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Ovil & Mechanical Engineer.
SAN FRANCISCO, CA .T>.
No. 9 ^IcQ 2.
25
American Practical Navigator
An Epitome of Navigation and
Nautical Astronomy
By NATHANIEL BOWDITCH, LL. D., Etc.
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E-S.S
ORDERS RELATING TO REVISION.
BuRKAU OF ^Navigation,
Wavy Departnwrif. January i, 1881.
In accoi'dance with the purpose contemplated in the pui'chase of the copyright of
the New American Practical Navigator, a thorough and complete revision has been
made by Commander P. H. Cooper, U. S. Navy, acting under th(> direction of the
Bureau. The revision Consists principally in the substitution of the more concise and
convenient methods of the present day for the obsolete methods of the past, and a
complete reari-angement under proper chapters and paragraphs for read}- reference,
keeping in view, however, the character of the work as a Practical Navigator.
The revision having been completed, it was submitted to Capt. Ralph Chandler,
U. S. Navy, for a final review, and having received a satisfactory report from that
officer it has been accepted bj^ the Bureau and will hereafter bo substituted for the
former editions of the work.
William D. Whiting,
Chief of Bureau.
Bureau of Equipment,
Navy JJe_partmetit, March 18, 190o.
A revision of Bowditch's American Practical Navigator having become neces-
sary, the work has been cooipletcd by Lieut. G. W. Logan, U. S. Navy, under the
supervision of the Hydrographer to the Bureau of Equipment. The revision was
approved by a Board consisting of Capt. Colby M. Chester, U. S. Navy, Commander
C. J. Badger, U. S. Navy, and Lieut. Commander C. C. Rogers, U. S. Navy. It
is directed that this revised edition be substituted for all former editions.
R. B. Bradford,
Chief of Bureau.
2
VK5BB
YEDDING OF PROMINENT COUPLE THIS | '31
^^^rnoon at First Presbyteri an Chf^rcb, ''^^
~ik-
ii't'.?
PREFACE.
The copyright of the New American Practical Navigator, by the late Dr.
Bowditch, became the property of the United States Government under the provision
of an act of Congress to establish a Hydrographic Office in the Navy Department,
approved June 21, 1866.
Under the direction of the Bureau of Navigation, at that time charged with such
publications, the work was revised in 1880 by Commander P. H. Cooper, U. S. Navy,
certain chapters being contributed by Lieuts. Richard Wainwright and Charles H.
Judd, U. S. Navy, and the whole being reviewed by Capt. Ralph Chandler, U. S.
Navj'. The object of this revision was to improve the general arrangement, and to
introduce the more convenient and precise methods of navigation that had come into
practice since the book was originally written.
The progress that has been made in the science of navigation since 1880 has
rendered necessary a second extensive revision, to take cognizance of the changes of
methods and instruments that have accompanied the general introduction of high-speed
vessels built of iron and steel. This work has been carried out, under the direction
of the Bureau of Equipment, by Lieut. G. W. Logan, U. S. Navy, who was aided in
the collection of data and preparation for publication by Lieut. T. A. Kearnej, U. S.
Navj; the chapters on Winds and Cyclonic Storms were contributed by Mr. James
Page, nautical expert, Hydrographic Office.
There has been an extensive rewriting of the text, with the object of amplifying
those matters that are of the greatest importance in the modern practice of navigation,
and of omitting or condensing those of lesser importance; and the revision of the
tables has proceeded along similar lines. This has involved, among other things, a
much wider treatment of the subject of the compass; an extension of the traverse
table for degi'ees to distances up to 600 miles; an improved table for reducing circum-
meridian altitudes; the combination of the tables of maritime positions and tidal data;
the omission of certain special methods for finding position by two observations; the
addition of a series of annotated forms for the working of all sights, atid the intro-
duction of a number of new tables of use to the navigator.
The explanation of the method of lunar distances, with its accompanying tables,
has been I'etained, in order to be available for use when required; but since this obser-
vation is so rarely employed in modern navigation, everything pertaining thereto has
been incorporated in an appendix, that it may be distinct from matter of every-day
use to the navigator.
For convenience in use the work has been divided into two parts, of which the first
comprises the text and its appendices, and the second the tables.
W. H. H. SOUTHERLAND,
Commander, U. S. Navy, HydrograpJwr,
Hydrographic Office,
Bureau of Equipment, Navy Department, ' •
Washington, D. C, March 19, 1903.
M767913
X O T E
Part I of this edition is a reprint of the revised edition of 1903 with typo-
graphical errors corrected. Part II was revised and enhirfjed August 10, 1911
(see p. 503).
Jonx J. Knapp,
Captain, U. S. Navy, H;/ilrograph^r.
Hydrographic Office.
Bi REAi- OF Navigation, Xavv Department,
Washin^on, D. C, January 15, 1912.
P J^ R T I
TEXT AND APPENDICES.
"Th» oe««Ln !■ th« •lemeut which
nrtffht eontaln such conditions. The )
oiigrinatlon of the oooan flta It to sus-
tain life better tljan any other en-
vironment, and the fundamental char-
acteristics of the ocean also encourasfp
•volution of active life. Can we not
therefore assume that the ocean Is the
Attest of known substances for the
creation of the origin of life?
"The orlsrln of lite itself depends
upon stability. Onr present existence
depends upon stability of climate and
other elements of onr environments.
Where conditions are most stable
there you will find most active and
progressive life. There Is one sub-
stance that posspsses more stability
than anythlnp else we know of and
that Is the ocean.
"In the ocean we see every degree of
development from the highest to the
lowest forms of life. It we are to be-
lieve In the theory of evolution mny
we not fro a step further and conclude
that Inorganic life under certain con-
ditions, such«aa those contained In the
ocean, will develop organic lite?"
OOISTTEN'TS OF P^RT I.
Page.
Orders relating to revision 2
Preface S
Abbreviations 9
Chapter I. Definitions relating to Navigation M
II. Instruments and Accessories in Navigation 13
III. The Compass Krror ?9
IV. Piloting 42
V. The Sailings 50
VI. Dead Reckoning 60
VII. Definitions relating to Nautical Astronomy 63
VIII. Instruments employed in Nautical Astronomy 66
IX. Time and the Nautical Almanac 74
X. Correction of Observed Altitudes 82
XI. The Chronometer Error 87
XII. Latitude 94
XIII. Longitude 103
XIV. Azimuth 109
XV. The Sumner Line 114
XVI. The Practice of Navigation at Sea 124
XVII . Marine Surveying 131
XVIII. Winds 142
XIX. Cyclonic Storms 147
XX. Tides 153
XXL Ocean Currents 158
Appendi.x I. Extracts from the American Ephemeris and Nautical Almanac for the year 1879,
which have reference to examples for that year given in this work 163
II. A collection of Forms for working Dead Reckoning and various Astronomical
Sights, with not«s explaining their application under all circumstances 171
III. Explanation of certain Rules and Principles of Mathematics of u.se in the Solu-
tion of Problems in Navigation 178
IV. Maritime Positions and Tidal Data 190
V. Lunar Distances 288
Index 333
7
ABBREVIATIONS USED IN THIS WORK.
Alt. (or A) Altitude.
A. M Ante meridian.
Amp Amplitude.
App ..Apparent.
App. t Apparent time.
Ast Astronomical.
Ast. t Astronomical time.
Aug Augmentation.
Az. (orZj Azimuth.
C Course.
C C Chronometer correction.
C— W Chronometer mmif.? watch.
Chro. t Chronometer time.
Co. L Co. latitude.
Col Column.
Corr Correction.
Coe Cosine.
Cosec Cosecant.
Cot Cotangent.
d (or Dec. ) Declination.
D (or DLo) Difference lorigitude.
Dep Departure.
Dev Deviation.
Diff Difference.
Dist Distance.
DL Difference latitude.
D. R Dead reckoning.
E. , Ely Ea.st, easterly.
Elap. t Elai)8ed time.
I'xj. eq. alt Equation equal altitude"
Kq. t Etjuation of time.
G. (or Gr. ) Greenwich.
G. A. T Greenwich apparent Jie.
G. M. T Greenwich mean time.
G. S. T. Greenwich sidereal time.
h Altitude.
H Meridian altitude.
H. A. (or() Hour angle.
H. D Hourly difference.
H. P. (or Hor. par. )... Horizontal parallax.
Hr-s Hour-s.
H.W High water.
I. C Index correction.
L. (or IM. ) Latitude.
L. A. T Local apparent time.
L. M. T Local mean time.
L. S. T Local sidereal time.
Lo. (or Long) Longitude.
Log Logarithm.
Lun. Int Lunitidal interval.
L. W Low water.
m Meridional difference.
Merid Meridian or noon.
Mag Magnetic.
M. D Minute's difference.
Mid Middle.
Mid. L Middle latitude.
M. T Mean time.
N. , Nly North, northerly.
N. A. ("or Naut. Aim. ). Nautical Almanac.
Np Neap.
Obs Observation.
p ( or P. D. ) Polar distance.
p. c Per compass.
P. D. (orp) Polar distance.
P. L. (or Prop. Log.) .Proportional logarithm.
P. M Post meridian.
p. <fc r Parallax and refraction.
Par Parallax .
R. A Right ascension.
R. A. M. S Right ascension mean sun.
Red Reduction.
Ref Refraction.
S., Sly South, southerly.
S. D Semi-diameter.
Sec Secant.
Sid Sidereal.
Sin Sine.
Spg Spring.
t Hour angle.
T Time.
Tab Table.
Tan Tangent.
Tr. (or Trans. ) Transit.
Var Variation .
Vert Vertex or vertical.
W., Wly West, westerly.
W. T Watch time
z Zenith distance.
Z Azimuth.
STMBOIvS.
o
The Sun.
° Degrees.
c
The Moon.
' Minutes of Arc.
*
A Star or Planet.
" Seconds of Arc.
r-x
Alt. upjx-r
limb.
' Hours.
(•)<(
Alt. lower limb.
" Minutes of Time
00
Azimuthal
angle.
• Seconds of Time
GREEK LETTERS.
Aa.
.Alpha.
Ny....
.Nu.
BIS.
.Beta.
Bi ....
.Xi.
I'y.
.Gamma.
Oo....
-Omicron.
4S.
.Delta.
nx....
-Pi.
Ee .
.Epsilon.
Pp. ...
.Rho.
z?.
.Zeta.
. 2<J(5)-
.Sigma.
Hv.
.Eta.
Tt ....
.Tau.
Bf) .
.Theta.
rv....
.Upsilon.
1 1 ..
.Iota.
$ <p
.Phi.
Kk.
. Kappa.
V;r....
.Chi.
AX.
.I.ambda.
y v....
.Psi.
Mft.
.Mu.
n at ...
.Omega.
T^l
npi
A
Uhi'INITlOU.S
KKLAllM,
ATIOif.
11
CHAPTER I.
DEFINITIONS EELATING TO NAVIGATION.
1. That science, generally termed Kavigcttion, which affords the knowledge necessary to conduct
a ship from point to point upon the earth, enabling the inariner to determine, with a sufficient degree
of accuracy, the position of his vessel at any time, is properly divided into two branches: yarix/ution
and Navllcat Astronomy.
2. Navigation, in its limited sense, is that branch which treats of the determination of the position
of the ship by reference to the earth, or to objects thereon. It comprises (a) Piloting, in which the
position is ascertained from visible objects upon the earth, or from soundings of the depth of the ssa,
and (h) Dead Reckoning, in which the position at any moment is deduced from the direction and
amount of a vessel's progress from a known point of departure.
3. Xauticat Adronotni/ is that branch of the science wliii-h treats of the determination of the
vessel's place by the aid of celestial objects — the sun, moon, planets, or stars.
4. Navigation and Nautical Astronomy have been respectively termed Geo-Namga'ion and Celo-
Niirigaiion, to indicate the processes upon which they depend.
5. As the method of piloting can not be employefl excepting near land or in moderate depths of
water, the navigator at sea must fix his position either hji dead reckoning or by obeervalion {of celestial
obiects); the latter method is more exact, but as it is not always available, the former must often be
depended upon.
6. The Earth. — The Earth is an oblate spheroid, being a nearly spherical Ixxiy slightly flsttened
at the poles; its longer or equatorial axis measures about 7,927 statute miles, antl its shorter axis,
around which it rotates, about 7,900 statute miles.
The Earth (assumed for purposes of illustration to be a
sphere) is represented in figure 1.
The A.ris of Rotation, usuallv spoken of simplv as the
Axis, is PP'.
The Poles are the points, P and P', in which the axis
intersects the surface, and are designated, respectively, as
the North Pole and the South Pole.
The E'juator is tlie great circle pjQMW, formed by the
intgrsection with the earth's surface of a plane perpendicular
to the axis; the equator is equidistant from the poles, every
])oint upon it teing 90° from each pole.
Meridians are the great circles PQP', PMP', PM'P',
formed by the intersection with the earth's surface of planes
secondary to the equator (that is, passing through \t» poles
an<i therefore perpendicular to its plane) .
Parallels of Latitude are small circles NT», N'»'T', lormeil
by the intersection with the earth's surface of planes passed
parallel to the etjuator.
The Ixititude of a place on the surface of the earth is the
arc of the meridian intercepted between the equator and
that place. I>atitude is reckoned North and South, from the
equator as an origin, through 90° to the poles; thus, the
latitude of the point T is MT, north, and of the point T', M'T', north. The Difference of iMtitude
))etween any two places is the arc of a meridian intercepted between their parallels of latitude, and is
called North or South, according to direction; thus, the difference of latitude between T and T' is Tn' or
T'u, noVth from T or south from T'.
The longitude of a place on the surface of the earth is the arc of the equator intercepted between
its meridian and that of some place from which the longitude is reckoned. Longitude is measured East
or West through 180° from the meridian of a designated place, such meridian being termed the lYtine
Meridian; the prime meridian used by most nations, including the United States, is that of Greenwich,
England. If, in the figure, the prime meridian be PCJQP', then the longitude of the point T is QM, east,
and of T', QM', east. The Difference of Longitude lietween any two places is the are of the equator inter-
cepted between their meridians, and is called East or West, according to direction; thus, the difference
of longitude between T and T' is MM', east from M or west from M'. The Departure is the linear distance,
measured on a parallel of latitude, between two meridians; unlike the various quantities previously
defined, departure is reckoned in miles; the departure l)etween two meridians varies with the parallel of
latitude upon which it is measured; thus, the departure between the meridians of T and T' is the number
of miles correspomling to the distance Tn in the latitude of T, or to n'T' in the latitude of T'.
12 DEFINITIONS BELATING TO NAVIGATION.
The curved line which joins any two places on the earth's surface, cutting all the meridians at the
same angle, is called the Hhumb Line, Loxodromic Curve, or Equiangular Spiral. In the figure, tliis line
is represented by TrT'. The constant angle which this line makes with the meridians is called the
Course; and the length of the line between any two places is called the Distance between those places.
The unit of linear measure employed by navigators is the Nautical or Sea Mile, or Knot. It is
equal to one minute of latitude — that is, to the length of that portion of a meridian which subtends at
the earth's center the angular measure of one minute; since, however, on account of the fact that the
earth is not a perfect sphere, this distance is not exactly the same in all latitudes, a mean value is adopted for
the length of the knot, and it is regarded as equal to 6,080.27 feet. For the purposes of navigation, the
variation from this value in different latitudes is so small that it may be neglected, and the knot may
be assumed equal to a minute of latitude in all parte of the earth; hence, when a vessel changes her
position to the north or south by one nautical mile, it may always be considered that the latitude has
changed 1'. Owing to the fact that the meridians all converge toward the poles, the difference of longi-
tude produced by a change of position of one mile to the east or west will vary with the latitude; tlius
a departure of one mile will equal a difference of longitude of I'.O at the equator, of I'.l in the latitude
of 30°, and of 2'.0 in the latitude of 60".
The Great Circle Track or Course between any two places is the route between those places along the
circumference of the great circle which joins them. In the figure, this line is represented by 'R/T'.
From the properties of a great circle (which is a circle upon the earth's surface formed by the inter-
section of a plane passed through its center) the distance between two points measured on a great circle
track is shorter than the distance upon any other line which joins them. Except when the two points
are on the same meridian or when both lie upon the equator, the great circle track will alwavs differ
from the rhumb line, and the great circle track will intersect each intervening meridian at a different
angle.
INSTRUMENTS AND ACCESSOBIES IN NAVIGATION. 13
CHAPTER II.
INSTEUMENTS AND ACCESSORIES IN NAVIGATION.
DIVIDERS OR COMPASSES.
7. This instrument consists of two legs movable about a joint, so that the ix>ints at the extremitiee
of the legs may be set at any requirerl distance from each other. It is used to take and transfer dis-
tances and to describe arcsand circles. When used for the former purpo.se it is termed diriders, and
the extremities of both legs are metal points; when used for describing arcs or circles, it is called a cmn-
pass, and one of the metal points is replaced by a jiencil or pen.
PARALLEL RULERS.
8. Parallel riilerx are used for drawing lines parallel to each other in any direction, and are particu-
larly useful in transferring the rhumb-line on the chart to the nearest compass-rose to ascertain the
course, or to lay off bearings and courses.
PROTRACTOR.
9. This is an instrument used for the measurement of angles upon paper; there is a wide variation in
the material, size, and ."hape in which it may be made. ( For a description of the Three Armed Protractor,
see art. 432, Chap. XVII. )
THE CHIP LOO.
10. This in.strument, for measuring the rate of sailing, consists of three parts; viz, the log-chip,
the log-line, and the log-glags. A light substance thrown from the ship ceases to partake of the motion
of the vessel as soon as it strikes the water, and will be left behind on the surface; after a certain inter-
val, if the distance of the ship from this stationary object te measured, the approximate rate of sailing
will l)e given. The log-chip is the float, the log-line is the measure of the distance, and the log-glau
defines the interval of time.
The log-chip is a thin wooden quadrant of aliout 5 inches radius, loaded with lead on the circular
edge sufficiently to make it swim upright in the water. There is a hole in each comer of the log-
chip, and the log-line is knotted in the one at the apex; at about 8 inches from the end there is seized
a wooden socket; a piece of line of proper length, being knotted in the other holes, has seized into its
bight a wooden jieg to fit snugly into the socket before the log-chip is thrown; as soon aa the line is
checked this peg pulls out, thus allowing the log-chip to Ije hauled in with the lea.st resistance.
The log-line is al)out 1.50 fathoms in length, one end made fast to the log-chip, the other to a
reel upon which it is wound. At a distance ot from 1.5 to 20 fathoms from the log-chip a permanent
mark of red bunting aV)out 6 inches long is placed to allow sufficient gtrau line for the log-chip to clear
the vessel's eddy or wake. The rest of the line is divided into lengths of 47 feet 3 inches called knots,
by pieces of fish-line thrust through the strands, with one, two, three, etc., knots, according to the
number from stray-line mark; each knot is further subdivided into five equal lengths of two-tenths of a
knot each, marked by pieces of white rag.
The length of a knot depends upon tlie numterof seconds which the log-glass measures; the length
of each knot must liear the same ratio to the nautical mile (^V ot a degree of a great circle of the earth
or 6,080 feet) that the time of the glass does to an hour.
In the United States Kavy all log-lines are marked f6r log glasses of 28 seconds, for which the
proportion is:
3600 : 6080 = 28- : a:,
X being the length of the knot.
Hence, .
a: = 47".29, or 47" 3'°.
The speed of the sliip is estimated in knots and tenths of a knot.
The Ujg-glam is a sand glass of the same shape and construction as the old hour-glass. Two gla-sses
are used, one of 28 seconds and one of 14 seconds; the latter is employed when the ship is going at a
high rate of speed, the number of knots indicated on a line marked for a 28-second glass being doubled
to obtain the true rate of speed.
11. The log in all its parts should be frequently examined and adjusted; the peg must be found to
fit sufficiently tight to keep the log-chip upright; the log-line shrinks and stretches and should often be
verified; the log-glass should be compared with a watch. One end of the glass is stopped with a cork,
by removing which the sand may be dried or its quantity corrected.
12. A ground log consists of an ordinary log-line, with a lead attached instead of a chip; in shoal
water, where there are no well-defined objects available for fixing the position of the vessel and the
course and speed are influenced by a tidal or other current, this log is sometimes used, its advantage
being that the lead marks a stationary point to which motion may be referred, whereas the chip would
drift with the stream. The speed, which is marked in the usual manner, is the speed over the
ground, and the trend of the line gives the course actually made good by the vessel.
14 INSTRUMENTS AND ACCKS80RIES IN NAVIGATION.
THE PATENT LOG.
1 3. This is a mechanical contrivance for registering the distance actually run by a vessel through the
water. There are various types of patent logs, but for the most part they act upon the same principle,
consisting of a registering device, a fly or rotator, and a log or tow line; the rotator is a small .spindle
with a number of wings extending radially in such manner as to form a spiral, and, when drawn
through the water in the direction of its axis, rotates about that axis after the manner of a screw pro-
peller; the rotator is towed from the vessel by means of a log or tow line from 20 to 50 fathoms in length,
made fast at its apex, the line teing of special make so that the turns of the rotator are transmitted
through it to the worm shaft of the register, to which the inboard end of the line is attached; the regis-
tering device is so constructed as to show upon a dial face the distance run, according to the numlx'r of
turns of its worm shaft due to the motion of the rotator; the register is carried at some convenient point
on the vessel's quarter; it is frequently found expedient to rig it out upon a small boom, so that tlie
rotator will be towed clear of the wake.
14. Though not a perfect instrument, the patent log affords the most accurate means available for
determining the ves-sel's speed through the water. It will usually be found that the indications of the
log are in error by a constant percentage, and the amount of this erior should be determined by careful
experiment and applied to all readings.
Various causes may operate to produce ina(«uracy of working in the patent log, such as the bending
of the wings of the rotator by accidental blows, fouling of the rotator by sea weed or refuse from the
ship, or mechanical wear of parts of the register. The length of the tow-line has much to do with the
working of the log, and by varying the length the indications of the instrument may sometimes be
adjuste<l when the percentage of error is small; it is particularly important that the line shall not be too
short. The readings of the patent log can not be depended upon for accuracy at low speeds, when the
rotator does not tow horizontally, nor in a head or a following sea, when the effect depends upon the
wave motion as well as upon the speed of the vessel.
15. Electrical registers for patent logs are in use, the distance recorded by the mechanical register
being communicated electrically to some point of the vessel which is most convenient for the purposes of
those charged with the navigation.
16. A number of instruments based upon different })hysical principles have been devised for
recording the speed of a vessel through the water and have been used with varying degrees of success.
1 7. The revolutions of the screw propeller afford in a steamer a valuable check upon the patent
log and a means of replacing it if necessary. To be of service the number of revolutions per knot must
be carefully determined for the vessel by experiment under varying conditions of speed, draft, and foul-
ness of bottom.
THE LEAD.
18. This device, for {iscertaining the depth of water, consists essentially of a suitably marked line,
having a lead attached to one of its ends. ' It is an invaluable aid to the navigator in shallow water,
particularly in thick or foggy weather, and is often of service when the vessel is out of sight of land.
Two leads are used for soundings — the hand-lead, weighing from 7 to 14 pounds, with a line marked
to about 25 fathoms, and the deep-sea lead, weighing from 30 to 100 pounds, the line being 100 fathoms or
upward in length.
Lines are generally marked as follows:
2 fathoms from the lead, with 2 strips of leather. , 17 fathoms from the lead, same as at 7 fathoms^
20 fathoms from the lead, w-ilh !J lk r io t8.<^«
25 fathoms from the lead, with 1 knot. *"
3 fathoms from the lead, with 3 strips of leather.
5 fathoms from the lead, w ith a white rag.
30 fathoms from the lead, with 3 knots.
35 fathoms from the lead, with 1 knot.
40 fathoms from the lead, with 4 knots.
An<l so on.
7 fathoms from the lead, with a red rag.
10 fathoms from the lead, with leather having a
hole in it.
13 fathoms from the lead, same as at 3 fathoms.
15 fathoms from the lead, same as at 5 fathoms.
Fathoms which correspond with the depths marked are called marks; the intermediate fathoms are
called deeps; the only fractions of a fathom used are a half and a quarter.
A practice sometimes followed is to mark the hand-lead line in feet around the critical depths of
the vessel by which it is to be used.
Lead lines should be measured frequently while wet and the correctness of the marking verilied.
The distance from the leadsman's hand to the water's edge should l>e ascertained in order that proi)er
allowance may be made therefor in taking soundings at night.
19. The deep-sea lead may be armed by filling with Tallow a hole hollowed out in its lower end,
by which means a sample of the bottom is brought up.
THE SOUNDING MACHINE.
SO. This machine possesses advantages over tlie deep-sea lead, forwhich it is a substitute, in that
soundings may be obtained at great depths and with rapidity and accuracy without stopping the ship.
It consists essentially of a stand holding a reel upon which is wound the sounding wire, and which is
controlled by a suitable brake. Crank handles are provided for reeling in the wire after the sounding
has been taken. Attached to the outer end of the wire is the lead, which has a cavity at its lower end
for the reception of the tallow for arming. Above the lead is a cylindrical case containing the depth-
registering mechanism ; various devices are in use for this purpose, all depending, however, upon the
increasing pressure of the water with increasing depths.
21. In the iMrd Kelvin machine a, slender glass tube is used, sealed at one end and open at the
other, and coated inside with a chemical substance which changes color upon contact with sea water;
this tube is placed, closed end up, in the metal cylinder; as it sinks the water rises in the tube, the
contained air being compressed with a force dependent upon the depth. The limit of discoloration is
marked by a clearly defined line, and the depth <]f the sounding corresponding to this line is read off
from a scale. TuImjs that have been used in comparatively shallow water may be useil again where the
water is known to be deeper.
IKSTRUMENTS AND ACCESSORIES IN NAVIGATION.
15
22. A tube whose inner surface is (fround has been substituted for the chemical-coated tube, ground
glass, when wet, showing clear. The advantage of these tubes is that they may be used an indefinite
number of times if thoroughly dried. To facilitate drying,arubbercapi8 fitted to the upper end, which,
when removed, admits of a circulation of the air through the tube.
23. As a substitute for the glass tubes a mechanical depth recorder contained in a suitable case has
been used. In this device the pressure of the water acts upon a piston against the tension of a spring. A
scale with an index pointer records the depth reached. The index pointer must be set at zero before
each sounding.
24. Since the action of the sounding machine, when glass tubes are used, depends upon the com-
pression of the air, the barometric pressure of the atmosphere must be taken into account when accurate
results are required. The correction consists in increasing the indicated depth by a fractional amount
according to the following table:
Bar. reading.
Increase.
//
29.75
30.00
30.50
30.75
One-fortieth.
One-thirtieth.
One-twentieth.
One-fifteenth.
THE KAKINER'S COMPASS.
25. The Marinefg Compaes is an instrument consisting either of a single magnet, or, more usually,
of a series of magnets, which, being attached to a graduated circle pivoted at the center and allowed to
• Fio. 2.
swing freely in a horizontal jdane, has a tendency to lie with its magnetic axis in the plane of the earth's
magnetic meridian, thus affording a means of determining the azimuth, or horizontal angular distance
from that meridian, of the ship's <ourse and of all visible o>)ject8, terrestrial or celestial.
16
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
46. The circular tard of the compass (fig. 2) is divided on its periphery into 360°, numbered from 0°
at North and South to 90° at East and West; also into thirty-two divisions of lip each, called yjoi'nte, the
latter being further divided into half-poii)ts and quarter-points ; still liner sulxlivisions, eighth-points, are
sometimes used, though not indicated on the card. A system of numbering the degrees from 0° to 360°,
always increasing toward the right, is shown in the figure. This system is in use by the mariners of
some nations, and its general adoption would carry with it certain undoubted advantages.
27. Boxing the Compass is the process of naming the points in their order, and is one of the first
things to be learned by the young mariner. The four principal points are called cardinal points and are
named North, South, East, and West; each differs in direction from the adjacent one by 90°, or 8 points.
Midway between the cardinal points, at an angular distance of 45°, or 4 points, are the inter-cardinal
points, named according to their position Northeast, Southeast, etc. Jlidway between each cardinal
and inter-cardinal point, at an angular distance of 22J°, or 2 points, is a point whose name is made uj)
of a combination of that of the cardinal with that of the inter-cardinal point: North-Northeast, East-
Northeast, East-Southeast, etc. At an angular distance of 1 point, or 11|°, from each cardinal and inter-
cardinal point (and therefore midway between it and the 22J°-division last described), is a point
which bears the name of that cardinal or inter-cardinal point joined by the word hy to that of the cardi-
nal point in the direction of which it lies: North by East, Northeast by North, Northeast by East, et(^
In boxing by fractional points, it is evident that each division may be referred to either of the
whole points to which it is adjacent; fot instance, NE. by N. J N. and NNE. J E. would describe the
same division. It is the custom in the United States Navy to box /j-ojji North and South toward East and
West, excepting that divisions adjacent to a cardinal or inter-cardinal point are always referred to that
point; as N. J E., N. by E. J E., NNE. J E., NE. J N., etc. Some mariners, however, make it a prac-
tice to box from each cardinal and inter-cardinal point toicard a 22}°-point (NNE., ENE., etc.) ; as
N. I E., N. by E. J E., NE. by N. J N., NE. J N., etc.
The names of the whole points, together with fractional points (according to the nomenclature of
the United States Navy), are given in the following table, which shows also the degrees, minutes, and
seconds from North or South to which each division corresponds:
N. toE.
N. to W.
S. toE.
S. to W.
Pts.
Angular
measure.
North:
N. JE
N. JE
N. IE
N. byE
N. byE. JE...
N. byE. JE...
N. byE. |E...
NNE
NNE. JE
NNE. JE
NNE. |E
NE. bvN
NE. iN
NE. JN
NE. t N
NE
NE. JE
NE. JE
NE. IE
NE. byE
NE. byE. J E..
NE. byE. JE..
NE. bvE. i E..
ENE ....:
ENE. JE
ENE. JE
ENE. |E
E. bvN
E. JN
E. JN
E. JN
East
North:
N. iW
N. J W
N. }W
N.by W
N. byW. iW.
N. bvW. JW.
N. by W. }W.
NNW
NNW. JW...
NNW. J W...
NNW. J W...
NW. by N
NW. JN
NW. +N
NW. i N
NW
NW. i W
NW. J W
NW. i W
NW. by W
NVV.byW.JW
NW. by W. JW
NW.byAV. |W
WNW
WNW. i W...
WNW. J W...
WNW. J W...
W. byN
W. JN
W. J N
W. IN
West
South:
S. JE
S. JE
S. }E
S.byE
8. byE. JE.
S. byE. JE.
S. by E. J E .
SSE ,
SSE. JE
SSE. JE
SSE. JE....
SE. bvS
SE. JS
SE. JS
SE. JS
SE
SE. JE
SE. JE
SE. JE
SE. byE
SE. by E. J E
SE. by E. J E
SE. by E. J E
ESE
ESE. JE....
ESE. JE....
ESE. JE....
E. byS
E. JS
E. JS
E. JS
East
South:
S. J W
S. JW
S. J W
S. by W
S. bvW. JW...
S. bvW. JW...
S. by W. JW...
ssw
i
i
1
U
li
2
SSW. JW '• 2J
ssw. J W .
SSW. J W
SW. byS
SW. J s . .
SW. JS..
SW. JS..
SW
2J
2J
3
3J
3J
3J
4
4J
SW. J w....
SW. JW....
SW. JW I 4|
SW. byW I 5
SW. byW. JW. 5 J
SW. hyW. JW.I 5J
SW. bvW. JW.I 5J
WSW....". 6
WSW. JW 6J
WSW. JW ! 6 J
WSW. JAV ! 6J
w.
by S .
W.
JS.
W. JS.
AV. J S .
West
7
7J
7*
2 48 45
5 37 30
8 26 15
11 15 00
14 03 45
16 52 30
19 41 15
22 30 00
25 18 45
28 07 30
30 56 15
33 45 00
36 33 45
39 22 30
42 11 15
45 00 00
47 48 45
50 37 30
53 26 15
56 15 00
59 03 45
61 52 30
64 41 15
67 30 00
70 18 45
73 07 30
75 56 15
78 45 00
81 33 45
84 22 30
87 11 15
90 00 00
28. The compass card is mounted in a bowl which is carried in gimbals, thus enabling the card to
retain a horizontal position whiie the ship is pitching and rolling. A vertical black line called the lub-
ber's line is marked on the inner surface of the bowl, and the compass is so mounted that a line joining
\\» pivot with the lubber's line is parallel to the keel line of the vessel; thus the lubber's line always
indicates the compass direction of the ship's head.
2S. According to the purpose which it is designed to fulfill, a compass is designated as a Standard,
Steering, Check, or Boat Compass.
INSTRUMENTS AND ACCESSOKIES IN NAVIGATION. 17
30. There are two types of compass in use, the vet or Umiid and the dri/; in the former the bowl is
filled with liquid, the card l)eing thus partially buoyed, with consequent increased ease of working on
the pivot, and the liquid further serving to decrease the vibrations of the card when deflectetl by reason
of the motion of the vessel or other cause. On account of its advantages the liquid compass is used In
the United States Navy.
31. The Navy Service 7J-inch Liquid Compass. — This consists of a skeleton card 7J inches in
diameter, made of tinned brass, resting on a pivot in liquid, with provisions for two pairs of magnets
symmetrically placed.
The magnet system of the card consists of four cylindrical bundles of steel wires; these wires are
laid side by side and magnetized as a bundle Ijetween tlie poles of a jiowerfiil electromagnet. They are
afterwards placed in a cylindrical ca.se, sealed, and secured to the card. Steel wires made up into a
bundle were adopted because they are more homogeneous, can be more perfectly tempered, and for the
same weight give greater magnetic power than a soliil steel bar.
Two of the magnets are placed parallel to the north and south diameter of the card, and on the
chords of 15° (nearly) of a circle passing througli their extremities. These magnets penetrate the air
vessel, to which they are soldered, and are further secured to the Iwttom of tlie ring of the card. The
other two magnets of the system are placed parallel to the longer magnets on the chords of 45° (nearly)
of a circle passing through their extremities, and arc secured to the bottom of the ring of the card.
The card is of a curved annular type, the outer riu" being convex on the upper and inner side, and
is graduated to read to one-fourth point, a card circle lieing adjusted to its outer edge and divided to
half-degrees, with legible figures at each 3°, for use in reading bearings by an azimuth circle or in laying
the course to degrees.
The card is ]irovi(le(l with a concentric spheroidal air vessel, to buoy its own weight and that of the
magnets, allowing a ])res.sure of between 60 and 90 grains on the pivot at 60° F. ; the weight of the card
in air is .3,060 grains. The air vessel has within it a hollow cone, ojieu at its lower end, and provided
with the pivot bearing, or cap, containing a sapi)hire, which rests upon the pivot and thus sujiports the
card; the cap is provided with adjusting screws foraccurately centering the card. The pivot is fastened
to the center of the lK)ttom of the bowl by a flanged plate and scivws. Through this plate and the
bottom of the bowl are two small holes which communicate with the expansi<m chamber and admit of
a circulation of the liiiuid between it and the Ik>w1. The pivot is of gun metal with an iridium cap.
The card is mounted in a bowl of cast bronze, the glass cover of which is closely packed with rubber,
preventing the evaporatiim or leakage of the liquid, which entirely fills the Ixiwl. This liquid is com-
posed of 45 per cent pure alcohol and 55 per cent distille<l water, and remains liquid below — 10° F.
The lubber's line is a fine line drawn on an enameled ])late on the inside of the bowl, the inner
."urface of the latter l>eing covered with an insoluble white paint.
Beneath the bowl is a metallic self-adjusting expansion chamber of elastic metal, by means of which
the lx)wl is kept constantly full without the show of bubbles or the development of undue pressure
<'aused by the change in volume of the liquid due to changes of temperature.
The rim of the compass l»wl is made rigid and its outer edge turned strictly to gauge to receive the
azimuth circle.
!J2. The Dky Compass. — The Lord Kelrin Cotnjyiim, which may l)e regarded as the standard for
the nonliquid type, consists of a strong jiaper card with the central parts cut away and its outer edge
stiffened bj- a thin aluminum ring. The pivot is fitte<l with an iridium point, u])on which rests a small
light aluminum 1m)SS fitted with a sapphire bearing. Radiating from this boss are 32 silk threads whose
outer ends are made fast to the inner edge of the compa.ss card; these threads sustain the weight of the
suspended card, and, as they ])os.ses8 some elasticity, teml to ilecrea.se the shocks due to motion.
Eight small steel w ire needles, 3| to 2 inches long, are secured normally to two i)arallel silk threads,
and are slimg from the aluminum rim of the card by other ."ilk threads which pass through eyes in the
ends of the outer pair of needles. The needles are below the radial threads, thus keeping the center of
gravity low.
33. The Azimuth CiKcle. — This is a necessary fitting for all compasses employed for taking
bearings — that is, noting the directions — of either celestial or terrestrial objects. The instrument varies
widely in its different forms; the essential features which all share consist in (o) a pair of sight vanes,
or equivalent device, at the extremities of the diameter of a circle that revolves concentrically with the
compass bowl, the line of sight thus always passing through the vertical axis of the compass; and (h)
a system, usually of mirrors and prisms, by which the point of the coiuiiass card cut by the vertical
plane through the line of sight — in other words, the compa.ss direction — is brought into the field of view
of the person making the observation. In some circles, for obser\ ing azimuths of the sun advantage is
taken of the brightness of that body to reflect a jtencil of light uix)n the card in such a manner as to
indicate the bearing; such an azimuth circle is used in the United .States Navy.
34. Binnacles. — Comi)a.sses are mounted for use in stands known as lihinacleK, of which there are
two principal tjpes — the ('uiiipensathtg and the yon-Compeiiiidthui Bhnmclr, so designated according as
they are fir are not e(|Hii)ped with appliances by which the deviation of the compa.ss, or error in its
indications due to disturbing magnetic features within the ship, may be compensated.
Binnacles may be of wood or of some nonmagnetic metal; all contain a compass chamlier within
which the compass is susjiended in its gimbal ring, the knife edges upon which it is suspended resting
in V-shaped bearings; an appropriate method is supplied for centering the compa,ss. A hood is provided
for the protection of the compass and for lighting it at night. Binnacles must be rigidly secured to the
deck of the vessel in such position thet the lubber's line of the compass gives true indications of the
direction of the ship's head.
The position of the various binnacles on shipboard and the height at which they carry the compass
must be chosen w ith regard to the purpose which the compass is to ser\'e, having in mind the magnetic
conditions of the ship.
Compensating binnacles contain the appliances for carrying the various correctf)rs used in the ccm-
pensation of the deviation pf the compass. These consist of (a) a system of permanent magnets for
24972°— 12 -2
18 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
semicircular deviation, placed in a magnet chamber lying immediately beneath the compass chamber,
so arranged as to permit variation in the height and direction of the magnets employed; (6) a pair of
arms projecting horizontally from the compass chamber and supporting masses of soft iron for quad -
ran tal deviation; (c) a central tuV)e in the vertical axis of the binnacle for a permanent m^net used to
correct the heeling error, and (d) an attachment, sometimes fitted, for securing a vertical soft iron rod,
or "Flinders bar," used in certain cases for correction of a part of the semicircular deviation. An
explanation of the various terms here used, together with the method of compensating the compass,
will be given in Chapter III.
THE PELORT7S.
35. This instrument consists of a circular plate, mounted liorizontally in gimbals upon a vertical
standard, at some point on board ship affording a clear view for taking bearings; radial scores upon a
raised flange on the periphery of this plate indicate true directions from its center parallel with the keel
line of the vessel and perpendicular thereto — in other words, lines of bearing directly ahead, astern, and
abeam. Revolving about a common center, which is also the center of the plate, are (a) a dumb com-
pass card, usually engraved on metal, whose face is level with the raised periphery of the plate on which
are marked the scores, and (6) a pivoted horizontal bar carrying at its extremities a pair of sight vanes
so arranged that the line of sight always passes through the vertical axis of the instrument, and having
an index showing the point at which the line of sight cuts the dumb compass. The dumb compass and
the sight-vane bar can each be rigidly clamped.
The insiruraent is used for taking bearings, and may be more convenient than the compass for that
purpose because of the better view that it affords, as well as because it may be made to eliminate the
compass error from observed bearings. Suppose that the dumb compass be revolved until the degree or
division which is coincident with the right-ahead score of the plate is the same as that which is abreast
the lubber's line of the ship's compass. Then all directions indicated by the dumb comi^ass will be
parallel to the corresponding directions of the live one, and all bearings taken by the pelorus will lie
identical with those taken by the compass (leaving out of the question the diffence due to the distance
that separates them). Suppose, now, that it is known that the ship's compass has a certain error and
that the correct direction that we seek (which is the one indicated on the charts) is a certain angular
distance to the right or left of that which the compass shows; if, in such a case, instead of setting tlie
pelorus for the direction indicated by compass, we set it for the correct direction in which we know the
ship to be heading, all Isearings observed by the pelorus will be correct liearings as given by the chart
and may be plotted directly thereon without the necessity for the intermediate process of correction to
which the bearings shown by compass are subject. It will at once be evident that the indications of the
pelorus will be accurate only when bearings are taken at an instant when the ship is heading exactly in
the direction for which it is set, and care must be taken accordingly in its use.
The most modern types of pelorus are fitted for illuminating the dumb compass, thus greatly facili-
tating night work.
THE CHABT.
!I6. A nautical chart is a miniature representation upon a plane surface, in accordance with a defi-
nite system of projection or development, of a portion of the navigable waters of the world. It generally
includes the outline of the a<ljacent land, together with the surface forms and artificial features tliat are
useful as aids to navigation, and sets forth the depths of water, especially in the near approaches to the
land, by somidings that are fixed in po.sition by accurate determinations. Except in charts of harbors
or other localities so limited that the curvature of the earth is inappreciable on the scale of construction,
a nautical chart is always framed over with a network of parallels of latitude and meridians of longitude
in relation to which the features to be depicted on the chart are located and drawn; and the mathematical
relation between the meridians and parallels of the chart and those of the terrestrial sphere determines
the method of measurement that is to be employed on the chart and the special uses to which it is
adapted.
37. There are three principal systems of projection in use: (a) the Mercator, (h) the polyconic, and
(c) the gtiommfiic; of these, the Mercator is by far the most generally used for purposes of navigation
proper, while the polyconic and the gnomonic charts are employe<l for nautical purposes in a more
restricted manner, as for plotting surveys or for facilitating great circle sailing.
3§. The Mercator Projection. — The Mercator I'rojection, so called, may be said to result from
the development, vmm a plane surface, of a cylinder which is tangent to the earth at the equator, the
various points of the earth's surface having been projected upon the cylinder in such manner that the
loxodromic curve or rhumb line (art. 6, Chap. I) appears as a right line preserving the same angle of bear-
ing with respect to the intersected meridians as does the ship's track.
In order to realize this condition, the line of tangency, which coincides with the earth's equator,
being the circumference of a right section of the cylinder, will appear as a right line on the develop-
ment; while the series of elements of the .cylinder corresponding to the projected terrestrial meridians
will appear as equidistant right lines, parallel to each other and perpendicular to the equator of the
chart, maintaining the same relative positions and the same distance apart on that equator as the
meridians have on the terrestrial spheroid. The series of terrestrial parallels will also appear as a
system of right lines parallel to each other and to the equator, and will so intersect the meridians as to
form a system of rectangles whose altitudes, for successive intervals of latitude, must be variable,
increasing from the equator in such manner that the angles made by the rhumb line with the meridian
on the chart may maintain the required equality with the corresponding angles on the spheroid.
39. Meridional Parts. — At the equator a degree of longitude is equal to a degree of latitude, but
in receding from the equator and approaching the pole, while the degrees of latitude remain always of
the same length (save for a slight change due to the fact that the earth is not a perfect sphere), the
degrees of longitude become less and less.
INSTRUMENTS AND ACCKS80RIE8 IN NAVIGATION. 19
Since, in the Mercator projection, the degrees of longitude are made to appear everywhere of tlie
same length, it becomes necessary, in order to preserve the proportion that exists at different parts- of
the earth's surface l)et\veen degrees of latitude and degrees of longitude, that the former be increased
from their natural lengths, and such increase must become greater and greater the higher the latitude.
The length of the meridian, as thus increased, between the equator and any given latitude,
expressed in minutes at the equator as a unit, constitutes the number of Meridional Parte corresponding
to that latitude. The Table of Meridional Parts or Increased Latitudes (Table 3) , computed for every
minute of latitude between 0° and 80°, affords facilities for constructing charts on the Mercator pro-
jection and for solving problems in Mercator sailing.
4©. To CoxsTRucT A Merc.\tor Chart. — If the chart for which a projection is to be made includes
the equator, the values to be measured off are given directly by Table 3. If the equator does not come
upon the chart, then the parallels of latitude to be laid down should be referred to a principal parallel,
preferably the lowest parallel to be drawn on the chart. The distance of any other parallel of latitude
from the principal parallel is then the difference of the values for the two taken from Table 3.
The values so found may either be measured off, without previous numerical conversion, by means
of a diagonal scale constructed on the chart, or they may be laid down on the chart by means of any
properlv divided scale of yards, meters, feet, or miles, after having been reduced to the scale of proportions
adopted for the {•hart.
If, for example, it be required to construct a chart on a scale of one-quarter of an inch to five minutes
of arc on the eiiuator, a diagonal scale may first be constructed, on which ten meridional parts, or ten
minutes of arc on the eijuator, have a length of half an inch.
It mav often be desirable to adapt the scale to a certain allotment of paper. In this case, the lowest
and the highest parallels of latitude may first be drawn on the sheet on which the transfer is to be made.
The distance between these parallels may then be measured, and the number of meridional parts
between them ascertained. Dividing the distance by this number will then give the length of one
meridional part, or the quantity by which all the meridional parts taken from Table 3 must be multi-
plied. This quantity will represent the urate of the chart. If it occurs that the limits of longitude are
a governing consideration, the case may be similarly treated.
E.vami-le: Let a projection be re^iuireil for a chart of 14° extent in longitude between the parallels
of latitude 20° .30' and 30° 25', and let the space allowable on the paper l)etween these parallels measure
10 inches.
Entering the column in Table 3 headed 20°, and running down to the line marked 30' in the side
column, will be found 1248.9; then, entering the column 30°, and ninning down to the line of 25', will
be found 1905.5. The difference, or 1905.5 — 1248.9 = 656.6, is the value of the meridional arc lietween
these latitudes, for which 1' of arc of the equator is taken as the unit. On the intended projection,
lAiD
therefore, V of arc of longitude will measure -^.~„ = 0.0152 inch, which will be the scale of the chart.
For the sake of brevity call it 0.015. By this quantity all the values derived from Table 3 will have to
be multiplied before laying them down on the projection, if they are to be measured on a diagonal scale
of one inch.
Draw in the center of the sheet a straight line, and assume it to be the middle meridian of the chart.
Construct very carefully on this line a perpendicular near the lower border of the sheet, and assume this
perpendicular to lie the parallel of latitude 20° 30'; this will lie the southern inner neat line of the chart.
From the intersection of the lines lay off on the parallel, on each side of the middle meridian, seven
degrees of longitude, or distances each equal to 0.015 X 60 X 7 = 6.3 inches; and through the points thus
obtained draw parallel lines to the middle meridian, and these will be the eastern and western neat lines
of the chart.
In order to construct the parallel of latitude for 21° 00', find, in Table 3, the meridional parts for
21° 00', which are 1280.8. 8ubtra<:ting from this number the number for 20° 30', and multiplying the
difference by 0.015, we obtain 0.478 inch, which is the distance on the chart between 20° 30' and
21° 00'. On the meridians lay off distances equal to 0.478 inch, and through the three points thus
obtained draw a straight line, which will be the parallel of 21° 00'.
Proceed in the same manner to lay down all the parallels answering to full degrees of latitude; the
distances will be respectively:
0'".015X (1344.9-1248.9) =1.440 inches,
0'°.015X (1409.5-1248.9) =2.409 inches,
0'».015X (1474.5-1248.9) =3.384 inches, etc.
Thus will be shown the parallels of latitude 22° 00', 23° 00', 24° 00', etc. Finally, lay down in the same
way the parallel of latitude 30° 25', which will be the northern inner neat line of the chart.
A degree of longitude will measure on this chart 0'°. 015X60=0'". 9. J^ay off, therefore, on the low-
est parallel of latitude drawn on the chart, on a middle one, and on the highest )>arallel, measuring
from the middle meridian toward each side, the distances of 0'".9, ]'".8, 2'". 7, 3'". 6, etc., in order to
determine the points where meridians answering to full degrees cross the parallels drawn on the chart.
Through the points thus found draw the meridians. Draw then the outer neat lines of the chart at a
convenient distance outside of the inner neat lines, and extend to them the meridians and parallels.
Between the inner and outer neat lines of the chart subdivide the degrees of latitude and longitude as
minutely as the scale of the chart will ])ermit, the sulxlivisions of the degrees of longitude being found
by dividing the degrees into equal parts, and the subdivisions of the degrees of latitude being accu-
rately found in the same manner as the full degrees of latitude previously deseril)ed, though it will
generally be found sufficiently exact to make even subdivisions of the degrees, as in the case of the
fongitude.
The subdivisions between the two eastern as well as those between the two western neat lines will
serve for measuring or estimating terrestrial distances. Distances Vjetween points l)earing North and
South of each other may be ascertained by referring them to the suV)divisions between the same paral-
lels. Distances represente<l by lines at an angle to the meridians (loxodromic lines) may l)e measured
20
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
by taking between the dividers a small number of the subdivisions near the middle latitude of the
line to be mea.sured, and stepping them off on that line. If, for instance, the terrestrial length of a line
running at an angle to the meridians between the parallels of latitude of 24° 00' and 29° 00' l)e required,
the distance shown on the neat space between 26° 15' and 26° 45' ( = 30 nautical miles) may be taken
between the dividers and stepjied off on that line.
41. Coast lines and other positions are plotted on the chart by their latitude and longitude. A
chart may be transferred from any other projection to that of Mercator by drawing a system of corre-
sponding parallels of latitude and meridians over botli charts so close to eacli other as to form minute
squares, and then the lines and characters contained in each square of the map to be transferred may
be copied l)y the eye in the corresponding squares of the Mercator projection. •
Since the unit of measure, the mile or minute of latitude, has a different value in every latitude, there
is an appearance of distortion in a Mercator chart that covers any large extent of surface; for instance,
an island near the pole will be represented as being much larger than one of the same size near the
equator, due to the different scale used to preserve the character of tlie jirojection.
42. The Poi.ycoxic Pko.iection. — This projection is based upon the development of the earth's
surface on a series of cones, a different one for each parallel of latitude, each one having the parallel as
its base, and its vertex in the point where a tangent to the earth at that latitude intersects the earth's axis.
The degrees of latitude and longitude on this chart are projected in their true length, and tlie general
distortion of the figure is less than in any other method of projection, the relative magnitudes ))eing
closely preserved.
A straight line on the jiolyconic chart represents a great circle, making a slightly different angle
with each successive meridian as the meridians converge toward the pole and are theoretically curved
lines; but it is only on charts of large extent that this curvature is apparent; the parallels are also
curved, this fact being apparent to the eye upon all excepting the largest scale charts.
This method of projection is especially adaj)ted to the plotting of surveys; it is also employed for
nearly all of the charts of the United States Coast and Geodetic Survey.
43. Gnomo.nic Projection. — This is based upon a system in which the plane of projection is tangent
to the earth at some given point; the eye of the spectator is situated at the center of the sphere, where,
being at once in the plane of every great circle, it will see all such circles projected as straight lines
where the visual rays passing through them intersect the plane of projection. In a gnomonic chart, a
straight line between any two points is projected as an arc of a great circle, and is therefore the shortest
line between those points.
Excepting in the Polar regions, for which latitudes the Mercator projection can not be constructed,
the gnomonic charts are not used for general navigating purposes. Their greatest application is to afford
a ready means of finding the course and distance at any time in great circle sailing, the methodoLdoing
which will be explained in Chapter \'.
44. Meeidi.\xs E.virLOYED in Ch.vrt Constklction. — The United States, England, Germany, Italy,
Eussia, Norway, Sweden, Denmark, Holland, Austria, Portugal, and Japan adopt as a prime meridian
the meridian of Greemvich.
France adopts the meridian of Paris in Long. 2° 20' I4".5 E. of Greenwich.
Spain adopts the meridian of fktn Fernando, Cadiz, in Long. 6° 12' 20" W. of Greenwich.
The Pulkowa Observatory of St. Petersburg (sometimes referred to in Russian charts) is in Long.
30° 19' 39".6 E. of Greenwich.
The Royal Observatory of Naples (sometimes referred to in Italian charts) is in Long. 14° 14' 06" E.
of Greenwich.
The meridian of Genoa is 8° 55' 21" E.; of Lisbon, 9° 08' 36" W.; of Rio de Janeiro, 43° 10' 21".2
W.; of Amsterdam, 4° 53' 03".8 E.; of Washington, 77° 03' 56".7 W.
45. Quality of Bottom. — The following table shows the qualities of tlie bottom, as expressed on
charts .of various nations:
I'nited States.
English.
French.
Italian.
Spanish.
German.
Olav
Coral
Gravel . . .
Mud
C.
Co.
G.
M.
Sh.
St.
....Wd.
fne.
crs.
stf.
sft.
Clay
Coral
Gravel . . .
Mud
Rock....
Sand
Shells ...
Stones....
Weed....
Fine
Coarse . . .
Stiit
Soft
Black ....
Red
Yellow..
cl.
....crl.
g-
m.
....rk.
8.
....fh.
.St.
...wd.
t.
c.
....stf.
....sft.
...blk.
....rd.
y-
Argile....
Corail....
Gravier ..
Vase
Roche....
Sable
Coquille .
Pierre
Herb
Fin
Gros
Dure
Molle....
Noire
Rouge ...
Jaune
....A.
...Cor.
....Gr.
....V.
....R.
S.
..Co^.
....H.
...fin.
m.
n.
r.
j.
Argila
Cor411o
RenaorGhiaja
Arcillo or Barro
Coral
CascAjo
Fangoor Luno.
Piedra or Roca .
Arena
Conchuela
Piedra
Alga
Fina
Gruesa...
.cl.
Co.
..F.
..P.
.A.
.ca.
..P.
.A.
..f.
Lehm
Korallen . . .
Grob sand . .
Schlemm ..
Fels
Sand
h.
K.
....g. s.
Sch.
Rocky
Roccia
F.
Sand
S4bia or Artoa
. S
Shells....
Muschel . . .
Stein.
Gras
Fein
Grob
Zahe
Welch
Schwarz...
Roth.
Gelb.
M.
Stone
pietre
Weed
Alga
G.
Fine
Fino
i.
Coarse . . .
Grosso
f-
Stiff
Soft
Molle
Muelle
\v.
Black....
bk.
rd.
yi.
gy.
Nero
Negro
, .schw.
Red
Yellow...
Giallo
Amarillo
Gray
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
21
46. Measures op Depth. — The following table shows the measures of depth employed in the charts
of certain foreign nations, with their equivalents in English measures:
I English feet.
Austrian fathom (klafter) . .
Danish and Norwegian fathom (farn)..
Dutch fathom ( vaden) . .
French /fathom ( brasse) . .
\meter (metre)
Portuguese fathom (braga) . .
Prussian fathom ( faden) . .
Russian fathom (sajen) . .
Spanish fathom (braza) . .
Swedish fathom (famn) . .
6.222
6.175
5.575
5.329
3.281
6.004
O.906
6.000
5.492
5. 843
Englisli
fathoms.
1.030
1.029
0.929
0.888
0.547
1.000
0.984
1.000
0.915
0.974
II
i
The Dutch elle, the Spanish, Portuguese, and Italian metro, and the French mrtre are identical.
Xpied ««i(f/= 13. 124 inches, or 1.094 feet. A mPtre is 'S pieds; a, pied da roi =12.7896 inches; t/)-asse
is used upon old French charts instead of metre. Tpon some Italian charts soundings are in French
pieds.
THE BABOKETEB.
47. The barometer is an instrument for measuring the pressure of the atmosphere, and is of jxreat
service to the mariner in affording a knowledge of existing meteorological con-
ditions and of the probable changes therein. There are two classes of barome-
ter — merc.imrd and aneroid.
48. The Mercuri.^l Barometer. — This instrument, invented by Torricelli
in 1643, indicates the pressure of the atmosphere by the height of a column
of mercury.
If a glass tube of uniform internal diameter somewhat more than 30 inches
in length and closed at one end be completely filled with pure mercury, antl
then placed, open end down, in a cu|) of^ mercury (the open end having been
temporarily sealed to retain the liquid during the process of inverting) , it will
be found that the mercurv in the tube will fall until the top of the colunm is
about 30 inches above the level of that which is in the cup, leaving in the upper
part of the tute a perfect vacuum. Since the weight of the column of mercury
thus left standing in the tube is equal to the pressure by which it is held in
position — namely, thatof the atmosi)heric air — it follows that the heightof the
column is subject to variation upon variation of that ])res8ure; hence the mer-
cury falls as the pressure of the atmosphere decreases and rises as tliat j)res-
sure iucrea-ses. The mean pressure of tlio atmosphere is equal to nearly 15
pounds to the square inch; the mean heightof the barometer is about 30 inches.
49. In the practical construction of the barometer the glass tube which
contains the mercury is encased in a brass tube, the latter terminating at the
top in a ring to be used for suspen.^ion, and at the bottom in a flange, to which
the several jiarts forming the cistern are attached. The up])er part of the brass
tui)e is partially cut away to expose the mercurial column for observation ;
abroa.«t this opening is fitted a scale for measuring the height, and along the
scale travels a render for exact reading; the motion of the vernier is controlled
by a rack and pinion, the latter having a milled head accessible to the observer,
by which the adjustment is made. In the middle of the brass tube is fixed a
thermometer, the bulb of which is covered from the outside but open toward
the mercury, and which, being nearly in contact with the glass tube, indicates
the temperature of the mercury and not that of the external air; tlie central
IX)sition of the column is selected in order that the mean temperature may be
obtained — a matter of importance, as tlie teni])eratureof the mercurial column
must be taken into account in every accuratt; application of its reading.
•50. In the arrangement of further details menturial barometers are di-
vide<l into two classes, according as they are to be used a.s Stii>id<irds (fig. 4)
on shore, or as Sea Barouielen (fig. 3) on shipboard.
In the Standard Barometer the scale and vernier are so graduated as to
enable an oVjserver to read the height of the mercurial column to the nearest
0.002 inch, while in the Sea Barometer the reading can not be made closer
than 0.01 inch.
The instruments also differ in the method of obtaining the true height of
the mercurial column at varying levels of the liquid in the cistern. It is evi-
dent that as the mercury in the tube rises, upon increase of atmospheric pres-
sure, themercury in the cistern must fall; and, conversely, when the mercurial
column falls the amount of fluid in the cistern will thereby be increased and a
Pj^_ 3 rise of level will occur. As the heightof tlie mercurial column is required pj,. 4
above the existing level in the cistern, some means must be adopted to obtain
the true height under varying conditions. In the Standard Barometer the mercury of the cistern is
contained in a leather l)ag, against t\\i\ bottom of which presses the i)oint of a vertical screw, the milled
22
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
head of the screw projecting from the bottom of the instrument and thus placing it under control of the
observer. By this means the surface of the mercury in the cistern (which is visible through a glass
casing) may be raised or lowered until it exactly coincides with that level which is chosen as the zero
of the scale, and which is indicated by an ivory pointer in plain view.
In the Sea Barometer there is no provision for adjusting the level of the cistern to a fixed point,
but compensation for the variable level is made in the scale graduations; a division representing an
inch on the scale is a certain fraction short of the true inch, proper allowance being thus made for the
rise in level which occurs with a fall of the column, and for the reverse condition.
Further modification is made in the Sea Barometer to adapt it to the special use for which intended.
The tube toward its lower end is much contracted to prevent the oscillation of the mercurial column
known as "pumping," which arises from the motion of the ship; and just below this point is a trap to
arrest any small bubl)les of air from finding their way upward. The instrument aboard ship is sus-
pended in a revolving center-ring, in gimbals, supported on a horizontal brass arm which is screwed
to the bulkhead; a vertical position is thus maintained by the tube at all times.
51. The wrnicc is an attachment for facilitating the exact reading of the scale of the barometer,
and is also applied to many other instruments of precision, as, for example, the sextant and theodolite.
It consists of a metal scale similar in general construction to that of the instrument to which it is fitted,
and arranged to move alongside of and in contact with the main scale.
The general principle of the vernier requires that its scale shall have a total length exactly e(iual
to some whole number of divisions of .the scale of the mstrument and that this length shall ))e subdivided
into a number of parts equal to 1 more or 1 less than the number of divisions of the instrument scale
which are covered; thus, if a space of 9 divisions of the main scale' be designated as the length of the
vernier, the vernier scale would to divided into either 8 or 10 parts.
Suppose that a barometer scale be divided into tenths of an inch and that a length of 9
divisions of such a scale be divided into 10 parts for a vernier (fig. 5) ; and suppose that the
31 divisions of the vernier \)e numbered consecutively from zero at the origin to 10 at the upper
extremity. If, now, by means of the movable rack and pinion, the bottom or zero division
of the vernier be brought level with the top of the mercurial column, and that division falls
into exact coincidence with a division of the main scale, then the height of the colunui will
correspond with the scale reading indicated. In such a case the top of the vernier will also
exactly coincide with a scale division, but none of the intermediate divisions will be evenly
abreast of such a division; the division marked "1" will fall short of a scale division by one-
tenth of 1 divison of the scale, or by 0.01 inch; that marked "2" by two-tenths of a division,
or 0.02 inch, and so on. If the vernier, instead of having the zero coincide with a scale
ao division, has the division " 1 " in such coincidence, it follows that the mercurial column stands
at 0.01 inch above that scale division which is next below the zero; for the division "2," at
0.02 inch; and similarly for the others. In the case portrayed in figure 5, the reading of the
column is 29.81 inches, the scale division next below the zero being 29.80 inches, while the
fact that the first division is abreast a mark of the scale shows that 0.01 inch must be added
to this to obtain the exact reading.
Had an example been chosen in which 8 vernier divisions covered 9 scale divisions — that
is, where the number of vernier divisions was 1 less than the number of scale divisions
covered — the principle would still have applied. But, instead of the length of 1 division of
the vernier falling short of a division of the scale by one-tenth the length of the latter, it would
have fallen beyond by one-eighth. To read in such a case it would therefore be necessary to
number the vernier divisions from up downward and to regard the subdivisions as jV instead
of 0.01 inch.
It is a general rule that the smallest measure to which a vernier reads is equal to the
length of 1 division of the scale divided by the number of divisions of the vernier; hence, by varying
either the scale or the vernier, we may arrive at any subdivision that may be desired.
52. The Sea Barometer is arranged as described for the instrument a.ssumed in the illustration; the
scale divisions are tenths of an inch, and the vernier has 10 divisions, whence it reads to 0.01 inch. It is
not necessary to seek a closer reading, as complete accuracy is not attainable in observing the height of a
barometer on a vessel at sea, nor is it essential. The Standard Barometer on shore, however, is capa-
ble of very exact reading; hence each scale division is made equal to half a tenth, or 0.05 inch, while
a vernier covering 24 such divisions is divided into 25 parts; hence the column maybe read to 0.002 inch.
53. To adjust the vernier for reading the height of the mercurial column the eye should be brought
exactly on a level with the top of the column; that is, the line of sight should be at right angles to the
scale. When properly set, the front and rear edges of the vernier and the uppermost point of the mer-
cury should all be in the line of sight. A piece of white paper, held at the back of the tube so as to
reflect the light, assists in accurately setting the vernier by day, while a small bull's-eye lamp held
behind the instrument enables the observer to get a correct reading at night. When observing the
barometer it should hang freely, not being inclined by holding or even by touch, l)ecause any inclina-
tion will cause the column to rise in the tube.
54. Other things being equal, the mercury will stand higher in the tube when it is warm than
when it is cold, owing to expansion. For the purposes of comparison, all barometric observations are
reduced to a standard which assumes 32° F. as the temi>erature of the mercurial column, and 62° F. as
that of the metal scale; it is therefore important to make this reduction, as well as that for instrumental
error (art. 56), in order to be enabled to compare the true barometric pressure with the normal that
may be expected for any locality. The following table gives the value of this correction for each 2° F.,
Fig. 5.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
23
the plus sign showing that the correction is to be added to the reading of the ship's barometer and the
minus sign that it is to be subtracted:
Tempera-
ture.
Correction.
Tempera-
ture.
Correction.
Tempera-
ture.
Correction.
Tempera-
ture.
Correction. !
o
Inch.
o
Inch.
o
Iruih.
Inch.
20
-1-0. 02
40
-0.03
60
-0.09
80
-0.14
22
-1-0. 02
42
-0.04
62
-0.09
82
-0.14
24
-1-0. 01
44
-0.04
64
-0.09
84
-0. 15
26
H-0. 01
46
-0.05
66
-0.10
86
-0.15
28
0.00
48
-0.05
68
-0.10
88
-0.16
30
0.00
50
-0.06
70
-0.11
90
-0.16
32
-0. 01
52
-0.06
72
-0.12
92
-0.17
34
- 0. 02
54
-0.07
74
-0.12
94
-0.17
36
-0.02
56
-0.07
76
-0.13
96
-0.18
38
-0.03
58
-0.08
78
-0.13
98
-0.18
As an example, let the observed reading of the mercurial barometer be 29.95 inches, and the tem-
perature as given by the attached thermometer 74°; then we have:
Observe<l lieight of the mercury 29. 95 '
Correction for temperature (74° ) —0. 12
Height of the mercury at standard temjierature 29. 83
55. Thk Aneroid Barometer. — This is an instrument in which the pressure of the air is measured
by means of the elawticity of a plate of metal. It consists of a cylindrical brass box, the metal in the
sides being very thin; the contained air having been partially, though not completely, exhausted, the
box is hermetically sealed. When the pressure of the atmosphere increases the inclosed air is compressed,
the capacity of the box is diminished, and the two flat ends approach each other; when the pressure of
the atmosphere decreases, the ends recede from one another in consequence of the expansion of the
inclosed air. By means of a combination of levers, this motion of the ends of the box is communicated
to an index pointer which travels over a graduated dial plate, the mechanical arrangement being such
that the motion of the ends of the box is magnifie<l many times, a very minute movement of the box
making a considerable difference in the indication of tlie pointer. The graduations of the aneroid scale
aie obtained by comparison with the correct readings of a standard mercurial barometer under normal
and reduced atmospheric pressure.
The thermometer attached to the aneroid barometer is merely for convenience in indicating the
temperature of the air, but as regards the instrument itself, no correction for temperature can be applied
with certainty. Aneroids, as now manufactured, are almost perfectly comjiensated for temperature by
the use of different metals liaving unequal coefficients of expansion; they ought, therefore, to show the
same pressure at all temperatures.
The aneroid barometer, from its small size and theea.se with wliich it may be transported, can often
be usefully employed under circumstances where a mercurial barometer would not be available. It also
has an advantage over the mercurial instrument in its greater sensitiveness, and the fact that it gives
earlier indications of change of jiressure. It can, however, be reliefl upon only when frequently com-
pared with a standard mercurial barometer; moreover, considerable care is re<]uired in its handling;
while slight shocks will not ordinarily affect it, a severe jar or knock may change its indications by a
large amount.
When in use the aneroid barometer may be suspended vertically or plaeetl flat, but changing from
one position to another ordinarily makes a sensible change in the readings; the instrument should
always, therefore, be kept in the same position, and the errors determined by comparisons made while
occupying its customary place.
56. Co.MP.\RisoN OF B.\Ro.METERs. — To determine the reliability of the ship's barometer, \\hether
mercurial or aneroid, comparisons should from time to time be made with a standard barometer.
Nearly all instruments read either too high or too low by a small amount. These errors arise, in a
mercurial barometer, from the improper placing of the scale, lack of uniformity of caliber of the gla.ss
tube, or similar causes; in an aneroid, which is less accurate and in which there is even more necessity
for fretiuent comparisons, errors may be due to derangement of any of the various mechanical featur«i
upon which itH working depends. The errors of the barometer should be determined for various
heights, as they are seldom the same at all parts of the scale.
In the principal ports of the world standard barometers are observed at specified times each day,
and the readings, reduced to zero and to sea level, are published. It is therefore only necessary to read
the barometer on sliipboard at those times, and, if a mercurial instrument is used, to note the attached
thenuometer and apply the correction for temperature (art. 54). It is evident that a comparison of the
heights by reduced standard and by the ship's barometer will give the correction to be applied to the
latter, including the instrumental error, the reduction to sea level, and the personal error of the
observer. In the United States, standard barometer readings are made Ijy the Weather Bureau and
Branch Hydrographic offices.
Aneroid barometers may be adjusted for instrumental error by moving the index hand, but this is
usually done only in the case of errors of considerable magnitude.
57. DpKRMiNATiox OF HEIGHTS BY' Babometer. — The barometer may be used to determine the
difference in heights between any two stations by means of the difference in atmospheric pressure
24
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
between them. An approximate rule ia to allow 0.0011 inch for each difference in Jevel of one foot, or,
more roughly, 0.01 inch for every 9 feet.
A very exact method is afforded by Babinet's formula. If B„ and B represent the barometric pres-
sure (corrected for all sources of instrumental error) at the lower and at the upper stations respectively,
and t„ and t the corresponding temperatures of the air; then.
Diff. in height=CX
B„-B
B.+B'
if the temperatures be taken by a Farhenheit thermometer.
<'
900
>
— — . .. ^ ^ — ,«(- — — — ^^ ..J — — ., — .^.v. .. [^.jj.
! are three classes of thermometer, distinguished according to the method of graduating the
Hows: the Fahrenheit, in which the freezmg point of water is placed at 32° and its boiling
C (in feet) = .52, 494 I i_|_
if a centigrade thermometer is used,
(in meters) = 16,000^1+?^^^^.
THE THERMOMETER.
58. The Thermometer is an instrument for indicating tenii)eraturc. In its construction advantage
is taken of the fact that bodies are expanded by heat and contracted by cold. In its most usual form
the thermometer consists of a bulb filled with mercury, connected with a tube of very fine cross-sectional
area, the liquid column rising or falling in the tube according to the volume of the mercury due to the
actual degree of heat, and the height of the mercury indicating upon a scale the temperature; the mer-
cury contained in the tube moves in a vacuum produced by the expulsion of the air through l)oiling tlie
mercury and then closing the top of the tube by means of the blowpipe.
There!
scale as follows
. point (under normal atmospheric pressure) at 212°; the' Ceiitif/mile, in which the freezing point is at 0°
and the boiling point at 100°; and the Reaumur, in which these points are at 0° and 80°, respectively.
The Fahrenheit thermometer is generally used in the United States and England. Tables will be
found in this work for the interconversion of the various scale readings (Table 31).
59. The thermometer is a valuable instrument for the mariner, not only by reason of the aid it
affords him in judging meteorological conditions from the temperature of the air and the amount of
moisture it contains, but also for the evidences it furnishes at times, through the temperature of the sea
water, of the ship's position and the probable current that is being encountered.
60. The thermometers employed in determining the temperature of the air ( wet and dry bulb)
and of the water at the surface, should be mercurial, and of some standard make, with the graduation
etched upon the glass stem; they should be Cf)mpared
with a<"curate standards, and not accepted if their read-
ings vary more than 1° from the true at any point of
the scale.
CI. The dry-bulb thermometer gives the tempera-
ture of the free air. The wet-bulb thermometer, an
exactly similar instrument the bulb of which is sur-
rounded by an envelope of moistened cloth, gives what
is known as the temperature of ernporntion, which is
always somewhat less than the temperature of the free
air. Froin the difference of these two temperatures the
observer may determine the proximity of the air to
saturation; that is, how near the air is to that )ioint
at which it will be obliged to precipitate some of its
moisture (water vapor) in the form of liijuid. With
the envelojie of the wet bulb removed, the two ther-
mometers should read precisely the same; otherwise
they are practically useless.
The two tliermoTneters, the wet and the dry bulb,
shciuld be hung within a few inches of each other, and
the surroundings should be as far as possible identical.
In ]iractice the two tliermometers are generally in<'losed
within a small lattice case, such as that shown in figure
6; the case should be placed in a position on deck
remote froiii any source of artificial heat, sheltered
from the <lirect rays of the sun, and from the rain and
spray, but freely exposed to tlie circulation of the air;
the door should be kept closed excei>t during the ])roc-
ess of reading. The cloth envelope of the wet bulb
should be a single thickness of fine muslin, tightly
stretched over the bulb, and tied with a fine thread.
Tlie wick which serves to carry the water from the
cistern to the bulb should consist of a few threads of
lampcotton, and should be of sufficient length to admit of two or three inches being coiled in the cistern. .
The muslin envelope of the wet bulb should be at all times thoroughly moist, but iU)t dripping.
When the temperature of the air falls to 82° F. the water in the wick freezes, the capillary action
is at an end, the bulb in consequence soon becomes (piite dry, and the thermometer no longer shows
the temperature of evaporation. At such times the bull) should be thoroughly wetted with ice-col<l
water shortly before the time of observation, using for this purpose a caiiiers hair tirusli or feather; by
Fig. 6.
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
25
this process the temperature of the wet bulb is temporarily raised above that of the dry, but only for a
brief time, as the water quickly freezes; and inasmuch as evaporation takes place from the surface of
the ice thus formed precisely as from the surface of the water, the thermometer will act in the same way
fts if it had a damp bulb. The wet-bulb thermometer can not properly read higher than the dry, and
if the reading of the wet bulb should be the higher, it may always be attributed to imperfections in the
instruments.
62. Knowing the temperature of the wet and dry bulbs, the relative humidity of the atmosphere
«t the time of observation may be found from the following table:
Tempera-
ture of the
air, dry-
Difference between dry-buJb and wet-bulb reading
s.
bulb ther-
mometer.
tv
2°
3°
4°
5°
CO
7°
8°
9°
10°
o
Perrt.
Perct.
Per el.
Per et.
Peret.
Peret.
Peret.
Perct.
Perct.
Perct.
24
87
75
62
50
38
26
26
88
76
65
53
42
30
28
89
78
67
56
45
34
24
30
90
79
68
58
48
38
28
32
90
80
70
61
51
41
32
23
34
90
81
72
63
53
44
35
27
36
91
82
73
64
55
47
38
30
22
38
92
83
75
66
57
50
42
34
26
40
92
84
76
68
59
52
44
37
30
22
42
92
84
77
69
61
54
47
40
33
26
44
92
85
78
70
63
56
49
43
36
29
46
93
86
79
72
65
58
51
45
38
32
48
93
86
79
73
66
60
53
47
41
35
50
93
87
80
74
67
61
55
49
43
37
52
94
87
81
75
69
63
57
51
46
40
54
94
88
82
76
70
64
59
53
48
42
56
94
88
82
77
71
65
60
55
50
44
58
94
89
83
78
72
67
61
56
51
46
60
94
89
84
78
73
68
63
58
53
48
62
95
89
84
79
74
69
64
59
54
50
64
95
90
85
79
74
70
65
60
56
51
66
95
90
85
80
75
71
66
61
57
53
68
95
90
85
81
76
71
67
63
58
54
70
95
90
86
81
77
72
68
64
60
55
72
95
91
86
82
77
73
69
65
61
57
74
95
91
86
82
78
74
70
66
62
58
76
95
91
87
82
78
74
70
66
63
59
78
96
91
87
83
79
75
71
67
63
60
80
96
92
87
83
79
75
72
68
64
61
82
96
92
88
84
80
76
72
69
65
62
84
96
92
88
84
80
77
73
69
66
63
86
96
92
88
84
81
77
73
70
67
63
88
96
92
88
85
81
77
74
71
67
64
90
96
92
88
85
81
78
74
71
68
a5
The table may be readily understood. For example, if the temperature of the air (dry bulb) be
60°, and the temperature of evaporation (wet bulb) be 56°, the ilifference teing 4°, look in the cohmm
heade<l "Temperature of the air" for 60°, and for the figures on the same line in column headed 4°;
here 78 will be found, which means that the air is 78 per cent saturated with water vapor; that is, that
the amount of water vapor present in tlie atmosphere is 78 per cent of the total amount that it could
<'arry at the given temperature (60°). This total amount, or saturation, is thus represented by 100, and
if there occurred any increase of the quantity of vapor beyond this point, the excess would be precipi-
tated in the form of liquid. Over the ocean's surface the relative humidity is generally about 90 per
cent, or even higher in the doldrums; over the land in dry winter weather it may fall as low as 40 per
cent.
63. The sea water of which the temperature is to be taken should be drawn from a depth of 3
feet below the surface, the bucket used being weighted in order to sink it. The bulb of the thermome-
ter should remain immersed in the water at least three minutes before reading, and the reading should
be made with the bulb immersed.
THE LOG BOOK.
64. The Tx)g Book is a record of the ship's cruise, and, as such, an imjjortant accessory in the navi-
gation. It should afford all the data from which the position of the ship is established by the method
of dead reckoning; it should also comprise a record of meteorological observations, which should be
made not only for the purpose of foretelling the weather during the voyage, but also for contribution to
the general fund of knowledge of marine meteorology.
65. A convenient form for Tecording the data, which is employed for the log books of United States
naval vessels, is shown on page 26; beside the tabulated matter thus arranged, to which one page of the
book is devoted, a narrative of the miscellaneous events of the day, written and signed by the proper
officers, appears upon the ojiposite jiage.
26
IN8TBUMENTS AND ACCESSORIES IN NAVIGATION.
State of
sea by
symbols.
1
o S o
is
111
s
H
-
■■^■si
1
Ipl
H S
ji
X
i
■a
5
Hi
Si's .
ill
m
5-
Reading
of
patent
log.
00
si
c
1
o
M .
S S 2
3^ CG 00 Xi a
6C M tic 2 5
INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
27
«6. For the most part, the nature of the information called for, with the method of recording it,
will he apparent. A brief explanation ia here given of such points as seem to require it.
67. The Wind. — In recording the force of the wind the scale devised by the late Admiral Sir F.
Beaufort is employed. According to this scale the wind varies from 0, a calm, to 12, a hurricane, the
greatest velocity it ever attains. In the lower grades of the scale the force of the wind is estimated
from the speed imparted to a man-of-war of the early part of the nineteenth century sailing full and by;
in the higher grades, from the amount of sail which the same vessel could carry when closehauled.
The scale, with the estimated velocity of the wind in both statute and nautical miles per hour, is as
follows:
Velocity.
Mean pressure
Conditions.
in pounds
per square
Foroe of wind.
Statute miles per
Nautical miles per
hotir.
hotir.
foot.
Oalm
Full-riwred ship, ail sails set, no headway .
Just sufficient to give steerage way
Speed of 1 or 2 knot.'i, "full and by "
to 3
8
13
to 2.6
6.9
11.3
0.03
0.23
■J.— Light breezo
0.62
3.— Gentle breeze
Speed of 3 or 4 knots, "fuUaud by"
18
15.6
1.2
4.— MtMlerate breeze..
Speed of 5 or 6 knots, "full and by "
23
20.0
1.9
28
24.3
2.9
6.— Strong breeze
Topgallantsailsoversingle- reefed topsails
34
29.5
4.2
7.— Moderate gale —
*.— Fresh gale
40
34.7
5.9
Treble-reefed topsails (or reefed upper-
48
41.6
8.4
topsails and courses).
9. — Str* »ng gale
Clase-reefedtopsailsandcourses(or lower
topsails and courses).
66
48.6
11.5
10.— Whole gale
Close-reefed main topsail and reefed fore-
sail (or lower main topsail and reefed
foresail).
&5
56.4
15.5
' 75
90 and over.
65.1
78. 1 and over.
20.6
29.6
6». When steaming or sailing with any considerable speed, the apparent direction and force of
the wind, as determined from a vane, flag, o"r pennant aboard ship, may differ materially froin the true
direction and force, the reason being that the air appears to come from a direction and with a force
dependent, not only upon the wind itself, but also upon the motion of the vessel. For instance,
suppose that the wind has a velocity of 20 knots an hour (force 4), and take the case of two vessels,
each steaming 20 knots, the first with the wind dead aft, the second with the wind dead ahead. The
former ve'<8el will be moving with the same velocity as the air and in the same direction; the velocity
of the wind relatively to the ship will thus Ije zero; on the vessel an apparent calm will prevail and the
pennant will hang up and down. The latter vessel will l)e moving with the same velocity as the air, but
in the opposite direction ; the relative velocity of the two will thus be the sum of the two velocities, or 40
knots an hour, and on the second vessel the wind will apparently have the velocity corresponding very
nearly with a fresh gale. Again, it might be shown that in the case of a vessel steaming west at the
rate of 20 knots, with the wind blowing from north with the velocity of 20 knots an hour, the velocity
with which the air strikes the ship as a result of the combined motion will be 28 knots an hour, and
the direction from which it comes will be NVV. If, therefore, the effect of the the speed of the ship is
neglected the wind will te recorded as N\V., force 6, when in reality it is north, force 4.
In order to make a proper allowance for this error and arrive at the true direction and force of the
wind, Table 32 may be entered with the ship's speed and the apparent direction and force of the wind
as arguments, and the true direction and force will be found.
69. We.vther. — To designate the weather a series of symbols devised by the late Admiral Beaufort
is employed. The system is as follows:
//. — Clear blue sky.
r. — Clouds.
)l. — Drizzling, or light rain.
/. — Fog, or foggy weather.
g. — (iloomy, or dark, stormy-looking weather.
//.—Hail.
/. — Lightning.
)/(. — Misty weather.
0. — Overcast.
p. — Passing showers of rain.
q. — Squally weather.
r. — Rainy weather, or continuous rain.
s. — Snow, or snowv weather.
/.—Thunder.
u. — Ugly appearances, or threatening weather.
r. — Visibility of distant objects.
«'. — Wet, or heavy dew.
z. — Hazv.
To indicate great intensity of any feature, its symbol may be underlined; thus: r., heavy rain.
?0. Cloi'ds. — The following are the principal forms of clouds, named in the order of the altitude
above the earth at which they usually occur, teginning with the most elevated. The symbols by which
each is designated follows its name:
1. Cirrus, {(1.). — Detached clouds, delicate and fibrous looking, taking the form of feathers,
generally of a white color, sometimes arranged in belts which cross a portion of the sky in great circles,
and, by an eflect of perspective, converging toward one or two opposite points of the horizon.
2. Cirro-Stratl's, (Ci.-S.). — A thin, whitish sheet, sometimes completely covering the sky and
only giving it a whitish appearance, or at others presenting, more or less distinctly, a formation like a
tangled web. This sheet often produces haloa around the sun and moon.
3. CiRRO-CuMULUs, (Oi.-ft*.).— Small globular masses or white flakes, having no shadows, or only
very slight shadows, arranged in groups and often in lines.
* 4. Alto-Cumulus, (A.-Cu.). — Rather large globular masses, white or grayish, partially shaded,
arranged in groups or lines, and often so closely packed that their edges appear confused. The detached
masses are generally larger and more compact at the center of the group; at the margin they form into
liner flakes. They'often spread themselves out in lines in one or two directions.
28 INSTRUMENTS AND ACCESSORIES IN NAVIGATION.
5. Alto-Stratus, (A.-S.). — A thick sheet of a gray or bluish color, showing a brilliant patch in the
neighborhood of the sun or moon, and which, without causing halos, may give rise to coronpo. This
form goes through all the changes like the Cirro-Stratus, but its altitude is only half so great.
6. Strato-C'i'mi-lus, (S.-Cu.). — Large globular masses or rolls of dark cloud, frequently covering the
whole sky, especially in winter, and occasionally giving it a wavy appearance. The layer of Strato-
(Ximulus is not, as a rule, very thick, and patches of blue sky are often visible through tlie intervening
spaces. All sorts of transitions between this form and the Alto-Cumulus are noticeable. It may be
distinguished from Nimbus by its globular or rolled appearance and also because it does not bring rain.
7. Nimbus, {N.). — Rain clouds; a thick layer of dark clouds, without shape and with ragged edges,
from which continued rain or snow generally falls. Through the openings of these clouds an upper
layer of Cirro-Stratus or Alto-Stratus may almost invariably be seen. If the layer of Nimbus separates
into shreds or if small loose clouds are visible floating at a low level underneath a large nimbus, they
may be describe<l as Fracto-Nimbus (Fr.-N. ), the " scud " of sailors.
8. Cumulus, {C'ti.). — Wool-pack clouds; thick clouds of which the upper surface is dome-shajjed
and exhibits protuberances, while the base is horizontal. When these clouds are opposite the sun the
surfaces usually presented to the observer have a greater brilliance than the margins of the protuter-
ances. When the light falls aslant, they give deep shadows; when, on the contrary, the clouds are on
the same side as the sun, they appear dark, with bright edges. The true Cumulus has clear superifir
and inferior limits. It is often broken up by strong winds, and the detached portions undergo continual
changes. These may be distinguished by the name of Fraeto-Cumulus (i^.-C((. ).
9. CuMULo-NiMBus, ( On. -N. ) . — The thunder-cloud or shower-cloud ; heavy masses of clouds rising in
the form of mountains, turrets, or anvils, generally having a sheet or screen of fibrous appearance above,
and a mass of clouds similar to Nimbus underneath. From the base there usually fall local shower*
of rain or of snow (occasionally hail or soft hail).
10. Stratus, (S.). — A horizontal sheet of lifted fog; when this sheet is broken up into irregular
shreds by the wind or bv the summit* of mountains, it mav be distinguished by the name of Fracto-
Stratus (Fr.-S.).
71. In the scale for the amount of clouds represents a sky which is cloudless and 10 a sky which
is completely overcast.
72. State of Sea. — The state of th^ sea is expressed by the following system of symbols:
B.— Broken or irregular sea. M. — Moderate sea or swell.
C. — Chopping, short, or cross sea. R. — Rough sea.
6. — Ground swell. S. — Smooth sea.
H. — Heavy sea. T. — Tide-rips.
L. — Long rolling sea.
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THE COMPASS ERROR. 29
■^
CHAPTER III
THE COMPASS ERROR.
<.^ CAUSES OF THE ERROP.
7:1. When two magnets are near enough together to exert a mutual influence, their properties are
such an to cause those poles whicli possess similar magnetism to repel, and those which possess magnet-
ism of opposite sorts to attract one another.
The earth is an immense natural m^net, having in each hemisphere a pole lying in the neighlx>r-
•>^ ii< i\ of the geographical pole, though not exactly coincident therewith; consequently, when a magnet,
^^^such as that of a compass, is allowed to revolve freely in a horizontal plane, it will so place itself as to
be parallel to the lines fif magnetic force in that plane created l)y the earth's magnetic poles, the
end which we name north pointing to the north, and the south end in the opposite direction. The
north end of the compass — north-seeking, as it is sometimes designated for clearness — will be that end
which has o|)j>osite polarity to the earth's north magnetic pole, this latter possessing the same sort of
-Vnagnetism as the so-called south pole of the compass.
74. By reason of tlie fact that the magnetic pole diffefsin position from the geographical pole, the
^t compass needle will not indicate true directions, but each compass point will differ from the corres[)ond-
ing true point by an amount dependent upon the angle between the geographical and the magnetic pole
at the position of the observer. The amount of this difference, expressed in angular measure, is the
Variation of the Compass (sometimes callefl also the Derlination, though this term is seldom employed by
navigatfirs).
The variation not only changes as one travels from point to point on the earth, being different in
different localities, but, as it has been found that the earth's magnetic poles are in constant motion, it
" '«rgoes certain changes from year to year. In taking account of the error it produces, the navigator
. therefore be sure that the variation used is correct not only for the place, but also for the lime
■r consideration. The variation is subject to a small diurnal fluctuation, but this is not a material
conitKeration with the mariner.
75. Besides the error thus produced in the indications of the compass, a further one, due to Loral
Attraction, may arise from extraneous influences due to natural magnetic attraction in the Vicinity of the
; vessel. Instances of this are quite common when a ship is in port, as she may be in close proximity to
vessels, docks, machinery, or other masses of iron or steel. It is also encountered at sea in localities wfiere
the mineral substances in the earth itself possess magnetic qualities — as, for example, at certain ])laces in
Lake Superior and at others off the coast of Australia. When due to tlie last-named cause, it may be a
source of great danger to the mariner, but, fortunately, the number of localities subject to local attraction
is limited. The amount of this error can seldom, if ever, be determined; if known, it might jiroperly
be included with the variation and treated as a part thereof.
76. In addition to the variation, the compass ordinarily has a still further error in its indications,
which arises from the effect exerted upon it by masses of magnetic metal within the ship itself. This
is known as the Di-riation of the Compass. For reasons that will be explained later, it differs in amount
for each heading of the ship, and, further, the character of the deviations undergo modification as a
vessel proceeds from one geographical locality to another.
APPLYING THE COMPASS ERROR.
77. From what has been explained, it may be seen that there are three methods by which bearings or
courses may be expressed: (a) tr>ie, whentheyreferto the angular distance from the earth's geographical
meridian; (';) magnetic, when they refer to the angular distance from the earth's magnetic meridian,
and must be corrected for variation to be converted into true; and (c) hy compass, when they refer to
the angular distance from the north indicated by the compass on a given headmg of the ship, and must
be corrected for the deviation on that heading for conversion to magnetic, and for both deviation and
variation for conversion to true bearings or courses. The process of applying the errors under all circum-
stances is one of which the navigator must make himself a thorougli master; the various problems of
conversion are constantly arising; no course can beset nor liearing plotted without involving the applica-
tion of this problem, and a mistJake in its solution may produce serious consequences. The student is
therefore ui^ed to give it his most careful attention.
30
THE COMPASS ERROR.
78. When the effect of a compass error, whether arising from variation or from deviation, is to
draw the north end of the compass needle to the right, or eastward, the error is named east, or is
marked + ; when its effect is to draw the north end of the needle to the left or westward, it is named
icest, ormarlied ~.
Figures 7 and 8 represent, respectively, examples of easterly and westerlj^ errors. In both cases
consider that the circles rep-
resent theobserver's horizon,
N and S being the correct
nortli and south points in
each case. If N' and S' repre-
sent the corresponding points
indicated by a com pass whose
needle is deflected by a com-
pass error, then in the first
case, the north end of the
needle being drawn to the
right or east, the error will
be easterly or positive, and
in the second case, the north
end of the needle being drawn
to the left or west, the com-
pass error will be westerly or
negative.
Considering ligure 7, if
we assume the easterly error to amount to one point, it will be seen that if a direction of N. by W. is
indicated by the compass, the correct direction should be north, or one point farther to the right. If
the compass indicates north, the correct bearing is N. by E. ; that is, still one point to the right
If we follow around the whole card, the same relation will be found in every case, the corrected bearing
being always one point to the right of the compass bearing. Conversely, if we regard figure 8, assuming
the same amount of westerly error, a compass bearing of N. by E. is the equivalent of a {'orrect bearing
of north, which is one point to the left; and this rule is general throughout the circle, the corret'ted
direction being always to the left of that shown by the compass.
79. Having once satisfied himself that the general rule holds, the navigator may save the necessity
of reasoning out in feach case the direction in which the error must be applied, and need only charge
his mind with some single formula which will cover all cases. Such a one Is the following:
When the correct direction, is to the right, the error is east.
The words correct-righl-east, in such a case, would be the key to all of his solutions. If he had a
compass course to change to a corrected one with easterly deviation, he would know that to obtain the
result the error must be applied to the right; if it were desired to change a correct course to the one indi-
cated by compass, the error being westerly, the converse presents itself— the correct must be to the
left— the uncorrected will therefore be to the right; if a correct bearing is to be compared with a com-
pass bearing to find the compass error, when the correct is to the right the error is east, or the reverse.
SO. It iiHist be remembered that the word east is equivalent to riyht in dealing with the compass
error, and west to left, even though they involve an apparent departure from the usual rules. If a
vessel steers NE. by compass with one point easterlv error, her corrected course is NE. by E. ; but if
she steers SE., the corrected course is not SE. by E., but SE. by S. Another caution may be necessary
to avoid confusion; the navigator should always regard himself as facing the point under consideration
when he applies an error; one point westerly error on South will bring a corrected direction to S. by
E.; but if we applied one point to the left of South while looking at the compass card in the usual
.„j.ay— north end up — S. by W. would l)e the point arrived at, and a mistake of two points would be the
result. . .
81. In the foregoing explanation reference has been made to " correct" directions and compass
errors" without specifying "magnetic" and "true" or "variation" and "deviation." This has been
done in order to make the statements apply to all cases and to enable the student to grasp the .^ubjei-t
in its general bearing without confusion of details.
Actually, as has already been pointed out, directions given may be true, magnetic, or bj; compass.
By applying variation to a magnetic bearing we correct it and make it true, by applying deviation to a
compass bearing we correct it to magnetic, and by applying to it the combined deviation and variation
we correct it to true. Whichever of these operations is undertaken, and whichever of the errors is
considered, the process of correction remains the same; the correct direction is always to the right,
when the error is east, by the amount of that error.
Careful study of the following examples will aid in making the subject clear:
Examples: A bearing taken by a compass free from deviation is N. 76° K.; variation, 0° W.;
required the true bearing. N. 71° E.
A bearing taken by a similar compass is NW. bv W. i W.; variation, i pt. W.; require<l the true
bearing. NW. by W. | W. . . , , ,.
A vessel steers S. 27° E. by compass; deviation on that heading, 8° W.; variation in the locality,
12° E.; required the true couree. S. 18° E.
A vessel steers S. bv W. i W.; deviation, i pt. W.; variation,
SSW. i W.
It is desired to steer the magnetic course N. 38° W.; deviation,
pass. N. 42° W.
The true course between two points is found to be W. ; X.
required the compass course. W. | S.
True course to be made, X. 5.5° E.; deviation, 7° E. ; variation, 14° W.
compass. N. H2° E.
1 ,,t
4° E.
E. ; required the true course,
required the course by coin-
variation U pt. E.; no deviation;
requirefl the coui'se by
THE COMPASS EKKOR. ' 31
A vessel passing a range whose direction is known to be S. 20° W., magnetic, observes the bearing
by compass to be S. 2° K. ; re(|uired the deviation. 22° E.
The sun's observed bearing i)y compass is S. 89° E. ; it is found by calculation to be N. 84° E. (true) ;
variation, 8° W. ; required the deviation. 1° E.
FINDING THE COMPASS EBBOB.
82. The variation of the compa.«!J for any given locality is found from the charts. A nautical
chart always contains infonnation hom which the navigator is enabled to ascertain the variation for
any place within the region embraced and for any year. Beside the information thus to be acquired
from local charts, special charts are published showing the variation at all points on the earth's surface.
83. The deviation of the compass, varying as it does for every ship, for every heading, and for
every geographical locality, must be determined by the navigator, for .which purpose various methods
are available.
Whatever method is used, the ship must be swung in azimuth and an observation made on each of
the headings upon which the deviation is required to be known. If a new iron or steel ship is being
swung for the first time, observations should be made on each of the thirty-two points. At later
swings, esjiecially after correctors have been applied, or in the case of wooden ships, sixteen points
will suffice — or, indeed, only eight. In case it is not practicable to make observations on exact compass
points, they should be made as near thereto as practicable and platted on the Napier diagram (to' be
explained hereafter), whence the deviations on exact points may be found.
84. In swinging ship for deviations the vessel should he on an even keel and all movable masses
of iron in the vicinity of the compa.ss secured as for sea. The vessel, upon being placed on any heading,'
should be stea<lied there for three to four minutes before the observation is made in order that the
compass card may come to rest and the magnetic conditions assume a .settled state. To a.ssure the
greatest accuracy "the ship should first be swung to starboard, then to port, and the mean of the two
deviations on each course taken. Ships may be swung under their own steam, or with the assistance
of a tug, or at anchor, where the action of the tide tends to turn them in azinuith (though in this case
it is difficult to get them steadied for the requisite time on each heading), or at anchor, by means of
springs and hawsers.
85. The deviation of all (ompas-ses on the ship may be obtained from the same swing, it teing
required to make observations with the standard only. To accomplish this it is necessary to record the
ship's head by all compasses at the time of steadying on each even point of the standard; applying
the deviation, as ascertained, to the hea<ling by standard, gives the magnetic heads, with which the
direction of the ship's Iiead by each other compass may be compared, and the deviation thus obtained.
Then a complete table of deviations may be constructed as explained in article 94.
86. There are four methods for ascertaining the deviations from swinging; namely, by reciprocal
hearings, by bearings of the sun, by rntigen, and by a distant object.
87. Reciproc.m, Be.\rin<;s. — One observer is stationed on shore with a spare compass placed in a
jiosition free from disturbing magnetic influences; a second observer is at the standard compass on
board ship. At the instant when ready for observation a signal is made, and each notes the bearing
of the other. The bearing by the shore compass, reversed, is the magnetic bearing of the shore station
from the ship, and the difference between this and the bearing by the ship's standard compass repre-
sents the deviation of the latter.
In determining the deviations of compasses placed on the fore-and-aft amidship line, when the
distribution of magnetic metal to starboard and port is symmetrical, the shore compass may be replaced
by a dumb compass, or pelorus, or bv a theodolite in which, for convenience, the zero of the horizontal
graduated circle may be ternie<l north; the reading of the shore instrument will, of course, not represent
magnetic directions, but by assuming that they do we obtain a series of fictitious deviations, the mean
value of which is the error common to all. Upon deducting this error from each of the fictitious devia-
tions, we obtain the correct values.
If ship and shore observers are provided with watches which have been compared with one
another, the times may te noted at each observation, and thus afford a means of locating errors due to
misunderstanding of signals.
88. Bearings of the Six. — In this method it is required that on each heading a Ijearing of the
sun be observed by compass and the time noted at the same moment by a chronometer or watch. By
means which will be exi)laine<l in Chapter XI\', the true bearing of the sun may be ascertained from
the known data, and tiiis, compared with the compass tearing, gives the total compass error; deducting
from the compass error the variation, there remains tlie deviation. The variation used may l)e that
given by the chart, or, in the case of a compass affected only by symmetrically placed iron or steel, may
be considered equal to the mean of all the total errors. Other celestial bodies may be observed for this
purpose in the same manner as the sun.
This meth(xl is important as being the only one available for determining the compass error at sea.
89. Ran<ie.s. — In many localities there are to be found natural or artificial range marks which are
clearly distinguishable, and which when in line lie on a known magnetic bearing. By steaming about
on different headings and noting the compass bearing of the ranges each time of crossing the line that
they mark, a series of deviations may be obtained, the deviation of each heading being equal to the
difference between the compass and the magnetic bearing.
90. Distant Ohiect. — A conspicuous object is selected which must be at a considerable distance
from the ship and upon which there should l)e some clearly defined point for taking bearings. The
direction of this object by compass is observed on successive headings. Its true or magnetic bearing is
then found and compared with the compass bearings, whence the deviation is obtained.
The true or the magnetic bearing may be taken from the chart. The magnetic bearing may also be
found by setting up a compass ashore, free from foreign magnetic disturbance, in range with the object
and the ship, and observing the bearing of the object; or the magnetic bearing maybe assumed to be the
mean of the compass tarings.
32
THE COMPASS ERROK.
In choosing an object for use in this method care must be taken that it is at such a distance that its
bearing from the ship does not practically tliffer as the vessel swings in azimuth. If the ship is swung
at anchor, the distance should be not less than 6 miles. If swung under way, the object must be so far
that the parallax (the tangent of which may be considered equal to half the diameter of swinging
divided by the distance) shall not exceed about .S(K.
91. in all of the methods described it will be found convenient to arrange the results in tabular
form. In one column record the ship's head by .standard compass, and abreast it in successive columns
the observations from whict the deviation is determined on that heading, and finally write the deviation
itself. When the result of the swing has been worked up another table is constructed showing simply
the headings and the corresponding deviations. This is known as tlie DerkUlon Table of the compass.
If compensation is to be attempted, this table is the basis of the operation; if not, the deviation tables
of the standard and steering compass should be posted in such place as to be accessible to all persons
concerned with the navigation of the ship.
92. Let it be assumed that a deviation table has been found and that the values are as follows:
Deviation table.
Ship's head by
standard compass.
Devia-
tion.
Ship's head by
standard compass, j
Devia-
tion.
North
N. by E .
NNE....
NE. by N
NE
NE. by E
ENE....
E. by N .
- 1 50
- 3 00
- 5 15
- 7 10
-10 15
-13 05
-17 10
1 00 i East -19 55 '■ South
E. by S... -22 00
ESE -23 30
SE. by E .'-24 00
SE -23 30
SE. bvS.. -20 30
SSK. '..... -16 00
S.by E... - 8 50
Ship's head by
standard compass.
Devitt-
tiOD.
Ship's head by Devia-
standard compass. tion.
00 West.
W. by N...
WNAV
NW. bvW.
S.bv W... -flO 20
SSW +17 00
SW. by S.. +21 50 i
SW^ +24 30 NW.
SW. bv W . 4-26 20 ' NW. Ijy N .
WSW" +25 00 NNW
W. hv S . . . Lo;; ;{o X. bv AV. . .
+19 30
+17 00
+ 13 00
+11 10
+ 7 40
-I- 5 05
+ 3 00
+ ! 00
We have from the table the amount of deviation on each compass heading; therefore, knowing the
ship's head by compass, it is easy to pick out the corresponding deviation and thus to obtain the mag-
netic heading. But if we are given the magnetic direction in which it is desired to steer and have to
find, the corres]ionding compass course, the problem is not so simple, for we are not given deviations
on magnetic heads, and where the errors are large it may not te assumed that they are the same as on
the corresponding compass headings. For example, with the deviation table just given, suppose it is
required to determine the compass heading corresponding to N. 79° W., magnetic.
The deviation corresponding to N. 79° W., per compass, is + 17° 00'. If we apply this to N. 79°
W., magnetic, we have S. 84° W. as the compass course. But, consulting the table, it may be seen that
the deviation corresponding to S. 84° W., per compass, is -f 21j°, and therefore if we steer that course
the magnetic direction will be N. 74J° W., and not N. 79° AV., as desired.
A way of arriving at the correct result is to make a series of trials until a (-(jurse is arrived at which
fulfills tlie conditions. Thus, in the example given:
Mag. course required . .
Try dev. on N. 79° W.,
p. c
FIrxt trial.
. . N. 79° W.
17° E.
. . S. 84° W.
21i°E.
g. course made good N. 74J° W.
Since this assumption carries the course 4J° too
far to the right, assume next a deviation on a
course 5° farther to the left than the one used here.
Trial comp. course
Dev. on S. 84° W., p. c
Mag. course required .
Try dev. on S. 79° W.,
Trial comp. course
Dev. on S. 77r W.
p. c
p. c...
Second trinl.
N. 79° W.
23i° E.
S. 77J° W.
24° E.
Mag. course made good N. 78 j ° W.
This is as close to the recpiired ccairse as the ship
can be steered. It may occur that further trials
will be necessarv in some cases.
93. TnE Napier Diaokam. — A much more expeditious method for the solution of this problem is
afforded by the Napier Diagram, and as that diagram also facilitates a number of other operations con-
necte<l with compass work it should be clearly understood by the navigator. This device admits of a
graphic representation of the table of deviations of the compass V)y means of a curve; besides furnishing
a ready means of converting compass into magnetic courses and the reverse, one of its chief merits is
tliat if the deviation has been determined on a certain nundier of headings it enables one to obtain the
most probable value of the deviation on any other course that the ship may head. The last-named
feature renders it useful in making a table of deviations of compasses other than the standard when their
errors are found as described in article 85.
THE COMPASS ERROR.
33
94. The Napier diagram (fig. 9) represents the margin of a compass card cut at the north point and
itraightened into a vertical line; for convenience, it is usually divided into two sections, representing,
respectively, the eastern and western semicircles. The vertical line is of a convenient length and divided
into thirtv-two equal parts corresponding to the points of the compass, beginning at the top with North
and continuing around to the right; it is also divided into 360 degrees, which are appropriately marked.
DEVIATION
WEST
DEVIATION
EAST
Fio. 9.
The vertical line is intersected at each compass point by two lines inclined to it at an angle of 60°,
that line which is inclined upward to the right bein^ drawn plain and the other dotted.
To plot a curve on the Napier diagram, if the deviation has been observed with the ship's head on
given ««Hpf(ji« courses (as is usually the case with th^. standard compass), measure off on the vertical
scale the number of degrees corre.sponding to the deviation and lay it down — to the right if easterly and
to the left if westerly — on the doited line passing through the point representing the ship's head; or, if
the observation was not made on an even point, then lay it down on a line drawn parallel to the dotted
ones through that division of the vertical line which represents the compa.s8 heading; if the deviation
has been observed with the ship on given magnetic courses (as when deviations by steering compass are
obtained by noting the ship's head during a swing on even points of the standard) , proceed in the same
way, excepting that the deviation must be laid down on a plain line or a line parallel thereto. Mark
each point thus obtained with a dot or small circle, and draw a free curve passing, as nearly as possible,
through all the points.
24972°— 12 3
34
THE COMPASS EBKOR.
To obtain a complete curve, a sufficient number of observations should be taken while the ship
swings through an entire circle. Generally, observations on every alternate point are enough to estab-
lish a good curve, but in cases where the maximum deviation reaches 40° it is preferable to observe on
every point.
the curve shown in the full line on figure 9 corresponds to the table of deviations given in article 92,
From a giren compass course to find the corresponding magnetic course, through the point of the vertical
line representing the given compass course, draw a line parallel to the dotted linen until the curve is
intersected, and from the point of intersection draw another line parallel to the plain lines; the point on
the scale where this last line cuts the vertical line is the magnetic course sought. The correctness of
this solution will be apparent when we consider that the 60° triangles are equilateral, and therefore the
distance measured along the vertical side will equal the distance measured along the inclined sides —
that is, the deviation; and the direction will be correct, for the construction is such that magnetic
directions will be to the right of compass directions when the deviation is easterly and to the left if
westerly.
From a given magnetic course to find the corresponding compass course, the process is 1 ho same, excepting
that the first line drawn should follow, or be parallel to, the plain lines, and the second, or return line,
should be parallel to the dotted; and a proof similar to that previously employed will show the correctness
of the result. As an example, the problem given in article 92 may be solved by the diagram, and the
result will be found to accord with the solution previously given.
THE THEORY OF DEVIATION."
95. Features of the Earth's Magnetism. — It has already been stated that the earth is an
immense natural magnet, with a pole in each hemisphere which is not coincident with the geographical
pole; it has also a magnetic equator which lies close to, but not coincident with, the geographical
equator.
A magnetic needle freely suspended at a point on the earth's surface, and undisturbeil by any
other than the earth's magnetic influence, will lie in the plane of the magnetic meridian and at an
angle with the horizon depending upon the geographical position.
The magnetic elements of the earth which must be considered are shown in figure 10. The earth's
total force is represented in direction and intensity by the line AB. Since compass needles are mechan-
ically arranged to move only in a horizontal plane, it becomes
necessary, when investigating the effect of the earth's mag-
netism upon them, to resolve the total force into two com-
ponents which in the figure are represented by AC and AD.
These are known, respectively, as the horizontal and vertical
components oi the earth's total force, and are usually designated
as H and Z. The angle CAB, which the line of direction
makes with the plane of the horizon, is called the magnetic
inclination or dip, and denoted by 6.
It is clear that the horizontal component will reduce to
zero at the magnetic poles, where tlie needle points directly
downward, and that it will reach a maximum at the magnetic
equator, where the free needle hangs in a horizontal direction.
The reverse is true of the vertical component and of the angle
of dip.
Values representing these different terms may Vie found
from special charts.
96. Induction; Hard and -Soft Iron. — When a piece of
unmagnetized iron or steel is brought within the influence of
a magnet, certain magnetic properties are immediately imparted
to the former, which itself becomes magnetic and continues to
remain so as long as it is within the sphere of influence of the
permanent magnet; the magnetism that it acquires under these
circumstances is said to be induced, and the properties of induc-
tion are such that that end or region which is nearest the pole
of the influencing magnet will take up a polarity opposite thereto. If the magnet is withdrawn, the
induced magnetism is soon dissipated. If the magnet is brought into proximity again, but with its
opposite pole nearer, magnetism will again te induced, but this time its polarity will be reversed. A
further property is that if a piece of iron or steel, while temporarily possessed of magnetic qualities
through induction, be subjected to blows, twisting, or mechanical violence of any sort, the magnetism
is thus made to acquire a permanent nature.
The softer the metal, from a physical point of view, the more quickly and thoroughly will induced
magnetism be dissipated when the source of influence is withdrawn; hard metal, on the contrary, is
slow to lose the effect of magnetism imparted to it ip any way. Hence, in regarding the different features
which affect deviation, it is usual to denominate as hard iron that which possesses retained magnetism
of a stable nature, and as soft iron that which rapidly acquires and parts with its magnetic qualities
under the varying influences to which it is subjected.
97. Magnetic Properties Acquired by an Iron or Steel Vessel in Building. — The inductive
action of the earth's magnetism affects all iron or steel within its influence, and the amount and
permanency of the magnetism so induced depends upon the position of the metal with reference to the
earth's total force, upon its character, and upon the degree of hammering, bending, and twisting that it
undergoes.
n As it is probable that the student will not have practical need of a knowledge of the theory of deviation and the
compensation of the compass until after he has mastered all other subjects pertaining to Navigation and Nautical
Astronomy, It may be considered preferable to omit the remnindcr of this chapter at first and return to it later.
Fig. 10.
THE COMPASS ERROR. 35
An iron bar held in the line of the earth's total force instantly becomes magnetic; if held at an
angle thereto it -nould acquire magnetic properties dependent for their amount upon its inclination to
the line of total force; when held at right angles to the line there would be no effect, as each extremity
would be ecjually near the poles of the earth and all influence would be neutralized. If, while such a
bar is in a magnetic state through inductive action, it should be hammered or twisted, a certain mag-
netism of a permanent character is impressed upon it, which is never entirely lost unless the bar is
subjected to causes eijual and opposite to those that produced the first effect.
A sheet of iron is affected by induction in a similar way, the magnetism induced by the earth
diffusing itself over the entire plate and separating itself into regions of opposite polarity divided by a
neutral area at right angles to the earth's line of total force. If the plate is hammered or bent, this
magnetism takes up a permanent character.
If the magnetic mass has a third dimension, and assumes the form of a ship, a similar condition
prevails. The whole takes up a magnetic character; there is a magnetic axis in the direction of the line
of total force, with poles at its extremities and a zone of no magnetism perpendicular to it. The distri-
bution of magnetism will depend upon the horizontal and vertifal components of the earth's force in
the locality and upon the direction of the keel in building; its permanency will depend upon the
amount of mechanical violence to which the metal has been subjected by the riveting and other inci-
dents of construction, and upon the nature of the metal employed.
98. Causes tii.\t Prodcce Deviation. — There are three influences that operate to produce devia-
tion; namely, («) siibperm<ment mngnetisiii; (fc) transient magnetism induced in vertical soft iron, and (c)
transient magnetism induced in horizontal soft iron. Their effect will be explained.
Subpermanent magnetism is the name given to that magnetic force which originates in the ship while
building, through the process explained in the preceding article; after the vessel is launched and has
an opportunity to swing in azimuth, the magnetism thus induced will suffer material diminution until,
after the lapse of a certain time, it will settle down to a condition that continues practically unchanged;
the magnetism that remains is denominated subpermanent. The vessel will then approximate to a
permanent magnet, in which the north polarity will lie in that region which was north in building, and
the south polaritv (that which exerts an attracting influence on the north pole of the compass needle),
in the region which was south in building.
Transient magnetism induced in vertical soft iron is that developed in the soft iron of a vessel through
the inductive aetion of the vertical component only of the earth's total force, and is transient in nature.
Its value or force in any given mass varies with and depends upon the value of the vertical component
at the place, and is proportional to the sine of the dip, Ijeing a maximum at the magnetic pole and zero
at the magnetic equator.
Transient magnetism induced in horizontal soft iron is that developed in the soft iron of a vessel through
the inductive action of the horizontal component only of the earth's total force, and is transient in
nature. Ita value or force in any given mass varies with and depends upon the value of the horizontal
component at the place, and is proportional to the cosine of the dip, being a maximum at the magnetic
equator and reducing to zero at the magnetic pole.
The needle of a compass in any position on board ship will therefore be acted upon by the earth's
total force, together with the three forces just described. The jwles of these forces do not usually lie in
the horizontal plane of the compa-ss needle, but as this needle is constrained to act in a horizontal i)lane,
its movements will be affected solely by the horizontal components of these forces, and its direction will
be determined by the resultant of those components.
The earth's force operates to retain the compass needle in the plane of the magnetic meridian, but
the resultant of the three remaining forces, when without this plane, deflects the needle, and the
amount of such deflection constitutes the deviation.
99. Classes op Deviation. — Investigation has developed the fact that the deviation produced as
described is made up of three parts, which are known respectively as semicircular, (juadrantal, and con-
stant deviation, the latter being the least important. A clear understanding of the nature of each of
these classes is essential for a comprehension of the methods of compensation.
too. iSemicircular Deviation is that due to the combined influence, exerted in a horizontal plane, of
the subpermanent magnetism of a ship and of the magnetism induced in soft iron by the vertical com-
ponent of the earth's force. If we r^ard the effect of these two forces as concentratefl in a single
resultant pole exerting an attracting influence upon the north end of the compass needle, it may be seen
that there will be some heading of the ship whereon that pole will lie due north of the needle and
therefore produce no <leviation; now consider that, from this position, the ship's head swings in azi-
muth to the right; throughout all of the semicircle first described an easterly deviation will be produced,
and, after completing 180°, the pole will be in a position diametrically opposite to that from which it
started, and will again exert no influence that tends to produce deviation. Continuing the swing,
throughout the next semicircle the direction of the deviation produced will be always to the westward,
until the circle is completed and the ship returns to her original neutral position. From the fact that
this disturbing cause acts in the two semicircles with etjual and opposite effect it is given the name of
semicircidar deviation.
\ In figure 9, a curve is depicted which shows the deviations of a semicircular nature separated from
those due to other disturbing causes, and from this the reason for the name will be apparent.
101. Returning to the two distinct sources from which the semicircular deviation arises, it may
be seen that the force due to subpermanent magnetism remains constant regardless of the geographical
position of the vessel; but since the horizontal force of the earth, which tends to hold the needle in the
magnetic meridian, varies with the magnetic latitude, the deviation due to subpermanent magnetism
varies inversely as the horizontal force, or as tt; this may be readily understood if it is considered that
the stronger the tendency to cling to the direction of the magnetic meridian, the less will be the deflec-
tion due to a given disturbing force. On the other hand, that part of the semicircular force due to
magneti.sm induced in vertical soft iron varies as the earth's vertical force, which is proportional to the
36 THE COMPASS ERROR.
sine of the dip; Its effect in producing deviation, as in the preceding case, varies inversely as the earth's
horizontal force— that is, inversely as the cosine of the dip; hence the ratio representing the change of
... 1 1 f , . . . sin &
deviation arising troni this cause on change of latitude is „„„ g, or tan 9.
If, then, we consider the change in the semicircular deviation due to a change of magnetic latitude,
it will be necessary to separate the two factors of the deviation and to remember that the portion pro-
duced by subperinanent magnetism varies as ^^, and that due to vertical induction as tan 0. But for
xl
any consideration of the effect of this class of deviation in one latitude only, the two parts may be
joined together and regarded as having a single resultant.
102. If we now resume our former assumption, that all the forces tending to produce semicircular
deviation are concentrated in a single pole exerting an attracting influence upon the north pole of the
compass, we may consider a line to be drawn joining that theoretical pole with the center of the com-
pass, then the angle made by this line with the keel line of the vessel, measured from right ahead,
around to the right is called the starboard ani;le. From this it follows that the disturbing force producing
semicircular deviation may be considered to have the same effect as a single magnet whose center is in
the vertical axis of the compass, and whose south pole (attracting to the north pole of the compass) is in
the direction given by the starboard angle; if, therefore, a magnet be placed with its center in the ver-
tical axis of the compa-ss, its north (or repelling) pole in the direction of the starboard angle, and its
distance so regulated that it exerts upon the compass a force equal to that of the ship's combined sub-
permanent magnetism and vertical induced magnetism, the disturbing effect of these two forces will be
counterbalanced, and, so far as they are concerned, the compass deviations will be corrected, provided
that tlie ship does not change her magnetic latitude.
103. It is evident that the force of the single magnet may be resolved into two components — one
fore-and-aft, and one athwartship; in this case, instead of being represented by a single magnet with its
south pole in the starboard angle, the semicircular forces will be represented by two magnets, one fore-
and-aft and the other athwartship, and compensation
may be made by two separate magnets lying respec-
tively in the directions stated, but with their north
or repelling poles in the position occupied by the
south or attracting poles of the ship's force.
Figure 11 represents theconditions that have been
de.scrihed. If O be the center of the compass, XX'
.. --'* and YY', respectively, the fore-and-aft and athwart-
ship lines of the ship, and OS the direction in which
the attracting pole of the disturbing force is exerted,
then XOS is the starboard angle, usually designated
a. Now, if OP be laid off on the line 0.S, represent-
ing the amount of the disturbing force according to
some convenient scale, then Oh and Oc, respectively,
represent, on the same scale, the resolved directions
of that force in the keel line and in the transverse
line of the ship. Each of these resolved forces will
exert a maximum effect when acting at right angles
to the needle, the athwartship one when the ship
heads north or south by compass, and the longitu-
dinal one when the heading is east or west. On any
other heading than those named the deviation produced ))y each force will bea fraction of its maximum
whose magnitude will depend upon the azimuth of the ship's head. The maximum deviation produced,
therefore, forms in each case a basis for reckoning all of the various effects of the disturbing force, and is
called a coefficient.
The coefficient of semicircular deviation produced by the force in the fore-and-aft line is called B,
and is reckoned as positive when it attracts a north pole toward the bow, negative when toward the
stern; that produced by the athwartship force is C, and is reckoned as positive to starboard and nega-
tive to port. These coefficients are expressed in degrees."
Referring again to figure 11, it will be seen that:
or ( what may be shown to be the same thing):
Oc
tan a=-^-^,
. sm C.
tan «= . ~|i
sinB
and when the maximum deviations are small, this becomes:
tan o'=vi.
B
Since the starboard angle is always measured to the right, it will be seen that, for positive values of
B and C, a will be between 0° and 90°; for a negative B and a positive C, between 90° and 180°; for
a It should be remarked that in a mathematical analysis of the deviations, it would be necessary to distinguish between
the approximate coefficients. B and C, here described, as also A, D, and E, to be mentioned later, and the eiact coefficients
denoted by the corresponding capital letters of the German alphabet. In the practical discussion of the subject here given,
the question of the difference need not be entered into.
THE COMPASS ERROB.
37
negative values of both B and C, between 180° and 270°; and for a positive B and negative C, between
270° and 3«0°.
104. The coefficient B is approximately equal to the deviation on East; or to the deviation on
West with reversed sign; or to the mean of these two. Thus in the ship having the table of deviations
previouslygiven(art. 92), Biseoualto -19° 55', or to —19° 30', or to J (—19° 55' —19° 30')= —19° 43'.
The coefficient O is approximately equal to the deviation on North; or to the deviation on South
with reversed sign; or to the mean of these two. In the example C is equal to —1° 00' or 0° 00', or
i (-1° 0O'±0° 00')= -0° sc
105. The value of the subpermanent magnetism remaining practically constant under all condi-
tions, it will not alter when the ship changes her latitude; but that due to induction in vertical softiron
undergoes a change when, by I'hange of geographical position, the vertical component of the earth's
force assumes a different value, and in such case the correction by means of one or a pair of permanent
magnets will not remain effective. If, however, by series of observations in two magnetic latitudes, the
values of the coefficients can be determined under the differing circumstances, it is possible, by solving
equations, to determine whateffect each force has in jjroducingthe semicircular deviation; having done
which, the subpermanent magnetism can be corrected by permanent magnets after the method previ-
ously described, and the vertical induction in soft iron can be corrected by a piece of vertical soft iron
placed in such a position near the compass as to produce an equal but opposite force to the ship's vertical
soft iron. This last corrector is called a Flinders bar.
Having thus opposed to each of the component forces a corrector of magnetic character identical -with
its own, a change of latitude will make no difference in the effectiveness of the compensation, for in every
case the modified conditions will produce identical results in the disturbing and in the correcting force.
106. iluadrantal Deviation is ihaX which arises from horizontal induction in the soft iron of the
vessel through the action of the horizontal component of the earth's total force. Let us consider, in figure
12, the effect of any piece of soft iron which is symmetrical with respect to the compass — that is, which
lies wholly within a plane passing through the center of the needle in either a fore-and-aft or an ath wart-
ship direction. It may be seen \a) that such iron produces no deviation on the cardinal points (for
on north and south headings the fore-and-aft iron, though strongly magnetized, has no tendency to draw
the needle from a north-and-soutli line, while the athwartship
iron, being at right angles to the meridian, receives no magnetic
induction, and therefore exerts no force; and on east and west
headings similar conditions prevail, the athwartship and the
fore-and-aft iron having simply exchanged positions) ; and (h)
the direction of the deviation produced is opposite in successive
quadrants. The action of unsymraetrical soft iron is not quite
so readily apparent, but investigation shows that part of its effe<;t
is to profluce a deviation which becomes zero at the inter-cardinal
points and is of opposite name in successive quadrants. From
the fact that deviations of this class change sign every 90°
throughout tlie circle, they gain the name of quadratdal deriatturm.
One of the curves laid down in the Napier diagram (fig. 11) is
that of quadrantal deviations, whence the nature of this disturb-
ance of the needle may te observed.
107. All deviations produced by soft iron may be considered
as fractions of the maximum deviation due to that disturbing
influence; and consequently the maxinuun is regarded as a
coefficient, as in the case of semicircular deviations. The coeffi-
cient due to symmetrical soft iron is designated as D, ancl is
considered positive when it produces easterly <leviations in the
quadrant betvveen North and East; the coeflicient of deviations arising from unsymraetrical soft iron is
called E, and is reckoned as positive when it produces easterly deviations in the quadrant between NW.
and NE. ; this latter attains importance only when there is some marked inequality in the distribution
of metal to starboard and to port, as in the "case of a compass placed off the midship line.
108. D is approxiniately etpial to the mean of the deviations on NE. and SW.; or to the mean of
those on SE. and N\V., with sign reversed; or to the mean of those means. In the table of deviations
given in article 92, D is equal to J (—7° 10' + 24° 30') = )- 8° 40'; or to J (+23° 30' - 7° 40')
= + 7° 55'; or to J ( 4- 8° 40' + 7° 55') = -p 8° 23'. By reason of the nature of the arrangement of iron
in a ship, I) is almost invariably positive.
E is approximately equal to the mean of the deviations on North and South; or to the mean of those
on East and West with sign reversed; or to the mean of those means. In the example, E is equal to
i (-1°00'±0°00') =-0°30'; or to i (-f- 19° 55' - 19° .30') =+0° 13'; or tot (~0° 30' J- 0° 13')
= - 0° 09'.
109. Quadrantal deviation does not, like semicircular, undergo a change upon change of magnetic
latitude; being due to induction in horizontal softiron, the magnetic force exerted to produce it is propor-
tional to the horizontal component of the earth's magnetism; but the directive force of the needle likewise
depends upon that same component; consequently, as the disturbing force exerted upon the needle
increases, .so does the power that holds it in the magnetic meridian, with the result that on any given
heading the deflection due to soft iron is always the same.
no. Quadrantal deviation is corrected by placing masses of soft iron (usually two hollow spheres
in the athwartship line, at equal distances on each side of the compass), with the center of mass in the
horizontal plane of the needle. The distance is made such that the force exerted exactly counteracts
that of the ship's iron. As the correcting effect of this iron will, like the directive force and the quad-
rantal disturbing force, vary directly with the earth's horizontal cdmponent, the compensation once
properly made will be effective in all latitudes.
In practice, the quadrantal deviation due to unsymmetrical iron is seldom corrected; the correction
may be accomplished, however, by placing the soft iron masses on a line which makes an angle to the
athwartship line through the center of the card.
Fig. 12.
38 THE COMPASS ERBOB.
111. Constant Dmation is due to induction in horizontal soft iron unsymmetrically placed about the
compass. It has already been explained that one effect of such iron is to produce a quadrantal deviation,
represented by the coefficient E; another effect is the constant deviation, so called tjecause it is uniform
in amount and direction on every heading of the ship. If plotted on a Napier diagram, it would appear
as a straight line parallel with the initial line of the diagram.
112. Like other classes of deviation, the effect of the disturbing force is represented by a coeffi-
cient; this coefficient is designated as A, and is considered plus fpr easterly and minus for westerly errors.
It is approximately equal to the mean of the deviations on any number of equidistant headings. In the
case previously given, it might be found from the four lieadings, North, East, South, and West, and
would then be equal to i (-1° 00'-19° 55'±0° OC+IQ" 30')=-0° 21'; or from all of the 32 headings,
when it would equal +0° 16'.
For the same reason as in the case of E, the value of A is usually so small that it may be neglected;
it only attains a material size when the compass is placed off the midship line, or for some similar
cause.
113. Like quadrantal deviation, since its force varies with the earth's horizontal force, the con-
stant deviation will remain uniform in amount in all latitudes.
No attempt is made to compensate this class of error.
114. Coefficients. — The chief value of coefficients is in mathematical analyses of the deviations
and their causes. It may, however, be a convenience to the practical navigator to find their approxi-
mate values by the methods that have been given, in order that he may gain an idea of the various
sources of the' error, with a view to ameliorating the conditions, when necessary, by moving the bin-
nacle or altering the surrounding iron. The following relation exists between the coefficients and the
deviation:
d=A + B sin 2' + C cos 2' -f D sin 22' -f E cos 22',
where d is the deviation, and 2' the ship's heading by compass, measured from compass North.
115. Me.\n Directive Force. — The effect of the disturbing forces is not confined to causing devi-
ations; it is only those components acting at right angles to the needle which operate to produce
deflection; the effect of those acting in the direction of the needle is exerted either in increasing or
diminishing the directive force of the compass, according as the resolved component is northerly or
southerly.
It occurs, with the usual arrangement of iron in a vessel, that the mean effect of this action
throughout a complete swing of the ship upon all headings is to reduce the directive force — that is,
while it varies with the heading the average value upon all azimuths is minus or southerly. The result
of such a condition is unfavorable from the fact that the compass is thus made more "sluggish," is
easily disturbed and does not return quickly to rest, and a given deflecting force produces a greater
deviation when the directive force is reduced. The usual methods of compensation largelv correct this
fault, but do not entirely do so; it is therefore the case that the mean combined horizontal force of earth
and ship to north is generally less than the horizontal force of the earth alone; but it is only in extreme
cases that this deficiency is serious.
1 16. Heeling Error. — This is an additional cause of deviation that arises when the vessel heels to
one side or the other. Heretofore only those forces have been considered which act when the vessel is
on an even keel; but if there is an inclination from the vertical certain new forces arise, and others
previously inoperative become effective. These forces are (a) the vertical component of the subperma-
nent magnetism acquired in building; (h) the vertical component of the induced magnetism in vertical
soft iron, and (c) the magnetism induced by the vertical component of the earth's total force in iron
■which, on an even keel, was horizontal. The first two of these disturbing causes are always present,
but, when the ship is upright, have no tendency to produce deviation, simply exerting a downward
pull on one of the poles of the needle; the last is a new force that arises when the vessel heels.
The maximum disturbance due to heel occurs when the ship heads North or South. When heading
East or West there will be no deviation produced, although the directive force of the needle will be
increased or diminished. The error will increase with the amount of inclination from the vertical.
117. For the same reason as was explained in connection with semicircular deviations, that part of
the heeling error due to subiiermanent magnetism will vary, on change of latitude, as , while that
due to vertical induction will vary as tan 0. In south magnetic latitude the effect of vertical induction
will be opposite in direction to what it is in north.
118. The heeling error is corrected by a permanent magnet placed in a vertical position directly
under the center of the compass. Such a magnet has no effect upon the compass when the ship is
upright; but since its force acts in an opjwsite direction to the force of the ship which causes heeling
error, is equal to the latter in amount, and is exerted under the same conditions, it affords an effective
compensation. For similar reasons to those affecting the compensation of B and C, the correction by
means of a permanent magnet is not general, and must be rectified upon change of latitude.
PRACTICAL COMPENSATION.
119. In the course of explanation of the different classes of deviation occasion has been taken to
state generally the various methods of compensating the errors that are produced. The practical
methods of applying the correctors will next be given.
120. Order of Correction. — The following is the order of steps to he followed in each case. It
is assumed that the vessel is on an even keel, that all surrounding masses of iron or steel are in their
normal positions, all correctors removed, and that the binnacle is one in which the semicircular
deviation is corrected by two sets of permanent magnets at right angles to each other.
1. Place quadrantal correctors by estimate.
2. Correct semicircular deviations.
THE COMPASS ERBOB. 89
3. C!orrect quadrantal deviations.
4. Swing ship for residual deviations.
The heeling corrector may be placed at any time after the semicircular and quadrantal errors are
corrected. A Flinders bar can be put in place only after observations in two latitudes.
121. The ship is first placed on some magnetic cardinal point. If North or South, the only force
^theoretically speaking) which tends to produce deflection of the needle will be the athwartship com-
ponent of the semicircular force, whose effect is represented by the coefficient C If East or West, the
only deflecting force will be the fore-and-aft component of the semicircular force, whose effect is repre-
sented by the coefficient B. This will be apparent from a consideration of the direction of the forces
producing deviation, and is also shown by the equation connecting the terms (where A and E are zero);
• (i = Bsinz' + Ccosz' + Dsin2y.
If the ship is headed North or South, z' being equal to 0° or 180°, the equation becomes d = ± C.
If on East or West, z' being 90° or 270°, we have d = ± B.
This statement is exact if we regard only the forces that have been considered in the problem, but
experience has demonstrated that the various correctors when in place create certain additional forces
by their mutual action, and in order to correct the disturbances thus accidentally produced, as well as
those due to regular causes, it is necessary that the magnetic conditions during correction shall approxi-
mate as closely as possible to those that exist when the compensation is completed; therefore the quad-
rantal correctors should first be placed on their arms at the positions which it is estimated that they
will occupy later when exactly located. An error in the estimate will have but slight effect under
ordinary conditions. It should be understood that the placing of these correctors has no corrective
effect while the ship is on a cardinal point. Its object is to create at once the magnetic field with which
we shall have to deal when compensation is perfected.
This having been done, proceed to correct the semicircular deviation. If the ship heads North or
South, the force producing deflection is, as has been stated, the athwartship component of the semi-
circular force, which is to be corrected by permanent magnets placed athwartships; therefore enter in
the binnacle one or more such magnets, and so adjust their height that the heading of the ship by
compass shall agree with the magnetic heading. VVhen this is done all the deviation on that azimuth
will be corrected.
Similarly, if the ship heads East or West, the force producing deviation is the fore-and-aft com-
ponent of the semicircular force, and this is to be corrected by entering fore-and-aft permanent magnets
in the binnacle and adjusting the height so that the deviation on that heading disappears.
With the deviation on two adjacent cardinal points corrected, the semicircular force has been com-
pletely compensated. Next correct the quadrantal deviation. Head the ship NE., SE., SW., or NW.
The coefficients B and C having been reduced to, zero by comjiensation, and 2z' , on the azimuths named,
being equal to 90° or 270°, the equation becomes d = ± D. The soft-iron correctors are moved in or
out from the positions in which they were placed by estimate until the deviation on the heading (all of
■which is due to quadrantal force) disappears. The quadrantal disturbing force is then compensated.
122. Deter.min.\tion op Magnetic Headixos. — To determine when the ship is heading on any
given magnetic course, and thus to know when the deviation has been corrected and the correctors are
in proper position, four methods are available:
{a) Swing the ship and obtain by the best available method the deviations on a sufficient number
of compass courses to construct a curve on the Napier diagram forone quadrant, and thus find the com-
pass headings corresponding to two adjacent magnetic cardinal points and the intermediate intercardinal
point, as North, NE., and East, magnetic." Then put the ship succ&ssively on these courses, noting the
corresponding headings by some other compass, and when it is desired to "head on the various magnetic
azimuths during the process of correction the ship may be steadied upon them by the auxiliary com-
pass. Variations of this method will suggest them.selves and circumstances may render their adoption
convenient. The compass courses corresponding to the magnetic directions may be obtained from
observations made with the auxiliary compass itself, or while making observations with another com-
pa.ss the headings by the auxiliary may be noted and a curve for the latter constructed, as explained
in article 94, and the required headings thua deduced.
(6) By the methods to be explained hereafter (Chap. XIV), ascertain in advance the true bearing
of the sun at frequent intervals during the period which is to be devoted to the compensation of the
compa.oses; apply to these the variation and obtain the magnetic bearings; record the times and
bearings in a convenient tabular form; set the watch accurately for the local apparent time; then
-when it is required to steer any given ma^etic course, set that jwint of the pelorus for the ship's
head and set the sight vanes for the magnetic bearing of the sun corresponding to the time by watch.
Maneuver the ship with the helm until the sun comes on the sight vanes, when the azimuth of the
ship's head will be that which is required. The sight vanes must Ije altered at intervals to accord with
the table of times and bearings.
(c) Construct a table showing times and corresponding magnetic bearings of the sun, and also set
the watch, as explained for the previous method. Then place the sight vanes of the azimuth circle of
the compass at the proper angular distance to the right or left of the required azimuth of the ship's
head; leave them so set and maneuver the ship with the helm until the image of the sun comes on with
the vanes. The cour.se will then be the required one. As an example, suppose that the table shows that
the magnetic azimuth of the sun at the time given by the watch is N. 87° E., and let it be required to
head magnetic North; when placed upon this heading, therefore, the sun must bear 87° to the right, or
east, of the direction of the ship's head; when steady on any course, turn the sight vane to the required
bearing relative to the keel. If on N. 11° W., for example, turn the circle to N. 76° E.; leave the vane
"This is all that is required for the purposes of compensation, but if there is opportunity it is alwavs well to make a
complete saving and obtain a full table of deviations, which may give interesting infonnation of the existing magnetic
conditions.
40 THE COMPASS EEROK.
nndisturbed and alter course until the sun comes on. The magnetic heading is then North, and adjust-
ment may be made accordingly.
{d) When ranges are available, they may be utilized for determining magnetic headings.
123. SuMM.\HY OF Ordinary Corrections. — To summarize, the following is the process of correct-
ing a compass for a single latitude, where magnets at right angles are employed for compensating the
semicircular deviation and where the disturbances due to unsymmetrical soft iron are small enough to be
neglected:
First. All correctors being clear of the compass, place the quadrantal correctors in the position
which it is estimated that they will occupy when adjustment is complete. The navigator's experience
will serve in making the estimate, or if there seems no other means of arriving at the probable position
they may be placed at the middle points of their supports.
Second. Steady the ship on magnetic North, East, South, or West, and hold on that heading by such
method as seems best. By means of permanent magnets alter the indications of the compass until the
heading coincides with the magnetic course. If heading North, magnets must be entered N. ends to
starboard to correct easterly deviation and to port to correct westerly^and the reverse if heading
South. If heading East, enter N. ends forward for easterly and aft fo^fwfesterly deviations, and the
reverse if heading West. (Binnacles differ so widely in the methods of cftrrying magnets that details
on this point are omitted. It may be said, however, that the magnetic intensity of the correctors may
be varied by alterini' either their number or their distance from the compass; generally speaking,
several magnets at a distance are to be preferred to a small number close to the compass. )
Third. Steady the ship on an adjacent magnetic cardinal point and correct the compass heading
by permanent magnets to accord therewith in the same manner as described for the first heading.
Fourth. Steady the ship on an intereardinal point (magnetic) and move the quadrantal correctors
away from or toward the compass, keeping them at equal distances therefrom, until the compass and
magnetic headings coincide.
124. The compensation being complete, the navigator should proceed immediately to swing ship
and make a table of the residual deviations. Though the remaining errors will be small, it is seldom
that they will be reduced to zero, and it nuist never be assumed that the compass may be relied upon
without taking the deviation into account. Observations on eight equidistant points will ordinarily
suffice for this purpose.
125. To Correct Semicircular Deviation with a Single Magnet. — In certain binnacles provision
is made for correcting the semicircular deviation by a single magnet (or series of magnets) in the star-
board angle, the magnet tray having motion in azimuth as well as vertically. In this case the process of
correcting semicircular deviation is somewhat different from that described for correction by rectangular
magnets. Either of the two following methods may be employed :
(a) By computation determine the starboard angle. An approximate method for doing this is
given in article 103, and a more exact one may be found in works treating this subject 'mathematically.
Head the ship on a cardinal point (magnetic); enter the magnets in the tray and revolve it until their
N. ends lie at an angular distance from ahead (measured to the right) equal to the starboard angle;
raise or lower the tray until the deviation disappears.
(6) Head the ship on a cardinal point (magnetic), enter the magnets, and turn the tray to an east-
and-west position, the N. ends in such direction as will tend to reduce the deviation; raise or lower the
tray until the deviation disappears. Alter course 90° and head on an adjacent magnetic cardinal point;
observe the amount of deviation that the compass shows; correct half of this by altering the starlioard
angle and the other half by raising or lowering the tray. Return to first course, note deviation, and
correct one-half in each way, as liefore. Continue the operation, making a series of trials until the
deviations disappear on both headings, when the compensation will be correct. This operation may be
considerably hastened by finding the first position of the magnets from a rough calculation of the
starboard angle (art. 103).
126. Correcting the Heeling Error. — The heeling error may be corrected by a method
involving computation, together with certain observations on shore. A more practical method, however,
is usually followed, though its results may be less precise. The heeling corrector is placed in its vertical
tube, N. end uppermost in north latitudes, as this is almost invariably the required direction; the ship
being on a course near North or South and rolling, observe the vibrations of the card, which, if the
error is material, will be in excess of those due to the ship's real motion in azimuth; slowly raise or
lower the corrector until the abnormal vibrations disappear, when the correction will be made for that
latitude; but it must be readjusted upon any considerable change of geographical position.
In making this observation care must be taken to, distinguish the vessel's "yawing" in a seaway,
from the apparent motion due to heeling error; for this reason it may be well to have an assistant to
watch the ship's head and keep the adjuster informed of the real change in azimuth, by which means
the latter may better judge the effect of the heeling error.
In the case of a sailing vessel, or one which for any reason maintains a nearly steady heel for a
continuous period, the amount of the heeling error may be exactly ascertained by observing the azi-
muth of the sun, and corrected with greater accuracy than is possible with a vessel which is constantly
rolling.
127. Flinders Bar.— The simplest method that presents itself for the placing of the Flinders
bar is one which is available only for a vessel crossing the magnetic equator. Magnetic charts of the
world show the geographical positions at which the dip becomes zero — that is, where a freely suspended
needle is exactly horizontal and where there exists no vertical component of the earth's total magnetic
force. In such localities it is evident that the factor of the semicircular deviation due to vertical induc-
tion disappears and that the whole of the existing semicircular deviation arises from subpermanent
magnetism. If, then, when on the magnetic equator the compass be carefully compensated, the effect
of the subpermanent magnetism will be exactly opposed by that of the semicircular correcting magnets.
Later, as the ship departs from the magnetic equator, the semicircular deviation will gradually acquire
a material value, which will be known to be due entirely to vertical induction, and if the Flinders bar
be so placed as to correct it, the compensation of the compass will be general for all latitudes.
THE COMPA88 ERROB. • 41
In following this method it may usually be assumed that the soft iron of the vessel is symmetrical
with respect to the fore-and-aft line and that the Flinders bar may be placed directly forward of the
tompass or directly abaft it, disregarding the effect of components to starboard or port. It is tnerefore
merely necessary to observe whether a vertical soft iron rod must be placed forward or abaft the
compass to reduce the deviation, and, having ascertained this fact, to find by experiment the exact
distance at which it completely corrects the deviation.
The Flinders bar frequently consists of a bundle of soft iron rods contained in a case, which is
secured in a vertical position near the compass, its upper end level with the plane of the needles; in
this method, the distance remaining fixed, the intensity of the force that it exerts is varied by increasing
or decreasing the number of rods; this arrangement is more convenient and satisfactory than the
employment of a single rod at a variable distance.
128. When it is not possible to correct the compass at the magnetic equator there is no ready
practical method by which the Flinders bar may be placed; the operation will then depend entirely upon
computation, and as a mathematical analysis of deviations is beyond the scope laid out for this work
the details of procedure will not be gone into; the general principles involved are indicated, and students
seeking more must consult t1i%, various works that treat the subject fully.
It has been explained that each coefficient of semicircular deviation (B and C) is made up of a sub-
permanent factor varying as ti and of a vertical induction factor varying as tan (I. If we indicate by the
subscripts , and ,., respectively, the parts due to each force, we may write the equations of the coefficients:
B=B, X jj + B, X tan 8; and
= C,Xh + 0, X tanO.
Now if we distinguish by the subscripts , and ^ the values in the first and in the second position of
observation, respectively, of those quantities that vary with the magnetic latitude, we have:
Bi = B,Xg- + B,.Xtan6„
B, = B, X g-f B, X tan 6.^ ; and
C, = C, X-i + C, Xtane,,
ill
Cj = C. X jj- + C, X tan 6.,.
The values of the coefficients in both latitudes are found from the observations made for deviations;
the values of the horizontal force and of the dip at each place are known from magnetic charts; hence
we may solve the first pair of equations for B, and B^, and the second pair for C, and C, ; and having
found the values of these various coefficients, we may correct the effects of B, and C, by permanent mag-
nets in the usual way and correct the remainder — that due to B„ and C, — by the Flinders bar.
Strictly, the Flinders bar should be so placed that its repelling pole is at an angular distance from
ahead equal to the " starboard angle" of the attracting pole of the vertical induced force, this angle
depending upon the coefficients B^ and C,; but since, as before stated, horizontal soft iron may usually
be regarded as symmetrical, C,. is assumed as zero and the bar placed in the midship line.
129. To CoKRECT Adjustment on C'h.vxge of Latiti-de. — The compensation of quadrantal devia-
tion, once properly made, remains effective in all latitudes; but uidess a Flinders bar is used a correction
of the semicircular deviation made in one latitude will not remain accurate when the vessel has
materially changed her position on the earth's surface. With this in mind the navigator must make
frequent observations of the compass error during a pa-ssage and must expect that the table of residual
deviations obtained in the magnetic latitude of compensation will undergo considerable change as that
latitude is departed from. The new deviations may l)ecoine so large that it will be found convenient
to readjust the semicircular correcting magnets. This process is very simple.
When corrector!! at rUjht angles are uneiJ, provide for steadying the ship, by an auxiliary compass or
by the pelorus, upon two adjacent magnetic cardinal points (art. 122). Put the ship on heading North
or South (magnetic), and raise or lower the athwartship magnets or alter their number until the
deviation disappears; then steady on East or West (magnetic) and similarly adjust the fore-and-aft
magnets. Swing ship for a new table of residual deviations.
When correctors in the starboard angle are used, arrange as before for heading on two adjacent cardinal
magnetic courses. Steady on one of these, observe amount of compass error, correct half by changing
the starboard angle and half by raising or lowering magnets; steady on the adjacent cardinal point and
repeat fhe operation. Continue until adjustment is made on both headings, then swing for residual
deviations.
42 PILdTING.
CHAPTER IV.
PILOTING.
130. Definition. — Piloting, in the sense given tiie word by modern and popular usage, is tiie
art of conducting a vessel in channels and harbors and along coasts, where landmarks and aids to
navigation are available for fixing the position, and where thedepth of wateraud dangers to navigation
are such as to require a constant watch to be kept upon the vessel's course and frequent changes to be
made therein.
131. Requisites. — As requisites to successful piloting, the navigator should be provided with
the best available chart of the locality to be traversed, together with the sailing directions and descrip-
tions of aids to navigation; and all of these should be corrected for the latest information, published in
notices to mariners or otherwise, that bear upon the locality. The vessel should be equipped with the
usual instrumentsemployed in navigation. The deep-sea sounding-machine, if provided, should be ready
for use when there is a chance that it may be needed. The lead lines should be correctly marked, and
a.s shoal water is entered one or two men should be stationed to sound. The index errors of the sextants
should be known, and, above all, there should be at hand a table showing correctly the deviation of
the compass on each heading.
1 32. Laving the Course. — Mark a point upon the chart at the ship's position; then mark another
point for which it is desired to steer; join the two by a line drawn with the parallel ruler, and, main-
taining the direction of the line, move the ruler until its edge passes through the center of the compass
rose and note the direction. If the compa,ss rose indicates true directions, this will be the true course,
and must be corrected for variation and deviation (by applying each in the opposite direction to its
name) to obtain the compass course; if it is a magnetic rose, the course need be corrected for deviation
only.
Before putting the ship on any course a careful look should be taken along the line over which it
leads to be assured that it clears all dangers.
133. Methods of Fixing Position. — A navigator in sight of objects whose positions are shown upon
the chart may locate his vessel by either of the following methods: (a) cross bearings of two known
objects; (b) the bearing and distance of a known object; (c) the bearing of a known object and the
angle between two known objects; (d) two bearings of a known object separated by an interval of time,
with the run during that interval; (f) sextant angles between three known objects. Besides the fore-
going there are two methods by which, without obtaining the precise position, the navigator may assure
himself that he is clear of any particular danger. These are: (/) the danger angle; (g) the danger
bearing.
The choice of the method will be governed by circumstances, depending upon which is best adapted
to prevailing conditions.
134. Cross Bearings of two Known Objects. — Choose two objects whose position on the chart
can be unmistakably identified and whose respective bearings from the ship differ, as nearly as possible,
by 90°; observe the bearing of each, either by compass or pelorus, taking one as quickly as possible
after the other; see that the ship is on an even keel at the time the observation is made, and, if using
the pelorus, be sure also that she heads exactly on the course for which the pelorus is set. Correct the
bearings so that they will be either true or magnetic, according as they are to be plotted by the true or
magnetic compass rose of the chart — that is, if observed by compa.ss, apjjly deviation and variation to
obtain the true bearing, or deviation only to obtain the magnetic; if
/'y observed by pelorus, that instrument sliould be set for the true or mag-
(Va netic heading, according as one or the other sort of reading is required,
jf^ and no further correction will be necessary. Draw on the chart, by
v' ( means of the parallel rulers, lines which shall pass through the resjjec-
y' \ tive objects in the direction that each was observed to bear. As the
jT \ ship's position on the chart is known to be at some point of each of
>/ \ these lines, it must be at their intersection, the only point that fulfills
•^/ \ c both conditions.
— yKr i"* ^^ figure 1.3, if A and B are the objects and OA and OB the lines
y^ \^ j passing through them in the observed directions, the ship's position
/ \^ 1 will be at O, their intersection.
\^ 1 135. If it be possible to avoid it, objects should not be selected
\^ \ for a cross bearing which subtend an angle at the ship of less than 30°
N^ or more than 150°, as, when the lines of bearing approach parallelism,
p^B a small error in an observed bearing gives a large error in the result.
V\. For a similar reason objects near the ship should l)e taken in prefer-
^ > ence to those at a distance.
Fig. 13. 1 36. When a third object is available a bearing of that may be
, taken and plotted. If this line intersects at the same point as the other
two (as the bearing 00 of the object C in the figure), the navigator may have a reasonable a.ssurance
that his " fix " is correct; if it does not, it indicates an error somewhere, and it may have arisen from
inaccurate observation, incorrect determination or application of the deviation, or a fault in the chart.
PILOTING.
43
137. What may be considered as a form of thia method can be used when only one known object
ia in sight by taking, at the same instant as the bearing, an altitude of the sun or other heavenly body
and noting the time; work out the sight and obtain the Sumner line (as explained in Chapter XV), and
the intersection of this with the direction-line from the object will give the observer's position in the
same wav as from two terrestrial bearings.
138. Bearing and Distance op a Known Object. — When only one object is available, the ship's
position may be found by observing its bearing and distance. Follow the preceding method in the mat-
ters of taking, correcting', and plotting the bearing; then, on this
line, lav off the distance from the object, which will give the
point occupied by the observer. In figure 14, if A represents the
object and AO the bearing and distance, the position sought will
Tie at O.
139. It is not ordinarily easy to find directly the distance
of an object at sea. The most accurate method is when its height
'is known and it subtends a fair-sized angle from the ship, in
which case the angle may be measured by a sextant," and the
distance computed or taken from a table. Table 3.3 of this work
gives distances up to 5 miles, corresponding to various heights
and angles. Captain Lecky's "Danger Angle and Offshore Dis-
tance Tables" carries the computation much further. The use
<5f this method at great distances must not be too closely relied
upon, as small errors, such a.s those due to refraction, may throw
•out the results to a material extent; but it affords an excellent approximation, and as this method of fixing
positjon is employed only when no other is available the best possible approximation has to suffice.
In measuring vertical angles, strictness requires that the
observation should l)e so made that the angle at the foot of the
object should equal 90° and that the triangle be aright triangle,
as OMN, figure 15, where the line OjVl j; truly horizontal, and
not as in the triangle O'MN, where the condition is not fulfilled.
This error is inai)preciable, however, save at very close dis-
tances, when it may be sufficiently corrected by getting down
as low as possible on board the vessel, so that the eye is near
the water-line. One condition exists, however, where the
error is material — that shown in figure 16, where the visible
shore-line is at M', a considerable distance from M, the point
vertically below the summit. In this case there is nothing to
mark M in the observer's eye, and it is essential that all angles
be measured from a point close down to the water-line.
If a choice of objects can be made, the best results will be
obtained by observing that one which subtends the greatest
angle, as small errors will then have the least effect.
There is another meth(xl for determining the distance of
an object, which is available under certain circumstances. This consists in observing, from a position
aloft, the angle between the object and the line of the sea horizon beyond. By reference to Table 34
will be found the distance in yards corresponding to different angles for various heights of the observer
from 20 to 120 feet. The method is not accurate beyond moderate distances (the table being limited to
5.000 vards) and is obviously only available for finding the distance of an isolated object, such as an
islet, vessel, or target, over which the horizon may be seen. In employing this method the higher the
position occupied bv the observer the more precise will be the results.
140. In observing small angles, such as those that occur in the methods just described, it is some-
times convenient to measure them on and off the limb of the sextant. First look at the bottom of the
object and reflect the top down into coincidence; then look through the transparent part of the horizon
glass at the top and bring the bottom up by its reflected ray. The mean of the two readings will be the
true angle, the index correction having been eliminated by the operation.
141. When the methods of finding distance by a vertical or a.horizon angle are not available, it
must be obtained by such means as exist. Estimate the distance by the appearance; take a sounding, and
note where the depth falls upon the line of bearing; at night, if atmospheric conditions are normal,
consider that the distance of a light when sighted is equal to its maximum range of visibility, remem-
bering that its range is stated for a height of eye of 15 feet; or employ such method as suggests itself
under the circumstances, regarding the result, however, as an approximation only.
142. The Bearing op a Known Object and the Angle between two Known Objects. — This
method is seldom employed, as the conditions always permit of cross bearings being taken, and the
latter is generally considered preferable.
Take a bearing of a known object by compass or pelorus and observe the sextant angle between some
two known objects. The line of bearing is plotted as in former methods. In case one of the objects of
the observed angle is that whose bearing is taken, the angle is applied, right or left as the case may be,
to the bearing, thus giving the direction of the second object, which is plotted from the compass rose
and parallel rulers. If the object whose bearing is taken is not one of the objects of the angle, lav off
the angle on a three-armed protractor, or piece of tracing paper, and swing it (keeping the legs or lines
always over the two objects) until it passes over the line of tearing, which defines the position of the
ship; there will, except in special cases, be two points of intersection of the line with the circle thus
described, and the navigator must know his position with sufficient closeness to judge which is correct.
143. Two Bearings of a Known Oriect. — This is a most aseful method, which is frequently
employed, certain special cases arising thereunder teing particularly easy of application. The process
aThe use of the sextant is explained in Chapter VIII.
44
PILOTING.
is to take a careful bearing and at the same moment read the patent log; then, after running a convenient
distance, take a second bearing and again read the log, the difference in readings giving the intervening
run; when running at a known speed, the time interval will also afford a means for determining the
distance run.
The problem is as follows: In figure 17, given OA, the direction of a known object, A, at the first
observation; PA, the direction at the second observation; and OP, the distance
traversed between the two; to find AP, the distance at the second observation.
Knowing the angle POA, the angular distance of the object from right ahead
at the first bearing; OPA, the angular distance from right astern at the second
bearing; and OP, the distance run; we have by Plane Trigonometry:
PAO = ]80°-(POA + OPA); and
AP=OP X
sin POA
sin PAO'
Fig,
If, as is frequently the case, we desire to know the distance of passing abeamr
we have:
AQ = AP X sin OPA.
Tables 5A and 5B give solutions for this problem, the former for intervals
of bearing of quarter points, the latter for intervals of two degrees. The first
column of each of these tables gives the value of AP, the distance of the ship
from the observed object at the time of taking the last bearing, for values of
OP equal to unity; that is, for a run between bearings of 1 mile. The .second
column gives AQ, the distance of the object when it bears abeam, likewise for
a value of OP of 1 mile. When the run between bearings is other than 1 mile,
the number taken from the table must be used as a multiplier of that run to give the required distance.
Example: A vessel steering north takes a bearing of a light NW. J W.; then runs 4.3 miles, when
the bearing is found to be WSW. Required the distance of the light at the time of the second bearing.
Difference between course and first bearing, 4J pts.
Difference between course and second bearing, 10 pts.
Multiplier from first column. Table 5A, 0.88.
4.3 miles X 0.88 = 3.8 miles, distance at second bearing.
Example: A vessel on a course S. 52° E. takes the first bearing of an object at S. 26° E., and the
second at S. 2° W., running in the interval 0.8 mile. Required the distance at which she will pass
abeam.
Difference between course and first bearing, 26°.
Difference between course and second bearing, 54°.
Multiplier from second colunm, Table 5B, 0.76.
0.8 mile X 0.76 = 0.6 mile, distance of passing abeam.
144. As has been said, there are certain special cases of this problem whei'e it is exceptionally
easy of application; these arise when the multiplier is equal to unity, and the distance run is therefore
equal to the distance from the object. When the angular distance on the bow
at the second bearing is twice as great as it was at tlie first bearing, the distance
of the object from the ship at second bearinf; is equal to the run, the multiplier
being 1.0. For if, in figure 18, when the ship is in the first position, O, the object
A bears a°on the bow, and at the second position, P, 2a°, we have in the triangle
APO, observing that APO = 180° - 2a, and POA = a:
PAO = 180° -{POA + APO),
= 180° —(a: + 180° — 2a:),
= a.
Or, since tli« angles at O and at A are equal to each other, the sides OP and AP
are equal, or the distance at second bearing is equal to the run. This is known
as doubling the angle on the bow.
145. A case where this holds good is familiar to every navigator as the bow
and beam bearing, where the first bearing is taken when the object is broad on
the bow (four points or 45° from ahead) and the second when it is abeam (eight
points or 90° from ahead); in that case the distance at second bearing and the
distance abeam are identical and equal to the run between bearings.
146. AVhen the first bearing is 263° from ahead, and the second 45°, the
-pjj, -j^g distance at which the object idll be passed abeam yfill eqna.1 the run between bear-
ings; this may be proved by computation or by reference to the tables and is a
very convenient fact to remember, as it shows the navigator at once, if about to pass a point, how wide
a berth he is going to give the offiving dangers. '
147. There is 0. graphic method of solving this problem that is considered by some more convenient
than the use of multipliers. Draw upon the chart the lines OA and PA (fig. 19), passing through the
object on the two observed bearings; set the dividers to the distance run, OP; lay down the parallel
rulers in a direction parallel to the course and move them toward or away from the observed object
until some point is found where the distance between the lines of bearmg is exactly equal to the
distance between the points of the dividers; in the figure this occurs when the rulers lie along the line
PILOTING.
45
Fig. 19.
OP, and therefore O represents the position of the ship at the first bearing and P at the second. For
any other positions O'P', 0"P", the condition is not fulfilled.
148. Another graphic solution is given by the Distance Finder, devised by Lieut. J. B. Blish, U. S.
Navy. This consists of a semicircle whose circumference is graduated in degrees. Two pieces of thread,
made to swing about a pin-head at the center, are laid down to
represent the lines of bearing, and ease in measuring distances is
afforded by series of cross lines similar to those on a piece of profile ^
paper.
149. The method of obtaining position by two bearings of the
game object is one of great value, l^y reason of the fact that it is
frequently necessary to locate the ship when there is but one land-
mark in sight. Careful navigators seldom, if ever, miss the oppor-
tunity for a lx)W and beam bearing in passing a light-house or other
well-plotted object; it involves little or no trouble, and always gives
a feeling of added security, however little the position may be in
doulrt. If about to pass an object abreast of which there is a
danger — a familiar example of which is wlien a light-house marks a
point off which are rocks or shoals — a good assurance of clearance
should be obtained before bringing it abeam, either by doubling
the angle on the bow, or by using the 26J°— 1.5° liearing; the latter
has the advantage over the former if the object is sighted in time
to permit of its use, as it may te a.ssumed that the 4h° (bow) bear-
ing will always be observed in any event, and this gives the distance
abeam directly, saving the necessity of plotting the position at
second Ijearing (as obtained by doubling the angle) and then carry-
ing it forward.
1 50. It must be rememiaered that, however convenient, the
fix obtained by two bearings of the same object will be in error unless
the course and distance are correctly estimate<l, the cours-e "made
good" and the distance "over the ground" ijeing required. Difficulty will occur in estimating the
exact course when there is bad steering, a cross current, or when a ship is making leeway; errors in
the allowed run will arise when she is being set ahead or back by a current or when the logging is
inaccurate. To take a not extreme case, a vessel making 10 knots through the water, running against a
2-knot tide, will overestimate her distance one-fifth of its true amount in taking a bow and beam bear-
ing if no allowance is made for the tide, or she will underestimate her distance by one-fifth of its
apparent amount if going with the same tide. Therefore, if in a current of any sort, due allowance
must be made, and it should be remembered that more dei)endence can be placed upon a position fixed
by simultaneous liearings or angles, when two or more objects are available, than by two bearings of a
single object.
151. Sextant Angles between Three Known Oriects. — This method, involving the solution of
the tlirre-point problem, will, it the objects be well chosen, give the most accurate results of any. It is
largely eniployed in surveying, because of its precision; and it is especially valuable in navigation,
because it is not subject to errors arising from imperfect knowledge of the compass error, improper log-
ging, or the effects of current, as are the methods previously described.
Three objects represented on the chart are selected and the angles measured with sextants of
known index error tetween the center one and each of the others. Preferably there siiould be two
observers and tlie two angles be taken simultaneously, but one observer may first take the angle which
is changing more slowly, then take the other, then repeat the first angle, and consider the mean of the
first and last observations as the value of the first angle. The position is usually plotted by means of
the three-armed protractor, or station-pointer (.see art. 432, Chap. XVII). Set, the right and left
angles on the instrument, and then move it over the chart until the three beveled edges pass respectively
and simultaneously through the three objects. The center of the instrument will then mark the ship's
position, which may i)e pricked on the chart or marked with a pencil point tiirough the center hole.
When the three-armed protractor is not at hand, the tracing-paper protractor will prove an excellent
substitute, and may in some ca,«es be preferable to it, as, for instance, when the objects angled on are
go near tlie olwerver as to be hidden by the circle of the
instrument. A graduated circle printed upon tracing
paper permits tlie angles Iieing readily laid off, but a
plain piece of tracing paper may be u.s'ed and the angles
marked by means of a small protractor. The tracing-
paper protractor ])ermits the laying down, for simultane-
ous trial, of a number of angles, where special accuracy is
sought.
1 .52. The three-point problem, by which results are
obtained in this method, is: To find a point such that
three lines drawn from this point to three given points
shall make given angles with each other.
Let A, B, and C, in figure 20, be tiiree fixed objects on
shore, and from the ship, at D, suppose the angles CDK
and ADB are found equal, respectively, to 40° and 60°.
With the complement of CDB, 50°, draw the lines
BE and CE; the point of intersection will be tlie center
of a circle, on some point of whose circumference the
ship must be. Then, with the complement of the angle ADB, 30°, draw the lines AF and BF, meeting
at F, which point will be the center of another circle, on some point of whose circumference the ship
must be. Then D, the point of intersection of the circumference of the two circles, will be the position
of the ship.
Fig. 20.
46
PILOTING.
The correctness of this solution may be seen as follows: Take the first circle, DBC; in the triangle
EEC, the angle at E, the center, equals 180°— 2X50°= 2 (90° -SO'' ), twice the complement of 50°, which
is twice the observed angle; now if the angle at the center subtended by the chord BC equals twice the
observed angle, then the angle at any point on the circumference subtended by that chord, which equala
half the angle at the center, equals the observed angle; so the required condition is fulfilled. Should
either of the angles exceed 90°, the excess of the angle over 90° must be laid off on the opposite side of
the lines joining the stations.
153. It may be seen that the intersection of the circleG Decomes less sharp as the centers E and F
approach each other; and finally that the problem becomes indeterminate when the centers coincide,
that is, when the three observed points and the observer's position all fall upon the same circle; the
two circles are then identical and there is no intersection; such a case is called a "revolver," because
the protractor will revolve around the whole circle, everywhere passing through the observed points.
The avoidance of the revolver and the emjiloyment of large angles and short distances form the keys
to the selection of favorable objects.
Generally speaking, the observer, in judging which objects are the best to be taken, cau picture
in his eye the circle passing through the three points and note whether it comes near to his own
position. If it does, he must reject one or more of the objects for another or others. It should be
remembered that he must avoid not only the condition where the circle passes exactly through his
position (when the problem is wholly indeterminate), but also all conditions approximating thereto,
for in' such cases the circles will intersect at a ver^ acute angle, and the inevitable small errors of the
observation and plotting will produce large errors in the resulting fix.
Without giving an analysis of reasons, which may lie found in various works that treat the
problem in detail, the following may be enumerated as the general conditions which Vesult in a i/ood fix:
(fl) When the center object of the three lies between the observer and a line joining the other two,
or lies nearer than either of the other two.
^6] When the sum of the right and left angles is equal to or greater than 180°.
(c) When two of the objects are in range, or nearly so, and the angle to the third is not less than 30°.
(d) When the three objects are in the same straight line.
A condition that limits all of these is that angles should be large — at least as large as 30° — excepting
in the case where two objects are in range or nearly so, and then the other angle must be of good size.
When possible, near objects should be used rather than distant ones. The navigator should not fall into
the error of assuming that objects which would give good cuts for a cross bearing are necessarily
favorable for the three-point solution.
In a revolver, the angle formed by lines drawn from the center object to the other two, added to
the sum of the two observed angles, equals 180°. A knowledge of this fact may aid in the choice of
objects.
If in doubt as to the accuracy with which the angles will plot, a third angle to a fourth oliject may
be taken. Another way to make sure of a doubtful fix is to take one compass
bearing, by means of which even a revolver may be made to give a good
position.
154. The D.4nger Angle. — When running in sight of the land, it is
frequently of the greatest importance for the navigator to assure liiniself that
the course leatls clear of outlying dangers, and the Dmiger Angle affords a con-
venient means of so doing. There are two sorts of danger angles — the hori-
zontal angle taken between two objects, and the vertical angle of a single one.
The former will be first described.
155. Suppose, in figure 21, that a vessel standing along the coast on the
course indicated must pass an offshore danger between two well-marked
objects, A and B, and that, allowing a safe margin, it is desired to approach
no closer than the point O. Through the points A, B, and O draw a circle,
by the usual methods of geometry, and observe that no portion of the danger
lies without the circle. Measure the angle AOB with a protractor, and con-
sider this the danger angle; as the ship draws near, take frequent observa-
tions with a sextant of the angle subtended by the objects A and B. As
long as the angle is less than the danger angle the
ship is without the circle; but if the angle increases
to the amount of the danger angle, she is on the
circle, and should at once sheer off to avoid approach-
ing closer. The reason will be evident from the con-
sideration that all angles AOB, AO'B, AO"B, AO'"B,
subtended at points on the circumference of the
circle by the chord AB, are equal.
15(8. The vertical danger angle is an application of the same principle |
where there is in sight only one well-charted object and that is of known height. ^
Draw a circle with that object as a center and of such radius that no neigh Ixiring
dangera lie beyond its circumference; note, from Table 33, the vertical angle
which is subtended by the known height at the distance chosen as a radius,
and, by frequent observations in passing, make sure that this danger angle is
not exceeded. By a simple modification, a ship passing inshore of an isolated z
rock or shoal could be navigated clear by means of a vertical danger angle which
was not allowed to decrease below that corresponding to a safe distance.
Considerations governing the taking of vertical angles are given in the
description of finding position by one bearing and the distance (arts. 139, 140). Y
157. The D.^nger Bearing.— This is a method by which the navigator is
warned by a compass bearing when the course is leading into danger. Suppose
a vessel to be steering a course, as indicated in figure 22, along a coast which must not be approached
within a certain distance, the landmark A being a guide. Let the navigator draw through A the line
Fig. 22.
PILOTING. 47
S.A, clear of the danger at all points, and note its direction by the compass rose; then let frequent
bearings be taken as the ship proceeds, and so long as the bearings, YA, ZA, are to the right of XA he
may be assured that he is on the left or safe side of the line.
If, as in the case given, there is but one object in sight and that nearly ahead, it would be very
difficult to get an exact position, but this method would always show whether or not the ship was on a
good course, and would, in consequence, be of the greatest value. And even if there were other objects
visible by which to get an accurate fix it would be a more simple matter to note, by an occasional glance
over the sight-vane of the pelorus or compass, that the ship was making good a safe course than to be
put to the neeessitv of nlotting the position each time.
15S. It will occaslonallv occur that two natural objects will so lie- that when in mnge they mark
a danger bearing; advantage 'should be taken of all such, as they are easier to observe than a compass
bearing; but if in a localitv with which the navigator has not had previous acquaintance the compass
bearing of all ranges should be observed and compared with that indicated on the chart in order to
make sure of the identity of the objects. The utility of ranges, either artificial or natural, as guides in
navigation is well recognized.
1 59. Soundings. — The practice should l)e followed of employing one or two leadsmen to take and
report soundings continuously while in shoal water or in the vicinity of dangers. The soundings must
not be regarded as fixing a' position, but they afford a check upon the positions obtained by other
methods. An exact agreement with the soundings on the chart need not be expected, as there may be
some little inaccuracies in reporting the depth on a ship moving with speed through the water, or the
tide may cause a discrepancy, or the chart itself may lack perfection; but the soundings should agree in
a general way, and a marked departure from the characteristic bottom shown on the chart should lead
the navigator to verify his position and proceed with caution; especially is this true if the water la more
shoal than expected.
160. But if the soundings in shallow water when landmarks are in sight serve merely as an auxiliary
guide, those taken (usually with the patent sounding machine or deep-sea lead) when there exist no
other means of locating the position, fulfill a much more important purpose. In thick weather, when
approaching or running close to the land, and at all times when the vessel is in less than 100 fathoms
of water and her position is in doubt, soundings should be taken continuously and at regular intervals,
and, with the character of the bottom, systematically recorded. By laying the soundings on tracing
paper, along a line which represents the track of the ship according to the scale of the chart, and then
moving the paper over the chart, keeping the various courses parallel to the corresponding directions
on the chart, until the observed soundings agree with those laid down, the ship's position will in general
be quite well det«rmine<l. While some localities, by the sharpness of the characteristics of their
soundings, lend themselves better than others to accurate determinations by this method, there are few
places where the mariner can not at least keep out of danger by the indications, even if thev tell him no
more than that the time has come when he must anchor or lie off till conditions are more favorable.
161. Lights. — Before coming within range of a light the navigator should acquaint himself with
its characteristics, so that when sighted it will be recognized. The charts, sailing directions, and light
lists give infonnation as to the color, character, and ranee of visibility of the various lights. Care should
be taken to note all of these and compare them when the light is seen. If the light is of the flashing,
revolving, or occulting variety the duration of its periods should be noted to identify it. If a fixed
light, a method that may be employed to make sure that it is not a vessel's light is to descend several
feet immediately after sighting it and observe if it disai)pears from view; a navigation light will usually
do so, excepting in misty weather, while a vessel's light will not. The reason for this is that naviga-
tion lights are as a rule sufficiently powerful to be seen at the farthest point to which the ray can reach
without being interrupted by the earth's curvature. They are therefore seen at the first moment that
the ray reaches an observer on a ship's deck, and are cut off if he lowers the eye. A vessel's light, on
the other hand, is usually limited by its intensity and does not carry beyond a distance within which it
it is visible at all heights.
Care must be taken to avoid being deceived on first sighting a light, as there are various errors into
which the inexperienced may fall. The glare of a powerful light is often seen beyond the distance of
visibility of its direct ravs by the reflection downward from particles of mist in the air; the same mist
may also cause a white light to have a distinctly reddish tinge, or it mav obscure a light except within
short distances. When a light is picked up at the extreme limit at which the height of the observer
will permit, a fixed light may appear flashing, as it is seen when the ship is on the crest of a wave, and
lost when in the hollow.
Many lights are made to show different colors in different sectors within their range, and by con-
sulting his chart or books, the navigator may be guided by the color of the ray in which he finds himself;
in such lights one color is generally used on bearings whence the approach is clear, and another covers
areas where dangers are to l>e encountered.
The visibility of lights is usually stated for an assumed height of the observer's eye of 15 feet, and
must be modified accordingly for any other height. But it should be remembered that atmospheric and
other conditions considerably affect the visibility, and it must not be positively assumed, on sighting a
light, even in perfectly clear weather, that a vessel's distance is equal to the range of visibility; it may be
either greater or less, as the path of a ray of light near the horizon receives extraordinary deflection under
certain circumstances; the conditions governing this deflection are discussed in article 301, Chapter X.
162. Buoys. — While buoys are valuable aids, the mariner should always employ a certain amount
of caution in being guided by them. In the nature of things itis never possible to be certain of finding
buoys in correct position, or, indeed, of finding them at all. Heavy seas, strong currents, ice, or collisions
with passing vessels may drag them from their places or cause them to disappear entirely, and they are
especially uncertain in unfrequented waters, or those of nations that do not keep a good lookout upon
their aids to navigation. When, therefore, a buoy marks a place where a ship must be navigated with
caution, it is well to have a danger angle or bearing as an additional guide instead of placing too much
dependence upon the buoy being in place.
Different nations adopt different systems of coloring for their buoys; an important feature of
many such systems, including those adopted by the United States and various other great maritime
48 PILOTING.
nations (though not all), consists in placing black buoys to be left on the starboard hand of a vessel
going out of a harbor or fairway, and red buoys (the color of the port side light) on the port hand. In
these various systems the color and character of the buoy are such as to denote the special purpose for
which it is employed.
163. Fogs and Fog Signals.— As with lights, the navigator should, in a fog, acquaint himself
with the eharacteristics of the various sound signals which he is likely to pick up, and when one is
heard, its periods should be timed and compared with those given in the light lists to insure its proper
identity.
Experiment has demonstrated that sound is conveyed through the atmosphere in a very uncertain
way; that its intensity is not always increased as its origin is approached, and that areas within its range
at one time will seem silent at another. Add to these facts the possibility that, lor some cause, the
signal may not be working as it should be, and we have reason for observing the rule to proceed with
the utmost caution when running near the land in a foj;.
The best guide is the lead, and that should be kept going constantly. The method of plotting
soundings described in article 160 will give the most reliable position that is obtainable. Moreover,
the lead will warn the navigator of. the approach to shallow water, when, if his position is at all in
doubt, it is wisest to anchor before it becomes too late.
When running slowly in a fog (which caution, as well as the law, requires that one should do) it
must be borne in mind that the relative effect of current is increa.sed; for instance, the angle of deflec-
tion from the course caused by a cross-set is greater at low than at high speed.
It is worth rememliering that when in the vicinity of a bold bluff shore vessels are sometimes
warned of a too close approach by having their own fog signals echoed back from the cliffs; indeed, from
a knowledge of the velocity of sound (art. 314, Chap. XI) it is possible to gain t-ome rough idea of the
distance in such a case.
164. Tides and Currents." — The information relating to the tides given on thechartand in other
publications should be studied, as it is of importance for the navigator to know not only the height of
the tide above the plane of reference of the chart, but also the direction and force of the tidal current.
The plane of reference adopted for soundings varies with different cliarts; on a large nuinber it is
that of mean low water, and as no plane of reference above that of mean low water is ever employed,
the navigator may with safety refer his soundings to that level when in doubt.
When traversing, waters in which the depth exceeds the vessel's draft by but a small margin,
account must be taken of the fact that strong winds or a liigh barometer may cause the water to fall
below even a very low plane of reference. On coasts where there is much diurnal inequality in the
tides, the amount of rise and fall can not be depended upon, and additional caution is necessary.
A careful distinction should be made lietween the vertical rife and fall of the tide, which is marked
at the transition periods by a stationary height, or stand, and the tidal current, which is the horizontal
transfer of water as a result of the difference of level, producing the flood and ebb, and the intermediate
condition, or sl((ck. It seldom occurs that the turn of the tidal stream is exactly coincident witli the
high and low water, and in some channels the current may outlast the vertical movement which pro-
duces it by as much as three hours, the effect being that w hen the water is at a stand the tidal stream
is at its maximum, and when the current is slack the rise or fall is going on with its greatest rapidity.
Care must be taken to avoid confounding the two. Usually, more complete data is furnished in charts
and tide tables regarding the rise and fall, and it frequently occurs that the information regarding the
tidal current is comparatively meager; the mariner nmst therefore take every means to ascertain for
himself the direction and force of the tidal and other currents, either from the set shown between suc-
cessive well-located positions of the ship, or by noting the ripple of the water around buovs, islets, or
shoals, the direction in which vessels at anchor are riding, and the various other visible efiects of the
current.
Current arrows on the chart must not be regarded as indicating absolutely the conditions that are
to be encountered. They represent the mean of the direction and force observed, but the observatious
upon which they are based may not be complete, or there may be reasons that bring about a departure
from the normal state.
Generally speaking, the rise and fall and strength of current are at their minimum along straight
stretches of coast upon the open ocean, while bays, bights, inlets, and large rivers operate to augment
the tidal effects, and it is in the vicinity of these that one finds the highest tides and strongei-t curients.
The navigator need therefore not be surprised, in cruising along a coast, to notice that his vessel is stt
more strongly toward or from the shore in passing an indentation, and that the evidences of tide will
appear more marked as he nears its mouth.
165. Charts, b — The chart should be carefully studied, and among other things all of its notes should
be read, as valuable information may be given in the margin which it is not practicable to place upon
the chart abreast the locality affected.
The mariner will do well to consider the source of his chart and the authority upon which it is based.
He will naturally feel the greatest confidence in a chart issued by the Government of one of the more
important maritime nations which maintains a well-equipped oftice for the especial purpose of acquiring
and treating hydrographic information. He should note the character of the survey from which the
chart has been constructed; and, finally, he should be especially careful that the chart is of recent issue
or bears correction of a recent date — facts that should always be clearly shown upon its face.
It is well to proceed with caution when the chart of the locality is based upon an old survey, or one
whose source does not carry with it the presumption of accuracy. Even if the original survey was a
good one, a sandy bottom, in a region where the currents are strong or the seas heavy, is liable to
undergo in time marked changes; and where the depth is affected by the deposit or removal of silt, as
in the vicinity of the estuaries of large river systems, the behavior is sometimes most capricious. Large
blank spaces on the chart, where no soundings are shown, may be taken as an indication that no sound-
oSee also Chapter XX. 6 See also article 36 and following articles, Chapter II.
PILOTING. 49
ings were made, and are to be regarded with suspicion, especially if the region abounds in reefs or pin-
nacle rocks, in which case only the the closest sort of a survey can be considered as revealing all the
dangers. All of these facts must be duly weighed.
When navigating by landmarks the chart of the locality which is on the largest scale should be
used. The hydrography and topography in such charts appear in greater detail, and — a most important
consideration — bearings and angles may be plotted with increased accuracy.
166. Records. — It will be found a profitable practice to pay careful attention to the recording of
the various matter relating to the piloting of the ship. A notebook should be kept at hand on deck or
on the bridge, in which are to be entered all bearings or angles taken to fix the position, all changes of
course, important soundings, and any other facts bearing upon the navigation. (This book should be
different from the one in which astronomical sights and offshore navigation are worked. ) The entries,
though in memorandum form, should be complete; it should be clear whether bearings and courses are
true, magnetic, or by compass; and it is especially important that the time and patent log reading should
be given for each item recorded. The value of this lx)ok will make itself apparent in various directions;
it will afford accurate data for the writing of the ship's log; it will furnish interesting information for \ \
the next run over the same ground; it will provide a means by which, if the ship be shut in by fog,
rain, or darkness, or if there be difficulty in recognizing landmarks ahead, the last accurate fix can be
plotted and brought forward; and, finally, if there should be a mishap, the notebook would furnish
evidence as to where the trouble has been.
The chart on which the work is done should also be made an intelligible record, and to this end
the pencil marks and lines should not be needlessly numerous, heavy, or long. In plotting bearings,
draw lines only long enough to cover the probable position. Mark intersections or positions by drawing
a small circle around them, and writing neatly abreast them the time and patent log reading. Indicate
the courses and danger bearings by full lines and mark them appropriately, preferably giving both
magnetic (or true) and compass directions. A great number of lines extending in every direction may
lead to confusion; however remote the chance may seem, the responsibilities of piloting are too serious
to run even a small risk.
Finally, on anchoring, record and plot the position by bearings or angles taken after coming to; 1
observe that the berth is a safe one, or, if in'doubt, send a boat to sound in the vicinity of the ship to |
make sure.
24972°— 12 4
60
THJC SAILINGS.
CHAPTER V.
THE SAILINGS.
167. In considering a ship's position at sea with reference to any other place, either one tliat has
been left or one toward which the vessel is bound, five terms are involved — the Course, the Distance,
the Difference of Latitude, the Difference of Longitude, and the Departure." The solutions of the various
problems that arise from the mutual relation of these quantities are called Sailings.
168. Kinds of Sailinos. — When the only quantities involved are the course, distance, difference
of latitude, and departure, the process is denominated Plane Sailing. In this method the earth is >^
^ regarded as a plane, and the operation proceeds an if the vessel sailed always on a perfectly level sur-^^
face. When two or more courses are thus considered, they are combined by the method ot Tracerse
Sailing. It is evident that the number of niiks of latitude and departure can thus be readily deduced;
but, while one mile always equals one minute in difference of latitude, one mile of departure corre-
sponds to a difference of longitude that will vary with the latitude in which the vessel is sailing. Plane
sailing, therefore, furnishes no solution where difference of longitude is considered, and for such solu-
tion resort must be had to one of several methods, which, by reason of their taking account of the
spherical figure of the earth, are called Spherical Sailings.
When a vessel sails on an east or west course along a parallel of latitude, the method of converting
departure into difference of longitude is called Parallel Sidling. When the course is not east or west,
and thus carries the vessel through various latitudes, the" conversion may be made either by Middle
Laiilude Sailing, in which it is assumed that the whole run has been made in the mean latitude, or by
Mercator Sailing, in which the principle involved in the construction of the Mercator chart (art. 38,
Chap. II) is utilized.
Great Circle Sailing deals with the courses and distances between any two points when the track
followed is a gre^t circle of the terrestial sphere. A modification of this method which is adopted
under certain circumstances is called Composite Sailing.
PLANE SAILING.
169. In Plane Sailing, the curvature of the earth being neglected, the relation between the elements
' of the rhumb track joining any two points may be considered from the plane
right triangle formed by the meridian of the place left, the parallel of the place
arrived at, and the rhumb line. In figure 23, T is the point of departure;
T', the point of destinatioli; T», the meridian of departure; T'/i, the parallel
of destination; and TT', the rhumb line between the points. Let C repre-
sent the course, T'Tn; Dist., the distance, TT'; DL, the difference of latitude,
Tn; and Dep. , the departure, T'n. Then from the triangle TT'n, we have
the following:
8inC=5?E.;
Dist.
COS C :
. DL .
Dist.'
Fig. 23.
tanC=^.
From these equations are derived the following formulae for working the various problems that may
arise in Plane Sailing:
Given.
Required.
Formulse.
Course and distance .
f Difference of latitude .
\Departure
D L =Di8t. cos C. Log D L =log Dist. -flog cos C.
Dep. =Dist. sin C. Log Dep. =log Dist. -flog sin C.
Difference of latitude
and departure.
f Course ..
Distance.
TanC=^E:.
Dist. =5^.
sinC
Course and difference of | Distance...
([Departure ,
Dist. =
DL
latitude.
Dep.
cos C
DLtanC.
Log tan C= log Dep.— log D L.
Log Dist. = log Dep. —log sin C.
Log Dist. =log D L — log cos C.
Log Dep. =Iog D L+log tan C.
<iFor tlie definition of tliese terms, see article 6, Cliapter I.
THE SAILINGS.
51
Given.
Course and departure.
Distance and difference
of latitude.
Distance and departure.
Required.
Distance
Difference of latitude.
Course
Departure
Course
Difference of latitude.
Fonnulae.
Dist. =^.
sin C
DL =^.
tan C
Log Dist. =log Dep. — log sin 0.
Log D L = log Dep.— log tan C.
Log cos C=log D L —log Dist.
Dep. =Dist. sin C. Jjog Dep. =log Dist. +log sin C.
CosC:
_ DL
'Dist.'
SinC=J^-?P-
Dist.
LogsinC=logDep.— log Dist.
D L =Di8t. cos C. Log D L =logDist.+logcosC.
1 TO. The solution of the plane right triangle may be accomplished either by Plane Trigonometry, by
Traverse Tables, or by construction. If the former method is adopted, the logarithms of numbers may
be found in Table 42, and of the functions of angles in Table 44. A more expeditious method is avail-
able, however, in the Traverse Tables, which give by inspection the various solutions. Table 1 contains
values of the various parts for each unit of Dist. from 1 to 300, and for each quarter-point (2° 49'), of C;
Table 2 contains values for each unit of Dist. from 1 to 600, and for each degree of C. The method of
solving by construction consists in laying down the various given terms by scale upon a chart or plain
paper, and mea-suring thereon the terms required.
171. Of the various problems that may arise, the first two given in the foregoing table are of much
the most frequent occurrence. In the first, the given quantities are course and distance, and those to be
found are difference of latitude and departure; this is the case where a navigator, knowing the distance
run on a given course, desires to ascertain the amount made good to north or south and to east or
west. In the second case the conditions are reversed ; this arises where the course and distance between
two points are to be obtained from their known difference of latitude and departure.
Example: A ship sails SW. by W., 244 miles. Required the difference of latitude and the departure
made good.
Bi/ liixpection.
In Table 1, find the course SW. by W. (5 points); it
occurs at the bottom of the page, therefore take the names
of the columns from the bottom as well; opposite 244 in
the Dist. column will be seen Lat. 135.6 and Dep. 202.9.
Sy Computation.
Dist.
C
244
56° 15'
135.6
log
log cos
log
2.38739
9.74474
DL
2.13213
Dist.
C
244
56° 15'
log
log sin
2.38739
9.91985
Dep. 202.9 log
2.30724
Example: A ship sails N. 5° E., 188 miles. Required the difference of latitude and the departure.
By Computation. By Inspection.
Dist.
C
DL
Dist.
C
Dep.
188
0°
187.3
188
5°
16.4
log 2.27416
log cos 9.99834
2.27250
log
log 2.27416
log sin 8.94030
In Table 2, find the course 5°; it occurs at the top of the
page, therefore take the names of' the columns from the
top; opposite 188 in the Dist. column will be seen Lat.
187.3 and Dep. 16.4.
1.21446
Example: A vessel is bound to a port which is 136 miles to the north and 203 miles to the west of
her position. Required the course and distance.
By Computation. By Inspection.
Dep. 203 log 2.30750 Enter Table 1 and turn the pages until a course
DL 136 log 2.13354 is found whereon the numbers 136 and 203 are
found abrea.st each other in the columns marked
respectively I^at. and Dep. This occurs most nearly
at the course for 5 points, the angle being taken
203 log 2.30750 from the bottom, because the appropriate names
56° 11' log sin 9.91951 of the columns are found there. The course is
therefore NW. by W. Interpolating for interme-
244.3 log 2.38799 diate values, the corresponding number in tke
Dist. column is about 244.3.
C (N.) 56° 11' (W.) log tan 0.17396
Dep.
C
Dist.
52
THE SAILINGS.
Exampl'e: As the result of a day's run a vessel changes latitude 244 miles to the south and makes a
departure of 171 miles to the east. What is the course and distance made good?
By Inspection.
Enter Table 2 and the nearest agreement will
be found on course (S.) 35° (E. ), the appropriate
names being found at the top of the page. The
nearest corresponding Dist. is 298 miles.
By Computat
ion.
Dep. 171
DL 244
log 2.23300
log 2.38739
C (S.) 35°02' (E.)
log tan 9.84561
Dep. 171
C 35° 02'
log 2.23300
log sin 9.75895
Dist.
297.9
log
2.47405
TRAVERSE SAILING.
ITS. A Traverse is an irregular track made by a ship in sailing on several different courses, and the
method of Traverse Sailing consists in hnding the difference of latitude and departure corresponding to
several courses and distances and reducing all to a single equivalent course and distance. This is done
by determining the distance to north or south and to east or west made good on each course, taking tlie
algebraic sum of these various differences of latitude and departure and finding the course and distance
corresponding thereto. The work can be most expeditiously performed by adopting a tabular form for
the computation and using the traverse tables.
Example: A ship sails SSE., 15 miles; SE.,34mibs; W. by S., 16 miles; WNW., 39 miles; S. by E.,
40 miles. Required the course and distance made good.
Courses.
Dist.
N.
s.
E.
w.
SSE.
SE.
W. by S.
WNW.
S. by E.
S. by W.
15
34
16
39
40
14.9
13.9
24.0
3.1
39.2
5.7
24.0
7.8
15.7
36.0
66.8
14.9
80.2
14.9
37.5
51.7
37.5
65.3
14.2
The result of the various courses is, therefore, to carry the vessel S. by W., 66.8 miles from her original
position.
PARALLEL SAILING.
173. Thus far the earth has been regarded as an extended plane, and its spherical figure has not
been taken into account; it has thus been impossible to consider one of the important terms involved —
namely, difference of longitude. Parallel Sailing is the simplest of the various forms of Spherical Sailing,
being the method of interconverting departure and difference of longitude when the ship sails upon an
east or west course, and therefore remains always on the same parallel of latitude.
In figure 24 T and T' are two places m the same latitude; P, the adjacent pole;
TT', the arc of the parallel of latitude through the two places; MM', the corre-
sponding arc of the equator intercepted between their meridians PM and PM';
and TT', the departure on the parallel whose latitude is TOM = OTC, and whose
radius is OT.
Let DLo represent the arc of the equator MM', which is the measure of
MPM', the difference of longitude of the meridians PM and PM'; R, the equa-
torial radius of the earth, CM = CT; r, the radius OT of the parallel TT'; and L,
the latitude of that parallel.
Then, since TT' and MM' are similar arcs of two circles, and are therefore
^proportional to the radii of the circles, we have: \
MM"'
. OT . Dep.
CM' ' DLo
From the triangle COT, ?■ = R cos L; hence
Dep. __ R cos L
DLo R
; or, DLo = Dep. sec. L; or, Dep. = DLo cos L.
Thus the relations are expres.sed between mimites of longitude and miles of departure.
174. Two cases arise under Parallel Sailing: First, where the difference of longitude between two
places on the same parallel is given, to find the departure; and, second, where the departure is given,
to find the difference of longitude.
THE SAILINGS.
53
In working these problems, the computation can be made by logarithms; but the traverse tables
may more conveniently be employed. Remembering that those tables are based upon the formulae,
DL=Dist. cos C, and Dist. =DL sec C,
we may substitute for the column marked Lat. the departure, for that marked Dist. the difference of
longitude, and for the courses at top and bottom of the page the latitude. The tables then become
available for making the required conversions.
Example: A ship in the latitude of 49° SCK sails directly east until making good a difference of
longitude of 3° SC. Required the departure.
By Computation.
L 49° 3(K log cos 9.81254
DLo 210' log 2.32222
Dep. 136.4 log 2.13476
By Inspection.
Enter Table 2 with the latitude as C and the difference
of longitude as Dist. As the table is calculated only to
single degrees, we must find the numbers in the pages of
49° and 50° and take the mean. Corresponding to Dist.
210 in the former is Lat. 137.8, and in the latter J>at. 135.0.
The mean, which is the required departure, is 136.4.
Ex.\.mple: a ship in the latitude of 38° sails due west a distance of 215.5 miles,
difference of longitude.
Required the
By Computation.
By Inspection.
L
Dep.
DLo-!
38°
215.5
273'. 5
4° 33'. 5
log
log
sec 0.10347
2.33345
2.43692
Entering Table 2 with the latitude, 38°, as a course,
corresponding with the number 215.5 in column of Lat.,
is 273.5 in the column of Dist. This is therefore the
required difference of longitude, being equal to 4° 33'.5.
MIDDLE LATITUDE SAILING.
C 175. When a ship follows a course obliquely across the meridian the latitude is constantly
changing, and the method of converting departure and difference of longitude by Parallel Sailing, just
described, ceases to be applicable.
Infigure25,T is the point of departure; T', the point of destination; P,
the earth's pole; TT', the rhumb tra<:k; jiiTT', the course; Tn, rijT', the
respective parallels of latitude; and MM', the equator.
The difference of longitude between T and T' is MPAI', which may
be measured by the arc of the equator, MM', intercepted between their
meridians. This corresponds to a departure Tii in the latitude of T, and
to the smaller departure T'?!, in the higher latitude of T'; but since the
vessel neither makes all of the departure in the latitude T, nor all of it
in the latitude T', the departure actually made in the passage must have
some intermediate value between these extremes. Dividing the total
difference of longitude into a number of equal parts MP/h,, jhjPh!,, etc.,
of such small extent that, for the purposes of conversion, the change of
latitude corresponding to each may be neglected, we have the total
departure made up of the sum of a number of small departures, each
equal to the same difference of longitude, but each different from the
other. These will be rfj r, in the latitude T, d, r, in the latitude )•„
etc. Hence we have:
MM'=rf] r, sec MT-f-ri2 1'ly sec »i, ri-~d, r,, sec m^ r„ + etc.
Now, if LL' be a parallel of latitude lying midway between Tn and I'n^, since there will be as many
of the small parts lying above as below it, and since for moderate distances the ratio to be employed in
the conversion of departure and difference of longitude may be regarded as varying directly with the
latitude, it mav be assumed for such distances that the sum of all of the different small departures
equals the single de[)arture between the meridians measured in the latitude LL', and therefore that the
departure obtained by the method of plane sailing on any course may be converted into difference of
longitude by multiplying by the secant of the Middle Latitude.
The method of conversion based upon this assumption is denominated Middle Latitude Sailing, and
by reason of its convenience and simplicity is usually employed for short distances, such as those covered
by a vessel in a dav's run.
176. In Middle Latitude Sailing, having found the mean of the latitudes, the solution is identical
l/tv "'''^ *''^' °^ Parallel Sailing (art. 173), substituting the Middle I^atitude for the single latitude therein
>[J^ employed.
177. It may be remarked that the Middle Ijatitude should not be used when the latitudes are of
opposite name; if of different names and the distance is small, the departure may be assumed equal to
the difference of longitude, since the meridians are sensibly parallel near the equator; but if the distance
is great the two portions of the track on opposites of the equator nmst be treated separately.
Example: A ship in I^t. 42° 30' N., Long. 58° 51' W., sails SE. by S., 300 miles. Required -the
latitude and longitude arrived at.
From Table 1: Course SE. by S., Dist, 300, we find I^t, 249.4 S. (4° 09'.4), Dep., 166.7 E.
Fig. 25.
42°
4
30'.0 N.
09 .4 S.
Latitude left,
DL,
Latitude arrived at, 38 20 .6 N.
Latitude left, 42° 30' N.
Latitude arrived at, 38 21 N.
Mid. latitude,
2)80 51
40 25 N.
54
THE SAILINGS.
Enter Table 2 with the middle latitude, 40°, as a course; the difference of longitude (Dist. ) cor-
responding to the departure (Lat. ) 166.7 is 217.6; entering with 41°, it is 220.9; the mean is 219.2
Longitude left, 58° Sl'.O W.
DLo, 3 39 .2 E.
Longitude arrived at, 55 11 .8 W.
Example: A ship in Lat. 39° 42' S., Long. 3° 31' E., sails S. 42° W., 236 miles. Required the lati-
tude and longitude arrived at.
From Table 2: Course, S. 42° W., Dist., 236 miles; we find Lat., 175.4 S. (2° 55'.4), Dep., 157.9 W.
Latitude left, 39° 42'.0 S. Latitude left, 39° 42' S.
DL, 2 55 .4 S. Latitude arrived at, 42 37 S.
Latitude arrived at, 42 37 .4 S.
2)82 19
Mid. latitude, 41 09 S.
From Table 2: Mid. Lat. (course), 41°, Dep. (Lat.), 157.9; we find DLo (Dist.), 209.3 (3° 29'.3).
Longitude left, 3° 31'.0 E.
DLo, 3 29 .3 W.
Longitude arrived at, 01 .7 E.
Example: A vessel leaves Lat. 49° 57' N., Long. 15° 16' W., and arrives at I./at. 47° 18' N., Long.
20° 10' W. Required the course and distance made good.
Latitude left, 49° 57' N. Longitude left, 15° 16' W.
Latitude arrived at, 47 18 N. Longitude arrived at, 20 10 W.
DL,
Mid. latitude.
f 2° 39'lc
t 159 'r-
2)97^15' N.
"48 38 N.
DLo,
/ 4° 54'Uy
1 294'/ ^^•
From Table 2: Mid. Lat. (course), 49°, DLo (Dist), 294; we find Dep. (Lat.), 192.9.
From Table 2: DL 159 S., Dep. 192.9 W., we find course S. 51° W., Dist., 251 miles.
17§, The assumption upon which Middle Latitude sailing is based — that the conversion may be
made as if the whole distance were sailed upon a parallel midway between the latitudes of departure and
destination — while sufficiently accurate for moderate distances, may be materially in error where the
distances are large. In such case, either the method of Mercator Sailing (art. 179) iimst be employed,
or else the correction given in the following table should be applied to the mean latitude to obtain what
may be termed the latitude of conversion, being that latitude in which the required conditions are
accurately fulfilled. The table is computed from the formula:
cos Lo=— ,
m
where Lc represents the latitude of conversion, and I and m are respectively the differences of latitude
and of meridional parts (art. 39, Chap. II) between the latitudes of departure and destination."
Mid.
Lat.
Difference of latitude.
Mid.
Lat.
1°
2°
3°
4° i 5°
6°
7°
8°
9°
" 10°
12°
14°
16°
1S°
20°
15
18
21
/
-86
-67
-54
/
-85
-67
-54
—44
-30
-22
-16
-11
— 8
/
-84
-66
-53
/
-83
-66
-52
/
-81
-63
-51
/
-79
-61
-49
/
-76
-59
-47
/
-73
-56
-44
/
-69
-53
-42
/
-65
-50
-39
/
-56
-43
-32
/
-46
-34
-24
/
-34
-23
—15
-21
-12
- 5
/
- 6
1
7
o
15
18
21
24
30
35
-44
-31
-23
-44
-29
-21
-42
-29
-21
-41
-28
-19
-40
-26
-18
-12
- 7
- 3
-38
-24
-17
-.36
-23
-15
-33
-20
-12
-31
-18
-10
-24
-12
- 5
-17
- 6
2
- 8
1
10
1
11
18
12
21
28
24
30
35
40
45
50
-17
-12
- 8
I^
- 3
-15
-11
- 7
-14
-10
— 6
-^13
- 8
- 5
-10
- 5
- 1
- 8
- 3
1
- 6
- 1
3
— 4
1
6
2
7
12
8
14
20
16
22
28
25
31
38
34
41
49
40
45
50
55
58
60
- 5
- 3
- 3
- 4
- 3
- 2
- 3
- 1
- 1
— 2
1
2
3
2
4
5
5
7
8
7
10
11
10
13
14
17
20
22
25
29
32
35
39
43
46
51
55
58
64
69
55
58
60
62
64
. 66
- 3
- 2
- 2
- 2
- 1
- 1
- 1
1
2
2
3
4
4
5
6
7
8
9
10
12
13
9
11
12
13
14
16
17
18
20
25
27
30
35
38
42
46
50
55
60
65
71
75
81
89
62
64
66
68
70
72
- 1
- 1
1
1
2
2
3
4
5
5
6
7
8
10
14
16
18
18
20
23
22
25
28
33
37
41
46
51
57
61
67
76
78
87
97
98
109
123
68
70
72
.- .J
a The statement often made, that the latitude of conversion is always greater than the middle latitude, is not correct
when the compression of the earth is taken into account, as an inspection of the table will show; that statement is based
upon an assumption that the earth is a perfect sphere, and it was upon that assumption that a table which appeared in early-
editions of this work was computed. The value of the compression adopted for this table is — - —
293.465
THE SAILINGS.
55
Example: A vessel sails from Lat. 10° 13' S. to Lat. 20° 21' S.
Bequire<l the difference of longitude.
Latitude left, 10° 13' S.
Latitude arrived at, 20 21 S.
making a departure of 432 miles.
2)30
34
For Mid. Lat. 15° and Diff. o
Mid. latitude,
Correction,
15
- 1
17 S.
05
Lc,
14
12 S.
Lo
Dep.
14° 12' logseo .01.348
432 log 2.63548
DLo
445'.6 log
2.64896
MEBCATOR SAILING.
1 79. Mercator Sailing is the method by which values of the various elements are determined from
considering them in the relation in which they are plotted upon a chart constucted according to the
Mercator projection.
180. Upon the Mercator chart (art. 38, Chap. II), the meridians being parallel, the arc of a par-
allel of latitude is shown as equal to the corresponding arc of the equator; the length of every such
arc is, therefore, expanded; and, in order that the rhumb line may appear as a straight line, the merid-
ians are also expanded by such amount as is necessary to preserve, in any latitude, the propier propor-
tion existing between a unit of latitude and a unit of longitude. The lengths of small portions of the
meridian thus increased are called meridional parts (art. 39, Chap. II), and these, computed for every
minute of latitude from 0° to 80°, form the Table of Meridional Parts (Table 3),
by means of which a Mercator chart may be constructed and all problems of
Mercator Sailing may be solved.
In the triangle ABC (fig. 26), the angle ACB is the course, C; the side AC, the b
distance, Dist.; the side BC, the difference of latitude, DL; and the side AB, the
departure, Dep. Then corresponding to the difference of latitude BC in the lati-
tude under consideration, if CE be laid off to represent the meridional difference
of latitude, in, completing the right triangle CEF, EF will represent the differ-
ence of longitude, DLo. The triangle ABC gives the relations involved in Plane
Sailing as previously described; the triangle CEF affords the means for the con-
version of departure and difference of longitude by Mercator Sailing.
181. To find the arc of the expanded meridian intercept e<l between any two
parallels, or the meridumal difference of latitude, when Iwth places are on the same
side of the equator, subtract the meridional parts of the lesser latitude, as given
by Tal)le 3, from the meridional parts of the greater; the remainder will be the
meridional difference of latitude; but if the places are on different sides of the
equator, the sum of the meridional parts will be the meridional difference of
latitude.
182. To solve the triangle CEF by the traverse tables it is only necessary to substitute merid-
ional difference for Lat., and difference of longitude for Dep. Where long distances are involved,
carrying the computation beyond the limits of the traverse table, as frequently occurs in this method,
either of two means may be adopted: the problems may be worked by the trigonometrical formulae,
using Idgarithms, or the given quantities involved may all be reduced by a common divisor until they
fall within the traverse table, and the results, when obtained, correspondingly increased. The former
method is generally preferable, especially when the distances are quite large and accurate result^ are
sought. The formulse for the various conversions are as follows:
tanC=
DLo
; DLo=m tan C; jh=DLo cot C.
E.xample: a ship in Lat. 42° 3(/ N., Long. 58° 51' W., sails SE. by S., 300 miles,
latitude and longitude arrived at.
From Table 1: Course, SE. by S., Dist., 300; we find Lat. 249.4 S. (4° 09.'4).
Latitude left, 42° 30'.0 N. Merid. parts, +2806.4
DL, 4 09 .4 S.
Required the
Latitude arrived at, 38 20 .6 N.
Merid. parts, —2480.4
m.
m
C
DLo
By Computation
326.0 log
33° 45'
f 217'.8
13° 37'.8
2.51322
log tan 9.82489
log
2.33811
326.0
Bij Inspection.
Enter Table 1, course 3 points; since the quantities
involved exceed the limits of the table, divide by 2;
abreast ^ (Lat.), 163.0, find ^- (sPep.), 108.9; hence
DLo=217'.8 or 3° 37'.8.
Longitude left,
DLo,
58° 51'.0 W.
3 37 .8 E.
Longitude arrived at, 55 13 .2 W.
56 THE SAILINGS.
Example: A ship in Lat. 4° 37' S., Long. 21° 05' W., sails N. 14° W., 450 miles. Required the
latitude and longitude arrived at.
From Table 2: Course, (N.) 14° (W.), Dist, 450; we find Lat. 436.6 N. (7° 16'.6).
Latitude left, 4° 37'.0 S.
DL, 7 16 .6 N.
Merid. parta, +275.4
Latitude arrived at, 2 39 .6 N.
Merid. parts, +159.0
m, 434.4
tatimi.
By Inspection.
m 434.4 log 2.63789 From Table 2: Course, 14°, m (Lat.), 434.4, we find
C 14° log tan 9.39677 DLo (Dep.) 108'.3 W., or 1° 48'.3.
v,T / 108'.3 log 2.03466
ULo 1^0 4g/ 3
Longitude left, 21° OS'.O W.
DLo, 1 48 .3 W.
Longitude arrived at, 22 53 .3 W.
Example: Required the course and distance by rhumb line from a point in J^t. 42° 03' X., Long,
70° 04' W., to another in Lat. 36° 59' N., Long. 25° 10' W.
Lat. departure, 42° 03' N. Merid. pts., +2770.1 Long, departure, 70° 04' \V.
Lat. destination, 36 59 N. Merid. pts., —2377.3 Long, destination, 25 10 W.
DL
{^;Ot;}s. m, 392.8 DLo ^^J^'}^
DLo 2694 log 3.43040
m 392.8 log 2.59417
C (S.) 81° 42' (E.) log tan .83623 log sec .84056
DL 304' log 2.48287
Dist. 2106 log 3.32343
The course is therefore S. 81° 42' E., and the distance is 2,106 miles. Since the figures involved
are so large, it is best to employ only the method by computation. The formula by which the Dist. is
obtained comes from Plane Sailing.
GREAT CIRCLE SAILING.
1§3. The shortest distance Ijetween any two points on the earth's surface is measured liy the arc of
the great circle which paisses through those points; and the method of sailing in which the arc of a great
circle is employed for the track of the vessel, taking advantage of the fact that it is the shortest route
possible, is denominated Great Circle tSailin;/.
184. It frequently happens when a great circle route is laid down that it is found to lea<l across
the land, or to carry the vessel into a region of dangerous navigation or extreme cold which it is expe-
dient to avoid; in such a case a certain parallel should be fixed upon as a limit of latitude, and a route
laid down such that a great circle is followed as far as the limiting parallel, then the parallel itself, and
finally another great circle to the port of destination. Such a modification of the great circle method is
called Composite Sailing.
I §5. The rhumb line (art. 6, Chapul) also called the loxodromic curve, which cuts all the meridi-
ans at the same an^le, has been largely employed as a track by navigators on account of the ease with
which it may be laid down on a Mercator chart. But as it is a longer line than the great circle Isetween
the same points, intelligent navigators of the present day use the latter wherever practicable. On the
Mercator chart, however, the arc of a great circle joining two points (unless both are on the equator or
both on the same meridian) will not be projected as a straight line, but as a curve which seems to be
longer than the rhumb line; hence the shortest route appears as a circuitous one, and this is doubtless
the reason that a wider use of the great circle has not been made.
It should be clearly understood that it is the rhumb line which is in fact the indirect route, and
that in following the great circle the vessel is always heading for her port, exactly as if it were in sight,
while on the course which is shown as a straight line on the Mercator chart the vessel never heads for
her port until at the very end of the voyage.
1S6. The method of great circle sailing is of especial value to steamers, as such vessels need not,
in the choice of a route, have regard for the winds to the same extent as must a sailing vessel ; but even in
navigating vessels under sail a knowledge of the great circle course may prove of great value. For example,
suppose a ship to be bound from Sydney to Valparaiso; the first great circle course is SE. by S., while
the Mercator course is almost due east. The distance is 748 miles shorter by the former route (if the
THB SAILINGS. 67
(treat circle is followed throughout, though this would lead to a latitude of 61° 8.)- With the wind at
E. i S. the ship would lie nearer to the Slereator course on tlie starboard tack, assuming that she sailed
within six points of the wind; but if she took that tack she would be increasing her distance from th^
port of destmation by 4^ miles in every 10 that she sailed; while on the port tack, heading one point
farther from the rhumb, the gain toward the port would be 9J miles out of every 10. Any course
between East and SSW. would be better than the Mereator course; and if the wind were anything to
the eastward of SE. by S., the ship would gain by taking the port tack in preference to the starboard.
187. As the great circle makes a different angle with each meridian that is crossed, it becomes
necessary to make frequent changes of the ship's course; in practice, the course is a series of chords
joining the various points on the track line.
If, while endeavoring to follow a great circle, the ship is driven from it, as by unfavorable weather,
it will not serve the purpose to return to the old track at convenience, but it is required that another
great circle be laid down, joining the actual position in which the ship finds herself with the port of
destination.
1§§. The methods of determining the great circle course may be divided generally into four
classes; namely, by Great Circle Sailing Charts, by Computation, by the methods of the Time Azimuth,
and by Graphic Approximations. >
189. (treat Circle S.\iling Ch.\rts. — Of the available methods, that by means of charts espe-
cially constructed for the purpose is considered greatly superior to all others.
A series of great circle sailing charts covering the navigable waters of the globe is published by the
United States Hydrographic Office. Being on the gnomonic projection (art. 43, Chap. II), all great
circles are represented as straight lines, and it is only necessary to join any two points by such a line to
represent the great circle track between them. The courses and distance are readily obtainable by a
method explained on the charts. The track may be transferred to a chart on the Mereator projection
by plotting a number of its points by their coordinates and joining them with a curved line.
The navigator who contemplates the use of great circle
tracks will find it of the greatest convenience to be pro-
vided witli these gnomonic charts for the regions which
his vessel is to traverse.
190. By CoMPiTATioN. — This method consists in de-
termining a series of points on the great circle by their
coordinates of latitude and longitude, plotting them upon
a Mereator chart, and tracing the curve that joins them.
The first point determined is the vertex, or point of highest
latitude, even when, as sometimes occurs, it falls without
that portion of the great circle which joins the points of
departure and destination. Fig. 27.
In figure 27, A represents the point of departure; B, the
point of destination; AVB, the great circle joining them, with its vertex at V; and P, the pole of the
earth.
Let Ca = PAB, the initial course;
Cb = PBA, the final course;
La,Lv,Lb = the latitudes of the respective pints a, V, B = (90° — PA), (90° — PV), (90° — PB).
Loab, Loat, Lobv = the differences of longitude between A and B, A and V, B and V, respectively, =
APB, APV, BPV.
D = the great circle distance between \ and B; and
(p = an auxiliary angle introduced for the computation.
We then have:
tan ip = cos Loab cot L b ;
cot Ca = cot Loab cos (La -\- cp) cosec <p;
cot D = cos Ca tan (La + <p);
cos Lt = sin Ca cos La ;
cot Loav = tan Ca sin Jy a .
Bv these formulse are determined the initial course and the total distance by great circle; also the
latitude of the vertex and its longitude with respect to A. By interchanging the subscript letters a and
B throughout, we should obtain the final course, and the longitude of the vertex with respect to B; also
the same total distance and latitude of the vertex as before.
In performing this comp, tation, strict regard must be had to the signs of the quantities. If the
points of departure and destin. tion are in different latitudes, the latitude of one of these points must be
regarded as negative with respect to the other, and they must be marked with opposite signs. Should
Loat or Lobv assume a negative value, it indicates that the vertex does not lie between A and B, and is
to be laid off accordingly.
To find other points of the great circle, M, N, etc., let their latitudes be represented by Lm, Lii,etc.,
and their longitudes from the vertex by Lovm, Lovk, etc.; then
tan Lm = tan Lv cos Lovm ; or, cos Lovm = tan Lm cot Lv ;
tan Ln = tan Lv cos Lovn; or, cos LovN = tan Ln cotLv;
and so on. By these formula; intervals of longitude from the vertex of 5°, 10°, or any amount, may be
assumed, and the corresponding latitudes deduced; or any Latitude may be assumed and its correspond-
ing interval of longitude from the vertex found. Two positions will result from each solution, and the
appropriate ones may be chosen by keeping in mind the signs involved.
58
THE SAILINGS.
Example: Given two places, one in Lat. 40° X., Long. 70° W., the other in Lat. 30° S., Long. 10°
W., find the great circle distance between them; also the initial course, and the longitude of equator
crossing.
L» = +40°; Lb = -30°; Loab=60°.
Loab 60° cos 9. 69897.. cot 9.76144
Lb — 30° cot (— ) .23856
Li +40° cos 9.88425 sin 9.80807
<p - 40° 54' tan( — ) 9.93753.. cosec(-) .18393
{La + 9') — 0° 54' cos 9.99995 tan (-) 8.19616
Ca 131° 24' orS.48°36' p:....cot (-)9.94532 cos (-) 9.82041 sin 9.87513 tan (-) .05472
D 89° 24' or 5,364 miles cot 8.01657
Lv + 54° 56' cos 9.75938
Loav - 53° 54' cot ( — )9.86279
The initial course is therefore S. 48° 3t)' E., and the distance 5,.364 nautical miles. (It may be
found that the course by rhumb line is S. 38° 45' E. and the distance 5,751 miles. ) The vertex of the
great circle is in Lat. 54° 56' N., and is 53° 54' in longitude from the point A, in a direction away from
B; hence it is in Long. 123° 54' W. To find the longitude of equator crossing let Lx = 0°; then in the
equation,
cos LovM=tan Lm cot L^-,
since tan Lm equals zero, cos Lovm also equals zero, or the longitude-interval from the vertex is 90°, which
is evident from the properties of the great circle; therefore the longitude of equator crossing is
123° 54' AV.— 90°=33° 54' VV.
191. By Time Azi.muth Methods. — A convenient method of obtaining the initial and final courses
in great circle sailing is afforded by the tables and graphic methods which are prepared for thfe solution
of the Time Azimuth problem (art. 359, Chap. XIV). It will be found by comparison that if the lati-
tude of the point of departure be substituted for the latitude of the observer in that problem, the latitude
of destination for the declination of the celestial body, and the longitude interval for the hour angle, the
solution for the initial course will coincide with that for the azimuth; by interchanging the latitudes of
the points of departure and destination the final course will be .similarly obtained. Advantage may
thus be taken of the various methods provided for facihtating the determination of the azimuth to ascer-
tain the great circle courses from one jjoint to another.
192. By Graphic Appro.'limations. — Of the numerous methods that fall within this class only two
need be given.
193. By the use of a Terrestrial Globe the two given points between which the great circle track
is required may be joined by the shortest line between them, either by means of a piece of thread or
by moving the globe until they are brought to the fixed horizon which is usually provide<l; the coordi-
nates of the various points of the track are then transferred to the chart. The number of minutes of
arc, as measured on the scale of the horizon between the points, equals the number of miles of distance;
if there be no horizon, the measure may be made by a thread along the equator or a meridian.
194. The Method of Professor Airy consists in drawing on the chart a rhumb line joining the two
points, and erecting at its middle [wint a iterpendicular; the following table should then be entered
with the middle latitude as an argument, and the "corresponding parallel" of latitude taken out
(noting whether it is the same or opposite in name to the middle latitude); where this parallel is inter-
sected oy the perpendicular that was drawn will be the center from wliicli may be swept an arc approx-
imately representing the great circle between the two points.
Middle lati-
Correspond-
Name.
Middle lati-
Correspond-
Name.
tude.
ing parallel.
tude.
ing parallel.
o /
/
20
81 13
Opposite.
52
11 33
Opposite.
22
78 16
Do.
54
6 24
Do.
24
74 59
Do.
56
1 13
Do.
26
71 26
Do.
58
4 00
Same.
28
67 38
Do.
60
9 15
Do.
30
63 37
Do.
62
14 32
Do.
32
59 25
Do.
64
19 50
Do.
34
55 05
Do.
66
25 09
Do.
36
50 36
Do.
68
30 30
Do.
38
46 00
Do.
70
35 52
Do.
40
41 18
Do.
72
41 14
Do.
42
36 31
Do.
74
46 37
Do.
44
31 38
Do.
76
52 01
Do.
46
26 42
Do.
78
57 25
Do.
48
21 42
Do.
80
62 51
Do.
50
16 39
Do.
THE SAILINGS. 59
COMPOSITE SAILING.
195. It has already been stated that when, for any reason, it is impracticable or unadvisable to
follow the great circle track to its highest latitude, a limiting parallel is choaen and the route modified
accordingly. This method is denominated Composite Sailing.
196. The shortest track between points where a fixed latitude is not exceeded is made up as
follows:
1. A great circle through the point of departure tangent to the limiting parallel.
2. A course along the parallel.
3. A great circle through the point of destination tangent to the limiting parallel.
The composite track may be determined by Great Cirde Sailing Chart, by Computation, or by
Graphic Approximation.
197. On a Great Circle Sailing Chart, draw lines from the points of departure and destination,
respectively, tangent to the limiting parallel; transfer these great circles to a Mercator chart in the
usual manner, by the coordinates of several points, including in each case the point of tangency to the
jiarallel. Follow the first ^reat circle to the parallel; then follow the parallel; then the second great
circle. Determine great circle courses and distances from the gnomonic chart as thereon described;
determine the distance along the parallel by Parallel Sailing.
198. Si/ compvialion, the problem consists in finding the great circl&s which pass, respectively,
through the points of departure and destination and have their vertices in the latitude of the limiting
parallel. Resuming the designation of terms already employed (art. 190), we have:
cos LoTA=tan La cot Lv ;
cos LovB=tan Lb cot Lv ;
where Lova and Lo™ represent the distances in longitude from A and from B to the respective points of
tangencv; other features of each of the great circles mav be detennined in the usual manner.
E.x.iMPLE: A vessel in Lat. 30° S., Long. 18° VV., is" bound to a point in Lat. 39° S., Long. 145° E.,
and it is decided not to go south of the parallel of 55° S. Find the longitude of reaching that parallel
and the longitude at which it should be left.
La =30° S.; Lb =39°S.; Lv=55°S.
Loa=18° W.; Lob =145° E.
La 30° tan 9.76144 L„ 39° tan 9.90837
Lt 55° cot 9.84528 Lv 55° cot 9.84523
Lova 66° 09' E. cos 9.60667 Lovb 55° 27' W. cos 9.75360
Ix)a 18 00 \V. - Lob145 00 E.
Lov 48 09 E. Lf.v 89 .33 E. .
199. A graphic approximation to the composite track may be obtained by drawing a straight line
between the given points on a Mercator chart and erecting at its middle point a perpendicular, which
should be extended until it intersects the limiting parallel. Then through this intersection and
the two points describe the arc of a circle, and this will approximate to the^hortest distance within the
assigned limit of latitude.
200. .\ terrestrial globe may be employed for the determination of the composite track; the
method of its use will suggest itself.
201. Another approximation is obtained by joining the two points with a single great circle,
and following this to its intersection with the limiting parallel; thence sailing along the parallel until
the great circle is again intersected; then resuming the circle and following it to the destination.
60 DEAD BECKONING.
chaptf:r VI.
DEAD BECKONING.
203. Dead Reckoning is the process by which the position of a ship at any instant is found by
applying to the last well-detemiined position the run that has since been made, using for the puriwse
the ship's course and the distance indicated by the log.
203. Positions by dead reckoning, also spoken of as positions by account, differ from those
determined by bearings of terrestrial objects or by observations of celestial bodies in being less exact,
as the correctness of dead reckoning depends upon the accuracy of the estimate of the run, and this is
always liable to be at fault to a greater or less extent. The course made good by a ship may differ from
that which it is believed that she is making good, by reason of imperfect steering, improper allowance
for compass error and leeway, and the effects of unknown currents; the allowed distance over the
ground may be in error on account of inaccurate logging and unknown currents.
/Notwithstanding its recognized defe(;ts as compared with the more exact methods, the dead
reckoning is an invaluable aid to the mariner. It affords him a means of plotting the position of the
ship at any desired time between astronomical determinations; it also gives him au approximate
y^ position at the moment of taking astronomical observations which is a great convenience in working up
' those observations; and finally it affords the only available means of determining the location of a
/"* vessel at sea during those periods (which may continue for several days together) when the weather is
I such as to render the observation of celestial bodies an impossibility.
r 204. Taking Departure. — Before losing sight of the land, and preferably while objects remain in
good view, it is the duty of the navigator to take a departure; this consists in fixing the position of the
ship by the best means available (Chap. IV), and using this position as the origin for dead reckoning.
There are two methods of reckoning the departure. The first and simpler consists in taking from the
chart the latitude and longitude of tlie position found, and applying the future run thereto. The other
requires that the bearing and distance of an object of known latitude and longitude be found; the
position of the object then forms the basis of the reckoning, and the reversed direction of the bearing,
with the distance, forms the first course and distance; thus if may be considered that the ship starts from
the position of the object and sails to the position where the bearing was taken; the correction for
deviation in such a case should be that due to the heading of the ship when the bearing was taken.
Each time that a new position is determined it is used as a new departure for the dead reckoning.
This meaning of the term departure should not be confounded with the other, which refers t(j the
distance run toward east or .west.
^ 205. Methods. — The working of dead reckoning merely involves an application of the methods of
^ Traverse Sailing (art. 172) and Middle Latitude Sailing (art. 175), as explained in Chapter V.
The various compass courses are set down in a colunm, and abreast each are written the errors by
reason of which the course steered by compass differs from the true course made good over the ground;
thence the true course made good is determined and recorded; next, the distance is written in, and
afterwards, by means of Tables 1 or 2 (according as the courses are expressed in quarter points or
degrees), the difference of latitude and departure are found, separate columns being kept for distances to
the north, south, east, and west.
When the position of the ship at any moment is required, add up all the differences of latitude and
departure, and write in the column of the greater the difference between the northing and southing,
and the easting and westing. Apply the difference of latitude to the latitude of the last determined
position, which will give the latitude by D. R., and from which may be found the middle latitude; with
the middle latitude find the difference of longitude corresponding to the departure, apply this to the
longitude of last position, and the result will be the longitude bv D. R.
^ The employment of the tabular form will be found to facilitate the work and guard against errors.
It will be a convenience to include in that form columns showing the hour, together with the reading
'"' of the patent log (if used) each time that the course is changed or the dead reckoning worked up.
^ The employment of minutes and tenths in dead reckoning rather than minutes and seconds is
^ recommended.
^ Example: A vessel under sail heading NE. J E. (on which course deviation is } pt. Easterly) takes
' departure from Cape Henry light-house (see Appendix IV for position), bearing SSW. \ W. per compass,
/■ distant 1.4 miles. She then sails on a series of courses, with errors and distances as indicated below;
'^ wind about SE. by E. Required the position by dead reckoning; also the course and distance made
good by dead recokning.
-yO^-Z^Cy
f^^-z^^^yy:!^
*^ <^^.SB^a^ ^^^^j:^ ^^-;^^^iZ^ ^:^.i^^:^Z^^ ^Sr^^^^^i-^^;^^--^-'
DEAD BECKONING.
61
Comp. course.
Var.
Dev.
Leeway.
Error.
True course.
Dist.
N.
s.
E.
W. D.
NNE. i E.
JW.
*E.
iw.
NNE. i E.
1.4
1.3
0.6
NE. i E.
W.
}E.
w.
w.
NE. i E.
27.6
18.5
20.5
S. by W.
W.
E.
w.
S. } W.
31.5
31.2
4.6
ENE.
W.
iE.
W.
V W.
NE. bv E. i E.
14.2
7.3
12.2
S. i E.
W.
E.
S. JE.
11.0
11.0
0.5
NE. } N.
iw.
JE.
iW.
iW.
NE. by N.
/
87.0
72.3
48.3
7 Z.7
99.4
42.2
82.1
4.6
Made good.
NE. i E.
96.5
57.2
^7,3)
97.0
Point of dejiarture,
Run,
By D. K.
Latitude.
36° 55'.6 N.
57 .2 N.
37 52 .8 N.
Mid. L., 37°
Longitude.
76° OC.o W.
1 37 .0 E.
74 23 .5 W.
Example: A steamer's position by observation at noon, patent log reading 27.3, is Lat. 49° 15' N.,
Long. 7° 32' W. Thence she steers S. 82° W. ( per compass ) , tlie total compass error on that course being
20° W., until 12.30, at which time, patent log reading 33.9, the course is changed to S. 80° W. {p. c.) ,
.«aiue error. At 4.12, patent log 80.5, sights are taken from which it is found that the true longitude is
8° 4(i' W., and the compass error 19° W. At 6.15, patent log reading 6.1, a sight is taken from which
it is found that the true latitude is 48° 34' 30" N. At 8 p. m. the patent log reads 27.5. Required the
positions by D. R. at each sight and at 8 o'clock.
Time.
Oomp. course.
Error.
True course.
Pat. Log.
Dist.
s.
w.
D.
Noon.
12.30
4.12
6.15
8.00
S. 82° W.
S. 80° W.
S. 80° \V.
S. 80° W.
20° W.
20° W.
19° AV.
19° \V.
s
s
62° W.
60° W.
61° W.
61° W.
27.3
33.9
80.5
6.1
27.5
6.6
46.6
25.6
21.4
3.1
23.3
5.8
40.3
70.3
34.1
27.9
26.4
12.4
10.4
46.1
22.4
18.7
By obs. at noon.
Run to 4.12 sight.
By p. R. at 4.12 sight,
By obs. at 4.12 sight.
Run to 6.15 sight.
By D. R. at 6.15 sight.
By obs. at 6.15 sight,
Run to 8 p. m..
Latitud
49° 15'.0
26.4
N.
S. Mid. L., 49°
N.
S. Mid. L., 49°
N.
N.
S. Mid. L., 48°
Longiii
7° 32'.0
1 10.3
ide.
W.
VV.
W.
"w.
W.
W.
W.
48 48.6
12.4
8 42.3
8 46.0
34.1
48 36.2
48 34.5
10.4
9 20.1
27.9
By I). R. at 8 p. m., 48 24.1 N.
9 48.0 W.
206. Allowance for Current. — When a vessel is sailing in a known current whose strength may
be estimated with a fair degree of accuracy, a more correct position may be arrived at by regarding the
set and drift of the current as a course and distance to be regularly taken account of in the dead
reckoning.
Example: A vessel in the Gulf Stream at a point where the current is estimated to set N. 48° E. at
the rate of 1.8 miles an hour, sails S. 3° W. (true), making 9.5 knots an hour through the water for
S*" 30". Middle latitude 35°. Required the course and distance made good.
True course.
Dist.
N.
s.
E.
w.
D.
Run
Current
Made good
S. 3° W.
N. 48° E.
S. 6° E.
33.3
6.3
29.3
4.2
33.3
4.7
1.7
3.6
29.1
3.0
62 DEAD BECKONING.
207. Finding the Cuekent. — It is usual, upon obtaining a good position by observation (as the
navigator usually does at noon), to compare that position with the one obtained by dead reckon-
ing, and to attribute such discrepancy as may bejound to the effects of current. It has already been
pointed out that other causes than the motion of the water tend to make the dead reckoning inaccurate,
eo that it must not be assumed that currents proper are thus determined with complete correctness.
Current is said to have set and drift, referring respectively to the direction toward which it is flow-
ing and the velocity with which it moves.
It is evident that, in calculating current by the method of comparing positions by observation with
those by account, the navigator must limit himself to the periods during which the dead reckoning has
been brought forward independently, without receiving any corrections due to new points of departure.
In case it is desired to find the current covering a period during which fresh departures have lieen used,
as from noon to noon, find the algebraical sums of all the differences of latitude and longitude from the
table, and apply these to the latitude and longitude of original departure — that of the preceding
noon; this gives the position from the ship's run proper, and the difference between tiiis and the posi-
tion by observation gives the set and drift for the twenty-four hours; if an allowance has been made
for current, as explained in the preceding article, that must be omitted in bringing up the position
which is to take account of the run only.
I20§. Day's Run. — It is usual to calculate, each day at noon, the ship's total run for the preceding
twenty-four hours. Having the positions at noon of each day, the course and distance between them is
found as explained in article 175, Chapter V. The position by observation is used in each case, if such
has been found; otherwise, the position by dead reckoning.
Example: At noon, January 22, the position of a vessel by observation was Lat. 35° KY N., Long.
134° OF W. During the next 24 hours, the run by account was (iO.l miles north and 153.2 miles east.
At noon, January 23, tlie position by observation was Lat. 36° 03' N., Long. 131° 14' W. Required
the position by D. R. at the latter time; also the nm and current for the 24 hours.
Latitude. Longitude.
By obs., noon, 22d, 35° lO'.O N. l^iriT 1R° \ 134° Ol'.OW.
Run, 1 00.1 N. ?J'^-V^o^°T,, 3 09 .4 E.
Dep., 153.2 E.<
By D. R., noon, 23d, 36 10 .1 N. J^' 189.4 E.| ^g^ 51 g-\y
By obs., noon, 23d, 36 03 .0 N. fD, 22.4 W.l 131 14 .OW.
Current, 6 .9 S. iDep., 18.1 W.J 22 .4 W.
Current for 24 hours, 6.9 S., 18.1 W.= S. 69° W., 19.4 miles.
Current per hour, S. 69° W., 0.8 mile.
Latitude. Longitude.
By obs., noon, 23d, 36° 03'.0 N. U,. , . .^o \ 131° i4'.0W.
By obs., noon, 22d, 35 10 .0 N. p i67 0E ^^* 01 .OW.
Run, 53 .ON. JDep., 135.1 [ g 47 .0 E.
Run for 24 hours, 53.0 N., 135.1 E.=N. 68° E., 146 miles.
DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
63
TO FIND THE LONGITUDE.
Departure miles areaJw© honest, but degrees of Longitude ^gTEONOMY,
e only true on the Equatpr, and as they go north or south
rmrrt, they contract, converging towards the Poles, and inste-
r . . , ., , , 1 r ..1 .. J • 3, Chap. I) as that branch of
of Betarm^ 6o miles to a degree they »*tU»ee-+r»fn-#Kit grad- ,j. the aid of celestial objects—
illy^untif reaching the Poles there is no longitude. Hence it^j^^ ^^^^j^ ^pp^^^ ^^ ^.^^, ^^^
ill be seen that the homst. departure must be proportioned fJ^'amlThativ^^Jan determine
xordine to the distance the ship is from the Equator. In' from each other or from the
., .,, radms, the •eye of the observer
her words a departure mile will run over a greater or less space dh this Cdestial. Sphere, or Celes-
, ... . , 1 • • 1 r ..1 >, IT 'sect the surface of the sphere.
lono^itude in proportion as the ship is removed from the h.qua- ^ii angular distances are meas-
r. Consequendy we will (unless on the Equator)^^t-more^e^-\t^l^sphe^^^^^^^^^
fference of longitude than departure. aeridians, equator, and all other
Proceed to find the correct difference of longitude miles ^P^f<^j|;^ "^tL^S^X
ade, and the latitude r)f the-ship as follows: 'tion upon its axis; second, the
VK~/t,4 ^ t J Ja ^ '*^ orbit; and tlnrd, the actual
.'\dd together yest'eFd^J'TS^to-day's latitude and clivide"|^;^J;f, t^«^<^Xlato^^^
/ 2. The answer of course will be the Middle Latitude, the ^ named are independent of the
, , _ , 1 1 • 1 1 r 111-1 • 1 *'■■ relatio" to the center of the
3int hall way between the latitude left and the latitude arrived dated in the Nautical Almanac
rations to govern the actual and
^■ , 1 • ^1 T \ ^ 1 • 'I- 1 I c» f the celestial sphere vertically
Aov. taking the Departure, turn to the page in lable 2
iowditch or Thoms) with that number of degrees on, and-^plr^^hhZtnTth o?1he
jply it in the Latitude column, and opposite in the Di.stance
)]umn will be found the Correct Difference of Longitude.
If the figures exceed sixty miles, divide them by 6o, antl
bplj'^the answer to the longitude left, addiri!:; it if the longi-
ide has been increased, but subtracling it \{ di.creas-ed. The-
iswer will Ix
; the i.oNT.iTUDE ok
HE SIJIl' HV DKAli R
iflKQNIXiJ.
Conrse.
Dihtimce .
North.
South.
Eftst.
West.
S. E. bv S.
S. E.
60 miles.
.50 mil PS,
49-9
35-4
33-3
35-4
Diiierence of Lntitnde, 85 — 3
69-0 Departure.
TrtMt! i gives the Conrse 39o=.S. E. I S, and the Distauce 110 miles.
n To-Day's Latitude, apply the difpekence ;>i' latitcide to yesterbay's g
■"■•• Fig. 28.
aftiTiliiy's latitude. 40° 20' North / Apyljing the Departure 69 in the
liffiriiK-e of Lititiide. 85 uiileH — 1° 25' South / circles of the celestial sphere
I Latitude column on page of ictial, and may be formed by
Lititiide by 1). U., Z^ri 55' \ ersect the celestial sphere. In
40° 20' 1 Middle Latitude, Table 2, I ins the zenith and is therefore
I { ects the horizon in N and S, its
2|79o 15' .; get the difference of Inngitude
lie latitude, 39" 37'
! ly's Inucitnde, . . - - 73 ' 50' West
;ice (vf lonsihide, 91 miles, — 1^ 31' E.ist
91 miles.
I made,
itial sphere which pass through
:he figure, ZH, WZE, NZS, are
1 the poles, coincides with the
eoo<l position bv observation (as the
QUESTION 2nd,
g2 BEAD RECKONING.
207. Finding the CcRRENT.-It is "^"^^l'^"" "i^fj^.^th^^he <5ne' obteined by dead recton-
navigator usually does at noon), *o coiyare that posiUo.i ^v itn tne ^^ has already been
STod-fo^u^teote^tuSTnth^^
so that it must not be assumed that curre of latitude always contains 6o full miles.
Current is said to have set and dnp, J
ing and the velocitv with which it movei
It is evident that, in calculating curr
those by account, the navigator must lire
been brought forward independently, wi
In case it is desired to find the current cc
as from noon to noon, find the algebraici
table, and apply these to the latitude
noon; this gives the position from the si
tion by observation gives the set and <l)
for current, as explained in the precei
which is to take account of the run only
208. Day's Kun.— It is usual to cal
twenty-four hours. Having the position
found as explained in article 175, Chapt(
has been found; otherwise, the position
Example: At noon, January 22, the
134° 01' W. During the next 24 hours.
At noon, January 23, the position by
the position by D. R. at the latter time;
EXPLAIN METHOD OF OBTAINING LATITUDE BY DI
RECKONING?"
By obs., noon.
Bun,
By D. R., noon, 23d,
By obs., noon, 23d,
Current,
Having^ corrected the courses sailed by applying i
iation and Leeway (if any), set them down in a Traverse
with the distance sailed on each course opposite; apply
courses separa ely in Table 1 (Bowditch or Thoms) on
22d, proper page, and looking opposite to the figures in the
tance column, corresponding to the number of miles ru
such course, the amount of Latitude and Departure w
seen, which must be read from either the top or bottor,:- (
page, accord'ng as the course was found. Having fo
Current for 24 hours, 6.9 s., 18.1 W the courses in a like manner, add the columns .sepa-
Current per hour, s. 69° w., 0.8 m subtract between the north and south and the east ana «
and the answer will be the Difference of Latitude and Dvl
ure the ship has made. If the difference of latitude ex^
sixty miles divide it by 6o, and apply it to the latitutle
adding it if you have increased your latitude, but subirai
it \{ decreased : the answer will be the latitude of thi:
HV DEAD RECKOMXG.
The difference of latitude is correct, because lati
By obs., noon.
By obs., noon
Run,
23d,
22d,
Bun for 24 hours, 53.0 N., 135.1 E.
1
is near enoughcorrecl
Xenith Distance. ' I'his method
some circumstances, but it is an ignorant way of working
should never be employed as there is no necessity for i*
case it is ever necessary to observe an altitude from alot
sometimes happens) the Zenith Distance obtained in the ai
manner will be very materially wrong and the latitude ir
sequence will be far from the truth.
PROPER MANNER OF CORRECTING AN ALTITUDE,
DEFINITIONS RELATING TO NAUTICAL ASTRONOMY.
63
. CHAPTER VII.
DEFINITIONS EELATING TO NAUTICAL ASTKONOMY.
209. Nautical Astronomy, or Celo-Xaflgation, has been defined (art. 3, Chap. I) as that branch of
the science of Navigation in which the position of a ship is determined by the aid of celestial objects —
the 8un, moon, planets, or stars.
210. The Celestial Sphere. — An observer upon the surface of the earth appears to view the
heavenly bodies a-s if they were situated itpon the surface of a vast hollow sphere, of which his eye is
the center. In reality we know that this apparent vault lias no existence, and that we can determine
only the relative directions of the heavenly bodies — not their distances from each other or from the
observer. But by adopting an imaginary spherical surface of an infinite radius, the«ye of the observer
being at the center, the places of the heavenly bodies can be projected upon this Celestial Sphere, or Celes-
tial Concare, at points where the lines joining them with the center intersect the surface of the spliere.
Since, however, the center of the earth should be the jtoint from which all angular distances are meas-
ured, the observer, by transferring himself tliere, will find projected on the celestial sphere, not only the
heavenly bodies, but the imaginary points and circles of the earth's surface. The actual position of the
observer on tlie surface will be projected in a point called the zenith; the meridians, equator, and all other
lines and points may also be projected.
211. An observer on the earth's surface is constantly changing his position with relation to the
celestial bodies projected on the sphere, thus giving to the latter an apparent motion. This is due to
three causes: first, the diurnal motion of the earth^ arising from its rotation upon its axis; second, the
annual motion of the earth, arising from its motion about the sun in its orbit; and third, the actual
niotion of certain of the celestial bodies themselves. The changes produced by the diurnal motion are
different for observers at different points upon the earth, and therefore depend upon the latitude and
longitude of the observer. But the changes arising from the other causes named are independent of the
observer's position, and may therefore be considered at any instant in their relation to the center of the
earth. To this end the elements necessary for any calculation are tabulated in the Nautical Almanac
from data based upon laws which have been found by long series of observations to govern the actual and
apparent motion of the various bodies.
212. The Zaiith of an ol)8erver on the earth's surface is the point of the celestial sphere vertically
overhead. Tlie Nudir is the point vertically beneath.
213. The Celestial Horizon is the great circle of the celestial sphere formed by passing a plane
through the center of the earth at right angles to the line which joins that point with the zenith of the
observer. The celestial horizon differs somewhat
from the Visible Horizon, which is that line appearing
to an observer at sea to mark the intersection of earth
and sky. This difference arises from two causes:
first, the eye of the observer is always elevated above
the sea level, thus permitting him a range of vision
excee<ling 90° from the zenith; and second, the
observer's position is on the surface, instead of at the
center of the earth. These causes give rise, respec-
tively, to dip of the horizon and parallax, which will
be explained later (Chap. X).
214. In figure 28 the celestial sphere is considered
to be projected upon the celestial horizon, represented
by NESVV. ; the zenith of the observer is projected at
■>, and that pole of the earth which is elevated above
the horizon, as.sumed for illustration to te the north
pole, appears at P, the Elerjted Pi.'.c of the celestial
sphere. The other pole is not shown in.the figure.
215. The Equinoctial, or Celestial Equator, is the
great circle formed by extending the plane of the
earth's equator until it intersects the celestial sphere.
It is shown in the figure in the line EQW. The equi-
noctial intersects the horizon in E and W, its east and
west points.
216. Jfour Circles, Declination Circles, or Celestial. Meridians are great circles of the celestial sphere
passing through the poles; they are therefore secondary to the e(iuinoctial, and may be formed by
extending the planes of the respective terrestrial meridians until they intersect the celestial sphere. In
the figure, PW, PS, PE, are hour circles, and that one, PS, which contains the zenith and is therefore
formed by the extension of the terrestrial meridian of the observer, intersects the horizon in N and S, its
north and south points.
217. Vertical Circles, or Circles of Altitude, are great circles of the celestial sphere which pass through
the zenith and nadir; they are therefore secondary to the horizon. In the figure, ZH, WZE, NZS, are
projections of such circles; the vertical circ e NZS, which passes through the poles, coincides with the
s
Fig. 28.
84
DEFINITIONS RELATING TO NAUTICAL ASTBONOMY.
meridian of the observer. The vertical cirde WZE, whose plane is at riglit angles to that of tlie merid-
ian, intersects the horizon in its eastern and western points, and, therefore, at the points of intersection
of the equinoctial; this circle is distinguished as the Prime Vertical.
21 §. The Declination of any point in the celestial sphere is its angular distance from the equinoctial,
measured upon the hour or declination circle which passes through that point; it is designated as North
or South according to the direction of the point from the equinoctial ; it is customary to regard north
declinations as positive (+), and south declinations as negative ( — )■ I" the figure, DM is the declina-
tion of the point M. Declination upon tlie celestial sphere corresponds with latitude upon the earth.
219. The Polar Distance of any point is its angular distance from the pole (generally, the elevated
pole of an observer), measured upon the hour or declination circle passing through the "point; it must
therefore equal 90° minus the declination, if measured from the pole of the same name as the declina-
tion, or 90° plus the declination, if measured from the pole of opposite name. The polar distance of the
point M from the elevated pole, P, is PJI.
220. The Altitude of any point in the celest'al sphere is its angular distance from the horizon,
measured upon the vertical circle passing through the point; it is regarded as positive when the body
is on the same side of the horizon as the zenith. The altitude of the point ^I is HM.
«221. The Zenith Distance of any point is its angular distance from the zenith, measured upon the
vertical circle passing through the point; the zenith distance of any point which is above the horizon of
an observer must therefore equal 90° minns the altitude. The zenith distance of M, in the figure, is ZM.
222. The Hour Anple of any point is the angle at the pole between the meridian of the observer
and the hour circle passmg through that point; it may also be regarded as the arc of the equinoctial
intercepted between those circles. Jt is measured toward the west as a positive direction through the
twenty-four liours, or 360 degrees, which constitute the interval between the successive returns to the
meridian, due to the diurnal rotation of the earth, of any point in the celestial sphere. The hour angle of
M is the angle C^PD, or the arc QD.
223. The Azimuth of a point in the celestial sphere is the angle at the zenith between the meridian
of the obser\-er and the vertical circle passing through the point; it may also be regarded as the arc of
the horizon intercepted between those circles. It is measured from either the north or the south point
of the horizon (usually that one of the same name as the elevated pole) to the east or west through 180°,
and is named accordingly; as, N. 60° W., or S. 120° W. The azimuth of M is the angle NZH, or the arc
NH, from the north point, or the angle SZH, or the arc SH, from the south point of the horizon.
224. The Amplitude of a point is the angle at the zenith between the prime vertical and the vertical
circle of the point; it is measured from the east or the west point of the horizon through 90°, as \W . 80°
N. It is closely allied with the azimuth and may always be deduced therefrom. In the figure, the
amplitude of H is the angle WZH, or the arc WH. The amplitude is only used with reference to points
in the horizon.
225. The Ecliptic is the great circle representing the path in which, by reason of the annual revo-
lution of the earth, the sun appears to move in the celestial sphere; the plane of the ecliptic is inclined
to that of the equinoctial at an angle of 23° 27 Y, and this inclination is called the obliquity of the ecliptic.
The ecliptic is represented by the great circle CVT.
226. The Equinoxes are those points at which the ecliptic and the equinoctial intersect, and when
the sun occupies either of these positions the days and nights are of equal length throughout the earth.
The Vernal Equino.v is that one at which the sun appears to an observer on the earth when passing from
southern to northern declination, and the Autumnal Equinox that one at which it appears when passing
from northern to southern declination. The Vernal Equinox is also designated as the First Point of Aries,
and is used as an origin for reckoning right ascension; it is indicated in the figure at V.
227. Tlie Solstitial Points, or Solstices, are points of the ecliptic at a distance of 90° from the equinoxes,
at which the sun attains its highest declination in each hemisphere. They are called respectively the
Summer and the Winter Solstice, according to the season in which the sun appears to pass these points in
its path.
22S. The Right Ascension of a point is the angle at the pole between the hour circle of the point
and that of the First Point of Aries; it may also be regarded as the arc of the equinoctial intercepted
between those circles. It is measured from the First Point of Aries to the eastward as a positive
direction, through twenty-four hours or 360 degrees. The right ascension of the point M is VD.
229. Celestial iMtUude is measured to the north or south of the ecliptic upon great circles secondary
thereto. Celestial Longitude is measured upon the ecliptic from the First Point of Aries as an origin,
being regarded as positive to the eastward throughout 360°.
230. CooKDiNATES. — 111 Order to define the position of a point in space, a system of lines, angles, or
planes, or a combination of these, is used to refer it to some fixed
line or plane adopted as the primitive; and the lines, angles, or
planes by which it is thus referred are called coordinates.
231. In figure 29 is shown a system of rectilinear coordinates
for a plane. A fixed line FE is chosen, and in it a definite ])oint C,
as the origin. Then the position of a point A is defined by CB = .r,
the distance from the origin, C, to the foot of a perpendicular let
^ fall from A on FE; and by AB = y, the length of the perpendicular.
The distance .r is called the abscissa and ■;/ the ordinate. Assuming
two intersecting right lines FE and HI as standard lines of refer-
ence, the location of the point A is defined by regarding the dis-
tances measured to the right hand of HI and above FE as positive;
those to the left hand of HI and below FEas negative.
An exemplification of this system is found in the chart, on which FE is represented bv the equator,
HI by the prime meridian; the "coordinates x and y being the longitude and latitude of the point A.
Fig. 29.
DEFINITIONS RELATING TO NAUTICAL ASTRONOMY. 65
232. The great circle is to the sphere what the straight line is to the i)lane; hence, in order to
detine the position of a point on the surface of a sphere, some great circle must be selected as the
primary, and some particular point of it as the origin. Thus, in figure 30, which represents the case of a
sphere, some fixed great circle, CBQ, is selected as the axis and called the
primary; and a point C is chosen as the origin. Then to define the position
of any point A, the abscissa x equals the distance from C to the point B,
where the secondary great circle through A intersects the primary; the
ordinate y equals the distance of A from the primary measured on the
secondary — that is, x = CB and y = AB.
233. In tlie case of the earth, the primary selected is the equator (its
Iilane being perpendicular to the earth's axis), and upon this are measured
the abscissae, while upon the secondaries to it are measured the ordinates of
all points on the earth's surface. The initial point for reference on the
equator is determined by the prime meridian chosen, West longitudes and
North latitudes being called positire, East longitudes and South latitudes,
negative.
234. In the case of the celestial sphere, there are four systems of coor-
dinates in use for defining the position of any point; these vary according to the circle adopted as the
primary and the point used as an origin. They are as follows:
1. Altitude and azimuth.
2. Declination and hour angle.
3. Declination and right ascension.
4. Celestial latitude and longitude.
235. In the system of AUUude and Azimuth, the primary circle is the celestial horizon, the seconda-
ries to which are the vertical circles, or circles of altitude. The horizon is intersected by the celestial
meridian in its northern and southern points, of which one — usually that adjacent to the elevated pole — is
selected as an origin for reckoning coordinates. The azimuth indicates in which vertical circle the point
to be defined is found, and the altitude gives the position of the point in that circle. In figure 28 the
point M is located, according to this system, by its azimuth NH and altitude HM.
236. In the system of Declination and Hour Angle, the primary circle is the equinoctial, the seconda-
ries to which are the circles of declination, or hour circles. The point of origin is that point of inter-
section of the equinoctial and celestial meridian which is above the horizon. The hour angle indicates
in which declination circle the point to be defined is found, and the declination gives the position of
the jioint in that circle. In figure 28 the point M is located, according to this system, by its hour angle
QD and declination DM.
237. Inthe system of Declination and Right Ancennimi, the primary and secondaries are the same as in
the system just described, but the point of origin differs, being assumed to be at the First Point of Aries, or
vernal equinox. The right ascension indicates in which declination circle the point to be defined may
l)e found, and the declination gives the jxjsition in that circle. In figure 28 the point M is located by V[),
the right ascension, and DM, the declination. It should be noted that this system differs from tlie
])receding in that the position of a point is herein referred to a fixed point in the celestial sphere and is
independent of the zenith of the observer as well as of the position of the earth in its diurnal motion,
while, in the system of declinationand hour angle, both of these are factors in determining the coordinates.
23l>i. In the system of Celestial Latitude and longitude, the primary circle is the ecliptic; the point
of origin, the First Point of Aries. The method of rei^koning by this system, whicli is of only slight
importance in Nautical Astronomy, will appear from the definitions of celestial latitude and longitude
already given (art. 229).
24972°— 12 5
66
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
CHAPTER VIII.
INSTEUMENTS EMPLOYED IN NAUTICAL ASTEONOMT.
THE SEXTANT.
339. The sextant is an instrument lor measuring the angle between two ol)jeotn by bringing into
coincidence at the eye of the observer rays of liglit received directly from the one and by reflection from
the other, the measure Ijeing afforded by the inclination of the reflecting surfaces. By reason of its
email dimensions, its accuracy, and, above all, the fact that it does not require a permanent or a stable
mounting but is available for use imder the conditions existing on shipboard, it is a most important
instrument for the purposes of the navigator. While the sextant is not capable of the same degree of
accuracy as fixed instrument", its measurements are sufficiently exact for navigation.
240. Descriptio.v. — A usual form of the sextant is represented in figure 31. The frame is of brass
or some similar alloy. The graduated arc, AA, generally of silver, is marked in appropriate divisions;
^ in the finer sextants, each divi-
sion represents 10', and the
vernier affords a means of
reading tf> 10". A wooden
handle, H, is provided for
holding the instrument. The
index mirrnr, M, and harizoa
mirror, m, are of plate glass,
and are silvered, though the
upper half of the horizon glass
is left ])lain to allow direct rays
to pass through uno))Structed.
To give greater distinctness to
the images, a small telearojie,
E, is placed in the line of
sight; it is supported in a ring,
K, which can l)e moved by a
screw in a direction at right
angles to the plane of the sex-
tant, thus shifting the axis of
the telescope, and therefore the
plane of reflection; this plane,
however, always remains par-
allel to that of the instrument,
the motion of the telescope
being intended merely to regu-
late the relative brightness of
the direct and reflected images. In the ring K are small screws for the purpose of adjusting the tele-
scope by making its axis parallel with the plane of the sextant. The vernier is carried on the end of an
index bar pivoted beneath the index mirror, M, and thus travels along the graduated scale, affording a
measure for any change of inclination of the index mirror; a reading glass, R, attached to the index bar
and turning upon a pivot, S, facilitates the reading of vernier and scale. The index mirror, M, is attached
to the bead of the index bar, with its surface perpendicular to the plane of the instrument; an adjust-
ing screw is fitted at the back to permit of adjustment to the perpendicular plane. The fixed glass m,
half silvered and half plain, is called the horizon glass, as it is through this that the horizon is observed
in measuring altitudes of celestial bodies; it is provided with screws, by which its perpendicularity to
the plan« of the instrument may t)e adjuste<l. At Pand Q are colored glasses of different shades, which
may be used separately or in combination to protect the eye fnjm th 3 intense light of the sun. In order
to observe with accuracy and make the images come ])recisely in contact, a tangent-screii; B, is fixed to
the index, by means of which the latter may be moved with greater precision than by hand; but this
screw does not act until the index is fixed by the screw C at the back of the sextant; when the inde^
is to be moved any considerable amount, the screw C is loosened ; when it is brought near to its required
position the screw must be tightened, and the index may then be moved gradually by the tangent-screw.
Besides the telesf^ope, E, the instrument is usually provided with an inverting telescope, I, and a
tube without glasses, F; also, with a cap carrying colored glasses, which may be put on the eye-end of
the telescoi^, thus dispensing with the necessity for the use of the colored shades, Pand Q, and elimina-
ting any possible errors which might arise from nonparallelism of their surfaces.
241. The tvniicr is an attachment for facilitating the exact reading of the scale of a sextant, by
which aliquot parts of the smallest divisions of the graduated scale are measured. The principle of the
sextant vernier is identical with that of the barometer vernier, a complete description of which will
be found in article 51, Chapter II. The arc of a sextant is usually divided into 120 or more parts, each
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. . 67
division representing 1°; each of these degree divisions is further subdivided to an extent dependent
upon the accuracy of reading of which the sextant is capable. In the instninients for liner worli, the
divisions of the scale correspond to 10' each, and the vernier covers a length corresponding to 59 such
divisions, which is subdivided into 60 parts, thus permitting a reading of KX'; all sextants, however, are
not so closely graduated.
Whatever the limits of subdivision, all sextants are fitted with verniers which contain one more
division than the length of scale covered, and in which, therefore, scale-readings and vernier-readings
increase in the same direction — toward the left hand. To read any sextant, it is merely necessary to
observe the scale division next below, or to the right of, the zero of the vernier, and to add thereto the
angle corresponding to that division of the vernier scale which is most nearly in exact coincidence with
a division of the instrument scale.
242. Optic.\l Principle. — When a ray of light is reflected from a plane surface, the angle of inci-
dence is equal to the angle of reflection. From this it ^^
may be proved that when a ray of light undergoes two \
reflections in the same plane the angle between its \^ f
first and its last direction is equal to twice the inclina-
tion of the reflecting surfa<-es. Upon this fact the con-
struction of the sextant is based.
In figure 32 let B and C represent respectively the
index mirror and horizon mirror of a sextant; draw
EF perjiendicular to B, and CF perpendicular to C;
then the angle CFB represents the inclination of the
two mirrors. Supjiose a ray to proceed from A and
undergo reflection at B and at C, its last direction being
CD; then ADC is the angle lietween its first and la.^t
directions, and we desire to prove that ADC = 2 CFB.
From the equality of the angles of incidence and
reflection:
ABE = EBC, and ABC = 2 EBC;
BCF = FCD, and BCD = 2 BCF.
From Geometrv:
ADC = ABC - BCD = 2 (EBC - BCF) = 2 CFB,
which is the relation that was to be proved.
243. In the sextant, since the index mirror is immovably attached to nie index arm, which also
carries the vernier, it follows that no change can occur in the inclination between the index mirror and
the horizon mirror, excepting such as is registered by the travel of the vernier upon the scale.
If, when the index mirror is so placed that it is nearly parallel with the horizon mirror, an observer
direct the telescope toward some well-<lefined object, there will be seen in the field of view two separate
images of the object; and if the inclination of the index mirror be slightly changed by moving the index
liar, it will be seen that while one of the images remains fixed the other moves. The fix«f image is
the direct one seen through the unsilvered part of the horizon glass, while the movable image is due to
rays reflected by the index and horizon mirrors. When the two images coincide these mirrors must be
parallel (assuming that the object is sufficiently distant to disregard the space which separates the mir-
rors); in this position of the index mirror the vernier indicates the true zero of the scale. If, however,
in8tea<l of observing a single object, the instrument is so placed that the direct ray from one object
appears in coincidence with the reflected ray of a second object, then the true angle between the objects
will be twice the angle of inclination between the mirrors, or twice the angle measured by the vernier
from the true zero of the scale. To avoid the neceasity of doubling the angle on the scale, the latter is
so marked that each half degree appears as a whole degree, whence its indications give the whole anple
directly.
244. Ar).irsTMENTS of the Sextant. — The theory of the sextant requires that, for accurate indi-
cations, the following conditions be fulfilled:
(a) The two surfaces of each mirror and shade glass must be i>arallel planes.
(ft) The graduated arc or limb must be a plane, and itn graduations, as well as those of the vernier,
must be exact.
(c) The axis must be at the center of the limb, and perpendicular to the plane thereof.
(d) The index and horizon glasses must be perpendicular, and the line of sight parallel, to the
plane of the limb.
Of these, only the last named ordinarily require the attention of the navigator who is to make use of
the sextant; the others, which may be called the permanent adjvittmenis, should be made before the
instrument leaves the hands of the maker, and with careful use will never be deranged.
245. The Adjimlmod of the Index Mirror consists in making the reflecting surface of this mirror
truly perpendicular to the plane of the sextant. In order to test this, set the index near the middle of
the arc, then, placing the eye very nearly in the plane of the sextant and close to the index mirror,
observe whether the <lirect image of the arc and its image reflected from the mirror appear to form one
continuous an-; if so, the gla.ss is perpendicular to the plane of the sextant; if the reflected image appears
to droop from the arc seen directly, the glass leans backward; if it seems to rise, the glass leans forward.
The adjustment is made by the screws at the back of the mirror.
246. The Adjustmeid of the Horizon Mirror consists in making the reflecting surface of this mirror
perpendicular to the plane of the sextant. The index mirror having been adjusted, if, in revolving it
by means of the index arm, there is found one position in which it is parallel to the horizon glass, then
the latter must also be perpendicular to the plane of the sextant. In order to test this, put in the tele-
scope and direct it toward a star; move the index until the reflected image appears to pass the direct
image; if one passes directly over the other the mirrors must be parallel; if one passes on either side of
the other the horizon glass needs adjustment, which is accomplished by means of the screws attached.
68 INSTRUMENTS EMPLOYED IN NATTTICAL ASTRONOMY.
The sea horizon may also be used for making this adjustment. Hold the sextant vertically and
bring the direct and the reflected images of the liorizon line into coincidence; then incline the sextant
until its plane makes but a small angle with the horizon; if the images still coincide the glasses are
parallel; if not, the horizon glass needs adjustment.
347. The Adjustment of the Telescope must be so made that, in measuring angular distances, the line
of sight, or axis of the telescope, shall be parallel to the plane of the instrument, as a deviation in that
respect, in measuring large angle.s, will occasion a consideral)le error. To avoid such error, a telescope is
employed in which are placed two wires, parallel to each other and equidistant from the center of the
telescope; by means of these wires tlie adjustment may l)e made. Screw on the telescope, and turn the
tube containing the eyegla.ss till the wires are parallel to the plane of the instrument; then select two
clearly-defined objects whose angular distance must l)e not less than 90°, because an error is more easily
discovered when tiie distance is great; bring the reflected image of one object into exact coincidence
with the direct image of the other at the inner wire; then, by altering slightly the position of the instru-
ment, make the objects appear on the other wire; if the contact still remains perfect, the axis of the
telescope is in its right situation; but if the two objects ajjpear to separate or lap over at the outer wire
the telescope is not parallel, and it must be rectified by turning one of the two screws of tlie ring into
which the telescope is screwed, having previously unturned the other screw; by repeating this ojieration
a few times the contact will be precisely the same at both wires, and the axis of the telescope will be
parallel to the plane of the instrument.
Another method of making this adjustment is to place the sextant upon a table in a horizontal
position, look along the plane of the limb, and make a mark upon a wall, or other vertical surface, at a
distance of about 20 feet; draw another mark above the first at a distance equal to the height of the axis
of the telescope above the plane of the limb; then so adjust the telescope that the upper mark, as
viewed through the telescope, falls midway between the wires. Some sextants" are accompanied by
small sights whose height is exactly equal to the distance between the telescope and the plane of the
limb; by the use of these, the necessity for employing the second mark is avoided and the adjustment
can t)e very accurately made.
248. The errors which arise from defects in what have been denominated the permanent adjustments
of the sextant may be divided into three classes, namely: Errors due to faulty centering of the axis,
called eccentricU;/; errors of graduation; and errors arising from lack of parallelism of surfaces in index
mirror and in shade glasses.
The errors due to eccentricity and faulty graduation are constant for the same angle, and should be
determined once for all at some place where proper facilities for doing the work are at hand; these
errors can only be ascertained by measuring known angles with the .sextant. If angles of 10°, 20°, 30°,
40°, etc., are first laid off with a theodolite or similar instrument and then measured by the sextant, a
table of errors of the sextant due to eccentricity and faulty graduation may be made, and the error at
any intermediate angle found liy interpolation; this table will include the error of graduation of the
theodoliteandalso the error due to inaccurate reading of the sextant, but such errors are small. Another
method for determining the combined errors of eccentricity and graduation is by measuring the angular
distance l)etween stars and comparing the observed and the computed arc between them, but this process
is liable to inaccuracies by reason of the uncertainty of allowances for atmospheric refraction.
Errors of graduation, when large, may be detected by "stepping off " distances on the graduated
arc with the vernier; place the zero of the vernier in exact coincidence with a division of the arc, and
observe whether the final division of the vernier also coincides with a division of the arc; this should be
tried at numerous positions of the graduated limb, and the agreement ought to be iierfect in every case.
The error due to a prismatic index mirror may be found by measuring a certain unchangeable angle,
then taking out the glass and turning the upper edge down, and measuring the angle again; half the dif-
ference of these two measures will be the error at that angle due to the mirror. From a number of meas-
ures of angles in this manner, a table similar to the one for eccentricity and faulty graduation can be
made; or the two tables may be combined. When possible to avoid it, however, no sextant should be
use<l in which there is an index mirror which produces a greater error than thatdue to the probable error
of reading the scale. Mirrors having a greater angle than 2" between their faces are rejected for use in
the United States Navy. Inde.x mirrors may be roughly tested by noting if there is an elongated image
of a well-defined point at large angles.
Since the error due to a prismatic horizon mirror is included in the index correction (art. 249), and
consequently applied alike to all angles, it may be neglected.
Errors due to prismatic shade glasses can be determined by measuring angles with and without the
shade glasses and noting the difierence. They may also be determined, where the glas.ses are so arranged
that they can Ije turned through an angle "of 180°, by measuring the angle first with the glass in its
usual position and then reversed, and taking the mean of the two as the true measure.
249. Inde.x: Error. — The Index Error of a sextant is the error of its indications due to the fact
that when the index and horizon mirrors are parallel the zero of the vernier does not coincide with
the zero of the sc^le. Having made the adjustments of the index and horizon mirrors and of the
telescope, as previously described, it is necessary to find that point of the arc at which the zero of the
vernier falls when the two mirrors are parallel, for all angles measured by the sextant are reckoned from
that point. If this point is to the left of the zero of the limb, all readings will be too great; if to the
right of the zero, all readings will be too small.
If desirable that the reading should be zero when the mirrors are parallel, place the zero of the
vernier on zero of the arc; then, by means of the adjusting screws of the horizon glass, move that glass
until the direct and reflected images of the same object coincide, after which the perpendicularity of
the horizon glass should again be verified, as it may have been deranged by the operation. This adjust-
ment is not essential, since the correction may readily be determined and applied to the reading. In
certain sextant work, however, such as surveying, it will be very convenient to be relieved of the
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 69
necessity of correcting each angle observed. Tlie sextant should never be relied upon for maintaining
a constant index correction, and the error should be ascertained frequently. It is a good practice to
verify the correction each time a sight is taken.
250. The Index Correction may be found (o) by a star, (h) by the sea horizon, and (c) by the sun.
(a) Bring the direct and reflected images of a star into <oincidence, and read off the "arc. The
index correction is numerically equal to this reading, and is positive or negative according as the read-
ing is on the right or left of the zero.
(6) The same method may be employed, substituting for a star the sea horizon, though this will be
found somewhat less accurate.
(c) Measure the apparent diameter of the sun by first bringing the upper limb of the reflected
image to touch the lower limb of tlie direct image, and then bringing the lower limb of the reflected
image to touch the upper limb of the direct image.
Denote the readings in the two cases by r and r'; then, if S = apparent diameter of the smi, and
B = the reading of the sextant when the two images are in coincidence, we have:
r =R + S,
)■' = R -- S,
K = J(r + r').
As R represents the error, the correction will be— R. Hence the rule: Mark the readings when on
the arc with the negcttire sign; when off, with th& positive sign; then the index correction is one-half the
algebraic sum of the two readings.
Example: The sun's diameter is measureil for index correction a.s follows: On the arc, 31' 20"; off
the arc, 33' 10". Required the correction.
On the arc, - 31' 20"
Off the arc, ~ 33 10
2)-p 1 50
I. C, -r 55
251. From the equations previously given, it is seen that:
.S = i (r-;-');
hence, if the observations are correct, it will be found that the sun's semidiameter, as given in the
Nautical Almanac for the day of observation, is equal to one-half the algebraic difference of the readings.
If required to obtain the index correction with great precision, several observations should 'oe taken and
the mean used, the accuracy being verified by comparing the tabulated with the observed semidiameter.
If the sun is low, the horizontal semidiameter should be observed, to prevent the error that may arise
from unequal refraction.
252. Use op the Sextant. — To measure the angle between any two visible objects, jxiint the tele-
scoi^e toward the lower one, if one is above the other, or toward the left-hand one, if they are in nearly
the same horizontal plane. Keep this object in direct view through the unsilvered part of the horizon
glass, and move the index arm until the image of the other object is seen by a double reflection from the
index mirror and the silvered portion of the horizon glass. Having gotten the direct image of one
object into nearly exact contact with the reflected image of the other, clamp the index arm and, by
means of the tangent-screw, complete the adjustment so that the contact may be perfect; then read the
limb.
In measuring the altitude of a celestial body above the sea horizon, it is necessary that the angle
shall Vie measured to that point of the horizon which lies vertically beneath the object. To determine
this point, the observer should move the instrument slightly to the right and left of the vertical,' swinging
it about the line of sight as an axis, taking care to keep the object in the middle of the field of view."
Tlie object will appear to describe the arc of a circle, and the lowest point of this arc marks the true
vertical.
The shade-glasses should Ix; employed as may be necessary to protect the eye when observing
objects of dazzling brightness, such as the sun, or the horizon when the sun is reflected from it at a low
altitude. Care must be taken that the images are not too bright or the eye will be so affected as to
interfere with the accuracy of the observations.
233. Choice of Sextants. — The choice of a sextant should he governed by the kind of work w iiich
is refiuired to be done. In rough work, such as survej^ing, where angles need only be measure<l to the
nearest 30" the radius may l)e as small as 6 inches, which will jx;rmit easy reading, and the instrument
can be correspondingly lightened. AV'here readings to 10" are desired, as in nice astronomical work, the
radius should beaboutTJinches, and the instrument, to be strongly built, should weigh aboutSJ pounds.
The parts of an instrument should move freely, without binding or gritting. The eyepieces shoulil
move easily in the telescope tubes; the bracket for carrying the telescope should be made very strong.
It is frequently found that the parallelism of the line of sight is destroyed in focusing the eyepiece,
either on account of the looseness of the fit or because of the telescope bracket being weak. The vernier
should lie close to the limbs to prevent parallax in reading. If it is either too loose or too tight at either
extremity of its travel, it may indicate that the pivot is not perpendicular. The balls of the tangent-
screw should fit snugly in their sockets, so that there may be no lost motion.
Where possible, the sextant shoulil always be submitted to expert examination and test as to the
accuracy of its permanent adjustments before acceptance by the navigator.
254. Resilvering Mirrors. — Occasion may sometimes arise for resilvering the mirrors of a
sextant, as they are always liable to be damaged by dampness or other causes. For this purpose some
70
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
clean tin foil and mercury are required. Upon a jtiece of glass about 4 int-hes siiuare lay a piece of
tin foil whose dimensions exceed by about a quarter of an inch in each direction those of the glass to be
silvered; smootli out the foil carefully by rubbing; put a small drop of mercury on the foil and spread
it with the finger over the entire surface, being careful that none shall find its way under the foil;
then put on a few more drops of mercury until the whole surface is fluid. The glass which is to be
silvered having been carefully cleaned, it should l)e laid upon a i)iece of tissue paper whose edge just
covers the edge of the foil and transferred carefully from the paper to the tin foil, a gentle jiressure
being kept upon the glass to avoid the formation of liubbles; finally, place the mirror face downward
and leave it in an inclined position to allow the suri)lus mercury to flow off, the latter ojjeration Ix^ing
hastened by a strip of tin foil at its lower edge. After five or six hours the tin foil around the edges
mav be removed, and the next day a coat of varnish made from spirits of wine and red sealing wax
should be applied. For a horizon mirror care must be taken to avoid silvering the plain half. The
mercury drawn from the foil should not be placed with clean mercury with a view to use in the artificial
horizon or the whole will be spoiled.
255. Octants .\n'd Quint.wts. — Properly speaking, a sextant is an instrument whose aic covers
one-sixth of a complete circle, and which is therefore capable of measuring an angle of 120°. Other
instruments are made which are identical in jirinciple with the sextant as heretofore described, and
which differ from that instrument only in the length of the arc. These are the octant, an eighth of a
circle, bv which angles may be measured to 1>0°, and the (jiiintaut, a fifth of a circle, which measures
angles up to 144°. The distinction between these instruments is not always carefully made, and in
such matters as have been touched upon in the foregoing articles the sextant may be regarded as the
type of all kindred reflecting instruments.
THE AKTIFICIAL HORIZON.
!256. The Artificial Horizon is a small, rectangular, shallow basin of mercury, over which, to protect
the mercurv from agitation by the wind,, is placed a roof consisting of two plates of glass at right angles
to each other. The mercury affords a perfectly hijrizontal surface
which is at the same time an excellent mirror. The different jiarts
of an artificial horizon are furnished in a compact form, a metal
bottle being provided for containing the mercury when not in use,
together with a suitable funnel for pouring.
• If MN, in figure 33, is the horizontal surface of the mercury; S'K
a ray of light from a celestial object, incident to. the surface at B;
BA "the reflected ray; then an observer at A will receive the ray BA
as if it proceeded from a point S", whose angular depression, ilBS",
below the horizontal plane is equal to the altitude, JIB.S', of the
object above that plane. If, then, SAis a direct ray from the object
parallel to S'B, an observer at A can measure with the sextant the
angle SAS"= S'BS"= 2 S'BM, by bringing the image of the object
reflected by the index mirrfir into coincidence with the image S"
reflected by the mercury and seen through the horizcjn gla.ss. The
instrumental measure, corrected for index error, will be double the
apparent altitude of the body.
The sun's altitude will lie measured by bringing the lower limb
of one image to touch the upper limb of the other. Half the cor-
rected instrumental reading will be the apparent altitude of the
sun's loicer or upper limb, according as the lower or upper limb of
the reflected image was the one employed in the observation.
In observations of the sun with the artificial horizon, the eye is
protected by a single dark glass over the eyepiece of the telescope through which direct and reflected
rays must pass alike, thereby avoiding the errors that might po.ssibly arise from a difference in the
separate shade glasses attached to the frauje of the sextant.
The glasses in the roof over the mercury should be made of plate-glass, with perfectly parallel faces.
If they are at all jirismatic, the observed altitude will be erroneous. The error may be removed l)y
observing a second altitude with the roof reversed, and, in general, by taking one half of a set of obser-
vations with the roof in one jiosition and the other half with the roof reversed. On the rare occasions
when the atmosphere is so calm that the unsheltered mercury will remain undisturbed, most satisfac-
tory observations may l>e made by leaving off the roof.
257. In setting up an artificial horizon, care should be taken that the basin is free from dust and
other foreign matter, as small particles floating upon the surface of the mercury interfere with a perfect
reflection. The basin should l>e so placed that its longer edge lies in the direction in which the observed
body will bear at the middle of the observations. The spot selected for taking the sights should be as
free as possible from causes which will produce vibration of the mercury, and precautions should be
taken to shelter the horizon from the wind, as the mere placing of the roof will not ordinarily be suf-
ficient to accomplish this. Embedding the roof in earth serves to keep out the wind, while setting the
whole horizon uiwn a thick towel or a piece of such material as heavy felt usually affords ample protec-
tion from wind, tends to reduce the vibrations from mechanical shocks, and also aids in keepmg out the
moisture from the ground. In damp climates the roof should be kept dry by wiping, or the moisture
deposited from the inclosed air will form a cloud upon the glass.
Molasses, oil, or other viscous fluid may, when necessary, be employed as a substitute for mercury.
Fig. 33.
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 71
958. Owing to the perfection of manufacture that is required to insure accuracy' of results with tiie
artificial horizon, navigators are advised to accept only such instrument as has satisfactorily stood the
necessary tests to prove the correctness of its adjustment as regards the glasses of the roof.
THE CHKONOMETEB.
259. The Chronometer is simply a correct time-measurer, differing from an ordinary watch in
having the force of its main-spring rendered uniform by means of a variable lever. Owing to the fact
that on a sea voyage a chronometer is exjwsed to many changes of temperature, it is furnished with an
expansion balance, formed of a combination of metals of different expansive qualities, which produces
the required compensation. In order that its working may not be deranged by the motion of the ship
in a seaway, the instrument is carried in gimbals.
As the regularity of the chronometer is essential for the correct determination of a ship's position,
it is of the greatest importance that every precaution lie taken to insure the accuracy of its indications.
There i» no more certain way of doing this than to provide a vessel with several of these instruments — •
preferably not less than three — in order that it an irregularity develop in one, the fact may be revealed
by the others.
260. C.\RE OF Chronometers ox Shipboard. — The box in which the chronometers are kept
should have a permanent place as near as practicable to the center of motion of the ship, and where it
will be free from excessive shocks and jars, such as those that arise from the engines or from the firing
of heavy guns; the location should be one free from sudden and extreme changes of temperature, and
as far removed as possible from ma.sses of vertical iron. The box should contain a separate compart-
ment for each chronometer, and each compartment should be lined with baize cloth padded with
curled hair, for the double purpose of reducing shocks and equalizing the temperature within. An
outer cover of baize cloth should be provided for the box, and this should be changed or dried out
frequently in damp weather. The chronometers should all be jilaced with the XII mark in the same
position.
For transiX)rtation for short distances by hand, an instrument should be rigidly clamped in its
gimbals, for if left free to swing, its performance may be deranged by the violent oscillations that are
imparted to it.
For transportation for a considerable distance, as by express, the chronometer should be allowed
to run down, and should then be dismounted and the balance corked.
261. Since it is not possible to make a perfect instrument which will be uninfluenced by the dis-
turbing causes incident to a sea voyage, it becomes the duty of the navigator to determine the error and
to keep watch upon the variable rate of the chronometer.
The error of the chronometer is i)\e difference between the time indicated and the standard time to
which it is referred — usually Greenwich mean time.
The amount the chronometer gaimt or tov.? daily is the daily rate.
The indications of a chronometer at any given iu-stant require a correction for the accumulated error
to that instant; and this can be found if the error at any given time, together with the daily rate, are
known.
262. Winding. — Chronometers are ordinarily constructed to run for 56 hours without rewinding,
and an indicator on the face always shows how many hours have elapsed since the last winding. To
insure a uniform rate, they must be wound regularly every day, and, in order to avoid the serious conse-
quences of their running down, the navigator should take some means to guard against neglecting this
duty through a fault of memory. To wind, turn the chronometer gently on its side, enter the key in its
hole and push it home, steadying the instrument with the hand, and wind to the left, the last half turn
being made .so as to bring up gently against the stop. After winding, cover the keyhole and return the
instrument to its natural position. Clironometers should always te wound in the same order to prevent
omissions, and the precaution taken to inspect the indicators, as a further a,«8urance of the proi^er
performance of the operation.
After winding each day, the comparisons should l)e made, and, with the readings of the maxinmm-
and-minimum thermometer and other necessary data, recorded in a book kept for the purpose.
The maximum-and-minimum thermometer is one so arranged that its highest and lowest readings
are marked by small steel indices that remain in place until reset. Every chronometer box should be
provided with such an instrument, as a knowledge of the temperature to which chronometers have
l)een subjected is essential in any analysis of the late. To draw down the indices for the purpose of
resetting, a magnet is used. This magnet should be kept at all times at a distance from the chronometers.
263. Comp.\risox of Chkono.meters. — The instrument telieved to be the best is regarded as the
Standard, and each other is compared with it. It is usual to designate the Standard as A, and the
others as B, C, etc. Chronometers are made to beat half-seconds, and any two may be compared by
following the beat of one with the ear and of the other with the eye.
To make a comparison, say of A and B, open the boxes of these two instruments and close all
others. Oiet the cadence and, commencing when A has just completed the beat of some even 5-second
division of the dial, count "half-one-half-two-half-three-half-four-half-five," glancing at B in time to
note the position of its second-hand at the last count; the seconds indicated by A will be five greater
than the number af the beginning of the count. The hours and minutes are al.so recorded for each
chronometer, and the subtraction made. A good check upon the accuracj is afforded by repeating the
operation, taking the tick from B.
Where necessary for exact work, it is po.ssible to estiuiate the fraction between Ijeats, and thus
make the comparison to tenths of a second; but the nearest half-second is sufficiently exact for the
purposes of ordinary navigation at sea.
72
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY.
264. The following form represents a convenient method of recording comparisons:
Stand. A, No. 777. Cheo. B, No. 1509. Chro. C, No. 1802.
Date, 1903.
Designation of
comparisons.
Chro. B
with
Stand. A.
2d diff.
Chro. C
with
Stand. A.
2d difl.
Therm.
Bar.
Remarks.
Max.
Min.
Air.
January
Stand. A.
B and C.
Difference.
A. m. «.
1 13 40
1 12 21.5
s.
A. m. s.
1 14 20
2 04 11
«.
o
63
59
o
60
//
30.07
Fomid errors
by t i m e -
ball.
1 18.5
11 10 09
2
Stand. A.
B and C.
Difference.
1 16 30
1 15 10
+L5
1 17 00
2 06 51. 5
-0.5
64
58
57
30.12
Left New
York for
San Juan,
P. E.
1 20
11 10 08. 5
265; The second difference in the form is the difference between the comparisons of the same
instruments for two successive days. When a vessel is equipped with only one chronometer there is
nothing to indicate any irregularity that it may develop at sea — and even the best instruments may
undergo changes from no apparent cause. When there are two chronometers, the second difference,
which is equal to the algebraic difference between their daily rates, remains imiform as long as the rates
remain vmiform, but changes if one of the rates iindergoes a change; in such a case, there is no means
of knowing which chronometer has departed from its expected performance, and the navigator nmst
proceed with caution, giving due faith to the indications of each. If, however, there are three chro-
nometers, an irregularity on the part of one is at once located by a comparison of the second differ-
ences. Thus, if the predicted rates of the chronometers were such as to give for the second difference of
A — B, -r l'-5, and of A — C, — 0'.5, suppose on a certain day those differences were i 4*.5 and — 0'.5,
respectively; it would at once be suspected that the irregularity was in B, and that that chronometer
had lost 3' on its normal rate during the preceding day. Suppose, however, the -second differences
were +4^5 and -f2'.5; it would then be apparent that A had gained 3'.
266. Te.mperature Curves. — Notwithstanding the care taken to eliminate the effect of a change
of temperature upon the rate of a chronometer, it is rare that an absolutely perfect compensation is
attained, and it may therefore be assumed that the rates of all chronometers vary somewhat with the
temperature. Where the voyage of a vessel is a long one and marked changes of climate are encoun-
tered, the accumulated error from the use of an incorrect rate may be very material, amounting to sev-
eral minutes' difference of longitude. Careful navigators will therefore take every means to guard
against such an error. By the employment of a temperature curve in connection with the chronometer
rate the most satisfactory results are arrived at.
267. There should be furnished with each chronometer a statement showing its daily rate under
various conditions of temperature; and this may be supplemented by the observations of the navigator
during the time that the chronometer remains on board ship. With all available data a temperature
curve should be constructed which will indicate graphically the performance of the instrument. It is
most convenient to employ for this purpose a piece of "prohle paper," on which paralfel lines are ruled
at equal intervals at right angles to each other. ]>et each horizontal line represent, say, a degree of tem-
perature, numbered at the left edge, from the bottom up; draw a vertical line in red ink to represent
the zero rate, and let all rates to the right be plus, or gaining, and those to the left minus, or losing; let
the intervals between vertical lines represent intervals of rate (as one-tenth of a second) numbered at
the top from the zero rate; then on this scale plot the rate corresponding to each temperature; when
there are several observations covering one height of the thermometer, the mean may be used.
Through all the plptted points draw a fair curve, and the intersection of this curve with each tempera-
ture line gives the mean rate at that temperature. The mean temperature given by the maximum and
minimum thermometer shows the rate to lie used on any day.
268. Hack or Comparing Watch. — In order to avoid derangement, the chronometers should
never be removed from the permanent box in which they are kept on shipboard. When it is desired to
mark a certain instant of time, as for an astronomical observation or for obtaining the chronometer
error by signal, the time is marked by a "hack " (an inferior chronometer used for this purpose only),
or by a comparing watch. Careful comparisons are taken — preferably both before and afterwards — and
the chronometer time at the required instant is thus deduced. The correction represented by the chrci-
nometer time minus the watch time (twelve hours being added to the former when necessary to make
the subtraction possible) is referred to as C — W.
Suppose, for example, the chronometer and watch are compared and their indications are as follows:
Chro. t.
W. T.,
5" 27"
2 36
30'
45.5
C-W, 2 50 44.5
If then a sight is taken when the watch shows 3" 01'" 27. '5, we have:
W. T., 3'' 01'" 27". 5
C-W,
Chro. t.,
-2 50 44.5
5 52 12.0
INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 73
It may occur that the values of C — W, as obtained from comparisons before and after marking the
desired time, will vary; in that case the value to be used will be the mean of the two, if the time marked
is about midway between comparisons, but if much nearer to one comparison than the other, allowance
should be made accordingly.
Thus suppose, in the case previously given, a second comparison had been taken after the sight as
follows:
Chro.t., 6" 12"' 45'
W. T., - 3 21 59.5
C-W, 2 50 45.5
The sight having been taken at about the middle of the interval, the C — W to be used would be the
mean of the two, or 2" 50"' 45'.0.
Let us assume, however, that the second comparison showed the following:
Chro.t., 6''38'"25''
W. T., -3 47 39
C-\V, 2 50 46
Then, the sight having been taken when only about one-third of the interval liad ela]>se(l between
the first and second comparisons, it would be assumed that only one-third of the total change in the
( ' — W had occurred up to the time of sight, and the value to be used would be 2'' 50'" 45'.0.
269. It is considered a good practice always to subtract watch time from chronometer time
whatever the relative values, and thus to employ C-W invariably as an additive correction. It is equally
correct to take the other difference, W — C, and make it subtractive; it may sometimes occur that a few
figures will thus be saved, but a chance for error arises from the possibility of inadvertently using the
wrong sign, which is almost impossible by the other method. Thus, the following example may be
taken:
fC, 10* 57"» 38"
r, W, -11 42 .35
Comparison i '
Sight
IC-W, U 15 03
fW, U 50 21
C-W,H-11 15 03
w.
11"
42'"
.35-
0,
-10
57
38
AV-C,
44
57
^v.
11
50
21
w-c-
-
44
57
11 05 24 C, 11 05 24
74 TIME AND THE NAUTICAL ALMANAC,
CHAPTER IX.
TIME AND THE NAUTICAL ALMANAC.
ii70. The subjects of Time and the Nautical Almanac are two of the most important ones to be
mastered in the study of Nautical Astronomy, as they enter into every operation for the astronomical
determination of a ship's position. They will be treated in conjunction, as the two are interdependent.
METHODS OF RECKONING TIME.
271. The instant at which any point of the celestial sphere is on the meridian of an observer is
termed the transit, culmination, or meridian passage of that point; when on that half of the me.idian
whicli contains the zenith, it is designated as superior or upper transit; when on the half containing the
nadir, as inferior or lower transit.
272. Three different kinds of time are employed in astronomy — (a) apparent or solar time, (6) mean
time, and (c) sidereal time. These depend upon the hour angle from the meridian of the points to which
they respectively refer. The point of reference for apparent or solar time is the Center of the Sun; for
mean time, an imaginary point called the Mean Sun; and for sidereal time, the Vernal Equ inox, also called
the First Point of Aries.
The unit of time is the Day, which is the period between two successive transits over the same
branch of the meridian of the point of reference. The day is divided into 24 equal parts, called Hours;
these into 60 equal parts, called Minutes, and these into 60 equal parts, called Seconds.
273. Apparent or Sol,\r Time. — The hour angle of the center of the sun affords a measure of
Apparent or Solar Time. An Apparent or Sohtr Day is the interval of time between two successive transits
over the same meridian of the center of the sun. It is Apparent Noon when the sun's hour circle coin-
cides with the celestial meridian. This is the meet natural and direct measure of time, and the unit of
time adopted by the navigator at sea is the apparent solar day. Apparent noon is the time when the
latitude can be most readily determined, and the ordinary method of determining the longitude by the
sun involves a calculation to deduce the apparent time first.
Sini'e, however, the intervals between the successive returns of the sun to the same meridian are not
equal, apparent time can not be taken as a standard. The apparent day varies in length from two causes:
first, the sun does not move in the equator, the great circle perpendicular to tlie axis of rotation of the
earth, but in the ecliptic; and, secondly, the sun's motion in the ecliptic is not uniform. Sometimes the
sun desci'ibes an arc of 57' of the ecliptic, and sometimes an arc of 61' in a day. At the points where
the ecliptic and equinoctial intersect, the direction of the sun's apparent motion is inclined at an angle
of 23° 27' to the equator, while at the solstices it moves in a direction parallel to the equator.
274. Mean Time. — To avoid the irregularity of time caused by the want of uniformity in the sun's
motion, a fictitious sun, called the Mean Sun, is supposed to move in the equinoctial with a uniform
velocity that equals the mean velocity of the true sun in the ecliptic. This mean sun is regarded as being in
coincidence witli the true sun at the vernal equinox, or Firat Point of Aries.
Mean Time is the hour angle of the mean sun. A Mean Day is the interval between two successive
transits of the mean sun over the meridian. Mean Noon is the instant when the mean sun's hour circle
coincides ■with the meridian.
Mean time lapses uniformly; at certain times it agrees with apparent time, while sometimes it is
behind, and at other times in advance of it. It is this time that is measured by the clocks in ordinary
use, and to this the chronometers used by navigators are regulated.
275. The difference between apparent and mean time is called the Equation of Time; by this
quantity, the conversion from one to the other of these times may be .made. Its magnitude and the
direction of its application may be found for any moment from the Nautical Almanac.
276. Sidereal Time. — Sidereal Time is the hour angle of the First Point of Aries. This point,
which is identical with the vernal equinox, is the origin of all coordinates of right ascension. Since the
position of the point is fixed in the celestial sphere and does not, like the sun, moon, and planets, have
actual or apparent motion therein, it shares in this respect the properties of the fixed stars. It may
therefore be said that intervals of sidereal time are those which are measured by the stars.
A Sidereal Day is the interval between two successive transits of the First Point of Aries across
the same meridian. Sidereal Noon is the instant at which the hour circle of the First Point of Aries
coincides with the meridian. In order to intenranvert sidereal and mean times an element is tabulated
in the Nauticul Almanac. This is the Sidereal Time of Mean Noon, which is also the Right Ascension
of the Mean Sun.
277. Civil and Astronomical Time. — The Oitril Day commences at midnight and comprises the
twenty-four hours until the following midnight. The hours are counted from to 12, from midnight to
noon;"then, again, from to 12, from noon to midnight. Thus the civil day is divided into two periods
of twelve hours each, the first of which is marked a. m. (ante meridian), while the last is marked p. m.
(post meridian) .
TIME AND THE NAUTICAL ALMANAC. 75
The Astronomical or Solar Day commences at noon of the civil day of the same date. It comprises
twenty-four hours, reckone<l from to 24, from noon of one day to noon of the next. Astronomical time
(apparent or mean) is the hourangle of the sun (true or mean) measured to the westward throughout
its entire circuit from the time of its upper transit on one day to the same instant of the next.
The civil day, therefore, begins twelve hours before the astronomical day, and a clear under-
standing of this fact is all that is required for interconverting the.se times. For example:
January 9, 2 a. m., ci\il time, is January 8, 14'', astronomical time.
Januarv 9, 2 p. ni., civil time, is January 9, 2'', astronomical time.
27§. tfoiTit Angle. — The hour angle of a heavenly boiiy Is the angle at the pole of the celestial
concave between the declination circle of the heavenly body and the celestial
meridian. It is measured by the arc of the celestial equator between the decli-
nation circle and the celestial meridian.
In figure 34 let P be the pole of the celestial sphere, of which VMQ is the
etjuator, PQ, the celestial meridian, and PM, PS, PV, the declination circles of
the mean sun, a heavenly body, and the First Point of Aries, respectively.
Then QPM, or it.s arc, QM, is the hour angle of the mean sun, or the mean y^
time; QPS, or (JS, tlie hour angle of the heavenly body; l^PV, or QV, the hour
angle of the First Point of Aries, or the right ascension of the meridian, both of
which are equivalent to the sidereal time; VPS, or VS, the right ascension of
the heavenly body; and VPM, or VM, the right ascension of the mean sun.
279. Time .\t Different Meridi.\ns. — The hour angle of the true sun at any meridian is called the
local apparent time; that of the mean sun, the local mean time; that of the First Point of Aries, the local
sidereal time. The hour angles of the same body and points from Greenwich are respectively the Qreen-
vrich apparent, menu, and sidereal times. The difference tetween the local time at any meridian and the
Greenwich time is e<iual to the longitude of that place from Greenwich expressed in time; the conver-
sion from time to arc may be effected by a simple mathematical calculation or by the use of Table 7.
In comparing corresponding times of different meridians the most easterly meridian may he distin-
guished a.s that at which the time is greate-^l or latest.
In figure 35 PM and PM' represent the celestial meridians of two places;
PS, the declination circle through the sun, and PG, the Greenwich meridian;
let To = the Greenwich time = GPS;
Tm = the corresponding local time at all places on the meridian PM = MPS;
TM'=the corresponding local time at all i>laces on the meridian PM' =
M'PS;
Lo = west longitude of meridian PM = GPM ; and
Lo' =ea.st longitude of meridian PM' = GPM'.
If west longitudes and hour angles Vje reckone<l as positive, and east lon-
gitudes and hour angles as negative, we have: Fig. 35.
Lo = To — Tk; and
Lo' = To — Tm-; therefore,
Lo-Lo' = T,— T,.
Thus it may be seen that the ilifferenee of longitude between two places equals the difference of
their local times. This relation may be shown to hold for any two meridians whatsoever.
Both local and (ireenwich times in the above formula' must be reckoned westward, always from
their respective meridians and from 0'' to 24''; in other words, it is the astronomical time which should
be used in all astronomical computations.
The formula Lo = To — Tm is true for any kind of time, solar or sidereal; or, in general terms.
To and Tm are the hour angles of any point of the sphere at the two meridians whose difference of
longitude is Lo. S may be the sun (true or mean) or the vernal equinox.
2§0. Finding the Greenwich Time. — Since nearly every computation made by the navigator
requires a knowledge of the Greenwich date and time as a preliminary to the use of the Nautical
Almanac, the first operation necessary is to deduce from the local time the corresponding Greenwich
date, either exact or approximate, and' thence the Greenwich time expressed astronomically.
The formula is:
To=Tk+Lo,
remembering that west longitudes are positive, east longitudes are negative. Hence the following rule
for converting local to Greenwich time:
Having expresseil the local time astronomically, .arf(/ the longitude if west, subtract it if east; the result
is the corresponding Greenwich time.
Example: In longitude 81° 15' W. the local time is, 1879, April, 15"' 10" 17°' 30 a. m. Required the
Greenwich time.
Local Ast. time, April, 14" 22" 17'" .30"
Longitude, -f 5 25 00
Greenwich time, 15 3 42 30
KxAMpiJi: In longitude 81° 15' E. the local time is, August, 5'' 2'' 10"' 30' p. m. *^Required the Green-
wich time.
Local Ast. time, 5'' 2" lO-" 30»
Longitude, — 5 25 00
Greenwich time, 4 20 45 30
76 TIME AND THE NAUTICAL ALMANAC.
Example: In longitude 17° 28' W. the local time is, May, 1^ S*" 10™ p. m. Required the Greenwich
time.
Local Aet. time, 1'' S" 10"' 00»
Longitude, + 1 09 52
Greenwich time, 1 4 19 52
Example: In longitude 125° SO' E. the local time is. May, 1" 8" 10™ 30' a. m. Required the Green-
wich time.
Local Ast. time, April, 30'* 20" 10"' .SO"
Longitude, — 8 22 00
Greenwich time, 30 11 48 30
281. From the preceding article we have:
Tg = Tm + Lo; hence,
Tm = Tg - Lo;
thus it will be seen that, to find the local time corresponding to any Greenwich time, the above process
is simply reversed.
Since all observations at sea are referred to chronometers regulated to Greenwich mean time, and
as these instruments are usually marked on the dial from 0'' to l"', it becomes necessary to distinguish
whether it is a.m. or p.m. at Greenwich. Therefore, an approximate knowledge of the longitude and
local time is necessary to determine the Greenwich date.
Example: In longitude 5' 00" 00» AV., about 3'' 30" p.m. April 15th, the Greenwich chronometer
read S" 25™, and was fast of Gr. time 3™ 15'. Required the local astronomical time.
Aprox. local time, 15" S^ 30™ Gr. chro., 8'' 25™ 00" Gr. Ast. time 15'', 8" 21™ 45
Longitude, + 5 00 Corr., — 3 15 Longitude, —5 00 00
Approx. Gr. time, 15 8 30 Gr. Ast. time 15", 8 21 45 Local Ast. time 15'*, 3 21 45
Example: In longitude 5" 00™ OO' E., about 8 a. m. May 3d, the Gr. ihro. read 3'" 15" 20', and was
fast of Gr. time 3" 15'. Required the local astronomical time.
Approx. local time, Mav, 2'' 20" Gr. chro., 3' 1.5™ 20' Gr. Ast. time 2", 1.5" 12™ 05
Longitude, " — 5 Corr., — 3 15 Longitude, -'r 5 00 00
Approx. Gr. time, 2 15 Gr. Ast. time 2", 15 12 05 Local Ast. time 2'^, 20 12 05
THE MTAtTTICAL ALMANAC. «
282. The American Ephemeris and Nautical Almanac is divided into four parts, as follows: Part I,
Ephemeris for the meridian of Greenwich, gives the ephemerides of the sun and moon, the geocentric
and heliocentric positions of the major planets, the sun's coordinates, and other fundamental astronom-
ical data for equidistant intervals of Greenwich mean time; Part II, Ephemeris for the meridian of
Washington, gives the ephemerides of the fixed stars, sun, moon, and major planets for transit over the
meridian of Washington; Part III, Phenomena, contains predictions of phenomena to be observed, with
data for their computation; and Part IV, Star Numbers and other data, contains matter relating to cer-
tain fixed stars. Tables are also appended for the intercon version of mean and sidereal time and for
finding the latitude by an altitude of Polaris.
The American Navtkal Almanac \s & smaller book made up of extracts from the "Ephemeris and
Almanac ".just described, and is designed especially for the use of navigators, being adapted to the
meridian of Greenwich. It contains the positions of the sun and moon, the distances of the moon from
the center of the sun, from the centers of the four most conspicuous planets, and from certain fixed
stars, together with the ephemerides of the planets Mercury, Venus, Mars, .Jupiter, and Saturn, and the
mean places of 150 fixed stars; solarand lunar eclipses are described, and the tables for the interconversion
of mean and sidereal time and for finding the latitude by Polaris are included.
The elements dependent upon the sun and moon are placed at the beginning of the book,
arranged according to the months of the year; eighteen pages are devoted to each month, numbered in
Roman notation from I to XVIII. Of these, page I contains the Apparent Right Ascension and Declina-
tion of the sun and the Equation of Time for the instant of Greenwich apparent noon; throughout the
remaining seventeen pages Greenwich mean time forms the basis of reckoning. Page I is used in com- ,
putations from observations that depend upon the time of the sun's meridian passage, at which instant
the local apparent time is 0", and the Greenwich apparent time is equal to the longitude, if west, or to
24" minus the longitude, if east; this page therefore affords a means for reducing the elements for such
observations from a knowledge of the longitude alone. In all other observations the calculation is
made for some definite instant of Greenwich mean time (usually as noted by the chronometer) , in which
case Pages II to XVIII are employed.
283. Reduction of Elements. — The reduction of elements in the Nautical Almanac is usually
accomplished by Interpolation, but in certain cases where extreme precision is necessary the method of
Second Differences must be used.
a See extracts Irora Ephemeris iind Nautical Almanac for 1879, Appendix I.
TIME AND THE NAUTICAL ALMANAC. 77
The Ephemeris, being computed for the Greenwich meridian, contains tlie right ascensions, declina-
tions, equations of time, and other elements for given equidistant intervals of Greenwich time. Hence,
before the value of any of these quantities can be found for a given local time it is necessary to determine
the corresponding Greenwich time. Should that time be one for which the Nautical Almanac gives the
value of the required element, nothing more is necessary than to employ that value. But if the time
falls between the Almanac times, the required quantity must be found by interpolation.
The Almanac contains the rate of change or difference of each of the principal quantities for some
unit of time, and, unless great precision is required, the first differences only need be regarded. In
order to use the difference columns to advantage, the Greenwich date should be expressed in the unit
of time for which the difference is given. Thus, for using the hourly differences, the Greenwich tinr.e
should be expressed in hours and decimal parts of an hour; when using the differences for one minute,
the time should be in minutes and decimal parts of a minute. Instead of using decimal parts, some may
prefer the use of aliquot parts.
Since thequantities in the Almanac are approximate numbers, given to a certain decimal, any inter-
polation of a lower order than that decimal is unnecessary work. Moreover, since, in computations at
sea, the Greenwich time is more or less inexact, too great refinement need not be sought in reducing the
Almanac elements.
Simple interpolation assumes that the differences of the quantities are proportional to the differences
of the times; in other words, that the differences given in the Almanac are constant; this is seldom the
case, but the error arising from the assumption wfll be smaller the less the interval between the times
in the Almanac. Hence those quantities which vary most irregularly are given for the smallest units
of time; as the variations are more regular, the units for which the differences are given increase.
In taking from the Almanac the elements relating to the fixed stars the data may be found either
in the table which gives the "mean place" of each star for the year or in that which gives the
" apparent place " occupied by each one on every tenth day throughout the year. As the animal varia-
tion of position of the fixed stars is small, the results will not vary greatly whichever table may be used.
Yet, as it is proper to seek always the greatest attainable accuracy, the use of the table showing the
exact positions is recommended. That table is, however, ])ublished in the "Ephemeris and Nautical
Almanac" only, and is omitted from the abridged "Nautical Almanac;" hence, where the larger book
is not at hand, the table of mean places must be employed.
2§4. To find from the Nautical Almanac a required element for any given time and place, it is
first necessary to express the time astronomically and to convert it to Greenwich time and date. Then
take from the Almanac, for the nearest given preceding instant, the required quantity, together with its
corresponding " Diff. for l"" " or " Diff. for l""," noting the name or sign in each case; for the sun use
Page I of the proper month in the Almanac when apparent time is to be the basis for correction, but
otherwise use Page II. Multiply the "Diff. for 1''" by the number of houre and fraction of an hour,
or the " Diff. for 1"'" by the number of minutes and fraction of a minute, corresponding to the interval
between the time for which the quantity is given in the Almanac and the time for which required;
apply the correction thus obtained, having regard to its sign.
A modification of this rule may be adopted if the time for which the quantity is desired falls con-
siderably nearer a subfefjuent time given in the Almanac than it does to one preceding; in this case the
iiiter]iolation may be made backward, the sign of application of the correction being reversed.
Example: At a place in longitude 81° lo' W., April 17, 1879, find the sun's declination and the
equation of time at apparent noon.
Ix)ng. =81° 1.5' W. G.
Dec, 17'' 0'', ( + ) 10° 26' 42".3 N.
Corr., + 4 46 .2
A.
T.
= 1?' 5" 25°' = 17'' + 5\42.
E(i. t., 1?' 0\ O" 24«.46
Corr., -i- 3 .18
Dec, 1?'5'>25'", 10 31 28 .5 N.
Eq.t.,17''5i'2.5'", 27.64
H. D., 4- 52".80
G. A. T., + 5\42
H. D., + 0».587
G. A. T., -f 5\42
Co„ + f286".18 Corr., + 3M82
■' \4'46".18 {Siibtract iroiu apparent time.)
Example: At a place in Long. 81° 1.5' E., April 17, 1879, find the sun's declination and the equation
of time at apparent noon.
Long. =81° 15' E. G. A. T. = 1 6'' 18'' 35'" = 17'* — 5''.42.
Dec, 17" 0'', ( + ) 10° 26'42".3N. Eq. t, 17'> 0^ C" 24".46
Corr., — 4 46 .2 Corr., -~ 3.18
Dec, 16'' 18" 35'»,
10 21 56 .1 N.
Eq. t., 16'' 18" 35'°, 21 .28
H. D.,
G. A. T.,
-f 52". 80
- 5\42
H. D., + 0".587
G. A. T., - 5".42
Por.'
; 286". 18
Corr., — 3M82
78
TIME AND THK NAUTICAL ALMANAC.
Example: April 16, 1879, at 11'' 55"" 30" a. ni., local mean time, in Long. 81° 15' W., required tltt
declination and semidiameter of the yun, the equation of time, and the right ascension, declination
horizontal parallax, and semidiameter of the moon and Jupiter.
Local mean time.
Longitude,
lo-i 23'' 55°' 30"
5" 25°' 00"
[16" 5" 20"' 30"
Greenwich mean time, { W 5'' 20°'.o
116'' 5".34
Dec, 0", ( + ) lO" 05' 30". 1 N.
Corr., 4- 4 44 . 3
For the >S')(»i.
S. D., 15' 58".
(Same as at G. A. Noon.)
Eq. t, 0',
Corr.,
O" 10». 15
3.22
Dec.,
+
+
+
0°,
't.,
10 10 14 . 4 N.
For the Moon.
(-) 7°59' 36".l S. Hor. Par.,0'',
+ 4 27 .1 Corr.,
Eq. t.,
13 . 37
H. D.
G. M.
+
, +
53". 24
5'. 34
H. D., -f
G. M. T., -i-
0'. 604
5\ 34
Corr.,
R. A., .5»,
Corr.,
22h 14" 39>.29
38.31
284". 30
4' 44". 30
Dee., .s\
Corr.,
DfO.,
M. D.,
Xo. min.,
Corr.,
35^ 54
9. 71
Corr., +
{Add to iitemi
5.5'13".6 S.D.,0k,
- 7 .2 Corr.,
3'. 22
time. )
1.V04".7
- 1 .8
R. A.,
22 15 17 .60
7 6.5 09 .0 S. Hor. Par.,
55 06 .4 S. P.,
15 02 .9
M. D.,
No. min..
1«.869
20».5
+ 13".03 H. D.,
+ 20-.5 (i. M. T.,
l."31 H. !>.,
+ 6\34 li. M. T.
T'.lo Corr..
Hor. Par., 16',
S. D., IB'',
- 0".34
Corr.,
R. A.,
Corr.,
38'.31
22'' 26"'
, ( 267". 12 Corr.,
^ \ 4'27".l
For Jupiter.
Dec, 0", (- ) 10° 40' 28". S.
Corr., - 53 . 6
1".S1
1". 6
R. A.,
22 26
45 . 25
Dec, 10 39 34 . 4S.
H. D.,
G. M.
+
I'. 819
5\ 34
H. D., + 10*. 03
G. M. T., + 5\ 34
16".9
Corr.,
9*. 71
Corr.,
53". 6
2§5. Should greater precision be required than that attainable by simple interpolation, resort must
be had to the reduction for second differences.
The differences between successive values of the quantities given in the Nautical Almanac are called
the first differences; the differences between successive first differences are called the second differences.
Simple interpolation, which satisfies the necessities of sea computations, assumes the first differences to
be constant; but if the variation of the first differences be regarded, a further interpolation is required
for the second difference.
The difference for a unit of time in the American Nautical Almanac abreast any element expresses
the rate at which the element is changing at that precise instant of Greenwich time. Now, regarding
the second difference as constant, the first difference varies uniformly with the Greenwich time; there-
fore its value may be found for any intermediate time by simple interpolation.
Hence the following rule for "second differences: Employ the interiwlated value of the first differ-
ence which corresponds to the middle of the interval for which the correction is to be computed.
Example: For the Greenwich' date 1879, April, 10' 18" 25'" 30% find the moon's declination.
Dec, 18", ( — )26° 19' 41".l S.
Corr., -H 2 .1
Dec,
26 19 39 .OS.
Firstdiff., i 0".044
Corr., -f .039
M. D., -i-0 .083
No. min., -h 25°'.5
Seconddiff.,-f 0".181
Interval, r-0".213
Corr.,
0".039
Corr.,
+ 2".12
The difference for one minute being ■- 0".044 at 18", and -;-0".225 at 19", the difference for one
minute undergoes a change of -f 0".181 during one hour. The time for which it is desired to obtain the
difference is at the middle instant between 18" 0'° and 18" 25"'.5— that is, at 18" 12™. 75, or its equivalent,
18".213. With a change of -|- 0".181 in' one hour, the change in 0".213 is readily obtainable; correcting
the minute's difference at 18".0 accordingly, the process of correcting the declination becomes the same
as in simple interpolation.
TIME AND THE KAUTICAL ALMANAC. 7^
CONVERSION OF TIMES.
386. Conversion of Time is the process by which any instant of time that is defined according to one
system of reckoning may be defined according to some other system; and also
by which any interval of time expressed in units of one system may be con-
verted into units of another.
287. Sidereal and Mean Times. — Mean time is the hour angle of the
Mean Sun; sidereal time is the hour angle of the First Point of Aries. Since
the Right Ascension of the Mean Sun is the angular distance Ijetween the hour
circles of the Mean Sun and of the First Point of Aries, mean time may be con-
verted into sidereal time by adding to it the Right Ascension of the' Mean Sun;
and similarly, sidereal time may be converted into mean time by subtracting from
it the Right Ascension of the Mean Sun.
This is explained in figure 36, which represents a projection of the celestial
sphere upon the equator. If P be the pole; QPQ', the meridian; V, the First
Point of Aries; M, the position of the mean sun (west of the meridian); then
QPV, or the arc QV, is the sidereal time; QPM, or the arc QM, is the mean
time; and VPM, or the arc VM, is the Right Ascension of the Mean Sun. From this it will appear that:
Qy=QM+VM, or
Sidereal time=Mean time-f Right Ascension of Mean Sun.
If the mean sun be on the opposite side of the meridian, at M', then the mean time equals
24''-M'Q. In this case:
QV = VM'-M'Q, or
Sidereal time=Right Ascension of Mean Sun— (24"— Mean time),
=Right Ascension of Mean Sun + Mean time— 24".
Right ascension being measured to the east and hour angle to the west, the sidereal time
will therefore always eqnal the sum of these two; but 24'' must be subtracted when the sum exceeds
that amount.
From the preceding equations, we also have:
QM=QV-VM; and
M'Q=VM'-QV, or
(24'>-M'Q) = (24''+QV)-VM'.
From this it may be seen that the mean time equals the sidereal time minus the Right Ascension
of the Mean Sun, but the former must be increased by 24'' when necessary to make the subtraction
jiossible.
288. Apparent and Mean Times. — Apparent time is the angle l>etween the meridian ajid the
hour circle which contains the center of the sun; mean time is the angle between the meridian and the
hour circle which contains the mean sun. Since the equation of time represents the angle between
the hour circles of the mean and apparent suns, it is clear that the conversion of mean time to apparent
time may be accomplished by the application of the equation of time, with its proper sign, to the mean
time; and the reverse operation by the application of the same ([uantity, in an opposite direction, to tlie
apparent time.
The resemblance of these operations to the interconversif>n of mean and sidereal times may be
observed if, in figure 36, we assume that PV is the hour circle of the true sun, PM remaining that of the
mean sun; then the arc QM will be the mean time; QV, the apparent time; and VM, the equation of
time; whence \.e have as before:
QV = QM-rVM, or
Apparent time = Mean time + Equation of time ;
the equation of time will be positive or negative according to the relative position of the two suns.
289. Sidereal a.vd Mean Time I.vtervals.— The sidereal year consists of 366.25636 sidereal days
or of 365.25636 mean solar days. If, therefore, M be any intervalof mean time, and S the corresponding
interval of sidereal time, the relations between the two may be expressed as follows:
S 366.25636 __^^^
M~ 365.25636"
M_ 365.25636
S "366.25636'
= 0.9972696.
Therefore, 8 = 1.0027379 M = M + . 0027379 M;
M = 0.9972696 S = S -.0027304 S.
If M = 24'', S = 24''-|-3'°56'.6; or, in a mean solar day, sidereal time gains on mean time 3" 56'. 6, the
gain each hour being 9'.8565.
If 8 = 24'', M=24'' — 3'" 55'.9; or, in a sidereal day, mean time loses on sidereal time 3"' 55'. 9, the
loss each hour being 9«.8296.
If M and S be expressed in hours and fractional parts thereof,
S = M-f 9'.8565M;
M = 8 - 9'. 8296 S.
Tables for the conversion of the intervals of mean into those of sidereal time and the reverse are
based upon these relations. Tables 8 and 9 of this work give the values for making these conversions,
and similar tables are to be found in the Nautical Almanac.
80
TIME AND THE NAUTICAL ALMANAC.
200> To Convert Mean Solar into Sidereal Time. — Apply to the local mean time the longitude,
adding if west and subtracting if east, and thus obtain the Greenwich mean time. Take from the Nau-
tical Almanac the Right Ascension of the Mean Sun at Greenwich mean noon, and correct it for the
Greenwich mean time by Table 9 or by the hourly difference of 9'. 857. Add to the local mean time this
corrected right ascension, rejecting 24'' if the sum is greater than that amount. The result will be the
local sidereal time.
Example: April 22, 1879, in Long. 81° 15' VV., the local mean time is 2" OO" 00= p. m. Required
the corresponding local sidereal time:
L. M. T., 220 2^ 00"' 00» R. A. M. S., 22" 0\ 2" 00'" 41».24 L. M. T.,
Long., + 5 25 00 Red. for 7" 25°' (Tab. 9), + 1 13.10 R.A.M.S.,
G.M.T., 22 7 25 00 R. A. M. S., 7'' 25"',
2 01 54 .34 L. S. T.,
2" 00'» OO"
2 01 54.34
4 01 54.34
Example: April 22, 1879, in Long. 75° E., the local mean time is 4" 00'" 00' a. m. Required the
local sidereal time.
L. M. T., 21'
Long., -
16'' 00"'
5 00
00»
00
G. M. T., 21 11 00 00
R. A M. S. 21" 0'',
Red. for 11" (Tab. 9),
R. A. M. S., 11\
1" 56'" 44".69
1 48 .42
L.M.T., 21" 16'' 00'" 00'
R.A.M.S.,+ 1 58 33.11
1 58 33 .11 L. S. T., 21 17 58 33.11
In these examples the reduction of the R. A. M. S. has fonned a separate operation in order to
make clear the process. It would be as accurate to add together directly L. M. T., R. A. M. S., and
Red., and the work would thus be rendered more brief.
291. To Convert Sidereal into Mean Solar Time. — Take from the Nautical Almanac the
Right Ascension of the Mean Sun for Greenwich mean noon of the given astronomical day, and apply
to it the reduction for longitude, either by Table 9 or by the hourly difference of 9'.857, and the result
will be the Right Ascension of the Mean Sun at local mean noon, which is equivalent to the local
sidereal time at that instant. Subtract this from the given local sidereal time (adding 24'' to the latter
if necessary), and the result will be the interval from local mean noon, expressed in units of sidereal
time. Convert this sidereal time interval into a mean time interval by subtracting the reduction as
^iven by Table 8 or by the hourly difference of 9'.830; the result will be the local mean time.
Example: April 22, 1879, a. m., in Long. 75° E., the local sidereal time is 17" 58" 33M1. What is
the local mean time?
Astronomical day, April 21.
L. S. T.,
R. A M. S.,
17"58"^33M1
- 1 55 55.41
Sid. interval from L. M. noon, 16 02 37 .70
Red. for sid. interval (Tab. 8), 2 37 .70
R. A. M. S., Gr. 21" 0",
Red. for -5" long. (Tab. 9)
R. A. M. S., local 0\
1" 56"
44". 69
49.28
1 55 55 .41
L. M. T., 21", 16 00 00 .00
Example: April 22, 1879, p. m., at a place in T,ong. 81° 15' W., the sidereal time is 4" 01"' M'.'M.
What is the eorresjionding mean time?
Astronomical day, April 22.
L. S. T.,
R. A. M. S.,
4" Ol-" 54'.34
-2 01 34.63
R. A. M. S , Gr. 22" 0", 2" 00'" 4P.24
Red. for +5" 25-° long. (Tab. 9), + 53.39
Sid. interval from L. M. Noon, 2 00 19 .71
Red. for sid. interval (Tab. 8), — 19 .71
R. A. M. S., local 0\
2 01 34 .63
L. M. T., 22",
2 00 00 .00
292. To Covert Mean into Apparent Time and the Reverse. — Find the Greenwich time corre-
sponding to the given local time. If apparent time is ^iven, find the Greenwich apparent time and take
the equation of time from Page I of the Almanac. It mean time, find the Greenwich mean time and
take the equation of time from Page II. Correct the equation of time for the required instant and
apply it with its proper sign to the given time.
Example: April 21, 1879, in Long. 81° 15' W., find the local apparent time corresponding to a local
mean time of 3" 05"' 00' p. m.
' 00' L. M. '
Eq. t..
L. M. T.^
Long. ,
21" 3" 05°' 00'
5 25 00
S. M. T., 21 8 30 00
L. A. T.,
21" 3'' 05°' OO"
1 22.01
Eq. t, 0", 1°' 17.61
Corr., -f 4.40
21 3 06 22.01
Eq.t., 1 22.01
H.D., -r 0'.518
G.M.T.,+ 8".5
Corr., ~r f.403
{Add t(j mean time.)
TIME AND THE NAUTICAL ALMANAC.
81
Example: April 3, 1879, in Long. 81° 15' E., tlie local apparent time is 8'' 45" 00' a. m. Required
the mean time.
L. A. T., 2'' 20" 45™ 00' L. A. T., 2"' 20" 45°" 00'
Long., - 5 25 00 B}. t., -4 3 30.90
Eq. t., 0", 3" 42».46
Corr., — 11 .56
G. A. T.,
2 15 20 00
L. M. T.,
2 20 48 30.90
Eq. t.,
3 30 .90
H. D., - 0^.754
G. M. T., - 15".33
Corr., — IP. 56
{Add to apparent time. )
293. To Find the Hour Angle of a Body from the Time, and the Rever.se. — In figure 36, if M
and M' represent tiie po.sitions of celestial bodies instead of those of the mean sun as before assumed,
then the hour angles of the boilies will be Q M and 24" — M' Q, respectively, and their right ascen-
sions will be V M and V M'.
As before, we have:
Q V = Q M + V M,
= V M' - M' Q;
QM =QV-VM;
M' Q = V M' - V Q, or
(24" - M' Q) = (24" + Q V) - V M'.
Substituting, therefore, hour angle of the body for inean time, and right ascension of the body for Right
Ascension of the Mean Sun, the rules previously given for the conversion of mean and sidereal times will
be applicable for the conversion of hour angle and sidereal time. Thus, the sidereal time is equal to the
sum of the right ascension of the body and its hour angle, subtracting 24" wlien the sum exceeds that
amount; and the hour angle equals the sidereal time minus the right ascension of the body, 24" being
added to the former when necessary to render the subtraction possible.
Example: In Long. 81° 15' W., on April 25, 1879, at 12" 10"" 30' (astronomical) mean time, find the
hour angle of Siriu.s.
L. M. T., 12" lO" 30»
Long., + 5 25 00
G. M. T.. 17 35 30
L. M. T., 12" 10°'3O'
R. A. M. S.,0",+ 2 12 30.91
Red. (Tab. 9), + 2 53.39
L. S. T., 14 25 54.30
R. A. Sirius, — 6 39 49.83
H. A. Sirius,
7 46 04.47
Example: May 9, 1879, Arcturus being 2" 27" 42».52 east of the meridian, find the local sidereal time
24" 00™ 00"
H. A., 2 27 42.52 E.
H. A., 21" 32"» 17'.48
R. A., 4- 14 10 11 .71
H. A., 21 32 17.48 W.
L. S. T., 11 42 29.19
Or thus:
24972°— 12
H. A., — 2" 27" 42-. 52
R. A., + 14 10 11 .71
L. S. T.,
U 42 29 .19
82
COBEECTION OF OBSERVED ALTITUDES.
CHAPTER X.
OOEREOTIOK OF OBSEEVED ALTITUDES.
S94. The fnw altitude of a heavenly body at any place on the earth's surface is the altitude of its
center, as it would be measured by an observer at the center of the earth, above the plane passed
through the center of the earth at right angles to the direction of the zenith.
Tlie ohxerred altitude of a heavenly body, as measured at sea, may be converted to the true altitude
by the application of the following-named corrections: Index Correction, Dip, Refraction, Parallax, and
Semidiamefer. The corrections for parallax and semidiameter are of inappreciable magnitude in
observations of the fixed stars, and with planets are so small that they need only be regarded in refined
calculations. In observations with the artificial horizon there is no correction for dip.
For theoretical accuracy, the corrections should be applied in the order in which they are named,
but in ordinary nautical practice the order of application makes no material difference, except in the
case of the parallax of the moon as explained in article 306.
INDEX CORRECTION.
a95. This c<jrrection is fully exjilained in articles 240 and 2.50, Chapter VIII.
REFRACTION.
296. It is known by various experiments that the ravs of light deviate from their rectilinear
course in passing obliquely from one meilium into another of a different density; if the latter be more
dense, the ray will be bent toward the jterpendicular to the line of junction of the media; if less dense,
it will be bent away from that perpendicular.
The ray of liglit Ijefore entering the second medium is calle<l the incident ray ; after it enters the
second medium it is called the refracted ray, and the
difference of direction of the two is called the refraction.
The rays of light from a heavenly body must pass
through the atmosphere before reaching the eye of an
observer upon the surface of the earth. The earth's
atmosphere is not of a uniform density, but is most
dense near the earth's surface, gradually decreasing in
density toward its upper limit; hence the path of a ray
of light, by passing from a rarer medium into one of
continually increasing density becomes a curve, which
is concave toward the earth. The last direction of the
ray is that of a tangent to the curved path at the eye of
the observer, and the diffcirence of the direction of the
ray before entering the atmosphere and this last direc-
tion constitutes the refraction.
297. To illustrate this, consider the earth's atmos-
phere as shown in figure 37; let SB be a ray from
a star S, entering the atmosphere at B, and bent into
the curve BA; then the apparent direction of the star
is AS', the tangent to the curve at the point A, the
refraction teing the angle between the lines Bi^ and
AS'. If CAZ is the vertical line of the observer, by a
law of Optics the vertical plane of the observer which
contains the tangent AS' must also contain the whole
curve BA and the incident ray BS. Hence refraction
increases the apparent altitude of a star without affect-
ing its azimuth.
At the zenith the refraction is nothing. The less
the altitude the more obliquely the rays enter the atmosphere and the greater will be the refraction. At
the horizon the refraction is the greatest.
298. The refraction for a mean state of the atmosphere (barometer 30'", Fahr. thermometer 50°)
is given in Table 20 A; the combined refraction and sun's parallax in Table 20 B; and the combined
refraction and moon's parallax in Table 24.
Since the amount of the refraction depends upon the density of the atmospliere, and the density
varies with the pressure and the temperature, which are indicated by the barometer and thermometer,
the Inie refraction is found by applying to the mean refraction the corrections to be found in Tables 21
and 22; these are deduced from Bessel's formula-, and are regarded as the mcist reliable tables
constructed. It should be remembered, however, that under certain conditions of the atmosphere a
very extraordinary defiection occurs in rays of light which reach the observer's eye from low altitudes
Fig. 37
(;OKRKCTl()N OF OBSKKVED ALTITUDES.
83
/
(that is, from points near t lie visible horizon), the amount of which is not covered by the ordinary
corrections for pressure and temperature; the error thus created is discussed under I>ip (art. 301); on
account of it, altitudes less than 10° should be avoided. .
Example: Required the refraction for the apparent altitude 5°, when the thermnmeter is at 20°
and the barometer at 30'" .67.
The mean refraction by Tal)le 20 A is, 9^ 52"
The correction for height of barometer is, + 13
The correction for the temperature, + 42
True refraction, ' 10 47
299. The correction for refraction' should always be .subtracte<l, as also that for combined refraction
and parallax of the sun; the correction for combined refraction and parallax of the moon is invariably
additive.
DIP.
300. Dij) of the Horizon is the angle of depression of the visible sea horizon l)eKnv the true horizon,
due to the elevation of the eye of the observer above the level of the sea.
In figure 38 suppose A to be the position f)f an
observer whose height above the level of the sea is
AB. CAZ is the true vertical at the pf)sition of the
observer, and .\H is tlie direction of the true hori- \^ iZ
zon, S being an observed heavenly body. Draw
.VTII' tangent to the earth's surface at T. Disre-
garding refraction, T will 1^ the most distant point
visible from A. t)wing to refraction, however, the
most distant visible point of the eartli's surface is h-
niore remote from the observer than the ])oint T,
and is to be found at a point T', in figure 39. But
to an observer at A the point T' will appear to lie
in the direction of AH", the tangent at A to the curve
AT'. Jf the vertical plane were revolved about CZ
as an axis, the line AH would generate the plane of
the true horizon, while the point T' would generate
a small circle of the terrestrial sphere called the
Visihie or Sen Horizon. The Di/) of the Horizon is
HAH", being the angle between the true horizon and
the apjxirent direction of the sea horizon. Values
of the tlip are given in Table 14 for various heights
of the observer's eye, and in the calculation of the
table allowance has been made for the effect of at-
mospheric refraction as it exists under normal con-
ditions.
Fig. 38.
301. The fact must Vie emphasized, liowever, that
under certain conditions the deflection of the ray in its path
from the horizon to the eye is so irregular as to give a value
of the dip widely different from that whicli is tabulated for
the mean state of atmosphere. These irregularities usually .
occur when there exists a material difference between the
temiierature of the sea water and that of the air, and they '
attain a niaxinnnn value in calm or nearly calm weather, V
when the lack of circulation permits the air to arrange itself ^ ^
iu a series of horizontal strata of different densities, Wifif ^' ^
denser strata l)eing below when the air is warmer, and the /
reverse condition obtaining when the air is cooler. The
effect of such an arrangement is that a ray of light from the
horizon, iu parsing through media of different densities,
undergoes a refraction quite imlike that which occurs in the ,.•
atmosphere of much more nearly homogeneous density that^- ,
exists under normal conditions. ' : ^
Varif)us methods have been suggested for computing , '
the amount of dip for different relative values of tempera- ,
« ture of air and water, but none of these afford a satisfactory .^
solution, there l>eing so many elements involved which are not 8uscei)tible of determination by an T
observer on shipboard that it will always be difficult to arrive at results that may be depended upon. «
As the amount of difference between the actual and tabulated values of the dip flue to this cause
may sometimes be very considerable — reliable oV)servations having frequently placed it above 10', and
values as high as 32' having been recorded — it is necessary for the navigator to be on his guard against
the errors thus produced, and to recognize the pfi.ssible inaccuracy of all i esults derived from oVjservations
taken under unfavoral)le ccmditions. Without attempting to give any method for the determination of
the amount of the extraordinary variati(jn in dip, the following rules may indicate to the navigator the
conditions under which caution nnist be observed, and the direction of probable error:
(<() A di.splacement of the horizon should always Ije suspected when there is a marked differences ■*
i^etween the temperatures (>( air and sca>vater; this fac^jghoilld b < esp qaaUx^^t in mind iu ^(^ons / >*
Buch as tho,ae of the Red Sea 'and tUl? (jrWl Ptreatn, 'wIfBr3*lie differeflWfi^lieml^exis^. - • ^ -
n K serfWltrt attarhm o m jtevised by XieutenantCoralhanderT. "R, Blish, ip. S.^Jfav^, en^i8^*ft- observer to measurer the
actual nip ^x any tiiuo. \ * *
/
■?.--A
^ •>
-i^N^ ,>2lN^ »4k%C
vxA
/
84
CORRKCTION OF OBSEKVED ALTITUDES.
(b) The error in the tabulated vahie of the dip will increase with an increase in the difference ol
temperature, and will diminish with an increase in the force of the wind.
(c) The error will decrea.se with the height of the observer's eye; hence it is expedient, especially
when error is suspected, to make the observation from the most elevated position available.
(d) When the sea water is colder than the air the visible horizon is raised and the dip is decreased;
therefore the true altitude is greater than that given by the use of the ordinary dip table. When the
water is warmer than the air, the horizon is depressed and the dip is increased. At such times the
altitude is really less than that found from the use of the table.
The same cause, it may be mentioned here, affects the kindred matter of the visibility of objects.
When the air is warmer, terrestrial objects aTe sighted from a greater distance and appear higher above
the horizon than under ordinary conditions. When the water is warmer than the air, the distance of
visibility is reduced, and terrestrial objects appear at a less altitude.
30i. What has been said heretofore about the dip supposes the horizon to be free from all inter-
vening land or other objects; but it often happens that an observation is required to be taken from a
ship sailing along shore or at anchor in harbor, when the sun is over the land and the shore is nearer the
ship than the visible sea-horizon would be if it were unconfined; in this case the dip will be different from
that of Table 14, and will be greater the nearer the ship is to that point of the shore to which the sun's
image is brought down. In such case Table 15 gives the dip at different heights of the eye and at
different distances of the ship from the land.
303. The dip is always to be subtracted from the observed altitude.
PARALLAX.
304. The parallax of a heavenly l)ody is, in general
terms, the angle between two straight lines drawn to the
body from different points. But in Nautical Astronomy
yeocentric parallax is s.lone considered, this being the differ-
ence between the positions of a heavenly body as seen at
the same instant from the center of the earth and from a
point on its surface.
The zenith distance of a body, S ( fig. 40) , seen from A, on
the surface of the earth, is Z.\S; seen from C it is ZCS; the
iHtrullax is the difference of these angles, ZA8— ZCS=ASC.
Parallax in altUude is, then, the angle at the heavenly
l)ody subtended by the radius of the earth.
If the heavenly body is in the horizon as at H', the
radius, being at right angles to AW, subtends the greatest
possible angle at the star for the same distance, and this
angle is called the horizontal parallax. The parallax is less
as the bodies are farther from the earth, as will be evident
j-j(. 40 from the figure.
Let par. = parallax in altitude, ASC;
Z = SAZ, the apparent zenith distance (corrected for refraction);
R = AC, the i-adius of the earth; and
D = CS, the distance of the object from the center of the earth.
' Then, since SAC = 180° - SAZ, the triangle ASC gives:
B sin Z
sm par.
D
If the object is in the horizon at H', the angle AH'C is the horizontal parallax, and denoting it by
P. the right triangle AH'C gives:
R
sin H. P.
D"
Substituting this value of f. in the above,
sin par. = sin H. P. sin Z.
If h = SAH', the apparent altitude of the heavenly body, then Z = 90° — A; hence,
[^ sin par. = sin H. P. cos h.
S Since par. and H. P. are always small, the sines are nearly profjortional to the angles; hence,
Sk par. = H. P. cos h.
V 305. The Nautical Almanac gives the horizontal parallax of the moon, as well as of the planets
lercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune.
.^^
CORRECTION OF OBSERVED ALTITUDES.
^'J
85 Si;
In Table 16 will be found the values of the sun's parallax for altitude intervals of 5° or 10°, while
Table 20 B contains the combined values of the sun's parallax and the refraction. In Table 24 is given
the parallax of the moon, combined with the refraction, at various altitudes and for various values of
the horizontal parallax.
306. Parallax is always additive; combined parallax and refraction additive in the case of the
moon, but subtractive for the sun.
As the correction for parallax of the moon is so large, it is essential that it be taken from the table
with considerable accuracy; the corrections for index correction, semidiameter, and dip should there-
fore be applied first, and the "approximate altitude" thus obtained should be use<l as an argument in
entering Table 24 for parallax and refraction.
SEMIDIAMETEB.
307. The i!cm.idimneter of a heavenly body is half the angle subtended by the diameter of the
visible disk at the eye of the observer. For the same body the semidiameter varies with the distance;
thus, the difference of the sun's semidiameter at different times of the year is due to the change of the
earth's distance from the sun; and similarly for the moon and the planets.
In the case of the moon, the earth's radius bears an appreciable and considerable ratio to the moon's
distance from the center of the earth; hence the moon is materiallv nearer to an observer when in or
near his zenith than when in or near his horizon, and therefore tfie semidiameter, besides having a
menstrual change, ha.s a semidiurnal one also.
The increa.se of the moon's semidiameter due to increase of altitude is called its augmentation. This
reduction may te taken from Table 18.
The semidiameters of the sun, moon, and planet* are given in their appropriate places in the Nautical
Almanac.
308. The seniidiameter is to be added to the observed altitude in case the lower limb of the body
is brought into contact with thff horizon, and to be subtracted in the case of the upper limb. When the
artificial horizon is used, the limb of the reflected image is that which determines the sign of this correc-
tion, it being additive for the lower and subtractive for the upper.
Exa,mple: May 6, 1879, the observed altitude of the sun's upper limb wa.s 62° 10' 40"; I. C, + 3' 10";
height of the eye, 2.5 feet. Required the true altitude.
Obs. alt. 0,
Corr.,
True alt.,
62° 10' 40"
18 04
61 52 36
I. C,
3' 10"
S. D. (Xaut. Aim. ), — 15' 53"
dip (Tab. 14), - 4 54
p.Jtr. (Tab. 20 B), - 27
Corr..
-21 14
- 18' 04"
Ex.^mi'I.e: The altitude of Sirius as observed with an artificial horizon was 50° 59' 30"; I.
1' 30". Required the true altitude.
C,
Obs. 2 alt. >>:,
I. C,
50° 59' 30"
1 30
2)50 58 00
Obs. alt., 25 29 00
ref. (Tab. 20 A),- 2 02
True alt..
25 26 58
E.xampj,e: April 16, 1879, observed altitude of Venus 53° 26' 10"; I. C, + 2' 30"; height of eve, 20
feet. Required the true altitude.
Obs. alt. *, 53° 26' 10"
Corr., — 2 32
53 23 38
par. (Tab. 17), -,- 0' 04"
I. C, + 2 30
Hor. Par. (Naut. Aim.), 7"
J 2 34
dip (Tab. 14), - 4' 23"
ref. (Tab. 20 A),- 43
Corr.,
-5 06
- 2' 32" .
4
4
^
'^^.
J^^
.^5T^
86
coer'ection of obskrvkd altititdes.
Example: May 6, 1879, at 13" 24"' G. M. T., the observed altitude of tlie moon's lower limb was 25°
30' 30"; I. C, —V 30"; height of eye, 20 feet. Required the true altitude.
Obs. alt.C,
Ist com,
25° SO' 30"
10 57
S. D. (Naut. Aim.),
Aug. (Tab. 18),
16' 42"
08
Hor. rar.(Xaut.Ahu.) 61' 10"
Approx. alt., 25 41 27
p. d-r. (Tab. 24), + 53 07
True alt.,
26 34 34
dip (Tab. 14),
I. C,
1st corr.,
Or, the following modification may be adopted:
;- 16 50
- 4' 23"
- 1 30
- 5 53
-I- 10' 57"
Obs. alt.C,
1st corr.,
Approx. alt.,
par..
True alt.,
25° 30' 30"
8 56
25 39 26
55 08
26 34 34
S. D.,
Aug. ,
dip,
ref.,
I. C,
+ 16' 42"
+ 08
-!- 16 50
- 4' 23"
- 2 01
- 1 30
tat corr., -}-
7 54
8' 56"
II. P., 3670"
App. alt., 25° 39'
log 3. .56467
cos 9. 95494
par..
/ 3308"
\55' 08"
log 3. 51961
ts_
>:
^ /■ Jt
t '-«.
■^ .^ V > f^-.
X
, >'^^-<^
T^-'
^ ^k. S WW ^^'.v .^^> X
THE CHKONOMETER ERROK. 87
CHAPTER XI.
THE CHRONOMETEE EEROR.
309. It has already btien explained (art. 201, Chap. A'llI) that the error of a chronometer is the
difference between the time indicated by it and the correct standard time to which it is referred; and
that the daili/ rate is the amount that it gains or loses each day. In practice, chronometer errors are
usually stated with reference to Greenwich mean time. It is not required that either the error or the
rate shall be zero, but in order to be enabled to determine the correct time it is essential that both rate
and error be known, and that the rate shall have been unifonn since its last determination.
310, Determixixg the Rate. — Since all chronometers are subject to some variation in rate under
the changeable conditions existing on shipboard, it is desirable to ascertain a new rate as often as possible.
The process of obtaining a rate involves the determination of the error on two different occasions sepa-
rated by an interval of time of such length as may be convenient ; the change of erro.r during this interval,
divided by the number of days, gives the daily rate.
Exa.mple: On March 10, "at noon, found chronometer No. 576 to be 0™ 32".o fast of G. JI. T. ; on March
20, at noon, the .same chronometer wag 0'" 48". fast of G. M. T. What was the rate?
Error, March 10^ 0\ -^ 0"' 32'. 5
Error, March 20" 0", -[- 48 .
Change in 10 days, ~ 15 . 5
Pally rate, -f 1'.55
The chronometer is therefore gainiiig 1".55 jier day.
311. Determixixo Error feo.m Rate. — The error on any given day l>eing known, together with
the daily rate, to find the error on any other day it is only necessary to multiply the rate by the number
of data that may have elapsed, and to apply the product, with projier sign, to the given error.
Exa.mple: On December 17 a chronometer is 3'" 27'.5 slow of G. M, T. and losing 0'.47 ilaily. What
is the error on Pecember 26?
Error Dec. 17, — 3" 27'.5 Daily rate, — 0'.47
Correction, — 4.2 No. days, 9
p:rror Dec. 26, - 3 31.7 Corr., -4.23
The chronometer is therefore shm of G. M. T. on December 26, 3" 31'. 7.
318. It is necessary to distinguish between the signs of the chronometer correction and of the
chronometer error. A chronometer fast of the standard time is considered as having a pomtive error,
since its readings are po.sitive to (greater than) those of an instrument showing correct time; but the
same chronometer has a negative correction, as the amount must be subtracteil to reduce chronometer
readings to correct readings.
313. Numerous methods are available for determining the error of a chronometer in port. The
principal of these will be given.
BT TIME SIGNALS.
314. In nearly all of the important ports of the world a time signal is made each dav at some
defined instant. In many cases this consists in the dropping of a time-ball— the correct instant being
given telegraphically from an ob-^ervatory. In a number of places where there is no time-ball a signal
may lie received on the instruments at tHe telegraph offices, wherebv mariners may ascertain the errors
of their chronometers. Such signals are to be had in almost every port of the United States.
The time signal may be given by a gun-fire or other sound, in which case allowance must \)q made
by the observer for the length of time necessary for the sound to travel from the point of origin to his
position. Sound travels l,090feet per second at 32° F., and its velocity increases at the rate of 1.15 feet
per second with each degree increase of temijerature. If V be the velocity of sound in feet per second
at the existing temperature, and D the distance in feet to Ix; traversed, y is the number of seconds to
be subtracted from the chronometer reading at the instant of hearing the signal, to ascertain the reading
at the instant the signal was made.
This method of obtaining the chronometer error consists in taking the difference between the
standard time and chronometer time at the time of observation and marking the result with appropriate
sign.
88 THE CHRONOMETER ERROR.
Example: A time-ball drops at S*" O" 0', G. M. T., and the reading of a clironometer at the same
moment is 4'' 57° 52».5. What is the chronometer error?
G. M. T., 5" 00"' 00"
Chro. t., 4 57 52 .5
Chro. error, — 2 07 .5
That is, clironometer slow 2'° 07'.5; chronometer cori-edion. additive.
BY TRANSITS.
315. The ni(i.«t accurate method of finding tlie clironometer correction is by means of a transit
instrument well adjusted in the meridian, noting the times of transit of a star or the limbs of the sun
across the threads of the in.struinent.
At the instant of the body's passage over the meridian wire, mark jfltt time by the chronometer.
The hour angle at the instant is O""; therefore the local sidereal time is er^I to the right ascension of
the body in the case of a star, or the local apparent time is 0'' in the case of the sun's center. By con-
verting this sidereal or apparent time into the corresponding mean time and applying the longitude, the
Greenwich mean time of transit is given. By comparing with this the time shown by chronometer the
error is found.
Example: 1879, May 9 (Ast. day), in Long. 44° 39' E., observed the transit of Arcturus over the
middle wire of the telescope, the time noted by a chronometer regulated to Greenwich mean time lieing
8" 05"' 33'.5. Kequired the error.
L. S. T. (R. A.*), 14'" 10"' 11'. 71
Long., - 2 58 36
G. S. T.,
R. A. M. S.,9"0",
11
- 3
11
07
35.71
42.69
Sid. int. from 0\
Reduction (Tab. 8),
S
03
1
53.02
19.27
G. M. T.,
Chro. t.,
8
8
02
05
33 . 75
33.50
Chro. fa.st,
9
59.75
Example: June 25, 1879, in Long. 60° E., observed the transit of botlt limbs of the sun oyer the
meridian wire of the telescope, noting the times bv a chronometer. Find the error of the chronometer
on G. M. T. " >
Transit of western limb, 8" 04'" 02". 5 Eq. t., 2'" 16\ 72
Transit of eastern limb, 8 06 20 . ——
H. D., -r 0».5,S2
Chro. time, loc. app. noon, 8 05 11 .25 Long., — 4''
8
05
11 .
25
0"
00"
2
' 00'
14
.59
4
02
00
14
00
.59
8
8
02
05
14
11 .
.59
,25
L. A. T., loc. app. noon, C' 00"' 00' Corr., — 2M28
Eq. t., - ^ -
Eq. t., 2"' 14-".59
L. M. T., loc. apji. noon, 02 14.59 Add to apparent tune.
Long.,
G. M. T., loc. app. noon,
Chro. time, loc. app. noon,
Chro. fast, 2 56 . 66
BY A SINGLE ALTITUDE ^TIME SIGHT).
316. The problem involved in this solution, by reason of its frequent application in determining
the longitude at sea, is one of the most important ones in Nautical Astronomy. It consists in finding
the hour angle from given values of the altitude, latitude, and polar distance. The liour angle thus
obtained is converted by moans of the longitude and equation of time in the case of the sun, or longi-
tude and right ascen.-ion in the case of other celestial bodies, into Greenwich mean time; and this, com-
pared with tiie chronometer time, gives the error.
317. It should be borne in mind that the most favorable position of the heavenly body for time
observations is when near the prime vertical. When exactlyin the prime vertical a small error in the
latitude produces no appreciable effect. Therefore, if the latitude is uncertain, good results may be
obtained by observing the sun or other body when bearing east or west. If observations are made at
the same or nearly the same altitude on each side of the meridian and the mean of the results is taken,
various errors are eliminated of which it is otherwise impossible to take account, and a very accurate
determination is thus afforded.
318. With a sextant 'and aititicial horizon or good sea horizon, several altitudes of a body should
be observed in quick succession, noting in each case the time as shown by a liack chronometer or com-
paring watch whose error upon the standard chronometer is known. Condensing the observation into
THE CHRONOMETER ERROR.
89
a brief interval justifies the assumption that the altitude varies uniformly witli the time. A very satis-
factory methofl is to set the sextant in atlvance at definite intervals of altitude and note the time as con-
tact is observed.
319. Correct the observed altitude for instrumental and other errors, reducing the apparent to the
true altitude.
If the sun, the moon, or a planet is observed, the declination is to be taken from the Nautical
Almanac for the time of the observation. If the chronometer correction is not approximately known
and it is therefore impossible
to determine the Greenwich
mean time of observation
with a fair degree of accu-
racy, the first hour angle
found will be an approximate
one; thedeclination corrected
by this new value of the time
will produce a more exact
value of the hour angle, and
the operation may be re-
peated until a sufficiently
precise value is determined.
320. In figure 41 there
are given:
AO = /(, the altitude of
the body O;
Yia. 41. DO = d, the declination;
and
QZ = L, the latitude of the place.
In the astronomical triangle POZ there may be found from the foregoing:
ZO = z, the zenith distance of the body, = 90° — h;
PO =p, the polar distance, = 90° ± d; and
PZ = co-L, the co-latitude of the place, =90° — J..
From this data it is required to find the angle OPZ, the hour angle of the V)ody,= (.
oy the formula:
* • ,,, cos i (h + h + p) sin i {h + p — h)
sm' i I =
This is given
If we let .s = J (/( -f L-^p), this becomes:
cos L sin p
sin i / = .y/ sec L coeecp cos « sin (s — h).
The polar distance is obtained by adding the declination to 90° when of different name from the
latitude anil subtracting it from 90° when of the same name. Like latitude and altitude it is always
positive.
If the sun is the body observed, the resulting hour angle i.'< the local apparent time and is to be
taken from the a. m. or p.' m. column of Table 44 according as the altitude is observed in the forenoon
or afternoon. If the moon, a star, or a planet be taken, the hour angle is always found in the p. m.
column.
Local apparent time as deduced from an observation of the sun is converted to local mean time by
the application of the equation of time; then, by adding the longitude if west, and subtracting it if east,
the Greenwich mean time is olitained.
The hour angle of any other body, added to its right ascension when it is west of the meridian at
observation or subtracted "therefrom when east, gives tne local sidereal time, which may be reduced to
Greenwich sidereal time by the application of the longitude, and thence to Greenwich mean time by
methods previously explained.
A comparison of the Greenwich mean time with the chronometer time of sight gives the error of
the chronometer.
Example: January 20, 1879, p. m., in Lat. 48° 41' 00" S., Ix)ng. 69° 03' 00" E., observed a series
of altitudes of the sun with a sextant and artificial horizon; mean double altitude, 59° 03' 10", images
approaching; mean of times by comparing watch, 4'' 40'° 56'; C — W, 7'' 23'" 25'; index correction,— 1' 30";
approximate chronometer correction, —0'" 10'. What was the exact chronometer error?
11"' ]4'.60
W. T.,
C— W,
4h40„, 5g. Obs. 2 alt. Q, 59° 03' 10" Dec,
7 23 25 I. C,
20° 08' 26". 6 S. Eq. t.
Chro. t., 04 21
App. C. C, - 10
App. G. M.T., 04 11 Corr.,
S. D.,
p. & r.,
Corr.,
—
1 30
2)59
01 40
29
+
30 50
14 43
29
45 33
-^ w. 17"
- 1' 34"
H. D.,
32". 5 H. D., + 0'.74
0^.07 G. M. T., O'.OV
2". 27
Corr. .
Corr.
Dec, 20° 08' 24". 3 S. Eq. t.,
P,
0».052
11"" 14'. 7
69° 51' 36"
{Add to apparent
time. )
14' 43"
90 THE CHRONOMETER ERROR.
h
L
29° 45' 33"
48 41 00
69 51 36
sec
cosec
cos
sin
.18031
.02740
9.43631
9.84483
L. A. T.,
Eq. t.,
L. M. T.,
Long.,
G. M. T.,
Chro. t.,
Chro. slow
4"
+
29"
11
■46'. 7
14.7
P
4
—4
41
36
01.4
12.0
2)148 18 09
74 09 05
44 23 32
s
s—h
04
04
49.4
21.0
2)19.48885
,
00
28.4
L. A.T., 4>'29"°46'.7 sin J f 9.74442
Ex.\mple: May 18, 1879, p. m., in Lat. 8° 03' 22" S., Long. 34° 51' 57" AV., observed a series of
altitudes of the star Arcturus, east of the meridian, using artificial horizon; mean double altitude,
60° 10'; mean watch time, 6" 50"" 32'; C— W, 2" 20'" 59'.5; 1. C, -J- 2' 00". Find the true error of the
chronometer.
W. T.,
c— w.
6" 50"' 32'
2 20 59.5
Obs. 2
LC,
ref.,
'',
sec
coseo
cos
sin
sin J t
alt.
*'
.00431
.026.50
9.44116
9.84096
60°
10' 00"
2 00
E. A
Dec.
;'.
., o\
)m o^
• *
+
, 14" 10'" IP. 7
19° 48' 33". 5 >."
Chro. t.
, 9 11 31.5
30° 04' 19"
8 03 22
109 48 34
160
30
12 00
06 00
1 41
109
141.
3
° 48' 34"
h
L
30
04 19
R. A. *,
H. A.,
L. S. T.,
Long.,
G. S. T.,
R. A. M. S
Sid. int. fn
Red. (Tab.
G. M. T.,
Chro. t.,
Chro. fast.
10"' 11».7
35 41
P
10
2
34 30.7
19 27.8
2)147 56 15
73 58 08
43 53 49
3" 35™ 41» E.
s
s-h
12
3
53" 58 .5
43 11.7
H. A.
2)19.31293
9.6.5647
9
10 46.8
1 30.2
9
9
09 16.6
11 31.5
2 14.9
BY EaUAL. AliTITTJDES.
321. The method of observing equal altitudes of the .same body on opposite sides of tlie meridian
is usually employed for accurate determinations of the chronometer error when the method of transits is
not available.
In the case of a star, the mean of the two chronometer times corresponding to the equal altitudes
is the chronometer time of transit; but in the case of the sun the mean of these times differs somewhat
froni the time of transit, since, in consequence of the change of the sun's declination between the
observations, the equal altitudes do not occur at equal intervals l>efore and after the transit.
The small correction necessary, when the sun is observed, to reduce the mean of the times to the
time of transit is called the equation of equal altitudes.
322. Eqi'al Altitudes of the Srx." — On shore, at a place whose longitude is accurateh/ known,
and whcjse latitude is approxivnatebi known, observe, with an artificial horizon, the same altitude both
before and after meridian passage, as near the prime vertical as convenient when the altitude is more
than 10°, noting the times. In low latitudes the method of equal altitudes will often give very accurate
results, even when tlie observations are quite near the meridian.
It ia most convenient, as well as conducive to accuracy, to take the observations in series, setting
the sextant in advance of the altitude and marking the time at the instant that the contact is observed;
about five or seven sights may compose a series, and several series may be observed, with the images of
the sun alternately approaching and separating; thus the mean of the results (working each series of
sights separately) will eliminate various possible errors. Ten minutes of double altitude will usually
be found a convenient interval for observing.
The sights may be taken on opposite sides of -the meridian for either upper or lower transit. If at
upper transit, the first altitudes are taken in the forenoon and the times recorded ; then in the afternoon
the times corresponding to the same altitudes are observed, the last altitude taken in the morning being
the first to come on in the afternoon; series taken with separating images in the forenoon should be
observed with approaching images in the afternoon, knd the reverse. If the time of lower transit is to
be determined, the first set of eights is taken in the afternoon of one day and the second set in the
forenoon of the next, care being taken as before to observe with images moving in opposite directions
on opposite sides of the meridian.
a Chauvenet's method.
THE CHRONOMETER ERROR.
91
323. The mean of the a. in. times call the .1. M. Chronometer Time, the mean of the p. m.
times, the P. M. Chronometer Time. If, instead of noting the times by the chronometer, a watch is
used (comparetl with the chronometer both before and after each observation), it will generally be
found necessary to make an allowance for its gain or loss on the chronometer, so as to obtain the exact
difference between the watch and chronometer at the instant of observation. The difference applied
to the mean of the watch times gives the. mean chronometer time the same as would have been found
by employing the chronometer directly.
The half sum of the A. M. and P. M. Chronometer Times is the Middle Chro)iometer Time; the P. M.
minus the A. M. time in the cas9 of observations for upper transit, or the A. M. mimM the P. M. time
for lower transit, gives the Elapsed Time. Twelve hours shoul<l be added to the chronometer time at
second observation in any case where the chronometer has passed XII'' during the interval between
eights.
Take from the Nautical Almanac, page I, the sun's declination, the hourly difference of declination,
and the equation of time, reducing each to the in.stant of local apparent noon by applying the differences
due to the longitude.
ilark norlli latitude and declination +, south latitude and declination — .
Mark hourly difference of declination when toward north -^, when toward south —.
Enter Table 37 with the elapsed time, and take out log A and log B, prefixing to each its proper
sign as given in the table at the head of the page.
To log A add the logarithm of the hourly diff. (Table 42) and the log tangent of the latitude (Table
44). Prefix to each logarithm the sign of the quantity it represents, and to their sum the sign which
results from the algebraic nmltiplication of the quantities. This sum is the logarithm (Table 42) of the
numl)er of seconds of time in ihe firat part of equation of equal altitudes, to l)e marked + or — , like its
logarithm.
To log B add the logarithm of the hourly diff. and the log tangent of the declination, marking the
signs as before. The sum is the logarithm of the second part of the equation of equal altitudes, to be
marked -r or — like its logarithm.
Combine the two part", having regard to signs, to obtain the eimation of equal altitudes; apply this,
with proper sign, to the Middle Chronometer Time and the result is the Chronometer Time of Local
Apparent Xoon. or Chronometer Time of Local Apparent Midnight, according as observations were taken on
opposite sides of the meridian at upper or at lower transit.
Apply tlie equation of time (adding when it is additive to mean time, otherwise subtracting); the
result is the Chronometer Time of Local Mean Noon, or Midnight, which, if the chronometer is regulated
to local time, will be 12'' 0"' 0» when the chronometer is right, more than 12'' when fast, less than 12''
when slow.
If the chronometer is regulated to Greenwich time, apply the longitude (in time) to the chronom-
eter time of mean noon (subtracting in west, adding in east longitude) ; the result will be more or less
than ]■_"', according a« the chronometer is fast or slow.
E\ampi.k: April l:?, 1879, at a place in I^t. 30° 25' X., I^jng. 5" 2.1™ 42» \V., oteerved the following
equal altitudes of the sun with a sextant and artificial horizon, noting the times by a watch compared
with a chronometer regulated to Greenwich mean time. What is the error of the chronometer?
A. M. COMPARISONS.
Chro., 21
Watcli, 8
22"
52
■30'
02
p. M. COMPAF
Chro.,
Watch,
C-W,
Chro.,
Watch,
C-W,
AI.TS.
91° 00'
10
20
30
40
Mean, W. T., P. M
C-W,
P. M. Chro. T.,
A. M. Chro. T..
Elapsed Time,
Eq. t.,
H. D.
Long.,
Corr.,
E.,. t.,
{yfinut! tome
IISONS,
8i>04'
2 34
30- Dec, 9° 00' 54".l N.
H. D. (18th),+54".40
H. D. (14th),+.54 .03
H T) Rf tinnn 4- 51" "Vf
C-W,
5
30
28
5 30
29 Ixmg., + 5l'.43
Diff., 24hrs., - .37
2'
9
' -Mt'
SI" 33" 30« (^,^||,|, f294".9«
3 03 01 " U'-55".0
Diff., 1 hr., -0".015
Watch,
2(i
02
Diff., 5'.43, -0 .08
C-W,
b
30
28
5 30
29 Dec, 90 05' 49" X.
H.D.atnoon,+.54".32
WATCH, A. M.
9'' 12" 30-
12 ffi
13 20
13 4.5
14 10
WATCH, P. M.
Oh 45™ 45'
45 20
44 55 Tab. 37 log Af-)9.4445
44 30 H. D. +.54".32 log ( + )1.7360
44 05 I.at. +30° 2.5' tan (+) 9.7687 (
211 44" 5.5' 1st I"art-8'.88 log (-)0.9482
+ 5 30 29 2d Part+1 .81
8 15 24 Eq.eq.l _7 „
- 2 43 48 alt. 1
logB( + )9.3193
log (+) 1.73.50
; -t 906' tan ( + )9.20-15
Mean, W. T., A.
C-W,
M., '>
.+ 5
13'"
30
20-
28
log ( + ) 0.2588
A. M. Chro. T.,
P. M. Chro. T.,
+ 8
43
15
4S
24
2)10
59
]2
5 31
36
Mid. Chro. T.,
Eq. fq. alt,,
.5
29
3(i
7.1
0'" 35>.02
+ o-.es
+ 5h.43
Chro. t. L. A. Noon, .'i
Eq. t..
29
28.9
31.5
+ 3'.53
0" 31'.5
an tfme. )
Chro. t. L. M. N
Long.,
oon, 5
- 5
28
25
67.4
42.0
Chro. fa.«t.
03
1.5.4
92
THE CHRONOMETER ERROR.
324. A quicker method of solving the same problem" is available when results are not required to
be accurate to the fraction of a second.
If // is the change of altitude in minutes of arc, due to the total change in declination in the
time elapsed between sights (the latitude and hour angle remaining the same), and t' the number of
seconds it requires for the sun to change its altitude one minute of arc, then:
Equation of equal altitudes = o ''' X !'■
Table 25 gives the change of altitude of an object arising from a change of 100 seconds In declination
at various altitudes, declinations, and latitudes. By multiplying the appropriate quantity taken from
this table by the total change of declination between sights, dividing by iOO, and converting the result
from seconds to minutes of arc, // is found. It is marked with the sign indicated in the table.
By dividing the number of seconds of time between the tirst and last sights of one of the series by
the number of minutes difference of altitude, we find ('. When the sights are taken on opposite sides
of the upper meridian t' is minus; for the lower meridian it is plus.
AVhen the artificial horizon is used, if /' is computed on a basis of the change of the double altitude,
its value is only half of the true one and the second term of the equation becomes // X t' instead of as
given above.
The example given in illustration of the preceding method when worked by this method is as
follows:
Change in declination tetween sights = H. P. X elapsed time = 54".32 X S^.oS = 300".
Change in altitude due to 100" declination (Tab. 25) = -f 56".
100 X 60
2''45'"45' -
2"44""05"
'' ~ 91° 40' — 91° OC
Eq. equal alt. = + 2.80 X -
_ UK)"
^~ 40'
2'.5 = - 7'.00.
= - 2».5.
325. If equal altitudes of a planet wereob.oerved, the correction due to change of declination could
be computed as in the case of the sun. It is not ordinarily expedient to use a planet, however, for if
night sights are to l)e taken facility of working would make it preferable to employ a fixed star.
On account of its rapid and excessive change of declination the moon would iiever be observed for
equal altitudes.
326. Equal Altiti'des op x Fixed Star. — In selecting stars for this observation, it is to be
remarked that the nearer to the zenith the star passes the less may the elapsed time be; and when a
star passes exactly through the zenith the two altitudes may be taken w ithin a few minutes of each
other. But, with the ordinary sextants, altitudes near 90° can not be taken with the artificial horizon,
as the double altitude is then nearly 180°. A limit is thus placed upon the extreme altitude that it
is practicable to observe.
The sextant should be set and the coincidences of the two images of the star awaited, as in the case
of the sun's limb, and the times by chronometer or watch noted as usual.
327. Take the mean of the times before the meridian passage as the ^1. j1/. Chronometer Time, and
the mean of those after the meridian passage as the I'. M. Chronometer Thtu. The mean of these two
(adding 12'' to the later one in case the chronometer has passed Xll" in the interval between sights) is
the Chronometer Time of Star's Transit. At the instant of transit the local sidereal time will equal the
right ascension of the star in case of the upper transit, or it will equal the right ascension 7)/!(,< 12" in
case of the lower transit. By converting local sidereal into Greenwich sidereal and thence into Green-
wicli mean time in the usual way, the chronometer error is found.
Exa.mple:— June 8, 1879, at Cape Town, Lat. 33° 56' S., Ix)ng. 18° 28' 40" E., using sextant and arti-
ficial horizon, observed equal altitudes of star Antares before and after upper transit, as stated below.
Required the clironometer error on Greenwich mean time.
Chro. t.,
Chro. t.,
t. Transit,
T. Transit,
SlOW;
Chro.
71, .-jO"'
7 32
7 32
A.M.
10'. 5
35.0
59.3
Altitudes.
125° 30'
40
50
P. M. Chro. t.,
L. S. T.(R. A. *),
Long.,
G. S. T.,
E. A. M. S., 0",
Sid. int. from 0",
Red. (Tab. 8),
G. M. T.,
Chro. P. M.
11" .34°' 20'. 3
11 33 56.0
11 .33 32.0
A. M.
F. M.
11
32
33
34.9
56.1
11 33 56.1
!)19
06
31.0
16" 22"' 03^5
1 13 54 7
Chro.
G. M.
9
9
33
59
15.5
30.9
15 08 08.8
5 05 59.4
Chro.
26
15.4
10 02 09.4
— 1 38 .5
10 00 ,30.9
« Suggested by Commander W. E. Sewell, IJ. S. Navy.
THE CHRONOMETER ERROR. 93
328. Degree op Depexdence. — An error of 5' in the latitude would not affect the corresponding
part of the equation of equal altitudes by more than one-hundredth of its amount in the most unfavorable
case, and in general would have no sensible effect. It is one of the advantages of the equal altitude
method, therefore, that it does not require an accurate knowledge of the latitude. It is also jplain that
errors in the longitude affecting the declination and its hourly difference produce but small propor-
tionate effects upon the computed equation. The absolute error of the chronometer on Greenwich will
be affected by the whole error in the longitude, but the rate will still be correct. Hence, we conclude
that by this method the chronometer may be accurately rated at a place whose latitude and longitude
are both imperfectly known.
The chief source of error is in the observation itself. The best observers with the sextant can not
depend on the noted time of a migle contact within W-b, and hence the intervals between the successive
chronometer times (which, if observations could be perfectly taken, would be sensibly equal) may
differ 2'. But the greatest probable error of the chronometer time of sun's or star's transit, from the
mean of six such observations on each side of the meridian, is found to be not more than 0'.2, provided
the rate of the chronometer between the observations is uniform.
94
LATITUDK.
CHAPTER XII.
LATITUDE. '^ g^v^ ;,. ^ -?^.^- .'
"1.
JZi ^-c "y-z^T^t^i.^ »
^ :::iaJ^/c^.^'4- . /.
BY MERIDIAN ALTITUDE.
329. The latitude of a place on the surface of the earth, being its angular distance from the equator,
is measured by an arc of the meridian between the zenith and the equator; lience, if tlie zenith distance
of any heavenly body when on the meridian be known, together
with the declination of the body, the latitude can thence be tound.
I^et figure 42 reprei^ent a projection of the celestial sjihere on
the plane of the meridian NZS; C, the center of thesphere; NS, the
horizon; P and P', the poles of the sphere; QCQ', the equator; Z,
the zenith of the observer. ' Then, by the above definition, ZQ will
be the latitude of the observer; and NP, the altitude of the elevated
pole, will also equal the latitude.
Let A be the position of a heavenly body north of the equator,
but south of the zenith; QA = </, its declination; AS = /(, its altitude;
and ZA = ; = 90°— /(, its zenith distance.
From the figure we have:
QZ = QA + AZ, or
L-=d-i-z.
Puj, 42. By attending to the names of z and rf, marking the zenith dis-
tance north or south according as the zenith is north or south of the
body, the alx)ve equation may be consideretl general for any position of the body at upper transit, as
A, A', A".
In ease the body is below the pole, as at k.'" — that is, at its lower culmination — the same formula
may be used by substituting 180°— rf for rf. Another solution is given in this case by observing that:
NP = PA'" + NA'", or
L =/> + ''•
330. A common practice at sea is to conunence ol)serving the altitude of the sun's lower limb
above the sea horizon about 10 minutes before noon, and then, by moving the tangent-screw, to.follow
the sun as long as it rises; as soon as the highest altitude is reached, the sun begins to fall and tlie lower
limb will appear to dtp. When the sun dips the reading of the limb is taken, and this is regarded as
the meridian observation.
It will, however, be found more convenient, and frequently more accurate, for the observer to have
his watch set for the local apparent time of tlie prospective noon longitude, or to know the error of the
watch thereon, and to regard as the meridian altitude that one wliich is observed when the watch indi-
cates noon. This will save time and try the patience less, for when the sun transits at a low altitude it
may remain "on a standi" without appreciable decrease of altitude for several minutes after noon ; more-
over, this method contribiites to accuracy, for when the conditions are such that the motion in altitude
due to change of hour angle is a slow one, the motion therein due to change of the observer's latitude
may be very material, and thus have considerable influence on the time of the sun's dipping. This
error is large enough to take account of in a fast-moving vessel making a course in which there is a goo<l
deal of northing or southing.
In observing the altitude of any other heavenly liody than the sun, the watch time of transit
should previously he computed and the meridian altitu<le taken by time rather than by the dip. This
is especially important with the moon, whose rapi<l motion in declination n>ay introdnce still another
element of inaccuracy.
331. The watch time of transit for the sun, or other heavenly body, may ))e found by the forms
given below, knowing the prospective longitude, the chronometer error, and the amount that the watch
IS slow of the chronometer.
For the Sun.
Fur other Bodies.
L. A. T. noon.
Long. (-1- if west),
G. A. T.,
Eq. t,
G. M. T.,
C. C. (sign reversed),
Chro. time,
C-W,
Watch time noon,
0" 00"" 00"
L. S. T. transit.
Long, (-f- if west),
G. S. T.,
R. A. M. S., 0^
Sid int. from 0'',
Ked. (Tab. 8),
G. M. T.,
C. C. (sign reversed)
Chro. time,
C-W,
Watch time transit.
(Right ascension.)
. — __ LATITUDE. ' - 95
' .^/-/r< / .
332. From the observed altitude deduce the true altitude, and thence the true zenith distance.
Mark the zenith distance North if the zenith is north of the body when on the meriilian, South it the
zenith ia south of the body.
Take out the declination of the body from the Nautical Almanac for the time of meridian passage,
having regard for its proper sign or name.
The algebraic sum of the declination and zenith distance will be the latitude. Therefore, add
together the zenith distance and the declination if they are of the same name, but take their difference if of
opposite names; this sum or difference will be the latitude, which will be of the same name as the greater.
Ex.\mple: At sea, June 21, 1879, in Long. 60° W., the observed meridian altitude of the sun's lower
limb was 40° 4'; sun bearing south; I. C.,+3'0"; height of the eye, 20 feet; required the latitude.
Obs. alt., 40° 04' 00"' S. D., + 15' 46" Dec, 23° 27' 20". 5 N.
Corr., + 13 21 I. C, + 3 00
A,
40 17 21
dip,
p.&r.,
+ 18 46
49° 42' .39" N.
23 27 22 N.
— 4' 23"
, - 1 02
H. D., + 0".32
Long., 4''.
Corr., + 1".28
73 10 01 N. - 5 25
Corr., + 13' 21"
Dec, 23° 27' 22"
Example: At sea, April 14, 1879, in Long. 140° E., the observed meridian altitude of the sun's lower
limb was 81° 15' 30"; sun bearing north; I. C.,— 2' 30"; height of the eye, 20 feet.
Dec, 9° 22' .35". 4 N.
Obs. alt.,
Corr.,
81°
15'
8
30"
59
S.
N.
N.
S. D.,
dip,
p. &T..
I. C,
Corr.,
4- 15' 59'
- 4 23
, - 07
- 2 30
A,
81
24
29
d.
S°
9
35'
14
31"
11
- 7 00
L,
38
40
+ 8' 59'
H. D., + .54''.03
Long., — 9\33
Pnrr / ^04".!
e.orr., - |g, 24". 1
Dec, 9° 14' 11" N.
Example: At sea, May 15, 1879, Long. 0°, the observed meridian altitude of the sun's lower limb
was 30° 13' 10"; sun liearing north; I. C, + 1' 30"; height of the eye, 15 feet.
Obs. alt., 30° 13' 10" P. D., + 15' 51" Dec, Gr. 0^ 18° 50'48".5 N.
Corr., 4- 12 02 I. C, + 1 30
30 25 12
z, .59° 34' 48" S.
d, 18 50 49 N.
40 43 59 S.
_!-
17
21
dip,
—
3'
48"
p. &T.^
1
31
5
19
^^_
^^
Corr.,
+
12'
02"
Example: Januarv 1, 1879, the observefl meridian altitu<le of Sirius was h?° 2.3' 40", bearing south;
I. C., + 5' 0"; height o'f the eye, 17 feet.
Dec *, 16° 33' 04" S.
Obs. alt.,
Corr.,
53°
23' 40"
15
I.e.,
dip,
ref. ,
Corr.,
T 5' 00"
- 4' 02"
43
h.
53
23 55
z.
36°
16
.36' 05" N.
33 04 S.
- 4 45
- 0' 1.5"
L,
20
03 01 N.
Example: June 13, 1879, in Long. 65° W., and in a high northern latitude, the meridian altitude of
the sun's lower limb was 8° 16' 10", below the pole; height of the eye, 20 feet; I. C, 0' 00".
Greenwich apparent time of lower culmination, June 13, 16'' 20'"' { = Long. + 12'") .
- 1.5' 47" Dec, 23° 13' 03".8 N.
Obs. alt., 8° 16' 10"
Corr., -\- 5 12
S. D.,
dip,
_•>. <& r.
/(, 8 21 22
z, 81° 38' 38" S.
180° -J, 1.56 44 36 N.
Corr.,
75 0.5 58 N.
AlkmalUe method,
h, 8° 21' 22"
p, 66 44 36
L, 75 05 58 N.
— . /
4 23
4> 12
10 35
5 12
H. D.
<i. M.
T.
+
8". 58
16" .33
Corr.,
H
140".5
2' 20". 5
Dec,
23°
15' 24"
P,
66°
44' 36"
N.
180°— rf, 1.56° 44' 36"
96
LATITUDE.
Example: June 26, 1879, in Long. 80° W., the observed meridian altitude of the moon's upiier limb
was 59° 6' 40", bearing south; I. C, -i- 2' 0"; height of the eye, 19 feet.
h, 59° 18' 00"
z, 30° 42' 00' N.
d, 4 51 06 S.
L, 25 50 54 N.
Obs. alt.,
I.e.,
S. D.,
Aug.,
dip,
l.st Corr.,
+ 2' 00"
_
16' 03'
-
H
-
4 16
-
20 33
G. M. T., Gr. trans., .!>■ iT^.O
Corr. for Long (Tab. 11),+ 11 .0
Dec. (ll'), 4°51'36".5 S.
L. M. T., local trans.,
Long.,
5 38 .0
+ 5 20 .0
M. D.,
No. min.,
G. M. T., local trans., + 10 58 .0
Corr.,
Dec.,
15''
'.07
2"
.0
30"
M
Approx. alt., 58° 48' 07"
p.d-r. (Tab. 24), + '29 63
Hor. Par.,
39 18 00
Example: At sea, September 16, 1879, in Long. 75° E., the observed meridian altitude <if .Tupitet
was 51° 25' 24", bearing north; I. C, +3' 0"; height of the eye, 16 feet.
Obs. alt., 51° 25' 24"
Corr., - 1 41
h, 51 23 43
par., +0'01"
I.e., +3 00
G.->r. T., Gr. trans.,
Corr. for Long.,
lO^ 49».8
f .9
38° 36' 17" S.
10 44 59 S.
dip,
ref..
+ 3 01
- 3' 55"
- 47
L. M. T., local trans., 10 50 .7
Long., - 5 00 .0
G. JI. T. local trans.
49 21 16 S.
-4 42
Corr., - 1'41"
Dec,
H. D.,
G. M. T.,
Corr.,
Dec,
H. r.,
I>ar. (Tab.l7) ,
10°44'20".5 S.
G".58
51.84
38".43
2".2
1"
333. Constant. — In working a meridian altitude, especially the daily noon observation of the sun,
it is frequently a convenience to so arrange the terms of the problem thkt all computation, excepting
the application of the observed altitude, is completed beforeliand ; then the ship's latitude will be known
immediately after the sight has been taken, it being necessary only to add or subtract the altitude.
It is assumed that the noon longitude will be sufficiently accurately known in advance to enable the
navigator to correct the declination; also the approximate meridian altitude to correct the parallax and
refraction; if the latter is not known, it may readily be found from the declination and approximate
latitude.
Generally speaking,
Lat. = Zenith distance -- Dec,
= 90° - True alt. !- Dec.,
= 90° — (Obs. alt. + Corr.) -^ Dec,
= (90° -i^ Dec - Corr.) - Obs. alt.,
in which the quantity (90° -J- Dec. — Corr.) may be termed a Constant for the meridian altitude of the
day, as it remains the same regardless of what the observed altitude ma^y prove to be. The constant
having been worked up before the observation is made, the latitude will be known as soon as the
observed altitude is applied.
To avoid the confusion that might arise from the necessity of combining the terms algebraically
according to their different names, it may be convenient to divide the problem into four cases and lay
down rules for the arithmetical combination of the terms, disregarding their respective names as follows:
Case I. Ijat. and Dec. same name, Lat. greater, -f- 90° ~r Dec — Corr. — Obs. alt.
Case If. Lat. and Dec. same name, Dec. greater, — 90° + Dec. H- Corr. + Obs. alt.
Case III. Lat. and Dec. opposite names, H- 90° — Dec. — Corr. — Obs. alt.
Case IV. Lat. and Dec same name, lower transit,-^ 90° — Dec. -,- Corr. -f Obs. alt.
The correctness of such an arrangement will become readily apparent from an inspection of figure 42.
The assumption has been made that the correction to the observed altitude is positive; when this is
not true the sign of the correction must be reversed.
As examples of this method, the first, second, third, and fifth of the examples previously given
illustrating the meridian altitude will be worked, using the constant; the details by which Corr. and
Dec. are obtained are omitted, being the same as in the originals.
Dec,
Corr.,
1st Exa.mple.
Case I.
+ 90° 00' 00"
+ 23 27 22
- 13 21
Dec,
Corr.,
2d Example.
Case II.
-90° 00' 00"
+ 9 14 11
+ 8 59
Dec,
Corr.,
3d Example.
Case in.
+90° 00' 00"
-18 50 49
- 12 02
Dec,
Corr. ,
OTH Example.
Case IV.
+90° 00' 00"
-23 15 24
^ 5 12
Constant,
Obs. alt,
Lat.,
-113 14 01
- 40 04 00
Constant, -
Obs. alt., -
80
81
36 50
15 30
Constant, -
Obs. alt.,-
70
-30
57 09
13 10
Constant, -
Obs. alt.,-
-66 49 48
- 8 16 10
73 10 01 (N.) Lat.,
38 40 (N.) Lat,
40 43 59 (S.) Lat,
75 05 58 (N.)
LATITUDE. 97
BY BEDTJCTION TO THE MEBIDIAN.
334. Should the meridian observation be lost, owing to clouds or for other reason, altitudes may be
taken near the meridian and the times noted by a watch compared with the chronometer, from which,
knowing the longitude, the hour angle may be deduced.
If the observations are within 26"' from the meridian, before or after, the correction to be applied
to the observed altitude to reduce it to the meridian altitude may be found by inspection of Tables 26
and 27. Table 26 contains the variation of the altitude for one minute from the meridian, expressed in
seconds and tenths of a second. Table 27 contains the product obtained by multiplying the square of
the minutes and seconds by the change of altitude in one minute.
Let a = change of altitude (in seconds of arc) in one minute from the meridian:
H = meridian altitude;
/t = corrected altitude at observation; and .;
t = interval from meridian passage.
The value of the reduction to the meridian altitude of each altitude is found by the formula:
H = ft -f at',
a being found in table 26, and afi in Table 27; hence the following rule:
Find the hour angle of the body in minutes and seconds of time. Take from Table 26 the value of
o corresponding to the declination and the latitude. Take from Table 27 the value of at" corresponding
to the (I thus found and to the interval, in minutes and seconds, from meridian passage. This quantity
will represent the amount necessary to reduce the corrected altitude at the time of observation to the
corrected altitude at the meridian passage; it is always additive when the body is near upper transit,
and always to be subtracted when near lower transit.
If the mean of a number of sights is to l)e taken, determine each reduction separately, take the
mean of all the reductions, and apply it to the mean of the altitudes; it is incorrect, in such a case, to
take the mean of the times and work the sight with this single value of /. The differences of altitude
being small, the parallax and refraction will be sensibly the same for all, and one computation of the
correction to the observed altitude will suffice.
Knowing the meridian altitude, the latitude is to be found as previously explained.
335. When several sights are taken, the most exjjeditious method of calculating will be to find
first the watch time of transit, and thence oljtain the hour angle of each observation by comparing the
watch time of observation. The watch time of transit may be found as already explained (art. .331)
for computing that quantity as a guide iu taking the meridian altitude, but the hour angle thus obtained
is subject to a correction. The differen(« between wat<'h time of transit and watch time of observation
gives the watch time — that is, the mean time^elapsing between transit and observation. A fixed star
covers in that time an angle corresponding to the sidereal and not to the mean time interval, and a
reduction should be made accordingly to give its true hour angle at the instant of observation. A
planet's hour angle should be corrected in the same way (for we may disregard its very small change
m right ascension). The correction may be entirely neglected in the case of the sun, as the difference
between mean and apparent time intervals is immaterial. The reduction of the hour angle in the case
of the moon be<tomes rather cumbersome, so much so that it is betterto find the hour angle of this body
by the more usual method of converting watch time to G. M. T., and thence to L. S. T., and finding
the difference between the latter and the R. A. ; an additional reason for this is that the G. M. T. of
observation must be known exactly, with the moon, for the correction of the declination (art. 338).
336. Table 26 includes values of the latitude up to 60°, and those of the declination up to 63°,
thus taking in all frequented waters of the globe and all heavenly bodies that the navigator is likelv to
employ. No values of a are given when the altitudes are above 86° or below 6°, as the method of reduc-
tion to the meridian is not accurate when the body transits very near the zenith, and the altitudes
themselves are questionable when very low. In case it is desired to find the change of altitude in one
minute from noon for conditions not given in .the tables, it may be computed by the formula:
_ 1"^9635 cos L cos d
sin (L — d)
In working sights by this method where great accuracy is required, as in determining latitudes on
shore for surveying purposes, it is well to compute the a rather than to take it from the table, as one
is thus enabled to employ the value as found to the second decimal i)lace.
Due regard nmst be paid to the names of the declination and latitude in working this formula; if
they are of opiwsite names, the declination is negative, antl L and d should be added together to obtain
L — (/.
337. Table 27 contains values of aC up to the limits within which the method is considered to
apply with a fair degree of accuracy. It must not be understood that the plan of reduction to the
meridian is not available for wider limits, but it would seem preferable to emplov the <p' <p" formula,
described hereafter, when the hour angle falls beyond that for which the table is computed. On the
other hand, the reduction is not exact in all cases covered by the table; while sufficiently so for sea
navigation, the limits given are far too wide for the precise determinations required in surveying, where
the aim should l)e to observe bodies under such conditions that the total reduction ai:' shall not exceed 1'.
33§. It should be ke^t clearly in mind when employing the method of reduction to the meridian
that the resulting latitude is that of the ship at the instant of observation, and to bring it up to noon
the run must be applied. The declination should properly be corrected for the instant of observation;
with the sun or a planet, it is sufficiently accurate to use the declination at meridian passage, unless the
interval from the meridian be quite large; but the moon's declination changes so rapidly that the exact
time of observation must be used iu its correction w-hen working with this body.
24972°— 12 7
98
LATITUDE.
Example: In latitude 47° S., having previously worked up the constant for meridian altitude,
78° 42' 10", observed altitude of sun near meridian, 31° 11' 50"; Dec. 11° N.; watch time, 11'' 40'" 21%
watch fact of L. A. T., 7'. Find the latitude.
Watch time, ll''40'»21'
Watch fast, 07
Obs. alt, 31° 11' 50"
aP, -(- 10 24
a (Tab. 26),
o<'''(Tab.27),
l."6
f ]."0 =
• 6 =
L. A. T., 11 40 14
Mer. alt., 31 22 14
Constant, 78 42 10
6' 30"
3 54
i, 19'°46»
1 R —
1A OJ
Lat.,
47 19 56 S.
E.x.\mple: At sea, July 12, 1879, in Lat. 50° N., Long. 40° W., observed circum-meridian altitude of
the sun's lower limb, 61° 48' 30", the time by a chronometer regulated to (Greenwich mean time being
2" 41-" 39'; chro. corr., -2'" 30'; I. C, -3' 0"; height of the eye, 15 feet. Find the latitude.
Chro.t.,
C. C,
2''
41'
2
'39>
30
Q
Corr.,
f>,
S. D.,
dip,
p. & r.,
I. C,
Corr.,
h,
a(\ +
61°
+
48' 30"
8 31
Dec,
H.D.,
Long.,
Corr.,
Dec,
22°
00'
2.S". 2
N.
N.
« (
aC
Eq. t.,
H. D.,
Ix)ng.,
Corr. ,
Eq. t.,
[Subtract
time. )
Tab. 26), 2.'
2.
(Tab. 27), °-
5"' 17».99
-
20". 7
2". 7
-r- 0^.32
2\7
G.M.T.,
Eq. t..
2
39
5
09
19
61
57 01
T
15' 46"
~
55". 9
86
G.A.T.,
Long.,
, .2
_ 2
33
40
50
00
-
3 48
2?
3 00
21°
59'
27"
5"' 18'.9
from mean
L.A.T.,
11
53
50
t,
6
10
~
7 15
61° 57'
1
8 31
01"
35
''5
"0 = V 16"
5 = 19
H, 61 58 36
12. 5 = 1 35
L,
28 01 24 N.
21 59 27 N.
50 00 51 N.
Example: May 31, 1879, in Lat. 30° 25' N., Long. 5" 25"' 42' W., about 9 p. m., observed with a
sextant and artificial horizon a series of altitudes of Spica; mean observed double altitude 98° 06' 34";
noted times as enumerated below by a watch compared with a chronometer which was 2°' 33' fast of
G. M. T.; C-W, 5" 29'" 40"; I. C, ~3' 00". Find the latitude.
R. A. * (L. S. T.tiansit) , 13" 18'" 52'.2
Long.,
r! a". >i'. S. Gr. 0",
Sid. int. from C,
Red. (Tab. 8),
G. M. T.,
C. C. (sign reversed),
Chro. time transit,
C^W,
Watch time transit,
5 25 42
LC,
18 44 34.2
4 34 26.9
14 10 07.3
- 2 19 .4
ref.
h,
14 07 47 .9
+ 2 33
14 10 20.9
- 5 29 40
8 40 41
Intervals from transit
Watch times.
8" 31" 18'.0
33 19.5
36 07.0
38 50.0
41 07.5
43 45.5
45 46.0
47 33.0
51 12.5
Meantime.
— 9"'23'.0
7 21.5
4 34.0
1 51.0
-r 26.5
3 04.5
5 05.0
6 52.0
10 31.5
Sid. time.
— 9"" 24'
7 23
4 35
1 61
+ 27
3 05
5 06
6 53'
10 33
k, 98°
06' 34"
3 00
R. A. *,
Dec,
a (Tab. 26),
13'' 18"' 52'.2
10° 3"'' 04" S
2)98
49
03 34
01 47
50
2". 5
49
00 57
ae (Tab. 27).
£o 05* I5 '
2' 56" 0' 44" 3' 40"
1 49 27 2 16
42 10 52
07 01 08
01 00 01
19 04 23
52 13 1 05
1 35 23 1 58
3 42 55 4 37
49° 00' 57"
1 40
H, 49 02 37
2,
d,
40 57 23 N.
10 32 04 S.
L, 30 25 19 N.
9)15 00
1 40
LATITUDE.
99
Example: Aueust 6, 1S79, Lat. 59° S., Long. 175° 27' E., during evening twilight, observed an
Jiltitude of Achernar, near lower transit, 26° 52'; watch time, 4" 31'" 12'; C - W, 0" 18- 07-; chro. fast of
G. M. T., 12'" 42'; I. C, + 1' 20"; height of eye, 24 ft. Find hour angle by both methods; thence the
latitude.
R. A. * -r 12" \
L. S. T. lower trans./
1.3''33"'lo».4
Long.,
RA'.M.'s. Gr.5«0",
Sid. int..
Red. (Tab. 8),
G. M. T.,
C. C. (sign reversed ),+
Chro. time,
C-W,
Watch time transit,
Watch time obs.,
. (Mean time,
iSid. time,
Obs. alt. *,
— 11 41 48
LC,
dip,
rel.,
Corr.,
at',
H,
P,
+
1
- 8
51
54
27.4
39.8
16
56
2
47.6
46.6
16
t-
54
12
01.0
42
5
-
06
18
43
07
4
4
48
31
36
12
26°
17
17
52'
24
27
00"
1'
20"
4'
1
48"
55
6
43
5' 23"
26°
46'
3
37"
03
26
32
43
09
.34
32
Watch time,
C-W,
Chro. t.,
C. C, ~
G. M. T. 5",
R. A.M.S. Gr.5''0", +
Red. (Tab. 9), +
G. S. T.,
Long., +
L. S. T.,
R. A. * + 12",
4" 31° 12'
+ 18 07
4 49
12
19
42
16 36
8 54
2
37
39.8
43.7
1 34
11 41
00.5
48
13 15
13 33
48.5
15.4
17 27
R. A. *,
Dec,
P,
a (Tab. 26),
at' (Tab. 27),
1" 33°' 15'. 4
57° .50' 28" S.
32° 09' 32"
0".6
3' 03"
58 53 06 S.
BY A SINGLE ALTITUDE AT A GIVEN TIME.
339. This observation should be limited to conditions where the body is within three iumrs of
meridian passage and where it is not more than 45° from the meridian in azimuth; also where the
declination is at least 3°. On the prime vertical the solution by this method is inexact, and when the
hour angle is 6'", or the declination 0°, it is inii)racticable.
The problem is: Given the hour angle, declination, and altitude, to find the latitude. The solution
is accomplished by letting fall, in the usual astronomical triangle, a perpendicular from the body to the
meridian, and considering separately the distances on the meridian, from the pole and zenith, respec-
tively, to the point of intersection of the perpendicular; the sum or difference of these distances is the
co-latitude.
Following the usual designation of terms and introducing the auxiliaries <p' and tp", the formulae are
as follows:
tan <f/'= tan d sec t;
cos ^ = sin h sin ip" cosec d;
L=^ + <p".
The terms <p' and <p" will haye different directions of application according to the position of the
body relatively to the observer. From a knowledge of the approximate latitude, the method of com-
bining them will usually be apparent; it is better, however, to have a definite plan for so doing, and
this may be ba.sed upon the following rule:
Mark (p" north or south, according to the name of the declination; mark cp/ north or south, accord-
ing to the name of the zenith distance, it being north if the body bears south and east or south and west,
and south if the body bears north and east or north and west. Then combine g/' and tp' according to
their names; the result will be the latitude, except in the case of bodies near lower transit, wnen
180° — ?/' must be substituted for ip" to obtain the latitude.
It may readily be noted that if we substitute <p" for declination and ip' for zenith distance, the
problem takes the form of a meridian altitude; indeed, the method resolves itself into the finding of
the zenith distance and declination of that point on the meridian at which the latter is intersected by a
perpendicular let fall from the observetl body.
The time should be noted at the instant of observation, from which is found the local time, and
thence the hour angle of the celestial object.
100
LATITUDE.
If the sun is observed, the hour angle is the L. A. T. in the case of a p. m. sight, or 12'' - - L. A. T.
for an a. m. sight. If any other body, the hour angle mav be found as hitherto explained.
E.xample: June 7, 1879, in Lat. 30° 25' N., Long. 81°' 25' 30" W., by account; ehro. time, 6" 22"" 52»;
obs. Q 75° 13', bearing south and east; I. C. —3' 00"; height of the eye, 25 feet; chro. corr. —2°' 36*.
Find the latitude.
Chro. t,
CO.,
G.M.T.,
Eq. t,
G.A.T.,
Long. ,
e" 22™ 52'
2 36
6
20
16
+
1
26
6
21
42
- 5
25
42
Obs. alt. Q, 75° 13' 00" Dec,
+ 7 40
H.D..
TAT-/ / 0" 56°' 00' E.
Corr.,
h,
S.D.,
dip,
p. &r.,
LC,
Corr.,
22° 45' 09".9 X. Eq. t., !■» 28'.85
75 20 40 G.M.T., H
Corr. , <
14".6
6". 3
H.D., - 0".46
G.M.T.,+ 6\3
+ 15' 48"
4' 54"
14
3 00
91". 98
1' 32"
Corr.,
2". 85
Dec.,
22° 46' 42" N.
Eq.t, l'"26'.
(Add to meantime. )
8 08
7' 40"
t
d
14°
22
00' 00"
46 42
sec
tan
h
75
23
20 40
24 07 N.
tan
f/
7
02 SON.
Lat.
30
26 37 N.
.01310
9.62317
9.63627
cosec .41210
sin 9.98563
sin 9.59898
cos 9.99671
Example: May 28, 1879, p. m., in Lat. 6° 20' S. by account, Long. 30° 21' 30" W.; chro. time,
7'' 35'° 10*; observed altitude of moon's upper limb, 75° 33' 00", bearing north and east; I. C, —3' 00";
height of eye, 26 feet; chro. fast of G. M. T., 1"" 37".5. Required the latitude.
Chro. t.,
C. C,
G. M. T.,
R. A. M. S.,
Red. (Tab. 9),
G. S. T.,
R. A. C.
H. A. fromGr.,
Long.,
(,
7k
35"
'lO-
-
1
37.5
7
33
S2.5
+ 4
■22
37.3
+
1
14.5
11
57
24.3
-10
22
17
1
3.5
07
2
01
26
w.
w.
Ok 26" 19" E.
. 6° 34' 4y'
Obs. alt.'J,
S. D.,
Aug.,
dip,
I.e.,
Ist Corr.,
Approx. alt.,
p. A r. (Tab. 24),
75° 33'
00"
- 15'
~
5
3
51"
16
00
00
- 24
07
75° 08'
+ 14
5,3"
37
R. A. C, lOk ai"" 07«.
M. D.,
No. min..
R. A.,
2<.06
33".54
69«.09
1»09«
Dec,
M. D.,
No. min.,
Corr.,
Dec,
6°49'52".4 N.
H".46
33".54
\ 8'(
486"
8' 05"
6° 41' 47"
N.
Hor. Par., 58' 03"
t
d
h
Lat.
6° 34' 45"
6 41 47
75 23 30
6 44 26 N.
13 05 40 S.
sec
tan
.00286
9.06973
tan 9.07259
sin
sin
.93324
9.98573
9.06959
9.98856
6 21 14 S.
Example: August 6, 1879, p. m., in Lat. 52° 47' S. by D. R., Long. 146° 32' E., observed altitudeof
Achernar, near lower transit, 24° 01' 20" bearing south and west; watch time, 6" 48'° 22«; C-W, 9' 46°'
27'; chro. corr. onG. M. T., + 1°' 57"; height of eye, 18 feet; I. C. H- 1' 00". Find the latitude.
Watch time, 6" 48'" 22'
C-W, + 9 46 27
Chro. t.,
C. C.
G. M. T., S'"
R. A. ivi. S.,
Red. (Tab. 9), +
G. S. T.,
E. A. *,
H. A. from Gr.,
Long.,
H. A,,
+
4 34
1
49
57 .
+
+
16 36
8 54
2
46
39.8
43.7
1 34
1 33
09.5
15.3
00
9 46
54 W.
08 E.
9 47
02 W.
Obs. alt. if., 24° 01' 20"
Corr., - 5 19
R. A. *, 1" 33'" 15'.3
Dpc .^7° ."yV 28" S
'',
23 56 01
LC,
dip,
ref.,
+ I'OO"
- 4' 09"
- 2 10
6 19
Corr.,
- 5' 19"
2" 12" 58«
. 33° 14' 30"
t
d
33°
57
23
-<f/' 117
64
14' 30"
50 28
56 01
44 18 S.
54 15 N.
LATITUDE.
see .07760
tan .20153
cosec
sin
sin
cos
.07233
h
180°-
tan .27913
9. 60818
9. 94699
f'
9.62750
Lat.
52
50 03 S.
101
BY THE POLE STAR.
340. This method, confined to northern latitudes, is available when the star Polaris and the hori-
zon are distinctly visible, the time of the observation being noted at the moment the altitude is measured.
Two methods will be given. The first is sufficiently precise for nautical purposes, involving the
computation of the formula:
'L = h~p coat,
in which,
/( = true altitude, deduced from the observefl altitude;
p = polar distance = 90° — d, the apparent declination being taken from the Nautical Almanac
for the date;
t = star's hour angle.
Find the right ascension and declination of Polaris from the Nautical Almanac; then find the hour
angle in the usual way.
To the log cosine of the hour angle ada toe logarithm of t.he polar distance in minutes; the number
corresponding to the resulting logarithm will be a correction in minutes to be subtracted from the star's
true altitude to find the latitude.
Attention must be paid to the sign of the correction p cos t. If ( is more than 6'" and less than IS"",
the sign of cos < is — ; hence the formula becomes arithmetically:
L = h+pcm t.
Example: June 11, 1879, from an observed altitude of Polaris the true altitude was found to be
29° 5' 55". The time noted by a Greenwich chronometer was 13'' 41"' 26"; chro. corr. — 2"° 22'; Long.
5' 25'» 42» W.
Chro. time,
C. C,
13" 41° 26-
2 22
G. M. T., 11", 13
R.A.M.S., + 5
Eed. (Tab. 9), +
39
17
2
04
49
15
G.S.T., 18
K. A. *, - 1
59
14
08
04
H. A.fromGr., 17
Long., 5
45
25
04 W.
42 W.
H. A., 12
19
22 W.
h,
p cos t,
Lat.,
29° 05' 55"
+ 1 19 54
30 26 49 N.
R. A. *,
1" 14"° 04'
Dec,
88° 39' 47" N.
/ 1° 20' 13"
^' \ 80'. 2
p, 80'.2 log 1. 90417
t, 175° 09' 30" cos ( - ) 9. 99845
«cos(-l^^-^'0ff(-) 1-90262
t.
f 11"
1175°
40'" 38» E.
09' 30"
341. The second method is more rigorous, and should be employed when greater accuracy is
sought. It is embodied in Table 28.
Reduce the observetl altitude of the star to the true altitude. Find from the Nautical Almanac the
apparent right ascension and declination of the star at the time of observation. Find the hour angle in
the usual manner.
With the hour angle take out the first correction, A, from Table 28, giving to it the sign — when the
hour angle is numerically less than 6''; the sign -)- when the hour angle is greater than 6''.
With the hour angle and altitude take out the second correction, B, from Table 28. The sign of this
correction is always -f-. (If the altitude is greater than 60°, this correction may be found by taking
that for 45° and multiplying it by the tangent of the altitude; adding, if desirable, the second term in
the expression for B, viz: + 0".0076 sin* ( tan' h. )
With B and the declination take out the third correction, C, from Table 28, giving it the sign -\-
when the declination is less than 88° 48'; — when the declination is greater than 88° 48'.
With A and the declination take out the fourth correction, D, from Table 28, giving it the same sign
as that of A when the declination is less than 88° 48'; the opposite sign when the declination is greater
than 88° 48'.
Combine these corrections with the true altitude according to their signs; the result is the latitude
of the place of observation.
If, when several sights are taken, great precision is required, or the intervals are great, it will be
necessary to take out the first and second corrections for each observation separately; in other cases the
102 LATITUDE.
mean of the times may be used. The means of these two corrections may always be used for finding
the third and fourth corrections; and these four quantities mav be combined With the mean of the
altitudes.
If the nearest 10" suffices for each, the corrections may be taken out for the nearest arguments
without interpolation, and all but the first may thus be taken out when a precision of 3" is required. If
a precision of 1' is sufficient for each correction, as is ordinarily the case at sea, an hour angle within
S" will suffice for A; and D may be neglected, and B used only when the altitude exceeds 47°.
Example: January 1, 1903, about 9 p. m.. Longitude 79° 54' 07" W., observed double altitude
of Polaris with artificial horizon, 81° 57' 20"; chro. time l"" 55°' 12'; chro. corr. on G. M. T. -f 1"° 07»;
I. C. — 0' 50". (The necessary quantities, taken from the Nautical Almanac for 1903, are given
below.) Required the latitude.
Chro. time, 1" 55" 12" Obs. 2 alt. *, 81° 57' 20" R. A. sk, 1" 24"" 33» 3
C. C, 4- 1 07 I. C, - 50 ^
Dec, 88° 47' 42" N.
O. M. T., 13 56 19 2)81 56 30
R. A. M. S., ' " " '-
Red. (Tab. 9), + 2 17. 4 40 58 15
ref., ~ 1 07
13
56
19
18
39
50.9
2
17.4
8
38
27.3
1
24
33.3
7
13
54 \V.
5
19
37 W.
G. S. T.,
R. A. *, 1 24 33.3 h,
A,
H. A.fromCir., 7 13 54 \V. B, +
Long., 5 19 37 W. C,
H. A., 1 54 17 W.
40 57
08
1 03
13.9
08.9
00.0
15.7
89 63
47 N.
LONGITUDE. 103
CHAPTER XIII.
LONGITUDE.
342. The longitude of a position on the earth's surface is measured bv the arc of the equator
intercepted Ijetween the prime meridian and the meridian passing througli the place, or by the angle
at the pole between those two meridians.
AferidianK are great circles of the terrestrial sphere passing through the poles.
The prime mrridinn is that one a.-i8unied as the origin, passing through the location of some principal
observatory, such a.« Cireenwich, Paris, or Washington. That of Greenwich is the prime mendian not
only for English but also for American navigators, and those of many other nations.
Secondary meridians are those connected with the primary meridian, directly or indirectly, by
exchange of telegraphic time signals.
Tertiary meridians are those connected with secondaries by carrying time in the most careful manner
with all possible corrections.
Longitude is found by taking the difference between the hour angle of a celestial body from the
prime meridian and its hour angle, at the same instant, from the local meridian. In determinations
ashore the hour angle from the prime meridian may Ije found either from chronometers or from
telegraphic signals; the local hour angle may be found by transit instruments or by sextant. In
determinations at sea the chronometer and sextant give the only means available.
DETEBMINATIOX ASHOBE.
34:1. Telegraphic Determination of Secondary Meridians. — In order to locate with accuracy
the positions of prominent points on the coasts, it is necessary to refer them, by chronometric measure-
ments, to secondary meridians of longitude which have been determined with the utmost degree of care.
Before the establishment of telegraphic cables, this was attempted principally through the observa-
tion of moon culminations, which seemed always to carry with them unavoidable errors, or by trans-
porting to and fro a large number of chronometers between the principal observatory and the position
to be lotated; and in this method it can be conceived that errors would Ije involved, no matter how
thorough the theoretical compensation for error of the instruments.
By the aid of the electric telegraph, differences of longitude are determined with great accuracy,
and an ever-increasing number of secondary meridional positions are thus established over the world:
these afford the necessary bases in carrying on the surveys to map correctly the various coast lines, and
render possible the j)ublication of reliable and accurate navigators' charts.
:t44. To detennine telegraphically the difference of longitude between two points, a small observa-
tory containing a transit instrument, chronograph, break-circuit sidereal chronometer, and a set of
telegraph ingtruments is established at each of the two points, and, teing connected by a temporary
wire with the cable or land line at each place, the two observatories are placed in telegraphic com-
munication with each other.
By mean.s of transit observations of stars, the error of the chronometer at each place on its own local
sidereal time is well determined, and the chronometers are then accurately compared by signals sent
first one way and then the other, the times of sending and receiving being very exactly noted at the
respective stations. The error of each chronometer on local sidereal time being applied to its reading,
the difference lietween the local times of the two places may be found, and consequently the difference
of longitude. The time of transmission over the telegraph line is eliminated by sending signals both
ways. By the employment of chronometers keeping sidereal time, the computation is simplified,
though mean-time chronometers may be used.
345. Estabmshment ok Tertiary Meridians. — Let it be supposed that the meridional distance
between A and B is to be measured, of which A is a secondary meridional position accurately deter-
mined, and B a tertiary meridional i>osition to be determined.
If possible, two sets of observations should be taken at A to ascertain the errors and rates of the chro-
nometers. The run is then made to B, and observations made to determine local time, and hence the
difference of longitude; and on the same spot altitudes of the sun, or of a number of pairs of stars, or
both, should be taken to determine the latitude.
Now, if chronometer rates could be relied on to be uniform, this measurement would suffice, but
since variations may always arise, the run back to A should Ite made, or to another secondary meridio-
nal position, C, and new rates there obtained. Finally, the errors of the chronometers on the day when
the observations were made at the tertiary position should be corrected for the loss or gain in rate, and
for the difference of the errors as thus determined.
When opportunity does not permit obtaining a rate at the secondary meridional station or stations,
both before and after the observations at B, the navigator may obtain the errors only, and a.ssume that
the rate has been uniform between those errors.
A modification of the foregoing method that may sometimes prove convenient is to make the first and
third sets of observations at the position of the tertiary meridian, and the intermediate one at the second-
ary meridian; in this caae the error will be obtained at thesecondary station, and the rate at the tertiary.
104
LONGITUDE.
Example: A vessel at a station A, of known longitude, obtained chronometer eirors as follows:
May 27, noon, chro. slow, 7'" 18'.9,
June 3, noon, chro. slow, 7 12 .7;
then proceeding to a station B a series of observations for longitude was taken on June 17; after which,
returning to A, the following errors were obtained:
July 3, noon, chro. slow, 7"" 00*. 7,
July 10, noon, chro. slow, 6 59 .8.
Required the correct error on June 17.
May 27, —7° 18".9
June 3, -7 12.7
July 3, -7°' 00% 7
July 10, -6 59 .8
Change, + 6.2
Change, + .9
Daily rate, + 0^.89
Daily rate, -+ (?'.*8
Therefore, assuming that these rates were correct at the middle of the periods for which they were
determined, we have,
May 30, Midnight, Rate, +0".89
July 6, Midnight, Rate, +0.13
Change of rate, 37 days, —0 .76
Daily change of rate, — 0'.021
Change of rate for 3^ days, — 0".07; rate June 3, noon, +0".89— 0».07=+0».82
Change of rate for 17i days, —O'.Sl; rate June 17, noon, -: .89—0 .37=-i-0 .52
Mean daily rate, June 3 to 17, -f .67
Total change of error, June 3 to 17,
Error, June 3,
-0™ 09'. 38
-7 12.7
Error, June 17, —7 03 .3
346. Single Altitudes. — The determination of longitudes ashore by single altitudes of a celestial
body is identical in principle with the determination at sea by that metnod, which will be explained
hereafter (art. 349). It may be remarked, however, that by taking observations on opposite sides of
the meridian, at altitudes as nearly equal as possible, a means is afforded, which is not available at sea,
of eliminating certain constant errors of oVjservation.
347. Equal Altitudes. — The method of equal altitudes, explained in article 321, Chapter XI, is
available for the determination of longitudes as well as for chronometer error. In the case of the sun,
the sight ^ives the chronometer time of L. A. noon or midnight; applying the chronometer correction
and equation of time (the latter with its sign for mean time), we obtain the G. A. T., which equals the
longitude, if west, or 24'' minus the longitude, if east. For any other body, the sight gives the chro-
nometer time of transit; apply the chronometer correction and there results G. M. T., which may be
reduced to G. S. T.; the difference between the latter and the R. A. of the body (this being L. S. T.),
is the longitude.
Example: April 20 p. m. and April 21 a. m., 1879, in Lat. 30° 25' N., Long, (approx.) 81° 26' W.,
chro. corr. — S" 11'.4, observed times and equal altitudes of the sun as stated below; C— W for p. ra.
sights, 5" 31°" 58».5, and for a. m. sights, 5" 32" 01". Required the longitude.
WATCH, P. M.
ALTS.
2'" 51« 40>
90° 0'
52 05
89 60
52 30
40
52 55
30
53 20
20
Mean, W.T., P.M., 2i'52»30'.0
Mean,
C - W, +6 31 58 .5
C - W
P. M. Chro. T., 8 24 28 .5
A.M.C
WATCH, A. M.
8b ij9» 00-
Dec,
.58 »4 .5
58 09 .5
H. D. at Mid.
57 46 .0
Long. +12'',
57 20 .0
., SI- 58"
+ 5 32
ir
' 29'
17".l ]
+ 51".10
1-1' .43
+
f
tl4'
890".7
.51"
H. D. (20th).
H. D. (2Ist).
Diff. 24\
Biff. in.
Dec,
11° 44' 08" N.
+51".45
+50 .97
.48
- 0".0i
- 0".35
A.M.Chro.,T.+12l',26
11 .0 P. M. Chro. T.,
30
24
2)10 54
Klapsed Time,
18 05 42 .5
Mid. Chro. T.,
Eq. eq. alt.,
5 27 19 .76
+ 19 .36 Kq. t.,
imoi'.g Tab. 37 log A ( + )9.9364
' H.D.+51".10Iog (+)1.7084
H. D. at Mid., +.-il".l(>
logB(-)9.7912
log (+)1.7084
Chro.t.,L.A.Mid., 5 27 39.1 H. D.,
Eq. t., + 1 14 .3 Long. + 12'',
Chro. t.,L.M. Mid., 5 28 53 .4 Corr.,
C. C. , - 3 11 .4
Eq. t.,
Long..W., /6h25.42..0
* ' ' 181° 25 30"
01.64 Lat. 30° 25' tan ( + )9.7687 d+11044'tan ( + )9.317&
17i>.43
1st Part +25'.911og( + )1.4135
9,4 2d Part - 6 .56 log (-)0.8171
(Plug to mean time.)
LONGITUDE.
105
34 §. In the same example the equation of equal altitudes may be found by the less exact method
heretofore given (art. 324), as follows:
Change in declination between sights = H. D. X Elapsed time = ol".10 X IS".! = 925".
Change in altitude due to 100" declination (Tab. 25) = + 53".
h' = +
t' = +
53 X925
100 X 60
2''53"'20'-
= + 8'. 19.
-2" 51"' 40"
90° 00' - 89° 20'
Eq. eq. alt. = + 8.19 X 2'.5 =
100'
' 40'
20«.5.
= + 2'.5.
DETEBMINATION AT SEA.
349. The Time Sight. — The method of determining longitude at sea which is employed almost to
the exclusion of all others Js.that of the lime sighi, sometimes called the chronometer method. The altitude
of tlie body above the sea- horizon is measured with a sextant and the chronometer time noted; the
hour angle of the body is then found by the process described in article 316, Chapter XI.
If the sun is observed, the hour angle is equal to the local apparent time; the Greenwich apparent
time may be determined by applying the equation of time to the Greenwich mean time as shown by the
chronometer; the longitude is then equal to the difference between the local and the Greenwich appar-
ent times, being east when the local time is the later, and west when it is the earlier of the two.
If any other celestial bodv is employed, the hour angle from the local meridian, found from the
sight, is compared with the liour angle from the Greenwich meridian to obtain the longitude; the
Greenwich hour angle is found by converting the (Jreenwich mean time into Greenwich sidereal time
in the usual manner, and then taking the diSerence between the latter and the right ascension of the
body, the remainder being marked east or west, according as the (Greenwich sidereal time is the lesser
or greater of the two quantities; and as the local hour angle may be marked east or west according to
the side of the meridian upon which it was observed, the name of the longitude will be indicated in
combining the quantities.
350. As has been stated, the most favorable position of the celestial body for finding the hour
angle from its altitude is when nearest the prime vertical, provided the altitude is not so small as to be
seriously affected liy refraction.
3Si. In determining the longitude at sea by this method, it is necessarj^ to employ the latitude
by account. This is seldom exactly correct, and a chance of error is therefore introduced in the result-
ing hour angle; the magnitude of such an error depends upon the position of the body relatively to the
observer. The employment of the Sumner line, which is to be explained in a later chapter, insures the
navigator against being misled from this cause, and its importance is to be estimated accordingly.
Example: At sea, May 18, 1879, a. m.; I^t. 41° .33' N.; Long. 33° 30' \V., by D. R., the following
altitudes of the sun's lower limb were observed, and times noted by a watch compared with the Green-
wich chronometer. Chro. corr., -f 4'" 59».2; I. C, — 30"; height of the eye, 23 feet; C- W, 2" 17'" 06'.
-Required the true longitude.
\v. T.,
7'' 20» 16'
20 47
21 14
G. A. T.,
Obs. alt. Q, 29° 36' 30"
41 20
46 10
Mean,
7
20
4.5.3
C-W,
+ 2
17
06
Chro. t.,
9
37
61.3
C. C,
+
4
69.2
G. M. T.,
17'1, 21
42
60.5
Eq. t.,
+
3
47.9
Mean,
Corr.,
S. D.,
dip,
p. & r.,
I.e.,
29 41 00
+ 9 05
1.')' 51"
4' 42"
1 34
30
6 46
Dec, 19° 32' 01".S N.
H. D., +
Q.M.t., -
33".09
2k.3
Corr., - |j,
Dec, 19° 30'
76".l
16"
46"
Eq. t.,
3" 47 '.68
H.D.,
G.M.T.,
- 0'.09
2l>.3
Corr.,
+ 0'.21
N.
70° 29' 14"
{Pius to mean time.)
Corr.,
9' 05"
h
L
P
»
s—h
29° 50' 05"
41 33 00
70 29 14
G. A. T.
.L. A. T.
Long.
2)141
52
19
70
41
56
06
09
04
21»
19
46'"
32
' 38'
07
r 2" 14'" 31'->,y
t33° 37' 45"/*^-
see
cosec
COS
sin
sin i t
.12588
.02569
9.51406
9.81782
2)19.48345
9.74172
106
LONGITUDE.
Example: At sea, April 16, 1879, p. m., in Lat. 11° 47' S., Long. 0° 20' E., by D. R., observed an
altitude of the star Aldebaran, west of tiie meridian, 23° 13' 20"; chronometer time, 6" 56"" 32^; chro-
nometer fast of G. M. T., 2"" 27"; I. C. - 2' 00"; lieight of eye, 26 feet. What was the longitude?
Chro. t,
CO.,
6" 56"° 32'
2 27
6
54
05
+1
37
01.9
+
1
08.0
8
32
14.9
4
28
59.6
G. M. T.,
R. A. M. S., +1
Red. (Tab. 9)
G. S. T.,
R. A. *,
H.A.fromGr., 4 03 15 W.
Obs.alt. *, 23° 13' 20"
Corr., — 9 16
R. A. H«, 4" 28°' 59". 6
Dec, 16° 15' 59" Is
h, 23 04 04
p, 106° 15' 59"
I.e., - 2' 00"
dip, — 5 00
ref., - 2 16
Corr. ,
h
L
P
23° 04' 04"
11 47 00
106 15 59
2)141 07 03
»
s—h
70 33 32
47 29 28
Gr.H.
H. A.
A. 4" 03™ 15' W.
4 05 50 W.
9 16
sec
cosec
.00925
. 01774
cos
sin
9. 52223
9. 86757
2)19.41679
sini( 9.70839
Tnn., /0''02-35»\p
Long. |qo 38/ 45//|E.
Example: At sea, April 17, 1879, a. m., in I.at. 25° 12' S., Long. 31° 32' W., by D. R., observed an
altitude of the planet Jupiter, east of the meridian, 45° 40'; watch time, 5'' 48"" 02'; C — W, 2'' 05" 42';
C. C, +2'° 18'; I. O., +1' 30"; height of eye, 18 feet. Required the longitude.
W.T.,
6«'48»02'
2 05 42
Obs. alt.
Corr.,
/'■
I.e.,
dip.
ref.,
Corr.,
h
L
P-
8
S —
Gr.
H.
*, 45° 40' 00" R.A. (!■
- 3^ RT,
^^0'^), 22l>27"19'.0
Dec. (n^ Ok), 10° 36' 28".l 8.
+ 1'.8
4'.1
7". 4
H.D., + 10".0
Chro. t..
7
+
63
2
44
18
45 36 24 G.M.T.
G.M.T., - 4''.1
C.C,
+ 1' 30" Corr..
4' 09" R. A.,
- 57
Corr.. — 41".
19
+ 1
+
66
37
3
02
01.9
16.5
G.M.T.,16'',
R.A.M.S.,0',
22h27n ll'.O
sec . 04343
cosec .00750
cos 9.41032
sin 9. 69217
Dec., 10° 37' 09" S.
Red. (Tab. 9),
p, 79° '22' 51"
- 5 06
G.S.T.,
21
22
36
27
20.4
11.6
R.A. *,
3' 36"
45° 36' 24"
25 12 00
79 22 51
H. A. from Gr.
,
60
51 E.
2)150 11 15
75 05 38
// 29 29 14
H. A. 0" .50™51'E.
A. 2 57 21 E.
2)19.1.5342
sin i I 9. 57671
T^„ / 2" 06™ 30' W
Long. |3io37,3o//|^^.
LONGITUDE. 107
Example: At sea, June 26, 1879, p. m,, in Lat. 49° SC N., Long. 6° W W., by account, observed an
altitude of the moon's lower limb 21° 18' 10", the body bearing east; chronometer time, 2" 26"" 58";
chronometer slow of G. M. T., 42"; I. C.,-1' 45"; height of eye, 22 feet. Find the longitude.
Chro. t..
2" 26-
+
'58'
42
Obs. alt. ^,
S. D.,
Aug.,
dip.
I.e.,
1st corr.,
Approx. alt
p.<tr. (Tab.
h
L
P
2):
s
$-h
Gr. H. A.
H. A.
21° 18' 10"
R. A.,
M. D., +
No. mill..
Corr. , 4-
R. A.,
Hor. par.,
cosec
cos
sin
sin J (
m 37" 41>.96
Dec.,
M. D.,
No. min.,
Corr.,
Dec.,
p.
2° 36' 36".4 S.
C. C,
+ 15' .i9"
+ 6
2'-07
27».7
15".l
G. M. T..
2 27
+ 6 16
+
40
57..i
24.3
27».7
R. A. M. S..
Red. (Tab. 9),
+ 16 05
67'.34
f 419".3
I 6' 69".3
- 4' 36"
- 1 45
U' 38» 39'.3
58' 35"
.19043
.00049
9.11923
9.93799
G S. T.,
R. A. a.
8 ia
11 38
01.8
39.3
2° 42' 36" S.
- 6 21
H. A. from Gr.
, 2 53
37 E.
+ 9' 44"
21° 27' .54"
24). + 52 06
•22 20 00
22° 20' 00"
49 50 00
92 42 36
164 52 36
82 26 18
60 06 18
2" 53™ 37" E.
3 19 04 E.
2)19,24814
9.62407
Long. I ^o fi/'ly/jw.
352. Equal Altiti'des. — The method of finding the longitude at sea by observation of equal alti-
tuden of a heavenly body is one that may be conveniently employed when applicable, though the limits
of applicability are narrow.
If, on board a vessel which is either stationary in position or moving at a uniform rate of speed in a
true east or west direction, equal altitudes of the sun, a planet, or a star be observefl before and after
transit, and the times noted by chronometer or watch, the interval from meridian being not greater than
ten minutes of time and the altitude not less than 75°, the mean of the times will be the time (by the
chronometer or watch used) of the meridian passage of the body; from this may be found the Green-
wich mean time of transit and thence the longitude.
If (the limits of time and altitude remaining as stated) observations be taken when the body bears
not less than 80° from the meridian, the tirne of meridian passage may with accurracy be regarded as
equal tf) the mean of the times of observation, no matter what course may have been steered by th(
vessel in the interval.
But if the azimuth of the body is less than 80° from the north or .south point of the horizon the
metho<l is not available for vessels making a material amount of northing or southing; and if the hour
angle is greater than 10"' or the altitude less than 75°, it can not be accurately employed by any veasel,
no matter what course is steered. The navigator should not yield to the temptation offered by the
simplicity of this method to follow it beyond the limits within which it may properly be considered
to apply.
!15!1. To deduce the longitude by this method take the mean of the watch times before and after
transit, which will give the watch time of transit; correct this watch time in the usual manner for
C -W and chronometer correction, from which is derived the Greenwich mean time of transit.
In the case of the sun, apply to the Greenwich mean time the equation of time, giving it its sign of
application to mean time; the result is the Greenwich apparent time of transit, whicli is ecjual to the
longitude if the latter is west, or to 24'' minnii the longitude if east.
For other bodies, convert Greenwich mean time into tireenwich sidereal time by the usual method;
the body being on the meridian, the local sidereal time is equal to the body's right ascension; the
difference between Greenwich and local sidereal times is the longitude — east if the local time is greater,
and west if it is less.
108 LONGITUDE.
Example: April 2, 1879, in Lat. 3° 30' N., Long. 86° 00' E., by D. R., observed equal altitudes of
Q before and afternoon, using same sextant and same height of eye. Watch: a. m.. 11'' 52" 37"; p.m.,
12" 07"" 22*; C — W, 6" IT" 48'; C. C, + 2°' 32'. Vessel steering west between sights. Required the longi-
tude at noon.
W. T., A. M.,
W. T., P. M.,
11"
12
52"
07
'37»
22
Eq. t, 3°'42^5
H. D., - . 0".75
G.M.T., - 5". 7
Corr., + 4'. 3
W. T.,L. A.,noon,
C-W,
2)23
11
+ 6
59
59
17
59
59.5
48
Eq. t., , 3"° 46'.8
(Subtract from mean t
Chro. t., L. A., noon,
C. C,
6
+
17
2
47.5
32
G. M. T., L. A., noon, I-",
Eq. t.,
18
20
3
19.5
46.8
G. A. T.,L. A., noon,
18
16
33
Longitude,
f 5" 43™27» 1,7
1 H'^° M ' 4.V' f ^*
Example: August 6, 1879, p. m., in Lat. 25° 55' S., bj- obs., and Long. 36° 58' W., by account,
observed equal altitudes of the star Antares, the chronometer times before and after passage being
9" 42°" 38' and 10" 00"" 26% and the true azimuths S. 81° E. and S. 81° W., respectively; chro. fast of
G. M. T., l" 27'. The ship was steaming on a course SSW. What was the longitude?
Chro. time before, 9" 42"' 38'
Chro. time after, 10 00 26
Chro. time passage,
C. C,
G. M. T. passage,
R. A. M. S.,
Red. (Tab. 9),
G. S. T. passage,
L. 8. T. passage (R. A
T •* ^ / 2" 28"" 15'\,i,
Longitude, ^.^^o 03/ 45'// W.
2)19
43
04
9
51
1
32
27
9
4- 8
+
50
58
1
05
36.3
36.9
18
1, 16
50
22
18.2
03.4
AZIMUTH. lOy
CHAPTER XIV.
AZIMUTH.
354. The (uimufh of a body has been defined (art. 223, Chap. VII) as the arc of the horizon
intercepted between the meridiari and the vertical circle passing through the body; and the amplitude
(art. 224) as the arc measured between the position of the body when its true altitude is zero and the
«ast or west point of the horizon. The amplitude is measured from the east point at rising and the west
point at .setting, and, if added to or subtracted from 90°, will agree with the azimuth of the body when
in the true horizon. The azimuth is usually measured from the north point of the horizon in north
latitude, and from the south point in south latitude, through 180° to the east or west; thus, if a body
bore X. bv K., its azimuth would be named N. 11J° E. in north, or S. 168J° E. in south latitude.
The determination of the azimuth of a celestial body is an operation of frequent necessity. At
sea, the comparison of the true bearing with a bearing by compass affords the only means of ascertain-
ing the error of the compass due to variation and deviation; on shore, tlie azimuth is required in order
to furnish a knowledge of the variation, and is further essential in all surveying operations, the true
direction of the base line being thus obtained.
355. There are various methods of obtaining the true azimuth of a celestial body, which will be
-described as follows: (a) Amplitudes, (b) Time Azimuthx, (c) Altitude Azimuths, {d) Time and Altitude
Azimuths. A further metho<l, by means of the Sumner line, will be explained later (Chap. XV).
Still another operation pertains to this subject, namely: (e) The determination of the True Bearing of a
Terrestrial Object.
AMPIilTTTDES.
356. The method of obtaining the comi)ass error by amplitudes consists in observing the compass
bearing of the sun or other- celestial body when its center is in the true horizon, the true bearing, under
such conditions, being obtained by a short calculation. Since the true horizon is not marked by any
visible line (differing as it does from the visible horizon by reason of the effects of refraction, parallax,
and dip), allowance may be made for the difference by an estimate of the eye, or else the observation
may be made in the visible horizon and a correction applied.
357. When the center of the sun is at a distance above the horizon equal to its own diameter it
is almost exactly in the true horizon; at such a time, note its bearing by compass, and also note (as in
all observations for determining compass error) the ship's head by compass, and the angle and direction
of the ship's heel.
Or, note the bearing at the instant at which the center of the body is in the visible horizon; in the
<»se of the sun and moon, the correct bearing at that time may be most accurately ascertained by taking
the mean of the bearings when the upper and the lower limbs of the disk are just appearing or disap-
pearing.
35§. To find the true amplitude h)j computation there are given the latitude, L, and declination, d.
The quantities are connected by the formula,
sin Amp. =8ec L sin d,
from a solution of which the amplitude is obtained.
To find the true amplitude by inspection enter Table 39 with the declination at the top and the lati-
tude in the side column; under the former and opposite the latter will be given the true amplitude.
To obtain accurate results, interpolate for minutes of latitude and declination.
To reduce the observed amplitude when taken in the visible horizon to what it would have been if
taken in the true horizon, enter Table 40 with the latitude and declination to the nearest degree and
apply the correction there found to the observed amplitude; the result will be the corrected amplitude
by compass, which, Ijy comparison with the true amplitude, gives the compass error. When the body
observed is the sun, a star, or a planet, apply the correction, at rising in north latitude or at .setting in
south latitude, to the right, and at setting m north latitude or at rising in south latitude, to the left.
For the moon, apply half the correction in a contrary direction.
Ex.\mple: At sea, in I^at. 1 1° 29^ N., the observed bearing of the sun, at the time of rising when its
center was estimated to be one diameter above the visible horizon, was E. 31° N.; corrected declination
22° 32' N. Required the compass error.
By inspection ( Table S9).
d! 22°.' I N;} '•'''"*' ^"'P- ^- 2^°- ° ^'•
Obsd. amp. E. 31 . N.
Error, 8°. K.
Error, 7° 59' E.
By computation.
L 11° 29^ sec
d 22 32 sin
.00878
9. 58345
True amp. E. 23° 01' N. sin
Obsd. iimp. E. 31 00 N.
9. 59223
110 AZIMUTH.
Example: At sea, in Lat. 25° 03' S., the observed bearing of Venus when in the visible horizon at
rising was E. 18° 30' N., its declination being 21° 44' N. Required the compass error.
By computation. Py inspection ( Table 39).
L 25° 03' sec .04290 L, -^'.OS.l^ E 24° 1 N
d 21 44 sin 9.56854 d, 21 . 7 N. J ^ "''^ '''"P- ^- ^* -^ ^-
Obsd. amp. E. 18°. 5 N. 1 f, v i c a xt
True amp. E. 24° 08' N. sin 9.61144 Corr. (Tab. 40) 0. 3 left.] ^^^^^- ""P" ^^- "* ' ^ ^■
Comp. amp. E. 18 48 N.
Error, 5° 20' W.
Error, 5°. 3 W.
E.xample: At sea, in Lat. 40° 27' N., the mean of the observed bearings of the upper and lower
limbs of the moon when in contact with the visible horizon at setting was W. 17° S.; declination,
21° 12' S. What was the error of the compass?
By computation. By in.'tpe.ction ( Table 39).
L 40° 27' see .11863 L, 40°.5N.l .p „. oco i o
d 2112 sin 9.55826 d, 21 . 2 S.f ^^e amp. W . 28°.4 S.
Obsd. amp. W. 17°.0S. Ip ,,.,,, „„
True amp. W. 28° 22' S. sin 9.67689 Corr. (Tab. 40) 0. 3 right.f *^"'"P- ^"'P' " • '" ■' *■
Comp. amp.AV. 16 42 S.
Error, 11° 40' W.
Error, 11°.7W.
TIME AZIMUTHS.
359. In this method are given the hour angle at time of observation, /, the polar distance, p, and
the latitude, L; to find the azimuth, Z.
Any celestial body bright enough to be observed with the azimuth cin'le may be employed for
observation; the conditions are, however, most favorable for solution when the altitude is low.
360. Take a bearing of the object, bisecting it if it has an appreciable disk, and note the time with
a watch of known error. Record, as usual, the ship's head by compass and the amount of heel. If
preferred, a series of bearings may be taken with their corresponding times; and the means taken.
361. First prepare the data as follows:
(a) Find the Greenwich time corresponding to the local time of observation.
(fe) Take out the declination of the body from the Nautical Almanac; if the method of computation
is employed the polar distance and the co-latitude should be noted.
(c) Find the hour angle of the body by rules heretofore given.
This having been done, the true azimuth may be determined either by Time Azimuth Tables, by the
graphic method of an Azimuth Diagram, or by Solution of the Astronomical Triangle. Owing to the pos-
sibility of more expeditious working, either of the first-named two is to be considered preferable to the
last, and the navigator is recommended to supply himself with a copy of a book of Azimuth Tables, or
with an Azimuth Diagram ; an explanation of the method of use accompanies each of these.
362. To solve the triangle:
Let S = J sum of polar distance and co-Lat.
D = I difference of polar distance and co-Lat.
it = i hour angle.
Z = true azimuth.
Then, tan X = sin D cosec S cot J t;
tan Y = cos D sec S cot J t;
Z = X 4- Y, or X ~ Y.
First Case. — If the half-sum of the polar distance and co-Lat. is less than 90°: take the sum of the
angles X and Y if the polar distance is greater than the co-Lat. ; take the difference if the polar distance
is less than the co-Lat.
Second Case. — If the half-sum of the polar distance and co-Lat. is greater than 90°: always take the
difference of X and Y, which subtract from 180°, and the result will be the true azimuth.
In either case, mark the true azimuth X. or S. according to the latitude, and E. or W. according
to the hour angle. It may sometimes be convenient to use the supplement of the true azimuth, by
subtracting it from 180° and reversing the prefix N. or S., in order to make it correspond to the compass
azimuth when the latter is less than 90°.
The cotangent of half the hour angle may be found from Table 44 abreast the wlmle hour angle in
the column headed "Hour P. M."
AZIMUTH.
Ill
Example: December 3, 1879, a. m., in Lat. 30° 25' N., Long. 5" 25" 42^ W., the observed bearing of
sun's center was N. 135° 30' E., and the Greenwich mean time, December 3, 2" 36"° 11'. The corrected
declination of the sun was 22° 07' S. ; the equation of time (additive to mean time) , 10"" 03'. Required
the error of the compass.
G.M.T. (Dec.3), 2" 36'» 11'
Long., - 5 25 42
co-Lat., 59° 35'
p, 112 07
L.M.T. (Dec.2),
Eq.t.,
L. A. T.,
t.
21 10 29
- 10 03
21 20 32
2" 39"'28»
t
8
D
X
Y
2" 39" 28'
85° 51'
26 16
50 44
88 19
cotjt .44051
cosec .00114
sin 9.64596
cotJ< .44051
sec 1.14045
cos 9.95267
tan
.08761
tan 1.53363
X+Y139 03
26 16
True azimuth, N. 139° 03' E.
Comp. azimuth, N. 135 30 E.
Compass error, 3 33 E.
Example: April 9, 1879, in Lat. 2° 16' N., the observed bearing of the sun's center was N. 85° 15' E:
a's hour angle, S"" 44" 16',- and its declination, 7° 38' N. Re<iuired the compass error.
co-Lat.,
P,
87°
82
44'
22
t
S
D
X
Y
Y-
Tru(
Con
Com
3" 44" 16' cot j < . 27372
85° 03' cosec .00162
2 41 sin 8.67039
cotji
sec
coa
tan
. 27372
1.06406
9. 99952
,
170
06
p + CO-L,
5 03 tan 8.94573
87 22
s,
85
03
1.33730
co-L —p,
5°
22'
-X82 19
; azimuth, N. 82° 19' E.
ip. azimuth, N. 85 15 E.
D,
2
41
pass error, 2 56 AV.
Example: April 26, 1879, Lat. 16° 32' S., observed bearing of Venus 56° 00' W., its hour angle
being 4'' 27" 31", and its declination 23° 12' N. What was the error of the compass?
co-Lat.,
P,
73° 28'
113 12
(
S
D
X
Y
Y-
Z
-X
4" 27" 31'
93° 20'
19 52
27 16
87 40
cotJ< .18022
cosec . 00074
sin 9. 53126
cot i
sec
cos
tan
( .18022
1.23549
9. 97335
p-f co-L,
186 40
tau 9. 71222
s,
93 20
1.38906
p — co-L,
39° 44'
60 24
119° 36'
D.
19 52
True azimuth, S. 119° 36' W.
Comp. azimuth, S. 124 00 W.
Compass error, 4 24 \V.
ALTITUDE AZIMUTHS.
363. This method is employed when the altitude of the body is observed at the same time as the
azimuth; in such a case the hour angle need not Vie known, though the time of observation should be
recorded with snfhcient accuracy for the correction of the declination of the sun, moon, or a planet.
There are given the altitude, h, the polar distance, p, and the latitude, L; to find the azimuth, Z.
364. Take a bearing of the body by compa*i8, bisecting it if the disk is of appreciable diameter, and
simultaneously measure the altitude; note the time' approximately. Observe also the ship's heading
(by compass) and the heel.
Or a series of azimuths, with corresponding altitudes, may be observed, and the mean employed.
365. Calculate the tnie altitude and declination from the observed altitude and the time. Then
compute the true azimuth from the following formula:
cx)s i Z = \/cos 8 cos (s — p) sec L sec h,
in which « = J(/i-rL-fp). The resulting azimuth is to be reckoned from the north in north latitude
and from the south in south latitude.
112 AZIMUTH.
It may occur that the term (« — ; ) will have a negative value, but since the cosine of a negative angle
less than 90° is positive, the result will not be affected thereby.
Example: December 3, 1879, in Lat. 30° 25' N., the observed bearing of the sun's center was
N. 135° 30' E., and.its corrected altitude 24° 59'; the approximate G. M. T. was 2\6, the declination at
that time being 22° 07' S. Required the compass error.
h
L
P
24°
30
112
59'
25
07
sec
sec
cos
cos
cos
.04267
. 06431
9. 03690
9.94445 '
True azimuth, K.
Comp. azinmth, N.
Compass error,
2)167
83
— 28
69
139
31
45
22
30
00
139° 00'
135 30
s-p
3 30
) 19. 08833
*i
9.54416
E.
E.
E.
TIME AND ALTITUDE AZIMUTHS.
366. When, at the time of observing the compass bearing of a celestial body, the altitude is meas-
ured and the exact time noted, the true azimuth may be very expeditiously determined, a knowledge
of the latitude being unnecessary.
In view of the simplicity of the computation this method strongly commends itself to observers not
provided with an azimuth table or diagram.
367. The observation is identical with that of the altitude azimuth (art. 364), with the exception
that the times of observation must be exactbj instead of approximately noted.
36S. Ascertain the declination of the body at time of sight, and correct the observed altitude; com-
pute the hour angle. We then have:
sin Z=sin t cos d sec h,
from which the azimuth may be found.
This method has a defect in that there is nothing to indicate whether the resulting azimuth is
measured from the north or the south point of the horizon; but as the approximate azimuth is always
known, cases are rare when the solution will be in question.
Ex.\mple: December 3, 1879, in Lat. 30° 25' N., Long. 5" 25°' 42" W., the observed bearing of the
sun's center was N. 135° 30' E. ; its altitude at the time was 24° 59'; hour angle, 2" 39- 28» (39° 52'), and
declination 22° 07' S. Find the compass error. (See example under Altitude Azimuths and. first
example under Time Azimuths. )
sin 9. 80686 True azimuth, N. 139° 04' E.
cos 9. 96681 Comp. azimuth, N. 135 30 E.
t
d
h
39° 52'
22 07
24 59
ZS.
40° 56'
sec .04267
E. sin 9. 81634
3 34 E.
TRUE BEARING OF A TERRESTRIAL OBJECT.
369. Thus far, sea observations for combined variation and deviation have been discussed, but if it
becomes necessary, as in surveying, to ascertain the True Bearing of a Terreslrud Object, or to find the
variation at a shore station, more accurate methods than the foregoing must be resorted to.
The most reliable method is that by an Astronomical Bearing. This consists in finding the true
bearing of some well-defined object by taking the angle between it and the sun or other celestial body
with a sextant or a theodolite, and simultaneously noting the time by chronometer, or measuring the
altitude, or observing both time and altitude. It should always be noted whether the object is right
or left of the sun.
370. By Sextant. — Measure the angular distance between the object and the sun's limb; and if there
is a second observer, measure the altitude of the sun at the same moment and note the time. In the
absence of an assistant, first measure the altitude of the sun; next, the angular distance between the
sun and the object; then, a second altitude of the sun, noting the time of each observation. Also
measure the altitude of the defined point above the sea or shore horizon.
By Theodolite. — This instrument is far more convenient than the sextant, for, being leveled, the
horizontal angle between the sun and the object is at once given, no matter what may be the altitudes of
the objects. In case the altitude of the sun is needed, it may be read accurately enough from the vertical
circle, although not a*finely graduated as the limb of the sextant. The error in altitude nmst, how-
ever, be found by the level" attached to the telescope, since it will usually be found to differ from the
levels of the horizontal circle. If, in directing the telescope to the sun, there is no colored eye-piece, an
image of the sun may be cast on a piece of white paper held at a little distance from the eye-piece, and
by adjusting the focus the shadow of the cross-wires will be seen.
It should be understood that any celestial body may be used as well as the sun, and there are, in
fact, certain advantages in the use of the stars; the sun is chosen for illustration, because it will usually
be found most convenient to employ that body.
AZIMUTH.
113
371. Find the true azimuth of the celestial body by any one of the methods previously explained
in this chapter and apply to it the azimuth difference, or horizontal angle between the celestial and the
terrestrial body, having regard to the direction of one from the other.
To find the azimuth difference from sextant observations, change the observed altitudes of the
bodies into apparent altitudes by correcting them for index error of the sextant, dip, and semidiameter;
change the observed angular distance into apparent angular distance, by correcting for index error and
semidiameter. Tlien if S = J (App. Dist. + App. Alt. Q + App. Alt. Object) , we have:
cos J Az. Diff. = x/sec App. Alt. Q sec App. Alt. Object cos S cos (S — App. Dist.),
whence the azimuth difference is deduced.
When the theodolite is used, the horizontal angle is given directly. If only one limb of the sun ia
observed, it will be necessary to apply a correction for semidiameter (S. D. X sec h), but it is usual to
eliminate this correction by taking the mean of observations of both limbs.
Example: December 10, 1879, a. m., in Lat. 30° 25' 24" N., Long. 81° 25' 24" W., made observa-
tions with a sextant and obtained the following data for finding the true bearing of a station:
Watch time, 11" 22'" 36"
C-W, 5 21 18
Chro. corr., + 2 16
I.e.,
Required the true bearing of the object.
Obs. Ang. Dist.0, 117° 07' Left.
Obs. 2Q, 71° 37' 20"
Obs. alt. Station, 20'
zero.
Dec. S.
, 22°
56'
27"
Eq.t.,
4-
7"'
OC
S.D.,
16'
17"
W. T.,
C-W,
Chro. t.,
C. C, H
G.M.T.,Dec.lO,
Eq. t, -i
G. A. T.,
Long.,
L. A. T.,
lib 22°' 36"
5 21 18
4
43
2
54
16
4
46
7
10
00
4
5
53
25
10
42
23
27
28
2 0, 7^
' 37' 20'
a 35
S.D., +
48 40
16 17
App. Alt., 36
p. & r., -
04 57
1 13
Kl:
8° 08' 00"
22 56 27
36 03 37
9° 17' E.
170 43 E.
sin 9.15069
cos 9.96422
sec .09239
sin 9.20730
'',
36 03 44
i,
(0'32"'
\8° 08'
32-
00"
Obs. Ang. Dist.,
117° 07' 00"
App. Dist.
117° 23'
True bearing 0, N. 170° 43' E.
G's S. D.,
+ 16 17
App. Alt.
36 06
sec 0.092.50
Az. Diff., 125 00 Left.
App. Alt. Object
S
20
2)153 48
sec 0.00001
cos 9.36536
App. Ang. Dist.,
117 23 17
True bearing object, N. 45° 43' E.
76 54
S — App. Dist.
-40 29
COS 9.88115
2)19.32902
J Az. Diff.
62° 30'
COS 9.66451
Az. Diff.
125 00
E.xamplk: Same date and place and same objects as in the preceding example; measurement
with a theodolite, angular distance 0, 123° 17'; object leftof sun. Watch time, 11" 16" 34'.5; watcl
of L. A. T., 4™ 53'.5. Dec. 0, 22° 56' S. Required the true bearing.
made
watch slow
W. T., 11"16»34".5
W. slow, 'r 4 53 .5
L. A.T., 23 21 28.0
t, 38 32
24972°— 12 8
co-Lat.,
p,
59° 35'
112 56
31
S
D
0" 38"" 32*
86° 15'
26 41
X
Y
79° 24'
89 39
p + co-L, 172
S, 86 15
;)-co-L, 53 21 X + Y 169 03
cot J t 1.07435
cosec .00093
sin 9.65230
tan
26 41
True bearing ©,
Az. Diff.,
True bearing object, N. 45 46 E.
.72758
N. 169° 03' E.
123 17 Left.
cot i t 1.07435
sec 1.18440
cos 9.95110
tan 2.20985
114
THE SUMNEB LIN fit
CHAPTER XV.
THE SUMNER LINE.
DESCRIPTION OF THE LINE.
372. The method of navigation involving tlie use of the Sumner line takes its name from Capt.
Thomas H. Sunmer, an American shipmaster, who discovered it and published it to the world. As a
proof of its value, the incident which led to its discovery may be related:
" Having sailed from Charleston, S. C, 25th November, 1837, bound for Greenock, a series of heavy
gales from the westward promised a quick passage; after passing the Azores the wind prevailed from
the southward, with thick weather; after passing longitude 21° W. no observation was had until near
the land, but soundings were had not far, as was sui)posed, from the bank. The weather was now more
boisterous, and very thick, and the wind still southerly; arriving about midnight, IVth December,
within 40 miles, by dead reckoning, of Tuskar light, the wind hauled SH true, making the Irish coast
a lee shore; the ship was then kept close to the wind and several tacks made to preserve her position
as nearly as possible until daylight, when, nothing being in sight, she was kept on ENE. under short
sail with heavy gales. At alxiut 10 a. m. an altitude of the sun was observed, and the chronometer time
noted; but, having run so far without observation, it was plain the latitude by dead reckoning was liable
to error and could not be entirely relied upon."
The longitude by chronometer was determined, using this uncertain latitude, and it was found to^
be 15' E. of the position by dead reckoning; a second latitude was then assumed 10' north of that by
dead reckoning, and toward the danger, giving a position 27 miles ENP'. of the former position; a third
latitude was assumed 10' farther north, and still toward the danger, giving a third position ENE. of the
second 27 miles. Upon plotting these three positions on the chart, they were seen to be in a straight
line, and this line passed through Smalls liglit.
" It then at once appeared that the observed altitude must have happened at all tlie three puints
and at Smalls light and at the ship at the same instant."
Then followed the conclusion that, although the absolute position of the ship was uncertain, she
must be somewhere on that line. The ship was kept on the course ENE., ai^d in less than an hour
Smalls light was made, bearing ENE. i E. and close aboard.
The latitude by dead reckoning was found to be 8' in error, and if the position given by that latitude
had been assumed correct the error would have been 8 miles too far S. and 31' 30'' of longitude too far
W., and the result to the ship might have been disastrfius had this wrong position been adopted. This
represents one of the practical applications of the Sumner line.
The properties of the line thus found will now be explained.
373. Circles of Eqial Altitude. — In figure 43, if EE'E" re
present the earth projected upon the
horizon of a point A, and if it be a.ssumed that, at some particular instant of time, a celestial body is in
the zenith of that point, then the true altitude of
the body as observed at A will be 90°. In such a
case the great circle EE'py, which forms tlie hori-
zon of A, will divKle the earth into two hemi-
spheres, and from any point on the surface of one
of those hemispheres the body will be \isible, while
over the whole of the other tiemisphere it will be
invisible. The great circle Efi'E", from the fact
of its marking the limit of illumination of the body,
is termed the circle of illuiiiination, and from any
point on its circumference the true altitlide of the
center of the body will be zero. If, now, we con-
sider any small circle of the sphere, BB'B", CC'C",
DD'D", whose plane is parallel to the plane of the
cin'le of illumination and which lies within the
hemisphere throughout which the body is visible,
it will be apparent that the true altitude of the
body at any point of one of these circles is equal
to its true altitude at any otiier point of the same
circle; thus, the altitude of the body at B is equal
to its altitude at B' or B", and its altitude at 1) is
the same as at D' or D".
It therefore follows that at any instant of time
there is a series of p(Jsitions on the earth at which
a celestial body appears at the same given altitude,
and these positions lie in the circumference of a
circle described upon the earth's surface whose
Fio. 43.
center is at that position which has the body in the zenith, and whose radius depends upon the zenith
distance, or — what is the same thing — upon the altitude. Such circles are termed circles of equal altitude.
THE SUMNEB LINE. 115
374. The data for an astronomical sight coipprise merely the time, declination, and altitude. The
first two fix the position of the body and may be regarded as giving the latitude and longitude of that
point on the earth in whose zenith the body is found; the zenith distanoe (the complement of the altitude)
indicates tiie distance of the observer's zenith from that point; but ^here is nothing to show at which
of ttie numerous positions fulfilling the required conditions the observation may have been talcen. A
number of navigators mav measure the same altitude of a body at the same instant of time, at places
thousands of miles apart;" and each proceeds to work out his piosition with identical data, so far as this
sight is concerned. It is therefore clear that a single observation is not enough, in itself, to locate the
point owupied by the observer, and it becomes necessary, in order to fix the position, to employ a
second circle, which may be either that of another celestial body or that of the game body given by au
observation when it is in the zenith of some other point than when first taken; knowing that the point
of observation lies upon each of two circles, it is only possible that it can be at one of their two points
of intersection; and since .the position of the ship is
always known within fairly close limits, it is easy to
choose the proper one of the two. Figure 44 shows
the plotting of observations of two bodies verticallv
over the points A and .V upon the earth, the zenith
distances corresponding respectively to the radii AO
and A'O.
375. The Sumner Line. — In practice, under
the conditions existing at sea, it is never necessary
to determine the whole of a circle of equal altitude,
as a very small portion of it will suffice for the pur-
poses of navigation; the position is always known
within a distance which will seldom exceed thirty
miles under tlie most unfavorable conditions, and
which is usually very much less; in the narrow limits
thus required, the arc of the circle will practically
coincide with the tangent at its middle point, and
may be regarded as a straight line. Such a line, Y\g. 44.
comprising so much of the circle of e^jual altitude as
covers the probable limits of position of the observer, is called a Sumner line or Line of position.
376. Since the direction of a circle at any point — that is, the direction of the tangent — must be
perpendicular to the radius at that point, it follows that the Sumner line always lies in a direction at
right angles to that in which the body bears from the observer. Thus, in figure 44, it may be seen that
TO m' and n n', the extended Sumner lines corresponding to the bodies at A and A', are respectively
perpendicular to the bearings of the lx)dies OA and OA'. This fact has a most important application
m the employment of the Sumner line.
377. Uses of the Simner Line. — The Sunmer line is valuable because it gives to the navigator
a knowledge of all of the probable positions of his vessel, while a sight worked with a single assumed
latitude or lorgitude gives but one of the probable positions; it must be recognized that, in the nature
of things, an error in the assumed coordinate will almost invariably exist, and its possible effect should
be taken into consideration; the line of position reveals the difference of longitude due to an error in
the latitude, or the reverse.
Since the Sunmer line is at right angles to the bearing, it may be seen that when the body bears
east or west — that is, when it is on the prime vertical — the resulting line runs north and south, coincid-
ing with a meridian; if, in this case, two latitudes are assumed, the deduced longitudes will be the same.
When the t)ody bears north or south, or is on the meridian, the line runs east and west and becomes
identical with a parallel of latitude; in such a case, two assumed longitudes will give the same latitude.
Any intermediate bearing gives a Sumner line inclined to both meridians and parallels; if the line
agrees in direction more nearly with the meridian, latitude should generally be assumed and the longi-
tude worked; if it is nearer a parallel, the reverse course is usually preferable. The values of the
assumed coordinates mav vary from IC to 1°, according to circumstances.
37§. The greatest benefit to be derived from the Sumner method is when two lines are worked
and their intersections found. The two lines may be given by different bodies, which is generally
preferable, or two different lilies may be obtained from the .»arae body from observations taken at
different times. The position given by the intersection of two lines is more accurate the more nearly
the lines are at right angles to each other, as an error in one line thus produces less effect upon the
result. When two oVjservations of the same body are taken, the position of the ship at the time of first
sight must be brought forward to that at the second in considering the intersection; if, for example, a
certain line is determined, and the ship then runs NW. 27 miles, it is evident that her new position is
on a line parallel with the first and 27 miles to the NW. of it; a second line being obtained, the inter-
section of this with the first line, as corrected for the run, gives the ship's position.
Besides the employment of two lines for intersections with each other, a single line may be made
to serve various useful purposes for the navigator. These are described in article 400, Chapter XVI.
METHODS OF DETEBMINATION.
379. Any line may be defined in either of two ways — by two of its points, or by one point and the
direction. There are thus two methods by which a Sumner line may be determined:
(a) Assume two values of one coordinate and find the corresponding values of the other. Two
values of the latitude may be assumed and the longitudes determined, as was done by Captain Sumner
on the occasion that led to the discovery of the method; or else two values of the longitude may be
assumed and the latitudes determined. Two points are fixed in this way, and the line joining them is
the line of position.
(6) Assume either one latitude or one longitude and determine the corresponding coordinate. This
gives one point of the line. The azimuth of the body is then ascertained, and a line is drawn through
116
THE SUMNEK LINE.
the determined point at right angles to the direction in which the body bore at the time of sight. This
will be the Hne of position.
3§0. It follows that if the Sumner line be located by the first method and its direction thus
defined, the azimutli of the observed body maybe determined by finding the angle made by tlie line
with the meridian and adding or substraoting 90°.
Example: At sea April 17, 1879, A. M., m Lat, 25° 12' S., Long. 31° 32' W., by D. R., observed an
altitude of the planet Jupiter, east of the meridian, 45° 40'; watch time, 5" 48'° 02"; C — W, 2'' 05" 42";
C. C, + 2°' 18'; I. C, + 1' 30"; height of eye, 18 feet. Required the Sumner line.
From a solution of this same problem for a single longitude (art. 351, Chap. XIII), the following
were found: H. A. from Gr., 0''50°' 51' E.; h, 45° 36' 24"; p, 79° 22' 51". Assume values of Lat. 25° 02'
and 25° 22' S.
;!
45°
36' 24"
I-,
25
02
00
sec
.04284
p
79
22
51
cosec
.00750
2)150
01
15
"i
75
00
38
cos
9.41270
■'i
-/i 29
24
14
sni
9.69105
L, 25° 22' 00"
sec
cosec
.04403
.00750
Gr. H. A. 0'- 50"» 51' E.
2)19.15409
H. A.,
2 57 29 E. sin \ t, 9.57704
h
h
. H.
75
-/(29
10
34
38
14
(ir
A. 0" 50°' 51'
H.
A.,
2
57
12
cos
sin
9.40794
9.69328
2)19.15275
sin J (j 9.57638
T / 2" 06'"38'K,.
lx>ng., J3^o 39/ 30'/j>vv.
/ 2" 06°'21'\,,,
It should be observed that % and Sj — h can be obtained, respectively, from .<!, and «, — A by adding
half the difference between Li and L^; also that log cosec p is the same for both hour angles. The
determination of the second hour angle is thus considerably simplified.
A comparison of these results with those obtained by the solution with a single latitude shows that
the hour angle, and consequently the longitude, corresponding to the latitude 25° 12' S. are the means
of those corresponding to the latitudes here used; and therefore that the assumption that the Sumner
line is a straight line is accurate.
The line of the same sight might also have been found as follows:
Working with the single latitude 25° 12' S., it was found that the corresponding longitude was
31° 37' 30" W. Now by referring to an azimuth table or azimuth diagram, the azimuth corresponding
to Lat., 25°.2 S., Dec., 10°.6 8., H. A., 2' 57". 3 E. is S. 100° 58' E.; therefore the Sumner line extenUs
S. 10° 58' E.
The line may therefore be defined in either of two ways, thus:
, /25° 02' 00" S.
^'\31 39 30 W.
Or,
/25°
131
00" S.
30 W.
. /25° 22' 00" S.
^»t'51 35 15 W.
Line runs S. 10° 58' E.
By inspection of the coordinates of Aj and A, it may be seen that —
-f 20' diff. lat. makes — 4'. 25 diff . long. ; 'or,
4- 20 miles diff. lat. makes — 3.8 miles departure.
Therefore by reference to Table 2 it appears that the line runs about S. 11° E., and the azimuth
of the body is S. 101° E.; thus the results obtained by the two methods agree.
Example: At sea. May 18, 1879, A. M., Lat. 41° 33' N., Long. 33° 30' W., by D. R., the mean of a
series of observed altitudes of the sun's lower limb was 29° 35' 30"; the mean watch time, 7'' 20'° 45'.3;
CO., +4-° 59'. 2; LC.,-30"; height of the eye, 23 feet; C- W, 2" 17°' 06'. Required the Sumner line.
From a solution of this same problem for a single longitude (art. 351, Chap. XIII) the following
were found: G. A. T., 21" 46°- 38'; h, 29° 50' 05"; p, 70° 29' 14". Assume values of the latitude 41° 03'
and 42° 03' N.
h
u
p
29° 50' 05"
41 03 00
70 29 14
sec . 12255
cosec . 02569
«1 — ll
2)141 22 19
70 41 09
40 51 04
cos 9.51950
sin 9,81564
G. A. T.
21" 46" 38'
19 32 08
2)19.48338
L. A. T.i
sini<, 9.74169
L,
42° 03' 00"
sec
cosec
. 12927
. 02569
71
s,—h 41
11
21
09
04
G. A. T. 21"
L. A. T.J 19
46°
32
'38'
06
cos 9. 50852
sin 9. 81999
2)19.48347
sin i <2 9. 74174
/ 2" 14" SO-lor
Long.,| 330 37, 3(y,|W.
4 / 41° 03' 00" N. . f42° 03'
■^\ 33 37 30 W. ^»\33 38
/ 2" 14" 32' \„,
i^ng.j -1^33038/ oo//|v>.
00" N.
00 W.
+ 60' diff. lat. makes4-0'.5 long.
-f 60 miles diff. lat. makes +0.4 mile departure.
Line runs, N. }° W. Azimuth, N. 89i° E.
THE SUMNEK LINE.
117
The same sight worked with a single latitude, 41° 33' N., as was done in the original example, with
azimuth taken from tables or diagram, gives:
.141° 33' 00" N.
^\33 37 45 W.
Azimuth, N. 89° 38' E.
Line runs, N. 0° 22' W.
This example illustrates the case in which an observation is taken practically on the prime vertical;
the azimuth shows the bearing to be within 0° 22' of true East, and the Sumner line is therefore within
0° 22' of the meridian; a variation of 30' in either direction from the dead reckoning latitude makes a
difference of onlv 15" in the longitude.
Example: May 28, 1879, in Lat. 6° 20' S. by account. Long. 30° 21' 30" W.; chro. time, 7" 35°' 10';
observed altitude of moon's upper limb, 75° 33' 00", bearing north and east; I. C, — 3' 00"; height of
eye, 26 feet; chro. fast of G. M. T., 1" 37».5. Required the Sumner line.
From a solution of the same problem with a single longitude (art. 339, Chap. XII), the following
values were obtained: H. A. from Greenwich, 1" 35- 07» W.; h, 75° 23' 30"; d, 6° 41' 47" N. Assume
the longitudes 30° 10' and 30° 30' W.
Gr. H. A. 1" 35°" 07» W.
Long.i 2 00 40 W.
Gr. H. A. l" 35"' 07'
Long. 2 2 02 00
, JO" 25" 33"
'i \6° 23' 15"
'.{
'k
6°
6
75
' 23'
41
23
15"
47
30
sec .00270
tan 9.06973
cosec
sin
.93324
h
9.98573
Cf/',
6
13
44
11
17 N.
20 S.
tan 9.07243
sin
cos
9.06942
^I
9.98839
Lat.,
I 6
27
03 S.
:?
6°
6
75
43'
41
23
15"
47
30
sec .00299
tan 9.06973
cosec
sin
.93324
A
9.98573
<P",
6
13
44
01
33
00
tan 9.07272
sin
cos
9.06972
■p',
9.98869
10" 26" 53'
\6° 43' 15"
. f 6° 27' 03" S.
^•tsO 10 00 W.
/ 6° 16' 27
'130 30 OC
00 W.
T.at. J 6 16 27 S.
Working by the other method, and finding the azimuth, we have:
^^{3oir3rw: Line runs N. 62° W.
It might be shown that the results check with each other, as in previous cases.
Example: At sea, July 12, 1879, in Lat. 50° N., Long. 40° W., observed circum-meridian altitude
of the sun's lower limb, the time by a chronometer regulated to Greenwich mean time being 2" 41" 39';
chro. corr., -- 2" 30'; I. C, — 3' 0"; height of the eye, 15 feet. Find the Sumner line.
From the solution of the same problem for a single latitude (art. 338, Chap. XII) the following
values were obtained: G. A. T., 2" .3.3" 50»; h, 61° hi' W; d, 21° 59' 27" N.; a (Tab. 26), 2" .5.
Assume longitudes 39° 46' and 40° 15' W.
Gr. H. A. 2" 33°' 50"
Long.i —2 39 00
h
ail'
H.
r
10
61° 57' 01"
+ 1 06
61 58 07
28 01 53 N.
21 59 27 N.
Gr. H. A. 2" 33° 50"
Long., —2 41 00
h
d
7 10
61°
57' 01'^
2 08
61
59 09
28
21
00 51
59 27
50 01 20 N.
The line given by these coordinates is then :
, r50° 01' 20" N.
'*^>\.39 45 00 W.
50 00 18 N.
/50<' 00' 18" N.
'n40 15 00 W.
118 THE SUMNER LINE.
This shows that the Sumner line lies so nearly in a due east-and-west direction that a difference of
longitude of 30' makes a difference of latitude of only V.
From an azimuth table or diagram, it is found that the azimuth of the sun corresponding to Lat. 50°
N. Dee. 22° N. and H. A. 6'" 10» E., is N. 177° E. Therefore, using the values given bv the earlier
solution, the line is defined as follows:
H
50° 00' 51" N. I . „ „_„ „
40 (XI 00 N. LmerunsN. 8^°E.
The direction of the line thus given and the one found from the double coordinates mav Ite shown
to agree as in examples before given.
futding the intersection of sumner lines.
3§1. The intersection of Sumner lines may be found either graphically or by computation.
3§2. Graphic Methods. — Each line may be plotted upon the chart of the locality in which the
ship is being navigated and the intersection thus found. The details of the plotting will be obvious,
whether the line is defined by two of its points, or by one point and its directiqji. This plan will com-
mend itself especially when the vessel is near shore, as the chart in use will then probably be one of
conveniently large scale, and it will be an advantage to see where the position falls with reference to
soundings and landmarks.
383. When clear of the land it is often inconvenient to follow this plan; a large scale chart may
not be at hand, it may not be desired to deface the chart with numerous lines, or the necessarv space for
chart work may not be available. In such a case, the following method « is recommended, as it obviates
the disadvantages of the other.
To understand the principle of this method, suppose that the lines are defined by the latitude and
longitude of two points of each, and consider that they are plotted on a chart which is constructed upon
a sheet of elastic rubber. It is evident that if, while hoUling it fast in the direction of the meridians,
we stretch this rubber along the lines of the parallels in a uniform manner until the length of each
minute of longitude is made to equal a minute of latitude, the chart, while losing its accuracv as por-
traying actual conditions on the earth's surface, still correctly represents the positions of the various
points in terms of the new coordinates which have been created, namely, those in which a minute of
latitude is equal to a minute of longitude. Thus, if on the true chart a point is m minutes north and n
minutes east of another, on the stretched one it will still be m minutes north and n minutes east, the
only difference lieing that the minutes of longitude will now be of a different length; and if on the orig-
inal chart the two Summer lines intersect at a point m minutes north and n minutes east (on the
original ec&le) of some definite point of one of the lines, the intersection on the stretched chart will lie
m minutes north and n minutes (of the new scale) to the east of the same point.
A stricter mathematical conception of the stretched chart and its properties may perhaps be
obtained by considering the chart of the locality to be projected (with the eye at the zenith) upon a
plane which passes through one of the meridians and makes an angle witli the plane of the horizon
which is equal to the latitude; each minute of longitude will then be increased by multiplying it by the
secant of the latitude, and thus becomes equal to a minute of latitude.
From a consideration of the properties of this hypothetical chart it may be seen that the following
rule may be laid down: If two or more Sumner lines be plotted by their latitude and longitude upon
any sheet of paper, using a scale whereon latitude and longitude are equal regardless of the latitude of
the locality, the intersection of those lines, measured by coordinates on the scale employed, correctly
represents the intersection of the lines as it would be measured upon a true chart.
It follows from this that we may plot Sumner lines upon any piece of paper, measuring the coordi-
nates with an ordinary scale ruler, and assigning any convenient length for the mile; the larger the
scale the more accurate will be the determination. Or, what is even more convenient, we may employ
" profile paper," whereon lines are ruled at right angles to each other and at equal distances apart, in
which case no scale ruler is needed.
One caution must be observed in using this method; all longitudes employed on the paper for any
purj)ose must be those of the scale, namely, one minute of longitude equals one minute of latitude.
For instance, if the two Sumner lines be taken at different times, in bringing the first up to the position
of the second by the intermediate run, that run must be laid down to scale; that is, the easting or
westing must appear as so many minutes of longitude, not so many miles. To do this enter the traverse
table with course and distance run, and pick out latitude and departure; then, by means of the middle
latitude, convert departure into minutes of longitude and bring the first line to the second by laying off
so many minutes of latitude north or south, and so many of longitude east or west.
In the case where the Sumner is defined by one position and its line of direction, it is not correct to
lay down the angle to the meridian on the hypothetical chart, for all angles are distorted thereon. The
best way is to find another position on the line by assuming a second latitude ten or twenty miles
removed from that of the point given, entering the traverse table with the angle that the line makes with
the meridian as a course, and abreast the latitude taking out the departure; convert departure into differ-
ence of longitude, and plot the second point by its coordinates from the first.
Example: Let it be required to find the intersection, by each of the methods, of the following lines :
, 140° 00' N. . f40° 20' N.
^'\63 15 W. '^'X&A 07 W.
T, r40 05 N. „/40 15 N.
">\63 03 W. "463 12 W.
a Suggested by Lieut. G. W. Logan, U, S. Navy.
THE SUMNER LINE.
119
Figure 45 shows the intersection, (1> by Mercator chart, (2) by scale, and (3) on profile paper,
as follow!-:
.A? -.20'
3''** '■/ I . . <w ,7v A^ io^
10- £5" 15- 12- 10- OT- 03- 63° ^" ^' "^
limle = .06in.cK
Fig. 45.
er
, . .. /40° 12'.8 N.
Intersection :<g3 09 .9 W.
Suppose, in the example just given, the first line had been defined as follows:
^{ef iT W. ^'"*' ™"*' ^'- ^^° ^•
To find a second coordinate by which to plot it, proceed as follows:
In Table 2, for 17°: Lat. 20' N., Dep. 6.1 m. E. For Mid. Lat.: 40°, Dep. 6.1 ra., diff. long. 8'.0 E.
Hence, as previously given :
. 140° 00' N.
-^>\63 15 W.
40° 20' N.
■i 07 W.
f4t
46:-
3§4. Methods by Co.mputation.o — The finding of the intersection of two Sumner lines by compu-
tation mav be divided into two cases:
Cow /. When one line lies in a NE.-S\V. direction, and the other in a NW.-SE. direction.
Case II. When both lie in a NE.-SW., or both in a NW.-SE. direction.
Suppose, first, that the lines are defined by the latitude and longitude of two points of each, and for
the simplification of the problem consider the lines projected on a plane passing through one of the
meridians and making an angle with the plane of the horizon equal to the latitude, the properties of
which were explained under the graphic method, (art. 383); this saves the necessity of convertine
minutes of longitude into miles of departure before the solution and converting them back again after-
wards; as all points are thus projected in corresponding relative
positions, the results are as exact as if the longer method be
tollowe<l of dealing with minutes of latitude and longitude of
unequal length.
3§5. Cnse I. One line NE.-SW., and the other ^■W.-SE.—
Suppose the two lines, projected as described, are as shown in
figure 46, A, A2 and B, B.^; for the present assume that the two
points. A, aii<l B,, have a common latitude. Drop the perpen-
dicular PO from the intersection; then the latitude of the inter-
section will be a distance OP above the common latitude of A;
and Bi, and its longitude will be a distance AjO to the right of
Ai and B,0 to the left of B,.
Find the angles a and /i from the traverse table (Table 2),
they being taken out with the difference of latitude between the
two points of the same line in the column Lat. and the differ-
■ence of longitude in the column Dep. (Do not overlook the
fact that we are dealing now with the plane of projection and
that a and ft are not the angles made by the Sumner line with
meridians on the earth's surface.) The solution may now be accomplished by either of two methods:
(a) Observe that the case is the same as if a ship were steaming along the line A, B, and took the
first bearing of the point P when at A,, at an angle from the course equal to 90°— *, and the second
bearing when at B,, at an anglS from the course equal to 90°-f /3, with an intervening run equal to the
difference of longitude A, B,; or, she may be considered as steaming from B, to A,, in which case the
first angle is 90°— /3 an<l the second 90°4-«. Picking out of Table 5 B, corresponding to the angles
given, tbo quantity in the second column, we shall have the ratio of the distance of passing abeam, OP,
to the distance A, B,; multiply the difference of longitude by this ratio, and we shall have the actual
length of OP. Then entering the traverse table with this as a latitude and a as a course, we find in the
departure column the distance A.O by which the longitude of OP is defined; it is recommended also
to pick out B,0, using the angle p, which affords a proof of the correctness of all work done after the
finding of ex and fi.
Fig. 46.
oSugKested by Lieut. G. W. Logan, t'. 8. Navy
120
THE SUMNER LINE.
(6) The second method is to find by trial and error some latitude such that its departure correspond-
ing fo a, plus its departure corresponding to /S, equals the difference of longitude A, Bj; then the point
will be defined by the latitude, and by its longitude from A, and B,, the agreement of the longitude as
established from the different points furnishing a check upon the operation.
Example: Find the intersection of the following Sumner lines:
A,
(49'
\6
4(K N.
55.3 W.
, f49 40 N.
''\ 6 32.5 W.
Longitude A, B,=22'.8.
f50°
aA 7
Ml
(xy N.
20.0 W.
00 N.
11.3 W.
+20'
+24.7
lat.
long.
+20 lat.
—21.2 long.
Line runs NW.
«=51°.
Line runs NE.-
/3=47°.
-SE.
■SW.
Fig. 47.
Hence, intersection:
First draw a rough sketch (fig. 47) to illustrate the direction
of coordinates.
Notice that A; is west of Bjf The line through Ai runs
NW.-SE. That through B„ NE.-SW. The intersection is
therefore south of both, east of A,, and west of Bj.
(a) To solve by Table 5 B: First bearing {90°- a) =39°;
second bearing (90° + /*) = 137°. Corresponding ratio, 0.43, mul-
tiplied by 22'.8 = 9'.8 lat. (The angles 90° -fJ and 90°+ a would
have given the same ratio, 0.43.) Then (Table 2) with a = 51°,
lat. =9'.8, dep. =12'.l; and with = 47°, lat.=9'.8, dep. =
9'.8S. of lat. 49°
12.1 E. of long. 6
10.5W. of long. 6
(6) To solve by Table 2:
Assuming lat
40' N. =49°30'.2N,
55.3 W. = 6° 43 .2 W
32.5 W. = 6° 43
•2 W.l .
.0 w.r
heck.
Dep. for 51° 6.2
Dep. for 47° 5.3
Hence, intersection:
Sum
9'.9 S.
12 .2 E.
10 .6 W.
...11.5
S'
9.7
8.5
18.2
10'
12.3
10.7
23.0
9'
12.2
10.6
22.8
of 49° 40' =49° 30'. 1
of 6 55.3= 6 43.1
of 6 32.5= 6 43
:!}
check.
It may be seen that the results by the two methods substantially agree.
3S6. Case II. Both lines NE.-SW., or both NW.-SE. — Consider the lines as drawn in figure 48, and
continue the assumption that A^ and B, have a common
latitude. The differences from the first case by both
methods simply involve a change of signs.
(a) If the ship is steaming from Aj toward Bj, the
first angle from the keel line is 90° — a, and the second,
90° — fi; if steaming from Bj toward Aj, the first angle is
90° + fi, and the second 90° -f- a; in other words, either
add both angles to 90° or subtract both from 90° and
enter with the smaller angle as the first bearing.
(6 ) It may be seen that O Aj — OB, = A, B, ; in other
words, to solve by the second method, the values must
be so found that the difference of the corresponding depar-
tures equals the difference of longitude, instead of their
Fici. 48. sums, as before.
Example: Find the intersection of the Sumner lines defined below:
P
•
a N.^'"'^
A^
k
^1
A
1
f
3.
^.{
■>.{1
49° 30' N.
5 24.8 W.
30 N.
25.8 W.
f49=
L 5
49
. 4
50'
21.5
50
52.1
+20'
—3.3
lat.
long.
-20 lat.
-33.7 long.
Line runs NE.-SW.
a=9°.
Line nms NE.-SW.
/3=59°.
Aj B,=1'.0.
In this case (fig. 49) B, is west of Aj, the lines
both run NE.-SW., and ^ is the greater angle; there-
fore intersection lies to the north and east of both points.
(a) By Table 5 B: First course (90° + a) = 99°;
second course (90° + /S)= 149°; ratio 0.67Xl'.0 =
0'.7; or, first course (90° — /3) = 31°; second course
(90° — a) = 81° ; ratio = 0.67, as before.
Fig. 49.
a = 9°, lat. =0'.7, dep. =0'.l; and /3 = 69°, lat. =0'.7, dep. =1'.2.
THE SUMNER LINE.
121
Hfii)ce, intersection:
(6) By Table 2:
0'.7 N. of 49° 3(y N. =49° 30'." N.
0.1 E. of 5 24.8W. = 5 24.7W.-| , ,
5 24 .6 W. I'^"'^^-
1 .2 E. of 5 2.5 .8 W.
Hence, intersection:
Assuming lat 2'.0 0'.5 0'.6
Dep. for 9° .. ..3 .1 0.1
Dep. for59° ,3.3 0.9 1.1
Difference 3.0 0.8 1 .0
O'.e N. of 49° 30' =49° 30'.6
0.1 E. of 5 24.8= 5 24.71 ..
• I.IE. of 5 25.8= 5 24 .7 P"^''-
387. In discussing these cases, we have assumed that there was a point of one line which had a
common latitude with a point of the other line; this would be the case if two lines were worked from
time sights taken at the same time. It may occur, however, either that they have not a common lati-
tude, but do have a common longitude, as in the case of two lines
worked from q/ ep" (latitude) sights taken at the same time; or that
they have neither a common latitude nor a common longitude, as
with one time sight and one
latitude sight, or witli two
sights taken at different
times.
In case there is a t;om-
mon longitude (fig. 50),
which will be rather a rare
one, the problem is worked
with OP as a lonyilude co-
ordinate; the modification
of the other method will
B suggest itself, the principal
change rendered necessary being due to the fact that the
angles from the course in Table 5 B will be complementary
to what they were before, as we are now dealing with angles
to the meridian instead of angles to the parallel.
When there is no common coordinate of either latitude
or longitude, the simplest way of solving is first to find some
point on one line which corresponds in latitude with one of
the points on the other line, then solve as before.
Thus, in figure 51, given A, Aj and Bj Bj, find a and fi, and
thence the longitude of a point A, corresponding to the difference of latitude between Aj and Bi on the
course a; then find intersection of A, K^ and B, B.^ i« the usual way.
Fig. 50.
Fig. 51.
Example: \^l it be required to find the intersection of Sumner lines as follows:
, / 25° 30' S. . / 25° 50' S. +20' lat. Line runs SE.-NW.
^'\115 22 E. ^2\115 40 E. +18 long. <t=42°.
B,
.{-
25 15 S.
B,
25 35 S.
+20 lat.
— 7 long.
Line runs NE.-SW.
/i=19°
Find where B, B^ crosses parallel 25° 30' S.
)S=19°, lat. = +15', dep. = — y.l. Hence, the line B, B2 becomes:
g f 25° 30' S. ^ -a _n/ n Uw runs NE.-SW.
115 31.9 E.
A, B,=9'.9
/S=19°.
The directions of the lines (fig. 52) require us to follow Case I. A, is west of B3. The line through
A, runs SE.-NW., and that through B3,SW.-NE. Therefore, /^ g
the intersection is south of Aj and B3, east of A„ and west '* ^ '
ofB,.
(a) By Table 5 B. (90°-a)=48°, (90°^/3)=109°. Ratio
0.81X9'.9=8'.0 lat.; a=42°, lat.=8'.0, dep.=7'.2. ^=19°;
lat. =8'.0, dep.=2'.7.
Hence, intersection:
(6) By Table 2:
8' S. of 25° 30' S. = 25° 38' 8.
7.2 E. of 115 22 E.=115 29.2 E.\ , ,
2.7W.ofll5 31.9E.=115 29.2 E.r'^'*'^''-
Assuming lat 6' 8'
Dep. for 42° 5.5 7.2
Dep. for 19° 2.1 2.7
Sum 7.6 9.9
122
THE SUMNER LINE.
Intersection:
8' S. of 25° 30' = 25° 38'
7.2 E. of 115 22 =115
2.7 W. of 115 31.9 =115
check.
3§§. The followmg is a summary of the method when lines are given by coordinates of two
points of each:
(a) By Table 5 B.
1. Write down lines; find a and /3.
2. If there are no points which have a common
latitude, reduce one point of one line to latitude of
some given point of the other.
3. Write down difference of longitude.
4. Draw rough sketch to illustrate direction of
point of intersection.
5. Enter Table 5 B:
Case I, angles (90° ~ a) and (90° + fi) or (90° —
/S) and (90° + a).
Case IT, angles (90° + a) and (90° + fi) or (90° —
/3) and (90° ~ a).
Take out ratio from second column, and multiply,
by difference of longitude; this gives difference of
latitude of intersection from the common latitude.
6. Find departure corresponding respectively to
a and /i with latitude; this gives differences of
longitude to the point of intersection from the re-
spective points of common latitude.
3§9. If the lines, instead of being defined by coordinates of two points, are defined by the coordi-
nates of one point of each with its direction as deduced from the azimuth of the body, it will be better
not to consider the projection on the fictitious plane through the meridian, as there will then be no
advantage in so doing. In this case, consider the angles of the lines with the meridian, as given, a and
yS; reduce the difference of longitude A^ B, to departure, and use this in miles instead of the A, Bi in
minutes; and when Afi and B,0 are found, being in miles of departure, they must be reduced to min-
utes of longitude before being applied to the longitude of A, and Bj.
Example: The Sumner lines of the last example being expressed by a single point and the direction,
as given below, find the intersection.
(6) By Table 2.
1. Write down lines; find a and fi.
2. If there are no points which have a common
latitude, reduce one point of one line to latitude of
some given point of the other.
3. Write down difference of longitude.
4. Draw rough sketch to illustrate direction of
point of intersection.
5. Enter Table 2, at pages a and ft; find by trial
some latitude at which —
Case I, the sum of the corresponding departures
equals the total difference of longitude;
Case II, the difference of the corresponding de-
partures equals the total difference of longitude.
These give differences of latitude and longitude
to the point of intersection from the respective
points of common latitude.
/ 25° 40'
1115 31
S.
■E.
f 25 25 S.
U15 33.5 E.
Line runs (a-=) N. 39° W.
Line runs (ft = ) N. 18° E.
First bring second line up to Lat. 25° 40' S. ft = 18°
-5'. 4; hence we have:
lat. = + 15'; dep. = — 4.9 m. ; diff. long. =
„,/ 25° 40' S.
'^ \115 28.1 E.
Line runs [ft =) N. 18° E.
Fig. 53.
Intersection:
AB' = 2'.9 = 2.6 miles.
B' being west of A (fig. 53), and the lines through the two
points running respectively NE. and NW., the intersection is north
of both, east of B', and west of A.
(a) By Table 5 B. (90° - a) =51°; (90° +/i) = 108°. Ratio
0.88 X 2.6 = 2'.3 lat. a = ;W°, lat. =2'.3, dep. = 1.8 m., diff. long. =
2.0. ft = 18°, lat. = 2'.3, dep. = 0.7 m., diff. long. = 0.8.
2'.3 N. of 25° 40' S. = 25° 37'.7 S.
2 .0 W. of 115 31 E. = 115 29 E
0.8E. of 115 28.1 E. =115 28 .9 E,
>^
heck.
(b) By Table 2:
Intersection:
Assuminglat 4' 2' 2'.3
Dep.for39° 3.2 1.6 1.9 = 2'.l
Dep.forl8° 1.3 0.7 0.7=0.8
Sum 4.5 2.3 2.6 = 2.9
2'.3 N. of 25° 40' = 25° 37'.7
2 .1 W. of 115 31 = 115 28 .91 „hepk
0.8E. of 115 28.1=115 28 .9 r'^'^-^'
THE SUMNER LINE.
123
The following summary gives the various steps when the lines are each given by the coordinates of
one point with the direction:
{a) By Table o S.
1. Write down lines as given.
2. If the points have not a common latitude,
reduce one point to latitude of the other.
3. Write down difference of longitude and con-
vert it to departure.
4. Draw rough sketch to illustrate direction of
point of intersection.
5. Enter Table 5 B:
Case J, angles {90°-a) and (90°+/J) or (90° -/i)
and (90°- a).
Case II, angles (90°+*) and (90°+/3) or (90°-/i)
and (90°-a).
Take out ratio from second column, and multiply
by departure between the two points; this gives
difference of latitude of intersection from common
latitude.
6. Find departure corresponding respectively to
a and /S with this difference of latitude, and con-
vert to difference of longitude; this gives differences
of longitude to the point of intersection from the
respective points of ct)mnion latitude. i
390. The modification of the methods for finding the intersection of two Sumner lines, where there
is a run between the observations from which they are deduced, will be readily apparent. It is known
that at the time of taking a sight the vessel is at one of the points of the Sumner line, but which of the
various points repre.-fents her precise position must remain in doubt until further data are acquired.
Suppose, now, that after an observation the vessel sails a given distance in a given direction; it is clear
that while her exact position is still undetermined it must be at one of the series of points comprised in
a line jiarallel to the Sumner line and at a distance and direction therefrom corresponding to the course
and distance made good; hence, if a second sight is then taken, the position of the vessel may be found
from the intersection of two lines — one, the Sumner line given by the second observation, and the other
a line parallel to the first Sumner but removed from it by the amount of the intervening run.
Positions may Ije brought forward graphically on a chart by taking the course from the compass
rose with parallel rulers, and the distance by scale with dividers. If the method given in article 383 be
employed, runs in latitude and longitude must each be applied on their own scales, as explained in the
description of the method. If one of the methods by computation be adopted, the point or points of
the first line are brought forward by the traverse table's, using middle latitude sailing. The direction of
a Sumner line as determine<l from the azimuth of the body always remains the same, whatever shift
may be made in the position of the point by which the line is further defined.
(h) By Tabled.
1. Write down lines as given.
2. If the points have not a common latitude,
reduce one point to latitude of the other.
3. Write down difference of longitude and con-
vert it to departure.
4. Draw rough sketch to illustrate direction of
point of intersection.
5. Enter Table 2 at pages a and /S; find by trial
some latitude at which —
Cajte I, the sum of the corresponding departures
equals the departure between the two points;
Cane II, the difference of the corresponding
departures equals the departure between the two
l)omte.
This difference of latitude, and these departures
(converted into difference of longitude) give dis-
tance of point of intersection m latitude and
longitude from the respective points of common
latitude.
124 THE PKACTICE OF NAVIGATION AT SEA.
CHAPTER XVI.
THE PEAOTIOE OF NAVIGATION AT SEA.
391. Having set forth in previous chapters the methods of working dead reckoning and of solv-
ing problems to iind the latitude, longitude, chronometer correction, and azimuth from astronomical
observations, it will be the aim of the present chapter to describe the conditions which govern the
choice and employment of the various problems, together with certain considerations by which the
navigator may be guided in his practical work at sea.
392. Departure and Dead RECKO.NiNd. — On beginning a voyage, a good departure must be taken
while landmarks are still in view and favorably located for the purpose; this becomes the origin of the
dead reckoning, which, with frequent new departures from positions by observation, is kept up to the
completion of the voyage, thus enabling the mariner to know, with a fair degree of accuracy, the posi-
tion of his vessel at any instant.
At the moment of taking the departure, the reatling of the patent log (which should have been
put over at least long enough previously to be regularly ruiming) must be recorded, and thereafter at
the time of taking each sight and at every other tnne when a position is required for any purpose, the
log reading must also be noted. It is likewise well to read the log each hour, for general information as
to the speed of the vessel as well as to observe that it is in proi)er running order and that the rotator
has not been fouled by seaweed or by refuse thrown overboard from the ship. It is a good plan to
record the time by ship's clock on each occasion that the log is read, as a supplementary means of arriv-
ing at the distance will thus be available in case of doubt. If a vessel does not use the patent log but
estimates her speed by the number of revolutions of the engines or the indications of the chip log, the
noting of the time becomes essential. A good sight is of no value unless one knows the point in the
ship's run at which it was taken, so that the position it gave may be brought forward with accuracy to
any later time.
393. Routine Day's Work. — The routine of a day's work at sea, no part of which should ever be
neglected unless cloudy weather renders it impossible to follow, consists in working the dead reckoning,
an a. m. time sight and azimuth taken when the sun is in its most favorable position for the purpose, a
meridian altitude of the sun (or, when clouds interfere at noon, a sight for latitude as near the meridian
as possible) , and a p. m. time sight and azimuth. This represents the minimum of work, and it may be
aniplified as circumstances render expedient.
394. Morning Sights. — The morning time sight and azimuth should be observed, if possible, when
the sun is on the prime vertical. As the body bears east at that time, the resulting Sumner line is due
north and south, and the longitude will thus be obtained without an accurate knowledge of the latitude.
Another reason for so choosing the time is that near this point of the sun's apparent path the body is
changing most slowly in azimuth, and an error in noting the time will have the minimum effect in
its computed bearing. The time when the sun will be on the prime vertical — that is, when its azimuth
is 90° — may be found from the azimuth tables or the azimuth diagram. Speaking generally, during
half the year the sun does not rise until after having crossed the prime vertical, and is therefore never
visible on a bearing of east. In this case it is best to take the observation as soon as it has risen above
the altitude of uncertain atmospheric effects — between 10° and 15°.
A series of several altitudes should be taken, partly because the mean is more accurate than a single
sight, and partly because an error in the reading of the watch or sextant may easily occur when there
is no repetition. If the sextant is set in advance of the altitude on even five or ten minute divisions of
the arc, and the time marked at contacts, the method will be found to possess various advantages. As
the sight is being taken the patent log should be read and ship's time recorded. It is well, too, to make
a practice of noting the index correction of the sextant each time that the sextant is used. The bearing
of the sun by compass should immediately afterward be observed, and the heading by compass noted,
as also the time (by the same watch as was used for the sight).
Before working out the sight, the dead reckoning is brought up to the time of observation, and the
latitude thus found used as the approximate latitude at sight. It is strongly recommended that every
tight be worked for a Sumner line, either by assuming two latitudes, or by using one latitude and the azi-
muth, the advantages derived therefrom being always well worth the small additional labor expended.
The compass error is next obtained. From the time sight the navigator learns that his watch is a
certain amount fast or slow of L. A. T., and he need only apply this correction to the watch time of
azimuth to obtain the L. A. T. at which it was observed; thence he ascertains the sun's true l)earing
from the azimuth tables or azimuth diagram, compares it with the compass bearing, and obtains the
compa.ss error; he should subtract the variation by chart and note if the remainder, the deviation, agrees
with that given in his deviation table; but in working the next dead reckoning, if the ship's course
does not change, the total compass error thus found may be used without separating it into its compo-
nent parts. It should be increased or decreased, however, as the ship proceeds, by the amount of any
change of the variation that the chart may show.
395. If there is any fear of the weather being cloudy at noon, the navigator should take the pre-
caution, when the sun has changed about 30° in azimuth, to observe a second altitude and to record
the appropriate data for another eight, though this need not actually be worked unless the meridian
THE PRACTICE OF NAVIGATION AT SEA. 125
observation is lost. If it is required, it may be worked for either a time sight or q/ q/' sight, according
to circumstances, a second Sumner line obtained, and the intersection of the earlier Sumner with it will
give the ship's position.
396. Noon Srihts. — Between 11 and 11.30 o'clock (allowing for gain or loss of time due to the
day's run) the ship's clocks should be set for the L. A. T. of the prospective noon position. The noon
longitude may be closely estimated from the morning sight and the probable run. The navigator
should also set his own watch for that time, to the nearest minute, and note exactly the number of.
seconds that it is in error. He may now compute the constant (art. 333, Chap. XII) for the meridian
altitude. The daily winding of the chronometer is a most imjjortant feature of the day's routine, and
may well be performed at this hour. At a convenient time before noon, the observations for meridian
altitude are commenced and continued until the watch shows L. A. noon, at which time the meridian
altitude is measured and the latitude deduced.
If the weather is cloudy and there is doubt of the sun being visible on the meridian, an altitude
may be taken at any time within a few minutes of noon, the time noted, and the interval from L. A.
noon found from the known error of the watch. It is then the work of less than a minute to take out
the a from Table 26, the aC from Table 27, and apply the reduction to the observed altitude to obtain
the meridian altitude. Indeed, the method is so simple that it may be practiced every day and several
values of the meridian altitude thus obtained, instead of only one.
397. It now becomes necessary to find the longitude at noon. This may be done graphically by
a chart, or by computation. The former plan needs no explanation. There are a number of variations in
the methods of computation, one of which will be given as a type.
By the ship's run, work back the noon latitude to the latitude at a. m. time sight. If the Sumner
line was found from two assumed latitudes which differed i m minutes, while the corresponding longi-
tudes differed ± n minutes, then V difference of latitude causes ± — minutes difference of longitude. If
m '
the true latitude at sight is ± .r minutes from one of the assumed latitudes, then ± x X — is the corre-
m
spending difference of longitude. If the Sumner line was found from one assumed latitude and an
azimuth, Z, it makes an angle with the meridian equal to 90°— Z. Enter the traverse table with this
as a course and with the difference between the true and assumed latitudes as a latitude, and the
departure will be found; convert this into difference of longitude at the latitude of observation, and
apply the result with its jiroper sign to the longitude corresponding to the assumed latitude. Having
thus the longitude at sight, the longitude at noon is worked forward for the run. If the sights show a
fonsiderable current it should be allowed for, lx)th in working back the latitude and in bringing up the
longitude for the run between the sight and neon.
39S. CfRRENT .\ND RuN. — The current may be found by comparing the noon positions as obtained
by observation and by dead reckoning; and the day's run is calculated from the difference between the
day's noon position by observation and that of the preceding dav. To "current" is usually attributed
all discrepancies between the dead reckoning and observations; but it is evident that this is not entirely
due to motion of the waters, as it includes errors due to faulty steering, improper allowance for the
compass error, and inaccurate estimate of the vessel's speed through the water.
The noon position by observation becomes the departure for the dead reckoning that follows.
399. .\pTERNOON SuiHTs. — The p. m. time sight and azimuth is similar to the morning observation.
400. SrM.NER Lines. — By performing the work that has just been described a good position is
obtained at noon each day, which, in a slow-moving vessel with plenty of sea room, may be considered
sufficient; but conditions are such at times as to render it almost inijjeratively necessary that a more
frequent determination of the latitude and longitude be made. If the vessel is near the land or in the
vicinity of off-lying dangers, if she is running a great circle course requiring frequent changes, if she is
making deep-sea soundings, if she has just come through a period of foggy or cloudy weather, or if the
indications are that she is about to enter upon such a period, it is obviously inexpedient to await the
coming of the next noon for a fix. The responsibilities resting upon the navigator require that he shall
earlier find his ship's position; and, generally speaking, the greater the speed made by the vessel the
more absolute is this requirement.
The key to all such determinations will lie in the Sumner line, and a clear understanding of the
properties of such a line will greatly facilitate the solutions. The mariner must keep in mind two facts:
First, that a single observation of a heavenly body can never, by itself, give the point occupied by an
observer on the earth's surface; and second, that whenever any celestial body is visible, together with
enough of the horizon to permit the measuring of its altitude, aii observer may thereby determine a litie
which passes through his own position on the earth's surface in a direction at right angles to the bearing
of the body.
It may readily be seen that if two Sumner lines are determined the observer's position must be at
their intersection, and that that intersection will be most clearly marked when the angle between the
lines equals 90°; hence, if two heavenly bodies are in sight at the same time the position may be found
from the intersection of their Sunmer lines, the angle of intersection being equal to the horizontal
angle between the bodies. If only one body is in sight, as is generally the case when the sun is shining,
one line of position may he gotten from an altitude taken at one time, and a second line from another
altitude taken when it has changed some 30° in azimuth — usually, a couple of hours later. Bringing
forward the first line for the intervening run, the intersection may be found.
With the general principles of the Sumner line clearly before him, the navigator will find no diffi-
culty in making the choice of available bodies. If about to take a star sight, and sky and horizon are
equally good in all quarters, two bodies should be taken whose azimuths differ as nearly as po.ssible by
90°. If one body can be taken on or near the meridian, its bearing being practically north or south,
the resulting Sumner line will be east and west— that is, it may be said that whatever the longitude
(within its known limits) the latitude will be the same; the other sight may then be worked as a time
sight with this 8ing;le latitude and time will thus be saved. The same is true if Polaris is observed, and
it is a very convenient practice to take an altitude of that star at dawn and obtain a latitude for working
126 THE PRACTICE OF NAVIGATION AT SEA.
the a. m. time sight of the sun. A similar case arises when a body is observed on the prime vertical;
its Sumner line then runs north and south and coincides with a meridian; if the other body is favorably-
located for a <p' <p" eight, it may be worked with a single longitude and the latitude thus found directly.
If it is not possible to obtain two lines and thus exactly locate the ship, the indications of a single
line may be of ^reat value to the navigator. A Sumner line and a terrestrial bearing will give the ship's
position by their intersection in the same manner as two lines of position or two bearings; or the posi-
tion of the ship on a line may be shown with more or less accuracy bv a sounding or a series of
soundings. If the body be observed when it bears in a direction at right angles to the trend of a
neighboring shore line, "the resulting line will be parallel with the coast and thus show the mariner his
distance from the land, which may be of great importance even if his exat^t position on the line remains
in doubt. If the bearing be parallel to the coast line, then the Sumner line will point toward shore;
the value of a line that leads to the point that the vessel is trying to pick up is anijily demonstrated by
the experience of Captain Sumner that led to the discovery of the method (art. 372, Chap. XV).
For especially accurate work three Sumner lines may be taken, varying in azimuth about 120°; if
they do not intersect in a point, the most probable position of the ship is at the center of the triangle
that they form.
If two pairs of lines be determined, each pair based upon observation of two bodies bearing in
nearly opposite directions and at about the same altitude, the mean position that results from the inter-
section of the four lines will be as nearly as j>ossible free from those errors of the instrument, of refrac-
tion, and of the observer, which can not otherwise lie eliminated. This is fullv explained in article 451,
Chapter XVII.
401. Use of Stars, Pl.\nets, .\nd Moon. — It may be judged that the employment in navigation
of other heavenly bodies than the sun is considered of the utmost importance, and mariners are urged
to familiarize themselves with the methods by which observations of stars, planets, and the moon may
be utilized to reveal to them^he position of their vessels at frequent intervals throughout the twenty-
four hours.
It should be remembered, however, that in order to be of value these observations must be accu-
rate; and to measure an accurate altitude of the body above the horizon it is recjuired not only that the
body be visible but also that the horizon be distinctly in view. Care should therefore be taken to make
the "observations, if possible, at the time when the horizon is plainest— that is, during morning and
evening twilight. It may be urgently reijuired to get a position during hours of darkness, and a dim
horizon line may sometimes be seen and an observation taken, using the star telescope of the sextant;
if the moon is shining, its light will be a material aid; but results obtained from such .sights should be
regarded as questionable and used with caution, .\ltitudes measured, however, just before sunrise and
just after sunset are open to no such criticism ; a fairly well-practiced observer who takes a series of sights
at such a time, setting the sextant for equal intervals of altitude, will find the regularity of the corre-
sponding time intervals such as to assure him of accuracy.
402. Identification of Unknown Bodies. — On aci'ount of the very great value to be derived froni
the use of stars and planets in navigation, it is strongly recommended that all navigators familiarize
themselves with the names and positions of those fixecl stars whose magnitude renders possible their
employment for observations, and also with the general characteristics — magnitude and color — of the
three planets (Venus, Jupiter, and Mars) which are most frequently used. A study of the different
portions of the heavens, with the aid of any of the numerous charts and books which bear upon the
subject, will enable the navigator to recognize the more important constellations and single stars by
their situation with relation to each other, and to the pole and the equator.
It may occur, however, that occasion will arise for observing a body whose name is not known,
either because it has not been learned, or because the surrounding stars by which it is usually identified
are obscured by clouds or renderetl invisible by moonlight or daylight. In such a case the observer
may estimate the hour angle and declination (the hour angle applied to local sidereal tinie giving the
right ascension), and the star or planet may thus be recognized from a chart or from an inspection of
the Nautical Almanac. This rough method will generally suffice when the body is the only one of its
magnitude within an extensive region of the heavens; but cases often arise where a much closer
approximation is necessary, and more exact data is required for identification.
403. If in doubt as to the name of the body at the time of taking the sight, it should be ma<le an
invariable rule to observe its bearing by comp'ass, whence the true azimuth may be approximately
deduced by applying the compass error. The method « to be described then affords a convenient means
of identification. The quantities given are the corrected altitude of observation, h, the (approximate)
true azimuth of the body, Z, and the latitude by dead reckoning, L; those to be determined are the
declination, d, and the hour angle, t. From the astronomical triangle we have:
sin Z_8in t , .
~ r; or, sin Z cos /t=sin ( cos a.
sin p cosh
The value of sin Z cos h (calculated from the given azimuth and altitude) must therefore equal
sin t cos (I, whatever the values of f and d may prove to be. , , , . , u • ^.u
From a given latitude, azimuth and declination, the hour angle may be found either by azimuth
tables or an azimuth diagram; or from a given latitude, azimuth and hour angle, the dechnation may
be found bv the same means. If, therefore, some probable value of the declination be assumed, using
the known"latitude and azimuth, we may ascertain the corresponding hour angle; or, if the hour angle
be assumed, the corresponding declination is obtained ; then the product of sin t cos d may be calculated,
and if it agrees substantiallv with sin Z cos h, the trial values of the hour angle and declination are the
correct ones; if not, other trials mav be made until the correct ones are found. It may be remembered
that absolutelv exact results are not sought, and in practice the operation may be made very short; the
a SiiKgested by Lieut. G. W. Logan, U. S. Navy.
THE PRACTICE OF NAVIGATION AT SEA.
127
values of the quantities may be taken in even degrees and the logarithms need not be carried beyond
the third place; the sum of the logarithms will suffice and the corresponding numbers do not have to be
taken out. The possibility that the observed body may have been a planet must always be kept in
mind in looking it up in the star table or chart.
ExAMrLE: ;ilay 16, 1879, in Lat. 5° 2^., Long. 2'' 53"' W. by D. R., a star is observed whose corrected
altitude is 38°, and true azimutli \. 107° E. The Greenwich'sidereal time (as computed for use in the
regular working of the sight) is 12"' 53"'. Let it be required to identify the body.
First find the logarithm of sin Z cos h.
107° sin 9. 981
38° cos 9. 897
sin Z cos /» log 9. 878
Now suppose the observer estimates from the position of the body that its declination is 3° S. Look
in the azimuth table on the page of latitude5° (declination contrary name to latitude), and find the hour
angle (P- m.) corresponding to Dec. 3° and Az. 107°; this is about 1" 40'"; then with d=3°, 1=1" 40;",
find sin t cos d. (Sin t may be obtained either by converting time into arc and taking from the table in
the usual way, or by multiplying by 2 and finding it from the column headed "Hour P. M." Thus in
the present case find the sine of 25° 00' or of S'' 20"'. In using the time column be careful to take the
name from the foot of the page when the double angle exceeds &'. )
t l''40°'
d 3°
sin 9. 626
cos 9. 999
sin ( cos d log 9. 625
As this logarithm should equal 9.878, it is seen that tlie assumption is incorrect. Try a value of the
declination 5° farther south — that is, 8° S. The corresponding liour angle is 2" 50".
( 2" 50" sin 9. 830
d 8° cos 9. 996
sin ( cos d log 9. 826
The logarithm is not yet quite large enough; assume declination 10° S. ; the hour angle is 3'' 20™.
t 3^ 20" sin 9. 884
d 10° cos 9. 993
sin t COB d log 9. 877
This is practically identical with the logarithm of sin Z cos h, and the correct values are, therefore,
1=3" 20", rf=10° S.
We now have :
G. S. T. 12" 53"
Long. _2 53 W.
L. S. T. 10 00
H.A. J 20 E.
R. A. 13 20
From the Nautical Almanac it is found that the right ascension of Spica is IS' 19" and the dech-
nation 10° 32' 8. This is therefore the body observed.
Example: March 18, 1879, in I^t. 26° S., Long. 5" 42" E., by D. R., the altitude of a body is 41°
and its azimuth S. 84° E., the Greenwich sidereal time being lO" '52". Rwjuired the name of the body.
Z 84° sin 9.998
h 41° cos 9.878
sin Z cos h log 9.876
Assume first an hour angle of 3" 00'". The corresponding declination is 23° (same name as lati-
tude).
t 3" 00" sin 9.849
d 23° cos 9.964
sin ( cos d log 9.813
Next assume an hour angle of 3" 30". The declination is then 21° 8.
t 3" 30" sin 9.899
d 21° cos 9.970
sin ( cos d log 9.869
128 THE PRACTICE OF NAVIGATION AT SEA.
Assume hour angle 3'' 35'". Declination is still nearest to 21° 8
/ 3" Sa™ sin 9.907
d 21° cos 9.970
sin<cosrf log 9.877
The last assumption is therefore correct.
We then have:
G. S. T. lO" 52"
Long. ^ 42 E.
L. S! T. 16 34
H. A. 3 35 E.
R. A. 20 09
As there is no fixed star corresponding to these coordinates the tables for the planets should be
consulted. On March 18, 1879, the right ascension of Mars is 20" Og"', and the declination 21° 06' 8.
This is therefore the body that was observed.
404. The following is a summary of the method employed:
1. Reduce time of observation to Greenwich sidereal time and find the true altitude to the nearest
degree. (These operations must be performed before any sight can be worked; they are, therefore, not
stnctly a part of the process of identification. )
2. Correct the observed azimuth for deviation and variation.
3. Find the logarithm of sin Z cos h to the third place.
4. Assume a declination and find the corresponding hour angle that will produce the given azimuth
at the given latitude; orassume an hour angle and find the corresponding declination. (Use an azimuth
table or diagram for the purpose. )
5. Find the logarithm of sin t cos d to the third place.
6. Observe whether this agrees with the logarithm of sin Z cos h, and if it does not, repeat trials
until an agreement is found.
7. Having found the hour angle and declination, convert the Greenwich sidereal time into local
sidereal time and subtract the hour angle if west, or add it if east; the result is the right ascension of
the observed body, by which, with the declination and magnitude, the identification is accomplished.
405. The exactness with which the comparison of logarithms is carried out will depend upon the
possibility of errors of identification in the region of the heavens involved. It will not usually be
necessary to find the correspondence as closely as has been done in the examples given, and the cases
will be rare when, with a fair estimate of hour angle or declination at beginning, a sufficiently accurate
knowledge of the values can not be arrived at after the second approximation; and frequently the first
will suffice for identificaton.
406. Value of the Moon in Observ.\tions. — Xext to the sun, the most conspicuous body in the
heavens is the moon, and it may therefore frequently be employed by the mariner with advantage.
Owing to its nearness to the earth and the rapidity with which it changes right ascension and declina-
tion, the various corrections entailed render observations vt this body somewhat longer to work out,
with consequent increased chances of error; and errors in certain parts of the work will have more
serious results than with other bodies; the navigator will therefore usually pass the moon by if a choice
of celestial bodies is offered for a determination of position; but so many occasions present themselves
when there is no available substitute for the moon that the extra time and care necessary to devote to
it are well repaid. During hours of daylight it is often clearlv visible, and its line of position may cut
with that of the sun at a favorable angle, giving a good fix from two observations taken at the same
time, when the only other method of finding the position would be to take two sights of the sun sepa-
rated by a time interval in which an imperfect allowance for the true run intervening would affect the
accuracy of the result, or a clouding-over of the heavens would preventany definite result whatever being
reached; and during the night, the gleam upon the water directly below the moon may define the
horizon and give opportunity for an altitude of that body when it is impossible to take an observation
of any other. Navigators are therefore recommended to make use of the moon with complete confidence
whenever it will serve their purposes. It has been the purpose of this work to point out the features of
the various sights wherein the practice with the moon differs from that of the sun, stars, or planets;
care and intelligent consideration will render these quite clear.
Besides its availability for determining Sumner lines of position, which it shares with other bodies,
the moon affords a means" for ascertaining the Greenwich meantime independently of the chronometer,
thus rendering it possible to deduce the longitude and chronometer error. This is accomplished by the
method of lunar distances, which is fully explained in Appendix V. If the Greenwich time given by
an observation of lunar distance could be relied upon for accuracy, the method would be a great boon
to the navigator; but this is not the case. The most practiced observer can not be sure of obtaining
results as close as modern navigation demands, and the errors to which the method is subject are larger
than the errors that may be expected in the chronometer, even when the instrument is only a moder-
ately good one and its-rate is carried forward from a long voyage. The method is not, therefore, recom-
mended for use except where the chronometer is disabled or where it is known to have acquired some
extraordinary error; and when lunar distances are resorted to care must be taken to navigate with due
allowance for possible inaccuracy of the results. In this connection it is appropriate to say that the
best safeguard against the dire consequences that may result from a disabled or unreliable chronometer
is for every vessel to carry two— or, far better, three— of those instruments, the advantages of which
plan are stated in article 265, Chapter VIII.
407. Employment op Bodies dependent upon their Position.— The practical navigator will soon
observe that there are certain conditions in which bodies are especially well adapted for the finding of
latitude, and others where the longitude is obtained most readily.
THE PRACTICK OF NAVIGATIOJT AT SEA. 129
Taking the sun for an example, when a vessel is on the equator and the declination is zero, that
body will rise due east of the observer and continue on the same bearing until noon, when for an instant
it will be directly overhead, with a true altitude of 90°, and will then change to a bearing of west, which it
will maintain until its setting. In such a case any observation taken throughout the day will give a true
north-and-south Sumner line, defining longitude perfectly, but giving no determination of the latitude,
excepting for a moment only when the body is on the meridian. With the exception noted, all efforts
to determine the latitude will fail. The reduction to the meridian takes the form , becoming inde-
terminate, and in the <)c/ q/' sight the cosine of <p' will assume a value that corresjwnds alike to any
angle within certain wide limits — the limits within which the circle of equal altitude has practically a
north-and-south direction. In conditions approximating to this we may obtain a longitude position
more easily than one for latitude, even within a few minutes of noon.
,\s the latitude and declination separate, conditions become more favorable for finding latitude and
less so for longitude; the intermediate cases cover a wide range, wherein longitude may be well determined
by observations three to five hours from the meridian, and latitude by those within two hours of
nieridian passage. As extreme conditions are approached the accuracy of longitude determinations con-
tinues to decrease; at a point in 60° north latitude, when the sun is near the southern solstice, its bear-
ing differs only 39° from the meridian at rising; or, in other words, even if observed at the most
favorable position, the resulting Sumner line is such that V in latitude makes a difference of 1 .."i miles of
departure, or 2'. 6 of longitude, and is far better for a latitude determination than for longitude. And in
higher latitudes still this condition is even more marked.
Having grasped these general facts, the navigator must adapt his time for taking sights to the cir-
cumstances that prevail, and when the sun does not serve for an accurate determination of either
latitude or longitude the ability to utilize the stars, planets, and moon as a substitute will be of the
greatest advantage.
40§. Use of V.\kiou8 Sights. — Having taken a sight, the navigator may sometimes be in <loubt as
to the best method of working it. No rigorous rules can be laid down, and experience alone must be
his ^uide. In a general way it may lie well, when the body is nearer to the prime vertical than to the
meridian, to work it for longitude, assuming latitude, and using the time sight; and when nearer the
meridian to work it for latitude, assuming longitude, by the cp' q/' method. The time sight is more
generally used than the other, it has w ider limits of accurate application and is probably a little quicker;
but as the meridian is approached and the hour angle decreases small errors in tlie terms make large
ones in the results. The q/ cp" or latitude method should not ordinarily be employed beyond three
hours from the meridian, and then only when the body is within 45° of azimuth from" the meridian and
has a tleclination of at least 3°; with an hour angle of 6'' (90°) or a declination of 0° the trigonometric
functions assume such form that the method is not available; nor does it give definite results when the
azimuth is 90° or thereabouts.
When the Viody is close enough to the meridian for the method of reduction to the meridian to be
applicable, that method is to be preferre<l because of its quickness and facility. It should be noted,
however, that, though close enough to employ the reduction, it may not be sufficiently correct to
assume that the lx)dy bears due north or south, and the sight should be worked with two longitudes,
or the Sumner line determined by the azimuth, unless the bearing nearly coincides with the direction
of the meridian.
In cases where a body transits near the zenith, a good fix both in latitude and longitude may be
obtained by sights, a few minutes apart, near its meridian passage. Various special methods have
been devised for doing this, V)ut it seems simpler to treat the problem as an ordinary one for Sumner
lines, except where it falls within the narrow limits of application of the equal altitude method (art.
352, Chap. XIII). The .solution is possible, l)ecause in the condition where it is available (that of ahigh
transit) the body makes a very rapid change of azimuth (from nearly east to nearly west) in a short
space of time, and two observations separated by a short interval give Sumiu r lines that cut at a
favorable angle. The time sight or latitude sight may be used according as the body's Ijearing is
greater or less than 45° from the meridian. If one observation he taken when the bearing is about SE.
and the other when it is about SW., the intersection, allowing for intervening run, will not only give
the longitude, but will also afford a good check upon the meridian obsenation for latitude, which, in
the case of high transits, it is difficult to make with perfect accuracy.
409. Working to Skcoxds and Accuh.\cv of 1)etermix.\tions. — The beginner who seeks counsel
from the more exiierienced in matters pertaining to navigation will find that he receives conflicting
advice as to whether it is more expedient to carry out the terms to seconds of arc, or to disregard seconds
and work with the nearest whole minute.
It is a well-recognized fact that exact results are not attainable in navigation at sea; the chro^
nometer error, sextant error, error of refraction, and error of observation are all uncertain; it is impos-
sible to make absolutely correct allowance for them, and the uncertainty increases if the position is
obtained by two oV)servations taken at different times, in which case an exactly correct allowance for
the intervening run of the ship is an essential to the correctness of the determination. No navigator
should ever assume that his position is not liable to be in error to some extent, the precise amount
depending upon various factors, such as the age of the chronometer rate, the (juality of the various
instruments, the reliability of the observer, and the conditions at the time the sight was taken; perhaps
a fair allowance for this possible error, under favorable circumstances, will be 2 miles; there.fore,
instead of plotting a position upon the chart, and proceeiiing with absolute confidence in the belief that
the ship's position is on the exact point, one may describe, around the point as a center, a circle whose
radius is 2 miles — if we accept that as the value of the possible error — and shape the future courses
with the knowledge that the ship's position may be anywhere within the circle.
It is on account of this recognized inexactness of the determination of position that some navigators
a.asiniie that the odd seconds may be neglected in dealing with the different terms of a sight; the average
possible error due to this course is probably about one minute, though under certain conditions it may
24972°— 12 9
130 THE PRACTICE OF NAVIGATION AT SEA.
be considerably more. It is possible that, in a particular case, the error thuw introduced through one
term would be offset by that from others, and the result would be the same as if the seconds had been
taken into account; but that does not affect the general fact that the neglect of seconds as a regular
thing renders any determination liable to be in error about one minute. Those that omit the seconds
argue, however, that since, in the nature of things, any sight may be in error two minutes, it is imma-
terial if we introduce an additional possibility of error of one minute, because the new error is as liable
to decrease the old one as to increase it; but the fallacy of the argument will be apparent when we return
to the circle drawn. around our plotted point. The eccentricity of the sextant may exactly offset the
improper allowance for refraction, and the mistake in the chronometer error may offset the observer's
personal error, but unless we know that such is the case — which we never can — we have no justification
for doing otherwise than assume that the ship maybe any place within the 2-mile circle. If, now,
we increase the possible error by 1 mile, our radius of uncertainty must be increa.«ed to 3 miles, and the
diameter of the circle, representing the range of uncertainty in any given direction, is thereby increased
from 4 to 6 miles.
It is deemed to be the duty of the navigator to put forth every effort to ol>tain the mod probable
position of the ship, which rpcjuires that he shall eliminate possible errors a.s completely as it lies
within his power to do. By neglecting seconds he introduces a source of error tliat might with small
trouble be avoided. This becomes of still more importance since modern instruments and modern
methods constantly tend to decrease the probability of error in the observation, and to place it within
the power of the navigator to determine his ship's position with greater accuracv.
410. There is a more exact way of defining the area of the ship's possibfe position than that of
describing a circle around the most probable p<iint, as mentioned in the preceding article, and that is to
draw a line on each side of each of the Sumner lines by whiih the position is defined, and at a uniform
distance therefrom equal to the possible error that the" navigator believes it most reasonable to assume
under existing conditions; the parallelogram fi rmed by these four auxiliary lines marks the limit to be
assigned for the ship's position; this method takes account of tlie errors due to poor intersections, and
warns the navigator of the direction in which his position is least clearly fixed and in which he must
therefore make extra allowance for the uncertainty of his determination.
It must be remembered in this connection that no position can ever be obtained except from the
intersection of two Sumner lines, whether or not the lines are actually plotted; thus, a meridian altitude
gives a Sumner line that extends due east and west, and a sight on the prime vertical a line that extends
north and south, though it may not have been considered necessary to work the former with two
longitudes or the latter with two latitudes.
411. The Work Book and Forms for Sights. — The navigation work book, or sight book, being
the official record of all that pertains to the navigation of the ship when not running by bearings of the
land, should be neatly and legibly kept, so that it will lie intelligible not only to the person who per-
formed the work, but also to any other who may have reason to refer to it.
Each day's work should be' begun on a new page, the date set forth clearly at the top, and prefer-
ably, also, a "brief statement of the voyage upon whicli the ship is engaged. It is a good plan to have
the dead reckoning begin the space allotted for the day, and then have the sights follow in the order in
which taken. The page should be large enough to permit the whole of any one sight to be contained
thereon without the necessity of carrying it forward to a second page. No work should be connnenced
at the bottom of a page if there is not room to complete it. Every operation pertaining to the working
of the sights should appear in the book, and all irrelevant matter should be excluded.
It is well to observe a systematic form of work for each sight, always writing the different terms in
the same position on the page; this practice will conduce to rapidity and lessen the chances of error.
In order to facilitate the adoption of such a method, there are appended to this work (Apiiendix II)
a series of forms that are reconmiended for dead reckoning, and for time sights, meridian altitudes, and
latitude sights (both by <f/ cp" formula and method of reduction to the meridian), for the stm, stars,
planets, and moon, respectively. For beginners, these are deemed of especial importance, and it is
recommended that, until ]ierfect familiarity with the different sights is acquired, the first step in work-
ing out an observation be to write down a" copy of the appropriate blank form, indicating the proper
sign of application of each quantity (for which"the notes will be a guide), and not to put in any figures
until the scheme has been completely outlined; then the remainder of the work will consist m writing
down the various quantities in their proper places and performing the operations indicated.
MAKINE SURVEYING.
131
CHAPTER XVII.
MARINE SUKVEYING.
413. Definitioxs. — Surreying is the art of representing upon paper the pnrface of the earth, giving
its characteristic features, such &f, on land, the position of prominent objects, lieightg, and depressions,
and on wat«r, the depth, character of bottom, and position of shoals.
Topographirid Surreii'mg delineates the land, and Ifydrof/raphic Stirrei/lng, the water.
Geode."!! is a higher kind of surveying, which takes into account the curvature of tlie earth. To
points determined l>y a geodetic sur\ey other surveys are referred.
It is not deemed appropriate to include in this work a complete treatise on JMarine Surveying. The
scoi)e of this chapter will be to set forth such general information regarding the principles of surveying
and the instruments therein employed as will give the navigator an intelligent understanding of the
subject sufficient to enable him to comprehend the methods by which marine (charts are made, and, if
occasion should arise, to conduct a survey with such accuracy as the instruments ordinarily at hand on
shipboard may permit. For a more detailed di.acussion of Marine Surveying, the student is referred to
the various publications which treat the suliject exhaustively.
INSTRUMENTS EMPLOYED IN MARINE SURVEYING.
413. The Theodolite
AND Tr.\nsit. — The Theodo-
lite (fig. 54) is an instrument
for the accurate measure-
ment of horizontal and ver-
tical angles. While these
instruments vary in detail
as to methods of construc-
tion, the essential principles
are »lways identical.
A telescope carrying cross-
hairs in the common focus
of the object-glass and eye-
piece is so mounted as to
have motion about two axes
at riglit angles to one an-
<?ther; graduated circles and
verniers are provided by
which angular motion in
azimuth and (usually) in
altitude may be measured;
and the instrument is capa-
ble of such adjustment by
levels that the planes of mo-
tion about the respective
axes will correspond exactly
with the horizontal and the
. vertical. .
The telescope is carried
in appropriate supports
upon a horizontal plate
which has, innnovably at-
tached to it, one or more
verniers, and which revolves
just over a graduated circle
that is marked upon the
periphery of a second hori-
zontal plate, a means of
measuring the motion of
the upper plate relatively to
the lower one Ijeing thus
provided. Thumb- screws
are fitted by which the up-
per plate may be clamped
to the lower, and (except-
ing in some simpler forms of
the instrument) others by
which the lower plate may
be made immovable in azi-
muth, or allowed free mo-
tion, at will; all clamping ^"^■- '^'*-
arrangements include slow-motion tangent-screws for finer control.
132 MARINE SURVEYING.
A vertical graduated circle, or arc, with a vernier, clamps, and tangent-screws, is fitted to most
theodolites, for the measurement of the angular motion of .the telescope in altitude.
The theodolite usually carries a magnetic needle, with a graduated circle and vernier for compass
bearings. The instrument is mounted upon a tripod, and levels and leveling-screws afford a means of
bringing the instrument to a truly horizontal jiosition.
The TranKtt used in surveying is a modified form of the theodolite, and is generally employed where
less accuracy is reijuired; it takes its name from the fact that the telescope may be turned completely
about its horizontal axis, or tranniled, without removal from its supports.
414. The line of collimatlon of a telescope is an imaginary line passing through the optical center of
the object-glass in a direction at right angles to that of its axis of rotation. This is also called the axis
of collimation. The Une of si;/lil if an imaginarv line i>aosing through the optical center of the object-
glass and the point of intersection of the cross-hairs.
A theodolite or transit, before it can be used for the accurate measurement of angles, must be in
adjustment in the following respects: (n) The vertical axes of revolution of the upper and lower hori-
zontal plates nmst be coincident; (6) the axis must be vertical and the plates horizontal when the
bubbles of the levels are in their central positions; (c) the vertical cross hair must be perpendicular
to the horizontal axis of the telescope; (rf) theline of collimation must coincide with the line of sight;
(e) the horizontal axis of the telescope must be perpendicular to the vertical axis of the instrument;
(/) the bubble of the telescope level must stand at the middle of its scale, and the vertical circle must
read zero, when the line of collimation is horizontal.
The last-named condition may be disregarded it vertical angles are not to be measured.
415. The instrument being in adjustment, to observe angles it should be set up, leveled, and
focused. This involves placing the tripod so that a plumb bob from the center of the instrument shall
hang directly over the spot at which the measurement is to be made. The legs of the tripod should be
firmly placed in such manner that the height shall be convenient for the observer and the instrument
shallbe nearly level. Then the horizontal plates are brought to a true level by means of the leveling
screws and bubbles. The telescope should next be focused by moving the object glass and eyepiece in
such manner that the object sighted and the cross hairs may be plainly seen and that the object will
not api>ear to have motion relatively to the cross hairs as the eye is moved to the right or left in front
of the eyepiece. This last condition insures the cross hairs being at the common focus of the eyepiece
and objective.
To observe a horizontal angle with a theodolite or transit, clamp the upper plate to the lower at zero,
leaving the lower plate undamped; swing the telescope so that its vertical cross hair bisects one of the
objects, and clamp the lower plate; unclamp the upper plate and bring the telescope to bisect the other
object, and the reading of the vernier on the scale will give the required angle. (The final nice motion
by which the cross-hair is brought exactly upon a point is always given by the tangent screw. )
In taking a round of ungles, this operation is repeated successively upon each object to be observed
about the horizon, the upper plate being always swung, while the lower is kept where set upon the
first f)bject, or origin. The result w ill give the angular distance of each object from the origin, and, if
the observations have been accurately made, upon finally sighting back to the origin, the reading
should be zero.
To repeat ati angle, having made the first measurement of it in the usual way, tmclamp the lower
circle and swing back the telescope until it again points to the first object, and clamp it; then unclamp
the upper circle, swing to the second object, and clamp. The .■•cale-reading should now be double that
of the first angle. Repeat as often as the importance of the angle requires, and the accepted value will
be the final reading divided by the number of measurements. All angles of the main triangulation,
and others of importance in the survey, are repeated.
Defects in adjustment of the instrument may be eliminated by taking one series of angles with
the telescope direct and another with the teleacope rererml. To reverse the telescope, revolve it about its
horizontal axis through 180°, then swing it about its vertical axis through 180°— in other words,
invert it.
Vertical angles are measured on the same principle as that described for horizontal ones.
The process of setting up the instrument at a station and observing the angles between the various
objects that are visible is called occuyiiiiitg the station.
416. The Plane Table.— This is an instrument by which positions are plotted in the field directly
upon a working sheet. It consists (fig. 55) of a drawing board mounted upon a tripod in such manner
as to be capable of motion in azimuth, and with facilities for being brought to a perfect level; in con-
nection with it is emi)loved an alidade, consisting of a straightedge ruler, upon which is moimted a
telescope with cross-hairs" whose line of sight is exactly parallel to the vertical plane through the edge
of the rule. It is evident that it a sheet representing a chart be placed upon such a board and turned
•BO that the true meridians, as portrayed thereon, lie in the direction of the earth's meridian at that
place, then all lines of bearings on the chart will coincide with the corresponding lines on the earth's
surface; from which it follow.s that if the alidade be so placed that its rule passes through the spot
on the chart representing the ])osition of the observer, while the telescope is dn-ected to some visible
object, the position of that object on the chart lies somewhere upon the line drawn along the edge of
the rule. Upon this general iiriuciple depend the various applications of the plane table.
The drawing board is usually made of several pieces of well-seasoned wood, tongued and grooved
together, with the grain running in different directions to prevent warping; abo\it its edge are several
metal clips for securing the jiaper in place. It is supported upon three strong brass arms, to which it is
attached by screws, thus permitting its removal at will. The arms are attached to a horizontal plate
which revolves upon a second horizontal plate lying immediately below it; a clamp and tangent screw
are fitted, by which the upper plate, and with it the drawing board, may te secured to the lower plate,
or may be given a fine motion in azimuth. Three equidistant lugs of brass, grooved on the under side,
project down from the lower plate, resting on screws in the top of the tripod, by which the instrument
IS leveled; when adjusted in this respect it is firmly clamped in position, and, as the tripod is made
unusually large, the adiustmont is not easily deranged.
MARINE SURVKYINCr.
133
The alidade is a metal straightedge with a vertical column at its center, at the top of which are the
supports which carrv the telescope; a vertical arc and vernier are jirovided for measuring the motion of
the telescope in altitude. The telescope is usually so fitted that it may he revolveil in azimuth through
an arc of exactly 180°, for the purpose of adjusting the line of collimation. On top of the rule near its
center is the level— sometimes replaced by two levels at right angles— by means of which it may be seen
when the table is in a true horizontal position.
A magnetic needle mounted in a rectangular metal box, whose outer straiglitedge is i)arallel to the
zero line of a graduated scale over which the needle swings, is provided for drawing tlie north-and-south
line on the chart; this is called a riedinatoire.
Fig. 5.1.
417. To be in coiTCct adjustment, a ])lane table must comply with the following conditions:
(a) The fiducial edge of the rule must be perfectly straight, (b) The level nuistliave the bubble in
its central position w hen the table is truly horizontal. {<■) Tlie vertical cros.s hair niu.st be perpendic-
ular to the horizontal axis of the telescope. (<?) The line of collimation must coincide with the line of
sight, (f) The horizontal axis of the telescoi)e must be parallel to the plane of the table. {/) The
vertical circle shfiuld read zero when the line of collimation is horizontal.
41S. The results derived from the use of the plane table, like all others dependent upon graphic
methods, must be regardeil as less accurate than those deduced by computation, and even less accurate
tiian those derived from the careful plotting of theodolite angles. Hence it is that, in a careful marine
survey, this instrument would be employed only for the topography aud shore line.
For whatever purpose used, the plane table would not ordinarily be called into requisition until the
survey had so far progressed that a chart could be furnished the olxserver showing certain stations
whose positions were already estahlisheil; with this cliait, the first steji would be to ucriipi/ one of the
determined points. The table must be set up with the point on the chart directly over the center of the
station; it must then he leveled and the telescope focuseri as described for the theodolite or transit; and
linally it must be oriental, that is, so turned in azimuth tliat all lines of the chart are parallel to similar
lines of the earth's surface. To orient, unclamp the table and swing it until the north-and-south lineof the
chart is approximately ])arallel to that of the earth, one means fif doing which is afforded by the decli-
iiatoire; place the alidade so tiiat the edge of the rule passes througlithe points on the chart representing
the station occupied and some second station which is clearly in view; then, sighting through the tele-
scope, perfect the adjustment of the table by swinging it until the second station is exactly bisected by
the vertical cross hair, the final slow motion Iteing obtained by clamping the table and working the
tangent screw. If the a<ljustrnent lias been correctly made, the rule may be laid along the line joining
the station occupied and any otiier on the chart, and the telescope will point exactly to that other station.
Being properly oriented, if the alidade be so placed that the edge of the rule pass through the station
occupied, and the telescope point directly to some unknown oVtject whose position is to be determineil,
134 MARINE SURVEYING.
then a line drawn alonf>; the rule will contain the point which represents the position of that object.
If, now, the plane table be set \ip at a second station, oriente<l for its new position, and a line be simi-
larly drawn from that station toward the one to be established, it will intersect the first line in the
required point. This is the method of determining positions by prosection. Actually, the surveyor does
not regard the point as well established until the intersection is checked by a line from a third station.
In practical work, of course, each station is not occupied separately for the determination of each
point; the instrument is set up at a station, lines are drawn to all required points in view, and each line
IS appropriately marked; then a second station is occupied, and the operation repeated, and so on, the
various intersections being marked as the work proceeds.
A second method of establishing positions is that of reaeclujn; iu this the iir.st line is drawn from
some known station, as in the preceding method, and the observer next proceeds to the place whose
position is rei^uired and occupies it; the plane table is there oriented Ijy means of tlie line already
drawn, placing the edge of the rule along the line, sighting back toward the first station, and swinging
the table until that station is in the lino of sight of the telesco].>e; then choose some other established
station as nearly as possible at right angles to the direction of the first; place the edge of the rule upon
the plotted position of this station and swing the alidade (the rule always being kept on the plotted
point) until the object is bisected by the telescope cros.s-hairs; draw this line, and its intersection with
the first will give the required point, the accuracy of which can be checked from some other i>lotted
station.
A third method of locating a point is by means of a single bearing from a known station, with tlie
distance from the occupied station to the required one, the process of jilotting lieing self-evident.
A fourth method is given by occupying an uudeteruiined position from which three established
stations are in view; the point occupied by the observer is then plotted by an application of the "three-
point problem."
419. It may be seen that where tlie greatest accuracy is not essential the plane table may be
employed for plotting all the points of a survey. In such a case.it would only be necessary to begin
with the two base stations, plotted on the sheet on any relative bearing whatsoever and at a distance
apart equal to the length of the base line (reduced t) scale), as measured by the most accurate mean.s
available. The work of plotting might eveu proceed before the base line ha:l been measured, the two
stations being laid off at any convenient distance apart; when, later, the base line was measured, the
scale of the chart would be determined, being equal to the distance on the chart between base stations
divided by the length of the base line.
420. A plane table could be improvised on shipboard which would greatly facilitate the operation of
any surveying work that a vessel not equipped with instruments might ba called U])on to perform. A
drawing board could be mounted upon a tripod (as, for example, the tripod sujiplied for compass work
on shore) in such manner as to l)e capable of motion in azinmth; it could be brought nearly to the
horizontal, if no better means offered, by moving the tripod legs, and this adjustment could be proved
by any small spirit level; sight vanes could be erected upon an onlinary ruler to take the place of the
alidade; in case there was difficulty in observing any object with such an alidade, because of its altitucle
or for other reasons, a horizontal angle might be observed with a sextant and plotted with a pro-
tractor. By this means work could l)e done which, even if it should lack complete accuracy, might be
of great value.
421. The Telemeter and St.adia. — Any telescope fitted with a pair of horizontal cross-hairs at
the focus may be used as a telemeter, and v/hen accompanied by a graduated staff, called a .itudki, affords
a means of measuring distance (up to certain limits) with a close degree of accuracy; the method con-
sists in observing the number of divisions of the scale subtended by the hairs when the stadia is held
up vertically and perpendicular to the line of sight of the teies^-ope, it being evident that the closer the
distance the fewer divisions will appear between them. The facility with which distances can Ije
measured by this method makes it most im|)ortant that all telescopes of theodolites, transits, and plane
tables be fitted as telemeters, and that stadia rods be provided for all surveying work.
Speaking approximately, it may be said that the number of divisions intercepted between the cross-
hairs will vary directly as the distance of the stadia rod. This would be exactly true if we looked at the
object through an empty tube, directly between the hairs. Since, however, the rays from the stadia are
refracted by the object glass before they are intercepted by the wires, the statement, to be absolutely
exact, must be slightly modified; but for practical surveying work it may be accepted as given.
422. There are two methods of installing the telemeter cross-hairs — the first, in which they are
immovably secured in the telescope and always remain at the same distance apart, and the second, in .
which the distance of the cross hairs is made variable, being under the control of the observer. The
former is generally regarded as the preferable method, and when it is employed it is evident that the
subtended height of the stadia bears a constant ratio to the distance of the staff from the telescope. It
proves most convenient in practic'e to space the hairs so that this constant ratio is some even multiple
of 10, for facility in converting scale readings into distance; it is also advantageous to mark the stadia
in the unit of the chart scale and decimals thereof; for example, if the ratio of stadia height to distance
were 100, and the stadia were marked in meters and decimals, a reading of 2.07 would at once be con-
verted into a distance of 207 meters. Any units and any ratio may, however, be employed, and fol-any
given setting of cross-hairs it is very easy to graduate a stadia, by experiment, for any desired units; for
example, if it is required to mark the stadia in feet, set up and level the telescope, measure off a distance
of exactly 100 feet from it, hold up an unmarked staff and mark upon it the points intersected by the
cross hairs; the interval between these marks will represent 100 feet of the scale; divide this length into
100 parts, each of which will represent a distance of one foot, and mark the whole staff on the same scale;
then if the stadia be held up at any distance, the cross-hairs will intercept a number of divisions corre-
sponding to the I umber of feet of distance.
MARINE SUEVEYTNG. 135
When the crosshairs are movable the ratio becomes variable, but the principle of measuring
/emains the same— namely, the distance of the staff from the teleseoiie is equal to the existing ratio
multiplied by the distance intercepted on the scale.
423. Tlie stadia is made of a light, narrow piece of wood and is usually lunged for convenience in
transporting. Ordinarily the backgrtmnd of the scale is painted white, while the main divisions are
marked in red, with minor divisions in black, and geometrical figures arc employed to facilitate the
reading of fractional parts of the scale. Devices are furnished by which the man holding the stadia
may know when it is at right angles to the line of sight of the telescope — an essential condition for
accuracy of measurements.
424. The use of the telemeter and stadia for measuring distances is limited to the distance at
which the scale divisions can be accurately read through the telescope. For fairly close work and with
the cla.ss of telescope usually supplied with surveying instruments, 400 meters represents about the
greatest distance at which it can be employed. With this limitation, the character of the survey
determines the nature of its employment. In a careful survey its greatest use would be in connection
with the theodolite or plane table in putting in shore lines, contour lines, and topography generally.
In a survey where only approximate results are sought it might afford the Best means for the measure-
ment of the base.
423. If the telemeter be applied to a theodolite, tran.sit, or plane table which is fitted with a
graduated vertical arc or circle, it is possible to measure the distance to the stadia not only in a horizontal
but also in a vertical direction. In this case the vertical angle nmet te observed as well as the stadia
reading. Tables are computed giving the solution of the triangles involved.
426. In making a survey with the ordinary resources of a ship, the principle of the telemeter and
stadia may l>e profitably employed, using a sextant and imiirovised staff. In this case it is usual to have
the stadia of some convenient fixed length, as, for example, 10 feet, and of slight width and thickness;
this is held at right angles to the line of sight from the observer, who notes the angle subtended by the
total length; tables are prepared by which the distance corresponding to each angle is given.
427. The Sext.vxt. — This instrument is of the greatest value in hydrographic surveying. It is
fully descril)ed elsewhere in this work and its adjustment explained (Chap. VIII).
Sextants are manufactured of a form especially adapted to surveying work; they are smaller and
lighter than those usually employed in iistronomiial ob,servations, but have a longer limb, by which
angles may be measureil up to 135°; the vernier is marked for quick reading and has no finer graduation
than half minutes; the telescope has a large field.
This instrument is principally emploved in measuring the horizontal angles by means of which
soundings are plotted. It may, however, be put to various uses when making an approximate survey,'
as has already been explained. It should be rememlx'red, in measuring terrestrial angles with a sextant,
that rigorous methods require a reduction to the horizontal if either of the objects has material altitude •
' above the horizon.
425. The Level. — This is an instrument for the accurate measure of differences of elevation. It
consists of a telescope, carried in a Y-shape<l rest, which is mounted uixin a triptxl and leveled in a man-
ner similar to a theodolite; but it differs from that instrument in that the telescope is not capable of
motion about a horizontal axis, and in having no graduated circle for measurements of a'titude and
azimuth. The principle of its use contemplates placing the line of coUimation of the telescope in a truly
horizontal plane and keeping it so fixed.
429. It is principally employed in marine surveying to determine heights and contour lines — the
latter being lines of ecjual elevation above the sea level — and for locating bench marks for tidal observa-
tions (Chap. XX). In connection with it is U8e<l a graduated staff called a leveling rod, carrying a con-
spicuous mark, adjustable in height, called a target. To ascertain the difference of level between any
two points, set up the level with the telescope horizontal at some place between them; let an assistant
take the leveling rod to one of the points, and, while holding it on the ground in a truly vertical posi-
tion, move the target, under the direction of the observer at the telescope, to a point where it is exactly
bisected by the horizontal cross-hair; the height of the target on the staff — that is, the height of the cross-
hair above the level of the first point — is then accurately rea<l with a vernier; now, withou,t moving the
level, shift the rod to the second point and again adjust the target and read it. It is evident that a com-
parison of the reading at the first position with that at the second will give the difference of height at
the two points. The difference that can be read from one location of the instrument is limited by the
length of the roil; but by making a sufficient number of shifts any clifference may lie measured. .
The work of the level may l)e performed equally well by a fhe<idolite whose telescope is adjusted
to the true horizontal.
4:lO. Heliotrope .\.\d Hemogr.\pi[. — These are instruments sometimes employed in surveying, by
means of which the sun's rays may be refiected in any given direction; the object of their use is to
render conspicuous a station which is to be obser\'ed at a distance and which would not otherwise be
distinguishable. The instruments vary widely in form of construction and, in the absence of those
made for the )iur]K>.se, substitutes may easily be devised.
4:|l. .\sTRo.NoMiCAL Tr.\nsit IxsTRiME.NTs. — Various instruments are employed for the a.stronom-
ical determinations necess'ary in a marine survey, .\mong these are the zenith tdescupe and portable
transit. While differing in detail they consist essentially of a telescope mounted upon a horizontal
axis that is placed truly in the prime vertical, thus insuring the revolution of the line of collimation in
the meridian; a vertical graduated circle ancl vernier are sup))lied, affording a measure of altitude; in
the focus are a number of equidistant vertical croas-hairs t)r lines; a small lamp is so placed that its
rays illuminate the cross-hairs and render, possible observations at night. Latitude is obtained by
observing the meridian altitude of stars; hour angle (and thence longitude) by observing the times of
their meridian transit, which is taken from the mean of the times of passing all of the vertical cross-hairs.
Excepting in surveys of a most accurate nature, the astronomical determination of position by the
sextant and artificial horizon is regarded as satisfactory.
136
MARINE SURVEYING.
432. The Three- Akmed Protkactok, or Station Pointer. — Tliis is an instrument whereby posi-
tions are plotted on tlie principle of the "three-point problem," of ■which an explanation is given in
article 152, Chapter IV. It consists (lig.
66) of a graduated circle with three arms
pivoted at the center; each arm has one
edge that, is a true rule, the direction of
which always passes through the center
of the circle. The middle arm is immov-
ably fixed at the zero of the scale; the
right and left arms each revolve about the
center on their own sides, and are pro-
vided with verniers giving the angular
distance from the middle arm. The pro-
tractor being set for the right and left
angles, it is so moved that the three arms
pass through the respective stations, when
the center marks the position of the ob-
server. Center pieces of varvms forms
are provided, being cylindrical plugs
made to fit into a socket at the pivot, and
by employing one or the other of them
the true center may be pricked with a
needle, dotted with a pencil, or its position
indicated by cross-hairs. Adjustable arms
are provided which can be fitted to the
ends of the ordinary arms when working
with distant signals.
The most valuable use of the three-
armed protractor is^n plotting the posi-
tions of^ soundings taken in boats, where
sextant angles between signals are ob-
served. It may occur, however, that
certain shore stations will be located by
its use.
433. In default of a three-anned
protractor, a piece of tracing paper may
be made to answer its purpose. To use
the tracing paper, draw a line, making a
dot on it to represent tlie center station,
and with the center of an ordinary pro-
tractor on the dot, lay off the two observed
angles right and left of the line; then,
laying f liis on the plan, move it about till
the tiiree lines pass exactly through the
three stations observed. The dot from
which thev were laid off will Ije on the
Fit;. 56.
position of the observer, and must be j>ricke<l lightly through or marked underneatli iu pencil.
434. The Beam Compass. — This instrument (tig. 57) is employed in chart drafting and performs
the functions of compasses and dividers when the dis-
tance that must be spanned i-* l^eyond the limits of
those instruments in their ordinary form. Itconsi.ats
of an angular bar of wood or metal upon wliich two
instruments termed beam hea<ls are fitted in such a
manner that the bar may slide eisily through tliem.
A clamping screw attached to one side of the beam
head will fix it iu any part of its course along the
beam. Upon each head a socket is constructed to
carry a plain point, exchangeable for an ink or a
jieucil point. For exact purposes the beam head
placed at the end of the beam has a fine adjustment,
which moves the point a short distance to correct
any error in the first rough setting of the instrument.
This adjustment generally consists of a milleil-head
."crew, which passes through a nut fixed upon the
end of the beam head, which it carries with its
motion.
435. PROPORTIONAL Dividers. — These are jirin-
cipally employed for reducing or enlarging drawings
in any given proportion. They consist (fig. 58) of
two narrow flat ]iicces of metal called Irr/K, which
turn upon a pivot whose position is movable in the
direction of their length. The ends of both legs are shaped into points like those of ordinary dividers.
AVhen the pivot is fixed at the middle of the legs, any distance measured V)y the points at one end is
just equal to that measured by those at the other; for any other location of the pivot, however, the
Fig. 57
MARINE SURVEYING.
137
clistiuu-es thus measureil will not he equal, but with a given setting of the pivot any distance measured
by one end bears a fixed ratio to that measured by the other. The path of travel of the pivot is gradu-
ated so that the ratio may be given any desired value. Being adjusted in this respect, if a distance is
taken off a chart with the legs at one end of the instrument, then those at the other
end will sliow the same distance on the scale of a chart enlarged or reduced in the pro-
portion represented by the ratio for which the pi\-nt was set.
METHODS EMPLOYED IN A HYDROGBAPHIC SURVEY.
436. A geodetic survey has for its object the determination, with the greatest
attainable accuracy, of points on the surface of the earth, by the eniployment of a pro-
cess of triangulation, all positions bein^ located either trigonometrically or astronomic-
ally, and the curvature of the earth being taken into account.
Before commencing a survey a general inspection of the field is made; a baseline
is located and its extremitie^marked by tiignalK; certain other positions, known as main
trumgulaliiin points, are selected and also marked with signals,- being so chosen that,
Etartmg with the ba-^e and proceeding thence from one to another of these points, a
eeries of w ell-conditioned triangles or quadrilaterals may cover the field of survey. The
base line is measured witli the greatest degree of accuracy which the resources of the
survey render possilile. Kach extremity of the base line and each other main tri-
angulation jjoint is occupied by an observer with a theodolite, who measures the angles
at each station lietween all the other stations which are in sight. An astranuyiiicol
tIcterminaliiiH is made (if the latitude and longitude of s(.)iii" point (if the survey (fre-
quently one of the extremities of the base) and of the true azimutli of some known line
(frequently the base line). Data is now at hand for the location upon the chart of the
base line and main triangulation points.
If the survey is one of considerable extent it is expedient to measure a rhed: late
near the end of the triangulation, a comparison between the measured and the comf)uted
distance between any two stations showing the accuracy of the work and affording a
means of reconciling discrepancies. The jnisition of a second observation spot may be
determined for a similar purpose.
The jrriiiiary triatiguliitio7i gives a skeleton of the field, but the points thus deter-
mined are not usually clofe enough together to afford a basis for all the detail work
that nmst be done. A second system of points is therefore selected and signals erected
thereon, and the position of these points is determined by a series of angles from the
main triangulation points and from each otlier. This is known as the seeoudtiry tri-
angulation. The jioints thus located are used in the plotting of the ti>jiograp}iii and Iii/drt-
(/raphy. It is not essential that their determination be as accurate as that of main
triangulation points.
The topography is put in, and includes the delineation of the features of the land —
shore line, light-houses, beacons, contour lints, peaks, buildings, and, in short, every-
thing that may be recognized by the navigator and utilized by him in locating the ship's Yic. 5,S.
position.
The hydrographic work is taken up and the dei)th of water and character of bottom detennined as
accurately as p08siV)le for the complete water area, especial care being taken to develop all shoals and
dangers to navigation and to locate all aids to navigation, such as buoys, light-ships, and beacons.
One or more tidal stations are established where observations are taken, continually and at frequent
intervals, of the height of the tide and direction and velocity of the tidal and other currents, whence
(lata is derived for the reduction of all soundings to the plane of reference and for the information al)out
tides and currents which is to appear upon the chart.
Observations are made to determine the magnetic variation and dij), and the intensity of the earth's
magnetic force.
437. The foregoing repre.sent, in outline, the various steps that must te taken in the accumulation
of the data necessary for the construction of a complete liydrographic chart. In the following i>ara-
graphs the details of the various operations will be more fully set forth.
The navigator who is called upon to conduct a marine survey without having available the time,
instruments, and general facilities necessary for the most thorough performance of the work must
exercL-e his discretion as to the modifications of method that he will make, and call upon his ingenuity
to adapt his means to the particular work in hand.
4!|S. The B.\se Line. — As the base line is the foundation for all distances on the chart, the cor-
rectness of the results of the survey will depend largely upon the degree of accuracy with which it ia
measured. The triangulation merely affords a measure of the various distances as compared with the
distances between the two initial jjoints from which it began; if that initial distance is 1,000 feet, we
have certain values for the sides of the various triangles; if the same base line is 2,000 feet, the value
of each side becomes twice as great as it was before; with the same triangulation, therefore, distances
vary directly with the length of the base line; it may thus be seen that if an error exists in measurement
which is only a small fraction oi tlie total length, the error will become much more material as the
more distant points of the survey are reached. In a base line 1,000 feet long, if a mistake of 10 feet be
made, all distances measured upon the chart will be in error 1 ])er cent, an(i a point plotted by trian-
gulation 10 miles from the oVjservation sp(jt (the point at which plotting begins), would be out of its
correct position one-tenth of a mile.
It IS important that the base line should be as long as possible, as an error in measurement will
thus constitute a smaller percentage of the total length and will not accumulate so rapidly as the work
proceeds. The position of the line must be such as to afford favorably conditioned triangles and quadri-
138 MARINE SURVEYING.
laterals with adjoining main triangulation points, and its extremities must be visible from those points
and from each other. The character of the ground and the facility for measuring will of course form an
important consideration in the choice.
439. In measuring a base l)y tape, chain, or similar means, a number of successive fleets are made
with the measure, whatever its nature, the distance travereed being approjjriately marked after each
fleet, while an observer, with a theodolite or transit, insures the measurement being made accurately
along the line.
440. The most careful measurements are made by a steel tape 100 feet long, stretched along a series
of battens which are supported by metal crutches and made exactly horizontal by a level. Tlie tape is
stretched to a uniform tension byaspring balance; its exact length at that tension is known from compar-
ison with some standard; a correction for temperature is applied. Tlie ends of the fleets are marked by
driving into the ground a peg carrying in its top a tack; the exact end of the tape is marked by a .score
filed on the head of the tack at a point marked by a plumb bob from the tape, and this score becomes the
origin for the next fleet. An assistant precedes the measuring party before each shift of the battens, and
is accurately aligned by the theodolite to mark the true direction of the base line. The result of this
method of measurement gives the horizontal distance between the points. It C'an be depended upon for
the greatest degree of accuracy of any 'method, excepting that with a special baw-meatmrinr/ apparatus,
which is seldom employed in marine surveys.
441. A second method of base measurement is with the surveyor's chain. This depends for accu-
racy upon the surface traversed being plane and level, a condition that is well fulfilled on a sandv
beach, where the chain is nearly as accurate as the tape and much more rapid. A surveyor's chain is
usually 100 feet long; the exact value of its length nuist l)e obtained by comparison with a standard,
and a correction applied for expansion or contraction due to temperature. The ends of the fleets are
maiked by steel pins driven into the grounl; the alignment is kept by the theodolite.
443. Where neither chain nor tape is available substitutes may be improvised from soundinir
wire taken from the deep-sea sounding machine, or, failing this, from well-stretched iixl line.
443. Measurements made by the telemeter and stadia aff(jrd a close a])i)roximation to the true
result, and if these instruments are not at hand the sextant angle of a rod of fixed length can l)e employed.
The masthead height of the vessel may be used in deteriiuning the length of base line on this principle,
either by making the ship itself mark one of the extremities and observing the masthead angle from
the other extremity, or liy simultaneously observing the masthead angle from both ends of a shore
base, and also the three horizontal angles of the triangle formed by the ship and the two ba-^e stations.
The latter plan is far preferable where accuracy is sought, as, if the angles are all taken by different
observers at the same instant (which can be marked by the hauling down of a flag), the error arising
from the motion of the ship about her anchor is eliminated, and, moreover, the data furnished offers a
double solution of the triangle and the mean may be taken as giving a closer result.
444. A crude method of measuring a base is by means of the velocity of sound, though this would
never be used where close results are expected. Fire a gun at one end of the base and at the other
note by the most accurate means available the time between seeing the flash and hearing the report.
Repeat several times in each direction. The mean numl)er of seconds and tenths of a second multiplied
by the velocity of sound per second at the temperature of observation (art. 314, Chap. XI) gives the
approximate length of base line.
443. When for any reason the existing conditions do not permit of a diret't measuroiuent being
made along the line between the two base stations, recourse must be had to a hrokrii ha«e, that is, one
in which the length of the base is obtained by reduction from the measured length of two or more
auxiliary lines. Necessity for resorting to a broken base arises frequently when the two stations are
situated on a curving shore line and the straight line between them passes across water, or where wooded
or unfavorable country intervenes, or where a stream must l)e crossed. The most common form of
broken base is that in which the auxiliary lines run from each extremity of the base at an acute angle
and intersect; in addition to measuring each of these lines, the angles of the triangle f(jrmed by them
with the base line must be observed and the true length of the base deduced by solution of tlie triangle.
The form that is most frequently used where only a short section of the ba.-'e is incapable of measure-
ment (as is the case where a deep stream flows across) is that of an auxiliary right triangle whose base
is the required distance along the base line and altitude a distance measured along a line perpendicular
thereto to some convenient point; by this measured distance and the angles which are observed, the
triangle is solved and the length of the unmeasured section determined.
446. In a survey of considerable extent, where good means are at hand for the correct determina-
tion of latitude and longitude, a ))ase line actually measured upon the earth may be dispensed with,
and, instead of that, the positions of the two stations which are most widely separated may l)e deter-
mined astronomically and plotted; the triangulation is then jilotted upon any assumed scale, and when
it has been brought up to connect the two stations the true value of the .scale is ascertained. This is
called the method of an astronomical liaxc.
44 'y. SiGN.^LS. — All points in tlie survey whose positions are to be located from other stations, or
from which other positions are to be located, must be marked l)y signals of such character as will render
them distinguishable at the distance from which they are observed. The methods of constructing signals
are of a wide variety.
A vessel regularly fitted out for surveying would carry scantlings, lumber, bolts, nuts, nails, white-
wash, and sheeting for the erection of signals; however meager the e(iuipment, the whitewa.sh and
sheeting (or some substitute for sheeting, preferably half of it white and half dark in color, ) should be
provided, if possible, before beginning any surveying work. Regular tripod signals, which are quickly
erected and are visible, under favorable circumstances, for many miles, are almost invariably employed
to niark the main triangulation stations; among other advantages the tripod form permits the occupation
with the theodolite of the exact center of the station, and avoids the necessity for the reiluctioii which must
otherwise be applied. Signals on secondary stations take an innumerable variety of forms, the require-
MAKINE SURVEYING. 139
merit being only that the^ shall be seen throughout the area over which they are to be made use of;
a whitewashed spot on a rock, a whitewashed trunk of a tree, a whitewashed cairn of stones, a sheeting
flag, a piece of sheeting wrapped about a bush or hung, with stones attached, over a cliff, or a white-
washed barrel or box filled with rocks or earth and surmounted by a flag, suggest soma of the secondary
signals that may be employed; sometimes objects are found that are sufficiently distinct In themselves
to be used as signals without further marking, as a cujxjla or tower, a hut, a lone tree, or a bowlder; but
it is seldom that an object is not rendered more conspicuous by the flutter of a flag above it, or by the
dead-white rav reflected from a daub of whitewash.
For convenience, each signal is given some short name by which it is designated in the records.
448. The Main Triaxgvlatiox. — The points selected as stations for the main triangulation mark
in outline the whole area to be surveyed; they are close enough together to afford an accurate means
of plotting all intermediate stations of the secondary triangulation; and they are so placed with relation
to one another that the triangles or quadrilaterals d'erived from them are well conditioned. The ])oints
are generally so chosen that small angles w ill be avoided. In order to fulfill the other conditions, it
frequently becomes necessary to carry forward the triangulation by means of stations located on points
a considerable distance inland, sucli as mountain peaks, which would not otherwise be regarded a.s
properlv within the limits of the survey.
Great care should be taken in observing all angles upon which the main triangulation is based; the
best available instrument should be employed; angles taken with a theodolite or transit should be
repeated, and observed with telescope direct and reversed, and the mean result taken; if the sextant is
used, a numl>er of separate observations of each angle should be taken and averaged for the most prob-
able value. It nmst be remembered that while, in any other part of the work, an error in an angle
affects only the results in its inuiiediate vicinity, a mistake in the main triangulation goes forward
through all the plotting that comes after it.
It frequently occurs that the purposes of the survey are sufficiently well fulfilled by a graphic plot-
ting of the main triangulation! but where more rigorous methods prevail, the results are obtained by
calculation. The sum of the angles of each triangle is taken, and if it does not exactly equal 180° the
values are adjusted to make them comply with this condition. The lengths of the various sides are
then computed, regarding the stations, usually, as forming a series of quadrilaterals, and allowing for
the curvature of the earth where the sides are sufficiently long to render it expedient to do so.
449. The Seco.nuary Triangulation. — The points of the secondary triangulation are located, as
far as jiossible, by angles from the main triangulation stations; these angles, having less dependent upon
them, need not be repeated. A graphic plotting of these stations, without calculation, will suflice.
450. Astronomical Work. — This comprises the determination of the correct latitude and longitude
of some j)oint of the survey, which is the first jjosition jilotted, and of the true direction of sofne other
point friim the oljservation spot, which is the first line to be laid down on the chart; it is evident that
these determinations form the origin of all positions and of all directions, without which the chart
coulil not be constructed.
The methods of finding latitude, longitude, and the true bearing of a terrestrial object are fully set
forth in jjrevious chapters. The feature that distinguishes such work in surveying from that of deter-
mining the position of a ship at sea lies in the greater care that is taken to eliminate iwssible errors.
At sea, results of absolute exactness are recognizetl as unattainable and are not required; but in a careful
survey no step which will contribute to accuracy should be neglected.
Tlie results should therefore be basefl upon a very large number of observations, employing the
best instruments that are available, and the various sights being so taken that probable errors are offset
in reckoning the mean.
4.51. Hy taking a number of sights the observer arrives at the most probable result of which his
instruments and his own faculties render him capable; but this result is liable to an error whose amount
is indeterminate and which is ecjual to the algebraic sum of a number of small errors due, resiiectively,
to his instruments (which must always lack perfection in some details), to an improper allowance for
refraction under existing atmospheric conditions, and to his own jiersonal error. Assuming, as we
may, that the personal error is approximately constant, these three causes give rise to an erriir by which
all altitudes appear too great or too small by a uniform but unknown amount. Let us assume, for an
illustration, that this error has the effect of making all altitudes appear 30" too great; if an observer
attempted to wciik his latitude from the meridian altitude of a star bearing south, the result of this
unknown error would give a latitude 30" south of the true latitude; if another star to the southward
were observed, this mistake would be rejieated; but if a star to the north were taken, the resulting
latitude would l»e 30" to the north. It is evident, therefore, that the true latitude will be the mean of
the results of observatifm of the northern and the southern star, or the mean of the average of several
northern stars and the average of several southern stars. A similar process of reasoning will show that
errorsinthedeterminationof hour angle are offset by taking the mean of altitudes of object.s respectively
east and west of the meridian.
4.52. It must be remembered that the uniformity of the unknown error only exists where the
altitude remains approximately the same, as instrumental and refraction errors may vary with the
altitude; another condition of uniformity requires that the instrument and the observer remain the same,
and that all observations be taken about the same time, in order that atmospheric conditions remain
unchanged; to preserve uniformity, if the artificial horizon is used, the same end of the roof should
always be the near one to the observer; in taking the sun, however, as the personal error may not be
the same for approaching as for separating limbs, every series of observations should be made up of an
equal number of sights taken under each condition.
453. With all of this in mind, we arrive at the general rule that astronomical determinations
shall be based upon the mean of observatimis, under similar conditions, of bodies whose respective dis-
tances from the zenith are nearly equal, and which bear in opposite directions therefrom.
140 MARINE SURVEYING.
454. This condition eliminates tlie sun from availability for observations for latitude, though it
properly admits the use of that body for longitude where ecjual altitudes or single a. m. and p. m. sights
are taken. Opposite stars of approximately equal zenith distance should always be used for latitude,
circum-meridian altitudes being observed during a few nunutes before and after transit ; excellent results
are also obtained from stellar observations for longitude; but very low stars should be avoided, on
account of the uncertainty of refraction, and likewise very high ones, as the reflection from the index
mirror of the sextant may not be perfectly distinct when the ray strikes at an acute angle.
455. It there is telegraphic communication, an endeavor should be made to obtain a time signal
from a reliable source, instead of depending upon the chronometers.
456. Toi"OGR.\i>nv. — The plane-table, with telemeter and stadia, affords the most expeditious means
of plotting the topography, and should be employed when available. Points on shore may also be
plotted by sextant angles, using the three-point problem, or by any other reliable method.
457. HynROGRAPHY. — The correct delineation of the hydrographic features being one of the most
important objects of the survey, great care should be devoted to this part of the work. Soundings are
run in one or more series of parallel lines, the direction and spacing of which depend upon the scope of
the survey. It is usual for one series of lines to extend in a direction normal to the general trend of the
shore line. In most cases a second series runs perpendicular to the first, and in surveys of im]>ortant
bodies of water still other series of lines cross the system diagonally. In developing rocks, shoals, or
dangers the direction of the lines is so chosen as will best illustrate the features of the bottom. When
lints cross, the agreement of the reduced soundings at their intersection affords a test of the accuracy of
the work.
As the depth of water increases, if there is no reason to suspect dangers, the interval between lines
may be increased.
Lines are run by the ship or boat in such manner as to follow as closely as possible the scheme of
sounding that has lieen laid out. The position is located by angles at the beginning of each line, at each
change of course, at frequent intervals along the line, and at the poiiit where each line is finished.
Soundings taken between prmtiov-t are plotted Ity the time interval or patent-log distances.
458. There are a number of methods for determining positions while sounding, which may be
described briefly as follows:
By tiro sexUmt angles. — Two observers with sextants measure simultaneously the angles between
three objects of known position, and the position is located by the three-point problem. This is the
method most commonly employed in boat work, and has the great adxantage that the results may be
plotted at once on the working sheet in the boat and the lines as run thus kept nearly in coincidence
with those laid out in the scheme. A study of the three-point problem (art. 158, Chap. IV) will give
the considerations that must govern in the selection of objects.
By two theodolite angles. — Two stations on shore are occujiied by observers with theodolites, and at
certain instants, indicated by a signal from the ship or boat, they observe the angular distance thereof
from some known point. Tlie intersection of the direction lines thus given is at the required position.
This method is expeditious where the signals are small or not numerous. Its disadvantage is that the
plotting can not be kept up as the work proceeds.
By one se.tiniit and one tlieodoKle angle. — 'An observer ashore occupies a station with a theodolite and
cuts in the ship or boat, while one on board takes a sextant angle between two objects, of which one
should preferably be the occupied station. It is plotted by laying off the direction line from the theodo-
lite and finding with a three-armed protractor or piece of tracing jiaper what point of that line subtends
the observed angle between the objects. Its advantages and disadvantages are the .same as those of the
preceding method.
In running lines of soundings offshore, where signals are lost sight of, the best method is to get an
accurate departure, before dropping the land, by the best means tliat offers, keeping careful note of the
the dead reckoning, and on running in again, to get a position as soon as jiossible, note the diift and
reconcile the plotting of intermediate soundings accordingly. Where circumstances require, the position
may be located by astronomical observations as usually taken at sea.
459. A careful record of soundings must be kept, showing the time of each (so that proper tidal
correction may be applied), the depth, the character of bottom, and such data as may be required to
locate the position.
460. Tidal Observ.\tions. — These should begin as early as practicable and continue thif)ughout
the survey, it being most important that they shall, if possible, cover the period of a lunar month. In
the chapter on Tides (Chap. XX) the nature of tlie data to be obtained is explained.
461. Magnetic Observations. — The feature of the earth's magnetism with which the navigator is
most concerned is the variation, which is set forth on the chart, and upon the determination of which
will depend the correctness of all courses and bearings on shipboard. It is usually obtained by noting
the compass direction from the observation spot of the object whose true bearing is known by calcula-
tion, and comparing the true and compass bearings; or it may be f>bserved 1)y mounting the ship's com-
pass in a place on shore free from foreign magnetic influence, and finding the compass error as it is found
on board. Observations for dip and intensity are also made when the proper instruments are at hand.
463. KiTNNiNG Survey.- — Where time and opportunity permit only a superficial examination of a
coast line or water area, or where the interests of navigation require no more, recourse is had to a Run-
ning Surrey, in which shore positions are determined and soundings are made while the ship steams
along the coast stopping only occasionally to fix her position, and in which the assistance of boat or
shore parties may or may not be employed.
In this method the ship starts at one end of the field from a known position, fixed either by astro-
nomical observations or by angles or bearings of terrestrial objects having a determined location. Care-
ful compass bearings or sextant angles are taken from this position to all objects ashore which can be
recognized, and a series of direction lines is thus obtained. The ship then steams along the coast, at a
convenient distance therefrom, keeping accurate account of her run by compass courses and patent log.
MABINK SURVEYING. 141
From time to time other series of bearings or angles are talten upon those objects ashore which are to be
located, the direction lines plotted from the estimated position of the ship, and the various objects located
by the intersections with tlieir otlier direction lines. During all the time that the ship is under way,
soundings are taken at regular intervals and plotted from the dead reckoning. As frequently as circum-
stances'permit, the ship is stopped and her position located by the best available means, anil the inter-
vening dead reckoning reconciled for any current that may be found.
If a steam launch can be employed in connection with a running survey, it is usually sent to run a
second line inshore of the ship. The boat's position is obtained by bearings of objects ashore which are
locateil by the ship, or by l^earings and ma.st-hetul angles of the ship, or by such other means as offer.
The duty of the boat is to take a series of soundings, and to collect data for shore line and topography.
If circumstances allow the landing of a shore party, its most important duty is to mark the various
objects on shore by some sort of signals which will render them unmistiikable. Beyond this, it can
perform such of the duties assigned to shore i)arties in a regular survey as opportunity permits.
142 WINDS.
CHAPTER XVIII.
WINDS.
463. TT7?irf is air in approximately horizontal motion. Observations of the wind should include
its true direction, and its force or velocity. The direction of the wind is designated by the point of the
compass from which it proceeds. The force of the wind is at sea ordinarily expressed in terms of
the Beaufort Scale, each degree of this scale corresponding to a certain velocity in miles per hour, as
explained in article 67, Chapter II.
464. The C.visk of the AVind. — Winds are produced by differences* of atmospheric pressure, which
are tliemselves ultimately, and in the main, attributable to differences of temperature.
To understand liow the air can be set in motion by these differences of pressure it is necessary to
have a clear conception of the nature of the air itself.
The atmosphere which ('ompletely envelops the earth may be considered as a fluid sea at the
bottom of which we live, and wliich extends upward to a considerable height, probably 200 miles,
constantly diminishing in density as the altitude increases.
The air, or material of which this atmosphere is composed, is a transparent gas, which, like all
other gases, is perfectly elastic and highly compressible, .\lthough extremely light, it has a perfectly
definite weight, a cubic foot of air at ordinary pressure and temperature weighing 1.22 ounces, or abon't
one seven hundred and seventieth part of the weight of an equal volume of water. In consequence fif
this weight it exerts a certain pressure upon the surface of the earth, amounting on the average to 15
pounds for each square inch. To accurately measure this pressure, which is constantly undergoing
slight changes, we ordinarily employ a mercurial barometer (art. 48, Chap. II), an instrument in which
the weight of a column of air of given cross section is balanced against that of a column of mercury
having an equal cross section; and instead of saying that the pressure of the atmosphere is a certain
number of pounds on each square inch, we say that it is a certain number of inches of mercury, meaning
thereby that it is equivalent to the pressure of a column of mercury that many inches in height, and
one square inch in cro.ss section.
All gases, air included, are highly sensitive to the action of heat, expanding or increasing in volume
as the temperature rises, contracting or diminishing in volume as the temperature falls. Suppose
now that the atmosphere over any considerable region of the earth's surface is maintained at a
higher temperature than that of its surroundings. Tlie warmed air will expand, and its upper layers
will flow ofi to the surrounding regions, cooling as they go. The atmosjjheric jiressure at sea level
throughout the heated areas will thus be diminished, while that over the circumjacent cooler areas will
be correspondingly increased. As the result of this difference of pressure, there will be movement of
the surface air away from the region of high i)ressure and towards the region of low, somewhat similar
to the flow of water which takes place through the connecting bottom sluice as soon as we attempt to
fill one compartment of a divided vessel to a slightly higher level than that found in the other.
A difference of atmospheric pressure at sea level is thus immediatelj' followed by a movement of
the surface air, or by winds; and these differences of pressure have their origin in differences of tempera-
ture. If the atmosi)here were everywhere of uniform temperature it would lie at rest on the earth's
surface — sluggish, torpid and oppressive — and there would be no winds. This, however, is lorrunaieiy
not the case. The temperature of the atmosphere is continually or periodically higher in one region
than in another, and the chief variations in the distribution of temperature are systematically repeated
year after year, giving rise to like systematic variations in the distribution of pressure.
465. The Nor-Mal Disthibitiox of Pressure. — The winds, while thus due primarily to differences
of temperature, stand in more direct relation to differences of pressure, and it is from this point of view
that they are ordinarily studied.
In order to furnish a compr'ehensive view of the distribution of atmospheric pressure over the
earth's surface, charts have been prepared showing the average reading of the barometer for any given
period, whether a month, a season, or a year, and covering as far as possible the entire globe. "These
are known as isobaric charts, from the fact that all points at which the barometer has the same reading
are joined by a continuous line or isobar.
The isobaric chart for the year (fig. 59) shows in each hemisphere a well-defined belt of high
pressure (.30.20 inches) completely encircling the globe, that in the northern hemisphere having its
middle line about in latitude 35° North, that in the southern hemisphere about in latitude 30° South,
these constituting the so-called meteorological tropics. From the summit or ridge of each of these belts
the pressure fails off alike toward the equator and toward the pole, although much less rapidly in the
former direction than in the latter. The equator itself is encircled by a belt of somewhat diminished
pressure (29.90 inches), the middle line of which is ordinarily found in northern latitudes. In the
northern hemisphere tlie diminution of pressure on the poleward slope is much less marked and much
less regular than in the southern hemisphere, minima (29.70 inches) occurring in the North Atlantic
Ocean near Iceland, and in the North Pacific Ocean near the Aleutian Islands, beyond which the
pressure increases. In the southern hemisphere no such minima are apparent, the pressure continuing
to diminish uninterruptedly as higher and higher latitudes are attained. Along the sixtieth parallel of
south latitude the average barometric reading is 29.30 inches.
WII^DS.
143
Fig. 59.
144 WINDS.
466. Seasonal Variations of Pressure. — As might be expecteci from its close relation to the
temperature, the whole system of pressure distribution exliibits a tendem-y to follow the sun's motion
in declination, the barometric equator occupying in July a position slightly to the nortliward of its
position in January. In either hemisphere, moreover, the pressure over the land during the winter
season is decidedly above the annual average, during the summer season decidedly below it; the
extreme variations occurring in the case of continental Asia, where the mean monthly pressure ranges
from 30.50 inches during January to 29.50 inches during July. Over the northern ocean, on the otlier
hand, conditions are reversed, the summer pressures being here .somewliat the higher. Thus, in January
the Icelandic and the Aleutian minima increase in depth to 29.50 inches, while in July these minima
fill up and are well-nigh obliterated, a tact which has much to do with the strengtli and fre(iuency of
the winter gales in high northern latitudes and tlie absence of these gales during the summei-. Over
the southern ocean, in keeping with its slight contrast between winter and summer temperatures,
similar variations of pressure do not exist.
467. The Prevailing "Winds. — As a result of the distribution of pre.ssure just described, there is
in either hemisphere a continual motion of the surface air away from the meteorological tropic — on one
side towards tbe equator, on the other side towards the pole, the first constituting in each case the
trade winds, the second the prevailing winds of higher latitudes. Upon a stationary earth the direction
of this motion would be immediately from the region of high towards the region of low l)arometer, the
moving air steadily following the barometric slope or gradient, increasing in force to a gale where these
gradients are steep, decreasing to a light breeze where they are gentle, sinking to a calm where they
are absent. The earth, however, is in rapid rotation, and this rotation gives rise to a force which
exercises a material influence over all horizontal motions upon its surface, whatever their direction,
serving constantly to divert them to the right in the northern hemisphere, to the left in the southern.
The air set in motion by the difference of pressure is thus constantly turned asiile from its natural
course down the barometric gradient or sloj)e, and the direction of tlie \vin<l at any point, instead of
being identical with that of the gradient at that point, is deflected by a certain amount, crossing the
latter at an angle which in practice varies between 45° and 90° (4 to 8 compass points), the wind in
the latter case blowing parallel to the isobars. As a consequence of this deflection the northerly winds
whii:h one would naturally e.xpect to find on the e(]uatorial slope of the belt of high jiressure in the
northern hemisphere become nortlieasterly, — the NE. trade; the southerly winds of the polar slope
become southwesterly, — the prevailing w esterly winds of northern latitudes. So, too, for the southern
hemisphere, the southerly winds of the equatorial slope here becoming southeasterly, — the SE. trades;
the northerly winds of the polar slope northwesterly, — the prevailing westerly winds of southern
latitudes.
468. The relation here described as existing between the distribution of atmospheric i>ressure and
the direction of the wind is of the greatest imjjortance. It may be briefly stated as follows:
In the northern hemisphere stand with the back to the wind; in this position the region of high
barometer lies on j'our right hand and somewhat behind you; the region of low liaroineter on your left
hand and somewhat in front of you.
In the southern hemisphere stand with the back to the wind; in this position the region of high
barometer lies on your left hand and somewhat behind \ou; the region of low l)arometer on your right
hand and somewhat in front of you.
This relation holds absolutely, not only in the case of the general distribution of pressure and cir-
culation of tlie atmosphere, but also in the case of the special conditions of high and low pressure which
usually accompany severe gales.
469. The Trade Winds. — The Trade Winds blow from the tropical belts of high pressure towards
the equatorial belt of low pressure — ih the northern hemisphere from the northeast, in the southern
hemisphere from the southeast. Over the eastern half of each of the great oceans they extend consid-
erably farther from the line and their original direction inclines more towards the pole than in mid-
ocean, where the latter is almost easterly. They are ordinarily looked U])on as the most constant of
winds, but while they may blow for days or even for weeks with slight variation in direction or
strength, their uniformity should not be exaggerated. There are times when the trade winds weaken
or shift. There are regions where tlieir steady course is deformed, notably among the island groiips of
the South Pacific, where tlie trades during January and February are practically nonexistent. They
attain their highest development in the South Atlantic and in the South Indian Ocean, and are every-
where fresher during the winter than during the summerseason. Tliey are rarely disturbed by cyclonic
storms, the occurrence of the latter within the limits of the trade wind region being furthermore con-
fined in point of time to the late summer and autumn months of the respective hemispheres, and in
scene of action to the western portion of the several oceans. The South Atlantic Ocean alone, however,
enjoys complete immunity from tropical cyclonic storms.
470. The Doldrums. — The equatorial girdle of low pressure occupies a position lietween the high-
pressure belt of the northern and the similar belt of the southern hemisphere. Throughout the extent
of tliis barometric trough the pressure, save for the slight diurnal oscillation, is practically uniform, and
decided barometric gradients do not exist. Here, accordingly, the winds sink to stagnation, or rise at
most only to the strength of fitful breezes, coming first from one point of tlie compass, tlien from another,
with cloudy, rainy sky and frequent thunderstorms. The region throughout which these conditions
prevail consists of a wedge-shaped area, the base of the wedge resting in the case of the Atlantic Ocean
on the coast of Africa, and in the case of the Pacific Ocean on the coast of America, the axis extending
westward. The position and extent of the belt vary somewhat with the season. Throughout February
and March it is found immediately north of the equator and is of inapprecialjle width, vessels following
the usual sailing routes frequently passing from trade to trade without interruption in both the Atlantic
and the Pacific Oceans. In July and August it has migrated to the northward, the axis extending east
and west along the parallel of 7° north, and the belt itself covering several degrees of latitude, even at
its narrowest point. At this season of the year, also, the southeast trades blow with diminished fresh-
ness across the equator and well into the northern hemisphere, being here diverted, however, by the
effect of the earth's rotation, into southerly and southwesterly winds, the so-called soutliwest monsoon
of the African and Central American coasts.
WINDS. 145
471. The Horse jl,atitudes. — On the outer margin of the trades, corresponding vaguely with the
summit of the tropical ridge of high pressure in either hem isjihere, is a second region throughout which
the barometric gradients are faint and undecided, and the prevailing winds correspondingly light and
variable, the so-called horite loliludes, or calms of Cancer and of Capricorn. Unlike the doldrums, how-
ever, the weather is here clear and fresh, and the periods -of stagnation are intermittent r;ither than
continuous, showing none of the persistency which is so characteristic of the ecpiatorial region. The
explanation of tliis difference will become obvious as soon as we come to study the nature of the daily
barometric cJianges of pressure in the respective regions, these in the one case being marked by the
uniformity of the torrid zone, in the other sharing to a limited extent in the wide and rapid variations
of the temperate.
472. The Prevailing Westerly Winds. — On the exterior or polar side of the tropical maxima
the j)ressure again diminishes, the barometric gradients being now directeil towards the pole; and the
currents of air set in motion along these gradients, diverted to the right and left of their natural course
by the earth's rotation, appear in tlie northern hemisphere as southwesterly winds, in the southern
hemisphere as northwesterly — the jjrevailing westerly winds of the temperate zone.
Only in the southern hemisphere do these winds exhibit anything approaching the jiersistency of
the trades, their course in the northern hemisphere being subject to frequent local interruption by
periods of winds from the eastern semicircle. Thus the tabulated results show that throughout the
portion of the North Atlanti<^ included between the parallels 40°-50° North, and the meridians 10°-50''
West, the winds from the western semicircle (South — NNW.) comprise about 74 per cent of the whole
number of observations, the relative frequency being somewhat higher in winter, somewhat lower in
summer. The average force, on the other hand, decreases from force 6 to force 4 Beaufort scale, with
the change of season. Over the sea in the southern hemisphere such variations are not apjiarent; here
the westeilies blow through the entire year with a steadiness little less than that of the trades them-
selves, and with a force which, though fitful, is very much greater, their boisterous nature giving the
name of the " Roaring Forties" to the latitudes in which they are most frequently observed.
The ex))lanation of this striking difference in the extra-tropical winds of the two halves of the globe
is found in the distribution of atmospheric pressure, and in the variations which this latter undergoes in
different jiarts of the world. In the landless southern hemisphere the atmospheric pressureafter cross-
ing the parallel of 80° South diminishes almost uniformly towards the pole, and is rarely disturbed by
those large and irregular fluctuations which form so important a factor in the daily weather of the
northern liemisi)here. Here, accordingly, a system of polar gradients exists quite comparable in
stability with the equatorial gradients which give rise to the trades; and the poleward movement of the
air in obedience to these gradients, constantly diverted to the left by the effect of the earth's rotation,
constitutes the steady westerly winds of the south temperate zone.
473. The Monsoon Winds. — The air over the land is warmer in summer and colder in winter than
that over the adjacent oceans. During the former season the continents thus iK'COnie the seat of areas
of relatively low pressure; during the latter of relatively high.. Pressure gradients, directed outward
during the winter, inward during the summer, are thus established l)etween the land and the sea, which
exercise the greatest influence over the winds prevailing in the region adjacent to th(f coast. Thus, off
the Atlantic seaboard of the United States southwesterly winds are most frequent in summer, north-
westerly winds in winter; while on the Pacific coast the reverse is true, the wind here changing from
northwest to southwest with the a<lvance of the colder season.
The most striking illustration of winds of this class is presented by the monsoons {}fausum, season)
of the China Sea and of the Indian Ocean. In January abnormally low temperatures and high pressure
obtain over the Asiatic plateau, high temperatures and low pressure over Australia and the nearby
portion of the Indian Ocean. As a result of the baric gradients thus established, the southern and
eastern coa.-'t of the vast Asiatic continent and the seas adjacent thereto are swept by an outflowing
current of air, which, diverted to the right of the gradient by the earth's rotation, appears as a north-
east wind, covering the China Sea and the northern Indian Ocean. Upon entering the southern
hemisphere, however, the same force which hitherto deflecte<l the moving air to the right of the
gradient now serves to deflect it to the left; and here, accordingly, we have the monsoon appearing as
a northwest wind, covering the Indian Ocean as far south as 10°, the Arafura Sea, and the northern
coast of Australia.
In July these conditions are precisely reversed. Asia is now the seat of high temperature and
correspondingly low pressure, Australia of low temijerature and high pressure, although the departure
from the annual average is by no means so pronounced in the case of the latter as in that of the former.
The baric gradients thus lead acro.ss the equator and are addressed toward the interior of the greater
continent, giving rise to a system of winds whose direction Ls southeast in the southern hemisphere,
southwest in the northern.
The northeast (winter) monsoon blows in the China Sea from October to April, the southwest
(summer) monsoon from May to September. The former is marked by all the steadiness of the trades,
often attaining the force of a moderate gale; the latter appears as a light breeze, unsteady in direction,
and often sinking to a calm. Its prevalence is frequently interrupted by tropical cyclonic storms,
locally known as tjiphoom, although the occurrence of these latter may extend well into the season of
the winter monsoon.
4 74. Land and Sea Breezes. — Corresponding with the seasonal contrast of temperature and
pressure over land and water, there is likewise a diurnal contrast which exercises a similar though more
local effect. In summer particularly, the land over its whole area is warmer than the sea by day, colder
than the sea by night, the variations of pressure thus established, although insignificant, sufficing to
evoke a system of littoral breezes directerl landward during the (laytime, seaward during the night,
which, in general, do not penetrate to a distance greater than 30 miles on and off shore, and extend but
a few hundred feet into the depths of the atmosphere.
The sea breeze liegins in the morning hours— from 9 to 11 o'clock — as the land warms. In the late
afternoon it dies away. In the evening the land breeze springs up, and blows gently out to sea until
24972°— 12 10
146 WINDS.
morning. In the tropics this process is repeated day after day with great regularity. In our own
latitudes, the land and sea breezes are often masked by winds of cyclonic origin.
475. A single important effect of the seasonal variation of temjMirature and pressure over the land
remains to be described. If there were no land areas to break the even water surface of the globe, the
trades and .westerlies of the terrestrial circulation wf)uld be developed in the fullest simplicity, with
linear divisions along latitude circles between the several members — a condition nearly approached in
the land-barren southern hemisphere during the entire year, and in the northern hemisphere during the
winter season. In the summer season, however, the tropical belt of high pressure is l)roken where it
creases the warm land, and the air shouldered off from the continents accumulates over the adjacent
oceans, particularly in the northern or land hemisphere. This tends to create over each of the oceans a
circular or elliptical area of high pressure, from the center of which the baric gradients radiate in all
directions, giving rise to an outflowing system of winds, which by the effect of the earth's rotation is
converted into an outflowing spiral eddy or (iiitici/clonic whirl. The sharp lines of demarcation which
would otherwise exist between the several members of the general circulation are thus obliterated,
the southwesterly winds of the middle northern latitudes becoming successively northwesterly, northerly,
and northeasterly, as we approach the e(iuator and round the area of high ])ressure by the east; the
northeast trade becoming successively southeasterly, southerly, and southwesterly, a-s we recede from the
efjuator and round this area by the west; similarly for the (jther hemisphere.
CYCLONIC STORMS. 147
CHAPTER XIX. .
CYCLONIC STOEMS.
476. Vakiations ok the Atmospheric rREssiRE. — The distribution of the atmospheric pressure
previously ilescribed (Chap. XVII I) and the attendant circulation of the winds are those which become
evident after tlie effects of many disturbing causes have been eliminated by the process of averaging, or
embracing in the summation observations covering an extended j>eriod of time. The distribution of
pressure and the system of winds which actually exist at a given instant will in general agree with
these in its main features, but may differ from them materially in detail.
Confining our attention for the time l)eing to the subject of atmospheric pressure, it may he said
that this, at any given point on the earth's surface, is in a constant state of change, the mercury rarely
becoming stationary, and then only for a few hours in succession. The variations which the pressure
undergoes may be divide<l into two cla.sses; viz, periodic, or those which are continuously in operation,
repeating theniselves within fixed intervals of time, long or short; and non-periodic or accidental, which
0('cur irregularly, and are of varying duration and extent.
477. Periodic Variations" — Of the former class of changes the most iiniwrtant are the seasonal^
which have been already to some extent descriljed, and the diurnal. The latter consists of the daily
occurrence of two barometric maxima, or points of highest pressure, with two intervening minima.
Under ordinary circumstances, with the atmosphere free from disturtances, the barometer each day
attains its first minimum about 4 a. m. As the day advances the pressure increases, and a maximum,
or point of greatest pressure, is reacheil about 10 a. m. From this time the pressure diminishes, and
a second mmimuin is reached about 4 p. m., after which the mercury again riseSj reaching its second
maximum al)out 10 p. m. The range of this diurnal oscillation is greatest at the equator, where it
amounts to ten hundredths (0.10) of an inch. It diminishes with increased latitude, and near the poles
it seems to vanish entirely. In middle latitudes it is much more apparent in sunmier than in winter.
47§. Xo.N-PERioDic Variations. — The equatorial slope of the tropical l«lt of high pressure which
encircles the globe in either hemisphere is characterized l)y the marked uniformity of its meteorological
conditions, the temj)erature, wind, and weather changes proper to any given season repeating them-
selves as (lay succeefls day with almost monotonous regularity. Here the diurnal oscillation of the
barometer constitutes the "main variation to which the atmosi)heric pressure is subjected. On the polar
slope of these belts conditions the reverse of these obtain, the elements which go to make uj) the daily
weather here passing from phase to phase without regularity, with the result that no two days are pre-
cisely alike; and as regards atmospheric pressure, it may be said that in marked contrast with the
uniformity of the torrid zone, the barometer in the temperate zone is constiUitly subjected to non-periodic
or accidental fluctuations of such extent that the periodic diurnal variation is scarcely api)arent, the
mercury at a given station frequently rising or falling several tenths of an inch in twenty-four hours.
479. PRo<iRB.ssivE Areas of IIioh and Low I'Ri-xsrHE. — The explanation of this rapid change of
conditions is found in the approach and passage of extensive areas of alternately high and low pressure,
which affect alike, although to a different degree, all the barometers coming' within their scope. The
general direction of motion of these areas is that of the prevailing winds: eastward, therefore, in the
latitudes which are under consideration.
Taken in conjunction, these areas of high and low pressure exercise a controlling influence ovei' the
Heather changes of tlie tein[)erate zones. As the low area draws near, the sky becomes overclouded,
the jirexailing westerly wind falls away, and is succe»>ded by a wind from some easterly direction, faint
at first, but increasing as the ))ressure continues to diminish; the lowest pressure having been reached,
the wind again goes to the westward, the gla.ss starts to rise, and the weather clears; all marking the
eastward recession of the 1(jw area and the api>roach of the gubsec|uent high.
The first stage in the development of the low is a slight diminution of the atmospheric pressure,
amounting in general to not more than one or two hundredths of an inch, throughout an area covering
a more or less extensive portion of the earth's surface, either land or water, but far more frequently
over the former than over the latter. Shortly after the advent of this initiatory fall the decrease of pres-
sure throughout some small region within the larger area assumes a more decided character, the mercury
here standing at a lower level than elsewhere and reading successively higher as we go outward, the
region thus becoming, as it were, the center of the whole barometric "depression. A system of baro-
metric gradients is by this means established, all directed radially inward, and in obeclience to these
gradients there is a movement of the surface air towards the center or point of lowest barometer. The
air once in hiotion, however, the effect of the earth's rotation is brought into play precisely as in the
case of the larger movements of the atmosphere, with the result that the several c:urrents, instead of
followiiig the natural course along these gradients, are deflected from them, in the northern hemisphere
to the right hand, in the southern hemisphere to the left, the extent of the deflection being from 4 to 8
compass jioints.
480. Cvi LONEs AND CvcLONic CiRCfLATioNS. — A Central area of low barometer will thus be sur-
rounded by a system of winds which constantly draw in towards the center but at the same time circulate
aljout it, the whole forming an inflowing spiral; the direction of this circulation being in the southern
hemisphfife with the motion of the hantls of a watch, in the northern hemisphere opjwsed to this
148
CYCLONIC STORMS.
motion. Where the barometric gradients are steep, these winds are apt to be strong; where they are
gentle, the winds are apt to be weak; where they are absent, as is the case at the lenter or lx)ttoui of
the depression, cahns are apt to prevail.
Around the center of the area of high pressure a similar system of wind will be found, but blowing
in a contrary direction. Here the barometric gradients are directed radially outward, with the result
that in place of the inflowing, we have an outflowing spii-al, the ('irculatory motion being right lianded
or with the hands of a watch in the northern hemisphere, left handed or against the hands of a watcii
in the southern.
All of these features are showii in the accompanying diagrams (fig. 60), which exhibit the general
character of cyclonic (around the low) and anticydonic (around the high) circulations in the northern
An'icyclonic.
NdKTHERN IIEMISIMIKH K.
Ci/dnnir.
Aittici/duui'
Cyclonk,
SdCTHEKN HEMISl'HEKi:.
Fig. 60.
The light arrows siiow the direction of tlie gradient**; tlie lieavy arrows the direetiou of the winds.
and the southern hemisphere, respectively. The closed curves represent the isobars, or lines along
which the barometric pressure is the same; the short arrdws show the direction of the gradients, which
are everywhere at right angles to the isobars; the long arrows give the direction of the winds, deflected
by the earth's rotation to the right of the gradients in the northern hemisphere, to tiie left in the
southern.
4SI. Fe.vtiues of Cyclonic a.vd Anticyclonic Regions. — Certain features of the two areas may
here be contrasted. In the anticydonic, the successive isobars are as a rule far apart, showing weak
gradients and consequently light winds; the areas themselves are of relatively great extent, and their
rate of progression is slow. During the summer they originate as extensions into higher latitudes of
the margins of the tropical belts of high i>ressure; during the winter, as offshoots of the strong anticy-
clone which covers the land throughout that season. Their approach and presence is accompanied by
polar or westerly winds, temperature lielow the seasonal average, fair weather, and clear skies. In the
cyclonic area the successive isobars are crowded together, showing steep gradients and strong winds;
they may appear either as trough-like extensions into the temperate zone of the polar l)elt of low pres-
sure, in which case the easterly winds proper to their polar side are nonexistent, or (in lower latitudes)
as independent areas, sometimes, indeed, as detached portions of theeciuatorial low-prsssure belt, which
move eastward and poleward across the temperate zone, and are ultimately merged into the great
cyclonic area surrounding the pole. The progress of these indeiiendent areas is invariably attended by
the strong and steadily shifting winds, foul weather, and other features whicli make up the ordinary
storm at sea. In the trough-like depressions of higher latitudes these features may or may not be
observed, their presence depending upon the depths of the barometric trough and the steepness of its
slopes. In these, moreover, the cyclonic circulation is never completely developed, the storm winds
having rather the character of right line gales, blowing from an equatorial oreasterly direction until the
axis ot the trough is at hand, and as this passes shifting by the west at one bound to a polar direction.
482. Cyclonic Storms. — Strong winds are the result of steep barometric gradients. These may
occur with cyclonic or with anticydonic areas, the latter being exemplified in the case of the northers
in the Gulf of Mexico and the northwesterly winter gales aloiig the Atlantic coast of the United States,
which are almost invariably accompanied by barometers above the average. They are, how^ever, so
much more frequent in the case of areas of low pressure and consequent cyclonic circulations, W'ith their
attendant foul weather characteristics, that the latter are generally known as cyclonic storms, i. e.,
storms in which the wind circulation is cyclonic.
Cyclonic storms may with convenience be divided into two clas-ses; viz, tropical, or those which
originate near but not on the equator; and extra-tropical, or those which first appear in higher
latitudes.
4§3. Tropical Cyclonic Storms. — The occurrence of tropical cyclonic storms is confined to the
summer and autumn months of the respective hemispheres, and to the western part of the several
oceans, the North Atlantic, the North Pacific, the South Pacific, and the Indian Ocean. They are
unknown in the South Atlantic Ocean.
The Arabian Sea and the Bay of Bengal are also visited by cyclonic storms, the season of their
occurrence extending from May to October.
484. Motion ok tiik Storm Center. — In the case of tropical cyclonic storms there is always a
tendency for the barometric depression, impelled by the general motion of the atmosphere in the
CYCLONIC STORMS.
149
aade wind region, to follow a jiath which tends at once westward and away from the equator. This
motion continues until the limits of the trades are reached, where the path ordinarily recurves, and
the suljsequent motion of the depression is eastward and towards the pole, the disturbance at the same
time assuming the features of the extra-tropical cyclonic storm.
4§5. Rate OF Progress op the Stor.m Centkh.— Within the tropics (in tli^; northern heniisphere)
the average velocity of the storm center along the track is about 17 miles per hour; in the latitudes of
recurv-ature this drops to 8 miles per hour, the center at the time frequently becoming stationary; in
higher latitudes it again increases, rising to 20 or even to 30 miles per hour.
In the southern liemisphere the average velocity of progress as far as determined is somewhat less
than iu the northern, l)ut shows about the same relation in different parts of the track.
The general path of the tropical cyclonic storm in either hemisphere and the cyclonic circulation of
the wind about the storm center are" given in figures 61 and 62; that for the northern hemisphere
applying to the West India hurricane; that for
the southern hemisphere to the hurricanes of ^ , -- , ,1 , - - , ., „ f
the South Pacific Ocean.
486. Character of Tropical Cyclonic
Storms. — Within the tropics the storm area is
suiall, the region covered by violent winds ex-
tending in general not more than 150 miles from
the center. The barometric gradient.s are, how-
ever, exceedingly steep, instances having been
recorded in which the difference of pressure for
this distance amounted to 2 inches. In the
typhoons of the North Pacific Ocean gradients
of one inch in 60 miles are not infrequent. The
successive isobars are ahnost circular. As a
consequence of this distribution of pressure the
winds on the slopes of the depre.ssion are fre-
quently of great violence, and in the matter of
direction they are more symmetrically disposed
about the center than is the case with the larger
and less regularly shaped depressions of higher
latitudes. In these low latitudes the average
values of the deflection of the wind from the
barometric gradient is in the neighborhood of
six compa.ss points, — to the right in the northern
hemisphere, to the left in the southern.
487. To Fix the Bearing op the Storm
Center from the Vessel. — On this assumption,
the following rules will enable an observer to
fix the bearing of the storm center from his
vessel : —
In the northern hemisphere, stand with the
back to the wind; the storm center will bear six
points to the observer's left.
In the southern hemisphere, stand with the
back to the wind; the storm center will l>ear six
points to the observer's right.
On the basis of these rules the tables here-
after given (art. 492) show the bearing ofthe
center corresponding to a wind of any direction.
488. To Fix tub Distance op the Stor.m Ce.n'ter pro.m the Vessel. — Tlie following table, taken
from Piddington's "Sailor's Horn Book," may prove <jf some assistance in estimating thedistance of the
Btorm center from the vessel:
Fig. 61.
Average fall ofthe fxirometer
per hour.
From 0.02 to 0.06 in.
From 0.06 to 0.08 in.
From 0.08 to 0.12 in.
From 0.12 to 0.15 in.
DiHtance from the xtorm center.
From 250 to 150 miles.
From 150 to 100 miles.
From 100 to 80 miles.
From 80 to 50 miles.
The table assumes that the vessel is hove-to in front of the storm, and that the latter is advancing
directly toward it.
489. To Avoid the Center op the Storm. — In the immediate neighborhood of the center itself
the winds attain full hurricane force, the sea is exceedingly turbulent, and there is danger of being
struck aback. Every effort should therefore be made to avoid this region, either by running or by
heaving-to; and if recourse is had to the latter maneuver, much depends upon the selection of the
proper tack ; this being in every case the tack which will cause the wind to draw aft with each successive
shift.
A vessel hove-to in advance of a tropical cyclonic storm will experience a long heavy swell, a falling
barometer with torrents of rain, and winds of steadily increasing force. The shifts of wind will depend
upon the position of the vessel with respect to the path followed by the storm center. Immediately upon
the path, the wind will hold steady in direction until the passage of the central calm, the "eye of
the storm," after which the gale wifl renew itself, but from a direction opposite to that which it previ-
150
CYCLONIC STORMS.
ously had. To the right of the path, or iu tlie right-liand semicircle of the storm (the observer being-
supposed to face along the track ) , the wind, as the center advances and jjasses the vessel, will constantly
shift to the right, the rate at which the successive shifts follow each other increasing with the prox-
imity to the center; in this semicircle, then, in order that the wind shall draw aft with each shift, the
vessel must be hove-to £>n the starboard tack; similarly, in the left-hand semicircle, the wind will con-
stantly shift to the left, and here the vessel nuist he hove-to on the port tack.
These rules hold alike for both hemispheres and for cyclonic storni.« in all latitudes.
The above shifts ol the wind are based upon the supposition that the vessel is lying-to. A vessel in
rapid westerly motion may, in low latitudes, readily overtake the storm center, in which cage the
observed shifts will be just the reverse of those here described.
49©. D.\NGERors AND Navig.\ble Semiciecxes.— Prior to recurving, the winds in tliat semicircle
of the storm which is more remote from the equator (the right-hand semicircle in the northern hemi-
sphere, the left-hand semicircle in the
180' 170° southern ) are liable to be more severe than
those of tlie opposite semicircle. A vessel
hove-to in the semicircle adjacent to the
equator has also the advantage of immu-
nity from becoming involved in the actual
center itself, inasmuch as there is a distinct
tendency on the part of the latter to move
away from the equator. For these reasons
the more remote semicircle has been called
the dam/eroui^; the less remote, theiiarigable.
491. MANECVERixfi. — A vessel sus-
pecting the dangerous proximity of a trop-
ical cyclonic storm should lie-to for a time
on the starT)oard tack to locate the center
by observing shifts of the wind and the
behavior of the barometer. If the former
holds steady and increases in force, while
the latter falls rapidly, say at a greater rate
than 0.03 of an inch per hour, the vessel
is probably on tlie track of the storm and
in advance of the center. In this position
the proper step (providing, of course, that
sea room permits) is to run, keeping the
wind, in the northern hemisphere, at all
times well on the starboard quarter; in the
p2 southern hemisphere, well on the port; and
tlius constantly increasing the distance to
the storm center. Thesame rule holds good
if the observation places the vessel at but
a scant distance within the forward quad-
rant of the dangerous semicircle. Here,
too, the natural course will be to seek the
navigable semicircle of the storm, even
though such a course involves crossing the
track in ad\ance of the center, always ex-
ercising due caution to keep the wind from
drawing too far aft.
The critical case is that of a ves.sel
which finds herself in tlie forwar<l quad-
rant of the dangerous semicircle and at a
considerable distance from the track, for
here the shifts of the wind are sluggish and
the indications of the barometer are unde-
cided, l)oth causes conspiring to render the
bearing of the center doubtful. If, upon
heaving-to, the barometer liecomes station-
ary, the position should be maintained
Fig. 62.
until indications of a rise are apparent, upon which the course may be resumed with safety and held as
long as the rise continues. If, however, the barometer falls, a steamer should make a run to tlie NNE.
or NE. (southern hemisphere, SSE. orSE. ), keeping the wind and sea a little on the port (southern
hemisphere, starboard) bow, and using suc^h speed as will at least keep the mercury stationary. ^ Such
a step will in general be attended with the assurance that the present weather conditions will m any
case grow no worse. For a sailing vessel, unable to stand closer to the wind than six points, the last
maneuver will be impossible, and driven-to leeward by wind, sea, and current, she may be compelled
to cross the track immediately in advance of the center, or may even become involved m the center
itself In this extremity the path of the storm center during the past twenty-four hours slionld be laid
down on a diagram as accurately as the observations permit, and the line prolonged for some distance
beyond the preseut position of the center. Having assumed an average rate of progress ffvr the center,
its probable position on the line should be frequently and carefully plotte<l. and the handling ot the
vessel should be in accordance with the diagram. . , , , • • ,.u
492. Summary of Rri.ES.— The following summary comprises the rules for maneuvering in the
Korthem Hemisphere, so far as they may be made general:—
CYCLONIC STORMS.
151
la th£ Right Semicircle: Haul by the wind on the starboard taek and larry sail as long as possible;
it" obliged to heave-to, do so on starboard tack.
In the Left Semicircle: Bring the wind on the starboard quarter, note course and I-.eep it; if obliged
to heave-to, do so on port tack. ,
In Front of Center: Bring wind two points on starboard (juarter, note course and keep it; if obliged
to heave-to, do so on jwrt tack.
In Rear of Center: Run out with wind on starboard quarter; if obliged to heave-t«, do so on star-
board tack.
The application of these rules for the various directions of the wind is shown in the following
table:—
Storm Table, Sorthern Hemisphere.
Direction
of wind.
North.
NNK.
NE.
ENE.
East.
ESE.
SE.
SSE.
South.
Direction
of center.
If wind I 1
stiifts to- If Hind sliifts towards tlie j If wind steady witli falling If wind steady with rising
wards the ' ^
right. '
left.
barometer.
ESE.
SE.
SSE.
South.
SSW.
SW.
WSW.
West.
WNW.
S Run SSW.
2 SI 2 i RunSW.
^-'^ §.- Run WSW.
p -• 2 -5" Run West.
S-o'^ ^ i RunWXW.
ggv; |.| RnnNW.
a'g 3 S- 1 Run XXW.
g-P-— o i Run North.
n Q » 3
n -« T
^1-%
Run NNE.
rule:
Run SSW.
Run SW.
Run WSW.
Run West.
Run WNW.
Run NW.
Run NNW.
Run North.
Run NNE.
P.I.. 'NTli'
■:3 o o
"■to' 3
fD
i 3^
TO FIND THK SE.MI-CIRei.E THE SHIP IS IN.
go 5-
Run SSW.
Run SW.
Run WSW.
Run West.
Run WNW.
Run NW.
Run NNW.
Run North.
Run NNE.
Run NE.
Run ENE. '
Run East.
Run ESE.
Run SE.
Run SSE.
Run South.
»
O i^
^ OTQ P
-1 rt> 3
7(3
g-^
In North Latitndes the Ships Position is 8 points to the ^ ^
,eft of the Wind; but in South Latitudes the Ship's Position ~„„.„,i „„,„„,„ it possi„ie.
8 (Pomt.^ to the ^Sghi of the wind.
ror example: If the ship experienced a North-east wind ii^-and keep it; if obliged to
le would be on the J^orth-west point, in North Latitudes; ry «iii as i,.n- as possible; if
ut the South-east point in South Latitudes. ,,,, and keep it; if oi,iige.i to
Draw a line through the centre of a circle in the direc- eav.-t,., ,ln so on port tack.
on the storm is traveling. Imagine yourself .standing on this
|ne and looking in the direction of the storm: The semi-
rcle on your right is called the Right Hand S^mi-circle, and
iial on vour Wi The Left Hard Semi-circle.
falling If wind steady witli rising
barometer.
TACK TO HEAVE TO ON.
In the Right Hand Semi-circle heave to on \.\\tt Star-
hard tack.
In the Left Hand Semi-circle heave to on the (Port %%
tck.
WSW.
West.
WNW.
NW.
NNW.
SE.
SSE.
South.
SSW.
SW.
Run NE.
Run ENE.
Run East.
Run ESE.
Run SE.
a..w
o .i.
a"
0.0 ..»
.OSS
Run NE.
Run ENE.
Run East.
Run ESE.
Run SE.
Run SSE.
a
o o.
Run South.
Run SSW.
Run SW.
old CO
if obh
port t
Run WSW.
m
Run West.
&:
-^c/:
Run WNW.
o a
%^
RunNW.
s-^
Run NNW.
^^
»*!
Run North.
7.=
Jx
Run NNE.
a.'S
Run NE.
o ^
Run ENE.
gl
s?
Run East.
Run ESE.
o
Run SE.
y»
a Conrses given are for wind two points on port ijuarter, but it is preferable to take wind broad on ii\iartcr, it possible.
150
CYCLONIC STORMS.
ously had. To the right of the path, or in tiie liglit-hand semicircle of the storm (the observer being
Bupjiosed to face along the track ), the wind, as the center advances and passes the vessel, will constantly
shift to the right, the rate at which the successive shifts follow each other increasing with the prox-
imity to the center; in this semicircle, then, in order that the wind shall draw aft witli each shift, the
vessel must lie hove-to f n the starboard tack; similarly, in the left-hand semicircle, the wind will con-
stantly shift to the left, and here the vessel must be hove-to on the port tack.
These rules hold alike for lx)th hemispheres and for cyclonic storms in all latitudes.
The above shift.') of the wind are based upon the supposition that the vessel is lying-to. A vessel in
rapid westerly motion may, in low latitudes, readily overtake the storm center, in which case the
oltserved shifts will be just the reverse of those here described.
'190. Dax«er()US and Naviuable Semicircles. ^Prior to recurving, the winds in that semicircle
of the storm which is more remote from the etiuator fthe right-hand semicircle in the northern hemi-
spliere, the left-hand semicircle in the
180° 170° southern ) are liable to be more severe than
those of the oppi:)site semicircle. A vessel
hove-to in the semicircle adjacent to the
equator has also the advantage of immu-
nity from becoming involved in the actual
center itself, inasmui h as there is a distinct
tendency on the part of the latter to move
away from the equator. For tliese reasons
the more remote sen dcircle has been called
the danf/erous; the less remote, theiitifigahle.
491. Maneiverixg. — A vessel sus-
jiecting the dangerous proximity of a trop-
ical cvclonic storm should lie-to for a time
QUESTION 59th."""'
"WHAT MOTIONS HAS A CYCLONE?"
The Motion.s of Cyclones may be d
progressive.
escribed a:
QUESTION 60th.
WHAT SIGNALS DO YOU MAKE FOR
A PILO
IN THE DAYTIME.
To be hoisted at the fnrp fl.« i i
'W..,. «fe,.,, «,W, Mealed b^r'p.T.*"
Fig. 62.
IN THE NIGimiME
imtil indications fif a rise are apparf
long as the rise continues. If, how
or NE. (southern hemisphere, SSF
hemisphere, starlioard) bow, and using su<;w of^^-wv.
a step will in general l)e attended v.ith tlie assurance thai ttie present weatner »-..,.«.«.
case grow no worse. For a sailing vessel, unable to stand closer to the wind than six ])ointS| the last
maneuver will be impossible, and driven'to leeward by wind, sea, and current, she may be compelled
to cross the track immediately in advance of the center, or may even become in\olved in the center
itself. In this extremity the path of the storm center during the past twenty-four hours should l)e laid
down on a diagram as accurately as the observations permit, and the line prolonged for some distance
beyond the present position of the center. Having assumed an average rate oi progress fur the center,
its probable position on the line should be frequently and carefully plotted, and the handling of the
vessel should be in accordance with the diagram.
492. Summary op Rii.es. — The following summary compri.ses the rules for maneuvering in the
Korthem Hemlsjthere, so far as they may be made general: —
CYCLONIC STORMS.
151
In the Right Semicircle: Haul by the wind on the starboard tack and carry .sail as long as possible;
if obliged to heave-to, do so on starboard tack.
In the Left Si'iiiit-a-de: Bring the wind on the starboard quarter, note course and heep it; if obliged
to heave-to, do so on port tack. ,
In Front of Center: Bring wind two ixjints on starboard quarter, note course and keep it; if obliged
to heave-to, do so on port tack.
In Rear of Center: Run out with wind on starboard quarter; if obliged to heave-to, do so on star-
boaril tack.
The application of these rules for the various directions of the wind is shown in the following
table:—
Storm Table, Northern Hemisphere.
If wind
■1
Direction
Direction
shifts to-
If wind shifts towards the
If wind steady
with falling
If wind steady with rising I
of wind.
of center.
wards the
^ left.
barometer.
barometer. |
right.
North.
ESE.
w
Run SSW.
—
Run SSW.
—
Run SSW.
K
NNE.
SE.
2 °'£ S
Run SW.
"x ^2-
Run SW.
old(
obli
port
Run SW.
cc I:;;© 1
NE.
SSE.
"^ t < —
Run WSW.
5- - ~
Run WSW.
Run WSW.
S »•
74* CJ' ft
ENE.
South.
» s." S -^
Run West.
-I- — c
Run West.
?S2
Run "West.
o^So
East.
SSW.
3-2;^^
Run WNW.
P-^i
Run WNW.
n =-§
Run WNW.
§11 i
ESE.
SW.
i ?.•" i-
Run NW.
^ ^r.
Run NW.
r^i
Run NW.
SE.
WSW.
3.^sS-
Run NNW.
^- ^
Run NNW.
Run NNW.
1= ' i
SSE.
West.
si^B§
Run North.
Run North.
^ —
Run North.
?r «-!-■ 05
South.
WNW.
Run NNE.
Run NNE.
Run NNE.
So
SSW.
NW.
. ^ ^ ^ rK
Run NE.
Run NE.
s-s
Run NE.
IM
SW.
NNW.
5 5 T
Run EXE.
Run ENE.
Run ENE.
: wsw.
North.
9^5
Run East.
S ^
Run East.
&0
Run East.
? g
West.
NNE.
JSI
Run ESE.
Run ESE.
SE
Run ESE.
0^
WNW.
NE.
- J, 3.
Run SE.
?i
Run SE.
ss
Run SE.
s
NW.
ENE.
fll
Run SSE.
Run SSE.
Run SSE.
2s
NNW.
East.
Run South.
gjf
Run South.
B s;
Run South.
2»
"Coursfs given are for wind tw<» v«>int.s on starlxiard quarter, hut it is preferable to take wincl broad on quarter if jtossible.
Similarly, the following rules and table apply for the Sinitlierii Ifeinixphere: —
[11 t!ie liight Si'mii-iri-le: Bring the wind on the port quarter, note coui-se and keep it; if obliged to
heave-to, do so on starboard tack.
7/i the Left Semicircle: Haul by the wind on the ]>ort tack ami carry sail as long as possible; if
obliged to heave-to, do so on port tack.
In Front of Center: Bring wind two points on pi>rt quarter, note course and keep it; if ol)liged to
heave-to, do so on starlioard tack.
In Rear of Center: Run out with wind on. j)ort (luartcr; it obliged to heave-to, do so on port tack.
Storm Table, Southern Hemisphere.
If wind
1
Direetion
Birection
If wind shifts towards the
.shifts to-
If wind steadv
with falling
If wiiulsteadj
with rising
of wind.
of center.
right.
wards the
left.
hiaroineter.
barometer.
i
North.
WSW.
Run SSE.
u
a
Run SSE.
w
Run SSE.
NNE.
NE.
ENE.
West.
AVNW.
NW.
Run South.
Run SSW.
Run SW.
0; "--C
— C C ?i
5 — » =
Run South.
Run SSW.
Run SW.
old CO
oblige
starbo
Run South.
Run SSW.
Run SW.
old course
if obliged
port tack.
East.
ESE.
NNW.
North.
Run AVSW.
Run West.
m
• wi
sail 1
1 to
ick.
Run WSW.
Run West.
Run WSW.
Run West.
SE.
NNE.
Run WNW.
?= '
^Z 2,
Run WNW.
l^s
Run WNW.
=
SSE.
NE.
Run NW.
rs-
§ c":
Run NW.
?^g "
RunNW.
s-1
South.
SSW.
ENE.
p:a8t.
Run NNW.
Run North.
9k
Run NNW.
Run North.
n
Run NNW.
Run North.
SW.
WSW.
p:se.
SE.
Run NNE.
Run NE.
0^1
Run NNE.
Run NE.
fi.O
Run NNE.
Run NE.
West.
SSE.
Run ENE.
^
.o|f
Run ENE.
jg
Run ENE.
§*g
WNW.
South.
Run East.
g «
55 u-TT
Run East.
0^
Run East.
95 S
NW.
SSW.
Run ESE.
= 5^
Run ESE.
Run ESE.
05:
NNW.
SW.
Run SE.
y«
^kH.
Run SE.
§«
Run SE.
^3
aConrses given are for wind two points on iwrt quarter, but it is preferable to take wind broad on quarter, ii possible.
152
CYCLONIC STORMS.
493. Extra-Tropical Cyclonic Storms. — On turning to the cyclones ot temperate latitudes, we
find many features in whicli they resemble those of the torrid zone, "but certain other features in which
they differ. Their fundamental resemblance to tropical cyclones is seen in their incurving winds, form-
ing" an inflowing left-handed spiral about tlR> center of low pressure in the northern hemisphere, an
inflowing right-handed spiral in the southern. The intensity of these winds varies with the dejjth of
the barometric depression. The depression itself, however, in place of covering a few miles, as is the
case in the tropics, will frequently have a diameter of several hundred or even a thousand miles, and for
some distance around the center the gradients will have a tolerably strong value. For this rea.son there
is less concentration of violence close to the center, and the calm and clear central space, or "eye," is
seldom sharply developed, although it is not uncommon to discover a gradual weakening or failing of
the winds, and sometimes even an imperfect breaking away of the clouds as the central area passes over
the observer. The form of tropical cyclones as defined by their isobaric lines is nearly circular.
Extra-tropical cyclones are as a rule less" symmetrical, and their isobars are often elongated into an oval
form, the longer axis of the oval trending (in the northern hemisphere) between north and east—
about, therefore, in the direction of })rogression. The steepest gradients, and consequently the strongest
winds, are apt to be found on the equatorial and westerly sides of the denj-esgion.'
Extra-tropical cyclones generally follow an easterly course, inclining somewhat towards the pole;
but they occasionally turn to one side or the other, become stationary, or even move backward. The
velocity of progression varies from 15 to 40 miles an hour. If they exist as independent barometric
depressions, with strong upward gradients on all sides of the center, the cyclonic circulation will be
complete, the wind shifting with the Bun for an observer situated in the equatorial semicircle of the
storm, against the sun for an observer situated in the polar semicircle.
494. Storms Along the Transatlantic Steamship Routes.— The storms which are so frequently
met during the winter season along the steamship routes between America and Europe are not, as a
^ rule, due to central barometric depressions, but
f to depressions having a trough or V shape, which
'• extend southerly from the extensive permanent
area of low pressure having its center in the
vicinity of Iceland. They are not attended by
complete cyclonic circulations, ina-^much as the
polar gradients which would otherwise give rise
to easterly winds on this polar side are lacking.
Their approach is heralded by a gradual hauling
of the wind to southward, which is later fol-
lowed (at the time of passage of the central line
of the trough ) by a change to N W. , accompanied
by heavy rain squalls and a rapid increase in
force. The general distribution of pressure and
the surrounding winds are shown in figure 63.
The changes in wind and pressure ensue much more rapidly in the case of a westward-bound vessel than
in that of one eastward bound, the rate at which the observer and the depression apjjroach each other
being in the former case the sum of his own westward velocity and the eastward velocity of the trough,
in the latter case, the difference of these velocities.
TIDES. 153
CHAPTER XX.
TIDES.
493. Definitioks. — Tidal phenomena present themselves to the observer xmder two aspects — as
alternate elevations and depressions of the sea, and as recurrent inflows and outflows of streams. The
word tide, m common and general usage, is made to refer without distinction to both the vertical and
horizontal motions of the sea, and confusion has sometimes arisen from this double application of the
term; in its strict sense, this word may be used only with reference to the changes of elevation, while
the recurrent streams are proj^erly distinguished as tidal currents.
The tide rises until it reaches a maximum height called high water or ]ii{/h tide, and then falls to a
minimum level called low imter or low tide; that period at high or low water marking the transition
between tlie tides, during which no vertical change can be detected, is called stand.
Of the tidal currents, that which arises from a movement of the water in a direction, generally
speaking, from the sea toward the land, is called Jlood, and that arising from an opposite movement,
ebb; the intermediate j)eriod betw"een the currents, during which there is no horizontal motion, is dis-
tinguished as slack. Set and drift are terms applicable to the tidal currents, the first referring to the
direction and the second to the velocity.
Care should be taken to avoid confusing the terms relating to tides with those which relate to tidal
currents.
496. Cause. — The cause of the tides is the unequal attraction of the sun and moon upon different
parts of the earth. These bodies attract the parts of the earth's surface which are nearer to them with
greater force than they do its center, and attract its center more than they <io its opi)osite surface; to
restore efiuilibriinn the waters take a spheroidal figure, whose longer axis lies in the diiection of the
attracting body. The mean force of the moon in raising the tides is two and a half times as great as
that of the sun, for though the mass of the sun is vastly greater than the nia's of the moon, the sun's
distance is so great that it attracts the different parts of the earth with nearly etjual force. Theory is
not sufficiently advanced to render possible a prediction of tides or tidal changes from a mere knowledge
of the positions of the sun and moon, but by theory, supplemented by observation of actual tidal condi-
tions during a certain jxTifxl of time, very accurate predictions may he arrived at.
497. KsTAiii-isuMENT. — High and low water occur, on the average < f the twenty-eight days com-
prising a lunar month, at about tlie same intervals after the transit of the moon over the meridian.
These nearly constant intervals, expressed in hours and minutes, are known respectively as the high
water lunitidul interval and low water lunitidal intirial.
The interval Ijetwecn the moon's meridian passage at any place and the lime of the next succeeding
high water, as observed on the days when the moon is at full or change, is called the rnlgar {or common)
establishment of that place, or, sometimes, simply the citablishmerit. This interval is friquently spoken
of as the time of high water on full and change days (abbreviated "H. W. F. & C."); for sinte, on such days,
the moon's two transits (upper and lower) over the meridian occur about noon and midnight, the vul-
gar establishment then corresponds closely with the local times of high water. When more extended
observations have been made, the average of all the high water lunitidal intervals for at least a lunar
month is taken to obtain what is termed, in distinction to the vulgar establishment, the corrected estab-
lishment of the port, or mean high ■neater lunitidal interval. In defining the tidal characteristics of a place
some authorities give the corrected establishment, and others the vulgar establishment, or ' ' high water,
full and change;" calculations ba.«ed upon the former will more accurately represent average conditions,
though the two intervals seldom differ by a large amount.
Having determined the time of high water by applying the establishment to the time of moon's transit,
the navigator may obtain the time of low water with a fair degree of approximation by adding or
subtracting 6'' 13'" (one-fourth of a mean lunar day); but a closer result will be given by applying to
the time of transit the mean Unv water bttvitidol interval, which occupies the same relation to the time of
low water as the mean high water lunitidal interval, or corrected establishment, does to the time of
high water.
498. R.\xGE. — The rattge of the tide is the difference in height between low water and high water.
This term is often applied to the difference existing under average conditions, and may in such a case
be designated as the mean range or mean riie and fall to distinguish it from the spring range or neaji range,
which are the ranges at spring and neap tides, respectively.
499. iSprino and Neap Tides. — At the times of new and full moon the relative positions of sun
and moon are such that the high water produced by one of those bodies occurs at the same time as that
produced by the other, and so also with the low waters; the tides then occurring, called spring tides,
have a greater range than any others of the lunar month, and at such times the highest high tides as
well as the lowest low tides are experienced, the tidal range being then at its maximum. At the flrst
and third <iuarters of the moon the positions are such that the high tide due to one body occurs at the
time of the low tide due to the other, so that the two actions are opposed; this causes the neap tides,
which are those of minimum range, the high waters being lower and the low waters higher than at
other periods of the month.
154
TIDES.
Since the horizontal motion of the water depends directly upon the rise and fall of the tides, it follows
that the currents will be greatest at springs and least at neaps.
The effect of the moon's being at full or change is not felt at once in all parts of the world, and the
greatest range of tides does not generally occur until one or two days thereafter; thus, on the Atlantic
coast of North America, the highest tides are experienced one day, and on the Atlantic coast of Europe,
two days afterward, though on the Pacific coast of North America they occur nearly at full and change.
500. The nearer the moon is to the earth the stronger is its attraction, and as it is nearest in perigee,
the tides will be larger then on that account, and consequently less in ajjogee. For a like reason, the
tides will be increased by the sun's action when the earth is near its perihelion, about the 1st of January,
and decreased when near its aphelion, about the 1st of July.
501. The height of the tides at any place may undergo modification on account of strong prevailing
winds or abnarraal barometric conditions, a wind blowing off the shore or a high bai-ometer tending to
reduce the tides, and the reverse. The effect of atmospheric ]iressure is to create a difference of about
2 inches in the height of tide for every tenth of an inch of difference in the barometer.
302. Pkimixg and Lagging. — The tidal daij is the variable interval, averaging 24'' 50"', between two
alternate high or low waters. The amount by which corresponding tides grow later day by day — that
is, the amount by which the tidal day exceeds 24'' — is called the daily retardation. When the sun's tidal
effect is such as to shorten the lunitidal intervals, thus reducing the length of the tidal day and causing
the tides to occur earlier than usual, there is said to be n priming of the tide; when, from .similar causes,
the interval is lengthened, there is said to be a tagging.
SOS. Types of Tides. — The observed tide is not a simple wave; it is a compound of several elemen-
tary undulations, rising and falling from the same common plane, of which two can be distinguished and
separated by a simple grouping ol the data. These two waves are known as the semi-diurnal and the
diurnal tides, because the first, if alone, would give two high and two low waters in a day, while the
second would give but one high and one low' water in an equivalent period of time. In nearly all ports
these two tides coexist, but the proportion between them varies remarkably for different seas. The
effect of the combination of these two types of tide is to produce a diurnal inefiualitg, both in the height
of two consecutive high or low waters, and in the intervals of time between their occurrence. The
height of the diurnal wave may be regarded as reaching a maximum fortnightly, soon after the moon
attains its extreme declination and is therefore near one of the tropics. The tides that then occur are
denominated tropic tides.
In undertaking to investigate the tides of a port it is important to ascertain as early as possible the
form of the tide; that is, whether it resembles the semi-diurnal, the diurnal, or the mixed type; because
not only may this information be of scientific value, but the knowledge thus gained at the outset will
enaVjle the observer to fix upon the best method of keeping liis record.
304. The type forms referred to are
illustrated in the diagram in figure 64,
where the waves are plotted in curves,
using the times as abscissa' and the
heights as ordinates. In this diagram,
the curve traced in the full line is a tide-
wave of the semi-diurnal type; that
traced by the dotted line one of the di-
urnal ; while the broken line is one of the
mixed type, in this case the compound
of the two others. >
In order to determine the type to
which the tide of any port belongs, it is
usually only necessary to make hourly
observations for a day or two at the date
of the moon's maximum declination, and
to repeat the series about a week later,
when the moon crosses the equator.
The reported irregularities of the rise
and fall at any place should not deter
jjersons from careful investigation.
When analyzed, even the most compli-
cated of tides are found to follow some
general law.
503. Tidal CruiiExxs. — It should
l)e clearly borne in mind l)y the naviga-
tor that the jjcriods of flood and ebb ('urrents do not necessarily coincide with those of rising and falling
tides, and that, paradoxical though it may seem at first thought, the inward set of the surface current
does not always cease when the water has attained its maximum height, nor the outward set when a
minimum height has been reached. Under some circumstances it may occur that stand and slack will
be simultaneous, while other conditions may produce a maximum current at stand, with a maximum
rate of rise or fall at slack water.
The varying effects which v.ill be produced according to local conditions may be considered by the
comparison of two tidal basins, to one of which the tide-wave has access from the sea by a channel of
ample capacity, while the other has an entrance that is narrow and constricted. In the first case, the
process of filling or emptying the basin keeps pace with the change of level in the sea and is practically
completed as soon as the height without becomes stationary; in this case slack and stand occur nearly
at the same time, as do flood and rise and ebb and fall. In the second case, the limited capacity of the
entrance will not permit the basin to fill or empty as rapidly as the tide changes its level without;
(
)T 2"3^4, 5 6'7 8 10 n 12 1.3 M 15 ]6 17 18 10 20 2122 23 24 |
fV
1
1 1
3
2
1
1
2
3
4
1
^
1
.
J f^
■''
— ^
"v.
,'
/■
I
/
I"
A
n;
/f
/
N
/
V
/
/
\
\
-,
/
\'i
K
/
/
,.
•\
\
/
/
\
1
\
—
/
^.
/
/
\
/
k~-
^
/
'
y
/
-
'd:
/
r-;
■•'
\
/
/>—
-\l 1
■—
A,
/\
\
, \A
- Semi-diurnal.
. diurnal .
Fk;. 64.
- mixed.
TIDES. 155
hence there ia still a difference of level to produce a current when the vertical motion in either direction
has ceased on the outside, and for a considerable time after motion in the reverse direction has been in
progress; under extreme conditions it may even occur that a connnon level will not be established
until mid-tide, and therefore the surface current at some places will ebb until three hours after low
water and flow until three hours after high water.
Localities that partake of the nature of the first case are those upon open coasts and wide-mouthed
bights. Examples of the latter class will l^ie found in narrow bays and long channels.
TIMES OF HIGH AND LOW WATER.
506. Tide Tables. — The most expeditious, as well as most exact, method of ascertaining the times
of high and low water and other features of the tides will l)e by reference to a Tide TafJe, and every
navigator is reconunended to provide himself with such a publication. The United States Coast and
Geodetic Survey publishes annually, in advance, tables giving, for every day in the year, the predicted
time and height of the tides at certain principal porta of the world, and from these, by a simple reduc-
tion, the times and heights at a multitude of other ports may readily be obtained; data for ascertaining
the tidal currents in certain important regions are also provided. General tide tables are also published
by the governments of other maritime nations, and special tables are to be had for many particulai
localities.
507. Where no tide tables are available, the method of calculation by applying the lunitidal Intf r
val to the time of the moon's meridian passage must be resorted to.
To do this, find first the time of the moon's meridian passage, upper or lower, as may lie require<l.
The Greenwich mean time of up))er transit at Greenwich is given in the Nautical Almanac (page IV oi
the month) ; the corresponding time of lower transit is most easily found by taking the mean of the two
adjacent upper transits; to the Greenwich time of Greenwich transit apply the correction for longitude
given in Table 11 (u.sing the daily variation of the moon's meridian pas.«age shown in the Almanac)
adding in west and subtracting in east longitude; the result is the local' mean time of local transit
Add to this the high-water or low-water lunitidal interval of the port from Appendix 1"\', according as
the time of high or low water may be re(|uired. The result is the time sought.
The astronomical date nmst he strictly adhered to, and in so doing it may be found necessary to
emi)loy the time of a lower transit, or the transit of a preceding day, to find "the time of the tide in
question.
Appendix IV contains, besides the geographical positions of all the more important jiositions in the
world, a series of tidal data relating to many of those places. In such data are comprised the mean
lunitidal intervals for high and low water; also, for places where the .semi-diurnal type of tide prevails,
the tidal range at spring and at neap tides, and for those where the tide is of the diurnal tvi>e, the tropic
range. An alphabetical index is appended to this table.
The corrected establishment taken from the charts may be substituted for the high-water lunitidal
interval of the table; or, with only slight variation in the results, the vulgar establishment (H. AV. F.
& C. 1 may be employed.
Example: Find the times of the high and low waters at the New York navv vard, occurring next
after noon on April 22, 1879.
G. M. T. of Gr. transit, U'?' 0'" 32"'.2
Corr. for -{-74° Long. (Tab. 11), -!- 10
L. M. T. of local transit, L':.' 4'J
Transit, 22^ 0^^ 42"' Transit, 22' 0'' 42"'
H. W.Lun. Int. (App. IV). 8 44 L. W. Lun. Int. (App. IV), " 2 49
I ^I T U W /-- •' -*^ T \r T T W- 122 3 31
• • ^•' ^*- •■ 1 April 22, 9.2(1 p. m. ^^ ^^- ^■' ^'- ^^ ' \ April 22, .S.31 p. n..
Exa.mple: Find the time of high water at the Presidio, San Francisco, Cal., on the afternoim of
May 7, 1879.
G. M. T. of Gr. transit, tV 12" 36"'.6
Corr. for -^ 122° Long. (Tab. 11), -^ 22
L. M. T. of local transit, (i 12 59
II. W. Lun. Int. (App. IV), -p 11 43
L. M. T.,H. W., IL '^JL ,,
' \ May 7, 12.42 1). m.
Example: Find the time of low water at Singapore on the night of May 28, 1879.
G. M. T. of Gr. transit, 28'i 5'' 5.5"'. ;!
VoTT. for —104° Long. (Tab. 11), — 13
L. M. T. of lo<:al transit, 28 5 42
L. W. Lun. Int. (App. IV), -f 4 02
T M T 1 W r 28 9 44
^•^'■^•'^•^^- I May 28, 9.44 p. m.
156 TICKS.
Kxami'i.e: Find the time of morning high wat*^ and afternoon low water at <;i))raltar on Juno 26,
1879.
G. M. T. of Gr. upper transit, 25" 4" 40"'. 1
G. M. T. of Gr. upper transit, 26 5 27 .0
2).51 10 07 .1
G. M. T. of Gr. lower transit, 2."> 17 04
Corr. for r 5° Long. (Tab. 11), -• 01
L. M. T. of local lower trans., 2.5 17 0.5
Transit, ' 2.V']7"05'" Transit, 2.5" 1 7'' 0.5™
H.W.Lun.Int. (App. IV), 18.5 L. W.Lun. Int. (App. IV)-, 7.55
L. M. T., H. W., I f \f'l „, L. M. T., L. W., I f ^ P'\
' ' . I June 2h, (>.4() a. 111. ' ' \ June 2(3, 1 ]i. m.
TIDAI. OBSERVATIONS.
508. Since navigators will frequently have oiijiortunity to observe tidal conditions, either in con-
nection with a hydrographic survey or otherwise, at i)laces where existing knowledge of the tides is
incomplete, an understanding of the methods employed in tidal observations may be important.
309. Tides. — For the proper study of tides, frequent and continuous observations are nece.ssary;
it will not suffice to observe the heights of the high and low waters only, even if they present them-
selves as distinct pha.ses, but the whole tidal curve for each day should be developed by recording the
height of water at intervals, which, preferably, should not exceed thirty minutes. Observations, to be
(»mplete, must cover a whole lunar month; or, if it be impracticable to observe the tides at night, the
day tides of two lunar months may be substituted.
510. When made for the purposes of a hydrographic survey the tidal observations are used to
correct the soundings, and care must be taken to malce sure that the gauge is placed in a situation visited
by the same form of tide as that which occurs at the place where soundings are being made. It will not
answer, for instance, to correct the soundings upon an inlet-bar by tidal observations made within the
lagoon with which this inlet communicates, because the range of the tide within the lagoon is less than
upon the outside coast. A partial obstruction, like a bridge, or a natural contraction of the channel
section, while it may not reduce the total range of the tide or materially affect the time of high or low
tides, will alter the relative heights above and below at intermediate stages, so that the hydrographer
must be careful to see that no such obstruction intervenes between his field of work and the gauge.
511. TiD.ti. 'CuRREN'Ts. — Observations for tidal currents should be made with the same regularity
as for tides; the intervals need not ordinarily be more frequent than once in every half hour. They
should always be made at the same point or points, wdiich should be far enough from shore to be repre-
sentative of the conditions prevailing in the navigable waters. The ordinary log may be employeil for
measuring the current, but it is better to replace the chip by a pole weighted to float upright at a depth
of about fifteen feet; the line should be a very light one, and buoyed at intervals by cork floats to keep it
from sinking; the set of the current should be noted by a compass bearing of the direction of the pole
at the end of the observation.
512. Record. — The record of observations should be kept clearly and in complete form. It should
include a description of the locality of observation, the nature of gauge and of instruments used for
measuring currents, and the exact position of both tidal and current stations, together with situation
and height of bench mark. The time of making each observation should be shown, and data given for
reduction to sohie standard time. In extended tidal observations the meteorological conditions should
be carefully recorded, the instruments used for the observations being properly compared with standards.
51 3. There are frequently remarkable facts in reference to tides and currents to be obtained from
persons having local knowledge; these should be examined and recorded. The date and circumstances
of the highest and lowest tides ever known form important items of information.
514. Planes of Reference. — The pUine of reference is the plane to which soundings and tidal data
are referred. One of the principal objects of observing tides when making a survey is to furnish the
means for reilucing the soundings to this plane. Four i)lanes of reference are used; namely, mean low
water, mean low water springs, mean lower low waters, and the harmonic or Indian tide plane..
Mean low voter is a plane whose depression below mean sea level corresponds with half the mean
semi-diurnal range, while the depression of mean low-water springs corresponds with half the mean range
of spring tide; meayi lower low water depends upon the diurnal inecjuality in high and low water; the
harmonic or Indian tide plane was adopted as a convenient means of expressing something of an approxi-
mation to the level of low water of ordinary spring tides, but where there is a large diurnal inequality
in low waters it falls considerably below the true mean of such tides.
As these planes may differ "considerably, it is important to ascertain which plane of reference is
adopted before making u.se of any chart or considering data concerning the tides.
515. The tides are subject to so many variations dependent upon the movements of the sun and
moon, and to so many irregularities due to the action of winds and river outflows, that a very long series
of observations would be neces.aary to fix any natural plane. In consideration of this, and keeping in
view the possibilities of repetitions of the surveys or subsequent discoveries within the field of work, it
is necessary to define the position of the plane of reference which has resulted from any series of obser-
vations. This is done by leveling from the tide gauge to a permanent bench, jirecisely as if the adopted
plane were arbitrary.
516. Bench Mark.— -The plinth of a light-house, the water table of a substantial building, the
base of a monument, and the like, are proper benches; and when these are not within reach, a mark
TIDES. 157
may be made on a rock not likely to l)e moved or started by the frost, or, if no rock naturally exists in
the' neigh borhofxl, a block of stoiie bu-ied l)elow the reach of frost and plowshare should be the resort.
When a bench is made on shore, it should be marked by a circle of 2 or 3 inches diameter with a cross
in the center, indicating the reference point. The levelings between this point and the gauge should be
be run over twice and the details recorded. A bench made upon a wharf or other i^erishable structure
is of little value, but in the absence of permanent objects it is better than nothing. The marks should
be cut in, if on stone, and if on wood, copper nails should be u.sed. The bench must be sketched and
carefully described, and its location marked on the hydrographic sheet, with a statement of the relative
position of the plane of reference.
517. The leveling from the tench mark to the tide gauge may be done, when a leveling instrument
is not available, by measuring the difference of height of a number of intermediate points by means of
a long straight-edged board, held horizontal by the aid-of a carpenter's spirit level, or even a plummet
square, taking care to repeat each step with the level inverted end for end. A line of sight to the sea
horizon, when it can be seen from the tench acro.«8 the tide staff, will afford a level line of sufficient
accuracy, especially when observed with the telescope. It may often be convenient to combine these
methods.
518. Tide Gauges. — The Staff Oauge is the simplest device for measuring the heights of tides, and
in perfectly sheltered localities it is the best. It consists of a vertical staff grailuated upward in feet and
tenths, an<i so placed that its zero shall lie telow the lowest tides. The same gauge may also be used
where the surface is rough, if a glass tube with a float inside is secured alongside of the staff, care teing
taken to practically close the lower end of the tube so as to exclude undulations; readings may also be
made by noting the point midway tetween the crest and trough of the waves.
A staff gauge should always be erected for careful tidal observations, even where other ('lasses of
gauge are to be employed, as it furnishes a standard for comparison of absolute heights, and also serves
to detect any defects in the mechanical details upon which all other gauges are to a greater or less extent
dependent.
519. Where there is considerable swell, and where, from the situation of the gauge or the great
range of the tide (making it inconvenient for the observer to see the figures in certain positions) the
staff gauge can not be used, recourse must be ha<l to the Bo.r Omigi'. This gauge consists of a vertical
box, closed at the bottom, with a few small holes in the lower part which admit suthcieut water to keep
the level within equal to the mean level without, but which do not permit the admission of water with
suiflcient rapidity to be affected by the waves. Within the box is a copper float; in some ca.ses this
float carries a graduated vertical rod whose position with reference to a fixed point of the box affords a
mea.<ure for the height of the water; in other gauges of this class the float is attached to a wire or cord
which passes over pulleys and terminates in a counterpoi.se whose position on a vertical graduated scale
shows the height of tide.
520. An Automatic Gauge requires a tex and float such as has just been described. The motion of
the float in rising and falling with the tide is communicated to a pencil which rests ni)on a moving
sheet of paper; uniform motion is imparted to the paper by the revolution of a cylinder driven by clock-
work; the motion of the jiencil due to the tide is in a direction perpendicular to the direction of motion
of the paper, and a curve is thus traced, of which one coordinate is time, and the other height. The
paper, which is usually of sufficient length to contain a month's record, is paid out from one cylinder,
pas.ses over a second whereon it receives the record, and is rolled upon a third cylintler, which thus
contains the completed tidal sheet.
This gauge, besides giving a perfectly continuous record, has the further merit of requiring but
little of the observer's time. But its indications, both of time and heights, should be checked by
occasional comparisons with the standard clock and the staff gauge, the readings of which should bs
noted by hand at appropriate points of the graphic re«ord.
158 OCEAN CURRENTS.
CHAPTER XXI.
OCEAN OUEEENTS.
521. An ocean current is a progressive liorizontal motion of the water ocourrin}; througlimit a
region of the ocean, a.« a result of which all Iwdies floating therein are carried with the stream.
The fet of a current is the direction toward which it flows, and its drift, the velocity of the flow.
522. Caise. — The principal cmike of ocean currents is the wind. Every breeze sets in motion, by
its friction, the surface particles of the water over which it blows; this motion of the upper stratum is
imparted to the stratum next beneath, and thus the general movement is connnunicated, eacli layer of
particles acting upon the one below it, until a current is established. The direction, depth, strength,
and permanence of such a current will depend upon the direction, steadiness, and force of the wind;
all, however, subject to modification on account of extraneous causes, i?uch as the intervention of land
or shoals and the meeting of conflicting currents.
A minor cause in the generation of ocean currents is the difference in density of the sea water in
different regions, a.s a result of which a set is produced from the more dense toward the less dense, in
the effort to establish equilibrium of pressure; the difference of density may be due to temperature, the
warmer water near the equator being less dense than the colder water of higher latitudes; or it may be
created by a difference in the amount of (■ontaine<l saline matter, resulting from evaporation, freezing,
or other causes. Another minor factor that may have influence upon ocean currents is the difference of
pressure exerted by the atmosphere ujion the water in different regions. But neither of the last-
mentioned causes may be regarded as <if great importance when compared with the influence, direct
and indirect, of the wind.
52il. Dkift .\xd Stre.\m Currents. — Ocean currents may be divide<l into two classes: Drift and
Stream Currents.
A Drift Current is one which arises from the effect of wind upon the surface water, impelling the
particles to leeward. Such currents reach only to shallow dei)ths, except in regions where caused by
winds whose prevalence is almost unbroken, and w here, in conseijuence, motion is communicated stratum
by stratum, during a long series of years, until the influence is felt at great dejiths.
' A Stream Current is one which arises 'when the Avater carried forward by a drift current encounters
an obstacle which prevents a further flow in the direction which it has been following, and the particles
are forced to acquire a new motion which takes such direction as may be imposed by the conditions
existing in the locality.
Some currents are compounded of both <lrift and stream; for a stream already formed may pass
through the region of a prevalent wind in such direction that it will receive an accelerating effect due to
the wind.
524. Submarine Currents. — In any scientific investigation of the circulation of ocean waters it is
necessary to take account of the submanne currents as well as those encountered upon the surface; but
for the practical purposes of the navigator the surface currents alone are of interest.
525. Methods of Deter.minatiox. — The methods of determining the existence of a current, with
its set and drift, may be divided into three classes; namely, (a) by observations from a vessel occupying
a stationary position not affected by the current ; ( ') ) by comparison of the position of a vessel under way
as given by observation with that given by dead reckoning; and (o) by the drift of objects abaniloned
to the current in one locality and reappearing in another.
526. Of these methods, the first named, by observations from a vessel at anchor, is by far the most
accurate and reliaVjle, but being possible only under special circumstances is not often available. The
most valuable information about ocean currents being that which pertains to conditions in the open sea,
the great depths there existing usually jireclude the possibility of anchoring a vessel; ships especially
fitted for the purpose have at times, however, carried out current observations with excellent results;
the most notable achievements in this direction are those of the survey of the Ciulf Stream, made by
United States naval officers acting under the Coast and Geodetic Survey, during which the vessel wa.s
anchored and observations were made in positions where the depth reached to upward of 2,000 fathoms.
52T. The method of determining current from a comparison of positions obtained, respectively,
bv observation and by dead reckoning is the one upon which our knowledge nuist largely depend.
This method is, however, always subject to some inaccuracy, and the results are frequently quite
erroneous, for the so-called current is thus made to embrace not only the real set and drift, but also
the errors of observation and dead reckoning. In the case of a modern steamer accurately steered and
equipped with good instruments for determining the speed through the water as well as the position by
astronomical observations, the current may be arrived at by this method with a fairly close degree of
accuracy. It is not always possible, however, to keep an exact reckoning, and this is especially true
in sailing vessels, where the conditions render it difticult to determine correctly the position by account;
this source of error may be combined with faulty instrumental determinations, giving apparent currents
differing widelv from those that really exist.
528. .Much useful knowledge regarding ocean currents has Ijeen derived from the observed drift
of objects from one to another localitv. This is true not only of the bottles thrown overboard from vessels
with the particular object of determining the currents, but also of derelicts, drifting buoys, and pieces
OCEAN CURRENTS. 159
of wreckage, which fulfill a similar mission. The deductions to be drawn from such drift are of a
general nature only. The point of departure, point of arrival, and elapsed time are all that are posi-
tively known. The route followed and the set and drift of current at different points are not indicated,
and in the case of objects floating otherwise than in a completely submerged condition account must
he taken of the fact that the drift is influenced by the wind. But even this general information is of
great value in researches as to ocean currents, and navigators who desire to aid in the work of investi-
gation may do so by throwing overboard, from time to time, sealed bottles containing a staten\ent of
date and position at which they are launched.
329. C'lKRENTS OF THE ATLANTIC OcE.^N. — A Consideration of the currents of the Atlantic most
cunvenientlv liegins with a de.«cription of the Eqwdorial Currents. The effect of the northeast and
southeast trade winds is to form two great drift currents, setting in a westerly direction across the
Atlantic from .\frica toward the American continent, whose combined width covers at times upward
of fifty degrees of latitude. These are distinguished as the Xorlhern or Soullicrn l-Jf/tiatorial Currents,
according as they arise from the trade winds of the northern or southern hemisi)here.
Of the two, the Southern Equatorial Current is the more extensive. It has its origin off the conti-
nent of Africa south of the Guinea coast, and liegins its flow with a daily velocity that averages about
15 miles; it maintains a general set of west, the portion near the equator acquiring later, however, a
northerly component, while the drift steadily increases imtil, on arriving off the South .Vmerican coa.st,
a rate of 60 miles is not uncommon. .\t.Cape San Roque the current bifurcates, the main or equatorial
branch flowing along the tiuiana coast, while the other l)ranch is deflected to the southward.
The Xorthern Equatorial (.'urrent originates to the northward of the Cape Verde Islands and sets
across the ocean in a direction that averages due west; though parallel to the corresponding southern
drift, its velocity is not so high.
530. Between the Xorthern and Southern Equatorial Currents is found the Equatorial Counter
Outwent, which sets to the eastward, being apparently a flowing ba<k, in the region of equatorial calms,
of water carried westward by the trade drifts. The extent and strength of this current varies with the
season, a maximum being attained in July or August, when its effect is apparent to ths westward of
the fiftieth meridian of west longitude, while at its minimum, in November or December. it.s influence is
but slight and prevails over a limited area only.
531. To the westward of the region of the Equatorial Counter Current the North and the South
l-xjuatorial Currents unite. A large part of the combined stream flows into the CariblK'an Sea through
the various passages between the Windward Islands, takes up a course first to the westward and then
to the northward and westward, finally arriving off the extremity of the peninsula of Yucatan; from
here some of the water follows the shore line of the tiulf of llexico, while another portion iiasses
directly toward the north Cuban coast; by the reuniting of these two branches in the Straits of Elorida
there is formed the most remarkable of all ocean currents — the Gulf Stream.
From that portion of the combined equatorial currents which fails to find entrance to the Caribbean
Sea a current of moderate strength and volume takes its course along the north coasts of Porto Kico,
Haiti, and Cuba, flows between the last-named island and the Bahama.", and enters the Gulf Stream off
the Florida coast, thus adding its waters to those of»the main branch of the equatorial current which
have arrived at the same point l)y way of the Caribbean, the Yucatan Passage, and the Gulf.
532. The Gulf Stream, which has it.'j origin, as has been described, in the Straits of Florida, and
receives an accession from a branch of the Equatorial Current off the Bahamas, flows in a direction that
averages true north as far as the parallel of 31°, then curves sharply to ENE. until reaching the latitude
of 32°, when a direction a little to the north of NE. is assumed and maintained as far as Cape Hatteras;
at this i)oint its axis is about 40 miles, while its inner edge is in the neighborhood of 20 miles off the
shore. Thus far in its flow the average position of the maximum current is from 11 to 20 miles outside
the 100-fathom curve, disregarding the irregularities of the latter, and the width of the stream — about
40 miles — is nearly uniform. From off Hatteras the stream broadens rapidly and curves more to the
eastward, seeking deeper water; its northern limit may Ix; stated to be 60 to 80 miles off Nantucket
Shoals and 120 to InO miles to the southward of Nova Scotia, in which latter place it has expanded to
a width of about 250 miles. Further on, its identity as the Gulf Stream is lost, but its general direction
is preserved in a current to be de.scrilx'fl later.
The water of the (iulf Stream is of a deep indigo-blue color, and its junction with ordinary sea
water may be plainly recognized; in moderate weather the edges of the stream are marked by ripi)les;
in cool regions the evaporation from its surface, due to difference of temperature between air aiid water,
is apparent to the e\'e; the stream carries with it a quantity of weed known as "gulf weed," which is
familiar to all who liave navigated its waters.
In its progress from the tropics to higher latitudes the transit is so rapid that time is not given for
more than a partial cooling of the water, and it is therefore found that the Gulf Stream is very much
warmer than the neighboring waters of the seas through which it flows. This warm water is, however,
divided by bands of markedly cooler water which extend in a direction parallel to the axis and are
usually found near the edges of the stream of warm water. The most abrupt change from warm to cold
water occurs on the inshore side, where the name of the Cold ]Vall has been given to that band which
has appeared to some oceanographers to form the northern and western boundary of the stream.
The investigatiims of Pillsbury tend to prove that the thermometer is^ only an approximate guide to
the direction and velocity of the current. Though it indicates the limits of the stream in a general way,
it must not be a.ssumed that the greatest velocity of flow coincides with the highest temperature, nor
that the northeasterly set will be lost when the thermometer shows a region of cold sea water.
The same authority has also demonstrated that in the vicinity of the land there is a marked varia-
tion in the velocity of current at different hours of the day, which may amount to upward of 2 knots,
and which is due to the elevation and depression of the sea as a result of tidal influences, the maximum
current being encountered at a period which averages about th ree hours after the moon's transit. Another
effect noted is that at those times when the moon is near the equator trie current presents a narrow
front with very high velocity in the axis of maximum strength, while at periods of great northerly or
160 OCEAN CUEBENTS.
southerly declination^ the front broadens, the current decreasing at the axis and increasing at the edges.
These tidal effects are not, however, observed in the open sea.
The velocity of the Gulf Stream varies with the seasons, following the variation in the intensity of
the trade winds, to which it largely owes its origin. The drift of the current under average conditions
may be stated as follows:
Between Key West and Habana: Mean surface velocity in axis of maximum current, 2| knots;
allowance to be made by a vessel crossing the entire widtli of the stream, 1.1 knots per hour.
Off Fowey Rocks: Mean surface velocity in axis, 3.5 knots; allowance in crossing, 2J- knots per hour.
Off Cape Hatteras: Mean surface velocity in axis, upward of 2 knots; allowance in crossing tiie
stream, 1 J knots per hour between the 100-fathom curve and a point 40 miles outside that curve.
533. After passing beyond the longitude of the easternmost portions of North America, it is gen-
erally regarded that the Gulf Stream, as such, ceases to exist; but by reason of the prevalence of westerly
winds the direction of the set toward Europe is continued until the continental shores are approached,
when the current divides, one branch going to the northeastward and entering the Arctic regions and
the other running off toward the south and east in the direction of the African coast. These currents
liave received, respectively, the designations of the Easterly, Northeast, and Southeast Drift Cm-rents.
534. The effect of the currents thus far described is to create a general circulation of the surface
waters of the North Atlantic, in a direction coinciding with that of the hands of a wati'h, about the
periphery of a huge eUipse, whose limits of latitude maybe considered as 10° N. and 45° N., and which
is bounded in longitude by the Eastern and Western continents. The central space thus inclosed, in
which no well-marked currents are observed, and in the waters of which great quantities of the Sargasso
or gulf weed are encountered, is known as the Sargasso Sea.
535. The Southeast Drift Current carries its waters to the northwest coast of Africa, whence they
follow the general trend of the land from Cape Spartel to Cape Verde. From this ijoint a large part of
the current is deflected to the eastward close along the upper Guinea coast. The steam thus formed,
greatly augmented at certain seasons by the prevailing monsoon and by the waters carried eastward
with the Equatorial Counter Current, is called the Guinea Current. A remarkable characteristic of this
current is the fact that its southern limit is only slightly removed from the northern edge of the west-
moving F^quatorial Current, the effect being that tlie two currents flow side by side in close jiroximity,
but in diametrically opposite directions.
536. The Arctic or Labrador Current sets out of Davis Strait, flows southward down the coasts of
Labrador and Newfoundland, and thence southwestward past Nova Scotia and the coast of the United
States, being found inshore of the Gulf Stream. It brings with it the ice so frequently met at certain
seasons off Newfoundland.
537. EenneU's Current is a temporary but extensive stream, whicli sets at times from the Bay of
Biscay toward the west and northwest, across the entrance to the English Channel and to the westward
of Cape Clear.
538. Of the two branches of the Southern Equatorial Current which are formed by its bifurcation
off Cape San Roque, the northern one, setting along the coasts of northeastern Brazil and of tniiana and
contributing to the formation of the Gulf Stream, ims already been described; the other, known as the
Brazil Current, flows to south and west, along the southeastern coast of Brazil, as far as the neighborhood
of the island of Trinidad; here it divides, one part continuing down the coast and having some slight
influence as far as the latitude of 45° S., and the other curving around toward east.
539. The last-mentioned branch of the Brazil Current is called the <S'OM//(fm Connecting Ciiirent and
flows toward the African coast in about the latitude of Tristan d'Acunha. It then joins its waters with
those of the general northerly current that sets out of the Antarctic region, forming a current which
flows to the northward along the southwest African coast and eventually connects with the Southern
Equatorial Current, thus completing the surface circulation of the South Atlantic.
540. There are two other currents whose effects are felt in the Atlantic, one originating in the
Indian Ocean and flowing around the Cape of Good Hope, the other originating in the Pacific and flow-
ing around Cape Horn. They will be descriVjed under the currents of the oceans in which they first
appear.
541. Currents of the Pacific Ocean. — As in the Atlantic, the waters of the Pacific Ocean, in
the region between the tropics, have a general drift toward the westward, due to the effect of the trade
winds, the currents produced in the two hemispheres being denominated, respectively, the Northern and
the Southern Equatorial Currents. These are separated, as also in the case of the Atlantic, by an east-
setting stream, about 300 miles wide, whose mean position is a few degrees north of the equator, and
which receives the name of the Equatorial Compter Current.
542. The major portion of the Northern Equatorial Current, after having passed the Mariana
Islands, flows toward the eastern coast of Formosa in a WNW. direction, whence it is deflected north-
ward, forming a current which is sometimes called the Japan Stream, l)ut which more frequently
receives its Japanese name of A'mi-o (Si'wo, or "black stream." This current, the waters of which are
dark in color and contain a variety of seaweed similar to "gulf weed," carries the warm tropical water
at a rapid rate to the northward and eastward along the coasts oi Asia and its oftlying islands, presenting
many analogies to the Gulf Stream of the Atlantic.
The limits and volume of the Kuro Siwo vary according to the monsoon, being augmented during
the season of southwesterly winds and diminished during the prevalence of those from northeast. The
current sets to the north along the east coast of Formosa, and in about latitude 26° N. changes its course
to northeast, arriving at the extreme southwestern point of Japan by a route to westward of the Meiaco-
sima and Loo-choo islands. A branch makes off from the main stream to follow northward along the
west coast <
toward the
runs parallel to the general trend of the south shores of the Japa
Nipon, attaining its greatest velocity between Bungo and Kii channels, where its average drift is
between 2 and 3 knots per hour. Continuing beyond the southeastern extremity of Nipon, the direction
OCEAN CURRENTS. 161
of the stream ))ecomes somewhat more northerly, and its width increases, with consequent loss of
velocity. In the Kuro Siwo, as in the (Julf Stream, the temperature of the sea water is an approximate,
though not an exact, guide as to the existence of the current.
543. Near 146° or 147° E. and nortli of the fortieth parallel the Kuro .Siwo divides into two parts.
One of these, called the Kamchatka Current, flows to the northeast in the direction of the Aleutian
Islands, and its influence is felt to a high latitude. The .second branch continues as the main stream,
and maintains a general easterly direction to the 180th meridian, where it is merged into the north and
northeast drift currents which are generally encountered in this region.
544. A cold counter current to the Kamchatka Current sets out of Bering Sea and flows to the
south and west close to the shores of the Kuril Island,", Yezo and Nipon, sometimes, like the Labrador
Current in the Atlantic, Ijringing with it quantities of Arctic ice. This is often called by its Japanese
name of Oya Siiro.
545. On the Pacific coast of North America, from about 50° N. to the mouth of the Gulf of
California, 23° N., a cold current, 200 or 300 miles wide, flows with a mean speed of thi-ee-quarters of a
knot, being generally .stronger near the land than at sea. It follows the trend of the land (nearly SSE.)
as far as Point Concepcion (south of Monterey ), when it begins to bend toward SSW., and then to WSW.,
off Capes San Bias and San Lucas, ultimately joining the great northern equatorial drift.
On the coast of Mexico, from Cape Corrientes (20° N.) to Cape Blanco (Gulf of Nicoya), there are
alternate currents extending over a space of more than 300 miles m width, which appear to be produced
by the jirevailing winds. During the dry season — January, February, and March — tbe currents generally
set toward southeast; during the rainy season — from May to October — especially in July, August, and
September, the currents set to northwest, particularly from Cosas Island and the Gulf of Nieova to the
parallel of 1.5°.
546. The Southern Equatorial Current prevails between limits of latitude that may Ije approxi-
mately given as 4° N. and 10° S., in a broad region extending from the American continent almost to
the one hundred and eightieth meridian, setting always to the west and with slowly increasing velocity.
In the neighborhood of the Fiji Islands this current divides; one part, known as the liossel Current, con-
tinues to the westward, following a route marked by the various passages between the islands, and later
at'quiring a northerly component and setting through Torres Strait and along the north coast of New
Guinea; the other part, called the Australia Current, sets toward south and west, arriving off the east
coast of Australia, along which it flows southward to about latitude 3.5° S., whence it bends toward
southeast and east and is soon after lost in the currents due to the ])revailing wind.
547. The general drift current that sets to the north out of the Antarctic regions is deflected until,
upon gaining tlie regions to the southwest of Patagonia, it has acquired a nearly easterly set; in striking
the shores fif the South American continent it is divided into two branches.
The first, known a." the Cape Horn Current, maintains the general easterly direction, and its influence
is felt, where not modified by winds and tidal cuiTents, throughout the vicinity of Cape Horn, and, in
the Atlantic Ocean, off the Falkland Islands and eastern Patagonia.
The second branch flows northeast in the tlirection of Valdivia and Valparaiso, follows generally
the direction of the coast lines of Chile and Peru (though at times setting directly toward the shore in
such manner as to constitute a great danger to the navigator), and forms the important current which
has been called variously the Perui'ian, Chilean, or Humboldt Current, the last name having been given
for the distinguished scientist who first noted its existence. The principal characteristic of the Peru-
vian Current is its relatively low t«nperature. The direction of the waters between Pisco and Payta is
between north and northwest; near Cape Blanco the current leaves the coa,st of America and bears
toward the Galapagos Islands, passing them on both the northern and southern sides; here it sets toward
WNW. and west; beyond the meridian of the Galapagos it widens rapidly, and the current is lost in the
equatorial current, near 108° W. As often happens in similar ca.ses, the existence of a counter-current
has been proved on different occasions; this sets toward the south, is very irregular, and extends only a
little distance from shore.
548. Currents of the Indun Ocean. — In this ocean the currents to the north of the equator
are very irregular; the periodical winds, the alternating breezes, and the changes of monsoon produce
currents of a variable nature, their direction dej)ending upon that of the wind which produces them,
upon the form of neighboring coasts, or, at times, \i\ion causes which can not be satisfactorily explained.
549. There is, in the Inciian Ocean south of the equator, a regular Equatorial Current which, by
reason of owing its source to the southeast trade winds, corresjionds with the Southern Equatorial Currents
of the Atlantic and Pacific. The limits of this west-movnig current vary with the longitude as well as
with the season. Upon reaching about the meridian of Rodriguez Island, a branch makes off toward
the .south and west, flowing jiai^t Mauritius, then to the south of Madagascar (on the meridian of which
it is 480 miles ls"oad) , and thereafter, rapidly diminishing its breadth, forming part of the Agulhas Cur-
rent a little to the south of Port Natal.
The main equatorial current continues westward until passing the north end of Madagascar, where,
encountering the obstruction presented by the African continent, it divides, one branch following the
coast in a tiortherly, the other in a southerly, direction. The former, in the season of the southwest
monsoon, is merged into the general easterly and northeasterly drift that prevails throughout the
ocean from the northern limit of the Equatorial Current on the south, as far as India and the adjacent
Asiatic shores on the north; but during the northeast monsoon, when there exists in the northern
regions of the Indian Ocean a westerly drift current analogous to the Northern Equatorial Currents
produced in the Atlantic and Pacific by the northeast trades, there is formed an east-setting Equatorial
Counter Current, which occupies a narrow area near the equator and is made up of the waters accumu-
lateil at the western continental boundary of the ocean by the drift currents of both hemispberes.
550. The southern branch of the Etiuatorial Current flows to the south and west down the
Mozambique channel, and, being joined in the neighborhood of Port Natal by the stream which
arrives from the open ocean, there is formed the warm Agulhas Current, which possesses many of the
characteristics of the Gulf and Japan streams. This current skirts the east coast of South Africa and
24972°— 12 11
162 OCEAN CURRENTS.
attains considerable velocity over that part between Port Natal and Algoa Bay. During the summei-
months its effects are felt farther to the westward; daring the winter it diminishes in force and extent.
The meeting of the Agulhas Current with the cold water of higher latitudes is frequently denoted by a
broken and confused sea.
Upon arriving at the southern side of the Agulhas Bank, the major part of the current is deflected
to the south, and then curves toward east, flowing back into the Indian Ocean with diminished strength
and temperature, on about the fortieth parallel of south latitude, where its influence is felt as far as the
eightieth meridian. A small part of the stream which reaches Agulhas Bank continues across the
southern edge of that bank, then turns to the northwest along the west coast of the continent until it
is united with the waters of the Southern Connecting Current of the Atlantic.
551. Along the fortieth parallel of south latitude, between Africa and Australia, there is a genera!
easterly set, due to the branch of the Agulhas current already described, to the continuation of the drift
current from the Atlantic which passes to southward of the Cape of Good Hojie, and to the westerly
winds which largely prevail in this region. At Cape Leeuwin, the southwestern extremity of Australia,
this east-setting current is divided into two branches; one, going north along the west coast of Australia,
blends with the Equatorial current nearly in the latitude of the Tropic of Capricorn; the other preserves
the direction of the original current and has the effect of producing an easterly set along the south coa.st
of Australia.
552. As in the other oceans, a general northerly current is observed to set into the Indian Ocean
from the Antarctic regions.
EXTBACX8 FROM NAUTICAL ALMANAC.
163
APPENDIX I.
EXTEAOTS FEOM THE AMERICAN EPHEMERIS AND NAUTICAL ALMA-
NAC, FOR THE YEAR 1879, WHICH HAVE REFERENCE TO THE
EXAMPLES FOR THAT YEAR GIVEN IN THIS WORK.
[Extraots: Page I.]
AT GREENWICH APPARENT NOON.
THE SUN'S
Apparent
Right Ascension,
Diff. fur
1 hour.
Apparent Diff. for
I>e<Sination. 1 hour.
Semi-
diameter.
Sidereal
Time of
the Semi-
diameter
passing
the
Meridian.
Equation of
Time, to be
added to
subtracted
from Appar-
ent Time.
Diff. for
1 hour.
JANUARY.
Sun.
19
Mon.
20
Tues.
21
20 4 60. 17
10.626
20 9 14.84
10. .595
20 13 28. 75
10.664
i
S. 20 21 9.
20 8 20. 4
S. 19 55 9. 1
+31.54
32.49
+33.43
16 17.58
69.72
16 17. 48
69.61
16 17. 38
69.51
10 56. 68
11 14.74
11 32.05
0.769
0.1SS
0.706
APRIL.
Tuee.
1
Wed.
2
Thur.
3
Sun.
13
Mon.
14
Tues.
15
Wed.
16
Thur.
17
Frid.
18
Sat.
19
San.
20
Mon.
21
41
45
49
1 25
1 29
1 33
1 36
1 40
1 44
1 47
1 51
1 .55
54.87
9.096
33.24
9.100
11.70
9.106
47.34
9.205
28.45
9.219
9.91
9.234
51.74
9.2S0
33.95
9.268
16.56
9.285
59.58
9.302
43.01
9.320
26.87
9.337
N. 4 30 43. 2
4 53 49. 1
5 16 49. 8
9 54. 1
9 22 35. 4
9 44 7.5
10 5 29. 9
10 26 42. 3
10 47 44. 7
11 8 36..4
11 29 17.1
N. 11 49 46.4
+57.85
57.64
57. 41
54.40
64.03
53.64
53.23
52.80
52.37
.51.92
51.45
+50.97
2.16
64.51
1.89
64.53
1.61
64.55
58.86
64.89
58.59
64.94
58. 31
64.99
6.5.04
58.04
57.77
65.09
57.50
65.15
57.24
65.21
56.98
6.5.27
56.72
65. 33
4 0.60
3 42. 46
3 24. 43
.35. 02
19.60
4.54
10. 15
24. 46
38.36
51. 85
1 4.93
1 17.60
0.758
0.754
0.748
0.649
0.635
0.620
0.604
0.587
0.670
0..553
0.536
0. 518
MAY.
Mon.
Tues.
Sat.
Sun.
I Thur.
' Frid.
Sat.
Sun.
2 48 30. 72
9.626
2 52 22. 03
9.650
3 7 53. 03
9.747
3 11 47.27
9.771
3 27 30. 07
9.871
3 31 27. 26
9.895
3 35 25.03
9.919
3 39 23. 37
9.942
N. 16 13 40. 4
16 30 40. 4
17 35 53. 8
17 51 29. 1
18 50 48. 5
19 4 51.6
19 18 35.5
X. 19 31 59. 8
+42.86
42.17
39.33
38. .59
35.52
34.72
33.91
+33.06
15 53. .36
66.37
15 53. 14
66.45
15 52. 25
66.78
15 52. 03
66.86
15 51. 20
67.19
15 51.00
67.27
15 50. 80
67.35
15 60. 61
67.43
3 25. 18
3 30. 40
3 45. 58
3- 47. 90
3 51.32
3 50.68
3 49. 47
3 47.69
0.229
0.206
0.109
0.084
0.014
0.039
0.062
0.086
-Mean Time of the Semidiameter passing may be found by substractintr 0".18 from the Sidereal Time.
+ prefixed to the hourly change of declination indicates that north declinations are increasing and south
aeclinations are decreasing; — indicates that north declinations are decreasing and south declinations
increasing.
164
EXTRACTS FROM NAUTICAL ALMANAC.
[Extracts: Pa^c I.J
AT GREENWICH APPARENT NOON— Continued.
1
1
1
&
THE SUN'S
Sidereal
Time of
the Semi-
diameter
passing
the
Meridian,
Equation of
Time, to be
subtracted !
from
Diff. for
1 liour.
Apparent
Right Ascension.
Dift. for
1 hour.
Apparent
Declination.
Diff. for
1 hour.
Semi-
diameter.
added to
Apparent
Time.
II. V}. s.
s.
o / //
//
/ //
g.
?fi, .»■,
».
JUNE.
Sat.
Tues.
Wed.
Frid.
Sat.
Frid.
Sat.
Wed.
Thur.
Frid.
7
10
11
13
14
20
21
25
26
27
5 33. 74
5 12 57. 61
5 17 6.09
5 25 23. 73
5 29 32. 85
5 54 30. 05
5 58 39. 75
6 15 18.00
6 19 27. 29
6 23 36. 42
10. 312
10.348
10. 3.58
10.376
10.383
10.402
10. 402
10.389
10.383
10.376
N. 22 45 9. 5
23 55. 9
23 5 22.9
23 13 3.8
23 16 17.4
23 27 0. 3
23 27 20. 5
23 24 .33. 1
23 22 49. 5
X. 23 20 41. 3
+14.64
11.63
10.62
8.58
"..55
1.36
•f 0.32
- 3.78
4.81
- 5.84
15 47.63
15 47. 30
15 47. 20
15 47.00
15 46. 91
15 46.48
15 46. 43
15 46. 27
15 46. 24
15 46. 22
68.70
68.81
68.84
68.90
68.92
68.98
68.98
68. 94
68.93
68.91
1 28.86
54, 76
42. 87
18.42
5.89
0. 455
0.490
0,500
0,518
0, 525
0, 546
0.546
0, 532
0,526
0,519
1 11.75
1 24.86
2 16. 72
2 29. 42
2 41. 97
. JULY.
Frid.
Sat.
Tues.
Wed.
Thur.
11
12
22
23
24
7 21 16. 72
7 25 21. 24
8 5 39. 82
8 9 38. 68
8 13 36. 94
10.197
10.179
9.964
9.939
9.914
X. 22 8 29. 2
22 23. 2
20 19 8.9
20 7 5.2
X. 19 54 41.3
-19.76
20.71
29.72
30.57
-31.41
15 46. 30
15 46. 33
15 46. 94
15 47. 03
15 47. 13
68.30
68.24
67.51
67. 43
67.35
5 10.04
5 17.99
6 10. 85
6 13. 15
6 14.84
0.339
0,321
0,108
0,083
0. 0.59
SEPTEMBER.
Tobestlhtract-
ed from Ap-
parent Time.
Wed.
Thur.
10
11
11 13 33. 93
11 17 9.68
8.993
8.988
X. 4 59 24. 2
N. 4 36 36. 2
—56.90
-57. 10
15 55.81
15 56. 06
64. 12
64.10
3 1.29
3 22.03
0,862
0,867
DECEMBER.
Mon.
Tues.
22
23
18 1 24.12
18 5 50:72
11. 108
11. 107
S. 23 27 17. 3
S. 23 26 54.3
+ 0.37
+ 1.56
16 18. 13
16 18.18
71. 30
71.30
1 16.61
46. 64
1.248
1.216
Not
+
sail Time of tlie Se
prefixed to tlie lie
declinations are d
increasing.
midiamoter passing may be found by subtracting O'.IS
urly change of declination indicates that north declit
ecreasing: — indicates that north declinations are d
from the S
lations are
ecreasing i
uiereal Time,
increasing a
nd south dec
nd south
linations
EXTKACIS FEOM NAUTICAL ALMANAC.
165
[Extracts: Page II.J
AT GREENWICH MEAN NOON.
Day of
the
Week.
Dav of
the
Month.
Appareyit Diff. for
Right Ascension. 1 hour.
h. VI.
Apparent
Declination.
Diff. for
1 hour.
E(juation of :
Time, to be j
added to Mean
Time.
Diff. for
1 hour.
Sidereal Time
or Ri^ht As-
cension of
Mean Sun.
h. m.
JANUARY.
Frid.
10
Sat.
11
lion.
20
Tues.
21
19 26 16.08
19 30 36.59
20 9 12.84
20 13 26. 71
10.866
10.842
10.593
10.562
S. 21 58 32.
+ 22.35
21 49 22. 7
23. Jl
20 8 26. 6
32. 48
S. 19 65 15. 6
+ 33.42
7 43. 42
8 7.37
11 14.60
U 31.91
1.010
0.986
0.738
0.706
19 18 32.66
19 22 29.22
19 57 58. 24
20 1 54.80
APRIL.
Tues.
1
Wed.
9
Tue?.
8
\XeA.
9
Tues.
15
Wed.
16
Thur.
17
Sun.
20
Mon.
21
Tue.s.
22
Wed.
23
Thur.
24
Frid.
25
Tues.
29
Wed.
30
41
45
1 7
1 11
1 33
1 36
1 40
1 51
1 .55
1 59
2 2
2 6
2 10
2 25
2 29
54. 27
9.098
32. 68
9.102
26. 22
9.146
5.87
9.157
9.91
9.236
51. 77
9.252
34. 02
9.269
43.19
9.321
27.08
9.338
11.41
9.366
.56. 19
9.375
41.42
9.394
27.11
9.414
.34. 67
9.494
22.79
9. .515
X. 4 30 39.
4 53 45.
7 10 20.
7 32 42.
9 44 7.
10 5 30.
10 26 42.
11 29 18.
11 49 47.
12 10 5.
12 30 11.
12 50 4.
13 9 45.
14 26 14.
X. 14 44 46.
4
+ .57. 86
6
67.65
3
,56.08
8
55.77
4
,53.65
53.24
1
8
.52.81
1
51.46
6
:«. 98
4
.50.48
9
49. 97
49.46
4
48.92
5
46, ta
7
+ 46. I>4
4 0.65
0.758
3 42. 50
0.754
1 56. 74
0.709
1 39.83
0.698
4. .'54
0.620
0.604
10. 15
24. 46
0.587
1 4.94
0.636
1 17.61
0..518
1 29.83
0.,500
1 41.61
0.481
1 52.93
0.462
2 3.80
0.442
2 42. 46
0.361
2 50.89
0.340
37
41
1 5
1 9
1 33
53. 62
50.16
29.48
26.04
5.37
1.92
58.48
48.13
44.69
41.24
37. 80
34. 35
30.91
17. 13
13.68
MAY.
Frid.
9
Sat.
10
Sun.
11
Mon.
12
Frid.
16
Sat.
17
Sun.
18
Wed.
28
Thur.
29
Frid.
30
Sat.
31
Sat.
/
Sun.
8
Wed.
U
Sat.
14
Sun.
15
Wed.
25
Thur.
26
Frid.
27
3 4
3 7
3 11
3 15
3 31
3 35
0.01
9.723
53.65
9.747
47.89
9.771
42.71
9.796
27.90
9.896
25. 67
9.919
24.01
9.942
36. 81
10. 155
40.75
10. 1»3
45. 12
10.190
49.91
10.207
N. 17 20 3.5
17 35 56.3
17 51 31.6
18 6 48.9
19 4 53.8
19 18 37.6
19 32 1.8
21 27 5.9
21 36 37.4
21 45 46.5
N.2] 54 3.3.0
-I- 40. 06
39.33
38. .59
37.84
34.72
33.91
33.09
24.28
23.,')4
22.40
+ 21. 45
JUNE.
5 .34. 00
10.311
5 4 41.64
10. 324
5 17 6.22
10. 3.57
5 2{» 32. 87
10.382
5 .33 42.11
10.388
6 15 17.60
10.888
6 19 26. 86
10.382
6 23 35.96
10. 375
N. 22 45 9. 9
22 50 49. 3
23 5 23.0
23 16 17. 4
23 19 6. 4
23 24 33. 2
23 22 49. 7
N. 23 20 41. 6
+ 14.64
13. 64
10.62
7. .55
+ 6. .52
-3.78
4.81
-.5.84
3 42. 68
3 45. 59
3 47. 91
3 49. 64
3 50. 68
3 49. 47
3 47. 68
3 0.46
2 .53. 08
2 45. 26
2 37.03
To he added to
'nhtrnrtfd/rmn
Mfiut Timt'.
1 28.85
1 17.77
42. 86
.5.89
6.80
2 16. 70
2 29.40
2 41.95
0.134
0.109
0.084
0.060
0.039
0.062
0.086
0.297
0.315
0.334
0.351
0.485
0. 467
0,.50O
0. .525
0.532
0.532
0. 526
0.519
Note.— The Semidiamt'ter.<iir Mean Noon may be assumed the .same as that for Apparent Noon.
+ prefixed to the hourly change of declination indicates that north declinations are
increasing and south declinations are decrea.sing; — indicates that north declinations are
decreasing and south declinations increasing.
3 7
3 11
3 15
3 19
3 35
42.69
39.24
35.80
32. 35
18.58
15.14
11.69
37. 27
33. 83
30.38
26.94
5 2 2.85
5 5 59. 41
5 17 49.08
5 29 38. 76
5 33 35. 31
6 13 0.90
6 16 57.46
6 20 54. 01
Diff. for 1 hour.
+ 9'.8566.
166
EXTRACTS FROM NAUTICAL ALMANAC.
[Extracts: Page 11.]
AT GREENWICH MEAN NOON— Continued.
Day of
the
Week.
Day of
the
Month.
THE SUN'S
Etjuation of
Time, io be
liiibtracted from
Jfean Time.
Diff. for
1 hour.
.Sidereal Time
or Ri^ht As-
cension of
Mean Sun.
Apparent
Right Ascension.
Dift. for
1 hour.
Apparent
Declination.
Dlff. for
1 hour.
fi. VI. a.
s.
Of n
It
vt. ^.
s.
h. 111. s.
AUGUST.
Tues.
Wed.
5
6
9 27.45
9 4 17. 82
9.610
9.586
]Sr. 17 1 29. 2
N. 16 45 8. 6
-40.52
-41.20
5 47.69
5 41.51
0.246
0.270
8 .54 39. 76
8 ,58 36.31
SEPTEMBER.
To be added to
Mean Time.
Wed.
Thur.
10
11
11 13 34. 39
11 17 10. 19
8.995
8.990
N. 4 59 21.3 '■ -S6-91
N. 4 36 32.9 , --^7.12
3 1.33
3 22.07
0.862
0.867
11 16 3,5.72
11 20 32. 26
OCTOBER.
Wed.
Thur.
Frid.
Tues.
Wed.
15
16
17
28
29
13 20 28. 07
13 24 11. 75
13 27 56. 01
14 9 44.78
14 13 37.03
9.309
9.333
9.S.i7
9.662
9.693
S. 8 29 16. 2
8 51 28. 1
9 13 32. 4
13 6 2.6
S. 13 26 4. 6
— .55. 65
.5.5.34
.5,5.02
.50.34
-49.82
14 7. 02
14 19.89
14 32. 18
16 ,5.51
16 9.82
0.548
0..524
0.-500
0.195
0.164
13 34 35. 08
13 38 .31.64
13 42 28. 19
14 25 50. 29
14 29 46. 84
JiOVEMBER.
Wed.
Thur.
12
13
15 9 14. 01
15 13 18.76
10. 180
10.216
S.17 41 18.4 -W-77
S.17 57 27.6 -■•»■'»
15 44. 60
15 36. 41
0.323
0.:i59
15 24 ,58. 61
15 28 55. 17
DECEMBER.
Wed.
Thur.
Mon.
Tues.
Wed.
Thur.
Mon.
Tues.
Wed.
3
4
8
9
10
11
22
23
24
16 37 40. 65
16 42 1. 22
16 .59 29.19
17 3.52.48
17 8 16.23
17 12 40.41
18 1 24.34
18 5 50.85
18 10 17. 33
'10.844
10.869
10.960
10.979
10.998
11.015
11.101
11.103
11.101
S. 22 6 24. 6
22 14 43.
22 43 35. 6
22 49 42. 3
22 .55 21. 9
23 34. 3
23 27 17.3
23 26 54. 3
S. 23 26 2. 9
-21.30
20.23
15.83
11.7;
13. .58
- 12.4.5
+ 0.37
1.55
+ 2.73
10 5.66
9 41.65
7 59. 91
7 33. 18
7 .5.99
6 .38. 37
1 16. .58
46. 63
16. 71
0.987
1.013
1.104
1.123
1.142
1.159
1.248
1.246
1.244
16 47 46. 31
16 51 42.87
17 7 29. 10
17 11 25.66
17 15 22. 22
17 19 18.78
18 2 40.92
18 6 37.48
18 10 34.03
NOTK.-
-The Se
+ prefl
incre
dec re
midiameter for Me
.xed to the hourly
astng and south de
asing and south de
m Noon m
change c
jlinations i
clinations
ay be assumed the same as tht
f declination indicates that
ire decreasing; — indicates th«
ncreasing.
it for .\pparcnt
north declinat
t north declina
S'oon.
ions are
ions are
Did. for 1 hour.
+ 9 •.8.56.5
EXTRACTS FROM NAUTICAL ALMANAC.
167
[Extracts: Page III.]
AT GREENWICH MEAN NOON.
Day of
the
Month.
Day of
the
Year.
THE SUN'S
Ix)garithm of
the Radius
Vector of the
Earth.
Difl. for
1 hour.
Mean time of
Sidereal O'.
True LONGITUDR
Diff. (or
1 hoxir.
I.ATITl-DE.
k
\'
o / ff
1 ff
ff
//
A. VI. 8.
APRIL.
21
22
Ill
112
,30 60 16. 5
31 58 46. 1
59 47. 4
58 16.9
146.27
146.19
+0.52
+0.52
0.0023923
0. 0025087
+48.8
+48.3
21 59 38. 53
21 55 42.62
[Extracts; Page IV.]
GREENWICH MEAN TIME.
c
THE .M<K>N's
SE.M1DIAMF.TER.
HOBIZOXTAI. PARAl.I.A.X.
MERIDUX PA.SSAdK.
AliK.
Noon.
Noon.
Midnight.
Noon.
Diff. for
1 hour.
Midnight.
Diff. for
1 hour.
Did. for
: 1 hour.
1
/ ff
/ ff
' f/
//
f ft
//
h. m.
m.
d.
APRIL.
16
15 4.7
15 0.6
.55 13.6
-l.M
54 58.5
-1.19
21 3.8
1.71
24.6
17
14 57.
14 53. 8
54 45.1
l.M
.54 33. 5
0.90
21 44.3
1.67
25. 6
18
14 51. 1
14 48. 9
54 23. 5
0.76
54 15.2
0.63
22 24. 6
1.68
26.6
19
14 47.0
14 45. 6
54 8.4
0.50
.54 3.1
0..S8
23 5.4
1.73
27.6
20
14 44. 5
14 43. 7
53 59. 1
0.27
53 56. 5
-0.16
23 47. 7
1.81
28.6
21
14 43.4
14 43. 4
53 55. 3
-o.a5
53 55. 3
+0.06
6
39.6
22
14 43. 8
14 44. 6
53 36. 7
+0.17
53 59. 4
0.29
32.2
1.90
0.9
23
14 45. 7
14 47. 2
54 3.6
0.41
.54 9.3
O..^
1 19.0
2.01
1.9
24
14 49. 2
14 51.6
.54 16.5
0.67
54 25. 3
0.80
2 8.2
2.10
2.9
25
14 54. 5
14 57. 8
54 S5. 8
0.94
54 48.
1.09
2 59.3
2.15
3.9
26
15 1.6
15 5.9
55 2.1
+1.24
55 17.9
+ 1.39
3 51.2
2.16
4.9
MAY.
6
16 44.6
16 42. 1
61 20.1
-0.53
61 11.3
-0.93
12 36.6
2.66
14.9
('
16 .38. 5
• 16 33. 7
60 57. 8
-1.29
60 40.2
-1.62
1.3 41. 2
2.09
1.5.9
28
15 47.0
15 53. 2
57 48. 8
+1.86
.58 11.4
+ 1.90
5 55.3
1.95
7.3
29
15 59. 4
16 5.6
58 34. 3
+1.90
58 57. 1
+1.88
6 42. 5
1.98
8.3
JUNE.
25
15 49. 8
15 54. 3
57 59. 1
1.37
58 15. 5
1.36
4 40. 1
1.94
5.7
26
15 58. 7
16 3.0
.58 31. 7
1.S4
.58 47. 6
1.30
5 27.0
1.98
6.7
27
16 7.2
16 n.i
59 3.0
1.23
.59 17.5
1.17
6 1.5.6
2.08
7. 7
168
EXTRACTS FROM NAUTICAL ALMANAC.
[Extracts: Pages V-XII.]
GREENWICH MEAN TIME.
THE moon's right ASCENSION AND DECLINATION.
Hour.
Right Ascension.' j^^\"^
Declination.
Diff.
for 1 m.
Honr.
Right Ascension. {^'^^
Declination.
Diff.
for 1 ra.
h. m. s. '' 8.
o , „
H
, li. m. «. ! s.
O f ft
II
THUESDAY, APRIL 10.
WEDNESDAY, MAY 28.
17
18
19
17 18 38.57
17 21 17. 16
17 23 55. 54
2,6448
2.6414
2.6379
S. 26 19 38. 3
26 19 41. 1
S. 26 19 33.0
- 0.138
+ 0.M4
+ 0.225
6
7
8
10 19 4. 23
10 21 7. 78
10 23 11. 34
2.0591
2. 0592
2. or.w
N. 7 4 18.5
6 49 52. 4
X. (J 35 23. 4
-11.411
14. 4.59
-14.507
WEDNESDAY, APRIL 16.
THURSDAY, .TUNE 26.
4
5
6
22 12 47. 08
22 14 39. 29
22 16 31. 30
1.8718
1.8685
1.86.53
8. 8 12 37. 4
7 59 36. 1
S. 7 46 33. 5
+13.010
13.032
+13.054
2
3
11
11 37 41.96
11 39 46.49
11 56 28. 42
2.0743
2. 0767
2.0889
S. 2 35 36. 4
2 50 44. 4
S. 4 51 36. 5
-1.5.135
1.5. 133
-15.069
FRIDAY, APRIL 25.
MONDAY, DECEMBER 8.
16
17
18
5 41 .33. 19
5 43 48. 55
5 46 3. 93
2.2.558
2.2562
2.2666
N. 26 5 43. 8
26 4 23. 5
N. 26 2 55. 2
- 1.272
1.405
- I..537
2
3
4
12 23 13. 52
12 25 23. 37
12 27 3.3.54
2.1615
2. 1668
2.1722
S. 8 9 24. 4
8 23 44. 9
S. 8 38 3. 8
14.354
14.328
34.302
TUESDAY, APRIL 29.
n
12
13
i
9 2 56.23 2.1384
9 5 4.49 2.1369
9 7 12.66 2.1356
N. 15 27 3. 6
15 14 52. 7
N. 15 2 36. 3
-12. 135
12.227
-12.318
EXTBACTS FROM NAUTICAL ALMANAC.
[Extracts: Pages relating to Planets.]
GREENWICH MEAN TIME.
169
JTJPIXKR.
April.
15
16
17
18
Apparent
Right
Ascension.
Noon.
Var. of
R. A.
fori
Hour.
Noon,
22 25 51.70
22 26 35.54
22 27 19.02
22 28 2.14
-Apparent
Declination.
8.
+1.S
1.819J
1.8041
+1.789
Var. of
Dec.
fori
Hour.
Noon.
-10 44 29.6
10 40 28.0
10 36 28.1
—10 32 30.0:
Meridian
+10.10 20 50.0
10.03' 20 46.8
9-961 20 43.6
+9.89! 20 40.3
VENXJS.
April.
Apparent
Right
Ascension.
Var. of
R. A.
fori
Hour.
Noon.
Noon.
h. m. 9. 8.
4 19 14.43 + 12.686
4 24 19.28 12.718
4 29 24.88+12-718
.\pparent
Declination.
Noon.
+22 40 33.2
22 55 4.9
+23 8 59.5
Var. of
Dec.
fori
Hour.
Noon.
Meridian
Passage.
A. ffi.
+37.08 210.7
35.-55, 2 11.9
+34.00: 2 13.0
Day of the Month.
Polar Semidiameter
Horizontal Parallax
1st.
16.4
1.5
11th.
16.7
1.6
17.1
1.6
Day of the month.
17.5
1.6
Semidiameter
Hor. Parallax
6th.
6.0
6.2
6.1
6.3
11th.
6.2
6.4
26th.
6.4
6.7
6.6
6.8
September.
>IA.RS.
16
17
Apparent
Ascension.
Var. of
R. A. Apparent
for 1 Declination.
Hour.
A. m. ».
22 32 5.11
22 31 .38.03!
Noon.
Niton.
-1.134
-1.120
-10 44 20.5
-10 46 57.2
Var. of
Dec.
for 1
Hour.
-6.58
-6.47
March.
Meridian
h. m.
10 49.8
10 4.5.5
Day of Month.
1st.
Polar Semidiameter
Horizontal Parallax
23.6
2.2
11th.
23.5
2.2
23.2
2.2
Apparent
Right
Ascension.
Noon.
fi. m. f
20 5 56.83
20 9 1.27
2012 5.45
Var. of
R.A.
fori
Hour.
Noon.
+7.1
7.680
+7.669
Apparent
Declination.
-21 13 58.1
21 5 40.4
-20 57 10.7
Var. of
Dec.
fori
Hour.
Noon.
+20.48
20.98
+21.48
Meridian
Passage.
A. ffl
20 26.4
20 25.6
20 24.
22.8
2.2
Note.— North declinations are marked +, south declinations — .
+ prefixed to the hourly change of declination, indicates that north declinations are increasing and south
declinations are decreasing; — indicates that north declinations ar^ decreasing and south declinations
increasing.
170
EXTRACTS t'ROM NAUTICAL ALMANAC.
[Extracts: Pact's relating to Fixed Stars.]
iniXBD ST.A.RS.
MEAN PLACES FOR 1879.0. (Jan. 0+''.016, AVashingtox. )
star's Name.
Magni-
tude.
Itiglit Ascension. An. Variation
Declination.
.\n. Varia-
tion.
a Ursse Min. (Polaris) * 2
a Eridani (Achemar) | 1
(rTauri (Aldebaran) | 1
/I Geniinorum '• 3
a Canis Maj. (Sirius) 1
a Virginia (Spica) 1
a Bootis (Arcturua) 1
a Scorpii {Aniares) 1.'.
1 14 24.861
1 .33 12.133
4 28 58.716
6 15 38.457
6 39 48.935
13 18 49.216
14 10 8.551
16 21 59.432
+21.485
+ 2.233
+ 3.437
3.633
2.645
3.154
2.735
3.670
+
+
+
+
+88 39 49.92
-57 51 5.79
+16 15 53.35
+22 34 26.94
-16 33 4.30
—10 31 44.21
+19 48 48.59
-26 9 41.94
+ 19.00
+18.40
-r 7.59
— 1.48
— 4.68
-18.90
-18.87
— 8.34
* Cireunipolar Star.
APPARENT PLACES FOR THE UPPER TRANSIT AT WASHINGTON.
a Ursse Minoris. ^Polaris.)
a Eridani. ^^Adtcn
(I?-.)
aTauri. {Aldebaran.)
Mean Solar
Date.
Right
Ascension.
Declination
North.
Mean Solar
Date.
Right
Ascension.
Declination
South.
Mean Solar Right
Date. Ascension.
Declination
North.
June 10.8
11.8
12.8
?l. VI.
1 13
63.54
64.35
65.21
o /
+88 39
ff
47.1
47.0
46.9
July 27. 7
Aug. 6.7
A. m.
1 33
14.91 +•«
16.37 +•''5
O f
-57 50
28.6 +0.6
28.3 0.0
Apr. 9.1
19.1
29.1
h. m.
4 28
59.66 -10
59.57 -07
59.52 --02
O f
+16 15
58.7 -0.2
.58.6 -0.1
58.5 0.0
a Canis Majoris. (Sirim.)
aVirginis. (Spicn.)
a Bootis. {Arclurug.)
Mean Solar
Date.
Kiglit
Ascension.
Declination
South.
Mean Solar
Date.
Right
Ascension.
Declination
South.
Mean Solar
Date.
Right Declination
Ascension, North.
(Dec. 30.5)
Jan. 9.5
Apr. 9.2
19.2
29.2
May 9.2
h. m.
6 39
51.06 +-10
51.14 +05
50.09 -18
49.92 16
49.77 -13
49.65 -10
O 1
-16 32
ri
63.7 -2.5
66.1 -2.3
76.2 +0.3
75.8 0.6
75.0 0.9
74.0 +1-1
Apr. 29.5
May 9.4
19.4
29.4
June 8.3
ft. m.
13 18
52128 +-02
52.29 00
52.28 --ttJ
52.24 .04
52.19 -60
o /
-10 31
64.6 -0.1
64.7 0.0
64.6 +0.1
64.4 0.3
64.1 +0.4
May 9.4
19.4
h. in.
14 10
s. "
11.71 +02
11.71 -01
O /
+19 48
"
32.1 +1.6
33.7 +1-6
1
a Scorpii. (Antaret.)
Mean Solar
Date.
Right
Ascension.
Declination
South.
May 9.5
19.5
29.5
June 8.5
18.4
July 28.3
Aug. 7.3
17.3
h. m.
16 21
■63.11 +19
63.28 16
63.43 12
63.53 -09
63.60 +05
63.49 -10
63.. 38 -13
63.24 -15
O 1
-26 9
n
53.8 -0.5
54.3 0.4
54.7 0.4
55.0 0.3
55.3 -0.3
56.0 0.0
55.9 +0.1
55.8 +0.2
FORMS FOR WORK.
171
APPENDIX II.
A COLLECTION OF FORMS FOR WORKING DEAD RECKONING AND VARI-
OUS ASTRONOMICAL SIGHTS, WITH NOTES EXPLAINING THEIR
APPLICATION UNDER ALL CIRCUMSTANCES.
(The figures in parenthesis refer to the Notes following these forms.)
FOBX FOB DAY'S WUBK, DEAD KECKOMXU.
Time.
Compass Courae.
Var.
Dev.
Lee-
way.
Total
error.
Tnie Course.
Patent
log.
Dist.
N.
S.
E.
W.
Diff.(>)
Long.
Longitude.
Left at departure (or noon)
Run to
ByD.R.at
.Run to
nS. or.S,
.V. or S.
N". or S.
N. or S.
(') E. or \V.
E. or W.
E. or W.
E. or W.
ByD.R.at S. or S. E. or W.
FORM FOR TI.1IG SKiHT OF SUA'S LOWER UXR (SINNER LINE).
W. T.
C-\V
Chro.
C.C.
(") G. M.
(') K(|. t.
G. A. T.
Obs. alt. Q, .
Corr. zh .
(») S. D.
(<) I. C.
(lip
p. & r.
+ .
+ -
o I rt
p)Dec -V.orS.
('■) I
H.It. --.
"
(l.M.T. .
h.
„
Dec
o
S'
/ rf
(°) Eq. t.
H. D.
G. M. T.
Corr.
Eq. t.
Corr. ± .
h
L,
V
sec
eosec
(')L.,
sec
eosec
/(. m.
G..\.T
L..\.T.,
ib. m. c.
6- •••,•■•»• E.orW.
cos
sin
sin i fi
2).
S-y-h
/i. in, s.
G..\.T
L.A.r..
Ih. 111. 8.
i /■">,■ E.orW.
cos
sin
sin i U
2).
172 FORMS FOR WORK.
FORM FOK TIME SKiHT OF A STAR (KUMNER LINE).
h. m. e. ° ' " h. m. s.
Obs. alt. >J: E. A
\V. T.
C-W
Chro.
. t
C. C.
;") G.M.
T.
R. A.
M.S.
Red.
(Tab. 9)
G.S.
T.
R. A.
*
Corr.
o / ft
Dec. N. or S.
(<)I-C. + Wi)
+ .
+ .
dip
ref.
{«) H. A. JromGr E. orW.
Corr.
P
A.
2).,
cosec
—
9i-h
Gr H
h.
m.
J.
2)
. E.orW.
<«) H. A.,
. E. or W. sin J (j
h.
m.
s.
(") Long.i
o
'
11
■[E.orW.
(6) Li sec
cosec
('») s, cos
S'l-h sin
Gr. H. A
H. A.o sin Ms
Long.o
W.T.
C-W
h, m. «.
+
Obs. alt. *
Corr. ±
Chro. t.
C. C.
A
(")G. M.T.
R. A. M. S. +
Red. (Tab.9) +
(IS) par. +
(<) I. C. +
G. S. T.
R. A.*
FORM FOR TIME SKJHT OF A I'LANET (SIM.NER I.INE).
" h. M. .'.
R.A. Dec.
dip
(«)H.A.fromGr E.orW. ref.
H. D. ± H. D.
h.
G. M. T. .- G. M. T.
Corr. i Corr.
R.A.
mp
For the remainder of the work, by which the hour angles and thence the longitudes are found, employ the method
given under " Form for Time Sight of a Star (Sumner Line)."
•
h. VI. s.
W. T.
C-W
+
Chro. t.
C. C.
±
(")G. M. T.
R. A. M. S.
+
Red. (Tab.9) +
G. 8. T.
R. A. (J
F0KM8 FOE WORK. 173
FORM FOR TIME KlUHT OF Hoax's LOWER LIMB (SUMNER LINE).
° ' " /i. m. s. oil,
Oba.alt.^ (i')R.A. (") Dec. N.orS.
(i»)S. D. + M. D. + M. D.
Aug. +
(*)I. C. + Xo. min. ± No. min. ±
dip
M. D.
+
7».
Xo. min.
i
«.
Corr.
±
h. m. s.
R. A.
Corr.
Dec.
<'2|H.A.(romGr E.orW. 1st corr. ± (8)p
O / II
Approx. alt
p.<t-r.(Tab.'24) +
For the remainder of the work, by which the hour angles and thence the longitudes are found, employ tlie method
given under " Form for Time Sight of a Star (Sumner Line)."
FORM FOR MGKIDIAX ALTITl'DK OF SIIX'S LOWER LIMB.
o I II II, ail,
C')S. D. + (»)Dec X.orS.
(♦)I.C. +
/,
mi
d
O 1
' rr
X.orS.
X.orS.
Lat.
X.orS.
dip
p.d:r.
H.D. i
h.
Long. ±
Ctorr.
Obs.
Corr.
alt.
*
h
■)5
d
X.orS.
X.orS.
Lat.
X.orS.
' " Dec X.orS.
Corr. ±
FORM FOR MERIDIAN ALTITUDE OF A STAR.
I If O t 11
C')I-C. + Dec N.orS.
dip ~
ref. -
(-orr. ±
FORM FOR MERIDIAN ALTITUDE OF A PLANET.
oil.
" li. m. ° ' "
Obs.alt. :+: (i5) pur. + G. M. T., Gr. trans Dec X.orS.
Corr. .-t (<)I.C. + Corr. for Long. + ^-,^_
('')z N.orS. dip- G. M. T., local trans.
rf N.orS. ri'f. -
L. M. T., local trans H. D. +
Long. ± /,.
G.M.T
Lat. N.orS.
Cor. ±.
Ootr. ± .
Dec N.orB.
174
FORMS FOR WOR"K.
FORM FOB MGRIDUK ALTITUDE «F MOOS'S LOWER LIMB.
o r It o I It /,_ .j,j_
Obs.alt. ^ G. M. T., Gr. trans. (':) Dec.
•^-^— — — Corr.forLong.(Tab.U)±
N.orS.
. N.orS. (16)S.D.
. N.orS. Aug.
(«)I.C.
Lat N.orS.
+ L. M. T., local trans.
+ Long.
+
— ; G. M. T., local trans.
+
M. D. ± .
No. rain. ± .
Corr.
dip
Dee.
. N.orS.
Approx. Alt.
p. <tr. (Tab.24) + .
ALTER.NATITE FORM FOR MERIDIAN ALTITUDE OF A BOOT. (»)
90° 00' 00" Rulefjor signs.
I«) Dec. ± .
Corr. ± .
Constant :
Obs. alt. :
Case I. Lat. & Dec. same name, Lat. greater + 90° + Dec. — Corr. — Alt-
Case II. Lat. & Dec. same name, Dec. greater -90° + Dec. + Corr. + Alt.
Case III. Lat. and Dec. opposite names + 90° — Dec. — Corr. — Alt.
Case IV. Lower transit + 90° — Dec. + Ohrr. + Alt.
Lat.
li. m. s.
.... N.orS.
FORM FOR LATITUDE SIGHTS OF SUN'S LOWER LIMB (SUMNER LINE).
oil! O f If
W. T.
C-W ±
Chro. t.
C.C. ±
Obs. alt. Q .
Corr. ± .
<")6.M.T.
(') Eq-t-
G.A.T.
Long. 1 ±
L.A.T.,
(«)<i
(«) Long. 2
L.A.T..
h. m.
VI
h. m. s.
(3) S.D.
(4) LC.
dip
p. & r.
Corr.
(») Dec.
H.D.
G.M.T.
Corr.
Dec.
N. or S.
(") Eq. t.
. N. or 1
H.D. ^ .
*
G.M.T.
h.
s.
Ea.t.
m.
A
d
h
(")9>l" •
<P\'
Lat.,
92
Lat.,
*' *" Method.
sec.,
tan .
. N. or S.
. N. ar S.
. N. or S.
sec.
tan .
sin.
sin.
sin.
sin.
. N. or S.
h
( -'■■ ) a ( , '-
(■") '1
d
Jiedudion to Meridian.
Lat.] N.orS.
a(,2
Hj
N.orS.
t-i
N.orS.
d
N.orS.
Lat.s
. N. or 8.
FORMS FOR WORK 17[
* FORM FOR LATITUDE SICHTS OF A STAR (SUMXER LINE).
h. m. s. ° ' " !i- »'• s-
W. T. Obs.alt.* R. A.
C-\v +
Chro.t. A Deo. N. op S.
O.C. ' ±
(11) G. M. T.
R. A. M. S. + .
Red.(Tab.9) + .
G. S. T.
R. A.*
(12) H.A.fromGr E. or W.
(») Long., E.orW.
(h. m. fA
i;>"';";,'\E.orvf.
Obs.alt.*
A
I.e.
+
dip
ref.
, „
Corr.
/ //
±
h. in. f.
(«) Long.s
For the remaiiwier of the work, by which the latitudes are found from either the <p' «p" formula or the reduction to the
meridian, employ the methods given under " Form for I.Atitude Sights of Sun's Ix)weT Limb (Sumner Line)."
FOB)! FOR LATITl'DE MGHTS OF A PLACET (SIIMXER LIKE).
o / " ;, „, p^ o I II
W.T. Obs.alt. :»: K. A. Dee. N. or S.
C-W
Chro.t. h H. n. ± H. D.
C. C.
Obs.i
Corr.
«lt.
*
4-
K. A.
h
H. n.
par.
T r
+
/ //
G. if. T,
+
/ //
R. A.
G. .M. T.
(ii)G. M. T.
R. A. M. S. +
Red.{Tab.9) + Corr. ± Corr.
G. S. T. , „ h. m. s.
RA.* .^^^^^^^^^ _ R.A Dec X.orS.
(«) H.A.fromGr E.orW. ref.
(")Long.i E.orW.
f ft. m. n.
Corr.
E. or W.
h.
m.
e.
h.
m.
8.
O / "
(») I»ng.;
For the remainder of the work, by which the latitudes are found from either the ip' <p" formula or the reduction to the
meridian, employ the methods given under " Forms for Latitude Sights of Sun's Lower Limb (Sumner Linfe)."
176
FORMS E'OE WORK.
FORM F<>B LATITUDK SIOHTS OF MOOS'S LOWEB LIMB (Sl!HNKB LIXE)
W.T.
C-W
Chro. t
C. C.
(ii)<J-M-T.
K. A. M. S. +.
Ucil.(Tab.9) +.
(i. S. T.
R. A.£
('=) H. A. from Gr E.wW.
(«')Long., E.oiW.
h. m. 8.
Long..
}E.or\V.
fi. ni. J*.
E.orW
{ h. m. g.
Obs.alt.(£
(«) 8. D.
Aug.
dip
1st Corr.
Approx. alt
p. ii r. (Tab. 24) +
_^^
f tf
+
+
+
—
' '/
±.
o
' //
+.
^^
O 1
' //
(1') R. A,
M. D.
+
Xo. mill.
+
Corr.
8.
4:
R. A.
A. in. s.
('-) Dec
^
mt^^
n
w
D.
±..
m.
So
.min
- ±.
1 tf
Corr.
_^
N.orS.
Dec.
.N.orS.
For the remainder of the work, by which the latitudes are found from eitlier the <p' <p" formula or the reduction to the
meridian, employ the methods given under " Forms for Latitude Sights of Sun's Lower Limb (Sumner Line)."
FORM FOB VHKO.VOillETEK COKBECTIOX BY EQUAL ALTITUDES «F SUX.
h. v\. ii. h. m. s. o I tl tl
W. T., A. M.
C-W
+
A. M. Chro. t.
P. M. Chro. t.
+
2)
Mid. Cliro. t.
Efj. eq. alt.
_4:.
Chro. t. L. A.
noon
('1 fA- 1.
}
Chro, t. L. Sr.
noon
(=5) Long.
1.
J
(*>) Chro. error on
G. M. T.
}-
W. T., p. M
.... (=»)Dec.
. N.
. X.
Of
Of
■s.
■s.
H. D. (prev.) ^
noon \ )
C-W +
+
II
A.
P.M.Chro.t
A.M.Chro.t.-
H. D. at
merid.
noon) J
Long.
Corr.
Dee.
' "
DifT. P' d=.
' "
DifT. for long. ±
(a«)Eq. t.
H. D.
Ix)ng.
Corr.
Kq. t.
H. D. at merid. ±
('i)Tab.37 logA(±).... logB( + ).
It
H. D. i log ( + ).... log (±).
o / o /
L ± tan (±) d i tan (±).
log (±)~.
1st pt. ± .
2dpt. ±.
Kq.eq.K
alt. /-■
log (±).
FORM FOB FISDIXO THE TIME OF HI«H (OB LOWi WATEB.
d. h. m.
G. M. T. of Greenwich transit
(32) Corr. for Long. (Tab. 11) ±
L. M. T. of local transit
Lunitidal int. ( App. IV) +
L. M. T. of high (or low) water
FORMS FOR WORK. 177
NOTES REIiATIXG TO THE FOBXS.
1. It is not necessary to convert departure into difference of longitude for each course, it will suflRce to make one
conversion for the snm of all the departures used in bringing forward the position to any particular time.
2. In D. R. it will be found convenient to work Lat. and Long, in minutes and tenths, rather than in minut«s and
seconds.
3. If upper limb is observed, the correction for S. D. should be negative, instead of positive.
4. A positive I. C. has been assumed for illustration throughout the forms; if negative, it should be included with the
tninu!^ terms of the correction.
5. For time sights and (p' <p" sights, take Dec. and Eq. t. from Naut. Aim., p. II (G. M. noon).
6. To obtain p. subtract Dec. from 90° if of same name as Lat.; add to 90° if of opposite name.
7. Sign of Eq. t. that of application to mean time.
8. If G. A. T. is later than L. A. T., Long, is west; otherwise it Ls east.
9. If Lat. is exactly known, a second latitude need not be employed.
10. «2 a.nd 8-2— h may be obtained by applying half the difference between Lj and L., with proper sign, tosi andsj— A,
respectively.
11. The G. M. T. must represent the proper number of hours from noon, the beginning of the astronomical day; to obtain
this it may be necessary to add 12*' to the Chro. t.
12. H. A. from Greenwich is the difference between G. S.T. and R. A., and should be marked W. if the former is greater;
otherwise, E.
13. Local H. A. is marked E. or W.. according as the body is east or west of the meridian at time of observation.
M. Subtract local hour angle from Greenwich hour angle to obtain longitude; that is, change name of local hour angle
and combine algebraically.
15. The forms include a correction for the parallax of a planet, but in most cases this is small, and may be omitted. When
used, take hor, par. from Xaut. Aim. and reduce to observed altitude by Table 17. The semidiameter of a planet may bie
disregarded in sextant W(^irk if the center of the body is brought to the horizon line.
1*>. If upper limb is observed, the corrections for S. D. and Aug. should be negative, instead of positive.
17. R. A. and Dec. are to be picked out of Naut. Aim. for nearest hour of G. M. T., and to be corrected for the inmiber
of minutes and tenths.
IS. Mark zenith distance N. or S. according as zenith is north or south of the body observe<l; mark Dec. according to its
name, subtracting it from IHO*^ for cases of lower transit; then, in combining the two for Lat., have regard to their names.
19. For meridian altitudes, take Dec. from Naut. Aim., p. I (G. A. noon).
20. This form enable" "Oonstant" to be worked up before sight is taken, and gives latitude directly on completion of
meridian observation. Ixingitude and altitude at transit must be known in advance with sufficient accuracy for correcting
terms.
21. The details of obtaining Dec. at transit and correction for altitude are shown in the meridian altitude forms for each
of the various bodies.
22. In an a. m. sight subtract L. A. T. from 24'> to obtain (; in a p. m. sight L. A. T. is equal to (.
23. If L<>ng. is exactly known, a second longitude need not be employed.
24 Mark 9" N. or S. according to name of Dec., and subtract it from 180° when body la nearer to lower than to upper
transit; mark?)' N. or S. according as zenith is north or south of the body; then combine for Lat. having regard to the names.
25. Take a from Table 2t; and at- from Table 27.
26. Add for upper, subtract for lower transits.
27. Subtract longitude from Greenwich hour angle to obtain local hour angle; that is, change name of longitude and
combine algebraically.
28. For equal altitude sights, take Dec. and Eq. t. from Naut. Aim., p. I (G. A. noon).
29. Add longitude if east; sublract if west. " ,
30. If error is +, the chronometer is fast, and the correction is subtractive; and the reverse.
31. Mark log A and log B as indicated in Table 37; mark N. Lat., N. Dec, and H. D. toward the north +, and the
reverse. If, in combining the three logarithms for the respective parts of the equations, one or three of them should be
tnimis. the sign of that part is minus; otherwise, plus.
32 Add for west, subtract for east longitude.
178
BULKS AND PEINCIPLES OF MATHEMATICS.
APPENDIX III.
EXPLANATION OF OEETAIN EULES AND PRINCIPLES OF MATHEMATICS
OF USE IN THE SOLUTION OF PROBLEMS IN NAVIGATION.
DECIMAL FRACTIONS.
Fractions, or Vulgar Fraction.^, are expressions for any a,ssignable part of a unit; they are usaually
denoted by two numbers, placed one above the other, with a line between them; thus i denotes the
fraction one-fourth, or one part out of four of some whole quantity, considered as divisible into four
equal parts. The lower number, 4, is called the denominator of the fraction, showing into how many
parts the whole is divided; and the upper number, 1, is called the numerator, and shows how many of
those equal parts are contained in the fraction. It is evident that if the numerator and denominator be
varied in the same ratio the value of the fraction will remain unaltered; thus, if both the numerator
and denominator of the fraction, \, be multiplied by 2, 3, 4, etc., the fractions arising will be f, -j^, f^,
etc., all of which are evidently equal to }.
A Decimal Fraction is a fraction whose denominator is always a unit with some number of ciphers
annexed and the numerator any number whatever; as, -^g, yf j, Tsiist etc. And as the denominator of
a decimal is always one of the numbers 10, 100, 1000, etc., the necessity for writing the denominator
may be avoided bv employing a point; thus, j^ is written .3, and yV% is written .14; the mixed number
3^>jjij, consisting of a whole number and a fractional one, is written 3. 14.
In setting down a decimal fraction the luimei-ator must consist of as many places as there are
ciphers in the denominator; and if it has not so many figures the defect must be supplied by placing
ciphers before it; thus, ^J'^ = .16, ji^f f = .016, t^Vjo = -0016, etc. And as ciphers on the right-hand side
of integers increase their value in a tenfold proportion, as 2, 20, 200, etc., so when set on the left hand
of decimal fractions they decrease their value in a tenfold proportion, as .2, .02, .002, etc.; but ciphers
set on the right hand of these fractions make no alteration in their value; thus, .2 is the .same as
.20 or .200.
The common arithmetical operations are performed the same way in decimals as they are in inte-
gers, regard being had only to the particular notation, to distinguish the integral from the fractional
part of a sum.
.\ddition op Db»im.\ls. — Addition of decimals is performed exactly like that of whole numbers,
])lacing the numbers of the same denomination under each other, in which case the separating decimal
points v,'ill range .straight in one column.
Ex.\MPLES.
Add:
Miles.
26.7
.32.15
143.206
.003
Feet.
1.26
2.31
1.785
2.0
7.355
Inches.
272.3267
.0134
2.1576
31.4
305.8977
Sum: 202.059
SuBTKACTiox OF Decim.\ls. — Subtraction of decimals is performed in the same manner as in whole
numbers, observing to set the figures of the same denomination and the separating points directly
under each other.
EX.\MPLES.
From:
Take:
.31.267
2.63
.36.75
.026
1.254
.316
1364.2
25.163
Difference:
28.637
.36.724
.938
1339.037
MrLTiPLic.VTioN OF DECIMALS. — Multiply the numbers together as if they were whole numbers,
and point off as many decimals from the right hand as there are decimals in both factors together; and
when it happens that there are not so many figures in the product as there must be decimals, then
prefix such number of ciphers to the left hand as will supply the defect.
Example I.
Multiply 3.25 by 4.5.
3.25
4.5
1.625
13.00
Answer: 14.625
In one of the factors is one decimal, and in the
other two; their sum, .3, is the number of decimals
of the product
Example II.
Multiply .17 by .06.
.17
.06
Answer:
.0102
In each of the factors are two decimals; the pro-
duct ought therefore to contain 4; and, there being
only three figures in the product, a cipher must be
prefixed.
RULES AND PRINCIPLES OF MATHEMATICS.
179
Example III.
Multiply 0.5 by 0.7
0.5
0.7
Answer:
0.35
E.XAMPLE
IV.
Multiply .18
by 24.
.18
24
72
36
Answer: 4. .32
Division op Dectmals.— Division of decimals is performed in the same manner as in whole num-
bers. The number of decimals in the quotient must be equal to the excess of the number of decimals
of the dividend above those of the divisor; when the divisor contains more decimals than the dividend,
ciphers must be affixed to the right hand of the latter to make the number equal or exceed that of the
divisor.
Example III.
Example I.
Divide 14.625 by 3.25.
3.25 ) 14.625 ( 4.5
1300
1625
1625
In thin example there are two decimals in the
divisor and three in the dividend; hence, there is
one decimal in the quotient.
Example II.
Divide 3.1 by .0062.
Previous to the division affix three ciphers to
the right hand of 3.1, to make the number of deci-
mals in the dividend equal the number in the
divisor.
.0062) 3.1000(500
310
000
Divide 17.256 by 1.16.
1.16 ) 17.25600 ( 14.875
116
565
464
1016
928
880
812
680
580
100
MULTIPLICATION OF DECIMALS BY CoNTKACTiox. — The Operation of multiplication of decimal fractions
may be very much abbreviated when it is not required to retain any figures beyond a certain order or
place; this will constantly occur in reducing the elements taken from the Nautical Almanac from Green-
wich noon to later or earlier instants of time.
In multiplying by this method, omit writing down that part of the operation which involves decimal
places below the required order, but inental note should be made of the product of the first discarded
figure by the multiplying figure, and the proper number of tens should be carried over to insure accuracy
in the lowest decimal place sought.
Example: Required the reduction for the sun's declination for 7''.43, the hourly difference being
58".18, where the product is required to the second decimal.
ordinary method.
58".18
7'. 43
By contraction
58".18
7\43
17454
23272
40726
1.74
23.27
407.26
432".2774
432. "27
In the contracted method, for the multiplier .03 it is not necessary to record the product of any
figures in the multiplicand below units; for the multiplier .4, none below tenths; but in eacli case
observe the product of the left-hand one of the rejected figures and carry forward the number of tens.
180
fiULE8 AND PRINCIPLES OF MATHEMATICS.
Reduction op Decimals. — To reduce a vulgar fraction to a decimal, add any number of ciphers to
the numerator a:;:! divide it by the denominator; tiie quotient will be the decimal fraction. The decimal
. point must be so placed tliat there may be as many figures to the right hand of it as there were added
ciphers to the numerator. If there are not so many figures in the quotient place ciphers to the left hand
to make up the number.
EXAMPLH 1.
Reduce ^5 to a decimal.
50)1.00
.02 Answer.
Example II.
Reduce f to a decimal.
8)3.000
.375 Answer.
Example III.
Reduce 3 inches to the decimal of a foot.
Since 12 inches = 1 foot this fraction is fV.
12)3.00
Example IV.
Reduce 15 minutes to the decimal of an hour.
Since 60'" = 1'', this fraction is Jg.
60)15.00
.25 Answer.
E.ka.mple V.
Reduce 17'" 22* to the decimal of an hour.
= 0"'.37
22'"
22» =
60
17".37
"'.37= =0".289 Answer.
60
.25 Answer.
Any decimal may be reduced to lower denominations of the same quantity by multiplying it by the
number representing the relation between the respective denominations.
Example VI: Reduce 7.231 days to "days, hours, minutes, and seconds.
0".231
21
924
462
5".544
0".544
60
32"'. 640
0'".640
60
38».400
Answer: 7'' 6'' 32"' 38'.4.
GEOMETRY.
Geometry is the science which treats of the description, properties, and relations of magnitudes, of
which there are three kinds; viz, a line, which has only length without either breadth or thickness; a
surface, comprehended by length and breadth; and a so'lkl, which has length, breadth, and thickness.
A paint, considered mathematically, has neither length, breadth, nor thickness; it denotes position
simply.
A line has length without breadth or thickness.
A surface has length and breadth without thickness.
A solid has length, breadth, and thickness.
A straight or right line is the shortest distance between two points on a plane surface.
K plane surface is one in which, any two points being taken, the straight line between them lies
wholly- within that surface.
Parallel lincK are such as are in the same plane and if extended indefinitely never meet.
A circle is a plane figure bounded by a curve line of which every point is
equally distant from a point within called the center. The bounding curve of
the circle is called the circumference.
The radius of a circle, or semi-diameter, is a right line drawn from the
center to the circumference, as AC (flg. 65) ; its length is that distance which
is taken between the points of the trompasses to describe the circle.
A diameter of a circle is a right line drawn through the center and termi-
nated at both ends by the circumference, as ACB, its length being twice that
of the radius. A diameter divides the circle and its circumference into two
equal parts.
An arc of a circle is any portion of the circumference, as DFE.
The chord of an arc is a"straight line joining the ends of the arc. It divides
the circle into two unequal parts, called segm.nti, and is a chord to them both;
thus, DE is the chord of the arcs DFE and DUE.
A semicircle, or half circle, is a figure contained between a diameter and the arc terminated by that
diameter, as AGB or AFB.
RULES AND PKINCIPLES OF MATHEMATICS. 181
Any part of a circle contained between two radii and an arc is called a sector, as GCH.
A ijuadrant is half a semicircle, or one-fourth part of a whole circle, as CAG.
Allcircles are supposed to have their circumferences divided into 360 equal parts, called degrees;
each degree is divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called
seconds; an arc is measured by the nuuxber of degrees, minutes, and seconds that it contains.
A .ijiltere is a solid bounded by a surface of which every point is equally distant from a point within
which, as in the circle, is called the center. Substituting »itrface for circumference, the definitions of the
radius and diameter, as given for the circle, apply for the sphere.
An finyle is the inclination of two intersecting lines, and is measured by the arc of a circle inter-
cepted between the two lines that form the angle, the center of the circle being the ix)int of intersection.
A right angle is one that is measured by a quadrant, or 90°. An acute angle is one which is less than
a right angle. An obtuse angle is one which is greater than a right angle.
A plane triangle is a figure contained by three straight lines in the same plane.
When the three sides are equal, the triangle is called equilateral; when two of them are equal, it is
called isosceles.. When one of the angles is 90°, the triangle is said to be right-angled. AVhen each angle
is less than 90°, it is said to be acute-angled. Wheu'one is greater than 90°, it is said to be obtuse-angled.
Triangles that are not right-angled are generally called oblique-angled.
A quadrilateral figure is one bounded by four sides. If the opposite sides are parallel, it is called a
parallelogram. A parallelogram having all its sides equal and its angles right angles is called a square.
When the angles are right angles and only the opposite sides equal, it is called a rectangle.
In a right-angled triangle the side opposite the right angle is called the hypotenuse, one of the other
sides is called the base, and the third sitie is called the perpendicular. In any oblique-angled triangle,
one side having been assumed as a l)ase, the distance from the intersection of the other two sides to the
base or the base extended, measured at right angles to the latter, is the perjjendicular. In a parallelo-
gram, one of the sides having been assumed as the base, the distance from its opposite side, measured
at right angles to its direction, is the perpendicular. The term altitude is sometimes substituted for
perpendicular in this sense.
I^Ivery section of a sphere made by a plane is a circle. A great circle of a sphere is a section of the
surface made by a plane which passes through its center. A synall circle is a section by a plane which
intersects the sphere without passing through the center.
A great circle may be drawn through any two points on the surface of a sphere, and the arc of that
circle lying between those points is shorter than any other distance between them that can be measured
upon the surface. All great circles of a sphere have equal radii, and all bisect each other.
The extremities of that diameter of the sphere which is perpendicular to the plane of a circle are
called the poles of that circle. In the case of a small circle the poles are named the adjacent pole and
the remote pole. All circles of a sphere that are parallel have the same poles. All points in the circum-
ference of a circle are equidistant from the poles. In the case of a great circle, the poles are 90° distant
from every point of the circle.
Assuming any great circle as a primary, all ^reat circles which pass through its poles are called its
secondaries. All secondaries cut the primary at right angles.
Useful Formul.e Derived from (jeometry.. — In these formulae the following abbreviations are
adopted :
>j, base of triangle or parallelogram. r, radius of sphere or circle.
/(, perpendicular of triangle or parallelogram. d, diameter of sphere or circle.
/, height of cylinder or cone. • A, major axis of ellipse.
*, ratio of diameter to circumference o, minor axis of ellipse.
(=3.141593). s, side of a cube.
Area of parallelogram = 6 X h.
Area of triangle = \bxh.
Area of any right-lined figure = sum of the areas of the triangles into which it is divided.
Sum of three angles of any triangle = 180°.
Circumference of circle = 2zr, or nd.
Area of circle = ?rc^, or —y--
Angle subtended by arc equal to radius = .57°.29578.
Volume of sphere = -^ -
Surface of sphere = nd^, or inr'.
Area of ellipse = -r—
Volume of cube = if.
Volume of cylinder = Area of base X I-
Volume of pyramid or cone = Area of base X ^-
182
RULES AND PEINCIPLES OF MATHEMATICS.
TBIGONOMETBIC FUNCTIONS.
The trigonometric function)! of the angle formed by any two hnea
are the ratios existing between the sides of a right triangle formed by
letting fall a perpendicular from any point in one line upon the
other line; no matter what point is chosen for the perj^endicular
nor which line, the ratios, and therefore the respective functions,
will be the same for any given angle.
Let ABC (fig. 66) be a plane right triangle in which C is the
right angle; A and 15, the other angles; c, the hypotenuse; a and
b the sides opposite the angles A and B, respectively. In considering
the functions of the angle A, its opposite side, ((, is regarded as the
perpendicular and adjacent side, b, as the base; for the angle B, b is
the perpendicular and a the base. Then the various ratios are
designated as follows:
a
c
b
a
v
b
a'
c
b'
c
a'
1-
1-
perpendicular . ,, , , , . ' , . , . .
hvnotennsp ' ^^ called the sine of angle A, abbreviated sin A;
'"^ hvno tenuse' ^ called the cosine of angle A, abbreviated cos A;
perpendicular .
base
is called the tangent of the angle A, abbreviated tan A;
;t^ — j— . is called the cotangent of the angle A, abbreviate<l cot A;
ypotenuse .
base ' '
hypotenuse
or - Pr > is called the seca7it of the angle A, abbreviated sec A;
or -.1------ - J called the cosecant of the angle A, abbreviated cosec A;
perpendicular
cosine A, is called the versed sine of A, abbreviated vers A.
sine A, is called the co-versed sine of A, abbreviated covers A.
The following relations may be seen to exist between the various functions:
1
sin A
1
cos A
1
tan A
a c-
; 1 H- - = - = cosec A;
c a '
= sec A;
-^- = - = cotA;
?!5_A=-^-^-?^ = ''=tanA.
cos A c c /<
Hence the cosecant is the reciprocal of the sine, the secant is the reciprocal of the cosine, the cotan-
gent is the reciprocal of the tangent, and the tangent equals the sine divided by the cosine.
The comph'ment of an angle is equal to 90° minus that angle, and thus in the triangle ABC the
angle B is the complement of A. The supplement is equal to 180° minus the angle.
From the triangle ABC, regarding the angle B, we have:
sin B = — = cos A;
tan B = — = cot A ;
sec B = - = cosec A.
BULKS AND PRINCIPLES OF MATHEMATICS.
183
/^ 2iqu.^i.
U qual. \,
p
I
^\?c
*** -/'^
t'
-J> ^^
\^^ *\
\
^^<^
"c^-^^^
/
)i
-a /
\i'
-
4th (^uaA. /
Fig. 67
Hence it may be seen that the sine of an an^le is the cosine of tlie complement of that angle; the
tangent of an angle is the cotangent of its complement,
and the secant of an angle is the cosecant of its com-
plement.
The functions of angles vary in sign according to
the quadrant in which the angles are located.
I^t AA' and BB' (fig. 67) be two lines at right
angles intersecting at the point O, and let that point
be tlie center about which a radius revolves from an
initial position OB, successively passing the points
A, B', A'. In considering the angle made bv this i
radius at any position, P', P", P'", P"", with the line /
OB, its position of origin, tlie functions will depend * f-
upon the ratios existing between the sides of a right
triangle whose base, b, will always lie within BB,'
and whose perpendicular, a, will always be parallel to
AA', while its hypotenuse, c (of a constant length
equal to that of the radius), will dejjend upon the
)X)sitioB occupied by the radius. Now, if OB and 0.\
be regarded as the positive directions of the base and
perpendicular, respectively, and OB' and OA' as their
negative directions, the sign of the hypotenuse being
always positive, the sign of any function may be deter-
mined by the signs of the sides of the triangle upon
which it"dei)ends.
For example, the sine of the angle P"OB is -, and since a is positive the quantity has a positive
value; its cosine is -, and as b is mea.sured in a negative direction from O the cosine must therefore be
negative.
In the first quadrant, between 0° and SK)°, all quantities Ix'ing positive, all functions will also he
positive.
In the second quadrant, between (H)° and 180°, sin .V f =^ J is positive; cos A (=- J has a nega-
ative value because b is negative; tan A { =t j is also negative because of b. The cosecant, secant, and
cotangent have, as in all cases, the same sighs as the sine, cosine, and tangent, respectively, being the
reciprocals of those quantities.
In the third quadrant, between 180° and 270°, sin A f = J and cos A ( =- J are both negative,
because both « and b have negative values; tan A ( —r ) is jwaitive for the same reason.
In. the fourth quadrant, between 270° and 360°, sin A ( =- ) is negative, cos A { =- ) is positive,
and tan -^ ( =i> ) is also negative.
From a consideration of the signs in the manner that has l)een indicated the following relations
will appear:
sin A = sin (180°-A) = — sin (180° -f A) = — sin (860°— A).
cos A = — cos (180°-A) = -cos (180° + A) = cos (360°— A).
tan A = — tan (180° -A )= tan (180° + A) = — tan (360°-A).
sin A = cos (90°-A) = -cos (90° -^A) = - cos (270°-A) = cos (270° +A).
Any similar relation may be deduced from the figure.
It is of great importance to have careful regard for the signs of the functions in all trigonometrical
solutions.
LOGABITHKS.
In order to abbreviate the tedious operations of multiplication and division with large numbers, a
series of numbers, called Logarithms, was invente<l by Lord Napier, by means of which the oi>eration of
multiplication may be performed by addition, and that of division by subtraction. Numljers may be
involved to any power by simple multiplication and the root of any power extracted by simple division.
In Table 42 are given the Togarithms of all numbers, from 1 to 9999; to each one must be prefixed
an index, with a period or dot to separate it from the other part, as in decimal fractions; the numbera
from 1 to 100 are given in that table with their indices; but from 100 to 9999 the index is left out for the
sake of brevity; it may be supplied, however, by the general rule that the index of the logarithm of any
184 RULES AND PBIISrCTPLES OF MATHEMATICS.
integer or mixed number is always one less than the number of integral places in the natural number.
Thus, the index of thelogarithm of any number (integral or mixed) between 10 and 100 is 1; from 100
to 1000 it is 2; from 1000 to 10000 it is 3, etc.; the method of finding the logarithms from this table will
be evident from the rules that follow:
To find the logixrithm of ani/ number less than 100, enter the first page of the table, and opposite the
given number will be found the logarithm with its index prefixed. Thus, opposite 71 is 1.85126, which
IS its logarithm.
To find the logarithm of any number between 100 and 1000, find the given number in the left-hand col-
umn of the table of logarithms, and immediately under in the next column is a number, to whit'h must
be prefixed the number 2 as an index (because the number consists of three places of figures), and the
required logarithm will be found. Thus, if the logarithm of 149 was required, this number being found
in the left-hand column, against it, in the column marked at the top (or bottom) is found 17319, pre-
fixing to which the index 2, we have the logarithm of 149, 2.17319.
To fmdthelogarithm of any number between 1000 and 10000, find the three left-hand figures of the given
number in the left-hand colunni of the table of logarithms, opposite to which, in the column that is
marked at the top (or bottom) with the fourth figure, is to be found thej.required logarithm, to which
must be prefixed the index 3, because the number contains four places of figures. Thus, if the logarithm
of 1495 was required, opposite to 149, and in the column marked 5 at the top (or bottom) is 17464, to
which prefix the index 3, and we have the logarithm, 3.17464. "
To find the logarithm of any number above 10000, find the first three figures of the given number in the
left-hand column of the table, and the fourth figure at the top or bottom, and take out the corresponding
logarithm as in the preceding rule; take also the difference between this logarithm and the next greater,
and multiply it by the remaining figure or figures of the number whose logarithm is sought, pointing off
as many decimal places in the product as there are figures in the multiplier. To facilitate the calcula-
tion of the proportional parts several small tables are placed in the margin, which give the correction
corresponding to the difference, and to the fifth figure of the proposed number. Thus, if the logarithm
of 14957 was required, opposite to 149, and under o, is 17464; the difference between this and the next
greater number, 17493, is 29; this multiplied by 7 (the last figure of the given number^ gives 203;
pointing off the right-hand figure gives 20.3 (or 20) to be added to 17464, which makes 17484; to this,
prefixing the index 4, we have the logarithm sought, 4.17484. This correction, 20, may also be found
by inspection in the small table in the margin, marked at tlie top 29; opposite to the fifth figure of the
number, 7, in the left-hand column, is the corresponding correction, 20, in the right-hand column.
Again, if the logarithm of 1495738 was required, the logarithm corresponding to 149 at the left, and
5 at the top, is, as in the last example, 17464; the difference between this and the next greater is 29;
multiplying this by 738 (the given number excluding the first four figures) gives 21402; crossing off the
three right-hand figures of this product (because the number 738 consists of three figures), we have the
correction 21 to be added to 17464; and the index to be prefixed is 6, because the given number consists
of 7 places of figures; therefore the required logarithm is 6.17485. This correction, 21, may be found as
above, by means of the marginal table marked at the top 29, taking at the side 7.38 (or 7J nearly), to
which corresponds 21 , as before.
To find the logarithm of any mixed decimal number, find the logarithm of the number, as if it were
an integer, by the preceding rules, to which prefix the index of the integral part of the given number.
Thus, if the logarithm of the mixed decimal 149.5738 was required, find the logarithm of 1495738, with-
out noticing the decimal point; this, in the last example, was found to be 17485; to this prefix the index
2, corresronding to the integral part 149; the logarithm sought will therefore be 2.17485.
To find the logarithm of any decimal fraction less than unity, it must be observed that the index uf,the
logarithm of any number 'less "than unity is negative; but, to avoid the mixture of positive and negative
quantities, it is common to borrow 10 in the index, which, iu most cases, may' afterwards be neglected
in gumming them with other indices; thus, instead of writing the index — 1 it is written + 9; instead
of — 2 we may write -f 8; and so on. In this way we may find the logarithm of any decimal frac'tion
by the following rule: Find the logarithm of a fraction as if it were a whole number; see how many
ciphers precede the first figure of the decimal fraction, subtract that number from 9, and the remainder
will be the index of the given fraction. Thus the logarithm of 0.0391 is 8.59218 — 10; the logarithm of
0.25 is 9.39794 — 10; the logarithm of 0.000002,^ is 4.;«t794 — 10, etc. In most cases the writing of - 10
after the logarithm may be dispensed with, as it will be quite apparent whether the logarithm has a
positive or a negative index.
To find the number corresponding to any logarithm, seek in the column marked at top and bottom
the next smallest logarithm, neglecting tlie index; write down the number in the side column abreast
which this is found and this will give the first three figures of the required number; carry the eye along
the line until the next smallest logarithm to the given one is found, and the fourth figure of the required
number will be at the top and bottom of the column in which this stands; take the difference between
this next smallest logarithm and the next larger one in the table, and also the difference between the
next smallest logarithm and the given one; entering the small marginal table whicli has for its heading
the first-named difference and finding in the right-hand column of that table the last-named difference,
there will appear abreast the latter, in the left-hand column, the fifth figure of the required number.
Where it is desired to determine figures beyond the fifth for the corresponding number, the difference
between the next lower logarithm and the given one may be divided by the difference between the
next lower and next higher ones, and the quotient (disregarding the decimal point, but retaining any
ciphers that may come between the decimal point and the significant figurea^will be the fifth and suc-
ceeding fjcuras^f^he munber sou^jt. ^kHaving found the figures of the coSesponding numberi^ point
off ffom-tb'e lefl!%'numbe(" of figur4sVhie*nrffti.lt*e one greater than th«- index uuhiber, and ■QSere place
a decimal point, tajhis operation o^placing the decimal point, proper accountj^ust ^ takei^f the
-.^iegative ^Th^lf a^Sindex. '"^ ^ i ■'" - "tj^Ot '■''
_ .Thus, if the number corresponding tdthe logarithm 1.52634 Were requir^, find 52634 in tliecWmnn
, <CV^v.'^jna*k^ a4t>ho toi> or bottom, and opposite toat is 3^; now, th««i»_dp_^bemgTVthe required ami^er
, must consist of two integral places; therefore it is 33.6. "v ' '' """^ i -^
SULES AND PRINCIPLES OF MATHEMATICS.
185
If the number corresponding to the logarithm 2.57345 were required, look in the column and find
in it, against the number 374, the logarithm 57287, and, guiding the eye along that line, find the given
logarithm, 57345, in the column marked 5; therefore the mixed number souglit is 3745, and since the
index is 2, the integral part must consist of 3 places; therefore the number sought is 374.5. If the index
be 1 the number will be 37.45, and if the index be the number will be 3.745. If the index be 8.
corresponding to a number less than unity, the number will be 0.03745.
Again, if the number corresponding to the logarithm 3.57811 were required, find, against 378 and
under 5, the logarithm 57807, the difference between this and the next greater logarithm, 57818, being
11, and the difference between 57807 and the given number, 57811, being 4; in the marginal table headed
11, find in the right hand column the lumiber 4, and abreast the latter appears the figure 4, which is the
fifth figure of the required number; hence the figures are 37854; pointing off from the left 3H-1 = 4
places, the number is 3785.4.
If the given logarithm were 5.57811, since the index 5 requires that there shall be six places in the
■whole number, it i.-J desirable to seek accuracy to the sixth figure. The logarithmic part being the
same as in the example immediately preceding, it is fouiul as before that the first four figures are J5785,*
the difference between the next lower and next greater logarithms is 11, and between the next lower
logarithm and the given one is 4; divide 4 by 11 and the <iuotient is .36; drop the decimal point, annex
and point off, and the number required is found to be 37S536.
It may be remarked that in using five-place logarithm tables it is not generally to be expecte<l that
results will be exact beyond the fifth figure.
To show, at one view, the indices corresponding to mixed and decimal numbers, the following
examples are given:
Mixed number. Logarithms.
40943.0 I^g. 4.61218
4094. 3 Log. 3. 61218
409. 43 Log. 2. 61218
40. 943 ! Log. 1. 61 218
4.0943 Log. 0.61218
Decimal number. Logariihnu.
0.40943 Log. 9.61218 — 10
0.040943 Log. 8.61218 — 10
0.0040943 Log. 7.61218 — 10
0.00040943 I^g. 6.61218 — 10
0. 000040943 Log. 5. 61218 — 10
To perform mullipliratlon bi/ logarithms, add the logarithms of the two numbers to Ixi multiplied and
the sum will be the logarithm of their product.
Example I.
Multiply 25 by 35.
25 Log. 1.39794
as Log. 1.54407
Product, 875 I^,g. 2. 94201
EXAMPI.K II.
Multiply 22.4 by 1.8.
22.4 Log. 1.35025
1.8 Log. 0.25527
Product, 40.32 Log. 1.60.5.5:
Example III.
Multiply 3.26 by 0.0025.
3.26 Log. 0.51322
0.0025 , Log. 7.39794
Product, 0. 00815 Log. 7. 91 116
Example W.
Multiply 0.25 by 0.003.
0. 25 Log. 9. 39794
0.003 Log. 7.47712
Product, 0. 00075 Log. 6. 87506
In the last example, the sum of the two logarithms is really 16.87506—20; this is the same as
6.87506— 10, or, remembering that the quantity is less than unity, simply 6.87506.
To perform ilirision bi/ logarithms, from the logarithm of the dividend subtract the logarithm of the
divisor; the remainder will be the logarithm of the quotient.
Example I.
Divide 875 by 25.
875 Log. 2.94201
25 Log. 1 . 39794
Quotient, 35 Log. 1.54407
Example II.
Divide 40.32 by 22.4.
40.32 Log. 1.605.52
22.4 Log. 1.35025
Quotient, 1.8 Log. 0.25527 Quotient, 0.03 Log. 8.47712
In Bxamjile III both the divisor and dividend are fractions less than unity, and the divisor is the
lesser; consequently the quotient is greater than unity. In Example IV botli fractions are less than
unity; and, smce the divisor is the greater, its logarithm is greater than that of the dividend; for this
reason it is neces.sary to borrow 10 in the index before making the subtraction, that is, to regard the
logarithm of .00075 as 16.87506 — 20; hence the quotient is less than unity.
EXAMPLK III.
Divide 0.00815 by 0.0025.
0.00815 Log. 7.91116
0.0025 Log. 7.39794
Quotient, 3.26 Log. 0.51322
Example IV.
Divide 0.00075 by 0.025.
0.00075 Log. 6.87506
0.025 L(w. 8.39794
186
KULES AND PRIIfCIPLES OF MATHEMATICS.
The arithmetical complement of a logarithm is the difference between that logarithm and the loga-
rithm of unity (10.00000—10, or 0.00000). It is therefore the logarithm of unity divided by that
number which is the reciprocal of the number; and, since the effect of dividing by any number is the
game as that of multiplying by its reciprocal, it follows that, in performing division by logarithms, we
may either subtract the logarithm of the divisor or add the arithmetical complement of that logarithm.
As the addition of a number of quantities can be performed in a single operation, while in subtraction
the difference between only two quantities can be taken at a time, it is frequently a convenience to deai
with the arithmetical complements rather than with the logarithms themselves.
Example I.
Divide 875 by 2.5.
875 Log. 2.94201
25 Log. ] .39794 Oolog. 8. 60206
Quotient, 35 Log. 1.54407
Ex.\MPLE II.
Divide 0.00075 by 0.025.
0.00075 Log. 6. 87506
0.025 Log. 8.39794 Colog. 1.60206
Simplify the expression.
Ex.\MPI.E III.
40.32 X .00815
22.4 X .0025
40.32 Log. 1.60552
.00815 Log. 7.91116
22.4 Log. 1.35025 Colog. 8.64975
.0025 Log. 7.39794 Colog. 2.60206
Result, 5.868
.Log. 0.76849
Quotient, 0.03 Log. 8. 47712
To perform involution hij logarilhmst, maltiply the logarithm of the given number by the index of the
power to which the quantity is to be raised; the product will be the logarithm of the power sought.
Example I.
Required the square of 1.8.
18.
.Log. 1.25.527
2
Answer, 324 Log. 2.51054
Example II.
Required the square of 6.4.
6.4 Log. 0.80618
o
Answer, 40.96 Log. 1.61236
Ex.\MPLE III.
Required the iHibe of 13.
13 Log. 1.11394
3
Answer, 2197 Log. 3.34182
Example IV.
Required the cube of 0.25.
0.25 Log.9..39794
3
Answer, 0.015625 Log. 8. 19382
In the last example, the full product of the multiplication of 9.39794—10 bv 3 is 28.19382—30, which
IS equivalent to 8.19382—10.
To perform evolution by logarithms divide the logarithm of the number by the index of the power;
the quotient will be the logarithm of the root sought. If the number whose root is to be extracted is a
decimal fraction less than unity, increase the index of its logarithm by adding a number of tens which
shall be less by one than the index of the power before making the division.
IjXAMPLE I.
Required the square root of 324.
324 Ix)g.2)2.51055
Answer, 18 Log. 1.25527
Example II.
Required the cube root of 2197.
2197 Log. 3) 3. 34183
Answer, 13 Log. 1.11394
Example III.
Required the square root of 40.96.
40.96 Log.2) 1.61236
An-swer, 6.4 Log. 0.80618
Example IV.
Require<l the cube root of 0.015625.
0.015625 Log. 8.19382
Add 20 to the index 3)28.19382
Answer, 0.25 Log. 9.39794
30.
In the last example thelogarithm8.19382— 10 was converted into its equivalentform of 28.19382
which, divided by 3, gives 9.39794—10.
To find the logarithm of any function of an angle, Table 44 must be employed. This table is so
arranged that on'every page there appear the logarithms of all the functions of a certain angle A,
together with those of the angles 90°— A, 90° + A, and 180°— A; thus on each page may be found the
logarithms of the functions of four different angles. The number of degrees in the respective angles
are printed in bold-faced type, one in each corner of the page; the number of minutes corresponding
appear in one column at the left of the page and another at the right; the names of the functions
RULES AND PRINCIPLES OF MATHEMATICS.
187
to which the various logarithms t-orrespond are printed at the top and bottom of the columns. The
invariable rule must be to take the name of the function from the top or the bottom of the page,
according as the number of degrees of the given angle is found at the top or bottom; and to take the
minutes from the right or left hand column, according as the numter of degrees is found at the
right or left hand side of the page; or, more briefly, take names of functions and number of minutes,
respectively, from the line and column nearest in position to the number of degrees.
Taking, as an example, the thirty-first page of the table, it will be found that 30° appears at the
upper left-hand corner, 149° at the upper right-hand, 59° at the lower right-hand, and 120° at the lower
left-hand corner. Suppose that it is desired to find the log. sine of 30° 10'; following the rule given, we
find 10' in the left-hand column and Sine at the top of the page, and abreast one and below the other Is
the required logarithm, 9.70115. But if the log. sine of 59° 10' were sought, as 59° appears below and at
the right of the page, the logarithm 9.93382 would be taken from the coliunn marked Sine at the bottom
and abreast 10' on the right. It may also be seen that log. sin 30° 10'=log. cos 59° 50'=log. cos
120° 10'=log. sin 149° 50'=9.70115, the equality of the functions agreeing with trigonometrical deductions;
(in this statement numerical values only are regarded, and not signs; the latter must, of course, be taken
into account in all operations).
Example II.
Required the log. sine, cosecant, tangent, cotan-
gent, secant, and cosine of 75° 42'.
Log. sin 9. 98633 Log. cot 9. 40636
Log. cosec 10. 01367 Log. sec 10. 60730
Log. tan 10. 59364 Log. cos 9. 39270
Example I.
Eetjuired the log. sine, cosecant, tangent, cotan-
gent, recant, and cosine of 28° 37'.
Log. sin 9. 68029 Log. cot 10. 26313
Log. cosec 10. 31971 Ix)g. sec 10. 05658
Log. tan 9. 73687 Log. cos 9. 94342
When the angle of which the logarithmic function is required is given to seconds, it tjecomea
necessary to interpolate Ijetween the logarithms given for the even minutes next below and next above;
this may be done either by computation or (except in a few cases) by inspection of the table.
To interpolate by computation, let n represent the number of seconds, D the difference between the
logarithms of the next less and next greater even minute, and d the difference between the logarithm
of the next less even minute and that of the required angle. Then,
It should lie noted when the number of seconds is 30, 20, 15, or some similar number, itemiitting
the reduction of the fraction wn to a simple value, such as J, J, 1, as the interpolation by this method
may thus be made with greater facilitv.
Having obtained the difference of the logarithm from that of the next lower even minute, it mu.st
be' applied in the proper direction — that is, if the function is such that its logarithm increases as the
angle increases, the logarithmic difference must be added; but if it decreases, then that difference must
be subtracted.
For example, let it l)e required to find the log. sin and log. cosec of 30° 10' 19". The log. sin of
30° 10' is 9.70115; the difference between this logarithm and that of the sine of 30° 11' (9.70137) is -f22,
which is D. Hence,
d = ^X( + 2-2) = +
and tlie required logarithm is 9.70122. The log. cosec of 30°
that and log. sin 30° 11' (10.29863) is — 22. In this case
10' is 10.29885; the difference, D, between
^' = Sx(-
22) = -7;
therefore, log. cosec 30° 10' 19" = 10.29878.
The method of interpolating by inspection consists in entering that column marked "Diff." which
is adjacent to tlie one from which the logarithmic function for the next lower minute is taken, and
finding, abreast the number in the left-hand minute column which corresponds to the seconds, the
reijuired logarithmic difference; and the latter is to be added or subtracted according as the logarithms
increa.se or decrease with an increased angle. Thus, if it be recjuired to find log. sin 30° 10' 19", find as
Wiore log. sin ,30° 10' = 9.70115; then, in the adjacent column headed " Diff." and abreast the numlter
of seconds, 19, in the left-hand minute column will be found 7, the logarithmic difference; add this, as
the function is increasing, and we have the required logarithm 9.70122. If log. cosec 30° W 19" be
sought, find log. cosec 30° 10' = 10.29885; then in the adjacent difference column, which is the same as
was used for the sines, find as before the logarithmic difference, 7; and since this function decreases iis
the angle increases, this must be subtracted; therefore, log. cosec 30° 10' 19" = 10.29878.
This method of interpolation by inspection is not available in that portion of the table where the
logarithmic differences vary so rapidly that no values will aiijily alike to all the angles on the same
page; on such pages the difference for one minute is given in a column headed "Diff. 1'," instead of
the usual difference for each second; in this case, the inten>olation must be made by computation, the
given difference for one minute being D. In other parts of the table the interpolation by inspection
may be liable to slight error becau.se of the variation in logarithmic difference for different angles on
the same page; but the tabulated values are sufficiently accurate for the usual calculations in navigation.
It will be evident that while the methods explained have contemplated entering the tables with a
smaller angle and interpolating ahead, it would be equally correct to enter with a greater angle and
interjiolate hack for the proper number of minutes, making the requisite change in the sign of the
correction.
188
RULES AND PRINCIPLES OF MATHEMATICS.
Example I.
Required the log. sine, cosine, and tangent of
!° 57' 06".
42° 57' 06'
Log. sin 9. 83338
Log. cos 9. 86448
Log. tan 9. 96890
+ 1
— 1
-r 3
For 42° 57' 06".
9. 83339
9. 86447
9. 96893
Example II.
Required the log. secant, cosecant, and cotangent
of 175° 32' 36".
For 175° 32'
d 1 For 175° 32' 3(i"
Log. sec
Log. cosec 11.108.^8
Log. cot 11. 10726
10.00132 — 1
+97
10. 00131
11. 10955
+98 I 11. 10824
It should be observed that, for uniformity and convenience, all logarithms given in Table 44 liave
been increased by 10 in the index, and it is understood tliat —10 ought properly to be written after
each; thus all logarithms under 10.00000 represent functions whose value is less than imity, and all
over 10.00000 those greater than unity; for example, 11.10726 is the logaritlim of a number in which
the decimal point should be placed after the second figure from the left.
To find the cmyle corresponding to any logiiriDimlc function, the process is the reverse of the one just
described. Find, in the column marked with the name of the function, either at top or bottom, the
two logarithms between which the given one falls; write down the degrees and minutes of the lesser of
the two corresponding angles, which will be the degrees and minutes of the angle required. Call the
difference between the two tabulate<l logarithm^ D, and the difference between the given logarithm and
that which corresponds to the le.sser angle, d; then if n represent the number of seconds, we have:
n = jj X 60.
Or, the same may be obtained by inspection (except where, a.s before explained, the differences
(or seconds are not tabulated ) bv finding, in the " I)i tf . " cohunn adjacent to that from which the logarithm
was taken, the logarithmic difference, rf, and noting the number of seconds abreast which it stands in
the left-hand minute column.
Interpolation may be also made in the reverse direction from the next greater even minute.
Thus, if it be required to find the angle corresponding to log. sin 9.614C)0, we find log. sin 24°. 16',
9.61382, and log. sin 24° 17', 9.61411; hence D = 29, and d = 18;
» = 29 X 60 = .37;
and the angle is 24° 16' 37". Or, in adjacent column headed "Diff.," 18 would be found abreast 38,
39, or 40 (seconds) in the left-hand minute column — a correspondence suflSciently close for navigation
work.
If the angle were known to be in the second quadrant, we find log. sin 155° 43', 9.61411, and log.
sin 155° 44', 9.61382; here, D = 29, and <? = 11 ;
n = 29 X 60
2,3;
therefore, the angle is 155° 4.3' 23". Or, in adjacent "Diff." column find, abreast 11, 23 or 24 seconds.
Example I.
Find angles less than 90° corresponding to log.
cot 10.33621, log. sec 10.11579, and log. cos 8.70542.
Example II.
Find angles in second quadrant corresponding to
log. tan 10.15593, log. sin 8.87926, and log. cosec
10.04944.
Log. cot 10. 33621 24 45
Log. sec 10.11579 40 00
Log. cos 8. 70542 87 05
8
15
4
22
116
28
o
/
d
"
124
55
19
42
175
39
69
25
116
49
3
27
Log. tan 10. 15.593
Log. sin 8. 87926
I Log. cosec 10. 04944
The Hour Columns in Table 44 give the measure in time corresponding to twice the angular distance
given in arc. Thus, abreast the angle 13° 00' stands in the P. M. column l"" 44"' 00', corresponding in
time to 2 X 13° 00', and in the A. M. column lO"" 16'» 00% which is the same subtracted from 12''. These
columns are of use in working the various formulse which involve functions of half the liour angle.
Interpolation for values intermediate to those given in the tables is made on the same principle as for
the angular measure; this operation may be performed by inspection by the use of the small tables at
the bottom of each page, where n, the number of seconds of time, is given in bold-faced type, and d, the
logarithmic difference for the respective columns, appears below.
Example I.
Given 1=1^ AW 44", find log. cot } t.
For 1" 48'° 40", log. cot. J t 10. 61687
Diff. for 4», Col B, - 28
For 1" 48-" 44",
log. cot J t 10. 61659
Example II.
Given log. sin i t 9.91394, find the Hour A. M.
corresponding.
For 9.91389, 4''39°'12"
Diff. for 5, Col. C, - 5
For 9.91394.
4 39 07
RULES AND PRINCIPLED OF MATHEMATICS.
189
UISCELiLANEOUS USEFUL DATA.
iCarth's Polar radius=6,356,583.3 meters.
Earth's Equatorial ra(lius=6,378,206.4 meters.
Earth's Compression =900 4^=
Earth's Eccentricity=0.6824846
Nmnhr of feet in one statute raile=5280
Number of feet in one nautical raile=6080.27
Sine of l"=0.0000048o
Sine 01 l'=0.00029089
The Napierian base £=2.7182818
The modulus of common logarithm8=0. 434^45
French meter in English feet, 3.2808333
French meter in English statute miles, 0.000021369
French meter in nautical viles, 0.000539593
1 pound Avoirdupois=7,000 grains Troy.
French trramme =0.00220606 Imperial pound Trov.
French kilogramme=0.0196969 English cwts.
Cubic inch of distilled water, in grains=252.458.
Cubic foot of water, in ounces Troy =908. 8488.
Cubic foot of water, in pounds Troy =75. 7374.
Cubic foot of water, in ounces Avoirdupols=997.1.366691.
Cubic foot of water, in pounds Avoir(.lupois=62.-"210606.J
Length of pendulum which vibrates second at Greenwich, 39.1393 inches.
log 8. 0163666.
log 3. 7226339.
log 3. 7839229.
log 4. 6855749.
log 6. 4637261.
log 0. 4342945.
log 9. 6377843.
log 0. 5159842.
log 6. 7933496.
log 6. 7320663.
Bar. 30.00 in.; th?r. 62° F.
APPENDIX IV.
MAEITIME POSITIONS AND TIDAL DATA.
The following table contains the latitude and longitude of a large number uf jilaces, together with
lunitidal intervals and tidal ranges at the more important ones. It is arranged geographically and
followed by an alphabetical index.
The geograi)hical position generally relates to some specified exact location, and is based upon the
best available authority. The tidal data relate to tlie waters adjacent to the point whose latitude
and longitude are given, being abstracted from the Tide Tables published by the United State? Coast and
Geodetic Survey for the year 1903.
The high water and low water lunitidal intervals represent the mean intervals between the moon's
transit and the time of next succeeding high and low waters throughont a lunar month. Tlie spring
and neap ranges are the differences in height between high water and low water at spring and at neap
tides. For those places where the tide is chiefly of a diurnal tyi)e, and w here there is usually but one
high and one low water during a lunar day, the tidal values are bracketed; in such cases the lunitidal
intervals are for the semi-diurnal part of the tide ( which, however, is onl v appreciable for a few days when
the m(X)n is near the equatf)r), and the range given in the column headed "Spg." does not, as in other
cases, apply to the spring tide, but to the greatest periodic daily range, which usually occurs a day or
two after the moon attains its extreme of declination, and is therefore near one of the tropics. As those
places where the diurnal type predominates seldom experience large tidal effects, the general data
furnished regarding such tides will suffice for the ordinary purpose of the navigator. The method
of finding the time of high or low water from this table is illustrated in article 507, Chapter XX.
lao
APPENDIX IV.
>rAEiTi:\rE positions and tidal data.
EAST COAST OF NORTK AMEKICA.
[Page 191
8
Place.
Lat. N.
Ix)ng. W
Lim.
Int.
Range.
H.W.
L. W.
Spg.
Neap.
o / //
63 27 00
63 06 00
62 37 00
62 35 00
62 48 00
62 50 00
62 30 00
62 07 00
61 18 00
60 10 00
60 40 00
60 52 00
60 33 00
61 21 00
61 40 00
60 00 00
59 48 00
69 07 00
57 35 00
57 00 00
56 32 45
55 27 04
55 13 33
54 65 60
54 26 55
54 00 05
53 50 00
63 42 37
63 34 25
53 26 00
52 40 07
52 21 16
52 15 36
52 06 00
51 53 00
51 38 48
50 42 10
49 59 54
49 53 00
49 45 29
49 35 40
49 41 20
49 36 50
49 15 20
49 04 20
48 42 01
48 30 15
48 16 55
47 53 10
48 08 58
47 42 45
47 48 30
47 34 02
46 39 24
46 37 04
4e VA iio
46 49 34
47 17 55
47 00 26
46 56 30
46 46 51
47 15 30
47 35 13
o / //
76 30 00
77 50 00
78 08 00
77 33 00
74 00 00
75 20 00
74 03 00
72 25 00
70 02 00
67 05 00
67 50 00
64 40 00
64 12 00
65 00 00
64 30 00
64 28 00
64 07 15
63 20 00
61 20 00
62 07 00
61 40 13
60 12 34
59 08 01
57 56 40
57 12 40
56 31 31
56 23 00
56 59 50
56 58 39
55 35 48
55 44 29
55 38 08
55 32 20
55 41 00
55 22 10
55 25 12
56 35 30
55 21 33
55 37 17
63 10 56
63 45 00
54 47 36
54 12 00
53 25 12
53 37 45
53 04 42
53 02 40
53 23 35
53 23 20
52 47 42
53 08 11
52 47 20
52 40 54
53 04 30
63 31 56
63 TL 10
54 11 42
53 68 43
55 08 49
66 32 00
66 10 36
66 51 40
67 36 62
A. m.
h. m.
/'.
jt-
Nottingham Iplaiidi S. pt .... ......
8 58
2 46
13.5
6.1
::::.... i:::;;;
1 1
W pt
Prince of Wales Sound: Center of ent ...
;
Grppn T«Ia.ii(l" \K lit
i
Button I.slands: N. \A
Oarte ( 'hidleich
e
! 1
Resolution Island: S. pt., Hutton h'dl'd
E. pt., C. Resolution
Rlark Head
1
\
1
8 00
7 00
145
48
5.0
5.2
2.0
2.1
Nachvack Bav: Islands off entrance
2
1
:::::::::: i
Nain : (Church
7.00
5 30
48
11 43
6.5
6.9
3.0
3.2
Hopedale Harbor: Hill to K*d
Ailfick Harbor: Cape Mokkivik
Cape ITarri.son' N extreme
::::::;::::::::::!:::: i
Indian Harbor: ( »bs
Outer ^ rannet Island: Summit
6 10
12 23
7.0
3.2
Cartwri)»lit Harbor: CarilKHi Castle
Indian Tickle: Summit
6 27
15
6.0
2.8
Occasional Harbor: E. summit of Twin I.
Cape St. Lewis: SE. pt
Battle Islands: NE. extreme, SE. I
Table Head .
6 38
6 30
26
18
5.0
3.5
2.3
1.6
:::":::i::::::
Belle Isle: Light-house
Cape Bauld : Light-house
Bell Island: S. end
Cape St. John: Gull Island light
Tilt Cove, Union Copper
Mine
::..'.:::
::::::::::: i
Funk Island : Summit
j
•i
s
Offer Wadham : Light-house
Toulinguet Islands: Light-house
Seldom-come-by Harbor: Shiphill
Cape Freels: Gull I
Greenspond Island
Cape Bonavista: Light-house
Catalina Harl)or: Green I. light-house ..
a
a
Hearts Content: Light-house
Baccalieu Island: Light-house
7 23
1 11
4.1
1.9
Harbfjr (irace: Light-house on beach ...
Cape St. Francis: Light-hf)use
7 15
1 03
3.3
1.5
£
St. Johns Harbor: Chain Rock Battery..
Cape Race: Light-house ". . .
Cape Pine: Light-house. .... ......
7 12
6 50
1 01
38
3.3
6.5
1.5
3.0
Trepassey Haroor : Sfungle jN eck
CapeSt. Marv: Light-house
6 60
8 20
38
2 08
6.6
7.2
3.1
3.3
Little Placent!ia Harbor: W. side Coopers
Cove
Burin Island : Light-house
Laun: Gr. Laun R. C. (Jhureh
8 05
8 23
8 53
8 22
1 53
2 11
2 41
2 10
7.0
6.6
6.5
6.2
3.2
3.1
3.0
2.9
St. Pierre: U. S. Coast Survey Station...
Brunei Island: Mercers Hd. light-house.
Boar Islands: Burgeo I. light-house
Page 192] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
Place.
a
«
Ml"
it
.9
La Poile Bay : Gr. Espic Church
Cape Ray : Light-house
Codrov island: S. side Boat Harbor
Cape St. George : Red I. , SE. pt
Cow Head : NW. extreme
Port Saunders: NE. point of entry
Rich Point: Light-house
FeroUe Point: Cove Point, NE. extreme .
Flower Cove: Capstan Pt
Green Island: 150 fnis. from NE. end . . ,
Cape Norman : Light-house
Chateau Bay : S. pt. Castle I
Amour Point : Light-house
Wood Island: S. pt
Greenly Island : Light-house
Bradore Bav: Obs. Spot, Jones Pt
Old Fort Island : Center
(xreat Mecatina Island: SK pt
Mecatina Harbor: S. point of Dead Cove.
Little Mecatina 1. : S. pt. C. McKinnon. ,
St. Mary Reefs
South Makers Ledge
Cape Whittle
Natashquan Point: S. edge
Clearwater Point: S\V. extreme..
Carousel Island: Light-houne
Point de Monts: Light-house
Quebec: Mann's Bastion, Citadel .
Montreal : Cathedral
Father Point: Light-house
Cape Chatte: Extreme
Cape Magdalen : Ligh t- house
Cape Rosier: Light-house
Cape Gaspe : Light-house
Anticosti Island: Heath Pt. light-house
SW. pt. light-house . .
Bona venture Island: E. pt
Leander Shoal
_Macquereau Point
'Chaleur Bay: Carlisle
Dalhousie I
Miscou Island: NE. pt., Point Birch .
Miramichi Bay: Portage I., N. pt
Point Escumenac: Light-house
North Point: Light-house
Richmond Harbor: Royalty Pt...
East Point: Light-house
Charlottetown:' Flag-staff on fort .
Gt. Bird Rock : Light-house
East Island: E. extreme
Entry Island : Light-house
Amherst Hbr. : N. side of entrance
Deadman Rock: W. pt
St. Paul Island: Light-house, NE. end.
Light-house, SW. end.
Cape North : Light-house
St. Anns Harbor: E. pt. entrance
Sydney Harbor: Light-house
Lat. N.
47 39 50
47 37 00
47 52 30
48 33 48
49 55 20
50 38 ,30
50 41 39
51 02 10
51 17 25
51 24 10
51 38 00
51 58 00
51 27 35
51 22 45
51 22 35
51 27 .30
51 21 40
50 47 30
50 46' 44
.50 31 40
.50 14 00
50 09 30
.50 11 00
50 06 00
50 12 27
50 05 40
49 19 ,35
46 48 17
45 30 24
48 31 25
49 06 00
49 1*5 40
48 51 37
48 45 15
49 05 20
49 23 45
48 29 30
48 24 00
48 12 00
48 01 00
48 04 24
48 01 00
47 14 00
47 05 00
47 03 46
46 34 00
46 27 15
46 13 55
47 50 40
47 37 40
47 16 30
47 14 23
47 16 03
47 13 50
47 11 20
47 01 45
46 21 00
46 12 25
Long. W.
.58 24 10
.59 18 00
59 23 40
,59 13 10
57 50 00
.57 17 07
57 24 20
57 02 40
56 44 45
56 ,33 40
55 53 52
55 50 20
56 51 05
57 08 00
57 10 50
57 14 12
57 46 00
58 51 00
58 59 20
59 20 00
59 45 00
,59 57 00
60 08 00
61 44 00
63 27 03
66 22 44
67 21 55
71 12 19
73 33 04
68 27 40
66 46 00
65 19 30
64 12 00
64 09 35
61 42 30
63 35 46
64 08 00
64 18 00
64 46 30
65 19 00
66 22 10
(U 29 00
65 02 00
64 47 33
63 59 19
63 43 00
61 58 05
63 07 23
61 08 32
61 24 30
61 41 20
61 49 ,38
62 12 25
60 08 32
60 09 50
60 23 27
60 27 00
60 12 50
Lull. Int.
H. W.
h. m.
8 50
8 50
'g'io'
1 25
1 43
1 48
6 07
1 52
1 46
1 33
1 25
1 20
1 25
1 55
2 20
3 10
2 00
4 16
4 20
5 15
8 17
11 07
8 30
35
25
10
L. \V.
2 38
2 32
Range.
Spg.
.ft-
6.0
4.3
'4.'9'
6 45
7 05
7 18
54
7 33
7 13
6 50
6 40
6 ,35
6 40
7 33
8 07
9 10
8 25
10 59
11 00
11 55
2 20
4 23
2 12
2 17
2 13
2 05
4.0
8.1
10.8
14.6
12.0
10.5
6.4
5.5
3.6
4.9
4.7
4.8
8.1
4.0
2.3
2.4
1.8
1.4
6.4
3.1
6.0
5.0
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NOBXH AMERICA— Continued.
[Page 193
Ȥ
a
e
3
u
oa
s
n
Place.
Lat. N.
Long. W.
Scatary Island: Light-house, NE. pt.
Louisburg: Light-house, NE. pt
Madame Island: S. pt
Port Hood: Just-au-corps I
Sable Island: Light- house, E. end .
Pictou: Custom-house
Cape St. George
North Canso: Light-house, NW. entrance.
Arichat Harbor: R. C. Church steeple . .
Cape Canso: Cranberry I., light-hou.se . .
White Head Island: Light-house
Green Island : Light-house
Wedge Island : Light-house
Halifax : Dock- yard observatory
Sambro Islanil: Light-house
Margaret Bay : Shut-in I
. Tancook Island
Lunenburg: Battery Pt. light
Cape Le Havre: Black Rock
Colli n Island : Ligh t-house
Little Hojje Island : Light-house
Shelburne Hbr.: Two lights, McNutts I.
Cape Sable: Light-house
Seal Island : Light-house
Yarmouth : Cape Fourchu light
Cape St. Mary I
Bryer Island : Light-house
Annapolis Harbor: Prim Pt. light
Haute Island : Light-house
Cape Chignecto.
Burntcoat Head: Light-house
Cape Enn^e : Light-house
Cape Quaco: Light-house
St. Johns: Partridge I. light
Cape Lepreau: Light-house
L'Etang Harbor: S. pt. tower
St. Andrew: S. pt. light
Campo Bello Lsland: Light-house, N. j)t.
Grand Manan Island: Light-house, NE. pt.
GannetRock: Light-house, NE. pt
Machias Island : Light-house
46 02 15
45 54 34
45 28 00
46 00 00
59 40 25
59 59 26
61 03 00
61 36 00
Lun. Int.
43 58 14 : 59 46 08
Calais: Astronomical station
Eastport : Cong. Church
Quoddy Head : Light-house
Machias: Town Hall
Petit Manan Island : Light-house
Bakers Island : Light-house
Mount Desert Rook: Light-house
Bangor: Thomas Hill
Belfast: Methodist Church
Rockland : Ejiiscopal Church
Matinicus Rock: Light-house
Monhegan Island: Light-house
Seguin Island : Light-house
Bath: Winter St. Church
Brunswick: College spire
Augusta: Baptist Church
Portland : Custom-house
Portland Head light-house
Cape Elizabeth: Light-house (west) .
Wood Island : Light-house
Boon Island: Light-house
45 40 50
45 52 00
43 41 42
45 30 48
45 19 49
45 11 58
45 06 15
45 00 35
44 39 38
44 26 10
44 34 00
44 29 00
44 21 45
44 12 00
44 02 00
43 48 30
43 37 15
43 23 19
43 23 34
43 47 28
44 05 20
44 14 57
44 41 .34
45 14 5.5
45 19 00
45 18 40
45 35 34
45 19 30
45 14 20
45 03 40
45 04 00
45 04 06
44 57 40
44 45 52
44 30 38
44 30 07
62 42 10
61 52 00
61 29 10
61 01 47
60 55 41
61 08 14
61 32 40
61 52 45
63 35 22
63 33 30
63 54 00
64 06 00
64 17 35
64 18 00
64 37 30
64 47 15
65 15 45
65 37 11
66 00 52
66 09 21
66 12 40
66 23 38
65 47 20
65 00 45
64 57 00
63 48 30
64 46 55
65 32 00
66 03 20
66 27 40
66 49 00
67 02 52
66 54 10
66 44 00
66 47 00
67 06 13
45 11 05
67 16 50
44 54 15
66 59 14
44 48 55
66 57 04
44 43 01
67 27 22
44 22 03
67 51 51
44 14 29
68 11 58
43 58 08
68 07 44
44 48 23
68 46 59
44 25 29
69 00 19
44 06 06
69 06 52
43 47 03
68 51 28
43 45 53
69 18 59
43 42 26
69 45 32
43 54 55
69 49 00
43 54 29
69 57 44
44 18 52
69 46 37
43 39 28
70 15 18
43 37 23
70 12 30
43 33 51
70 12 11
43 27 24
70 19 46
43 07 17
70 28 37
H. W.
7 45
7 55
9 05
9 34
9 20
9 26
7 55
7 43
7 45
34
32
'39
8 17
9 35
10 00
10 29
10 49
11 07
27
11 21
11 07
11 04
11 09
11 00
11 02
"io'Si
11 36
11 09
U 02
23
11 35
11 09
10 45
12 13
2 54
11 06
11 12
L. W.
h. m.
1 35
1 47
2 47
3 13
3 00
3 10
1 47
1 31
1 38
Range.
Spg.
ft-
5.0
5.0
3.5
3.9
2.8
3.1
5.0
6.5
6.6
1 46 5.2
1 30 7.1
1 36
7.0
2 05
3 23
3 41
8.5
12.8
16.0
4 36
4 41
5 27
20.8
27.5
33.0
7 27
50.5
5 56
4 58
5 26
5 08
5 00
30.0
23.9
24.5
23.3
24.9
5 21
'•i'se'
5 40
5 05
22.5
"is.o'
23.3
20.9
4 59
15.5
6 47
5 22
4 .55
4 31
15.1
11.7
11.0
10.2
6 16
7.9
10 18
4 51
4.9
10.1
4 51
10.2
Neap.
/(.
3.1
3.1
1.8
2.0
1.4
1.6
3.1
4.0
4.1
3.2
4.4
4.3
5.2
9.5
11.8
15.4
20.4
24.4
37.4
22.2
17^7
18.2
17.1
18.2
16.
13.2
17.1
15.2
11.3
11.0
8.6
.8.1
7.5
5.8
3.6
7.3
7.5
24972°— 12-
-13
Page 194] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
Place.
^
e
B
e
a
a
e
V
Whale Back: Light-house
Portsmouth : Navy-yard flagstaff
Fort Constitution
Hampton : Baptist Church
Isles of Shoals: White I. light-house ...
Newburyport: Aca<;lemv
Plum I. light-house
Ipswich : Light-house ( rear)
Annisquam Harbor: Light-house
Cape Ann: Thatchers I. light-house (N.)
Gloucester: Universalist Church
Ten-pound I. light-house . .
Beverly: Hospital Pt. light-house
Salem : Derbys Wharf light-house
Marblehead : Light-house
Cambridge: Harvard Observatory
Boston : Navy-yard flagstaff
State house
Little Brewster I. light-house. .
Minotg Ledge: Light-house
Plymouth : Pier head
Gurnet light-house
Barnstable: IJght-house
Cape Cod : Highlands light-house
Chatham : Light-house (south )
Monoraoy Point : Light-house
Nantucket : South Church
Nantucket South shoal: Light ship
Sankaty Head : Light-house
Tarpaulin Cove: Light-house
Vineyard Haven: W. Chop light-house.
Gay Head : Light-house
Cutty hunk: Light-house
New Bedford : Baptist Church
Sakonnet Point : Light-house
Beaver Tail: Light-house
Newport: Flagstaff, torpedo station
Bristol Ferry : Light-house
Providence: Unitarian Church
Point Judith : Light-house
Block Island: Light-house (SE)
Watch Hill Point: Light-house
Montauk Point : Light-house
Stonington: Light-house
New London : (t rot on Monument
Little Gull Island: Light-house
Gardners Island: Light-house, N. pt...
Plum Island: Light-house, W. pt
Say brook: Light-house, Lynde Pt
New Haven: YaleCollegespire( middle)
Bridgeport Harbor: Light-house
Norwalk Island : 1 Jght-house
Shinneeock Bay: Light-house
Fire Island : Light-house
Albany: Dudley Observatory
New York ; Nav v-y ard flagstaff
Citv'Hall
Fort Wadsworth : Light-house
Lat. X.
43 03 32
43 04 56
43 04 16
42 .56 15
42 58 02
42 48 30
42 48 55
42 41 07
42 39 43
42 38 21
42 36 46
42 36 07
42 32 48
42 31 00
42 30 20
42 22 48
42 22 22
42 21 28
42 19 41
42 16 11
41 58 44
42 00 12
41 43 20
42 02 23
41 40 17
41 33 34
41 16 55
40 37 05
41 17 01
41 28 08
41 28 51
41 20 55
41 24 52
41 38 10
41 26 30
41 26 58
41 29 07
41 .38 34
41 49 26
41 21 40
41 09 10
41 18 14
41 04 16
41 19 31
41 21 16
41 12 23
41 08 29
41 10 25
41 16 17
41 18 28
41 09 24
41 02 56
40 51 03
40 37 57
42 39 50
40 42 02
40 42 44
40 36 20
Long. W.
Lun. Int.
70 41 49
70 44 22
70 42 34
70 50 12
70 37 25
70 52 28
70 49 10
70 46 00
70 40 55
70 34 31
70 39 59
70 39 58
70 51 23
70 53 03
70 50 03
71 07 43
71 03 05
71 03 50
70 53 26
70 4.5 35
70 39 12
70 36 04
70 16 52
70 03 40
69 57 01
69 59 39
70 05 57
69 3(> 33
69 57 57
70 45 29
70 36 01
70 50 08
70 57 01
70 55 36
71 13 30
71 24 00
71 19 40
71 15 39
71 24 19
71 28 55
71 33 08
71 51 32
71 51 27
71 54 49
72 04 47
72 06 26
72 08 44
72 12 43
72 20 37
72 .55 45
73 10 49
73 25 11
72 30 16
73 13 08
73 44 56
73 58 51
74 00 24
74 03 15
H. w.
h. vt.
'ii'23
11 19
11 23
11 17
11 13
11 02
11 16
11 09
L. w.
ft. Ml.
's'og'
4 58
5 10
5 04
5 00
4 49
5 03
4 57
11 27
'ii'69"
5 17
'4"56
Range.
ft.
i6."5'
10.0
9.1
10.2
10.6
10.6
11.0
'i6."9'
7 51
11 34
7 31
7 36
7 57
7 40
7 4a
7 48
7 53
8 12
7 32
7 33
8 49
8 20
9 09
9 26
9 26
9 40
10 29
11 08
11 09
11 03
7 48
7 19
5 13
8 44
1 51
4 33
1 20 i
59 I
1 18 ;.
1 05
1 09
1 00
40
57
1 17
1 25 I
2 38 j
2 03
3 03
3 32
3 04
3 35
2.8
2.0
3.7
4.3
5.2
4.5
4.7
4.4
5.2
5.4
3.8
3.7
3.2
2.3
3.2
2.9
3.0
2.5
11
54
04
56
.38
20
46
2 49
41
1 38 5.4
4.3
7.0
8.4
8.2
3.0
2.2
2.8
5.3
Neap.
ft-
7.3
6.6
10. 1 7. 4
10.1 7.4
7.5
7.7
7.7
8.1
'i'.b
i
11 23
11 36
5 11
5 25
10.8
11.6
7.9
8.5
12 11
12 00
04
5 57
5 48
6 00
4.6
4.3
3.8
3.4
3.1
2.3
1.7
L2
2.2
2.6
3.1
2.6
2.8
2.6
3.6
3.4
2.3
2.2
2.1
1.5
2.1
1.0
2.0
1.7
2.8
4.9
5.9
5.7
2.0
1.4
1.8
3.4
3.5
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
[Page 195
Place.
Lat. N.
•0
a
n
a
«
e
c
h
e
■c
e
Sandy Hook : Light-house (rear)
Light-ship
Navesink Highlands: N. light-house ...
Barnegat Inlet: Light-houae
Tuckers Beach : Light-house
Absecon Inlet: Li":ht-house
Five Fathom Bank: Light-ship
Cape May: Light-house
Philadelphia, Pa. : Statehouse ,
Navy-yard flagstaff,
I>eague I
AVilmington, Del. : Town hall
Cape Henlopen: Light-house
Assateague Island : Light-house ,
Hog Island: Light-house
Cape Charles; Light-house ,
Baltimore: Washington Monument
Annapolis: Naval Academy observatory
Point Lookout: Light-house
Washington, D. C. : Navy-yard flagstaff
Naval Observatory
Capitol dome
Old Point Comfort : Light-house
Norfolk : Navy-yard flagstaff
Richmond, Va. : Capitol
Cape Henry : Light-house
Elizabeth City : Court-house
Edenton : Court-house
Currituck Beach: Light-liouse .
Bodie Island: Light-house
Cape Hatteras: Light-house
Ocracoke: Light-house
Newbern, -Episcopal spire
Cape Lookout: Light-house
Beaufort, N. C. : Court-house . .
Frying-Pan Shoals: Light-ship
Georgetown : Episcopal Church
Light-house, North I
Cape Romain : Light-house
Charleston: Light-house, Morris I
St. Michael's Church
Beaufort, S. C. : Episcopal Church
Port Royal: .Martins Industry light-ship.
Ty bee Island: Light-house.
Savannah: Exchange si)ire .
Sa]ielo Island: Light-house.
Darien: Winnowing House.
St, Simon: Light-house
Brunswick: Academy
Amelia Island: Light-house
Femandina: Astronomical station ..
St. Johns River: Light-house
Jacksonville: Methodist Church
St. Augustine; Presbyterian Church
Light-house
Cape Canaveral : Light-house
Jupiter Inlet: Light-house
Fowey Rocks; Light-house
Carysfort Reef; Light-house
40 27 42
40 28 15
40 23 48
39 4.5 52
39 30 22
39 21 59
38 47 20
38 55 59
39 56 53
39 53 14
39 44 27
38 46 42
37 54 40
37 23 46
37 07 22
39 17 48
38 58 53
38 02 19
38 52 30
38 .i5 14
38 53 20
37 00 06
36 49 33
37 32 16
36 55 35
36 17 58
36 03 24
36 22 36
35 49-07
35 15 17
35 06 32
35 06 21
.34 37 22
34 43 05
.33 34 26
33 22 08
33 13 21
33 01 06
32 41 43
32 46 34
32 26 02
32 05 33
32 01 20
32 04 52
31 23 28
31 21 54
31 08 02
31 08 51
30 40 23
30 40 18
.30 23 36
.30 19 43
29 53 20
29 .53 07
28 27 37
26 56 54
25 35 25
25 13 17
Long. W.
74 00 09
73 50 09
73 59 10
74 06 24
74 17 08
74 24 52
74 34 36
74 57 39
75 09 03
75 10 32
75 33 03
75 05 03
75 21 23
75 41 59
75 54 24
76 36 59
76 29 08
76 19 20
76 59 45
77 03 57
77 00 36
76 18 24
76 17 46
77 26 04
76 00 27
76 13 23
76 36 31
75 49 51
75 33 49
75 31 16
75 .59 11
77 02 24
76 31 29
76 39 48
77 49 12
79 16 49
79 10 55
79 22 19
79 52 54
79 55 49
80 40 27
80 33 15
80 50 37
81 05 26
81 17 01
81 25 39
81 23 .30
81 29 26
81 26 26
81 27 47
81 25 27
81 .39 14
81 18 41
81 17 12
80 32 30
80 04 48
80 05 41
80 12 40
Lun. Int.
Range.
H.W.
A. m.
7 30
7 .50
7 48
9 59
8 16
1 28
53
12 00
8 17
8 03
6 34
4 39
31
7 42
8 44
9 05
4 30
7 53
7 37
7 00
6 29
7 21
8 39
"659'
7 20
8 10
7 10
8 13
7 30
7 40
7 30
8 00
7 39
7 36
8 12
8 00
8 00
8 20
8 21
L.W.
Spg.
h. m.
1 23
1 43
1 42
3 57
1 47
8 58
8 02
6 40
1 50
2 19
44
10 53
6 52
1 56
2 17
2 47
11 55
1 43
1 26
45
20
1 08
3 38
'o'so'
1 10
2 06
04
07
24
1 44
27
57
1 31
1 33
2 00
1 52
2 00
2 16
2 08
5.6
2.7
4.2
4.7
5.6
6.2
7.0
6.7
5.4
8.0
1.4
1.0
1.7
3.5
3.0
3.2
4.3
3.2
3.4
2.2
4.4
.3.3
4.3
T9'
6.0
8.5
7.9
7.6
8.4
7.5
7.5
7.8
6.9
5.4
5.3
5.9
1.8
2.6
2.7
Neap.
ft.
3. 6
1.7
2.7
.3.0
3.6
4.4
5.2
4.9
3.5
2.0
1.0
0.8
1.1
2.5
2.0
2.1
2.8
2.1
2.2
1.5
3.0
2.3
2.9
'■i.'i
4.2
5.9
5.3
5.8
5.2
.5.3
5.4
4.8
3.7
3.6
4.0
1.2
1.3
1.4
Page 196J APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NOKTH AMERICA— Continued.
Plac
Alligator Reef: Light-house
Sombrero Ke v : Light-house
Sand Key: Light-house
Key West: Light-house
Loggerhead Key : Light-house
Sanibel Island : Light-house
Gasparilla Island: Light-house
Tampa Bay : Egmont Key light
Cedar Keys: Ast. station, Depot Key
Seahorse Kev light
St. Marks: Fort St. Marks"
Apalachicola: Flag-staff
Cape St. George: Light-house
Cape San Bias: Light-house
Pensacola: Light-house
Navy-yard chimney
Lat. N.
Sand Island : Li^ht^house (front)
Mobile Point: Light-house
Mobile: Episcopal Church
Horn Island: Light-house
East Pascagoula: Coast^Survey station . . .
Mississippi City: Coast-Survey station. . .
Ship Island: Light-house
Cat Island: Light-house
Chandeleur: Light-house
Mouth Mississippi River: Pass a 1' Outre
light
S. Pass light
(East Jetty)
SW. Pass light
New Orleans: United States Mint
Barataria Bay : Light-house
Tim bailer Island : Light-house
Ship Shoal : Light-house
Southwest Reef: Light-house
Calcasieu Pass: Light-house .■
Sabine Pass: Light-house
Galveston: Cathedral, N. spire
Light-house, Bolivar Pt
Matagorda: Coast-Survey station
Light-house
Indianola: Coast-Survey station :
Lava<'a: Coast-Survey station
Aransas Pa.ss: Light-house
Brazos Santiago: Light, 8. end Padre I .
Point Isabel : Light-house
Rio Grande del Norte: Obs. N. side of
entrance
San Fernando River: Entrance
Santander River: Entrance. ."
Mount Mecate: Summit
Tampico: Light-house
Cape Roxo
LobosCay: Light-house
Tuspan Reefs: Middle islet
Mexico: National Observatory
Bernal Chico: Middle of islet
Zempoala Point: Extreme
Vera Cruz: San Juan d' UUoa light. .
Sacrificios Island
Orizaba Mountain : 17,400 feet
Cofre de Perote Mount: 14,000 feet .
Alvarado: E. side of entrance
Roca Partida: Summit
Tuxtla, volcano: Summit
Montepio: Landing place
24 51 02
24 37 36
24 27 10
24 32 58
24 38 04
26 27 11
26 43 06
27 36 04
29 07 29
29 05 49
30 09 03
29 43 32
29 35 18
29 40 00
30 20 47
.30 20 49
30 11 19
30 13 44
30 41 26
30 13 23
30 20 42
.30 22 54
30 12 53
30 13 57
30 02 58
29 11 30
28 59 28
28 58 22
29 57 46
29 16 30
29 02 49
28 54 56
29 23 36
29 46 55
29 43 04
29 18 17
29 22 05
28 41 29
28 20 18
28 32 28
28 37 30
27 51 53
26 04 16
26 04 36
25 57 22
25 23 40
23 46 20
22 38 40
22 15 50
21 35 00
21 28 12
21 03 00
19 26 01
19 .39 50
19 27 26
19 12 29
19 10 10
19 04 00
19 29 30
18 49 00
18 44 00
18 29 00
18 40 00
Long. W.
80 37 08
81 06 40
81 52 40
81 48 04
82 55 42
82 00 43
82 15 34
82 45 40
83 01 57
83 03 58
84 12 42
84 59 12
85 02 54
85 21 .30
87 18 32
87 16 06
88 03 02
88 01 26
88 02 28
88 31 39
88 32 45
89 01 57
88 57 56
89 09 41
88 52 19
89 02 28
89 08 08
89 23 30
90 03 28
89 .56 43
90 21 25
91 04 15
91 30 14
93 20 43
93 51 00
94 47 26
94 46 00
95 57 26
96 25 28
96 31 01
96 37 21
97 03 23
97 10 00
97 12 28
97 08 57
97 21 25
97 46 55
98 04 55
97 49 55
97 22 00
97 13 00
97 13 35
99 06 39
96 24 39
96 20 22
96 07 57
96 05 30
97 15 55
97 07 30
95 44 48
95 11 14
95 08 00
95 05 12
Lun. Int.
H.W.
k. m.
8 22
8 24
8 40
9 20
9 44
12 17
42
U 32
42
2 00
[12 10]
[11 10]
iii'28i
[11 25]
[1 35^
[12 00
[0 20
[0 23]
[11 53]
[11 15]
[10 .551
[10 54]
L. W.
2 00
2 05
2 20
2 36
3 21
6 10
6 19
5 07
7 13
Range.
ft-
2.6
1.9
1.5
1.6
1.4
2.3
1.4
1.8
3.1
Neap.
/(.
1.3
1.0
0.8
0.9
0.8
1.2
0.7
0.9
1.5
8 .30 2. 6 i
[5 3.5] I [2.5]:
1.2
[4 55]
[4 20]
[2.1]!
[1.7]L.
rs 09]
'6 ,50]
o40]
5 45]
[11 00]
[11 50"
[0 18'
[0 40
2 17
3 17
[4 18]
[4 07]
[6 35]
[5 33]
[5 00]
[4 42]
[4 41]
[4 35]
[4 25]
[1 55]
4 47
5 38'
6 33'
6 56'
8 41
9 36
[10 33]
[10 23]
[10 47]
[10 .35]
[8 03]
[1 06] [7 19]
[2 49], [8 38]
1.5
2.1'
[2.01
"2.3;
[2.1]
[1.8]
[1.6]
[1-7]
[1-9]
2.1
2.0'
2.2'
[2. 0]
1.7
0.9
[1.4]
[1.6]
[1.6]
[1.6]
[L4]
[1-3]
[2.4]
1.3
0.6
APPENDIX IV. [Page 197
MARITIME POSITIONS AND TIDAL DATA.
BAST COAST OF NORTH ABIEBICA— Continued.
1
Place.
Lat.N.
Long. W.
Lun
.Int.
Range. i
H. W.
L. W.
Spg.
Neap.
g
•
V
a
Zapotitlan Point: Light-house
o / t/
18 34 00
18 19 45
18 08 56
18 18 49
18 26 44
18 39 30
18 47 08
18 38 44
19 38 00
19 48 24
19 50 20
19 51 36
21 02 00
21 10 06
21 26 30
21 17 00
21 23 00
21 36 30"
21 35 50
20 12- 45
20 29 00
20 32 00
20 54 54
20 58 00
21 50 00
22 07 10
22 23 36
21 33 00
21 12 00
21 03 00
20 35 50
20 16 20
19 46 55
18 23 20
17 12 15
17 36 15
16 42 20
17 19 30
17 33 15
16 57 50
16 48 50
17 29 20
16 57 40
16 47 45
16 48 10
16 30 54
16 14 15
15 54 00
15 49 45
15 38 00
15 24 20
15 52 20
15 57 45
16 08 00
15 47 11
15 48 45
15 38 00
15 55 45
16 03 40
15 58 00
16 18 00
16 24 20
16 28 00
18 44 00
O / If
94 50 00
94 38 57
94 24 46
93 51 53
93 25 25
92 42 00
91 30 50
91 50 17
90 43 27
90 36 11
90 32 20
90 30 51
90 22 00
90 02 37
90 18 27
89 39 30
88 54 27
88 10 27
87 04 10
91 57 45
92 13 27
91 52 27
92 12 47
92 18 57
92 04 26
91 24 21
89 41 45
86 48 00
86 43 39
86 46 45
86 4:5 55
86 59 04
87 28 27
87 23 40
87 32 30
87 46 30
87 50 .50
88 03 20
88 04 45
88 06 05
88 05 36
88 11 20
88 13 48
88 15 15
88 37 40
88 22 13
88 35 51
88 56 20
88 46 22
89 01 36
89 09 44
88 33 22
88 38 .50
88 20 15
88 04 31
87 27 46
86 55 00
85 59 18
86 59 15
86 32 09
86 34 27
86 18 41
85 55 00
84 02 00
A. m.
A. m.
/I-
ft
San Juan Point : Light-house
Coatzacoalcop : Light-house .,
Santa -Ana Lagoon : Entrance
Tupilco River: Entrance
Tabasco River: Light-house
Laguna <le Terniinoa: Vigia tower, W.
end Carmen I
[12 16]
[6 00]
[1.6]
Pay poton Mount: Summit
Lerma: C'hurcli
Campeclie: Light-iiouse
2 59
9 28
2.1
1.3
Port San Jos6
Point Palmas
Sisal : Fort Hght
10 20
4 10
1.8
0.9
Madagascar Reef: Center
Progreso: Light-house
Silan : Village
Lagartos: N'illage
Cape Catoche: Light-hf)use
9 .30
[12 06]
3 19
[5 50]
1.5
[1-6]
0.8
Areas Cavs: Light-house
Obispo Shoal : 16-foot spot
New Bank: Center
ii2 66]
[5 45]
[1.6]
Triangles, W. reef: Cay at S\V. end
Baj" Nuevo Reef: Center
Arenas Cavs: N\V. Cay
.\lacran Reef: Perez Cav
Coutov Island : Light-house ..
Mugeres Island : Light-house
Cancun Island : Nisuc Pt
9 20
3 08
1.6.
0.9
Cozumel Island: N. pt. light-house
S. pt. light-house
Ascension Bav: Allen Pt
8 20
2 08
1.5
0.8
Chinchorro Bank: Cayo Lotos light
Half-Moon Cay: Light-house
Mauger Cav, XW. end: Light-house
&
a
s
V
i
2
s
1
n
Glover Reef: SW. Cav
English Cav: Light-house
St. Georges" Cav : Center
1
Sand-Fly Cavs: Hut, S. end
Sout h Water Cav : Center
Belize: Fort (ieorge light
8 00
1 50 1.5
0.8
North Standing Creek: Entrance
Sittee Point: Cav
Cockscomb Mount: Summit, 4,000 feet..
Placentia Point: Huts on point
1
Icacog Point: S. extreme
Sarstoon River: Entrance
Dulce River: Entrance, W. side
Dulce Gulf: Fort St. Philip
9 00
2 50
2.0
1.1
Isabel
Hospital Bight: Hut, N. pt. of entrance.
Cape Three Points: NW. extreme
Seal Cavs: S. Cav
1
Omoa: Entrance
Cape Triunfo: Bluff pt
Congrehoy Peak: Summit, 8,040 feet
Truxillo: Fort
Utilla Island: S. Cay
1
Hog Islands: Highest hill on W. islet. . .
Roatan: Center of Coxen Cay
................. 1
7 35
1 23
3.5
1.8
PortRoyal, NW. pt. of GeorgeCav
Bonacca Island: Summit, 1,200 feet... .".
Misteriosa Bank: S. Point
8 50
2 38
1.5
0.8
Swan Islands: NW. pt. of W. I
17 24 30 83 56 27 1
1
!
.: -.. 1
Page 198] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF NORTH AMERICA— Continued.
s .
at
©>•
B
Place.
Great Rock Head : Bluff extreme
Cape Camaron
Brewers Lagoon : E. side of entrance
Patook River: E. side of entrance
Carataska Lagoon: E. side of entrance .,
Cape Gracias-ii-Dios: Light-house.
Caxones Reef: Great Hobby Islet
Gorda Bank : Gorda Cay
Farrall Rock: Center
Half -Moon Cay: Center
Alargate Reef: E. pt
Mosquito Cays: S. end
Rosalind Bank: NW. extreme
Serranilla Bank: Beacon Cay
Serrana Bank: Little Cay
Quita Sueno Bank: S. extreme of reef...
Spit at NW. end...,
Roncador Cay: S. pt
Old Providence: Isabel House ,
St. Andrews Island : SW. cove, Entrance I
Courtown Cays: Middle Cay
Albuquerque Bank: Smith Cay ,
Brangmans Bluff: Extreme ,
Pearl Cays : Colombilla Cay ,
Pearl Cays Lagoon: Mosquito Pt ;
Oookra Hill: Summit
Blueflelds: Schooner Pt ,
Little Corn Island : Gun Pt
Great Cornlsland: WellsN. of Quin Bluff
Grey to wn : Light-house :
Mount Cartago: Peak, 11,100 feet.
Port Limon: Grape Cay light
Carreta Point: Extreme
Tirby Point: Extreme
Columbus Island : Lime Pt
Blanco Peak: Summit, 11,740 feet
Shepherd Island: Hut on summit
Cobbler Rock: Center
Valiente Peak: Summit, 722 feet
Escudo de Veragua: W. pt. of island...
Lit. X.
15 53 00
16 00 00
15 51 50
15 48 50
15 23 40
15 00 00
16 03 30
15 52 00
15 51 00
15 08 50
15 07 00
14 21 12
16 54 00
15 47 45
14 21 33
14 08 00
14 30 00
13 34 30
13 22 .54
12 31 40
12 24 00
12 10 00
14 03 00
12 22 35
12 20 39
12 15 30
11 .59 00
12 17 30
12 09 17
10 56 15
1
10 01 30 i
10 00 05
9 38 30
9 25 45
9 24 47
9 16 .30
9 14 22
9 14 30
9 10 30
9 06 30
Long. W.
Lull
Int.
Range.
H. W.
L.W.
Spg.
Neap.
o / //
85 27 10
h. m.
h. vi.
ft-
ft.
85 03 00
84 38 33
84 17 10
83 42 36
83 10 00
83 08 20
10 20
4 07
2.0
1.1
82 23 27
82 18 07
82 42 08
82 20 00
82 45 57
80 51 27
79 50 53
80 15 20
81 08 21
4 00
4 00
10 13
10 13
2.0
2.0
1.1
1.1
81 07 21
80 05 05
81 21 26
81 43 06
4 00
10 13
1.0
0.5
81 27 53
81 49 54
83 21 27
83 23 10
83 37 12
1 50
8 03
2.0
1.1
83 45 57
83 41 57
82 58 35
1 40
7 52
2.0
1.1
S3 03 35
83 42 15
83 47 27
1 35
1 00
7 47
7 13
2.0
1.5
1.1
0.8
83 02.00
82 39 06
1 00
7 13
1.6
6.9
82 21 47
1
82 20 31
1
'■
83 03 27
1
82 20 33
82 07 51
81 55 02
81 33 57
WEST COAST OF NORTH AMERICA.
Point Barrow: Highest lat. of U. S
Icy Cape: Extreme
Cape LisVjurne : 849 feet
Cape Krusenstern : Extreme*
Chamisso Island: Summit ,
Cape Espenberg: Extreme
Diomede Island : fairway Rock . . .
Cape Prince of Wales: W. pt ,
Port Clarence: Point Spencer
King Island: N. pt
Cape Nome: Extreme
St. Michael: Fort ,
Stuart Island: W. pt
Cape Romanzof : Extreme ,
St. Lawrence Island : E. pt
NW.pt
St. Matthew Island: SE. pt
Pinnacle Islet: Summit, 930 feet..
Kuuivak Island: Cape Etolin
Hagenmeister Island
71 23 30
156 27 00
70 16 00
161 47 30
68 52 00
166 06 00
67 09 00
163 34 00
66 14 30
161 45 00
66 32 00
163 36 00
65 35 30
168 40 00
65 33 30
168 00 00
65 16 40
166 46 30
65 00 00
168 02 00
64 26 00
165 05 00
63 26 00
162 02 30
63 34 30
162 42 ,30
61 40 00
166 15 00
63 16 00
168 41 00
63 50 00
171 31 00
60 18 00
172 02 00
60 13 00
172 36 00
60 25 22
166 08 .30
.58 48 31
160 50 00
11 41 : 5 33 0. 6 ! 0. 2
1
7 45 1 1 50
2.0 1 0.6
1
6 10 ! 1 10
1.1 0.9
[2 05] [8 25]
:8 05] i [1 2o;
[2.]]-
:4.5]i
4 40 I 11
3.1
L6
APPENDIX IV.
MARITIME POSITIONS AXD TIDAL DATA.
"WEST COAST OF NORTH AMERICA— Continued.
[Page 199
Place.
s
5
3
m
3
s
«
5
i
5
Cape Menchikof : Extreme
Port MoUer
St. George Island: S. side
Attn Island : Chichagof Harbor
Kiska Island : Kiska Harbor, Ast. sta . . .
Amchitka Island: Constantine Harbor..
Adakli Island : Bay of Islands
Atka Island: Nazan Bay (church)
Pribilof Island: St. Paul I., village
Unalaska Island: C. S. station, Iliuliuk .
Sannakh Reefs: S. edge "
Sannakh Island : NE. end
Unga Island
Popof Island : Humboldt I
Nagai Island : Sanborn Harbor
Koniushi Island : N W. harbor
NE. harbor
Simeonof Island: Simeonof Harbor
Lat. X.
Cape Strogonof : P^xtreme
Chignik Bay : Anchorage
Anowik Island: S. end
Chiachi Islands
Light-House Rocks
Chirikof Island
Kodiak Island, St. Paul Harbor: Cove
NW. of village
Port Patches
Middleton Island
Mount St. Elias: Sununit
Yakutat Bay : Port Mulgra ve
Lituya Bay
Sitka: Middle of parade ground.
Juneau
Wrangell: Ast. station
57 30 24
55 54 59
56 34 23
52 56 01
51 59 04
51 23 39
51 49 18
52 10 36
57 07 19
53 52 54
54 13 30
.54 26 12
55 20 45
55 19 17
55 07 36
55 03 17
54 58 25
54 .55 30
North Island: N. pt
Cape Knox: Extreme
Port Kuper: Sansum I
Forsyth Point: Extreme
St. James Cape: S. extreme
Cumshewa Harbor: N. side of entrance
Skidegate Bay: Rock on bar
Rose Spit Point: Extreme
Mafisett Harlwr: Uttewas village
Cape Edensha w : Extreme
Hecate Bay: Observatory Islet
Stamp Harlx)r: Observatory Islet
Island Harbor: Observatory Islet...
Cape Beale: Light-house
Refuge Cove: Village on W. side
Hesquiat Harbor: Boat Cove
Estevan Point: S. extreme
Nootka Sound : Friendly Cove
Port Langford : Colwood Islet
Esperanza Inlet: Observatory Rock.
Kyuquot Sound : Shingle Point
Nasparti Inlet: Head Beach
Cook Cape: Solander I
North Harbor: ObservatorvRock...
.56 48 00
56 19 20
.56 05 13
55 51 58
55 45 24
55 48 22
57 47 57
60 20 43
59 27 22
60 20 45
.59 33 42
58 36 57
57 02 52
58 18 00
56 27 00
54 15 00
54 10 30
52 56 31
52 09 07
51 .54 00
53 02 00
53 22 20
.54 13 00
54 01 40
54 04 30
49 15 22
49 13 46
48 54 41
48 47 23
49 20 50
49 27 31
49 22 07
49 35 31
49 47 20
49 52 45
49 59 55
50 11 21
50 06 31
50 29 25
Long. W.
157 58 30
160 34 54
169 39 50
Long. E.
173 12 24
177 30 00
179 12 06
Long. W.
176 52 00
174 15 18
170 17 52
166 31 44
162 38 00
162 18 00
160 38 39
160 31 14
159 56 06
159 23 05
1.59 22 18
159 15 03
158 46 00
158 24 24
1.56 39 19
1.59 05 24
157 27 04
155 42 51
152 21 21
146 37 38
146 18 45
141 00 12
139 46 16
137 40 06
135 19 31
134 24 00
132 23 00
132
132
132
131
131
131
131
131
132
132
56 20
57 50
09 06
03 20
01 26
31 00
51 00
34 00
10 OO
20 .56
125 55 43
124 .50 07
125 16 54
125 13 14
126 16 06
126 24 .53
126 31 58
126 36 58
126 56 31
126 59 21
127 08 56
127 37 24
127 56 46
128 03 05
Lun. Int.
H. W.
h. m.
3 35
3 30
3 25
4 17
3 50
12 13
2 40
L. w.
Range.
Spg.
9 48
9 43
ft-
9 38 5.
10 29
9 58
6 10
2 20
1 45
16
50
34
06
45
30
12 15
45
12 20
"i2'G5'
12 05
11 55
11 50
11 47
2.7
2.9
5.7
55 8.2
8 33 7. 5
58 8. 1
6 24
7 05
6 41
6 17
6 56
6 39
00 6 12 11.5
9.0
10.1
9.5
9.9
18.6
17.7
07 I 6 19 12. 8
6 08
7 20
6 15
'5'56
5 55
5 45
5 38
5 34
10.0
12.4
9.9
Ib'.s
9.8
9.7
9.3
9.3
Neap.
ft-
2.9
2.7
2.6
1.4
1.5
28
4.1
3.8
4.0
4.5
5.1
5.0
5.2
9.7
9.2
6.1
6.7
5.8
7.1
5.7
*5.'9
5.5
5.3
5.3
Page 200J APPENDIX IV.
MARITIME POSITIONS AXP TIDAL DATA.
WEST COAST OF NOBTH ABIEBICA— Continued.
Place.
Koprino Harbor: Observatory Rock
Hecate Cove: Kitten Islet
Triangle Island: W. side
Cape Scott: Summit -
Bull Harbor, Hope Island :N.pt. Indian I.
Port Alexander: Islet in center
Beaver Harbor: Shell Islet
Cormorant I. : Yellow Bluff in Alert Bay.
Baynes Sound: Beak Pt
Nanoose Harbor: Entrance Rock
Nanaimo: Light-house
Benson's House
Victoria: Light-house
Esquimalt: Fisgard I. light
Race Island : Light-house
Sooke Inlet : Secretary I
Port San Juan : Pinnacle Rock ^
Port Harvey: Tide Pole Islet
Port Neville : Robber's Nob
Knox Bay, Thurlow Island: Stream at
head of bav
Valdes Island: S. pt
Howe Sound : Plumper Cove
Atkinson Point: Light-house
Vancouver, Burrard Inlet: Govt. Re-
serve, English Bay
Eraser River: Garry Pt
New Westminster: Military barracks...
Point Roberts: Parallel station
Semiamoo Bay: Parallel station. . . .
Admiralty Head: Light-house
Steilacoom: Methodist Church
Seattle: C. S. ast. station
Port Townsend: C. S. ast. station
Smith Island : Light-house
New Dungeness: Light-house
Port Angeles: Ediz Hook light-house . .
Cape Flattery: Light-house
Cape Shoal water: Light-house
Cape Disappointment : Light-house
Kalama: Methodist Church
Bremerton: Navy-yard flagstaff
Tacoma: St. Luke Church
Astoria: Flagstaff
Yaquina Head : Light-house
Cape -i^rago, or Gregory: Light-house . .
Cape Blanco: Light-house
Crescert City : Light-house
Trinidad Head: Light-house
Eureka: Methodist Church
Humboldt: Light-house
Cape Mendocino : Light-house
Pomt Arena: Light-house
Point Reyes: Light-house
San Francisco: Coast Survey ast. station
Presidio station
Mare Island: Stone block, obs. station..
Benicia: Church
Farallon Islet: Light-house
Santa Clara: Catholic Church
Mount Hamilton : Obs. peak
San Jose: Spire
Pigeon Point: Light-house
L«t. X.
Long. W.
50 30 00
50 32 20
50 51 53
50 46 41
50 54 47
50 50 49
50 42 36
50 35 02
49 36 29
49 15 43
49 12 50
49 10 15
48 25 26
48 25 50
48 17 53
48 19 35 i
48 33 30
50 33 58
50 31 09
50 24 15
50 02 42
49 24 39
49 19 42
49 16 18
49 07 04
49 13 01
49 00 00
49 00 00
48 09 19
47 10 20
47 35 54
48 06 56
48 19 07
48 10 52
48 08 24
48 23 30
46 43 00
46 16 29
46 00 26
47 33 24
47 15 32
127 51 42
127 35 44
129 05 58
128 26 11
127 55 29
127 39 23
127 24 33
126 56 56
124 50 44
124 07 32
123 48 11
123 56 02
123 23 28
123 26 46
123 31 47
123 42 40
124 27 37
126 16 06
126 03 47
125 38 26
125 14 34
123 28 46
123 15 54
123 U 26
123 11 27
123 53 52
123 04 52
122 44 56
122
122
122
122
122
123
123
124
124
! 124
: 122
122
I 122
40 34
35 51
19 59
44 58
50 36
06 31
24 07
44 06
04 25
03 11
50 39
37 33
26 26
41 44 36
41 03 01
40 48 11
40 41 37
40 26 18
38 57 12
37 59 39
37 47 55
37 47 30
38 05 53
38 03 05
37 41 51
37 20 49
37 21 03
37 19 58
37 10 49
Llm. Int.
H.W.
li. m.
46 11 19 , 123 49 42
44 40 35 ! 124 04 40
43 20 36 124 22 31
42 50 22 1 124 33 30
124 12 10
124 09 03
124 09 41
124 16 26
124 24 25
123 44 27
123 01 24
122 24 32
122 27 49
122 16 24
122 09 23
123 00 07
121 56 26
121 36 40
121 53 39
122 23 39
1
10
32
.0 30
55
4 45
4 52
4 40
[2 17]
[2 00]
1 55
2 30
3 40
4 45
5 38
5 20
5 28
5 11
4 59
4 46
4 22
3 47
3 40
2 42
2 10
08
12 22
3 39
4 27
4 32
15
11 50
11 55
11 33
11 27
11 57
11 33
11 00
10 36
11 23
12 07
11 43
1 05
1 35
10 40
L. W.
h. 111.
6 22
6 44
6 42
7 08
11 00
11 18
11 05
[8 31]
[8 14]
8 10
8 47
10 00
10 15
11 58
11 35
12 01
11 23
11 10
11 04
10 33
9 32
9 28
8 34
8 23
6 16
6 19
11 25
10 35
10 45
6 42
5 37-
5 49
15
11
45
19
50
21
08
34
07
7 15
7 48
4 25
Range.
Spg. Neap.
10.7
11.6
11.5
12.8
10.6
10.2
9.8
[5.7],
[5.8]
14.1
16.0
15.7
7.2
9.0
7.8
8.2
7.0
7.1
11.0
9.2
6.2
5.6
5.0
5.3
7.1
7.7
3.2
9.4
9.8
7.8
7.3
6.0
5.8
5.7
5.7
5.3
4.7
4.1
5.1
5.1
4.6
5.6
5.6
4.5
APPENDIX IV.
:n[aritime positions and tidal data.
WEST COAST OF NORTH AMERICA— Continued.
[Page 201
Place.
Lat. N.
Umg. W.
Lun. Int.
H. W.
L. W.
Range.
Spg. Neap.
u
e
Santa Cniz: Warehouse flagstaff
Monterey : C. S. azimuth station
Point Pines: Light-house
Piedras Blancas: Light-house
Point Conception: Light-house
Santa Barbara: N. tower, Mission Church
San Buenaventura: C. S. ast. station
Pt. Fermin, San Pedro Bay: Light-house.
Los Angeles: Court-house
Point Lonia : Light-h(jnse
San Diego: C. S. ast. station
Mexican Boundary: Obelisk
San Miguel Island : Seal Pt
Santa Rosa Island: E. pt.
Santa Cruz Island : NE. pt
Anacapa Island: E. pt
Santa Barbara Island: Summit
San Nicolas Island: Summit
Santa Catalina Island : Catalina Peak . . .
Ensenada Harbor: Head of bay, close to
beach
San Tonias: N\V. shore of cove
Colnett Bay: Head of bav
San Martin Island : Ha^sler Cove
Port San Quentin: Sextant Pt
San Geroninio Island: Bight at E. end . .
Canoas Point: High bluff
Guadeloupe: North pt
La Playa Maria: Mound on W. side
Santa Rosalia Bay: t>bs. spot, Cairn
Lagoon Head: Highest pt. of crater
Cerros Island: SE. extremity
San Benito Island: Summit of W. island.
San Bartolome: X. side of entrance
Asuncion Island: Summit of island
San Ignacio Point: Kxtreme
Abreojos Point: Extreme of rocky ledge.
San Domingo Point: E<Ige of cliff
San Juanico Point: Knoll
Alijos Rocks: South Rock
Cape San J./azaro: Extreme
Magdalena Bay: Obs. spot (post) N. of
Port Magdalena
Cape Tosco: Extreme
El Conejo Point : Extreme
Todos Santos: Foot of hill, Lobos Pt
San Lucas: Steep sand beach, NW. pt.
of liay
San .Jose del Cabo: NE. side of entrance.
Arena Point : Extreme
Arena de la Ventana: Extreme
Pichilinque Bay: SE. pt. of San Juan,
Neponiezeino I
La Paz: Obs. spot. El Mogote
Lupona Point: Extreme
San Evaristo: 3 m. S. of S. Evaristo Hd.
San Marcial Point : Extreme
Salinas Bay: Beach, NE. pt. of bay
Loreto: Cathedral
Pulpito Point: Summit
Muleje: E(|uipalito Pt
San Marcos Island: S. sand spit
Santa Maria Cove: Beach on NW. shore.
San Carlos Point: Extreme
Santa Teresa Bay: Beach on N. side
36 57 31
36 35 21
36 37 55
35 ,39 50
34 26 49
34 26 10
34 15 46
33 42 14
34 03 05
32 39 48
32 43 06
32 31 58
34 04 19
33 56 30
34 03 12
34 00 25
33 28 16
33 14 55
33 23 09
31 51 10
31 33 04
30 57 39
30 28 58
30 22 16
29 47 20
29 25 29
29 10 50
28 56 06
28 40 16
28 14 26
28 03 52
28 18 08
27 39 35
27 06 10
26 45 45
26 42 49
26 18 56
26 03 18
24 58 00
24 47 31
122 01 29
121 52 59
121 56 02
121 17 06
120 28 18
119 42 42
119 15 56
118 17 41
118 14 32
117 14 37
117 09 41
117 07 32
120 21 55
119 58 29
119 33 51
119 23 04
119 02 29
119 31 19
118 24 05
116 38 05
116 40 51
116 17 28
116 06 46
115 59 07
115 48 12
115 12 14
118 18 30
114 31 06
114 14 15
114 06 21
115 11 32
115 36 10
114 54 27
114 17 25
113 16 25 !
113 35 04
112 41 44
112 17 52
115 51 54
112 18 25
24 38 23 112 08 54
24 18 12 i 111 42 54
24 20 17 111 ,30 21
23 27 14 : 110 14 07
22 53 07
23 03 35
23 32 48
24 03 52
24 15 31
24 10 10
24 24 10
24 52 03
26 29 23
25 59 37
26 (K) 41
26 ,30 44
26 53 37
27 10 21
27 26 06
28 00 07
28 25 04
109 64 .60
109 40 43
109 28 57
109 ,60 29
110
110
110
110
111
111
111
111
111
112
112
112
112
20 34
20 41
20 35
41 47
01 43
06 53
21 03
27 14
58 04
06 39
19 56
47 36
51 59
A. m.
10 54
10 43
h. m.
4 27
4 24
9 37
9 53
9 36
9 29
9 32
9 23
'929
9 20
9 28
9 28
9 27
9 23
9 15
9 05
9 00
9 00
8 29
8 25
8 36
9 40
I
3 15
3 21
3 13
3 07
3 20
3 02
's'oe
3 04
3 08
3 06
3 05
3 00
2 53
2 42
2 37
2 48
2 17
2 12
2 20
3 34
5.2
4.8
ft-
3.3
3.1
4. 8 2. 2
4.9 1 2.2
5,5 ! 2.5
5.2 ! 2.3
6.1 2.3
4.9 ' 2.2
"4.'9':"'2.'2
I
4.9
6.1
5.0
7.6
7.8
'8.'2'
6.7
'5."7'
5.5
4.5
5.4
2.2
2.3
2.2
6. 8 2. 6
•i.'i) |"'2."2
3.4
3.6
"2." 8
11 ,60 : 6 47
11.2
2.3
'i.'e
1.5
1.2
1.3
2.6
Page 202] APPENDIX IV.
MARITIME POSITIONS AXD TIDAL DATA.
WEST COAST OF NOBTH AMEBIOA— Continued.
«
«
Place.
Las Animas: Low pt
Kaza Island: Landing place, S. side.
Angeles Bay: Bight on NW. shore..
Remedies Bay: Beach on W. sliore .
Mejia Island : S. side
San Luis Island : SE. side
San Firmin: Beach, N. of l)ight
San Felipe Point: Peak, 1,000 feet . .
Philips Point: Beacon
Georges Island: NE. shore
Cape Tepoca: Hill, 300 feet
Libertad Anchorage : Beach
Patos Island : SE. end
Tiburon Island: SE. end
Kino Point: 0.2 mile N. 88° W. of mound.
San Pedro: N. side of bay
(iuaymas: Light-house
Claris Island : NW. part
Santa Barbara: NW. side of bay
Agiabampo: SE. side of entrance
Topolobampo : SE. end of Santa Maria I . .
Navachista: W. side of creek
Playa Colorado: N. side of entrance
Altata: N. side of entrance
Mazatlan : Light-house
Palenita Village: Boca Tecapan
San Bias: Custom-house
Maria Mad re Island: SE. extreme
Mita Point: Extreme
Peiias Anchorage: Mouth of Rio Real . . .
Cape Corrientes : Extreme
Perula Bay: Smooth Rock
San Benedicto Island: S. extreme
Socorro Island : SE. part
Roca Partida: Summit
Clarion Island : S. end
Clipperton Island: Summit
Navidad Bay: W. end of sandy beach...
ManzanillaBay: Flagstaff, L^ S.consulate
Sacatula River: Beach, W. side of bay...
Isla Grande: Tripod on NW. summit ..
Sihuatanejo Point : Tree on beach
Morro Petatlan: Junction of stony and
sandy beaches
Tequepa Harbor: Limekiln
Acapulco: Light-house
Maldonado: El Recordo Pt ,
Port Angeles: Light-house ,
Sacrificios Point: Highest pt. of cape
Port Guatulco: Cross ,
Morro Ayuca : Summit of N. edge of cape
Salina Cruz : Light-house
I-at. N.
Champerico: Inshore end of iron wharf.
San Jos6 de Guatemala: Light-house
Acajutla: Light-house
Libertad : Light-hpuse
La Union : Light-nouse
Chicarene Point: Extreme
Corinto: Light-house
San Juan del Sur: Signal station
Salinas Bay: Salinas Islet
Port Culebra: Extremity of Mala Pt
Ballena Bay: N. Estero Toussa
Parida Anchorage: S. pt. of Deer Id
Port Nuevo: Entrada Pt
Bahia Honda: W. end of Centinela I. . .
Coiba (Quibo) Island: Observation pt. .
28 47 40
28 49 11
28 56 39
29 13 52
29 33 08
29 57 27
30 25 16
31 02 57
31 46 10
31 00 54
30 16 05
29 54 12
29 16 12
28 45 55
28 45 28
28 03 22
27 50 28
26 58 59
26 41 09
26 16 35
25 33 56
25 23 06
25 11 42
24 38 52
23 10 40
22 30 26
21 32 30
21 30 45
20 45 50
20 36 26
20 25 00
19 34 48
19 17 15
18 42 57
18 59 41
18 20 55
10 17 00
19 13 25
19 03 15
17 58 21
17 40 15
17 37 50
17 31 28
17 16 13
16 49 10
16 19 37
15 39 09
15 40 41
15 44 58
15 52 17
16 09 49
14 17 44
13 55 15
13 .34 20
13 28 49
13 20 00
13 17 09
12 27 54
11 14 45
11 03 10
10 36 46
9 43 45
8 10 13
8 04 30
7 43 32
7 24 20
Loilg, W.
113 12 48
113 00 05
113 34 35
113 40 00
113 35 19
114 25 49
114 39 47
114 52 10
114 43 31
113 16 .30
112 53 26
112 45 04
112 28 51
112 21 46
111 58 37
111 16 00
no .54 28
109 57 17
109 40 48
109 17 30
109 10 23
108 49 00
108 23 37
107 59 37
106 26 47
105 44 25
105 18 40
106 33 14
105 ,33 37
105 16 00
105 39 21
105 08 54
110 49 22
110 56 53
112 04 07
114 44 17
109 13 00
104 43 26
104 19 50
102 07 06
101 40 25
101 33 23
101 27 14
101 04 32
99 55 50
98 35 05
96 30 43
96 15 04
96 08 10
95 46 43
95 12 31
91 55 .36
90 49 45
89 50 26
89 19 25
87 51 00
87 47 06
87 12 31
85 52 59
85 43 38
85 42 46
85 00 46
82 14 32
81 43 30
81 31 58
81 41 51
Range.
H.W.
h. m.
L.W.
Spg.
h, m.
ft.
11 30
10 07
9 08
9 08
9 07
9 07
50
2 50
2 50
2 55
3 05
3 15
2 no
3 00
2 50
2 45
3 15
3 10
5 26 1 5.0 1.2
3 59
2 51
5.8
3.8
2 52 I 3.2
2 53 I 2. 5
2 54 i 1.9
2 38 ! 2.
9 02
9 02
9 08
9 18
9 28
8.5
9.0
9.5
10.0
10.5
9 08
9 12
9 02
8 58
10.5
10.0
9.5
9.0
9 28
10. 5 5. 7
9 22
11.0
APPENDIX IV.
:maritime positions and tidal
west coast of north america—
DATA.
Continued.
[Page 203
"x
Place.
JUt. N.
Long. W.
Lun
Int.
Range.
H. W.
L. W.
Spg.
Neap.
i
u
5
Cocos Island: Head of Chatham Bay
Panama: NE. bastion, ast. station .".
TaVjoga Island : Church
o / //
5 32 57
8 57 12
8 47 45
7 27 40
4 03 00
o / //
86 59 17
79 32 05
79 33 16
79 59 25
81 36 00
/(. VI.
!t. in.
ft.
/'•
3 00
3 00
3 10
9 14
9 13
9 22
j 16.0
' 15.4
! 13.0
8.7
8.3
7.0
Alalpelo Island : Summit
"
1
WEST INDIA ISLANDS.
i
S
s
7
m
a
S
a
i
s
Memorv Rock : Center
26 56 53
79 06 54
79 (X) 38
77 10 45
76 57 36
78 23 48
79 06 00
79 18 26
78 06 02
77 34 26
75 44 39
75 10 34
75 45 17
75 28 20
75 51 41
74 51 .54
75 46 24
74 59 00
76 13 00
76 51 48
77 21 58
77 46 45
77 53 55
77 57 06
75 26 00
75 07 27
74 28 20
74 50 08
74 20 37
74 22 ,54
74 20 21
74 22 48
73 49 15
73 38 03
72 47 03
73 .50 29
73 40 17
73 42 33
72 28 18
72 12 51
72 07 14
71 31 12
71 07 29
70 29 .54
69 21 24
68 47 24
74 09 41
74 29 34
74 53 44
75 33 18
75 36 59
75 47 18
75 47 40
75 52 18
76 07 48
76 35 34
7 40
1 28
3.2
1.7
*
Bahama Island; \V. pt
26 41 18
25 51 30
26 31 10
27 15 42
26 02 00
25 34 30
22 45 10
22 22 30
21 42 00
22 01 15
22 14 02
22 20 44
22 31 15
22 51 00
23 32 15
23 €6 (X)
25 (K) 00
25 31 20
25 05 37
24 43 45
25 49 40
25 49 12
24 06 15
23 50 50
23 56 40
23 37 45
22 06 40
22 32 40
22 47 30
22 51 00
23 05 30
22 34 38
22 16 .30
21 40 30
20 56 00
21 30 40
21 37 30
21 30 00
21 .54 00
21 29 33
21 30 55
21 06 30
20 35 00
20 02 00
20 15 10
20 21 40
20 41 41
20 47 14
21 04 24
21 09 00
21 07 00
21 07 .30
21 07 05
21 18 30
Abaco Island: Light-house
Little tjuana Cav : Light-house
Walker Cav: Highest part
Great Isaac Cav: Light-house
Gun Cay: Light-house
8 20
2 08
3.0
1.5
Ginger Cay : Center
Cay Lobos: Light-house
St. Domingo Cav : Center
'
Cav Verde: Hill at S. end
Ragged Island: (lun Pt
... J
Xairn Cay: E. pt
Nurse ( ^hannel Cav : Beacon
1
1
Long Island: S. pf
1
( ireat Emma Island : Beacon
Clarence Harbor: Light-house
Eleuthera Island : Light-house
\<i )y al Island : Eastern Pass
Nassau : Light-house
8 20
7 00
2 08
48
4.1
4.0
2.1
2.1
7 20
7 40
1 08
1 28
4.0
3.0
2.1
1.5
Andros Island: Light-house
Great Stirrup Cay: Light-house
Little Stirrup Cay: W. end
San Salvador (Cat I.): Light-house
Concepcion Island: W. bay
Watlings Island: Ilunchinbroke Rock ..
Rum Cay : Harbor Pt
7 00
48
4.0
2.1
1
1
Castle Island: Light-house
:::::;::
""T. ""I
Fortune Island : S.end
'
Crooked Island: Mossflag.«taff..
Bird Island: Light-house
Samana Cav : \\ . pt
:::::::::::::;::;:::::;::::: i
Plana Cav :' N \V. pt
i 1
Mariguana Island : SE. pt
Hogstv Reef: N\V. Cay
7 20
1 08
3.0
1.5
Inagua Island : Light-house
7 50
1 38
3.5
L8
Little Inagua Island: N\V. pt
AV. Caicos Cav: Hill, SE. end
::;::::::::::::::::::::: i
French Cay : W. pt
1
i
Fort George Cay: Old magazine
Caicos Island: Parsons Pt., S. islet
Turk Island : Light-house
i
1
!
1
7 30
1 18
3.0
1.5
Square Handkerchief Bank: NE. breaker
Silver Bank: E. extreme
Navidad Bank : Center of E. side
Cape Maysi : Light-house
5 40
11 53
2.8
1.6
Port Baracoa : Light-house
Port Cavo Moa: Carenero Pt
Port Nipe: Roma Pt
Lucrecia Point: Light-house
Port Sama: E. side of entrance
Peak of Sama: Summit, 885 feet
Port Naranjo: E. side of entrance
.libara: Fort San Fernando
6 20
08
2.4
L4
Port Padre: Guinehos Pt
Port Nuevitas: Light-house
21 38 54 77 05 3-> 1
7 00
48
2.2
1.2
'
Page 204]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST INDIA ISLANDS— Continued.
Place.
Maternillos Point: Light-house
Cay Verde: NW. end
Cay Confltes: S. pt
Paredon Grande Cay: Light-hout-o.
Cay Sal: Light-house
Bahia de Cadiz Cay: Light-house..
Piedras Cay : Light-house
Matanzas; Summit of peak
Habana: Morro hght-house
Transit pier, arsenal yard
Cape San Antonio: Light-house ...
San Felipe C3,ys: SW. pt
Isle of Pines : Port Frances
Piedras Cay: Light-house
Cienfuegos: Colorados Pt. light
Cape Cruz : Light-house
Santiago de Cuba: Light-house
Port Guantanamo: Fisherman Pt . .
Cayman Brae: E. pt
Little Cayman: W. pt
Grand Cayman: Fort George, W. end.
Morant Point: Light-house
Port Antonio: Folly Pt. Light
Port Maria: NW. wharf.
St. Ann Bay: Long wharf
Falmouth : Fort
Montego Bay : Fort
St. Lucia: Fort
Savanna-la-Mar: Fort
Kingston : Plum Pt. light
Port Royal : Fort Charles, flagstaff
Morant Cavs: NE. Cay
Pedro Bank: Portland Rock, E. end...
Baxo Nuevo: Sandy Cay
Lat. K.
Samana Town: Fort
Cape Cabron : Extreme
Port Plata: Light-house
Grange Point: W. end
Manzanilla Point: Presidente Pt
Cape Haitien : Town fountain
Port Paix: Wharf
Nicolas Mole: Fort Ge<^)rge, flagstaff
Gonaives: Verreur Pt
Gonave Island: W. pt
Arcadius Islands: Light-house
Port an Prince: F"ort Islet light
Petite Riviere Village: Sand beach in
front of huts
Jeremie: Fort
Navassa Island: N. extreme
Fonnigas Bank : Shoal spot
Vache'Island: Sand beach, near NW. j)t
Jacmel : Wharf
Beata Island: NW. pt
Frayle Rock: Center
Alta Vela: Summit
A varena Point: Extreme
Salinas Point (Caldera) : Extreme
St. Domingo City: Light-house
Point Espada: Extreme
40 02
08 45
U 14
29 10
56 30
12 84
14 10
01 54
09 21
08 03
51 44
55 00
85 80
57 45
01 58
50 13
57 31
54 39
19 45 15
19 39 10
19 17 45
17 55
18 11
18 28
18 26
18 30
18 29
18 27
18 12
17 55
17 55
17 26
17 06
15 53
19 12
19 21
19 48
19 54
19 45
19 46
19 57
19 49
19 25
18 55
18 48
18 38
18 87
18 38
18 25
18 83
18 06
18 13
17 36
17 37
17 28
18 07
18 12
18 27
18 19
05
31
00
24
34
25
45
20
32
56
30
20
00
29
17
51
45
34
20
40
15
42
26
13
54
15
15
10
M
00
30
45
00
50
00
00
54
48
Lun. Int.
Long. W.
Range.
79 46 07
80 07 17
81 23 17
11 08
26 31
54 22
12 52
39 52
56 16
10 52
08 54
46 45
50 38
58 20
26 28
39 04
19 23
16 00
41 27
39 03
47 20
U 42
49 45
23 07
42 52
18 84
39 05
22 01
28 55
05 54
02 03
44 24
43 40
34 30
33 44
41 00
39 11
59 18
35 18
52 59
27 34
H. W.
h. VI.
20
8 30
8 18
8 30
4 47
8 20
: 50
L. W.
h. VI.
I 08
2 18
1 56
2 18
11 00
2 30
2 00
9 00
Spg. j Neap.
ft.
2.8
2.2
1.3
1.5
2.0
2.2
2.6
[1.3]
[LI]
[1.2]
[1.1]
2 48 3.
6 50 39 I 5. 5
[1.2]
[2.5]
[2. 2]
/'•
1.6
o.;
0.9
1.1
i'i
1.3
1.5
2.9
APPENDIX IV.
MARITIME POSITK^XS AND TIDAL DATA.
WEST INDIA ISLANDS— Continued.
[Page 205
1
Placs.
Lat. X.
Long. W.
Lun.
Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
s
t
Mona Tflland • Ijicht-housp
o / It
18 02 43
18 11 56
18 25 09
18 28 56
18 23 05
17 57 10
18 18 44
18 05 20
18 20 23
18 18 08
18 25 04
18 30 39
18 45 11
18 36 30
17 45 09
18 35 37
18 16 42
18 13 06
18 04 07
17 53 .58
17 39 10
17 29 10
17 18 12
17 13 38
17 07 52
17 35 50
17 00 00
17 06 54
16 55 18
16 42 12
15 59 50
16 25 09
16 11 57
16 13 14
16 13 56
16 19 56
16 10 17
15 52 59
15 51 32
15 34 34
15 17 27
15 42 00
14 35 44
14 43 54
14 46 13
14 23 23
O f ft
67 50 30
67 09 04
67 16 08
66 07 28
65 36 31
66 54 11
65 13 34
65 25 26
64 55 52
64 42 03
64 36 47
64 21 48
64 24 58
64 10 45
64 42 16
63 28 13
63 16 00
(!3 04 39
6:5 05 45
62 51 30
63 15 16
62 59 09
62 43 14
62 35 25
62 37 29
61 49 54
61 46 07
61 55 11
62 19 10
02 13 24
61 44 09
61 32 15
61 29 40
61 32 05
61 33 15
61 00 44
61 06 45
61 19 15
61 35 55
61 28 14
61 23 52
03 37 46
61 04 30
61 11 12
60 53 20
60 52 33
A. m.
h. in.
fl-
ft-
Mayaguez: Mouth of Mayaguez K
7 04
2 00
2.0
1.0
San Juan de Porto Rico: ^Morro liglit-
8 21
2 20
1.3
0.9
Oanp San .Tuan* Liffht-house
[1.0]
[1.0]
[1.1]
[L2]
Culebi'ita Island; Lieht-hous*^ ...
[7 31]
[7 35]
[7 11]
[1 30]
[1 4o;
[0 58]
Vieques (Crab) Island: Port Ferro light.
St. Thomas: Fort Christian, SW. bastion.
St John Island" Raiu Hea4.1
Tortola: Fort Burt
Virsfin ( lorda : Vixen Pt .........
Christians! ed, Santa Cruz: S\V. bastion
Sombrero: Light-Iiouse
St. Martin : Fort Marigot light
[1.5]
Saba: Diamond Kock
St. Christopher; Basseterre Church
Booby Island: Center
Nevis: Fort Charles . . ..'
Barbuda: Flagstaff, Martello Tower
Antigua, English Harlwr: Flagstaff,
dockyard
[2.0]
Sandy Island: Light-house
Redonda Islet : Center
^lontserrat: Plymouth Wharf
Guadeloupe, Basseterre: Light on mast..
Port Louis: IJght on mast .
Cozier Islet: Light-house..
Manroux Id. : Light-house .
Point a Pitre: Jarry Mill. . .
Desirade: E. pt
[1.3]
Petite Terre: Light-hf)use
jNIarie (ialante: Light-house
Saintes Islands: Tower on Chameauhill.
Dominica, Prince Ruperts Bay: Sand
beach W. of church
Roseau: Flagstaff, Fort Young.
Aves Island : Center ". .
Martinique, Fort de France: Fort St.
Louis light
4 00
10 12
1.5
"■"*'"
0.8
St. Pierre:' Ste. Marthe Bat-
Caravel le Pen. : Light-hou.se-
Cabrit Islet: Summit
St. Lucia, Port Castries: Light-house
Barbados, Bridgetown: Flagstaff, Rick-
ett's Battery
S. Point: Light-house
Ragged Point: Light-house ..
St. Vincent, Kingstown: Liaht-house . . .
Bequia Island, Admiralty Bay: Church .
Grenada: St. Cieorge light-house
Tot>agc 1, Rocky Bay : Light-houije
3 50
10 02
1.1
• 0.6
14 01 54 ' 61 00 48
13 05 42
13 02 45
13 09 40
13 09 19
13 00 25
12 03 02
11 10 08
59 37 19
59 31 50
59 26 04
61 14 34
61 14 09
61 45 06
60 42 38
2 50
9 02
3.0
1.5
1
;:;::;:;:;: i
2 50
9 05
1.6
0.8
2 30
3 50
8 42
10 02
1.5
2.1
0.8
.1.1
Page 206]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
"WEST INDIA ISLANDS— Continued.
Place.
Testigos Islets : Center of Testigo Grande .
Sola Island : Center
Panipatar, Margarital. : San Carlos Ca.stle.
Tortugas Islanfl: S. end of W. Tortugillo
Islet
Orchila Island : S. side
Roques Islands: Pirate Cay
Bonaive Island : Light-house
Little Cura(,>ao Island: Light-house
Curasao Island ; Fort Nassau
Light-house
Oruba Island: Light-house
lAt. N.
o / n
11 25 02
11 19 00
10 59 43
10 57 45
11 47 57
11 5(5 16
12 02 00
u .59 ao
12 06 59
12 06 17
12 31 05
Ix)ng. W.
63 05 48
63 36 00
63 48 00
65 26 38
66 12 31
66 39 10
68 14 10
68 39 19
68 55 50
68 56 16
70 02 34
Lun. Int.
Range.
H. W.
L. W.
Neap.
NORTH AND EAST COASTS OF SOUTH AMERICA.
Chagres: San Lorenzo Castle
Toro Point: Light-house
Colon: Light-house
Porto Bello: Ft. St. Geroninio
Caledonia Harhor: Scorpion Cay
Carreto Port: Peak
( 'aribana Point: Extreme
Fuerte Island : N. extreme
Cispata Port : Zapote Pt
Cartagena : Light-house
Savanilla: Light-house ,
Magdalena River: NW. pt. of Gomez I. .
Santa .Marta: Light-house
Rio de la Hacha: Light on church
Cape La Vela: Sand beach inside cape .
Bahia Honda: E. pt., S. side
Espada Point : Extreme
Maracaibo: Zapara I. light
Estangues Point: 500 ft. from extreme ..
Cape San Roman : Extreme
Marjes Islets: N. islet
Vela de Coro : Light-house
Tucacas Island : Ore house
St. Juan Bay: Cay
Puerto ('aliello: Light-house
La Gilaira: Light-house
Cape Codera: Morro
Corsarios Bay: W. pt
Centinela Islet: Center
Barcelona: Morro
Cumana: Light-house
Escarseo Point: Extreme
Chacopata: Morro
Esmeralda Islet: Center
Carupano : Light-house
Pt. Herman Vasquez
Puerto Santo Bay: Sand spit S. of Morro.
Tres Puntas Cape : Extreme
UnareBay: Obs. spot, 200 yds. S. of Morro
Pena Point: Extreme
Pato Island: H pt ;
Mocomoco Pt. : Extreme
19 27
22 39
22 09
32 30
.54 52
47 00
37 .30
24 00
24 00
25 50
00 15
07 00
15 28
33 30
12 34
23 09
Port of Spain : King's AVharf light
Chacachacare Island: Rocks off SW. pt. .
Galera Point: NE. extreme, light-house.
Icacos Point: I>ight-house
San Fernando: Pierhead
12 04 00
10 57 30
11 48 56
12 11 00
12 29 15
11 27 56
10 47 00
11 10 00
10 29 53
10 36 57
10 35 00
10 34 06
10 49 30
10 13 30
10 27 20
10 40 00
10 42 00
10 40 00
10 40 15
10 42 00
10 43 27
10 45 00
10 44 19
10 43 48
10 38 15
8 39 25
10 38 37
10 40 03
10 50 02
10 03 29
10 16 59
00 22
57 16
54 45
39 40
42 25
38 00
52 55
10 45
48 00
32 50
57 55
49 51
14 33
54 50
09 42
45 42
71 07
71 37
70 17
70 04
70 57
69 34
68 19
68 22
68 00
66 56
66 06
66 04
66 09
64 44
64 11
64 17
63 50
63 31
63 18
63 14
63 09
62 41
62 44
61 50
61 51
60 10
61 30 38
61 45 54
60 54 10
61 55 41
61 28 12
06
11 30
5 05
6 00
6 18
1.1
0.6
5 17
1.5
0.8
11 17
2.5
1.5
12 12
2.8
4 20
10 30
3.2
1.9
APPENDIX IV. [Page 207
MARITIME POSITIONS AXD TIDAL DATA.
NOKTH AND EAST COASTS OF SOUTH AMERICA— Continued.
g
ga
Denierara: Georgetown light-house
Nickerie River: Light-house
Par.'unaribo : Stone steps
Maroni River: W. liglit-liouse
Salut Islands: Light-house
Enfant Perdu Islet: Light-house
Cayenne: Light-house
Connetable Islet : Center
Carimare Mount: Summit
Orange Cape: Extreme
Maye Mountain: Summit
No^th Cape: Extreme
Cape Magoari : Extreme
Para: Custom-liouse
Atalaia Point: Light-house
Itatolomi Point: Liglit-house
Jlaranhao Island: Landing place
Santa Anna Island : Light-house
Tutoya: Entrance
Paranahiba River: Aniar(,-ao Village
Ceara: Light-house
Jaguaribe River: Pilot station
Caivara: Village
Cape St. lloque: Extreme
Rio Grande do Norte: Light-house
Natal : Cathedral
Parahiba River: Light-house at entrance.
Parahiba: Cathedral
Olinda: Light-house
Pernainbuco: I'icao light-h<juse
Cape St. Augustine: Light^house
Tamandare : Village
Maceio: Light-house
San Francisco River: Light-house at en
trance
Cotinguiba River: Light-house at en-
trance
Vaza Harris River: Semaphore at en-
trance
Real River: Liglit-house
Conde: ' Village
Garcia d' .Vvila: Tower
Bahia: Santo Antonio light-house
Itaparica: Fort on N. pt ,
Morro de Sao Paido: Light-house
Caniamu: Village
Contas : Church
Ilheoa: Church
Oliven^'a: Center of village
Una: Center of village
Coniandatuba : Center of village
Santa Cruz : Church
Porto Seguro: Matrix Church
Prado : River entrance
Alcoba^a: Center of village
Caravellas: Center of village.,
Abrolhos Island : Light-house
Porto Alegre: Center of village
Espiritu Santo Bay: Light-house
Guarapiri Islets: E; islet
Benevente: Village
Itapeniiriin: Moscas Islet
Sao Joao da Barra: Lightrhouse
Cape St. Tl .ome : Extreme
Macahc : Fort at entrance
Lat. N.
6 49 20
5 58 30
5 49 30
.5 44 50
5 16 50
5 02 40
4 56 20
4 49 30
4 23 20
4 20 45
2 46 30
1 40 17
Lat. S.
17 00
1 26 59
35 03
2 10 n
31 48
16 22
41 55
53 20
42 05
25 35
03 15
29 15
45 05
46 41
6 56 .30
7 06 ,35
8 00 50
8 03 22
8 20 45
8 43 40
9 39 35
10 30 30
10 58 20
11 09 45
11 27 40
12 12 05
12 33 40
13 00 37
12 52 48
13 22 37
13 56 42
14 17 40
14 47 40
14 56 40
15 13 27
15 21 00
16 17 20
16 25 38
17 21 40
17 31 45
17 43 30
17 57 31
18 06' 15
20 19 23
20 38 25
20 49 00
20 57 35
21 38 40
22 02 00
22 23 45
Long. W.
58 11 30
57 00 30
55 08 48
54 00 30
52 34 53
52 21 11
52 20 26
51 55 36
51 50 36
51 27 46
50 54 46
49 56 46
48 23 30
48 30 01
47 20 .54
44 25 56
44 18 45
43 37 30
42 18 02
41 40 .35
38 28 25
37 44 .55
36 02 52
35 15 .52
35 11 55
35 12 43
34 49 30
34 53 04
34 .50 36
34 51 57
34 66 05
35 05 06
35 44 54
36 21 51
37 04 00
37 12 .36
37 24 00
37 45 46
38 02 16
38 32 06
38 41 28
38 54 38
39 07 05
39 00 45
39 03 25
39 01 45
.39 01 15
.39 16 45
39 02 05
39 04 15
39 13 15
39 12 00
39 14 36
38 41 46
.39 31 16
40 16 36
40 23 46
40 40 45
40 46 ,35
41 02 21
40 .59 00
41 47 35
Lun. Int.
H. W.
h. in.
4 18
5 50
4 27
11 50
6 50
5 35
5 05
5 25
5 50
4 05
4 33
4 20
4 17
4 10
3 50
3 50
3 35
3 25
3 10
3 15
2 50
'2"46
2 20
L. W.
h. m.
9 50
12 00
10 30
5 37
38
11 47
11 17
11 37
12 00
10 17
10 50
10 32
10 29
10 22
10 00
10 00
9 47
9 37
9 23
9 27
9 00
'8'52'
30
Range.
Spg.
Neap.
ft-
8.6
9.5
6.0
11.0
16.5
13.1
11.7
8.2
8.0
7.0
8.5
7.8
7.6
6.0
6.3
6.4
6.0
6.4
7.5
4.0
'5.'6'
9.2
ft.
3.9
4.3
2.7
5.2
7.9
6.2
5.6
3.9
3.8
4.2
3.3
4.1
.3.7
3.6
2.9
3.0
3.1
3.1
3.6
1.9
4.4
Page 208] APPENDIX IV.
MARITIME POSITIONS AND TICAL DATA.
NORTH AND EAST COASTS OF SOUTH AMERICA— Continued.
Place.
Lat. S.
Santa Anna Island : Summit
Barra Sao Joao: Vills^e
Busiest Church
Cape Frio: Light-house
Port Frio: Village
Maricas Islands: S. islet
Kio de Janeiro: Fort Villegagnon Light.
Imperial Observatory
Raza Island : Light-house
Petropolis: Center of town
Cape Guaratiba: Summit
Marambaya Island: Summit of SW. end.
Mangaratiba: Village
Palinas Bay: Beach at head of bay
Angra dos Keis: Landing-place
Ilha Grande: Light-house
Parati : Fort
I'batuba: Cathedral
Porcoa Grande Islet: Sunimit
Busios Islets: Summit
St. Sebastian Island: Boi Pt. light
Villa Nova da Princessa: Center
Santos: Moela I. light-house
Quay
Alcatrasses Island: Summit, 880 ft
Conceigao: Church
Quemada Grande Island: Summit, 623 ft..
Iguape: Quay
Bom Abrigo Islet: Light-house
Ilha do Mel : Light-house
Paranagua: Quay
Antonina: Quay
Coral Islet: Center
Itacolomi Islet: Center
Sao Francisco : Center of town
Itapacaroya: Church
Cambria: Church
Arvoredo Island : Light-house
Anhatomirim : Light-house
St Catharine Island : Rapa Pt
Naufragados light .
Nostra Senhora do Deserto: Quay
Coral Island : Summit, 230 feet
Cape St. Martha: Light-house
Torres Point: Extreme
Rio Grande do Sul: Light-house
Castillos: Beuna Vista Hill, 184 feet.
Cape Santa Maria: Light-house
Lobes Island: Center
Maldonado : Light-house
Flores Island : Light-house
Montevideo: Cathedral, SE. tower..
Colonia: Light-house
Martin Garcia Island: Light-house
Buenos Ayres: Cupola of custom-house.
La Plata
Indio Point: Light-house
Piedras Point: Extreme
Cape San Antonio: Light-house
Mfidanas Point: Light-house
Cape Corrientes: E. summit
Port Belgrano: Anchor-Stock Hill
Argentina: Fort
22 26 00
22 37 00
22 46 00
23 00 42
22 53 15
23 01 43
22 54 46
22 54 15
23 03 40
22 32 00
23 03 40
23 04 20
22 57 20
23 09 20
23 00 30
23 0(1 50
23 12 20
23 25 55
23 32 57
23 45 15
23 58 30
23 47 20
24 03 06
23 56 00
24 06 30
24 10 32
24 28 45
24 42 35
25 06 40
25 30 55
25 31 20
25 26 30
25 44 10
25 50 15
26 14 17
26 46 45
27 01 35
27 18 00
27 25 30
27 22 55
27 50 27
27 36 00
27 56 40
28 38 00
29 20 20
32 06 40
34 21 19
34 40 01
35 01 39
34 58 15
34 56 55
34 54 33
34 28 20
10 50
36 30
54 30
15 45
26 50
18 24
53 00
05 30
57 00
43 50
Long. W.
43 15
59 45
54 05
00 00
01 15
54 05
09 24
10 16
08 45
11 01
33 24
59 26
02 29
08 24
19 04
05 45
42 04
04 04
03 50
00 39
15 20
21 04
15 57
19 09
40 49
47 44
41 04
32 54
51 50
19 "53
31 03
43 14
23 14
25 51
39 29
36 59
36 44
22 20
34 25
26 09
35 16
34 14
33 44
49 45
43 39
07 44
58 15
58 22
57 54
57 10
57 05
56 44
56 38
57 30
61 59
62 15
Lun. Int.
H. W.
h. m.
53 47 16
54 09 14
54 53 16
54 57 10
55 55 04
56 12 15
57 52 27
2 30
2 50
1 35
2 50
2 55
2 35
4 00
8 20
2 00
6 30
6 43
9 50
6 00
L. W.
h. VI. ft.
Range.
Spg.
8 42 j 4. 9
9 00 i 4. 2
47 i 5.3
00 I 5.0
9 05 6. 4
8 47 5. 9
10 12 1.
2 08
2.0
8 12
00
3.5
4.0
12 15
3 35
'6 '66
2.1
5.3
'i.5.'8"
APPENDIX IV. [Page 209
IIAEITIME POSITIONS AND TIDAL DATA.
NORTH AND EAST COASTS OF SOUTH AMEKICA— Continued.
i
Place.
Lat. S.
Labyrinth Head: Summit
Union Bav: Indian Head
San Bias Ilarljor: SW. end of Hog Islet. .
San Bias Bay : Summit of Rubia Pt
Rio Negro; Main Pt
Bermeja Head : E. summit
Port San Antonio: Point Villarino
San Antonio Sierra: Summit
Port San Jos6: San Quiroga Pt
Delgado Point: SE. cliff
Cracker Bay: Anchorage
Port Madryn: Anchorage off cave bluff .
Chupat River: Entrance
Port St. Elena: St. Elena pen
Leones Island: SE. summit
Melo Port: W. pt
Port Malasphia: S. pt
Cape Three Points: NE. pitch
Port Desire: Largest ruin
Sea Bear Bay : Wells Pt
Port San Julian : Sholl Pt
Port Santa Cruz: Mount at entrance
Coy Inlet: Height S. side of entrance
Gallegos River: Observation mound
Cape V'irgins: SE. extreme
Cape San Diego: Extreme
Staten Island, Cape St. John: Light-
house, W. pt
Port Cork: Observation
mark, summit
Cape St. Bartholomew-
Middle pt
Good Success Bav: S. end of beach
Lennox Cove: Bluff, N. end of beach .
Goree Road : Guanaco Pt
Wollaston Island : Middle Cove
Barneveldt Islands: Center
Cape Horn: South summit, 500 ft
Hermite Island: St. Martin Cove
39 26 30
39 57 30
40 32 52
40 36 10
41 02 00
41 11 00
40 49 00
41 41 10
42 14 15
42 46 15
42 57 00
42 45 40
43 20 45
44 30 40
45 04 00
45 03 00
45 10 10
47 06 20
47 45 05
47 57 15
49 15 20
.50 08 30
50 58 27
51 33 21
52 18 35
.54 40 35
54 43 24
54 45 16
54 53 45
54 48 02
•55 17 00
.55 19 00
55 35 30
55 48 54
55 58 41
55 51 20
Long. W.
I
62 03 22
62 07 46
62 09 .30
62 10 12
62 45 11
63 08 16
64 .54 41
65 12 29
64 27 56
63 37 16
64 28 20
64 59 00
65 03 36
65 22 10
65 36 01
65 52 30
66 32 .36
65 51 46
65 54 45
65 45 40
67 42 30
68 23 00
69 09 47
69 00 31
68 22 12
65 05 53
63 47 00
64 03 00
64 45 45
ft5 13 48
66 49 00
67 10 00
67 19 00
66 43 48
67 16 15
67 34 00
Lun, Int.
H.VV. L.W.
h. m.
h. m.
10 50
10 35
7 05
3 50
00
10 35
9 20
•9 00
8 40
8 18
4 20
4 19
3 50
4 07
4 38
4 23
52
10 03
Range.
Spg. t Neap.
fl-
14.7
13.2
6 12 18.3
4 23
3 08
2 47
2 28
2 06
10 33
10 32
10 03
10 02
29.5
39. 6
40.0
45.6
38.7
9.9
7.8
6.:
4.8
7.7
23.5 1 12.3
6.9
16.8 ! 8.8
9.6
15.4
20.7
20.9
23.9
20.2
5.2
6.0
5.2
3.8
WKST COAST OF SOUTH AWCfeBICA.
False Cape Horn : S. extreme
lldefonso Island : Highest summit
Diego Ramirez Island: Highest summit .
York Minster Rock: Summit, 800 ft
Cape Desolation : S. summit ,
Mount Sky ring: Summit, 3,000 ft
Noir Island: SE. extreme
Landfall Island: Summit of Cape Inman.
Cape Deseado: Peaked summit
Apostle Rocks: W. rocks
Cape Pillar: N. cliff
Dungeness Point: Light-house
Cape Espiritu Santo: NE. cliff
Catharine Point: NE. extreme
Cape Possession : Light-house
Cape Orange: N. extreme
Delgada Point: Light-house
Cape Gregory : Ligh t-house
Cape San Vicente : W. extreme
55 43 15
55 52 30
56 28 50
55 24 50
54 45 40
.54 24 48
54 30 00
53 18 30
52 .55 30
52 46 15
52 42 .50
52 23 55
52 39 00
52 32 00
52 17 54
52 28 40
52 28 00
52 38 18
52 46 20
69
68
70
71
72
73
74
74
74
74
68
68
68
68
69
69
70
70
04 40
17 30
41 30
01 30
36 10
10 20
00 00
18 15
36 30
46 50
42 20
25 45
.34 00
45 20
57 10
24 00
33 00
14 16
25 25
3 50
2 20
1 50
32
8 19
8 20
8 24
8 35
8 47
9 23
10 03
33
03
6 45
2 07
2 08
2 12
2 25
2 40
3 20
5.0
4.8
4.7
4.0
39.4
39.0
30.0
39.0
39.0
21.0
3.9
3.7
3.7
3.1
20.6
20.4
15.7
20.4
20.4
11.0
24972°— 12-
"14
Page 210] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMERICA— Continued.
Place.
Long. W.
Elizabeth Island : NE. bluff
Sandy Point : Light-house
Cape St. Valentine: Summit, at extreme-
Port Famine: Observatory , |
Cape San Isidro : Extreme
Cape Froward : Summit of bluff 1
Mount Pond: Summit
Port Gallant : Wigwam Pt \
Charles Island : White rock near N W. endj
Rupert Island : Summit
Mussel Bay : Entrance
Till y Bay : Sara h 1 1
Borja Bay: Bluff on W. shore
Cape Quad : Extreme :
Barcelo Bay : Entrance
Swallow Bay: Shag I
Cape Notch : Extreme I
Playa Parda Cove: Summit of Shelter I . .
Pollard Cove: Entrance
Port Angosto: Hay Pt
St. Anne Island : Central summit
Half Port Bay : Point
LTpright Port: Entrance
Port Tamar: Mouat Islet
Port Churruca: Summit of Blaiica Pen ..'
Valentine Harbor: Observation mount..
Cape Parker: W. summit
Mercy Harbor: Summit of Battle I
Mayne Harbor: Observation spot
Port Grappler: Observation spfit
Port Riofrio: Vitalia I
Eden Harbor: Observation spot
Halt Bay : Observation islet
Westminster Hall Islet: E. summit
Evangelistas Island: 1 jght-house
Cape \'ictory : Extreme
Cape Isabel : W. extreme
Cape Santiago : Summit
Moly neux Sound : Romalo I
Cape Tres Puntas: Summit, 2,000 ft
Port Henry: Observation sjjot
Mount Corso: SW. summit
Rock of Dundee : Summit
Santa Barbara Port: N. extreme obs. pt .
Guaineco Islands: Speedwell Bav, hill,
NE.pt -
Port Otway : Observation spot
Cape Tres Montes : Extreme
Cape Raper: Rock close to cape
Christmas Cove: SE.extreme
Hellyer Rocks: Middle
Cape" Taytao: W. extreme
Socorro Island: S. extreme
Mayne Mountain: Sunnnit, 2,080 ft
Port Low : Observation islet
Huafo Island : S. extreme
Port San Pedro: Cove on S. shore
Cape Quilan : S W. extreme
Corcovado Volcano: Summit, 7,510 ft...
Minchinmadiva Volcano: S. summit,
8,000 feet
Castro: E. en<l of town
.52 49 18
53 10 10
53 33 30
53 38 12
53 47 00
53 53 43
53 51 45
53 41 45 ,
53 43 57 I
53 42 00
53 37 10
53 34 20
53 31 45
53 32 10
53 30 50
53 30 05
53 25 00
53 18 45
53 15 30
53 13 40
53 06 30
53 11 40
53 06 35
,52 55 46
53 01 00
52 55 00
52 42 00
52 44 58
51 18 29
49 25 19
49 12 40
49 07 30
48 54 20
52 37 18
52 24 00
52 16 10
51 51 .50
.50 42 00
.50 17 20
50 02 00
50 OO 18
49 48 00
48 06 15
48 02 20
47 39 30
46 49 31
46 58 57
46 49 10
46 35 00
46 04 00
45 53 20
44 55 .50
44 09 00
43 48 30
43 41 .50
43 19 35
43 17 10
43 11 20
42 48 00
42 27 45
70 37 51
70 54 24
70 34 27
70 58 31
70 55 03
71 17 15
71 55 30
71 59 41
72 04 45
72 10 42
72 19 30
72 27 10
72 34 15
72 32 25
72 38 00
72 47 30
72 47 55
73 00 30
73 12 05
73 21 30
73 15 30
73 17 45
73 16 15
73 44 28
73 59 33
74 17 45
74 13 30
74 38 14
74 04 00
74 17 39
74 23 27
74 25 10
74 20 55
74 23 10
75 06 00
74 55 00
75 13 20
75 27 45
74 51 30
75 22 00
75 13 20
75 34 00
75 40 30
75 28 20
75 10 00
75 18 20
75 25 30
75 37 55
75 31 .30
75 12 00
V5 06 00
75 08 45
74 07 45
73 59 ,35
74 42 00
73 41 .50
74 22 00
72 44 40
72 30 30
73 45 20
Lun. Int.
H. W.
It. m.
10 24
11 03
11 58
12 21
28
1 20 7 40 8. 4. 2
1 54
1 53
1 31
1 09
55
55
15
10
00
12 20
12 10
01
L. w.
A. Hi.
4 24
5 03
5-58
6 21
6 53
Range.
Spg. Neap.
ft-
8.0
5.0
6. 3.1
8. 4. 2
7.0 1 3.
8 11 5.5
8 08 5.0
44
21
07
08
30 6 45
6 30
6 25
4.5
4.0
6.0
4.4 3.4
4.5
5.3
6 13
6 10
6 00
6 21
4.4
6.2
6.1
18.0
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMERICA— Continued.
[Page 211
Place.
Dalcahue: Chapel
Oscuro head : Observation pt
Comaii Inlet: Olvidada I
Port C'albuco:- 1« Picuta
San Carlos de Ancud: Light-house
Condor Cove : Landing
Rann Cove: Anchorage
Muilcalpue Cove: I^anding place '•
Milagro Cove : Landing jAa.ce
Laruehuapi Cove: Landing place
Valdivia : Niebla Fort light
Queule Bay: Choros Pt
Mocha I.«land : Light-house
I.«bu River; Tueapel Head
Yaiiez Port : Anchorage
Lota: Light-house
Santa Maria Island; Light-house
Talcahuano: Fort Galvez
Light on Quinquina I
Llico; Village
Port San Antonio: Village
Aconcagua Mountain: Summit
Santiago : Observatory
Valparaiso; Playa Ancha Pt. light
Site of Fort San Antonio
Quintero Point ; Summit
Pichidanqne: SE. ])t. of island
Tablajs Point: SW. extreme
Ch\iapa River: S. entrance pt
Maitencil Ip Cove : N . head
Talinay Mount; Summit
Lengua de Vaca: Light-house
Port Tongoi : Obs. spot. \V. of village
Coquimbo: Tortuga Pt. light
Smelting works, X. of town.
N. islet
Pajaros Islets: Light-house
Choros Islands: S\V. pt, of largest id
Chafiaral Island: Liglit-house
Huasco: Light on mole
Herradura de Carrizal; Ijinding place...
Port Carrizal : .Middle Point
Matanioras Cove: Outer pt.S. side
Salado Bay: Sunnnit of Cachos Pt
Cf)piapo: Landing jjlace
Caldera; Light-house
Light on mole head
Cabeza de Vaca Point; Extreme
Flamenco: SE. corner of bay
Chafiaral Bay ; Observation pt
St. Felix I. : I'eterborough Cathedral Rock
Pan de .\zucar Island: Summit
Lavata; Cove near SW. pt
San Pedro Point : Summit
Port Taltal ; Light-house
Grande Point; Outer summit 1 . . .
Paposo Road; Huanillo Pt
Reyes Head : Extreme pitch
Cobre Bay: Pt. W. of village
•Tara Head; Summit
Antofaga.sta: Light-house
Chimba Bay; E. pt. of large island
42 23 00
42 04 00
42 03 00
41 46 08
41 46 40
40 46 19
40 43 18
40 35 52
40 21 04
40 11 47
.39 51 37
39 23 00
38 21 22-
37 35 20
37 22 30
37 05 20
36 59 07
36 42 00
36 36 45
34 46 02
33 .34 13
33 38 30
33 26 42
33 01 08
33 01 52
32 46 00
32 07 55
31 51 45
31 39 30
31 17 05
30 50 45
30 14 00
.30 15 14
29 56 15
29 .56 24
29 .55 10
29 34 40
29 15 45
29 00 .50
28 27 20
28 ft5 45
28 04 30
27 .54 10
27 .39 20
27 20 00
27 03 15
27 03 1.?
26 51 05
26 .34 30
26 20 00
26 16 12
26 09 15
25 39 30
25 31 00
25 25 20
25 07 00
25 05 25
24 34 30
24 15 00
23 53 00
23 38 50
23 33 05
Long. W.
73 36
73 25
72 45
73 07
73 52
73 51
73 49
73 45
73 45
73 41
73 26
73 14
73 58
73 .39
73 40
73 11
73 32
73 07
73 02
72 06
71 38
69 56
70 41
71 38
71 38
71 32
71 33
71 34
71 35
71 39
71 39
71 39
71 31
71 21
71 21
71 22
71 33
71 15
71 12
71 11
71 09
71 03
70 58
70 52
70 53
70 51
70 44
70 37
80 11
70 43
70 44
70 41
70 34
70 30
70 29
70 36
70 33
70 32
70 25
70 26
H. W.
h. in.
1 10
04
00
10 25
10 18
10 20
10 15
10 10
10 05
10 10
10 04
10 05
9 57
9 44
9 37
9 35
9 30
9 26
9 15
8 58
8 23
8 50
8 21
8 50
9 00
9 05
9 10
9 05
L. W.
7 35
6 20
6 13
4 13
4 05
5 07
4 02
3 55
3 50
3 55
3 51
3 53
3 48
3 34
Range.
Spg. Neap.
ft
14.8
5.9
3 26
7.2
5.6
4.9
3.3
4.9
5.3
4.9
6.0
5.3
5.0
4.1
4.0
3.9
3 25
3 20
3 16
3 05
2 48
4.1
3.9
4.2
"4^i
4.9
2 10
2 38
4.9
4.9
2 08
2 37
6.0
4.9
2 47
2 52
5.0
4.9
2 57 5.
2 52
4.7
(. o
3.0
3.7
2.8
2. 5
1.7
2.5
2.7
2.5
3.0
2.7
2.5
2.1
2.0
2.0
2.1
2.0
2.1
2.1
2.5
2.5
2.5
2.5
2.5
2.5
2.5
9 20 i 3 07 4. 9
9 35 I 3 22 5.
9 30 I 3 17 4. 9
2.4
Page 212J APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF SOUTH AMERICA— Continued.
Place.
Moreno Mountain: Summit
Constitution Cove: Shingle pt. of island,
Mexillones Mount: Summit
Port Cobija: Landing place
Tocopilla: Extremity Point
San Erancisco Head : W. pitch
Loa River: Mouth
Lobos Point: Outward pitch
Pabellon de Pica: Summit
Patache Point: Extreme
Iquique: Light-house
Mexillon Bay : Landing place
Pisagua: Pichalo Pt., extreme
Gorda Point: W. low extreme
Lobos Point: Summit
Arica: Iron church
Schama Mount: Highest summit
Lat. s.
Coles Point: Extreme
Ilo: Mouth of rivulet
Port Mollendo : Light-house
Isla y : Custom-house
Quiica: W. head of cove
Pescadores Point: SW. extreme
Atico: E. cove
Chala Point: Extreme
Lomas: Flagstaff on pt
San Juan Port: Needle Hummock
Nasca Point : Summit
Mesade Dona Maria: Central summit...
Carreta Mount: Summit
San Gullan Island: N. summit
Paraca Kay : N. extreme of W. pt
Pisco: Light-house
Chincha Islands: Boat slip, E. side N. id.
Fray les Point : Extreme
Asia Rock: Summit
Chilca Point: SW. pitch : . .
Morro Solar: Summit
San Lorenzo Island: Light-house
Callao: Palominos Rock Light
Pescadores Islands: Summit of largest.. .
Pelado Island: Summit
1 Sup^: W. end of village
Huarmey : W. end of sanily beach
Colina Redonda: Smnmit
Samanco Buy : Cross Pt
; Chimbote: Village, N. jiart
' Chao Islet: Center
Guanape Islands: Summit of highest
Huanchaco Point: SW. extreme
Malabrigo Bay : Rocks
Pacasmay o : Light-house
Eten Head : Light-house
Lambayeque: Beach opposite
Lobos de .Vfuera Island: Cove on ¥.. side.
Lobos de Tierra Island: Central summit.
Aguja Point: W. cliff summit
Paita, Saddle: S. summit
Paita: Light-house
Parinas Point: Extreme
Cape Blanco: XTnder middle of high cliff.
Tuml)ez: Malpelo Pt
23 28 30
23 26 42
23 06 30
22 34 00
22 06 00
21 55 50
21 28 00
21 05 30
20 57 40
20 51 05
20 12 30
19 05 01
19 36 30
19 19 00
18 45 40
18 28 43
17 58 a5
17 42 00
17 37 00
17 01 00
17 00 00
16 42 20
16 23 50
16 13 30
15 48 00
15 33 15
15 20 56
14 57 00
14 41 00
14 09 50
13 50 00
13 48 00
13 45 00
13 38 20
13 01 00
12 48 00
12 31 00
12 11 30
12 04 03
12 08 15
11 47 10
11 27 10
10 49 45
10 06 15
9 38 .35
9 15 30
9 04 40
8 46 30
8 34 50
8 05 40
7 42 40
7 23 40
6 55 50
6 46 00
6 46 45
6 26 45
5 55 30
5 12 00
5 05 00
4 40 50
4 16 40
3 30 42
Long. W.
I
70 34 56
70 37 11
70 31 39
70 17 42
70 13 40
70 11 17
70 02 45
70 12 12
70 10 26
70 14 40
70 11 20
70 10 30
70 15 21
70 17 50
70 21 50
70 20 00
70 52 31
71 22 31
71 20 01
72 02 53
72 07 16
72 27 16
73 16 41
73 41 31
74 27 16
74 51 01
75 09 36
75 30 46
75 49 56
76 16 36
76 27 31
76 18 31
76 10 00
76 24 15
76 31 06
76" 38 11
76 48 56
77 02 31
77 15 44
77 14 45
77 16 11
77 50 04
77 43 42
78 10 02
78 21 33
78 30 03
78 35 57
78 45 16
78 56 53
79 06 46
79 26 00
79 33 15
79 51 30
79 57 55
'80 42 54
80 51 56
81 09 19
81 05 36
81 07 03
81 17 01
81 12 01
80 28 12
Lun. Int.
h, m.
9 35
9 44
8 55
9 00
8 35
"8'32
7 49
7 55
L. W.
Range.
3 22 3.9
. 3 31 4.
2 42 4. 8
2 47 4.9
2 22 : 5.0
2 20
1 37
1 43
39
1 27
6 47
35
16 04
5.0
5.6
5.3
6.2
3.9
3.8
5 47 12 00
5 08 I 11 21
'4'56'i ii 03
4 19
4 04
3 20
10 32
10 17
3.5
2.1
2.0
2.1
2.5
9 33
3.5
APPENDIX IV.
MARITIME POSITIONS AND TIDAL
WEST COAST OF SOUTH AMERICA—
DATA.
Continued.
[Page 213
o
C
e
?
s
1
s
e
s
Place.
Lat. S.
Long. W.
i Lun
Int.
Range.
H. W.
L. W.
Spg.
Keap.
Guayaquil River: Ligiiton Santa Clara I.
Guayaquil, Concejot S. pt. of city
Puna : Mandinga Pt. light
r ft
3 10 40
2 12 24
2 44 30
/ tf
80 25 29
79 52 19
79 53 45
80 59 00
81 03 55
80 55 55
80 42 50
80 25 24
80 30 37
80 05 40
80 07 55
79 42 00
79 03 30
78 45 29
78 24 24
78 11 16
77 11 45
77 29 44
77 33 28
77 30 31
77 40 55
78 54 40
78 05 35
79 31 15
79 07 55
79 41 45
A. m
4 00
7 00
b. m.
10 13
1 00
/I-
10.0
11.0
/I-
5.1
5.6
Point Santa Elena: Veintemilla light 2 12 00
Plata Isle: E. pt 1 16 55
Cape San Lorenzo: Marlingspike Rock.. 1 03 30
Manta Bay: Light-hou.«e 56 50
Caraques Bay : Punta Playa i 35 25
Cape Pasado: Extreme ; 21 ;«)
Lat. N.
Point Galera: X. extreme 50 10
Cape San Francisco: SW. extreme 40 00
3 00
9 13
7.9
4.0
3 10
9 23
7.5
3.8
3 15
9 28
9.9
5.0
Esmeralda River: Light-house
1 03 30
1 36 00
1 49 36
2 37 10
2 58 10
3 49 27
4 17 06
5 28 46
6 41 19
6 49 45
8 12 30
8 28 50
8 54 30
Mangles Point: S. pt. of creek entrance. .
Tumaco: S. pt. of El Morro I
3 35
9 48
13.2
7.1
Guascama Point: Extreme
Gorgona Island : Watering Bav
1
Buenaventura: Basan Pt
6 00
12 13
13.2
7.1
Chirambiri Point: N. extreme
Cape Corrientes: SW. extreme
3 40
3 30
9 53
9 43
13.1
13.3
7.0
7.2
Cupica Bay: Entrance to Cupica River. .
Cape Marzo: SE. extreme
Isla del Rey : Extreme of Cocos Pt
Darien Harljor: Graham Pt
3 00
9 13
15.7
8.5
Flamenco Island: N. Pt
Chepillo Island: Center 8 56 32
Point Chame: Extreme 8 39 00
3 05
3 30
9 18
9 42
16.0
15.0
8.7
8.1
ISLANDS IN THE ATLANTIC OC
EAN.
i
m
2:
N
i
1
i
Fseroe Islands, Strom Islet: Thorshaven
Fort flagstaff
62 02 26
62 18 20
61 23 00
57 35 52
6 43 08
7 00 36
6 45 30
13 42 21
31 08 00
31 08 49
28 34 00
28 37 39
28 44 00
28 28 12
28 13 00
28 00 45
27 13 45
25 40 40
25 08 21
25 10 00
24 47 06
16 16 20
16 33 30
16 55 16
16 39 31
16 57 30
17 16 a5
Halderoig Islet: Halde-
roig Church
Numken Rock
Rockall Islet: Summit, 70 feet
Corvo Island : S. pt
39 40 07
Klures Island : Santa C^ruz Fort 1 39 27 00
Fayal Channel: N. Magdalen Rock \ 38 32 09
Fayal Island, Horta: C'astleofSantaCruz.: 38 31 45
Caldera: summit 3,351 ft ..! 38 34 30
11 30
5 18
3.9
1.8
Pico Island : Summit
38 25 00
38 40 30
39 OH 24
38 38 20
37 44 16
37 49 20
36 56 00
37 16 44
33 03 15 ,
32 35 45 I
32 37 42
32 43 14
32 45 00 i
32 48 07 1
St. George Island : Light-house
::::;:;:;:::::
Graciosa Island : Santo Fort light
Terceira Island: Monte del Brazil, near
Angra
20
6 32
4.4
2.0
St. Micliael Island: Custom-house, Ponta
Delgada
Pt. Arnel light
Santa Maria Island: Villa do Porto light.
Formigas Islands: Highest rock ....
Porto Santo Island : Light-house
Deserta.s: Chao I., Sail Rock
15
6 27
5.7
2.6
40
6 52
6.6
3.0
Madeira Island: Funchal light ..
35
6 47
6.6
3.0
Fora I. light-house
Pico Ruivo, summit
6,056 ft
Pargo (W.) Pt
Page 214] APPENDIX IV.
THARITIME POSITIONS AND TIDAL DATA.
ISLANDS IN THE ATLANTIC OCEAN— Continued.
Salvage I.«land»: Light-house, Gran Sal-
vage I : :» 08 00
Jit
Alegranza Island: Delgada Pt. light
Lanzarote Island: Port Naos light
Pechinguera Pt. light.
Lobos Island: Martino Pt. light
Fuerta Ventura Island; Jandia Pt. light.
Gran Canaria: I.-<leta Pt. light
Palma.« light
Teneriffe Island : Anga Pt. light
Santa Cruz, Br. con-
sulate
Suniraitof peak, 12, 180
ft
Gomera Island: Port Goniera
Ferro Island : Port Hierro
Palma Island: Light, XK. i)t
29 23 50
28 .57 24
28 50 56
28 45 25
28 03 00
28 10 42
28 07 06
28 .35 25
28 28 12
28»16 35
28 08 00
27 46 30
2'8 .50 06
Ireland Island: Dock yard clock tower..; 32 19 22
Bastion C j 32 19 37
Hamilton Island: Gibbs Hill light ..:...! 32 15 05
St. Davids Island: Light-house ' 32 21 40
St. Paul Rocks: Summit, 64 ft 55 30
Lat. S.
Rocas Reef: NW. sandy islet 3 51 30
Fernando Noronha: The Pyramid | 3 50 30
Ascension Island: Fort Thornton I 7 55 20
St. Helena Island: Obs. Ladder Hill 15 55 00
Martin Vaz Rocks: Largest islet i 20 27 42
Trinidad Island: SE. pt ' 20 30 32
Inaccessible Island : Center 37 19 00
Tristan d' Acunha Islands: NW. pt 37 02 48
Long. \V.
H. W.
15 54 00
13 29 31
13 33 07
13 52 05
13 49 13
14 31 35
15 25 11
15 24 56
16 08 11
16 15 09
16 38 02
17 05 55
17 54 22
17 47 01
San Antonio Island: Bull Pt. light : 17 06 50 | 24
Summit, 7,400ft...' 17 04 00
St. Vincent Island: Porto Grande light . 16 54 36
St. Lucia Island: N. pt 16 49 00
Raza Island: E. pt. 16 38 00
St. Nicholas Island: Light-house 16 34 00
Sal Island: N. pt. light : 16 50 50
S. pt ' 16 34 00
Boa vista Island: NW.pt ; 16 13 20
NE.pt ' 16 11 00
Light-house ; 16 09 10
Mayo Island: English Road 15 07 30
St. Jago Island: Tleta Pt. light 15 18 06
Porto Prava, S. light ... 14 53 40
Fogo Island: N. S. da Luz,"village 14 53 00
Brava Island: Light-house | 14 50 30
59 15
17 00
01 12
47 08
38 08
16 00
54 55
55 42
55 44
42 00
57 20
12 42
47 06
31 45
30 38
40 00
64 49 35
64 49 15
64 49 40
64 38 40
29 22 28
.33 49 29
32 25 29
14 24 35
5 43 03
28 46 57
29 14 56
12 23 00
11 18 39
Gough Island: Penguin Islet 40 19 11 9 56 11
Port Egmont : Observation spot. . .
Mare Harbor: Observation spot . .
Port Louis: Flagstaff, govt, house.
Port Stanley: Governor's house ..
Cape Pembroke: Light-house
South Georgia Islan<l : N . cape
Shag Rocks: Center
Sandwich Islands: S. Thule _-.
Traverse I. volcano
51 21 26 I 60 04 52
51 04 11 i 58 .30 56
51 32 20 i 58 08 04
51 41 10 57 51 30
51 40 40 I 57 41 48
54 04 45 ! 38 15 00
53 48 00 I 43 25 00
59 34 00 : 27 45 00
55 57 00 26 33 00
50
40
1 15
20
5 50
30
5 50
Hange.
L. \y. \ Spg. Neap,
7 04
5 05
5 00
5 20
3 00
3 35
3 40
12 50
20
7 00 ' 8.5
6 50 9.3
6 30
12 00
1 20
12 00
52
11 18
11 13
U 30
9 10
9 48
9 53
7.8
8.6
3.3
4.4
4.8
4.0
5 40
1 08
5 31 I 11 27
10.0
6.0
2.0
2.8
3.5
4.0
5.2
10.7
4.3
APPENDIX IV.
MARITIME POSITIONS AXD 'xIDAL DATA.
ISLANDS IN THE ATLANTIC OCEAN— Continued.
[Page 215
Place.
Lat. S.
Long W.
New 8. Orkney Is. : E. pt. Laurie I
E. summit Corona-
tion I., 5,397 ft ...
New S. Shetland Islands, Deception
Island : Port Foster
Bouvets Island (Circumcision): Center..
60 5-i 00 44 25 00
60 46 00 45 53 00
62 55 36 60 35 00
54 16 00
Long. E.
6 14 00
Lun. Int.
H. W.
h. VI.
L. \V.
A. m.
Range.
Spg.
Neap.
ATLANTIC COAST OF EUROPE.
I Lat. N.
Greenwich: Observatory i 51*8 38
Oxford: University Observatory ..: 51 45 34
Cambridge: Observatory ". j 52 12 52
North Foreland: Light-house
South Foreland: Light-house.
Dungeness: Light-house
Beacny Head: Light-house. . .
Southsea Castle : Light-house
Portsmouth : Observatory
Southampton : Royal Pier light
Hurst Castle: W. light
Needles Rocks: Old light-house
St. Catharine: New light-house
Portland : Notch Bill light
Start Point: Light-house ,
Plymouth : Breakwater light
Eddystone: Light-house
Falmouth: St. Anthony Pt. light
Lizard Point: W. light-house
Porthcurnow: SE. cor. telegraph co.'s sta.
Lands End: Longships light-house
Scilly Hands: St. Agnes light-house
Tre vose Head : Light-house
Bideford : High light-house
Lundy Lsland: Light-house, N. pt
Bristol : Cathedral
Cardiff: Light-house, W. pier
Swansea: Light-house, W. pier
Caldy Island : Light-house
St. Anns: Upper light-house
Smalls Rocks : Light-house
Aberystwith : Light-house
Bardsey Island : Light-house ..:..;
South Stack: Light-house on rocks
Holyhead : Light-house on old pier
Skerries Rocks: Light-house, highest I..
Bidstone: Light-house on hill
Liverpool: Rock light
Observatory
Morecambe Bay: Fleetwood high light..
Calf of Man: Upper light-house
Isle of Man: Ayre Pt. light-house
St. Bees: Light-house
White Haven: AV. pier-head light
Mull of Galloway: Light-house
Ayr,Firth of Clytle: Light-house, N. side
harbor
Troon : Light-house, inner pier
51 22 28
51 08 23
50 54 47
50 44 15
50 46 35
50 48 03
50 53 45
50 42 07
50 39 42
50 34 30
50 31 10
50 13 18
50 20 02
60 10 49
50 08 .30
49 57 40
50 02 44
50 04 10
49 53 33
50 33 00
51 04 00
51 12 05
51 27 24
51 27 48
51 36 50
51 37 52
51 41 00
51 43 15
52 24 20
52 45 00
53 18 30
53 18 54
53 25 15
53 24 02
53 26 38
53 24 04
53 55 03
54 03 14
54 24 56
54 30 50
54 33 00
54 38 10
55 28 10
55 32 55
Long. \V.
00 00
1 15 04
05 40
Long. E.
1 26 48
1 22 22
58 18
13 00
Long. \V.
1 05 15
05 58
24 00
33 04
35 25
17 47
27 30
38 28
09 27
15 53
01 00
5 12 06
5 39 18
5 44 45
6 20 38
5 01 55
4 12 30
4 40 35
2 35 55
3 09 42
3 56 00
4 40 59
5 10 30
5 40 15
4 05 40
4 47 50
4 42 00
4 37 01
4 36 20
3 10 42
3 02 27
3 04 16
3 00 20
4 49 37
4 22 01
3 37 50
3 36 00
4 51 20
4 38 10
4 41 00
1 10
11 24
11 09
10 35
11 10
11 31
35
11 05
6 29
5 25
5 20
4 45
4 15
5 45
5 00
7 00
6 45
5 45
5 40
5 41
5 40
7 25
7 24
10 00
11 08
11 00
7 46
18.8
5 53
5 43
4 23
4 58
10 55
11 00
11 05
11 40
4 19
6 48
4 53
09
11 38
11 33
10 58
10 28
11 58
11 13
48
33
11 58
11 53
11 54
11 53
1 13
1 12
16.8
19.8
21.5
19.8
13.2
12.8
12.2
6.7
14.9
15.3
14.2
15.9
22.7
26.9
31.3
36.2
27.1
25.3
24.0
20.9
14.2
14.9
3 48 i 15. 8
5 27 27.6
4 48 j 27.4
4 43
4 48
4 53
5 28
19.7
25.9
14.8
8.7
12.6
8.4
10.0
11.0
10.1
6.7
6.5
0.2
1.0
6.8
7.0
6.5
7.3
11.4
13.5
15.7
18.1
13.6
12.7
12.0
10.5
7.1
7.5
7.9
14.0
13.9
10.0
'i3."i
5.2
Page 216]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
Place.
Lat. N.
Ardrossan : S. breakwater light
Pladda Island : Light-house
Glasgow: Observatory
Cantyre: Light-house
Rhynns of Islay : Light-house
Oban : Light-house on N. pier
Skerryvore Rocks: Light-house
Barra Head : Light-house
Glas Island: Light-house, Scalpay I
Stornoway : Arnish Pt. light
Butt of Lewis : Light-house
Cape Wrath : Light-house
Dunnet Head : Light-house
Kirkwall (Orkneys): New pier-head
light :
Startpoint (Orkneys): Light-house i
North Ronaldsay: Light-house
Fair Isle Skroo: Light-house
Suniburgh Head : Light-house
Blackness (Shetland Is.): Light-house
pier
Lerwick (Shetland Is. ) : Fort
Hillswickness (Shetland Is. ) : S. extreme.
Balta I. (Shetland Is.): Cairn on E. side.
Pentland Skerries: Upper light-house ...
Tarbertness: Light-house
Buchanness: Light-house
Aberdeen (Girdleness) : Light-house
Buddonness: Upper light-house
Bell Rock: Light-house
May Island : Light-house
Inch Keith Rock : Light-house
Edinburgh : Observatory
Berwick: Light-house
Farn Island: NW. light-house
Co<,aet Island : Light-house •
Tynemouth: Souter Point light-house
North Shields: Light-house |
Sunderland: N. pier light
Hartlepool : Light-house
Flamborough : New light-house
Humber River: Killingholme middle
light
55 38 27
55 26 00
55 52 48
55 18 39
55 40 20
56 24 50
56 19 22
56 47 08
57 51 25
58 11 28
58 30 40
58 37 30
58 40 16
5i?59 15
59 16 45
59 23 24
59 33 00
59 51 15
60 08 02
60 09 22
60 27 20
60 44 25
58 41 22
57 51 54
57 28 15
57 08 33
56 28 07
56 26 03
56 11 00
56 02 09
55 57 23
55 46 00
55 37 00
55 20 06
54 58 10
55 00 30
54 55 07
54 41 51
54 07 00
53 39 00
Spurn Head: Upper light-house 53 34 45
Lowestoft: Light-house ! 52 29 14
Orfordness: N. light-house 52 05 00
Harwich: Landguard Pt. light ! 51 56 05
Cape Clear: Old light -house
Fastnet Rock : Light-house
Mount Gabriel : Ordnance survey station .
Ca.stlebaven : Light-house
Mizen Hill: Ordnance survey station
Bantry Bay: Roancarrig light
Bull Rock: Light-house
Skelligs Rocks : Light-house
Valentia: Light-house
Port Magee
Dingle Bay: Light at entrance
Blasket Islands: Westernmost rock
Smerwick : Signal tower
Tralee Bay: Light-house
Beeves Rocks : Light-house
Limerick : Cathedral
Shannon River: Ijoop Head light
Long. W.
4 49 28
5 07 09
4 17 39
5 48 00
6 30 46
5 28 20
7 06 .32
7 39 09
38 28
22 10
1£ 01
59 41
22 25
2 57 33
2 22 25
2 22 45
1 36 30
1 16 20
1 16
1 08
1 29
47
2 55
3 46
1 46
2 04
2 44
2 23
2 33
3 08
3 10
05
12 00
Long. E.
07 10
1 45 24
1 34 30
1 19 10
Long.
9 29
9 36
9 32
9 10
9 48
9 44
10 18
10 32
10 19
10 23
10 15
10 40
10 21
9 52
9 01
8 37
9 55
Lun. Int.
H. W.
A. m.
11 35
55
10 20
5 10
535
"6*35'
9 57
10 50
9 35
10 20
9 30
10 00
24
50
1 56
1 58
2 08
3 11
3 12
3 21
4 20
5 16
9 47
11 05
11 56
3 50
"iib
w
03
25
44
20
19
49
03
45
16
17
30
00
40 I 3 40
53 ! 3 50
23 ! 6 00
54 i
5 23
7 08
4 08
Range.
Spg. Neap.
8.8
11.2
4.0
3 44 9.
4 37
3 22
5.0
5.2
4 17
6.0
3 17
3 47
6.4
9.8
6 36 ] 11.2
7 02 i 11.7
8 08 15. 5
8 11
8 28
16.5
1.5.0
9 31 14.8
9 32 14.5
9 43 14.2
10 ,36 15. 8
11 29 18.5
3 35 6. 2
4 .53 I 7.8
5 44 11.2
10 03 j 8. 8
'i6'23Ti6.'6
3 30
'3'46'
9 43
"9'53'
9 53
10 03
13
10.8
i6."7'
10.7
12.3
18.7
ft-
5.3
6.7
2.4
11 22 j 12. 8 I 7. 7
ii'47'] ii.'i, "i's
"6'22Ti3.'4T"5.'7
4.2
2.2
2.2
2.6
2.7
4.2
6.1
6.4
8.5
7.4
7.3
7.0
8.8
10.2
3.6
4.5
6.6
4.4
'"5.';!
4. ()
"4.6
4.6
5.3
8.0
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF ETTBOPE— Continued.
[Page 217
a
■c
n
Place.
Eeragh Island : Light-house
Arran Island : Light-house
Galwav : Mutton I. light
Golam Head : Tower
Slyne Head: N. light-house
Clifden Bay: Gortrumnagh Hill
Tully Mountain: Ordnance survey station
Inishboffin: Lyon Head light
Inishturk Island : T(jwer
Clew Bay: Inishgort light
Newport: Church ^
Clare Island : Light-house
Blacksod Point: Light-house
Eagle Island: W. light-house
Broadhaven: (iuba Ca^hel light
Dounpatriek Head: Ordnance survey
station
Anghris Hea<l: Ordnance survey station.
Knocknarea: Tumulus
Sligo Bay : Black Rock light
Knocklane: Ordnance survey station
Killvbegs (Donegal Bay): St. Johns Pt.
light ;
Rathlin O'Birne Islet: Light-house
Aran Island: Rinrawros light
Bloody Foreland: Ordnance survey sta-
tion
Tory Island : Light-house
Horn Head: Ordnance survey station . . .
Mehnore Head : Tower
Fanad Point: Light-house
Glashedy Island: Ordnancesurveystation
Malin Head: Tower
Inishtrahull : Light-house
Inishowen Head: E. light-house
Moville: New Pier
Londonderry : Cathedral
Scalp Mountain : Ordnance survey station
Benbane Head : Summit
Rathlin Island: Altacarry light-house...
Maiden Rocks: W. light-house
Lough I.ame: Farres Pt. light-house
Belfast Bay: Light, east side
Mew Islands : Light-house
Donaghadee: Light-house
South Rock: Light vessel
Diindrum Bay: St. John Pt. lif^it
Carlingford Lough: Haulbowline Rk. It..
Droglieda: Light-house
Rockabill : Light-house
Howth Peninsula: Bailey light
Dublin : Observatory
N. wall light
PooUjeg: Light-house
Kingstown: K. pier light.;
Killiney Hill: Mapas obelisk
Bray Head: Ordnance survey station
Wicklow : Upper light
Tara Hill: Sununit ,
Black Stairs Mountain : Ordnance survey
station
Tory Hill: Ordnancesurveystation
Wexford : College
Forth Mount: (Jrdnance survey station . .
Tuskar Rock : Light-house
Great Saltee: S. end
Waterford : Hoop Pt. light
53 08 55
53 07 38
53 15 13
53 13 46
53 23 58
53 29 47
53 35 00
53 36 40
53 42 27
53 49 34
53 53 06
53 49 30
54 05 45
54 17 00
54 16 00
54 19 36
54 16 33
54 15 30
54 18 00
54 20 50
54 34 08
54 39 47
55 00 52
55 08 13
55 16 26
55 12 31
55 15 14
55 16 33
55 19 07
55 22 50
55 25 55
55 13 38
55 10 20
54 59 40
55 05 23
55 15 03
55 18 05
54 55 47
54 51 07
54 40 20
54 41 50
54 38 45
54 24 04
54 13 30
54 01 10
53 43 00
53 35 47
53 21 40
53 23 13
53 20 47
53 20 30
53 18 10
53 15 52
53 10 39
52 57 54
52 41 55
52 32 55
52 20 53
52 20 04
52 18 57
52 12 09
52 06 41
52 07 25
I.oag. W.
9 51 30
9 42 06
9 03 10
9 46 03
10 14 01
10 03 54
10 00 15
10 09 40
10 06 41
9 40 12
9 32 56
9 59 00
10 03 34
10 05 31
9 53 00
9 20 41
8 46 02
8 34 25
8 37 00
8 40 14
8 27 33
8 49 52
8 33 48
8 15 38
8 15 00
7 57 15
7 47 12
7 37 .53
7 23 51
7 22 22
7 13 37
6 .55 38
7 02 20
7 19 25
7 21 51
28 45
10 45
44 18
47 21
49 30
5 31 30
5 32 01
5 22 20
5 39 30
6 04 45
6 15 00
6 00 20
6 03 06
6 20 30
6 13 33
6 09 00
6 07 30
6 06 37
(i 04 55
6 00 08
6 13 01
6 48 17
7 07 31
6 28 15
6 33 41
6 12 35
6 37 15
6 55 53
Lun. Int.
Range.
H. W.
h. in.
4 15
4 19
4 16
4 20
4 50
5 10
L. W.
Spg.
/(.
10 28
10 19
13.4
15.1
10 29
13.2
10 33
12.1
11 03
10.4
11 23
5 03 11 16
11.4
11.2
.1
5 28 11 41
11.6
6 55 43
7 48 1 ;»
10 30
10 42
"ii '66
10 46
10 45
10 55
11 00
10 52
10 30
10 10
7 05
5 30
"5'65'
7.5
8.0
4 18
6.7
4 06
9.3
"ii.i"
4 33
4 33
15.8
11.6
4 43
12.7
4 48
4 27
13.0
10.9
4 18
3 58
11.8
8.7
53
4.9
11 43
ii'is'
8.8
12.3'
Neap.
/«■
5.7
6.4
5.7
.5.2
4.5
5.3
4.8
5.3
3.4
3.6
4.5
6.3
"7.'4
9.2
6.8
7.6
6.4
6.9
5.1
2.9
5.1
'6.2
Page 218] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EtTROPE— Continued.
a
s
a
9
Place.
Lat. N.
Waterf ord : Cathedral
lireat Newton Head: Sletal Man Tower
Dungarvan: Ballinacourty light
Knockniealdown Mount; Ordnance sur-
vey station
Helvick Head: Ordnance survey station
Mine Head : Light-house
Youghal : Light-house
Capel Island : Tower
Ballycottin : Light-house
Cork Harbor: Haulbowline Coal Wharf
Queenstown : Roches Pt. light
Kinsale; Light-house, S. pt
Seven Heads: Tower
Galley Head : Light on summit
Stag Kocks: Largest
Alderney Harbor: Old pier light
St. Hellers: Light on Victoria Pier
A'ardo: Fortress
Vadso: Light-house
North Cape: Extreme
Fruholni : Light-house
Hammerfest: Light-house
Tromso : 01)servatory
Hekkingen : Light-house
Andenes: Light-house
J^odingen (Hjertholm): Light-house .. -
Lofoten Island: Skraaven I. light
Glopen light
Gryto: i/ight-house ^ . .
Stot: Light-house -
Tra;nen : Soe Islet light
Bronnosund : Light-house
Villa: Light-house
Halten Island : Light-house
Koppem
Agdenes: Light-house
Trondheim: Mumkhohnen flagstaff
Grip: Church
Christiansund: Storvaden
Freikallen
Hestskjaer: Light-house
Stemshesten
yErstenen : Light-house
Svinoen Islet
Hjoerringa Mountain: Summit
Hornelen ^Mountain: Summit
Batalden Island : Store
Kinnsund : Light-house
Alden
Helliso: Light-house
Bergen : Cathedral
Lorstakken Mountain: Summit
Marstenen Islet: Light-house
Furen Islet
Ulsire: Light-house
Hvidingso: Light-house
Port Stavanger: Light-house
Obristadbra'kke: Light-house
Synesvarde Mountain : Summit
Kompas Mountain : Summit
Lister: Light-house
Lindesnes : Light-house
Kyvingen Island: Light-house
Christianssand: Odderoen light
52 15 33
52 08 13
52 04 27
52 13
52 03
51 59
51 56
51 52
51 49
51 50
51 47
51 36
51 34
51 31
51 28
49 43
49 10
70 22 00
70 04 00
71 11 00
71 06 00
70 40 15
69 .39 12
69 36 05
69 19 30
68 24 40
68 09 20
67 .53 15
67 23 15
66 56 35
66 2.T .50
65 28 40
64 32 .55
64 10 25
63 48 25
63 38 45
63 27 04
63 13 11
as 07 01
63 03 04
63 05 00
62 58 49
62 48 20
62 19 38
62 11 12
61 51 21
61 38 40
61 33 35
61 19 16
60 45 06
60 23 37
60 21 39
60 07 50
59 57 44
59 18 20
59 03 10
58 58 30
58 39 25
58 36 56
58 25 51
58 06 25
57 58 55
57 58 00
58 07 50
Long. W.
06 24
10 15
33 05
54 .54
32 39
35 08
50 34
51 10
59 00
18 20
15 14
31 58
42 51
57 10
13 27
12 00
06 44
Long.
31 07
29 45
25 40
23 59
23 40
18 57
17 50
16 08
16 02
14 40
13 04
13 .52
13 28
11 .59
12 13
10 42
9 24
9 44
9 45
10 23
7 36
7 43
7 46
7 29
7 12
6 36
5 16
5 01
5 15
4 47
4 46
47
42
20
19
01
03
52
24
45
33
49
58
6 34
7 03
7 29
8 00
E.
30
00
00
00
00
00
15
00
30
40
30
30
50
50
30
10
50
45
20
30
05
35
04
.55
32
10
25
59
11
38
45
14
55
15
;i5
00
30
35
20
20
35
08
49
20
10
50
30
Lun. Int.
h. m.
5 00
5 02
4 40
4 33
4 30
4 20
6 21
6 09
5 40
h. m.
11 13
11 15
10 53
10 59
10 43
10 33
Range.
ft.
12.4
12.6
11.8
11.6
11.4
10.7
16
00
11 57
ir.2
3L2
9.0
2 20
1 35
42
8 40 I 8. 3
7 48 I -7. 8
6 55 7.
Neap.
11 35
5 23 6. 9
11 18 ! 5 04
"ii"66 4'48"
10 15
9 43
4 16
3 55
8.4
4.1
3 40
10 15
6.2
6.3
5.9
5.8
5.7
5.3
7.6
13.6
5.1
4.7
4.4
4.0
3.3
4.1
5. 2. 9
2.1
0.8
1.1
0.5
APPENDIX IV.
MARITIME POSITION'S VXD TIDAL DATA.
ATLANTIC COAST OF EUKOPE— Coatinued.
(Page 219
Place.
Lat. N.
e
Okso: Light-houae
Hamberg: Mill
.Vreiulal Inlet: Inner Torungerue light..
Jonif ruland : Light-house - . .
Langotangen : Light-house
Langesund : Church
Freileriksva^rn : Ixjokout tower
Svenor: Light-house
Foerder Islet: Light-house
Fulehuk : Light-house
Basto: Light-house
Horten: Church
Holmestrand: Church
Drobak : Church
Oscarsberg: Fort flagstaff
Christiania: Observatory
Stronitangen (Torgauten): Light-house.
Fredriksten : Fort clock tower
Torbjoruskja;r: Light-house
Koster: Light-house
58 04
58 15
58 24
.58 51
58 59
59 00
58 59
58 .58
59 01
.59 10
59 23
59 25
.59 29
.59 39
59 40
59 54
59 09
.59 07
58 .59
58 54
Stromstad: Steeple
Xord Koster Islands: Light-house
Wadero Island: Light-house
Hollo Island: Light-house
Paternoster Rocks: Light-house
Gottenburg: Signal station
Xidingen Islet: Light-house
Warberg: Castle tower
Falkenberg: Church
Hahnstad: Palace
Fngelhohn : Church
KuTlen Point.- Light-house
Helsingborg: Lighthouse
Landskrfnia: Light-house
Malnio: Light-hou.ie
Falsterbo : Light-house
Trelleborg: Light-house
Ystad : Light-house
Sandhamniaren : Light-house
Hano Island : Light-house
Karlshanm: Light-house
Karlskrona: Stunihohn Tower
Oland Island : Light on S. pt
Oottland Island: Hoburg light, S. pt.
Ostergarns light
Faro Island: Hoi madden light
Sparo Vestervik: Orans-o light
Haradsskar Islet : Light-house
Xorrkoi)ings Inlopp: Light-house
Landsort: Light-house
Stockholm: Observatory
Upsala: Observatory
Xorrtelge: Inn
Soderarm : Light-house
SvartkluVtben: Light-house
Osthammar: Church
Oregrund : Clock tower
Djursten : Light-liouse
Forsmark : Church
Orskar Rock : Light-house
Gefle: Church
Eggegrund Islet: Light-house
Hamrange: Church
Soderhamm : Court-house
Enanger: Church
58 .56 24
.58 ,54 12
58 32 45
.58 20 12
57 53 49
57 40 58
.57 18 15
57 06 26
56 54 08
.56 40 21
.56 14 40
.56 18 06
.56 02 37
55 52 00 i
55 3('> 47 ;
.55 23 00
55 22 00
55 25 42
.55 22 58
56 00 .54
56 10 04
.56 09 45
.56 11 .50
.56 55 18
57 26 29
57 57 24
57 45 ,38
58 08 52
58 17 .55
58 44 26
.59 20 .'5.5
.59 51 31
59 45 24
.59 45 15
60 10 35
60 15 19
60 20 26
60 22 15
60 22 26
60 31 41
60 40 29
60 43 48
60 .55 57
61 18 22
61 32 54
Long. K.
8 03
8 31
8 47
9 36
9 45
9 45
10 03
10 09
10 31
10 36
10 32
10 29
10 19
10 38
10 36
10 43
10 .50
11 24
10 47
11 00
30
36
55
15
50
14
28
26
.55
25
45
52
15
08
•55
;«
15
09
20
45
28
36
16
24
04
54
16
32
48
38
47
11
30
48
49
02
20
38
10
57
02
05
04
06
27
36
36"
22
28
09
30
39
34
34
49
36
33
21
49 i
38 i
29 i
50
57 ,
18 !
51 I
Lun. Int.
Range.
H. W.
L. W.
Spg.
Neap.
h. III.
h. m.
ft-
ft.
4 17
10 10 ! 1.0
0.7
j
1
4 34
10 00
L3
1.0
5 22
io 37 j i.2
I
0.9
1
j
.
1
i
1
I
1
1
........
1
Page 220] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUBOPE— Continued.
^'
Place.
Lat. N.
Long. E.
o r n
17 07 37
17 16 22
17 19 05
18 05 05
19 02 .50
20 45 35
20 18 35
Lun. Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
1
t
f
s
PS
Hudiksvalls: Court-house
O / W
61 43 57
62 02 51
62 23 30
62 38 35
63 11 55
63 35 34
63 39 33
64 28 50
65 19 10
65 18 .53
65 31 30
65 48 30
65 02 20
A. m.
h. m.
/(.
ft.
Giiarp: Church
Suiidsvall : Church ,.
Lungo: Light-house
Skags Head : Jjight-house
Holmogadd : Light-house
Umea: Bredekar Light
Bjuroklubb: Light-house
21 34 45
21 30 00
22 21 55
23 34 00
24 12 00
24 34 00
23 27 00
20 37 40
21 11 24
21 22 34
21 01 00
22 17 03
19 34 00
19 31 20
19 54 05
20 25 50
21 22 00
22 58 08
24 24 43
24 ,57 17
25 25 51
25 37 30
26 41 05
27 01 40
26 58 44
27 33 46
2i 58 36
29 03 01
29 47 12
29 46 07
30 19 22
30 19 40
29 54 54
29 46 38
28 23 01
28 03 31
26 23 00
25 48 58
25 02 37
24 46 10
24 44 45
24 31 57
24 24 05
24 04 30
23 23 15
22 36 15
22 11 36
21 49 ,56
22 04 15
23 59 .34
24 49 25
24 00 ,59
24 08 25
23 15 00
22 39 15
21 34 00
20 59 40
Pitea
1
Rodkallen : Light-house
Maloren : Light-house
Tornea: Light-house
L^leaborg: Karlo I. light
Ulko Kalla Rock: Light-house
64 20 05
63 14 08
62 20 06
Norrsher Islet: Kvarken light
Kaske: Shelgrund I. light
Bierneborg: Sebsher light
Nuistad: Ensher light
61 28 29
60 43 10
60 26 57
60 24 45
60 13 20
Aland Island : Shelsher light
Ekkere light
Logsher light i 59 50 50
Bogslier: Beacon 59 31 11
Ute Islet: Light-house 59 46 30
Gange: Gange I. light i 59 46 00
Rensher: Light-house ! 59 56 10
Helsingfors: Observatory 60 09 43
Soder Skars: Light-house 60 06 40
Kalboden Island: Light vessel 59 58 4.5
Rodsher Island: Light-house
59 58 08
60 00 40
Upper light 60 06 22
VieborgBav: Nelva I. light ' 60 14 43
Stirsudden : Light-house
Kronstadt: Light on Frederikstadt bas-
60 11 05
59 58 14
Cathedral
59 59 44
59 56 30
59 46 19
59 53 26
59 .55 40
60 02 08
59 '^8 04
Pulkowa: Observatory
Oranienbaum : Light-house
Seskar Islet' Light-house
Stensher Rock- Light-house 59 49 10
j
.59 41 06
r,Q -19 on
Koksher' Light-house
Revel: Light N. end of W. mole 59 27 05
Cathedral 59 26 28
Nargen Island : Light-house 59 36 22
Surop: W. light... 59 27 .55
Baltic Port: Light-house i .59 21 30
Odenskholm Island: Light-house 59 18 06
Takhkona Point: Light-house j .59 05 25
Dawo Island- Dagerort light ' 58 .55 02
58 23 02
57 54 37
58 05 50
58 23 10
57 03 28
56 56 36
57 48 02
57 48 10
57 24 00
56 31 01
Pernau: Light at S entrance
Riga: Light on Fort Kametskoi dike
Cathedral
Libau: Light at entrance of port
i 1
APPENDIX IV.
MARITIME POSITION? AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
[Page 221
Place.
Men)el: Light-house
Heihgen Creutz: Church tower
Brusterort: Light-house
Pillau: Light-house
Fischausen: City-hall tower
Konigsberg: Ohi-ervatory
Tolkemit: Church tower
Elbing: Church tower
Tiegenort: Church tower
Danzig: Observatory
Neufahrwasser light
Weichselmunde: Fortress tower
Putziger Heisternest: Church tower ..
Oxhof t ; Light-house
Hela: Light-house
Eixhoft: Light-house
Leba: Church tower
Stopelinunde: Church i
Jershoft: Light-house i
Rugenwalde: St. Mary's Church...". I
Coslin: St. Mary's Churcli :
Funkenlmgen : Light-house
Colberg: St. Mary's Church j
Gross-Horst: Light-hou.><e
Cammin: Cathedral tower
WoUin : C'hurch tower ;
Stettin: N. Castle tower |
Swinenuinde: Light-house I
Streckelsberg: Survey station near beacon[
Usedoni: Church tower
Lassau : Church tower [
Wolgast: Church tower
Griefswald: St. Nicholas Church
Griefswalder Oie: Light-house
Granitz: Castle tower
Bergen : Church tower
Arkona: Light-house
Stralsund : St. Mary's (Jhurch
Darsserort: Light-house
Wustrow : Church
Ribnitz: Churcli tower
Wameuiunde : Church
Rostock : St. Jacob's Church
Diedrichshagen : Survey station
Basdorf: Survey station
Wismar: St. Nicholas Church
Hohenschonberg: Survey station
Travemunde: Light-house '
Burg: Church tower i ;
Marienleuchte: I.,ight-house i
Petersdorf : Churcli tower i
Hessenstein : Flagstaff of lookout tower . .
Schonberg: Church
Bulk: Light-house
Kiel : Observatory
Eckemforde: C!liurch |
Schleswig: Cathedral j
Kappeln: Churcli I
Flensberg: Church
Duppel: Survey station
Schleimunde: Light-house
Augustenburg: Church
Hugeberg: Survey station
Apenrade: Church
Skoorgaarde: Survey station I
Ballum: Church
List: K. light-house
55 43 45
54 53 47
54 57 40
54 38 25
.54 43 49
54 42 51
54 19 19
54 Q9 44
54 16 30
54 21 18
54 24 28
54 23 51
54 12 16
54 33 09
54 36 06
54 49 55
54 45 29
.54 35 16
54 32 29
.54 25 27
.54 11 28
54 14 40
51 10 40
54 05 47
53 58 29
.53 .50 41
.53 25 41
53 55 03
54 03 08
.53 52 17
53 56 .59
54 03 18
.54 05 49
.54 15 02
54 22 .56
.54 25 08
54 40 53
54 18 42
.54 28 28
.54 20 47
.54 14 42
.54 10 42
.54 05 27
.54 06 32
54 08 00
53 53 50
53 58 54
.53 57 44
54 26 16
54 29 43
54 28 54
.54 19 47
54 23 52
54 27 25
54 20 30
54 28 25
54 30 55
54 39 48
54 47 05
54 54 28
.54 40 23
54 56 48
54 58 05
55 02 46
55 03 52
.55 05 31
55 03 04
Lun. Int.
Long. E.
Range.
H. W.
21
20
19
19
20
20
19
19
19
18
18
18
18
18
18
18
17
16
16
16
16
15
15
15
14
14
14
14
14
13
13
13
13
13
l.T
13
13
13
12
12
12
12
12
11
11
11
11
10
11
11
11
10
10
10
10
9
9
9
9
9
10
9
9
9
9
06 06
01 25
59 06
53 .55
tX) 39
29 44
31 .58
23 58
08 37
39 46
39 59
41 03
40 35
.33 46
49 04
20 29
33 38
51 35
32 50
24 52
11 05
52 39
34 44
04 06
46 36
37 12
.33 52
17 19
01 17
55 26
51 13
46 51
22 53
55 42
37 .54
26 11
26 12
05 30
30 23
24 02
26 04
05 19
08 10
46 04
41 .54
28 09
05 54
52 59
11 .59
14 29
04 18
32 59
22 24
12 04
08 56
50 23
34 23
56 13
26 20
45 .35
02 23
52 20
58 41
25 18
23 35
39 41
26 50
h. m.
L. W.
Spg.
Neap.
h. m. Jt. \ ft.
20 6 33
5.2
3.0
Page 222] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
Place.
Keitum: Church
Fohr: St. Nicholas Church
Galgenberg: Survey station
Husuni : Church
Tonning: Church
Busum : Church
Helgoland: liight-house
Scharhorn : Beacon
Neu werk : Li^ht-house
Cuxhaven : Light-house
Stade: Church steejjle
Steinkirchen ; Church
Altona : Observatory
Hamburg: Observatory
Berlin : Observatory
Harl)nrg: Light-liouse
Hohe Wog: Light-house
Langvvarden : Church
Brenierhaven: New harbor light.
Minsener Sand: ]>ight vessel
Schillighorn : Light-house
Wilhelmshaven: Observatory
AVangeroog: Light-house
Spikeroog: Church
Langeoog: Belvedere
Balstrum : Church
Norderney : Light-house
Juist; Church
Emden : Citv Hall tower
Lat. N.
54 54 13
54 41 51
.54 41 21
54 28 43
54 19 08
.54 07 52
54 10 57
53 57 15
53 55 01
53 52 25
.53 36 12
53 33 43
53 32 45
53 33 07
52 30 17
53 28 30
53 42 50
53 36 20
53 32 52
53 46 57
■53 42 21
53 31 52
53 47 25
53 46 19
.53 45 06
53 43 46
53 42 39
53 40 45
53 22 06
Falster: Gjedser light : 54 33 50
Moen Island: Stege Church spire i 54 59 03
Moen light, SE.pt ] 54 56 46
Proeste: Church spire ' 55 07 24
Kjorge: Church tower '. 55 29 44
Amager Island: HoUcenderbvCh. spire.. ^ .55 35 45
Nordse Rase" light 55 38 1
Copenhagen: New observatory 55 41 14
Bornholm: Ronne light ' .5.5 05 40
Christianso Island: Great tower .55 19 19
Kronberg: High spire 56 02 20
Nakkehooe<l: Upper light .56 07 10
Hesselo Island: Light-house .56 11 .50
Anholt Island: Light-house 56 44 16
Spodsbjerg: Light-house 55 58 36
Roeskilde: Cathfjdral .55 38 34
Nykjobing: Church tower .55 55 30
Oddensby : C^hurch tower .55 57 .52
Sejro Island: Sejro Point liglit 55 55 09
Kallnndborg: Church .55 40 .50
Omo Island: Church i ,55 09 48
Vordingborg: Waldeniar's tower .55 00 26
Yeiro Island: Light-house .55 02 19
Langeland Island: Fakkebjerg light .54 44 23
jEro Island: Church spire 54 51 14
Lyo Island : Church tower | 55 02 34
Assens: Church tower ' .55 16 09
Baago Island: Light-house i 55 17 44
Kolding: Ca.stle tower '• .55 29 31
Bogense: Church spire \ .55 34 03
Nyborg: Churchspire ! 55 18 41
Turo Island: Churchspire \ .55 03 00
Svendborg: Frue Church j 55 03 37
Endelave Island: Church tower i 55 45 32
Samso Island: Koldby Church tower j 55 48 02
Horgens: Preiser Church spire ! 55 51 44
Long. E.
8 22 03
8 33 13
8 33 58
9 03 21
8 56 38
8 51 53
7 53 11
8 24 35
8 29 58
8 42 43
9 28 48
9 36 40
9 56 .35
9 58 25
13 23 44
9 .59 37
8 14 48
8 18 30
8 34 25
8 04 47
8 01 43
8 08 48
7 54 09
7 41 45
7 a5 41
7 22 03
7 13 58
6 59 53
7 12 25
11 .58
12 17
12 .32
12 03
12 07
12 38
12 41
12 34
14 42
15 11
12 32
12 20
11 42
11 39
U 51
12 05
11 40
11 24
11 05
11 05
11 09
11 .54
11 22
10 42
10 24
10 09
9 53
9 48
9 28
10 05
10 47
10 40
10 36
10 16
10 33
9 51
Lun. Int.
H. W.
h. m.
1 35
2 10
1 45
•1 11
11 29
39
25
54
10
04
11 27
11 05
24
9 33
L. w.
h. m.
7 47
8 23
7 57
7 24
5 17
Range.
7.8
10.8
11.0
11.7
8.1
51 10. 1
4 00 10 13
5 00 ! 11 12
6 38
7 07
6 23
6 17
5 15
4 53
6 36
3 21
8.5
6.1
10.1
10.4
9.5
8.9
0.6
Neap.
4.5
6.2
6.4
6.8
4.7
5.8
4.9
3.5
5.8
5.3
13.2
8.0
7.4
4.5
4.1
5.0
0.3
APPENDIX IV.
MARIXniE POSITIONS AXn TIDAL DATA.
ATLANTIC COAST OF EUROPE— Continued.
[Page 223
Place.
Lat.N.
Long. E.
Lun
. Int. 1 Range.
H. W.
L.W. j Spg.
[ Neap.
s
a
i
1
s
S
.
s
a
u
i
i
a
2
Tuno Island : Light-house
o / //
55 56 58
1 65 57 06
56 09 26
56 08 00
56 26 36
66 59 54
: 57 02 54
57 43 46
67 .35 06
57 06 50
56 30 48
56 05 27
55 47 17
.5.5 44 .50
55 31 .52
.56 26 26
.55 16 11
o / //
10 26 51
10 33 00
10 12 50
10 48 32
10 57 40
10 18 53
9 55 22
10 36 38
9 66 44
8 36 10
8 07 23
8 14 52
8 14 36
8 14 43
8 24 12
8 24 03
8 32 38
4 46 36
4 53 01
5 07 50
4 29 03
4 18 .30
4 15 10
4 10 45
4 28 50
4 07 40
4 26 26
3 .58 35
3 35 48
3 .34 32
4 22 18
4 24 44
4 24 12
3 06 .54
2 .55 51
2 55 22
2 45 .34
2 20 14
2 22 31
2 06 :m
1 51 07
1 .3.5 02
1 33 47
1 49 .56
1 .30 46
1 06 01
57 35
42 ,34
22 12
04 08
06 22
13 43
LoilK, W.
21 10
27 24
31 08
1 16 21
1 15 56
1 43 44
1 38 08
1 57 15
2 22 41
fi. in.
A. m. ' /I.
ft-
-
Samsoe Island: Nordby Church tower ..
Aarhus: Cathedral spire
Hjelm Islet : Light-house
Fomies : Light-house
Hals: Church tower
Aalborg: St. Rudolph's Churcli
Cape Skaw, or Skagen: Old light-house .
Hirtshals: Light-house
j
I
1
5 46
4 18
11 58 : 1.0
10 30 i 1.2
0.5
0.7
Haustholm : Light-house
Boobjerg: Light-house -
Ringkjobing: Church spire
;:::::::: i
Ijoune: t^hurch tower
2 35
8 47 2. 1
1.2
Blaabjerg: Summit, 100 ft
(iuldager: Church
Fano Island: Nordby Church
2 36
2 34
8 47 4. 5
8 46 1 4. 7
1 2.6
I 2.7
Mano Island: Church spire. .
Niewe Diep: Time-ball station
52 57 50
52 22 30
.52 05 10
52 09 20
52 04 40
52 06 16
51 .54 29
51 .54 ao
51 49 19
51 41 48
51 49 08
61 26 33
51 26 24
50 51 11
51 12 2g
51 13 17
51 18 47
51 14 13
51 13 50
51 07 53
48 50 11
51 02 09
.51 00 18
50 57 45
.50 .52 10
.50 41 57
50 07 05
50 11 42
49 .56 (16
49 55 04
49 52 28
49 46 a5
49 30 04
49 29 01
49 25 32
19 11 14 1
7 17
1 05 3.9
i '■'
Amsterdam : W. church tower
Utrecht: Observatory
Levden : Observatorv
The Hague: Church tower
Scheveningen: Light-house
Brielle: Light-house
Rotterdam : Time-ball station
2 50
3 a5
2 20
3 20
9 02 i 4.8
9 47 1 6. 7
8 32 5. 2
9 32 ! 9. 8
1
2.5
3.5
2.8
5.2
Hellevoetsluis: Time-ball station
Will^mstadt: Light-house
Goedereede: Light on church tower .. ..
Flushing: Time-ball station
Light, Westhaven bastion
Brussels; Observatory
Antwerp: Observatorv
::;::::i:: i
44
6 56
14.7
, 7.8
4 15
10 27
14.8
7.8
Notre Dame Cathedral
Blankenberghe: Fort light-house
Ostend : Light-house
05
02
6 17
6 32
12.5
16.1
6.7
8.4
Cliurch tower
Nieuport: Templars tower
10
6 22
15.7
8.4
Paris: Observatory
Dunkerque: Tower
11 58
11 .59
11 .39
11 17
11 18
5 58
6 16
6 13
5 51
5 52
16.8
19.0
21.0
21.5
25.2
8.5
9.6
10.7
11.0
12. S
Gravelines: Light on N. breakwater
Calais: Light oh old fort
Cape Gris Nez: Light-house
Boulogne, C. Alprech: Light-house
Abbeville: Tower
Cayeux: Light-house
Dieppe: W. jetty light
Ailly Point: Light-house
10 54
5 48
27.3
13.3
St. Valery en Caux : Light on W. break-
water
10 29
10 06
5 33
5 02
26.8
23.3
13.1
11.4
Fecamp: N. iettv Hght
Cape La Heve: S. light i
Havre: S. jetty light
Honfieur: Hospital jetty light
9 03
4 14
22.5
11.0
Caen : Church tower
Port CorseuUes: W. jetty light
49 20 18
49 20 28
49 34 19 i
49 41 50 ;
49 40 29
49 38 54
49 43 22
49 43 17 :
i
Point De Ver: Light-house
Cape La Hougue : Ligh t-house
8 13
8 14
2 45
2 37
18.5
17.0
8.2
7.5
Cape Barfleur: Light-house
Cherbourg: Light, W. head of break-
water
Naval Observatory
7 30
1 44
17.6
7.8
Cape La Hague: Light-house '
Casquets Rocks: Lighi on NW. rock i
6 20
15
1.5.6
6.9
Page 224]
APPENDIX IV.
^MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF ETJBOPE— Continued.
Place.
Lat. N.
•Port St. Peter, Guernsey: Light on Cas-
tle Coonet Breakwater
Douvres Rock.s; Light-house
Cape Carteret : Light-house
Coutances: Cathedral tower
Granville: Light-house
Chausey Is. : Light on SE. end of large id .
St. Malo: Roehebourne light
Cape Frehel : Light-house
Heau de Brehat; Light-house
Morlaix, He Noire: Light-house
De Bas Islet : Light-house
Abervrach : Light on Vrach Islet
Ushant: StiH Point light
Brest: Observatory
Brest (approach ) : Quelern light
De Sein Islet: Light-house
Bee du Raz: Light-house
Audierne: Pier-head lijiht
Penniarch Rocks: Light-house
(ilenan Islands: Light, Penfret I
De Groix Island : Light-house
Lorient: Church-tower light
Belle Isle: Light-house
Port Haliguen : Light on N. jetty
Haedic Island: Light-house
Port Navalo: Light-house
Yannes : St. Pierre Church
Jje Four Rock : Light-house
Croisic: PJnd of breakwater
Guerande: Steeple
Port St. Nazaire: Light-house
Paimlxcuf : Steeple
Nantes: Cathedral •.
Noir Moutier Island: Light-house
Le Pilier Island: Light-house
D'Yeu Island: Light-house
La Chaume: Light-house
Point de Grouin du Con: Light-house. . .
Re Island : Light, NW.pt
Rochelle; E. Quay light
Aix Island : Light-house
Rochefort: Hospital
Oleron Island : Light N W. pt
Point de la Coubre: Light-house
Point Cordouan; Light-house
Point de Grave: Light-house
Bordeaux: St. Andre
Bayonne: Cathedral _
Biarritz: Light-house
St. Jean de Luz: St. Barbe Point light ..
Fuenterrabia: Light on Cape Higuera. . .
Port Pasages: Light at entrance
San Sebastian: Monte Igueldo light
Bilbao: Light on Galea Castle
Castro Urdiales: Santa Ana Castle light .
Santona: Pescador Point light
Santander: Cape Mayor light
San Martin de la Arena: Light-house
San Vincent de la Barquera: End of new
mole
Ri vadesella: Mount Sonios light
Gijon: Santa Catalina light
Aviles: Light-house
Rivadeo: Light-house
E.staca Point: Light-house
Long. W. "
49 27 1.3
49 06 28
49 22 27 I
49 02 54
48 50 07
48 52 13
48 40 18
48 41 05
48 54 33
48 40 23
48 44 45
48 36 57
48 28 31
48 23 32 ;
48 19 10
48 02 40
48 02 28
48 00 47
47 47 52
47 43 17
47 38 51
47 44 53
47 18 42
47 2!) 10 1
47 19 18 !
47 32 53
47 39 30
47 17 53
47 18 .30
47 19 44
47 16 18
47 17 17 j
47 13 08
47 00 41
47 02 35
46 43 04
46 29 38
46 20 41
46 14 40
46 09 25
46 00 36
45 56 37
46 02 49
45 41 39
45 35 14
45 34 10
44 50 19
43 29 29
43 29 38
43 23 58 (
43 23 30 i
43 20 05
43 19 22
43 22 36
43 24 20 \
43 28 36
43 29 30
43 26 50 1
I
43 23 35 i
43 31 00
43 32 48 I
43 38 05
43 34 40
43 47 20
Lun. Int.
H. W.
L. W.
2 31 31
2 48 49
1 48 25
1 26 39
1 36 46
1 49 20
1 .58 41
2 19 08
3 05 11
3 52 33
4 01 38
4 34 34
5 03 26
4 29 36
34 28
52 03
45 25
32 50
22 30
57 15
:30 35
3 21 .31
3 13 38
3 06 09
2 50 07
2 55 08
2 45 28
2 38 05
2 31 25
2 25 48
2 11 50
2 02 09
1 32 .59
2 13 16
2 21 37
2 22 56
1 47 45
1 27 49
1 33 40
1 08 57
1 10 40
57 .50
1 24 37
1 15 16
1 10 24
1 04 27
34 42
1 28 43
1 33 16
1 39 53
1 47 30
1 56 05
2 01 40
3 04 06
3 16 10
3 28 06
3 47 40
4 01 00
24 55
07 10
40 11
56 00
03 00
42 00
A. m. I h. m.
I
6 12 ' 07
6 07
5 50
5 55
5 43
5 .35
5 00
4 .35
4 00
3 :K
3 23
3 25
3 04
3 05
3 00
3 09
3 25
3 35
3 20
3 45
5 47
3 25
3 35
4 18
5 ,50
3 05
3 18
3 20
3 27
3 27
3 45
3 35
2 55
2 50
2 50
2 55
3 05
3 00
3 00
2 .50
2 45
2 45
15
09
04
04
12 00
11 25
11 00
10 25
10 00
9 45
Range.
Spg. Neap.
26.0
30.8
36.7
34.7
.36.0
30.4
23.1
22.0
20.6
18.9
19.5
9 53 17.2
9 31
9 34
9 27
9 36
9 50
9 58
9 46
10 08
12 11
11.1
13. 3
1,3.0
9 47
9 56
10 39
12 28
,9 26
9 40
9 44
9 22
9 22
9 55
9 53
6 30 12
3 07 9 14
9 05
9 03
9 03
9 07
9 18
9 14
9 14
13.8
16.6
16.9
16.7
16.6
15.-8
16.;
16.6
17.0
16.5
16.7
14.:
12.;
16.6
16.6
16.7
16.8
15.3
12.3
11.7
12.7
11.8
12.3
14.8
11.7
10.4
9 03
8 58
8 58
13.5
12.0
14.4
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ATLANTIC COAST OF ETIROFE— Continued.
[Page 226
1 i Place.
Lat. N.
Long. W.
Lun.
Int.
Range.
H. W.
L.W.
Spg.
Neap.
Port Cedeira: Light-house
o / //
43 39 00
43 29 30
43 27 30
43 23 10
42 52 45
42 12 30
41 09 10
40 10 47
39 24 49
39 21 00
38 46 49
38 42 31
38 29 15
37 01 20
37 07 48
36 58 23-
37 11 00
37 15 08
36 43 58
36 27 40
36 31 30
36 10 50
35 59 53
36 07 19
36 07 10
36 06 25
o / //
8 05 30
8 13 29
8 20 20
8 24 26
9 15 28
8 54 00
8 40 35
8 54 15
9 30 29
9 22 30
9 29 46
9 11 10
8 56 00
8 58 00
8 39 53
7 51 48
7 24 00
6 57 12
6 26 30
6 12 20
6 19 00
6 02 08
5 36 31
5 26 12
5 21 17
5 20 42
h. m.
2 43
2 44
h. m,
8 56
8 57
ft.
14.8
14.9
6^.'l
6.1
Ferrol ' Old naval observatory .... ,
Corufia: Hercules Tower light
2 43
2 42
8 56
8 55
14.8
10.0
6.1
4.6
i
s
t
e
i,
•0
s
X
e
I
Cape Finisterre: Light-house
2 25
2 20
8 38
8 35
10.0
7.0
4.3
3.0
Cape Mondego: Light-house
Berlanga Island: Light-house
2 05
8 15
7.8
3.4
Cape Roca : Light-house
2 20
2 10
8 05
8 20
11.1
11.6
4.8
5.0
Cape St. Vincent: I.,ight-house .
Lagos: Church
1 55
8 08
13.0
5.6
Cape Sta. Maria: Light-house
Ayamonte: Light-house
San Lucar: Chipiona light
1 15
7 28
12.3
5.6
Cadiz: Observatory of San Fernando
1 45
7 58
n.8
5.4
Cape Trafalgar: Light-house
Tarifa: Light-house
1 32
7 52
5.6
2.6
Algeciras: Verde I. light
Gibraltar: Dockvard flagstaff
-Europa Pt. light ... . .
1 35
7 55
3.7
1.7
COASTS OF THE MEDITERRAl
J-EAN, A
DRIATIC
AND BLACK SEAS
I
c
36 42 39
36 50 12
36 42 57
37 33 28
37 35 50
37 33 22
37 34 38
38 12 30
38 20 12
38 30 00
38 30 57
38 33 30
38 38 36
38 40 51
38 48 06
38 51 00
39 12 15
39 28 05
39 27 50
39 53 57
40 04 53
40 27 48
40 33 30
40 43 10
41 06 00
41 22 10
41 50 04
42 16 15
42 19 10
42 30 59
42 31 18
4 24 38
2 27 50
2 11 12
1 15 12
59 09
57 58
50 20
30 12
28 48
11 42
10 06
04 02
Long. E.
02 52
09 17
12 02
07 30
Long. W.
13 37
19 48
18 50
Long. E.
41 19
08 56
28 48
39 45
53 55
1 14 42
2 10 52
3 08 28
3 17 10
3 18 55
3 07 30
3 06 50
2 15
8 35
2.9
1.5
Almeria: Light-house
Cape de Oata: Light-house
Mazarron : Light-house
Cartagena: Arsenal gate
Escombrera light
Porman : Light-house
Santa Pola Bay : J>ight-house
Alicante: Js. mole light
Villajoyose: Light house
Benidonne: Tower
Altea: Light-house
C'alpe: Church tower
Morayva: Tower
Jarea: Cape San Antonio light
Denia: Mole-head light
Cape CuUera: Light-house
Valencia: Light-house
Mole-end light
5 00
11 30
1.5
0.8
Columbretes Islands: Light-house
Oropesa Cape: Light-house
Vinaroz: Mole-head light
Port Alfaques: Bafia light
Cape Tortosa: Light-house
Tarragona: E. mole light
Barcelona: E. mole-head light
Palamos Bay : Molino Pt. light
Cadaques: Clock tower
Cape Creux : J jght-house
Cape Bear: Light-house
Port Vendres: Fort Fanal light
24972°— 12-
-15
Page 226] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued.
Place.
Lat. N.
Port Nouvelle: S. jetty light ; 43 00 47
Cette: Light, St. Louis mole : 43 23 50
AiguesMortes: Espignette Pt. light | 43 29 17
Planier Rock: Light-house : 43 11 57
Marseille: Janet Cliff light 43 20 43
New observatory 43 18 22
Ciotat: Berouard mole light 43 10 21
Toulon: St. Mandrien light 43 05 10
Grand Riband Island : Light-house 43 01 01
Cannes: Light-house 43 32 51
Antibes: (jaroupe light 43 33 51
Nice: Light-house 43 41 32
Ville tranche: Mole-headlight 43 41 58
Cape Ferret light | 43 40 30
Port Ibiza: Light-house '.. 38 54 10
Cabrera Island: Light-house 39 06 34
Pi (Majorca): Light-house '. 39 33 00
PortMahon (Minorca): Light-house ! 39 51 53
Cape Spartivento: Light^house
Cape Sandalo: Light on San Pietro I .
Porte Conte: Cape Caccia light
Port Torres: Light-house ,
Cape Testa: Light-house
Kazzoli Island: Light-house
Caprera Island : Galera Pt
Cape Figari : Signal station
Cape Tavolara: Light-house
Cape Bellavista: Light-house
Cape Carbonera: Cavoli I. light
Cagliari: Light on mole
Bonifacio: Mount Pertusato light.
Ajaccio: Light-house
Corti: Church tower
Calvi : Light-house
Cape Corso: Giraglia I. light
Bastia: Light-house '.
Porto Vecchio: Chiape Pt. light . .
Cape Melle : Light-house
Genoa: San Benigno light
Spezzia: Fort Santa Maria light
Florence : Observatory
Leghorn (Livorno): Light on S. end of
curved breakwater
Capraia Island: Cape Ferrajone light
Elba Island, Porto Longone: Fort For-
cado light -
Pianosa Island: Light on battery, W.
side of fort
Africa Rock : Light-house
Monte Christo Islet: Summit
Giglio Island, Cape Rosso: Light-house .
Civita V'ecchia: Light N. end of break-
water
Rome: Observatory
Gaeta: Orlando tower
Ponza Islet: Punto della Guardia light . .
Naples: Observatory
Light on elbow of mole
Capri Island: Carena Pt. light
Lipari Island : Casa Bianca light
Ustica Island: NE. point light
Faro of Messina: Capo di Faro light
Milazzo: Light-house
Palermo: Observatory
Light on mole head
Trapani : Palumbo Rock light
38 52 34
39 08 44
40 33 50
40 50 25
41 14 36
41 18 24
41 14 15
40 59 52
40 54 55
39 55 45
39 05 15
39 12 35
41 22 10
41 52 50
42 18 14
42 35 10
43 01 45
42 41 47
41 35 45
43 57 17
44 24 15
44 04 00
43 46 04
43 32 33
43 02 57
42 45 14
42 36 06
42 21 28
42 20 15
42 19 13
42 05 38
41 53 54
41 12 27
40 52 38
40 51 46
40 50 15
40 32 07
38 28 43
38 42 40
38 16 02
38 16 10
38 06 44
38 07 56
38 00 39
Long £.
3 04
3 42
6 08
Lun. Int.
1 27 25
2 57 20
2 37 00
4 18 20
8 51 08
8 13 29
8 10 00
8 23 56
9 08 35
9 20 21
9 29 40
9 39 07
9 44 22
9 43 25
9 32 35
9 07 20
9 11 15
8 36 45
9 09 04
8 43 25
9 24 10
9 27 00
9 22 05
8 10 22
8 54 19
9 50 48
11 15 22
10 17 25
9 51 07
10 24 38
10 05 50
10 03 54
10 18 39
10 56 24
11 46 50
12 28 40
13 35 15
12 57 17
14 14 44
14 15 38
14 11 40
14 51 40
13 12 00
15 39 11
16 13 42
13 21 16
13 22 04
12 29 50
H. w.
L. W.
7 31
8 22
2 00
2 24
Range.
Spg. Neap.
ft.
0. 6 0. 3
0.6
4 00
0.2
10 13
o.;
0.2
APPENDIX IV. [Page 227
MARITIME POSITIONS AND TIDAL DATA.
COASTS or THE MEDITEBRANEAIT, ADRIATIC, AND BLACK SEAS— Continued.
Place.
Lat. N.
Long. E.
Lim. Int.
H.W.
L. W.
Range.
Neap.
Maritimo Island: Light on SW. pt
Marsala: W. mole light
Girgenti: Port Empedoohe light
Gozo Island : Light on NW. pt
Malta Island, Valetta Harbor: Light-
house.
Linosa Island : Landing Cove
Lampedusa Island: Carallo Bianco light.
Cape Passaro: Light-house
Syracuse: Maniace Castle light
Augusta Port: Torre d' Avola light
Catania: Sciari Biscari light
Cape Taormina: Semaphore
Messina: San Ranieri light
Cape Peloro : Light-house
Cape Spartivento: Light-house
Cape Colonna: Light-house '.
Cotrone: Mole-head light
Taranto: Cape St. Vito light
Gallipoli: St. Andrea light
Cape Sta. Maria di Leuca: Light-house. .
Cape Otranto: Light-house
Port Otranto: Caatle
Brindisi : Light-house
Bari:_St. Catalolo light
Viesti: Light on St. Croce Rock
Manfredonia: Light-house
Tremiti Islands: Caprara I. light
Ancona: Monte Cappncini light
Malamocco: Rocchetta Mole light
Venice: Site of tower of St. Mark
Grade: Church tower
Monfalcone: Church tower
Trieste: Observatory Nautical Academy.
Theresa Mole light
Capo d'Istria: Light-house
Isola : Light-house
Pirano: Light-hou.se
Salvore Point: Light-house
Citta Nuova: Light-house
Parenzo: Cathedral tflwer
Rovigno: St. Eufemia light
Pola: N. cupola of observatory
Promontore Point: Porer Rock light
Nera Point: Light-house
Fiume : Cathedral tower
Porto R^: Light-house
Veglia: Mole hea/1
Prestenizza Point: Lisjht-house
Chereo: Kimen Point light
Galiola Rock: Light-house
Unie Island: Netak Point light
Lussin Piccolo: Sta. Maria Church
St. Pietrodi Nembo Island: Health office.
Gruizza Rock : Light-house
Zengg: Mole-head light
Terstenik Rock: Light-house
Carlobago: Light-house
Zara: Church tower
Blanche Point: Light-house
Zara Vecchia: Church tower
Port Tajer: Lestrice I. light
Lucrietta Island : Light-house
Sebenico: Mount Tartaro
Rogosnizza Port : Mulo Rock light
Zirona Grande Island: St. George
Church tower
Trani : Cathedral tower
37
37
37
38
38
37 57 13
37 47 10
37 16 55
36 04 10
35 54 00
35 51 50
35 29 37
36 41 03
37 03 04
12 39
29 35
.50 25
11 .33
16 02
37 55 29
39 01 29
39 04 38
40 24 41
40 02 48
39 47 43
40 06 23
40 09 06
40 39 36
41 08 19
41 53 17
41 37 39
42 08 14
43 37 14
45 20 30
45 25 58
45 41 06
45 48 33
45 38 51
45 38 54
45 33 00
45 32 34
45 31 54
45 29 24
45 19 16
45 13 45
45 05 00
44 51 49
44 45 30
44 57 24
45 19 36
45 16 18
45 01 30
45 07 12
44 57 36
44 43 36
44 37 20
44 31 49
44 27 42
44 24 42
44 59 24
44 40 06
44 31 30
44 07 05
44 09 06
43 .56 16
43 51 15
43 37 36
43 45 08
43 31 00
43 27 00
43 31 02
12 02 55
12 25 59
13 32 27
14 12 55
14 31 30
12 52 09
12 36 12
15 07 45
15 17 37
15 13 20
15 05 19
15 18 30
15 34 36
15 39 11
16 03 31
17 12 09
17 08 07
17 12 23
17 56 55
18 22 17
18 31 25
18 28 45
17 59 37
16 50 52
16 11 13
15 55 34
15 31 36
13 31 18
12 19 09
12 20 29
13 22
13 32
13 46
13 45
13 43
13 39
13 33
13 29
13 33
13 35
13 38
13 50
13 .53
14 08
14 26
14 33
14 34
14 16
14 23
14 10
14 14
14 28
14 33
14 34
14 53
14 34
15 04
15 14
14 49
15 26
15 12
15 34
15 58
15 55
16 08 51 1.
16 15 09 I.
3 12
9 25
0.7
0.2
3 00
9 13
0.9
0.3
3 30
10 15
« 20
9 00
8 15
8 10
6 10
9 43
4 45
1.8
0.5
3.3
0.9
3 50 2.0
0.6
3 25
"2'35'
3.4
0.9
I
1.2 [ 0.3
I
2 25
1.1
20 ! 1.
0.3
0.3
Page 228] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
COASTS OF THE ICEDITEBBANEAN, ASBIATIC, ASH BLACK SEAS— Continued.
Place.
Lat. N.
Port Spalato: Cathedral tower
Soltal., PortOlivetto: St. Nicliolas tower.
Spalato Passage: Spec Ft. light
Makarska: Church tower
Pomo Rook : Center
St. Andrea Rock: Summit
Lissa Island : Hoste Rock light
Pakonjidol Rock: Light-house
Leaina Island: Port Gelsa light
St. Giorgio Pt. light
Sabioncello Peninsula: Cape (jomena
light
Sorelle Rocks: Light-house
Curzola Island: Porto Bema mole head. .
Porto Valle Grande,
church tower
Lagostini Island: Glavat Rock light
Lagosta Island: St. George Chapel
Cazza Island : Light-house
Pelagosa Rock : Light-house
Meleda Island : Port Palazzo Ruin
Olipa Rock : Light-house
Pettini di R^usa Rocks: Light-house...
Bobara Rock: Summit ..
Molonta Peninsula: Summit
Ostro Point: Light-house
Cattaro: Health office
Budua: Mole-head light
Katie Rock: St. Domenica Chapel
Antivari: Pt. Valovica light.
Dulcigno: W. windmill
Cape Rodoni: Guard-house
Cape Pali ; Guard-house
Durazzo: Light-house
Cape Laghi: Ruin
Skumbi River: Pyramid at mouth.
Semeny River: Saraana Pt. light..
Vojazza River: Pyramid at mouth
Saseno Island : Light-house
Avlona: Light-hou.se
Cape Linguelta : Extreme
Mount Cica: Pyramid
Port Palermo: Pyramid
Cape Kiefali: Pyramid
Fano Island: Pt. Ka.stri light
Port Pagonia: Ruin
Port Gomenitza: Well Dogana
Port Parga: Madonna I
Port St. Spiridione: Convent
Corfu: Light-house
Paxo Island: Madonna I. light
Prevesa; Fort Nuovo minaret
Port Drepano: Observation island
Port Vliko: Custom-house
Port Vathi: Lazaretto light
Port Argostoli : St. Theodore light
Patras: Light-house
Katakolo: Light-hou.«e
Zante: Mole light - -
Strovathi, or Strivali Island: Staniphani
Llight
Proti Pa.ssage: Marathon Pt
Navarin : Light-house
Mothoni: Round tower
Koroni Anchorage: Mole light
Petalidi Bay: Petalidi Pt
Candia Island, Port Buda: Light-house..
Megalo Kastron: Mole
light
43 30 07
43 23 50
43 19 12
43 17 46
43 0.5 28
43 01 43
43 04 30
43 09 24
43 09 50
43 07 30
43 02 50
42 57 42
42 54 19
42 57 37
42 45 54
42 45 05
43 45 05
42 23 30
42 47 06
42 45 30
42 39 00
42 35 08
42 27 04
42 23 36
42 25 30
42 16 42
42 11 43
42 05 15
41 55 47
41 35 10
41 23 31
41 18 40
41 08 44
41 02 12
40 47 00
40 36 14
40 30 12
40 25 30
40 25 17
40 12 00
40 02 57
39 54 29
39 51 53
39 39 27
39 29 50
39 16 32
39 39 54
39 37 05
39 11 30
38 56 30
38 47 25
38 40 40
38 22 04
38 11 36
38 15 (X)
37 38 20
37 47 10
37 15 12
37 03 38
36 54 10
36 48 40
36 47 50
36 57 20
X) 28 55
35 20 30
Long. E.
Lun. Int.
H. W.
16 26 06
16 11 10
16 24 30
17 01 36
15 27 30
i5 45 29
16 12 28
16 27 14
16 41 55
17 12 00
17 00 19
17 12 44
16 51 32
16 43 07
17 08 54
16 51 45
16 29 29
16 15 12
17 22 51
17 46 48
18 03 08
18 10 49
18 25 36
18 32 00
18 46 12
18 50 36
18 56 25
19 04 19
19 12 29
19 27 15
19 24 54
19 27 14
19 26 47
19 26 30
19 20 14
19 19 14
19 16 15
19 27 55
19 17 45
19 38 33
19 47 53
19 54 55
19 26 06
20 07 12
20 17 09
20 24 55
19 43 09
19 56 30
20 12 34
20 45 40
20 44 16
20 42 44
20 43 37
20 29 30
21 43 50
21 18 .55
20 55 26
21 01 14
21 34 35
21 40 29
21 42 40
21 58 00
21 56 42
24 09 39
25 09 44
4 00
Range.
Spg. Neap.
10 30
3 40
9 53
2.4
0.7
1.0
0.3
APPENDIX IV. [Page 229
MARITIME POSITIONS AND TIDAI. DATA.
COASTS OF THE MEDITEBBANRAJT, ADRIATIC, AND BLACK SEAS— Continued.
o
Place.
Lat. N.
Long. E.
Lun. Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
«
9
i
8
B
Pt
Kandeliuea Island: Light-house
Stanipali Island, Mahezana Port: Agios
loanes
o / //
36 29 40
36 34 25
36 15 20
36 40 27
36 59 12
37 06 32
37 00 01
37 08 38
37 26 12
37 07 36
37 25 55
37 38 00
37 39 28
37 44 00
37 57 30
36 47 05
37 18 42
37 31 45
37 44 .30
37 56 14
37 58 20
37 38 45
37 52 48
O / H
26 59 25
26 24 28
25 13 00
24 23 15
24 40 30
25 23 00
25 14 21
25 14 08
24 56 14
24 32 23
24 23 .35
24 44 32
24 19 44
24 04 12
24 42 30
23 05 40
23 08 53
23 25 45
23 25 30
23 38 10
23 43 55
24 02 15
24 03 00
h. m.
A. m.
ft-
ft-
Christiana Islands: N. pt
Milo Island: Summit, Mt. St. Elias
Naxos Island, Naxia: Gate on Bacchus I.
Paros Island, Port Trio: Trio Pt
Port Naussa: St. Yanni
Church
Syra: Mole light
Sermo Island : Amyno Pt
Thermia Island: Ruins of Cythnus
Jura Island: North pt
Port St. Nikolo: Light-house
St. Nikalao Island: Port Mandri
Andros Island, Cape Fasse: Light-house.
leraka : Acropolis
Port Kheli: Light-house
./iijgina: Light-house
: 1
Pireeus: Light-house
Athens: Observatory
Cape Colonna: Extreme
Port Raphti: Statue I
Petali Island : Trago I. peak
Euripo Strait: Light-house
Skiathos Island: Mount Stavros
Salonika: S. bastion
Port Haklar: Cape Xeros
LemnoB Island : Kastro Castle
38 01 28 ; 24 16 42
38 28 15 23 36 45
39 10 48 23 27 07
40 37 28 22 58 00
40 32 40 26 45 00
39 52 10 25 03 20
39 50 52 25 14 14
Port Moudros: Sangrada Pt
Strati Island : St. Strati Church
39 31 58
39 12 35
24 59 13
25 50 00
Mityleni Island, PortSigri: Light-house.
Mitvleni: LightonMity-
leni Pt
39 06 10
26 34 54
26 31 .39
Port lero: Sidero Islet .
Psara Island : Fort
39 03 20
38 32 00 J 25 35 00
38 19 55 ! 26 17 45
37 41 24 1 26 58 42
37 16 33 27 36 55
36 .55 00 : 27 18 25
36 48 00 28 18 00
36 39 33 29 06 13
.36 26 00 28 16 24
Tchesm^: C. K6zil light
Samos Island : Fonia Pt. light
Port Isene: Tower
Kos : Lieht-honse
Marmonce Harbor: Adassi Pt. light
Makrv Harbor: Kasil I
Rhodes Port: Arab's Tower light
Port Lindo: Tower
36 05 .53
40 02 30
40 24 27
41 01 20
41 01 02
41 00 35
41 00 16
41 21 15
41 .52 Ot
28 08 10
26 10 54
26 41 24
29 01 00
29 00 29
29 01 14
28 58 59
28 42 14
27 ,58 45
Dardanelles: Hellas Pt. light
Gallipoli: Light-house
Boap lorus: Tofana Pt. light
Scutari: Leander Tower light
Constantinople: Seraglio Pt. light
St. Sophia Mosque
Cape Kara Burnu: Light-house
Yuiada Road : Fort Tersana
Burghaz: Light-house
Varna Bay : Light-house
Kusterjeh: Cape Kusterjeh light
Danube River: Salina light
Fidonisi Island: Light-house
42 27 52 27 35 .54
43 10 00 27 58 35
44 10 20 ! 28 ,39 14
45 09 47 29 41 14
45 16 00
46 28 36
46 34 27
44 36 55
44 29 50
45 21 03
46 45 00
42 58 00
41 39 30
30 14 14
.30 45 .34
31 33 36
33 36 26
33 36 25
Odessa: Observatory
Dnieper Bay: Fort Nikolaeo light
Seba.stopol: E. light-house
Balaklava Bay: Hospital
Kertch : Light-house
36 28 30
Berdiansk: Breakwater light
36 46 40
40 55 10
41 38 15
Sauk houm : Light-house
Batoum : Light-house
Page 230] APPENDIX IV.
MAEITIME POSITIONS AND TIDAL DATA.
COASTS OF THE MEDITERRANEAN, ADRIA.TIC, AND BLACK SEAS— Continued.
. I
place.
Lat. N.
Trebizond : Light-house
Sinope: Light-house '.
Bender ErekH: Light-house
Marmora Island: Light off E. pt
Artaki Bay: Zeitijn Adasi Islet
Tenedos Island: Ponente Pt. light . . .
Port Ajano: Nikolo Rock
Port Ali-Agha: W. pt. <if entrance...
Smyrna: English consulate flag-staff .
Vourlah : Custom-house
Sighajik Harbor: Beacon on islet
Budrum : Light-house
Adalia: liight-house
Alexandretta: Light-house
Latakiyah : Light-house
Tripoli Roadstead: Bluff Islet light . .
Euad Island : Light-house
Beirut: Light-house
Saida( ancient Sidon): Light-house ...
Stir (ancient Tyre) : Light-house
Acre: Light-house
Haifa: Light-house
Famagusta: Light-house .
C. Gata: Light
Lamaka : Light-house
01 00
01 20
18 03
38 10
23 30
50 00
01 21
50 10
25 40
21 48
12 21
02 00
52 00
35 30
.30 30
29 25
52 00
54 10
34 20
16 ,30
54 35
47 40
Port Said : H igh light-house
River Nile: Damietta Mouth
Rosetta Mouth light.
Aboukir Bay: Nelson I. peak
Alexandria: Eunostos Pt. light..
Ben Ghaz;: Castle
Tripoli Harbor: Light-house
Sfax: Ras Tina light
Mehediah : Sidi Jubber
Monastir: Burj el Kelb battery . . .
Hammaniet Bay: Castle flag-staff .
Kalibia Road : Light-house
Cape Bon : Light-house
Tunis: Goletta light
Cape Farina: Extreme
Benzert: N. Jetty light
Galita Island: Monte Guardia
Bona: Fort Genois light
Stora: Singe I. light
Cape Bougaroni: Light-house
Cape Carbon : Light-house
Algier: Light-house near Admiralty
Cape Tenez: Light-house
Oran: Mers el Kebir light
Habibas Island: Light-house .
Zafarin Islands: Light Isabel Segunda I.
Alboran Island : Light-house
Ceuta: Light-house
Tangier: Casbah tower
Cape Spartel : Light-house
35 07 10
,34 33 45
34 54 00
31 15 41
31 31 40
31 29 30
31 21 23
31 11 43
32 06 51
32 54 03
34 39 01
35 30 24
35 45 24
36 23 20
.36 50 12
37 04 45
36 48 19
37 10 42
37 16 38
37 31 16
36 57 15
36 .54 29
37 05 17
36 46 41
36 47 16
36 33 07
35 44 21
,35 43 22
35 11 05
.35 58 00
3.5 53 44
35 47 00
35 47 14
Long. E.
39 46 25
35 13 20
31 25 49
27 46 09
27 47 30
25 58 34
26 47 57
26 57 20
27 09 10
26 47 00
26 47 32
27 27 05
30 45 34
36 10 20
35 46 30
35 44 24
35 51 00
35 28 25
35 21 ,30
35 14 40
35 08 00
35 05 00
33 57 22
33 01 30
33 38 59
32 18 45
31 51 00
30 19 10
30 06 00
29 51 40
20 02 40
13 10 50
10 41 17
11 05 15
10 50 42
10 37 10
11 07 00
11 03 15
10 18 31
10 17 30
9 ,53 21
8 56 12
7 46 40
6 53 11
6 28 37
5 06 22
3 04 13
1 20 36
Long. W.
41 38
1 07 57
2 25 45
3 03 29
5 16 46
5 48 31
5 55 41
Lun. Int.
H. W.
L. W.
•h, m. I A. m.
9 40
9 40
9 45
9 55
10 00
3 35
3 33
2 46
Range.
Spg. i Neap.
ft- I ft-
15 3 15 2.5 0.7
9 45 I 3 35 I 1.2
3 30
1.4
3 30 1.0
3 15
3 45
3 50
9 57
LI
1.2
1.9
4.2
9 55
3.0
8 58 1 2. 6
8 07
7 40
3.3
8.0
WEST COAST OF AFRICA.
El Araish: S. pt. of entrance . . .
SaU; Fort
Cape Dar el Beida: Light-house
35 12 50
34 04 10
33 36 00
6 09 13
6 48 00
7 33 00
1 35
7 45
10.4
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF AFRICA— Continued.
[Page 231
Cape Blanco, North : Extreme
Mogador Harbor: English consulate
Cape Ghir: Extreme
Cape Noun : Extreme
Cape Juby : Extreme
Cape Bojador: Extreme
Penha Grande
Ouro River entrance: Dumford Pt
Pedra de (ialha
Cape Blanco, South: Extreme
Portendik: Village
St. Louis: Light-house
Almadie Point: Light-house
Cape Verde: "Light-house ,.
Port Dakar: Light-house
Cape Manoel : Light-house
Goree Island: Fort
Bird Island : Flagstaff
Bathurst: Flagstaff :
Carabane: Light-house
Nunez River: Sand I
Ponga River entrance: Observation pt . .
Isles de Los: Light-house
Matacong Island: House
Scarcies River: W. end of Yellaboi I
Sierra Leone: Light on cape
N. battery
Sherbro Island: N. island
Sherbro River: Manna Pt
Gallina.s River: W. elbow of Kamasounl.
Cape Mount: \V. peak
Caj* Mesurado: Light-house
Monrovia: Light-house
Marshall : Agent's house
Grand Bassa: Agent's house
Cestos: Factory
Sangwin River: Sangwin Pt
Sinon : Bloobarra Pt
Cape Palma.s: Light-house
Tabou River: Talwu Pt
Axim Bay: Ft. St. Anthony
Cape Three Points: Light-house
Dix Cove: Fort
Tacorafly Bay: Tacorady Pt
Chama Bay: Dutch Fort
EI Mina Bay: Ft. St. George
Cape Coast Castle: Light-house
Accra: Light-house
Lat. N.
Volta River entrance: Dolbens Pt
Lagos River: Light-house
Benin River entrance: N. pt
Bra.ss River: Entrance (approx.)
Calebar River (New) : Rough Corner . . .
Opobo River: W. pt. beacon (approx. ) . .
Quaebo River: Bluff Pt
Calebar River (Old) : Townsend flagstaff
( Dunketown )
Fernando Po Island: Light-house
San Bento River: Joho Pt. (approx.) . . .
Princes Islandr Diamond Rocks, center
of largest
St. Thomas Island: Ft. San Sebastian
light
Anno Bon Island: Turtle Islet.
Cape Lopez: Light-house
Mayumba Bay: Light- house
33 08 00
31 30 30
.30 38 00
28 45 00
27 56 00
26 07 57
25 07 06
23 36 03
22 12 37
20 46 27
18 18 45
16 01 31
14 44 45
14 43 20
14 40 30
14 38 55
14 39 55
13 .39 45
13 28 00
12 35 00
10 36 37
10 03 15
9 30 30
9 16 10
8 57 05
8 30 00
8 29 57
7 40 36
7 22 45
7 00 08
6 44 30
6 19 10
6 19 00
6 08 06
5 54 08
5 26 25
12 42
.59 15
22 10
24 47
52 18
45 00
47 45
53 00
5 01 00
5 04 48
5 06 20
5 31 50
5 46 00
6 25 15
5 46 01
4 16 40
4 23 07
4 27 00
4 30 40
4 56 24
3 46 10
1 .35 00
1 40 42
20 30
Lat. S.
1 24 IS
36 25
3 23 00
Long. \V.
8 35 05
9 43 30
9 50 00
11 02 00
12 56 00
14 29 00
14 50 44
15 58 00
16 48 11
17 05 40
16 02 00
16 30 22
17 32 25
17 30 55
17 25 28
17 26 47
17 24 30
16 40 30
16 35 00
16 44 00
14 42 00
14 04 30
13 44 00
13 26 20
13 18 25
13 18 30
13 14 30
13 04 30
12 31 55
11 38 45
n 22 51
10 49 25
10 50 00
10 22 45
10 04 05
9 34 45
9 20 16
9 02 05
7 44 15
7 21 30
2 14 45
05 45
56 40
45 00
38 00
21 05
13 50
11 30
Long. E.
41 00
3 25 15
5 03 05
6 15 00
7 07 00
7 40 00
7 59 00
8 20 46
8 47 05
9 39 00
7 27 56
6 42 45
5 38 12
8 43 10
10 38 00
Lun. Int. 1 Range.
H.W.
h. m.
'i'bh'
11 55
11 50
11 36
L.W.
Spg.
h. m. . ft.
"i\i\'\ki'.\
Neap.
5 43 j 8. 5
5 38 7. 3
5 23
9 00
7 30
7 40
5 50
5 40
4 50
4 30
4 00
4 25
2 50
1 20
1 30
12 00
11 54
11 05
10 43
10 13
4 20 I 10 32
4 20 ! 10 33
4 50 11 05
10 38
5.9
11.4
11.6
10.4
6.0
4.8
4.3
4.7
6.0
4.2
3.3
7.0
ft-
"5."6
3.9
3.4
5.5 I 2.5
2.7
5.2
5.3
4.8
2.5
3.0
1.8
1.9
2.5
1.8
1.3
2.9
Page 232] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
WEST COAST OF AFRICA— Continued.
1
Place.
j ^
Lun. Int. 1 Range. 1
H. W.
L. W. i Spg. Neap. 1
Loango Bay : Indian Pt. light
O / ft
4 40 00
4 49 00
5 18 30
5 32 30
6 04 36
6 31 50
8 48 24
12 20 00
12 34 43
13 12 30
13 26 05
15 09 00
15 47 30
16 30 00
18 23 00
22 57 00
26 17 00
26 37 52
26 58 30
29 15 12
30 18 33
30 33 07
o / //
11 46 30
11 45 00
12 08 00
12 11 00
12 15 00
12 25 25
13 13 20
13 32 00
13 23 45
12 48 55
12 36 00
12 12 00
11,52 40
11 42 00
11 57 12
14 30 00
14 57 20
15 07 02
15 12 22
16 52 02
17 16 20
17 27 .30
*. m.
4 13
h. m.
10 26
6.5
2.7
Black Point Bay: Sandy Pt
Malemba Bay : Landing Cove
Kabenda Bay : Kabenda Pt. light
Congo River entrance: Sliark Pt
Margate Head : Summit
4 10
10 25
6.0
2.5
St. Paul de Loando: Flagstaff, Ft. San
Miguel
4')
3 40
9 53
4.8
2.0
Lobito Point: Extreme
Benguela: Telegraph office
3 30
9 43
5:5
2.3
Elephant Bay : Friar Rocks
St. Mary Bay: Bav I
Little Fish Bay : tight-house
Port Alexander: Bateman Pt
Great Fish Bay: Tiger Pt
3 66
9 12
5.7
2.4
Walfisch Bay: Light-house
Angra Pequena: Diaz Pt
Elizabeth Bay: S. pt. of Possession I
Port NoUoth: Magistrate's house
2 35
2 25
8 47
8 38
5.5
5.3
2.3
2.2
Roodewal Bay
::;::::::::::::
Saldanha Bay: Constable Hill
33 07 51 18 Oi 2i
33 48 52 18 22 33
33 56 04 1 18 28 40
34 21 12 i 18 29 26
2 20
8 33
5.1
2.1
Table Bay: Robben I. light
Cape Town : Observatory ...
1 36
7 47
4.6
2.0
Cape of Good Hope: Light-house
EAST COAST OF AFSICA AND THJB RED SEA.
Simons Bay : Light-house
34 10 45
34 23 48
34 46 45
34 49 45
34 23 47
34 11 10
34 04 35
34 06 15
34 12 30
34 01 41
33 57 43
33 50 27
33 36 09
33 28 00
33 23 10
33 05 10
33 01 45
32 42 00
32 02 30
31 48 15
31 38 06
31 26 15
29 52 40
29 00 12
28 32 30
28 09 36
25 58 49
24 05 30
23 45 30
22 05 00
21 31 00
20 38 10
20 10 42
18 52 50
18 01 24
17 51 .W
18 27 30
18 50 20
19 38 17
20 00 37
20 48 40
22 09 31
23 03 38
23 24 23
24 50 20
25 42 12
25 37 21
26 17 13
26 54 10
27 03 00
27 20 48
27 49 12
27 55 02
28 22 36
29 06 40
29 21 15
29 33 16
29 48 40
31 03 50
31 51 39
32 27 39
32 38 10
32 35 52
35 29 45
35 31 41
35 29 00
35 29 30
34 53 30
34 46 00
36 11 47
.36 58 30
.<{7 01 09
2 35
8 48
5.2
2.2
Quoin Point" Extreme
Cape Agulhas : Light-house
2 40
8 53
5.2
2.2
Port Beaufort • Flai?-staff
St. Blaize: Light-house
3 18
9 31
5.6
2.0
Knysna Harbor: Fountain beacon
Plettenberg Bay: Summit of Seal Pt
St Francis* Licht-houHP
Port Elizabeth : Light-house
3 21
9 33
5.4
1.9
Port Alfred- Sieiial staff
Waterloo Bay: Maitland Signal Hill
Cove Rock- Center
East London : Light-house
Cape Morgan : Extren\e
Hole-in-the-Wall
3 37
9 50
5.0
1.8
Rama Head: Extreme
Waterfall Bluff
Port Natal ( Durban ) : Light-house
Diiinford Point* Extreme
3 58
10 11
5.6
L6
Cape Vidal : Extreme
Delagoa Bay: Reuben Pt. light
CaDe Corrientea* Small rook
5 10
11 22
11.9
3.4
Innamban Bay: Barrow Hill light
4 30
10 42
11.0
3.2
Sofala : Fort on N. side of entrance
Zambesi River: Kangoni Mouth
4 15
10 27
13.5
3.9
Quillimane: Town
Mazemba River: Entrance
17 15 00 "^s 04. no
1
APPENDIX IV.
MARITIME POSITIONS AXI) TIDAL DATA.
EAST COAST OF AFBICA AND THE BED SEA— Continued.
[Page 233
Place.
Lat. S.
Premeira Islands: Center of Casuarina I.
Angoxa Islands: Center of Hurd I
Mafamale Island: Center
Port Mokamba: Mokambo Pt
Port Mozambique: St. George I. light...
San Sebastian light..
Cape Cabeceira: Lighf^house
Port Conducia: Bar Pt
Lurio Bay : Pando Pt
Pemba Bay: N. pt. light
Querimba Islands: Ibo I. light
Numba Island: E. pt
Cape Delgado: Light-house
Msimbati : Ras Matunda
Mikindini Harbor: Kinizi
ilgan Mwania: Madjori Rock
Lindi River: Fort flagstaff
Mchinga Bay : Observation spot
Kiswere Harbor: Rustinigi
Kilwa Kisiwani: Fort j
Mafia Island : Moresby Pt '
Dar-Es-Salaam : Flagstaff I
Baganioyo: French Mission
Zanzibar: English consulate
Tanga Bay: Light-house
Mombasa: Light-house
Port Melinda: Vasco de Gama's Pillar ..
Laino Bay : Lamo Castle
Manda Roads: E. side of Manda Toto I .
Port Durnford : Foot Pt
Kisimayu Bay: S. pt. of Kisimayu I
Brava: Well
Meurka .\nchorage: S. pt. of town .
Magadoxa: Tower
MuratHill: Peak
Ras Hafun: K. extreme of Africa . .
Cape Guardafui: E. pt
Kal Farun Islet: Center
.\bd-al-Kuri I.sland: NE. pt
Socotra Island : Tamarida, mosque.
Ras Antareh: Extreme of rocky pt
Mait Island: Center
Port Berbera: IJght-house
Zeyla: Mosque
Perim Island : Light-house
Hanf elah Bay : Hanf elah Pt
Disei Island : Village Bay
Ma-ssaua Harbor: N. pt. of entrance ...
Kh6r Nowarat: Shatireh Islet
Suakin : Light-house
Makaua Island: S. pt
St. Johns Island: Peak
Dsedalus Shoal : Light-house
Kosair Anchorage: SVV. angle of fort. . .
Brothers Island : Light-house
Safajah Island: \. summit
Ashrafi Island : Light-house
Ras Gharib: Light-house
Zafarana: Light-house
Suez: Newport Rock
Tor: Ruined fort
Sherra Yahar: Entrance
Sherm Joobbah : Entrance
Sherm Wej : Light-house
Sherm Hassejy : Anchorage
Yeml/j: Anchorage
17 06 30
16 33 24
16 20 30
15 08 00
15 02 12
15 00 45
14 58 20
14 53 00
13 23 40
12 55 45
12 19 30
11 09 18
10 41 20
10 19 22
10 16 31
10 06 43
9 59 30
9 44 22
9 25 36
8 57 15
7 38 10
6 49 41
6 26 10
6 09 43
00 35
04 30
12 48
15 42
13 35
13 00
Long. K
22 35
Lat. N.
1 06 48
1 42 06
2 01 48
2 30 00
10 26 30
11 50 30
12 26 00
12 11 15
12 39 00
11 27 30
11 13 00
10 25 00
11 22 00
12 39 00
44 00
28 10
37 12
15 12
07 00
44 00
36 20
56 30
06 24
18 50
45 48
47 21
20 52
06 29
53 05
13 47
35 45
33 00
13 00
38 35
05 15
40 52
39 45
39 27
38 19
37 19
37 15
36 10
.35 51
34 17
34 50
33 59
33 42
33 06
32 39
32 32
33 36
35 30
35 32
36 27
37 17
38 02
Lun. Int.
39 06 27
39 49 57
40 03 57
40 36 12
40 48 45
40 45 06
40 45 10
40 40 00
40 46 00
40 31 15
40 40 09
40 43 21
40 38 35
40 26 34
40 10 33 i
40 02 14 i
39 46 41
39 47 07
39 39 31
39 30 42
39 54 42
.39 17 05
38 54 27
39 11 08
39 10 20
39 41 13
40 11 21
40 .56 21
40 59 40
41 54 15
42 33 57
44 03 27
44 53 49
45 24 39
46 07 00
51 22 55
51 16 45
52 09 35
52 25 35
53 59 31
49 35 40
47 17 00
44 59 35
43 29 35
43 25 35
4 00
3 59
Range.
Spg. Neap.
ft
.1.
10 12 ! 11.8
10 11
1L3
3 55
10 08
4 05
10 17
4 00
4 30
4 15
10 13
10 42
10 27
6 00 12 12
7 05
1 17
7 30
7 50
45
2 10
6 40
10 35
10 40
10 45
1 18
1 38
6 57
8 22
10.9
14.5
12.1
n.7
7.5
8.5
7.2
4.0
1.7
28 2.
I
4 23
4 28
4 32
1.5
5.5
6.8
ft-
3.4
3.3
4.5
6.0
"5.' 6
"4.9
3.1
6. 1 2. 5
7. 5 .3. 1
3.5
3.0
1. ^
'o.'i
0.8
0.6
2.3
2.8
Page 234] APPENDIX IV.
:\IARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF AFRICA AND THE BED SEA Continued.
u
Place.
Lat. N.
Long. E.
Lun. Int.
Range. 1
H.W.
L.W.
Spg.
Neap.
1
Sherm Rabigh : Anchorage
o / //
22 43 50
21 28 00
20 09 00
19 55 30
19 07 40
18 15 50
16 50 15
16 53 00
15 42 00
15 20 30
14 47 00
14 03 53
13 19 43
o / //
39 00 30
39 10 38
40 12 00
40 30 00
41 03 20
41 27 30
41 58 15
42 29 00
42 38 45
42 34 00
42 56 00
42 45 28
43 13 36
h. m.
A. m.
ft-
/(.
Jiddah: Jezirah el Mifsaka I
3 30
9 42
2. 6 1 6. 8 1
Lith : Agha Islet
Kunfidah : Islet _
Farisan I. Anchorage: Jebel Mandhakh .
,
Loheiya: HillFort
1 15
7 27
2.9
1.2
Hodeida Road
Jebel Zukur Island: X. pt
Mokha: N. Fort
11 45
5 33
4.5
1.9
ISIiANDS OF THE INDIANT OCKATT.
»
V
a
m
m •
m
c
>
1
1
»
«
1
Chitlac Islet: S. end
Betrapar Islet : N. Island
Kittan Islet: S. end
11 40 45
11 35 00
11 27 30
11 13 00
11 06 00
10 47 00
10 32 00
10 06 00
10 03 00
8 16 00
6 55 00
6 59 00
6 25 00
5 26 30
5 01 30
4 25 45
4 44 00
4 10 15
3 41 00
2 57 00
3 16 00
2 10 30
2 07 00
14 30
Lat. S.
41 30
5 40 56
4 52 26
5 53 00
4 37 15
3 43 06
5 15 00
7 13 37
16 25 12
19 40 22
19 52 36
19 59 45
20 08 46
20 24 20
72 42 54
72 09 54
72 59 00
72 44 00
72 41 00
73 40 00
72 37 40
72 15 10
73 35 54
73 01 15
72 55 54
73 12 54
72 41 54
73 20 00
72 53 00
72 57 24
73 28 00
73 30 24
73 24 54
73 34 24
72 48 00
73 03 00
73 35 54
73 13 00
73 06 54
53 41 03
53 23 38
55 27 10
55 27 23
55 12 19
71 43 47
72 23 50
59 46 40
63 25 38
57 39 14
57 32 35
57 29.26
57 47 14
•
10 20
4 00
6.3
3.0
Ameni Islet' N. end
Cabrut Islet: E. end
Seuheli Par: N. islet
Kalneni Islet: S end
11 27
5 15
2.5
1.2
j^g^_l^li Island' N. end
Mah Kundu Island: NE. extreme
Nar Foree Island
To-du Island' Center
Male, or Kings Island : Flagstaff
20
6 25
2.9
1.4
Moluk Island* (Center
Kimbeedso Island" S end
Wahdn Island: E. end
Addii Atoll- Guner I
Amirante Islands: Iledes Roches, N. beach
African Islands
Seychelle Is. , Platte I. : S. end
Port Victoria: End of Ho-
4 22
10 35
4.3
1.2
Bird Island: Tree
Chagos Archipelago, Peros Banhos: Dia-
mond Islet
Diego Garcia: N.end
of Middle I
Cargados Carajos: Establishment I., flag-
staff
1 30
1 50
20
7 43
8 03
6 32
5.8
4.0
5.5
1.7
1.2
1.6
Rodriguez Island : MathurinaBay, Point
Tn'lnt Inland' ljii?ht-house
II
Port Louis: Martello tower, Ft. George..
48
7 00
1.6
0.3
1
APPEJ^DIX IV. [Page 235
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE INDIAN OCEAN— Continued.
1
Place.
Lat. s.
Long. E.
Lun. Int.
Range.
H. W. L. W.
Spg. 1 Neap.
E^union Island: St. Deiiiw li^ht
Bel- \ir lieht
o / //
20 51 38
20 .53 11
20 59 45
21 19 47
15 51 37
10 21 30
10 06 45
O f ft
55 26 59
55 36 18
55 16 IS
55 28 58
54 28 46
56 32 00
51 10 '21
A. m. ! h. m.
/'. /'.
i
St Paul light
;
1
Si
«
If
n
St. Pierre light
11 50
5 38
3.5 1 0.6
AssdassLS Island : NW. i)t - . - -
::::::!:;; i
Farouhar Islands* Hall's house
Alnhonse Island* SE nart f Trees)
7 on .30 ! r,9 44 57
; 1
Coetivy Island: N. end 7 06 00
Cape St. Mary: S. extreme ] 25 39 10
Leven Island: Center ..! 25 12 30
56 22 00
i i
45 06 50
44 17 57
\"" \ \"'
Port Machikora: Barracouta I 25 03 00 44 07 20
!
St. Augustine Bav : Nosi Vei I | 23 38 25
Murderers Bay: Center of Murder I j 22 05 18
Cape St. Vincent: Extreme 21 54 24
Mourondava: Village : 20 18 18
Tsmano: Village .i 19 49 30
Kovra Rvthi Point: Extreme 1 7 .53 00
43 38 20
43 15 20
43 20 21
44 19 21
44 31 30
44 02 20
43 45 18
5 40
11 52 9. 8 2. 9
_ _ _
j 1
1
■*"• 1*'' **'
[
Coffin Island: NosiVao .
17 29 00
16 12 10
16 07 00
15 46 30
1
44 29 05
t
Boyanna Bay : Barabata Pt
45 17 09
45 43 09
46 18 45
46 57 29
47 24 36
47 58 21
47 48 05
47 59 30
48 17 34
1
Cape Tauzon: Extreme
Majunga (Mojanga): Light-house
15 43 45
15 11 42
14 40 18
4 15
11 28
10:9
3.2
Narendri Bav: Moormora Pt
■:::::.::::::: i
Port Kadama: Pt. Blair
13 .59 00
Radama Islandfe: N. pt. Nossuvee 1 i 13 .5.5 40
Baratoube Bav: AmbubukaPt
13 27 15
13 23 38
12 49 30
12 27 20
12 03 18
11 57 30
Nosi B6: Hellville jetty
Minow Islands: N. pt. Great I
48 38 57
48 45 45
49 11 21
49 17 25
49 35 56
49 45 06
49 54 00
49 56 25
50 01 59
Cape San Sebastian : Extreme
Port Liverpool: N. pt. of entrance
Cape Amber: NE. extreme
12 23 20
Port Looke: Pt. Bathurst
12 44 02
12 49 00
J2 56 48
13 21 15
15 15 48
15 54 50
15 27 55
16 14 00
17 00 05
16 42 30
17 23 16
18 09 47
19 55 00
21 58 10
24 46 25
24 59 42
24 58 50
25 01 30
22 22 30
21 29 00
12 26 30
12 47 02
12 16 20
12 25 00
11 34 48
11 40 44
9 46 20
9 22 35
9 41 20
Port Leven: S. pt. Nosi Hau I
Vohemar: Flagstaff. . ..-^-.. .
Cape East: Ugoncv I .
50 31 21
,50 16 05
49 49 11
49 50 59
49 50 59
49 56 15
49 32 04
Venangue B^ Bav : Entrance
Port Choiseul: Maran Seelzy Village
Cape Bellone: Extreme
3 45
9 57
5. i i.5
St. Marvs Island: Light on Madame I ..
Port Taiitang: Flagstaff
Fenerive Point: Flagstaff
Tamatave: Pt. Ilastie
Mahanuru: Town
Matatane : Village
49 25 31
48 52 10
4 00
10 12
7.3
2.1
48 14 50
47 10 34
47 07 20
47 04 24
46 59 11
40 24 10
.39 40 39
46 32 35
45 16 27
44 24 54
43 47 00
47 24 09
43 19 15
46 31 07
46 14 52
47 32 25
Santa Lucia: N. end of town, Obs. Rock.
Point Ytapere: Extreme
Ytapere Bav: N. pt
Fort Dauphin : Flagstaff
4 15
10 27
"T?" ""l.'3 1
Europa Island : Center
Bassas da India: E. pt
......
Geyser Reef: SE. extreme
Ma votta Island : Zaoudzi
4 66
10 13
11.9
2.0
Johanna Lsland: I^anding place, Pomoni
Harbor
Mohilla Island: Numa Choa Harbor
Glorioso Islands: AV. islet
Comoro Island: Islet in Mauroni Bay . . .
Assumption Island: Hummock .. ..
4 45
10 58
10.0
1.7
Aldabra Island: Westl., E. sideentrance.
Cosmoledo Islands: Observation islet
^^^
Page 236] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISIiANDS OF TBE INDIAN OCEAN— Continued.
Prince Edwards Islands: Marion I., Obe.
spot, NE. side
Penguin Islands: Center of SW. islet ..
Possession Island: NW. pt
Twelve Islands: Summit NE. I
Navire Bay
Hog Island: Summit -
East Island: Center
Lat. 8.
46 49 30
46 36 00
46 22 00
46 01 00
46 28 18
46 10 40
46 26 00
Christmas Harbor 48 40 00
BlighsCape 48 26 45
Cape Bourbon 49 42 00
Mollov, Port Roval Sound: U. S. Tr. of
Venus Obs., 1874 49 21 22
Cape Challenger 49 41 00
Balfour Rock 49 29 00
Heard Island: Cape Laurens, NW. end. .
Sealing station
McDonald Island, Summit
St. Pauls Island : Ninepin Rock
Amsterdam Island: Summit, 2,750 feet..
Keeling or Cocos Islands: Direction 1 . . .
Christmas Island : Flying Fish Cove
Long. £.
53 02 45
53 13 00
53 02 50
38 42 51
37 50 00
12 06 22
10 25 19
37 49 15
50 41 30
51 30 15
50 40 00
51 50 00
50 35 00
52 13 00
69 04 00
68 48 20
68 54 00
70 04 31
70 15 00
70 29 50
73 15 30
73 52 00
72 31 45
77 31 53
77 29 15
96 .53 02
105 45 57
Range.
H. W.
A. m.
L. W.
h. m.
Spg.
/t.
14
6 36
4.6
10 40
10 50
5 20
7 10
4 28
4 38
11 32
1 00
3.0
3.3
5.1
4.5
Neap.
1.3
0.9
1.0
1.5
1.3
SOTTTH COAST OF ASIA.
Aden : Telegraph station
Sughra: Sheik's house
Mokatein : Black ruin
Howaiyuh: Sheik's house
Banderburum: SE. house of town
Makalleh Bay: Flagstaff
Shahah Roads: Custom-house
Sharmoh : Single house
Kosair: High house
Sihut: Center of town
Ras Fartak : Extreme pt
Damghot: Town
Merbat: Town
Kuria Maria Is., HuUaniyeh I. : NE. bluff
Ras Sherbe<iat: Point .'.
Cape Isolette: Islet
Masirah Island : Point Abu-Rasas
Point Ras Ye
Ras-al-Hed : Extreme pt
Maskat ( Muscat) : Ma.skat Pt
Deimaniyeh Islands: E. islet
Sneik : Fort
Sohar: SE. tower of town hall
Khaur Fakan Bay: W. end of village...
Ras Musendom : N. end of island
Great Quoin Islet: Center
Sharjah : High tower with flagstaff
Abu-Thabi : Fort flagstaff
Al Beda'a Harlior: Nessah Pt., N. extreme
Ras Rakkin: NW. pt
Bahrain Harbor: Portuguese fort . .
Basrah : Custom-house flagstaff
Kuweit Harbor: N. end of town...
Khdrig Islet: Fort flagstaff
Abu Shahr: Residency flagstaff
Shaikh Shu'aib Islet: "E. end
Kais Islet: NE. pt
Lat. N.
12 47 16
13 22 00
13 24 50
13 28 45
14 20 10
14 31 15
14 43 50
14 49 00
14 54 40
15 12 00
15 .38 00
16 30 00
16 59 00
17 ,32 45
17 53 15
19 00 25
20 10 00
20 31 30
22 32 40
23 38 00
23 52 00
23 51 ,30
24 21 ,50
25 21 00 -
26 24 13
26 30 00
25 21 34
24 29 02
25 17 24
26 10 .55
26 13 56
30 32 00
29 22 56
29 15 25
28 59 07
26 47 40
26 .33 37
Long.
44 59
45 40
46 26
46 39
48 56
49 07
49 35
49 57
50 16
51 10
52 14
52 48
54 43
56 03
56 20
57 51
58 38
.58 58
59 48
58 30
58 08
57 26
56 46
56 22
56 32
56 31
55 24
54 22
51 .33
51 13
50 32
47 51
48 00
E.
07
50
35
00
45
35
05
05
35
30
20
00
29
05
35
35
.35
35
35
50
00
00
12
56
22
29
12
14
32
46
17
23
55
49
8 20
8 50
9 45
9 15
9 30
1 41
4.9
2 07
6.8
2 38
7.0
3 32
3 03
3 20
9.6
8.9
6.0
.50 21 11
50 50 35
53 23 36
54 02 21
5 15
05
7 12
30
11 30
6 17
6.4
'8.' 3'
1 13
2.6
6 40
6.6
2.0
2.8
2.9
4.4
4.1
4.8
1.5
"3.8
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
SOUTH COAST OF ASIA— Continued.
[Page 237
s
s
Place.
Biisiduh: Chapel
Haujam Islet: Ruined mosque
Kasm : Fort
Jashak Bay: Telegraph office
Kub Kalat: High peak, 1,680 feet.
Chahbar Bay: Telegraph office
Gwatar Bay : Islet
Gwadar Bay: Telegraph office
Pasni : Telegraph office
Ormarah : Telegraph office
Sunmiyani: Jam's house
Cape Monze: Peak
Karachi : Manora light
Observatory
Mandavi : Light-house
Bey t ( Bet ) : Light-house
Dwarka: Light- house
Temple spire
Porebander: Light-house
Mangarol : Light-house
Diu Head : Light-house
Kutpur: Light-house
Bhaunagar: Ligiit-house
Perim Island: Light-house
Canibay : Flagstaff
Surat River: Tapti light
Sural: Minaret Adrusah
Ba.ssein : Center of town
Bombay : Observatory
Kenery Island light
Bankot: Fort Victoria
Ratnagherry : Fort
Vizladrug: Fort flagstaff
Cape Ramas: W. bastion of fort ..
Goa : St. Denis Ch urch
Agaa<la light
Vingorla: Signal-station light
Vingorla Rocks: Light-house
Sedashigar Bay: Oyster Rock light
Kuinpta: Light-house
Hind war; Monument
Kundapur: Light-house
Mangalore: Light-house
Kannanur: Liglit-house
Tellicherri : Flagstaff
Maho: Light-house
Calicut: Light-house
Cochin: Light-house
Alipee : Light-house
Quilon : Tongacherri Point light . .
Trevandrum: Observatory
Cape Comorin : Light-house
Trichendore: Pagoda on pt
Tuticorin : Light-house
Paumljen Pass: Light-house
Manaar: Center of town
Colombo: Light-house
Dondra Head: Light-house
Point de Galle: Light-house
Great Bassas Rocks: Light-house .
Little Bassas Rocks: Light-house .
Batticaloa: Light-house
Trincomali: Dock-yard flagstaff. . .
Calimere Point: Light-house
Ncgapatam : Light-house
Pondicherri: Light-house
Lat. N.
26 39 12
26 40 49
26 57 27
25 38 19
25 29 45
25 16 43
25 03 17
25 07 19
25 15 52
25 11 55
25 25 19
24 50 03
47 37
49 .50
50 00
29 20
14 00
14 00
38 00
06 00
41 20
02 21
47 00
35 54
17 00
05 20
12 19
20 10
53 45
42 08
58 00
59 30
33 26
05 12
21 24
29 25
51 10
53 20
49 00
25 00
17 28
38 15
■52 17
51 10
45 00
42 00
15 10
58 00
.30 00
53 20
30 47
04 00
29 55
47 10
17 20
8 59 00
6 55 40
5 55 30
6 01 25
6 10 10
6 25 00
7 45 00
8 33 30
10 18 00
10 45 28
11 55 40
Long. E.
55 16 47
55 54 25
56 17 37
57 46 14
59 40 32
60 37 40
61 26 24
62 19 42
63 28 37
64 37 02
66 35 39
66 39 58
66 58 06
67 01 33
69 20 15
69 04 40
68 57 06
68 58 54
69 36 00
70 06 32
70 50 45
71 49 35
72 14 00
72 21 08
72 35 10
72 38 40
72 49 27
72 48 44
72 48 56
72 48 49
73 02 40
73 15 56
73 19 39
73 54 50
73 54 00
73 46 10
73 37 00
73 27 15
74 03 40
74 22 30
74 26 40
74 39 50
74 50 40
75 21 51
75 29 40
75 31 10
75 46 40
76 14 40
76 20 40
76 34 00
76 56 45
77 32 35
78 07 47
78 11 26
79 12 50
79 53 52
79 50 40
80 34 12
80 13 04
81 28 15
81 44 00
81 41 00
81 13 42
79 51 30
79 50 47
79 50 10
Lull. Int.
H. W.
10 50
9 20
9 20
8 50
10 15
'i2"6.5
4 27
11 26
10 34
10 34
10 50
11 21
11 33
18
1 52
1 37
1 55
2 02
8 10
8 37
L. W.
4 35
3 05
3 05
2 35
4 00
'5'39
11 18
5 08
4 10
4 11
4 28
4 59
5 06
6 16
7 51
7 36
7 49
8 07
1 44
2 37
Range.
Spg.
11.6
7.8
Neap.
7.3
10. 8 5. 2
5.2
'h'.o
6.5
2.7
2.1
2.5
3.0
2.0
2.0
1.9
2.0
2.1
5.3
3.6
8.1 I 3.'
8.1 3.8
3.4
29. 8 1 15. 1
12.0 4.9
2.5
2.4
3.4
1.4
1.0
1.3
0.8
0.5
0.4
"6." 4
0.5
"6." 9
Page 238]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
SOUTH COAST OF ASIA— Continued.
Place.
Madras: Observatory
Light-house
Pulicat: Light-house
Armeghon: Light-house
Kistna: Light-house
Masulipatam: Flagstaff
Coconada: Liglit-house
Vizagapatam: Fort flagstaff
Kalingapatam: Light-house
Gopalpur: Light-house
Gaujam : Fort
Juggernath: Great temple
False Point: Light-house
Balasor River: Chandipur light . .
Saugor Island: Light-house
Diamond Harbor: Flagstaff
Calcutta: Ft. William semaphore.
Lat. N.
Chittagong River: Light-house ,
Akyab: Oyster Reef light ,
old temple ,
Ramree Island: S. pt
Chedubah Island: N\V. peak
Cape Negrais : Extreme
Bassein River: Alguada Reef light
Bassein : Port Dalhousie
Andaman Is. : Table Id., Light-house .
Port Cornwallis, Rock in
entrance
Port Blair, Light-house.
Little Andaman Island,
SE.pt
Krishna Shoal: Light vessel
Rangoon River: Grove Pt. light
Rangoon : (ireat Dagon pagoda
Moulmein: Docks
Moulmein River: Amherst Pt. Hght...
Double Island : Light-house
Tavoy River: Light-house
Mergui: Court-house
Tenasserim
St. Matthew Island: Hasting.-) Harbor.
Pak Chan River: Light-house
13 04 06
13 05 15
13 25 15
13 53 08
15 47 00
16 09 45
16 56 21
17 41 34
18 19 00
19 13 00
19 22 30
19 48 17
20 20 20
21 27 15
21 38 40
22 11 10
22 33 25
22 11 00
20 05 00
20 08 53
18 51 00
18 50 30
16 01 30
15 42 14
16 01 30
14 12 30
13 18 40
11 40 40
10 27 00
15 37 26
16 30 01
16 46 00
16 26 00
16 04 45
15 52 00
13 36 40
12 26 15
12 06 00
10 05 05
9 58 00
Tongka Harbor, Junkseylon Island:
Light-liou.>;e
Pulo Penang: Fort Cornwallis
Dinding Channel : Hospital Rook
One Fathom Bank: Light-house
Cape Rachado: Light-house
Malacca; Stat. St. Pauls Hill
Singapore Strait: Coney Island light...
Singapore: Fullerton Battery
Singapore Strait: Pedra Branca light . . .
Summit Bintang great
hill, 1,25-! feet.....
Rhio Straits, Pulo Sauh: Light-house ..
Terkolei: Light-house
Little(iarras: Light-house
Rhio, Bintang Island: Residency flag-
staff
Pitong Island : Peak
Abang Besar Island : N. pt
Linga Island : Flagstaff
Singkep Island: Mountain summit.
Menali Island: N. pt
Nicobar Islands, Car Nicobar: N. pt .
50 00 i
24 45 I
13 05
52 10
24 08
U 30 i
09 57
1 17 11
1 19 57
Long. E.
80 14 51
80 17 00
80 19 12
80 12 30
80 59 00
81 11 00
82 15 05
83 17 42
84 07 30
84 52 06
.8.5 03 29
85 49 09
86 44 00
87 02 20
88 02 00
88 11 07
88 20 12
91 49 00
92 39 00
92 52 40
93 56 30
93 31 00
94 13 16
94 12 00
94 23 00
93 22 30
92 57 10
92 45 15
92 31 10
95 37 32
96 23 00
96 07 30
97 38 00
97 33 05
97 35 00
98 13 00
98 35 59
99 03 00
98 10 15
97 3.5 00
98 25 30
100 21 44
100 34 15
100 59 12
101 51 02
102 15 00
103 44 47
103 51 15
104 24 08
1 04 20 ; 104 27 21
1 03 13 j 104 10 30
57 10 i 104 19 52
44 30 104 21 19
55 50
36 52
36 30
Lat. S.
12 34
26 13
57 51
Lat. N.
9 15 40
104 25 43
104 04 42
104 11 31
104 36 14
104 30 15
105 38 20
92 48 00
Lun. Int.
H.W.
8 41
8 42
8 48
9 21
1 25
1 02
9 40
3 05
9 50
9 40
4 26
3 07
2 12
10 50
10 40
11 50
5 50
"7'26'
'io'is'
L. W.
ft. m.
■Range.
Spg.
2 26 3. 1
2 35
2 34
4.5
4.4
3 00
9 06
7 56
11.2
13.1
3 28
7.6
9 55
18.7
3 37
3 27
8.6
6.3
11 15
10 49
8 49
16.9
11.7
19.2
4 20
4 10
1.5.6
18.0
5 40
12 00
14.4
1 08
4 02
10.5
""7.'6'
9 40
6 00
3 14
7.1
12 13
11.5
APPENDIX IV.
MAEITIMP; POSITIONS AND TIDAL DATA.
SOUTH COAST OF ASIA— Continued.
[Page 239
Place.
Nieobar Islands, Nancowrv Harbor:
Naval Pt
Great Nieobar: W.
pt, Galathea Bay . .
Acheen(Acheh) Head: Pulo Bras light
N. extreme
Diamond Point : Light-house
Point Baru or Datu : Extreme
Point Bon or Djabon: Extreme
Moeara-Konipehi : Fort
Djani bi : Flagstaff of fort
Palembang: Residency flagstaff
Lam pong Bay : Telok Betong light
Blimbing Bay
Kroe : Village
Engano Island : Barioe anchorage
Bintican : Ri ver mouth
Mega Island : N. pt
Benkulen : Light-house
Bantal: Village
Indrapura Point: Extreme
Pisang: Light-house
Padang: Light-house
Siberaet Island : Sigeb Pt
Katiagam: V'illage
Batoe Islands: N. point of Simoe Islet.
Summit of Tello
Lat. N.
Ayer Bangis: Fort flagstaff
Natal: Fort flagstaff.
Nias Island : Lagoendi Bay
Sitoli
Ijapan
Siboga: Flagstaff
Singkel : Post-office
Bangkaru Islands: Bay
Simaloe Island: NW. pt
Tampat Toewon; Flagstaff
Analaboe
Batve Toetong: Landing place.
8 02 10
6 46 20
5 45 00
5 34 40
5 15 58
Lat. S.
00 32
1 00 55
23 13
35 33
59 26
27 00
55 02
11 24
18 50
48 35
59 25
47 22
2 44 54
2 10 35
59 56
57 53
53 58
07 41
03 13
02 56
Lat. X.
11 41
33 11
34 47
1 17 36
24 16
44 24
16 47
02 32
51 30
14 59
08 14
38 21
Long. E.
93 29 42
93 49 20
95 04 33
95 19 00
97 30 11
103 47 58
104 21 ,30
103 59 14
103 36 41
104 45 34
105 15 58
104 32 36
103 55 42
102 07 28
103 20 18
101 00 58
102 14 50
101 17 25
100 50 06
100 19 28
100 20 19
98 53 58
99 45 20
98 05 55
98 16 43
Lun. Int.
Range.
99 22
99 06
97 43
97 36
97 12
98 46
97 45
97 06
95 56
97 10
96 07
95 34
H. W.
A. m.
9 05
10 00
11 50
L. W.
Spg.
Neap.
h. m.
2 52
3 44
5 34
5 40 I 11 52
5 50 i 12 03
5 35
29
11 48
ft-
8.3
2.8
5.2
8.7
2.3
3.7
2.6
4.0
1.1
5.5
1.4
11 42 2.8
EAST COAST OF ASIA.
s
Java Head : First Pt. light
Sunda Strait: Krakatoa I. peak
North Watcher Island: Light-house. . .
Lucipara I. : Beacon
Banka Island : Tobol Ali Fort
Berikat, summit
Nanka I. : Light-house
Banka Island : Mintok light
Blinyu
Crassok Pt
Shoalwater Island : Light-house
Pulo Lepar: Light-house
Pulo Jelaka: Light-house
Billiton Island: Tandjong Pandan flag-
staff.. 1
Langkuas I. light
Gaspar Island : Peak
Lat. S.
6 44 30
6 08 46
5 12 17
3 13 05
3 00 48
2 34 18
2 23 20
2 04 03
1 38 26
1 29 00
3 19 10
2 56 52
2 52 05
2 44 40
2 32 12
2 24 30
105 11 48
105 26 58
106 27 33
106 13 02
106 27 22
lot) 50 36
105 44 30
105 09 45
105 46 28
106 57 30
107 12 42
106 54 38
107 00 43
107 38 46
107 37 15
107 03 33
5 30
6 50
11 42
37
[9 05]
'[ebb]
[2 08]
[3 17]
[2 52]
'[6 '38]
[8 21]
[9 29]
2.5
3.8
0.7
1.1
[10. 1]
[9.3]
[5.6]
[6.6],
Page 240]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
*
s
Place.
Carimata Island : Sharp peak .
Pulo Eu: Center
Pulo Aor: S. peak, 1,805 feet.
St. Barbe Island: Center of W. side
Direction Island: S. pt
Dato Island : Summit
St. Julian Island : Summit
Tambelan Island: S. pt
Tamban I. obs. station
Victory Island: S. pt
Anamba Islands: White rock
Pulo Repon
Pulo Domar
St. Pierre Rock: S. pt
Natuna Islands: Pyramidal rocks
Semione I
Pulo V'arella: Center ,
Pulo Brala: Center ,
Tringano River: N. pt
Great Redang Harbor: Bukit Maria I . ,
Kalantan: Entrance small river
Cape Patani: NE. pt
Singora: SW. pt. of Ticos I
Koh Krah Islet: SE.pt
Bangkok: Old British factory
Cape Liant: NW. rock of Koh Mesan .
Chentabun River: Entrance, Bar I
Koh Chang: Small island on W. side .
Koh Kong: S. pt. of river entrance
Kusrovie Rock: Center
Koh Tang Rocks: SW. rock of group .
Panjang Island : NW. corner of S W. bay
Obi Islands: Light-house
Saigon : Observatory
Mitho: S. gate of citadel
Cape St. James: Light-house
Cape Padaran : Extreme
Cape Varella: Extreme
Quin Hon : Battery flagstaff
Condore Islands: Light-house
Safatu Island: Summit
CeicerdeMer Island: SW. hill
Natuna Islands: Murundura I., SE. pt.
Low I
Lun. Int.
Lat. S.
Canton Pulo: Light-house
Cham-Callao Islet: Watering place.
Tourane Bay : Light-house
Hon-M^': Summit
Nam-Dinh: Citadel tower
Hon Dau Island: Light-house
Hai-Fong: Observation pagoda
Hai-Duong: Citadel tower
Ha-Noi: Citadel towef
Pak-Hoi: Custom-house flagstaff
Hainan Island: Cape Bastion, extreme .
Gaalong Bay, E. Brother
1 33 24
2 07 00
2 26 30
Lat. N.
07 26
14 19
06 37
55 00
56 52
00 27
.34 41
18 10
25 00
44 31
51 42
03 00
31 00
3 17 00
4 53 00
5 21 40
5 44 21
6 11 53
6 58 01
7 13 54
8 24 47
13 44 20
12 35 08
12 27 43
12 01 20
11 33 00
11 06 25
10 21 20
9 18 14
8 25 20
10 46 47
10 21 16
10 19 51
11 21 00
12 53 40
13 45 23
8 40 06
9 58 23
10 32 36
2 02 55
3 00 GO
15 23 34
15 57 10
16 07 00
19 22 14
20 25 30
20 40 03
20 51 44
20 56 29
21 01 57
21 29 00
18 09 00
18 U .30
Long. E.
Range.
108 55 13
104 17 00
104 34 06
107 13 00
108 01 47
108 37 05
106 45 00
107 32 57
106 24 10
106 18 27
105 35 58
105 52 00
105 22 57
108 38 55
107 21 40
107 42 30
103 40 00
103 38 00
103 08 00
103 01 37
102 20 47
101 18 39
100 36 12
100 45 27
100 28 42
100 56 47
102 04 19
102 15 47
102 57 14
102 47 49
102 56 34
103 29 14
104 48 30
106 42 10
106 20 38
107 04 55
108 58 00
109 23 42
109 14 52
106 41 42
109 06 00
108 56 27
109 06 10
107 48 00
109 05 35
108 32 47
108 11 .30
105 55 22
106 08 41
106 47 10
106 41 08
106 17 .56
105 48 40
109 06 00
109 35 00
109 41 30
H. W.
L. W.
Spg.
Neap.
8 00
1 48
5.8
2.5
8 20
2 08
2.8
8 00
2 00
7.3
1.2
l.'i
10 00
3 50
4.5
2.1
5 00
11 20
9.8
4.2
9 00
2 48
4.3
2.1
5 00
11 12
14.0
6.6
APPENDIX IV. [Page 241
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
a
Place.
Lat. N. i Long. E.
1
Lun. Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
i
3
B
o / //
20 01 15
15 46 30
16 36 00
16 40 07
16 49 55
20 42 03
21 22 30
21 24 15
21 31 00
21 34 00
21 28 00
O f fl
110 16 10
111 14 30
111 40 .30
112 43 32
112 20 44
116 43 07
111 10 30
111 15 25
111 38 30
111 46 43
112 21 30
113 34 00
113 33 25
113 16 30
113 47 00
113 56 20
114 09 31
114 10 02
114 19 25
114 22 07
114 36 45
114 39 12
114 50 00
115 01 00
115 06 54
115 47 56
116 04 26
116 29 44
116 47 00
116 40 22
117 17 04
117 42 00
117 36 48
118 13 30
118 10 00
118 30 11
118 41 00
118 58 00
119 27 07
119 10 36
119 35 00
119 45 00
119 56 07
119 59 02
119 27 16
119 37 35
120 24 06
120 29 40
120 10 00
120 11 12
120 22 42
h. m.
h. m.
ft-
/(.
Observation bank
Tien-pak Harl,or: Pauk Pyah Islet ....
Song-yui Point: Extreme
Hui-lang-san Harbor: Mamechow Islet.
Mandarins Cap: Summit, 200 ft
Macao; Fort Guia liglit
11 50
5 37
8.2
3.8
22 11 40
22 11 24
23 06 35
99 09 nn
9 50
3 38
6.3
3.0
Canton- Dutch Follv lieht
2 00
8 00
5.i
2.4
Gap Rock: Light-house ' 21 48 50
Hnnakonw Cathedral i 5>9 Ifi .52
Wellington Battery
22 16 23
22 03 40
22 15 45
22 27 06
9 20
2 52
4.4
2.0
Nine-pin Rock: Center
22 24 06
22 30 42
22 32 54
22 18 30
22 48 14
22 48 07
22 56 24
Pank Piah Rook' Summit
Pedra Blanca Rock: Summit, 130 ft
Cnnohi Point- Hill
"Rrpakpr Point' Tjicht-house
Cape of Good Hope : Light-house
23 14 00
23 20 43
23 15 43
2 50
9 00
7.5
3.5
BrotherH Islets- SE. Islet I 2.S 32 30
Tong-sang Harbor: Fall Peak
23 47 15
24 09 49
1 24 23 16
24 25 44
11 20
5 08
12.0
7.6
Chapel Island : Light-house ..
05
6 13
15.5
9.9
Chinchin Harbor: Pisai Islet 24 49 13
Pyramid Point: Extreme 24 52 12
Ockseu Island: Light-house i 24 59 36
Sorrel Rock: Summit i 25 02 18
Lam vit Island: High Cone Peak 25 12 00
Hungwha Channel: Sentry I < 25 16 30
Turnabout Island: Light-house 25 26 10
East Dog Island: Light-house | 25 58 10
Min River: Pagoda, Losing I ' 25 59 00
Temple Pt ' 26 08 26
Alligator Island: Summit 26 09 29
Tung-yung Islands: Peak, N. end : 26 22 37
Coney Island: Summit ' 26 .30 00
Double Peak Island: Highest peak l 26 36 06
Pih-seang Island: Town I ! 26 42 30
Dangerous Rock : Summit 26 51 25
Tae Islands: Summit ' 26 .58 ,52
1
30
9 45
7 00
3 33
19.3
19.0
12.2
12.0
120 .32 33
120 42 34
120 25 .50
120 32 42
i 27 09 20
i 27 09 42
9 50
3 38
17.2
10.9
Ping-fong Island : Summit
Pi h-q nan Peak: Summit ! 27 19 18
PortNamki: E. horn ! 27 26 18
Pih-ki-shan Island: Summit i 27 37 36
Pe-shan Islands: Summit, SW. end i 28 05 07
Tung-chuh Island: Summit i 28 43 45
Kweshan Islands: Patahecock 29 22 45
Nimrod Sound: Middle islet 29 34 20
Tong-ting Islet: Summit ' 29 51 53
Chin-hai: Citadel 1 29 57 08
Ning-po: Square I. light 29 .59 21
Chusan Islands: Ting-hai Harbor 1 .30 04 .30
120 27 14
121 06 36
121 12 09
121 30 04
121 55 21
122 13 16
121 43 15
122 35 24
121 43 06
121 45 22
122 03 47
i
1
1
1
1 00
7 12
8.8
4.6
1
24972°— 12-
-16
Page 242]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
Place.
Video Island : Summit
West Volcano Island : Light-house .
Chapu : Battery
Gutzlaff Island : Light-house
Saddle Islands: N. Saddle light
West Barren Island: Suniniit
Shanghai: Eng. consulate flagstaff .
Wusung: Light-hoiise
Shaweishan Island: Light-house...
Pescadores Islands: Fisher I. light
Second pt.on N.side
Makung Harbor. .
South Cape: Light-house
Takau : Saracen Head
Port Heongsan
Tum-sui Harbor: White Fort
Kelung Harbor: Light-house
Soo (Sauo) Bay: Beach near village
Botel Tobago Sima: S. extreme
Lat. N.
Tanjong Datu
Sarawak River: Po Pt. light ,
Sanlwak : Fort
Cape Sirik: Light-house
Tanjong Barram
Bruni River: Light-house
Labuan I., Victoria Hbr. : Light-house.
Sandakhan Harbor: Light-house ,
I'nsang: Anchorage ,
Cape Kaniongan: E. pt. of Borneo
Pamaroongl. : E. pt. delta River Koetei.
Pulo Lant: S. pt. Koengit Islet
Selatan Point: Extreme of Sita Pt
Bandjerma.sin : Residency flagstaff
Sampit Bay: Bandaran Pt
Kottaringin Bay: Samadra 1
Succadana: Town
Padang Tikar: Point
Port Laykan: 8W. pt. of Celebes
51aca.ssar: Fort light
Palos Bay: Village at head
Cape Rivers: NE. Cape, Slime Islet...
Gorontalo: Light-house
Manado Bay : Light-house
Bajuren Island: Summit
Tagulanda Island: Peak
Seao Island : Conical peak
Sauguir Island : S. pt. t'ape I'alurabatu .
Taluat Island: Kabruang I., SE. pt...
Cape Flesko: Extreme
Cape Talabo: E. end...
Wowoni Island: N. pt .
Bouton Island: N. pt ..
E. pt . .
Fort...
Cape Lassa: Extreme . .
Salavar Ifjland: N. pt . .
S. pt . .
30 08 04
30 20 50
30 36 00
30 48 37
30 51 41
30 44 07
31 14 42
31 23 18
31 25 27
Long. E.
122 45 48
121 51 25
121 03 00
122 10 12
122 40 17
123 08 27
121 28 .55
121 29 36
122 14 12
23 32 53 I 119 28 05
23 32 54 I 119 30 12
21 65 00
22 36 14
24 46 00
25 10 24
25 09 12
24 35 28
22 01 40
05 15
43 50
33 55
45 20
36 15
02 00
15 25
50 10
16 30
04 00
Lat. .S.
45 00
05 42
10 40
18 55
16 00
54 00
14 00
40 00
5 36 00
5 08 09
57 00
Lat. N.
1 20 00
29 41
1 31 00
2 07 00
2 22 00
2 44 00
3 21 00
3 49 00
27 00
Lat. S.
46 00
3 58 00
23 30
15 00
29 15
35 00
47 00
26 00
Lun. Int.
H. W.
120 51 00
120 15 54
120 55 00
121 25 00
121 44 28
121 49 20
121 39 45
109 39 07
110 30 30
109 20 40
111 21 20
113 58 57
115 03 00
115 16 05
118 07 20
119 16 00
118 56 00
117 37 00
116 01 40
114 42 18
114 34 56
113 08 00
111 24 00
109 58 00
109 16 00
119 26 00
119 23 55
119 47 30
120 43 30
123 03 08
124 50 00
125 22 00
125 24 30
125 26 00
125 39 00
127 02 30
124 26 00
123 27 00
123 00 00
123 04 00
123 16 00
122 36 41
120 29 00
120 30 00
120 28 30
12
9 45
10 00
10 15
6 00
9 35
12 00
[7 45]
00
4 40
6 00
L. w.
fu m, /t
Range.
Spg.
8 06 I 9. 1
3 32
3 47
4 03
12 13
10 12
11 35
3 23
5 50
4.0
8.0
3.0
5.8
9.0
14.1
5.5
5.2
[1 33], [7.0]
47 i 7. 2
10 55 i 3. 9
12 15
4.3
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
[Page 243
^
Place.
LatS.
Long. E.
Lun
Int.
Range.
H. W.
L.W.
Spg.
Neap.
it
>
m
V
s
Anjer: Fourth pt. light
6 04 15
6 01 20
() 07 40
6 35 45
5 56 15
6 43 00
6 51 09
6 51 29
6 57 09
6 42 18
7 12 10
7 37 30
7 02 00
7 02 30
7 43 25
7 49 00
8 12 30
8 47 00
8 32 00
7 46 30
7 25 00
5 52 57
5 51 18
5 32 28
5 05 46
8 05 30
8 21 00
8 42 30
8 23 00
8 34 15
8 32 00
8 12 30
8 27 00
6 31 00
7 30 00
7 35 00
6 05 50
6 07 00
5 15 00
6 17 00
6 43 00
5 28 .30
8 16 15
8 50 55
8 04 45
7 48 00
8 20 30
8 .33 00
8 34 00
8 12 00
8 34 00
9 00 00
10 09 54
10 46 00
10 29 00
9 35 03
7 53 00
7 38 00
o / //
105 53 05
106 08 20
106 48 37
106 49 11
108 22 37
108 34 00
109 08 07
109 41 08
110 25 03
111 20 32
112 43 58
112 55 00
112 41 09
113 53 45
113 41 10
114 26 .53
114 22 55
114 25 13
113 15 00
109 02 12
106 24 30
110 25 29
112 .39 10
114 23 42
114 35 00
115 03 48
115 28 00
115 08 47
116 27 ,30
116 04 09
117 20 33
117 57 00
118 43 55
118 43 00
117 56 00
117 22 00
118 56 50
122 40 00
123 .32 00
123 59 00
126 43 ,30
127 30 00
120 29 55
121 38 40
122 .52 00
123 31 00
123 15 00
123 22 00
124 06 00
124 23 00
125 33 57
124 52 00
123 33 57
122 52 00
121 46 00
120 14 30
126 22 00
127 19 00
A. m.
7 11
h. m.
58
i-.
ft.
0.7
Batavia; Obyerv'atorv
[11 58]
[5 46]
[3.0]
Buitenzorg: Palace tower
Boompjeo Island: Racket I. light
Cheribon: Light-house
Tegal: Flagstaff
Pekalongan: Light W. of entrance
Samarang: Light-house
[6 00]
[12 13]
[4.0]
Rem bang: Residency flagstaff
Surabaya : Time-ball station
12 07
11 44
5 54
5 31
4.9
6.2
1.7
2.3
Pasuruan :' Light-house
Soemenep flagstaff
Besuki: Light-house
Cape Sedano : NE. pt. of Java
I
Banjuwangi: Fort
10 00
3 45
7.8
2.6
Barung Island : S. pt
Kambangau Island: Light-house
Cape Anjoe : Extreme
8 33
2 21
5.2
1.8
Karimon Djawa Island: Flagstaff
Rawean Island : Sangkapura flaastaff . . .
Great Solombo Island: N W. pt
Arentes Island : S. pt
Bali Island: Billing light-house
Peak, 11,326 ft
......... 1
• Badong Bav, Kotta village.
Lombok Island: Peak ]'2,379 ft
Ampenam light
Sumbawa I. : Sumbawa village
Tambora \'()l('ano, sum-
mit E. side of crater . . .
Bima, flagstaff
Postilion Islands: N. island
10 50
4 38
8.7
3.0
7 50
1 37
5.8
2.0
00
6 12
5.7
2.0
Maria Reigersbergen I
Ardassier Islands: S. id
Brill Reef: Light-house
Hegadis Island
.
Token Bessi I. : Wangi-Wingi, NW. pt.
Binongko, S. pt
Gunong Api : V'olcano '.
Lucipari Islands: N. islet
Flores Island: Reo village
Ende village
Flores Head, extreme...
Komba Island: Peak, S. part
Adenara Island : Summit, Mount Woka.
Lombata Island: Mount Lamararap
Pantar Island: S. jteak of saddle on S. ])t
Ornbay Island: Dololo anchorage
Timor Island: Deli, custom-house
Atapopa
45
6 58
5.7
2.0
Koupang, Fort Concor-
dia
10 50
4 37
8.5
2.9
Rotti Island: W. pt
Saru Island: Seba Bay, on NW. side...
Sandalwood Island : Nangamessie
Wetta Island : 11 waki road
11 20
5 07
16.5
5.6
Roma Island: W. pt
Page 244]
APPENDIX IV.
3IARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
Place.
Moa Island: Buffalo Peak, 4,100 ft
Sermalta I.sland : NE. pt
Damma Island : Kulewatta Harbor, N.pt
Nila Island : Center
Mano or Bird Island: NW. extremity.
Timor Laut Island: Olilet, on E. coast.
Vordate Island : S. pt
Mulu Island: N. pt
Arru Islands: S. island
N. pt
Great Ki Island : S. pt ,
Tello Islands: S. island, summit
Tehor Island: NE. pt
Matabella Islands: Kukur
Gorani Islands: Goram Mosque
Banda Island : Mole
Bouro Island, Kajeli: Fort Defense
Ceram Island : Kawa
Amboina Island: Light-liouse
Xulla Islands, Taliabo Island: NW. pt.
Mangola Island: E. pt .
Besi Island: E. pt
Oby Major Island : W. pt
Popa Island: Outer Extremity Bay
Mysole Island : Ef be Harbor
Gebey Islands: NW. pt ,
Gillolo Island: (Jape Tabo: E. extreme
Cape Salawag: NE. pt . ,
D3rrick Point: N. ex-
treme
Molucca Is. , Makkian I. : Fort Reeburgh
Ternate Island: Residency
Batian Island : Church ..
Meiaco-Sima Is., Kumi I; N. Beach .
Broughton Bay: Land-
ing pla(«
Port Haddington:
Hamilton pt
Tai-pin-san: Hirara,
Karimata Anch
Raleigh Rock: Summit, 270 ft
Ti-ao-usu Island: Summit, 600 ft
Hoa-pin-su Island: N. face
Loo Choo Islands, Great Loo Choo:
Nafa-Kiang
Yori-sima, 413 ft..
Yerabu-sima peak,
687 ft
Kakirouma: Sum-
mit. 2,207 ft
Iwo-sima: Volca-
no, 541 ft
Oho-sima: N. ex-
treme
Kikai-jinia: Sum-
mit, 867 ft
8 12 00
8 14 00
7 03 00
6 44 00
5 32 50
55 00
04 00
35 00
10 00
20 00
56 00
20 00
44 00
33 00
: 03 05
31 53
22 48
55 52
41 00
44 00
48 12
28 00
30 00
11 21
04 00
Lat.N.
02 02
11 00
1 26 00
2 12 00
24 00
47 13
Lat. S.
38 03
Lat. N.
24 26 00
24 21 30
24 25 00
24 48 18
25 55 00
25 58 30
25 47 07
26 12 25
27 02 00
27 21 00
27 44 00
27 53 00
28 31 40
28 18 00
Lun. Int.
Long. E.
Range.
128 01
129 00
128 28
129 29
130 17
131 23
131 55
131 40
134 24
134 40
132 .54
131 58
131 47
131 50
131 25
129 53
127 06
128 07
128 10
122 20
126 21
126 01
127 18
129 55
130 12
129 17 30
128 52 00
128 37 00
128 03 30
127 21 00
127 22 39
127 28 21
122 56 00
124 17 40
124 06 40
125 17 57
124 35 00
123 40 00
123 30 31
127 40 10
128 25 24
128 .33 10
128 59 00
128 14 30
129 42 30
129 59 00
H. W.
L. W:
A. m.
Neap.
1 45
1 20
7 57
7 32
9.0
4.2
6.6
3.1
2 20
8 32
7.5
5.5
5 00
11 10
3.9
2.9
7 27
1 14
4.9
2.1
6 30
15
5.8
2.5
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
[Page 245
BaliSbac Island, Cape Melville: Light-
house
Palawan Island, Cape Bovliluyan: S.
extreme
Victoria Peak, 5,680 ft.
Port Royalist: Tide
Pole Pt. Light
TavtavFort
Port Barton : Bubon Pt .
Kabuli I. : Summit, N.
extreme
Cuyo Island: Obs. spot
Agutaya Islet: Summit of Mt. Aguade. .
Quiniluban Islet: Summit
Culion Island: Fort
Busuanga Island: Mt. Tundalara
Apo Islet: Summit
Caluya Island : Summit
Semerara Island : N. extremity
Mindoro Island: Mangarin Pt., SE. ex-
tremity
Sablayan Pt.,Vantay-
Monte Calavite
Escarceo Pt
Pt. Dumaly
Ylin Island
Lubang Island, Port
Tulig
Luzon Island, Batangas: Ast. station...
Balayan : Plaza Rizal
Loro Peak : Suiiimit, 3,985
feet
CaballoL: Light-house .
Corregidor Island: Light-
house
Cavite: Sangley Pt. light.
Manila: Pasig light-house
Manila: Cathedral
Subig: Town
Capones Islet: Light-house
Iba: Ast. station
Port Masinloc: Bani Pt..
Santa Cruz: Plaza
Sual: Army Hospital
Silaqui Islet: Summit ...
Port San Fernando:
Main street
Candon: Ast. station
Port Santiago: Remark-
able tree S. of port
Vigan : Race track
Salomague Island: Port
Salomague flagstaff
Currimao: Town
Capa Bojeador: Light-
house
Mairaira Pt. : Semaphore
Aparri: Plaza
Port San Vicente: San
Vicente Islet
CapeEngaiio: Rofia Islet
Camiguin I. : Summit
Fuga Island: W. summit.
Dalupiri Island : Peak . . .
Calayan Island: NE. pt
Babayan Claro Island : W. pt
Lat. N.
7 49 25
8 20 25
9 22 30
9 43 43
10 50 00
10 29 19
11 26 25
10 51 26
11 09 09
11 25 47
11 53 53
12 02 09
12 39 46
11 54 28
12 06 45
12 20 03
12 50 15
13 28 40
13 31 35
13 06 05
12 17 15
13 49 30
13 45 22
13 56 17
14 12 20
14 21 48
14 22 27
14 29 50
14 35 49
14 35 31
14 52 36
14 55 33
15 19 30
15 .'54 48
15 45 43
16 04 06
16 27 15
16 37 15
17 11 43
17 16 55
17 33 56
17 47 17
18 01 09
18 31 08
18 39 02
18 21 43
18 28 32
18 32 02
18 50 26
18 52 54
19 03 03
19 22 00
19 30 00
Lun. Int.
Long. E.
H.W.
" I h.
117 00 00
117 09 35
118 17 30
118 43 03
119 31 10
119 05 36
119 29 55
121 00 25
120 56 26
120 45 38
120 00 48
120 12 56
120 27 18
121 30 24
121 20 10
121 03 33
120 44 42
120 22 33
120 59 17
121 29 20
121 01 53
120 09 58
121 02 56
120 43 37
120 38 10
120 36 40
120 33 48
120 54 40
120 57 19
120 58 06
120 13 52
120 00 15
119 57 11
119 54 16
119 54 00
120 06 01
119 56 10
120 18 25
120 26 14
120 25 07
120 22 SI
120 25 04
120 28 44
120 35 ,35
120 50 53
121 37 27
122 04 14
122 05 49
121 48 26
121 15 42
121 11 28
121 32 00
121 52 00
L.W.
[11 30] [5 20]
[11 07]
[10 22]
10 44
'[9 '42]
[4 50]
[3 66]
[4 10]
'i4"33i
[10 20]
[10 21]
[9 40]
5 43
6 00
[3 33]
[3 44]
[3 29]
-0 02
-0 12
Range.
Spg. Neap.
/(.
[6.5]
[4.9]
[4.4]
[4.6]
[3.1]
[2.4].
[2.3],
[2.6],
3.2
1.9
5.0
2.7
Page 246]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
i
8
•a
a
g
Place.
Balingtang Islands
Bataii Iwland: Mount Irada
Ibayat Island: Mount Santa Rosa
Yami Island : Islet off S\V. part
Luzon Island, Port Dima8ala.san: En-
trance
Polillo I.: Port Polillo. .
Tabaco: Church belfry .
Cautanduanco Islands:
N. islet
Cautanduanco Islands:
S. extreme
Point Calaan: S. extreme
Port Sorsogon, Tinacos
Islet
Masbate Island, Palanog: Pier
Bugui Pt. light-house..
Camasusu I.: Summit .
Tintolo Point: Extreme
Burias Island : Busainga
Marinduque I. : Summitof MountCatala.
Maestro de Campo Island, Port Con-
cepcion : Point Fernandez
Ban ton Island: Ban ton Mountain
Tablas Island : Tablas Head
Sanguilan Pt
Carabao Island: AV. pt
Romblon Island: Sabang Pt. light
Summit over port
Sibuyan Island: Summit
Samar Island, Guiuan: Pier .'
Catbalogan : Fort
Maripipi Island: Summit
Leyte, Tacloban
Ormoc: Ast. station
Palompon: Church
Maa.«in
Bohol I., Lapiniu I. ; Mount Basiao
Cebu Island, Cebu : Plaza
Siquiquor Island, Port Canoan: S. pt. of
entrance
Negros Island, Port Bunbonon: E. pt.
of entrance
Dumaguete : Tt)wn
Volcano of Malaspina,
8,192 ft
Bacalod: Town
Guimaras I., Inampulugan I., SW. pt ..
Panay Island, Iloilo: Fort
San Jos6
Pan de Azucar .«.
Batbatan Island: Summit
Pucio Point: Extreme...
Port Batan: Village
Capiz: Town
Siargao Island, Port Sapao: Semaphore.
Gibdo Island : Semaphore
Bucas Island : E. pt. of Port Sibanga . . .
Mindanao Island : Surigao
Cape St. Augustin . . .
Mindanao Island, Da vao : Mole
Saranguni Islets: W.
islet
Ba-sianang Bay: N.
pt. of Donauang I.
Polloc: Small hill
back of town
19 58 30
20 28 30
20 48 00
21 04 56
17 20 17
14 51 00
r.i 21 33
14 09 00
13 28 30
12 31 20
12 52 20
12 22 10
12 36 00
12 10 03
11 56 m
13 07 40
13 18 10
12 54 03
12 56 56
12 38 42
12 33 44
12 03 15
12 36 00
12 35 33
12 24 55
11 01 30
11 46 44
11 47 30
11 15 08
11 00 17
11 02 37
10 07 .39
10 03 22
10 17 30
9 15 17
9 03 87
9 18 25
10 24 a5
10 40 21
10 26 38
10 41 27
10 44 08
11 16 47
11 28 20
11 45 30
11 35 40
11 35 06
10 11 26
9 53 00
9 41 34
9 47 53
6 14 30
7 01 22
5 22 ,30
6 28 50
7 21 15
Long. E.
122 14 00
122 01 20
121 52 30
121 58 24
122 19 20
121 54 48
123 43 53
124 06 48
124 04 48
124 04 18
123 49 22
123 35 58
123 14 36
123 12 47
123 07 34
123 02 45
121 54 33
121 43 08
122 04 48
122 08 38
121 58 32
121 53 53
122 17 08
122 16 26
122 33 23
125 43 14
124 51 37
124 18 15
124 59 56
124 .36 20
124 22 07
124 50 15
124 32 35
123 54 18
123 34 26
123 06 09
123 18 43
123 07 05
122 55 42
122 40 20
122 34 26
121 54 27
122 09 09
121 52 .36
121 58 59
122 28 50
122 45 03
126 02 53
125 31 17
125 58 22
125 28 30
125 47 48
125 34 ,35
125 13 48
123 57 37
124 11 42
Lun. Int.
H. W.
ft. m.
6 08
[4 30]
6 53
11 47
11 06
[11 40]
6 00
L. W.
A. m.
00
[10 20]
1 25
4 50
5 22
Range.
Spg. Neap.
5.2
[5.5],
1.5
1.1
2.8
2.0
4.2
1.9
[6 15]
-o'is'
[6.5]
6.9
5.1
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
[Page 247
Place.
Lat. N.
Long. £.
Lun. Int.
Range.
H. W.
L. W.
Spg. Neap.
■8
S
a
Mindanao Island, Santa Cruz Islands:
SE. islet
Zamboanga: Fort...
Sibuoo Bay: Hill S.
of beach
Port Sta. Maria:
Fort
Dapitan: Village
Misamis: Fort
Camiguin Island: Mount Camiguin
Sombrero Rock: Center
Piedra Blanca: Center
Cagayanes Islands: Rocky islet be-
tween two larger islands
San Miguel Isles: E. pt. of Manuk Ma-
nukan .■
Cagayan Jolo Island: Middle of W.
coast
Omapui Lsland: NW. extreme
Sibutu Island: Hill on E. coast
Simonor Island: NW. pt
Bahaltolis Island: Sandakan Harbor
Bongao Island : S. pt
Keenapoussan Island: Center
Bubuan Island : Lagoon entrance
Cuad Ba.sang Island : SW. pt
Siassi: Town
Bulipongpong Island: Center hill
Tapul Island: Center hill, 1,676 ft
Jolo Islands: Maimbun Anchorage, dry
bank
Dalrymple Harbor, Tul-
yan Islet
Jolo light-house
Doc Can Islet: W. extreme
Pangituran Island : SW. pt
Basilan Island : La Isabela
Wang-kia-tia Bay: Langwang temple ..
Kyauchau Bay: Yunuisan light
Staunton Island: Landing place, N. side.
Shantung Promontory: Light-house
Weihaiwei: Light, S. side harlx)r
Chifu : Light-house
Fort flagstaff
Miautao Island: Peak of N. Island
Pei-ho: S. Taku Fort, S. Cavalier
Tientsin: Shore opp. NJ;. angle of wall. .
Shahiitien Island: Light-house
Niuchwang: Lightship
Hulu-shan Bay : N. side
Port Adams: Entry
Liao-ti-shan Promontory: SW. pt. light
Port Arthur: Obs. spot
Ta-lien-wan Bay: Isthmus on S. San-
shan I
Round Island : Summit
Thornton Haven, Hai-yun-tan Island:
Beach opposite Temple Point
Choda Island: S. pt
Sir James Hall Islands: N. island
Chemulpo: So Wolmi
Marjori banks Harbor: Manzoc Islet
Tas de toin Islet: Center
Guerin Island: Summit, 969 ft
6 52 15
6 54 03
7 18 05
7 45 41
8 40 15
8 08 29
9 10 19
10 43 00
10 27 00
9 35 30
7 43 00
7 00 38
4 54 10
4 49 30
4 55 30
5 .50 00
5 00 30
5 13 00
25 15
27 10
32 40
41 30
44 30
5 54 45
6 02 30
6 03 40
5 52 30
6 15 15
6 42 43
35 39 00
36 02 50
36 45 29
37 24 00
37 27 41
37 34 10
37 32 51
38 23 37
38 58 16
39 09 00
38 56 00
40 35 00
39 30 46
39 16 00
38 43 17
38 47 50
38 52 38
38 40 00
39 04 00
38 27 00
37 58 00
37 27 40
36 26 45
36 24 30
36 07 00
122 04 00
122 04 52
122 03 18
122 04 58
123 23 13
123 50 44
124 42 50
121 33 00
121 03 00
121 23 30
118 27 00
118 26 06
119 22 45
119 48 00
119 46 45
118 11 00
119 44 15
120 40 45
120 35 00
120 11 30
120 48 25
120 49 45
120 55 00
121 00 40
121 18 20
120 58 40
119 55 55
120 29 30
121 56 50
119 51 30
120 17 30
122 16 48
122 42 00
122 15 05
121 31 09
121 21 27
120 55 00
117 42 48
117 11 44
118 31 00
122 00 00
121 18i)3
121 35 59
121 08 26
121 15 54
121 51 59
122 11 30
123 10 34
124 34 40
124 34 30
126 36 27
126 28 00
126 24 00
126 01 09
A. m.
A. m.
ft.
6 50
42 i 3. i
[10 48]
[4 50]:
[5.1].
5 54
[9 38]
4 50
4 00
9 20
10 25
-0 18
8.6
6.4
[3 10]
[5.0]
11 03
11.4
6.0
10 12
3 08
4 13
6.8
9.0
8.1
5.0
6.6
6.0
6 50
4 30
10 05
4 19
LOO
10 50
4.5
3.3
3 53
7.5
5.5
10 31
28.8
1L6
Page 248]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
Place.
Kokoun-tan Islands: Camp Islet
Barren Island : Center, 600 ft
Sea Rock: Center, 160 ft
Modeste Island: N. peak, 1,228 ft
Ross Island: Peak, 1,920 ft
Kuper Harbor : NE. extreme of Josling I
Port Hamilton: W. pt. of Obs. Island.
Bate Islands: Summit Thornton Islet..
Montravel Island: Center, 1,041 feet. . .
Quelpart Island: Beaufort I., middle
of W. side
Observation Island: Point of W. arm. .
Sentinel Island: Summit, 400 feet
Broughton Head: Extreme
Tsau-Iiang-hai Harbor: Light-house . . .
Tsu Sima : Observation rock
Iki Sima: Summit, S. end of island
Oro No Sima: Summit, 277 ft
Kosime NoOsima: Summit Wilson I..
Yeboshi Sima: Light-house
Yobuko Harbor: Bluff opi)osite Nicoya
Hirado NoSeto: Taske light
Goto Island : Ose Saki light
Pallas Rocks: S. rock
Meiaco Sima: Ears Peak
Nagasaki: Transit Venus Station
Kuchinotsu: Light-house
Kagoshima: Breakwater light
Tsukarase Rocks: Summit, 96 ft
UjiShima: High peak, 1,097 ft
Yamagawa Harbor: Spit N. of town
Satano Misaki: Light-house
Kusakaki Jima: Ingersoll Rocks, 530 ft
Kuro Sima: 2, 160 ft.
Iwo Shima: Peak, 2,469 ft
Yakuno Shima : Mount Matomi, 6,252 ft
Firase Rocks: Highest, 92 ft
Kuchino Shima: Summit, 2,230 ft
Guaja Shima: Summit, 1,687 ft
Naka no Shima: Peak, 3,400 ft
Suwanose Jima: Volcano, 2,706 ft
Tokara J ima: Summit, 860 ft
Yoko Shima: Summit, 1,700 ft
Shimonoseki Strait: Meji Zaki, extreme
Rokuren Island: Light-house
Shirasu Reef: Light-house
Susaki: SW. battery
Tomo Roads: Tamatsu Sima
Port Okayama: Take Sima temple
Wusimado Pt. : Wusimado Peak, 548 ft
Akashi-no-seto: Maico Fort
Hiogo: Wada Misaki light
Kobe: Light-house
Osaka: Fort Temposan light
Sakai: Pier-head light
Osaki Bay : Tree Islet, S. pt
Yura No Uchi: Pier
Tanabe Bay: Fossil pt
Oo-.sima Hbr. : Kashinosaki light, E. pt
Uragami Harbor: Village pt ,
Owa.shi Bay: Hikimoto ,
Mura Harbor: Osima Islet ,
35 48 08
35 21 00
34 42 00
34 42 30
34 06 00
34 17 20
34 01 23
33 57 00
33 59 00
33 29 40
34 39 00
34 33 00
34 48 00
35 07 15
34 18 55
33 44 30
33 52 10
33 53 50
33 41 30
33 32 30
33 23 31
32 36 45
32 13 12
32 03 00
32 43 21
32 36 05
31 35 39
31 20 00
31 12 00
31 12 43
30 59 30
30 51 00
30 50 00
30 47 00
30 17 00
30 05 00
29 59 00
29 54 00
29 52 00
29 38 00
29 08 00
28 47 30
33 57 46
33 58 53
33 59 11
33 23 19
34 22 37
34 35 58
34 37 27
34 38 05
34 39 20
34 41 18
34 39 45
34 35 12
34 07 42
33 57 34
33 41 14
33 28 15
33 33 37
34 06 10
34 13 52
Lun. Int.
Long. E.
Range.
126 31 00
125 58 00
126 19 45
125 16 00
125 07 00
126 35 28
127 18 34
126 18 00
126 55 00
126 58 25
128 14 00
128 40 00
128 44 00
129 02 10
129 13 06
129 42 30
130 02 OO
130 25 20
129 58 50
129 52 43
129 33 21
128 36 10
128 04 39
128 25 00
129 52 25
130 13*40
130 33 49
129 46 20
129 29 00
130 37 00
130 39 30
129 28 00
129 55 30
130 18 00
1.30 32 00
130 03 00
129 56 00
129 33 00
129 52 30
129 42 00
129 13 30
129 01 30
130 57 50
130 52 07
130 47 36
133 17 OO
133 23 23
133 59 24
134 09 21
135 01 51
135 10 56
135 11 34
135 26 00
135 27 44
135 08 19
135 07 21
135 23 04
135 51 59
135 54 25
136 14 35
136 48 51
H. w.
h. m.
7 35
8 56
9 23
7 54
'e'io'
7 20
8 30
5 55
11 16
7 30
6 23
Spg. Neap.
A. m.
fl.
2 52
10.5
1 23
2 44
7.0
6.7
3 10
6.4
1 41
'i'66'
8.4
'io'.h'
1 08
9.5
2 20
6.7
12 08
5 04
5.0
10.2
1 25
4.;
10
4.7
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
[Page 249
Place.
Matoya Harbor: Anori-saki light
Omoi Saki: Light-house
Shimizu Bay: Mound on pt
Mikomoto Island : Light-house
Sinioda Harbor: Center I
Yokosuka Harbor: Eyj Yama pt
Yokohama: P^nglish Hlitoba light
Tokio: Naval Observatory
No Sima Saki: Light-house
Vries Island (O Sima) Volcano: Sum-
mit, 2,512 ft
Kozu Shima Volcano: Summit, 2,000 ft.
MikakeJima: Summit, 2,690 ft
Redfield Rocks: S. rock
Mikura .lima: Summit
Broughton Rock: Summit, 60 ft
Fatsizio Island : Observation spot
Aoga Shima: Center
Bavonnaise Island: Summit, 26 ft
Sm'ith Island : Summit, 250 ft
Ponafidin Island: Summit, 1,328 ft
Lots Wife Rock : Summit, 300 ft
Inaboye Saki : Light-house
Kinkwosan Island : Light-house
Kamaishi Harbor: SE. end of village ..
Yamada Harbor: Ko Sima, 90 ft
Siriva Saki: Light-house
Toriwi Saki : Center of Low Islet off . . .
Awomori : Light-house
Tatsupi Saki: N. side
Bittern Rocks: SW. rock
Tobi Shima: Takamori Yama
Awa Sima: NE. extreme
Sado Island: Ya Saki
Fushiki Harbor: Light-house
Cape Roigen: Extreme
Niigata: Buddhist temple
Mana Sima: Smnmit, 200 ft
Manao Harbor: Sorenjo Pt
Taurnga: T(j»n
Oki Islands: N. ])t
Taka Yama ( Cape Louisa ) : Extreme
AiSima: Summit, 300 ft
Mino Sima: Sunmiit, 492 ft
Kado Sima: Tsuno Shima light
Hakodate: lyight-ship
Endenno Harl)or: Bluff on E. side
Okishi Bay: Light-house
Noshiaf Saki: Light-house
Nemuro: Benteii Sima light
Notsuke Anchorage: Village
Noshiaf Misaki : Light-house
Risiri Islet: Peak, 5,713 ft
Lat. N.
34 21 57
34 35 52
35 00 51
34 34 25
34 39 49
35 17 30
35 26 52
;i5 39 18
34 54 17
34 43 30
34 13 15
34 05 00
33 56 50
33 52 00
33 .39 00
33 04 24
32 29 00
32 00 40
31 27 00
30 28 26
29 46 28
35 42 13
,38 16 57
39 16 30
39 27 17
41 25 58
41 as 34
40 .50 00
41 16 17
40 31 00
39 12 02
38 29 23
38 19 55
36 47 47
37 28 00
37 55 14
37 35 00
37 02 37
35 40 24
.36 .30 00
34 40 00
34 32 00
34 48 00
34 21 12
41 47 36
42 19 .54
42 56 52
43 22 56
43 20 22
43 .33 11
45 26 30
45 11 00
Kunashir Island: St, Anthonys Peak.. .- 44 20 00
Iturup Island: NE. pt i 45 38 30
Ump Island : Cape Vanderlind 45 37 00
Broughton Island: Summit 46 42 .30
Simusir Island : Prevost Peak : 47 02 50
Ketov Island: S. pt i 47 17 30
Mataiia Island: Peak I 48 06 00
Shiash-Kotan Island: Center 48 .52 00
Kharim-Kotan Lsland: Peak ; 49 08 00
Oune-Kotan Island: SW. pt j 49 19 00
Moukon rushi Island: Center 49 51 00
Poro musir Island: Fool's Peak 50 15 .36
Soumshu Island : Center 50 46 00
Long. E.
136 54 09
138 13 49
138 31 19
138 56 30
138 57 30
139 39 43
139 38 41
139 44 30
139 53 24
Lun. Int.
Range.
H. W.
139
139
139
138
139
139
139
139
140
140
140
140
140
141
141
141
141
140
140
140
139
139
1.39
138
137
137
139
1.36
136
1.36
133
131
131
131
1.30
140
140
144
145
145
145
141
141
23 00
08 00
31 00
48 15
34 00
17 45
50 24
43 31
00 00
02 00
14 02
19 40
52 22
35 33
52 50
59 00
27 32
56 36
44 40
22 37
31 00
32 58
15 .31
27 09
03 15
22 00
03 01
54 00
58 24
01 22
23 (XI
36 00
18 00
09 00
50 29
41 49
59 33
52 38
49 10
34 40
18 00
38 40
19 00
146 15 00
149 14 00
149 34 00
1,50 28 30
151 .52 50
152 24 00
1.53 12 30
154 08 00
154 39 00
1.54 44 00
1.54 32 00
1.56 15 20
1.56 26 00
5 52
5 52
5 25
5 04
4 30
2 30
11 41
3 40
3 32
3 41
3 48
3 33
4 50
L. W.
Spg.
12 04
12 04
11 30
"nil
10 45
8 42
'.5 "28
10 00
9 45
9 ,53
10 00
9 46
11. a5
ft-
4.3
3.9
.4.9
"3.' 7'
Neap.
3.4
0.6
'i.'i I
3.0
3.5
.3.0
3.1
2.1
3.7
1.;
1.9
'i.'i
1.3
0.4
'o.h
1.2
1.5
1.4
1.4
0.5
1.8
Page 250] APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
EAST COAST OF ASIA— Continued.
«;
Place.
Lun. Int.
Range. 1
H. W.
L. W.
Spg.
Neap.
e
Cape Clonard: Kxtreme
° ' "
36 05 45
36 36 00
37 09 30
37 30 00
o / ;/
129 33 30
129 20 00
131 55 00
130 53 00
h. VI,
h. m.
ft.
/(.
Ping-hai Harbor
Liancourt Kocks: Summit, 410 ft
Matu Sima: Peak, 4,000 ft
Port Lazaref: S. IJ miles from the S.
end of Bontenef I
39 19 12 i 127 32 48
Wawoda Rock: Summit, 12 ft
42 14 30 1.37 17 00
1
Expedition Bay: Lip^ht-house
42 38 05
42 33 40
43 05 13
42 41 00
43 22 00
130 48 45
131 10 00
131 53 56
133 02 00
135 15 00
Port Novogorod: Light-house
Vladivo.stok: Cape Oaldobin light
Cape Povorotiiyi: Light-house
2 45
9 00
1.9
0.8
Port Olca: Uffht-hnnse
St. Vladimir Bav: Orekhera Pt
43 53 40 i 135 27 19
44 30 00 ! 136 02 00
44 43 45 136 22 30
44 46 15 136 27 15
45 05 00 136 44 00
45 19 30 137 10 15
45 41 30 137 .38 15
i
t
«
Shelter Bay
Sybillo Bay
Pique Bay . . -
j
Luk6 Point: Extreme
Capo Disappointment: P>xtreme
Cape Suffreii: Extreme
47 20 00
48 59 30
51 28 00
45 53 10
46 01 20
54 24 30
53 08 05
55 11 00
56 25 28
56 22 30
59 19 45
51 02 00
52 .52 37
53 04 30
54 56 00
54 32 24
•56 10 00
58 26 00
59 55 00
62 14 30
60 18 00
63 12 00
64 16 00
64 25 55
64 24 30
64 46 00
64 50 00
65 00 30
66 02 00
138 58 00
140 23 40
140 48 00
142 04 51
143 26 30
142 46 30
140 42 58
137 40 00
138 25 50
143 15 45
143 07 14
156 46 00
1.58 46 42
160 04 00
166 43 00
168 09 00
163 24 00
163 34 00
170 22 00
179 04 30
Long. W.
172 04 00
159 50 00
173 10 00
173 07 15
172 12 30
172 07 00
Long. E.
178 40 00
Long. W.
175 54 00
169 32 30
Cape St. Nikolaia: Light-house
De Kastri : Light-house
9 50
10 45
3 40
4 40
2.7
6.3
1.1
2.6
Sakhalin I., Cape Notoro: Light-house.
Cape Siretoku : Extreme . .
Cape Elizabeth: N. pt
Nikolaevsk: Cathedral
11 20
5 08
4.2
1.7
Port Aian : Cape Vneshni
10
7 30
8.4
3.4
St. Jona Island: Summit, 1,200 ft
Okhotsk: Battery
Cape Lopatka: Extreme
3 55
3 30
10 08 1 4. 6
1.9
2.1
Petropavlovsk : Rakof light
9 45
5.1
Cape Shipunski: Extreme
Mednoi, or Copper Island : SE. extreme.
Cape Kamchatka: Extreme
Cape Oliutorski: Extreme, 2,480 ft
Cape Navarin: Extreme, 2,512 ft
St.Matthew Island: Cape Upright, SE. pt
6 00
12 15
4.5
1.8
Car>p Trhoiikotfikoi* Extreme
Port Providence: P^mma Harbor
Oarx^ Indian* Kxtreme
Arakani Island: Cape Kiguinin
Anadir River: Moutli
East Oane" Extreme
ISIiANDS OF TTTT! PACIFIC.
Hi
i
P,
*
Malpelo Island: Summit, 1,200 ft
Cocos Island: Head of Chatham Bay . . .
■Redondo Rock- Summit 85 ft
4 03 00
5 32 57
13 30
20 00
18 50
34 25
1 22 55
81 36 00
86 59 17
91 03 00
89 58 43
90 30 08
90 44 23
91 49 43
Towers Island- W cliff
Abingdon Island : Summit, 1,950 ft
AVenman Inland: Summit, 550 ft
::::
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
[Page 251
£
3
•
m
9
a
a.
a
"i
£
s
•
w
5
c
•8
fl
iS
«
8
1
Place.
Lat. s.
Long. W.
Lun.
Int.
Range.
H. W.
L. W.
Spg.
Neap.
Albemarle Island : Iguana Cove
Marlborough Island: Cai)e Hammond..
James Island: Sugarloaf, 1,200 ft
Off/
59 00
31 00
15 20
25 00
36 30
33 25
50 30
1 19 00
1 25 00
44 15
Lat. N.
1 57 17
3 51 26
4 41 10
5 52 15
13 30
49 00
Lat. S.
2 40 54
2 35 00
1 50 00
1 29 14
1 23 42
1 17 14
36 00
Lat. N.
11 10
20 54
51 30
1 38 45
1 44 15
2 03 00
3 01 30
4 35 25
5 55 07
6 14 00
7 05 30
7 09 17
7 15 00
8 14 00
8 27 00
8 19 00
8 54 21
9 28 09
10 03 40
10 17 25
11 48 00
11 19 21
11 24 00
11 07 00
11 40 00
10 05 00
11 40 00
9 39 00
o / //
91 29 12
91 36 00
90 52 53
90 43 30
90 41 00
90 33 58
90 06 13
90 28 13
89 40 08
89 16 58
157 27 45
159 21 50
160 24 30
162 05 00
176 32 39
176 43 09
Long. E.
177 01 13
176 07 00
l'?5 ,39 00
175 12 20
176 31 33
175 57 09
174 24 00
173 32 40
173 51 14
173 03 30
173 03 00
173 07 00
173 25 30
172 45 40
168 41 31
169 39 31
171 46 00
171 24 30
171 55 51
168 46 00
168 03 00
168 26 00
171 09 00
170 49 00
170 16 05
169 01 57
169 59 20
170 07 00
167 24 57
167 35 00
166 35 00
166 24 25
166 04 00
162 15 00
161 08 30
A. m.
2 00
h. m.
8 13
t.
ft-
3.1
2 45
8 58
5.2
2.6
Duncan Island' Center liill
Indefatigable Island: NW. bay
Barrington Island: W. summit, 900 ft..
Charles Island : Summit, 1,780 ft
Fatu Huku or Hood Island : E. summit,
640 ft ...
2 00
8 13
6.2
3.1
2 10
8 23
6.0
3.0
Chatham Island: Mount Pitt, 800 ft
Christmas Island: N. pt. of Cook Islet. .
Fanning Lsland: Flagstaff, entrance to
English Hbr
2 20
4 25
6 00
8 33
10 38
12 15
6.5
2.4
2.4
3.3
1.4
1.4
5 25
11 40
1.5
0.9
Baker Islet : Center
Howland Islands: Center island
Arorai or Hurds Island : S. pt
7 10
1 00
6.2
3.6
Tamana Island : Center
Onoatoa Island : Center
TaputcueaorDrummondlsland: SE. pt.
Nukunau vir Byron Island: SE. pt
Peru or Francis Island: NW. pt
Nonuti or Sydenham Island
1
1
Aranuka or Henderville Island: W. pt.
of W. island
Apamama or Hoppers Island : Entrance
islet
4 30
10 45
4.7
2.7
Maiana Island: S. pt
Tarawa Island: NE. pt
Apaiang Island: S. pt
Maraki Island: N. pt
4 45
11 00
4.7
2.7
Taritari Island: S. pt
1
Ebon Atoll: Rube Pt
4 45
11 00
4.7
2.7
Jaluit or Bonhain Islands: Jarbor Pier.
Burrh Island: Port Rhin, N. pt. of en-
5 00
11 15
5.0
2.8
Majuro or Arrowsmith Islands: An-
chorage Djarrit I
Arno .\tol!: NE. pt
Odia Islands: S. islet
Namu Island : S. pt
Jabwat Island : Center
Aurh or Ibbetson Island: NE. end, an-
chorage
Maloclab Islands: NW. end Karen Islet.
WotjeorRomanzov Islands: Christmas
Harbor
Litkieh Island: NW.pt
Ailuk Islands: Capenmr Islet
4 50
11 00
6.2
3.6
Bigar Islet: Center
Kongelab or Pescadores Islands: Center
of group
Rongerik or Radakala Islands: Obser-
vation spot
Ailinginae Island: Easternmost Islet. . .
Bikini or Eschholtz Islands: W. ex-
treme
Wottho or Schanz Island : Center
Eniwetok Islands: North or Engibi I..
Ujelang or Providence Island: Center
of atoll
Page 252]
APPENDIX IV.
maritijME positions and tidal data.
ISLANDS OF THE PACIFIC— Continued.
a
Place.
Greenwich Island: Northern islet.
Lat. N.
Matelotaa group: Easternmost of the
S. islands
Yap Island : Light in Tomil Bay
Eau Island : Center ,
Uluthi or Mackenzie Islands: Mograog
Islet
Feys or Tromelin Island: E. extreme .
Sorol or Philip Island : Center
Eauripik or Kama Islands: E. islet
Oleai group: Raur Islet, N. pt
Ifalik or Wilson Islets: N. end
Faraulep Island: S. end
W. Faiu Islet: Center
Olimarao Islet: Center
Toass Island: Center
Satawal Island: Center
Coquille or Pikelot Island: Center .^...
Suk or Polusuk Island : S. end
Los Martires: Ollap Islet, N. pt
Namonuito Islands: Magur Islet
Hall Island : Namuine Islet
Hogolu (Hogulu) Group: N. end of
Tsis Islet. .'.
Namoluk Islands: N\V. islet
Mortlock Islands: Lukanor, Port Oha-
misso
Nukuor or Monteverde Islands: H pt..
Oraluk or Bordelaise Island: Center . . .
Ngatik or Valientes Islands: E. extreme.
Ponapi Island: Jamestown Harbor
MokilorDuperrey Islands: Aoura, NE.pt
Pingelasp or MacAskill Islands: E. end
of island
Ualan or Strong Island: Chabrol Harbor.
Angaur Island: SW. pt
Pililu Island: S. pt
Earakong or Akamokan Island: Center.
Korror Islands: Korror Harbor, Mal-
akal pier
Baubeltaub Island: Cape Artingal
Kyangle Islets: Center of largest
Warren Hastings Island: Center
Nevil or Lord North Island: Center.
Sonserol Island: Approx
Guam Island: Fort Sta. Cruz, San Luis
d'Apra
Rota Island: Summit
Tinian Island : Sunharon village
Saipan Island: Magicienne Bay, land-
ing
Tanapag Hbr., Garapag
Anataxan Island: Center
Sariguan Island: Center
Guguan Island: Center
Alamaguan Island : Center
Pagan Island : SW. pt
Agrigan Island : SE. pt
Asuncion Island: Crater, 2,600 ft
Urracas Islands: Largest islet
Farralon de Pajaros: S. end
1 04 00
8 18 30
9 29 00
9 52 30
10 06 00
9 46 00
8 06 00
6 40 00
7 21 45
7 15 00
8 35 00
8 03 00
7 43 30
7 29 30
7 22 00
8 09 00
6 40 00
7 38 00
8 59 45
8 25 30
7 18 30
5 55 00
5 29 18
3 51 00
7 39 00
5 48 00
7 00 35
6 41 45
6 14 00
5 20 06
6 53 55
7 02 00
7 08 00
7 19 00
7 40 30
8 08 00
4 20 00
3 02 00
5 20 00
13 25 48
14 07 30
14 59 22
15 08 30
15 17 10
16 20 00
16 41 00
17 17 00
17 36 00
18 04 00
18 46 20
19 45 00
20 00 00
20 32 54
Long. E.
154 47 55
137 33 30
138 04 00
139 42 00
139 46 00
140 35 00
140 52 00
143 11 00
143 57 30
144 31 00
144 36 00
146 50 00
145 55 45
146 24 30
147 06 48
147 42 00
149 21 00
149 27 30
150 14 30
151 49 15
151 56 30
153 13 30
153 58 00
155 00 54
155 05 00
157 31 30
158 12 21
159 50 00
160 38 43
163 00 45
134 05 24
133 18 03
134 27 00
I
134 32 30 ;.
134 39 30 ;.
134 17 00 ■.
J
132 21 00 i.
131 11 00 !.
132 16 00 I.
Lun. Int.
Range.
H.W.I
Spg.
Neap.
144 39 30
145 13 04
145 36 20
145 43 55
145 42 50
145 39 00
145 47 00
145 57 00
145 55 00
145 52 00
145 41 45
145 30 00
145 21 00
144 54 00
7 15
1 00
3.4
1.9
4 00
10 15
4.3
2.4
6 00
12 15
3.5
2.0
20
1 20
2.6
1.5
7 00
50
2.0
1.1
•a
a
e
a
it
APPENDIX lY.
.MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
[Page 253
Place.
d
a
Wake Island: Obs. spot
Gaspar Kico Reef: N. clump of rocks. . ,
.Johnston or Cornwallis Islands: Flag-
staff on \V. island
Clipperton Island: Center
Hawaii Island: Hilo, Kanaha Pt. light
Kawaih'ae light
Kealakeakua Bay light
Kailua, stone church. .
Kahoolawe Island: Summit
Maui Island : Kanahena Pt. light
Lahaina light
Molokai Island: Light-house
Oahu Island: E. pt. Makapuu station .
Diamond Head
Honolulu, Tr. of V. Obs
Honolulu, Reef light
Kauai Island: Hanalei, Black Head
Wainiea, stone church .
Bird Island: Center
Necker Island : Center
French Frigate Shoal: Islet (120 ft.) ..
Gardiner Island : Center
Maro Reef: NW. pt
Laysan Island : Light-house ,
Lisiansky Island: Light-hou.se
Pearl and Hermes Reef: NE. extreme.
Midway Islands: N. end Sand Islet
Ocean Island: Sand Islet ,
Marcus Island: Center
Bonin Is., Parrys Group: N. rock ,
Kater Island : N. rock ,
Peel Island: Port Lloyd, ob-
servatory
Volcano Is., San Alessandro or North
Island : Center
Sulphur Island
San Augustine Island:
Center
Rosario Island: Center, 148 ft
Douglass Rocks: Center
Borodino Islands: Center of N. island.
Center of S. island .
Rasa Island: Center
Fatu Hiva Island: S. pt ,
Motane Island : SSE. pt
Tahuata Island: Port Resolution, wa-
tering i)lace ,
Hiva-Oa Island: C. Balguerie
Fatu Huku Island: Center
Roa Poua Island: Obelisk Islet
Nuka-Hiva Island: Port Tai-o-hae light
Hiaou Island: S. pt ,
Motu-ili Island: Summit, 130 ft ,
Ua-Huka or Ua-Una Island: N. pt
Fetouhouhou Island: NE. pt...
Caroline Islands: Solar Eclipse Transit
Pier
Vostok Island: Center ,
Flint Island; S. extremity
Lat. N.
19 15 00
14 41 00
16 44 48
10 17 00
19 46 14
20 03 00
19 28 CK)
19 38 26
20 33 39
20 36 00
20 52 00
21 06 17
21 18 16
21 15 08
21 17 57
21 17 55
22 12 51
21 57 17
23 05
23 35
23 46
25 00
25 31
25 48
26 00
27 56
28 13
28 24
24 14 00
27 45 00
27 81 00
27 05 37
25 14 00
24 48 00
24 14 00
27 15 32
20 30 00
25 59 38
25 52 45
24 27 00
Lat. S.
10 32 00
10 01 40
9 56 00
9 45 00
9 27 30
9 29 30
8 55 13
8 03 30
8 44 00
8 54 00
7 55 00
Long. E.
166 31 30
168 54 28
Ijong. W.
169 32 24
109 13 00
155
1.55
1.55
1.56
156
156
156
157
157
1.57
157
157
159
159
161
164
166
168
170
171
173
175
177
178
05 31
48 00
55 00
W) 15
35 04
26 00
35 00
18 32
39 07
48 14
51 34
51 54
30 47
40 08
58 17
40 47
17 57
00 52
39 20
44 00
57 00
46 00
21 30
27 45
Long. E.
154 00 00
142 06 53
142 11 53
142 11 23
141 11 00
141 13 00
141 20 00
140 50 28
136 10 00
131 19 30
131 12 17
131 01 50
Long. Vi.
138 39 20
138 48 30
139 09 00
138 47 40
138 55 10
140 04 45
140 04 00
140 44 00
140 38 30
139 33 30
140 34 40
10 00 01 150 14 30
10 06 00 152 23 00
11 25 23 151 48 34
Lun
Int.
Range.
H.W.
L.W.
Spg.
Neap.
A. VI.
h. m.
fi-
ft-
3 09
9 06
2.3
1.3
2 20
8 10
1.6
0.9
"
3 32 1 9 58
2 38 , 8 56
2.2
2.1
1.2
1.1
3 46
9 59
1.5
0.8
4 00
10 20
2.0
1.1
3 30
9 45
1.1
0.6
6 10
00
2.4
1.4
2 30
8 45
3.1
1.9
3 50
10 05
3.5
2.1
4 00
10 14
1.1
0.7
Page 254]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
Place.
Lat. S.
Long. W.
Lun. Int.
H. W.
Range.
Spg. Neap.
Maklen Island: Flagstaff, W. side 4 03 00
Starbuck Island: Flagstaff, W. side 5 37 00
PenrhvnorTongarewaIsland:NN\V.pt. 8 55 15
Jarvis'lsland : Center 22 33
Reirson Island : Church 10 02 00
Humphrey Island: N. pt i 10 20 30
Union or Tokelau Islands: Spot N. of 1
Fakaofu or Bowditch Islet 9 23 02
Union or Tokelau Mands: Nuku-nono,
or SE. island, Duke of Clarence I 9 13 06
Union or Tokelau Islands: Clump on
S. island, Oataf u or Duke of York I . . . ' 8 39 40
Canton or Mary Island: N. pt.
Enderbury Island: W. pt
Phwnix Island, N. pt
Birneys Island : S. pt
Gardners Island: Center
McKean Island: Center
Hulls Island: W. pt
Mukulaelae or Mitchells Island : S. pt . . .
Funafuti or Ellice Island: E. j)t
Nukufetau or De Peysters Island: S. pt ,
Vaitupu Island : S. end
Nui or Netherland Island: S. pt
Nauomaga Island : Center ,
Niutao Island : Church
Nanomea Island: Center
2 44 25
3 08 30
3 42 28
3 34 15
4 37 42
3 35 10
4 30 95
9 18 00
8 25 19
8 04 02
7 32 00
7 15 45
6 12 00
6 06 00
5 39 00
Ocean or Paanopa Island: Center (appx).i 52 00
Pleasant Island: Center J 25 00
Indispensable Reefs: S. pt. of S. reef i 12 50 15
Rennel Island: SE. extreme 11 52 15
W.end 11 33 45
Bay,
San Christoval Island: Point Wanga
laha
Guadalcanar Island: Wanderer
mouth of Boyd Creek
Florida Island: Mboli Harbor, Tree Islet.
Malaita Island: Village, Mary I., Port
Adam
Stewart Islands: Largest islet
Isabel Island: N. side of Cockatoo Islet.
Gizo or Shark Island: N. point village. .
Choiseul Island: Choiseul Bay en-
trance
Treasury Islands: Observation Islet
Bougainville Island: Hiisker Pt, Gt;-
zelle Harbor
Buka Island : Cape North
Lord Howe Group: Center, small SA\'.
islet
Center, small NE.
islet
NW. pt. of Ham-
mond I
New Britain, Blanche Bav: Matupi I.
N. pt ".
Duke of York Island: Makada Har-
bor, Spit Pt ,
10 17 32
9 41 47
9 01 30
9 30 00
8 23 00
5 30 50
8 05 40
6 42 40
7 24 30
(') 35 00
5 00 00
5 38 00
5 18 00
5 18 00
4 14 12
4 06 25
155 01 00
155 56 00
158 07 00
159 54 11-
161 05 30
161 01 12
171 14 46
171 44 40
172 28 10
171 45 29
171 10 00
170 42 37
171 32 07
174 40 18
174 17 26
172 13 28
Long. E.
179 50 00
179 07 25
178 28 51
178 41 01
177 16 50
176 16 30
177 20 01
176 06 15
169 35 00
167 05 00
160 26 00
160 40 15
159 55 00
161 33 30
159 39 .30
160 27 20
161 27 40
162 58 15
159 38 20
156 50 15
156 23 16
155 34 00
155 05 00
154 35 00
159 21 00
159 34 00
159 17 00
152 11 35
152 06 15
A. VI. h. m.
St. ft.
6 00 i 12 15
1.5
0.9
6 00 12 13 I 2.4
1.4
5 00
11 15 1 4.6
2.\
6 45
5 00
12 00
9 00
33
11 15
3.3 I 2.0
3.5 i 2.1
5 47 I 2. 7 1.6
2 45 2. 1
1.3
APPENDIX IV. [Page 255
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
u
Place.
Lat. S.
Long. E.
j Lun. Int.
Range. 1
H.W.
L.W.
Spg.
Neap.
i
m
M
i
s
•i
s
S
»
t
e
s
a
a
e
id
•
s
2
5
i
m
N
e
5
s
«
New Ireland: Carteret Harbor, Cocoa-
nut I....
Katharine Haven
Holz Haven, E. side
New Hanover Island: Water Haven,
creelc mouth .
North Haven
anchorage . . .
St. Matthias Island: S\V. extreme
Admiralty Island: Nares Harbor, obs.
islet
/ //
4 41 26
3 11 00
2 47 30
2 33 43
2 26 30
1 35 00
1 55 10
2 25 40
2 22 00
45 00
53 15
1 28 00
2 51 00
1 25 40
2 44 00
3 47 00
8 22 00
8 41 00
9 25 30
10 14 30
10 43 35
10 37 00
6 43 00
8 24 00
9 03 30
9 38 00
9 41 00
9 43 53
10 42 00
10 52 40
11 23 25
11 29 10
16 50 00
16 55 50
17 43 00
17 07 20
17 24 39
19 08 00
19 14 00
22 10 30
23 15 02
9 48 00
10 21 00
10 23 30
10 40 00
U 17 30
11 40 24
o / //
152 42 25
151 35 30
150 57 35
150 04 33
149 55 36
149 37 00
146 40 56
147 28 35
147 55 00
145 17 00
145 33 04
145 08 00
146 15 00
135 28 12
132 04 00
134 06 00
137 40 00
143 36 04
147 07 04
148 30 30
150 14 20
150 40 34
147 53 20
151 01 24
152 47 00
150 30 00
150 58 00
150 44 43
152 42 04
152 47 12
154 08 00
154 25 14
149 58 00
149 11 54
150 42 04
152 06 20
155 52 24
158 40 00
159 00 00
155 28 24
155 33 04
166 53 15
166 17 15
165 47 30
166 00 30
166 32 14
166 57 45
h. m.
A. m.
ft-
/(.
2 50
9 03
2.4
1.4
2 30
8 43
2.4
1.4
St. Andrew Island: Violet Islet, 60 ft ..
Jesus Maria Island: SE. pt
Commerson Island: Center of largest
islet
;::;::: i
Anchorite Island: N. pt
Hermit or Loaf Island : Pem6 Islet
Purdy Island : Mole Islet
:::::: i
Point d'LTville: extreme
Drei Cap Peninsula: Wass Islet
Triton Bay: Fort Dubus, Dubus Haven.
Cape Walsche: Extreme
55
7 08
7.3
4.3
Fly River: Free Islet, S. pt
Port Moresby: N. end of Jane I
Cape Rodney : Extreme
8 50
2 38
8.0
4.8
South Cape: S. pt. Su Au I
9 15 i 3 00
8 25 I 2 12
8.1
5.8
4.8
3.4
Havter Island: W. end
Cape Cretin: Cretin Islets
Trobriand Islands: NE. pt. Cape Denis.
Woo<llark Islands: N. pt
4 45 10 58
7 05 53
3.0
4.2
1.8
2.5
D'EntrecasteauxIs. ; Ferguson I., S\V.
extreme
Well Island, E. pt.
Norman by I., obs.
islet
St. Aignan Island: Summit
Renard Islands: W. pt
Roseel Island : E. pt
Adele Island: S. extreme
Coringa Islands: Chilcott Islet
Herald Cavs: NE. Cav
. . _ .
Tregosse Islands; S. islet
i
Lhou Reef: Observation Cav
1
Mellish Reef: Cay beacon . ."
t
Bampton Island
Renard Island : Center
Wreck Reef: Bird Islet
Cato Island: Center
Duff or Wilson Group: N. island
Matema or Swallow Group: Nimanu
Islet
1
Tinakula Island: Summit, 2,200 ft
Nitendi Island: NE. pt.. Cape Byron ..
Tapua Island: Ba.silisk Harbor, S. pt. of
entrance ."
1
1
Vanikoro: Ocili village
4 50
11 05
3.8
"l.'s 1
Page 256]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISIiANBS OF THE PACIFIC— Continued.
■0
V
a
Place.
Torres or Ababa Island: Hayter Bay,
Middlel
Vanua Lava Island: Port Patterson,
Nusa Pt
Santa Maria Island: Lasolara Anehor-
pt.
age
Aurora Island: Laka-rere
Mallicollo Island: Port Sandwich,
on E. side
Vat(S or Sandwich Island: Havannah
Harbor, Matapou Bay flagstaff
Erromango Island: Dillon Bay, Pt.
Williams
Tanna Island : Port Resolution, Mission ,
Erronan or Futuna Island: NW. pt
Aneitvum Island: Port Anatom, Sand
Islet
Matthew Island: Peak, 465 feet
Hunter Island: Peak, 97-i feet ,
Walpole Island: S. pt
Mitre Island: Center
Rotumah Island: Epipigi Peak .
Kandavu Island : N. rock Astrolabe Reef
light
Mt. Washington, N.
peak
N'galoa Harbor, outer
beacon
Vatu Lele Island: S. pt
Ovalau Island : Levuka light-house
Viti Levu Island: Summit of Malolo
Islet
Suva Harbor, low
light
Mbega or Mbengha Island: Swan Har-
bor, Leaven Pt
Matuku Island : N. side of Matuku en-
trance
Moala Island: Rocks off N. pt
Ngau Island: Herald Bay, E. side
Wakaya Island : Rocky Peak
Makongai Island: Dilliendreti Peak
Goro Island: NW. pt
Vanua Levu Island: Mount Dana
Nandi, observation
islet
Savu Savu Pt. ; ex-
treme
NE. Pt
Taoiuni Island: Somu-Somu town..
Thikombia Island: E. hummock...
Naitamba Island : Center
Vatu Vara Island: N. end, summit.
Kanathea Island : S. pt
Vanua Mbalavu Island: NW. pt . . .
Mango Island : Pier end
Thithia Island: Highest peak
Tuvutha Island: Peak
Naian Island: Summit, 580 ft
Lakemba Island: Kendi Pt
Oneata Island: Summit of Loa I...
Mothe Island : Summit
Mamuka Island: Center, 260 feet ..
Lat. s.
o / //
13 15 00
1.3 48 00
14 11 00
14 58 00
16 26 00
17 44 58
18 47 30
19 31 17
19 31 20
20 15 17
22 20 12
22 24 02
22 38 07
11 55 00
12 30 10
18 38 15
19 07 09
19 05 30
18 36 00
17 40 45
17 44 45
18 06 50
18 22 00
19 09 38
18 32 49
17 59 32
17 37 11
17 27 14
17 lo 21
16 42 01
16 57 53
16 49 19
16 08 00
16 46 00
15 44 45
17 03 00
17 25 33
17 17 20
17 10 00
17 25 26
17 44 12
17 39 33
17 59 00
18 14 10
18 25 46
18 38 56
18 46 00
Long. E.
Lun. Int.
Range.
H. W.
166 33 00
167 30 31
167 30 00
168 02 00
167 47 15
168 18 50
168 58 00
169 27 30
170 11 15
169 44 45
171 20 30
172 05 15
168 56 45
170 10 00
177 07 15
178 32 15
177 57 09
178 10 24
177 38 00
178 49 00
177 09 00
178 24 40
178 06 53
179 44 27
179 56 25
179 14 08
178 59 29
178 57 46
179 20 44
178 54 15
178 48 32
179 16 08
Long. W.
179 58 46
179 51 00
179 54 26
179 17 00
179 32 17
179 10 00
179 05 45
179 10 33
179 19 49
178 50 27
179 04 00
178 52 00
178 27 04
178 30 54
178 44 00
6 40
4 38
5 15
5 10
6 15
6 40
6 .30
L. W.
Neap.
K m.
30
3.8
2.3
10 50
11 27
3.8
3.0
1.9
1.8
11 23
3.1
1.9
00
4.2
2.5
25
4.0
2.4
15
3.6
2.2
6 00
6 10
12 13
4.3
2.6
00
3.1
1.9
APPENDIX IV.
MARITIME rOSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Contiuued.
[Page 257
e
9)
i
Place.
Kambara I^iland: Highest peak 18 oti 15
Totoya Island: Black Rock Bay, W. side [ 18 58 57
Fulanga Island: W. bluff : 19 0;5 00
OngeaLevn Island: Center 19 04 00
Vatoa or Turtle Island: Hummock | 19 49 11
Ono Islands: Peak I 20 39 10
Michaeloff Island: Center ' 21 00 09
Simonoff Island: Center ' 21 01 39
Fatuna or Home Island: Mt. Schouten . i 14 14 20
Ilea or Wallis Island: Fenua-fu Islet.. J 13 23 35
Niua-fu or (iood Hope Island: XW.
extreme 15 34 00
Keppel Island : Center 15 52 00
Boscawen Island: Center 15 58 00
Savaii Island: Paluale village 13 45 00
Upulols. : Apia Harbor, obs. spot : 13 48 56
Tutuila Island: Pago-Pago, obs. pt ! 14 18 06
.Manna Island: Village, N\V. side 14 19 00
Rose Island: Center 14 32 00
19 10 00
10 52 47
Nine or Savage Island : S. pt
Danger, or Bernardo, I.s. : Middle rock
Suwarrow or Souwaroff Island: Cocoa-
nut Islet
Palmerston Islands: W. islet
Scilly Islands: E. islet 16 28 00
Bellingshausen Island: Center I 15 48 00
Mopeha (Lord Howe) Island: Center..' 16 52 00
13 14 30
18 05 50
Maitea Island : Summit
Tahiti Island : Light-house
Tubuai-Manu or ilaia-iti I. : NW. pass. .
Eimeo Island : Talu libr. , Vincennes Pt .
Huaheine Island: Light-house
Ulietea Island : Regent Pt
Tahoa Island : Center .-
Bola-Bola Island: Otea-Vanua village..
Tubai or Motu-iti Island: N. pt. of reef. .
Mama or Maupili Island : Center
I
Ducie Island : NE. entrance
Pitcaini Island : Village
Henderson or Elizabeth Island: Center.
Oeno Island: N. pt
Mangareva or Gambler Island : Flagstaff
Marutea or Lord Hood Island: Center. .
Maria or Moerenhout Island: Center. . .
Vahanga Island: W. pt
Morane or Cadmus Island : Center
Tureia or Carysfort Island : E. pt
Mururoa or Osnabrug Island: Obs. spot.
Tematangi or Bligh Island: N. pt
Nukutipipi: SW. pt
Hereheretue or St. Paul Island: Center.
Vanavana or Barrow Island: Center
Nukutavake or Queen Charlotte I. : N. pt
Reao or Clermont Tonnere Island: NW.
point
Puka-ruha or Series Island: NW. pt
Vahitahi Island : W. pt
Ahunui or Byam Martin Island: NW. pt.
Pinaki or Whitsunday Island: E. pt ...
Tatakoto or Clerke Island: Flagstaff on
western coast -.
17 53 00
17 29 10
17 36 39
17 29 23
16 42 30
16 50 00
16 35 00
16 31 35
16 11 00
16 26 00
24 40 20
25 03 50
24 21 20
24 01 20
23 07 36
21 31 .30
22 01 00
21 20 00
23 07 50
20 46 20
21 50 00
21 38 00
20 43 00
19 53 17
20 46 07
19 16 30
18 29 00
18 16 00
18 43 30
19 37 00
19 25 00
17 19 30
Long. W.
178 59 05
179 52 58
178 47 25
17S 33 25
178 13 38
178 43 27
178 44 03
178 49 47
8 06 45
6 11 47
175 40 40
173 .52 00
173 52 00
172 17 00
171 44 56
170 42 14
169 32 00
168 09 00
169 50 00
165 51 30
163 04 10
163 10 00
1.54 30 00
154 31 00
154 00 00
148 05 00
149 29 00
150 36 56
149 50 30
151 01 28
151 27 21
151 35 00
151 46 00
151 48 00
152 12 00
124 48 00
130 08 30
128 19 00
130 41 00
134 57 54
135 33 05
136 10 15
136 38 53
137 06 15
138 27 45
138 56 30
140 38 45
143 03 15
144 57 00
139 08 45
138 48 30
136 26 30
137 03 30
138 53 15
140 15 45
138 40 45
138 26 26
R&nge.
H. \V.
L. W. Spg.
Neap.
A. m. ft.
ft-
6 35 20 I 3.5
6 10 00 3. 1
2.1
"i.'9
6 40
28
6 25
7 00
6 00
13
45
12 13
3 10
12 00
12 10
9 23
5 48
6 00
4.4
2.7
3.1
2.7
4.6
1.9
1.6
2.7
2.4
1.4
1.0
0.6
1.4
0.8
1 50
03
2.4
1.4
24972="— 12-
-17
Page 258]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
ISLANDS OF THE PACIFIC— Continued.
Place.
Lat. S.
s
S
S
9"
Hao or La Harpe Island: NW. pass
Paraoa or Glocester Island : Center
Eavahere Island : S. pt
Reitoru or Bird Island: N. Ijeach
Hikueru or Melville Island, E. pt
Tauere Island: NW. pt
Puka-puka Island : E. pt
Napuka Island : W. pt
Angatau or Araktcheff Island: W. pt ..
Tukunie or Wolkonsky Island: NW. pt.
Tuanske Island: N W.'pt
Nihiru Island (Tuanake): SW. pt .
Anaa Island: Islet in N. pa^s
Tepoto Island: N. pt
Haraiki or Crocker Island: SW. pt
Makenio_or Phillips Island: W. pass . . .
Fakarana or Wittgenstein Island: 8E.
pass
Taiaro or Kings I. : Middle of W. shore.
Aratika Island: E. pt
Toau or Elizabeth Island: AmyotBay.
Takapoto Island: S. pt
Aheu Island: Lagoon Entrance
Rangiroa Island: E. pt
Makatea Island : W. pt
Matahiva Island : W. pt
18 05
19 08
18 18
17 49
17 35
17 20
14 49
14 12
15 .50
15 44
16 39
16 44
17 20
16 47
17 28
16 26
16 31 00
15 43 15
15 30 00
15 50 00
14 43 00
14 29 10
15 14 30
15 50 30
14 53 00
Juan Fernandez Island: Fort S. Juan
Batista
Mas-afuera Island: Summit, 4,000 ft ...
St. Ambrose Island: N. part creek
St. Felix Island : Center
Sala y (lomez: NW. pt
Easter Island: Cooks Bay, mission
Rapa or Oparo Island: Tauna Islet
Bass Islets (Morotiri): SE. islet, 344 ft .
Tubuai or Austral Is. , Vavitoa I. : Center.
Tubuai I.: Flag
staff, N. side
Rurutu I. : N. pt . .
Rimitara I. : Cen-
ter
.33 37
33 46
26 18
26 16
26 27
27 10
27 35
27 55
23 55
Hull Island: NW. pt
Mangaia Island: Center
Rarotonga Island : NW.pt
Mauki or Parry Island: Center .
Mitiero Island : Center
Vatiu or Atiu Island : Center . . .
Hervey Islets: Center
Aitutaki Island: Center
Vavau Island: Port Valdes, Saudv Pt..
Kao Island : Summit, 5,000 ft
Tofua Island: Summit, 2,800 ft
Tongatabu Island: Light-house
Minerva Reefs, N. Minerva: NE. side..
S. Minerva: S. side of
entrance
Keimadec Is., Eaoul or Sunday I. : Den-
ham B. fl£^ staff
Macauleyl.: Center
Curtis I. : Center
Conway Reef : Center.
Long. W.
140 59 30
141 41 10
142 11 31
143 05 23
142 35 16
141 29 43
138 46 45
141 15 37
140 53 35
142 08 40
144 14 45
142 53 34
145 30 54
144 17 18
143 31 17
143 57 59
145 22 45
144 38 34
145 24 45
146 02 45
145 11 00
146 20 00
147 11 00
148 15 00
148 .39 45
I
' 23 21 45
I 22 29 00
I 22 45 00
21 47 00
21 49 00
I 21 11 35
20 17 00
20 01 00
20 04 00
19 18 00
18 54 (X)
18 39 02
19 41 35
19 45 00
21 08 00
23 37 06
23 55 00
29 15 .30
30 15 00
30 .35 00
21 44 45
Lun. Int.
H.W.
78 50 02
80 46 00
79 54 56
80 06 56
105 28 00
109 26 00
144 17 20
143 28 21
147 48 00
149 35 35
151 23 41
152 55 00
154 51 00
157 56 00
159 47 00
157 23 00
157- 34 00
158 08 00
158 54 00
1.59 32 00
174 01 00
174 .59 50
175 03 00
175 12 00
178 55 45
179 07 45
177 55 40
178 31 45
178 37 00
Long. E.
174 37 45
/(. m.
2 40
L. W.
h. m. ft.
8 55 2.4
' Range.
Spg. Neap.
1.4
4 30 1 10 43
2.1
4 00
40
10
10 15
6 53
6 25
3 00
9 13
6 00 12 15
6 20
6 20
7 50
, 6 00
3.3
2.8
2.4
2.4
2.7
1.3
2.0
1.7
1.4
1.4
10 3. 8
10
1 35
12 13
3.8
5.5
3.3
2.3
2.3
3.3
2.7
Page 260J
APPENDIX IV.
MARITIME POSITION'S AND TIDAL DATA.
AXTSTBALiIA— Continued.
MacLeay Islets: Rock off X. end
Port Usiiorne: S. pt
Fitz Roy River: Escape Pt
Cape L'Eveque: Extreme
Lacepede Island : NW. islet
Cape Baskerville: Extreme
Cape Latouehe Tr^ville : fiXtreme
Turtle Isles: Cen'ter of N. isle
Cape Lambert : Extreme
Legendre Island : NW. extreme
Rosemary Island : W. summit
Enderby Island : Rocky Head
Montebello Island: N. extreme of reef. .
Barrow Island: N. pt
Northwest Cape: Extreme
Cape Cuvier: Extreme
Cape Inscription : Extreme
Houtnian Rocks: N. islet
Port Gregory
Cape Leschenault: Extreme ,
Rottnest Island: Light-house
Perth (Fremantle): Arthur Head light.
Peel : Robert Pt
Cape Naturaliste: Extreme
Cape Leeuwin . Light-house
D'Entrecasteaux Point: Extreme
Nuy ts Point : Extreme
West Cape Howe: Extreme
Eclijjse Islets: Summit of largest
King George Sound: Commissariat
house near Albany jetty
Bald Isle: Center
Hood Point: Doubtful Isles
Recherche Archipelago: Termination
Isle
Cuiver Point : Extreme
Dover Point: Extreme
Fowler Point: Extreme
Streaker Bay : Port Blanche
Coffin Bay: 'Mount Dutton
Cape Catastrophe: W. pt
Neptune Isles: SE. islet
Port Lincoln: English Church
Franklin Harbor: Observation spot
Port Augusta: Flagstaff
Port Victoria: Wardang Island hut
Cape Spencer: S. pt
Investigator Strait: Troubridge light. . .
Port Wakefield : Light-house
Port Adelaide: Wonga Shoal light
Cape Jervis: Light-house
Cape Borda: Light-house
Cape Willoughby: Light-house
Port Victor: Flagstaff
Cape Jaffa: Margaret Brock light-house.
Cape Northumberland: Light-house ...
I^t. s.
15 52 00
15 39 25
17 24 25
16 23 a)
16 .50 00
17 09 CX)
18 29 00
19 54 00
20 36 00
20 19 00
20 27 00
20 35 00
20 16 45
20 40 40
21 46 41
24 00 00
25 29 19
28 18 05
28 12 00
31 18 00
32 00 20
32 03 12
32 27 00
33 31 45
34 21 ,55
34 52 00
35 05 00
35 09 00
35 11 54
35 02 20
34 55 00
34 24 00
,34 .30 00
32 57 00
32 34 00
.32 01 ,30
32 48 00
34 29 29
35 00 15
35 20 15
34 43 22
33 44 08
32 29 42
34 28 25
35 18 21
35 07 31
34 12 00
34 50 25
35 3(i 45
35 45 30
35 51 00
35 34 06
36 57 00
38 04 18
Cape Nelson: S. extreme 38 26 00
Portland Bay: Lawrence Rock 38 24 39
Port Fairy: Griffith Island summit 38 23 47
Cape Otwav: Light-house 38 51 45
King Island: Cape Wickham light 39 35 38
Port Phillip: Point Lonsdale light 38 18 00
Geelong: Custom-house ! 38 08 .52
Melbourne: Observatorv ! 37 49 53
Long. E.
123 45 00
123 36 27
123 39 47
122 55 45
122 05 30
122 15 00
121 ,54 00
118 48 00
117 11 00
116 45 00
116 30 00
116 23 00
115 22 00
115 27 45
114 10 08
113 21 00
112 57 09
113 35 .33
114 14 30
115 30 00
115 30 12
115 44 23
115 44 00
115 00 15
115 08 00
116 01 00
116 38 00
117 40 00
117 53 45
117 .54 04
118 27 00
119 34 00
121 58 00
124 39 00
125 30 00
1.32 33 00
1,34 13 40
135 24 56
135 56 09
1.36 06 24
135 51 03
136 57 22
137 45 24
1.37 22 21
136 53 30
137 49 39
138 09 00
138 26 .58
1.38 05 29
136 .34 39
138 07 45
1.38 37 09
139 39 39
140 39 40
Lun. Int.
141 32 39
141 40 02
142 14 37
143 ,30 39
143 57 03
144 37 00
144 21 47
144 58 35
H. V.'.
11 30
[10 16]
[10 53]
11 ,50
35
8 20
4 31
4 04
L. \V.
h. m.
5 10
Range.
/(• A
17.6
[3 43]
[4 40]
9 35
6 55
[2. 1]
[2.6],
5.1
5.5
2 15
11.4
10 45
10 22
10.2
6.3
4 00
11 52
"6"26'
10 43
2 02
2 19
10 15
5.8
5 40
'h'sh'
4.2
4 30
8 20
8 41
2.5
3.0
1.9
APPENDIX IV. [Page 261
MAKITI^n-: POSITIONS AXD TIDAL DATA.
AUSTRALIA— Continued.
1
Place.
Lat. S.
Long. E.
Lnn. Int.
Range. 1
H.W. L.W.
Spg.
Neap.
o / w
38 29 42
3« 90 1.T
O / 1,
144 52 51
145 01 34
146 25 16
147 18 39
148 04 00
147 47 39
148 07 24
146 37 43
149 55 10
149 .^8 SO
/*. m. h. m.
ft.
ft-
I'ort AVpMtern' EvtrpiTtp of W lipnd
1 1 Wilson Promontory: Light, SE.pt 39 08 00
•2 Kent Island: Deal Island light .39 29 45
e 1 Flinders Is.: Strzelecki Peaks, SE. peak 40 11 45
ij ! Goose Island : Light on S. end ! 40 1 8 40
> i Hanks Strait: Swan Tslflnd lii^ht 40 43 40
1 i;::::"
1 1
10 38
4 25
8.1
6.2
.38 45 06
1
::;:;::::::: i
Gabo Island : Light-house
Cape Howe (east): Extreme
37 .34 15
37 .30 10
8 40
2 27
4.5
3.4
CaDe Green: SE. nt
37 15 40 150 03 04
Twofold Bay: Lookout Pt. light
Drniiu'darv Arnnntaiti- Summit
37 04 18 ' 149 54 45
36 18 30 i 1.50 01 .34
8 05
1 52
5.2
3.1
Montagu Island : Light-house
. Ratpman Rav: Observatirm head
36 14 30
35 43 58
35 21 41
35 09 15
34 40 25
,34 25 .30
1.50 13 ,34
1.50 12 34
150 29 29
150 46 26
150 .52 19
1,50 ,55 14
8 20
2 07
5.3
3.2
i.
Ulladulla: Inner end of pier
8 20
2 07
5.4
3.3
«
.Tervis Bav: Light-house
^
Kiania Harbor: Outerextremeof S. head
:::::: i
1
Sydney : Observatory
Port Jackson: Onter S. hea<l liebt . . _ .
33 51 41 ' 151 12 23
,33 51 .30 i 151 18 15
8 40
2 27
4.2
2.5
si Broken Bay: Baranjo Head light ' 33 35 00
Z Newcastle: Kohbv Head light 1 32 55 15
^ Port Stephens : Light-house 1 32 45 10
Snsar Loaf Point : Liffht-honse ; 32 26 20
151 20 30
151 48 19
1.52 13 20
1,59 M 40
i
8 35
8 15
2 23
2 00
4.7
5.8
2.8
3.6
Port Macquarie: Entrance
31 25 30 1,52 .55 19
9 00
2 46
4.1
2.4
Solitary Islands: S. Isle light
30 12 00
1.53 17 00
153 23 10
153 35 55
1.53 01 48
1.53 33 50
1.53 28 04
153 13 00
1,53 23 00
1.53 13 40
1,52 25 00
1,52 45 15
151 41 04
151 37 15
151 23 ,50
151 14 04
1,50 45 44
Clarence River: S. Head light
Richmond River: X. Head light
Brisbane: Signal station .
29 25 ,30
28 51 30
27 27 32
27 26 20
27 02 10
8 15
2 00
4.0
2.4
■0
s
•
B
»
a
9
10 45
4 30
6.4
3.9
Lookout Point: Extreme
Cape Moreton : J..ight-house
1 1
Double Island Point: Light-house
25 56 00
! 1
Indian Head : Extreme 25 00 15
Sandy Cape: Light-house 24 43 20
1
■---"■■
1
Burnett River: S. Head light
24 45 00
24 07 00
24 01 20
! i .
Lad V Elliot Met : Light-house
Bustard Head: Light-house
RoddBay: Spit end 1 24 01 20
Port Curtis: (jatconibe Head light 23 53 00
i
Cape Capricorn : Light-house
23 29 30
22 31 40
21 39 00
Port Bowen : Observation rock
Percy Isles: Pine I. light
1.50 14 00
1
Northumterlandlsles: Summitof Prud-
hoe I
21 19 15
21 ,32 00
20 32 20
20 18 50
20 15 30
20 00 50
19 57 30
19 41 50
19 19 20
19 11 25
18 45 .30
18 09 30
17 40 40
149 43 ,30
149 31 04
148 58 00
148 53 15
149 00 00
148 16 54
148 27 ,34
148 23 00
147 27 40
147 01 10
146 42 50
146 11 04
146 n 00
Cape Pahnerston: N. extreme
Cape Conway: SE. pt
1
Port Molle: S. side of entrance
Cumberland Island: Whitsunday I.,
summit on W. side
1
Port Denison: Obs. pt., W^. side of Stone
Isle
10 05
3 53
9.0
.5.4
Gloucester Island: Summitnear N. end.
Holborne Islet: Center
. Cape Bowling Green: Light-house
Cape Cleveland : Light-house
Pa m Islands: SE. point of SE. island..
Rockingham Bay: Peak of Goold Isle..
Barnanl Island: Light-house
......
1
Frankland Island: High islet
17 09 45 , 146 02 30
C \\)e Tribulation: Extreme
16 04 20 1 145 29 34
Hope Island: S. islet 1 15 45 00 1 145 28 .30
Cook Mountain: Summit ,
Cape Bed ford : SE. extreme
15 29 45
15 16 30
145 17 30
H5 23 15
8 55
2 43
7.5
4.5
Page 262] APPENDIX R'.
MARITIME POSITIONS AND TIDAL DATA.
AUSTRAIilA — Continued.
6
1
Place.
Lat. S.
Long. K.
Lull. Int. 1 Range. 1
H.W.
B.W. Spg.
Neap.
•i
e
"S
s
Mnr<lofk Point* ExtreMie
O f 1/
14 37 15
14 10 00
14 07 45
14 00 30
13 24 45
/ //
144 57 30
144 32 34
144 15 19
143 42 15
143 .36 19
143 34 00
143 15 15
143 29 00
143 06 00
142 56 19
142 32 24
142 39 20
142 21 19
142 10 50
141 53 49
140 37 06
139 45 56
139 38 36
/(. m.
Ii. m. ft.
ft-
Cape Melville: NE. extreme
1 i
Flinders Island: N. extreme of N. island.
9 00
2 47 9. 6
5.8
12 51 no
Cape Grenville: Extreme ' 11 58 15
Sir Charles Hardy Island: N. extreme
of SE. isle 11 55 00
Bird Island: N\y. isle . . . . . 11 4fi .SO
Hannil>al Isles* E. isle
11 36 30
10 41 .30
10 37 45
10 22 00
10 46 00
10 36 05
17 36 40
17 35 10
17 06 50
i
Cape York : Sextant Rock
1 00
7 10 i 8.0
4.7
Mount Adolnlius' Summit
Prince of Wales Island: Cape Cornwall,
extreme _ - ---. .
4 20
10 30 1 7. 8
4.7
Albert River* Kaneraroo Pt
1
TASMANIA.
Cape Portland: NW. pt
Port Dalrymple: Low Head light
Port Sorrell: NW. entrance head
40 44 15
41 03 25
41 07 05
41 10 00
41 08 30
41 02 50
40 23 40
40 40 10
40 22 00
41 04 00
41 41 00
42 11 37
42 11 00
43 19 00
43 .33 30
43 44 .30
43 29 40
43 21 00
42 53 25
43 14 00
42 52 00
42 13 00
41 .34 00
40 59 40
147 56 09
146 47 54
146 33 30
146 24 30
146 12 00
145 56 39
144 47 45
144 .39 44
144 39 19
144 44 00
144 57 00
145 12 34
145 10 .30
145 .53 00
146 01 04
146 22 04
147 08 49
147 23 40
147 20 07
148 02 00
148 00 00
148 18 04
148 19 30
148 20 50
11 10
5 00
9.0
6.9
Leven River; W. entrance head
Cape Grim : Outer Doughboy Islet
Pieman River: Rocks clowe to entrance.
Macquarie Harbor: Entrance Islet
Hnrte Rnrrell' Tjiffht-house
7 20
1 07
2.7
2. i
Afpwstorip Rock' Center
Hobart Town : Transit of Venus station .
8 05
1 52
4.2
3.2
Cape Frederik Hendrik: Extreme
St. Patrick Head: N. pt...
'
NEW ZEALAND.
m
f
1
Three Kings Islands: NE. extreme of
NE island
34 06 20
34 25 07
34 31 00
35 00 20
35 01 44
35 17 00
172 08 49
173 03 34
173 00 54
173 32 39
173 45 48
174 06 06
Parenga-renga Harbor: Kohan Pt
Wangaroa Harbor: Peach Islet
Bay of Islands: Motu Mea Islet
7 40
7 26
1 30
1 55
6.4
5.9
4.5
4.2
APPENDIX IV.
MARITIME POSITIONS AXD TIDAL DATA.
NEW ZEALAND— Continued.
[Page 263
Place.
Lat. S.
Wanganiru Harbor : Gro ve Pt
Wangari Harbor: Loot Pt
Great Barrier Island : Needles Pt
Auckland Harbor: Light-hoiise
Coromandel Harbor: Tuhnia I
Cape Colville: N. pt
Cuvier Island : Light-house
Tauranga Harbor: Mount Maunganui,
860 ft
White Island: Summit, 863 ft
Cape Runaway : Extreme
F^st Cape: Islet, 420 ft
TolagaBay: Matu-heka Islet
Mahia Peninsula: S. extreme of Port-
land I
Ahuriri Harbor: Light-house
Kidnappers Cape: Extreme
Cape Palliser: Light-house
Port Nioholson; Pencarrow li^ht
Wellington: Queen's Wharf light
Mana-watu River: Light-house
Wanganui River: N. head
Egmont Mountain: Summit, 8,270 ft
New Plymouth: Flag-staff
Kawhia Harbor: S. head
Aotea Harix)r: S. head
Whaingaroa Harbor: S. entrance pt
Manukau Harbor: Paratutai flag-staff..
Kaipara Harl^r: Light-house
Hokianga River: Flag-staff at entrance.
Cape Campbell : Light-house
Port Cooper: Lyttleton custom-house . .
Akaroa Island: Light-house
Ashburton River: N. entrance pt
Waitangi River: N. entrance head
Otago Hartx)r: Taivoa Head light
Moiyneux Bay: landing place
Nugget Point : Light-house
Bluff Harbor: Light-house
Tewaewae Bav: Pahia Pt
Solander Islands: Summit, 1,100 ft
Preservation Inlet: Light-house
West Cape: Extreme
Queenstown: U. S. Tr. of Venus station.
Milford Sound: Freshwater Basin
Cascade Point: N. extreme
Grey River: Entrance
Hokitika: Entrance light
Cape Foul wind: Light-house
Cape Farewell : Extreme
Nelson: Bowlder Bank light
D' Urville Island : Port Hardy
Port Gore: Head of Melville Cove
Port Underwood: Flag Pt
35 23 48
35 51 09
36 01 15
36 50 06
36 48 .35
36 28 20
Long. E.
36 26 20 175 49 00
Port William: Howell's House ,
Paterson Inlet : Glory Cove
Port Adventure: White Beach, S. end..
Port Pegasus: Cove abreast Anchor-
age I
Codfish Island: NW. extreme
Snares Islands: SW. islet.
37 36 25
37 30 00
37 30 45
37 40 00
38 20 50
39 18 00
39 28 30
39 38 00
41 36 45
41 21 40
41 17 17
40 27 10
39 57 00
39 18 00
39 03 35
38 04 50
37 59 35
37 46 22
37 03 00
36 23 00
35 32 on
41 44 00
43 46 40
43 54 00
44 04 50
44 .54 50
45 46 55
46 24 05
46 27 10
46 37 00
46 20 40
46 36 00
46 10 00
45 .54 50
45 02 07
44 40 20
44 00 .30
42 26 20
42 42 20
41 45 40
40 29 50
41 16 05
40 46 .35
41 01 55
41 20 28
46 .50 .30
46 .58 .30
47 03 52
174 21 24
174 31 14
175 25 34
174 51 00
175 24 34
175 21 04
Lun. Int.
H. W.
176
177
177
178
178
177
176
177
i 175
174
175
1 174
I 174
! 174
; 174
174
t 174
', 174
174
173
174
172
173
171
171
1 170
I 169
169
168
167
166
166
166
168
167
168
171
170
171
172
173
173
174
174
10 14
10 49
59 34
35 09
20 14
53 15
.54 14
06 44
18 45
51 04
47 25
14 40
,59 44
03 59
04 35
48 04
50 04
52 19
31 14-
08 00
21 59
17 14
44 17
00 20
48 34
11 14
44 02
47 53
50 04
23 00
42 19
54 04
,38 15
25 49
40 06
54 45
21 ,34
11 ,54
59 30
27 44
41 04
17 30
54 04
11 22
08 24
168 05 34
168 09 54
168 10 57
47 11 40 167 40 51
46 45 45 167 36 49
48 Or> 43 106 27 44
L.W.
15
05
7 05
8 10
8 00
6 05
4 40
4 52
9 40
9 15
9 10
9 08
9 05
9 00
8 40
4 45
3 45
1 05
9 .55
9 45
6 00
1 00
11 45
1 05
55
1 10
55
55
2 00
1 50
12 15
'io'bb
10 54
3 30
3 05
300
Range.
Spg. Neap.
ft-
6.5
6.7
10.8
10.7
6.1
6.6
3.5
5.7
3.6
6.3
11.6
11.9
2 55 12. 3 !
2 50 12. 6
2 50
2 30
11 00
10 00
3 31 9 39 5. 6
10.0
9.2
7.5
7.4
15 7.8
11 10 I 5 00 7. 5
10 10 i 4 00 9. 8
10 20 I 4 10 9.5
3 45 12.
3 35 I 11.6
12 15 i 7. 6
9 15
5 40
7.8
7.9
ft-
4.6
4.8
7.7
7.6
4.4
4.7
5.8
3.0
3.1
5.4
8.2
8.5
8.7
9.0
7.1
6.5
6.5
5.8
4.4
"6."2
'5.' 9
7.5
9.4
9.2
6.6
6.2
6.2
Page 264]
APPENDIX IV.
MARITIME POSITIONS AND TIDAL DATA.
THE ABCTIC REOIOKS.
Cape Walsingham : Extreme
Mile Island : N. pt
Marble Island : E. end
Cape Kendall : Extreme
Iglooik Island : E. pt
Victoria Harbor: N. shore
Elizabeth Harbor: Entrance
Magnetic Pole, 1831
Port Neill: N. pt. of entrance
Port Bowen : N. cove
Battv Bav: S. pt. of entrance
Port" Leopold : Whaler Pt
Careys Islands
Discovery Harbor
Alert's Winter Quarters
Cape Joseph Henry: N. extreme.
Cape Hecla: N. extreme
Cape Columbia: Extreme
Melville Island: "Winter Harbor .
Ijit. N.
Liakhov Islands: E. pt. of New Siberia.
Cape Tscheljuskin : E. pt
Nova Zembla: Vaigats I., N. pt
CapeCostin (Kostina) ..
NE. pt., Cape Desire
Franz Josef Land: Wilczek I
Mezen: Epiphany Church . .'
Morjovetz Island : Light-house
Archangel: Trinity Church
Jighinsk Island : Light-house
Onega: St. Michael's Church
Salovetski : Light-house
Cape Sviatoi Nos: Light-house
Bear Island
Spitzbergen Island : S. cape
Cloven Cliff
Danes I., Robbe
Bav
(«)
Thank God Harbor
Cape York : Extreme
Uperni vik : Flagstaf*
Proven: Village
Omenak Island: Village
Godhavn: Village
Jacobshavn : Village
Claushavn: Village
Christianshaab: Village
Egedesmunde: Village
Whalefish Island : Boat Inlet
Holsteinberg: Village
Kanganiint
Ny Sukkertop: Village
Godthaab: Flagstaff
Sermelik Fjord: Kasuk Peak
Fiskernaes: Village
.lensen Nunatak : Peak
Ravn Storo: Peak
Frederikshaab: Church :
Kangarssuk Havn : Village
Arsuk: Pingo Beacon
Kajartalik Island : Summit
Ivigtuk: House
Bangs Havn : Anchorage
Aurora Harbor
North Cape 68
00 00
04 00
.3.3 00
42 00
21 00
09 17
38 14
05 00
09 13
13 39
13 00
.50 05
49 00
04 40
27 00
40 00
54 00
07 00
47 10
55 00
75 10 00
77 41 00
70 25 00
70 55 00
76 58 00
79 .55 00
65 50 18
66 45 50
64 32 06
65 12 17
63 53 36
65 07 00
68 08 51
74 30 00
76 35 00
79 .50 00
79 42 00
81 38 00
75 55 00
72 47 48
72 20 42
70 40 00
69 14 04
69 13 12
69 07 30
68 49 06
68 42 30
68 58 30
66 55 54
65 48 42
65 24 30
64 10 30
63 29 12
63 05 12
62 50 00
62 42 36
61 .59 36
61 28 20
61 10 24
61 09 42
61 12 12
60 47 30
60 48 36
Loug. W.
69
77
91
87
81
91
92
96
89
88
91
90
73
64
61
63
64
70
110
179
28 00
50 00
06 00
15 00
31 00
30 33
10 56
47 00
00 54
54 48
08 00
12 00
10 00
45 00
18 00
38 00
45 00
20 00
48 15
57 00
Long. E.
150 30 00
104 01 00
.59 10 00
.53 01 50
65 40 00
58 45 00
44 17 00
42 30 00
40 33 30
36 51 30
38 08 30
35 37 00
39 48 54
20 00 00
17 23 00
11 40 30
11 07 00
Ijong. W.
61 44 00
65 .30 00
.55 53 42
.55 20 00
51 .59 00
53 24 07
50 56 30
50 55 30
51 00 00
52 46 IX)
53 27 00
53 40 18
53 23 00
52 54 00
51 45 48
51 10 48
.50 43 .36
48 57 00
50 20 48
49 44 00
48 51 00
48 26 00
48 .30 42
48 10 30
47 52 00
47 46 48
Lun. Int.
H.W.
4 00
6 50
10 35 4 20
10 00
7 18
5 05
9 02
9 05
14
12 14
10 50
8 05
6 20
L.W.
h. m. h. m.
10 15
40
11 38 5 29
1 20 . 7 40
3 50
2 00
11 30
3 10
Range.
Spg. Neap.
/'.
12.0
"s.'o"
5.5 2.9
2.6
3.8 , 1.9
7.0
2.2
8.8
9.1
2 55
6 25
58
4 38
1 52
07
6 40 I 27
6 12
00
6 15
03
13.9
5.3
5.4
l.'o
7.5
10.0
12.5
9.0
12.0
<i('rti* M orris .lesiip (thu must northern known Iimill, n:^" :!li' N.. :iu° 40' W. (Hpiiro.x.
APPENDIX IV.
MAKITLME POSITIONS AND TIDAL DATA.
THE ARCTIC REGIONS— Continued.
[Page 265
1
Place.
Lat. N.
Long. W.
Lun.
Int.
Range.
H. W.
L. W.
Spg.
Xeap.
1
S
£
Julianshaab; Village .,
/ //
60 43 07
60 08 12
60 00 00
59 49 00
60 09 00
61 25 00
62 01 00
63 14 00
64 30 00
65 18 00
66 19 02
69 00 12
74 40 00
74 55 00
76 47 00
71 04 00
71 OS 00
71 00 00
66 22 45
66 32 40
66 33 42
66 07 30
66 27 29
66 26 30
65 30 15
64 48 04
64 08 40
64 04 09
63 48 06
63 48 19
64 35 42
64 55 27
65 16 14
65 45 00
Of//
46 01 00
45 16 00
44 40 00
44 01 42
42 55 00
42 15 00
42 00 00
40 50 00
39 30 00
38 30 00
35 11 00
26 10 24
18 17 00
17 33 00
18 40 00
7 36 00
7 26 00
8 28 00
14 30 46
16 10 24
17 57 36
20 05 26
22 23 04
23 08 00
24 31 26
23 45 08
21 55 00
22 39 04
22 39 00
16 36 13
14 08 31
13 41 10
13 32 22
14 23 ;w
A. m.
4 66
5 33
2 55
4 00
h. VI.
11 09
11 46
9 10
10 13
ft.
7.0
8.6
9.4
7.5
2.8
3.4
3.8
3.0
Neunortalik: Village
Frederiksthal: Village
Cape Farewell: Staten Huk
Aleuk Islands: Center
Cape Tordenskjold: Kx,trenie
Cape Bille: Extreme. . .'*.
Cape Juul : Extreme
Cape Lo wenorn : Extreme
Dannesbrog Island : Beacon
;
Ingolsfjeld
Rignv Mount: Summit
i_
11 05
11 10
4 53
4 58
6.7
3.7
3.9
2.1
Cape Philipp Broke
Cape Bismark : Extreme
Jan May en Island: Mt. Beerenberg,
6,870 ft
Youngs Fore-
land, or Cape
Xorthea.st
Mary Muss Bay. .
Langanaes Point
11 21
5 06
3.8
2. 2
Rissnaes Point
Grimsey Norddranger: Tr. Station
Skagataaa Point
North Cape: Kalfatindr
Straumnes.s Point
Fugle or Staabierg Huk : Point
Snaefells Yokul : Tr. Station
:::::::;;;;; i
B
1
m
Reykiavik: Observatory . .
5 10
11 25
14.5
"
Cape Skagi : Light-house
Reykianaes: Light-house
Ingolfshofde: Tr. Station
Papey Island : Tr. Station
ReythurFjeld: Tr. Station
Balatangi : Light-house
Dia Fjeld: Tr. Station
1
^^^^
Page 266]
INDEX TO APPENDIX IV.
Page.
Admiralty Islands 255
Adriatic Sea 22&-228
Africa, east coast 232, 233
north coast- 230
west coast 230-232
Alabama 196
Alaska 198,199
A lentian Islands 199
Alfreria 230
AraV)ia 236
Arctic regions 264,265
Argentina 208, 209
Asia, east coast 239-250
islands . 243, 244
south coast 236-239
Atlantic Ocean, islands. 213-215
Australia 259-262
Austria 227, 228
Azores Islands 213
Bahama Islands 203
Balearic Islands 226
Baluchistan 237
Banka Strait 239
Belgium 223
Belize .*. 197
Bermuda Islands 214
BlackSea 229,230
Borneo 242
Brazil 207,208
British Columbia 200
Burma 238
California 200, 201
Canary Islands . . 214
Cape Breton Island 192, 193
Verde Islands 214
Caroline Islands 252
Celebes Island 242
Central America, east
coast . . . 197, 198
west coast... 202,203
Ceylon 237
Chile 209-212
China 240-242,247
— Sea 240
Entrance 240
Cochin China 240
Colombia, north coast . 198, 206
west coast 213
Connecticut 194
Cooklslands 258
Coral Sea Archipelago 255
Corsica 226
Costa Rica 198
Crozet Islands 236
Cuba 203,204
Cyprus 230
Delaware 195
Denmark 222,223
REGIONS AND COASTS.
Page.
Ecuador 213
Egvjit 230
EUice Islands 254
Europe, Atlantic coast. 215-225
Falkland Islands 214
Fiji Islands 256, 257
Florida 195,196
Formosa Island 242
France, north and west
coasts 223, 224
France, south coast 225,226
Galapagos Islands 250, 251
Caspar Strait 239
Georgia 195
Germany 221,222
Gilbert Islands 251
Great Britain 215-218
Greece 228, 229
Greenland 264,265
Guatemala 197
Guiana 207
Haiti 204
Hawaiian Islands 253
Holland 223
Honduras 197,198
Iceland 265
India 237,238
Indian Ocean, islands. . 234-236
Italy 226,227
Jamaica 204
Japan 248, 249
Jaya 243
Kerguelen Islands 2,36
Korea 247, 248, 250
Kuril Islands 249
Labrador 191, 192
Laccadiye Islands 234
Ladrone Islands 252
Linschoten Islands 248
Louisiade Archipelago 255
Louisiana 196
Lower California 201, 202
Madagascar 235
Madeira Islands 213
Magdalen Islands 192
Maine 193
Malaysia 238, 239
Mald'i ve Islands 234
Mariana Islands 252
Man) uesas Islands 253
Marshall Islands 251
Maryland 195
Page.
Massachusetts 194
Mauritius Island 234
Mediterranean Sea 225-230
Mexico, east coast 196, 197
west coast 202
Mississippi 196
Morocco 230
Mosquito Coast 198
New Brunswick 192, 193
Caledonia 259
Newfoundland 191,192
New Guinea Island 255
Hampshire 194
Hebrides Islands 256
Jersey 195
Soutli AVales 261
York 194
Zealand 262,263
Nicaragua 198
North -America, east
coast . . . 191-198
• west coast . . . 198-203
Australia 259
Carolina 195
Island, New Zea-
land 262, 263
Norway : 218-219
Nova Scotia 193
Oregon 200
Pacific Ocean, Islands . . 250-259
Pelew Islands 252
Persia 23(i, 237
Peru 212
Philippine Islands 245-247
Pha'nix Islands 254
Porto Kico 205
Portugal 224, 225
Prince Edward Island 192
Queen Charlotte Islands . . . 199
Queensland 261 , 262
Red Sea 233-234
Rhode Island 194
Russia, south coast 229
west coast 220
St. Lawrence, Riyer and
Gulf 192
Samoan Islands 257
Santa Cruz Islands 2.55
Sardinia 226
Siam, Gulf 240
Siberia 250
Society Islands 257
Solomon Islands 2.54
South America, north and
east coasts 206-209
INDEX TO APPENDIX IV.
[Page 267
Page.
South America, W. coast 209-213
Australia 260
Carolina 195
Island, New Zealand.. 263
Spain, north and west
coasts 224,225
south and east coasts.. 225
Stewart Ireland 263
Sumatra 239
Sweden 219,220
Aalborg 223
Aarhus -. 223
Ababa Island 256
Abaco Island 203
Abang Besar Island 238
Abbeville 223
Abd-al-Kuri Island 233
Abenleen 216
.\l>ervrach 224
Aberystwith 215
Abingdon Island 250
Mk>:. 220
AboukirBay 230
Abreojos Point 201
Abrolhos island 207
Absecon Inlet 195
.\cajutla 202
Acapulco 202
Accra 231
Acheen Head 239
.\concagua Mountain 21 1
.\cre 230
Adakh Island 199
Adalia 230
Adams, Port 247
A.ldu Atoll 234
Adelaide, Port 260
River 259
Adele Island 255
Aden 236
Adenara Island 243
Admiralty Head 200
Islands 255
Adolphus Mountain 262
Adventure, Port 263
.-Egina 229
Aero Island 222
.Erstenen 218
Africa Rock 226
Agalegas Island 235
Agdenes 218
.\giabainpo 202
Agrigan Island 252
.\guadilla Bay 205
Aguja Point 212
Agulhas.Cape 232
Agutava Islet 245
Aheu Island 258
Ahunui Island 257
Ahuriri 263
AiSiina 249
Aian 250
Aignan, St., Island 255
Aigues MorteS 226
Ailinginae Islands 251
Aillick Harbor 191
Aillv Point 223
Aihik Islands 251
REoioxs .\Ni> COASTS— continued.
Page.
Tasmania 262
Texas 196
Tonga Islands 258
Trinidad 206
Tuamotu Archijielago. . 257, 258
Tunis 230
Turkey 228,229,230
Uruguay 208
PLACES.
Aitutaki Island 258
Aix Island 224
Ajatcio 226
Ajano 230
A kamokan Island 252
Akaroa Island 263
.\kashi-no-8eto 248
Akpatok Island 191
Akyab 238
Alacran Reef 197
Alamaguan Island 252
Aland Island 220
Alargate Reef 198
Albany 194
Albatross Islet 262
Albemarle Island 251
Albert, Port 261
River 262
Alboran Island 230
Albuquerque Bank 198
.•Vlcatcasses Island 208
Alcmene 259
Alcoba^a 207
A Idabra Island 235
Alden 218
Alderney Harbor 218
Alegranza Island 214
Alegre, Porto 207
Alert's Winter (Quarters 264
Alessandro, San, Island ... 253
Aleuk Islands 265
Alexander, Port 232
Vancouver 200
Alexandretta 230
Alexandria 230
Alfaques, Port 225
.Alfred, Port 232
Algeciras 225
Algier 230
Ali-Agha, Port 230
Alicante 225
Alijos Rocks 201
Alipee 237
Alligator Island 241
Reef 196
Almadie Point 231
Almeria 225
Alphonse Island 235
Alta Vela 204
Altata 202
Altea 225
Altona 222
Alvarado 196
Amager Island 222
Amter, Ca[)e 236
Aniboina Island 244
Ambrose, St. , Island 258
Amchitka Island 199
Page.
Vancouver Island 199, 200
Venezuela 206
Victoria 260, 261
Virginia 195
Washington 200
Western Australia 259, 260
West India islands 203-206
Yucatan 197
Amelia Island j 195
Ameni Islet 234
Amherst Harbor 192
Amirante Islands 234
Amour Point 192
Anioy 241
Amsterdam 223
Island 236
Ana, Sta., Lagoon 197
Anaa Island 258
Anacapa Island 201
Anadir River 259
Analaboe 239
Anamba Islands 240
Anataxan Island 252
Anchorite Island 255
Ancona 227
Andaman Islands 238
Andenes 218
Andrava Bav 235
Andrea, St. ," Rock 228
Andrew, St 193
Cape 235
Island 255
Andrews, St. , Island 198
Andros Island, Bahamas... 203
Grecian Arch 22?»
Anegada 205
Aueityum Island 256
Angatau 258
Angaur Island . . .■ 252
Angeles Bay 202
^Los 201
Port, Mexico 202
, Washington 200
Anghris Head 217
Angosto, Port 210
Angoxa Island 233
AngradosReis 208
• Pe<iuena 232
Anguilla 205
Anhatomirim 208
Anholt Island 222
Animas, Las 202
Anjer 243
Anjoe, Cape 243
Ann, Cape 194
St., Bay 204
Anna, Sta. , Island, N. Brazil . 207
; S. Brazil 208
Annapolis, Maryland 195
Nova Scotia 193
Anne, St., Island 210
Annisquam 194
Anno Bon Island 231
Anns, St., C. Breton I 192
England 215
Anowik Island 199
Page 268]
INDEX TO APPENDIX IV.
Page.
Antareh, Eas 233
Antibes 226
Anticosti Island 192
Antigua 205
Antipodes Island 259
Antivari 228
Antofagasta 211
Antonina 208
Antonio, Port 204
San, Cape, Argentina . 208
Cuba 204
Mt. and Island. . . 214
Port, Argentina. . 209
Chile 211
Sierra 209
Antwerp 223
AogaShima 249
Aor, Pulo 240
Aotea 263
Apaiang Island : 251
Apalaehicola 196
Apamama 251
Aparri 245
Apenrade 221
Apo Islet 245
Apostle Rocks 209
AragoCape 200
Araish, El 230
Arakam Island 250
Araktcheff Island 258
Aran Island 217
Aransas Pass 196
Arauuka Island 251
Aratika Island 258
Aroadius Islands 204
Areas Cays 197
Archangel 264
Ardassier Islands 243
Ardrossan 216
Arena de la Ventana 201
Point, California 200
L. California 201
Arenas Cay 197
Arendal Inlet 219
Arentes Island 243
Argentina 208
Argostoli, Port 228
Arica 212
Arichat Harbor 193
Arkona 221
Armeghon 238
Arnheim, Cape 259
Arno Atoll 251
Arorai Island 251
Arran Island 217
Arrowsmith Islands 251
Arru Islands 244
Arsuk 264
Artaki Bay 230
Arthur River 262
Port 247
Arvoredo Island 208
Ascension Bay 197
Island 214
Ashburton River 263
Ashrafi Island 233
Asia Rock 212
Assateagne Island 195
Assens 222
Assumption Island 235
Astoria 200
PLACES — continued.
Page.
Asuncion Island, Ladrones. 252
• L.Calif 201
Atalaia Point 207
Athens 229
Atico 212
Atiu Island 258
Atka Island 199
Atkinson Point 200
Attn Island 199
Auckland 263
Islands 259
Audierne 224
Augusta 193
Port, Australia 260
Sicily 227
Augustenberg 221
Augustin, St.,Cai)e, Brazil. 207
Philippines . 246
Augustine, San, Island 253
St., Bay 235
Harbor 195
.\urh Island 251
Aurora Harbor 264
Island 256
Austral Islands 258
Avareua Point 204
Aves Island 205
Aviles 224
Avlona 228
Axim Bay 231
.Iwa Sinia 249
Awomori 249
Ayamonte 225
Ayer Bangis 239
Ayr 215
Baago Island 222
Babayan Claro Island 245
Baccalieu Island 191
Bagamovo 233
Bahaltolia Island 247
Bahama Island 203
Bahia,Brazil 207
Colombia 206
de Cadiz Cay 204
Honda, C. America... 202
Bahrain Harbor 236
Bajo Nuevo 197
Bajuren Island 242
Baker Islet 251
Bakers Island 193
Baklar 229
Balilbac Island 245
Balaklava Bav 229
Balari Pass.." 259
Balasor River 238
Balatangi 265
Balayan 245
Bald Isle 260
Balfour Rock 236
Bali Island 243
Balingtang Islands 246
BallenaBay 202
Balls Pvramid 259
Ballum" 221
Ballvcottin 218
Balstrum 222
Balta Island 216
Baltic Port 220
Baltimore 195
Bampton Island 255
Pagv.
Banda Island 244
Banderbunmi 236
Bandjennasin 242
Bangkaru Islands 239
Bangkok 240
Bangor 193
Bangs Havn 264
Banjnwangi 243
Banka Island 239
Strait 239
Bankot 237
Banks Strait 261
Bantal 239
Bantam 243
Bantenan 243
Banton Island 246
Bantry Bay 216
Baracoa 203
Barataria Bay 1 96
Baratoube Bay 235
Barbados Island 205
Barbara, Santa, C'alifornia . 201
Island 201
Mexico 202
Port 210
Barbe, St. , Island 240
Barbuda 20."i
Barcelo Bay 210
Barcelona, Spain 225
Venezuela 206
Bardsey Island 215
Barfleur, ('ape 223
Bari 227
Barker Isletjj 259
Barnard Island 2()1
Barnegat Inlet 195
Barneveldt Islands 209
Barnstable 194
Barra Head 216
Sao Joao 208
Barren Island 248
West 242
Barrier, Great, Island 263
Barrington Island 251
Barrow Island, Australia . . 260
Tuamotu Arch... 257
Point 198
Bartholomew, St 205
Cape. 209
Bartolomi?, San 201
Barton, Port 245
Baru, Point 239
Barung Island 243
Bas, De, Island 224
Basdorf 221
Basianang Bay 246
Basiduh 237
Basilan Island 247
Baskerville, Cape ' 260
Basrah 236
Basslslet« 258
Bassa, (^rand 231
Bassas Rocks 237
da India 235
Bassein, Burma 23S
India 237
River 238
Basseterre 205
Bastia 226
Bastion, C^ape 240
INDEX TO APPENDIX IV.
[Page 269
Basto . . -•
Batalden Island
Batan Island
Port
Batangas
Batavia
Batbatan Island
Bate I^^land8
Batfiiian Bay
Bath
Bathun-t
Island
Batian Island
Batoe Islands
Batouni
Batticaloa
Battle Islands
Batty Bay
Batve Toetong
Baubeltaub Island
Bauld Cape
Baxo Xuevo
Bay of Islands
Baynes Sound
Bayonnaise Island
Bayonne
Bazariito Island
Beai'hy Head
Beale Cape
Bear Island
Cape
Beata Island
Beaufort, N. Carolina. .
S. Carolina
Port
Beaver Harbor
Beaver-tail light
Bee du Raz
Beda'a, Al
Bedford, CajX'
Bees, St
Beeves Rocks
Beirut
Bel Air
Belfast
Bay
Belgrano
Belize
Bell Island
Rock, Scotland
Bellavista Cape
Belle Isle, France
Labrador
Bellingshausen Island .
Bellone, Cape
Ben Ghazi
Benbane Head
Bender Erekli
Benedicto, San, Island.
Bene.vente
Beriguela
Benicia
Benidonne
Benin River
Benito, San, Island
Benkulen
Bento, San, River
Benzert
Bequia Island
Berbera
Berdiansk
Page.
. 219
. 218
. 246
. 246
. 245
. 243
. 246
. 248
. 261
. 193
. 231
. 259
. 244
. 239
. 229
. 237
. 191
. 264
. 239
. 252
. 191
. 204
. 262
.. 200
,. 249
.. 224
. 232
.. 215
.. 199
. 264
. 225
,. 204
.. 195
.. 195
.. 232
.. 200
.. 194
.. 224
.. 236
.. 261
.. 215
.. 216
.. 230
.. 235
.. 193
.. 217
.. 208
.. 197
.. 191
.. 216
.. 226
.. 224
.. 191
.. 257
.. 235
.. 230
.. 217
.. 230
.. 202
.. 207
.. 232
.. 200
.. 225
.. 231
.. 201
.. 239
.. 231
.. 230
.. 205
.. 233
.. 229
PLACKs — continued.
Page.
Bergen, Germanv 221
Norwav...'. 218
Berikat 239
Bering, Cape 250
Island 250
Berlanga Island 225
Berlin 222
Bernieja Head 209
Bermudas 214
BernalChico 196
Bernardo Islands 257
Berwick 216
Besuki 243
Betrapar Islet 234
Beverly 194
Beyt 237
Bhaunagar 237
Blanche Point 227
Biarritz 224
Bickerton Island 259
Bideford 215
Bidstone 215
Bierneborg 220
Bigar Islet 251
Bikini Islands 251
Bilbao 224
Bille, Cape 265
Billiton Island 239
Bindloe Island 250
Bintang Hill 238
IMntoean 239
Bird Island, Australia 262
Bahamas 203
Banda Sea 244
N. Pacific 253
Sevchelle Islands. 234
Tu'amotu Arch ... 258
AV. Africa 231
Islands, Magdalen Is. . 232
Birneys Island 254
Bismark, Cape 265
Bittern Rocks 249
Bjuroklubb 220
Blaabjerg 223
Black Head 191
Point Bay 232
Stairs Mountain 217
Blackness 216
Blacksod Point 217
Blair, Port 238
Blaize, St 232
Blanco Cape, N., Africa 231
Oregon 200
Peru 212
S., Africa 231
Peak 198
Blankenberghe 223
Bias, San, Argentina 209
Cape, Florida 196
Mexico 202
Blasket Islands 216
Bligh Island 257
Blighs Cai)e 236
BlimbingBav 239
Blinyu '. 239
Block Island 194
Bloody Foreland 217
Bluefields 198
Bluff Harbor 263
Boar Islands 191
Boavista Island 214
Page.
BobaraRock 228
Bodie Island 195
Bogense 222
Bogsher 220
Bohol Island 246
Bojador, Cape 231
Bojeador, Cape 245
Bola-Bola Island 257
Bom A brigo Islet 208
Bombay 237
Bon, C;ape 230
Point 239
Bona 230
Bonaeca Island 197
Bonaive Island 206
Bonaventure Head 191
Island 192
Bonavista Cape 191
Bongao Island 247
Bonham Islands 251
Bonifacio 226
Benin Islands 253
Boobjerg 223
Booby Island, Leeward Is. . 205
Queensland 262
Boompjeo Island 243
Boon Island 193
Borda, Cape 260
Bordeaux 224
Bordelaise Island 252
Borja Bay 210
Bornholui 222
Borodino Islands 253
Boscawen Island 257
Bosphorus 229
Boston 194
Botel Tobago Sinia 242
Bougainville, Cape 259
— Island 254
Bougaroni, Cape 230
Boulogne 223
Bounty Islands 259
Bourbon, Cape 236
Bouro Island 244
Bouton Island 242
Bouvets Island 215
Bovliluvan, Cape 245
Bo wditch Islet 254
Bowen, Port, Australia 261
Baffins Bay 264
Bowling Green , Cape 261
Boyanna Bay 235
Bradore Bay 192
Brala, Pulo" 240
Brangmans Bluff 1 98
Bras, Pulo 239
Brass River 231
Brava Island, C.Verde Is.. 214
E. Africa 233
Brazos Santiago 196
Bray Head 217
Breaker Point 241
Bremerhaven 222
Bremerton 200
Brest 224
Brewers Lagoon 198
Bridgeport 194
Brielle 223
BrillEeef 243
Brindisi 227
Brisbane 261
Page 270]
INDEX TO APPENDIX IV.
Page.
Bristol, England 215
Rhode li-land 194
Britannia Island 259
Broadhaven 217
Broken Bay 261
Bronnosund 218
Brothers Island, Red Sea . . 233
Islets, China 241
Broughton Bay 244
Head...: 248
Island 249
Rock 249
Brunet Island 191
Bruni River 242
Brunswick, Georgia 195
Maine 193
Bruny, Cape 262
Island 262
Brussels '223
Brusterort 221
Bryer Island 193
Bubuan Island 247
Bucas Island 246
Buchanness 216
Buddonness 216
Budruni 230
Budiia 228
Buenaventura 213
San 201
Buenos Avres 208
Bu^ui Point 246
Buitenzorg 243
Buka Island 254
Bulipongpong Island 247
Biilk... 221
Bull Harbor 200
Rock 216
Bullock Bay 250
Burg 221
Burghaz 229
Burias Island 246
Burin Harbor 191
Burnett River 261
Burntcoat Head 193
Burrh Island 251
Busios 208
Islets 208
Bustard Head 261
Busuanga Island 245
Biisum 222
Butt of Lewis 216
Button Islands 191
Byam Martin Island 257
Byron Island 251
Caballo Island 245
Cabeceira, Cape 233
Cabeza de Vaca 21 1
Cabrera Island 226
Cabron Cape 204
Cabrutlslet 234
Cadaques 225
Cadiz 225
Cadmus Island 257
Caen 223
Cagayan Jolo Island 247
Cagayanes Islands 247
Cagliari 226
Cai^ara 207
Caicos Island 203
West, Cay 203
PLACES — continued.
P.'ge.
Calaan, Point 246
Calais, France 223
Maine 193
Calavite, Monte 245
Calavan Island 245
Calbuco 211
Calcasieu Pass 196
Calcutta 238
Caldera 211
Caldy Island 215
Calebar River, New 231
Old 231
Caledonia 206
Calf of Man 215
Calicut 237
Calimere Point 237
Callao 212
Calpe 225
Cain va Island 245
Calvi 226
Canianiu 207
Camaron Cape 198
Camasusu Island 246
Cam bay 237
Cambria 208
Cambridge, England 215
Tnited States . ... 194
Caniiguin Lsland, Luzon 245
Mindanao 247
Cammin 221
Campbell, Cape 263
Island 259
Canipeche 197
Campobello Island 193
Canaria, Oran, Island 214
Canaveral Cape 195
Cancun Island 197
Candia Island 228
Candon 245
Cannes 226
Cannonier Point 234
Canoas Point 201
Canso, Cape 193
North 193
Cantf)n 241
Island 254
Pulo 240
Cantvre 216
Cape" Town 232
Cape Verde Islands 214
Capel Island 218
Cape d'Istria 246
Capones Islet 245
Capraia Island 226
Caprera Island 226
Capri Island 226
Capricorn, Cape 261
Car Nicobar 238
Carabane 231
Carabao Island 246
Caraques Bay 213
Carataska Lagoon 198
Caravellas 207
Carbon, Cape 230
Carbonera Cape 226
Cardamum Islet 234
Cardiff 215
Careys Islands 264
Cargados Carajos 234
Caribana Point 206
Carimare Mountain 207
Page.
Carimata Island '. . . . 240
Carlingford Lough 21 7
Carlobago 227
Carlos, San, de Ancud 211
Point 201
Carmen Island 197
Caroline Islands, N. Pacific. 252
S.Pacific 253
Carousel Island 192
Carreta Mountain 212
^ Point 198
Carreto, Port 206
Oarrizal, Port 211
Cartagena, Colombia 206
Spain 225
Cartago Mountain 198
Carteret Cape 224
Harbor 2.55
Cartwright Harbor 191
Carupano 206
Carvsfort Island 257
^Reef 195
Cascade Point 263
Casquets Rocks 223
Cassini Island 2.59
Castillos 208
Castle Island 203
Castlehaven 216
Castro 210
Urdiales 224
Cat Island 196
Catalina Harbor 191
Sta., Island 201
Catania 227
Catastrophe, Cape 260
Catbalogan 246
Catharine Point 209
St 215
Island 208
Cato Island 255
Catoche Cape 197
Cattaro 228
Cautanduaneo Islands 246
Cavite 245
Caxones 198
Cayenne 207
Cayeux 223
Caymans 204
Cazzalsjand 228
Ceari'i 207
Cebu Island .' 246
Cedar Keys 196
Cedeira 225
Ceicer de Mer Island 240
Celebes 242
Centinela Islet 206
Ceram Island 244
Cerros Island 201
Cestos 231
Cette 226
Ceuta 230
Ceylon 237
Chacachacare Island 206
Chacopata 206
ChagosArch 2.34
Chagres 206
ChahbarBay 237
Chala Point 212
ChaleurBay 192
Challenger, Cape 236
ChamaBay 231
INDEX TO APPENDIX IV.
[Page 271
Pago.
Cham-Callao Island 240
Chame, Point 213
Chaniisso Island 198
Chaniperico 202
ChanaralBay 211
Island 211
Chandeleur Islands 196
Chao Islet 212
Chapel Island 241
Chapu 242
Charles Cape 195
Island, Chile 210
Galapagos Group. 251
Hudson Strait ... 191
Charleston 195
Charlotteto wn 1 92
ChateauBav 192
Chatham Harbor 194
Island, Galapagos
Group 251
S.Pacific 259
ChatteCape 192
Chaume, La 224
Chausey Islands 224
Cheduhah Island 238
Chemulpo 247
Chentabun River 240
Chepillo Island 213
Cherbourg 223
Cherilx)n 243
Cherso 227
Chiachi Islands 199
Chicarene Point 202
Chidleigh Cape 191
Chifu 247
Chignecto Cape 193
Chignik Bay 199
Chilca Point 212
Chiniba Bay 211
Chinibote 212
Chincha Islands 212
Chinohin Harbor 241
Chinchorro Bank 197
Chin-hai 241
ChinoBay 241
Chirambiri Point 213
Chirikof Island 199
Chitlac Islet 2.34
Chittagong River 2.38
Choda Island 247
Choiseul Island 254
I'ort 235
Choros Islands 211
Christiana Islands 229
Christiania 219
Christiansliaab 264
Christianso Island 222
Christianssand 218
Christiansted 205
Christiansund 218
Christmas Cove 210
Harbor 2.36
I., Indian Ocean 236
N. Pacific 251
Christopher, St 205
Christoval, San, Island 254
Chuapa River 211
Chuluwan Island 232
Chupat River 209
Churruca, Port 210
Chusan Islands 241
PLACES — continued.
Page.
Ciaris Island 202
Cica, Mount 228
Cienfuegos 204
Ciotat 226
Cispata, Port 206
CittaXuova 227
Ci vita Vecchia 226
Clara, Sta 200
Clare Island 217
Claremont Point 262
Clarence Harbor, Bahamas. 203
Port, .\laska 198
River 261
Clarion Island 202
Claushavn 264
Clear Cajie 216
Clearwater Point 192
Gierke Island 257
Clermont Tonnere Island 257
Cleveland, Cape 261
ClewBav 217
Clifdenfiay 217
Clipi)erton Island, Mexico . 202
N. Pacific 253
Clonard, Cape 250
Coast Castle, Cape 231
Coatzacoalcos 197
Cobbler Rock 198
Cobija 212
CobreBay 211
Cochin 237
Cockell Islet 259
Cockscomb Mountain 197
Coconada 238
Cocos Island, C. America .. 203
N. Pacific 250
Cod, Cape 194
Codera Cape 206
Codfish Island 263
Cod rov Island 192
Coeti vv Island 235
Coffin Bay 260
Island, Madagascar 2.35
Nova Scotia 193
Cofre de Perote Mt 196
Coiba Island 202
Colberg 221
Colbert Islet 259
Coles Point 212
Colina Redonda 212
Colnett Bay 201
Colombo 237
Colon 206
Colonia 208
Colonna, Cape, Greece 229
Italy 227
Columbia, Cape 264
Colunibretes Islands 225
Columbus Island 198
Colville, Cape 263
Coman Inlet 211
Comandatuba 207
Commerson Island 255
Comorin, Cape 237
Comoro Island 235
Concei(;ao 208
Conception Island 203
Point 201
Conde 207
CondorCove 211
Condore Islands 240
I Conducia
; Conejo, El, Point
Coney Island
; Confites Cay
, Congo River
j Congrehoy Peak
j ConnStable Islet
j Constantinople
I Constitution Cove
Contas
! Conte, Port
Contoy Island
Conway, Cape
Reef
Cook Cape
Mountain
CookraHill
Cooper, Port
Cojienhagen
Copiapo
Copper Island
Coquet Island
Coquille Island
Coquimbo
Coral Island
Islet
Corcovado Volcano
Cordouan, Point
Corfu
Coringa Islands
Corinto
Cork, Ireland
Port, Staten Island . . .
Cormorant Island
Corn Islands
Corn wal lis Islands
-Port
Coro, Vela de
Coromandel Harbor
Coronation Island
Corregidor Island
Corrientes, Cape, Argentina .
Colombia
Mexico
S. Africa
Corsarios Bay
Corseulles, Port
Corso, Cape
Mountain
Corti
Coru na
Corvo Island
Coslin
Cosmoledo Island
Cotinguiba
Cotrone
Coubre, Point de la
Courtown Cays
Coutances
Cove Rock
Cow Head
Coy Inlet
Cozumel Island '.
Cracker Ba^
Crassok Pomt
Crescent City
Cretiii, Cape
Creux, Cape
Crocker Island
Croisic
Croker, Cape
age.
233
201
241
204
232
197
207
229
212
207
226
197
261
258 .
199
261
198
263
222
211
250
216
252
211
208
208
210
224
228
255
202
218
209
200
198
253
238
206
263
215
245
208
213
202
232
206
223
226
210
226
225
213
221
235
207
227
224
198
224
232
192
209
197
209
239
200
2.55
225
258
224
259
Page 272]
INDEX TO APPENDIX IV.
Page.
Crooked Island 203
Crozet Islands 236
Cruz Cape 204
i^ita., Brazil 207
California 201
Island 201
Islands, Philip-
pines 247
S. Pacific ... 255
Leeward Islands . 205
-. Luzon 245
Port 209
Cuad Basang Island 247
Cuba 203,204
Culebra 202
Culebrita Island 205
Culion Island 245
Cullera, Cape 225
Culver Point 260
Cumana 206
Cumberland Island 261
Cuinshewa Harbor 199
Cupohi Point 241
Cupica Bay 213
Curaf;ao Island 200
Little 206
( 'urrimao 245
Currituck Beach 195
Curtis Island 258
Port 261
Curzola Island 228
Cutty hunk Light 194
Cuvi'er, Cape 260
Island 263
Cuxhaven 222
Cuyo Island 245
Cyprus 230
Dfcdalus Shoal 233
Dago Island 220
Dakar, Port 231
Dakahue 211
Dale Point 259
Dalrvmple Harbor 247
'Port 262
Dalupiri Island 245
Danighot 236
Danima Island 244
Danger Islands 257
Dangerous Rock 241
Dannesbrog Island 265
Danube River 229
Danzig 221
Dai)itan 247
Dardanelles 229
Dar el Beida, Cape 230
Dar-es-Salaam 233
Darien, Colombia 213
Georgia, IT. S 195
Darsserort 221
Darwin, Port 259
Date-Island 240
Datu, Point 239
Dauphin, Fort 235
Davao 246
Davey, Port 262
Davids, St., Island 214
De Kastri 250
De Peysters Island 254
Deadman Rock 192
PLACES — continued.
Page.
Deception Island 215
Deiinaniveh 236
DelagoaBay 232
Delgada Point 209
Delgado,Cape 233
Point 209
Demerara 207
Denia 225
Denis,St 235
Denison, Port 261
D' Entrecasteaux Islands 255
-Point 260
Deseado Cape 209
Desert, Mt. , Rock 193
Desertas 213
Desirade 205
Desire, Port 209
Desolation Cape 209
DiaFjeld 265
Diamond Harbor 238
^ Point 239
Diedrichshagen 221
Diego Garcia 234
Ramirez Island 209
San 201
-Cape ,... 209
Dieppe 223
Digges Islands 191
Dima-salasan, Port 246
Dinding Channel 238
Dingle Bay 216
Diomede Island 198
Direction, Cape 262
— Island 240
Disappointment, Cape, Sib. 250
Washington 200
Discovery Harbor 264
Diseilsland 233
DiuHead 237
Dix Cove 231
Djabon, Point 239
Djambi 239
Djursten 219
Dnieper Bay 229
Doc Can Islet 247
Dodd Island 241
Dog Island 205
Domar, Pulo 240
Domesnes 220
Domingo, San, Point 201
St., Cay 203
City 204
Dominica 205
Donaghadee 217
Dondra Head 237
Donegal Bay 217
Double Island 238
Point 261
— - Peak Island 241
Douglass Rocks 253
Dounpatrick Head 217
Dou vres liwVa 224
Dover Point 260
Drei Cap Peninsula 255
Drepano, Port 228
DrObak 219
Drogheda 217
Dromedary Mountain 261
Drummond Island 251
Dublin 217
Ducie Island 257
Page.
Duff Islands 255
Duke of CJlarence Island . . . 254
York I., N.Britain. 254
S. Pac... 254
Dulce Gulf 197
River 197
Dulcigno 228
Dumaguete 246
Dumalv Point 245
Dumford Point ; 232
Duncan Island 251
Dundee, Rock of 210
Dundrum Bay 217
Dungarvan ..' 218
Dungeness 215
New 200
Point..; 209
Dunkerque 223
DunnetHead 216
Duperrey Islands 252
Duppel." 221
Durazzo 228
Durnford, Port 233
D'Urville Island 263
-Point 255
Dussejour, Cape 259
Dwarka 237
Eagle Island 217
Earakong Island 252
East Cape, Madagascar 235
New Zealand 263
-Siberia 250
Dog Island 241
Island, Crozet Is .i... 236
Magdalen Is 192
Easter Island 258
Eastport 193
Eau Island 252
Eauripik Islands 252
Ebon Atoll 251
Eckemforde 221
Eclipse Harbor 191
Islands 260
Eddvstone 215
"Point 262
Eden Harbor 210
Edenshaw Cape 199
Edenton 195
Edinburgh 216
Eeragh Island 217
Egedesmunde 264
Eggegrund Islet 219
Egmont Mountain 263
Port 214
Eimeo Island 257
Ekholm Islet 220
Elbal.sland 226
Elbing 221
Elena, St., Port 209
Sta., Point 213
Elei)hant Bay 232
Eleuthera Island 203
Elias, St., Mount 199
Elizaljeth Bay 232
Cape...' 193
Citv 195
Harbor 264
Island, Chile 210
TuamotuArch 257,258
Port 232
INDEX TO APPENDIX IV.
[Page 273
I'agc.
Klizalaeth Reef 259
KUice Islands 254
Eiiiiien 222
Emma, Great, Island 203
Emu Bay 262
Enanger 219
Endelave Island 222
Enderbury Island 254
Enderby Island 260
Endermo 249
Enfant Perdu Island 207
Engano, Cape 245
fjngano Island 239
Engelholm 219
English Cay 197
Eniwetok Islands 251
Enrag^Cape 193
P^nsenada 201
Entry Island 192
Erromango Island 256
Erronan Island 256
Kscarceo Point 245
Escarseo Point 206
Eschholtz Islands 251
Escudo de Veragua 198
Escunienae Point 192
Esdu Island 234
Esmeralda Islet 206
River 213
Espada Point, Colombia 206
Hayti 204
Espenberg, Cape 198
P^peranza Inlet 199
Espiritu Santo Bay 207
Cape 209
Esquimau 200
Essington, Port 259
Estaca Point 224
Estangues Point 206
Estevan Point 199
Etches, Port 199
EtenHead 212
Eu, Pulo 240
Eureka 200
ICuripo Strait 229
Europa Island 235
Eustatius, St 205
Evangelistas Island 210
Evarifto, San 201
Expedition Bay 250
Faero Islands 213
Fair Isle Skroo 216
Fairy, Port 260
Faiu, W., Islet 252
Fakaof u Islet 254
Fakarana Island 258
Falkenl)erg 219
Falkland Islands 214
Falmouth, England 215
Jamaica 204
False Cape Hf irn 209
Point 238
Falster Island 222
Falsterbi) 219
Famagusta 230
Famine, Port 210
Fanad Point 217
Fanning Island 251
Fano Island, Adriatic 228
Denmark 223
PLACES — continued.
Page.
Farallon Islet 200
Faraulep Island 252
Farewell, Cape, Greenland. 265
New Zealand 263
Farina, Cape 230
Farisan Island 234
Fam Island 216
Faro Island, Sweden 219
of Messina 226
Farquhar Islands 2,35
FarrallRock 198
Farralon de Pajaros 252
Fartak, Has 236
J'astnetRock 216
Father Point 192
Fatsizio Island 249
Fatu Hiva Island 253
HukuIsland,Galapagos 251
Marljuesas . . 253
Fatuna Island 257
Fayal Channel 213
Island 213
Fecamp 223
Felipe, San, Cavs '. 204
Point" 202
Felix, St., Island, Chile ... 211
• S. Pacific ... 258
Feneri ve Point 2;ii5
Fermin Point 201
Fernandina 195
Fernando Noronha 214
Po Island 231
San, River 196
— Port 245
— Trinidad 206
FgroUe I'oint 192
Ferro Islan<l 214
Ferrol 225
Fetouhouhou Island 253
Fevs Island 252
Fi(ionisi Island 229
Figari Cape 226
Filzand Island 220
Finisterre, Cape 225
Firase Rocks 248
Fire Island 194
Firmin, San 202
Fischausen 221
Fish, (ireat, Bay 232
— Little, Bay 232
Fiskernaes 264
Fitz Roy River 260
Fiunie 227
Five Fathom Bank 195
Flamborough 216
Flamenco 211
Island 213
Flat Island 234
Flattery, Cajie 200
Flensberg 221
Flesko, Cape 242
Flinders Island 262
Islands 261
River 262
Flint Island 253
Florence 226
Floros Island, Azores 213
Indian Arch 243
Uruguay 208
Florida Island 254
Flower Cove 192
Page.
Flushing 223
Fly River 255
Foerder Islet 219
Fogo Island 214
Fohr 222
Foreland, North 215
South 215
Formigas Islands 213
Shoal 204
Formosa Island 242
Fornses 223
Forsmark 219
Forsyth Point 199
Forth Mountain 217
Fortune Island 203
Foul wind, Cape 263
Four, Le, Rock 224
Fowey Rocks 195
Fowler Point 260
Francis Island 251
St., Cape, C. Colony. . . 232
— Ncwf'dl'd . . 191
Francisco, San 200
Cape 213
Head 212
River 207
Sao 208
Frankland Island 261
Franklin Harbor 260
Franz Josef Land 264
Fra.ser River 200
Frayle Rock 204
Fravles Point 212
Frederick, Port 262
Frederik Ilendrik, Cape... 262
Frederikshaab 264
Frederiksthal 265
Frederiksvaern 219
Fredriksten 219
Freels Cape 191
Frehel, Cape 224
Freikallen 218
Fremantle 260
French Cay 203
Frigate Shoal 253
Freycinet, De, Islets 259
Peninsula 262
Frio, C'ape, Brazil 208
W. Africa 232
Port 208
Frowaril Cape 210
Fruholm 218
Frying Pan Shoals 195
Fuenterrabia 224
Fuerta \'cntura Island 214
Fuerte Island 206
Fuga Island 245
Fugle Huk 265
Fulanga Island 257
Fulehuk 219
Funafuti Island 254
Funk Island 191
Funkenhagen 221
Furen Islet 218
Fushiki 249
Futuna Island 256
Gaalong Bay 240
Gabo Island 261
Gabriel Mountain 216
Gaeta 226
24972°— lU
-18
Page 274]
INDEX TO APPENDIX IV.
Page.
Gafor Island 234
Galapagos Islands 250, 251
Galera Point, Ecuador 213
Trinidad 206
Galgenbcrp 222
Galiola Kuck 227
Galita Island 230
Gallant, Port 210
Galle, Point de 237
Gallegos River 209
Galley Head 218
Gallinas Kiver 231
Gallipoli, Italy 227
Turkey 229
Galloway, Mull of 215
Galveston 196
Galway 217
Gambler Island 257
Gange 220
Gannet, Outer, Island 191
Rock 193
Gap Rock 241
Garcia d' Avila 207
Gardiner Island 253
Gardners I., Ix)ng Island .. 194
S. Paciric 254
Garras, Little 238
Gaspar, Island and Strait . . 239
Rico Reef 253
Gasparilla Island 196
Gaspe Cape 192
Gata, Cape, Cyprus 230
de, Spain 225
Gaujam 238
Gay Head 194
Gebey Islands 244
Geelong 260
Gefle :... 219
Genoa 226
George, Fort, Cay 203
St., Cape, Florida 196
Newf'dl'd . . 192
Nova Scotia. 193
Island, Alaska .. . 199
Azores 213
Georges Island 202
— St., Cay 197
Georgetown 1 95
Georgia, South, Island 214
Geronimo, San, Island 201
Geyser Reef 235
Gharib, Ras 233
Ghir,Cape 231
Gibdo Island 246
Gibraltar 225
Giglio Island 226
Gijon 224
Gilbert Islands 251
Gillolo Island 244
Ginger Cay 203
Girgenti 227
Gizau 234
Gizo Island 254
Glas Island 216
Glasgow 216
Glashedy Island 21 7
Glenan Islands 224
Glocester Island 258
Glorioso Islands 235
Gloucester Island, A.us 261
Massachusetts 194
PL.\CEs — continued .
Page.
Glover Keef 197
Gnarp 220
Goa-. 237
Godhavn 264
Godthaab 264
Goedereede 223
Golani Head 217
Gonienitza 228
Gomera Island 214
Gonaives 204
Gonave Island 204
Good Hope, Cape, Africa . . 232
China 241
Island 257
-Success Bay 209
tJoose Island 261
Gopalpur 238
Goram Islands 244
Gorda Cay 198
Point 212
Gore, Port 263
Goree Island 231
Road 209
Gorgona Island 213
Goro Island 256
Gorontalo 242
Goto Island 248
Gottenburg 219
Gottland Island 219
Gough Island 214
Gozier Islet 205
Gozo Island 227
Gracias a Dios Cape 198
Graciosa Island 213
Grado 227
Grand Manan Island 193
Port 234
Riband Island 226
Grande Point 211
Grange Point 204
Granitz 221
Granville 224
Grai>pler, Port 210
Grave, I'oint de 224
Gravelines 223
Greadv Harbor 191
Great Bird Rock 192
Rock Head 198
< xreen. Cape 261
Island, Labrador 191
Newfoundland... 192
Nova Scotia 193
Greenly Island 1 92
Greenspond Island 191
Greenwich 215
Island 252
( iregorv, Caj>e 209
Port 260
Grenada 205
Grenville, C!ape 262
Grey River 263
Greytown 198
Griefswald 221
Gr-efswalder Oie 221
Grim, Cape 262
Grimsev Nordd ranger 265
(irip . .". 218
GrisNezCape 223
Groate Eylandt 259
Groix, Island de 224
Gross-Horst 221
Pase.
Grouin du Cou, Point de. . . 224
Gruizza Rock 227
Gryto 218
(iuadalcanar Island 254
(juadeldupe, L. California. . 201
West Indies 205
Guaineco Islands 210
Guaira, La 206
Guaja Shima 248
Guam Island 252
Guana, Little, Cay 203
Guanape Islands 2] 2
(iuanica 205
Guantanamo 204
Guarajiiri Islets 207
Guaratiba Cape 208
Guardafui, Cape 233
Guascama Point 213
Guatulco, Port 202
Guayaquil 213
Gua} mas 202
Guerande 224
Guerin Island 247
Guguan Island 252
Guiniaras Island 246
Ciuiuan 246
Guldager 223
(iull Island, Little 194
Gullan, San, Island 212
Gun Cay 203
Gunong Api Island 243
G utzlaff 1 sland 242
Gwadar Bay 237
Gwatar Bay 237
Habana 204
Habibas Island 230
Hacha, Rio de la 206
Haddington, Port 244
Haedic Island 224
Hafun, Ras 233
Hagenmeister Island 198
Hague, Cape la 223
The 223
Hai-Duong 240
Hai-Fong 240
Haifa 230
Hainan Island 240, 241
Haitien, Cafx- ". 204
Hai-vun-tan Island 247
Hakodate 249
Half Port Bay 210
Half-Moon Cay, Belize 197
Nicaragua 198
Halgan Island 259
Halifax 193
Haliguen, Port 224
Hall Island... 252
Islands, Si r James 24 7
Halmstad 219
Hals 223
Halt Bay 210
Halten Island 218
Hamberg 219
Hamilton Island 214
Mountain 200
Port 248
Hammamet Bay 230
Hammerfest 218
Hampton 194
Hamrange 219
INDEX TO APPENDIX IV.
[Page 275
Page.
Hanalei 253
Hanfelah Bay 233
Hangkliii, Cape 232
Hannibal Isles 262
Hano Island 219
Ha-Xoi -- 240
Hao Island 258
Haradsskar Islet 219
Haraiki Island 258
Harbor Grat'e 191
HarburK 222
Hardy, .^irC, Island 262
Harpe, La, Island 258
Harrison Cape 191
Hartlepool 216
Harvey, Port 200
Harwich 216
HatterasCape 195
Haujani Islet 237
Hanstholm 223
Haute Island 193
Havre 223
Capele 193
Hawaii 253
Havter Island 255
Heiird Island 236
Hearts Content 191
ll.'au <Ie Brehat 224
Heaw aiidu Island 234
Hecate Bay 199
• Cove". :. 200
Heila, Cape 264
Hed, Ka.sal 236
Hee-tah-doo Island 234
Hegadis Island 243
Heiligen Creutz 221
Hekkingen 218
Hela 221
Helena, 8t., Island 214
Helgoland 222
Heliers, St 218
Hellevoetrfuis 223
Helliso 218
Hellyer Rocks 210
Helsinborg 219
Helsingfors 220
HelvickHead 218
Henderson Island 257
Henderville Island 251
Henlopen Cape 195
Henrv Cai>e 195
^Port 210
Heongsan, Port 242
Herald Cays 255
Hereheretue Island 257
Hermes, Cape 232
Hermit Island 255
Hermite Island 209
Herradura de Carrizal 21 1
Hervey Islets 258
Hesquiat Harbor 199
Hesseli) Island 222
Hessenstein 221
Hestskjaer 218
Heve, Cape la 223
Hiaou Island 253
Hik ueni Island 258
Hillswickness 216
Hilo 253
Hinimittee Island 234
Hinawar 237
PLACES — continued. •
Page.
Hiogo 248
Hirado No Seto 248
Hirtshals 223
Hiva-Oa Island 253
Hjelm Islet 223
Hjertholm 218
Hjoerringa Mountain 218
Hoa-pin-su Island 244
Hobart Town 262
Hodeidah Koad 234
Hog Island, Indian Ocean. . 235
Virginia.i 195
Islands 197
Hcigland Island 220
Hogolu Islands 252
Hogsty Reef 203
Hogulu Islands 252
HoheWeg 222
Hohenschonherg 221
Hokianga River 263
Hokitika 263
Holborne Islet 261
Hole-in-the-Wall 232
Hollo Wand 219
Holmestrand 219
Holmogadd 220
Hol.«teinberg 264
Holvhead 215
Hoii Dau Island 240
Hondeklij) Bay 232
Honfleur 223
Hongkong 241
Hon-Me.. 240
Honolulu 253
Hood Island 251
Lord, Island 257
Point, Australia 260
Port, Cape Breton Id. . 193
Hope Island 261
Hopedale Harbor 191
Hopes Advance, Cape 191
Hoppers Island 251
Horn, Cape 209
Head 217
Island 196
Home Island 257
Hornelen Mountain 218
Horsens 222
Horten 219
Hospital Bight 197
Hougvie, Cape La 223
Houtman Rocks 260
Ho wai vuh 236
Howe, Cape, East 261
• West 260
Lord, Island 257, 259
-Islands 254
Sound 200
1 lowland Islands 251
Howtli Peninsula 217
Huafo Island 210
Huaheine Island 257
Huanchaco Point 212
H uarmey 212
Hua.«co 211
Hudiksvalls 220
Huelva 225
Hiigeberg 221
Hui-lang-.«an 241
Hull Island 258
Hulls Island 254
Page.
Hulu-shan Bay 247
Humber River 216
Humboldt 200
Humphrey Island 254
Hungwha Channel 241
HunterIsland,N. Hebrides. 256
Tasmania 262
Hurds Island 251
Hurst Castle 215
Husum 222
Hvidingso 218
lUa 245
Ibayat Island 246
Ibbetson I.sland 251
Ibiza, Port 226
leacos Point, Belize 197
Trinidad 206
Ichabo Island 2.32
Icy Cape 198
leraka 229
Ifalik Islands 252
Iglooik Island 264
Ignacio, San, Point 201
Iguape 208
IkiSima 248
Ildefonso Islands 209
Ilha (irande 208
Ilheos 207
Ho 212
Iloilo 246
Inaboye Saki 249
Inaccessible Island 214
Inagua Islands 203
Inch Keith Rocks 216
liidefatigable Island 251
Indian, Ca]w 250
Harbor 191
Head 261
Tickle 191
Indianola 196
Indio Point 208
Indispensable Reefs 254
Indrapura Point 239
Ingol fshofde 265
Ingolsfjeld 265
Inishboffin 217
Inishowen Head 21 7
Inishrahull 217
Inishturk Island 217
Iniue Island 257
Innamban Bay 232
Inscription, ( 'ape 260
Investigator Strait 260
Ipswich 194
Iquique 212
Ireland Island 214
Isaac, Great, Cay 203
Isabel Cape •. 210
Island.. 254
Point 196
Isene 229
Isidro, San, Cajie 210
IslaGrande 202
Island Harbor 199
Islav 212
Isle"of Man 215
Isola 227
Isolette, Cape 236
Istria, Caped' 227
Page 276J
INDEX TO APPENDIX IV
Page.
Itacolomi Islet 208
Point 207
Itapacaroya Point 208
Itaparica 207
Ita))emirini 207
Iturup Island 249
Ivijituk 264
Iwo Shima 248
Iwo-sima 244
Jab wat Island 251
Jackson, Port 261
Jacksonville 195
Jacniel 204
Jacobshavn 264
Jaffa, Cape 260
Jago, St. , Island 214
Jaguaribe River 207
Jaluit Island 251
Jamaica 204
James Island 251
St., Cape, C. China... 240
Vancouver 1 . 199
Jan ilayen Island 265
Jara Head 211
Jarea 225
Jarvis Island 2.54
Jashak Bav 287
Java ■- 243
Head 239
Jean, St., de Luz 224
Jebel Zukui- Island 234
Jelaka, Pnlo 239
Jelalil 234
Jensen Nunatak 264
Jeremie 204
Jershoft 221
Jervis Bav 261
Cape 260
Island 251
Jesus Maria Island 255
Jibara 203
Jiddah 234
Jighinsk Island 264
Joao, San, da Barra 207
Johanna Island 235
John, St., Cape, Newf dl'd. 191
Staten Island 209
Island 205
Johns, St., Island, Red Sea. 233
N. Brunswick ... 193
Newfoundland. . . 191
Kiver 195
Johnston Islands 253
Jolo Islands 247
Jomfruland 219
Jona, St. , Island 250
Jose, San, California 200
^ de Guatemala 202
delCatx) 201
-Port 209
Joseph Henry, Cape 264
Juan Fernandez Island 258
San 205
Cape 205
delSur 202
Point 197
Port, Pern 212
Vancouver 1 . 200
St., Bay 206
Juanico, San, Point 201
; PLACES — continued.
Page.
Jubv, Cape 231
Judith Point 194
Juggernath 238
Juist 222
Julian, San, Port 209
St., Island 240
Julianshaab 265
Juneau 199
Jupiter Inlet 195
Jura Island 22S)
Juul, Cape 265
Kabenda Bav 232
Kabuli Island 245
Kado Sima 249
Kagoshima 248
Kahoolawe Island 253
Kaipara Harbor 263
Kais Islet 236
Kajartalik Island 264
Kakirounia 244
Kal Fanm Islet 233
Kalama ' 200
Kalantan 240
Kalboden Island 220
Kalibia 230
Kalingapatam 238
Kallundborg 222
Kalpeni Islet 2.34
Kama Islands 252
Kamaishi 249
Kaniardn Bay 2.34
Kamhangan Island 243
Kambara Island 257
Kamchatka, Cajie 250
Kanala, Port 259
Kanathea Island 256
Kandavu 256
Kandeliusa Island 229
Kangamint 264
Kangarssuk Havn 264
Kaniongan Point 242
Kannanur 237
Kao Island 258
Kappeln 221
Kara Burnu, Cape 229
Karachi 237
Karajinski Island 250
Karimon Djawa Island 243
Karlshamu 219
Karlskrona 219
Kaske 220
Ka-^m 237
KatakoloBay 228
Kater Island 253
Katiagani 239
Katie Rock 228
Kauai Island 253
Kawhia Harbor 263
Keats, Port 259
Kee-lah Island 234
Keeling Islands.... 236
Keenapoussan Island 247
Keitum 222
Kelung 242
Kendall, Cape 264
Kent Island 261
Keppel Island 257
Kermadec Islands 258
Kertch 229
Ketoy Island 249
Page.
Kev West ; 196
Kharig Islet 236
Kharim-Kotan Island 249
Khaur Fakan Bav 236
Kheli ". 229
KhorNohud 234
Nowarat 233
Ki Islands 244
Kiama Harbor 261
Kidnappers Cape 263
Kiefali, Cape 228
Kiel 221
Kikai-jinia 244
Killiney Hill 217
Killybegs 217
Kilwa Kisiwani 233
Kimbeedso Island 234
King George Sound 260
Island, Alaska 198
■• Australia 260
Kings Island 258
Kingston 204
King.stown 217
Kinkwosan Island 249
Kinnsiind 218
Kino I'oint 202
Kinsale 218
Kirkwall 216
Kisimayu Bav 233
Ki.«ka Island ." 199
Kistna 238
Kiswere 233
Kittan Islet 234
Kjorge 222
Knocklane 217
KnockmealdowuMouiitain. 218
Knocknarea 217
Knox Bay 200
Cape 199
Knysna 232
Kobe 248
Kodiak Island 199
Koh Chang 240
Kong 240
Krah Islet 240
— — Tang Rocks 240
Kokonn-tan Islands 248
Koksher 220
Kolding 222
Koniba Island 243
Kompas .Mountain 218
Kongelab Islands 251
Konigsberg 221
Koniushi Island 199
Koppem 218
Koprino Harbor 2{X)
Koroni Anchorage 228
Korror Islands 252
Kos ,229
Kosair, Arabia 236
Red Sea 233
Kosime No Osima 248
Koster 219
Kottaringin Bay 242
Kovra Rjthi Point 235
Kozu Shima Mountain 249
Krakatoa Island 239
Krishna Shoal 238
Kroc 239
Kronberg 222
Kronstadt 220
INDEX TO APPENDIX IV.
[Page 277
Page.
K ruseiistern Cape 198
Kiib Kalat 237
Kuchino Shima 248
Kuohinoteu 248
Kuino 220
Kullen Point '.. 219
Kumi Island 244
Kumpta 237
Kunashir Island 249
Kundapur 237
Kunfidah 234
Kuper Harbor 248
Port 199
Kiiria Maria Islands 236
KuroSinia • 248
Kusakaki Jiina 248
Kusrovie Rock 240
Kusterjeh 229
Kutpiir .■ 237
Kuweit 236
Kweshan Islands 241
Kyangle Islets 252
K yauchau Bay 247
Kyuquot Sound 199
Labuan Island 242
Labyrinth Head 209
Lacoadive Islands 234
Laoepede Island 260
Lad V Elliot Island 261
■' Frances, Port 235
Lagartos 197
Laghi, Cape 228
Lagoon Head 201
Lagos 225
River 231
Lagosta Island 228
Lagostini Island 228
Lakemba Island 256
Lainaka 230
I^anibayeque 212
Lambert, Cape 260
Lame Bay 233
Laniock Island 241
Lampednsa Island 227
I^anipong Bay 239
Laniyit Island 241
Landfall Island 209
Lands End 215
Landskrona 219
Landsort .■ 219
Langanaes Point 265
Langeland Island 222
Langeoog 222
Langesund 219
Langford, Port 199
Langkuas Island 239
1-angotangen 219
Langwarden 222
Lanzarot« Island 214
Laruehuapi Cove 211
Lassa, Cape 242
J-assau 221
Latakivah 230
]>atouche Tr^ville, Cape ... 260
Laun 191
I^urie Island 215
Laut, Pnlo 242
Lavaca 196
Lavata 211
PLACES — continued .
Page.
Lawrence, St. , Island, Alaska 198
Siberta 2.50
I^ykan, Port 242
Laysan Island 253
Lazaref, Port 250
r.azaro, San, Cape 201
Leander Shoal 192
Leba 221
Lebu River 211
Leeuwin, Cape 260
Legendre Island 260
Leghorn 226
I^ema Island 241
Leninos Island 229
l>engua de Yaca Point 211
Lennox Cove 209
Leon es Island 209
Leopold, Port 264
I^par, Pulo 239
I.«preau Cape i 193
Lenna 197
Lerwick 216
Leschenault, Cape 260
Lesina Island 228
L'Etang Harbor 193
Leven Island 235
Port :.. 235
River 262
L'Eveque, Cape 260
Lewis, St. , Cape 191
Leyden... 223
Levte Island 246
LhouReef 255
Liakhov Islands 264
Lianconrt Rocks 250
Liant, Cape 240
Liao-ti-shan 247
Libau 220
Libertad, C. America 202
Mexico 202
Lifu Island 259
Lighthouse Rocks 199
Limerick 216
Ijimon, Port 198
Lincoln Island 241
Port 260
Lindesnes 218
Lindi River 233
Linilo, Port 229
Linga Island 238
Linguelta, Cape 228
Linosa Island 227
Lipari Island 226
Lisbon 225
Lisburne Cape 198
Lisiansky Island 253
Lissa Island 228
List 221
Lister 218
Lith 234
Litkieh Island 251
Little Hope Island 193
Lituya Bay 199
Liverpool 215
Port 235
River 259
Livorno 226
Lizard Point 215
Llico 211
Loa River 212
Page.
Loango Bay 232
Lobito Point 232
Lobos Cay, Bahamas 203
Mexico 196
de Afuera Island 212
-— Tierra 212
Island, Canaries 214
Uruguay 208
Point, N. Chile 212
S.Chile 212
Lodingen 218
Lofoten Island 218
Ix)ggerhead Key 196
Loheivah 234
Loma'Point : 201
Lomas Point 212
Lombata Island • 243
Lombok Island 243
London, j;a8t 232
Londonderry 21 7
Cape .". ; 2.59
Long Island, Bahamas 203
United States 194
Loo Choo Islands 244
Look^"', Port 235
Lookout Cape, N. Carolina. 195
Point, Australia 261
Maryland 195
Lopatka, Cape 250
Lopez, Cape 231
Lorenzo, San, Cajie 213
Island 212
Loreto 201
Lorient 224
Loro, Mount 245
Lorstakken Mountain 218
Ix)s, Isles de 231
Lota 211
LotwWifeRock 249
Lough Lame 217
Louis, Port, Falkland Is . . . 214
Guadeloupe 205
Mauritius Island. 234
St 231
Ix)uisburg 193
Loui.sia<le Archipelago 255
Loune 223
Low Island 240
Port 210
Lowenorn, Cape 265
Lowestoft 216
Loyalty Islands 259
Lu bang Island 245
Lucar, San j . 225
Lucas, San 201
Lucia, Santa 235
St 204
-Cape 232
Id., C. Verde Is. . 214
Windward Is 205
Lucipara Is\and 239
Lucipari Islands 243
Lucrecia Point 203
Lucrietta Island 227
Liiis, San, Island 202
Luk<> Point 250
Lundy Island 215
Lunenburg 193
Lungo 220
Lupona Point 201
Page 278]
INDEX TO APPENDIX IV
Page.
LurioBay 2:53
Lussin Piccolo 227
Luzon Island 245, 246
Lyo Island 222
Maasin 246
MacaM 207
Macao 241
MacAskill Islands 252
Macassar 242
^lacanley Island 258
Maeeio 207
Machias .' 19:5
Island 193
^lachikora..^ 235
Mackenzie Islands 252
INIacLeay Islets 260
JIacqnarie Harbor 262
Island 259
Port 261
ISIacquereau Point 192
Madagas-car 235
Reef, Africa 232
Yucatan .. 197
Madame Island 193
IMadanas Point 208
Madeira Island 213
Madras 2:58
Ma<lrvn, Port 209
Madura Island 243
Maestro de Campo Island.. 246
Mafainale Islancl 233
Mafia Island 233
Magadoxa 233
Magdalen Cape 192
— Islands 192
MagdalenaBay 201
River 206
Magnetic Pole 264
Magoari Cape 207
Mah Kundu Island 234
Mahanuru 235
Maho 237
Mahia Peninsula 263
Mahon, Port 226
Maiana Island 251
Maiden Rocks 217
Mairaira Point 245
Miiit Island 233
Maitea Island 257
Maitencillo Cove 211
Majamba Bay 235
Majorca 226
Majunga 235
Majuro Islands 251
MakallehBay 236
Makarska 228
Makatea Island 258
Makaua Island 233
Makenio Island 258
Makers Ledge, South 192
Mak kian Island 244
Makongai Island 256
Makry 229
Mala Point 203
MalabrigoBay 212
Malacca 238
Malaga 225
Malaita Island 254
Malamocco 227
Malaepina, Port 209
I'LACEs — continued.
Page.
Maiden Island 254
Maldonado,' Mexico 202
U ruguav 208
Male Island " 234
MaleinhaBav 232
Malin Head ". 217
Mallicollo Island 256
Malmo 219
Malo, St 224
Malodab Islands 251
Maloren 220
Mali)elo Island, Galapagos. 250
Panama 203
Malta 227
Manuika Island 256
Manaar 237
ManaSiina 249
Manado Ba v 242
Manao ". 249
Mana-watu River 263
Manda Roads 233
Mandarins C?ap 241
Maiidavi 237
Maiifre<lonia 227
Mangalore 237
Mangara Island 258
Mangafatiba 208
Mangareva Island 257
Mangarin Point 245
Mangarol 237
Mangles Point 213
Mango Island 25(>
Manila 245
Mano Island, Asia 244
Denmark 223
Manoel, Cape 231
Manta Bay 213
Manna Island 257
Manukau Harbor 263
Man vers. Port 191
Manzanilla Bav 202
Point...." 204
Maracaibo 206
Maraki Island 251
Marambaya Island 208
Maranhiio Island 207
Marble Island 264
Marblehead 194
Marcial, San, Point 201
Marcos, San, Island 201
Marcus Island 253
Mare Harbor 214
Island, California 200
^ S.Pacific 259
Maret Islets 259
Margaret Bay 193
Margate Head 232
Maria Island 257
Madre Island 202
Port 204
Sta., Cape, Portugal. . . 225
• Uruguay ... 208
Cove 201
di Leuca, Cape 227
Island, Azores... 213
Chile 211
S. Pacific ... 256
• Port 247
Mariana Islands 252
MaricAS Islands 208
Marie Galante 205
Page.
Marienleuchte 221
Mariguana Island 203
Marinduque Island 246
Marion Island 236
Maripipi Island 246
Maritinio Island 227
Marjes Islets 206
Marjoribanks 247
Marks, St 196
Marlborough Island 251
Marmora Island 230
Marniorice 229
Maro Reef 253
Maroni River 207
Marsala ..-.._ 227
Marseille 226
Marshall 231
• Islands 251
Marstenen Islet.,. 218
Marta, Sta 206
Martha, St., Cape 208
Martin de la Arena, San . . . 224
( iarcia Island 208
San, Island, L. Calif . . 201
• St., I., Leeward Is 205
Vaz Rocks 214
Martiid<jue 205
Martires, Los .'. 252
Marua Island 257
Marutea Island 257
Marv Island 254
"St., Bay 232
Cape, Madagascar. 2:55
Newfound-
land 191
Nova Scotia. 193
Reefs 192
Marys, St. , Island 235
Marzo Cajjc 213
Mas-afuera Island 258
Masbate Island 246
Masinloc 245
Masi rah Island 2:56
Maskat 236
Massaua Harbor 233
Masset Harbor 199
Masulipatam 238
Mataliella Islands 244
Matacong Island 23 1
Matagorda 196
Matahiva Island 258
Matamoras Cove 211
Matana Island 249
Matanzas Peak 204
Matatane 235
Matelotas Islands 252
Matema Islands 255
Maternillos Point 204
Matinicus Rock 193
Matoya 249
Matthew Island 256
St., Island, Alaska 198
• Burma 238
Siberia 250
Matthias, St., Island 255
Matu Sinia 250
Matuku Island 256
Manger Cay 197
Maui Island 253
Mauki Island 258
Maunganui Harbor 262
INDEX TO APPENDIX IV.
[Page 279
Page.
Maupili Island 257
Jlauritius 234
Mav, Cape 195
^Island 216
Mayaguez 205
Maye Mountain 207
Mayne Harbor 210
Mountain 210
Mayo Island 214
Mayotta Island 235 \
MaysiCape 203
May umba Bay 231 |
Mazarron 225
Mazatlan 202
Mazemba River 232
Mtega Island 256
MehingaBay 233
McKean Island 254
Mecate Mountain 190
Mecatina Islands 192
Med noi Island 250
Mega Island 239
Megalo Kastron 228
Mehediah ....: 230
Meiaco Sima 248
Meiaco-sima Islands 244
Mejia Island 202
Mel, Ilhado 208
Melbourne 260
Meleda Island 228
Melinda 233
Melle, Cape 226
MellishEeef 255
Melniore Head 217
Melo, Port 209
Melville, Cape, Bahlbac I.. 245
:- Queensland 262
Island, Australia 259
Barrows Strait. . . 264
Tuamotu Arch... 258
Memel 221
Memory Kock 203
Menali Island 238
Menchikof Cape 199
Mendocino Cape 200
Mendoza Island 241
Merbat... 236
Mercy Harbor 210
Mergui 238
Mesa de Dona Maria 212
Messina 227
Mesurado, Cape 231
Meurka 233
Mew Islands 217
Mewstone Rock 262
Mexican Boundary 201
Mexico, City of 196
MexillonBay 212
Mexillones Mountain 212
Mezen 264
Mugan Mwania 233
Miautao Island 247
Michael, St. , Fort 198
Island 213
Michaeloff Island 257
Middleton Island 199
Midway Islands 253
Miguel, San, Island 201
-Islands 247
MikakeJiraa 249
Mikindini 233
PLACES — continued.
Page.
Mikomoto Islaind' 249
MikuraJima 249
Milagro Cove 211
Milazzo 226
Mile Island 264
Milford Sound 263
Milo Island 229
Min River 241
MinaBay, El 231
Minchininadiva Mountain . 210
Mindanao Island 246, 247
Mindoro Island 245
Mine Head 218
Minerva Reefs 258
Minikoi Island 234
MinoSima 249
Minorca 226
Minots Ledge 194
Minow 235
Minsener Sand 222
Mintok 239
MiramichiBay 192
Misamis 247
Miscou Island 192
Mississippi River, mouth . . 196
City 196
Misteriosa Bank 197
MitaPoint 202
Mitcliells Island 254
Mitho 240
Mitiero Island 2.58
Mitre Island 256
Mityleni Island 229
MizenHill 216
Moa Cavo, Port 203
Island 244
Moalalsland 256
Mobile 196
Mocha Island 211
Mocomoco Point 206
Modeste Island 248
Moeara Konipehi 239
Moen Island 222
Moeren hout Island 257
Mogador 231
Mohilla Island 235
Mojanga 235
Mokaniba, Port 233
Mokateui 236
Mokha 234
Mokil Islands 252
Molle, Port 261
MoUendo, Port 212
MollerPort 199
Molloy 236
Molokai Island 253
Molonta Peninsula 228
Molucca Islands 244
Moluk Island 234
Molyneux Bav 263
Sound..". 210
Mombasa 233
Mona Island 205
Monastir 230
Mondego, Cape 225
Monfalcone 227
Monhegan Island 193
Monomoy Point 194
Monrovia 231
Montagu Island 261
Montalivet Islands 259
Page.
Montauk Point 194
Monte Christo Islet 226
Montebello Island 260
MontegoBay 204
Montepio 196
Monterey 201
Monteverde Islands 252
Montevideo 208
Montravel Island 248
Montreal 192
Monts, Point de 192
Montserrat 205
Monze, Cai>e 237
Mopelia Island 257
Morane Island 257
Morant Cavs 204
Point". 204
Moray va 225
Morecanibe Bay 215
Moreno Mountain 212
Moresby, Port 255
Moreton, Cape 261
Morgan, Cape 2.32
Morjovetz Island 264
Morlaix 224
Morotiri Islands 258
Morro A vuca 202
de i^ao Paulo 207
Petatlan 202
Solar 212
Mortlock Islands 252
Mosquito Cays 198
Motane fsland 253
Mothe Island 256
Mothoni 228
Motu-ili Island 253
Motu-iti Island 257
Moudros 229
Moukon rushi Island 249
Moulmein 238
River 238
Mount, Cape 231
Mourondava 235
Moville 217
Mozambique 233
Msimbati 233
Mugeres Island 197
Muilcalpue Cove 211
Mukulaelae Island 254
Muleje 201
Mulu Island 244
Mura Harbor 248
MuratHill 233
Murderers Bay 235
Murdock Point 262
Murundum Island 240
Mururoa Island .257
Muscat 236
Musendum, Ras 236
Mussel Bay 210
Mysole Island 244
Nachvack Bay 191
Nafa-Kiang 244
Nagai Island 199
Nagasaki 248
Naian Island 256
Nain 191
Nairn Cay 203
Naitamba Island 256
Naka no Shima £48
Page 280]
INDEX TO APPENDIX IV.
Page.
Nakkehooed 222
Xam-Dinh 240
Namki, Port 241
Nanioluk Islamig 252
Namonuito Islands 252
Nam-quan 241
Naniu Island 251
Nanaimo 200
Nanoowry Harbor 239
Nanka Island 239
Nanomea Island 254
Nanoose Harbor •. 20O
Nantes 224
Nantucket Island 194
S.Shoal 194
Naples 226
Napuka Island 258
Nar Foree Island 234
Naranjo, Port 203
Narendri Bay 235
Nargen Island 220
Narva 220
Nasca Point 212
Naspartilnlet 199
Nassau 203
Natal, Brazil 207
Port, Africa 232
Sumatra 239
Natashquan Point 192
Natuna Islands 240
Naturaliste, Cape 260
Nauomaga Island 254
Navachista ' 202
Navalo, Port 224
Navarin 228
• • Cape 250
Navassa Island 204
Navesink Highlands 195
Navidad Bank 203
Bay 202
Navire Bay 236
Naxos Island 229
Nazaire, St., Port 224
Necker Island 253
Needles Rocks 215
Negapatam 237
Negrais, Cape 238
Negro, Rio 209
Negros Island 246
Neill, Port 264
Nelson 263
Cape 260
Port 259
Nemuro 249
Neptune Isles 260
Nera Point 227
Netherland Island 254
Neunortalik 265
Neuwerk 222
Nevil Island 252
Neville, Port 200
Nevis 205
New Bank 197
Bedford 194
Britain 254
Caledonia 259
— - Guinea 255
Hanover 255
Haven 194
Hebrides 256
Ireland 255
PLACES — continued.
Page.
New London....' 194
Orleans 196
Plymouth 263
.South Orkneys 215
Shetland 215
Westminster 200
York 194
Newbern 195
Newburyport 194
Newcastle 261
Newfoundland 191,192
Newport, Ireland 217
Rhode Island 194
Newton Head, Great 218
Ngatik Islands 252
Ngau Island 256
Nias Island 239
Nice 226
Nicholas, St. , Island 214
Nicholson, Port 263
Nickerie River 207
Nicobar, (ireat. Island 239
Islands 238, 239
Nicolas Mole 204
San, Island 201
Nidingen I.«let 219
Nieuport 223
NieweDiep 223
Nihiru I.-land 258
Niigata 249
Nikalao, St., Island 229
Xikolaevsk 250
Nikolaia, St., Cape 250
Nikolo, St., Port 229
Nila Island 244
Nile River 230
Nimrod Sound 241
Nine-pin Rock 241
Ning-po 241
Nipe, Port 203
Nitendi Island 255
Niua-fu 257
Niuch wang 247
Niutao Island 254
NoSiniaSaki 249
Noir Island 209
Noir Moutier Island 224
NoUoth, Port 232
Nome Cape 198
Nonuti Island 251
Nootka Sound 199
Nord Koster Islands 219
Norderney 222
Norfolk 195
Island 259
Norman C'ape 192
Norrkojiings Inlopp 219
Norrsher Islet 220
Norrtelge 219
North Cape, Arctic Amer. . 264
• Brazil 207
C. Breton 1 192
Iceland 265
New Zealand 262
Norway 218
Harbor . . . ." 199
Island, Vancouver 199
Volcano Islands.. 253
Lord, Island 252
• Standing Creek 197
Northumberland Cape 260
Page.
Northumberland I.sles 261
Northwest Cape 260
Norwalk Island 194
Noshiaf Misaki 249
Saki 249
Nosi Be 235
Nostra Senhora do Deserto. 208
Notch Cape 210
Notsuke 249
Nottingham Island 191
N(>Un«a 2.59
Noun, Cape 231
Nouyelle, Port 226
Nova Zembla ^64
Novogorod, Port 2.50
Nuevitas, Port 203
Nuevo, Port 202
Nugget Point 263
Nui Island 254
Nuistnd 220
Nuka-Hiyi 253
Nukufetau Island 254
Nukunau Island 251
Nuku-nono 254
Nukuor Islands 252
Nukutavake Island 257
Nukutipipi Island 257
Numba Island 233
Nunez River 231
Nunivak Island 198
Nurse Channel Cav 203
Nuyts Point ". 260
Ny Sukkertop 264
Nyborg 222
Nykjobing 222
Oahu 2.53
Oatafu Island 254
Oban 216
Obi Islands 240
Obispo Shoal 197
Obristadbroekke 218
Observation Island 248
Oby Major Island 244
Occasional Harbor 191
Ocean Island, N. Pacific ... 253
S. Pacific 254
Ockseu Island 241
Ocracoke 195
Oddensby 222
Odenskholm 220
Odessa 229
Odia Islands _. . . . 251
Oeno Island '. ... 257
Offer Wadham 191
Oho-sinia 244
Okayama, I'ort 248
Okhotsk 2.50
Oki Islands 249
Okishi Bay 249
Okso 219
Oland Island 219
Old Fort Island 192
Point Comfort 195
Providence 198
Oleai Islands 252
Oleron Island 224
Olga, Port 2.50
Olimarao Islet 252
Olinda 207
OHpaRock. 228
INDEX TO APPENDIX IV.
[Page 281
Page.
Oliutorski, Cape 250
Olivenca 207
Omapui Island 247
Oniena!i Island 264
Omo Island 222
Omoa 197
OmoiSaki 249
One Fathom Bank 238
Oneata Island 256
Onega 264
Ongea Levu Island .-r -3^7
Ono Islands "257
Onoatoa Islands 251
06-Sima Harbor 248
Oparo Island 258
Opobo River 231
Oporto 225
Oraluk Island 252
Oran 230
Orange Cape, Brazil 207
Magellan Strait. . 209
Oranienbaum 220
Orchila Island 206
Oregrund 219
Orfordness 216
Orizaba Mountain 196
Orkney Islands 216
Ormarah 237
Ormoc 246
Ornbay Island 243
Oro No Sima 248
Oropesa Cape 225
OrskarRock 219
Oruba Island 206
Osaka 248
Osaki Bay 248
Oscarsbefg 219
OscuroHead 211
Osnabrug 257
Ostend 223
Osthammar 219
Ostro Point 228
Otago Harbor 263
Otranto, Cape and Port 227
Otwav, Cape 260
Port 210
Oune-Kotan Island 249
Ouro River 231
Ovalaii Island 256
OwashiBay 248
Oxford 215
Oxhoft 221
Paanopa Island 254
Pabellon de Pica 21 2
Paoasmavo 212
Padang." 239
Tikar 242
Padaran, Cape 240
Padre, Port 203
Pagan Island 252
Pagonia, Port 228
Paimboeuf 224
Paita 212
Paix, Port 204
Pajaros Islets 211
Pak Chan River 238
Pak-Hoi 240
Pakonjidol Rock 228
Palamos Bay 225
PalaiK >g 246
TL ACES — continued .
Page.
Palawan Island 245
Palembang 239
Palenita 202
Palermo 226
Port 228
Pali, Cape 228
Pallas Rocks 248
Palliser, Cape 263
Palm Islands 261
Pahna Island 214
PalmasBay 208
Cape 231
Point 197
Palmerston, Cape 261
Islands 257
Palmyra Island 251
Palompon 246
Paloa Bay 242
Pamaroong Island 242
Pampatar Island 206
Pan de Azuear Island 211
Panama ....• 203
Panay Island 246
Pangituran 247
Panjang Island 240
Pank Piah Rock 241
Pantar Island 243
Papey Island 265
Paposo Road 211
Para 207
Paraca Bay 212
Paracel Islands 241
ParahiV)a River and Port.. 207
Paramaribo 207
Paranagiia 208
Paranahiba River 207
Paraoa Island 258
Parati 208
Paredon ( Jrande Cay 204
Parenga-renga 262
Parenzo 227
Parga 228
Parida 202
Parinas Point 212
Paris 223
Parker Cape 210
Pares Island 229
Parry Island 258
Parrys Group 253
Pasado Cai>e 213
Pasages, Port 224
Pascagoula, East 196
Pasni 237
Passaro, Cape 227
Pasuruan 243
Patache Point 212
Patani, Cape 240
Paternoster Rocks 219
Paterson Inlet 263
Pato Island 206
Patook River 197
Patos Island 202
Patras 228
Patrick, St. , Head 262
Patterson, Port 259
Paul, St., de Loando 232
Island, N. Araer. 192
:- Tuamotu ... 257
R<?union Island.. 235
Rocks 214
Pauls, St. , Island 236
Page.
Paumben Pass 237
Paxo Island 228
Paypoton Mountain 197
Paz, La 201
Pearce Point. '. 259
Pearl and Hermes Reef 253
-Cays..'. 198
Pedra Blanca Rock 241
Branca 238
de Galha 231
Pedro Bank 204
San 202
Point 211
Port 210
Peel 260
Island 253
Pegasus, Port 263
Pei-ho 247
Pekalongan 243
Pelado Island 212
Pelagosa Rock 228
Peloro, Cape 227
Pemba Bay 233
Pembroke Cape 214
Pena Point 206
Peuang, Pulo 238
Peflas Anchorage 202
Pendulum Islands 265
Penguin Islands 236
Penha Grande 231
Peniche 225
Penniarch Rocks 224
Penrhyn Island 254
Pensacola 196
Pentland Skerries 216
Percy Isles 261
Perim Island, .\frica 233
— India 237
Pernambuco 207
Pernau 220
Peros Banhos Islands 234
Perth 260
Peru Island 251
Perula Bay 202
Pescadores Islands, Asia, E.
coast 242
N. Pacific 351
— Peru 212
Point 212
Pe-shan Islands 241
Petali Island 229
Petalidi Bay 228
Peter, St., I'ort 224
Peterhof 220
Petersburg, St 220
Petersdorf 221
Petit Manan Island 193
Petite Riviere 204
Terre 205
Petrojiavlovsk 250
Petropolis 208
Pha-li-dn Island 234
Philadelphia 195
Philip Island 252
Philipp Broke, Cape 265
Philips Point 202
Phillip, Port 260
Phillips Island 258
Phoenix Island 254
Pi 226
Pianosa Island 226
Page 282]
INDEX TO APPENDIX IV.
i I
Pichiflanqne 211
I'ichilinque Bay 201
Pico Island .. .'. 213
Pictcm Harbor 193
Piedra Blanca 247
Piedras Blancas 201
Cay, Cuba, N. coast. . . 204
S. coast 204
Point 208
Pieman River 262
Pierre, St., Ne\yf'dl'd 191
Reunion 1 235
Rock 240
PietrodiNembo, St., Island. 227
Pigeon Point 200
Pih-ki-shan Island 241
Pih-quan Peak 241
Pih-seang Island 241
Pikelot Island 252
Pilier, Le, Island 224
Pililu Island 252
Pillau 221
Pillar, Cape, Chile ". 209
Tasmania 262
Pinaki Island 257
Pine; Cape 191
Pines, Isle of 204
Pingelasp Islands 252
Ping-fong Island 241
Ping-hai Harbor 250
Pinnacle Islet 198
Pinos Point 201
Pique Bay 2.50
Piraeus 229
Pirano 227
Pisagua 212
Pisang 2,39
Pisco 212
Pitcaim Island 257
Pitea 220
IMtong Island 238
Placentia Harbor 191
Point 197
Pladda Island 216
Plana Cav 203
PlanierRock 226
Plata, Isle 213
La 208
— — Port 204
Platte Island 2,34
Playa Colorado 202
.Maria, La 201
PardaCove 210
Pleasant Island 254
Plettenburg Bay 232
Plum Island .. 194
Plymouth, England 215
U. S 194
PoileBav 192
Pola ". 227
Sta.,Bay 225
Polillo Island 246
Pollard Cove 210
PoUoc 246
Polusuk Island 252
Porno Rock 228
Ponafidin Island 249
Ponapi Island 252
Pond Mountain 210
Pondicherri 237
Ponga River 231
PLACES — continued.
Page.
Ponza Islet 226
Poolbeg 217
Popa Island 244
Popof Island 199
Porcos Grande Islet 208
Porebander 237
Porman 225
Poro niusir Island 249
Poros Island 229
Port au Prince 204
of Spain 206
• Royal , Jamaica 204
S. Carolina 195
Said 2;W
Portendik 231
Porthcurnow 215
Portland, Bay 260
dpe 262
England 215
Maine 193
Porto Bello 206
Re 227
Rico 205
Santo... 213
Seguro 207
Vecchio 226
Portsmouth, England 215
V. S 194
Possession, Cape 209
Island 236
Postilion Islands 243
Povorotnyi,Cape 250
Prado 207
Pratas Island 241
Premeira Islands 2.33
Preservation Inlet 263
Prestenizza Point 227
Prevesa 228
Pribilof Island 199
Prince Edward Island 192
Ed wards Islands 236
Prince of Wales Cape 198
Island 262
Sound 191
Regent River 259
Princes Island 231
Proeste 222
Progreso 197
Promontore Point 227
Proti Passage 228
Proven 264
Providence 194
Island 2.51
Port 250
Psara Island 229
Pucio Point 246
Puerto Cabello 1 206
Santo Bay 206
Puka-puka Island 258
Puka-ruha Island 257
Pulicat 238
Pulkowa 220
Pulpito Point 201
Puna 213
Purdy Island 255
Putziger Heisternest 221
Pyramid Point 241
Pyramidal Rocks 240 i
Quaco, Cape 193
Quad, Cai)e 210
PaKC.
Quaebo River 231
Quebec 192
Queen Charlotte Lsland 257
Queenstown, Ireland 218
N. Zealand 263
Quel part Island 248
Quemada Grande Island. . . 208
Quentin, San, Port 201
Querimba Islands 233
Queule Bay 211
Quilan, Cape 210
Quilca 212
Quillimane 232
^ River 232
Quilon 237
Quin Hon 240
Quiniluban Islet 245
Quintero Point 211
Quita Sueno Bank 198
Quoddy Head 193
Quoin Great, Island 236
Point 232
Race, Cape 191
Island 200
Rachado, Cape 238
Radakala Islands 251
Radama Islands 235
Port 2.35
Ragged Island 203
Ragusa Rocks, Pettiui di . . 228
Rakkin, Ras 236
Raleigh Rock, China 241
• Formosa 244
Ramas, Cape 2,37
Rame Head 232
Rauiree Island 238
Rangiroa Island 258
Rangoon 2.38
River 238
Ranu Cove 211
Raoul Island 258
Rapa Island 258
Raper Cape 210
Raphti, Port 229
Rarotonga Island 258
Rasa Island 253
Rathlin Island 217
O'Birne Island 217
Ratnagherry 237
Ravahere Island 258
Ravn Storo 264
Rawean Island 243
RavC'ape 192
Raita Island, Brazil 208
C.Verde Is 214
L. California 202
Razzol i Island 226
Re Island 224
Real River 207
Reafi Island 257
Recherche Archipelago 260
Recife Cape 232
Red Islet 2.59
Redang, Great, Harbor 240
Redfield Rocks 249
Redonda Islet 205
Redondo Rock 250
Refuge Cove 199
Reirson Island 254
Reitoru 258
INDEX TO APPENDIX IV.
[Page 283
Page.
Rembang 243
Kenie<lios Bay 202
Renard iRlaml 255
Islands 255
Rennel Island 254
Rensher 220
Repon, Pulo 240
Kesolntion Island 191
R(''Uiiion Island 235
Revel 220
Rey, Isladel 21:5
Reyes Head 211
Point 200
Reykianaes 265
Reykiavik 265
Revthur Fjeld 205
Rhio 238
Rhodes, Port 229
Rhvnns of May 216
RiVjnitz 221
Rich Point 192
Richmond 195
Harbor 192
River 261
Riga 220
R'gny Mount 265
Riniitara Island 258 j
Hingkjobin 223
Rio Grande del \orte 196
do \orte 207 !
Sul 208
Janeiro 208
Riofrio, Port 210
Risiri Islet 249
Rissnaes Point 265
Ri vadeo 224
Rivadesella 224
Rivers, Cajie 242
Rixhdft 221
Roa Poua Island 253
Roatan 197
Roljerts Point 200
Roca, Cape 225
Partida, Mexico, E.
coast 196
— "\V. coast 202
Rocas Reef 214
Rochefort 224
Rochelle 224
Rockabill 217
Rockall Islet 213
Rockingham Bav 261
Rockland 1 193
Rodd Bay 261 j
Rodkallen 220 j
Rodney, Cape 255
Rodoni, Cape 228 j
Rodriguez Island . 234 [
Rotlsher Island 220 1
Roeskilde 222
Rogosnizza 227
Roigen, Cape 249
Rokuren Island 248
Roma Island 243
Remain Cape 195
Roman, San, Cape 206
Romanzof Cape 198
Romanzov Islands 251
Romblon Island 246;
Rome 226 i
Ronaldsay, North 216
PLACES — continued.
Page.
Roncador Cay 198
Rongerik Islands 251
Roodewal Bay 232
Roijue, St., Cape 207
Roques Islands 206
Rosa, Sta., Island 201
Rosalia, Sta. , Bav 201
Rosalind Bank . .' 198
Rosario Island 253
Rose Island 257
Spit Point 199
Rosemary Island 260
RosierCape 192
Ross Island 248
Rossel Island 255
Rostock 221
Rota Island 252
Rotterdam 223
Rotti Island 243
Rottnest Island 260
Rotumah Island 256
Round Island 247
Roundhill Island 191
Rovigno 227
Roxo Cape 196
Roval Island 203
Royalist, Port 245
Ruad Island 230
Riigenwalde 221
Rum Cay 203
Runaway, Cape 263
Runii Island 220
Rui)ert Island 210
Rurutu Island 258
Ry vingen Island 218
Saba 205
Sabine Pass 196
Sabioncello Peninsula 228
Sablayan Point 245
Sable Cape 193
Island 193
Sacatula River 202
Sacrificios Island 1 96
Point 202 1
Saddle Group 242
Island 191
Sado Island 249
Safajah Island z'i^
Safatu Island 240
Saida -230
Saigon 240
Saintes Islands 205
Saipan Island 252
Sakai 248
Sakhalin Island 250
Sakonnet Point 194
Sal Cay 204
Island 214
Sala V Gomez 258
Salado Bay 211 ,
Salavar Island 242
SaldanhaBav 232
Salem 194
Sali 230
Salina Cruz 202
Salinas Bav, C. America 202 ,
— • L. California 201
Point 204
Salisljury Island 191
Salomague Island 245
Salonika 229
Salovetski 264
Saltee, Great 217
Saint Islands 207
Salvador, San 203
Salvage Islands 214
Salvore Point 227
Sama, Port and Peak 203
Samana 204
Cay 203
Samanco Bay 212
Samar Island 24(>
Samarang 243
Sanibro Islands 193
Sauioan Islands 257
Samos Island 229
Sanipit Bay 242
Samso Island 222
Sani-soe Island 223
Sandlsland 196
Kev 196
Sandaklian Bay 242
Sandalo, Cape ." 226
Sandalwood Island 243
Sandfly Cay 197
Sandhamniaren 219
Sandwich Island 256
Islands 214
Sand v Cape 261
Hook 195
Point 210
Sangnin River 231
Sanibel Island 196
Sankatv Head 194
Sannakh Island 199
Santander 224
River 196
Santiago Cape 210
-de Chile 211
• Cuba 204
I'ort 245
Santofia 224
Santos 208
Sapelo Island 195
Sarage Island 257
Sarangnni Islands 246
Sarawak 242
River 242
Sariguan Island 252
Sarstoon River 197
Sam Island 243
Saseno Island 228
Satano Misaki 248
Satawal Island 252
Saugor Island 238
Sauguir Island 242
Sauh, Pulo 238
Sauklioum 229
Saunders, Port 192
Sauo Bay 242
Savaii Island 257
Sa vanilla 206
Savannah 195
Savanna-la-Mar 204
Saybrook 194
Scalp Mountain 217
Scarcies River 231
Scatary Island 193
Schama Mountain 212
Schank, Cape 261
Schanz Island 251
Page 284]
INDEX TO APPENDIX IV.
Page.
Scharhorn 222
Scheveningen 223
Schillighorn 222
Schleiiiiunde 221
Schlenwig 221
Schonberg 221
Scillv Islands, England 215
S. Pacific 257
Scott Cape 200
Scutari 229
Sea Bear Bav 209
Rock.." 248
Seal Cays 197
• -Island 193
Seao Island 242
Seattle 200
Sebastian,San,Cape,M'g'sc'r 235
Spain 224
St., Cape, S. Africa... 232
Island 208
Sebastopol 229
Sebenico 227
Sedano, Cape 243
SedashigarBay 237
Seguin Island 193
Sein, I. de 224
Sejro Island 222
Selatan Point 242.
Seldom-come-bv Harbor... 191
Semeny Kiver. ". 228
Senierara Island 245
Semianioo Bay 200
Semione Island 240
Sentinel Island 248
Series I.«land 257
Sermalta Island 244
Sernielik Fjord 264
Sermo Island 229
Serrana Bank 198
Serranilla Bank 198
Seskarlslet 220
Setubal 225
SeuheliPar. 234
Seven Heads 218
Seychelle Islands 234
Sfax 230
Shag Rocks 214
Shahah 236
Shahr, Abu 236
Shaikh Shu' aib Islet 236
Shaluitien Island 247
Shanghai 242
Shannon River 216
Shantar Islands 250
Shantung 247
Sharjah 236
Shark Island 254
Shannoh 236
Shaweishan Island 242
Shelburne Harbor 193
Shelter Bav 250
Shepherd Island 198
Sherliedat, Ras 236
Sherbro Island 231
^ River 231
Sherm Hassejy 233
Joobbah 233
Rabigh 234
Wej 233
Yahar 233
Shetland Islands 216
PLACES — continued.
Page.
Shiash-Kotan Island 249
Shields, North 216
ShiniizuBay 249
Shimonoseki Strait 248
Shinnecock Bay 194
Ship Island 196
Shoal 196
Shipunski, Cape 250
ShirasuReef 248
Shoals, Isles of 194
Shoal water Cape 200
Island 239
Siargao Island 246
Siassi 247
Siberaet Island 239
Siboga 239
SibucoBay 247
Sibutu Island 247
Sibuyan Island 246
Sidniouth, Cape 262
Sierra Leone 231
Sighajik 230
Sigri, Port 229
Sihuatanejo Point 202
Sihut 236
Silau 197
Silaqui Islet 245
Silver Bank 203
Sinialoe Island 239
Si meonof Island 199
Siraoda 249
Simon, St., Island 195
Simonoff Island 257
Siinonor Island 247
Simons Bay 232
Simusir Island 249
'Singapore 238
Singkel Island 239
Singkep Island 238
Single Island 241
Singora 240
Sinon 231
Sinope 230
Siphano Island 229
"Siquiquor Island 246
Sirik, Cape 242
Siri va Saki 249
Sisa'l 197
Sitka 199
Sittee Point 197
Skafiataas Point 265
Skagi, Cape 265
SkagsHead 220
Skaw, Cape 223
Skelligs Rocks 216
Skerries Rocks 215
Skerrvvore Rocks 216
Skiathos Island 229
Skidegate Bay 199
Skoorgaarde 221
Skunibi River 228
Skyring Mountain 209
Sligo Bav 217
SlyneHead 217
Smalls Rocks 215
Smerwick 216
Smith Island, Japan 249
Washington 200
Smyrna 230
Snaefells Yokul 265
Snares Islands 263
Page.
Socorro Island, Chile 210
- — -•' Mexico 202
Socotra Island 2.33
SoderSkars 220
Soderarm 219
Soderhamm 219
Sofala 232
Sohar 236
Sola Wand 206
Solander Islands 203
Solitary Islands 261
Solombo, Great, Island 243
Solomon Islands 254
Solta Island 228
Sombrero 203
Key 196
Rock 247
Sommer Island 220
Song-yui Point 241
Sonserol Island 252
SooBay 242
Sooke Inlet 200
Sorelle Rocks 228
Sorol Island 252
Sorrel Rock 241
Sorrell, Cape 262
Port , . 262
Sorsogon, Port 246
Soumshu Island 249
South Cape, Formosa 242
N. Guinea 255
Rock 217
Water Cay 197
Southampton 215
Southsea Castle 215
Southwest Cape 262
Reef 196
Spalato Passage 228
Port.. 228
Sparo Vestervik 219
Spartel, Cape 230
Spartivento Cape, Italv 227
— Sardinia ..."..... 226
Spencer, Cape 260
Spezzia 226
Spikeroog 222
Spiridione, St.. Port 228
Spitzbergen 264
Spodsbjerg 222
Spurn Head 2H)
Square Handkerchief Bank . 203
Staabierg Huk 265
Stack, South 215
Stade 222
Stag Rocks 218
Stamp Harbor 199
Stampali Island 229
Stanley, Port 214
Starbuck Island 254
Start Point 215
Startpoint 216
Staten Island 209
Staunton Island 247
Stavanger 218
Steilacoom 200
Steinkirchen 222
Stemshesten 218
Stensher Rock 220
Stephens, Port 261
Stettin 221
Stewart, Cape 259
INDEX TO APPENDIX IV.
[Page 285
Page.
Stewart Islands 254
Stirrup Cays 203
Stir^iudden 220
Stockholm 219
Stonington 194
Stopelmiinde 221
Sl»ra 230
Storiioway 216
Stot 218
Stralsund !:21
Stratllsland 229-
Straumuess Point 265
Streaker Bay 260
Streckelsberg 221
Strogonof Cape 199
Stronii^tad 219
Stromtangen 219
Strong Island 252
Strovathi Island 228
Stuartlsland 198
Suakin 233
Snal 245
Subig 245
Succadana 242
Suda,Port 228
Sneik 236
Suez 233
Suffren, Cape 250
Sugar Loaf Point 261
Sughrah 236
Suk Island 252
Sulphur Island 253
Suml)awa Island 243
Sumburgh Head 216
Sunda Strait 239
Sunday Island 258
Sunderland 216
Sun<lsvall 220
Sunmivani 237
Sujie .'. 212
Sur 230
Surabaya 243
Surat 237
Kiver 237
Surigao 246
Surop 220
Susaki 248
Suwanose Jinia 248
Suwarrf)W Island 257
Svalferort Tzerel 220
Svartklubben 219
Svendborg 222
Svennr 219
Sviatoi Nos 264
Svinoen 218
Swallow Bay 210
Islands 255
Swan Islands 197
Swansea 215
Swatau 241
Sweers Island 262 i
Swinemunde 221 I
SybilloBay 250 |
Sydenham Island 251 '
Svdnev, Australia 261
^ — Harbor, C. Breton I .. 192
Svnesvarde Jlountain 218
Syra 229 ;
Syracuse 227
Tabaco 246!
Tabasco River 197
PLACES — continued.
Page.
Tablas Island 246
Point 211
Table Bay 232
Head 191
Island 238
Taboga Island 203
Tabou River 231
Taclobau 246
Tacoma 200
TacoradvBay 231
Tae Islands 241
Tagulanda Island 242
Tahiti 257
Tahoa Island 257
Tahuata Island 253
Taiaro Island 258
Tai-pin-san 244
Tajer, Port 227
TakaYama 249
Takapoto Island 258
Takau 242
Takhkona I'oint 220
Talabo, Cape 242
Talcahuano 211
Ta-lien-w an Bay 247
Talinay Mountain 211
Taltal, Port 211
Tahiat Island 242
Taniana Island 251
Tanianilare 207
Tamar Port 210
Tauiatave 235
Tambelan Island 240
Tampa Bav 196
Tampat Toewon Point 239
Tanipico 196
Tauisni Harbor 242
Tanabe Bay 248
Tancook Island 193
Tandjong Pandan 239
Tanga Bav 233
Tangier .'. 230
Tanjong Barram 242
Datii 242
Tanna Island 256
Tantang, I'ort 235
Taoiunii 256
Taoruiina Cape 227
Tapua Island 255
Tapnl Island 247
Taputeuea ." 251
TaraHill 217
Taranto 227
Tarawa Island 251
Tarbertness 216
Tarifa 225
Taritari Islan<l 251
Tarpaidin Cove 194
Tarragona 225
Tas de Foin Islet 247
Tatakoto 257
Tatsupi Saki 249
Tauere Island 258
Tauranga Harbor 263
Tauzon, Cape 235
Tavolara Cape 226
Tavov River 238
Tavtao Cape 210
Tavtav Fort 245
Tchesme 229
Tchonkotskoi, Cape 250
Tegal 243
Page.
Tehor Island 244
Tellicherri 237
Tello Islands 244
Tematangi Island 257
Tenasserim 238
Tenedos Island 230
Teneriffe Island 214
Tenez.Cape 230
Tepoca Cape 202
Tepoto Island 258
Tequepa 202
Terceira Island 213
Teresa, Sta. , Bav 201
Terkolei " 288
Terminos Lagoon 197
Ternate Island 244
Terstenik Rock 227
Testa, Cape 226
Testigos Islets 206
Tewaewae Bav 263
Thabi, Abu. .". 236
Thank God Harbor 264
Thermia Island 229
Thikombia Island 256
Thithia Island 256
Thomas, St.,Id.,B.ot'Biafra 231
AVest Indies. 205
Thome, St. , Cape 207
Three Kings Islands 262
Points Caf>e, Africa . . . 231
Argentina . . 209
Honduras . . 197
Ti-ao-iisu Islanil -244
Tiburon Island 202
Tiegenort 221
Tien-pak 241
Tientsin 247
Tillv Bav 210
TinibaliiV Island 196
Timor Island 243
Laut Island 244
Tinakula Islan<l 255
Tinian Island 252
Tintolo Point 246
Tirbv Point 198
Toass Island 252
Toau 258
Tobago 205
Tobi Shima 249
TobolAli 239
Tocopilla 212
Todos Santos 201
To-du Island 234
Tofua Island 258
Tokara Jima 248
Tokelau Islands 254
Token Bessi Island 243
Tokio 249
Tolaga Bav 263
Tolkeniit 221
Tomas, San 201
Tomo Roads 248
Tongarewa" Island 254
Tongatabu Island 258
Tongka Harbor 238
Tongoi 211
Tong-sang Harbor 241
Tong-ting Islet. 241
Tonning. 222
Topolobampo 202
Tor 233
Torbjornskjaer 219
Page 286]
INDEX TO APPENDIX IV.
Page.
Tordenskjold, Cape 265
Torgauten 219
TorivviSaki 249
Tornea.... 220
Toro Point 206
Torres Island 256
Point : 208
Port 226
Tortola 205
Tortosa, ("ape 225
Tortugas Island 206
Toryllill 217
Island 217
Tosco Cape 201
Totoya Island 257
Touhnguet Islands 191
Toulon 226
TouraneBay 240
Towers Island 250
Townsend, Port 200
Tr-enen 218
Trafalgar, Cape 225
Tralee Bay '. 216
Trani 227
Trapani 226
Travemvmde 221
Travel s Islands 262
Treasury Islands 254
Trebizond 230
Tregosse Islands 254
Trelleborg 219
Tremiti Islands 227
Trepass^ey Harbor 191
Tres Monies Cape 210
Puntas Cape, Chile ... 210
Venezuela . . 206
Trevaiidrum 237
Trevose Head 215
Triangle Island 200
Triangles 197
Tribulation, Cape 261
Trichendore 237
Trieste 227
Trincomali 237
Tringano River 240
Trinidad Head 200
Island 214
Tripoli, Africa 230
Turkey 230
Tristan d' .\cunlia 214
Triton Bav 255
Island 241
TriunfoCape 197
Trobriand Islands 255
Tronielin Island, Carolinels. 252
I ndian Ocean 235
Tronisi) 218
Trondheim 218
Troon 215
Tru.xillo 197
Tsau-liang-hai 248
Tscheljuskin, Cape..* 264
Tsmano 235
TsuSima 248
Tsukarase Rocks 248
Tsuruga ... 249
Tuanske Island 258
Tubal Island 257
Tubuai Islands 258
Tubuai-Manu Island 257
Tucacas Island 206
Tuckers Beach 195
i'L.icES — continue<l.
Page.
Tukume Island 258
Tully Mountain 217
Tumaco 213
Tunibez 212
Tung-ehuh Island 241
Tung-yung Islands 241
Tuni-ang Island 241
Tunis 230
Tuni> Island 223
Tupilco River 197
Tureia Island 257
Turk Island 203
Turnabout Island 241
Turi) Island 222
Turtle Island 257
Isles 260
TuskarBock 217
Tuspan Reefs 196
Tuticorin 237
Tutova 207
Tutu'i la Island 257
Tuvutha Island 256
Tuxtla Volcano 196
Twelve Islands '. 236
Twofold Bav 261
Tvbec Island 195
Ty-fung-kyoh Island 241
Tynemouth 216
I'a-Huka Island 253
Talan Island 252
Ubatnba 208
Uea Island 257
Ujelang Island 251
Uji Shima 248
r leaborg 220
Ulietea Island 257
Ulko Kalla Rock 220
Ulladulla 261
Ulsire 218
Uluthi Islands 252
Umea 220
Una 207
I'nalaska Island 199
I'nareBav 206
Underut islet 234
Underwood, Port 263
I'nga Island 199
XTnie Island 227
Union Bay 209
Islands 254
Port de la 202
Unsang 242
I'perni vik 264
Upright Port 210
Upsala 219
Upulo Islands 257
Uragaini 248
Urracas Islands 252
Urup Islan<i 249
Usborne, Fort 260
Usedoiu 221
Ushant 224
Ustica Island 226
Ute Islet 220
Utilla Island 197
Utrecht 223
Uvea Island 259
Vache Island 204
Vadso 218
Vahanga Island 257
Pago.
A'ahitahi Island 257
Vaitupu Island 254
Valdes Island 200
Valdivia 211
Valencia 225
Valentia 216
Valentine Harbor 210
St., Cape 210
Valery en Caux, St 223
Valiente Peak 198
Valientes Islands 252
Valparaiso 211
Vanavana Island 257
Vancouver 200
Vanikoro 255
Vannes 224
Vanua Lava Island 256
Le vu Island 256
IMbalavu Island 256
Vardo 218
Varella Cape 240
Pulo 240
Varna Bav 229
Vat<'' I slaiid 256-
Vathi, Port 228
Vatiu Island 258
Vatoa Island 257
Vatu Lele Island 256
Vara Island 256
Vavau Island 25S
Vavitoa Island 258
Vaza Barris River 207
Veglia 227
Veiro Island 222
Vela, La, Cape 206
Venangue Be Bay 235
Vendres, Port 225
Venice 227
Ver, Pointde 223
Verj Cruz 196
Verde Cape 231
Cav, Bahamas 203
— ^Cuba 204
Vicente, San, Cape 209
— Port • 245
Victor, Port 260
Victoria 200
Harbor 264
Port, Australia 260
Sevchelle Islands. 234
River.". 259
Victory Cape 210
Island 240
Vidal, Cape 232
Video Island 242
Vieborg Bay 220
Vieques Island 205
Vieste 227
Vigan '245
Vigo 225
Villa 218
Nova da Princessu 208
Villajoyose 225
Ville Franche 226
Vinaroz 225
Vincent, San, de la Barqiiera 224
St., Cape, Madagascar. 235
Portugal 225
Id., C. Verde Is. . 214
Wind ward Is . 205
Port, S. Pacific. . . 259
Vineyard Haven 194
INDEX TO APPENDIX IV.
[Page 287
Page.
Vingorla 237
Rooks 237
Virgin Gorda 205
Virgins, Cape 209
Viti' Levii 256
Vizagapatam 238
Viziadrug ^ 237
Vladimir, St. , Bav 2.50
Madivostok 250
Vliko, Port 228
Vohemar 235
Vojazza River 228
Volcano Island, West 242
Inlands 253
Volta River 231
Voltaire, Cape 259
Vordate Island 244
Vordingborg 222
Vostok Island 2.53
Vourlah 230
Vries Island 249
Wadero Island 219
Wadsworth, Fort 194
Wahdu Island 2;}4
Waiinea 253
Waitangi River 263
Wakaya Island 256
Wake Island 253
Wakefield, Port 260
Walfisch Bay ; 232
WalkerCav 203
Wallis Island 257
Walpole Island 2.56
Walsche, Cape 255
Walsingham, Cape 264
Wanganui River 263
Wangari Harbor 263
Wangaroa Harbor 262
Wangaruru 263
Wangeroog 222
Wang-kia-tia Bay 24"
Warberg 219
Wamemunde 221
Warren Hastings Island . . . 2.52
Washington 195
Island 251
Watch Hill Point 194
AVatcher, North, Island 239
Waterfall Bluff 232
Watcrford 217, 218
pi,.\CES —continued.
Page.
Waterloo Bav 232
Watlings Island 203
Wawoda Rock 250
Wedge Island 193
AVeggs Cape 191
Weichselmunde 221
Weihaiwei 247
Wellington 263
Wenman Island 250
Wessel, Cape 259
West Cape 263
Western, Port 261
Westminster Hall Islet 210
AVetta Island 243
Wexford 217
AVhaingaroa Harbor 263
AVhale Back 194
AVhalefish Island 264
AA'hite Haven 215
Head Island 193
Island 263
Rock 240
AVhitsunday Island 257
AVhittleCape 192
AVicklow 217
AVilberforce, Caiie 259
AVilhelmshaven 222
AVillemstadt 223
William, Port 263
AVilloughby, Cape 260
AA'ilmington 195
AA'ilson I.»lands 255
Islets 252
Proniontorv 261
AVindau " 220
AVinter Harbor 264
AVismar 221
AVittgenstein Island 258
Wolgast 221
Wolkonsky Island 258
Wollaston Island 209
WoUin 221
AVolIongong 261
AA'ood Island, Labrador 192
• -Maine 193
AA'oodlark Islands 255
AA'oody Island 241
AVostenholme Cape 191
AVotje Islands 251
Wottho Island 251
AVowoni Island 242
Pago.
Wrangell 199
AVrath, Cape 216
AA'reck Reef 255
AVusimado Point 248
AVustrow 221
AA^usung 242
Xulla Islands 244
YakunoShima 248
YakutatBay 199
Yamada 249
Yamagawa 248
Yami Island 246
Yanez 211
Yap Island 252
Yaquina Head 200
Yarmouth 193
YeboshiSima 248
Yembo 233
Yerabu-sima 244
Yeu, Island de 224
Ylin Island 245
Yobuko 248
Yoko Shima 248
Yokohama 249
Yoko-shima 244
Yokosuka » 249
York, Ca|H', Greenland 264
Queensland 262
Minster Rock 209
Youghal 218
Ystad V 219
Ytapere Bav 235
• Point ." 2.35
Yuiada Road 229
Yura \o Cchi 248
Zafarana 233
Zafarin Islands 230
Zambesi River 232
Zamboanga 247
Zante 228
Zanzibar 233
Zapotitlan Point 197
Zara 227
A'ecchia 227
Zempoala Point 196
Zengg 227
Zeyla 233
Zirona Grande Island 227
288 LUNAR DISTANCES.
APPENDIX V.
LUNAR DISTANCES.
By reason of the comparative rapidity of motion of tlie moon relatively to the earth, it occurs that
the angular distance, measured from the earth, between the moon and a body that occupies a fixed, or
nearly fixed, position in the celestial sphere, is constantly changing. If, therefore, an observer accu-
ratelv measures with a sextant the angle between the moon and one of the various celestial bodies for
whicK the lunar distance is tabulated in the Nautical Almanac, this observed distance, reduced to true
distance, affords a means for determining the absolute instant of time at which the observation was
taken; and from this may be deduced the longitude and the chronometer error.
If it were practicable to obtain results with a close degree of accuracy by this method, it would be an
invaluable aid to the navigator, eliminating all anxiety as to change of rate of the chronometer, and
even rendering it possible to navigate a vessel without such an instrument. It is unfortunately the case,
however, that the method does not afford results that may be regarded as reliable within small limits,
since a very small error in the observed angle, which it may not be possible to avoid even though every
care be taken, causes a large error in the deduced time. Navigators of the present day do not, there-
fore, employ the method of lunar distances except under extraordinary circumstances, such as when an
accident to the chronometer occurs, or, on a very long voyage, when there is reason to suspect the cor-
rectness of the chronometer error as brought forwanl by the rate.
In order to facilitate the method of determining the longitude from lunar distances, there is pub-
lished in the Nautical Almanac, for every third hour of Greenwich mean lime, the angular distances of
the center of the moon froin the center of the sun, from the briglitest planets and from certain blight
fixed stars selected in the path of the moon. All the distances that can be observed on the same day
are grouped together under that date, and the columns are read from left to right across both pages of
the same opening. The letter W. or ¥,. is affixed to the name of the sun, planet, or star to indicate
that it is on the west or east side of the moon. An observer on the surface of the earth having meas-
ured a lunar distance, corrected it for instrumental errors and for the semidiameters of the objects, and
cleared it from tWe effects of refraction and parallax, finds the hme or geocentric distance. With this
distance and the distances in the Nautical Abuanac of the same bodies ou the same day, the Greenwich
mean time of the observation can be found, as will hereafter be described.
The unavoidable errors to which the observation of lunar <Hstance is subject are diminished by
making a number of measurements. Errors of the instrument may be diminished by measuring
distances on opposite sides of the moon, when possible, and combining the results.
Before taking the observation, the Nautical Almanac must be examined to see from what objects the
distances are computed. If the star or planet selected for observation is not recognized from its position
relatively to other bodies in the heavens, it can easily be identified from the distance given in the
Almanac; for the observer may set the sextant to the distance computed roughly for the estimated time
at the meridian of Greenwich, and direct his sight to the east or west of the moon, according as the
object is marked E. or W. in the Nautical Almanac, and, having found the reflected image of the moon
upon the horizon glass, sweep the instrument to the right or left, and the image will pass o\er the star or
planet sought, if above the horizon and the weather clear; the star or planet is always one of the brightest,
and is situated nearly in the arc passing through the moon's center, perpendicular to the line connecting
the two horns.
Although all the instruments used in these observations ought to be well adjusted, yet particular
care should be taken of the sextant used in measuring the angular distance of the moon from the sun or
star, since an error of V in this distance will cause an error of nearly 30' in the longitude deduced
therefrom. When a great angular distance is to be measured it is absolutely necessary to use a telescope,
and its parallelism with respect to the plane of the instrument must be carefully examined; but in
measuring small distances the use of the telescope is not of such great importance, and a sight tube may
then be used, taking care, however, that the eye and point of contact of the objects on the horizon glass
be equally distant from the plane of the instrument. It is always conducive to accuracy to use a
telescope, and, after a little practice, this is easily done.
While one person is observing the distance of the objects, two others should observe the altitudes.
The chronometer should be under the eye of a fourth pereon appointed to note the time; the observer
who takes the angular distance gives previous notice to the others to be ready with their altitudes by
the time he has finished his observation, which, being done, the time, altitudes, and distance should be
carefully noted; if other sets of observations are taken it must be done within the space of fifteen
minutes, and the mean of all the observations should be worked as a single one.
When a ship is rolling considerably it is difficult to measure the distance of the objects, but when
steady there is much less difficulty, especially in small distances, which are nuich more easily measured
than large ones, and are not so liable to error from an ill adjustment of the telescope; an observer would
therefore do well to choose those times for observation when the distance of the objects is less than 70°
or 80°. But it must lie observed that neither of the objects, if possible, ought to be at a less altitude
than 10°, on account of the uncertainty of the refraction near the horizon, for tlie horizontal refraction
varies from 33' to 36' 40" by an alteration of 40° in the thermometer; this alteration might cause an
error of 2° in the longitude with an observer who uses the mean refraction.
LUNAR DISTANCES. 289
In measuring the distance of the moon from the auu we must bring the moon's round limb in
contact with tlie nearer limb of the sun. In measuring the distance of the moon from a planet or fixed
star tlie round limb must be brought in contact with the center of the star or planet, observing that, the
semidiameter of the planet being only a few seconds, the center of it can be estimated sufficiently near
for all the purposes of this observation.
In taking the altitude of the moon, the round limb, whether it be the upper or lower, must be
brought to the horizon. In misty weather it is rather difficult to observe the altitude of the stars on
account of tlieir dimness. Sometimes they are so dim tliat they can not te seen through the telescope
of a sextant, particularly if the mirrors are not well silvered. In this case the telescope must be laid
aside and the altitude taken with a sight tube.
It has been assumed that there were observers enough to measure the altitudes when the distance
was observed, but if that Is not the case the altitudes may be estimated in a manner to be explained
hereafter.
The method here given is that of Professor Chauvenet, and involves the use of tlie tables in this
Appendix. The object of these tables is to give the true correction of a lunar distance in all cases when,
with the apparent distance of the moon from the sun, a planet, or star, the apparent altitudes of the
two objects have also been obtained by observation. They enable us readily to take into account:
First, the parallax of the moon in the latitude of the observer, allowing for the spheroidal figure of the
earth; second, the parallax of the sun or a planet; third, the true atmospheric refraction, allowing for
the actual state of the air as shown by the barometer and thermometer; and, fourth, that effect of
refraction which gives tlie apparent <lisks of the moon and sun an oval or elliptical figure.
The longitude deduced from a lunar observation, when no attention is paid to the spheroidal figure
«f the earth, to the barometer and thermometer, or to the elliptical figure of the disks, may in certain
cases be in error a whole degree. It is true these extreme cases are rare in practice, but cases are
common in which from such neglect the error in the longitude is ICK, 15', or 20', and it is absolutely
necessary to get rid of such errors and to leave no other inaccuracy in the result than that which
unavoidably follows from the observations.
The Observation. — The record of a complete observation embraces:
1. The latitude and approximate longitude of the place of observation.
2. The approximate local time.
3. The time of observation as shown by a chronometer, and the error of the chronometer, or ita
difference from mean (ireenwich time.
4. The apparent distance of the moon's bright limb from a star or planet, or from the nearer limb
of the sun.
5. The apparent altitude of the moon's upper or lower limb above the sea horizon.
6. The apparent altitude of the star, planet, or lower limb of the sun above the sea horizon.
7. The height of the barometer and thermometer.
.S. The height of the eye above the level of the sea.
9. The index correction of the sextant.
The index correction of the sextant may be supposed to be previously determined; but, since even
in the best instruments it is not constant, its determinataon should be considered a necessary part of the
observation.
The error of the chronometer alluded to is that which is obtained by applying the daily rate
(multiplied by the jiroper number of days) to the error found before leaving port. The agreement or
disagreement of the error thus found with that found by the lunar observation will be the test of the
accuracv of the chronometer, subject, of course, to the accepted limits of accuracy of the observation
itself.
Prepahatiox of the Data. — Greemoich Date. — Correct the chronometer time for its error from
Greenwich time and deduce the Greenwich date, i. e., the Greenwich day and hour (mean time), reck-
oning the hours in succession from to 24, l)eginning at noon. .
S'ljtilical Almiinac. — With the Greenwich date enter the Almanac and take out the moon's semi-
diameter and horizontal parallax; if the sun is observed, take its semidiameter; in the case of a planet,
take its horizontal parallax only.
ApjMircnt Altitude of tlie Moon. — To the altitude given by the sextant apply the index correction of
the instrument and subtract the dip of the horizon (Table 14). « If the lower limb is observed, add the
semidiameter and augmentation (Table 18) ; if the upper limb is observed, subtract the augmented semi-
diameter. The result is the apparent altitude of the moon's center, denoted " ([ 's App. Alt."
Apparent AUttade of the Sun, Planet, or Star, — To the observed altitude apply the index correction of
the sextant, and subtract the dip (Table 14); and if the sun is used, add its semidiameter when the lower
limb is oliserved, or subtract it when the upper limb is observed. The result is the apparent altitude
required, denoted by "Q's or >)c'8 App. Alt."
Apparent Distance. — First, when the sun is used, to the observed distance (corrected for index error
when necessary) add the moon's augmented semidiameter and the sun's semidiameter; second, when a
planet nr star is used, add the moon's augmented semidiameter if its nearer limb is ol^erved, but
subtract it if its farther limb is observed. The result is "Ap/i. Diet."
.Vooh'.i Rednred Paralla.€ and Refraction. — Enter Table 19 with the latitude of the place of observa-
tion and the moon's horizontal jiarallax, and take out the correction, which add to the horizontal
parallax. Call the result the moon's reduced parallax, or " ^ 's Red. P."
Enter Table I with the moon's apparent altitude, and take out the mean reduced refraction, and
apply to this mean refraction the corrections given in 'Tables 21 and 22, adding or subtracting these cor-
rections according to the directions in the tables. The result is the moon's r^uced refraction, or " (T 's
Red. R."
a The tables designated by their numbers in Arabic notation are to be found in Part II. The tables contained in thl«
Appendix, which are for exclusive use with lunar-distance observations, are denoted by Roman numbers.
24972°— 12^ 19
290 LUNAK DISTANCES.
Subtract the "d's Red. R." from the "d'a Red. P." and mark the result as "C's Red. P. mid R."
Reduced Parallax and Refraction of Sim, Planet, or Star." — With the apparent altitude of the sun,
planet, or star, take from Table I the mean reduced refraction, which correct by Tables 21 and 22. If
the sun is observed, subtract its horizontal parallax (which may always be taken at 8". 5) from its reduced
refraction, and mark the result as "Q's Red. P. and R." If a planet is observed subtract ita horizontal
parallax, and mark the result as " >f;'s Red. P. and R." If a star is observed, its reduced refraction is
at once the required " -Jf' s Red. P. and R."
Computation of the True Distance. — Take from Tables II, III, IV, and V respectively the four
logarithms A, B, C, D, '' and place these logarithms each at the head of a column, marking the columns
A, B, C, and D; then put the —
log of C 's Red. P. and R. (Table IX) in columns A and B.
log of Q's or >f;'s Red. P. and R. (Table IX) in columns and D.
log sin C's App. Alt. (Table 44) in columns A and D.
log sin O's or :if:'s App. Alt. (Table 44) in columns B and C.
log cot App. Dist. (Table 44) in columns A and C.
log cosec App. Dist. (Table 44) in columns B and D.
The sum of the four logs in Col. A is the log (Table IX) of the First Part of C 's Correction, which is
to be marked 4- when the app. dist. is less than 90°, but — when the app. dist. is greater than 90°.
The sum of the four logs in Col. B is the log (Table IX) of the Second Part of C 's Correction, which
is always to be marked — .
The sum of the four logs in Col. C is the log (Table IX) of the First Part of the Q's or >)c's Correction,
which is to be marked — when the app. dist. is less than 90°, but -|- when the app. dist. is greater
than 90°.
The sum of the four logs in Col. D is the log (Table IX) of the Second part of the Q's or >)c's Correc-
tion, which is always to be marked -p.
Combine the first and second parts of the C ' s correction according to the signs prefixed; that is,
take their sum if they have the same sign, but their difference if they have different signs, and prefix the
sign of the greater to the result, which call " d'a whole correction."
In the same manner form the "0's or >(c's whole correction."
First Correction of Distixnce. — Combine the ([ 's whole corr. and the Q's or '^'s whole corr., according
to their signs; the result is the First Correction of Distance, which is to be added to or subtracted from
the apparent distance, according as its sign is + or ~.
Second Correction of Distance. ^Enter Table VI with the Apparent Distance and the First Correction
of Distance, and take out the Second Correction of Distance, which is to be applied to the distance
according to the directions in the side columns of the Table.
Correction for the Elliptical Figure of the Moon's Disk, or Contraction of the Moon's Semi-diameter. — Enter
Table VII A with the C's App. Alt. and (L's Red. P. and R., and take out the number. With this
number and the C's whole correction enter Table VII B and take out the required contraction, which is
to be added to the app. dist. when the farther limb is observed, but subtracted when the nearer limb is
observed.
Correction for the Elliptical Figure of the Sun's Disk, or Contraction of the Sun's Semi-diameter. — Enter
Table VIII A with the Q's App. Alt. and Q's Red. P. and R., and take out the number. .With this
number and the Q'a whole corr. enter Table VIII B and take out the required contraction, which is
always to be subtracted from the distance (the nearer limb of the sun being always observed).
Correction for Compression, or for the Spheroidal Figure of the Earth.— Take frpm the Nautical Alma-
nac for the Greenwich date the declinations of the bodies to the nearest whole degree. With the moon's
declination and apparent distance, take from Table XI A the jfirst part of N, and mark it with the sign
in the table if the declination is North; but if the declination is South, change the sign from -}- to — or
from — to +. With the sun's or star's declination and the apparent distance, take from Table XI B the
second part of N, giving it the same sign •aa the declination. Take the sum, or difference, of the two parts,
according as their signs are the same or different, and to the resulting number prefix the sign of the
greater. The logarithm of this number of seconds, taken from Table IX, with its sign prefixed, is the
required log N. To log N add the log sine of the latitude of the place of observation; the sum is the log
(Table IX) of the required correction for compression. In north latitude add this correction if log X is -(-,
or subtract it if log N is — ; in south latitude subtract the correction when log N is +, and add it when
log N is — .
All these corrections being applied to the Apparent Distance, the result is the True Distance.
To Find the Greenwich Time. — Find in the Nautical Almanac the two distances between which the
true distance falls. Take out the first of these, together with the Prop. Log following it, and the hours
of Greenwich time over it. Find the difference between the distance taken from the Almanac and the
true distance, and to the log of this difference (Table IX) add the Prop. Log from the Almanac; the
sum is the log (Table IX) of an interval of time to be added to the hours of Greenwich time taken from
the Almanac. The result is the approximate Greenwich time.
To correct this Greenwich time, take the difference between the two Prop. Logs in the Almanac
which stand against the two distances between which the true distance falls. With this difference and
the interval of time just found enter Table X and take out the seconds, which are to be added to the
approximate Greenwich time when the Prop. Logs are decreasing, but subtracted when the Prop. Logs
are increasing. The result is the true Greenwich time.
By comparing with this the local mean time the longitude will be found; or, if testing the time
shown by chronometer, the difference between the true Greenwich time and the time shown l)y the
chronometer is the error of the chronometer as determined by the lunar observation.
a The parallax of a star being zero, iti " reduced parallax and refraction " become, of course, merely its " reduced refrac-
tion; " but as no mi-stake can arise from marking it as " >|c's Red. P. r tid R.," this designation has been retained in order to
give simplicity and uniformity at once to the rules and the tables.
b No interpolation is necessary in taking out these logarithms.
LUNAR DISTANCES.
291
Degree of Dependence. — If the error thus determined agrees with that deduced by means of the
rate and original error, it may be accepted as a confirmation of the rate of the chronometer; if otherwise,
more or less doubt is thrown upon the chronometer, according to the degree of accuracy of the lunar
obser\'ation itself. An error of 10" in the measurement of the distance produces about 20' error in the
Greenwich time; and since, even with the best observers, a single set of distances is subject to a possible
error of 10", it may be well to consider the chronometer as still to be trusted so long as it does not
differ from the lunar by more than 20'. Since, however, so much depends upon skill in measuring the
distance, the observer can only form a correct judgment of the degree of dependence to be placed upon
his own observations by repeated trials and a careful comparison of his several results.
Example: In Lat. 35° 30' N., Long. 30° VV., by account, at the local mean time, 1855, September 6,
18" 8"" 0», the observed distance of 0's andC 's nearer limbs was 43° 52' 10"; observed alt. C, 49° 32' 50";
observed alt. Q, 5° 27' 10"; barometer, 29'°. 1; thermometer, 75°; height of the eye above the sea, 20";
I. C, 0' 00"; required the longitude.
Preparation of the Data.
L. M. T., Sept. 6,
Long., D. R.,
G. iL T., approx.,
Obs. Alt. C,
Dip, Table 14,
C'sAug. S. D.,
C's App. Alt.,
C'sRed. R., Table I,
Bar. 29'M, Table 21,
Ther. 75°, Table 22,
C'sRed. R.,
C'sRed. P.,
C'sRed. P. andR.,
IS'-OS-'jC'sS. D.,
- 2 00 I Aug. Table 18,
20 08 ! C'sAug. S. D,
49° 32' 50'
4 23
I- 15 01
49 43
28
1'
16"
3
4
1
54
09
23
53 14
Obs. Alt. Q,
Dip,
O'sS. D.,
0'8 App. Alt,
O's Red R., Table I,
Bar., Table 21,
Ther., Table 22,
O's Red. R.,
O's Par.,
O's Bed. P. and R.,
14' 50".0 C's Par., N. A.,
I- 11 .2 Aug., Table 19,
Obs. Dist. 01 |C,
C'sAug. S.D.,
O'sS. D.,
54' 19".4
+ 3 .6
15 01 .2
5=
+
27'
4
15
10"
23
55
5
38
42
-
8'
57"
16
28
8
13
8
05
App. Dist.,
C's Dec, N. A.,
O's Dec., N. A.,
54 23 .0
43'=
+
+
52'
15
15
10"
01
55
44
23
06
25° N.
6°N.
A.
log A, Table II, 0. 0021
log C '8 Red. P. and R., 3. 5043
log sin C 's App. Alt., 9. 8825
log cot App. Dist., 0. 0093
(log. Table IX,
\lst Part C's corr.,
B.
3. 3982
+41' 42"
log B, Table III, 9. 9951
log C 's Red. P. and R., 3. 5043
log sin O's App. Alt., 8. 9929
log cosec App. Dist., 0.1552
/log, Table IX,
\2dPart C's corr.,
C's whole corr.,
2.6475
- 7' 24"
+34' 18"
log N, Tabs. XIandIX, (-)0.845
, log sin Lat, + 35° 30', ( + ) 9. 764
(log. Table IX, (-) 0.609
\Corr. for Compression, — 4"
Qmtputaiion of tlie True Distance.
G.
log C, Table IV, 9. 9949
log O's Red. P. and R., 2. 6857
log sm O's App. Alt, 8. 9929
log cot App. Dist., 0. 0093
flog, Table IX,
\lst Part O's corr.,
1. 6828
-0' 48"
D.
log D, Table Y, 9. 9992
log O's Red. P. and R., 2. 6857
log sm C 's App. Alt, 9. 8825
log cosec App. Dist, 0. 1552
flog, Table IX,
\2d Part O's corr.,
O's whole corr..
2. 7226
--8' 48"
+8' 00"
App. Dist, 44° 23'
1st Corr., + 42
2d Corr., Table VI, —
Contraction of C 'si
S.D., Table VII, f
Contraction of 0's\
S.D., Table Vni,/
Corr. for Comp. —
True Distance,
06"
18
16
.
20
45 04 44
292
LUNAR DISTANCES.
Extract from Nautical Almanac, September, 1855.
GREENWICH MEAN TIME: LUNAK DISTANCES.
star's name and
position.
Midnight.
P. L.
of
Difl.
XVb.
P. L.
of
Dlff.
XVIII''.
P. L.
of
Difl.
XXI''.
— ^
P. L.
of
Difl.
6
Sux E.
48° 46' 55"
1
3422 1 47° 25' 3"
i
3427
46° 3' 17"
3433
44° 41' 38"
3438
Computation of Greenwich Mean Time.
True Distance,
Distance, N. A., at XXllV,
45°
46
04'
03
44"
17
Difference,
58
33
Approximate interval.
2"
18
09"
04'
Approx. G. M. T.,
Corr., Table X,
20
09
04
o
True G. M. T.,
L. M. T.,
20
18
09
08
02
00
P. L., 0.3433
log. Table IX, 3.5457
log. Table IX, 3.8890
Longitude,
+ 2 01 02 = 30° 15' 30" W.
Diff. P. logs
Example: In Lat. 55° 20' S., Long. 120° 25' W., by account, on August 29, 1855, at 9" 40°' 00' p. m.,
local mean time, the following distance and altitudes were found, being the mean of six observations
corrected for index error. Observed distance of Fomalhaut and moon's farther limb, 46° 30' 23";
observed alt. C, 6° 26' 10"; observed alt. Fomalhaut, 52° 34' 40"; barometer, 31'"; thermometer, 20°;
height of the eye above the sea, 18".
Preparation of the Data.
L.M.T., August 29, O"" 40'" 00"
Long, by D. R., +8 01 40
Approx. G. M. T.,
Obs. alt. £
Dip,
C'saug. S. D., +
C's App. Alt.,
C's Red R., Table!
Bar., Table 21, +
Ther., Table 22, +
C'sRed R.,
C'sRed. P.,
C'sRed. P. andR., 51 44
17
41 40
6°
26' 10"
4 00
16 28
6
38 29
7' 48"
16
32
8 36
60 20
C'8S.D.,Naut.Al., 16' 26".3
Aug., Table 18, + 2 .0
C's aug S. D.,
Obs. alt. >f:,
Dip,
•^'s App. Alt,
*'sRed.R.,TableI,
Bar., Table 21, +
Ther., Table 22, +
*'sRed. R.,
*'s Red P.,
*'s Red. P. and R.,
16
•28
.3
52°
34'
4
40'
09
52
30
31
13"
2
5
20
1 20
C'sPar., N. A.,
Aug., Table 19,
V Red p.,
Obs. Dist. -)f IC,
C's aug., S. D.,
App. Dist.,
C 's Dec, N. A.,
i^i'a Dec., N. A.,
+
60' 11".8
8 .3
60 20 .1
46° 30' 23"
— 16 28
46 13 55
4° N.
30° S.
LUNAR DISTANCES.
293
log A, Table II,
log C'sRed. P. andR.^
log sin C 's App. Alt.,
log cot App. Dist.,
I log, Table IX,
\lst Part C's corr., -r
B.
log B, Table III,
log d 's Red. P. and R.,
log sin >)i:'s App. Alt.,
log cosec App. Dist.,
0.0274
3.4919
9.0632
9.9813
2.5638
6' 06"
0.0001
3.4919
9.8995
0.1414
/log, Table IX,
\2dPart C'scorr.,
C's whole corr.,
log N, Tabs. XI and (
IX,
log sin Lat. , -55'
3.5329
- 56' 51"
— 50 45
-)
flog Table IX,
(.Corr. for Comp.,
(-)
(+)
+
Computation of the True Distance.
C.
log C, Table IV,
log *'s Red. P. and R.,
log sin >|c's App. Alt.,
log cot App. Dist.,
(log, Table IX,
\lst Part i^'s corr.,
D.
log D, Table Y,
log 5t:'8 Red. P. and R.,
log sin C's App. Alt,,
log cosec App. Dist.,
9.9999
1.9031
9.8995
9.9813
1.7838
1' 01"
0.0267
1.9031
9.0632
0.1414
log. Table IX,
,2d Part >)<'s corr.,
3(c's whole corr.,
1.1344
+ 0' 14"
— 47
1.230
9.913
1.143
14"
Extract from Nautical Almanac, Augu^l, 1855.
GREENWICH MEAN TIME: LUNAR DISTANCES.
App. Dist., 46=
13'
Py
1st corr., —
51
32
2dcorr., Table VI, —
22
Contraction of C'sli
S. D., Table VII, j +
17
Corr. for Comp., +
14
True Distance, 45
22
32
.-5
5
Star's name and
position.
Midnight.
P. L.
of
Dlfl.
XV\
P.L.
of
Dill.
XVIIIl'.
P.L.
of
Difl.
XXI >.
P.L.
of
Dlfl.
29
Fomalhaut W.
42° 11' 34"
2535
43° 51' 59"
2527
45° 32' 35"
2521
47° 13' 19"
2516
Computation of Greenwich Mean Time.
True Distance,
Dist., N. A., at XV"
Difference,
Approx. interval.
Add—
Approx. G. M. T.,
Corr., Table X,
TrueG. M. T.,
L. M. T.,
Long. ,
45° 22' 32"
43 51 59
1
30 33
2h
15
42»01»
17
+
42 01
01
17
9
42 02
40 00
P. L.,
log. Table IX,
0.2527
3.7350
Diff . P. logs — 6
log. Table IX, 3.9877
+ 8 02 02 = 120° 30' 30" W.
Method ov T.^kixg a Lunar Obsekvation by One Observer. — Three observers are required to
make the necesssary obser\'ations for determining the longitude — one to measure the distance of the
bodies, and the others to take the altitudes. In case of not having a sufficient number of instruments
or observers to take the altitudes, the latter may be calculated, there being given the latitude of the place,
the time, the right ascensions, and the declinations of the objects. These calculations are long, however,
especially in the case of the moon, and a considerable degree of accuracy is required in finding from the
Nautical Almanac the moon's right ascension and declination, which must be liable to some error on
account of the uncertainty of the ship's longitude. The following method of obtaining those altitudes
is far more simple, and sufficiently accurate. This method depends on the supposition that the altitudes
increase or decrease uniformly.
294
LUNAR DISTANCES.
Before measuring the distance of the bodies, take their altitudes, and note the times by a chro-
nometer; then measure the distance and note the time (or measure a number of distances, and note
the corresponding times, and take the means); after having measured the distances, again measure tlie
altitudes, and note the times; then, from the two observed altitudes of either of the objects, the required
altitude of that object may be found from the following formula, which is based upon simple proportion:
^ — r~'
where x = change of altitude, in minutes, between first altitude and time of measuring the lunar
distance, being positive or negative according as body is rising or falling;
d = difference between first and second altitudes, in minutes;
e = time, in seconds, between first altitude and lunar observations; and
t — time in seconds, between first and second altitudes.
The change of altitude thus deduced, applied with proper sign to the first altitude, gives the
altitude at time of observing the hmar distance.
Example: Suppose the distances and altitudes of the sun and moon were observed, as, in the
following table; it is required to find the altitudes at the time of measuring the mean distance.
Mean,
Times by chro-
nometer.
2" 03"' 20'
2 04 20
2 05 50
Lunar dis-
tance.
40° 00' 00"
40 00 30
40 01 30
Times bji chro-
nometer.
2'' 02 "OO'
2 06 10
Obs. all.
(I's L. L.
20° 46'
21 20
Times by chni-
nometer.
2" 02" 30^
2 07 00
068
0'»
40°
39
. alt.
L.L.
20'
12
2" 04" 30'
2 02 00
10 d, 34
SSO'
ForQ.
Time of lunar obs..
Time of 1st alt.,
«,
^ _ 68 X 120 _
270
First altitude,
f 4 30
''\ 270^
2" 04"
2 02
30'
30
08
68'
2 04 30
Time of lunar
Time of 1st alt
40 00 40.
For C.
obs.,
^ = + 20'.4
^ _ ^ 34 X 1
250
First altitude.
f 2 30
\ 150»
= + 20' 24"
20° 46' 00"
+ 20 24
30'. 2 = — 30'
40° 20'
- 30
00
120'
12"
00"
12
Required altitude, 21 06 24 Required altitude, 39 49 48
To obtain the altitudes by calculation the following fornmlai may be employed:
tan A = tan d sec I;
cos (A — L) sxnd.
sin /(
sin A
in which d is the declination; t, the hour angle; L, the latitude; h, the true altitude of the center of the
object; A, an arc which has the same n^me or sign as the declination and is numerically in the .same
quadrant as i. In the solution, strict regard must be had for the signs.
Example: Required the apparent altitude of the sun's center on December 22, 1879, in Lat. 48° 23'
N., Long. 60° W., at 10" 01" 14' a. m., app. time.
L. A. T., December 21, 22" Ol" 14" (, 1" 58°' 46"
Long.,
December 22,
+
4
00 00 O's
Dec, 23° 27' 16" S.
G. A. T.
2
01 14
t
d
29° 41' 30"
— 23 27 16
sec 0.06113
tan ( — ) 9.63735
sin (-) 9.59991
A
L
— 26 32 20
+ 48 23 00
tan ( — ) 9.69848
cosec(— ) 0.34989
A-L
-74 55 20
cos (+) 9.41520
h
ref.— par
13 23 58
+ 3 50
sin (+) 9.36500
App. alt. 13 27 48
APPENDIX V:
TABLE I.
[Page 295
Mean Reduced Eefraction for Lunars.
Barometer 30 inches. Fahrenheit's Thermometer 60°.
Apparent al-
Reduced re-
Diff. to
Apparent al-
Reduced re-
Apparent al-
Reduced re-
Apparent al-
Reduced re-
titude.
fraction.
1'.
tttude.
fraction.
titude.
fraction.
titude.
fraction.
O 1
5
9 54.2
II
1.6
o /
10
/ II
5 24.1
O 1
15
/ //
3 41.7
o /
27
' II
2 7.8
5
9 46.3
1.5
6
6 21.6
10
3 39.4
27 30
2 5.7
10
9 38.6
1.5
10
5 19.2
20
3 37.1
28
2 3.7
15
9 31.0
1.5
15
5 16.8
30
3 34.9
28 30
2 1.7
20
9 23.7
1.4
20
5 14.4
40
3 32.7
29
1 59.8
25
9 16.5
1.4
26
5 12.1
50
3 30.6
29 30
1 58.0
5 30
9 9.5
1.4
ig 30
5 9.8
16
3 28.5
30
1 56.2
35
9 2. 7
1.3
35
5 7.6
10
3 26.5
30 30
1 54.5
40
8 56.0
1.3
40
5 5.3
20
3 24.5
31
1 52.8
46
8 49.5
1.3
45
5 3.1
30
3 22.6
31 30
1 61.2
50
8 43.1
1.2
50
5 0.9
40
3 20.7
32
1 49.7
55
8 36.9
1.2
55
4 68.8
60
3 18.8
32 30
1 48.2
. 6
8 30. 9
1.2
11
4 66.7
17
3 16.9
33
1 46.7
5
8 24.9
1.2
5
4 64.6
10
3 15.1
33 30
1 45.3
10
8 19.1
1.1
10
4 62.5
20
3 13.4
34
1 44.0
15
8 13.4
1.1
15
4 50. 5
30
3 11.6
34 30
1 42.7
20
8 7.8
1.1
20
4 48.6
40
3 9.9
35
1 41.4
25
8 2.4
1.1
26
4 46.6
60
3 8.2
35 30
1 40.2
6 30
7 57.0
1.0
11 30
4 44.6
18
3 6.6
36
1 39.0
35
7 51.8
1.0
35
4 42.7
10
3 6.0
36 30
1 37.8
40
7 46. 7
1.0
40
4 40.8
20
3 3.4
37
1 36.7
45
7 41.7
1.0
45
4 38.9
30
3 1.8
37 30
1 35.6
50
7 36.7
1.0
60
4 37.1
40
3 0.3
38
1 34.5
65
7 31.9
0.9
55
4 35.3
50
2 58.8
38 30
1 33.5
7
7 27. a
0.9
12-0
4 33.5
19
2 57.3
39
1 32.6
5
7 22.6
0.9
5
4 31.7
10
2 55.9
39 30
1 31.6
10
7 18.0
0.9
10
4 30.0
20
2 64.4
40
1 30.6
15
7 13.6
0.9
15
4 28.3
30
2 53.0
40 30
1 29.6
20
7 9.2
0.9
20
4 26.6
40
2 51.6
41
1 28.7
26
7 30
7 4.9
0.8
25
4 24.9
50
2 50.3
41 30
1 27.8
7 0.8
0.8
12 30
4 23.2
20
2 49.0
42
1 27.0
35
6 56.6
0.8
36
4 21.6
10
2 47.6
42 30
1 26.2
40
6 52.6
0.8
40
4 20.0
20
2 46.4
43
1 25.4
45
6 48.6
0.8
45
4 18.4
30
2 45.1
43 30
1 24.6
50
6 44.8
0.8
50
4 16.8
40
2 43.8
44
1 23.8
55
6 40.9
0.7
55
4 15.2
50
2 42.6
44 30
1 23.1
8
6 37.2
0.7
13
4 13.7
21
2 41.4
45
1 22.4
5
6 33.5
0.7
5
4 12.2
10
2 40.2
46
1 21.0
10
6 29.9
0.7
10
4 10.7
20
2 39.0
47
1 19.6
15
6 26.3
0.7
15
4 9.2
30
2 37.9
48
1 18.4
20
6 22.8
0.7
20
4 7.7
40
2 36.7
49
1 17.2
25
6 19.4
0.7
25
4 6.3
50
2 36.6
50
1 16.0
8 30
6 16.0
0.7
13 30
4 4.8
22
2 34.5
51
1 15.0
35
6 12.7
0.6
35
4 3.4
10
2 33. 4
52
1 13.9
40
6 9.5
0.6
40
4 2.0
. 20
2 32.4
53
1 13.0
45
6 6.3
0.6
45
4 0.6
30
2 31.3
54
1 12.0
50
6 3.1
0.6
50
3 59.3
40
2 30.3
65
1 11.1
56
6 0.0
0.6
56
3 57.9
60
2 29.2
56
1 10.3
9
5 67.0
0.6
14
3 56.6
23
2 28.2
57
1 9.6
5
5 54.0
0.6
6
3 56.3
20 -
2 26.3
58
1 8.7
10
5 51.1
0.6
10
3 54.0
40
2 24.4
59
1 8.0
15
5 48.2
0.6
15
3 52.7
24
2 22.5
60
1 7.3
20
6 46. 3
0.6
20
3 51.4
20
2 20.7
62
1 6.0
26
5 42.5
0.6
25
3 60.1
40
2 18.9
64
1 4.9
9 30
6 39.8
0.6
14 30
3 48.9
26
2 17.2
m
1 3.8
36
5 37.0
0.5
35
3 47.6
20
2 15.5
68
1 2.9
40
5 34.4
0.5
40
3 46.4
40
2 13.9
70
1 2.0
45
5 31.7
0.5
45
3 45. 2
26
2 12.3
73
1 1.0
50
6 29.2
0.5
50
3 44.0
20
2 10.8
76
1 0.1
55
6 26.6
0.6
55
3 42.8
40
2 9.3
80
59.2
10
5 24.1
15
3 41.7
27
2 7.8
90
58.3
Page 296]
APPENDIX V:
TABLE II. 1
Log
. A, for computing the First Correction of the Lunar Distance.
- App
alt. of
moon.
Reduced parallax and refraction of moon. 1
41'
42'
4S'
44'
45'
46'
47'
48'
49'
50'
51'
52'
58'
54'
55'
5° (/
.0288
0295
0301
0308
0315
0321
0.328
0335
0341
0348
0355
0361
0368
2
.0286
0293
0299
0306
0313
0319
0326
0333
0339
0346
0852
0359
0366
4
.0284
0291
0297
0304
0311
0317
0324
0330
0337
0344
0350
0357
0363
6
.0282
0289
0296
0302
0309
0315
0322
0328
0335
0341
0348
0354
0361
8
.0281
0287
0294
0300
0298
0307
0305
0313
0320
0326
0333
0331
0339
03.37
0346
0352
0359
5 10
.0279
0285
0292
0311
0318
0324
0344
0350
0356
12
.0277
0284
0290
0296
0303
0309
0316
0322
0329
0335
0341
0348
0.S54
14
.0275
0282
0288
0295
0301
0307
0314
0320
0327.
0333
0339
0346
0852
16
.0274
0280
0286
0293
0299
0306
0312
0318
0325
0331
**W
0344
03.=i0
18
5 20
.0272
0278
0285
0283
0291
0289
0297
0296
0304
0302
0310
0316
0323
0321'
0.329
0327
0335
0333
0341
0339
0348
.0270
0277
0308
0314
0,346
22
.0269
0275
0281
0288
0294
0300
0306
0313
0319
0325
0331
0337
0344
24
.0267
0273
0280
0286
0292
0298
0304
0311
0317
0323
0329
0335
0341
26
.0265
0272
0278
0284
0290
0296
0303
0309
0315
0321 •
0327
0333
0339
0346
,
28
.0264
0270
0276
0282
0289
0287
0295
0293
0301
0307
0313
0319
0325
0323
0331
0329
0337
0335
0344
5 30
.0262
0268
0275
0281
0299
0305
0311
0317
0342
32
.0261
0267
0273
0279
0285
0291
0297
0303
0309
0315
0321
0327
0334
0340
34
.0259
0265
0271
0277
0283
0290
0296
0302
0308
0314
0320
0326
0332 0338
36
.0258
0264
0270
0276
0282
0288
0294
0300
0306
0312
0318
0324
0330 : 0336
38
0262
0268
0274
0280
0279
0286
0285
0292
0290
0298
0296
0304
0302
0310
0308
0316
0314
0322
0320
0328
'0326
0334
5 40
0261
0267
0273
0332
42
0259
0265
0271
0277
0283
0289
0295
0301
0306
0312
0318
0324 : 0330
44
0258
0264
0270
0275
0281
0287
0293
0299
0305
0311
0316
0322 0328
46
0256
0262
0268
0274
0280
0286
0291
0297
0303
0309
0315
0320
0326
48
5 50
0255
0261
0267
0272
0271
0278
0284
0290
0296
02i)4
0301
"0300
0307
0305
0313
0319
0324
0253
0259
0265
0277
0282
0288
0311
0317
0323
52
0252
0258
0264
0269
0275
0281
0287
0292
0298
0304
0309
0315
0321
54
0251
0256
0262
0268
0274
0279
0285
0291
0296
0302
0308
0313
0319
56
0249
0255
0261
0266
0272
0278
0283
0289
0295
0300
0306
0312
0317
58
0248
0254
0259
0265
0263
0271
0269
0276
0275
0282
0280
0287
0293
0299
0297
0304
0303'
0310
0308
0316
6
0247
0252
0258
0286
0291
0314
<>
0245
0251
0256
0262
0268
0273
0279
0284
0290
0295
0301
0307
0312
4
0244
0249
0255
0261 0266
0272
0277
0283
0288
0294
0299
0305
0310
6
0243
0248
0254
0259
0265
0270
0276
0281
0287
0292
0298
0303
0309
8
0241
0247
0252
0258
0263
0269
0267^
0274
0280
0278
0285
0284"
0291
0296
0302
0307
0306
6 10
0240
0246
0251
0256
0262
0273
0289 , 0295
0300
12
0239
0244
0250
0255
0261
0266
0271
0277
0282
0288
02{)3
0299
0304
14
0237
0243
0248
0254
0259
0265
0270
0275
0281
0286
0292
0297
0302
16
0236
0242
0247
0252
0258
0263
0269
0274
0279
0285
0290
0295
0301
18
6 20
0235
0240
0246
0251
0257
0262
0267
0266'
0273
0278
0283
0289
0294
0299
-- —
0234
0239
0245
0250
0255
0261
0271 0276
0282 1 0287
0292
0298
22
0233
0238
0243
0249
0254
0259
0264
0270 0275
0280 ! 0286
0291
0296
24
0231
0237
0242
0247
0253
0258
0263
0268 ' 0274
0279 1 0284
0289
0295
26
0236
0241
0246
0251
0257
0262
0267 ' 0272
0277 ! 0283
0288
0293' 1
28
0234
0233
0240
0238
0245
0244
0250
0249
0255
0254
0260
0259"
0266 j 0271
0276
0275
0281
0280
0286
0292
02971
6 30
0264
0270
0285
0290
0295 1
32
0232
0237
0242
0248
0253
0258
0263
0268 1 0273
0278
0284
0289 , 0294
34
0231
0236
0241
0246
0251
0257
0262
0267 0272
0277
0282
0287 ' 0292
36
0230
0235
0240
0245
0250
0255
0260
0266
0271
0276
0281
0286 0291
38
0229
0234
0239
0244
0249
0254
0253
0259
0264
0269
0274
0273
0279
0284 0290
6 40
0227
0232
0238
0243
0248
0258
0263 ; 0268
0278
0283
0288
42
0226
0231
0236
0241
0246
0252
0257
0262
0267
0272
0277
0282
0287
44
0225
0230
0235
0240
0245
0250
0255
0260
0265
0270
0275
0280
0285
46
0224
0229
0234
0239
0244
0249
0254
0259
0264
0269
0274
0279 i 0284
48
0223
0222
0228
0233
0238
0237
0243
0242
0248
024'7"
0253
0252
0258
0257
0263
0262
0268
0266
0273
0278 I 0283
0276 1 0281
6 50
0227
0232
0271
52
0221
0226
0231
0236
0241
0246
0250
0255
0260
0265
0270
0275 0280
54
0220
0225
0230
0235
0239
0244
0249
0254
0259
0264
0269
0274 0279
56
0219
0224
0229
0233
0238
0243
0248
0253
0258
0263
0267
0272 , 0277
58
0218
0223
0227
0232
0237
0242
0247
0252
0257
0261
0266
0271 i 0276
7
0217
0222
0226
0231
0236
0241
0246
0251
0255
0260
0265
0270
02751
APPENDIX V: TABLE II.
[Page 297
Log. A, for computing the Mrst Correction of the Lunar Distance.
App.
alt. of
moon.
Reduced parallax and refraction of moon.
44'
46'
46' 47'
48' 49'
50'
51'
5*'
68'
sc
56'
56'
57'
7° 0'
.0222
0226
0231
0236
0241
0246
0251
0255
0260
0265
0270
0275
3
.0220
0225
0230
0234
0239
0244
0249
0254
0258
0263
0268
0273
6
.0218
0223
0228
0233
0238
0242
0247
0252
t)257
0261
0266
0271
9
.0217
0222
0226
0231
0236
0241
0245
0250
0255
0260
0264
0269
12
.0215
0220
0225
0223
0230
0234
0239
0244
0248
0253
0251
0258
0256
0262
0267
7 15
.0214
0219
0228
0233
0237
0242
0247
0261
0265
18
.0213
0217
0222
0226
0231
0236
0240
0245
0250
0254
0259
0263
21
.0211
0216
0220
0225
0230
0254
0239
0243
0248
0253
0257
0262
24
.0210
0214
0219
0223
0228
0233
0237
0242
0246
0251
0255
0260
27
.0208
0213
0217
0222
0227
0231
0230
0236
0240
0239
0245
0243
0249
0248
0254
0258
7 30
.0207
0211
0216
0220
0225
0234
0252
0257
33
.0206 ! 0210
0215
0219
0224
0228
0232
0237
0241
0246
0250
0255
36
.0204 0209
0213
0218
0222
0227
0231
0235
0240
0244
0249
0253
39
.0203 1 0207
0212
0216
0221
0225
0229
0234
0238
0243
0247 ^ 0252
42
.0202 1 0206
.0200 0205
0210
0209
0215
0219
0224
"0222
0228
022/
0232
"0231
0237
C)235
0241
"0240
0246 1 0250
"0244 0248
7 45
0213
0218
48
.0199 0203
0208
0212
0216
0221
0225
0229
0234
0238
0242
0247
51
.0198 ! 0202
0206
0211
0215
0219
0224
0228
0232
0237
0241
0245
0249
54
.0196 i 0201
0205
0209
0214
0218
0222
0227
0231
0235
0239
0244
0248
57
.0195
0200
0204
0208
0212
0217
0221 0225
0219 , 0224
0229
0228
0234
0232
0238
0242
0246
"0245"
8
.0194
0198
0203
0207
0211
0215
0236
0241
3
.0193
0197
0201
0206
0210
0214
0218 1 0222
0227
0231
0235
0239
0243
6
.0192
0196
0200
0204
0208
0213
0217 i 0221
0225
0229
0233
0238
0242
9
0195
0199
0203
0207
0211
0215 i 0220
0224
0228
0232
0236
0240
12
0193
0198
0202
0206
0210
0214
0218
0217
0222
0221
0227
0225
0231
0235
0239
0237
8 15
0192
0196
0201
0205
0209
0213
0229
0233
18
0191
0195
0199
0203
0207
0212
0217
0220
0224
0228
0232
0236
21
0190
0194
0198
0202
0206
0210
0214
0218
0222
0226
0231
0235
24
0189
0193
0197
0201
0205
0209
0213
0217
0221
0225
0229
0233
27
0188
0192
0191
0196
0195
0200
0204
0208 1 0212
0216
0220
0219
0224
0228
0226
0232
0230
8 30
0187
0199
0203
0207
0211
0215
0223
33
0186
0190
0193
0197
0201
0205
0209
0213
0217
0221
0225
0229
36
0184
0188
0192
0196
0200
0204
0208
0212
0216
0220
0224
0228
39
0183
0187
0191
0195
0199
0203
0207
0211
0215
0219
0223
0226
42
0182
0186
0190
0194
0198
0202
0201
0206
"0205
0210
"0208
0214
0212
0217
0216
0221
0220
0225
0224"
8 45
0181
0185
0189
0193
0197
48
0180
0184
0188
0192
0196
0200
0203
0207
0211
0215
0219
0223
51
0179
0183
0187
0191
0195
0198
0202
0206
0210
0214
0218
0221
54
0178
0182
0186
0190
0193
0197
0201
0205
0209
0212
0216
0220
57
0177
0181
0180
0185
0184
0189
0i8"8
0192
0196
0200
0204
0208
0211
0215
0219
9
0176
0191
0195
0199
0203
0206
0210
0214
0218
O
0175
0179
0183
0186
0190
0194
0198
0201
0205
0209
0213
0216
6
0174
0178
0182
0185
0189
0193
0197 1 0200
0204
0208
0211
0215
9
0173
0177 I 0181
0184
0188
0192
0196 i 0199
0203
0207
0210
0214
12
0172
0176
0180
0179
0183
0187
0191
0194
0193
0198
0197
0202
0201
0206
0204
0209
0213
9 15
0171
0175
0182
0186
0190
0208
0212
18
0170
0174 1 0178
0181
0185
0189
0192
0196
0200
0203
0207
0211
21
0170
0173 0177
0180
0184
0188
0191
0195
0199
0202
0206
0209
24
0172 0176
0179
0183
0187
0190
0194
0198
0201
0205
0208
27
0171
0175
0174
0179
0182
0186
0189
0193
0196
0195
0200
0199"
0204
0207
9 30
0170
0178
0181
0185
0188 , 0192
0203
0206
33
0170 : 0173
0177
0180
0184
0187 i 0191
0194
0198
0201
0205
36
0169 i 0172
0176
0179
0183
0186 : 0190
0193
0197
0200
0204
39
0168 1 0171
0175
0178
0182
0185 ; 0189
0192
0196
0199
0203
42
0167
0170
0174
0173
0177
0176
0181
0180
0184 j 0188
0191
0190
0195
"0194"
0198
"0197"
0202
"0201"
9 45
0166
0169
0183
0187
1
48
0165
0169
0172
0176
0179
0182
0186
0189
0193
0196
0200
0203
51
54
0164
0168
0171
0175
0178
0182
0185
0188
0192
0195
0199
0202
0163 ! 0167
0170
0174
0177
0181
0184
0187
0191
0194
0198
0201
0/
10
0163 1 0166
0169
0173
0176
0180
0183
0186
0186
0190
0189
0193
0197
0200
0162 1 0165
0169
0172
0175
0179 0182
0192
0196 ! 0199
Page 298] APPENDIX V:. TABLE II.
Log. A, for computing the First Correction of tlie Lunar Distance.
App
alt. of
moon.
Reduced parallax and refraction of moon. 1
46'
4J'
48'
49'
sec
51'
52'
58'
54' 55'
5«'
57'
58'
10° 0'
5
10
15
20
25
.0162
.0160
.0159
.0158
.0156
.0155
0165
0164
0162
0161
0160
0158
0169
0167
0166
0164
0163
0162
0172
0171
0169
0168
0166
0165
0175
0174
0172*
0171
0170
0168
0179
0177
0176
0174
0173
0171
0182
0181
0179
0178
0176
0175
0186
0184
0182
0181
0179
0178
0189 ■. 0192
0187 0191
0186 i 0189
0184 , 0187
0183 0186
0181 0184
0196
0194
0192
0191
0189
0188
0199
0197
0196
0194
0192
0191
10 30
35
40
45
50
55
11
5
10
15
20
25
11 30
35
40
45
50
55
.0154
.0153
.0151
.0150
.0149
.0148
0157
0156
0155
0153
0152
0151
0160
0159
0158
0157
0155
01.54
0153"
0152
0151
0149
0148
0147
0146
0145
0144
0143
0142
0141
0164
0162
0161
0160
0158
0157
0156
0155
0154
0152
0151
0150
0167
0166
0164
0163
0162
0160
0170
0169
0167
0166
0165
0163
0173
0172
0171
0169
0168
0167
0165
0164
0163
0161
0160
0159
0158
0157
0156
0154
0153
0152
0177
0175
0174
0172
0171
0170
0168
0167
0166
0164
0163
0162
0180
0178
0177
0175
0174
0173
0183
0181
0180
0179
0177
0176
0186
0185
0183
0182
0180
0179
0189
0188
0186
0185
0183
0182
0181
0179
0178
0176
0175
0174
.0147
.0146
0150
0149
0148
0146
0145
0144
0159
0158
0157
0155
0154
0153
0152
0151
0150
0149
0148
0146
0162
0161
0160
0158
0157
0156
0171
0170
0169
0167
0166
0165
0174
0173
0172
0170
0169
0168
0177
0176
0175
0173
0172
0171
0143
0142
0141
0140
0139
0138
0149
0148
0147
0146
0145
0144
0155
0154
0153
0151
0150
0149
0161
0160
0158
0157
0156
0155
0164
0162
0161
0160
01.59
0158
0167
0165
0164
0163
0162
0161
0159
0158
0157
0156
0155
0154
0170
0168
0167
0166
0165
0163
0172
0171
0170
0169
0167
0166
12
5
10
15
20
25
12 30
35
40
45
50
55
0137
0136
0135
0134
0133
0132
0140
0139
0138
0137
0136
0135
0143
0142
0141
0140
0139
0138
0145
0144
0143
0142
0141
0140
0148
0147
0146
0145
0144
0143
0151
0150
0149
0148
0147
0146
0154
0153
0152
0151
0150
0148
0147
0146
0145
0144
0143
0142
0157
0156
0154
0153
0152
0151
0162
0161
0160
0159
0158
0157
0165
0164
0163
0162
0160
0159
0131
0130
0129
0129
0128
0127
0134
0133
0132
0131
0130
0129
0137
0136
0135
0134
0133
0132
0139
0138
0137
0136
0136
0135
0142
0141
0140
0139
0138
0137
0145
0144
0143
0142
0141
0140
0150
0149
0148
0147
0146
0145
0153
0152
0151
0150
0149
0148
0155
0154
0153
0152
0151
0150
0158
0157
0156
0155
0154
0153
0158
0156
0155
13
5
10
15
20
25
0126
0125
0124
0123
0123
0122
0129
0128
0127
0126
0125
0124
0131
0130
0129
0129
0128
0127
0134
0133
0132
0131
0130
0129
0129
0128
0127
0126
0125
0124
0136
0135
0135
0134
0133
0132
0131
0130
0129
0128
0128
0127
0139
0138
0137
0136
0135
0134
0141
0141
0140
0139
0138
0137
0144
0143
0142
0141
0140
0139
0147
0146
0145
0144
0143
0142
0149
0148
0147
0146
0145
0144
0143
0142
0142
0141
0140
0139
0152
0151
0150
0149
0148
0147
01.54
0153
0152
0151
0150
0149
13 30
35
40
45
50
55
0121
0120
0120
0124
0123
0122
0121
0120
0120
0126
0125
0124
0124
0123
0122
0133
0133
0132
0131
0130
0129
0136
0135
0134
0133
0132
0132
01,38
0138
0137
0136
0135
0134
0141
0140
0139
0138
0137
0136
0146
0145
0144
0143
0142
0141
0148
0147
0146
0145
0145
0144
14
5
10
15
20
.25
14 30
3,5
40
45
50
55
0119
0118
0117
0117
0116
0115
0121
0121
0120
0119
0118
0118
0124
0123
0122
0121
0121
0120
0126
0125
0124
0124
0123
0122
0121
0121
0120
0119
0118
0118
0128
0128
0127
0126
0125
0124
0131
0130
0129
0128
0128
0127
0133
0132
01,32
0131
01,30
0129
01.36
01,%5
0134
01,33
0132
0131
0138
0137
0136
0135
0135
0134
0140
0139
0139
0138
0137
0136
0135
0134
0134
0133
0132
01,31
0143
0142
0141
0140
0139
0138
0114
0114
0113
0112
0112
0111
0117
0116
0115
0115
0114
0113
0119
0118
0118
0117
0116
0116
0124
0123
0122
0121
0121
0120
0126
0125
0124
0124
0123
0122
0128
0128
0127
0126
0125
0124
0131
0130
0129
0128
0127
0127
0133
0132
0131
0130
0130
0129
0137
0137
0136
0135
0134
0133
15
0110
0113
0115
0117
0119
0121
0124
0126
0128
Ol.M
0133
APPENDIX Y: TABLE 11. [Page 299
Log;. A, for computing the First Correction ot the Lunar Distance.
App.
alt. ot
nnx>n.
Reduced parallax and refraction of moon. 1
43' 49'
50'
5t'
52'
58'
54'
55' 66' 1 87'
58'
59'
15° 0'
.0110 ' 0113
0115
0117
0119
0121
0124
0126 i 0128
0130
0133
10
.0109
0111
0113
0116
0118
0120
0122
0124
0127
0129
0131
20
.0108
0110
0112
0114
0116
0119
0121
0123
0125
0127
0129
30
.0107
0109
0111
0113
0115
0117
0119
0121
0124
0126
0128
40
.0105
0107
0110
0112
0114
0116
0118
0117
0120
0122
0124
0126
0125
50
.0104
0106
0108
0110
0112
0115
0119
0121
0123
16
.0103
0105
0107
0109
0111
0113
0115
0117
0119
0121
0124
10
.0102
0104
0106
0108
0110
0112
0114
0116
0118
0120
0122
20
.0101
0103
0105
0107
0109
0111
0113
0115
0117
0119
0121
30
.0100
0102
0103
0105
0107
0109
0111
oiia
0115
0117
0119
40
.0098
0100
0102
0104
0106
0108
0110
0112 10114
0116
0118
50
.0097
0099
0101
0103
0105
0107
0109
0111 '0113
0115
0117
17
.0096
0098
0100
0102
0104
0106
0108 i 0110 1 0112
0114
0116
10
.0095
0097
0099
0101
0103
0105
0107 ! 0109 ' 0110
0112
0114
20
.0094
0096
0098
0100
0102
0104
0106 ; 0107 j 0109 1 0111
0113
30
0095
0097
0099
0101
0103
0104 i 0106 1 0108 ! OHO
0112
40
0094
0096
0098
0100
0101
0103
0105 ! 0107 ! 0109
0111
50
0093
0095
0097
0099
0100
0102
0104
0106 0108
0109
18
0092
0094
0096
0098
0099
0101
0103
0105 0107
0108
10
0091
0093
0092"
0095
0097
0098
0100
0102
0104
0105
0107
0109
20
0090
0094
0096
0097
0099 1 0101
0103
0104
0106
0108
30
0089
0091
0093
0095
0096
0098 1 0100
0102
0103
0105
0107
40
0088
0090
00!i»2
0094
0095
0097 l0099
0101
0102
0104
0106
50
0088
0089
0091
0093
0094
0096 0098 ! 0099 j 0101
0103
0105
19
0087
0088
0090
0092
0093
0095
0097 1 0098
0100
0102
0104
10
0086
0087
0089-
0091
0092
0094
0096
0098
0099
0101
0103
20
0085
0087
0088
0090
0092
0093
0095
0097- 1 0098
0100
0102
30
0084
0086
0087
0089
0091
0092
0094
0096 10097
0099
0101
40
0083
0085
0087
0088
0090
0091
0093 0095 0096
0098
0100
50
20
0082
0084
0086 0087
0089
0090 1 0092 0(194
0090 0091 0093
0095
0097
0099
0082
0083
0085 i 0086
0088
0094 0096
0098
10
0081
0082
0084
0086
0087
0089 0090 0092 0093 0095
0097
20
0080
0082
0083
0085
0086
0088 0089 0091 0093 0094
0096
30
0079
0081
0082
0084
0086
0087 , 0089 0090 0092 0093
0095
40
0079
0080
0082
0083
0085
0086 1 0088
0085 , 0087
0089
0091 0092
0094
50
0078
0079
0081
0082
0084
0088
0090 0091
0093
21
0077
0079
0080
0082
0083
0085 i 0086
0088
0089 0091
0092
10
0076
0078
0079
0081
0082
0084 ! 0085
0087
0088 0090
0091
20
0076
0077
0079
0080
0082
0083 i 0085
0086
0087 1 0089
0090
30
0075
0076
0078
0079
0081
0082 0084
0082 0083
0085
'0084"
0087
"0086
0088
0090
40
0074
0076
0077
0079
0080
0087
0089
50
0074
0075
0076
0078
0079
0081 : 0082
0084
0085 ! 0086
0088
22
0073
0074
0076
0077
0079
0080 : 0081 0083
0084
0086
0087
10
0072
0074
0075
0076
0078
0079 0081
0082
0083
0085
0086
20
0072
0071
0073
0074
0076
0077
0076
0079
0078
0080
0081
0083
0084
0086
30
0072
0074
0075
0079
0081
(X)82
0083
0085
40
0070
0072
0073
0074
0076
0077
0079
0080
0081
0083
0084
50
0070
0071
0072
0074
0075
0076
0078
0079
0081
0082
0083
23
0069
0070
0072
0073
0074
0076
0077
0078
0080
0081
0082
10
0068
0070
0069
0071
0070
0072
0074
0075
0076
0O76
0078
0077
0079
0080
0082
20
0068
0072
0OZ3
0074
0078 : 0080
0081
30
0067
0069
0070
0071
0072
0074
0075
0076
0078 i 0079
0080
40
0067
0068
0069 0071
0072
0073
0074
0076
0077
0078
0080
50
0066
0067
0069 0070
0071
0073
0074
0075
0076
0078
0079
24
0067
0066
0068 0069
0067 '0069"
0071
0070
0072
0073
0073
0074
0074
0076
0077
0078
10
0071
0075
0076
0078
20
0066
0067 , 0068
0069
0071
0072
0073
0074
0076
0077
30
0065
0066
0068
0069
0070
0071
0072
0074
0075
0076
40
0065
0066
0067
0068
0069
0071 ; 0072
0073
0074
0076
50
0064
0065
(X)65
0066
0066
0068
0069 1 0070
0071
0072
0074
0075
25
0063
0067
0068
0069
0071
0072 0073
0074
Page 300] APPENDIX V: TABLE II
Log. A, for computing the First Correction of the Lnniir Distance.
App.
alt. of
moon.
Reduced parallax and refraction of moon. 1
50'
51'
52'
58' 54'
oC 56'
5J' 58'
59'
80'
25° 0'
.0063
0065
0066
0067 ' 0068
0069 0071
0072 0073
0074
20
.0062
0064
0065
0066 0067 : 0068 0069 1 0071
0072
0073
40
.0061
0062
0064
0065 0066 i 0067 ; 0068 ! 0069
0071
0072
26
.0060
0061
0063
0064 0065 : 0066 0067 | 0068
0069
0071
20
.0059
.0058"
0060
0062
0063 0064 0065 i 0066 : 0067
0062 0063 0064 [ 0065 ; 0066
0068
0067
0069
40
0059
0061
0068
27
.0057
0058
0060
0061 0062 i 0063 [ 0064 j 0065
0066
0067
20
.0056
0057
0059
0060 0061 ' 0062
0063 ! 0064
0065
0066
•
40
.0055
0057
0058
0059 0060 : 0061
0062 ' 0063
0064
0065
28
20
.0055 1 0056
0057
0056
0058 0059 •0060
0061 : 0062
0063
0062
0064
.0054
0055
0057 0058 0059 ; 0060 I 0061
0063
40
.0053
0054
0055
0056 0057 0058 I 0059 | 0060
0061
0062
29
.0052
0053
0054 ' 0055 0056 0057 1 0058 1 0059
0060
0061
20
.0051 , 0052
0053 : 0054 0055 0056 ; 0057 , 0058
0059
0060
40
30
.0050 [ 0051
.00501 0051"
0052 ! 0053 0054 0055 ! 0056 ; 0057
0b5"l"j 0052" 0053 ;"0054 ; 0055 ; 0056
0058
0057
0059
0058
20
.0049 I 0050
0051 '■ 0052 0052 0053 i 0054 0055
0056
0057
1
40
.0048 1 0049
0050 , 0051 0052 0053 ! 0053 ' 0054
0055
0050
'
31
.0047 1 0048
0049 : 0050 i 0051 0052
0053 i 0053
0054
0055
20
40
.0047
.0046
0047
0048
0049 I 0050 0051
0052
0053
0052
0054
0053
0054
0054
0055
0047
0048
0048 1 0049 0050'
0051
0054
32
.0045 0046
0047
0048 ! 0048 0049
0050
0051
0052
0053
0054
1
20
.0044 0045
0046
0047 1 0048 . 0049
0049 : 0050
0051
0052
0053
40
.0044
0045
0045 { 0046 ! 0047 0048
0049 i 0049
0050
0051
0052
33
.0043
0044
0045 ! 0045 ! 0046 0047
0044 '' 0045 1 0046 0046
0048 1 0049
0047 1 0048
0049
0050
0050
0051
0050
1
20
.0042
0043
0049
40 .0042
0043
0043 : 0014 : 0045 0045
0046 : 0047
0048
0049
0050
34 .(X)41
0042
0043 0043 0044 0045 ' 0046 0046
0047
0048
0049
20 .0040
0041
0042 1 0043 , 0043 0044
0045 i 0046
0047
0047
0048
40 .0040
0041
0041
0042 1 0043
0044
0043
0044
0044"
0045
0044
0046
0047
0047
35 .0039
0040
0041
0041 i 0042
0045
0046
0047
20 .0039
0039
0040
0041 ! 0042 : 0042
0043
0044
0044
0045
0046
40
.0038
0039
0039
0040 1 0041 ; 0042 ; 0042
0043
0044
0044
0045
36
.0037
0038
0039
0040 1 0040 0041
0042
0042
0043
0044
0044
20
40
.0037
0038
0038
0039 ! 0040 0040
0041
0042
0042
0043
0044
.0036 1 0037
0038
0038 i 0039 i 0040
0040
0041
0042
0042
0043
37
.0036 0036
0037 0038 ; 0038 1 0039
0040
0040
0041
0042
0042
20
.0035
0036
0037
0037
0038
0039
0039
0040
0040
0041
0042
40
.0035
0035
0036
0037
0037
0038
0039
0039
0040
0040
0041
1
38
.0034
0035
0034
0035
0035
0036
0037
0037
0038
0039
0039
0040
0040
H
20
.0034
0036
0036
0037 1 0037
0038
0039
0039
0040
40
.0033
0034
0034
0035
0036
0036
0037
0037
0038
0039
0039
!
39
0033
0034
0034
0035
0036
0036
0037
0037
0038
0039
20
0033
0033
0034
0035
0035
0036
0036
0037
0037
0038
40
40
0032
0033
0033 ! 0034
0035
0035
0035
0036
0036
0037
0037
0032
0032
0033 0033
0034
0035
0036
0036
0037
20
0031
0032
0032 i 0033 i 0034
0034
0035
0035
0036
0036
40
0031 ' 0031
0032 ! 0032
0033
0034
0034
0035
0035
0036
41
0030
0031
0031 '' 0032
0033
0033
0034
0034
0035
0035
1
20
0030
0029
0030
0030
0031
0031
0032
0033
0033
0034
0034
0035
40
0030
0031
0032
0032
0033
0033
0034
0034
42
0029
0029
0030
0031
0031
0032
0032
0033
0033
0034
20
0029
0029
0030
0030
0031
0031
0032
0032
0033
0033
40
0028
0029
0029
0030 0030
0031
0031
0032
0032
0033
43
0028
0027
0028
0028
0029
0028
0029 i 0030
0030
0031
0031
0032
0032
0032
20
0029
0029 0030
0030
0031
0031
40
0027
0027
0028
0028
0029 0029
0030
0030
0031
0031
44
0026
0027
0027
0028
0028 0029
0029
0030
0030
0031
20
0026
0026
0027
0027 0028 1 0028
0029
002!)
0030
0030
40
0026
0026
0026
0027
0027
0028
0028
0028
0029
0028'
0029 i 0030
45
0025
0026
0026
0027
0027
0027
0029
0029
APPEKDIX V: TABLE II. [Page 301.
Log. A, for computing the First Correction of tlie Lunar Distance.
Apr.
alt. of
moon.
Reduced parallax and refraction of moon.
51'
52'
58'
64'
55'
56'
67'
58'
59'
60'
45° 0'
30
46
.30
47
30
48
.30
49
30
.0025
.0025
.0024
.0023
.0023
.0022
.0022
.0021
.0021
.0020
.0020
.0019
.0019
.0018
.0018
0026
0025
0024
0024
0023
0026
0025
0025
0024
0024
0027
0026
0025
0025
0024
0027
0026
0026
0025
0025
0024"
0023
0023
0022
0022
0027
0027
0026
0026
0025
0028
0027
0027
0026
0025
0028
0028
0027-
0026
0026
0029
0028
0027
0027
0026
0025"
0025
0024
0024
0023
0023
0022
0021
0021
0020
0029
0028
0028
0027
0026
0023
0022
0022
0021
0021
0023
0023
0022
0022
0021
0024
0023
0022
0022
0021
0024
0024
0023
0023
0022
0025
0024
0024
0023
0022
"0022
0021
0021
0020
0020
0025
0024
0024
0023
002;}
0022
0022
0021
0021
0020
0026
0025
0025
0024
0023
50
30
51
30
52
0020
0020
0019
0019
0018
0020
0020
0020
0019
0019
0021
0020
0020
0019
0019
0021
0021
0020
0020
0019
0022
0021
0020
0020
0019
0023
0022
0022
0021
0021
30
53
30
54
.30
.0018
.0017
.0017
.0016
.0016
0018
0017
0017
0016
0016
0018
0018
0017
0017
0016
0018
0018
0017
0017
0017
0019
0018
0018
0017
0017
0019
0018
0018
0018
0017
0019
0019
0018
0018
0017
0020
0019
0019
0018
0018
0020
0019
0019
0018
0018
0020
0020
0019
0019
0018
55
,30
56
30
57
30
58
30
59
30
.0015
.0015
.0015
.0014
.0014
0016
0015
0015
0014
0014
0016
0015
0015
0015
0014
0016
0016
0015
0015
0015
0016
0016
0016
0015
0015
0014
0014
0014
0013
0013
0017
0016
0016
0015
0015
0017
0016
0016
0016
0015
0017
0017
0016
0016
0015
0017
0017
0017
0016
0016
0018
0017
0017
0016
0016
.0014
.0013
.0013
.0012
.0012
0014
0013
0013
0013
0012
0014
0014
0013
0013
0012
0014
0014
0013
0013
0013
■0015
0014
0014
0013
0013
0015
0014
0014
0014
0013
0015
0015
0014
0014
0013
0015
0015
0014
0014
0014
0015
0015
0015
0014
0014
60
61
62
63
64
65
66
67
6S
69
.0012
.0011
.0011
.0010
.0009
.0009
.0008
.0008
.0007
.0007
0012
0011
0011
0010
0010
0009
0008
0008
0007
0007
0012
0011
0011
0010
0010
0012
0012
0011
0010
0010
0013
0012
0011
0011
0010
0009"
0009
0008
0008
0007
0007
0006
0006
0006
0(X)5
0013
0012
0011
0011
0010
(KX)9
0009
0008
0008
0007
0013
0012
0011
0011
0010
0010
0009
0008
0008
0007
0013
0012
0012
0011
0010
0013
0012
0012
0011
0010
0013
0013
0012
0011
0011
0010
0009
0009
0008
0008
0009
0009
0008
0008
0007
0009
0009
0008
0008
0007
0010 I 0010
0009 0009
0009 1 0009
0008 !0008
0008 '0008
70
71
72
73
74
.0007
.0006
.0006
. 0005
. 0005
. 0005
.0004
.0004
.0004
.0004
.0004
.0003
.0003
.0003
.0003
0007
0006
0006
0005
0005
"0005
0005
0004
0004
0004
0004
0003
0003
0003
0003
0003
0003
0003
0003
0003
0007
0006
0006
0006
0005
0007
0006
0006
0006
0005
0007
0006
0006
0006
0005
0007
0007
0006
0006
0005
0007
0007
0006
0006
0005
0005
0005
0C04
0004
0004
0007
0007
0006
0006
0005
0005
0005
0004
0004
0004
0004
0003
0003
0003
0003
0003
0003
0003
0003
0003
0007
0007
0006
0006
0006
0005"
0005
0004
0004
0004
75
76
77
78
79
0005
0005
0004
0004
0004
0004
0003
0003
0003
0003
0003
0003
0003
0003
0003
0005
0005
0004
0004
0004
0004
0003
0003
0003
0003
0003
0003
(X103
0003
0003
0003
0005
0005
0004
0004
0004
0005
0005
0004
0004
0004
0005
0005
0004
0004
0004
80
81
82
83
84
a5
86
87
88
89
0004
0003
0003
0003
0003
0003"
0003
0003
(K103
0003
0003
0004
0003
0003
0003
00.03
0003
0003
0003
0003
0003
0003
0004
0003
0003
0003
0003
0003"
0003
0003
0003
0003
0004
0003
0003
0003
0003
0004
0003
0003
0003
0003
.0003
.0003
.0003
.0003
.0003
0003
0003
0003
0003
(X103
0003 1
0003
0003 i
0003
0003
90
.0003
0003 1 0003
0003
0003
0003
0003
Page 302] APPENDIX V: TABLE III.
Log. B, for computing the First Correction of the Lunar Distance.
App. alt.
of sun
or star.
Reduced refraction and parallax of sun or star. 1
0' 0"
0' 80"
V 0"
1' 80"
2' 0" i 2' 80"
8' 0" 8' 80"
4' 0"
4' 30"
0' 0"
5' 30"
5° 0'
10
20
30
40
•
50
6
20
40
7
9.9976
9. 9970
9. 9972
9. 9974
20
40
8
20
40
9. 9981
9. 9982
9. 9982
9. 9983
9. 9984
9.9985
9.9985
9. 9986
9. 9987
9. 9977
9. 9978
9. 9979
9. 9980
9. 9981
9. 9982
9.9983
9. 9983
9. 9984
9. 9986
9. 9987
9.9989
9.9990
9.9991
9. 9975
9.9976
9. 9977
9.9978
9. 9979
9
20
40
10
11
9.9992
9.9989
9. 9991
9, 9986
9. 9986
9. 9987
9.9988
9. 9989
9. 9980
9. 9981
9. 9982
9. 9982
9. 9984
9.9986
9.9987
12
13
14
15
16
9.'9997
9.9997
9. 9995
9.9995
9. 9996
9.9996
9. 9993
9. 9994
9.9994
9.9995
9. 9995
9. 9992
9.9992
9. 9993
9.9994
9. 9994
9. 9990
9. 9991
9. 9992
9. 9993
9. 9993
9.9995
9.9996
9. 9989
9.9990
9. 9991
9. 9992
9. 9993
18
20
25
30
50
0.0001
0.0001
0.0001
0.0000
0.0000
0.0001
0.0001
9.9999
9.9999
0.0000
0.0000
0.0001
9. 9998 i 9. 9997
9.9998 9.9998
9. 9999 i 9. 9999
0. 0000 i 0. 0000
0. 0001 0. 0001
9.9996
9. 9997
9.9998
9.9999
9. 9995
9.9996
9. 9998
90
0.000110.0002
0. 0002 i 0. 0002
App. alt.
of sun
or star.
Reduced refraction and parallax of sun or star. 1
6' 0"
6' 80"
T 0" 1 J' 80"
8'0"
8' 80"
9' 0"
0' 80"
10' 0"
10' 80"
11' 0"
11' 80"
5° 0'
10
20
30
40
9. 9959
9.9960
9. 9962
9. 9963
9. 9965
9. 9967
9.9968
9. 9970
9.9971
9. 9973
9.9974
9. 9975
9.9951
9.9953
9.9954
9.9956
9.9957
9.9947
9. 9949
9. 9951
9. 9952
9. 9954
9.9944
9.9946
9. 9948
9. 9949
9. 9951
9. 9940
9. 9942
9. 9944
9. 9946
9.9948
9. 9949
9. 9951
9. 9954
9.9956
9. 9958
9. 9960
9.9962
9. 9964
9. 9937
9. 9939
9. 9941
9. 9943
9.9944
9. 9946
9. 9948
9. 9951
9.9953
9. 9956
9. 9958
9. 9933
9.9935
9. 9937
9. 9939
9.9941
9.9929
9.9932
9.9934
9.9936
9. 9938
9. 9926
9. 9928
9. 9931
9. 9933
9. 9935
9. 9922
9. 9925
9. 9927
9.9929
9.9932
9. 9919
9. 9921
9. 9924
50
6
20
40
7
9.9965
9.9966
9. 9968
9.9969
9.9971
9. 9972
9. 9974
9.9975
9.9976
9.9977
9.9958 9.9955
9.9960 9.9957
9.9962 9.9959
9.9964 9.9961
9.9966 9.9963
9. 9952
9. 9954
9. 9956
9. 9959
9. 9961
9. 9963
9.9965
9. 9966
9.9968
9. 9943
9. 9945
9. 9948
9. 9951
9. 99.53
9. 9940
9. 9942
9. 9945
9. 9948
9. 9937
9. 9939
20
40
8
20
40
9. 9968
9.9969
9. 9971
9. 9972
9.9973
9.9974
9. 9975
9. 9976
9. 9977
9. 9965
9. 9967
9. 9968
9.9970
9.9971
9.9972
9
20
40
10
11
9. 9978
9.9979
9.9980
9. 9981
9.9983
9. 9976
9.9977
9. 9978
9. 9979
9.9981
12
13
14
15
16
9.9985
18
20
25
30
50
•
90
APPENDIX V: TABLE IV. [Page 303
Log. C, for computing the First Correction .of the Lunar Distance.
App. alt.
of sun
or star.
Reduced refraction and parallax of sun or star. 1
O'O"
O'SO"
I'O"
I'SO"
ro"
4' 80"
8'0"
S'80"
t'O"
*'80"
O'O"
S'80"
.5° (T
20
40
6
20
9. 9969
40
S
9
10
9.9990
9.9991
9.9992
9.9993
9. 9993
9. 9994
9.9994
9. 9994
9. 9995
9. 9996
9.9988
9.9984
9.9986
9. 9987
9. 9988
9. 9989
9.9990
9.9991
9.9980
9.9982
9. 9984
9. 9986
9. 9987
9. 9988
9. 9989
9.9990
9.9990
9. 9991
9.9974
9. 9978
9. 9980
9. 9982
'979984
9.9985
9.9987
9.9988
9.9989
9. 9970
9. 9972
9. 9975
9. 9978
9.9981
11
12
13
14
15
9.9995
9.9993
9.9994
9.9994
9.9995
9.9995
9. 9995
9. 9996
9. 9997
9.9989
9. 9990
9.9991
9. 9991
9.9992
9. 9982
9. 9984
9. 9985
16
17
18
20
25
9.9998
9.9999
9.9997
9.9998
9.9998
9.9996
9.9996
9.9996
9.9997
9. 9998
9.9998
9. 9999
9. 9999
9. 9993
9. 9993
9. 9994
9. 9994
9. 9996
9.9992
9.9992
9.9993
9.9993
.
30
40
50
90
0.0000
o.axK)
0.0000
0.0000
0.0000
0.0000
9.9999
9.9999
0.0000
0.0000
9.9999
9. 9999
9.9999
0.0000
9.9998
9.9999
9.9997
3
App.alt.
of sun
or star.
Reduced refraction and parallax of sun or star. 1
6'0"
6' 80"
7'0"
7' 80" 8' 0" 8' «aC
. 9'0"
»' 80" 10' 0"
10'80"
H'O"
11' 80"
5° (y
20
40
6
20
9.9962
9.9964
9. 9966
9.9956
9.9959
9.9961
9.9963
9. 9965
9.9967
9.9971
9. 9974
9. 9977
9.9949
9.9953
9. 9955
9. 9958
9. 9960
9. 9962
9. 9964
9.9969
9. 9972
9.9975
9.9946 9.9942 9.9938
9.9949 9.9946 9.9942
9. 9952 ; 9. 9949 9. 9946
9.995519.9952 9.9949
9. 9957 i 9. 9955 9. 9952
9. 993.5
9. 9939
9. 9943
9. 9946
9. 9949
9. 9951
9. 9954
9.9960
9.9931
9. 9936
9. 99,39
9. 9943
9. 9946
9.9949
9.9951
9. 9927
9. 9932
9. 9936
9. 9940
9. 9943
9.9924
9.9929
9.9933
9.9937
9.9920
9. 9925
9.9930
9.9916
9.9922
40
7
8
9
10
9. 9968
9. 9969
9. 9973
9.9976
9. 9979
9. 9960 i 9. 9957
9. 9962 9. 9959
9. 9966 i 9. 9964
9. 9970 1 9. 9968
9. 9954
9. 9956
9.9962
9.9946
11
12
13
14
15
9.9981
9.9983
9. 9979
16
17
18
20
25
r
30
40
50
90
1
1
Page 304]
APPENDIX V: TABLE V. 1
Log. D, for computing the First Correction of the Lunar Distance.
App
alt. of
moon.
Reduced parallax and refraction of moon.
41'
42'
4S'
44'
45'
46'.
47'
48' j 4»'
50'
61' 52' 1 53'
54'
55'
5° 0'
.0283
0290
0296
0303
0310
0316
0323
0329
0336
0343
0349 0356 ' 0362
0369
3
.0280
0287
0293
0300
0307
0313
0320
0326
0333
0339
0346
0.^52 ' 03.59
0365
6
.0277
0284
0291
0297
0304
0310
0317
0323
0330
0336
0342
0349
0,355
0362
9
.0275
0281
0288
0294
0301
0307
0313
0320
0326
0333
0339
0345
0352
0358
12
5 15
.0272
0279
0285
0282
0291
0289
0298
0295
0304
0310
0317 j 0323
0330
0336
0333
0342
0349
03.55
.0270
0276
0301
0308
0314
0320
0326
0339
0345
0351
18
.0267
0273
0280
0286
0292
0298
0305
0311
0317
0323
0330
0336
0342
0348
21
.0264
0271
0277
0283
0289
0296
0302
0308
0314
0320
0327
0333
0339
0345
2-i
.0262
0268
0274
0281
0287
0293
0299
0305
0311
0317
0324
.0330
0336
0342
27
5 m
.0260
".0257"
0266
0263
0272
0278
0284
0282
0290
"0288
0296
0294"
0302
"0300"
0308
0306"
0314
0312
0321
0318
0327
"0324
0333
"0330
0339
0336
0269
0275
33
.0255
0261
0267
0273
0279
0285
0291
0297
0303
0309
0315
0321
0327
0333
36
.0253
0259
0265
0271
0276
0282
0288
0294
0.300
0306
0312
0318
0324
0330
39
0256
0262
0268
0274
0280
0286
0292
0298
0303
0309
0315
0321
0327
42
0254
0260
0266
0272
0277
0275
0283
0289
028"7
0295
0292
0301 0306
0312
"0310
0318
0315"
0324
5 45
0252
0258
0263
0269
0281
0298
0304
0321
48
0250
0255
0261
0267
0273
0278
0284
0290
0295
0301
0307
0313
0318
51
0247
0253
0259
0265
0270
0276
0282
0287
0293
0299
0304
0310
0316
54
0245
0251
0257
0262
0268
0274
0279
0285
0290
0296
0302
0307
0313
57
0243
0241
0249
0247
0254
0252
0260
0266
0271
0269
0277
0275
0282
0288
0294
"0291
0299
0297'
0305
"0302
0310
6
0258
0263
0280
0286
0308
3
0239
0245
0250
0256
0261
0267
0272
0278
0283
0289
0294
0300
0305
6
0237
0243
0248
02.54
0259
0265
0270
0275
0281
0286
0292
0297
0302
9
0235
0241
0246
0252
0257
0262
0268
0273
0279
0284
0289
0295
0300
12
0233
0239
0244
0249
0255
0260
0266
0263
0271
0269
0276
0282
0287
0292
"0290"
0298
6 15
0231
0237
0242
0247
0253
0^58
0274
0279
0285
0295
18
0230
0235
0240
0245
0251
0256
0261
0267
0272
0277
0282
0288
0293
21
0228
0233
0238
0243
0249
0254
0259
0264
0270
0275
0280
0285
0290
24
0226
0231
0236
0342
0247
0252
0257
0262
0267
0273
0278
0283
0288
27
0229
0227
0234
0233
0240
"0238
0245
0243
0250
"0248
0255
0253"
0260
0258
0265
"0263
0271
0268
0276
0281
0286
0291
6 30
0274
0279
0284
0289
33
0226
0231
0236
0241
0246
0251
0256
0261
0266
0271
0276
0281
0287
36
0224
0229
0234
0239
0244
0249
0254
0259
0264
0269
0274
0279
0284
39
0222
0227
0232
0237
0242
0247
0252
0257
0262
0267
0272
0277
0282
42
0220
0225
0230
0235
02.34
0240
0239
0245
"0244
0250
0248
0255
0260
0265
0270
0275
0280
6 45
0219
0224
0229
0253
0258
0263
0268
0273
0278
48
0217
0222
0227
0232
0237
0242
0247
0251
0256
0261
0266
0271
0276
51
0216
0220
0225
0230
0235
0240
0245
02.50
0254
0259
0264
0269
0274
54
0214
0219
0224
0228
0233
0238
0243
0248
0253
0257
0262
0267
0272
57
0212
0217
0222
0220
0227
0225
0232
0230
0236
0235"
0241
02.39
0246
0244
0251
0249
0255
0260
0265
0270
7
0211
0216
0254
0258
0263
0268
3
0209
0214
0219
0223
0228
0233
0238
0242
0247
0252
0256
0261
026<i
6
0208
0212
0217
0222
0227
0231
0236
0241
0245
0250
0255
0259
0264
9
0211
0216
0220
0225
02.30
0234
0239
0243
0248
0253
0257
0262
12
0209
"0208
0214
0219
0223
0228
0226
0232
"0231
0237
0235
0242
0246
0251
0255
0260
7 15
0212
0217
0222
0240
0245
0249
0254
0258
18
0206
0211
0216
0220
0225
0229
0234
0238 1 0243
0247
0252
0256
21
0205
0209
0214
0219
0223
0228
0232
0237 1 0241
0246
0250
0255
24
0204
0208
0213
0217
0222
0226
0230
0235 j 0239
0244
0248
0253
27
0202
0207
0211
0210
0216
0214
0220
0224
0229
0233 i 0238
0242
0247
0251
0249
7 30
0201
0205
0218
0223
0227
0232 , 0236
0241
0245
33
0199
0204
0208
0213
0217
0221
0226
0230
0234
0239
0243
0248
36
0198
0202
0207
0211
0215
0220
0224
0229
0233
0237
0242
0246
39
0197
0201
0205
0210
0214
0218
0223
0227
0231
0236
0240
0244
42
0195
0200
0204
0203
0208
0213
0217
0221
0225
0230
0234
0238
0243
7 45
0194
0198
0207
0211
0215
0220
0224
0228
0232
0237
0241
48
0193
0197
0201
0205
0210
0214
0218
0222
0227
0231 i 0235
0239
51
0191
0196
0200
0204
0208
0213
0217
0221
0225
0229 0234
0238
54
0190
0194
0198
0203
0207
0211
0215
0219
0224
0228 ] 0232
0236
57
0189
0193
0197
0201
0200
0206
0204"
0210
0208
0214
0212
0218
0217
0222
0226 ! 0230
0235
8
0188
0192
0196
0221
0225 , 0229
0233
APPENDIX V: TABLE V. [Page 305
hon. D, for computing the First Correction of the Lunar Distance.
App.
alt. of
moon.
Reduced parallax and refraction of moon. 1
io'
46'
4J'
48'
49'
50'
51'
52'
58'
64'
65'
66' 67'
58'
8° O'
5
10
. 15
20
.0192
.0190
.0188
.0186
.0184
0196
0194
0192
0190
0188
0200
0198
0196
0194
0192
0204
0202
0200
0198
0196
0208
0206
0204
0202
0200
0212
0210
0208
0206
0204
0217
0214
0212
0210
0207
0205'
0203
0201
0199
0197
0221
0218
0216
0214
0211
0209
0207
0205
0203
0201
0199
0197
0195
0193
0191
0189
0187
0186
0184
0182
0180
0179
0177
0175
0174
0225
0222
0220
0218
0215
0229
0227
0224
0222
0219
0233
0231
0228
0226
0223
0237
0235
0232
0230
0227
25
8 30
35
40
45
50
55
9
5
10
15
20
25
9 30
35
.0182
.0180
.0178
.0176
.0174
0186
0184
0182
0180
0178
0190
0188
0186
0184
0182
0194
0192
0190
0188
0186
0197
0195
0193
0191
0189
0201
0199
0197
0195
0193
0213
0211
0209
0207
0205
0202
0200
0198
0197
0195
0217
0215
0213
0210
0208
0206
0204
0202
0200
0198
0221
0219
0216
0214
0212
0210
0208
0206
0204
0202
0225
0223
0220
0218
0216
. 0173
.0171
.0169
.0167
.0166
0176
0175
0173
0171
0169
0180
0178
0177
0175
0173
0184 i 0188
0182 j 0186
0180 0184
0178 0182
0177 1 0180
0191
0189
0188
0186
0184
0195
0193
0191
0189
0187
0214
0212
0209
0207
0205
0203
0201
0199
0198
0196
.0164
.0163
.0161
0168
0166
0165
0163
0161
0171
0170
0168
0166
0165
0175
0173
0172
0170
0168
0179
0177
0175
0173
0172
0182
0180
0179
0177
0175
0174
0172
0170
0169
0167
0186
0184
0182
0180
0179
0177
0175
0174
0172
0171
0169
0167
0166
0164
0163
0193
0191
0189
0187
0185
0184
0182
0180
0179
0177
0196
0194
0193
0191
0189
0200
0198
0196
0194
0192
40
45
50
55
10
5
10
15
20
25
0160
0158
0157
0156
0154
0163
0162
0160
0159
0157
0167
0165
0164
0162
0161
0170
0169
0167
0165
0164
0187
0185
0184
0182
0180
0191
0189
0187
0185
0184
0194
0192
0190
0189
0187
0195
0194
0192
0190
0153
0151
0150
0149
0147
0156
0155
0153
0152
0150
0159
0158
0156
0155
0154
0162
0161
0160
0158
0157
0165
0154
0153
0151
0150
0166
0164
0163
0161
0160
0158
0157
0156
0154
0153
0152"
0150
0149
0148
0147
0172
0171
0169
0168
0166
0175
0174
0172
0171
0169
016'8
0166
0165
0163
0162
0179
0177
0175
0174
0172
0182
0180
0179
0177
0175
0185
0183
0182
0180
0179
0188
0187
0185
0183
0182
10 30
35
40
45
50
55
11
5
10
15
0146
0145
0143
0142
0141
0149
0148
0147
0145
0144
0152
0151
0150
0148
0147
0162
0160
0159
0157
0156
0155'
0153
0152
0151
0150
0165
0163
0162
0160
0159
0158
0156
0155
0154
0152
0171
0169
0168
0166
0165
0174
0172
0171
0169
0168
0177
0175
0174
0172
0171
0170
0168
0167
0165
0164
0180
0179
0177
0175
0174
'0172
0171
0170
0168
0167
0140
0139
0137
0143
0142
0140
0139
0138
0146
0145
0143
0142
0141
0149
0147
0146
0145
0144
0161
0159
0158
0157
0155
0164
0162
0161
0159
0158
0167
0165
0164
0162
0161
20
25
11 30
35
40
0137
0136
0135
0133
0132
0140
0139
0137
0136
0135
0143
0141
0140
0139
0138
0145
0144
0143
0142
0141
0148
0147
0146
0145
0143
0151
0150
0149
0147
0146
0154
0153
0151
0150
0149
0157
0156
0154
0153
0152
0160
0158
0157
0156
0154
0163
0161
0160
0159
0157
0166
0164
0163
0161
0160
45
50
55
12
5
0131
0130
0129
0128
0127
0134
0133
0132
0131
0130
0137
0136
0135
0134
0132
0140 0142
0138 0141
0137 0140
0136 0139
0135 0138
0145
0144
0143
•0142
0140
0148
0147
0145
0144
0143
0142
0141
0140
0139
0138
0150
0149
0148
0147
0146
0153
0152
0151
0150
0148
0156
0155
0153
0152
0151
0169
0167
0156
0155
0154
10
15
20
25
12 30
0126
0125
0124
0123
0122
0129
0128
0127
0126
0125
0131
0130
0129
0128
0127
0134
0133
0132
0131
0130
0137
0136
0135
0133
0132
0139
0138
0137
0136
Oia5
0145
0143
0142
0141
0140
0147
0146
0145
0144
0143
0150
0149
0147
0146
0145
0162
0161
0160
0149
0148
35
40
45
50
55
0121
0120
0119
0118
0118
0124
0123
0122
0121
0120
0126
0125
0124
0123
0123
0129
0128
0127
0126
0125
0131
0130
0129
0128
0127
0134
0133
0132
0131
0130
0136
0135
0134
0133
0132
0139
0138
0137
0136
0135
0141
0140
0139
0138
0137
0144
0143
0142
0141
0140
0147
0145
0144
0143
0142
0141
0147
0146
0145
13
0117
0119
0122
0124
0126
0129
0131
0134
0136
0139
0143
24972°— 12-
-20
Page 306] APPENDIX V: TABLE V.
Log. D, for computing the First Correction of the Lunar Distance.
App.
alt. of
moon.
Reduced parallax and refraction of moon.
47'
48'
49'
50'
51'
52'
53'
54'
55'
66'
5J'
58'
50'
13° 0'
10
20
30
40
.0117
.0115
.0113
.0112
0119
0117
0116
0114
0112
0122
0120
0118
0116
0114
0124
0122
0120
0119
0117
0126
0125
0123
0121
0119
0129
0127
0125
0123
0121
0131
0129
0127
0125
0124
0134
0132
0130
0128
0126
0136
0134
0132
0130
0128
0139
0137
0134
0132
0131
0141
0139
0137
0135
0133
0131
0129
0127
0125
0123
0143
0141
0139
0137
0135
0133
0131
0129
ai27
0126
50
14
10
20
30
0111
0109
0107
0106
0104
0113
0111
0110
0108
0106
0115
0113
0112
0110
0109
0117
0116
0114
0112
0111
0120
0118
0116
0114
0113
0122
0120
0118
0117
0115
0124
0122
0121
0119
0117
0126
0125
0123
0121
0119
0129
0127
0125
0123
0121
40
50
15
10
20
30
40
50
16
10
0103
0101
0100
0099
0097
0105
0103
0102
0101
0099
0107
0106
0104
0103
0101
0109
0108
0106
0105
0103
0111
0110
0108
0107
0105
0113
0112
0110
0109
0107
0106
0104
0103
0101
0100
0115
0114
0112
0111
0109
0108
0106
0105
0103
0102
0118
0116
0114
0113
0111
0110"
0108
0107
0105
0104
0120
0118
0116
0115
0113
0112
0110
0108
0107
0106
0122
0120
0118
0117
0115
0113
0112
0110
0109
0107
0124
0122
0120
0119
0117
0096
0094
0093
0092
0091
0089"
0088
0087
0086
0085
0098
0096
0095
0094
0093
0100
0098
0097
0096
0094
0102
0100
0099
0098
0096
0104
0102
0101
0099
0098
0115
0114
0112
0111
0109
1
20
30
40
50
17
0091
0090
0089
0088
0087
0093
0092
0091
0089
0088
0095
0094
0092
0091
0090
0097
0096
0094
0093
0092
0099
0097
0096
0095
0093
0100
0099
0098
0096
0095
0102
0101
0100
0098
0097
0104
0103
0101
0100
0099
0097"
0096
0095
0094
0092
0091
0089
0087
0084
0082
0106
0105
0103
0102
0100
0108
0106
0105
0104
0102
0101"
0099
0098
0097
0096
"0094
0092
0090
0087
0085
1
10
20
30
40
50
0084
0083
0085
0084
0083
0082
0081
0087
0086
0085
0084
0083
0089
0088
0086
0085
0084
0091
0089
0088
0087
0086
0092
0091
0090
0089
0087
0094
0093
0091
0090
0089
0088
0086
0083
0081
0079
0096
0094
0093
0092
0091
0090
0087
0085
0083
0081
0099
0098
0096
0095
0094
0093
0090
0088
0086
0084
18
20
40
19
20
0080
0078
0076
0074
0072
0082
0079
0077
0075
0073
0083 0085
0081 i 0083
0079 ! 0080
0077 1 0078
0075 1 0076
0086
0084
0082
0080
0078
0093
0091
0089
0086
40
20
20
40
21
20
40
22
20
40
0070
0068
0067
0065
0063
0072
0070
0068
0066
006.5
0073
0071
0069
0068
0066
0074
0073
0071
0069
0067
0076
0074
0072
0070
0068
0077
0075
0073
0072
0070
0079
0077
0075
0073
0071
0080
0078
0076
0074
0072
0081
0079
0077
0075
0074
0083 i 0084
0081 0082
0079 ] 0080
0077 i 0078
0075 1 0076
0062
0060
0059
0057
0056
0063
0061
0060
0058
0057
0064
0063
0061
0059
0058
0065
0064
0062
0061
0059
0067
0065
0063
0062
0060
0068
0066
0065
0063
0061
0069
0067
0066
0064
0062
0070
0069
0067
0065
0064
0072
0070
0068
0066
0065
"0063
0061
0060
0058
0057
0055"
0054
0053
0051
Q050
0073
0071
0069
0068
0066
0064
0063
0061
0059
0058
0056
0055
0053
0052
0051
0074
0072
0070
0069
0067
0065
0064
0062
0060
0059
0057
0056
0054
0053
0052
23
20
40
24
20
0054
0053
0052
0050
0055
0054
0053
0051
0050
0057
0055
0054
0052
0051
0058
0056
0055
0053
0052
0059
0057
0056
0054
0053
0060
0058
0057
0055
0054
0061
0059
0058
0056
0055
0062
0060
0059
0057
0056
40
25
20
40
26
0049
0047
0046
0045
0044
0050
0048
0047
0046
0045
0051
0049
0048
0047
0046
0052
0050
0049
0048
0046
0053
0051
0050
0049
0047
0053
0052
0051
0049
0048
0054
0053
0052
0050
0049
20
40
27
20
40
0043
0041
0040
0039
0038
0043
0042
0041
0040
0039
0044
0043
0042
0041
0040
0045
0044
0043
0042
0040
0046
0045
0044
0042
0041
0047
0046
0044
0043
0042
0048
0046
0045
0044
0043
0048
0047
0046
0045
0043
0042
0049
0048
0047
0045
0044
0043
0050
0049
0047
0046
0045
28
0037
0038
0039
0039
0040
0041
0042
0044
1
APPENDIX V: TABLE V. [Page 307
Log. D, for computing the First Correction of the Lunar Distance. 1
App.
alt. of
moon.
Reduced parallax and refraction of moon. 1
50' 1 51'
52'
5S'
64'
56' 56'
57' 58'
59'
60'
28° 0'
0.0037
0.0038
0.0039
0.0039
0.0040
0.0041
0.0042
1
0. 0042 ! 0. 0043
0.0044
30
0.0036
0. 0036
0. 0037
0. 0038
0.0038
0.0039
0.0040
0. 0040 : 0. 0041
0.0042
29
0.0034
0. 0035
0.0035
0.0036
0.0037
0. 0037 ' 0. 0038
0. 0039 0. 0039
0. 0040
30
0.0033
0. tX)33
0.0034
0.0035
■0.0035
0. 0036 1 0. 0036
0. 0837 ! 0. 0038
0.0038
30
0.0031
0. 00.30
0.0032
0. 0032
0.0033
0.0031
0. 0034
0.0032
0. 0034 I 0. 0035
0. 0033 1 0. 0033
0.0035
0.0034
0.0036
0.0037
30
0.0030
0.0031
0.0034
0.0035
31
0. 0028
0. 0029
0.0029
0. 0030
0. 0031
0. 0031 1 0. 0032
0.0032
0.0033
0. 0033
30
0.0027
1 0.0028
0.0028
0.0029
0.0029
0. 0030 ! 0. 0030
0. 0031
0. 0031
0.0032
0.0032
32
0. 0026 0. 0026
0.0027
0.0027
0.0028
0. 0028 1 0. 0029
0.0029 0.0030
0. 0030
0.0031
30
0. 0024 0. 0025
0. 0025
0.0026
0. 0026
0.0027
0. 0025
0. 0027
0.0028 0.0028
0.0026 0.0027
0.0029 0.0029
33
0. 0023 0. 0024
0.0024
0.0025
0. 0025
0. 0026
0. 0027
0. 0028
30
0. 0022 0. 0022
0. 0023
0. 0023
0.0024
0. 0024 j 0. 0025
0. 0025
0. 0025
0. 0026
0. 0026
34
0. C021 0. 0021
0.0022
0. 0022
0. 0022
0. 0023 i 0. 0023
0.0024
0.0024
0. 0024
0. 0025
30
0. 0020 0. 0020
0. 0020
0.0021
0. 0021
0.0022
0.0022
0. 0022
0. 0023
0. 0023
0. 0023
35
0.0018
0.0019
0. 0019
0. 0020
0. 0020
0.0020
0.0019
0.0021
0. 0019
0.0021
0. 0020"
0.0021
0. 0020
0.0022
0. 0022
30
0.0017
0.0018
0. 0018
0.0018
0. 0019
0.0020
0.0021
36
0.0016
0.0017
0.0017
0.0017
0.0018
0.0018
0.0018
0. 0019
0.0019
0.0019
0. 0019
30
0. 0015
0.0016
0.0016
0.0016
0. 0016
0.0017
0.0017
0.0017
0.0018
0.0018
0.0018
37
0. 0014 0. 0014
0.0015
0. 0015
0. 0015
0.0016
0.0016
0. 0016
0.0016
0.0017 0.0017
30
0. 0013 , 0. 0013
0.0014
0. 0014
0.0014
0. 0014
0. 0015
0. 0015
"0.0014
0. 0015
0. 0014
0. 0015 ! 0. 0016
0.0014 0.0014
38
0.0012 0.0012
0.0013
0.0013
0.0013
0.0013
0.0014
30
0.0011 0.0011
0.0012
0.0012
0. 0012
0.0012
0.0012
0.0013
0.0013
0.0013 0.0013
39
0.0010 1 0.0010
0. 0011
0.0011
0. 0011
0.0011
0.0011
0. 0012
0.0012
0.0012 0.0012
30
, 0.0009
0.0010
0.0010
0. 0010
0.0010
0.0010
0.0010
0.0011
0.0011
0. 0011
40
0.0008
0.0009
0.0009
0.0007
0.0009
0.0007
0.0009
0.0007
0.0009
o:ooo7
0.0009
0. 0010
0.0007
0. 0010
0. 0010
41
0.0007
0.0007
0. 0007
0.0008
0.0008
42
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0.0005
0. 0005 ! 0. 0006
43
0.0003
0.0003
0.0003
0.0003
0.0003
0.0003
0. 0003
0.0003
0. 0003 \ 0. 0004
44
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
0.0002
0.0002
0. 0002 i 0. 0002
45
0.0000
0.0000
9.9998
0.0000
0.0000
9. 9998
0.0000
9:9998
0.0000
0.0000
9. 9998
0.0000
0. 0000 1 0. 0000
46
9.9998
9.9998
9.995)8
9. 9998 i 9. 9998 1 9. 9998
47
9.9997
9.9997
9. 9997
9.9997
9.9996
9.9996
9.9996
9.9996
9.9996 9.9996
48
9.9995
9.9995
9. 9995
9. 9995
9. 9995
9. 9995
9. 9995
9. 9995
9.9994 9.9994
49
9.9994
9.9994 ,9.9994
9. 9993
9. 9993 ! 9. 9993 i 9. 9993
9. 9993
9.9993 9.9993
50
9.9992
9.9992
9.9992
9. 9992
9.9991"
9. 9992 1 9. 9992
9.9992
9. 9990
9.9991
9. 9991 ; 9. 9991
51
9.9991
9.9991
9.9991
9. 9990
9. 9990
9. 9990 9. 9990 1 9. 9990
52
9.9990
9.9990
9.9990
9. 9989
9. 9989
9. 9989
9.9989
9.9989 9. 9988 1 9. 9988
53
9.9989
9.9988
9.9988
9.9988
9.9988
9.9988
9.9987
9. 9987
9. 9987
9.9987
54
9. 9988
9.9987
9.9987
9. 9987
9.9987
9.9986
9. 9986
9. 9986
9.9986
9.9985
55
9. 9986
9.9986
9.9986
9.9986
9. 9984
9.998.5
9.9985
9.9984"
9.9985
9. 9984
9. 9984
9. 9983
9.9984
9. 9983
9.9984
9. 9983
56
9.9985
"9.9985
9.9985
9. 9984
57
9.9984
9. 9984
9. 9984
9. 9983
9. 9983
9. 9983
9.9982
9. 9982
9.9982
9.9981
58
9.9983
9. 9983
9. 9983
9. 9982
9. 9982
9. 9982
9.9981
9.9981
9.9981
9.9980
59
9. t>982
9. 9982
9.9981
9.9981
9. 9981
9. 9980
9.9980
9. 9980
9. 9979
9. 9979 1
60
9. 9981
9.9981
9.9980
9.9980
9.9980
9.9979
9. 9979
979978
9.9979
9.9978
9.9978
9. 9978 1
61
9. 9980
9.9980
9. 9980
9. 9979
9.9979
9.9978
9.9977
9. 9977
62
9. 9979
9.9979
9. 9979
9.9978
9.9978
9. 9977
9.9977
9. 9977
9.9976
9. 9976
63
9.9979
9. 9978
9.9978
9. 9977
9.9977
9. 9976
9.9976
9.9976
9.9975
9.9975
64
9.9978
9. 9977
9.9977
9. 9976
9.9976
9. 9976
9. 9975
9.9975
9. 9974
9. 9974
65
9.9977
9.9977
9.9976
9. 9976
9.9975
9.9975
9. 9975
9. 9974
9.9974
9.9974
9. 9973
9.9973
9.9972
66
9.9976
9.9976
9. 9975
9. 9974
9.9973
9.9973
9. 9972
67
9.9976
9; 9975
9. 9975
9.9974
9.9974
9.9973
9. 9973
9.9972
9. 9972
9.9971
68
9.9975
9.9974
9. 9974 i 9. 9973
9. 9973
9.9972
9.9972
9.9971
9.9971
9.9970
69
9. 9974
9.9974
9. 9973 1 9. 9973
9.9972
9. 9972
9. 9971
9.9971
9. 9970
9.9970
70
9. 9974
9.9973
9.9972
9. 9973 1 9. 9972
9.9971 9.9971
9. 9972
9. 9971
9. 9970
9. 9970
9.9969
9.9969
9. 9968
9.9969
72
9. 9972
9.9970
9. 9970 1 9. 9969
9.9968
74
9. 9971
9. 9971
9.9970 9.9970
9.9969
9. 9969 i 9. 9968
9.9968
9. 9967
9.9966
76
9.9971
9.9970
9. 9969 i 9. 9969
9.9968
9.9968 9.9967
9.9966
9.9966
9.9965
78
9.9970
9.9969
9. 9969 1 9. 9968
9.9967
9.9967 9.9966
9. 9966
9.9965
9.9964
«0
9.9969
9. 9969
9. 9968 1 9. 9967
9. 9967
9. 9966 i 9. 9965
9.9965
9.9964
9.9964
9.9962
90
9.9968
9.9967 1
9. 9966
9. 9966
9.9965
9. 9964 9. 9964
9.9963
9.9963
Page 308]
APPENDIX V:
TABLE VI.
Second Correction of the Lunar Distance.
Appar-
ent dis-
tance.
First correction of distance.
Appar-
8'
J'
10
12'
14'
16'
18'
ac
21'
22'
28'
24'
26'
26'
27'
28'
tance.
Sub.
//
II
II
II
II
II
//
11
II
II
II
II
n
It
II
II
Add.
15° (K
2
3
a
6
8
11
13
14
16
17
19
20
22
24
26
30
2
3
5
6
8
10
13
14
15
17
18
20
21
23
25
16
3
4
6
8
10
12
13
15
16
18
19
21
22
24
30
3
4
6
8
10
12
13
14
16
17
18
20
21
23
17
3
3
4
4
6
5
7
9
11
13
14
15
16
18
19
21
22
30
7
9
11
12
13
15
16
17
19
20
22
18
3
4
5
7
9
11
12
13
14
15
17
18
20
21
30
3
4
5
7
8
10
12
13
14
15
16
18
19
20
19
3
4
5
6
8
10
11
12
13
15
16
17
18
20
30
2
2
4
3
5
5
6
8
10
11
12
13
14
15
17
18
19
20
6
8
10
n
12
13
14
15
16
17
19
21
2
3
4
6
/
9
10
11
12
13
14
15
17
18
22
2
3
4
6
7
9
10
10
11
12
14
15
16
17
23
2
3
4
5
/
8
9
10
11
12
13
14
15
16
24
2
2
3
3
4
4
5
6
8
9
9
10
11
12
13
14
15
25
5
6
7
8
9
10
11
12
13
14
15
26
2
3
4
5
6
I
8
9
9
10
11
12
13
14
27
2
2
3
4
6
7
8
8
9
10
11
12
12
13
28
2
2
3
4
5
/
7
8
9
9
10
11
12
13
29
2
2
3
4
5
6
7
8
8
9
10
11
11
12
30
2
2
3
4
5
6
7
7
8
9
9
10
11
12
31
2
3
4
5
6
6
7
8
8
9
10
11
11
32
2
3
4
5
6
6
7
7
8
9
9
10
11
33
2
3
3
4
5
6
7
7
8
8
9
10
11
34
2
2
3
3
4
5
6
6
7
7
8
9
9
10
35
2
3
4
5
5
6
7
7
8
8
9
10
36
2
2
3
4
5
5
6
6
7
8
8
9
9
37
2
2
3
4
5
5
6
6
7
7
8
8
9
38
2
2
3
4
4
5
5
6
6
7
8
8
9
39
2
2
2
2
3
3
4
5
5
6
6
7
7
8
8
40
3
3
4
5
5
6
6
7
(
8
8
140°
42
2
2
3
4
4
5
5
6
6
7
7
8
138
44
2
2
3
4
4
4
5
5
6
6
7
1
136
46
2
2
3
3
4
4
4
5
5
6
6
(
134
48
2
2
3
3
3
4
4
5
5
5
6
6
132
50
2
2
3
3
4
4
4
5
5
5
6
130
52
2
2
3
3
3
4
4
4
5
5
5
128
54
0.
ol
2
2
3
3
3
3
4
4
4
5
5
126
56
2
2
2
3
3
3
3
4
4
4
5
124
58
— j-
2
2
2
3
3
3
3
4
4
4
122
60
2
2
2
2
3
3
3
3
4
4
120
62
■0
2
2
2
2
2
3
3
3
3
4
118
64
.0
1
1
2
2
2
2
2
3
3
3
3
116
66
1
2
2
2
2
2
2
3
3
3
114
68
1
1
2
2
2
2
2
2
3
3
112
70
1
1
1
2
2
2
2
2
2
2
110
74
1
1
1
1
1
1
2
2
2
2
106
78
1
1
1
1
1
1
1
1
1
1
102
82
1
1
1
1
1
1
1
1
98
86
94
90
14'
90
Appar-
ent dis-
tance.
S'
7'
w
12'
16'
18'
20'
21'
22'
28'
24'
25'
26'
27'
28'
Appar-
ent dis-
tance.
First correction of
distun
CO.
APPENDIX V: TABLE VL
Page
309
Second Correction of the Lunar IMstance.
Appar-
ent dis-
tance.
First correction of distance.
Appar-
ent dis-
tance.
29'
SC
81'
11
82'
11
88'
84'
85'
36'
37'
88'
89'
40'
41'
42'
48'
44'
Sub.
It
11
ff
II
It
ff
9
It
ff
n
II
II
//
It
Add.
15° C
27
29
31
33
35
38
40
42
45
47
•50
52
55
57
60
63
30
26
28
30
32
34
36
39
41
43
45
48
50
53
56
58
61
16
26
27
29
31
33
35
37
39
42
44
46
49
51
54
56
59
30
25
27
28
30
32
34
36
38
40
43
45
47
50
52
54
57
17
30
24
26
27
29
31
33
35
34
37
36
39
41
43
46
48
50
53
55
23
25
27
28
30
32
38
40
42
44
47
49
51
54
18
23
24
26
28
29
31
33
35
37
39
41
43
45
47
50
52
30
22
23
25
27
28
30
32
34
36
38
40
42
44
46
48
50
19
21
23
24
26
28
29
31
33
35
37
39
41
43
45
47
49
30
21
22
22
24
25
27
28
30
32
34
36
37
39
41
43
46
48
20
20
23
25
26
28
29
31
33
35
36
38
40
42
44
46
21
19
20
22
23
25
26
28
29
31
33
35
36
38
40
42
44
22
18
19
21
22
24
25
26
28
30
31
33
35
36
38
40
42
23
17
19
20
21
22
24
25
27
28
30
81
33
35
36
38
40
24
16
16
18
17
19
18
20
19"
21
20
23
24
25
27
28
30
31
33
35
36
38
25
22
23
24
26
27
28
30
31
33
35
36
26
15
16
17
18
19
21
22
23
25
26
27
29
30
• 32
33
35
27
14
15
16
18
19
20
21
22
23
25
26
27
29
30
32
33
28
14
15
16
17
18
19
20
21
22
24
25
26
28
29
30
32
29
30
13
13
14
14
15
14
16
15
17
16
18
17
19
20
22
23
24
25
26
28
29
30
19
20
21
22
23
24
25
27
28
29
31
12
13
14
15
16
17
18
19
20
21
22
23
24
26
27
28
32
12
13
13
14
15
16
17
18
19
20
21
22
23
25
26
27
33
11
12
13
14
15
16
16
17
18
19
20
22
23
24
25
26
34
11
12
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
35
10
12
13
14
14
15
16
17
18
19
20
21
22
23
24
36
10
11
12
12
13
14
15
16
16
17
18
19
20
21
22
23
37
10
10
n
12
13
13
14
15
16
17
18
19
19
20
21
22
38
9
10
11
11
12
13
14
14
15
16
17
18
19
20
21
22
39
9
10
10
11
12
12
13
14
15
16
16
17
18
19
20
19
21
20
140°
40
9
9
10
11
11
12
13
13
14
15
16
17
17
18
42
8
9
9
10
11
11
12
13
13
14
15
16
16
17
18
19
138
44
8
8
9
9
10
10
11
12
12
13
14
14
15
16
17
17
136
46
7
8
8
9
9
10
10
11
12
12
13
13
14
15
16
16
134
48
7
7
7
8
8
9
9
10
10
11
11
12
13
13
14
15
15
132
50
6
7
8
8
8
9
9
10
11
11
12
12
13
14
14
130
52
6
6
7
7
7
8
8
9
9
10
10
11
11
12
13
13
128
54
5
6
6
6
7
7
8
8
9
9
10
10
11
11
12
12
126
56
5
5
6
6
6
7
7
8
8
9
9
9
10
10
11
11
124
58
5
5
5
6
6
6
7
7
7
8
8
9
9
10
10
11
122
60
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
10
120
62
4
4
4
5
5
5
6
6
6
7
7
7
8
8
9
9
118
64
4
4
4
4
5
5
5
6
6
6
6
7
7
8
8
8
116
66
3
4
4
4
4
4
5
5
5
6
6
6
/
7
7
8
114
68
3
3
3
3
3
4
4
4
4
5
5
5
6
6
6
7
7
112
70
3
3
3
4
4
4
4
5
5
5
5
6
6
6
110
74
2
2
2
3
3
3
3
3
3
4
4
4
4
4
5
5
106
78
9
2
2
2
2
2
2
2
3
3
3
3
3
3
3
4
102
82
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
98
86
1
1
1
81'
1
1
1
1
1
1
1
1
1
1
1
1
1
94
90°
29'
30
.
90°
Appar-
ent di.s-
tanf-e.
82'
SS'
34'
85'
36'
87'
88'
89'
40'
41'
42'
48'
44'
Appar-
ent dis-
tance.
Firs
t corre
jtion o
distar
ce.
Page 310]
APPENDIX V: TABLE VI.
Second Correction of the Lunar Distance.
Appar-
ent dis-
, First correction of distance.
Appar-
ent dis-
tance.
46'
48'
47'
48'
49'
60'
51'
54'
58'
54'
56'
58'
57'
58'
59'
60'
tance.
Sub.
//
N
ft
II
II
//
II
tt
//
II
ft
//
"
II
II
Add.
15° 0'
66
69
72
75
78
81
85
88
91
95
99
102
106
110
113
117
30
64
67
70
72
76
79
82
85
88
92
95
99
102
106
110
113
16
62
64
67
70
73
76
79
82
85
89
92
95
99
102
106
110
30
60
62
65
68
71
74
77
80
83
86
89
92
96
99
103
106
17
30
58
56
60
59
63
'61
66
69
71
69
74
77
80
83
86
90
93
96
99
103
64
66
72
75
78
81
84
87
90
93
96
100
18
54
57
59
62
64
67
70
73
75
78
81
84
87
90
94
97
30
53
55
58
60
63
65
68
71
73
76
79
82
85
88
91
94
19
51
54
56
58
61
63
66
69
71
74
77
79
82
85
88
91
30
50 ; 52
49 j 51
54
53
57
55
59
58
62
60
64
67
69
72
70
75
73
77
80
83
86
89
20
62 65
67
75
78
81
83
86
21
46 1 48
50
52
55
57
59 61
64
66
69
71
74
76
79
82
22
44 46
48
50
52
54
56 58
61
63
65
68
70
73
75
78
23
42
44
45
47
49
51
53 56
58
60
62
64
67
69
72
74
24
40
38
41
40
43
41
45
43
47
45
49
47
51
53
55
57
59
61
64
66
68
71
25
49
51
53
55
57
59
61
63
65
67
26
36
38
40
41
43
45
47
48
50
52
54
56
58
60
62
64
27
35 , 36
38
39
41
43
45
46
48
50
52
54
56
58
60
62
28
33 i 35
36
38
39
41
43 i 44
46
48
50
51
53
55
57
59
29
32
33
32
35
33
36
35
38
39
41 ' 43
44
46
48
49
51
53
55
57
30
31
36
38
39 41
42
44
46
47
49
51
53
54
31
29 31
32
33
35
36
38 39
41
42
44
46
47
49
51
52
32
28 30
31
32
34
35
36 38
39
41
42
44
45
47
49
50
33
27 28
30
31
32
34
35 j 36
38
39
41
42
44
45
47
48
34
35
26 27
25 i 26
29
28
30
31
32
34 ! 35
36
38
39
41
39
42
44
45
47
29
30
31
32 1 34
35
36
38
40
42
43
45
36
24 25
27
28
29
30
31 32
34
35
36
38
39
40
42
43
37
23 ; 25
26
27
28
29
30
31
33
34
35
36
38
39
40
42
38
23 i 24
25
26
27
28
29
30
31
33
34
35
36
38
39
40
39
22 1 23
24
25
26
25
27
28
29
30
31
33
34
35
36
35
38
39
40
21 i 22
23
24
26
27
28
29
30
31
33
34
36
37
140°
42
20 21 21
22
23
24
25
26
27
28
29
30
31
33
34
35
138
44
18 I 19
20
21
22
23
24
24
25
26
27
28
29
30
31
33
136
46
17 1 18
19
19
20
21
22
23
24
25
26
26
27
28
29
30
134
48
50
16 : 17
17
16
18
17
19
20
20
21
22
23
24
22
25
23
26
26
27
28
132
15
16
18
18
19
20
21
21
24
25
25
26
130
52
14
14
15
16
16
17
18
18
19
20
21
21
22
23
24
25
128
54
13
13
14
15
15
16
16
17
18
18
19
20
21
21
22
23
126
56
12
12
13
14
14
15
15
16
17
17
18
18
19
20
20
21
124
58
10
12
11
12
11
13
12
13
14
14
15
15
16
16
15
17
16
18
16
18
19
20
122
60
12
13
13
14
14
15
17
18
18
120
62
9
10
10
11
11
12
12
13
13
14
14
15
15
16
16
17
118
64
9
9
9
10
10
11
11
12
12
12
13
13
14
14
15
15
116
66
8
8
9
9
9
10
10
11
11
11
12
12
13
13
14
14
114
68
7
7
8
8
8
9
9
10
10
10
11
11
11
12
12
13
112
70
6
7
7
7
8
8
8
9
9
9
10
10
10
11
11
11
110
74
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
106
78
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
7
102
82
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
98
86
90°
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
94
90°
Appar-
ent dis-
45'
48'
47'
48'
49'
hW
51'
5»'
58'
54'
55'
56'
57'
68'
69'
60'
Appar-
ent dis-
tance.
First eorrec
tion o
distance.
tance.
APPENDIX V: TABLE VII.
[Page 311
For finding the Correction of the Lunar Distance for the Contraction of the Moon
's Semidiaineter. 1
TABLE
VII A.— GIVING THE ARGUMENT FOR TABLE
VII
B.
Red.
Apparent altitude of moon.
R. of
moon.
8°
5i°
6°
Bi"
JO
JJO
|8c
81=
9°
n"
10<
11=
12<
18<:
14<
18°
10°
17°
18°
20°
26°
80°
40°
50°
41'
65
56
1
42
63
54
47
41
43
62
53
46
40135
44
60
51
45
39
34
30
27
45
58
50
43
38
33
30
26
24
21
20
46
57
49
42
37 '33
29
26
23
21
19
17
15
47
56
48
41
36 32
28
25
23
20
19
17
14
12
10
48
54
46
40
35
31
28
25
22 ; 20 1 18
17
14
12
10
9
8
7
6
49
53
45
39
3,5
30
27
24
22
19 18
16
14
12
10
9
8
7
6
6
5
3
50
52
44 38
34
30
26
24
21
19! 17
16
13
11
10
9
8
7
6
5
5
3
3
2
51
50
43 38i33
29
26
23
21
19; 17
15
13
11
10
8
7
7
6
5
5
3
2
2
2
52
49
42
37
32
28
25
23
20
18
17
15
13
11
9
8
7,
7
6
5
4
3
2
2
2
53
48
41
36
32
28
25
22
20
18
16
15
12
11
9
8
7
6
6
5
4
3
2
2
2
64
47
41
35
31
27
24
22
19
18
16
15
12
10
9
8
7
6
6
5
4
3
2
2
2
00
35
30
27
24
21
19
17
16
14
14
12
12
10
10
9
9
8
8
7
7
6
6
6
5
5
5
4
4
3
3
2
2
2
2
2
2
56
26
23
21
19
17
15
57
18
17
15
14
12
10
9
7
7
6
5
5
4
3
2
2
2
58
13
11
10
8
7
7
6
5
5
4
3
2
2
2
5!'
8
7
6
6
5
5
4
3
2
2
2
60
4
3
2
2
2
TABLE
VII B.— CONTRACTION OF MOON'S SEMI-DIAMETER.
Argument, number from Table VII A.
2 i
6
8
10
12
14
16
18
20
22
24
26
28
30
82
81
36
38
10
44
48
62
66
60
64
,
tt
/ It
tt
a
n
tf
//
//
tt
tt
tt
tt
//
tt
tt
tt
//
tt
tt
tt
tt
II
tt
tt
tt
(
)
5
(
)
10
(
)
1
1
1
1
1
1
1
1
1
1
1
1
1
1
15
(
)
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
20
(
)
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
3
4
4
4
4
5
5
22
(
) 1
1
1
1
3
2
2
2
2
3
3
3
3
3
3
4
4
4
5
5
5
6
6
24
(
) 1
1
1
2
2
2
2
3
3
3
3
3
4
4
4
4
5
5
6
6
6
7
7
26
. 1
1
2
2
2
2
3
3
3
4
4
4
4
5
5
5
5
6
6
7
%
8
9
28
. 1
2
2
2
3
3
3
3
4
4
4
5
5
5
6
6
6
7
8
8
9
10
30
I 1
I 1
~2
2
2
2
2
3
3
3
3
3
4
4
4
4
5
4
5
5
5
5
6
5
6
6
7
6
7
6
7
8
7
8
8
9
9
10
9
11
10
11
11
12
12
13
32
34
I 1
2
2
3
3
4
4
5
5
6
6
6
7
7
8
8
9
9
10
11
12
13
14
15
36
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
12
13
15
16
17
38
. 2
2
3
3
4
5
5
6
6
7
8
8
9
9
10
10
11
12
13
14
15
16
17
18
40
Y"
I 2
I 2
3
3
3
4
4
5
5
6
6
6
6
7
7
8
8
8
8
9
9
10
9
11
10
11
11
12
12
13
12
"13
13
14
14
16
15
17
17
18
18
20
19
21
20
23
42
4 4
44
I 2
3
4
5
5
6
7
8
9
9
10
11
12
12
13
14
15
15
17
19
20
22
23
45
I 2
3
4
5
6
6
7
8
9
10
11
11
12
13
14
15
15
16
18
19
21
23
24
46
2 3
3
4
5
6
7
7
8
9
10
11
12
13
14
14
15
16
17
19
20
22
24
47
Y"
2 3
I 3
4
4
4
5
5
6
6
6
7
7
8
8
9
9
10
10
11
11
U
12
12
13
13
14
14
15
15
16
16
17
17
18
18
18
19
20
21
22
23
24
25
26
48
49
J 3
4
5
6
7
8
9
10
11
12
12
13
14
15
16
17
18
19
21
23
25
50
2 3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
22
24
26
51
2 3
4
5
6
7
8
9
10
11
12
14 15
16
17
18
19
20
21
23
25
27
52
2 3
4
5
6
8
9
10
11
12
13
14
15
16
17
18
19
21
22
24
26
53
2 3
4
6
7
8
9
10
11
12
13
15
16
17
18
19
20
21
22
25
27
54
2 3
5
6
7
8
9
10
12
13
14
15
16
17
19
20
21
22
23
26
55
2 4
5
6
7
8
10
11
12
13
15
16
17
18
19
21
22
56
i 4
5
6
8
9
10
11
13
14
15
16
57
4
5
7
When the nearer limb is observed, stibstract this correction; when the fnrlher, add.
Page 312] APPENDIX V: TABLE VIII.
For finding the Correction of the Lunar Distance for the Contraction of the Sun's Semidiameter.
TABLE VIII A.— GIVING THE ARGUMENT FOR TABLE VIII B.
Red. P.
and R.
of sun.
Apparent altitude of sun. 1
5°
5i°
6°
61°
7°
74°
8°
8J°
9°
9t°
10°
n°
12°
18°
14°
15°
16°
17°
18°
20°
26°
30°
40°
50°
V 0"
30
2
30
3
44
46
40
49
42
51
60
6^
35
44
53
62
37
47
57
67
30
42
53
34
46
59
22
24
46
18
29
30
4
30
5
30
47
50
47
52
50
55
47
52
57
49
54
60
45
51
57
62
68
74
49
55
61
67
74
45
52
59
66
72
48
55
63
70
51
59
66
74
54
62
70
57
65
6
30
7
30
8
55
59
62
66
69
73
51
55
59
63
66
70
74
77
50
54
58
62
66
70
74
78
49
53
58
62
66
70
74
79
52
56
61
65
70
74
79
55
59
64
69
73
78
57
62
67
72
77
60
65
70
75
63
68
74
66
71
30
9
30
10
30
I
11
30
76
80
81
-
TABLE VIII B.— CONTRACTION OF SUN'S SEMIDIAMETER.
Whole
correction
of sun.
Argument, number from Table VIII A.
30
24
28
32
36
40
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
1
2
30
3
1
1
ff
1
2
1
2
1
2
3
2
3
4
2
3
4
ft
2
2
4
2
2
3
//
1
2
3
//
1
2
3
//
1
2
3
1
2
3
//
1
2
3
"
1
2
3
4
5
6
7
8
9
10
11
12
13
1
2
3
4
5
5
6
7
8
9
10
12
13
//
1
2
3
3
5
5
6
7
8
9
10
11
13
ti
1
2
2
3
4
5
6
7
8
9
10
11
12
//
1
2
2
3
4
5
6
7
8
9
10
11
12
1
2
2
3
4
5
6
6
8
9
10
11
1
2
2
3
4
5
5
6
7
8
9
10
11
12
13
15
16
17
19
20
22
23
25
27
28
1
2
2
3
4
5
5
6
7
8
9
10
11
12
13
14
16
17
18
20
21
23
24
26
28
1
1
2
3
4
4
5
6
7
8
9
10
11
12
13
14
15
16
18
19
21
22
24
25
27
29
1
1
2
3
4
4
5
6
7
7
8
9
10
11
12
14
15
16
17
19
20
22
23
25
26
28
30
30
4
20
40
5
«
—
—
—
—
5
7
5
6
7
9
10
5
6
7
8
9
11
12
4
6
7
8
9
10
12
13
14
16
4
6
7
8
9
10
11
12
14
15
4
5
6
7
8
9
11
12
13
15
4
5
6
7
8
9
10
12
13
14
4
5
6
7
8
9
10
11
12
14
20
40
6
20
40
7
20
40
8
20
18
17
19
16
18
20
21
16
17
19
21
15
17
18
20
22
15
16
18
19
21
14
16
17
19
20
14
15
17
18
20
13
15
16
17
19
13
14
16
17
18
13
14
15
16
18
19
21
22
24
26
28
40
9
20
40
10
23
23
22
24
21
23
25
20
22
24
25
20
21
23
25
26
20
40
11
20
Suhiract this correction from the distance.
APPENDIX V: TABLE IX.
[Page 313
Logarithms of Small Arcs in
Space or Time.
Arc. 1
0"
1"
S"
3"
4"
5"
6" 1
'" i
8" 9"
o /
ft
0'
0.0000
0. 3010
0. 4771
0. 6021
0.6990
0. 7782
0. 8451
0. 9031 0. 9542
10
1.0000
1.0414
1.0792
1.1139
1. 1461
1. 1761
1. 2041
1. 2304 1. 2553 I 1. 2788 |
20
1. 3010
1. 3222
1. 3424
1.3617
1. 3802
1. 3979
1.4150
1. 4314 ; 1. 4472 ! 1. 4624 |
30
1.4771
1. 4914
1.5051
1. 5185
1.5315
1.5441
1. 5563
1.5682
1.5798
1.5911
40
1. 6021
1.6128
1.6232
1. 6335
1.6435
1.6532
1. 6628
1. 6721
1.6812
1. 6902
50
1.6990
1. 7076
1.7160
1. 7243 1. 7324
1. 7404
1. 7482
1. 7559
1. 8261
1. 7634
1. 8325
1.7709
1
1. 7782
1.7853
1. 7924 1. 7993
1.8062
1.8129
1. 8195
1. 8388
1
10
1. 8451
1.8513
1. 8573
1. 8633
1. 8692
1.8751
1.8808
1.8865
1. 8921
1. 8976
1
20
1. 9031
1.9085
1.9138
1.9191
1.9243
1.9294
1.9345
1. 9395
1. 9445
1. 9494
1
30
1. 9542
1.9589
1.9638
1.9685
1. 9731
1.9777
1. 9823
1. 9868 i 1. 9912
1. 9956
1
40
2.0000
2. 0043
2.0086
2.0128 2.0170
2.0212
2. 0253
2. 0294 * 2. 0334
2. 0374
1
50
2.0414
2. 0453
2. 0492
2. 0531 2. 0569
2.0607
2.0645
2. 0682
2. 0719
2. 1072
2.0755 1
2
2. 0792
2. 0828
2. 0864
2. 0899
2.0934
2.0969
2.1004
2.1038
2.1106 J
2.1430 !
2
10
2. 1139
2. 1173
2.1206
2. 1239
2. 1271
2. 1303
2. 1335
2. 1367 1 2. 1399
2
20
2. 1461
2. 1492
2. 1523
2. 1553
2. 1584
2. 1614
2.1644
2.1673 12.1703
2. 1732
2
30
2. 1761
2. 1790
2. 1818
2. 1847
2. 1875
2. 1903
2. 1931
2. 1959 1 2. 1987
2. 2014
2
40
2.2041
2.2068
2. 2095
2. 2122
2. 2148
2. 2175
2. 2201
2. 2227 1 2. 2253
2. 2279
2
50
2.2304
2. 2330
2.2355
2. 2380
2. 2405
2. 2430
2. 2455
2. 2695
2. 2480 1 2. 2504
2. 2529
3
2. 2553
2. 2577
2. 2601
2. 2625
2.2648
2. 2672
2.2718
2. 2742
2. 2765
3
10
2. 2788
2. 2810
2. 2833
2. 2856
2. 2878
2.2900
2. 2923
2. 2945
2. 2967
2. 2989
3
20
2. 3010
2. 3032
2.3054
2. 3075
2. 3096
2.3118
2.3139
2. 3160
2.3181
2. 3201
3
30
2. 3222
2. 3243
2. 3263
2. 3284
2. 3304
2. 3324
2. 3345
2. 3365
2. 3385
2. 3404
3
40
2. 3424
2. 3444
2. 3464
2. 3483
2. 3502
2. 3522
2. 3541
2.3560
2. 3579
2. 3598
3
50
2. 3617
2. 3636
2. 3655
2.3674
2. 3692
2. 3711
2. 3729
2. 3747
2. 3766
2. 3945
2. 3784
4
2. 3802
2. 3820
2. 3838
2.3856
2. 3874
2. 3892
2. 3909
2. 3927
2. 3962
4
10
2. 3979
2. 3997
2. 4014
2. 4031
2. 4048
2.4065
2. 4082
2.4099
2. 4116
2. 4133
4
20
2. 4150
2. 4166
2. 4183
2.4200
2. 4216
2. 4232
2. 4249
2. 4265
2. 4281
2. 4298
4
30
2. 4314
2. 4330
2. 4346
2. 4362
2.4378
2. 4393
2.4409
2. 4425
2. 4440 ! 2. 4456
4
40
2. 4472
2. 4487
2. 4502
2.4518
2. 4533
2. 4548
2. 4564
2. 4579
2. 4594 i 2. 4609
4
50
2. 4624
2. 4639
2.4654
2.4669
2.4683
2. 4698
2. 4713
2.4857
2. 4728
2. 4871
2. 4742 1 2. 4757
2. 4886 : 2. 4900
5
2. 4771
2. 4786
2.4800
2. 4814
2.4829
2. 4843
5
in
2. 4914
2. 4928
2. 4942
2. 4955
2. 4969
2.4983
2. 4997
2.5011
2. 5024 , 2. 5038
5
20
2. 5051
2.5065
2. 5079
2.5092
2. 5105
2.5119
2. 5132
2. 5145
2. 5159 1 2.5172
5
30
2. 5185 ; 2. 5198
2.5211
2. 5224
2. 5237
2. 5250
2. 5263
2. 5276
2. 5289
2. 5302
5
40
2. 5315
2. 5328
2. 5340
2. 5353
2.5366
2.5378
2. 5391
2. 5403
2. 5416
2. 5428
5
50
2. 5441
2. 5453
2. 5575
2.5465
2. 5587
2.5478
2. 5490
2:56il
2. 5502
2.5514
2. 5635"
2. 5527
2. 5539
2. 5551
6
2. 5563
2.5599
2. 5623
2. 5647
2. 5658
2. 5670
6
10
2. 5682
2. 5694
2. 5705
2. 5717
2. 5729
2. 5740
2. 5752
2. 5763
2. 5775
2. 5786
6
20
2. 5798
2.5809
2. 5821
2. 5832
2. 5843
2. 5855
2. 5866
2. 5877
2. 5888
2. 5899
6
30
2. 5911
2. 5922
2. 5933
2.5944
2. 5955
2. 5966
2. 5977
2. 5988
2. 5999
2. 6010
6
40
2. 6021
2.6031
2.6042
2. 6053
2.6064
2. 6075
2. 6085
2.6096
2. 6107
2.6117
6
50
2. 6128
2.6232
2.6138
2. 6243
2. 6149
2. 6253
2. 6160
2. 6263
2. 6170
27(5274
2. 6180
2.6284
2. 6191
2. 6201
2.6212
2. 6222
7
2. 6294
2. 6304
2. 6314
2. 6325
10
2. 63,35
2. 6345
2. 6355
2.6365
2. 6375
2. 6385
2. 6395
2. 6405
2. 6415
2. 6425
7
20
2. 64;»
2.6444
2. 6454
2.6464
2. 6474
2. 6484
2. 6493
2. 6503
2. 6513
2. 6522
7
30
2. 6532
2. 6542
2. 6551
2.6561
2.6571
2. 6580
2. 6590
2. 6599
2.6609
2. 6618
7
40
2. (i628
2. 6637
2.6646
2.6656
2. 6665
2. 6675
2. 6684
2. 6693
2. 6702
2. 6712
7
50
2. 6721
2. 6730
2. 6739
2:6830^
2. 6749
2. 6839
2. 6758
2.684'8"
2. 6767
2. 6776
2. 67a5
2. 6794
2.6884
2. 6803
8
2. 6812
2. 6821
2. 6857
2. 6866
2. 6875
2. 6893
8
10
2. 6902
2. 6911
2. 6920
2. 6928
2. 6937
2. 6946
2. 6955
2.6964
2. 6972
2. 6981
8
20
2.6990
2. 6998
2. 7007
2. 7016
2. 7024
2. 7033
2. 7042
2. 7050
2. 7059
2.7067
8
30
2. 7076
2. 7084
2. 7093
2. 7101
2.7110
2.7118
2. 7126
2. 7135
2. 7143
2. 7152
8
40
2.7160
2. 7168
2.7177
2. 7185
2. 7193
2. 7202
2. 7210
2. 7218
2. 7226
2. 7235
8
50
0^
2. 7243
2. 7251
2. 7259
2. 7267
2. 7275
2.7284
2.7292
2. 7372
2.7300
2. 7308
2. 7388
2. 7316
2. 7396
9
2. 7324
2. 7332
2. 7340
2. 7348
2. 7356
2. 7364
2. 7380
9
10
2.7404
2. 7412
2. 7419
2. 7427
2. 7435
2. 7443
2. 7451
2. 7459
2. 7466
2. 7474
9
20
2. 7482
2. 7490
2. 7497
2. 7505
2. 7513
2. 7520
2. 7528
2. 7536
2. 7543
2. 7551
9
30
2. 7559
2. 7566
2. 7574
2. 7582
2. 7589
2. 7597
2.7604
2. 7612
2. 7619
2. 7627
9
40
2. 7634
2. 7642
2. 7649
2. 7657
2.7664
2. 7672
2. 7679
2. 7686
2. 7694
2. 7701
9
50
2. 7709
2.7716
2. 7723
2. 7731
2. 7738
2. 7745
2. 7752
2. 7760
2. 7767
2. 7774
Page 314]
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or
Time.
Arc.
0"
1"
2"
8"
4"
6"
6"
7"
8"
9"
'
(y 10"
n
0"
2. 7782
2. 7789
2.7796
2. 7803
2. 7810
2. 7818
2. 7825
2. 7832
2. 7839
2.7846
10
10
2. 7853
2. 7860
2. 7868
2. 7875
2. 7882
2. 7889
2. 7896
2. 7903
2. 7910
2. 7917
10
20
2. 7924
2. 7931
2. 7938
2. 7945
2. 7952
2. 7959
2. 7966
2. 7973
2. 7980
2. 7987
10
30
2. 7993
2.8000
2. 8007
2.8014
2. 8021
2. 8028
2.8035
2. 8041
2. 8048
2. 8055
10
40
2. 8062
2. 8069
2. 8075
2. 8082
2. 8089
2. 8096
2. 8102
2.8109
2.8116
2. 8122
10
50
2. 8129
2. 8136
2. 8202
2. 8142
2. 8209
2. 8149
2. 8156
2. 8162
2. 8169
2.8176
'2. 8241
2. 8182
"2. 8248
2. 8189
11
2. 8195
2. 8215
2. 8222
2. 8228
2. 8235
2. 8254
11
10
2. 8261
2. 8267
2. 8274
2. 8280
2. 8287
2. 8293
2.8299
2. 8306
2.8312
2. 8319
11
20
2. 8325
2. 8331
2. 8338
2. 8344
2. 8351
2. 8357
2. 8363
2. 8370
2. 8376
2. 8382
11
30
2. 8388
2. 8395
2. 8401
2. 8407
2. 8414
2. 8420
2. 8426
2. 8432
2. 8439
2. 8445
11
40
2.8451
2. 8457
2. 8463
2. 8470
2. 8476
2. 8482
2. 8488
2. 8494
2. 8500
2.8506
11
50
2. 8513
2:8573'
2. 8519
2. 8525
2. 8531
2. 8537
2. 8543
2. 8549
2. 8555
2. 8561
2. 8567
12
2. &579
2. 8585
2. 8591
2. 8597 2. 8603
2. 8609
2. 8615
2. 8621
2. 8627
12
10
2. 8633
2. 8639
2. 8645
2. 8651
2. 8657 2. 8663
2. 8669
2. 8675
2. 8681
2.8686
12
20
2. 8692
2. 8698
2. 8704
2. 8710
2. 8716 2. 8722
2. 8727
2. 8733
2. 8739
2. 8745
12
30
2. 8751
2. 8756
2. 8762
2. 8768
2. 8774
2. 8779
2. 8785
2. 8791
2. 8797
2. 8802
12
40
2. 8808
2. 8814
2. 8820
2. 8825
2. 8831
2. 8837
2. 8842
2.8848
2. 8854
2. 8859
12
50
2. 8865
2. 8871
2. 8876
2. 8882
2. 8887
2. 8893
2. 8949
2.8899
2. 8904
2. 8910
2. 8915
13
2. 8921
2. 8927
2. 8932
2. 8938
2. 8943
2. 8954
2. 8960
2. 8965
2. 8971
13
10
2. 8976
2. 8982
2. 8987
2. 8993
2. 8998
2.9004
2.9009
2. 9015
2. 9020
2. 9025
13
20
2. 9031
2. 9036
2.9042
2.9047
2. 9053
2. 9058
2. 9063
2. 9069
2.9074
2. 9079
13
30
2.9085
2.9090
2.9096
2. 9101
2. 9106
2.9112
2.9117
2. 9122
2. 9128
2. 9133
13
40
2. 9138
2. 9143
2. 9149
2. 9154
2. 9159
2. 9165
2.9170
2, 9175
2.9180
2. 9186
13
50
~
2. 9191
2. 9196
2. 9248
2. 9201
2. 9253
2. 9206
2. 9212
2.9217
2. 9222
2. 9227
2. 9232
2. 9238
14
2. 9243
2. 9258
2.9263
2. 9269
2. 9274
2. 9279
2. 9284
2. 9289
14
10
2. 9294
2. 9299
2. 9304
2.9309
2. 9315
2. 9320
2. 9325
2. 9330
2. 9335
2.9340
14
20
2. 9345
2.9350
2. 9355
2. 9360
2.9365
2. 9370
2. 9375
2. 9380
2. 9385
2. 9390
14
30
2. 9395
2.9400
2. 9405
2. 9410 i 2. 9415
2. 9420
2. 9425
2. 9430
2. 9435
2.9440
14
40
2. 9445
2. 9450
2.9455
2.9460
2.9465
2. 9469
2. 9474
2. 9479
2. 9484
2. 9489
14
50
2. 9494
2. 9499
2.9504
2.9509
2. 9513
2. 9518
2. 9523
2. 9528
2. 9533
2. 9538
15
2. 9542
2.9547
2. 9552
2. 9557
2.9562
2. 9566
2. 9571
2. 9576
2. 9581
2. 9586
15
10
2.9590
2. 9595
2.9600
2.9605
2.9609
2.9614
2. 9619
2. 9624
2.9628
2. 9633
15
20
2. 9638
2.9643
2. 9647
2.9652
2. 9657
2. 9661
2. 9666
2. 9671
2. 9675
2. 9680
15
30
2.9685
2. 9689
2.9694
2. 9699
2. 9703
2. 9708
2. 9713
2. 9717
2. 9722
2. 9727
15
40
2. 9731
2. 9736
2. 9741
2.9745
2. 9750
2. 9754
2. 9759
2. 9763
2. 9768
2. 9773
15
50
2. 9777
2. 9823"
2. 9782
2. 9786
2. 9791
2. 9795
2.9800
2. 9805
2.9809
2.9814
2.9818
16
2. 9827
2. 9832
2. 9836 ; 2. 9841
2.9845
2. 9850
2.9854
2. 9859
2. 9863
16
10
2. 9868
2. 9872
2. 9877
2.9881 2.9886
2. 9890
2. 9894
2. 9899
2. 9903
2. 9908
16
20
2.9912
2. 9917
2. 9921
2.9926 : 2.9930
2. 99,34
2. 9939
2. 9943
2. 9948
2. 9952
16
30
2. 9956
2. 9961
2. 9965
2.9969 2.9974
2. 9978
2. 9983
2.9987
2. 9991
2. 9996
16
40
3.0000
3.0004
3.0009
3. 0013 3. 0017
3. 0022
3. 0026
3.0030
3. 0035
3.0039
16
50
3.0043
3.0048
3.0052
3. 0056 3. 0060
3.0065
3.0069
3. 0073
3.0077
3.0082
17
3. 0086
3.0090
3.0095
3. 0099 3. 0103
3. 0107
3.0111
3.0116
3. 0120
3. 0124
17
10
3. 0128
3. 0133
3. 0137
3.0141 3.0145
3. 0149
3. 0154
3. 0158
3. 0162
3. 0166
17
20
3. 0170
3. 0175
3. 0179
3. 0183 3. 0187
3.0191
3. 0195
3. 0199
3.0204
3. 0208
17
30
3. 0212
3. 0216
3.0220
3. 0224 3. 0228
3.02.33
3.0237
3. 0241
3. 0245
3. 0249
17
40
3. 0253
3. 0257
3. 0261
3. 0265
3. 0269
3. 0273
3. 0278
3. 0282
3. 0286
3. 0290
17
50
3. 0294
3. 0298
3.0302
3. 0342
3. 0306
.3.0346
3. 0310
3.0350
3. 0314
3. 0318
3. 0322
3. 0326
3. 0366
3. 0330
3. 0370
18
3. 0334
3. 0338
3. 01554
3.0358
3. 0362
18
10
3. 0374
3. 0378
3. 0382
3. 0386
3. 0390
3. 0394
3. 0398
3. 0402
3. 0406
3. 0410
18
20
3.0414
3. 0418
3. 0422
3. 0426
3. 0430
3.0434
3. 0438
3. 0441
3. 0445
3. 0449
18
30
3. 0453
3. 0457
3. 0461
3. 0465
3. 0469
3. 0473
3. 0477
3.0481
3. 0484
3. 0488
18
40
3. 0492
3. 0496
3. 0500
3.0504
3. 0508
3. 0512
3. 0515
3. 0519
3. 0523
3. 0527
18
50
3. 0531
3. 0535
3. 0538
3. 0542
3. 0546 ! 3. 0550
3. 0554
3. 0558
3. 0561
3.0565
3.0603
19
3. 0569
3. 0573
3. 0577
3. 0580
3. 0584
3. 0588
3. 0592
3. 0596
3.0599
19
10
3.0607
3.0611
3.0615
3.0618
3. 0622
3.0626
3. 06.30
3. 0633
3.0637
3.0641
19
20
3. 0645
3. 0648
3.0652
3.0656
3.0660
3. 0663
3. 0667
3.0671
3.0674
3.0678
19
30
3.0682
3. 0686
3. 0689
3.0693
3.0697
3.0700
3. 0704
3. 0708
3. 0711
3. 0715
19
40
3. 0719
3. 0722
3. 0726
3. 0730
3.0734
3.0737
3. 0741
3. 0745
3. 0748
3. 0752
19
50
3. 0755
3.0759
3. 0763
3. 0766
3. 0770
3. 0774
3. 0777
3. 0781
3. 0785
3. 0788
APPENDIX V: TABLE IX.
[Page 315 j
Logarithms of Small Arcs in
Space or Time.
Arc.
0"
1"
i"
8"
4"
»"
0"
7" 8"
9"
C" '
0" 20""
O"
3. 0792
3. 0795
3.0799
3. 0803
3.0806
3. 0810
3. 0813
3. 0817
3. 0821
3. 0824
20
10
3. 0828
3. 0831
3.0835
3. 0839
3.0842
3. 0846
3.0849
3. 0853
3. 0856
3.0860
20
20
3. 0864
3. 0867
3. 0871 ' 3. 0874
3. 0878
3. 0881
3. 0885
3. 0888
3. 0892
3. 0896
20
30
3.0899
3. 0903
3.0906 3.0910
3. 0913
3.0917
3. 0920
3. 0924
3. 0927
3.0931
20
40
3. 0934
3. 0938
3. 0941 3. 0945
3. 0948
3. 0952
3. 0955
3. 0959
3. 0962
3. 0966
20
50
3. 0969
3.0973
3. 0976 3. 0980
3.0983
3.0986
3. 0990
.371024"
3. 0993
3. 0997
3.1031
3.1000
21
3. 1004
3.1007
3.1011 3.1014
3.1017
3. 1021
3. 1028
3. 1035
21
10
3. 1038
3. 1041
3. 1045 1 3. 1048
3. 1052
3. ia55
3. 1059
3. 1062
3. 1066
3. 1069
21
20
3. 1072
3. 1075
3. 1079 ! 3. 1082
3. 1086
3. 1089
3. 1092
3. 1096
3. 1099
3.1103
21
30
3.1106
3.1109
3.1113 3.1116
3.1119
3. 1123
3.1126
3. 1129
3.1133
3.1136
21
40
3. 1139
3. 1143
3.1146
3.1149
3. 1153
3.1156
3.1159
3. 1163
3.1166
3.1169
21
50
3. 1173
3. 1176
3. 1179
3.1183
3. 1186
3.1189
3. 1222
3.1193
3. 1196
3. 1199
3. 1232
3. 1202
22
3.1206
3. 1209
3.1212
3. 1216
3. 1219
3. 1225
3. 1229.
3. 1235
■?o
10
3. 1239
3. 1242
3, 1245
3.1248
3.12.52
3.12.55
3. 1258
3. 1261
3. 1265
3. 1268
90
20
3. 1271
3. 1274
3. 1278
3. 1281
3. 1284
3. 1287
3.1290
3. 1294
3. 1297
3.1300
OO
30
3. 1303
3. 1307
3. 1310
3. 1313
3. 1316
3. 1319
3. 1323
3. 1326
3. 1329
3. 1332
90
40
3. 1335
3. 1339
3. 1.342
3. i;i45
3. 1U8
3. 1351
3. 1355
3. 1358
3.1361
3. 1364
22
50
3. 1367
3. 1370
3. 1374
3. 1377
3. 1380
3. 1383
3. 1386
3. 1389
3. 1392
3. 1396
23
3.1399
3. 1402
3.1405
3.1408
3. 1411
3. 1414
3. 1418
3. 1421
3. 1424
3. 1427
23
10
3. 1430
3. 1433
3.1436
3.1440
3. 1443
3.1446
3. 1449
3.1452
3. 1465
3. 1458
23
20
3. 1461
3. 1464
3. 1467
3. 1471
3. 1474
3. 1477
3. 1480
3. 1483
3. 1486
3. 1489
23
30
3. 1492
3. 1495
3. 1498
3. 1501
3. 1504
3. 1508
3. 1511
3. 1514
3. 1517
3. 1620
23
40
3. 1523
3. 1526
3. 1529
3. 1532
3. 1535
3. 1538
3.1541
3.1544
3. 1547
3. 1,550
23
50
3. 1553
3.1584"
3. 1556
3. 1587
3. 15.59
3. 1.590
3. 1562
3.1566
3. 1569
3. 1572
3. 1576
3. 1578
3. 1581
24
3. 1593
3. 1596
3. 1.599
3. 1602
3.1605
3.1608
3. 1611
24
10
3. 1614
3.1617
3. 1620
3. 1623
3. 1626
3. 1629
3. 1632
3. 1636
3. 1638
3. 1641
24
20
3.1644
3.1647
3.1649
3. 1652
3. 1655
3.1658
3. 1661
3. 1664
3.1667
3. 1670
24
30
3. 1673
3. 1676
3. 1679
3. 1682
3.1685
3. 1688
3. 1691
3. 1694
3. 1697
3. 1700
24
40
3. 1703
3.1706
3. 1708
3.1711
3. 1714
3.1717
3.1720
3. 1723
3. 1726
.3. 1729
24
50
3. 1732
3.1735
3.1738
3. 1741
3.1744
3. 1746
3. 1749
3. 1762
3. 1755
3. 1758
25
3. 1761
3.1764
3. 1767
3. 1770
3. 1772
3. 1775
3. 1778
3. 1781
3.1784
3. 1787
25
10
3.1790
3. 1793
3. 1796
3. 1798
3. 1801
3.1804
3. 1807
3. 1810
3. 1813
3.1816
25
'20
3. 1818
3. 1821
3. 1824
3. 1827
3.1830
3. 1833
3. 1836
3. 1838
3. 1841
3. 1844
25
30
3.1847
3.1850
3. ia53
3.1855
3.1858
3. 1861
3. 1864
3. 1867
3. 1870
.3.1872
25
40
3. 1875
3. 1878
3. 1881
3.1884
3. 1886
3. 1889
3. 1892
3. 1895
3. 1898
3. 1901
25
50
3. 1903
3.1906
3. 1909
3.1912
3. 1915
3.1942
3.1917
3.1945
3. 1920
3. 1923
3. 1926
3. 1928
26
3. 1931
3.1934
3. 1937
3.1940
3.1948
3. 1951
3. 1953
3. 1956
26
10
3. 1959
3. 1962
3.1965
3.1967
3. 1970
3.1973
3. 1976
3. 1978
3. 1981
3.1984
26
20
3. 1987
3. 1989
3. 1992
3.1995
3. 1998
3.2000
3.2003
3.2006
3.2009
3. 2011
26
30
3. 2014
3. 2017
3. 2019
3. 2022
3. 2025
3. 2028
3. 2030
3. 2033
3. 2036
3. 2038
26
40
3.2041
3.2044
3.2047
3.2049
3. 2052
3.2055
3. 2057
3.2060
3.2063
3.2066
26
50
3.2068
3. 2071
"3. 2098
3. 2074
3. 2076
3. 2079
3. 2082
3. 2084
3. 2087
3.2090
3. 2092
27
3. 2095
3.2101
3. 2103
3. 2106
3.2109
3.2111
3. 2114
3. 2117
3. 2119
2-
10
3.2122
3. 2125
3. 2127
3.2130
3. 21.33
3. 2135
3. 21,38
3. 2140
3. 2143
3. 2146
27
20
3. 2148
3.2151 3.2154
3. 2156
3. 2159
3. 2162
3.2164
3. 2167
3.2170
3. 2172
27
30
3. 2175
3. 2177 3. 2180
3.2183
3. 2185
3. 2188
3. 2191
3.2193
3. 2196
3. 2198
27
40
3. 2201
3.2204 1 3.2206
3.2209
3. 2212
3. 2214
3. 2217
3. 2219
3. 2222
3. 2225
27
50
3. 2227
3. 2230
3. 2232
3. 22a5
3. 2261
3. 2238
3. 2240
3. 2243
3. 2245
3. 2271
3. 2248
3. 2250
28
3. 2253
3.2256
3. 2258
3. 2263
3. 2266
3. 2269
3. 2274
3. 2276
28
10
3. 2279
3. 2281
3. 2284
3. 2287
3. 2289
3.2292
3. 2294
3. 2297
3.2299
3. 2302
28
20
3.2304
3. 2307
3. 2310
3. 2312
3. 2315
3.2317
3. 2320
3. 2322
3. 2325
3. 2327
28
30
3. 2330
3. 2333
3. 2335
3. 2338
3.2340
3. 2.343
3. 2345
3. 2348
3. 23.50
3. 2353
28
40
3. 2355
3.2358 ! 3.2360
3.2363
3. 2365
3. 2368
3. 2370
3. 2373
3. 2375
3. 2378
28
50
3. 2380
3.2383
3. 2.385
3. 2.388
3.2390
3. 2393
3. 2395
3. 2398
3.2400
3. 2425
3. 2403
29
3. 2405
3. 2408
3. 2410
3.2413
3. 2415
3. 2418
3. 2420
3. 2423
3. 2428
29
10
3. 2430
3. 2433
3.2435
3. 2438
3.2440
3. 2443
3.2445
3.2448
3.2460
3. 2453
29
20
3. 2455
3. 2458
3.2460
3. 2463
3. 2465
3. 2467
.3. 2470
3. 2472
3. 2476
3. 2477
29
30
3. 2480
3. 2482
3. 24a5
3. 2487
3. 2490
3. 2492
3. 2494
3. 2497
3. 2499
3. 2.502
29
40
3. 2504
3. 2507 I 3. 2509
3. 2512
3. 2514
3. 2516
3. 2519
3. 2521
3. 2524
3. 2626
29
.50
3. 2529
3.2531 3.2.533
3. 2536
3. 2538
3. 2541
3. 2543
3. 2546
3.2548
3.2560
Page 316J
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in
Space or Time.
Are.
0"
1"
2"
8"
4"
5"
6"
<" I 8"
fl"
o /
0" 30"
n
0'
3. 2553
3.2555
3. 2558
3.2560
3. 2562
3.2565
3. 2567
3. 2570 j 3. 2572
3. 2574
30
10
3. 2577
3. 2579
3. 2582
3.2584
3. 2586
3. 2589
3. 2591
3. 2594 ! 3. 2596
3. 2.598
30
20
3. 2601
3. 2603
3. 2605
3.2608
3. 2610
3.2613 •■ 3.2615
3. 2617 i 3. 2620
3. 2622
30
30
3. 2625
3. 2627
3. 2629
3. 2632
3. 2634
3.2636 i 3.2639
3.2641 13.2643
3. 2646
30
40
3. 2648
3. 2651
3. 26.53
3. 2655
3. 2658
3.2660 3.2662
3. 2665 i 3. 2667
3. 2669
30
50
3. 2672
3. 2674
3. 2676
3. 2679
3. 2681
3.2683 ' 3.2686
3. 2688
3. 2711
3. 2690
3. 2693
31
3. 2695
3. 2697
3. 2700
3. 2702
3. 2704
3. 2707
3. 2709
3.2714
3. 2716
31
10
3. 2718
3. 2721
3. 2723
3. 2725
3. 2728
3. 2730
3. 2732
3. 2735
3. 2737
3. 2739
31
20
3. 2742
3. 2744
3. 2746
3. 2749
3. 2751
3. 2753
3. 2755
3. 2758
3. 2760
3. 2762
31
30
3. 2765
3. 2767
3. 2769
3. 2772
3. 2774
3. 2776
3. 2778
3. 2781
3. 2783
3. 2785
31
40
3. 2788
3.2790
3. 2792
3. 2794
3. 2797
3. 2799
3. 2801
3. 2804
3. 2806
3. 2808
31
50
3. 2810
3. 2813
3. 2815
3. 2817
3. 2819
3. 2822
3. 2824
3. 2826
372849
3. 2828
3. 2831
32
3. 2833
3.2835
3. 2838
3. 2840
3. 2842
3. 2844
3. 2847
3. 2851
3. 2853
32
10
3. 2856
3.2858
3.2860
3. 2862
3. 2865
3. 2867
3. 2869
3. 2871
3. 2874
3. 2876
32
20
3. 2878
3. 2880
3. 2882
3. 2885
3. 2887
3. 2889
3. 2891
3. 2894
3. 2896
3. 2898
32
30
3.2900
3.2903
3.2905
3. 2907
3.2909
3. 2911
3. 2914
3.2916
3. 2918
3. 2920
32
40
3. 2923
3. 2925
3.2927
3. 2929
3. 2931
3. 2934
3. 2936
3. 2938
3. 2940
3. 2942
32
50
3. 2945
3. 2967
3. 2947
3.2949
3. 2951
3. 2953
3. 2956
3.2978
3. 2958
3:2980
3. 2960
3. 2982
3. 2962
3. 2984
3. 2964
3. 2986
33
3.2969
3.2971
3. 2973
3. 2975
33
10
3. 2989
3. 2991
3.2993
3. 2995
3. 2997
3. 2999
3. 3002
3.3004
3. 3006
3. 3008
33
20
3. 3010
3. 3012
3. 3015
3. 3017
3. 3019
3. 3021
3. 3023
3. 3025
3. 3028
3. 3030
33
30
3. 3032
3. 3034
3. 3036
3. 3038
3. 3041
3.3043
3. 3045
3. 3047
3. 3049
3. 3051
33
40
3. 3054
3. 3056
3. 3058
3.3060
3.3062
3.3064
3. 3066
3.3069
3. 3071
3. 3073
33
50
3. 3075
3. 3077
3. 3079
3. 3081
3. 3084
3. 3086
3. 3088
3. 3090
3. ,3092
3. 3094
34
3. 3096
3. 3098
3. 3101
3. 3103
3. 3105
3. 3107
3. 3109
3.3111
3.3113
3. 3115
34
10
3.3118
3. 3120
3. 3122
3. 3124
3. 3126
3. 3128
3. 3130
3. 3132
3. 3134
3. 31,37
34
20
3. 3139
3. 3141
3.3143
3. 3145
3. 3147
3. 3149
3. 3151
3. 3153
3. 3156
3. 3158
34
30
3. 3160
3. 3162
3. 3164
3. 3166
3. 3168
3. 3170
3.3172
3. 3174
,3.3176
3.3179
34
40
3.3181
3.3183
3. 3185
3.3187
3. 3189
3. 3191
3. 3193
3. 3195
3. 3197
3. 3199
34
50
3. 3201
3.3204
3. 3206
3. 3226
3. 3208
3. 3228
3. 3210
3. 3230
3. 3212
3. 3214
3.3235
3. 3216
3. 3218
3. 3220
35
3. 3222
3. 3224
3. 3233
3. 3237
3. 3239
3. 3241
35
10
3. 3243
3. 3245
3. 3247
3. 3249
3. 3251
3. 3253
3. 3255
3. 3257
3. 3259
3. 3261
35
20
3. 3263
3. 3265
3. 3267
3. 3269
3. 3272
3. 3274
3. 3276
3. 3278
3. 3280
3. 3282
35
30
3. 3284
3.3286
3. 3288
3. 3290
3. 3292
3. 3294
3. 3296
3. 3298
3.3300
3. 3302
35
40
3.3304
3.3306
3. 3308
3. 3310
3. 3312
3. 3314
3.3316
3; 3318
3. 3320
3. 3322
35
50
3. 3324
3. 3326
3. 3347
3. 3328
3. 3349
3. 3330
3. 3;»1
3. 3332
3. 3353"
3. 3334
3. 3336
3. 3339
3. 3,341
3. 3343
36
3. 3345
3.3355 i .3.3.357
3. 3359
3. 3.361
3. 3363
36
10
3. 3365
3. 3367
3. 3369
3. 3371
3. 3373
3. 3375
3. 3377
3. 3379
3. 3381
3. 3383
36
20
3. 3385
3. 3387
3. 3389
3. 3391
3. 3393
3. 3395
3. 3397
3. 3398
3.3400
3. 3402
36
30
3.3404
3. ,3406
3. 3408
3. 3410
3. 3412
3. 3414
3. 3416
3. 3418
3. 3420
3. 3422
36
40
3. 3424
3. 3426
3. 3428
3. 3430
3. 3432
3. 3434
3. 3436
3. 3438
3. 3440
3. 3442
36
50
3. 3444
3. 3446
3. 3448
3. 3450
3. 3452
3. 3454
3. 3456
3. 3458
3. 3460
3. 3462
37
3. 3464
3. 3465
3. 3467
3. 3469
3. 3471
3. 3473
3. 3475
3. 3477 1 3. 3479
3. 3481
37
10
3. 3483
3. 3485
3. 3487
3. 3489
3. 3491
3. 3493
3. 3495
3. 3497
3. ,3499
3. 3.501
37
20
3. 3502
3. 3504
3. 3506
3. 3508
3. 3510
3. 3512
3. 3514
3. 3516
3. 3518
3. 3520
37
30
3. 3522
3. .3524
3. 3526
3. 3528
3. 3530
3.3531
3. 3533
3. 3535
3. 3537
3. 3.539
37
40
3. 3541
3. 3543
3. 3545
3. 3547
3. 3549
3. 3551
3. 3553
3. 3555
3. 3556
3. 3558
37
50
3. 3560
3. 3579
3. .3562
3. 3564
3. 3566
3. 3568
3. 3570
3. 3589
3. 3572
3. 3574
3. 3576
3. :i577
38
3. 3581
3. 3583
3. 3585
3. 3587
3. 3591
3. 3593
3. 3595
3. 3,596
38
10
3. 3598
3. 3600
3. 3602
3. 3604
3. 3606
3. 3608 .
3. 3610
3. 3612
3. 3614
3. ,3615
38
20
3. 3617
3. 3619
3. 3621
3. 3623
3. 3625
3. 3627
3. 3629
3. 3630
3. 3632
3. 3634
38
30
3. 3636
3. 3638
3.3640
3. 3642
3. 3644
3. 3646
3. 3647
3. 3649
3. 3651
3. 3653
38
40
3. 3655
3. 3657
3. 3659
3. 3660
3. 3662
3. 3664
3. 3666
3. 3668
3. ,3670
3. 3672
38
50
3. 3674
3. 3692
3. 3675
3. 3677
3. 3679
3. 3681
3. 3683
3. 3685
3. 3687
3. .3705
3.3688
3. 3707
3. 3690
3. 3709
39
3. 3694
3. 3696
3. 3698
3.3700
3. 3701
3. 3703
39
10
3. 3711
3. 3713
3. 3714
3.3716
3.3718
3. 3720
3. 3722
3. 3724
3. 3725
3. 3727
39
20
3.3729
3. 3731
3. 3733
3. 3735
3. 3736
3. 3738
3. 3740
3. 3742
3. 3744
3. 3746
39
30
3. 3747
3. 3749
3. 3751
3. 3753
3. 3755
3. 3757
3. 3758
3. 3760
3. 3762
3. 3764
39
40
3. 3766
3. 3768
3. 3769
3. 3771
3. 3773
3. 3775
3. 3777
3. 3779
3. 3780
3. 3782
39
50
3.3784
3. 3786
3. 3788
3. 3789
3. 3791
3. 3793
3. 3795
3. 3797
3. 3798
3. 3800
APPENDIX
V: TABLE IX.
[Page 317 |
Logarithms of Small Arcs in Space or Time.
Arc.
0"
1"
*"
8"
4"
5" i 6"
7"
8"
»"
' t
0" 40"
It
0'
3. 3802
3. 3804
3.3806
3. 3808
3. .3809
3. 3811
3. 3813
3. 3815
3. 3817
3. 3818
40
10
3. 3820
3. 3822
3. 3824
3. 3826
3. 3827
3. 3829
3. 3831
3. 3833
3.3835
3. 3836
40
20
3. 3838
3.3840
3. 3842
3.3844
3.3845
3. 3847
3. .3849
3. 3851
3. 3852
3.3854
40
30
3. 3856
3. 3858
3.3860
3. 3861
3. 3863
3.3865
3. 3867
3. 3869
3. 3870
3. 3872
40
40
3. 3874
3. 3876
3. 3877
3.3879
3. 3881
3. 3883
3. 3885
3. 3886
3. 3888
3. 3890
40
50
3. 3892
3. 3893
3. 3895
3. 3897
3.3899
3.3901
3.3902
3.3904
3.3906
3.3908
41
3. 3909
3. 3911
3. 3913
3. 3915
3. 3916
3.3918 ! 3.3920
3. 3922
3. 3923
3. 3925
41
10
3. 3927
3.3929
3. 3930
3. 3932
3. 3934
3.3936 1 3.3938
3. .39.39
3. 3941
3. 3943
41
20
3. 3945
3. 3946
3.3948
3. 3950
3. 3952
3.3953 3.3955
3. 3957
3. 3959
3.3960
41
30
3. 3962
3. .3964
3.3965
3. 3967
3. 3969
3. 3971
3. 3972
3. 3974
3. 3976
3. 3978
41
40
3. 3979
3. 3981
3. 3983
3.3985
3. 3986
3. 3988
3.3990
3. 3992
3. 3993
3. 3995
41
50
3. 3997
3. 3998
3.4000
3.4002
3. 4019
3.4004
3. 4021
3.4005
3.4007
3.4024
3.4009
3. 4011
3. 4012
42
3. 4014
3. 4016
3. 4017
3. 4023
3. 4026
3. 4028
3.4029
42
10
3. 4031
3. 4033
3.4035
3.4036
3.4038
3.4040
3. 4041
3. 4043
3. 4045
3.4047
42
20
3. 4048
3. 4050
3. 4052
3. 4053
3. 4055
3. 4057
3. 4059
3. 4060
3. 4062
3.4064
42
30
3.4065
3. 4067
3.4069
3.4071
3.4072
3. 4074
3. 4076
3.4077
3. 4079
3. 4081
42
40
3. 4082
3. 4084
3. 4086
3.4087
3. 4089
3.4091
3. 4093
3.4094
3. 4096
3.4098
42
50
3.4099
3. 4101
3. 4103
3.4104
3.4106
3. 4108
3. 4125
3.4109
3.4111
3.4113
3.4115
43
3.4116
3.4118
3. 4120
3. 4121
3. 4123
3. 4126
3. 4128
3. 4130
3. 4131
43
10
3.4133
3.4135
3. 4136
3.4138
3. 4140
3. 4141
3. 4143
3. 4145
3. 4146
3. 4148
43
20
3. 4150
3. 4151
3. 4153
3. 4155
3. 4156
3. 4158
3.4160
3.4161
3. 4163
3. 4165
43
30
3. 4166
3. 4168
3.4170
3. 4171
3. 4173
3. 4175
3.4176
3. 4178
3. 4180
3. 4181
43
40
3. 4183
3.4185
3. 4186
3. 4188
3.4190
3. 4191
3. 4193
3. 4195
3.4196
3. 4198
43
50
3.4200
3. 4201
3.4203
3.4205
3.4206
3.4208
3. 4224
3.4209
3.4211
3. 4213
3. 4214
44
3. 4216
3. 4218
3. 4219
3. 4221
3. 4223
3. 4226
3. 4228
3. 4229
3. 4231
44
10
3. 4232
3. 4234
3.4236
3. 4237
3. 4239
3. 4241
3. 4242
3. 4244
3. 4246
3. 4247
44
20
3. 4249
3. 4250
3. 4252
3.4254
3. 4255
3. 4257
3. 4259
3.4260
3. 4262
3. 4263
44
30
3. 4265
3. 4267
3. 4268
3. 4270
3. 4272
3.4273
3. 4?75
3. 4276
3. 4278
3. 4280
44
40
3. 4281
3. 4283
3. 4285
3. 4286
3. 4288
3. 4289
3. 4291
3. 4293
3.4294
3.4296
44
50
3.4298
3.4299
3. 4301
3. 4302
3. 4304
3. 4306
3. 4307
3. 4309
3. 4310
3. 4312
45
3. 4314
3. 4315
3.4317
3. 4318
3.4320
3. 4322
3. 4323
3.4325
3. 4326
3. 4328
45
10
3. 4330
3. 4331
3.4333
3. 4334
3. 4336
3. 4338
3. 4339
3. 4341
3. 4342
3.4344
45
20
3. 4346
3. 4347
3. 4349
3. 4.350
3.4352
3.4354
3.4355
3. 4357
3.4358
3.4360
45
30
3. 4362
3. 4363
3.4365
3.4366
3. 4368
3. 4370
3. 4371
3. 4373
3. 4374
3. 4376
45
40
3. 4378
3. 4379
3. 4381
3. 4382
3. 4384
3. 4385
3. 4387
3. 4389
3. 4.390
3. 4392
45
50
3. 4393
3. 4395
3. 4396
3. 4398
3.4400
3. 4401
3.4403
3.4404
3. 4406
3. 4408
46
3.4409
3.4411
3.4412
3. 4414
3. 4415
3.4417
3.4419
3. 4420
3.4422
3.4423
46
10
3. 4425
3.4426
3.4428
3. 4429
3. 4431
3.4433
3.4434
3. 4436
3. 4437
3. 4439
46
20
3. 4440
3. 4442
3.4444
3.4445
3. 4447
3. 4448
3. 4450
3. 4451
3. 4453
3. 4454
46
30
3. 4456
3.4458
3.4459
3. 4461
3. 4462
3.4464
3.4465
3.4467
3.4468
3. 4470
46
40
3. 4472
3.4473
3.4475
3.4476
3. 4478
3.4479
3.4481
3.4482
3. 4484
3.4486
46
50
3.4487
3.4489
3.4490
3. 4492
3. 4493
3.4495
3. 4496
3. 4498
3.4499
3. 4501
47
3. 4502
3.4504
3.4506
3. 4507
3.4509
3. 4510
3. 4512
3.4513
3.4515
3. 4516
47
10
3. 4518
3. 4519
3. 4521
3. 4522
3. 4524
3. 4526
3.4527
3. 4529
3.4530
3.4532
47
20
3. 4533
3. 4535
3.4536
3. 4538
3. 4539
3. 4541
3. 4542
3.4544
3. 4545
3.4547
47
30
3. 4548
3. 4550
3. 4551
3. 4553
3. 4555
3. 4556
3. 4558
3. 4.559
3.4561
3. 4562
47
40
3. 4564
3. 4565
3. 4567
3. 4.568
3. 4570
3. 4571
3.4573
3. 4574
3. 4576
3. 4577
47
50
3. 4579
3. 4580
3. 4582 3. 4583
3. 4597 3. 4598
3.4585
3.4600
3. 4.586
3.4601
3.4588
374603"
3. 4589
3. 4591
3. 4592
3. 4607
48
3. 4,594
3. 4.595
3. 4604
3.4606
48
10
3. 4609
.3. 4610
3. 4612 3. 4613
3. 4615
3. 4616
3. 4618
3. 4619
3. 4621
3. 4622
48
20
3. 4624
3. 4625
3.4627 ' 3.4628
3. 4630
3. 4631
3. 4633
3. 4634
3. 4636
3. 4637
48
30
3. 4639
3.4640
3.4642 I 3.4643
3. 4645
3.4646
3.4648
3.4649
3.4651
3.4652
48
40
3. 4654
3.4655
3.4657
3. 4658
3. 4660
3. 4661
3. 4663
3.4664
3.4666
3. 4667
48
50
3. 4669
3.4670
3. 4672
3.4673
3. 4675
3. 4676
3. 4678
3. 4679
3. 4681
3.4695
3.4682
49
3.4683
3.4685
3.4686
3. 4688
3. 4689
3. 4691
3. 4692
3. 4694
3. 4697
49
10
3. 4698
3.4700
3. 4701
3. 4703
3. 4704
3.4706
3. 4707
3. 4709
3. 4710
3.4711
49
20
3. 4713
3. 4714
3.4716
3.4717
3. 4719
3. 4720
3. 4722
3. 4723
3. 4725
3. 4726
49
30
3. 4728
3.4729
3. 4730
3. 4732
3. 4733
3.4735
3. 4736
3. 4738
3. 4739
3. 4741
49
40
3. 4742
3. 4744
3. 4745
3. 4747
3. 4748
3. 4749
3. 4751
3. 4752
3. 47.54
3. 4755
49
50
3. 4757
3. 4758
3. 4760
3. 4761
3. 4763
3.4764
3. 47a5
3. 4767
3. 4768
3. 4770
Page 318]
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in
Space or Time.
Arc.
0"
1"
2"
8"
4"
6"
6"
I" [ 8"
9"
o /
0" 50"
n
3. 4771
3. 4773
3. 4774
3. 4776
3.4777
3. 4778
3. 4780
3. 4781
3. 4783
3. 4784
50
10
3. 4786
3. 4787
3. 4789
3. 4790
3. 4791
3. 4793
3. 4794
3. 4796
3. 4797
3. 4799
50
20
3. 4800
3. 4802
3.4803
3.4804
3. 4806
3. 4807
3.4809
3. 4810
3. 4812
3.4813
50
30
3. 4814
3. 4816
3. 4817
3. 4819
3. 4820
3. 4822
3. 4823
3. 4824
3. 4826
3. 4827
50
40
3. 4829
3. 4830
3.4832
3. 4833
3. 4834
3. 4836
3. 4837
3. 4839
3. 4840
3. 4842
50
50
3. 4843
3.4844
3. 4846
3. 4860
3. 4847
3. 4861
3. 4849
3. 4863
3. 4850
3. 4864
3. 4852
3. 4853
3. 4854
3. 4869
3. 4S56
51
3.4857
3. 4859
3. 4866
3. 4667
3. 4870
51
10
3. 4871
3. 4873
3. 4874
3. 4876
3. 4877
3. 4878
3. 4880
3. 4881
3. 4883
3. 4884
51
20
3. 4886
3. 4887
3. 4888
3.4890
3. 4891
3. 4893
3. 4894
3. 4895
3. 4897
3. 4898
51
30
3. 4900
3. 4901
3. 4902
3. 4904
3. 4905
3. 4907
3. 4908
3. 4909
3. 4911
3. 4912
51
40
3. 4914
3.4915
3. 4916
3.4918
3. 4919
3.4921
3. 4922
3. 4923
3. 4925
3. 4926
51
50
3. 4928
3. 4929
3. 4930
3. 4932
3. 4933
3. 4935
3. 4936
3. 4937
3. 4939
3. 4940
52
3. 4942
3. 4943
3. 4944
3. 4946
3. 4947
3. 4949
3. 4950
3. 4951
3. 4953
3. 4954
52
10
3. 4955
3. 4957
3. 4958
3. 4960
3. 4961
3. 4962
3. 4964
3. 4965
3. 4967
3.4968
52
20
3. 4969
3. 4971
3. 4972
3. 4973
3.4975
3. 4976
3. 4978
3. 4979
3. 4980
3. 4982
52
30
3. 4983
3.4984
3. 4986
3. 4987
3. 4989
3. 4990
3. 4991
3. 4993
3. 4994
3. 4995
52
40
3.4997
3. 4998
3. 5000
3.5001
3.5002
3.5004
3. .5005
3.5006
3. 5008
3. 5009
52
50
3.5011
3. 5012
3.5013
3. 5015
3.5028
3. 5016
3. 5030
3.5017
3. 5031
3. 5019
3. 5032"
3. 5020
3. 50,34
3. 5022
"3.5035
3. 5023
53
3. 5024
3. 5026
3. 5027
3. 5037
53
10
3. 5038
3. 5039
3.5041
3. 5042
3. 5043
3. 5045
3. 5046
3. 5047
3. 5049
3. 5050
53
20
3. 5051
3. 5053
3.5054
3. 5056
3.5057
3. 5058
3.5060
3. 5061
3. 5062
3. 5064
53
30
3. 5065
3. 5066
3. 5068
3.5069
3. 5070
3. 5072
3. 5073
3. 5075
3. 5076
3. 5077
53
40
3. 5079
3. 5080
3. 5081
3. 5083
3. 5084
3. 5085
3. 5087
3. 5088
3. 5089
3. 5091
53
50
3.5092
3. 5093
3. 5107
3. 5095
3. 5108
3.5096
3.5097
3. 5099
3.5100
3.5113
3. 5101
3.5115
3. 5103
3. 5104
3.5117
54
3. 5105
3. 5109
3.5111
3. 5112
5.5116
54
10
3.5119
3. 5120
3. 5122
3. 5123
3. 5124
3. 5126
3.5127
3.5128
3. 5130
3. 5131
54
20
3. 5132
3. 5134
3. 5135
3. 5136
3. 5138
3. 5139
3. 5140
3.5141
3. 5143
3.5144
54
30
3. 5145
3. 5147
3. 5148
3. 5149
3. 5151
3. 5152
3.5153
3. 5155
3. 5156
3. 51.57
54
40
3. 5159
3. 5160
.3.5161
3. 5163
3.5164
3.5165
3.5167
3. 5168
3.5169
3.5171
54
50
3. 5172
3.5173
3. 5175
3. 5176
3.5177
3. 5179
3. 5180
3.5181
3. 5183
3.5184
55
3. 5185
3.5186
3. 5188
3. 5189
3. 5190
3. 5192
3. 5193
3. 5194
3. 5196
3. 5197
55
10
3. 5198
3. 5200
3. 5201
3. 5202
3. 5204
3. 5205
3. 5206
3. 5207
3.5209
3. 5210
55
20
3. 5211
3. 5213
3.5214
3. 5215
3. 5217
3. 5218
3. 5219
3. 5221
3. 5222
3. 5223
55
30
3. 5224
3. 5226
3. 5227
3. 5228
3. 5230
3. 5231
3. 5232
3. 5234
3.5235
8. 5236
55
40
3.5237
3. 5239
3. 5240
3. 5241
3. 5243
3.5244
3. 5245
3. 5247
3. 5248
3. 5249
55
50
3. 5250
3. 5252
3. 5253
3. 5254
3. 5256
3. 5257
3. 5270
3. 5258
3. 5260
3. 5261
3. 5274
3. 5262
56
3. 5263
3. 5265
3. 5266
3. 5267
3. 5269
3. 5271
3. 5272
3. 5275
56
10
3. 5276
3. 5278
3. 5279
3. 5280
3. 5281
3. 5283
3. 5284
3. 5285
3. 5287
3. 5288
56
20
3. 5289
3. 5290
3. 5292
3.5293
3.5294
3.5296
3.5297
3. 5298
3.5299
3.5301
56
30
3. 5302
3. 5303
3. 5305
3. 5306
3. 5307
3. 5308
3. 5310
3.5311
3. 5312
3. 5314
56
40
3.5,315
3. 5316
3. 5317
3. 5319
3. 5320
3.5321
3. 5322
3. 5324
3. 5,325
3.5326
56
50
3. 5328
3.5329
3. 5330
3. 5331
3. 5333
3. 5334
3.5335
3. 5336
3. 5338
3. 5350
3. 5339
3. 5352
57
3. 5340
3. 5342
3. 5343
3.5344
3. 5345
3. 5347
3. 5348
3. 5349
57
10
3.5353
3. 5354
3.5355
3. 5357
3. 5358
3.5359
3.5361
3. 5362
3. 5363
3. 5,364
57
20
3. 5366
3. 5367
3. 5368
3. 5369
3. 5371
3. 5372
3. 5373
3. 5374
3. 5376
3. 5377
57
30
3. 5378
3. 5379
3. 5381
3. 5382
3. 5383
3. 5384
3. 5386
3. 5,387
3. 5388
3. 5390
57
40
3. 5391
3. 5392
3. 5393
3. 5395
3. 5396
3. 5397
3. 5398
3.5400
3. 5401
3.5402
57
50
3. 5403
3.5405
3.5406
3. 5407
3.5408
3. 5410
3. 5411
3.5412
3. 5413
3. .5415
58
3.5416
3. 5417
3. 5418
3.5420
3. 5421
3.5422
3.5423
3. 5425
3. 5426
3.5427
58
10
3. 5428
3.5429
3. 5431
3.5432
3.5433
3.5434
3. 5436
3. 5437
3.5438
3.5439
58
20
3. 5441
3.5442
3.5443
3.5444
3. 5446
3.5447
3. 5448
3. 5449
3. 5451
3.5452
58
30
3.5453
3.5454
3.5456
3. 5457
3.5458
3.5459
3.5460
3. 5462
3. 5463
3. 5464
58
40
3.5465
3.5467
3.5468
3. 5469
3. 5470
3. 5472
3. 5473
3. 5474
3. 5475
3.5477
58
50
3. 5478
3.5479
3. 5480
3.5481
3.5483
3. 5495
3. 5484
3. 5485
3.5486
3. 5499
3. 5488
3. 5489
59
3.5490
3.5491
3. 5492
3.5494
3. 5496
3. 5497
3.5500
3. 5501
59
10
3. 5502
3. 5504
3. 5505
3.5506
3. 5507
3. 5508
3.5510
3.5511
3. 5512
3. 5513
59
20
3. 5514
3. 5516
3. 5517
3.5518
3. 5519
3. 5521
3. 5522
3. 5523
3. 5524
3. 5525
59
30
3. 5527
3. 5528
3. 5529
3. 5530
3. 5532
3. 5533
3. 5534
3. 5535
3. 5536
3. 5538
59
40
3. 5539
3. 5540
3.5541
3. 5542
3.5544
3. 5545
3. 5546
3. .5547
3. 5549
3. 5550
59
50
3. 5551
3. 5552
3. 55.53
3. 5.555
3. 5.556
3. 5557
3. 5.558
3. 5.559
3. 5561
3. 5562
1
APPENDIX V: TABLE IX.
[Page 319
Logarithms of Small Arcs in Space or Time.
Arc.
0"
1"
2"
8"
4"
5"
6"
7"
8"
8"
o t
l" 0"
0'
3. 5563
3.5564
3. 5565
3.5567
3. 5568
3. 5569
3. 5570
3. 5571
3. 55''3
3. 5574
10
3. 5575
3. 5576
3. 5577
3. 5579
3. 5580
3. .5581
3. 5582
3. 5583
3. 5585
3. 5586
20
3. 5587
3. 5.588
3. 5589
3. 5591
3. 5592
3. 5593
3. 5594
3. 5595
3. 5597
3. 5598
30
3. 5599
3.5600
3. .5601
3. 5603
3. 5604
3. 5605
3.5606
3. 5607
3.5609
3. 5610
40
3. 5611
3. 5612
3. 5613
3. 5615
3. 5616
3.5617
3. 5618
3. 5619
3. 5621
3. 5622
.50
3. 5623
3. 5624
3. 5625
3. 5626
3. 5628
3. 5629
3. 5630
3. 5631
3. 5632
3. 5634
3. .5645
1 1
3.5635
3. 5636
3. 5637
3.5638
3.5640
3. 5641
3.5642
3.5643
3. 5644
10
3. 5647
3. 5648
3. .5649
3.5650
3. 5651
3. 5653
3.5654
3. 5655
3. 56.56
3. 5657
20
3.5658
3.5660
3. 5661
3. 5662
3. 5663
3. 5664
3. 5666
3.5667
3. 5668
3. 5669
30
3. 5670
3. 5671
3. 5673
3. 5674
3. 5675
3. 5676
3. 5677
3. 5678
3. 5680
3. 5681
40
3. 5682
3. 5683
3. 5684
3. 5686
3. 5687
3. 5688
3. 5689
3. 5690
3. .5691
3. 5693
50
3. 5694
3. 5695
3. 5696
3. 5697
3. 5698
3. 5700
3. 5701
3. 5702
3. 5703
3. 5704
1 2
3. 5705
3. 5707
3. 5708
3. 5709
3.5710
3. 5711
3.5712
3. 5714
3.5715
3. 5716
10
3. 5717
3.5718
3. 5719
3. 5721
3. 5722
3. 5723
3. 5724
3. 5725
3. 5726
3. 5728
2
20
3. 5729
3. 5730
3. 57.31
3. 5732
3. 5733
3. 5735
3. 5736
3. 5737
3. 5738
3. 5739
2
30
3. 5740
3.5741
3. 5742
3. 5744
3. 5745
3. 5746
3. 5747
3. 5748
3. 5750
3. 5751
2
40
3. 5752
3. 5753
3. 5754
3. 5755
3. 5756
3. 5758
3. 5759
3.5760
3. 5761
3. 5762
2
■iO
3. 5763
3. 5765
3. 5766
3. 5767
"3. 5778
3.5768
3. 5769
3.5770
3. 5771
3.5773
3. 5774
1 3
3. 5775
3. 5776
3. 5777
3. 5780
3. 5781
3. 5782
3. 5783
3. 5784
3. 5785
3
10
3. 5786
3.5788
3. 5789
3. 5790
3. 5791
3. 5792
3.5793
3. 5794
3. 5796
3. 5797
3
20
3. 5798
3. 5799
3.5800
3. 5801
3.5802
3. 5804
3. 5805
3.5806
3. 5807
3. 5808
3
30
3.5809
3. 5810
3. .5812
3. 5813
3. 5814
3. 5815
3. 5816
3. 5817
3. 5818
3. 5819
3
40
3. 5821
3. 5822
3. 5823
3. 5824
3. 5825
3. 5826
3. 5827
3. 5829
3. 5830
3. 5831
3
1 4
50
3. 5832
3.5843
3. 5833
3. 5834
3. 5846
3. 5835
3. 5837
3. 5838
3. 5839
3. 5840
3. 5841
3. 5842
37,5853
3. 5844
3. 5847
3. 5848
3.5849
3. 5850
3. 5851
3. 5852
4
10
3. 5855
3. 58.56
3. 5857
3. 5858
3. 5859
3. 5860
3. 5861
3. 5862
3. 5864
3. 5865
4
20
3. 5866
3. 5867
3. 5868
3. 5869
3. 5870
3. 5871
3. 5873
3. 5874
3. 5875
3. 5876
4
30
3. 5877
3. 5878
3. 5879
3. 5880
3. 5882
3. 5883
3. 5884
3. 5885
3. 5886
3. 5887
4
40
3. 5888
3. 5889
3. 5891
3. 5892
3.5893
3. 5894
3. 5895
3. 5896
3. 5897
3. 5898
4
50
3. 5899
3. 5901
3. 5902
3.5903
3.5904
3. 5905
3.5906
3. 5907
3. 5908
3.5910
1 5
3. 5911
3. 5912
3. 5913
3. 5914
3. 5915
3. 5916
3. 5917
3. 5918
3. ,5920
3. 5921
5
10
3. 5922
3. 5923
3.5924
3. 5925
3. 5926
3. 5927
3. 5928
3. 5930
3. 5931
3. 5932
5
20
3. 5933
3. 5934
3.5935
3. 5936
3. 5937
3. 5938
3. 5940
3. 5941
3. 5942
3. 5943
5
30
3. 5944
3. 5945
3.5946
3.5947
3. 5948
3. 5949
3. 5951
3. 5952
3. 5953
3. 5954
5
40
3. 5955
3. 59.56
3. 5957
3. 5958
3. 5959
3.5960
3.5962
3.5963
3. 5964
3. 5965
5
1 6
50
3.5966
3.5967
3.5968
3.5969
3. 5970
3. 5971
3. 5973
3. 5974
3. 5975
3. 5976
3. 5977
3. 5978
3. 5979
3.5980
3, 5981
3. 5982
3.5984
3. 5985
3. 5986
3. 5987
6
10
3. 5988
3. 5989
3.5990
3.5991
3.5992
3.5993
3. 5994
3. 5996
3. 5997
3. 5998
6
20
3. 5999
3.6000
3.6001
3.6002
3.6003
3.6004
3. 6005
3.6006
3.6008
,3.6009
6
30
3.6010
3.6011
3.6012
3.6013
3.6014
3.6015
3.6016
3. 6017
3. 6018
3. 6020
6
40
3.6021
3.6022
3.6023
3.6024
3.6025
3. 6026
3. 6027
3. 6028
3.6029
3. 6030
6
50
3. 6031
3.6042
3. 6033
3.6034
3.6035
3. 6036
3.6037
3.6038
3. 60.39
3.6040
3. 6041
1 7
3.6043
3.6044
3.6046
3.6047
3. 6048
3.6049
3.6050
3.6051
3.6052
7
10
3.6053
3.6054
3.6055 1 3.60.56
3.6057
3. 60.58
3.6060
3.6061
3.6062
3.6063
7
20
3.6064
3.6065
3. 6066 i 3. 6067
3.6068
3.6069
3.6070
3.6071
3.6072
3.6073
7
30
3. 6075
3.6076
3.6077 3.6078
3.6079
3.6080
3. 6081
3.6082
3.6083
3. 6084
7
40
3.60a5
3.6086
3.6087 3.6088
3.6090
3. 6091
3.6092
3.6093
3.6094
.3.6095
7
50
3.6096
3.6097
3. 6098 j 3. 6099
3.6100
3. 6101
3. 6102
3. 6103
3.6104
3.6106
1 8
3. 6107
3. 6108
3.6109
3.6110
3.6111
3. 6112
3. 6113
3.6114
3.6115
3.6116
8
10
3.6117
3. 6118
3.6119
3. 6120
3. 6121
3.6123
3. 6124
3. 6125
3. 6126
3. 6127
8
20
3. 6128
3.6129
3.6130
3.6131
3. 6132
3. 61.33
3. 6134
3.6135
3. 6136
3. 6137
8
30
3.6138
3.6139
3. 6141
3. 6142
3. 6143
3. 6144
3.6145
3. 6146
3. 6147
3. 6148
8
40
3. 6149
3. 61.50
3. 6151
3. 6152
3. 6153
3. 61.54
3. 6155
3. 6156
3. 6157
3. 6158
8
50
3. 6160
3. 6161
3. 6162
3.6163
3.6164
3.6165
3. 6166
3. 6167
3. 6168
3. 6169
1 9
3.6170
3.6171
3. 6172
3. 6173
3. 6174
3. 6175
3.6176
3. 6177
3.6178
3. 6179
9
10
3. 6180
3. 6182
3.6183
3.6184
3.6185
3. 6186
3. 6187
3. 6188
3. 6189
3.6190
9
20
3. 6191
3.6192
3. 6193
3.6194
3. 6195
3. 6196
3. 6197
3.6198
3. 6199
3.6200
9
30
3.6201
3. 6202
.3.6203
3.6204
3.6206
3.6207
3.6208
3.6209
3. 6210
3. 6211
9
40
3. 6212
3. 6213
3.6214
3. 6215
3. 6216
3. 6217
3. 6218
3. 6219
3.6220
3.6221
9
50
3. 6222
3. 6223
3. 6224
3.6225
3. 6226
3. 6227
3. 6228
3. 6229
3.6230
3. 6231
Page 320J
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or
Time.
Are.
0"
1"
i" 1 8" 1 4" 5"
C"
l"
8"
9"
o /
1" 10"
0»
3. 6232
3. 6234
3. 6235
3. 6236 3. 6237
3. 6238
3. 6239
3. 6240
3. 6241
3. 6242
10
10
3. 6243
3. 6244
3. 6245
3. 6246 3. 6247
3. 6248
3. 6249
3. 6250
3. 6251
3. 6252
10
■20
3. 6253
3. 6254
3. 6255
3. 6256 ' 3. 6257
3. 6258
3. 6259
3. 6260
3. 6261
3. 6262
10
30
3. 6263
3. 6264
3. 6265
3. 6266 3. 6268
3. 6269
3. 6270
3. 6271
3. 6272
3. 6273
10
40
3. 6274
3. 6275
3. 6276
3. 6277
3.6278
3. 6279
3. 6280
3. 6281
3. 6282
3. 6283
10
50
3. 6284
3.6294
3.6285
3. 6295
3. 6286
3. 6296
3. 6287
3.6297
3. 6288
3. 6289
3. 6290
3. 6300
3.6291
3. 6292
3. 6293
1 11
3. 6298
3. 6299
3. 6301
3. 6302
3. 6303
11
10
3. 6304
3. 6305
3. 6306
3. 6307
3.6308
3.6309
3. 6310
3.6311
3. 6312
3. 6313
11
20
3.6314
3. 6315
3.6316
3. 6317
3. 6318
3. 6320
3. 6321
3. 6322
3. 6323
3. 6324
11
80
3. 6.325
3. 6326
3. 6327
3. 6328 3. 6329
3. 6330
3.6331
3. 6332
3. 6333
3. 6334
11
40
3. 6335
3. 6336
3. 6337
3. 6338 3. 6339
3. 6340
3. 6341
3. 6342
3. 6343
3. 6344
11
50
3. 6345
3. 6346
3. 6356
3. 6347
3. 6357
3. 6348 3. 6349
3. 6350
3. 6351
3. 6352
3. 6353
3. 6363
3. 6354
3. 6364
1 12
3. 6355
3. 6358 3. 6359
3. 6360
3. 6361
3. 6362
12
10
3. 6365
3. 6366
3. 6367
3. 6368 3. 6369
3. 6370
3. 6371
3. 6372
3. 6373
3. 6374
12
20
3. 6375
3. 6376
3. 6377
3. 6378 3. 6379
3. 6380
3.6381
3. 6382
3. 6383
3. 6384
12
30
3. 6385
3. 6386
3. 6387
3.6388 ; 3.6389
3. 6390
3. 6391
3. 6392
3. 6393
3. 6394
12
40
3. 6395
3. 6396
3. 6397
3. 6398 3. 6399
3.6400
3.6401
3. 6402
3. 6403
3. 6404
12
50
3.6405
3. 6406
3. 6407
3.6408 ; 3.6409
3. 6410
3.6411
3. 6412
3.6413
'3.6423
3.6414
3. 6424
1 13
3.6415
3. 6416
3.6417
3.6418 ! 3.6419
3. 6420
3. 6421
3. 6422
13
10
3. 6425
3. 6426
3. 6427
3.6428 : 3.6429
3. 6430
3. 6431
3. 6432
3. 6433
3. 6434
13
20
3. 6435
3. 6436
3.6437
3.6437 ! 3.6438
3. 6439
3. 6440
3. 6441
3. 6442
3. 6443
13
30
3.6444
3.6445
3. 6446
3.6447 ' 3.6448
3.6449
3. 6450
3. 6451
3. 6452
3. 6453
13
40
3. 6454
3. 6455
3. 6456
3. 6457
3. 6458
3.6459
3. 6460
3. 6461
3. 6462
3. 6463
13
50
3.6464
3. 6465
3. 6466
3.6467
3.6468
3. 6469
3.6470
3.6471
3.6472
3. 6473
1 14
3. 6474
3. 6475
3. 6476
3.6477
3. 6478
3. 6479
3. 6480
3.6481
3.6482
3.6483
14
10
3. 6484
3. 6485
3. 6486
3.6487
3. 6488
3. 6488
3. 6489
3. 6490
3. 6491
3. 6492
14
20
3. 6493
3. (-:494
3. 6495
3. 6496
3. 6497
3.6498
3. 6499
3. 6500
3. 6501
3. 6502
14
30
3. 6503
3. 6504
3. 6505
3. 6506
3. 6507
3. 6508
3. 6509
3. 6510
3.6511
3. 6512
14
40
3. 6513
3. 6514
3. 6515
3. 6516
3. 6517
3. 6518
3.6519
3.6520
3. 6521
3. 6521
14
50
3. 6522
3. 6523
3. 6524
3.6525 i 3.6526
3.6527
3.6528
3.6529
3. 6539
3. 6530
3.6540
3. 6531
3. 6541
1 15
3.6532
3. 6533
3. 6534
3.6535
3. 6536
3. 6537
3.6538
15
10
3.6542
3. a543
3.6544
3.6545
3.6546
3.6547
3. 6548
3.6549
3.6549
3. 6550
15
20
3. 6551
3. 6552
3. 6553
3. 6554
3. 6555
3. 6556
3. 6557
3. 6558
3.6559
3.6560
15
30
3. 6561
3. 6562
3. 6563
3.6564
3.6565
3. 6566
3. 6567
3. 6568
3. 6569
3. 6570
15
40
3. 6571
3. 6572
3. 6572
3. 6573
3. 6574
3. 6575
3. 6576
3. 6577
3. 6578
3. 6579
15
50
3.6580
3.6681
3. 6582
3. &583
3. 6584
3. 6585
3. 6586
3. 6587
3. 6588
3.6589
1 16
3. 6590
3. 6591
3. 6592
3. 6593
3.6593
3. 6594
3. 6595
3.6596 3.6597
3. 6598
16
10
3. 6599
3. 6600
3.6601
3. 6602
3. 6603
3.6604
3. 6605
3. 6606 3. 6607
3. 6608
16
20
3. 6609
3.6610
3.6611
3.6611
3. 6612
3. 6613
3. 6614
3.6615 3.6616
3. 6617
16
30
3. 6618
3. 6619
3. 6620
3. 6621
3. 6622
3. 6623
3. 6624
3. 6625 3. 6626
3. 6627
16
40
3. 6628
3. 6629
3. 6629
3. 6630
3. 6631
3. 6632
3. 6633
3. 6634 3. 6635
3. 6636
16
50
3. 6637
3. 6638
3. 6639
3. 6640
3. 6641
3.6650
3. 6642
3. 6643
3. 6644 1 3. 6645
3. 6645
1 17
3. 6646
3. 6647
3.6648
3. 6649
3. 6651
.3.6652
3. 6653
3.6654
3.6655
17
10
3.6656
3.6657
3. 6658
3.6659
3. 6660
3. 6660
3.6661
3. 6662
3. 6663
3. 6664
17
20
3. 6665
3. 6666
3. 6667
3. 6668
3. 6669 .
3. 6670
3. 6671
3. 6672
3. 6673
3. 6674
17
30
3. 6675
3. 6675
3. 6676
3. 6677
3. 6678
3. 6679
3. 6680
3. 6681
3. 6682
3. 6683
17
40
3. 6684
3.6685
3. 6686
3. 6687
3. 6688
3. 6689
3. 6689
3. 6690
3. 6691
3. 6692
17
50
3. 6693
3. 6702
3. 6694
3. 6703
3. 6695
3. 6696
3. 6705
3. 6697
3. 6698
3. 6707
3. 6699
3. 6700
3. 6701
3. 6702
3.6711
1 18
3. 6704
3.6706
3. 6708
3. 6709
3.6710
18
10
3. 6712
3. 6713
3. 6714
3. 6715
3. 6715
3. 6716
3.6717
3. 6718 ! 3. 6719
3. 6720
18
20
3. 6721
3. 6722
3. 6723
3. 6724
3. 6725
3. 6726
3. 6727
3. 6727 ; 3. 6728
3. 6729
18
30
3. 6730
3. 6731
3. 6732
3. 6733
3. 6734
3. 6735
3. 6736
3.6737 3.6738
3. 6738
18
40
3. 6739
3. 6740
3. 6741
3. 6742
3. 6743
3.6744
3. 6745
3.6746 3.6747
3. 6748
18
50
3. 6749
3. 6750
3. 6759
3. 6750
3. 6760
3. 6751
3. 6752
3. 6753
3. 6754
3. 6755
3. 6756
3. 6765
3. 6757
3. 6766
1 19
3. 6758
3. 6761
3. 6761
3. 6762
3. 6763
3. 6764
19
10
3. 6767
3. 6768
3. 6769
3. 6770
3. 6771
3.6772
3. 6772
3. 6773 ' 3. 6774
3. 6775
19
20
3. 6776
3. 6777
3. 6778
3. 6779
3. 6780
3. 6781
3. 6782
3. 6782
3.6783
3. 6784
19
30
3. 6785
3. 6786
3. 6787
3. 6788 , 3. 6789
3.6790
3. 6791
3. 6792
3. 6792
3. 6793
19
40
3. 6794
3. 6795
3.6796
3.6797 1 3.6798
3. 6799
3. 6800
3. 6801
3. 6802
3. 6802
19
50
3. 6803
3. 6804
3. 6805
3. 6806 3. 6807
3. 6808
3. 6809
3. 6810
3.6811
3. 6812
APPENDIX V: TABLE IX.
[Page 321
Logarithms of Small Arcs in Space or Time.
Arc.
0"
1"
2"
8"
4"
5"
6"
7"
8"
9"
o t
Ih 20"
fl
0'
3. 6812
3. 6813
3.6814
3. 6815
3. 6816
3. 6817
3. 6818
3. 6819
3.6820
3.6821
20
10
3. 6821
3. 6822
3. 6823
3.6824
3.6825
3.6826
3. 6827
3. 6828
3.6829
3. 6830
20
20
3. 6830
3. 6831
3.6832
3.6833
3. 6834
3.6835
3. 6836
3. 6837
3. 6838
3. 6839
20
30
3. 6839
3. 6840
3.6841
3.6842
3.6843
3.6844
3. 6845
3. 6846
3.6847
3. 6848
20
40
3. 6848
3. 6849
3.6850
3. 6851
3.6852
3.6853
3.6854
3.6855
3.6856
3. 6857
20
50
3.6857
3.6858
3. 6867
3.6859
3. 6860
3. 6861
3. 6862
3. 6871
3. 6863
3. 6864
3.6865
3. 6874
3.6865
3. 6874
1 21
3. 6866
3.6868
3. 6869
3. 6870
3. 6872
3. 6873
21
10
3. 6875
3. 6876
3. 6877
3. 6878 3. 6879
3. 6880
3. 6881
3. 6882
3. 6882
3. 6883
21
20
3. 6884
3. 6885
3. 6886
3. 6887
3. 6888
3. 6889
3.6890
3. 6890
3. 6891
3. 6892
21
30
3. 6893
3. 6894
3. 6895
3. 6896
3. 6897
3. 6898
3. 6898
3.6899
3.6900
3. 6901
21
40
3.6902
3. 6903
3. 6904
3. 6905
3.6906
3. 6906
3. 6907
3. 6908
3.6909
3. 6910
21
50
3.6911
3. 6912
3. 6913
3.6913
3. 6914
3. 6915
3. 6916
3. 6917
3. 69ia
'3.6927
3. 6919
1 22
3. 6920
3. 6921
3. 6921
3. 6922
3. 6923
3. 6924
3. 6925
3. 6926
3. 6928
22
10
3.6928
3. 6929
3. 6930
3. 6931 3. 6932
3. 6933
3. 6934
3. 6935
3. 6936
3. 6936
22
20
3. 6937
3. 6938
3. 6939
3. 6940 3. 6941
3. 6942 ; 3. 6943
3. 6943
3.6944
3. 6945
22
30
3. 6946
3. 6947
3. 6948
3.6949 1 3.6950
3. 6950 1 3. 6951
3. 6952
3. 6953
3. 6954
22
40
3. 6955
3. 6956
3. 6957
3.6957 3.6958
3.6959 3.6960
3. 6961
3. 3962
3.6963
22
50
3.6964
3.6964
3.6965
3. 6966 i 3. 6967
3. 6968 ! 3. 6969
3. 6977 1 3. 6978
3. 6970
3. 6978
3.6971
3. 6979
3. 6971
1 23
3. 6972
3. 6973
3. 6974
3.6975 i 3.6976
3. 6980
23
10
3. 6981
3. 6982
3.6983
3. 6984
3. 6984
3.6985 3.6986
3. 6987
3. 6988
3. 6989
23
20
3.6990
3.6991
3. 6991
3. 6992
3. 6993
3.6994
3. 6995
3. 6996
3.6997
3. 6998
23
30
3. 6998
3.6999
3.7000
3. 7001
3.7002
3. 7003
3.7004
3.7004
3.7005
3.7006
23
40
3.7007
3.7008
3.7009
3. 7010
3. 7010
3.7011
3. 7012
3. 7013
3. 7014
3. 7015
23
50
3. 7016
3. 7017
3. 7025
3. 7017
3. 7018
3. 7019
3. 7020
3. 7021
3. 7022
3. 7023
3. 7023
1 24
3. 7024
3. 7026
3. 7027 i 3. 7028
3.7029
3.7029
3. 7030
3. 7031
3. 7032
24
10
3. 7033
3. 7034
3. 7035
3. 7035
3. 7036 1 3. 7037
3.7038
3. 7039
3. 7040
3.7041
24
20
3.7042
3. 7042
3.7043
3.7044
3. 7045 3. 7046
3.7047
3.7048
3. 7048
3. 7049
24
30
3. 7050
3. 7051
3. 7052
3. 7053
3. 7054 , 3. 7054
3. 7055
3. 7056
3. 7057
3. 7058
24
40
3.7059
3.7060
3.7060
3.7061
3.7062
3.7063
3.7064
3.7065
3.7065
3.7066
24
50
3.7067
3.7068
3.7069
3. 7070
3. 7071
3. 7071
3. 7072
3. 7073
3. 7074
3. 7075
1 25
3. 7076
3. 7077
3. 7077
3. 7078
3. 7079 i 3. 7080
3. 7081
3. 7082
3.7083
3.7083
25
10
3.7084
3. 70a5
3. 7086
3. 7087
3. 7088 ! 3. 7088
3. 7089
3.7090
3.7091
3.7092
25
20
3. 7093
3. 7094
3.7094
3. 7095
3. 7096 i 3. 7097
3.7098
3.7099
3.7099
3.7100
25
30
3. 7101
3. 7102
3. 7103
3.7104
3. 7105 1 3. 7105
3.7106
3. 7107
3. 7108
3.7109
25
40
3.7110
3.7110
3.7111
3. 7112
3.7113 i 3.7114
3.7115
3.7116
3. 7116
3.7117
25
50
3. 7118
3. 7119
3. 7127
3. 7120
3. 7121
3. 7121 1 3. 7122
3. 7123
3. 7124
3. 7125
3. 7126
1 26
3.7126
3. 7128
3.7129
3.7130 3.7131
3. 7132
3. 7132
3. 7133
3. 7134
26
10
3. 7135
3. 7136
3.7137
3. 7137
3. 7138 3. 7139
3. 7140
3. 7141
3. 7142
3. 7142
26
20
3. 7143
3. 7144
3. 7145
3. 7146
3. 7147 3. 7147
3. 7148
3. 7149
3. 7150
3. 7151
26
30
3. 7152
.3. 7153
3. 7153
3. 7154
3.7155 3.7156
3. 7157
3. 7158
3. 7159
3. 7159
26
40
3. 7160
3. 7161
3. 7162
3. 7163
3.7163 j 3.7164
3.7165
.3. 7166
3. 7167
3. 7168
26
50
3. 7168
3. 7177
3. 7169
3.7170
.3. 7171
3.7172
3.7180
3. 7173
3.7181
3. 7173
377182'
3. 7174
3. 7175
3. 7183
3. 7176
1 27
3. 7178
3. 7178
3. 7179
3. 7183
3.7184
27
10
3. 7185
3. 7186
3. 7187
3. 7188 1 3.7188
3. 7189
3.7190
3. 7191
3. 7192
3. 7192
27
20
3. 7193
3. 7194
3. 7195
3. 7196
3. 7197
3.7197
3. 7198
3. 7199
3. 7200
3. 7201
27
30
3. 7202
3. 7202
3. 7203
3. 7204
3. 7205
3. 7206
3. 7207
3.7207
3.7208
3.7209
27
40
3. 7210
3.7211
3. 7212
,3.7212
3. 7213
3. 7214
3. 7215
3. 7216
3. 7216
3.7217
27
50
3. 7218
3. 7219
3.7220
3. 7221
3. 7229
3. 7221
3. 7230
3. 7222
3. 7230
3. 7223
3. 7224
3. 7225
3. 7233
3. 7226
377234
1 28
3. 7226
3. 7227
3. 7228
3. 7231
3. 7232
28
10
3. 7235
3. 7235
3. 7236
3. 7237
3. 7238
3. 7239
3. 7239
3. 7240
3. 7241
3. 7242
28
20
3. 7243
3. 7244
3. 7244
3. 7245
3. 7246
3. 7247
3. 7248
3. 7248
3. 7249
3. 7250
28
30
3. 7251
3. 7252
3. 7253
3. 7253
3. 7254
3. 7255
3. 7256
3. 7257
3. 7257
3. 7258
28
40
3. 7259
3. 7260
3. 7261
3. 7262
3. 7262
3. 7263
3. 7264
3.7265
3. 7266
3. 7266
28
50
3. 7267
3.7268
3. 7269
3. 7270
3.7278"
3. 7271
3."7279"
3. 7271
3. 7279
3. 7272
3. 7280
3. 7273
3. 7274
3. 7282
3. 7275
1 29
3. 7275
3. 7276
3. 7277
3. 7281
3. 7283
29
10
3. 7284
3. 7284
3. 7285
3. 728()
3. 7287 1 3. 7288
3. 7288
3. 7289
3. 7290
3. 7291
29
20
3.7292
3. 7292
3. 7293
3.7294
3. 7295 1 3. 7296
3. 7297
3. 7297
3. 7298
3. 7299
29
30
3. 7300
3. 7301
3. 7301
3. 7302 3. 7303 \ 3. 7304
3. 7305
3. 7305
3. 7806
3. 7307
29
40
3. 7308
3.7309
3. 7309
3. 7.310
3.7311 3.7312
3. 7313
3. 7313
3.7314
3. 7315
29
50
3. 7316
3. 7317
3. 7317
3. 7318
3. 7319 1 3. 7320
3. 7321
3. 7322
3. 7322
3. 7.323
24972°— 12-
-21
Page 322] APPENDIX V: TABLE IX.
Logarithms of Small Arcs in
Space or Time.
Arc.
0" 1"
2"
a" I -1"
o"
6"
j»
ii". 9" 1
/ //
1" 30'" 0"
3. 7324
3. 7325
3. 7326
3. 7326
3. 7327
3. 7328
3.7329
3. 7330
3. 7330
3. 7331
80 10
3. 7332
3. 7333
3. 7334
3. 7334
3. 7335
3. 73,36
3. 7337
3. 7338
3. 7338
3. 7339
.30 20
3. 7340
3. 7341
3. 7342
3. 7342
3. 7343
3. 7344
3. 7345
3. 7346
3. 7346
3. 7347
30 30
3. 7348
3. 7349
3. 7350
3. 7350
3. 7351
3. 7352
3. 7353
3. 7354
3. 73.54
3. 7355
30 40
3.7356
3. 7357
3. 7358
3. 7358
3. 7359
3. 7360
3. 7361
3. 7362
3. 7362
3. 7.363
30 50
3. 7364
3. 7365
3. 7366
3. 7374
3. 7366
3. 7367
3. 7368
3. 7376
3. 7369
3. 7377"
3. 7370
3. 7370
3. 7378
3. 7371
1 31
3. 7372
3. 7373
3. 7374
3. 7375
3. 7377
3. 7379
31 10
3. 7380
3. 7381
3. 7381
3. 7382
3. 7383
3. 7384
3. 7385
3. 7385
3. 7386
3. 7387
31 20
3. 7388
3. 7389
3. 7389
3. 7390
3. 7391
3. 7392
3. 7393
3. 7393
3. 7394
3. 7395
31 30
3. 7396
3. 7397
3. 7397
3. 7398
3. 7399
3. 7400
3. 7400
3. 7401
3. 7402
3. 7403
31 40
3. 7404
3. 7404
3. 7405
3. 7406
3. 7407
3. 7408
3. 7408
3. 7409
3. 7410
3. 7411
31 60
3. 7412
3. 7412
3. 7420"
3. 7413
3. 7421
3. 7414
3. 7422
3. 7415
3. 7423
3. 7415
3. 7416
3. 7417
3. 7425
3. 7418
3. 7426
3. 7419
3. 7426
1 32
3. 7419
3. 7423 3. 7424
32 10
3. 7427
3. 7428
3. 7429
3. 7430
3. 7430
3. 7431 3. 7432
3. 7433
3. 7434
3. 7434
32 20
3. 7435
3. 7436
3. 7437
3. 7437
3. 7438
3. 7439 3. 7440
3. 7441
3. 7441
3. 7442
32 30
3. 7443
3. 7444
3.7444
3. 7445
3. 7446
3. 7447 : 3. 7448
3. 7448
3.7449
3. 74.50
32 40
3. 7451
3. 7452
3. 7452
3. 7453
3. 7454
3. 7455 i 3. 7455
3. 7456
3. 7457
3. 7458
32 50
3. 7459
3. 7459
3. 7467
3.7460
3. 7461
3. 7462
"3. 7469
3. 7462 ! 3. 7463
3. 7470 [ 3. 7471
3. 7464
3. 7465
3. 7466
1 33
3. 7466
3. 7468
3. 7469
3. 7472
3. 7473
3. 7473
33 10
3. 7474
3. 7475
3. 7476
3. 7476
3. 7477
3. 7478 ! 3. 7479
3. 7480
3. 7480
3. 7481
33 20
3. 7482
3. 7483
3. 7483
3. 7484
3. 7485
3. 7486
3. 7487
3. 7487
3. 7488
3. 7489
33 30
3. 7490
3. 7490
3. 7491
3. 7492
3. 7493
3. 7493
3. 7494
3. 7495 j 3. 7496
3. 7497
33 40
3. 7497
3. 7498
3. 7499
3. 7500
3. 7500
3. 7501
3. 7502
3. 7503
3. 7504
3. 7504
33 50
3. 7505
3. 7506
3. 7507
3. 7507
3. 7508
3. 7509
3. 7510
3.7510
3. 7511
3. 7512
1 34
3. 7513
3. 7514
3. 7514
3. 7515
3. 7516
3.7517
3.7517
3. 7518
3. 7519
3. 7520
34 10
3. 7520
3. 7521
3. 7522
3. 7523
3. 7524
3. 7524
3. 7525
3. 7526
3. 7527
3. 7527
34 20
3. 7528
3. 7529
3. 7530
3. 7530
3. 7531
3. 7532
3. 7533
3. 7534
3. 7534
3. 7535
34 30
3. 7536
3. 7537
3. 7537
3. 7538
3. 7539
3. 7540 3. 7540
3. 7541
3. 7542
3. 7543
34 40
3. 7543
3. 7544
3. 7545
3. 7546
3. 7547
3. 7547 3. 7548
3. 7549
3. 7550
3. 7550
34 50
1 35
3. 7551
3. 7559
3. 7552
3. 7560
3. 7553
"3. 7560"
3. 7553
3. 7554
3. 7555 3. 7556
3. 7556
3.7564
3. 7557
3. 7558
3.7566
3. 7561
3. 7562
3. 7563
3. 7563
3. 7565
35 10
3. 7566
3. 7567
3. 7568
3. 7569
3. 7569
3. 7570
3. 7571
3. 7572
3. 7572
3. 7573
35 20
3. 7574
3. 7575
3. 7575
3. 7576
S. 7577
3. 7578
3. 7579
3. 7579
3. 7580
3. 7581
35 30
3. 7582
3. 7582
3. 7583
3. 7584
3.7585
3. 7585 1 3. 7586
3. 7587
3. 7588
3. 7588
35 40
3. 7589
3. 7590
3. 7591
3. 7591
3. 7592
3. 7593
3. 7594
3. 7594
3. 7595
3. 7596
35 50
3. 7597
3. 7597
3. 7605
3. 7598
3. 7606
3. 7599
3. 7600
3. 7600
3. 7601
3. 7602
3. 7603
'3"."7610"
3. 7603
3.76il
1 36
3. 7604
3. 7606
3. 7607
3. 7608
3. 7609
3. 7609
36 10
3. 7612
3. 7613
3. 7613
3. 7614
3. 7615
3. 7616
3. 7616
3.7617
3. 7618
3. 7619
36 20
3. 7619
3. 7620
3. 7621
3. 7622
3. 7622
3. 7623
3. 7624
3. 7625
3. 7625
3. 7626
36 30
3. 7627
3. 7628
3. 7628
3. 7629 ' 3. 7630
3. 7631
3. 7631
3. 7632
3. 7633
3. 7634
36 40
3. 7634
3. 7635
3. 7636
3.7637 1 3.7637
3. 7638
3.7639
3. 7640
3. 7640
3. 7641
36 50
3. 7642
3.7643
3. 7643
3. 7644 ; 3. 7645
3. 7645
3. 7646
3. 7647
3."7654
3. 7648
3. 7648
1 37
3. 7649
3. 7650
3. 7651
3. 7651 3. 7652
3. 7653
3. 7654
3. 7655
3. 7656
37 10
3. 7657
3. 7657
3. 7658
3. 7659 : 3. 7660
3. 7660
3. 7661
3. 7662
3. 7663
3. 7663
37 20
3. 7664
3. 7665
3. 7666
3. 7666
3. 7667
3. 7668
3. 7669
3. 7669
3. 7670
3. 7671
37 30
3. 7672
3. 7672
3. 7673
3. 7674
3. 7675
3. 7675
3. 7676
3. 7677
3. 7677
3. 7678
37 40
3. 7679
3. 7680
3. 7681
3. 7681
3. 7682
3. 7683
3. 7683
3. 7684
3. 7685
3. 7686
37 50
3. 7686
3. 7687
3. 7688
3. 7689
3. 7689
3. 7690
3. 7691
3. 7692
3. 7692
3. 7693
1 38
3. 7694
3. 7695
3. 7695
3. 7696
3. 7697
3. 7697
3. 7698
3. 7699
3.7700
3. 7700
38 10
3. 7701
3. 7702
3. 7703
3. 7703
3. 7704
3. 7705
3.7706
3. 7706
3. 7707
3. 7708
38 20
3. 7709
3. 7709
.3. 7710
3. 7711
3.7711
3. 7712
3. 7713
3.7714
3. 7714
3.7715
38 30
.3.7716
3.7717
3. 7717
3. 7718
3. 7719
3. 7720
3. 7720
3. 7721
3. 7722
3. 7722
38 40
3. 7723
3. 7724
3. 7725
3. 7725
3. 7726
3. 7727
3. 7728
3. 7728
3. 7729
3. 7730
38 50
3. 7731
3. 7731
3. 7732
3. 7733
3. 7733
3. 7734
3. 7735
3. 7736
3. 7736
3. 7737
1 39
3. 7738
3. 7739
3. 7739
3. 7740
3. 7741
3. 7742
3. 7742
3. 7743
3. 7744
3. 7744
39 10
3. 7745
3. 7746
3. 7747
3. 7747
3. 7748
3. 7749
3. 7750
3. 7750
3. 7751
3. 7752
39 20
3. 7752
3. 7753
3. 7754
3. 7755
3. 7755
3. 7756
3. 7757
3. 7758
3. 7758
3. 7759
39 30
3. 7760
3. 7760
.3. 7761
3. 7762
3. 7763
3. 7763
3. 7764
3.7765
3. 7766
3. 7766
39 40
3. 7767
3. 7768
3. 7768
3. 7769
3. 7770
3. 7771
3. 7771
3. 7772
3. 7773 ! 3. 7774
39 50
3. 7774
3. 7775
3. 7776
3. 7776
3. 7777
3. 7778
3. 7779
3. 7779
3.7780 3.7781
APPP:NDIX Y: table IX.
[Page 323
Logarithms of Small Arcs in Space or Time.
Arc. 1
0" 1"
2"
8"
4" ] 5"
6"
J"
8"
9"
o /
l" 40"
//
0=
3. 7782
3. 7782
3. 7783
3.7784
3.7784
3.7785
3. 7786
3. 7787
3. 7787
3. 7788
40
10
3. 7789
3. 7789
3. 7790
3. 7791
3. 7792
3. 7792
3. 7793
3. 7794
3. 7795
3. 7795
40
20
3. 7796
3. 7797
3. 7797
3. 7798
3. 77i)9
3. 7800
3.7800
3. 7801
3. 7802
3. 7802
• 40
30
3. 7803
3. 7804
3. 7805
3. 7805
3. 7806
3. 7807
3. 7807
3. 7808
3.7809
.3. 7810
40
40
3. 7810
3. 7811
.3. 7812
3. 7813 3. 7813 i 3. 7814
3. 7815
3. 7815
3. 7816
3. 7817
40
50
3. 7818
3. 7818
3. 7819
3."7826
3. 7820 3. 7820 3. 7821
3. 7822
3. 7823
3. 7823
3. 7830
3. 7824
1 41
3. 7825
3. 7825
3. 7827 ! 3. 7828 3. 7828
3.7829
3. 7830
3. 7831
41
10
3. 7832
3. 7833
3. 7833
3. 7834 : 3. 7835 3. 7835
3. 7836
3. 7837
3. 7838
3. 7838
41
20
3. 7839
3. 7840
3. 7840
3. 7841 1 3. 7842 \ 3. 7843
.3. 7843
3. 7844
8.7845
3. 7845
41
30
3. 7846
3. 7847
3. 7848
3. 7848 1 3. 7849 ; 3. 7850
3. 7850
3. 7851
3.7852
3. 7853
41
40
3. 7853
3. 78.54
3. 7855
3. 7855 ! 3. 7856 : 3. 7857
3. 7858
3.7858
3.7859
3. 7860
41
50
3. 7860
3. 7861
3. 7868
3. 7862
3. 7863
3. 7863
3. 7870
3. 7864
3. 7865
3. 7865
3.7866
3. 7867
3. 7874
1 42
3. 7868
3. 7869
3. 7870
3. 7871
3. 7872
3. 7872
3. 7873
42
10
3. 7875
3. 7875
3. 7876
3. 7877 3. 7877 j 3. 7878
3. 7879
3. 7880
3. 7880
3. 7881
42
20
3. 7882
3. 7882
3. 7883
3. 7884 3. 7885 1 3. 7885
3. 7886
3. 7887
3. 7887
3. 7888
42
30
3. 7889
3. 7889
3. 7890
3. 7891 1 3. 7892 3. 7892
3. 7893
3. 7894
3. 7894
3. 7895
42
40
3. 7896
3. 7897
3. 7897
3. 7898 3. 7899 3. 7899
3. 7900
3. 7901
3. 7901
3. 7902
42
50
3. 7903
3.7904
3. 7904
3. 7905 ' 3. 7906 3. 7906
3. 7907
3. 7908
3.7908
3.7909
3.7916
1 43
3. 7910
3.7911
3. 7911
3.7912 1 3.7913 | 3.7913
3. 7914
3. 7915
3. 7916
43
10
3. 7917
3. 7918
3. 7918
3. 7919 1 3. 7920
3. 7920
3. 7921
3. 7922
3. 7923
3. 7923
43
20
3. 7924
3. 7925
3. 7925
3. 7926 : 3. 7927
3. 7927
3. 7928
3. 7929
3. 79.iO
3. 79,30
43
30
3. 7931
3. 7932
3. 7932
3. 7933
3. 7934
3.7934
3. 7935
3. 7936
3. 7937
3. 7937
43
40
3. 7938
3. 7939
3. 7939
3. 7940
3. 7941 • 3. 7941
3. 7942
3. 7943
3. 7943
3. 7944
43
50
3. 7945
3. 7946
3. 7946
3. 7947
3. 7948 1 3. 7948
3. 7949
3. 7950
3. 7950
3. 7957
3. 7951
3. 7958
1 44
3. 7952
3. 7953
3. 7953
3. 7954
3. 7955 1 3. 7955
3. 7956
3. 7957
44
10
3. 7959
3. 7959
3.7960
3.7961
3. 7962 3. 7962
3. 7963
3.7964
3. 7964
3.7965
44
20
3. 7966
3. 7966
3. 7967
3. 7968
3. 7969 3. 7969
3. 7970
3. 7971
3. 7971
3. 7972
44
30
3. 7973
3. 7973
3. 7974 i 3. 7975
3.7975 ; 3.7976
3. 7977
3. 7978
3. 7978
3. 7979
44
40
3. 7980
3. 7980
3. 7981 ! 3. 7982
3. 7982 1 3. 7983
3. 7984
3. 7984
3. 7985
3. 7986
44
50
3. 7987
3. 7987
3. 7994
3. 7-988 3. 7989
3. 7989 ; 3. 7990
3. 7991
3. 7991
3. 7992
3.7999
3. 7993
3. 8000
1 45
3. 7993
3. 7995 3. 7995
3. 7996 1 3. 7997 i 3. 7998
3. 7998
45
10
3. 8000
3. 8001
3.8002
3. 8002
3. 8003
3. 8004
3.8004
3. 8005
3. 8006
3.8006
45
20
3.8007
3. 8008
3. 8009
3. 8009
3. 8010
3. 8011
3.8011
,3.8012
3.8013
.3.8013
45
30
3. 8014
3. 8015
3. 8015
3. 8016
,3.8017
3. 8017
3. 8018
3. 8019
3. 8020
3. 8020
45
40
3. 8021
3. 8022
3. 8022
3. 8023
3. 8024
3. 8024
3. 8025
3. 8026
3. 8026
3. 8027
45
50
3. 8028
3. 8028
3. 8029
3.8030 1 3.8030
3. 8031
3.~8038
3. 8032
3. 8033
3. 8033
3. 8034
1 46
3. 8035
3. 8035
3. 8036
3. 8036
3. 8037
3. 8039
3. 8039
3.8040
3.8041
46
10
3. 8041
3. 8042
3. 8043 : 3. 8043
3. 8044
3. 8045
3. 8045
3.8046
3. 8047
3.8048
46
20
3. 8048
3. 8049
3. 8050
3. 8050
3. 8051
3. 8052
3. 8052
3. 8053
3. 80,54
3. 80,54
46
30
3. 8055
3. 8056
3. 8056
3. 8057
3. 8058
3. 8058
3.8059
3. 8060
3. 8060
3.8061
46
40
3. 8062
3. 8062
3. 8063
3. 8064
3. 8065
3. 8065
3. 8066
3. 8067
3. 8067
3. 8068
46
50
3. 8069
3. 8069
3. 8070
3.8071
3. 8071
3. 8072
3. 8073
3. 8073
3. 8074
3. 8075
1 47
3. 8075
3. 8076
3. 8077
3. 8077
3. 8078
3. 8079
3. 8079
3. 8080
3. 8081
3. 8081
47
10
3. 8082
3. 8083
3. 8083
3. 8084
3. 8085
3. 8085
3. 8086
3. 8087
3. 8088
3. 8088
47
20
3. 8089
3. 8090
3.8090
3. 8091
3.8092
3. 8092
3. 8093
3. 8094
3. 8094
3. 8095
47
30
3. 8096
3. 8096
3. 8097
3. 8098
3. 8098
3. 8099
3. 8099
.3. 8100
3.8101
3. 8102
47
40
3. 8102
3.8103
3. 8104
3.8104
3.8105
3. 8106
3. 8106
3. 8107
3.8108
3. 8108
47
50
3.8109
.3. 8110
.3. 8110
3.8111
3.8112
3.8112
3.8113
3. 8114
3.8114
.3.8115
1 48
3.8116
3.8116
3.8117
3.8118
3.8118 i 3.8119 1 3.8120
3. 8120
3.8121
3.8122
48
10
3. 8122
3. 8123
3. 8124
3. 8124
3.8125 ' 3.8126
3.8126
3. 8127
3.8128
3. 8128
48
20
3. 8129
.3.8130
3. 8130
,3. 81,31
.3.8132 i 3.8132
3. 8133
3. 8134
3. 81,34
3. 8135
48
30
3. 8136
.3.8136
3.8137
3. 8138
3.81.38 . 3.8139
3. 8140
3. 8140
3.8141
3.8142
48
40
3. 8142
3. 8143
3. 8144
3. 8144
3.8145 1 3.8146
3.8146
,3. 8147
3. 8148
3.8148
48
50
3. 8149
3. 81.50
3. 8150
3. 8151
3.8152 j 3.8152
3. 8153
3.81,54
3. 8160
3. 8154
3.8161
3. 8155
3. 8162
1 49
3. 8156 .3. 8156
3.81.57
3.8158
3. 81.58 : 3. 81.59
3. 8160
49
10
3.8162 3.8163
3. 8164
3. 8164
3. 8165 1 3. 8166
3. 8166
3.8167
3. 8168
3. 8168
49
20
3.8169 3.8170
3. 8170
3.8171
3.8172 ; .3.8172
3.8173
3.8174
3.8174
3.8175
49
30
3.8176 3.8176
3.8177 ; 3.8178
3.8178 1 3.8179
3. 8180
.3.8180
.3.8181
3.8182
49
40
3.8182 3.8183
3. 8184
3. 8184
3. 8185
3 8185
3.8186
,3. 8187
3.8188
,3.8188
49
50
3.8189 3.8190
3. 8190
3.8191
3. 8191
3.8192
3. 8193
.3.8193 .3.8194
3.8195
Page 324]
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or
Time.
Arc.
0"
1"
S"
8"
4"
5"
6"
7"
8"
9"
o /
l" 50"
It
0«
3. 8195
3.8196
3. 8197
3.8197
3. 8198
3. 8199
3. 8199
3.8200
3.8201
3. 8201
50
10
3. 8202
3. 8203
3. 8203
3. 8204
3. 8205
3. 8205
3. 8206
3. 8207
3.8207
3. 8208
50
20
3.8209
3. 8209
3. 8210
3. 8211
3. 8211
3. 8212
3. 8213
3. 8213
3. 8214
3. 8214
50
30
3. 8215
3. 8216
3. 8216
3. 8217
3. 8218
3. 8218
3. 8219
3. 8220
3. 8220
3. 8221
50
40
3. 8222
3. 8222
3. 8223
3. 8224
3. 8224
3. 8225
3. 8226
3. 8226
3. 8227
3. 8228
50
50
3. 8228
3. 8229
3. 8230
3. 8230
3. 8231
3. 8231
3. 8232
3. 8233
3. 8233
3. 8234
1 51
3.8235
3.8235
3. 8236
3. 8237
3. 8237
3.8238
3. 8239
3. 8239
3. 8240
3. 8241
51
10
3. 8241
3. 8242
3. 8243
3. 8243
3.8244
3. 8245
3. 8245
3. 8246
3. 8246
3. 8247
51
20
3. 8248
3. 8248
3. 8249
3. 8250
3. 8250
3. 8251
3.8252
3. 8252
3. 8253
3. 8254
51
30
3. 8254
3. 8255
3. 8256
3. 8256
3. 8257
3. 8258
3. 8258
3. 8259
3. 8259
3. 8260
51
40
3. 8261
3. 8261
3. 8262
3. 8263
3. 8263
3.8264
3.8265
3. 8265
3. 8266
3. 8267
51
50
3. 8267
3. 8268
3. 8269
3. 8269
3. 8270
3. 8270
3. 8271
3. 8272
3. 8272
3. 8273
3. 8280
1 52
3. 8274
3. 8274
3. 8275
3. 8276
3. 8276
3. 8277
3. 8278
3. 8278
3. 8279
52
10
3. 8280
3. 8281
3. 8281
3. 8282
3. 8283 .
3. 8283
3. 8284
3. 8285
3.8285
3. 8286
52
20
3. 8287
3. 8287
3. 8288
3. 8289
3. 8289
3. 8290
3. 8290
3. 8291
3. 8292
3.8292
52
30
3. 8293
3.8294
3. 8294
3.8295
3. 8296
3.8296
3. 8297
3.8298
3.8298
3.8299
52
40
3.8299
3.8300
3. 8301
3. 8301
3. 8302
3.8303
3. 8303
3.8304
3. 8305
3.8305
52
50
3.8306
3. 8307
3. 8307
3. 8308
3. 8308
3.8309
3. 8310
3. 8310
3. 8311
3. 8312
1 53
3. 8312
3. 8313
3. 8314
3. 8314
3.8315
3. 8315
3. 8316
3.8317
3. 8317
3. 8318
53
10
3. 8319
3. 8319
3. 8320
3. 8321
3. 8321
3. 8322
3. 8323
3. 8323
3. 8324
3. 8324
53
20
3. 8325
3. 8326
3. 8326
3. 8327
3. 8328
3. 8328
3. 8329
3. 8330
3. 8330
3. 8331
53
30
3. 8331
3. 8332
3. 8333
3. 8333
3.8334
3.8335
3.8335
3. 8336
3. 8337
3. 8337
53
40
3. 8338
3. 8338
3. 8339
3. 8340
3. 8340
3. 8341
3. 8342
3. 8342
3. 8343
3. 8344
53
50
3. 8344
378351
3. 8345
3. 8345
3. 8346
3. 8347
3. 8a53
3. 8347
3. 8348
3. 8349
3. 8349
3. 8356
3. 8350
3.'8356
1 54
3. 8351
3.8352
3.8352
3. 8354
3.8354
3.8355
54
10
3.8357
3.8358
3.8358
3. 8359
3. 8359
3. 8360
3. 8361
3. 8.361
3. 8362
3. 8363
54
20
3. 8363
3. 8364
3.8365
3.8365
3. 8366
3. 8366
3. 8367
3. 8368
3. 8368
3. 8369
54
30
3. 8370
3. 8370
3. 8371
3. 8371
3. 8372
3. 8373
3. 8373
3. 8374
3. 8375
3. 8375
54
40
3. 8376
3. 8377
3. 8377
3. 8378
3. 8378
3. 8379
3. 8380
3. 8380
3. 8381
3. 8382
54
50
3. 8382
3. 8383
3. 8383
3. 8384
3. 8385
3. 8385
3. 8386
3. 8387
3. 8393
3. 8387
3. 8,394
3. 8388
3. 8394
1 55
3. 8388
3. 8389
3.8390
3. 8390
3. 8391
3. 8392
3. 8392
55
10
3. 8395
3. 8395
3. 8396
3. 8397
3. 8397
3. 8398
3. 8399
3. 8399
3. 8400
3. 8400
55
20
3. 8401
3. 8402
3. 8402
3. 8403
3. 8404
3. 8404
3. 8405
3. 8405
3. 8406
3. 8407
55
30
3. 8407
3. 8408
3.8409
3.8409
3. 8410
3. 8410
3. 8411
3. 8412
3. 8412
3. 8413
55
40
3. 8414
3. 8414
3. 8415
3. 8415
3. 8416
3. 841/
3. 8417
3. 8418
3. 8419
3. 8419
55
50
3. 8420
3. 8420
3. 8427
3. 8421
3. 8427
3. 8422
3. 8422
3. 8422
3. 8424
3. 8424
3. 8430
3. 8425
3. 8425
3. 8432
1 56
3. 8426
3. 8428
3.8429
3.8429
3.8430
3. 8431
56
10
3. 8432
3.8433
3. 8434
3. 8434
3.8435
3. 8435
3. 8436
3. 8437
3. 8437
3. 8438
56
20
3. 8439
3. 8439
3.8440
3. 8440
3. 8441
3. 8442
3. 8442
3. 8443
3. 8444
3.8444
56
30
3. 8445
3.8445
3. 8446
3.8447
3. 8447
3.8448
3.8448
3.8449
3. 8450
3. 8450
56
40
3. 8451
3. 8452
3. 8452
3. 8453
3. 8453
3. 8454
3. 8455
3. 8455
3. 8456
3. 8457
56
50
3. 8457
3. 8458
3. 8458
3. 8459
3. 8465
3. 8460
3. 8460
3. 8461
3.8462
3. 8468
3. 8462
3. 8468
3. 8463
1 57
3. 8463
3.8464
3.8465
3. 8466
3. 8466
3. 8467
3. 8469
57
10
3. 8470
3. 8470
3. 8471
3. 8471
3. 8472
3. 8473
3. 8473
3. 8474
3. 8474
3. 8475
57
20
3. 8476
3. 8476
3. 8477
3. 8478
3. 8478
3. 8479
3. 8479
3. 8480
3. 8481
3. 8481
57
30
3. 8482
3. 8483
3. 8483
3. 8484
3.8484
3. 8485
3. 8486
3. 8486
3. 8487
3. 8487
57
40
3. 8488
3. 8489
3. 8489
3.8490
3. 8491
3. 8491
3. 8492
3. 8492
3. 8493
3.8494
57
50
3. 8494
3. 8495
3. 8495
3. 8496
3. 8497
3. 8497
3. 8498
3.8499
3. 8499
3.8500
1 58
3.8500
3. 8501
3. 8502
3. 8502
3.8503
3. 8503
3.8504
3. 8505
3. 8505
3.8506
58
10
3. 8506
3. 8507
3.8508
3. 8508
3.8509
3. 8510
3. 8510
3. 8511
3. 8511
3. 8512
58
20
3. 8513
3. 8513
3. 8514
3. 8514
3. 8515
3. 8516
3. 8516
3. 8517
3. 8517
3. 8518
58
30
3. 8519
3. 8519
3. 8520
3. 8521
3. 8,521
3. 8522
3. 8522
3. 8523
3. 8524
3. 8524
58
40
3. 8525
3. 8525
3. 8526
3. 8527
3. 8527
3.8528
3. 8528
3. 8529
3. 8530
3. 8530
58
50
3. 8531
3. 8532
3. 8532
3. 8533
3. 8533
3. 8534
3. 8535
3. 8535
3.85T1
3. 8536
3.8,542'
3.8536
1 59
3. 8537
3. 8538
3. 8538
3. 8539
3. 8539
3. 8540
3.8541
3.8542
59
10
3. 8543
3. 8544
3. 8544
3. 8545
3. 8545
3. 8546
3. a547
3. 8547
3. 8.548
3. 8549
59
20
3. 8549
3. 8550
3. 8550
3. 8551
3. 8552
3. 8552
3. 8553
3. 8553
3. 8554
3.8555
59
30
3. a555
3. 8556
3. 8556
3.8557
3. 8558
3. 8558
3. 8559
3. 8559
3. 8560
3.8561
59
40
3. 8561
3. 8562
3. 8562
3. 8563
3. 8564
3.8564
3. 8565
3. 8565
3. a566
3. 8.567
59
50
3. 8567
3. ai68
3. 8568
3. 8569
3. 8570
3. 8570
3. 8571
3. 8572
3. 8572
3. 8573
APPENDIX V: TABLE IX.
[Page 325
Logarithms of Small Arcs in
Space or Time.
Arc.
0"
1"
i"
8"
4"
6"
6"
7"
8"
9"
o t
2" 0"
//
0»
3.8573
3.8574
3. 8575
3.8575
3.8576
3. 8576
3. 8577
3.8578
3.8578
3. 8579
10
3. 8579
3. 8580
3. 8581
3. 8581
3.8582
3. 8582
3. 8583
3. 8584
3.8584
3. 8585
20
3. 8585
3.8586
3. 8587
3. 8587
3. 8588
3.8588
3. 8589
3. 8590
3. 8590
3. 8591
80
3.8591
3. 8592
3. 8593
3. 8593
3. 8594
3. 8594
3. 8595
3. 8596
3. 8596
3. 8597
40
3. 8597
3. 8598
3. 8599
3. 8599
3.8600
3.8600
3. 8601
3. 8602
3. 8602
3. 8603
50
3. 8603
3.8604
3. 8605
3. 8611
3.8605
3. 8611
3.8606
3. 8612
3.8606
3. 8612
3. 8607
3. 8608
3.8608
3. 8609
2 1
3.8609
3. 8610
3. 8613
3. 8614
3. 8614
3. 8615
10
3. 8615
3. 8616
3. 8617
3. 8617
3. 8618
3. 8618
3. 8619
3. 8620
3. 8620
3. 8621
20
3. 8621
3. 8622
3.8623
3. 8623
3. 8624
3. 8624
3. 8625
3.8625
3. 8626
3. 8627
30
3. 8627
3. 8628
3. 8628
3.8629
3. 8630
3. 8630
3. 8631
3. 8631
3. 8632
3. 8633
40
3. 8633
3. 8634
3. 8634
3.8635
3. 86.36
3. 8636
3. 8637
3.8637
3. 8638
3. 8(!39
50
3. 8639
3. 8640
3.8640
3. 8641
3.8642
3.8647
3.8642
3.8648
3.8643
3.8643
3.8644
3.8650
3. 8645
3.8650
2 2
3.8645
3.8646
3. 8646
3. 8647
3.8649
3. 8649
2
10
3.8651
3.8652
3.8652
3.8653
3.8653
3. 8654
3.8655
3. 8655
3. 8a56
3.8656
2
20
3.8657
3.8658
3.8658
3.8659
3.8659
3. 8660
3.8661
3. 8661
3.8662
3. 8662
2
30
3.8663
3. 8663
3.8664
3.8665
3.8665
3.8666
3.8666
3.8667
3.8668
3.8668
2
40
3.8669
3.8669
3. 8670
3. 8671
3. 8671
3. 8672
3.8672
3.8673
3. 8673
3. 8674
2
50
3. 8675
3. 8675
3. 8676
3. 8676
3. 8677
3. 8678
3. 8678
3. 8679
3. 8679
3.8680
118686
2 3
3. 8681
3.8681
3. 8682
3. 8682
3. 8683
3.8684
3. 8684
3. 8685
3. 8685
3
10
3. 8686
3. 8687
3. 8688
3. 8688
3. 8689
3. 8689
3. 8690
3. 8691
3. 8691
3. 8(>92
3
20
3. 8692
3. 8693
3. 8693
3. 8694
3.8695
3. 8695
3. 8696
3. 8696
3. 8697
3. 8698
3
30
3. 8698
3. 8699
3.8699
3.8700
3. 8701
3. 8701
3. 8702
3. 8702
3. 8703
3. 8703
3
40
3. 8704
3. 8705
3. 8705
3. 8706
3.8706
3. 8707
3. 8708
3. 8708
3. 8709
3.8709
3
50
3. 8710
3. 8710
3. 8711
3. 8717
3. 8712
3. 8712
3.8713
3.8713
3. 8719
3. 8714
3. 8715 i 3. 8715 |
2 4
3. 8716
3. 8716
3. 8717
3. 8718
3. 8719
3. 8720
3.8720
3. 8721
4
10
3. 8722
3. 8722
3. 8723
3. 8723
3. 8724
3. 8724
3. 8725
3.8726
3. 8726
3. 8727
4
20
3. 8727
3. 8728
3. 8729
3.8729
3. 8730
3. 8730
3. 8731
3. 8731
3. 8732
3.8733
4
30
3. 8733
3. 8734
3. 8734
3.8735
3. 8736
3. 8736
3. 8737
3. 8737
3. 8738
3. 8738
4
40
3. 8739
3. 8740
3.8740
3. 8741
3. 8741
3. 8742
3. 8742
3. 8743
3. 8744
3. 8744
4
50
3. 8745
3. 8745
3. 8751
3.8746
3. 8747
3. 8747
3. 8748
3. 8748
3. 8754
3. 8749
3. 8749
3.8750
2 5
3.8754
3. 8752
3. 8752
3. 8753
3. 8754
3. 8755
3. 8755
3.8756
5
10
3.8756
3. 8757
3.8758
3. 8758
3. 8759
3. 8759
3.8760
3.8760
3. 8761
3. 8762
5
20
3. 8762
3. 8763
3.8763
3.8764
3.8764
3.8765
3. 8766
3.8766
3. 8767
3. 8767
5
30
3. 8768
3. 8769
3. 8769
3. 8770
3. 8770
3. 8771
3. 8771
3. 8772
3. 8773
3. 8773
5
40
3. 8774
3. 8774
3. 8775
3. 8775
3. 8776
3.8777
3. 8777
3. 8778
3. 8778
3. 8779
5
50
3. 8779
3. 8780
3. 8786
3. 8781
3. 8781
3. 8782
3. 8782
3. 8783
3. 8783
3. 8784
3.8790
3.8785
2 6
3.8785
3. 8786
3. 8787
3.8788
3. 8788
3. 8789
3. 8789
3. 8790
6
10
3.8791
3. 8792
3. 8792
3. 8793
3. 8793
3. 8794
3. 8794
3. 8795
3. 8796
3. 8796
6
20
3. 8797
3. 8797
3. 8798
3. 8798
3.8799
3.8800
3.8800
3. 8801
3. 8801
3. 8802
6
30
3.8802
3. 8803
3. 8804
3.8804
3.8805
3.8805
3.8806
3.8806
3. 8807
3. 8808
6
40
3. 8808
3.8809
3.8809
3. 8810
3. 8810
3.8811
3. 8812
3. 8812
3.8813
3.8813
6
50
3. 8814
3. 8814
.3. 8815
3. 8816
3. 8816
3. 8817
3. 8822
3. 8817
3. 8818
3.8818
3. 8819
2 7
3. 8820
3. 8820
3. 8821
3. 8821
3. 8822
3. 8823
3. 8824
3. 8824
3. 8825
7
10
3. 8825
3. 8826
3. 8826
3.8827
3. 8828
3. 8828
3.8829
3.8829
3. 8830
3. 8830
7
20
3. 8831
3. 8832
3. 8832
3.8833
3.8833
3. 8834
3.8834
3.8835
3.8835
3. 8836
7
30
3.8837
3.8837
3.8838
3.8838
3.8839
3.8839
3. 8840
3.8841
3.8841
3.8842
7
40
3. 8842
3.8843
3.8843
3.8844
3.8845
3.8845
3. 8846
3. 8846
3. 8847
3.8847
7
50
3. 8848
3.8849
3.8849
3.8850
3.8850
3. 8851
3.8851
3.8852
3.8862
3.8853
2 8
3. 8*54
3.8854
3.8855
3.8855
3.8856
3.8856
3.8857
3.8858
3.8858
3.8859
8
10
3.8859
3.8860
3.8860
3.8861
3. 8862
3.8862
3. 8863
3. 8863
3. 8864
3.8864
8
20
3. 8865
3.8865
3.8866
3.8867
3. 8867
3. 8868
3.8868
3. 8869
3. 8869
3. 8870
8
30
3.8871
3. 8871
3. 8872
3. 8872
3. 8873
3. 8873
3. 8874
3. 8874
3. 8875
3. 8876
8
40
3.8876
3. 8877
3. 8877
3. 8878
3. 8878
3. 8879
3.8880
3.8880
3. 8881
3.8881
8
50
3. 8882
3. 8882
3. 8883
3. 8883
3. 8884
3.8885
3.8885
3. 8886
3. 8886
3. 8887
2 9
3. 8887
3. 8888
3. 8889
3. 8889
3.8890
3.8890
3. 8891
3.8891
3. 8892
3.8892
9
10
3. 8893
3. 8894
3. 8894
3. 8895
3. 8895
3. 8896
3. 8896
3. 8897
3. 8897
3. 8898
9
20
3. 8899
3.8899
3.8900
3.8900
3.8901
3. 8901
3.8902
3.8903
3.8903
3.8904
9
30
3.8904
3.8905
3. 8905
3.8906
.3.8906
3.8907
3.8908
3. 8908
3.8909
3.8909
9
40
3. 8910
3. 8910
3. 8911
3. 8911
3. 8912
3. 8912
3. 8913
3.8914
3. 8914
3.8915
9
50
3. 8915
3. 8916
3. 8916
3. 8917
3. 8918
3. 8918
3. 8919
3. 8919
3.8920
3.8920
Page 326]
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or Time.
Arc.
0"
1" ! 2"
8"
4"
5"
6"
7"
8"
9"
2'' 10'" 0'
3. 8921
3. 8922 3. 8922
3. 8923
3. 8923
3. 8924
3. 8924
3.8925
3. 8925
3. 8926
10 10
3. 8927
3.8927 1 3.8928
3. 8928
3.8929
3.8929
3. 8930
3. 8930
3. 8931
3. 8932
10 20
3. 8932
3.8933 i 3.8933
3. 8934
.3.8934
3. 8935
3. 8935
3. 8936
3. 8937
3. 8937
10 30
3. 8938
3. 8938
3. 8939
3. 8939
3. 8940
3. 8940
3. 8941
3. 8941
3. 8942
3. 8943
10 40
3. 8943
3. 8944
3.8944
3. 8945
3. 8945
3. 8946
3. 8946
3. 8947
3. 8948
3. 8948
10 50
3. 8949
3. 8949
3.8950
3. 8950
3. 8951
3. 8951
3. 8952
3. 8953
3. 8953
3.8959
3. 8954
2 11
3. 8954
3. 8955
3. 8955 ; 3. 8956 ' 3. 8956 i 3. 8957
3. 8958
3. 8958
3. 8959
11 10
3. 8960
3. 8960 : 3. 8961 3. 8961 ! 3. 8962 3. 8963
3. 8963
3. 8964
3. 8964
3. 8965
11 20
3. 8965
3. 8966 3. 8966 3. 8967 j 3. 8967 : 3. 8968
3. 8969
3. 8969
3. 8970
3. 8970
11 30
3. 8971
3. 8971
3. 8972 3. 8972
3. 8973 ; 3. 8974
3. 8974
3. 8975
3. 8975
3. 8976
11 40
3. 8976
3. 8977
3. 8977
3. 8978
3. 8978 1 3. 8979
3. 8980
3. 8980
3. 8981
3. 8981
11 50
3. 8982
3. 8982
3. 8983
3. 8983
3. 8984 i 3. 8985
3. 8985
3. 8991
3. 8986
3. 8986
3. 8992
3. 8987
3. 8992
2 12
3. 8987
3. 8988
3. 8988
3. 8989
3. 8989 1 3. 899a
3.8991
12 10
3. 8993
3. 8993
3. 8994
3. 8994
3.8995 1 3.8995
3. 8996
3. 8997
3. 8997
3. 8998
12 20
3. 8998
3. 8999
3. 8999
3.9000
3. 9C00 ; 3. 9001
3.9001
3.9002
3. 9003
3. 9003
12 30
3. 9004
3. 9004
3.9005 i 3.9005
3.9006 1 3.9006
3.9007
3. 9007
3. 9008
3. 9009
12 40
3. 9009
3. 9010
3.9010 ! 3.9011
.3.9011
3. 9012
3.9012
3. 9013
3. 9013
3. 9014
12 50
3. 9015
3. 9015
3. 9016 I 3. 9016
3. 9017
3. 9017
3. 9018
3. 9018
3.9019
3.9024
3. 9019
2 13
3. 9020
3. 9021
3. 9021 3. 9022
3.9022
3. 9023
3. 9023
3. 9024
3. 9025
13 10
3. 9025
3. 9026
3. 9027 3. 9027
3.9028
3. 9028
3. 9029
3.9029
3. 9030
3.9030
13 20
3. 9031
3. 9031
3. 9032 3. 9033
3. 90,33 3. 9034
3. 9034
3. 9035
3. 9035
3. 9036
13 30
3. 9036
3. 9037
3. 9037
3. 9038
3. 9038
3. 9039
3. 9040
3. 9040
3. 9041
3. 9041
13 40
3. 9042
3. 9042
3. 9043
3. 9043
3. 9044
3. 9044
3. 9045
3. 9046
3. 9046
3. 9047
13 50
3. 9047
3. 9048
3. 9048
3.9054
3. 9049
3. 9054
3. 9049
3.9055"
3. 9050
3. 9055
3. 9050
3.9056
3. 9051
3.9051
3. 9052
3. 9057
2 14
3. («)53
3. 9053
3. 9056
3. 9057
14 10
3. 9058
3. 9058
3.9059
3.9060
3. 9060
3. 9061
3. 9061
3. 9062
3.9062
3.9063
14 20
3. 9063
3. 9064
3.9064
3.9065
3.9066
3. 9066
3.9067
3.9067
3. 9068
3.9068
14 30
3. 9069
3. 9069
3. 9070
3.9070
3.9071
3. 9071
3.9072
3. 9073
3. 9073
3. 9074
14 40
3. 9074
3. 9075
3. 9075
3. 9076
3. 9076
3.9077
3. 9077
3. 9078
3. 9078
3. 9079
14 50
3. 9079
3. 9080
3. 9081
3. 9081
3. 9082
3. 9082
3. 9083
3. 9083
3. 908a
3. 9084
3.9089
3. 9084
3. 9090
2 15
3.9085
3. 9085
3.9086 1 3.9086
3. 9087
3.9088 i 3.9088
15 10
3.9090
3.9091
3.9091 3.9092
3.9092
3. 9093
3. 9093
3. 9094
3. 9094
3. 9095
15 20
3.9096
3. 9096
3.9097 1 3.9097
3. 9098
3.9098
3.9099
3. 9099
3. 9100
3.9100
15 30
3.9101
3.9101
3.9102 1 3.9103
3. 9103
3. 9104
3.9104
3. 9105
3. 9105
3. 9106
15 40
3. 9106
3.9107
3.9107 ! 3.9108
3. 9108
3. 9109
3.9109
3.9110
3. 9111
3.9111
15 60
3.9112
3.9112
3.9113
3.9113
3.9114 i 3.9114
3.9115
3.9115
3. 9116
3.9116
2 16
3.9117
3.9117
3.9118
3.9118
3.9119 3.9120
3.9120
3. 9121
3.9121
3. 9122
16 10
3.9122
3.9123
3. 9123
3. 9124
3. 9124 3. 9125
3.9125
3. 9126
3.9126
3.9127
16 20
3. 9128
3.9128
3. 9129
3.9129
3.9130 i 3.9130
3. 9131
3. 9131
3. 9132
3. 9132
16 30
3. 9133
3. 9133
3. 9134
3.9134
3. 91,35
3. 9135
3. 9136
3. 9137
3. 9137
3. 9138
16 40
3. 9138
3.9139
3. 9139
3.9140
3. 9140
3.9141
3.9141
3. 9142
3. 9142
3. 9143
16 50
3. 9143
3. 9144
3.9149,
3. 9144
3. 91.50
3. 9145
3.9146
3.9146
3. 9147
3.9152
3. 9147
3. 9148
3. 9i53^
3. 9148
,3.9153
2; 17
3. 9149
3.9150
3. 9151
3.9151
3. 9152
17 10
3. 91.54
3.91.55
3. 9155
3. 9156
3. 9156
3.9157
3.9157
3. 9158
3.9158
3.9159
. 17 20
3. 9159
3. 9160
3. 9160
3.9161
3.9161
3. 9162
3.9162
3. 9163
3. 9163
3. 9164
17 30
3.9165
3. 9165
3. 9166
3. 9166
3.9167
3.9167
3. 9168
3. 9168
3. 9169
3. 9169
17 40
3. 9170
3. 9170
3. 9171
3.9171
3.9172
3. 9172
3.9173
3. 9173
3. 9174
3.9175
17 50
3.9175
3. 9176
3. 9176
3. 9177
3.9177
3. 9178
3.9178
3.9179
3. 9184
3. 9179
3. 9180
2 ,18
3. 9180
3.9181
3.9181
3. 9182
3. 9182
3. 9183
3. 9183
3. 9184
3. 9185
18 10
3. 9186
3.9186
3.9187
3. 9187
3.9188 ! 3.9188
3. 9189
3. 9189
3. 9190
3. 9190
18 20
3.9191
,3. 9191
3. 9192
3. 9192
3.9193 1 3.9193
3. 9194
3. 9194
3. 9195
3. 9195
18 30
3. 9196
3. 9197
3. 9197.
3. 9198
,3.9198 : 3.9199
3. 9199
3.9200
3. 9200
3. 9201
18 40
3. 9201
3. 9202
3. 9202
3. 9203
3.9203 1 3.9204
3. 9204
3. 9205
3. 9205
3. 9206
18 50
3. 9206
3. 9207
3. 9207
3.9213
3. 9208
3. 9213
3.9209 i 3.9209
379214 i 3.9214
3. 9210
3. 9215
3. 9210
3.9215
3.9211
3. 9216
3. 9211
2 19
3.9212
3.9212
3. 9216
19 10
3.9217
3. 9217
3. 9218
3.9218
3. 9219
3. 9219
3. 9220
3. 9221
3. 9221
3. 9222
19 20
3. 9222
3. 9223
3. 9223
3. 9224
3. 9224
3. 9225
3. 9225
3. 9226
3. 9226
3. 9227
19 30
3. 9227
3. 9228
3. 9228
3. 9229
3. 9229
3. 9230
3. 9230
3. 9231
3. 9231
3. 9232
19 40
3. 9232
3. 9233
3. 9233
3. 9234
3. 9235
3. 92:35
3. 92.36
3. 9236
3. 9237
3. 92.37
19 50
3. 9238
3. 9238
3. 92.39
3. 9239
3. 9240
3. 9240
3. 9241
3. 9241
3. 9242
3. 9242
APPENDIX V: TABLE IX.
[Page 327
Logarithms of Small Arcs in Space or Time.
Arc.
0"
l"
£"
8" 4"
5"
6"
7"
8"
9"
1
2" 20"
I!
0"
3. 9243
3. 9243
3. 9244
3. 9244
3. 9245
3. 9245
3. 9246
3. 9246
3. 9247
3. 9247
2(1
10
3. 9248
3. 9248
3. 9249
3. 9250
3. 9250
3. 9251
3. 9251
3. 9252
3. 9252
3. 9253
20
20
3. 9253
3. 9254
3. 9254
3. 9255
3. 9255
3. 9256
3.9256
3. 9257
3. 9257
3. 9258
20
30
3. 9258
3. 9259
3. 9259
3. 9260
3. 9260
3. 9261
3. 9261
3.9262 3.9262
3. 9263
20
40
3. 9263
3. 9264
3. 9264
3.9265
3. 9265
3. 9266
3. 9267
3. 9267
3. 9268
3. 9268
20
50
3. 9269
3. 9269
3. 9270
3. 9270
3. 9271
3. 9271
3.9272
3. 9272
3. 9277
3. 9273
"3.9278
3. 9273
3. 9278
2 21
3. 9274
3. 9274
3. 9275
3.9275 1 3.9276
3. 9276
3. 9277
■21
10
3. 9279
3.9279
3. 9280
3. 9280
3. 9281
3. 9281
3.9282
3. 9282
3. 9283
3. 9283
21
20
3. 9284
3. 9284
3. 9285
3. 9285
3. 9286
3. 9287
3. 9287
3. 9288
3. 9288
3. 9289
21
30
3. 9289
3. 9290
3. 9290
3.9291
3. 9291
3. 9292
3.9292
3. 9293
3. 9293
3. 9294
21
10
3. 9294
3.9295
3. 9295
3. 9296
3.9296 3.9297
3. 9297
3. 9298
3. 9298
3. 9299
21
50
3.9299
3.9300
3.9300
3. 9301
3.9301 1 3.9302
3. 9302
3. 9303
3. 9303
3. 9304
2 22
3. 9304
3. 9305
3. 9305
3. 9306
3.9306
3. 9307
3. 9307
3. 9308
3. 9308
3.9309
■>9
10
3. 9309
3. 9310
3.9311
3.9311
3.9312
3. 9312
3. 9313
3.9313
3. 9314
3. 9314
' ^9
20
3. 9315
3. 9315
3. 9316
3. 9316
3. 9317
3.9317
3. 9318
3. 9318
3. 9319
.3.9319
■}•->
30
3. 9320
3. 9320
3. 9321
3. 9321
3. 9322
3. 9322
3. 9323
3. 9323
3.9324
3. 9324
oi>
40
3. 9325
3. 9.325
3. 9326
3. 9326
3. 9327
3. 9327
3. 9328
3. 9328
3. 9329
3. 9329
22
2 23
50
3. 9330
3. 9335
3. 9330
3.9335
3. 9331
3.9336
3. 9331
3.9336
3. 9332
3. 9332
3. 9337
3. 9333
3. 9333
3. 9334
3. 9334
3. 9337
3. 9338
3. 9338
3. 9339
3. 9339
23
10
3. 9340
3. 9310
3. 9341
3.9341
3.9342 i 3.9.342 | 3.9343
3. 9343
3. 9.344
3. 9344
23
20
3. 9345
3. 9345
3. 9346
3.9346
3.9347 3.9348 : 3.9348
3. 9349
3. 9349
3.9350
23
30
3. 9350
3. 9351
3.9351
3. 9352
3.93.52 ,3.9:5.53 ; 3.93.53
3. 9354
3. 9354
3. 9355
23
40
3. 9355
3. 9356
3. 9356
3.9357
3. 9357
3.9358
3. 9358
3. 9359
3. 9359
3. 9360
23
50
3. 9360
3. 9361
3. 9366
3. 9361
3. 9366
3. 9362
3. 9362
3. 9363
3. 9363
3. 9364
3. 9369
3. 9364
3.9369
3. 9365
2 24
3.9365
3. 9367
3. 9367
3. 9368
3. 9368
3. 9370
24
10
3. 9370
3. 9371
3. 9371
3. 9372
3. 9372
3. 9373
3. 9373
3. 9374
3. 9374
3. 9375
24
20
3. 9375
3. 9376
3. 9376
3. 9377
3. 9377
3. 9378
3. 9378
3. 9379
3. 9379
3. 9380
24
30
3.9380
3. 9381
3.9381
3. 9382
3. 9382
3. 9383
3. 9383
3.9384
3. 9384
3. 9385
24
40
3. 9385
3. 9386
3.9386
3. 9387
3. 9387
3. 9388
3. 9388
3. 9389
3. 9389
3.9390
24
2 25
50
0"
3.9390
3. 9391
3. 9391
3. 9392
3. 9397
3. 9392
3. 9397
3. 9393
3. 9393
3. 9394
3. 9394
379399
3. 9395
3. 9395
3. 9396
3. 9396
3. 9398
3. 9398
3. 9399
3. 9400
25
10
3. 9400
3. 9401
3. 9401
3. 9402
3. 9402
3. 9403
3. 9403
3. 9404
3. 9404
3. 9405
25
20
3. 9405
3. 9406
3. 9406
3. 9407
3. 9407
3. 9408
3. 9408
3. 9409
3. 9409
3. 9410
25
30
3. 9410
3.9411
3.9411 1 3.9412
3.9412
3. 9413
3. 9413
3. 9414
3. 9414
3. 9415
25
40
3. 9415
3. 9416
3. 9416 ; 3. 9417
3.9417
3. 9418
3. 9418
3. 9419
3. 9419
3. 9420
25
50
3.9420
3. 9421
3. 9421
3. 9426
3. 9422
3. 9422
3. 9423
3.9428
3. 9423
3. 9424
3. 9424
3. 9429
3. 9425
2 2«
3. 9425
3. 9426
3. 9427
3. 9427
3. 9428
3. 9429
3. 9430
2t)
10
3. 9430
3. 9430
3.9431 ; 3.9431
3. 9432
3. 9432
3. 9433
3. 9433
3. 9434
3. 9434
26
20
3. 9435
3. 9435
3. 9436
3. 9436
3. 9437
3. 9437
3. 9438
3. 9438
3. 9439
3. 9439
26
30
3. 9440
3. 9440
3. 9441
3.9441
3.9442
3. 9442
3.9443
3. 9443
3. 9444
3. 9444
26
40
3. 9445
3. 9445
3. 9446
3. 9446
3. 9447
3. 9447
3. 9448
3. 9448
3.9449
3. 9449
26
50
3. 9450
3. 94.50
3.9451 1 3.94.51
3. 94.52
.3.94.52 i 3.9453
3. 9453
3.9454
3, 9454
2 27
3. 94.55
3. 9455
3. 9456
3. 9456
3. 9457
3.94.57 3.9458
3. 9458
3. 9459
3. 9459
27
10
3.9460
3. 9460
3. 9461
3. 9461
3. 9462
3. 9462 i 3. 9463
3. 9463
3. 9464
3.9464
27
20
3.9465
3. 9465
3. 9466
3. 9466
3. 9466
3. 9467
3. 9467
3. 9468
3. 9468
3. 9469
0-^
30
3. 9469
3. 9470
3. 9470
3. 9471
3.9471
3. 9472
3. 9472
3. 9473
3. 9473
3. 9474
27
40
3. 9474
3. 9475
3. 9475
3. 9476
3. 9476
3. 9477
3. 9477
3. 9478
3. 9478
3. 9479
27
50
3. 9479
3. 9484
3. 9480
3. 9485
3. 9480
3. 9481
3. 9481
3. 9482
3. 9482
3.9483
3. 9488
3. 9483
3. 9488
3. 9484
2 28
3.9485
3. 9486
3. 9486
3. 9487
3. 9487
3. 9489
28
10
3. 9489
3. 9490
3. 9490
3. 9490
3. 9491
3. 9491
3. 9492
3. 9492
3. 9493
3. 9493
28
20
3. 9494
3. 9494
3. 9495
3. 9495
3. 9496
3. 9496
3. 9497
3. 9497
3. 9498
3. 9498
28
30
3. 9499
3.9499
3.9500
3. 9500
3. 9.501
3. 9501
3. 9502
3. 9.502
3. 9503
3. 9503
28
40
3.9504
3. 9504
3. 9505
3. 9505
3. 9506
3. 9506
3. 9507
3. 9.507
3. 9508
3. 9508
28
50
3. 9509
3. 9509
3.9509
3. 9510
3. 9510
3.9511
3.9511
3. 9512
3.9512
3. 9513
2 29
3.9513
3. 9514
3. 9514
3. 9515
3. 9515
3. 9516
3. 9516
3. 9517
3. 9517
3. 9518
29
10
3.9518
3. 9519
3. 9519
3. 9520
3. 9520
3. 9521
3. 9521
3. 9522
3. 9522
3. 9523
29
20
3. 9523
3. 9524
3. 9524
3. 9525
3. 9525
3. 9526
3. 9526
3. 9526
3. 9527
3. 9527
29
30
3. 9528
3. 9528
3.9529
3. 9529
3. 9530
3. 9530
3. 9531
3. 9531
3. 9532
3. 9532
29
40
3. 9533
3. 9533
3. 95.34
3. 9534
3. 9535
3. 9435
3.9536
3. 9536
3. 9537
3. 9537
29
50
3. 9538
3. 9.538
3. 9539
3. 9539
3. 9540
3. 9540
3. 9540
3. 9.541
3. 9.541
3.9542
Page 328]
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or Time.
Are.
0"
1"
2" «"
4"
5"
6"
7"
8" 9"
o /
2'' 30°'
II
0'
3. 9542
3. 9543
3.9543
8. 9544
3.9544
3. 9545
3.9545
3. 9546
3.9546 3.9547
30
10
3. 9547
3. 9548
3. 9548
3. 9549
3.9549
3. 9550
3. 9550
3. 9551
3. 9551
3. 9552
30
20
3. 9552
3.9553
3. 9553
3. 9554
3. 9554
3. 9554
3. 9555
3. 9555
3. 95.56
3. 9556
30
30
3. 9557
3. 9557
3.9558
3. 9558
3. 9559
3. 9559
3. 9560
3. 9560
3. 9561
3. 9561
30
40
3. 9562
3.9562
3.9563
3. 9563
3.9564
3. 9564
3.9565
3. 9565
3. 9566
3.9566
30
50
3.9566
3. 9567
3. 9567
3. 9568
3. 9568
3. 9569
3:9574
3. 9569
3. 9570
3. 9570
379575
3. 9571
2 31
3. 9571
3. 9572
3. 9572
3. 9573
3. 9573
3. 9574
3. 9575
3. 9576
31
10
3. 9576
3. 9577
3. 9577
3. 9578
3. 9578
3. 9578
3. 9579
3. 9579
3. 9580
3. 9580
31
20
3. 9581
3. 9581
3. 9582
3. 9582
3. 9583
3. 9583
3. 9584
3. 9584
3. 9585
3. 9585
31
.30
3. 9586
3. 9586
3. 9587
3.9587
3. 9588
3. 9588
3. 9.589
3. 9589
3. 9589
3. 9590
31
40
3. 9590
3. 9591
3. 9591
3. 9592
3. 9592
3. 9593
3. 9593
3. 9594
3. 9594
3. 9595
31
50
3. 9595
3. 9596
3. 9596
3. 9597
3. 9597
3. 9598
3. 9598
3.9599
3. 9599
3.9599
2 32
3.9600
3.9600
3.9601 ! 3.9601
3.9602
3/9602
3. 9603
3.9603
3. 9604
3.9604
32
10
3. 9605
3.9605
3. 9606 3. 9606
3.9607
3. 9607
3. 9608
3. 9608
3. 9609
3. 9.609
32
20
3.9609
3.9610
3. 9610
3. 9611
3. 9611
3. 9612
3.9612
3. 9613
3.9613
3. 9614
32
30
3. 9614
3. 9615
3. 9615
3. 9616
,3.9616
3.9617
3. 9617
3. 9618
3. 9618
3. 9618
32
40
3. 9619
3. 9619
3. 9620
3. 9620
3. 9621
3. 9621
3. 9622
3. 9622
3. 9623
3. 9623
32
50
3. 9624
3.9628
3. 9624
3. 9625
3. 9625
3. 9626
3. 9626
3. 9627
3.9627
3.9627
3. 9632
3. 9628
2 33
3.9629
3.9629
3.9630
3.9630
3. 9631
3. 9631
3.9632
3. 9633
33
10
3. 9633
3. 9634
3. 9634
3. 9634
3.9635
3. 96,35
3. 9636
3. 9636
3. 9637
3. 9637
33
20
3. 9638
3. 9638
3.9639
3.9639
3. 9640
3. 9640
3.9641
3.9641
3. 9642
3.9642
33
.30
3. 9642
3. 9643
3. 9643
3.9644
3. 9644
3.9645
3. 9645
3. 9646
3. 9646
3. 9647
33
40
3. 9647
3.9648
3. 9648
3. 9649
3. 9649
3. 9650
3.9650
3. 9651
3. 9651
3. 9652
33
50
3.9652
3.9653
3. 9653
3. 9653
3. 9654
3. 9654
3.9655
3. 9655
3.9656
3. 9656
2 34
3.9657
3.9657
3. 96.58
3.9658
3.9658
3. 9659
3.9659
3.9660
3.9660
3.9661
34
10
3.9661
3. 9662
3.9662
3.9663
3.9663
3. 9664
3.9664
3.9665
3.9665
3.9665
34
20
3.9666
3.9666
3.9667
3.9667
3.9668
3.9668
3.9669
3. 9669
3.9670
3.9670
34
30
3. 9671
3. 9671
3. 9672
3.9672
3.9672
3. 9673
3.9673
3. 9674
3. 9674
3. 9675
34
40
3. 9675
3.9676
3. 9676
3. 9677
3. 9677
3. 9678
3. 9678
3. 9679
3. 9679
3.9680
34
50
3.9680
3. 9681
3. 9681
3. 9682
3.9682
3. 9682
3. 9683
3. 9683
3. 9684
3. 9684
2 35
3. 9685
3.9685
3.9686
3. 9686
3.9687
3. 9687
3. 9688
3. 9688
3. 9689 ' 3. 9689 1
35
10
3.9689
3.9690
3.9690
3. 9691
3.9691
3. 9692 i 3. 9692
3.9693
3. 9693 i 3. 9694 |
35
20
3.9694
3. 9695
3.9695 ! 3.9696
3. 9696
3. 9696
3. 9697
3.9697
3.9698
3.9698
35
.30
3. 9699
3.9699
3.9700
3.9700
3.9701
3. 9701
3. 9702
3. 9702
3.9703
3. 9703
35
40
3. 9703
3. 9704
3.9704
3.9705
3. 9705
3.9706
3.9706
3. 9707
3. 9707
3. 9708
35
50
3. 9708
3.9713
3.9709
3.9713
3.9709
3. 9710
3. 9710
3. 9710
3. 9711
3. 9711
3.9712
3. 9712
2 36
3. 9714
3. 9714
3. 9715
3. 9715
3.9716
3. 9716
3. 9716 : 3. 9717 1
36
10
3.9717
3.9718
3. 9718
3.9719
3. 9719
3. 9720
3. 9720
3. 9721
3. 9721 i 3. 9722 |
36
20
3. 9722
3. 9722
3. 9723
3. 9723
3. 9724
3. 9724
3. 9725
3. 9725
3. 9726
3. 9726
36
.30
3. 9727
3. 9727
3. 9728
3. 9728
3.9729
3. 9729
3.9729
3. 9730
3. 9730
3.9731
36
40
3. 9731
3. 9732
3. 9732
3. 9733
3. 9733
3. 9734
3. 9734
3. 9735
3. 9735
3.9735
36
50
3. 9736
3. 9736
3. 9737
3. 9737
3. 9738
3. 9738
3. 9743
3. 9739
3. 9739
3.9740
3. 9740
2 37
3.9741
3. 9741
3. 9741
3. 9742
3. 9742
3. 9743
3. 9744
3.9744
3. 9745
37
10
3. 9745
3. 9746
3. 9746
3. 9746
3. 9747
3. 9747
3. 9748
3. 9748
3. 9749
3. 9749
37
20
3.9750
3. 9750
3. 9751
3. 9751
3. 9752
3. 9752
3. 9752
3. 9753
3. 9753
3. 9754
37
30
3. 9754
3. 9755
3. 9755
3. 9756
3. 9756
3. 9757
3. 9757
3. 9758
3. 9758
3. 9758
37
40
3.9759
3. 9759
3.9760
3. 9760
3. 9761
3. 9761
3. 9762
3. 9762
3. 9763
3. 9763
37
50
3. 9763
3.9764
3.9764
3.9765
3.9765
3. 9766
3. 9766
3. 9767
3. 9767
3. 9768
2 38
3. 9768
3. 9769
3. 9769
3. 9769
3. 9770
3. 9770
3. 9771
3. 9771
3. 9772
3. 9772
38
10
3. 9773
3. 9773
3. 9774
3. 9774
3. 9774
3. 9775
3. 9775
3. 9776
3. 9776
3. 9777
38
20
3. 9777
3. 9778
3.9778
3. 9779
3. 9779
3. 9779
3. 9780
3. 9780
3. 9781
3. 9781
38
.30
3. 9782
3.9782
3. 9783
3.9783
3.9784
3. 9784
3.9785
3. 9785
3. 9785
3. 9786
38
40
3. 9786
3. 9787
3. 9787
3.9788
3.9788
3. 9789
3. 9789
3.9790
3.9790
3.9790
38
50
3. 9791
3.9791
3.9792
3. 9792
3.9793
3. 9793
3. 9798
3. 9794
3. 9794
3. 9795
3. 9795
3.9800
2 39
3. 9795
3.9796
3. 9796
3. 9797
3.9797
3. 9798
3. 9799
3. 9799
39
10
3.9800
3.9800
3. 9801
3. 9801
3. 9802
3. 9802
3. 9803
3. 9803
3. 9804
3. 9804
39
20
3.9805
3. 9805
3. 9805
3.9806
3.9806
3. 9807
3. 9807
3. 9808
3. 9808
3.9809
39
,30
3.9809
3. 9810
3. 9810
3. 9810
3.9811
3. 9811
3. 9812
3. 9812
3. 9813
3. 9813
39
40
3. 9814
3. 9814
3. 9815
3. 9815
3.9815
3. 9816
3. 9816
3. 9817
3. 9817
3.9818
39
50
3. 9818
3. 9819
3. 9819
3. 9819
3.9820
3. 9820
3. 9821
3. 9821
3. 9822
3. 9822
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in Space or Time.
[Page 329
Arc.
0"
1"
2" I 3"
4"
5"
6"
7"
8"
V
O 1 ft
9h 4o» 0"
3. 9823
3. 9823
3. 9824
3. 9824
3. 9826
3. 9825
3.9825
3. 9826
3. 9826
3. 9827
40
10
3. 9827
3. 9828
3. 9828
3.9829
3. 9829
3.9829
3. 9830
3. 9830
3. 9831
3. 9831
40
20
3. 9832
3.9832
3. 9833
3. 9833
3. 9834
3. 9834
3. 9834
3. 9835
3. 9836
3. 9836
40
30
3. 9836
3. 9837
3. 9837
3. 9838
3. 9838
3. 9839
3. 9839
3. 9839
3. 9840 3. 9840
40
40
3. 9841
3. 9841
3. 9842
3. 9842
3. 9843
3. 9843
3. 9843
3. 9844
3.9844 3.9846
40
50
3. 9845
3. 9846
3. 9846
3. 9847
3. 9847
3. 9848
3. 9848
3. 9848
3. 9849 3. 9849
2 41
3. 9850
3. 9850
3. 9851
3. 9851
3. 9852
3. 9862
3.9862
3. 9853 i 3. 9863 3. 9864
41
10
3. 9854
3. 9855
3. 9855
3. 9866
3. 9856
3. 9857
3. 9867
3. 9867 j 3. 9868 : 3. 9868
41
20
3.9859
3. 9859
3. 9860
3. 9860
3. 9861
3. 9861
3. 9861
3. 9862 ! 3. 9862 3. 9863
41
30
3. 9863
3. 9864
3. 9864
3.9865
3. 9865
3. 9865
3. 9866
3.9866
3. 9867 1 3. 9867
41
40
3. 9868
3. 9868
3. 9869
3.9869
3. 9870
3.9870
3. 9870
3. 9871
3. 9871 : 3. 9872
41
50
3. 9872
3. 9873
3. 9873
3. 9878
3. 9874
3. 9874
3. 9874
3.9875
3.9875
3. 9876 1 3. 9876
2 42
3. 9877
3. 9877
3. 9878
3. 9878
3. 9879
3. 9879
3.9880
3. 9880 3. 9881
42
10
3. 9881
3. 9882
3. 9882
3. 9882
3. 9883
3. 9883
3.9884
3.9884
3. 98a5 . 3. 9885
42
20
3. 9886
3. 9886
3. 9886
3. 9887
3. 9887
3. 9888
3. 9888
3. 9889 j 3. 9889 3. 9890
42
30
3.9890
3. 9890
3. 9891
3. 9891
3. 9892
3. 9892
3. 9893
3. 9893 1 3. 9894 3. 9894
42
40
3. 9894
3. 9895
3. 9895
3. 9896
3. 9896
3. 9897
3. 9897
3. 9898 i 3. 9898 3. 9898
42
50
3.9899
3. 9899
3.9900
3.9900
3.9905
3. 9901
3. 9905
3. 9901
3.9902
3.9902
3. 9903 3. 9903
3. 9907 1 3. 9907
2 43
3.9903
3.9904
3. 9904
3.9906
3.9906
3.9906
43
10
.3.9908
3. 9908
3.9909
3.9909
3. 9910
3.9910
3.9910
3.9911
3.9911 ' 3.9912
43
20
3. 9912
3. 9913
3. 9913
3. 9914
3. 9914
3. 9914
3. 9915
3. 9915
3. 9916 3. 9916
43
30
3. 9917
3. 9917
3.9918
3. 9918
3. 9918
3. 9919
3. 9919
3. 9920
3. 9920 \ 3. 9921
43
40
3. 9921
3. 9922
3. 9922
3.9922
3. 9923
3. 9923
3. 9924
3. 9924
3. 9925 3. 9925
43
50
3. 9926
3.9926
3. 9926
3. 9931
3.9927
3. 9927
3.9928
3. 9928
3.9929
3.9929 ,3.9930
2 44
3.9930
3.9930
3. 9931
3.9932
3.9932
3.9933
3. 9933
3.9933 3.9934
44
10
3. 9934
3. 9935
3.9935
3.9936
3. 9936
3. 9937
3.9937
3. 9937 ! .^. 99.38 3. 9938
44
20
3. 9939
3.9939
3.9940
3.9940
3.9941
3. 9941
3.9941
3. 9942 i 3. 9942 3. 9943
44
30
3. 9943
3.9944
3.9944
3.9944
3.9945
3.9945
3.9946
3. 9946 1 3. 9947 3. 9947
44
40
3.9948
3.9948
3.9948
3.9949
3.9949
3.9960
3.9950
3. 9951 i 3. 9951 3. 9952
44
.50
3.9952
3.9952
3. 9953
3.9963
3. 9954
3. 9954
3.9959
3.9955
3.9955
3. 9955 : 3. 9956
2 45
3. 9956
3. 9967
3.9967
3. 9968
3. 99.58
3. 9959
3.9959
3. 9960 3. 9960
45
10
3.9961
.3.9961
3. 9962
3.9962
3.9962
3.9963
3.9963
3.9964
3. 9964 3. 9965
45
20
3.9965
.3.9966
.3.9966
3.9966
3.9967
3.9967
3.9968
3.9968
3. 9969 3. 9969
45
30
3.9969
3. 9970
3. 9970
3.9971
3.9971
3. 9972
3.9972
3. 9973
3. 9973 3. 9973
45
40
3. 9974
3.9974
3.9975
3.9975
3.9976
3.9976
3.9976
3.9977
3. 9977 3. 9978
45
50
3.9978
3. 9979
3. 9979
3.9980
3.9980
3.9980
3.9985
3. 9981
3.9985
3.9981
3.9986
3. 9982
3. 9986
3. 9982
3. 9987
2 46
3. 9983
3.9983
3.9983
3.9984
3.9984
46
10
3.9987
3. 9987
3. 9988
3. 9988
3.9989
3.9989
3.9990
3.9990
3. 9990
3. 9991
46
20
3. 9991
3.9992
3.9992
3. 9993
3. 9993
3.9993
3.9994
3.9994
3. 9995
3. 9996
46
30
3. 9996
3.9996
3. 9997
3.9997
3.9997
3. 9998
3.9998
3.9999
3. 9999
4.0000
46
40
4.0000
4.0000
4.0001
4.0001
4.0002
4.0002
4.0003
4.0003
4.0003
4.0004
46
50
4.0004
4.0005
4.0006
4.0010
4.0006
4.0006
4. 0010
4.0007
4.0011
4.0007
4.0007
4.0012
4.0008
4.0008
2 47
4.0009
4.0009
4.0010
4.0011
4.0012 i 4.0013
47
10
4. 0013
4.0013
4.0014
4.0014
4.0015
4.0016
4.0016
4.0016
4.0016 1 4.0017
47
20
4.0017
4.0018
4.0018
4.0019
4.0019
4.0019
4.0020
4.0020
4. 0021 ; 4. 0021
47
30
4.0022
4.0022
4.0023
4.0023
4.0023
4.0024
4.0024
4.0025
4. 0025
4.0026
47
40
4.0026
4.0026
4.0027
4.0027
4.0028
4.0028
4.0029
4.0029
4.0029
4.0030
47
50
4.0030
4.0031
4.0031
4.0032
4.0032
4.0032
4.0033
4.0037
4.0033
4.0038
4.0034
4.0038
4.0034
4.0038
2 48
4.0035
4.0036
4.0035
4.0036
4.0036
4.0037
48
10
4.0039
4.0039
4.0040
4.0040
4.0041
4.0041
4.0041
4.0042
4.0042
4.0043
48
20
4.0043
4.0044
4.0044
4.0046
4.0045
4.0045
4.0046
4.0046
4.0047
4.0047
48
30
4.0048
4.0048
4.0048
4.0049
4.0049
4.0060
4. 0050
4.0051
4. 0051
4.0051
48
40
4.0052
4.0052
4.0053
4. 0053
4. 00.54
4.0054
4. 0054
4.0055
4. 0055 i 4. 0056 1
48
50
4. 0056
4.00.57 i 4.0057
4.0057
4.0058
4.0058
4.0059
4.0059
4. 0060 ! 4. 0060 |
2 49
49
10
4. 0060
4.0065
4. 0061 j 4. 0061
4. 0066 4. 0066
4.0062
4.0066
4.0062
4.0066
4.0063
4.0067
4.0063
4.0067
4.0063
4.0068
4.0064
4.0068
4.0064
4.0069
49
20
4.0069
4.0069
4.0070
4.0070
4.0071
4.0071
4.0072
4.0072
4.0072
4.0073
49
30
4.0073
4.0074
4.0074
4.0074
4. 0075
4.0075
4.0076
4.0076
4.0077
4.0077
49
40
4.0077
4.0078
4.0078
4.0079
4.0079
4.0080
4.0080
4.0080
4.0081
4.0081
49
50
4.0082
4.0082
4.0083
4.0083
4. 0083
4.0084
4.0084
4.0085
4.0085
4.0086
Page 330]
APPENDIX V: TABLE IX.
Logarithms of Small Arcs in
Space or Time.
Arc.
0"
1"
2"
3"
4"
w
G"
7"
8"
9"
o /
2" 50°
0'
4.0086
4.0086
4.0087
4. 0087
4. 0088
4.0088
4.0089
4.0089
4.0089
4.0090
50
10
4.0090
4.0091
4.0091
4.0092
4. 0092
4. 0092
4.0093
4.0093
4.0094
4.0094
50
20
4.0095
4.0095
4. 0095
4. 0096
4. 0096
4. 0097
4.0097
4. 0097
4. 0098
4. 0098
50
30
4.0099
4. 0099
4.0100
4. 0100
4. 0100
4. 0101
4. 0101
4. 0102
4. 0102
4. 0103
50
40
4. 0103
4.0103
! 4.0104
4.0104
4. 0105
4.0105
4.0106
4. 0106
4.0106
4. 0107
50
50
4. 0107
4. 0108
i 4. 0108
4. 0109
4. 0109
4. 0109
4.0110
4.0110
4.0111
4.0111
2 51
4.0111
4.0112
4.0112
4.0113
4.0113
4.0114
4. 0114
4.0114
4.0115
4. 0115
51
10
4.0116
4.0116
4. 0117
4.0117
4.0117
4. 0118
4.0118
4.0119
4. 0119
4. 0120
51
20
4.0120
4. 0120
4. 0121
4. 0121
4. 0122
4.0122
4. 0122
4. 0123
4. 0123
4. 0124
51
30
4. 0124
4.0125
1 4.0125
4. 0125
4.0126
4. 0126
4.0127
4. 0127
4.0128
4. 0128
51
40
4.0128
4.0129
! 4.0129
4. 0130
4. 0130
4. 0130
4. 0131
4.0131
4. 0132
4. 0132
51
50
4. 0133
4.0133
i 4.0133
4. 0134
4. 0134
4. 0135
4.0135
4. 0136
4. 0136
4. 0136
2 52
4. 0137
4.0137
: 4. 0138
4. 0138
4. 0138
4. 0139
4.0139 1 4.0140
4.0140
4. 0141
52
10
4. 0141
4. 0141
4. 0142
4.0142
4. 0143
4. 0143
4. 0144
4.0144
4.0144
4. 0145
52
20
4. 0145
4. 0146
i 4. 0146
4. 0146
4. 0147
4. 0147
4. 0148
4. 0148
4. 0149
4. 0149
52
30
4. 0149
4. 01.50
! 4.01.50
4.0151
4.0151
4. 0152
4. 0152
4. 0153
4.0153
4. 0153
52
40
4. 0154
4.0154
1 4. 0154
4. 0155
4. 0155
4. 0156
4. 0156
4.0157
4. 0157
4. 0157
52
50
4. 0158
4. 0158
! 4.0159
4. 0159
4. 0159
4. 0160
'^0164
4. 0160
4.0164
4. 0161
4. 0161
4. 0162
2 53
4. 0162
4. 0162
1 4.0163
4.0163
4.0164
4.0165
4.0165
4. 0166
53
10
4. 0166
4.0167
4. 0167
4. 0167
4. 0168
4. 0168
4. 0169
4. 0169
4. 0169
4. 0170
53
20
4.0170
4.0171
4.0171
4. 0172
4.0172
4.0172
4. 0173
4.0173
4. 0174
4. 0174
53
30
4. 0175
4. 0175
4. 0175
4. 0176
4.0176
4.0177
4.0177
4.0177
4.0178
4.0178
53
40
4. 0179
4. 0179
4. 0180
4.0180
4. 0180
4.0181
4.0181
4.0182
4. 0182
4.0182
53
50
4. 0183
4. 0183
4. 0184
4. 0184
4. 0185
4. 0185
4. 0185
4. 0186
4. 0186
4. 0187
2 54
4.0187 1 4.0187
4. 0188
4.0188
4. 0189
4. 0189
4. 0190
4. 0190
4.0190
4.0191
54
10
4. 0'191
4. 0192
4. 0192
4. 0192
4. 0193
4. 0193
4.0194
4. 0194
4. 0194
4. 0195
54
20
4. 0195
4. 0196
4. 0196
4. 0197
4. 0197
4. 0197
4. 0198
4. 0198
4.0199
4. 0199
54
30
4.0199
4. 0200
4.0200
4. 0201
4. 0201
4. 0202
4. 0202
4. 0202
4. 0203
4. 0203
54
40
4. 0204
4.0204
4. 0204
4. 0205
4. 0205
4.0206
4. 0206
4. 0207
4. 0207
4. 0207
54
2 55
50
4. 0208
4. 0208
4.0209
4. 0209
4.0209
4. 0210
4. 0210
4.0211
4.0211
4,0211
4. 0212
4.0212
4. 0213
4. 0213
4. 0214
4. 0214
4. 0214
4.0215
4. 0215
4.0216
rin
10
4. 0216
4. 0216
4. 0217
4. 0217
4. 0218
4. 0218
4. 0219
4. 0219
4. 0219
4. 0220
00
20
4. 0220
4. 0221
4. 0221
4. 0221
4. 0222
4. 0222
4. 0223
4. 0223
4. 0223
4. 0224
55
30
4. 0224
4. 0225
4. 0225
4. 0225
4. 0226
4. 0226
4. 0227
4. 0227
4. 0228
4. 0228
00
40
4.022-i
4. 0229
4. 0229
4. 0230
4. 02.30
4. 0230
4. 0231
4. 0231
4. 0232
4. 0232
55
50
4. 0233
4. 0233
4. 0237
4. 0233
4. 0237
4. 0234
4. 0234
4. 0235
4.0239"
4. 0235
4. 0239
4. 0235
4. 0240
4. 0236
4. 0240
4. 0236
4. 0240
2 56
4. 0237
4. 0238
4. 0238
56
10
4. 0241
4. 0241
4. 0242
4. 0242
4. 0242
4. 0243
4. 0243
4. 0244
4. 0244
4. 0244
56
20
4. 0245
4. 0245
4. 0246
4. 0246
4. 0246
4.0247
4.0247
4. 0248
4. 0248
4. 0249
56
30
4. 0249
4. 0249
4. 0250
4. 0250
4. 0251
4. 0251
4. 0251
4. 0252
4. 0252
4. 0253
56
40
4. 0253
4. 0253
4. 0254
4. 0254
4. 0255
4. 0255
4. 0256
4. 02.56
4. 02-56
4. 0257
56
50
4. 0257
4. 0258
4. 0262
4. 0258
4. 0262
4. 0258
4. 0259
4. 0259
4. 0260
4. 0260
4. 0260
4. 0261
4.026.5
2 57
4. 0261
4. 0262
4. 0263
4. 0263
4. 0264
4.0264
4. 0265
0(
10
4. 0265
4. 0266
4. 0266
4. 0267
4. 0267
4. 0267 4. 0268
4. 0268
4. 0269
4. 0269
57
20
4. 02G9
4. 0270
4. 0270
4. 0271
4. 0271
4. 0271 4. 0272
4. 0272
4. 0273
4. 0273
57
30
4. 0273
4. 0274
4. 0274
4. 0275
4. 0275
4. 0276 4. 0276
4. 0276
4. 0277
4. 0277
57
40
4. 0278
4. 0278
4. 0278
4. 0279
4. 0279
4. 0280
4. 0280
4. 0280
4. 0281
4. 0281
57
50
4. 0282
4. 0282
4. 0282
4. 0283
4. 0283
4. 0284
'4. 0288
4. 0284
4. 0284
4. 0285
4. 0285
2 58
4. 0286
4. 0286
4. 0287
4. 0287
4. 0287
4. 0288
4. 0289
4. 0289
4. 0289
58
10
4. 0290
4.0290
4. 0291
4. 0291
4. 0291
4. 0292
4.0292
4. 0293
4. 0293
4.0293
58
20
4. 0294
4. 0294
4. 0295
4. 0295
4. 0295
4. 0296
4. 0296
4. 0297
4. 0297
4. 0297
58
30
4. 0298
4. 0298
4. 0299
4. 0299
4.0300
4.0300
4. 0300
4. 0301
4. 0301
4. 0302
58
40
4. 0302
4. 0302
4. 0303
4. 0303
4.0304
4. 0304
4. 0304
4. 0305
4. 0305
4.0306
58
50
4. 0306
4. 0306
4. 0307
4.0307
4. 0308
4. 0308
4. 0308
4. 0309
4. 0309
4.0310
2 59
4. 0310
4. 0310
4.0311
4. 0311
4. 0312
4. 0312
4. 0312
4. 0313
4. 0313
4. 0314
59
10
4. 0314
4. 0314
4. 0315
4. 0315
4. 0316
4. 0316
4.0317
4. 0317
4. 0317
4. 0318
59
20
4. 0318
4. 0319
4. 0319
4. 0319
4. 0320
4. 0320
4. 0321
4. 0321
4. 0321
4. 0322
59
30
4. 0322
4. 0323
4. 0323
4. 0323
4. 0324
4. 0324
4. 0325
4. 0325
4.0325
4. 0326
59
40 4. 0326
4. 0327
4. 0327
4. 0327
4. 0328
4. 0328
4. 0329
4. 0329
4. 0329
4. 03,30
50
50 4. 0330
4. 0331
4. 0,331
4.0331
4. 0332
4. 0332
4. 0333
4. 0333
4. 0333
4. 03.34
APPENDIX V: TABLE X. [Page 331
Table showing the correction required, on account of Second Differences of the Moon's Motion, in
Finding the Greenwich Time corresponding to a Corrected Lunar Distance.
Approximate
interval.
Difference of the proportional logarithms in the Ephemeris. 1
2
4
6
8
10
12
14
16
18
20
22
24
26
1 28 30
82
34
86
h. m.
10
20
/,. m.
3
2 50
2 40
».
8.
8.
1
1
1
2
2
2
2
2
8.
1
1
2
2
2
2
2
3
3
8.
1
1
2
2
3
3
3
3
3
8.
1
2
2
3
3
3
4
4
4
8.
1
2
2
3
4
4
4
4
4
8.
1
2
3
3
4
4
5
5
5
8.
1
2
3
4
5
5
5
6
6
8.
1
2
3
4
5
6
6
6
6
8.
1
3
4
5
5
6
6
7
7
8.
2
3
4
5
6
7
7
7
8
8.
•2
3
!
8.
2
3
a.
2
4
8.
2
4
8.
2
4
«.
2
4
30
40
50
2 30
2 20
2 10
1
5
6
6
7
8
8
8
5
6
7
5
6
7
6
7
8
6
7
8
6
8
9
10 12
1 10 1 1 50
1 20 1 1 40
1 30 1 30
i
1
1
1
1
8
8
9
9
8
9
9
9
9
9
10
10
9
10
10
11
10
11
U
11
Differenoe of the proportional logarithms in the Ephemeris. 1
S8
«.
2
5
40
».
3
5
7
9
10
11
12
12
12
42
».
3
5
7
9
10
12
12
13
13
44
8.
3
5
8
10
11
12
13
14
14
46
8.
3
6
8
10
12
13
14
14
14
48
8.
3
6
8
10
12
13
14
15
15
50
8.
3
6
9
11
13
52 54
56
58
60
62 1 64
66 68
.70
A. M.
10
20
h. VI.
3
2 50
2 40
8.
3
6
8.
4
7
8.
4
7
8.
4
7
8.
4
7
8.
4
8
8.
4
8
8. 8.
4 1 4
8 i 8
8.
5
9
30
40
50
1
1 10
1 20
1 30
2 30
2 20
2 10
2
1 50
1 40
1 30
7
8
9
10
11
12
12
9
11
13
9
12
14
10
12
14
10
13
15
10
13
15
1^
16
11
14
16
12 ' 12
14 i 15
16 : 17
12
15
17
14
15
15
16
14
15
16
16
15
16
17
17
16
17
16
17
18
18
17
18
19
19
17
18
19
19
18
19
20
20
18 19
19 20
20 21
21 21
19
21
21
22
1
Difference of the proportional logarithms in the Ephemeris. 1
/(. m.
10
20
30
40
50
h. m.
3
2 50
2 40
2 30
2 20
2 10
"2 0~
1 50
1 40
1 30
72
s.
5
9
13
16
18
20
21
22
23
74
76
78
80
82
84
86
88
90
92 { 94
96
98 100
102
104
8.
5
9
13
16
19
21
22
23
23
8.
5
9
13
16
19
21
22
23
24
8.
5
10
14
17
20
22~
23
24
24
8.
5
10
14
17
20
22
24
.25
25
8.
5
10
14
18
21
23
24
25
25
8.
6
10
14
18
21
23
25
26
26
8.
6
11
15
19
22
24
25
26
27
8.
6
11
8.
6
11
8.
6
11
8.
6
12
8.
6
12
17
21
24
8.
6
12
8.
7
12
8,
1
13
8.
7
13
15
19
22
16
19
22
16
20
23
16
20
23
17
21
24
17
22
25
18
22
26
18
22
26
1
1 10
1 20
1 30
24
26
27
27
25
27
28
28
25 26
27 28
28 29
29 29
27
28
29
30
27
29
30
31
38
30
31
31
28
30
31
32
29
31
32
32
[
Difference of the proportional logarithms in the Ephemeris. 1
k. m.
10
20
30
40
50
1
1 10
1 20
1 30
ft. m.
3
2 50
2 40
2 30
2 20
2 10
106
108
110
112
114
116
118
120
122
124
120
128
ISO 182
184
186
138
8.
7
13
18
23
26
29
31
33
33
«.
7
13
19
23
27
30
32
33
34
».
7
14
19
24
27
30
32
34
34
8.
7
14
19
24
28
31
33
34
35
8.
7
14
20
25
29
31
34
35
35
8.
8
14
20
25
29
8.
8
15
20
25
29
8.
8
15
8.
8
15
8.
8
15
8.
8
15
«.
8
16
8.
8
16
8.
9
16
8. 8.
9 9
16 17
8.
9
17
21
26
30
21
26
30
21
27
31
22
27
31
22
28
32
22
28
32
23
28
33
23
29
33
24
29
34
24
30
34
2
1 50
1 40
1 30
32
34
35
36
33
35
36
36
33
35
37
37
34
36
38
38
34
37
38
39
35
J7
?9
39
35
38
39
40
36
38
40
40
37
39
41
41
37
40
41
42
38
40
42
42
38
41
42
43
The corrfotion is to be added to the approximate Greenwich time when the proportional logarithms in the Ephemeris
^re decreasing, and subtracted when they are increasing.
Page 332]
APPENDIX V
: TABLE XI.
1
For finding the value of N for Correcting Lunar Distances for the Compression of the Earth. 1
Table XI A, giving Ist part of N.
Table XI B, giving 2d part of N.
Moon's declination.
Other body'
5 declination.
App.
dfst.
App.
di8t.
00
8°
6°
9°
12°
15°
18°
21°
24°
27°
80°
0°
8°
6°
»°
12°
15°
18°
21°
24°
ff
80°
o
//
ft
It
„
II
If
ft
o
//
20
-0
3
6
10
13
16
19
22
25
28
31
20
+0
3
7
10
14
17
20
24
27
.30
33
22
3
6
9
12
14
17
20
23
25
28
22
3
6
9
13
16
19
22
25
27
.30
24
3
5
8
11
13
16
18
21
23
25
24
3
6
9
12
14
17
20
23
25
28
26
2
5
7
10
12
14
17
19
21
23
26
3
5
8
11
13
16
18
21
23
26
28
2
"2
4
4
7
6
9
8
11
10
13
12
15
14
17
16
19
21
28
+0
3
2
5
5
8
7
10
9
12
12
15
14
17
16
20
18
22
21
24
23
30
-0
18
20
30
32
2
4
6
8
9
11
13
15
16
18
32
2
4
7
9
11
13
15
17
19
21
34
2
4
5
7
9
10
12
14
15
17
34
2
4
6
8
11
13
15 1 16
18
20
36
2
3
5
7
8
10
11
13
14
16
36
2
4
6
8
10
12
14. 16
17
19
38
2
3
5
6
8
9
10
12
13
14
38
2
4
6
8
10
11
13, 15
17
18
40
-0
3
4
6
7
8
10
11
12
13
40
+0
2
4
6
7
9
11
13
14
16
18
42
3
4
5
7
8
9
10
11
13
42
2
4
5
7
9
10
12
14
15
17
44
2
4
5
6
7
8
10
11
12
44
2
3
5
7
8
10
12
13
15
16
46
2
3
5
6
7
8
9
10
11
46
2
3
5
6
8
10
11 ' 13
14
16
48
2
3
4
5
6
7
8
9
10
48
2
3
5
6
8
9
11
12
14
15
50
-0
2
3
4
5
6
7
8
9
10
50
+0
2
3
5
6
8
9
11
12
13
15
52
2
3
4
5
5
6
7
8
9
52
2
3
4
6
7
9
10
12
13
14
54
2
3
3
4
5
6
7
7
8
54
3
4
6
7
9
10
11
13 1 14l
56
1
2
2
3
4
6
5
6
7
8
56
3
4
6
7
8
10
11
12 14 [
58
y
Y
2
2"
3
3
4
3
4
4
5
5
6
5
6
6
7
58
Y
3
3
4
4
6
5
7
7
8
8
10
9
11
11
12
12
13
13
60
~0
7
60
+0
62
2
3
3
4
4
5
5
6
62
3
4
5
7
8
9
10
12
13
64
2
2
3
3
4
4
5
6
64
3
4
5
7
8
9
10
11 13
66
2
2
3
3
4
4
5
5
66
3
4
5
6
8
9
10
111 12
68
Y
1
2
2
2
2
3
3
3
3
4
3
4
4
5
4
68
Y
3
3
4
4
5
5
6
6
8
7
9
9
10
10
Hi 12
70
-0
70
+0
11
12
72
2
2
2
3
3
3
4
72
2
4
5
6
7
9
10
11
12
74
2
2
2
3
3
3
74
2
4
5
6
(
8
10
11
12
76
2
2
2
3
3
76
2
4
5
6
7
8
9
11 12 1
78
1
2
2
2
2
78
2
4
5
6
7
8
9
11
12
80
-0
1
1
2
2
2
80
+0
2
4
5
6
7
8
9
10
82
1
1
1
1
1
2
82
2
4
5
6
7
8
9
10
84
1
1
1
1
1
84
2
4
5
6
7
8
9
10
86
1
1
1
1
86
2
4
5
6
7
8
9
10
88
88
Y
2
2
4
4
5
5
6
6
7
7
8
8
9
9
10
90
-0
90
+0
101 11
92
+0
92
2
4
5
6
7
8
9
10' 11
94
1
1
1
1
94
2
4
5
6
7
8 9
10! 11
96
1
1
1
1
1
96
2
4
5
6
7
8i 9
10 1 11
98
+0
_0
-y
1
1
1
1
1
2
1
2
98
2
2
4
4
5
5
6
6
7
7
8
8
9
9
10! 11
100
2
2
100
+0
10! 11
102
1
2
2
2
2
102
2
4
5
6
7
8
9
11: 12
104
2
2
2
3
3
104
2
4
5
6
7
8
9
11
12
106
2
2
2
3
3
3
106
2
4
5
6
7
8
10
11
12
108
Y
"Y
2
2
2
2
2
3
3
3
3
3
3
4
4
108
Y
2
3
4
4
5
5
6
6
7
7
9
9
10
10
11
12
110
+0
4
110
+0
11' 12
112
2
2
3
3
4
4
5
112
3
4
6
6
8
9
10
Hi 12
114
2
2
3
3
4
4
5
5
114
3
4
6
6
8
9
10
11
12
116
2
2
3
3
4
4
5
6
116
3
4
5
8
9
10
11
13
118
120
+0
J
Y
2
2
3
3
3
3
4
4
4
5
5
5
5
6
6
7
118
1
3
3
4
4
5
6
8
8
9
9
10
11
12
12
13
13
120
+0
122
2
3
4
4
5
6
6
7
122
3
4
6
8
10
11
12
13
124
2
2
3
4
5
5
6
7
8
124
3
4
6
8
10
11
12
14
126
2
3
3
4
5
6
7
7
8
126
3
4
6
9
10
11
13
14
128
Y
2
2
3
3
4
4
5
5
5
6
6
7
7
8
8
9
9
128
2
2
3
3
4
5
6
6
~T
9
9
10
11
12
12
13
14
130
+0
10
130
+0
13
15
The signs in the 0° column apply to all the numbers in the same
When the declination is South change the sign + to — and — to +.
line, and are to be used when the declination is North,
INDEX TO PART I.
Subject.
Abbreviations
Account. (See Dead reckoning.)
Adjustments, horizon mirror
index mirror
plane table
sextant
permanent
theodolite or transit
Afternoon sights
Agulhas current
Airy's method for great circle sailing. .
Alidade, plane table
Almanac, Nautical. [See Nautical Al-
manac. )
Altitude and azimuth
time azimuth
azimuth
circle, definition
circum-meridian
forms for . . .
definition
ex-meridian
forms for
meridian, constant
form for . .
forms for
latitude by
observation of
reduction to
forms.
observed, how corrected
of Polaris for latitude
single, for chronometer error.
latitude
longitude ashore . .
at sea. . .
true, definition
Altitudes, equal, forchro. error
form . . .
longitude a.shore . .
at sea...
Amplitude, definition
determination of
Anchorage, position to be plotted
Angle, danger. (See Danger angle.)
hour. (>S'fe Hour angle.)
to repeat
Angles, between three known objects .
horizon, for finding distance..
round of
sextant and theodolite in hy-
drography
vertical terrestrial, to measure.
26J°-4o° on Ijow
Anticyclonic regions, features of
Apparent day, definition
variation in length
noon, definition
time, conversion to mean . .
definition ,
246
245
417
244
248
414
399
550
194
416
235
366
363
217
334
220
334
333
329
330
334
294
340
316
339
346
349
294
321
347
352
224
357
166
415
151
139
415
458
139
146
481
273
273
273
292
273
Page.
9
67
67
133
67
68
132
125
161
58
133
65
112
111
63
97
174
64
97
174
96
174
173
94
94
97
174
82
101
88
99
104
105
82
90
176
104
107
64
109
49
132
45
43
132
140
43
44
148
74
74
74
80
74
Subject.
Art.
Page.
Apparent time, inequality of
relation to mean
Arctic current
Aries, first point of, definition
Arming of lead
Artificial horizon, description
method of use
should be tested
.\scension, right. (See Right ascen-
sion. )
Astronomical base
bearing
time
transit instruments
work of survey
Atlantic ocean currents
storms
Attraction, local
Australia current
Axis of rotation, definition
Azimuth, altitude
and altitude
circle '
definition
from Sumner line
how determined
named
of body determines use
terrestrial object
time and altitude
determination
diagram
for compass errors
in great circle sailing .
tables
Barometer, aneroid
comparisons
definition
effect of, on tides
mercurial
standard
temperature correction
to determine height
vernier
Base, astronomical
line, description
Beam compass, description
Bearing and angle, position by
distance, position by
danger
method of observing and plot-
ting ---.-
of terrestrial object
Bearings, bow and beam
cross
sun, for compass error
two, of object, with run be-
tween
Beaufort's scale for wind
273
288
536
226
19
256
257
258
446
369
277
431
450
529
494
75
546
6
363
235
33
223
380
355
354
407
369
366
359
361
88
191
361
55
56
47
501
48
50
50
54
57
51
446
438
434
142
138
157
134
369
145
134
88
143
67
74
79
160
64
14
70
70
71
138
112
74
135
139
159
152
29
161
11
111
65
17
64
116
109
109
128
112
112
110
110
31
58
110
23
23
21
154
21
21
21
22
23
22
138
137
136
43
43
46
42
112
44
42
31
43
27
333
334
INDEX TO PABT 1.
Subject.
Bench mark, definition
Binnacles, description
Bottom, quality of, on chart
Boxing the compass
Brazil current
Buoys
C — W, definition
Cape 1 lorn current
Celestial coordinates
equator, definition
horizon, definitii n
latitude and lougitu le
definition
longitude and latitude
definition
meridian, definition
sphere or concnvp, definition.
Celo-Xavigation, definition
Chart (See alio Projection).
aa record of ]nlotiiig
employment in piloting
general features
great circle
for composite sailing.
isobaric
measures of depth on
Mercator, to construct
quality of bottom on
standard meridians on
Chilean current
Chronometer, advantage of more than
one
C — \V, defiyitiim
care on shipboard
comparison
record
correction. (.S'fe Chro-
nometer error. )
descriiition
error, by equal alts
form.
single altitude .
time sight...
signals .
transits
definition
differs from corr .
from rate
hack, use of
max. and min. ther-
mometer
minus watch, definition.
second difference
sight. (.Sff Time sight. )
temperature curve
transportation of
winding
Circle, declination, definition
hour, definition *.
of altitude, definition
equal altitude
illumination
vertical, definition
Circum-meridian altitude
forms
Civil time
Clouds, description and symbols
CoeflScients, constant ...'.
quadrantal
semicircular
value and relation
I ollimation, line of, definition
516
34
45
27
538
162
268
547
234
215
213
238
229
238
229
216
210
4
166
165
36
189
197
465
46
40
45
44
547
265
268
260
263
264
259
321
316
316
314
315
261
312
311
268
262
268
265
266
260
262
216
216
217
373 !
373
217
334
Page.
277
70
112
107
103
114
414
156
17
20
16
160
47
72
161
65
63
63
65
64
65
64
63
63
11
49
48
18
57
59
143
21
19
20
20
161
72
71
71
72
71
90
176
88
88
87
88
71
87
87
72
71
72
72
72
71
71
63
63
63
114
114
63
97
174
74
27
38
37
36
38
132
Subject.
Page.
Comparing watch, use of
Comparison, baron leter
chronometer, method
record
Compass, beam, description
boxing
compensation. {See Bevia-
tion. )
declination
definition
deviation. [See Deviation.)
divisions on card
dry
error. { See Error, compass. )
local attraction
Lord Kelvin
Navy service, 7^-inch
variation '
wet
Compasses (drawing) i
Compensation, compass. (See Devia- I
tion.)_ ^ !
Composite sailing, computation |
definition '
graphic approxima-
tion
shortest course for. .
terrestrial globe
Concave, celestial, definition
Constant deviation. (.SVr Peviation.)
for meridian altitude
form ! .
Conversion of tiuje, apparent to mean.]
definition
mean to apparent.
sidereal .
sidereal to mean . .
Coordinates, celestial ;
definilijK ;
Correction, chro. (.See Chronometer. ) '
index, sextant
of observed altitude
Course, definition
to lay
Culmination, definition
Current, Agiilha.=
allowance for
Arctic
Australia
Brazil
Cape Horn
Chilean
determined at noon
effect in piloting
equatorial, Atlantic
Indian
Pacific ..
Guinea
Gulf Stream '
Humboldt
Japan Stream
Kamchatka
Kuro >Si wo
Labrador
ocean, Atlantic
cause of
definition
determination of
drift, definition
of jVtlantic
Indian
Pacific
268
56
263
264
4.34
74
25
26
30
75
32
31
74
30
198
184
199
196
200
210
333
292
286
292
ho
291
234
230
250
294
6
132
271 I
550 I
206 ;
.536 i
546 I
538 I
547
547
398 '
l(i4
529
549
541
535
532
547
542
.")43
542
536
529
522
.521
525
523
533
.548
.541
72
23
71
72
136
16
29
15
16
17
29
17
17
29
17
13
59
56
59
59
59
m
96
174
80
79
80
80
80
65
64
69
82
12
42
74
161
61
160
161
160
161
161
125
48
159
161
160
160
159
161
160
161
160
160
159
158
158
158
158
160
160
161
INDEX TO PART I.
335
Subject.
Current, ocean, stream, definition ..
submarine
Oya Siwo
Peruvian
Rennell's
Kossel
Southern connecting
tidal, definitions
description of
observation of
. to find
Curve, temperature, chronometer...
Cyclones and cyclonic circulations ..
Cyclonic regions, features of
storms, description
maneuvering in...
summary of rulej. .
tropical
character .
Danger angle, horizontal
vertical
bearing
Data, useful, miscellaneous
Day's work, loutine
Dead reckoning, always kept
definition
form for
method of working . .
value of
Decimal fractions
Declination and hour angle
right ascension
circle, definition
definition
of compass
Declinatoire, plane table
Definitions, nautical astronomy
navigation
Departure, definition
on beginning voyage
to take
Depth, measures of, on charts
recorder, sounding machine
Deviation, causes of
classes of
compensation of
constant, coefficient
<lefinition
definition
heeling error, compensation
definition . . .
Napier diagram for
qnadrantal, coefficients
definition
recompensation
semicircular, coefficients . . .
definition
table
theory of
to apply
find
Diagram, time azimuth
Difference, second. {See Second dif-
ference. )
Dip of horizon, definition
how applied
none with artificial
horizon
523
524
544
547
537
546
539
495
505
511
207
266
480
481
482
491
492
483
486
155
156
157
393
392
202
205
203
Page.
variation in
when land intervenes.
Distance and l)earing
by horizon angle
236
237
216
218
74
416
209
1
6
392
204
46
23
98
99
119
112
111
76
126
116
93
107
106
129
103
100
91
95
77
83
361
300
303-
294
301
302
138
139
158
158
161
161
160
161
160
153
154
156
62
72
147
148
148
150
150
148
149
46
46
46
189
124
124
60
171
60
60
178
65
65
63
64
29
133
63
11
11
124
60
21
16
35
35
38
38
38
29
40
38
32
37
37
41
36
35
32
34
29
31
110
83
84
82
83
84
43
43
Subject.
Page.
Distance, definition
lunar. ( <See Lunar distance. )
of objects of known height. .
polar, definition
zenith. (.Se« Zenith distance. )
Distant object for compass error
Diurnal inequality of tide
type of tide
Dividers, description
proportional, description
Doldrums
Doubling angle on bow
Drift current, definition
currents, Atlantic
Earth, definitions relating to
Eccentricity, se.xtant
Ecliptic, definition
Elevated pole
Ephemens. {See Nautical Almanac. )
Equal altitudes for chro. error
form . . .
longitude ashore . .
at sea . . .
Equation of time, definition
- in conversion of time.
Equator, celestial, definition
earth' s
Equatorial currents. {See Current. )
Equiangular spiral
Rjuinoctial, definition
Equinox, definition ,
vernal. {See First point of
Aries. )
Error, chro. {See Chronometer. )
compass, causes
to applv
find".....
heeling.- (-SVe Deviation.)
index, sextant, description
probable, of position, how
shown '
sextant. {.S'fe Sextant. )
Establishment, tidal, definitions .
Ex-meridian altitudes
forms
Extraordinary refraction near horizon
Extra-trojiical cyclonic storms
First ijoint of Aries, definition
hour angle is si-
dereal time
Flinders bar, definition
to place
Fogs and fog signals
Forms for sights, etc.- •.
notes on
use recommended
Fractions, decimal
Gauges, tide, description
Geodesy, definition
Geometry
formuliP derived from
Geo-Navigation, definition
Gimbals, compass
chronometer
Glasses, shade. {See Shade glasses. )
Globe, terrestrial, tor comp. sailing. .
gt. circle sailing.!
Graduation, sextant, error J
Great circle charts
for comp. sailing. . .'
course I
sailing, advantages ''
139
219
90
503
503
7
435
470
144
523
533
6
248
225
214
321
347
352
275
288
215
6
6
215
226
73
77
82
...! 249
410
497
334
301
493
22»i
27()
105
127
163
411 I
518
412
4
28
259
200
193
248
189
197
6
186
12
43
64
31
154
154
13
1.36
144
44
158
160
n
68
64
63
90
176
104 .
107
74
79
63
11
12
63
64
29
29
31
130
153
97
174
83
152
64
74
37
40
48
171
177
130
178
i57
131
180
181
11
16
71
59
58
68
57
59
12
56
336
INDEX TO PART I.
Subject.
Oreat circle sailing, Airy's method ..
computation
definition
graphic approx . .
methods
terrestrial globe,
time azimuth
methods
Greenwich adopted as prime meridian
time, to find
Guinea current
Gulf Stream, description
extraordinary dip in
Hack chronometer, use of
Heading, magnetic, determination of..
Heeling error. ((S'e« Deviation. )
Height, determination by barometer..
Heliograph, use in surveymg
Heliotrope, use in surveying
Horizon angle, distance by
artificial, description
method of use
no dipwith^
should be tested
celestial, definition
dip of, definition
how applied
none with artificial
horizon
variation in
when land intervenes .
mirror, adjustment
description
prismatic
visible or sea, definition
Horse latitudes
Hour angle and declination
time, conversion
definition
how measured
circle, definition
Humboldt current
Hydrographic survey, method of
surveying, definition...
Hydrography in survey, description ..
to plot
Identification of unknown bodies
Index correction, sextant, to find
error, sextant, description
mirror, adjustment
description
prismatic
Induction, magnetic
Instrument", astronomical transit
nautical a,stronomy
navigation
surveying
Interpolation, Nautical Almanac
Intersection, Sumner. (See Sumner. )
Intervals, lunitidal, definitions
list of
mean and sidereal time
Iron, hard and soft
Isobars, chart showing
Japan stream
Kamchatka current
Knot, length of
Kuro Si wo current
Lalirador current
Lagging of tide
Land and sea breezes
194
190
183
192
188
193
191
342
280
535
532
301
268
122
5"
430
430
139
256
257
294
258
213
300
303
294
301
302
246
240
248
213
471
236
293
222
278
216
547
436
412
457
458
402
250
249
245
240
248
96
431
239
7
413
283
497
289
96
465
542
543
6
542
536
502
474
Page.
58
57
56
58
57
58
58
103
75
160
1.59
83
72
39
23
135
135
43
70
70
82
71
63
83
84
82
83
84
67
66
68
63
145
65
81
64
75
63
161
137
131
140
140
126
69
68
67
66
68
34
135
66
13
131
76
153
190
79
34
143
160
160
12
160
160
154
145
Subject.
Latitude, by meridian altitude
forms ..
Polaris
reduction to meridian
reduction to meridian,
forms
single altitude
forms
g/ q/' method
forms
celestial, definition
definition
difference of, definition
horse
Lead, arming
descrii)tion
line, marking of
Level of bench mark
surveying, use of
description
Lights, employment in piloting
Line, base, description of
of collimation, definition
position. ( See Sumner line. )
sight, definition
Sumner. (See Sumner line.)
Local attraction
time, to find
Log book
chip
ground
patent
electric registers
revolutions as substitute . .
Logarithms, explanation
Ix)ngitude, by equal altitudes ashore . .
at sea
single altitude ashore . .
at sea . . .
time sights, forms
transit observations
celestial, definition
definition
difference of
of secondary meridians
tertiary meridians
Loxodromic Curve
Lubber's line
Lunar distance, explanation of
tables
observations, value of
Lunitidal intervals, definitions
list of
Magnetic observations in survey
Magnetism, acquired in building vessel.
features of earth's
subpermanent
transient
Main triangidation
Maneuvering, cyclonic storms
summary of rules
Marine surveying
Mean day, definition
directive force
noon, definition
sun, definition
time, conversion to apparent
sidereal
definition
intervals, relation to side-
real
329
340
334
339
'339'
229
6
6
471
19
18
18
517
429
428
161
438
414
414
75
281
64
10
12
13
15
17
347
352
346
349
344
229
6
6
343
345
6
28
406
497
461
97
95
98
98
448
491
492
412
274
115
274
274
292
290
274
289
INDEX TO PAKT I.
337
Subject.
Mean time, relation to apparent
sidereal
Mercator-projection, description
to construct
sailing
Meridian altitude, constant
forma for
latitude by
observation of
reduction to
celestial, definition
of earth, definition
passage, definition
prime, Greenwich adopted . .
secondary, definition
determination of .
standard , on charts
tertiary, defi nition
determination of
Meridional parts
Middle latitude sailing
correction
Mile, nautical or sea, length of
Mirror, horizon. (See Horizon mirror. )
index. (<See Index mirror)
sextant, resilvering
Monsoon winds
Moon, correction of observed altitude .
form for latitude sights
meridian altitude
time sight
planets, and stars, use of
value of observations of
Morning sights
Nadir, definition
Napier diagram
Nautical Almanac, description
for 1879, extrai'ts..
gives horizontal
parallax
interpolation
reduction of ele-
ments
second differences .
Astronomy, definitions
instruments
mile, length of
Navigation, definitions
instruments and accessories
Neap tides
Noon sights
Notes on f<jrms for sights, etc
Occupying a station
Ocean current. (See Current, ocean. )
Octant, description . ,
Optical principle of sextant. ..'
Orient, to, a plane table
Oya Siwo current
Parallax, definition
horizontal, in Nautical Al-
manac
how applied
of planet or star
Parallel of latitude, definition
riders, description
sailing, description
Passage, meridian, definition
Pelorus, description
Peruvian current
Piloting, definition
requisites
24972°— 12 22
288
287
38
40
179
333
329
330
334
216
6
271
342
342
343
44
342
345
39
175
178
6
254
473
294
Page.
401
406
394
212
93
282
305
283
283
285
209
239
6
1
7
499
396
415
255
242
418
544
304
305
306
294
6
8
173
271
35
547
130
131
79
79
18
19
55
96
173
94
94
97
63
11
74
103
103
103
20
103
103
18
53
54
12
145
82
176
174
173
126
128
124
63
32
76
163
84
76
76
78
63
66
12
11
13
153
125
177
132
70
67
133
161
84
84
85
82
11
13
52
74
18
161
42
42
Subject.
Plane of reference, tidal
sailing
table, adjustments .
d^8cription
to improvise
use of
Planet, correction of observed altitude.
form for latitude sights
meridian altitude
time sight
identification of tinknown
Planets, stars, and moon, use of
Polar distance, definition
Polaris, latitude by
Pole, elevated
star, latitude by
Poles of earth
Portable transit
Position by angles between 3 objects..
26J°-15°onbow...
bearing and angle
distance...
bow and beam bearings . .
cross bearings
doubling angle on bow. .
two bearings and run
methods of fixing
of anchorage to be plotted. .
body determines its use..
soundings in survey
probable error of by Sumner
lines, how shown
Pressure, effect in wind
progressive areas of
seasonal variations in
variation of atmospheric . . .
Prime meridian, Greenwich adopted ..
vertical, definition
Priming of tide
Projection, gnomonic
Mercator
polyconic
systems in use
Proportional dividers, description...
Prosection method, plane table
Protractor, ordinary
three armed, description . .
substitute..
use of
Quadrantal deviation. [See Deviation. )
Quintant, description
Range of tide at various places
definitions
llanges for finding compass error
in piloting
Rate, chronometer. (.SVf Chronometer
rate. )
Reciprocal Ijearings for compass error.
Reckoning, dead. (See Dead reckon-
ing-)
Record of astronomical work
chronometer comparisons . .
piloting
tidal
Red sea, extraordinary dip in
Reduction to meridian
forms for
Reference, planes of, tidal
Refraction, correction for
definition
effect on dip
Art.
514
169
417
416
420
418
294
402
401
219
340
214
340
6
431
151
146
142
138
145
134
144
143
133
166
407
458
410
465
479
466
476
342
217
502
43
38
42
37
435
418
9
432
433
151
255
498
89
158
87
411
264
166
512
301
334
514
298
296
300
Page.
156
50
133
132
134
133
82
175
173
172
126
126
64
101
63
101
11
135
45
44
43
43
44
42
44
43
42
49
128
140
130
142
147
144
147
103
64
154
20
18
20
18
136
134
13
136
136
45
70
190
153
31
47
31
130
72
49
156
83
97
174
156
82
82
83
338
INDEX TO PAET I.
Subject.
Eefraction, extraordinary,near horizon
how applied
Relative humidity
Rennell's current ; .
Bepeat, to, an angle
Resection method, plane table
Residual deviation
Rhumb line, definition
not shortest course
Right ascension and declination
definition
Roaring forties
Rossel current
Round of angles
Run, calculation of
determined at noon
Running survey, description
Sailing, composite. {See Composite. )
great circle. (<Se«^ Great circle. )
Mercator
middle latitude
correction
parallel
plane
spherical
traverse
Sailings, definition
kinds of
Sargasso sea
Sea and land breezes
mile, length of
symbols for state of
water temperature
Second difference, chronometer
Nautical Almanac. .
Secondary meridian, definition
determination of.
triangulation
Seconds, employment in naut. sights..
Semicircles, storm
Semicirculardeviation. (/SseDeviation. )
Semidiameter, definition
how applied
measured
of planet or star
Semidiurnal type of tide
Sextant adjustments
permanent
angles for plotting soundings .
choice of
definition
description
eccentricity
graduation errors
index correction, to find
error, description
method of use
optical principle
prismatic mirrors
shade glasses
resilvering mirrors
surveying
vernier
Shade glasses, for artificial horizon
sextant, description
prismatic
Sidereal day, <leflnition
noon, definition
time, conversion to mean
definition
intervals, relation to '
mean
Art. Page.
301
299
62
537
415
418
124
6
185
237
228
472
546
415
208
398
462
179
175
178
173
169
168
172
167
168
534
474
6
72
63
265
285
342
343
449
409
490
307
308
251
294
503
244
248
458
253
239
240
248
248
250
249
252
242
248
248
254
427
241
256
240
248
276
276
291
276
289
83
83
25
160
132
134
40
12
56
65
64
145
161
132
62
125
140
55
53
54
52
50
50
52
50
50
160
145
12
28
25
72
78
103
103
139
129
150
85
85
69
82
154
67
68
140
69
66
66
68
«8
69
68
69
67
68
68
69
135
66
70
66
68
74
74
80
74
79
Subject.
Art.
Page.
Sidereal time, relation to mean
287
79
Sight, chronometer. ( See Time sight. )
equal alts. (&« Equal altitudes.)
latitude. (S?e latitude. )
line of, definition
414
132
longitude. (See, Longitude.)
time. ( See Time sight. )
Sights, afternoon
399
125
employment of various
408
129
morning
394
124
noon
.396
125
Signals, surveving, description
447
138
time, for chronometer error
314
87
; Silvering sextant mirrors
254
6»
Solar time. ( See Apparent time. )
Solstice, definition
227
64
Sound, velocity of
314
87
Sounding machine, barometric corr
24
15
depth recorder
23
15
description
20
14
tubes
21
458
14
Soundings, surveying, how plotted
140
use in piloting
159
47
Southern connecting current
539
160
Sphere, celestial, definition
210
168
63
Spherical sailing
50
Spring tides
499
153
Stadia. ( See Telemeter. )
Star, correction of observed altitude. . .
294
K2
equal altitudes for cliro. error
326
92
form for latitude sights
175
meridian altitude
173
time sight
172
identification
402
454
126
observations in surveving
140
Starboard angle, definition
102
36
Stars, planets, and moon, use of
401
126
Station pointer. ( Sec Protractor, three
armed. )
Storm center, motion of
484
485
148
rate of progress
149
to avoid
489
487
149
fix bearing
149
distance
488
490
492
494
149
150
tables
151
Storms, along transatlantic routes
152
cvclonic. (.SecCyclonicstorms. )
Stream current, definition
523
158
Submarine ocean currents
524
158
Sumner line, always recommended
394
124
applications of
400
125
c loice of bodies .*. ..
400
125
description
372
114
determination
379
115
uses
377
115
lines, intersection, computation
384
119
graphicallv .
382
118
when run in-
tervenes. .
390
123
Sun, correction of observed altitude. . .
294
82
equal altitudes for chro. error
322
90
long, ashore . .
347
104
176
• latitude sights '
174
meridian altitude
173
time sight
171
274
454
74
1 observations in surveying
140
450
436
139
hvdrographic, method of . . . ; .
137
running, description . . * -.-..
462
140
INDEX TO PART I.
339
Subject.
Three-armed
Survey, to plot soundings in
Surveying, hydrographic, definition
instruments
marine, definition
topographic, definition
transit, description
Symbols for clouds
sea
w eather
Table, plane. ( See Plane table. )
tide
time azimuth
Telemeter, description
substitute for
use of
Telescope, direct and reversed
sextant, adjustment
description
zenith
Temperature curve, chronometer
Terrestrial object, true bearing of
Tertiary meridian, definition
determination of . .
Theodolite, adjustments
angles for plotting sound-
ings
description
method of use
Thermometer, da-sses of
description
dry and wet bulb
max. and min., chro
protractor. {See Pro-
tractor. )
point problem, conditions
explanation
Tidal current. (.See Current, tidal.)
day, definition
establishment, definitions
observations in survey
instructions for
record
Tide, bench mark, definition
cause of
definitions relating to
diurnal inequality
type
effect of, in piloting
wind and barometer on
gauges, description
observation of
planes of reference of
primi^lg and lagging of
range of, at various places
definitions
semidiurnal type
spring and neap
tables
time of high and low
form for
tropic
types of
Time and altitude azimuth
hour angle, conversion of . . .
apparent. ((Si e Apparent time.)
astronomical
at different meridians
azimuth. (<Spe Azimuth, time.)
civil
conversion of. (-See Conversion.)
equation of. (-See Etjuation of
time.)
458
412
413
412
412
413
70
72
69
506
361
421
426
424
415
247
240
431
266
369
.342
345
414
458
413
415
58
58
61
262
153
152
502
497
460
508
512
516
496
495
503
503
164
501
.518
509
514
502
498
503
499
506
506
503
503
366
293
277
279
277
Page.
140
131
131
131
131
131
27
28
27
155
110
134
135
135
132
68
66
135
72
112
103
103
132
140
131
132
24
24
24
71
46
45
154
153
140
156
156
156
153
153
154
154
48
1.54
157
156
156
154
190
153
154
153
155
155
176
154
154
112
81
74
75
Subject.
Time, Greenwich, to find
local, to find
mean. (.See Mean time. )
of high and low water
form for . .
transit, liow found
sidereal. {See Sidereal time. )
signals for chronometer error
sight for chronometer error
longitude ashore
at sea
forms for
solar. {See Apparent time.)
Topographic surveying, definition
Topography in hydrographic survey . .
Tracing paper to plot soundings
3 -point problem .
Trade wind
Transit, astronomical
definition
observations for chronometer
error
longitude
portable
surveying. {See Theodolite. )
time of, how found
Traverse sailing
tables, use of
Triangulation, main
secondary
Trigonometric functions
logarithms
Tropic tide ...
Tropical cyclonic storms .■ . .
chara' ' sr
Tubes, sounding machine
Unknown bodies, identification of
Useful data, miscellaneous
Variation of compass, definition
to apply
find
Variations, atmospheric
non-periodic . .
j>eriodic
Vernier, barometer
sextant
theodolite
Vertical angles, terrestrial, to measure.
circle, definition
prime
Visible horizon, definition
Watch, comparing, use of
Weather symbols
Wind, Beaufort's scale
causes of
definition
doldrums
effect of, on tides
land and sea breezes
monsoon
normal ]jre.ssure
prevailing
westerly
" Roaring forties "
storms. (<See Cyclonic storms. )
Trade
true direction and force
Zenith, definition
distance, definition
how named
telescope
Page.
280
281
506-
331
314
316
346
349
412
456
160
433
469
431
271
315
344
431
331
172
170
448
449
503
483
486
21
402
74
77
82
476
478
477
51
241
413
139
217
217
213
268
69
67
464
463
470
501
474
473
405
467
472
472
469
68
212
2'21
329
431
P^RT II
TABLES
501
PREFACE.
The following tables comprise Part II of the American Practical Navigator, by the late Nathaniel
Bowditch, LL. D., as revised in 1880 under the direction of the Bureau of Navigation, Navy Department,
and further revised in 1903 and 1910 under the direction of the Bureau of Equipment, Navy Department.
In the present edition, the former tables liave been extended by incorporating Table 37A, The
Equation of Equal Altitudes near Noon; Table 45, Logarithmic and Natural Haversines; Table 46,
Consolidated Altitude Corrections; Table 47, The Longitude Factor; and Table 48, The Latitude Factor.
Ukited States IIvdrographic Office,
Department op the Navy,
Wagliington, D. C, August 10, 1911.
603
CONTENTS OF PART II.
P.age.
Explanation of the Tables 507
Table 1. Traverse Table, Quarter Points 515
2. Travers-e Table, Degrees ; 531
3. Meridional Parts 621
4. Length of Degrees of Latitude and Longitude 629
5A. Distance of an Object by Two Bearings, Quarter Points 631
5B. Distance of an (Object by Two Bearings, Degrees 634
6. Distance of Visibility of Objects of different Heights 640
7. Conversion of Arc and Time 641
8. Conversion of Sidereal into Mean Solar Time 642
9. Conversion of Mean Solar into Sidereal Time 645
10. Local mean time of Sun's visible Rising and Setting 648
11. Reduction of Moon's Meridian Passage for Longitude 672
12. Reduction of Quantities from Nautical Almanac 673
13. Change of Sun's Right Ascension 683
14. Dip of Sea Horizon 6S5
15. Dip at Distances short of Horizon OH.')
16. Parallax of Sun 68.'>
17. Parallax of Planet. 6,S()
18. Augmentation of Moon's Semidianieter '. 687
19. Augmentation of Moon's Horizontal Parallax 687
20A. Mean Refraction 688
20B. Mean Refraction and Parallax of Sun 689
21. Correction of Refraction for Barometer 690
22. Correction of Refraction for Thermometer 691
23. Mean Refraction and Mean Parallax of Moon 693
24. Mean Refra(>tion and Parallax of Moon 693
25. Variation of Altitude due to change of Declination 702
26. Variation of .Altitude in one minute from Meridian 704
27. Variation of .\ltitude in given time from Meridian 714
28.\. First Correction of Polaris 717
28B. Second Correction of P(jlarts 718
28C. Third Correction of Polaris 718
28D. Fourth Correction of Polaris 723
29. Nautical and Statute Miles 725
30. Conversion of Metric and English Linear Measure 726
31. Fahrenheit, Centigra<le, and Reaumur Temperatures 727
32. True Force and Direction of Wind 728
33. Distance by Vertical Angle 729"
34. Distance bv Horizon Angle 731
35. Speed Table for Measured M ile 732
.36. Jx)cal Mean and Standard Meridian Times 733
37. Logarithms for Equation of Equal .Altitudes 1 7.34
37A. The Equation of Equal Altitudes near Noon 738
38. Error in 1-ongitude produced by Error in Latitude 7.39
39. Amplituile's 740
40. Correction for Amplitude observed in Apparent Horizon 745
41. Natural Sines and Cosines 746
42. Logarithms of Nu mbers 755
43. Logarithms of Trigonometiic Functions, Quarter Points 771
44. Logarithms of Trigonometric Functions, Degrees " 772
4.5. Logarithmic and Natural Haversines 817
46. Consolidated table of Altitude Corrections 922
47. The Longitude Factor 928
48. The Latitude Factor 931
505
EXPLANATION OF THE TABLES.
TABLES X, 2: TRAVERSE TABLES.
Tables 1 and 2 were originally calculated by the natural sines taken from the fourth edition of
Sherwin's Logarithms, which were previously examined, by differences; when the proof sheets of the
first edition were examined the numbers were again calculated by the natural sines in the second edition
of Hutton's Logarithms; and if any difference was found, the numbers were calculated a third time by
Taylor's Logarithms.
The first table contains the difference of latitude and departure corresponding to distances not
exceeding 300 miles, and for courses to every quarter point of the compass. Table 2 is of the same
nature, but for courses consisting of whole degrees; it was oijginally of the same extent as Ta>)le 1, but
ha.s been extended to include distances up to 600 miles. The manner of using these tables is particularly
explained under the different problems of Plane, Middle Latitude, and Mercator Sailing in Chapter V.
The tables may be employed in the solution of any right triangle.
TABLE 3: MERIDIONAL PARTS.
This table contains the meridional parts, or increased latitudes, for every degree and minute to 80°,
calculated by the following formula:
m
in which
=^ log tan (^45° + j J " « («' »'" I^ + J f * si"' "i' + ie^ sin^ L + . . .
the Equatorial radius a = — - — = 3437'.74677 (log 3.5362739);
M, the modulus of common logarithms = 0.4342945;
jj= 2. 3025851 ( log 0. 3622157 ) ;
C, the compremon or meridional eccentricity of the earth
according to Clarke ( 1880) = 393465 = 0.003407562 (log 7.5324437) ;
e=v/ 2c -0^ = 0.0824846 (log 8.i
from which
^ = 7915'.7044558 (log 3.8984895) ;
ae» = 23'.38871 (log 1.3690072);
Jae*= 0'.0o3042 (log 8.7246192);
iae«= 0'.000216523 (log 6.3355038).
The results are tabulated to one decimal place, which is sufficient for the ordinarj' problems of
navigation.
The practical application of this table is illustrated in Chapters II and V, in articles treating of the
Mercator Chart and Mercator Sailing.
TABLE 4: LENGTH OF DEGREES OF LATITUDE AND LONGITUDE.
This table gives the length of a degree in V)oth latitude antl longitude at each parallel of latitude on
the earth's surface, in nautical and statute miles and in meters, based upon Clarke's value (1866) of the
earth's compression, „„» i= ' In tlie case of latitude, the length relates to an arc of which the given
degree is the center.
TABLES 5 A, 5B: DISTANCE BY TWO BEARINGS.
These tables have been calculated to facilitate the ojieration of finding the distance from an object by
two bearings from a given distance run and course. In Table 5A the arguments are given in points,
in Table 5B in degrees; the first colunm contains the multiplier of the distance run to give the distance
of observed object at second bfearing; the second, at time of passing abeam.
The method is explained in article 143, Chapter IV.
507
508
EXPLANATION OF THE TABLES.
TABLE 6: DISTANCE OF VISIBILITY OF OBJECTS.
This table contains the distances, in nautical and statute miles, at which any object is visible at sea.
It is calculated by the formulae:
d = 1. 15 x/x; and rf' = 1.32 s/^,
in which d is the distance in nautical miles, d' the distance in statute miles, and x the height of the eye
or the object in feet.
To find the distance of visibility of an object, the distance given by the table corresponding to its
height should be added to that corresponding to the height of the observer's eye.
Example: Required the distance of visibility of an object 420 feet high, the observer being at an
elevation of 15 feet.
Dist. corresponding to 420 feet, 23.5 naut. miles.
Dist. corresponding to 15 feet, 4.4 naut. miles.
Dist. of visibility,
27.9 naut. miles.
TABLE 7: CONVERSION OF ABC AND TIME.
In the first column of each pair in this table are contained angular measures expressed in arc
(degrees, minutes, or seconds), and in the second column the corresponding angles expressed in time
(hours, minutes, or seconds). As will be .seen from the headings of columns, the time corresponding
to degrees (°) is given in hours and minutes; to minutes of arc ('), in minutes and seconds of time;
and to seconds of arc ("), in seconds and sixtieths of a second of time.
The table will be especially convenient in dealing with longitude and hour angle. The method of
its employment is best illustrated by examples.
Ex.\MPLE I.
Required the time corresponding to 50° 31' 21*.
50° 00' 00" = 3'' 20"' 00'
31 00 = 2 04
21 = m
50 31 21 = 3 22 05. 4
Example II.
Required the arc corresponding to 6'' 33"' 26'.5.
6" 32"' 00»
1 24
: 98° 00' 00"
21 00
37.5
6 33 26. 5 = 98 21 37. 5
TABLES 8 AND 9: SIDEREAL AND MEAN SOLAR TIMES.
These tables give, respectively, the reductions necessary to convert intervals of sidereal time into
those of mean solar time, and intervals of mean solar into those of sidereal time. The reduction for any
interval is found by entering with the number of hours at the top and the number of minutes at the side,
adding the reduction for seconds as given in the margin.
The relations between mean solar and sidereal time intervals, and the methods of conversion of
these times, are given in articles 289-291, Chapter IX.
TABLE 10: SUN'S RISING AND SETTING.
This table gives the local mean time of the sun's visible rising and setting — that is, of the appearance
and disappearance of the sun's upper limb in the unobstructed horizon of a person whose eye is 15 feet
above the level of the earth's surface, the atmospheric conditions being normal.
The local apparent times of rising and setting were determined from the formula for a time sight,
the altitude employed being —0° 56' 08", made up of the following terms: Refraction, — 36' 29"; semi-
diameter, — 16' 00"; dip, —3' 48"; and parallax, +9".
To ascertain the time of rising or setting for any given date and place, enter the table with the
latitude and declination, interpolating if the degrees are not even. In the line R will be found the time
of rising; in the line S, the time of setting. Be careful to choose the page in which the latitude is of
the correct name, and in which the "approximate date" corresponds, nearly or exactly, with the
given date.
This table is computed with the intention that, if accuracy is desired, it will be entered with the
declination as an argument — not the date — as it is impossible to construct any table based upon dates
whose application shall be general to all years. But as a given degree of declination will, in the
majority of years, fall upon the date given in the table as the "approximate date," and as, when it
does not do so, it can never be more than one day removed therefrom, it will answer, where a slight
inaccuracy may be admitted, to enter the table with the date as an argument, thus avoiding the neces-
sity of ascertaining the declination.
Example: Find the local mean time of sunset at Rio de Janeiro, Brazil (lat. 22° 54' S., long.
48° 10' W.), on January 1, 1903 (dec. 23° 04' S.).
Exact method.
Approximate method.
Lat. 22° \
Dec. 23° /
Corr. for -f 54' lat .
Corr. for + 04' dec.
6" 48""
+ 02
00
Lat. 22°.. \
January 2 / ' ' •'
Corr. for + 54' lat.
Corr. for 1 dav
6" 48°'
+ 02
-01
L. M. T. sunset
6 50
L. M. T. sunset 6 49
EXPLANATION OF THE TABLES. . 509
TABIiE H: KEDTJCTION FOB MOON'S TRANSIT.
This table was calculated by proportioning the daily variation of the time of the moon's passing the
meridian.
The numbers taken from the table are to be added to the Greenwich time of moon's transit in weet
longitude, but subtracted in east longitude.
TABLE 12: BED0CTIONS FOB NAUTICAL ALMANAC.
This is a table of proportional parts for finding the variation of the sun's right ascension or declination,
or of the equation of time, in any number of minutes of time, the horary motion being given at the top of
the page in seconds, and the number of minutes of time in the side column; also for finding the variation
of the moon's declination or right ascension in anv number of seconds of time, the motion in one minute
being given at the top, and the numbers in the side column being taken for seconds.
TABLE 13: CHANGE OF STJN'S BIGHT ASCENSION.
This is a table that may be employed for finding the change of the sun's right ascension for any
given numljer of hours, the hourly change, as taken from the Nautical Almanac, being given in the
marginal columns.
TABLE 14: DIP OF SEA HORIZON.
This table contains the dip of the sea horizon, calculated by the formula:
D = 58".8v/F,
in which F = height of the eye above the level of the sea in feet.
It is explained in article 300, Chapter X.
TABLE 15: DIP SHORT OF HORIZON.
This table contains tlie dip for various distances and heights, calculated by the formula:
D = f d + 6.56514 X h
I a
in which D represents the dip in miles or minutes, rf, the distance of the land in sea miles, and h, the
height of the eye of the observer in feet.
TABLE 16: PARALLAX OF SUN.
This table contains the sun's parallax in altitude calculated by the formula:
par. = sin z X 8". 75,
in which z = apparent zenith distance, the sun's horizontal parallax being 8".75.
It is explained in article 304, Chapter X.
TABLE 17: PABALLAX OF PLANET.
Parallax in altitude of a planet is found by entering at the top with the planet's horizontal parall£ix,
and at the side with the altitude.
TABLE 18: AUGMENTATION OF MOON'S SEMIDIAMETER.
This table gives the augmentation of the moon's semidiameter calculated by the formula:
X = c if sin h.-\-\ <? ^ sin' 7t + i e* »*,
where h = moon's apparent altitude;
8 = moon's horizontal semidiameter;
X = augmentation of semidiameter for altitude h; and
log c = 5.25021.
TABLE 19: AUGMENTATION OF MOON'S HORIZONTAL PARALLAX.
This table contains the augmentation of the moon's horizontal parallax, or the correction to reduce
the moon's equatorial horizontal parallax to that point of the earth's axis which lies in the vertical of
the observer in any given latitude; it is computed by the formulee:
A»r = jr(6-1), 6 =
v/(l-e»8in»L)'
where Tt = equatorial horizontal parallax;
L = latitude;
« = eccentricity of the meridian; log e* = 7.81602; and
A Jf = augmentation of the horizontal parallax for the latitude T..
510 . EXPLANATION OF THE TABLES.
TABLE 20A: MEAN BEFBACTION.
This table gives the refraction, reduced from Bessel's tables, for a mean atmospheric condition in
which the barometer is 30.00 inches, and thermometer 50° Fahr.
TABLE SOB: MEAN REFRACTION AND PARALLAX OF SUN.
This table contains the correction to be applied to the sun's apparent altitude for mean refraction
and parallax, being a combination of the quantities for the altitudes given in Tables 16 and 20A.
TABLES 21, 22: CORRECTIONS OF REFRACTION FOR BAROMETER AND
THERMOMETER.
These are deduced from Bessel's tables. The method of their employment will be evident.
TABLE 23: MEAN REFRACTION AND MEAN PARALLAX OF MOON.
This table contains tlie correction of the moon's altitude for refraction and parallax corresponding
to the mean refraction (Table 20A), and a horizontal parallax of the mean value of 57' 30".
TABLE 24: MEAN REFRACTION AND PARALLAX OF MOON.
This table contains the correction to be applied to the moon's apparent altitude for eacli minute of
horizontal parallax, and for every 10' of altitude from 5°, with height of barometer 30.00 inches, and
thermometer 50° Fahr.
For seconds of parallax, enter the table abreast the approximate correction and find the seconds of
horizontal parallax, the tens of seconds at the side and the units at the top. Under the latter and
opposite the former will be the seconds to add to the correction.
For minutes of altitude, take the seconds from the extreme right of the page, and apply them as
there directed.
TABLE 25: CHANGE OF ALTITUDE DUE TO CHANGE OF DECLINATION.
This table gives the variation of the altitude of any heavenly body arising from a change of 100" in
the declination. It is useful for finding the equation of equal' altitudes by the approximate method
explained in article 324, Chapter XI, and for other purposes.
If the change move the body toward the elevated pole, apply the correction to the altitude with the
signs in the table; otherwise change the signs.
TABLE 26: CHANGE OF ALTITUDE IN ONE MINUTE FROM MERIDIAN.
This table gives the variation of the altitude of any heavenly body, for one minute of time from
meridian passage, for latitudes up to 60°, declinations to 63°, and altitudes between 6° and 86°. It is
based upon the method set forth in article 334, Chapter XII, and the values may be computed by the
formula:
1".9635 cos L cos d
sin (L— d)
where a ^variation of altitude in one minute from meridian,
L = latitude, and
(? = declination — positive for same name and negative for opposite name to latitude at upper
transit, and negative for same name at lower transit.
The limits of the table take in all values of latitude, declination, and altitude which are likely to
be required. In its employment, care must be taken to enter the table at a place where the declination
•is appropriately named (of the same or opposite name to the latitude) ; it should also be noted that at
the bottom of the last three pages values are given for the variation of a body at lower transit, which can
only be observed when the declination and latitude are of the same name, and in which case the reduc-
tion to the meridian is subtractive; the limitations in this case are stated at the fool of the page, and
apply to all values below the heavy rules.
TABLE 27: CHANGE OF ALTITUDE IN GIVEN TIME FROM MERIDIAN.
This table gives the product of the variation in altitude in one minute of a heavenly body near the
meridian, by the square of the number of minutes. Values are given for every half minute between
0" 30' and 26'" 0', and for all variations likely to be employed in the method of "reduction to the
meridian."
The formula for computing is: • .
Hed. = a X l\
where a = variation in one minute (Table 26) , and
I = number of minutes (in units and tenths) from time of meridian passage.
The table is entered in the column of the nearest interval of time from meridian, and the value
taken out corrresponding to the value of a found from Table 26. The units and tenths are picked out
separately and combined, each being corrected by interpolation for intermediate intervals of time.
The result is the amount to be applied to the observed altitude to reduce it to the meridian altitude,
which is always to be added for upper transits and subtracted for lower.
EXPLANATION OF THE TABLES. 511
TABLE 28, A, B, C, D: LATITUDE BY POLABIS.
The formula on which these tables are based is:
L = A — pcoa t + ip' sin 1" sin'' ( tan h
— Jp'sin' 1" cos t sin' ( + ip* sin' 1" sin*« tan' h;
in which L = the latitude of the place;
h = the true altitude;
p = the polar distance; and
i = the hour angle of the star.
Table A contains for the declination 88° 48', or p„ = 1° 12' =4320", the/rsi correction,
A= ^p„ cos t — ip\ sin* 1" cos i sin' t;
Argument, the hour angle of the star, or 24'" — the hour angle.
Table B contains the second correction, ^
B = Jp'o gin 1" sin= ti3,nh+ \p\ sin' 1" sin* <tan'A;
Arguments, the true altitude of the star and the hoxir angle, or 24'' — the hour angle. This
correction is always additive.
Table C contains the third correction,
C = J (p* — P^o) s'" 1" sin''' t tan h;
Arguments, B and the declination of the star from 88° 47' 20" to 88° 49^ 20".
Table D contains the fourth correction,
— (p —p„) cos t — ilp" — p'„) sin' 1" cos t ain't;
Arguments, A and the declination of the star from 88° 47' 20" to 88° 49' 20".
The method of employing this table is illustrated in article 341, Chapter XII.
TABLES 29, 30, 31: CONVEBSION TABLES.
These are self-explanatory.
TABLE 32: TRUE FOBCE AND DIBECTION OF WIND.
This table enables an observer on board of a moving vessel to determine the true force and direction
of the wind from its apparent force and direction. Enter the table with the apparent direction of the
wind (number of points on the bow) and force (Beaufort scale) as arguments, and pick out the direc-
tion relatively to the ship's head and the force corresponding to the known speed of the ship.
Example: A vessel steaming SE. at a speed of 15 knots appears to have a wind blowing from three
points on the starboard bow with a force of 6, Beaufort scale. What is the true direction and force?
In the column headed 3 (meaning three points on l)ow, apparent direction) and in the line 6
(apparent force, Beaufort scale), we find abreast 15 (knots, sjieed of vessel) that the true direction is 5
points on starboard tow, i. e., S. by \V., and true force 4.
TABLE 33: VERTICAL ANGLES.
This table gives the distance of an object of known height by the vertical angle that it subtends at
the position of the observer. It was computed by the formula:
h
tan rt = J I
where a = the vertical angle;
h = the height of the observed object in feet; and
d = the distance of the object, also converted into feet.
The employment of this method of finding distance is explained in article 139, chapter IV.
TABLE 34: HORIZON ANGLES.
This shows the distance in yards corresponding to any observed angle between an object and the
sea horizon l)eyond, the observer being at a known height.
The method of use is explained in article 139, chapter IV.
TABLE 35: SPEED TABLE.
This table shows the rate of speed, in nautical miles per hour, of a vessel which traverses a measured
mile in any given number of minutes and seconds. It is entered with the number of minutes at the top
and the number of seconds at the side; under one and abreast the other is the number of knots of speed.
512 EXPLANATION OF THE TABLES.
TABLE 36: LOCAL AND STANDARD TIMES.
This table contains the reduction to be applied to the local time to obtain the corresponding time
at any other meridian whose time is adopted as a standard. The results are given to the nearest minute
of time only, being intended for the reduction of such approximate quantities as the time of high water
or time of sunset. More exact reductions, when required, may be made by Table 7.
TABLE 37: LOGARITHMS FOR EQUAL ALTITUDE SIGHTS.
I^ogarithms of A and B, for computing the Equation of Kqual Altitudes, are calculated by the
formuhe:
A ^^, B- ^
"1800 sin } E "~1800 tan i E
where 1", in the numerator is the elapsed time in minutes, and E in the denominator the elapsed time
expressed in arc.
If we put
we have
L =latitude of the place of observation, + north, — south,
d =declination of the sun, -j- north, — south,
n =hourly change of declination, + north, — south,
C =correction to reduce the middle chronometer time to chronometer time of apparent
noon, algebraically additive,
C =the same for midnight,
C = —A n tan L + B n tan d;
C'= A n tan L -f B m tan d.
This is Chauvenet's table to aid the solution of the problem of Equal Altitudes, and is explained in
article 322 and following articles. Chapter XI.
TABLE 37A: EQUATION OF EQUAL ALTITUDES NEAR NOON.
When equal altitudes of the sun are timed within about 30 minutes of noon, on azimuths not less
than 15°, a fairly reliable longitude can be found by applying to the mean of the chronometer times a
correction known as the Equation of Equal Altitudes near Noon. This correction depends upon tlie
speed with which the ship and sun are nearing or parting, being + to the mean of the times of the
sights when they are parting; and the table contains the factors by which the relative speed of the ship
and sun must be multiplied to obtain the value of the "Equation."
Ex.\MPLE. — At Ship Apparent Noon, Latitude was 11° 5' N.; Declinations" 4' N., decreasing 55" per
hour; Equation of Time 16 sec. + to M.T. Ship was steaming N. 42° W. at 15.2 knots, pjjual Altitudes
were timed, and the G.M.T. for the mid-time was Ih. 19m. SOs. Required longitude at noon.
Speed of ship=d. Latitude for 15.2, N. 42° W. = 11.3 knots=678" N. per hour.
" " sun= = 55" S. " "
Relative speed, partinq =733" " "
(E)fromTable=.054-'.039 =.015
Equation of Equal Altitude8=. 015X733 =11 sec. plus to mean.
Mid-time of Sights = 1 19 30 G.M.T.
Equation of E<jual Altitudes = -|-11
Time of Apparent Noon = 1 19 41 G.M.T.
Equation of time -|-16
Time of Apparent Noon = 1 19 57 G.A.T.
= 19° 59i' West Longitude.
EXPLANATION OF THE TABLES. 513
TABLE 38: EFFECT UPON LONGITUDE OF ERROR IN LATITUDE.
Table 38 shows, approximately, the error in longitude in miles and tenths of a mile, occasioned by
an error of one mile in the latitude.
Thus, when the sun's altitude is .30°, the latitude 30°, and the polar distance 100°, the error is
eight-fentha of a mile.
The effect of an increase of latitude is as follows:
In nVsHongitude, f East \ of meridian, the / decieased 1 except where marked f increased \
the body being 1 West ) longitude is \ increased i ' l)y *, when it is \ decreased j '
In Enst longitude, f East \ of meridian, the / increased ) except where marked ( decreased 1
the body being (West! longitude is \ decreased j ' . by *, when it is \ increased J "
A decrease of latitude has the contrary effect.
The direction of error may readily be seen by drawing the Sumner line in a direction at right angles
to the approximate bearing of the body.
TABLE 39: AMPLITUDES.
This table contains amplitudes of heavenly bodies, at ri^^ing and setting, for various latitudes and
declinations, computed by the formula:
sin amp. =sec Lat. Xsin dec.
It is entered with tlie declination at the top and the latitude at the side.
Its use is explained in article 358, Chapter XIV.
TABLE 40: CORRECTION FOR AMPLITUDES.
This table gives a correction to be applied to the observed amplitude to counteract the vertical
displacement due to refraction, parallax, and dip, when the body is observed with its center in the
visible horizon.
The correction is to be applied for the sun, a planet, or a star, as follows:
At Rising in N. Lat. 1 i 41 »• 4 iu • ui.
Setting in S. Lat. \ "I^'''^' *''« <'0>-rection to the right.
"^^^Int Lat I^PP'y "'« ^'"•■•^^tion to the left.
For the moon, apply half the correction in the contrary manner.
TABLE 41: NATURAL SINES AND COSINES.
This table contains the natural sine and cosine for every minute of the quadrant, and is to be
entered at the top or bottom with the degrees, and at the side marked JI., with the minutes; the
corresponding numbers will be the natural sine and cosine, resjiectively, observing that if the degrees
are found at the top, the name sine, cosine, and 11. nmst also be found at the top, and the contrary if
the degrees are found at the bottom. It should be understood that all numbers given in the table
should be divided by 100,000 — that is, pointed off to contain five decimal places. Thus, .43366 is the
natural sine of 25° 42', or the cosine of 64- 18'.
In the outer columns of the margin are given tables of proportional parts, for the purpose of finding,
approximately, by insi>ection, the proportional part corresponding to any number of seconds in the
proposed angle, the seconds being found in the marginal column marked M., and the correction in
the adjoining column. Thus, if we suppose that it were required to find the natural .«ine corresponding
to 25° 42' 19", the difference of the sines of 25° 42' and 25° 43' is 26, being the same as at the top of the
left-hand column of the table; and in this column, and o])posite 19 in the column !M., is the correc-
tion 8. Adding this to the above number .43366, because the numbers are increasing, we get .43374 for
the sine of 25° 42' 19". In like manner, we find the cosine of the same angle to be .90108— 4=. 90104,
using the right-hand columns, and «M6(rac(i»^ because the numbers are decreasing; observing, however,
that the number 14 at the top of this column varies 1 from tlie difference between the cosines of 25° 42'
and 25° 43', which is only 13; so that the table may give in some cases a unit too much between the
angles 25° 42' and 25° 43'; but this is, in general, of but little importance, and when accuracy is required,
the usual method of proportional parts is to be resortied to, using the actual tabular difference.
TABLE 42: LOGARITHMS OF NUMBERS.
This table, containing the common logarithms of numbers, was compared with Sherwin'a, Hutton's,
and Taylor's logarithms; its use is explained in an article on Logarithms in Appendix III.
TABLE 43: LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, QUARTER POINTS.
This table contains the logarithms of the sines, tangents, etc., corresponding to points and quarter
points of the compass. This was compared with Sherwin's, Hutton's, and Taylor's logarithms.
24972°— 12 23
514 EXPLANATION OF THE TABLES.
TABLE 44: LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, DEGREES.
This table contains the common logarithms of the sines, tangents, secants, etc. It was compared
with Sherwin's, Mutton's, and Taylor'^ tables. Two additional columns are given in this table, wliicli
are very convenient in finding the time from an altitude of the sun; also, three columns of proportional
parts for seconds of space, and a small table at the bottom of each page for finding the proportional parts
for seconds of time. The degrees are marked to 180°, which saves the trouble of subtracting the given
angle from 180° when it exceeds 90°.
The use of this table is fully explained in Appendix III in an article on Logarithms.
TABLE 45: LOGARITHMIC AND NATURAL HAVERSINES.
The haversine is defined by the following relation:
hav. A=J vers. A=J(1— cos A)=sin- JA.
It is a trigonometric function which simplifies the solution of many problems in nautical astronomy
as well as in plane trigonometry. To afford the maxinuim facility in carrying out the processes of
Bolution, the values of the natural haversine and its logarithm are set down together in a single table
for all values of angle ranging from 0° to 3(50°, expressed both in arc and in time.
TABLE 46: CORRECTIONS TO BE APPLIED IN ORDER TO FIND THE TRUE ALTI-
TUDE OF A STAR AND ALSO OF THE SUN FROM THE OBSERVED ALTITUDE
ABOVE THE HORIZON.
This is a consolidated table in which the tabulated correction for an observed altitude of a star
combines the mean refraction and the dip, and that for an observed altitude of the sun's lower limb
combines the mean refraction, the dip, the parallax, and the mean semidiameter, which is taken as
16'. A supplementary table at the foot of the main table takes account of the variation of the sun's
semidiameter in the different months of the year.
TABLE 47: THE LONGITUDE FACTOR.
The change in longitude due to a change of V in latitude, called the longitude factor, F, is given in
this table at suitable intervals of latitude and azimuth. The (juantities tabulated are computed from
the formula —
F=sec. Lat. Xcot. Az.
When a time sight is solved with a dead-reckoning latitude, the resulting longitude is only true
if the latitude be correct. This table, by setting forth the number of minutes of longitude due to each
minute of error in latitude, gives the means of finding tlie correction to the longitude for any error that
may subsequently be disclosed in the latitude used in tlie calculation.
Regarding the azimuth of the observed celestial body as less than 90° and as measured from either
the North or the South point of the horizon towards East or West, the rule for determining whether the
correction in longitude is to be applied to the eastward or to the westward will be as follows: If the
change in latitude is of the same name as the first letter of the bearing, the change in longitude is of the
contrary name to that of the second letter, and vice versa.
Thus, if the body bears S. 45° E. and the change in latitude is to the southward, the change in
longitude will be to the westward; and, if the change in latitude is to the northward, the change in
longitude will be to the eastward.
The convenient application of the longitude factor in finding the intersection of Sumner lines is
explained in article 389.
TABLE 48: THE LATITUDE FACTOR.
The change in latitude due to a change of 1' in the longitude, called the latitude factor, f, is given
in this table at suitable intervals of latitude and azimuth. The quantities tabulated, being the reciprocals
of the values of the longitude factor, are computed from the formula —
f=F=sec. LatXcot. Az.=«°«- Lat.Xtan. Az.
When an ex-meridian sight is solved with a longitude afterwards found to be in error, this table, by
setting forth the number of minutes of latitude due to each V of error in longitude, gives the means
of finding the correction in the latitude for the amount of error in the longitude used in the calculation.
Regarding the azimuth of the observed celestial body as less than 90° and as measured from either
the North or the South point of the horizon towards East or West, the rule for determining whether tlie
correction in latitude is to be applied to the northward or to the southward is as follows: If the change
in longitude is of the same name as the second letter of the bearing, the change in latitude is of the
contrary name to the first letter, and vice versa. Thus, if the body bears S. 14° PI and the change in
longitude is to tlie westward, the change in latitude will be to the southward, and, if the change in
longitude is to the eastward, the change in latitude will be to the northward.
The convenient application of the latitude factor in finding the intersection of Sumner lines is
explained in article 390.
. y
/
/ .5/
/>'
"7-
I
/ P-t^o^'v-tpt:*
t>
4pt^
^^
/.
/
/
TABLE 1.
[Page 615 [
Difference of Latitude and
Departure for \ Point.
Dist.
N. JE.
N. i W.
S.
JE.
S. JW.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.0
61
60.9
3.0
121
120.9
♦5.9
181
180.8
8.9
241
240.7
11.8
2
2.0
0.1
62
61.9
3.0
22
121.9
6.0
82
181.8
8.9
42
241.7
11.9
3
3.0
0.1
63
62.9
3.1
23
122.9
6.0
83
182.8
9.0
43
242.7
11.9
4
4.0
0.2
64
63.9
3.1
24
123.9
6.1
84
183.8
9.0
44
243.7
12.0
5
5.0
0.2
65
64.9
3.2
25
124.8
6.1
85
184.8
9.1
45
244.7
12.0
6
6.0
0.3
66
6.5.9
3.2
26
125.8
6.2
86
185.8
9.1
46
245.7
12.1
7
7.0
0.3
67
66.9
3.3
27
126.8
6.2
87
186.8
9.2
47
246.7
12.1
8
8.0
0.4
68
67.9
3.3
28
127.8
6.3
88
187.8
9.2
48
247.7
12.2
9
.9.0
0.4
69
68.9
3.4
29
128.8
6.3
89
188.8
9.3
49
248.7
12.2
10
10.0
0.5
70
69.9
3.4
30
129.8
6.4
90
189.8
9.3
60
249.7
12.3
U
11.0
0.5
71
70.9
3.5
131
130.8
6.4
191
190.8
9.4
261
250.7
12.3
12
12.0
0.6
72
71.9
3.5
32
131.8
6.5
92
191.8
9.4
62
251.7
12,4
13
13.0
0.6
73
72.9
3.6
33
132.8
6.5
93
192.8
9.5
53
252.7
12.4
14
14.0
0.7
74
73.9
3.6
34
1.33. 8
6.6
94
193.8
9.5
54
253.7
12.5
15
15.0
0.7
75
74.9
3.7
35
134.8
6.6
96
194.8
9.6
55
254.7
12.5
16
16.0
0.8
76
75.9
3.7
36
135.8
6.7
96
195.8
9.6
56
265.7
12.6
17
17.0
0.8
77
76.9
3.8
37
136.8
6.7
97
196.8
9.7
67
266.7
12.6
18
18.0
0.9
78
77.9
3.8
38
137.8
6.8
98
197.8
9.7
58
257.7
12.7
19
19.0
0.9
79
78.9
3.9
39
138.8
6.8
99
198.8
9.8
59
258.7
12.7
20
20.0
1.0
1.0
80
81
79.9
3.9
40
139.8
6.9
200
199.8
9.8
60
269. 7
260. r
12.8
12.8
21
21.0
80.9
4.0
141
140.8
6.9
201
200.8
9.9
261
22
22.0
1.1
82
81.9
4.0
42
141.8
7.0
02
201.8
9.9
62
261.7
12.9
23
23.0
1.1
83
82.9
4.1
43
142.8
7.0
03
202.8
10.0
63
262.7
12.9
24
24.0
1.2
84
83.9
4.1
44
143.8
7.1
04
203.8
10.0
64
263. 7
13.0
25
25.0
1.2
85
84.9
4.2
45
144.8
7.1
05
204.8
10.1
65
264.7
13.0
26
26.0
1.3
86
85.9
4.2
46
146.8
7.2
06
205.8
10.1
66
265. 7
13.1
27
27.0
1.3
87
86.9
4.3
47
146.8
7.2
07
206.8
10.2
67
266.7
13.1
28
28.0
1.4
88
87.9
4.3
48
147.8
7.3
08
207.7
10.2
68
267.7
13.2
29
29.0
1.4
89
88.9
4.4
49
148.8
7.3
09
208.7
10.3
69
268.7
13.2
30
30.0
1.5
90
89.9
4.4
50
149.8
7.4
10
209.7
210.7
10.3
70
269.7
13.2
31
31.0
1.5
91
90.9
4.5
151
150.8
7.4
211
10.4
271
270.7
13.3
32
32.0
1.6
92
91.9
4.5
52
151.8
7.6
12
211.7
10.4
72
271.7
13.3
33
33.0
1.6
93
92.9
4.6
53
152.8
7.5
13
212.7
10.5
73
272.7
13.4
34
34.0
1.7
94
93.9
4.6
54
153.8
7.6
14
213.7
10.5
74
273.7
13.4
35
36.0
1.7
95
94.9
4.7
55
154.8
7.6
15
214.7
10.5
75
274.7
13.0
36
36.0
1.8
96
95.9
4.7
56
165.8
7.7
16
215.7
10.6
76
275.7
13.5
37
37.0
1.8
97
96.9
4.8
57
166.8
7.7
17
216.7
10.6
77
276. 7
13.6
38
38.0
1.9
98
97.9
4.8
58
157.8
7.8
18
217.7
10.7
78
277.7
13.6
39
39.0
1.9
99
98.9
4.9
59
158.8
7.8
19
218.7
10.7
79
278.7
13.7
40
41
40.0
2.0
100
99.9
4.9
60
169.8
7.9
20
219.7
10.8
80
279. 7
280. 7
13.7
41.0
2.0
101
100.9
5.0
161
160.8
7.9
221
220.7
10.8
281
13.8
42
41.9
2.1
02
101.9
5.0
62
161.8
7.9
22
221.7
10.9
82
281.7
13.8
43
42.9
2.1
03
102.9
5.1
63
162.8
8.0
23
222.7
10.9
83
282.7
13.9
44
43.9
2.2
04
103.9
5.1
64
163.8
8.0
24
223.7
11.0
84
283.7
13.9
45
44.9
2.2
05
104.9
5.2
65
164.8
8.1
25
224.7
11.0
85
284.7
14.0
46
45.9
2.3
06
105.9
5.2
66
166.8
8.1
26
226.7
11.1
86
285. 7
14.0
47
46.9
2.3
07
106.9
5.3
67
166.8
8.2
27
226. 7
11.1
87
286.7
14.1
48
47.9
2.4
08
107.9
5.3
68
167.8
8.2
28
227.7
11.2
88
287.7
14.1
49
48.9
2.4
09
108.9
5.3
69
168.8
8.3
29
228.7
11.2
89
288.7
14.2
50
49.9
2.5
10
109.9
110.9
5.4
70
169.8
8.3
30
229.7
11.3
90
289.7
14.2
51
50.9
2.5
111
5.4
171
170.8
8.4
231
230.7
11.3
291
290.6
14.3
52
51.9
2.6
12
111.9
5.5
72
171.8
8.4
32
231.7
11.4
92
291.6
14.3
53
52.9
2.6
13
112.9
5.5
73
172.8
8.5
33
232.7
11.4
93
292.6
14.4
54
53.9
2.6
14
113.9
5.6
74
173.8
8.5
34
233.7
11.5
94
293.6
14.4
55
54.9
2.7
15
114.9
5.6
75
174.8
8.6
36
234.7
11.5
95
294.6
14.5
56
55.9
2.7
16
115.9
5.7
76
176.8
8.6
36
235.7
11.6
96
295.6
14.5
57
56.9
2.8
17
116.9
5.7
77
176.8
8.7
37
236.7
11.6
97
296.6
14.6
58
57.9
2.8
18
117.9
5.8
78
177.8
8.7
38
237.7
11.7
98
297.6
14.6
59
58.9
2.9
19
118.9
5.8
79
178.8
8.8
39
238.7
11.7
99
298.6
14.7
60
59.9
2.9
20
119.9
5.9
80
179.8
8.8
40
239.7
11.8
300
299.6
14.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
E.
IN.
E. JS
W. }N.
^
S^. }S.
[Fc
r7|Po
nts.
Page 516]
TABLE 1. 1
Difference of Latitude and Departure for i Point. " 1
N. *E.
N. i
w.
s. i E. s.i \y. 1
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. j Lat.
Dep.
Dist.
Lat. 1 Dep.
Dist. Lat. Dep. 1
1
1.0
0.1
61
60.7
6.0
121
• 120. 4
11.9
181
180.1
17.7
241 239. 8
23.6
2
2.0
0.2
62
61.7
6.1
22
121.4
12.0
82
181.1
17.8
42 240. 8
23.7
3
3.0
0.3
63
62.7
6.2
23
122.4
12.1
83
182.1
17.9
43 241.8
23.8
4
4.0
0.4
64
63.7
6.3
24
123.4
12 2
84
183.1
18.0
44 242. 8
23.9
5
5.0
0.5
65
64.7
6.4
25
124.4
12! 3
85
184.1
18.1
45 ! 243.8
24.0
6
6.0
0.6
66
65.7
6.5
26
125.4
12.4
86
185.1
18.2
46 1 244.8
24.1
7
7.0
0.7
67
66.7
6.6
27
126.4
12.4
87
186.1
18:3
47 j 245.8
24.2
8
8.0
0.8
68
67.7
6.7
28
127.4
12.5
88
187.1
18.4
48 ' 246.8
24.3
9
9.0
0.9
69
68.7
6.8
29
128.4
12.6
89
188.1
18.5
49 247. 8
24.4
10
10.0
1.0
70
69.7
6.9
30
129.4
12.7
90
189.1
18.6
50 248.8
24.5
11
10.9
1.1
71
70.7
7.0
131
130. 4
12.8
191
190. 1
18.7
251 249. 8
24.6
12
11.9
1.2
72
71.7
7.1
32
131.4
12.9
92
191.1
18.8
52 250. 8
24.7
13
12.9
1.3
73
72.6
7.2
33
132.4
13.0
93
192.1
18.9
53 251.8
24.8
14
13.9
1.4
74
73.6
7.3
34
133.4
13.1
94
193.1
19.0
54 i 252. 8
24.9
15
14.9
1.5
75
74.6
7.4
35
134.3
13.2
95
194.1
19.1
55 ' 253.8
25.0
16
15.9
1.6
76
75.6
7.4
36
1,35. 3
13.3
96
195. 1
19.2
56 \ 254.8
25.1
17
16.9
1.7
77
76.6
7.5
37
136.3
13.4
97
196.1
19.3
57 i 255.8
25.2
18
17.9
1.8
78
77.6
7.6
38
137.3
13.5
98
197.0
19.4
58 256. 8
25.3
19
18.9
1.9
79
78.6
7.7
39
138.3
13.6
99
198.0
19.5
59 257. 8
25.4
20
19.9
2.0
80
79.6
7.8
40
139. 3
13.7
200
199.0
19.6
60
258. 7
25.5
21
20.9
2.1
81
80.6
7.9
141
140.3
13.8
201
200.0
19.7
261
259.7
25.6
22
21.9
2.2
82
81.6
8.0
42
141.3
13.9
02
201.0
19.8
62 1 260. 7
25.7
23
22.9
2.3
83
82.6
8.1
43
142.3
14.0
03
' 202.
19.9
63 ' 261. 7
25.8
24
23.9
2.4
84
83.6
8.2
44
143.3
14.1
04
203.0
20.0
64
262.7
25.9
25
24.9
2.5
85
84.6
8.3
45
144.3
14.2
05
204.0
20.1
65
263. 7
26.0
26
25.9
2.5
86
85.6
8.4
46
14.5.3
14.3
06
205.0
20.2
66
264.7
26.1
27
26.9
2.6
87
86.6
8.5
47
146.3
14.4
07
206.0
20.3
67
265. 7 i 26. 2 |
28
27.9
2.7
88
87.6
8.6
48
147.3
14.5
08
207.0
20.4
68
26(1. 7
26.3
29
28.9
2.8
89
88.6
8.7
49
148.3
14.6
09
208.0
20.5
69
267.7
26.4
30
29.9
2.9
90
89.6
90.6
8.8
50
149.3
14.7
10
209.0
20.6
70
268.7
269. 7
26.5
31
30.9
3.0
91
8.9
151
150.3
14.8
211
210.0
20.7
271
26.6
32
31.8
3.1
92
91.6
9.0
52
151.3
14.9
12
211.0
20.8
72
270.7
26.7
33
32.8
3.2
93
92.6
9.1
53
152.3
15.0
13
212.0
20.9
73
271.7
26.8
34
33.8
3.3
94
93.5
9.2
54
153.3
15.1
14
213.0
21.0
74
272.7
26.9
35
34.8
3.4
95
94.5
9.3
55
154. 3
15.2
15
214.0
21.1
75
273.7
27.0
36
35.8
3.5
96
95.5
9.4
56
155.2
15.3
16
215.
21. 2
76
274.7
27.1
37
36.8
3.6
97,
96.5
9.5
57
156.2
15.4
17
216.0 1 21.3
77
275. 7
27.2
38
37.8
3.7
98
97.5
9.6
58
157.2
15.5
18
217.0 i 21.4
78
276.7
27.2
39
38.8
3.8
99
98.5
9.7
59
158. 2
15.6
19
217.9 i 21.5
79
277.7
27.3
40
39.8
3.9
100
99.5
9.8
60
159.2
15.7
20
218.9
21.6
80
278.7
27.4
27.5
41
40.8
4.0
101
100.5
9.9
161
160.2
15.8
221
219.9
21.7
281
279.6
42
41.8
4.1
02
101.5
10.0
62
161.2
15.9
22
220.9
21.8
82
280.6
27.6
43
42.8
4.2
03
102.5
10.1
63
162.2
16.0
23
221.9
21.9
83
281.6
27.7
44
43.8
4.3
04
103.5
10.2
64
163.2
16.1
24
222.9
22.0
84
282.6
27.8
45
44.8
4.4
05
104.5
10.3
65
164.2
16.2
25
223.9
22.1
85
283.6
27.9
46
45.8
4.5
06
105.5
10.4
66
165.2
16.3
26
224.9
22.2
86
284.6
28.0
47
46.8
4.6
07
106.5
10.5
67
166.2
16.4
27
225.9
22.2
87 : 285. 6
28.1
48
47.8
4.7
08
107.5
10.6
68
167.2
16.5
28
226.9
22.3
88 ! 286.6
28.2
49
48.8
4.8
09
108.5
10.7
69
168.2
16.6
29
227.9
22.4
89 i 287. 6
28.3
50
49.8
4.9
10
109.5
10.8
70
169.2
16.7
30
228.9
22.5
22.6
90
288.6
28.4
28.5
51
50.8
5.0
111
110.5
10.9
171
170. 2
16.8
231
229.9
291
289.6
52
51.7
5.1
12
111.5
11.0
72
171.2
16.9
32
230.9
22.7
92
290.6
28.6
53
52.7
5.2
13
112.5
11.1
73
172.2
17.0
33
231.9
22.8
93
291.6
28.7
64
53.7
5.3
14
113.5
11.2
74
173.2
17.1
34
232.9
22.9
94
292.6
28.8
55
54.7
5.4
15
114.4
11.3
75
174.2
17.2
35
233.9
23.0
95
293.6
28.9
56
55.7
5.5
16
115.4
11.4
76
175.2
17.3
36
234.9
23.1
96
294.6
29.0
57
56.7
5.6
1?
116.4
11.5
77
176.1
17.3
37
235.9
23.2
97
295.6
29.1
58
57.7
5.7
18
117.4
11.6
78
177.1
17.4
38
236.9
23.3
98
296.6
29.2
59
58.7
5.8
19
118.4
11.7
79
178.1
17.5
39
237.8
23.4
99
297.6
29.3
60
59.7
5.9
20
119.4
11.8
80
179.1
17.6
40
238.8
23.5
300
298.6
29.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
E. iN
K. i S.
W. }N
W i S. [For 7J Points.
!
TABLE 1.
[Page 617
Difference of Latitude and Departure for \ Point.
N^ 1 E.
S\ 1 w
S. 1 E.
S. 1 W
Dist.
Lat.
Dcp.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. 1
Dep.
1
1.0
0.1
61
60.3
9.0
121
119.7
17.8
181
179.0
26.6
241
238.4
35.4
o
2.0
0.3
62
61.3
9.1
22
120.7
17.9
82
180.0
26.7
42
239.4
:i5.5
3
3.0
0.4
63
62.3
9.2
23
121.7
18.0
83
181.0
26.9
43
240.4
35.7
•1
4.0
0.6
64
63.3
9.4
24
122.7
18.2
84
182.0
27.0
44
241.4
35.8
5
4.9
0.7
65
64.3
9.5
25
123.6
18.3
85
183.0
27.1
45
242.3
35.9
6
5.9
0.9
66
65.3
9.7
26
124.6
18.5
86
184.0
27.3
46
243.3
36.1
7
6.9
1.0
67
66.3
9.8
27
125.6
18.6
87
185.0
27.4
47
244.3
36.2
8
7.9
1.2
68
67.3
10.0
28
126.6
18.8
88
186.0
27.6
48
245.3
36.4
9
8.9
1.3
69
68.3
10.1
29
127.6
18.9
89
187.0
27.7
49
246.3
36.5
10
9.9
1.5
1.6
70
71
69.2
10.3
30
128.6
19.1
90
187.9
27.9
50
247.3
.36.7
36.8
11
10.9
70.2
10.4
131
129.6
19.2
191
188.9
28.0
251
248.3
12
11.9
1.8
72
71.2
10.6
32
130.6
19.4
92
189.9
28.2
52
249.3
37.0
13
12.9
1.9
73
72.2
10.7
33
131.6
19.5
93
190.9
28.3
53
250.3
37.1
14
13.8
2.1
74
73.2
10.9
34
132.5
19.7
94
191.9
28.5
54
251.3
37.3
15
14.8
2.2
75
74.2
11.0
35
133. 5
19.8
95
192.9
28.6
55
252.2
37.4
16
15.8
2.3
76
75.2
11.2
36
134.5
20.0
96
193.9
28.8
56
253. 2
37.6
17
16.8
2.5
77
76.2
11.3
37
135.5
20.1
97
194.9
28.9
57
254.2
37.7
18
17.8
2.6
78
77.2
11.4
38
136.5
20.2
98
195.9
29.1
58
255. 2
37.9
19
18.8
2.8
79
78.1
11.6
39
137.5
20.4
99
196.8
29.2
59
256.2
38.0
20
19.8
2.9
80
79.1
11.7
40
"141
138. 5
20.5
200
197.8
29.3
60
257.2
38.1
38.3
21
20.8
3.1
81
80.1
11.9
139.5
20.7
201
198. 8
29.5
261
258.2
22
21.8
3.2
82
81.1
12.0
42
140.5
20.8
02
199.8
29.6
62
259.2
38.4
23
22.8
3.4
83
82.1
12. 2
43
141.5
21.0
03
200.8
29.8
63
260.2
38.6
24
23.7
3.5
84
83.1
12! 3
44
142.4
21.1
04
201.8
29.9
64
261.1
38.7
25
24.7
3.7
85
84.1
12.5
45
143.4
21.3
05
202.8
30.1
65
262.1
38.9
26
25.7
3.8
86
85.1
12.6
46
144.4
21.4
06
203.8
30.2
66
263.1
39.0
27
26.7
4.0
87
86.1
12.8
47
145.4
21.6
07
204.8
30.4
67
264.1
39.2
28
27.7
4.1
88
87.0
12.9
48
146.4
21.7
08
205.7
30.5
68
265.1
39.3
29
28.7
4.3
89
88.0
13.1
49
147.4
21.9
09
206.7
30.7
69
266.1
39.5
30
31
29.7
4.4
90
91
89.0
90.0
13.2
.50
148.4
22.0
22.2
10
211
207. 7 • 30. 8
70
267.1
39.6
39.8
30.7
4.5
13.4
151
149.4
208.7 i 31.0
271
268. 1
f
1 32
31.7
4.7
92
91.0
13.5
52
150.4
22.3
12
209. 7 : 31. 1
72
269.1
39.9
33
32.6
4.8
93
92.0
13.6
53
151.3
22.4
13
210.7 i 31.3
73
270.0
40.1
34
33.6
5.0
94
93.0
13.8
54
152.3
22.6
14
211.7
31.4
74
271.0
40.2
35
34.6
5.1
95
94.0
13.9
55
153.3
22.7
15
212.7
31.5
75
272.0
40.4
36
35.6
.5.3
96
95.0
14.1
56
154. 3
22.9
16
213.7
31.7
76
273.0
40. 5
37
36.6
5.4
97
96.0
14.2
57
1.55. 3
23.0
17
214.7
31.8
77
274.0
40.6
38
37.6
5.6
98
96.9
14.4
58
156.3
23.2
18
215.6
32.0
78
275.
40.8
39
38.6
5.7
99
97.9
14.5
59
157.3
23.3
19
216.6
32.1
79
276.0
40.9
40
39.6
5.9
100
98.9
14.7
60
158. 3
159. 3
23.5
20
217.6
2"18.6
32.3
80
281
277.0
278.0
41.1
41.^2
41
40.6
6.0
101
99.9
14.8
161
23.6
221
32.4
42
41.5
6.2
02
100.9
15.0
62
160. 2
23.8
22
219.6
32.6
82
278.9
41.4
43
42.5
6.3
03
101.9
15.1
63
161.2
23.9
23
220.6
32.7
83
279.9
41.5
44
43.5
6.5
04
102.9
15. 3
64
162.2
24.1
24
221.6
32.9
84
280.9
41.7
45
44.5
6.6
05
103.9
15.4
65
163. 2
24.2
25
222.6
33.0
85
281.9
41.8
46
45.5
6.7
06
104.9
15.6
66
164.2
24.4
26
223.6
33.2
86
282.9
42.0
47
46.5
6.9
07
105.8
15."
67
165.2
24.5
27
224.5
.33.3
87
283.9
42.1
48
47.5
7.0
08
106.8
15.8
68
166.2
24.7
28
225.5
33.5
88
284.9
42.3
49
48.5
7.2
09
107.8
16.0
69
167.2
24.8
29
226. 5
33. 6
89
285.9
42.4
50
49.5
7.3
10
111
108.8
109.8
16.1
70
168.2
24.9
30
227. 5
33.7.
90
286.9
42. 6
42.7
51
50.4
7.5
16.3
171
169.1
25.1
231
228.5
33.9
291 j 287. 9
52
51.4
7.6
12
110.8
16.4
72
170.1
25.2
32
229.5
34.0
92 ' 288.8
42.8
53
52.4
7.8
13
111.8
16.6
73
171.1
25.4
33
230.5
34.2
93 , 289.8
43.
54
53.4
7.9
14
112.8
16.7
74
172.1
25.5
34
231.5
34.3
94
290.8
43.1
55
54.4
8.1
15
113.8
16.9
75
173.1
25.7
35
232. 5
34.5
95
291.8
43. 3
56
55.4
8.2
16
114.7
17.0
76
174.1
25.8
36
233.4
34.6
96
292.8
43.4
57
56.4
8.4
17
115.7
17.2
77
175. 1
26.0
37
234.4
34.8
97
293.8
43.6
58
57.4
8.5
18
116.7
17.3
78
176.1
26.1
38
235.4
34.9
98
294.8
43.7
59
58.4
8.7
19
117.7
17.5
79
177.1
26.3
39
236.4
35.1
99
295. 8
43.9
60
59.4
8.8
20
118.7
17.6
80
178.1
26.4
40
237.4
35.2
300
296.8
44.0
Dist.
Dep.
lat.
Dist.
Dcp.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
K. \ X
K. 1 S.
W. J N.
w. 3 s.
[For 7i Points.
Page 518]
TABLE 1.
Difference of Latitude and Departure for 1 Point.
N. byE
N. by
W.
S. by E.
5. by
W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.8
11.9
121
118.7
23.6
181'
177.5
35.3
241
236.4
47.0
2
2.0
0.4
62
60.8
12.1
22
119.7
23.8
82
178.5
3.5.5
42
237.4
47.2
3
2.9
0.6
63
61.8
12.3
23
120.6
24.0
83
179.5
35.7
43
238.3
47.4
4
3.9
0.8
64
62.8
12.5
24
121.6
24.2
84
180.5
35.9
44
239. 3
47.6
5
4.9
1.0
65
63.8
12.7
25
122.6
24.4
85
181.4
36.1
45
240.3
47.8
6
5.9
1 *'
66
64.7
12.9
26
123.6
24.6
86
182.4
36.3
46
241.3
48.0
7
6.9
l!4
67
65.7
13.1
27
124.6
24.8
87
183.4
36.5
47
242.3
48.2
8
7.8
1.6
68
66.7
1,3. 3
28
125.5
25.0
88
184.4
.36.7
48
243.2
48.4
9
8.8
1.8
69
67.7
13.5
29
126.5
25.2
89
185.4
36.9
49
244.2
48.6
10
9.8
2.0
70
68.7
13.7
30
127.5
12875
25.4
90
191
186.3
37.1
37.3
50
251
245.2
48.8
49:0
11
10.8
2.1
71
69.6
13.9
131
25.6
187.3
246.2
12
11.8
2.3
72
70.6
14.0
32
129.5
25.8
92
188. 3
37.5
52
247.2
49.2
13
12.8
2.5
73
71.6
14.2
33
130.4
25.9
93
189. 3
37.7
53
248.1
49.4
14
13.7
2.7
74
72.6
14.4
.34
1»1.4
26.1
94
190.3
37.8
54
249.1
49.6
15
14.7
2.9
75
73.6
14.6
35
132.4
26.3
95
191.3
38.0
55
250. 1
49.7
16
15.7
3.1
76
74.5
14:8
36
133.4
26.5
96
192.2
38.2
56
251. 1
49.9
17
16.7
3.3
77
75.5
15.0
37
134.4
26.7
97
193.2
38.4
57
252.1
50.1
18
17.7
3.5
78
76.5
15.2
38
135.3
26.9
98
194.2
38.6
58
253.0
50.3
19
18.6
3.7
79
77.5
15.4
39
136. 3
27.1
99
195.2
38.8
59
254.0
50.5
20
19.6
3.9
80
78.5
15.6
40
137.3
27.3
200
196.2
.39.0
60
255.0
50.7
21
20.6
4.1
81
79.4
15.8
141
138.3
27.5
201
197.1
39.2
261
256.
50.9
22
21.6
4.3
82
80.4
16.0
42
139.3
27.7
02
198.1
39.4
62
257.0
51.1
23
22.6
4.5
83
81.4
16.2
43
140.3
27.9
03
199.1
39.6
63
257.9
51.3
24
23.5
4.7
84
82.4
16.4
44
141.2
28.1
04
200.1
39.8
64
258.9
51.5
25
24.5
4.9
85
83.4
16.6
45
142.2
28.3
05
201.1
40.0
65
259.9
51.7
26
25.5
5.1
86
84.3
16.8
46
143. 2
28.5
06
202.0
40.2
66
260.9
51.9
27
26.5
5.3
87
85.'9
17.0
47
144. 2 ' 28. 7
07
203.0
40.4
67
261.9
.52. 1
28
27.5
5.5
88
86.3
17.2
48
145.2
28.9
08
204.0
40.6
68
262.9
52.3
29
28.4
5.7
89
87.3
17.4
49
146.1
29.1
09
205.
40.8
69
263.8
52.5
30
29.4
5.9
90
88.3
89.3
17.6
50
147.1
29.3
10
206.0
206.9
41.0
70
264.8
52.7
31
30.4
6.0
91
17.8
151
148.1
29.5
211
41.2
271
265.8
52.9
32
31.4
6.2
92
90.2
17.9
52
149.1
29.7
12
207.9
41.4
72
266.8
53.1
33
32.4
6.4
93
91.2
18.1
53
150.1
29.8
13
208.9
41.6
73
267.8
53.3
34
33.3
-6.6
94
92.2
18.3
54
151.0
30.0
14
209.9
41.7
74
268.7
53.5
35
34.3
6.8
95
93.2
18.5
55
1.52.
30.2
15
210.9
41.9
75
269.7
53.6
36
35.3
7.0
96
94.2
18.7
56
153.0
30.4
16
211.8
42.1
76
270.7
53.8
37
36.3
7.2
97
95.1
18.9
57
154.0
30.6
17
212.8
42.3
77
271.7
.54.0
38
37.3
7.4
98
96 1
19.1
58
155.0
30.8
18
213.8
42.5
78
272.7
54.2
39
38.3
7.6
99
97.1
19.3
59
155.9
31.0
19
214.8
42.7
79
273.6
54.4
40
39.2
7.8
100
98.1
19.5
60
156.9
31.2
20
215. 8
42.9
80
274.6
54.6
41
40.2
8.0
101
99.1
19.7
161
157.9
31.4
221
216.8
43.1
281
275.6
54.8
42
41.2
8.2
02
100.0
19.9
62
158. 9 31. 6
22
217.7
43.3
82
276.6
55.0
43
42.2
8.4
03
101.0
20.1
63
159.9
31.8
23
218.7
43.5
83
277.6
55.2
44
43.2
8.6
04
102.0
20.3
64
160.8
32.0
24
219.7
43.7
84
278.5
55.4
45
44.1
8.8
05
103.0
20.5
65
161.8
32.2
25
220.7
43.9
85
279.5
55.6
46
45.1
9.0
06
104.0
20.7
66
162.8
32.4
26
221.7
44.1
86
280.5
55.8
47
46.1
9.2
07
104.9
20.9
67
163.8
32.6
27
222.6
44.3
87
281.5
56.0
48
47.1
9.4
08
105.9
21.1
68
164.8
32.8
28
223.6
44.5
88
282.5
56.2
49
48.1
9.6
09
106.9
21.3
69
165.8
33.0
29
224.6
44.7
89
283.4
56.4
50
49.0
9.8
10
107.9
21.5
21.7
70
166.7
33.2
30
225.6
44.9
90
284.4
56.6
51
50.0
9.9
111
108.9
171
167.7
33.4
231
226.6
45.1
291
285.4
56.8
52
51.0
10.1
12
109.8
21.9
72
168.7
33.6
32
227.5
45.3
92
286.4
57.0
53
52.0
10.3
13
110.8
22.0
73
169.7
33.8
33
228.5
4.5.5
93
287.4
57.2
54
53.0
10.5
14
111.8
22.2
74
170.7
33.9
34
229.5
45.7
94
288.4
57.4
55
53.9
10.7
15
112.8
22.4
75
171.6
.34.1
35
230.5
45.8
95
289.3
57.6
56
54.9
10.9
16
113.8
22.6
76
172.6
34.3
36
231. 5
46.0
96
290.3
57.7
57
55.9
11.1
17
114.8
22.8
77
173.6
34.5
37
232.4
46.2
97
291.3
57.9
58
56.9
11.3
18
115.7
23.0
78
174.6
34.7
38
233.4
46.4
98
292.3
58.1
59
57.9
11.5
19
116.7
23.2
79
175.6
34.9
39
234.4
46.6
99
293.3
58.3
60
58.8
11.7
20
117.7
23.4
80
176.5
35.1
40
235.4
46.8
300
294.2
58.6
Dist.
|Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
E.
byN.
E. I
)ys.
W. by N.
W. by S.
Tor 7 p
oints.
TABLE 1.
[Page 519 |
Difference of Latitude and Departure for IJ Points.
N.
by E. i E.
N. by W. J \V. S. by
E. i E. S. by W. J W.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Diat.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.2
14.8
121
117.4
29.4
181
175.6
44.0
241
233.8
58.6
?
1.9
0.5
62
60.1
15.1
22
118.3
29.6
82
176.5
44.2
42
234.7
58.8
3
2.9
0.7
63
61.1
15.3
23
119.3
29.9
83
177.5
44.5
43
235. 7
.59.0
4
3.9
1.0
64
62.1
15.6
24
120.3
30.1
84
178.5
44.7
44
236.7
59.3
5
4.9
1.2
65
63.1
15.8
25
121.3
30.4
a5
179.5
45.0
45
237. 7
,59.5
6
5.8
1.5
66
64.0
16.0
26
122.2
30.6
86
180.4
45.2
46
238.6
59.8
7
6.8
1.7
67
65.0
16.3
27
123.2
30.9
87
181.4
45.4
47
239.6
60.0
H
7.8
1.9
68
66.0
16.5
28
124.2
.31.1
88
182.4
45.7
48
240.6
60.3
9
8.7
2.2
69
66.9
16.8
29
125.1
31.3
89
183.3
45.9
49
241.5
60.5
10
11
9.7
2.4
70
67.9
17.0
30
126.1
31.6
90
184.3
46.2
.50
242.5
243.5
60.7
10.7
2.7
71
68.9
17.3
131
127.1
31.8
191
185.3
46.4
251
61.0
^?.
11.6
2.9
72
69.8
17.5
32
128.0
32.1
92
186.2
46.7
52
244.4
61.2
13
12.6
3.2
73
70.8
17.7
33
129.0
,32.3
93
187.2
46.9
53
245.4
61.5
14
13.6
3.4
74
71.8
18.0
34
130.0
32.6
94
188.2
47.1
54
246.4
61.7
15
14.6
3.6
75
72.8
18.2
.35
131.0
32.8
95
189.2
47.4
no
247.4
62.0
16
15.5
3.9
76
73.7
18.5
.36
131.9
33.0
96
190.1
47.6
56
248.3
62.2
17
16.5
4.1
77
74.7
18.7
37
132.9
.33.3
97
191.1
47.9
57
249.3
62.4
18
17.5
4.4
78
75.7
19.0
38
133. 9
33.5
98
192.1
48.1
58
250.3
62.7
19
18.4
4.6
79
76.6
19.2
39
134.8
33.8
99
193.0
48.4
59
251.2
62.9
20
19.4
4.9
- 5.1
80
81
77.6
19.4
40
135.8
34.0
34.3
200
194.0
48.6
48.8
60
252.2
63.2
?.-!
20.4
78.6
19.7
141
136.8
201
195.0
261
253.2
63.4
?.?.
21.3
5.3
82
79.5
19.9
42
137.7
34.5
02
195.9
49.1
62
2.54. 1
63.7
23
22.3
5.6
83
80.5
20.2
43
138.7
34.7
03
196.9
49.3
63
255. 1
63.9
24
23.3
5.8
84
81.5
20.4
44
139.7
35.0
04
197.9
49.6
64
256.1
64.1
25
24.3
6.1
85
82.5
20.7
45
140.7
36.2
05
198.9
49.8
65
257.1
(W.4
26
25.2
6.3
86
83.4
20.9
46
141.6
35.5
06
199.8
50.1
66
258.0
64.6
27
26.2
6.6
87
84.4
21.1
47
142.6
.^5.7
07
200.8
50.3
67
2.59.
64.9
28
27.2
6.8
88
85.4
21.4
48
143.6
36.0
08
201.8
50.5
68
260.0
6.5.1
29
28.1
7.0
89
86.3
21.6
49
144.5
36.2
09
202.7
50.8
69
260.9
6,5.4
30
29.1
7.3
90
87.3
88.3
21.9
50
145. 5
36.4
10
203.7
51.0
70
261.9
65.6
31
30.1
7.5
91
22.1
151
146.5
36.7
211
204.7
51.3
271
262.9
65.8
32
31.0
7.8
92
89.2
22.4
52
147.4
36.9
12
205.6
51.5
72
263.8
66.1
a3
32.0
8.0
93
90.2
22.6
53
148.4
37.2
13
206.6
51.8
73
264.8
66.3
34
33.0
8.3
94
91.2
22.8
54
149.4
37.4
14
207.6
52.0
74
265.8
66.6
35
34.0
8.5
95
92.2
23.1
.55
150.4
.37.7
15
208.6
.52.2
75
266.8
66.8
36
34.9
8.7
96
93.1
23.3
56
151.3
37.9
16
209.5
.52. 5
76
267.7
67.1
37
9.0
97
94.1
23.6
57
152.3
38.1
17
210.5
.52.7
77
268.7
67.3
38
9.2
98
95.1
23.8
58
153. 3
.38.4
18
211.5
53.0
78
269.7
67.5
39
37.8
9.5
99
96.0
24.1
59
1.54. 2
38.6
19
212.4
53.2
79
270.6
67.8
40
41
38.8
9.7
100
97.0
24.3
60
155.2
38.9
20
213.4
53.5
80
271.6
68.0
68.3
39.8
10.0.
101
98.0
24.5
161
156.2
39.1
221
214.4
53.7
281
272.6
42
40.7
10.2
02
98.9
24.8
62
157.1
39.4
22
215.3
53.9
82
273. 5
68.5
43
41.7
10.4
03
99.9
25.0
63
158. 1
39.6
23
216.3
54.2
83
274.5
68.8
44
4^.7
10.7
04
100.9
25.3
64
159.1
.39.8
24
217.3
54.4
84
275.5
69.0
45
43.7
10.9
05
101.9
25.5
65
160.1
40.1
25
218. 3
.54.7
85
277.5
69.2
46
44.6
11.2
06
102.8
25.8
66
161.0
40.3
26
219.2
54.9
86
277.4
69.5
47
45.6
11.4
07
103.8
26.0
67
162.0
40.6
27
220.2
55.2
87
278.4
69.7
48
46.6
11.7
08
104.8
26.2
68
163.0
40.8
28
221.2
55.4
88
279.4
70.0
49
47.5
11.9
09
105.7
26.5
69
163.9
41.1
29
222.1
55.6
89
280.3
70.2
50
48.5
12.1
10
106.7
26.7
70
164.9
41.3
.30
231
223.1
55.9
90
281.3
70.5
51
49.5
12.4
111
107.7
27.0
171
165.9
41.5
224.1
56.1
291
282.3
70.7
52
50.4
12.6
12
108.6
27.2
72
166.8
41.8
32
225.0
56.4
92
283.2
71.0
53
51.4
12.9
13
109.6
27.5
73
167.8
42.0
33
226.0
56.6
93
284.2
71.2
54
52.4
1.3.1
14
110.6
27.7
74
168.8
42.3
34
227.0
56.9
94
285. 2
71.4
55
53.4
13.4
15
111.6
27.9
75
169.8
42.5
35
228.0
.57.1
95
286.2
71.7
56
54.3
13.6
16
112.5
28.2
76
170.7
42.8
,36
228.9
57.3
96
287.1
71.9
57
55.3
13.8
17
113. 5
28.4
77
171.7
43.0
37
229.9
57.6
97
288.1
72.2
58
56.3
14.1
18
114.5
28.7
78
172.7
43.3
38
230.9
57.8
98
289.1
72.4
59
57.2
14.3
19
115. 4
28.9
79
173.6
43.5
39
231.8
58.1
99
290.9
72.7
60
58.2
14.6
20
116.4
29.2
80
174.6
43.7
40
232.8
58.3
300
291.0
72.9
Diiit.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Di»t.
Dep.
Lat.
Dist.
Dep.
Lat.
E
NE. JE
E
?E. J E.
WNW. i W.
\
VSW. f w.
[For 61 P
oints.
Page 520]
TABLE 1.
Difference of Latitude and Departure for IJ Points.
N
. byE.
JE.
N. by
VV. i w.
S. by E. i E.
s.
by W. i W.
Dist.
Lnt.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. j Lat.
Dep.
1
:.o
0.3
61
58.4
17.7
121
115.8
35.1
181
173.2
52.5
241
230.6
70.0
2
1.9
0.6
62
59.3
18.0
22
116.7
35.4
82
174.2
52.8
42
231.6
70.2
3
2.9
0.9
63
60.3
18.3
23
117.7
35.7
83
175.1
63.1
43 i 232.5
70.5
4
3.8
1.2
64
61.2
18.6
24
118.7
36.0
84
176.1
53.4
44
233.5
70.8
5
4.8
1.5
65
62.2
18.9
25
119.6
36.3
85
177.0
53.7
45
234.5
71.1
6
5.7
1.7
66
63.2
19.2
26
120.6
36.6
86
178.0
54.0
46
235. 4
71.4
7
6.7
2.0
67
64.1
19.4
27
121.5
36.9
87
178.9
54.3
47
236.4
71.7
8
7.7
2.3
68
65.1
19.7
28
122.5
37.2
88
179.9
54.6
48
237.3
72.0
9
8.6
2.6
69
66.0
20.0
29
123.4
37.4
89
180.9
54.9
49
238.3
72.3
10
9.6
2.9
70
67.0
20.3
20.6
30
124.4
37.7
90
181. a
55.2
50
239.2
240.2
72.6
11
10.5
3.2
71
67.9
131
125. 4
38.0
191
182.8
55.4
251
72.9
12
11.5
3.5
72
68.9
20.9
32
126.3
38.3
92
183.7
5.5.7
52
241.1
73.2
13
12.4
3.8
73
69.9
21.2
33
127.3
38.6
93
184.7
56.0
53
242.1 ' 73.4
14
13.4
4.1
74
70.8
21.5
34
128.2
38.9
94
185.6
56.3
54
243.1 1 73.7
15
14.4
4.4
75
71.8
21.8
35
129.2
39.2
95
186.6
56.6
55
244.0 ; 74.0
16
15.3
4.6
76
72.7
22.1
36
130.1
39.5
96
187.6
56.9
■56
245. 74. 3
17
16.3
4.9
77
73.7
22.4
37
131.1
39.8
97
188.5
57.2
57
245. 9 74. 6
18
17.2
5.2
78
■74.6
22.6
38
132. 1
40.1
98
189.5
57. 5
58
246.9 i 74.9
19
18.2
5.5
79
75.6
22.9
39
133.0
40.3
99
190.4
57.8
59
247.8 1 75.2
20
19.1
5.8
80
76.6
23.2
40
134.0
134.9
40.6
200
191.4
58.1
60
248.8 1 75.5
249. 8 i 75. 8
21
20.1
6.1
81
77.5
23.5
141
40.9
201
192.3
58.3
261
22
21.1
6.4
82
78.5
23.8
42
135. 9
41.2
02
193.3
.58.6
62
250. 7 ' 76. 1
23
22.0
6.7
83
79.4
24.1
43
136.8
41.5
03
194.3
58.9
63
251.7 : 76.3
24
23.0
7.0
84
80.4
24.4
44
137.8
41.8
04
195. 2
59.2
64
2,52.6 76.6
25
23.9
7.3
So
81.3
24.7
45
138.8
42.1
05
196.2
59.5
65
2.53.6 1 76.9
26
24.9
7.5
86
82.3
25.0
46
139.7
42.4
06
197.1
59.8
66
254.5 [ 77.2
27
25.8
7.8
87
83.3
25.3
47
140.7
42.7
07
198.1
60.1
67
2.55. 5 :'7.b
28
26.8
8.1
88
84.2
25. 5
48
141.6
43.0
08
199.0
60.4
68
256. 5 i 77. 8
29
27.8
8.4
89
85.2
25.8
49
142.6
43.3
09
200.0
60.7
69
257. 4 : 78. 1
30
28.7
8.7
90
86.1
26.1
50
143. 5
43.5
10
201.0
61.0
70
258.4 i 78.4
31
29.7
9.0
91
87.1
26.4
151
144.5
43.8
211
201.9
61.3
271'
259. 3 : 78. 7
32
30.6
9.3
92
88.0
26.7
52 ; 145.5
44.1
12
202.9
61.5
72
260.3 ' 79.0
33
31.6
9.6
93
89.0
27.0
53 1 146.4
44.4
13
203.8
61.8
73
261.2 i 79.2
34
32.5
9.9
94
90.0
27. 3
54 1 147.4
44.7
14
204.8
62.1
74
262. 2 i 79. 5 .
35
33.5
10.2
95
90.9
27.6
55 1 148.3
45.0
15
205.7
62.4
75
263.2 1 79.8
36
34.4
10.5
96
91.9
27.9
56
149. 3
45.3
16
206.7
62.7
76
264.1
80.1
37
35.4
10.7
97
92.8
28.2
57
150. 2
45.6
17
207.7
63.0
77
265.1
266.(7
80.4
38
36.4
11.0
98
93.8
28.4
58
151.2
45.9
18
208.6
63.3
78
80.7
39
37.3
11.3
99
94.7
28.7
59
152. 2
46.2
19
209.6
63.6
79
267.0 ; 81.0
40
38.3
11.6
100
95.7
29.0
60
153.1
46.4
20
221
210.5
63.9
80
267.9 1 81.3
41
39.2
11.9
101
96.7
29.3
161
154.1
46.7
211.5
64.2
281
268.9 1 81.6
42
40.2
12.2
02
97.6
29.6
62
155.0
47.0
22
212.4
64.4
82
269.9 81.9
43
41.1
12.5
03
98.6
29.9
63 : 156.0
47.3
23
213.4
64.7
83
270.8 1 82.2
44
42.1
12.8
04
99.5
30.2
64 i 1.56.9
47.6
24
214.4
6.5.0
84
271.8 1 82.4
46
43.1
13.1
05
100.5
30.5
65 ; 157.9
47.9
25
215. 3
6.5.3
85
272.7 ' 82.7
46
44.0
13.4
06
101.4
30.8
66 i 1.58.9
48.2
26
216. 3
65.6
86
273.7 i 83.0
47
45.0
13.6
07
102.4
31.1
67 , 159.8
48.5
27
217.2
65.9
87
274. 6 1 83. 3
48
45.9
13.9
08
103.3
31.4
68 ; 160.8
48.8
28
218.2
66.2
88
275.6
83.6
49
46.9
14.2
09
104.3
31.6
69 i 161.7
49.1
29
219.1
66.5
89
276.6
83.9
50
51
47.8
14.5
10
105.3
31.9
3"2. 2 '
70 1 162. 7
171 ! 163.6
49.3
30
220.1
66.8
90
277.5
84.2
48.8
14.8
111
106.2
49.6
231
221.1
67.1
291
278.5 1 84.5 1
52
49.8
15.1
12
107.2
32. 5
72 ! 164.6
49.9
32
222.0
67.3
92 j 279. 4 i 84. 8 I
53
50.7
15.4
13
108.1
32.8
73 i ia5.6
.50.2
33 ' 223.0
67.6
93 ! 280. 4
85.1
54
51.7
15.7
14
109.1
.33.1
74 \ 166.5
.50.5
34 i 223.9
67.9
94 ; 281.3
85. 3
55
52.6
16.0
15
110.0
33.4
75 1 167.5
50.8
35
224.9
68.2
95 1 282.3
85.6
56
53.6
16.3
16
111.0
33.7
76 i 168. 4
51.1
36
225.8
68.5
96 1 283.3
85.9
57
54.5
16.5
17
112.0
34.0
77 ! 169.4
51.4
37
226.8
68.8
97 1 284.2
86.2
58
55.5
16.8
18
112.9
34.3
78
170.3
51.7
38
227.8
69.1
98
285.2
86.5
59
56.5
17.1
19
113.9
34.5
79
171.3
52.0
39
228.7
69.4
99
286.1
86.8
60
57.4
17.4
20
114.8
34.8
80
172.2
52.3
40
229.7
69.7
300
287.1
87.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. 1 Dep.
Lat.
Dist,
Dep.
Lat.
Dist.
Dep.
Lat.
E^
IE. i E.
ESI
^. * E.
AVNW. * W.
W8W. i \\
[For 6J Points, j
TABLE 1.
[Page
621
Difference of Latitiu
e and Departure for If Points.
y. by
E. JE.
N. by
w. 1
W. S. by
E. J E. .
S. by W. 1 W.
Dist.
ijit.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.3
61
57.4
20.6
121
113.9
40.8
181
170.4
61.0
241
226.9
81.2
2
1.9
0.7
62
58.4
20.9
22
114.9
41.1
82
171.4
61.3
42
227.9
81.5
3
2.8
1.0
63
59.3
21. 2
23
115.8
41.4
83
172.3
61.7
43 228.8
81.9
4
3.8
1.3
64
60.3
2l!6
24
116.8
41.8
84
173.2
62.0
44 : 229. 7
82.2
5
4.7
1.7
65
61.2
21.9
25
117.7
42.1
85
174.2
62.3
45 230. 7
82. 5
6
5.6
2.0
66
62.1
22. 2
26
118.6
42.4
86
175.1
62.7
46 ; 231.6
,H2. 9
7
6.6
2.4
67
63.1
22! 6
27
119.6
42.8
87
176.1
63.0
47 232. 6
83.2
8
7.5
2.7
68
64.0
22.9
28
120.5
43.1
88
177.0
63.3
48 : 233.5
83. 5
9
8.5
3.0
69
65.0
23.2
29
121.5
43.5
89
178.0
63.7
49 234. 4
83. 9
10
9.4
3.4
70
65.9
23.6
30
122.4
123. 3^
43.8
44.1
90
191
178.9
64.0
50
235.4
236. 3
84.2
84. 6
11
10.4
3.7
71
66.8
23.9
131
179.8
64.3
251
12
11.3
4.0
72
67.8
24.3
32
124.3
44.5
92
180.8
64.7
,52 237.3
84.9
13
12.2
4.4
73
68.7
24.6
33
125.2
44.8
93
181.7
65.0
,53 i 238.2
85.2
14
13.2
4.7
74
69.7
24.9
34
126.2
4.5.1
94
182.7
65.4
54 1 239.2
85. 6
15
14.1
5.1
75
70.6
25.3
35
127.1
4.5.5
95
183.6
65.7
55 : 240.1
85. 9
16
15. 1
5.4
76
71.6
25.6
36
128.0
4.5.8
96
184.5
66.0
56
241.0
86. 2
17
16.0
5.7
77
72.5
25.9
37
129.0
46.2
97
185.5
66.4
57
242.
86. 6
18
16.9
6.1
78
73.4
26.3
38
129. 9
46.5
98
186.4
66.7
58
242. 9
86. 9
19-
17.9
6.4-
79
74.4
26.6
39
130.9
46.8
99
187.4
67.0
59
243. 9
87.3
20
21
18.8
19.8
6.7
80
75.3
27.0
40
131.8
132.8
47.2
47. 5"
200
188.3
67.4
60
261
244. 8
245.7"
.S7.6
87.9
7.1
81
76.3
27.3
141
201
189.3
67.7
22
20.7
7.4
82
77.2
27.6
42
133.7
47.8
02
190.2
68.1
62
246.7
88.3
23
21.7
7. 7
83
78.1
28.0
43
134.6
48.2
03
191.1
68.4
63 i 247.6
88.6
24
22.6
8.1
84
79.1
28.3
44
135. 6
48.5
04
192.1
68.7
64 248.6
88.9
25
23.5
8.4
85
80.0
28.6
45
136. 5
48.8
05
193.0
69.1
65 : 249.5
89.3
26
24.5
8.8
86
81.0
29.0
46
137. 5
49.2
06
194.0
69.4
66 2.50.5
89.6
27
25.4
9.1
87
81.9
29.3
47
138. 4
49.5
07
194.9
69.7
67 i 251.4
89.9
28
26.4
9.4
88
82.9
29. 6
48
139. 3
49.9
08
195.8
70.1
68 ' 2.52.3
90.3
29
27.3
9.8
89
8.3.8
30.0
49
140. 3
,50.2
09
196.8
70.4
69 253. 3
90.6
30
28.2
10.1
90
84.7
30.3
50
151
141.2
142. 2
,50. 5
.50. 9
10
197.7
198.7
70.7
70 254. 2
271 2,5,5.2
91.0
91.3
31
29.2
10.4
91
8.5.7
30.7
211
71.1
32
30.1
10.8
92
86.6
31.0
52
143. 1
51.2
12
199.6
71.4
72 256. 1
91.6
33
31.1
11.1
93
87.6
31. 3
,53
144.1
51. 5
13
200.5
71.8
73 ; 2,57.0
92.0
34
32.0
11.5
94
88.5
31.7
54
145.
51.9
14
201.5
72.1
74 ' 2.58.0
92. 3
35
33.0
11.8
95
89.4
32.0
55
145. 9
,52.2
15
202. 4
72.4
75 ' 258.9
92.6
36
.33.9
12.1
96
90.4
32. 3
,56
146. 9
,52. 6
16
203.4
72.8
76 1 2.59.9
93.
37
34.8
12.5
97
91.3
32.7
57
147.8
52. 9
17
204. 3
73. 1
77
260.8
93. 3
38
35.8
12.8
98
92.3
33.0
58
148.8
,53.2
18
205. 3
73.4
78
261.7
93. 7
39
,36. 7
13.1
99
93.2
33.4
59
149.7
53. 6
19
206. 2
73.8
79
262.7
94.0
40
37.7
13.5
100
94.2
33.7
60
150. 6
53. 9
20
207.1
74.1
80
263.6
94.3
41
38.6
13.8
101
95.1
34.0
161
151. 6
54. 2
221
208.1
74.5
281
264.6
94.7
42
39.5
14.1
02
96.0
34.4
62
152.5
54.6
22
209.0
74.8
•82
265.5
95.0
43
40.5
14.5
03
97.0
34.7
63
153. 5
54.9
23
210.0
75.1
83
266.5
95.3
44
41.4
14.8
04
97.9
35.0
64
154.4
5,5.2
24
210. 9
75.5
84
267.4
95. 7
45
42.4
15.2
05
98.9
3.5.4
65
15.5. 4
5,5.6
25
211.8
75.8
85
268.3
96.0
46
43.3
15.5
06
99.8
35.7
66
1.56. 3
,55. 9
26
212.8
76.1
86
269.3
96.4
47
44.3
15.8
07
100.7
36.0
67
157.2
56.3
27
213. 7
76.5
87
270.2
96.7
48
4.1.2
16.2
08
101.7
.36.4
68
1.58. 2
56. 6
28
214.7
76.8
88
271.2
97.0
49
46.1
16.5
09
102.6
36.7
69
1.59. 1
.56.9
29
21.5. 6
77.1
89
272.1
97.4
50
51
47.1
48.0^
16.8
17."2"
10
103.6
37.1
70
160.1
161.0
57.3
30
216.6
77.5
90
273.0
97.7
98.0
111
104.5
37.4
171
.57.6
231
217. 5
77.8
291
274.0
52
49.0
17.5
12
105. 5
37.7
72
161.9
57.9
32
218. 4
78.2
92 : 274.9
98.4
53
49.9
17.9
13
106.4
,38.1
73
162.9
58.3
33
219.4
78.5
93 ! 275.9
98.7
54
50.8
18.2
14
107.3
38.4
74
163. 8
.58.6
34
220.3
78.8
94
276.8
99.0
55
51.8
18.5
15
108.3
38.7
75
164.8
59.0
35
221.3
79.2
95
277.8
99.4
56
52.7
18.9
16
109.2
39.1
76
165.7
.59.3
36
222.2
79.5
96
278.7
99. 7
57
53.7
19.2
17
110.2
39.4
77
166.7 1 .59.6
37
223! 1
79.8
97
279. 6
100.1
58
54.6
19.5
18
111.1
39.8
78
167.6
60.0
38
224.1
80.2
98
280.6
100.4
59
55.6
19.9
19
112.0
40.1
79
168. 5
60.3
,39
225.0
80.5
99
281.5
100.7
60
56.5
20.2
20
113.0
40.4
80
169.5
60.6
40
226.0
80.9
300
282. 5
101.1
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
ENE. i
E.
]
?SE. J I
]^
^^
rNW. i W.
A
VSW. }
W.
[For 6J Po
int>?.
Page 522]
TABLE 1.
Differenc 3 of Latitude and Departure for
2 Points.
NNE.
.
NNW.
SSE.
ssw.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.4
23.3
121
111.8
46.3
181
167.2
69.3
241
222.7
92.2
9
1.8
0.8
62
57.3
23.7
22
112.7
46.7
82
168.1
69.6
42
223.6
92.6
3
2.8
1.1
63
58.2
24.1
23
113.6
47.1
83
169.1
70.0
43
224.5
93.0
4
3.7
1.5
64
59.1
24.5
24
114.6
47.5
84
170.0
70.4
44
225. 4
93.4
5
4.6
1.9
65
60.1
24.9
25
115.5
47.8
85
170.9
70.8
45
226.4
93.8
6
5.5
2.3
66
61.0
2.5.3
26
116.4
48.2
86
171.8
71.2
46
227.3
94.1
7
6.5
2.7
67
61.9
25.6
27
117.3
48.6
87
172.8
71.6
47
228.2
94.5
8
7.4
3.1
68
62.8
26.0
28
118.3
49.0
88
173.7
71.9
48
229.1
94.9
9
8.3
3.4
69
63.7
26.4
29
119.2
49.4
89
174.6
72.3
49
230.0
95.3
10
9.2
3.8
70
64.7
65.6
26.8
27.2
30
131
120.1
121.0
49.7
50.1
90
191
175. 5
72.7
50
231.0
95.7
11
10.2
4.2
71
176.5
73.1
251
231.9
96.1
12
11.1
4.6
72
66.5
27.6
32
122.0
50.5
92
177.4
73.5
,52
232.8
96.4
13
12.0
5.0
73
67.4
27.9
33
122.9
50.9
93
178. 3
73.9
53
233.7
96.8
14
12.9
5.4
74
68.4
28.3
34
123.8
51.3
94
179.2
74.2
54
234.7
97.2
15
13.9
5.7
75
69.3
28.7
35
124.7
51.7
95
180.2
74.6
55
235.6
97.6
16
14.8
6.1
76
70.2
29.1
36
125.6
52.0
96
ISl.l
75.0
56
236.5
98.0
17
15.7
6.5
77
71.1
29.5
37
126.6
52.4
97
182.0
75.4
57
237.4
98.3
18
16.6
6.9
78
72.1
29.8
38
127. 5
52.8
98
182.9
75.8
58
238.4
98.7
19
17.6
7.3
79
73.0
30.2
.39
128.4
53.2
99
183.9
76.2
•59
239.3
99.1
20
18.5
7.7
80
73.9
30.6
40
129.3
53.6
54.0
200
184.8
185. 7
76.5
60
240.2
99.5
21
19.4
8.0
81
74.8
31.0
141
130.3
201
76.9
261
241.1
99.9
22
20.3
8.4
82
75.8
31.4
42
131.2
54.3
02
186.6
77.3
62
242.1
100.3
23
21.2
8.8
83
76.7
31.8
43
132.1
54.7
03
187.5
77.7
63
243.0
100.6
24
22.2
9.2
84
77.6
32.1
44
133.0
55.1
04
188.5
78.1
64
243.9
101.0
2.5
23.1
9.6
85
78.5
32.5
45
134.0
55.5
05
189.4
78.0
65
244.8
101.4
26
24.0
9.9
86
79.5
32.9
46
134. 9
55.9
06
190.3
78.8
66
245.8
101.8
27
24.9
10.3
87
80.4
33.3
47
135. 8
56.3
07
191.2
79.2
67
246.7
102.2
28
25.9
10.7
88
81.3
33.7
48
136.7
56.6
08
192.2
79.6
68
247.6
102.6
29
26.8
11.1
89
82.2
34.1
49
137.7
57.0
09
193.1
80.0
69
248.5
102.9
30
27.7
11.5
90
83.1
34.4
50
138.6
57.4
10
194.0
80.4
80.7
70
249.4
103.3
31
28.6
11.9
91
84.1
34.8
151
139.5
57.8
211
194.9
271
250.4
103.7
32
29.6
12.2
92
85.0
35.2
52
140.4
58.2
12
195.9
81.1
72
251.3
104.1
33
30.5
12.6
93
85.9
35.6
53
141.4
.58.6
13
196.8
81.5
73
252.2
104.5
34
,31.4
13.0
94
86.8
36.0
.54
142.3
58.9
14
197.7
81.9
74
253. 1
104.9
35
32.3
13.4
95
87.8
36.4
55
143.2
,59.3
15
198.6
82.3
75
254.1
105.2
36
33.3
13.8
96
88.7
36.7
56
144.1
59.7
16
199.6
82.7
76
255.
105.6
37
34.2
14.2
97
89.6
37.1
57
145.0
60.1
17
200.5
83.0
77
255. 9
106.0
38
35.1
14.5
98
90.5
37.5
58
146.0
60.5
18
201.4
83.4
78
256.8
106.4
39
36.0
14.9
99
91.5
37.9
59
146.9
60.8
19
202.3
83.8
79
257.8
106.8
40
37.0
15.3
100
92.4
38.3
60
147.8
148.7
61.2
20
221
203.3
84.2
80
258.7
259.6
107.2
41
37.9
15.7
101
93.3
38.7
161
61.6
204.2
84.6
281
107.5
42
38.8
16.1
02
94.2
39.0
62
149.7
62.0
22
205.1
85.0
82
260. 5
107.9
43
39.7
16.5
03
95.2
39.4
63
150.6
62.4
23
206.0
85.3
83
261.5
108.3
44
40.7
16.8
04
96.1
39.8
64
151.5
62.8
24
206.9
85.7
84
262.4
108.7
45
41.6
17.2
05
97.0
40.2
65
152.4
63.1
25
207.9
86.1
85
263.3
109.1
46
42.5
17.6
06
97.9
40.6
66
153.4
63.5
26
208.8
86.5
86
264.2
109.4
47
43.4
18.0
07
98.9
40.9
67
154.3
63.9
27
209.7
86.9
87
265.2
109.8
48
44.3
18.4
08
99.8
41.3
68
155.2
64.3
28
210.6
87.3
88
266.1
110.2
49
45.3
18.8
09
100.7
41.7
69
156.1
64.7
29
211.6
87.6
89
267.0
110.6
50
51
46.2
19.1
10
101.6
42.1
70
157.1
158.0
65.1
30
212.5
88.0
90
267.9
111.0
47.1
19.5
111
102.6
42.5
171
65.4
231
213.4
88.4
291
268.8
111.4
52
48.0
19.9
12
103.5
42.9
72
158.9
65.8
32
214.3
88.8
92
269.8
111.7
53
49.0
20.3
13
104.4
43.2
73
159.8
66.2
33
215.3
89.2
93
270.7
112.1
54
49.9
20.7.
14
105.3
43.6
74
160.8
66.6
34
216.2
89.5
94
271.6
112.5
55
50.8
21.0
15
106.2
44.0
75
161.7
67.0
35
217.1
89.9
95
272.5
112.9
56
51.7
21.4
16
107.2
44.4
76
162.6
67.4
36
218.0
90.3
96
273.5
113.3
57
52.7
21.8
17
108.1
44.8
77
163. 5
67.7
37
219.0
90.7
97
274.4
113.7
58
53.6
22.2
18
109.0
45.2
78
164.5
68.1
38
219.9
91.1
98
275.3
114.0
59
54.5
22.6
19
109.9
45.5
79
165.4
68.5
39
220.8
91.5
99
276.2
114.4
60
55.4
23.0
20
110.9
45.9
80
166.3
68.9
40
221.7
91.8
300
277.2
114.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat,
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
ENE.
ESE.
WNW
WSW
[F
or 6 Poi
nts.
TABLE 1.
[Page 523 j
Difference of Latitude and Departure for 2i Points.
NNE
iE.
NNW
. i AV. SSE.
iE.
ssw.
iW.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
55.1
26.1
121
109.4
51.7
181
163.6
77.4
241
217.9
103.0
2
1.8
0.9
62
56.0
26.5
22
110.3
.52.2
82
164.5
77.8
42
218.8
103.5
3
2.7
1.3
63
57.0
26.9
23
111.2
.52.6
83
165.4
78.2
43
219.7
103.9
4
3.6
1.7
64
57.9
27.4
24
112.1
53.0
84
166.3
78.7
44
220.6
104.3
5
4.5
2.1
65
58.8
27.8
25
113.0
53.4
85
167.2
79.1
45
221.5
104.8
6
5.4
2.6
66
59.7
28.2
26
113.9
53.9
86
168.1
79.0
46
222.4
105.2
7
6.3
3.0
67
60.6
28.6
27
114.8
54.3
87
169.0
80.0
47
223.3
105.6
8
7.2
3.4
68
61.5
29.1
28
115.7
54.7
88
169.9
80.4
48
224.2
106.0
9
8.1
3.8
69
62.4
29.5
29
116.6
55. 2
89
170.9
80.8
49
225.1
106.5
10
11
9.0
4.3
70
71
63.3
29.9
30
117. 5
118. 4"
55.6
90
171.8
81.2
50
251
226.0
226.9
106.9
107.3
9.9
4.7
64.2
30.4
131
56.0
191
172.7
81.7
12
10.8
5.1
72
65.1
30.8
32
119.3
56.4
92
173.6
82.1
52
227.8
107.7
13
11.8
5.6
73
66.0
31.2
33
120.2
56.9
93
174.5
82.5
53
228.7
108.2
14
12.7
6.0
74
66.9
31.6
34
121.1
57.3
94
175.4
82.9
54
229.6
108.6
15
13.6
6.4
75
67.8
32.1
35
122.0
57. 7
95
176.3
83.4
55
230.5
109.0
16
14.5
6.8
76
68.7
32.5
,36
122.9
58.1
96
177.2
83.8
56
231. 4
109.5
17
15.4
7.3
77
69.6
32.9
37
12,3.8
58.6
97
178.1
84.2
57
232. 3
109.9
18
16.3
7. 7
78
70.0
3,3.3
38
124.8
59.0
98
179.0
84.7
58
233.2
110.3
19
17.2
8.1
79
71.4
.33.8
39 125. 7
59.4
99
179.9
85.1
59
234.1
110.7
20
21
18.1
8.6
80
72.3
73.2
34.2
40 126. 6
59.9
60.3
200
180.8
85.5
60
235.0
235.9
111.2
19.0
9.0
81
34.6
141 127. 5
201
181.7
85.9
261
111.6
22
19.9
9.4
82
74.1
35.1
42 128. 4
60.7
02
182.6
86.4
62
236.8
112.0
23
20.8
9.8
83
75.0
35.5
43 129. 3
61.1
03
183.5
86.8
63
237.7
112.4
24
21.7
10.3
84
75.9
35.9
44 130. 2
61. 6
04
184.4
87.2
64
238.7
112.9
25
22.6
10.7
85
76.8
36.3
45 I 131. 1
62.0
05
185.3
87.6
65
239.6
113. 3
26
23.5
11.1
86
77.7
36.8
46
132.0
62.4
06
186.2
88.1
66
240.5
113.7
27
24.4
11.5
87
78.6
37.2
47
132.9
62.9
07
187.1
88.5
67
241.4
114.2
28
25.3
12.0
88
79.6.
37.6
48
133.8
63.3
08
188.0
88.9
68
242. 3
114.6
29
26.2
12.4
89
80.5
38.1
49
1,34.7
63.7
09
188.9
89.4
69
243.2
115.0
30
27.1
12.8
90
81.4
82.3
.38.5
50
135.6
64.1
64.6
10
189.8
89.8
70
244.1
115.4
31
28.0
13.3
91
38.9
151
136.5
211
190.7
90.2
271
245.0
115.9
32
28.9
13.7
92
83.2
39.3
52
137. 4
65.0
12
191.6
90.6
72
245.9
116.3
33
29.8
14.1
93
84.1
39.8
53
138. 3
65.4
13
192.5
91.1
73
246.8
116.7
34
30.7
14.5
94
85.0
40.2
54
139.2
6,5.8
14
193.5
91.5
74
247. 7
117.2
35
31.6
15.0
95
85.9
40.6
55
140.1
66.3
15
194.4
91.9
75
248.6
117.6
36
32.5
15.4
96
86.8
41.0
.56
141.0
66.7
16
195.3
92.4
76
249. 5
118.0
37
33.4
15.8
97
87.7
41.5
57
141.9
67.1
17
196.2
92.8
77
250.4
118.4
38
34.4
16.2
98
88.6
41.9
58
142.8
67.6
18
197.1
93.2
78
251.3
118.9
39
35.3
16.7
99
89.5
42.3
59
143.7
68.0
19
198.0
93.6
79
252. 2
119.3
40
41
36.2
37.1
17.1
100
90.4
42.8
60
144.6
14,5. 5
68.4
20
198.9
94.1
80
253.1
254.
119.7
120.1
17.5
101
91.3
43.2
161
68.8
221
199.8
94.5
281
42
38.0
18.0
02
92.2
43.6
62
146. 4
69.3
22
200.7
94.9
82
254.9
120.6
43
38.9
18.4
03
93.1
44.0
63
147.4
69.7
23
201.6
95.3
83
255. 8
121.0
44
39.8
18.8
04
94.0
44.5
64
148.3
70.1
24
202.5
95.8
84
256.7
121.4
45
40.7
19.2
05
94.9
44.9
65
149.2
70.5
25
203.4
96.2
85
257. 6
121.9
46
41.6
19.7
06
95.8
45.3
66
150.1
71.0
26
204.3
96.6
86
258.5
122.3
47
42.5
20.1
07
96.7
45.7
67
151.0
71.4
27
205. 2
97.1
87
259. 4
122.7
48
43.4
20.5
08
97.6
46.2
68
151.9
71.8
28
206.1
97.5
88
260. 3
123.1
49
44.3
21.0
09
98.5
46.6
69
152.8
72.3
29
207.0
97.9
89
261.3
123.6
50
45.2
21.4
21.8
10
111
99.4
100.3
47.0
70
153.7
154. 6
72.7
30
207.9
98.3
90
262.2
263.1
124.0
124.4
51
46.1
47.5
171
73.1
231
208.8
98.8
291
52
47.0
22.2
12
101.2
47.9
72
155. 5
73.5
32
209.7
99.2
92
264.0
124.8
53
47.9
22.7
13
102.2
48.3
73
156.4
74.0
33
210.6
99.6
93
264.9
125.3
54
48.8
23.1
14
103.1
48.7
74
157.3
74.4
34
211.5
100.0
94
266.8
125.7
55
49.7
23.5
15
104.0
49.2
75
1.58. 2
74.8
35
212.4
100.5
95
266.7
126.1
56
50.6
23.9
16
104.9
49.6
76
159.1
7.5.2
36
213.3
100.9
96
267.6
126.6
57
51.5
24.4
17
105.8
50.0
77
160.0
75.7
37
214.2
101.3
97
268.5
127.0
58
52.4
24.8
18
106.7
50.5
78
160.9
76.1
38
215.1
101.8
98
269.4
127.4
59
53.3
25.2
19
107.6
50.9
79
161.8
76.5
39
216.1
102.2
99
270. 3
127.8
60
54.2
2.5.7
20
108.5
51.3
80
162.7
77.0
40
217.0
102.6
300
271.2
128.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NI
:. by E.
IE.
SI
:. by E. f E.
NW. by W. 1 W.
sw
. by W.
JW.
U
For 5| P
ointe.
j
Page 524]
TABLE 1.
Bifterence of Latitude and Departure for 2J Points.
NNE
. iE.
NNW
. i w.
SSE
} E. SSW
JW.
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
53.8
28.8
121
106.7
57.0
181
159.6
85.'3
241
212.5
113.6
2
1.8
0.9
62
54.7
29.2
22
107.6
57.5
82
160. 5
85.8
42
213.4
114.1
3
2.6
1.4
63
55.6
29.7
23
108.5
58.0
83
161.4
86.3
43
214.3
114.5
4
3.5
1.9
64
56.4
30.2
24
109.4
58.5
84
162. 3
86.7
44
215.2
115.0
5
4.4
2.4
65
57.3
30.6
25
110.2
58.9
85
163.2
87.2
45
216.1
115.0
6
5.3
2.8
66
58.2
31.1
26
111.1
59.4
86
164.0
87.7
46
217.0
' 116.0
7
6.2
3.3
67
59.1
31.6
27
112.0
59.9
87
164.9
88.2
47
217.8
116.4
8
7.1
3.8
68
60.0
32.1
28
112. 9
60.3
88
165.8
88.6
48
218.7
116.9
9
7.9
4.2
69
60.9
32.5
29 ' 113.8
60.8
89
166.7
89.1
49
219.6
117.4
10
8.8
4.7
5.2
70
71
61.7
62.6"
33.0
30
114.6
115.5
61.3
61.8
90
191
167.6
89.6
90.0
50
251
220.5
221. 4
117.8
118.3
n
9.7
33.5
131
168.4
12
10.6
5.7
72
63.5
33.9
32 116.4
62.2
92
169. 3
90.5
52
222. 2
118.8
13
11.5
6.1
73
64.4
34.4
33 117.3
62.7
93
170.2
91.0
53
223.1
119.3
14
12.3
6.6
74
65.3
34.9
34 118.2
63.2
94
171.1
91. 5
54
224.0
119.7
15
13.2
7.1
10
66.1
35.4
35 j 119.1
63.6
95
172.0
91.9
55
224.9
120.2
16
14.1
7.5
76
67.0
35.8
36
119.9
64.1
96
172.9
92.4
56
225. 8
120.7
17
15.0
8.0
77
67.9
36.3
37
120.8
64.6
97
173.7
92.9
57
226.7
121.1
18
15.9
8.5
78
68.8
36.8
38
121.7
65.1
98
174. 6
93. 3
58
227.5
121. 6
19
16.8
9.0
79
69.7
37.2
39
122.6
65.5
99
175.5
93.8
59
228.4
1 122. 1
20
17.6
9.4
80
70.6
37.7
40
123.5
66.0
200
201
176.4
94.3
60
229. 3
' 122.6
21
18.5
9.9
81
71.4
38.2
141 1 124.4
66.5
,177.3
94.8
261
330. 2
123.0
22
19.4
10.4
82
72.3
38.7
42
125. 2
66.9
02
178.1
9.0.2
62
2.31.1
123.5
23
20.3
10.8
83
73.2
39.1
43
126. 1
67.4
03
179.0
95. 7
63
231.9
124,0
24
21.2
11.3
84
74.1
39.6
44
127.0
67.9
04
179. 9
96. 2
64
232. 8
124.4
25
22.0
11.8
85
75.0
40.1
45 127. 9
68.4
05
180.8
96. 6
65
233. 7
124.9
26
22.9
12.3
86
75.8
40.5
46
128.8
68.8
06
181.7
97.1
66
234.6
125. 4
27
23.8
12.7
87
76.7
41.0
47
129.6
69.3
07
182.6
97.6
67
235.0
125.9
28
24.7
13.2
88
77.6
41.5
48
130.5
69.8
08
183. 4
98.1
68
236.4
126. 3
29
25.6
13.7
89
78.5
42.0
49
131.4
70.2
09
184.3
98.5
69
237. 2
126. 8
30
26.5
14.1
90
91
79.4
80.3
42.4
50
151
132.3
133. 2
70.7
10
185.2
99.
70
238.1
239.
127.3
31
27.3
14.6
42.9
71.2
211
186.1
99.5
271
127. 7
32
28.2
15.1
92
81.1
43.4
52
134. 1
71.7
12
187.0
99.9
72
239.9
128.2
33
29.1
15.6
93
82.0
43.8
53
134.9
72.1
13
187. 8
100.4
73
240.8
128.7
34
30.0
16.0
94
82.9
44.3
54
135.8
72.6
14
188.7
100. 9
74
241.6
129. 2
35
30.9
16.5
95
83.8
44.8
00
136. 7
73.1
15
189. 6
101.4
75
242. 5
129. 6
36
31.7
17.0
96
84.7
45.3
56
137.6
73.5
16
190. 5
101.8
76
243. 4
130. 1
37
32.6
17.4
97
85.5
45.7
0/
138.5
74.0
17
191.4
102.3
77
244. 3
130.6
38
33.5
17.9
98
86.4
46.2
58
139. 3
74.5
18
192.3
102.8
78
245.2
131.0
39
;«.4
18.4
99
87.3
46.7
59
140.2
75.0
19
193.1
103.2
79
246.1
131.5
40
35.3
18.9
100
88.2
47.1
60
141.1
75.4
20
221
194.
194.9
103. 7
80
246.9
132.
41
36.2
19.3
101
89.1
47.6
161
142.0
75.9
104. 2
281
247.8
132. 5
42
37. ' 19. 8
02
90.0
48.1
62
142.9
76.4
22
195.8
104.7
82
248.7
132. 9
43
37. 9 20. 3
03
90.8
48.6
63
143.8
76.8
23
196.7
105. 1
83
249.6
133. 4
44
38. 8 i 20. 7
04
91.7
49.0
64
144.6
77.3
24
197.6
105. 6
84
250. 5
133. 9
45
39.7 1 21.2
05
92.6
49.5
65
145. 5
77.8
25
198.4
106.1
85
251. 3
1.34.3
46
40. 6 : 21. 7
06
93.5
50.0
66
146.4
78.3
26
199.3
106.5
86
252.2
134. 8
47
41.5 22.2
07
94.4
50.4
67
147.3
78.7
27
200.2
107.
87
253.1
135. 3
48
42.3 22.6
08
95.2
50.9
68
148.2
79.2
28
201.1
107.5
88
254.
135. 8
49
43. 2 23. 1
09
96.1
51.4
69
149.0
79.7
29
202.0
107.9
89
254. 9
136.2
50
44. 1 i 23. 6
10
97.0
51.9
70
149.9
80.1
30
202.8
203. 7
108.4
108.9
90
255. 8
256.6
136.7
137.2
51
45.0 I 24.0
111
97.9
52.3
171
150. 8
80.6
231
291
52
45.9 24.5
12
98.8
52.8
72
151.7
81.1
32
204.6
109. 4
92
257. 5
137.6
53
46.7 25.0
13
99.7
53.3
73
152.6
81.6
33
205.
109.8
93
258.4
138.1
54
47.6 1 25.5
14
100.5
53.7
74
153. 5
82.0
34
206. 4
110.3
94
259. 3
1.38.6
55
48.5 25.9
15
101.4
54.2
10
154.3
82.5
35
207. 3
110.8
95
260.2
139.1
56
49. 4 1 26. 4
16
102.3
54.7
76
155.2
83.0
36
208.1
111.2
96
261.0
139.5
57
50.3 ! 26.9
17
103.2
55.2
1 /
156.1
83,4
37
209.
111.7
97
261.9
140.0
58
51.2 1 27.3
18
104.1
55.6
78
157.
83.9
38
209.9
112.2
98
262.8
140. 5
59
52.0
27.8
19
104.9
56.1
79
157. 9
84.4
39
210.8
112.7
99
263.7
140. 9
60
52.9
28.3
20
105.8
56.6
80
158. 7
84.9
40
211.7
113.1
300
264.6
141.4
Dlst.
Dep. Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat. |
Dist.
Dep.
Lat.
NE
. by E. i E.
SE
. by E. i E.
N\V. by W.
§AV.
SW. by W. J AV.
[I
V,,r 5} P
ointii.
TABLE 1.
[Page 525
Difference of Latitude and Departure for 2| Points.
NNE. i E.
NNW.
i W. SSE. J E. SSW. 1 W. j
Pist.
Lat. ! Dep.
Dist.
Lat. Dep. J
Dist.
Lat. j Dep. 1
Dist.
Lat. Dep.
Dist.
Lat. \ Dep. 1
1 ',
0.9 ' 0.5
61
52.3
31.4
121
103.8
62.2
181
155.2 ' 93.1
241
206.7
123.9
■2 '
1.7 ! 1.0
62
53.2
31.9,
22
104.6
62.7
82
156.1 1 93.6
42
207.6
124.4
3
2.6 i 1.5
63
54.0
32.4
23
105.5
63.2
83
157. 94. 1
43
208.4 i
124.9
4
3. 4 ' 2. 1
64
54.9
32.9
24
106.4
63.7
84
157.8 ; 94.6
44
209.3
125.4
5
4. 3 i 2. 6
65
55.8
33.4
25
107.2
64.3
85
158.7
95.1
45
210. 1 !
126.0
6
5.1 3.1
66
56.6
33.9
26 108. 1 ! 64. 8 1
86
159. 5
95.6
46 1
211.0
126.5
4
6. i 3. 6
67
57.5
34.4
27 i 108.9
65. 3
87
160.4
96.1
47
211.9
127.0
8
6.9 1 4.1
68
.58.3
3.5.0
28 1 109. 8
65.8
88
161.3
96.7
48
212. 7
127.5
9
7. 7 4. 6
69
59.2
35.5
29 110.6
66.3
89
162.1
97.2
49
213.6
128.0
10
8.6
5.1
70
60.0
36.0
30
111.5
66.8
90
163. 97. 7
163. 8 : 98. 2
50
251
214.-4
215.3 i
128.5
11
9.4
5.7
71
60.9
36.5
131
112.4
67.3
191
129.
12
10.3
6.2
72
61.8
37.0
32
113.2
67.9
92
164.7 ! 98.7
52
216.1
129.6
13
11.2
6.7
73
62.6
37.5
33
114.1
68.4
93
165.5 1 99.2
53
217.0 I
130. 1
14
12.0
7.2
74
63.5
38.0
34
114.9
68.9
94
166. 4 1 99. 7
.54
217.9
130.6
15
12.9
7.7
75
64.3
38.6
35
115. 8
69.4
95
167. 3 1
100.3
55
218.7
131. 1
16
13.7
8.2
76
65.2
39.1
36
116.7
69.9
96
168.1
100.8
56
219.6
131. 6
17
14.6
8.7
77
66.0
39.6
37
117.5
70.4
97
169.0
101.3
57
220.4
132. 1
18
15.4
9.3
78
66.9
40.1
38 118.4
70.9
98
169. 8
101.8
58
221.3
132. 6
19
16.3
9.8
79
67.8
40.6
39
119.2
71.5
99
170.7
102. 3
59
222.2
133.2
20
17.2
10.3
80
68.6
41.1
40
120.1
l20. 9
72.0
200
171.5
102.8
60
223.0
223. 9"
133. 7
134. 2
21
18.0
10.8
81
69.5
41.6
141
72.5
201
172.4
103.3
261
22
18.9
11.3
82
70.3
42.2
42
121.8
73.0
02
173.3
103. 8
62
224.7
134.7
23
19.7
11.8
83
71.2
42.7
43
122.7
73.5
03
174.1
104.4
63
225. 6
135.2
24
20.6
12.3
84
72.0
43.2
44
123.5
74.0
04
175.0
104.9
64
226.4
135. 7
25
21.4
12.9
85
72.9
43.7
45
124.4
74.5
05
175.8
105. 4
65
227.3
136. 2
26
. 22.3
13.4
86
73.8
44.2
46
125.2
75.1
06
176.7
105.9
66
228.2
136.8
27
23.2
13.9
87
74.6
44.7
47
126.1
75.6
07
177. 5
106.4
67
229.0
137.3
28
24.0
14.4
88
7.5.5
45.2
48
126. 9
76.1
08
178.4
106.9
68
229. 9
137.8
29
24.9
14.9
89
76.3
45.8
49
127.8
76.6
09 i 179.3
107.4
69
230.7
138. 3
30
31
25. 7 15. 4
90
77.2
46.3
50
128.7
77.1
10 1 180. 1
108.0
70
231.6
138.8
139.3
26.6
15.9
91
78.1
46.8
151 1 129.5
77.6
211
181.0
108.5
271
232. 4
32
27.4
16.5
92
78.9
47.3
52
130. 4
78.1
12
181.8
109.0
72
233. 3
139.8
33
28.3
17.0
93
79.8
47.8
53
131.2
78.7
13
182.7
l«t, 5
73
234. 2
140.4
34
29.2
17.5
94
80.6
48.3
.54
132.1
79.2
14
183. 6
110.0
74
235.
140.9
35
30.0
18.0
95
81.5
48.8
55
132.9
79.7
15
184.4
110.5
75
2.35.9 141.4
36
,30:9
18.5
96
82.3
49.4
56
133.8
80.2
16
185. 3
111.0
76
236.7 141.9
37
31.7
19.0
97
83.2
49.9
57
134.7
80.7
17
186.1
111.6
77
237.6 i 142.4
38
82.6
19.5
98
84.1
50.4
58
135.5
81. 2
18
187.
112. 1
78
238.4 142.9
39
33.5
20.1
99
84.9
50.9
59
1,36. 4
81.7
19
187.8
112.6
79
239. 3
143. 4
40
34.3
20.6
21.1
100
101
85.8
86.6
51.4
60
137.2
82.3
20 j 188. 7
221 1 189.6
113.1
113. 6
80
281
240.2
241.0
143. 9
"144. 5
41
35.2
51.9
161
138.1
82.8
42
36.0
21.6
02
87.5
52.4
62
139.0
83.3
22 1 190.4
114.1
82
241.9
145.
43
36.9
22.1
03
88.3
.53.0
63
139.8
83.8
23
191.3
114.6
83
242.7
145. 5
44
37.7
22.6
04
89.2
53. 5
64
140.7
84.3
24
192.1
115.2
84
243. 6
146.0
45
38.6
2,3.1
05
90.1
54.
65
141.5
84.8
25
193.
11.5, 7
85
244. 5
146.5
46
39.5
23.6
06
90.9
.54. 5
66
142.4
85.3
26
193.8
116.2
86
245. 3
147.
47
40.3
24.2
07
91.8
55.
67
143.2
8,5.9
27
194.7
116.7
87
246. 2
147.5
48
41.2
24.7
08
92.6
55. 5
68
144.1
86.4
28
195. 6
117.2
88
247.
148.1
49
42.0
25.2
09
93.5
56.0
69
145.0
86,9
29
196.4
117.7
89
247. 9
148.6
50
51
42.9
25.7
10
111
94.4
95. 2
56.6
"57. 1
70
171
145. 8
146. 7
87.4
30
197. 3
198.1
118.2
118. 8
90
291
248.7
149.1
149. 6
43.7
26.2
87.9
231
249. 6
52
44.6
26.7
12
96.1
.57.6
72
147. 5
88.4
32
199.0
119.3
92
250. 5
150.1
53
45.5
27.2
13
96.9
.58. 1
73
148.4
88.9
33
199.9
119.8
93
251.3
1.50. 6
54
46.3
27.8
14
97.8
58.6
74
149.2
89.5
34
200. 7
120.3
94
252. 2
151.1
55
47.2
28.3
15
98.6
59.1
75
150.1
90.0
35
201.6
120.8
95
253.
151.7
56
48.0
28.8
16
99.5
.59.6
76
151.0
90.5
.36
202.4
121.3
96
253. 9
1.52. 2
57
48.9
29.3
17
100.4
60.2
77
151.8
91.0
37
203.3
121.8
97
2.54.7
152. 7
58
49.7
29.8
18
101.2
60.7
78
152. 7
1 91.5
38
204.1
122.4
98
255. 6
153. 2
59
50.6
30.3
19
102.1
61.2
79
1.53. 5
1 92.0
39
205.
122.9
99
256. 5
1.53. 7
60
51.5
30.8
20
102.9
61.7
80
154. 4 1 92. 5
40
205. 9
123. 4
300
257.3
1.54. 2
Dist.
Dep.
Lat.
Dist.
! Dep.
Lat.
Dist.
Dep. 1 Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
N
E. by E. i E.
S
E. by E. J E.
NW. by W. \ W.
S\V. by \V. 1 W.
[For 5i Point!!. 1
Page 526]
TABLE 1.
Difference of Latitude and Depart
are for 3 PointB.
NE. by
N.
NW.
byN
SE. by S.
SW. by S.
Dlst.
Lat.
. Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
1 Dep.
1
0.8
0.6
61
50.7
33.9
121
100.6
67.2
181
150.5
100.6
241
200.4
1.33. 9
2
1.7
1.1
62
51.6
34.4
22
101.4
67.8
82
151.3
101.1
42
201.2
134.4
3
2.5
1.7
63
.52.4
35.0
23
102.3
08. 3
83
152.2
101.7
43
202.0
1,3.5.
4
3.3
2.2
64
53.2
35.6
24
103.1
68. 9
84
153.0
102.2
44
202.9
1,35. 6
5
4.2
2.8
65
54.0
36.1
25
103.9
69.4
85
153.8
102.8
45
203. 7
136. 1
6
5.0
3.3
66
54.9
36.7
26
104.8
70.0
86
154.7
103. 3
46
204.5
136. 7
7
5.8
3.9
67
55.7
37.2
27
105.6
70.6
87
155. 5
103.9
47
205.4
137. 2
8
6.7
4.4
68
56.5
37.8
28
106.4
71.1
88
156. 3
104.4
48
206.2
137.8
9
7.5
5.0
69
57.4
38.3
29
107.3
71.7
89
157. 1
105.0
49
207.0
138.3
10
8.3
5.6
70
58.2
38.9
30
108.1
108.9
72.2
90
158.0
158.8
105.6
50
207.9
208. 7
138.9
139. 4
11
9.1
6.1
71
59.0
39.4
131
72.8
191
106.1
251
12
10.0
6.7
72
59.9
40.0
32
109.8
73.3
92
159.6
106.7
52
209.5
140.
13
10.8
7.2
73
60.7
40.6
33
110.6
73.9
93
160. 5
107.2
53
210.4
140. 6
14
11.6
7.8
74
61.5
41.1
34
111.4
74.4
94
161.3
107.8
54
211.2
141.1
15
12.5
8.3
75
62.4
41.7
35
112.2
75.0
95
162.1
108.3
55
212.
141.7
16
13.3
8.9
76
63.2
42.2
36
113.1
75. 6
96
163.
108.9
56
212.9
142.2
17
14.1
9.4
77
64.0
42.8
37
113.9
76.1
97
163.8
109.4
57
213.7
142.8
18
15.0
10.0
78
64.9
43.3
38
114.7
76.7
98
164.6
110.0
58
214. 5
14.3.3
19
15.8
10.6
79
65.7
43.9
.39
115.6
77.2
99
165.5
110.6
59
215.4
143. 9
20
16.6
11.1
80
66.5
67.3
44.4
45.0
40
116.4
77.8
200
166.3
111.1
60
216.2
217.0
144.4
21
17.5
11.7
81
141
117.2
78.3
201
167.1
111.7
261
145.0
22
18.3
12.2
82
68.2
45.6
42
118.1
78.9
02
168.0
112.2
62
217.8
145. 6
23
19.1
12.8
83
69.0
46.1
43
118.9
79.4
03
168.8
112.8
63
218.7
146,1
24
20.0
13.3
84
69.8
46.7
44
119.7
80.0
04
169.6
113.3
64
219. 5
146.7
25
20.8
13.9
85
70.7
47.2
45
120.6
80.6
05
170.5
113.9
65
220.3
147.2
26
21.6
14.4
86
71.5
47.8
46
121.4
81.1
06
171.3
114.4
66
221.2
147.8
27
22.4
15.0
87
72.3
48.3
47
122.2
81.7
07
172.1
11.5.
67
222.0
1'48. 3
28
23.3
15.6
88
73.2
48.9
48
123.1
82.2
08
172.9
115.6
68
222.8
148.9
29
24.1
16.1
89
74.0
49.4
49
123.9
82.8
09
173.8
116.1
69
223.7
149.4
30
24.9
16.7
90
74.8
50.0
50
124.7
83.3
10
174. 6
116.7
70
224.5
225.3
150.0
31
25.8
17.2
91
75.7
50.6
151
125.6
83.9
211
175.4
117.2
271
1,50. 6
32
26.6
17.8
92
76.5
51.1
52
126.4
84.4
12
176.3
117.8
72
226.2
151. 1
33
27.4
18.3
93
77.3
51.7
53
127.2
85.0
13
177.1
118.3
73
227.0
151. 7
34
28.3
18.9
94
78.2
52.2
54
128.0
85.6
14
177.9
118.9
74
227.8
152. 2
35
29.1
19.4
95
79.0
52". 8
55
128.9
86.1
15
178.8
119.4
75
228.7
152. 8
36
29.9
20.0
96
79.8
53.3
56
129.7
86.7
16
179.6
120.0
76
229. 5
1,53. 3
37
30.8
20.6
97
80.7
53.9
57
130.5
87.2
17
180.4
120.6
77
230.3
153. 9
38
31.6
21.1
98
81.5
54.4
58
131.4
87.8
18
181.3
121.1
78
231.1
1,54.4
39
32.4
21.7
99
82.3
5.5.0
59
132.2
88.3
19
182.1
121.7
79
232.0
155.0
40
33.3
22.2
100
83.1
55.6
60
133.0
133. 9
88.9
20
182.9
183.8
122.2
80
232.8
233.6
155. 6
41
34.1
22.8
101
84.0
56.1
161
89.4
221
122.8
281
1,56. 1
42
34.9
23.3
02
84.8
56.7
62
134.7
90.0
22
184.6
123.3
82
234.5
156.7
43
35.8
23.9
03
85.6
57.2
63
1,35. 5
90.6
23
185.4
123.9
83
235.3
157.2
44
36.6
24.4
04
86.5
57.8
64
136.4
91.1
24
186.2
124.4
84
236.1
157. 8
45
37.4
25.0
05
87.3
58.3
65
137.2
91.7
25
187.1
125.0
85
237.0
158. 3
46
38.2
25.6
06
88.1
58.9
66
138.0
92.2
26
187.9
125.6
86
237.8
158.9
47
39.1
26.1
07
89.0
59.4
67
138.9
92.8
27
188.7
126.1
87
238.6
159.4
48
39.9
26.7
08
89.8
60.0
68
139.7
93.3
28
189.6
126.7
88
239.5
160.0
49
40.7-
27.2
09
90.6 j
60.6
69
140.5
93.9
29
190.4
127.2
89
240.3
160.6
50
41.6
27.8
28.3
10
91.5 !
92.3
61.1
70
141.3
94.4
30
191.2
127.8
90
241.1
161.1
51
42.4
111
61.7
171
142.2
95.0
231
192.1
128.3
291
242.0
161.7
52
43.2
28.9
12
93.1
62.2
72
143.0
95.6
32
192.9
128.9
92
242.8
162.2
53
44.1
29.4
13
94.0
62.8
73
143.8
96.1
33
193.7
129.4
93
243.6
162.8
54
44.9
30.0
14
94.8
63.3
74
144.7
96.7
34
194.6
130.0
94
244.5
163. 3
55
45.7
30.6
15
95.6
63.9
75
145.5
97.2
35
195.4
130.6
95
245.3
163.9
56
46.6
31.1
16
96.5
64.4
76
146.3
97.8
36
196.2
131.1
96
246.1
164.4
57
47.4
31.7
17
97.3
65.0
77
147.2
98.3
37
197.1
131.7
97
246.9
165.
58
48.2
32.2
18
98.1
65.6
78
148.0
98.9
38
197.9
132.2
98
247.8
165. 6
59
49.1
32.8
19
98.9
66.1
79
148.8
99.4
39
198.7
132.8
99
248.6
166.1
60
49.9
33.3
20
99.8
66.7
80
149.7
100.0
40
199.6
133.3
300
249.4
166.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. Lat |
Dist.
Dep.
Lat.
Dist.
rep.
Lat.
NE. by E.
S
E. byE
N\
V. by W.
SW. by W.
[For 5 PointB. 1
TABLE 1.
[Page 527 |
Difference of Latitude and Departure for Sj^ Points.
JTE. 1 N.
NW.
JN.
SE. J S.
SW. f s.
Dist.
Lat. 1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
49.0
36.3
121
97.2
72.1
181
145. 4
107.8
241
193.6
143.6
2
1.6
1.2
62
49.8
36.9
22
98.0
72.7
82
14ti.2
108. 4
42
194.4
144.2
3
2.4
1.8
63
50.6
37.5
23
98.8
73.3
83
147.0
109.0
43
195.2
144.8
4
3.2
2.4
64
.51.4
38.1
24
99.6
7.3.9
84
147.8
109.6
44
196.0
145.4
5
4.0
3.0
65
52.2
38.7
25
100.4
74.5
85
148. 6
110.2
45
196.8
145. 9
6
4.8
3.6
66
53.0
39.3
26
101.2
75.1
86
149.4
110.8
46
197.6
146.5
7
5.6
4.2
67
53.8
39.9
27
102.0
75. 7
87
150. 2
111.4
47
198.4
147.1
8
6.4
4.8
68
54.6
40.5
28
102. 8
76.2
88
151.0
112.0
48
199.2
147.7
9
7.2
5.4
69
55.4
41.1
29
103.6
76.8
89
151.8
112.6
49
200.0
148.3
10
8.0
6.0
70
56.2
41.7
30
104.4
77.4
90
152.6
113.2
50
200.8
148.9
149.5
11
8.8
6.6
71
57.0
42.3
131
105.2
78.0
191
153.4
113. 8
251
201.6
12
9.6
7.1
72
57.8
42.9
32
106.0
78.6
92
154.2
114.4
52
202.4
150.1
13
10.4
7. 7
73
58.6
43.5
33
106.8
79.2
93
155.0
115.0
53
203.2
150.7
14
11.2
8.3
74
59.4
44.1
34
107.6
79.8
94
155.8
115.6
54
2tH.O
151.3
15
12.0
8.9
75
60.2
44.7
35
108.4
80.4
95
156.6
116.2
55
204.8
151.9
16
12.9
9.5
76
61.0
45.3
36
109.2
81.0
96
157.4
116.8
56
205.6
152.5
17
13.7
10.1
77
61.8
45.9
37
110.0
81.6
97
158.2
117.4
57
206.4
153. 1
18
14.5
10.7
78
62.7
46.5
38
110.8
82.2
98
159.0
117.9
58
207.2
153. 7
19
15.3
11.3
79
63.5
47.1
39
111.6
82.8
99
159.8
118.5
59
208.0
1.54. 3
20
16.1
11.9
80
64.3
47.7
40
112.4
83.4
200
201
160.6
161.4
119.1
60
208.8
154.9
21
16.9
12.5
81
65.1
48.3
141
113.3
84.0
119.7
261
209.6
155. 5
22
17.7
13.1
82
65.9
48.8
42
114.1
84.6
02
162.2
120.3
62
210.4
156.1
23
18.5
13.7
83
66.7
49.4
43
114.9
85.2
03
163.1
120.9
63
211.2
1.56. 7
24
19.3
14.3
84
67.5
50.0
44
115.7
85.8
04
16.3.9
121.5
64
212.0
1.57. 3
25
20.1
14.9
85
68.3
50.6
45
116.5
86.4
05
164.7
122.1
65
212.8
1,57.9
26
20.9
15.5
86
69.1
51.2
46
117.3
87.0
06
165.5
122.7
66
213.7
158.5
27
21.7
16.1
87
69.9
51.8
47
118.1
87.6
07
166.3
123.3
67
214.5
159.1
28
22.5
16.7
88
70.7
52.4
48
118.9
88.2
08
167.1
123.9
68
215.3
159.6
29
23.3
17.3
89
71.5
53.0
49
119.7
88.8
09
167.9
124.5
69
216.1
160.2
30
24.1
17.9
90
91
72.3
53.6
50
120.5
89.4
10
168.7
125.1
70
216.9
160.8
31
24.9
18.5
73.1
54.2
151
121.3
90.0
211
169.5
125.7
271
217.7
161.4
32
2.5.7
19.1
92
73.9
54.8
52
122.1
90.5
12
170.3
126.3
72
218.5
162.0
33
26.5
19.7
93
74.7
55.4
53
122.9
91.1
13
171.1
126.9
73
219.3
162.6
34
27.3
20.3
94
75.5
56.0
54
123.7
91.7
14
171.9
127.5
74
220.1
163. 2
35
28.1
20.8
95
76.3
56.6
55
124.5
92.3
15
172.7
128.1
75
220.9
163. 8
36
28.9
21.4
96
77.1
•57.2
56
125.3
92.9
16
173.5
128.7
76
221.7
164.4
37
38
29.7
30.5
.22.0
22.6
,,97
77.9
57.8
58.4
57
58
126.1
120.9
93.5
94.1
17
18
174.3
175.1
129.3
129.9
77
78
222.5
223.3
165.0
165.6
98
78. 7
39
31.3
23.2
99
79.5
59.0
59
127.7
94.7
19
175.9
130.5
79
224.1
166.2
40
32.1
23.8
100
101
80.3
59.6
60
128.5
9,5.3
20
176.7
131.1
80
224.9
166.8
167.4
41
32.9
24.4
81.1
60.2
161
129.3
95.9
221
177.5
131.6
281
225.7
42
33.7
25.0
02
81.9
60.8
62
130.1
96.5
22
178.3
132.2
82
226.5
168.0
43
34.5
25.6
03
82.7
61.4
63
1,30. 9
97.1
23
179.1
132. 8
83
227.3
168.6
44
35.3.
26.2
04
83.5
62.0
64
131.7
97.7
24
179.9
133.4
84
228.1
169.2
45
36.1
26.8
05
84.3
62.5
65
132. 5
98.3
25
180.7
134.0
85
228.9
169.8
46
36.9
27.4
06
85.1
63.1
66
133.3
98.9
26
181.5
134.6
86
229. 7
170.4
47
37.8
28.0
07
85.9
63.7
67
134.1
99.5
27
182.3
135.2
87
230.5
171.0
48
38.6
28.6
08
86.7
64.3
68
134.9
100.1
28
183.1
135.8
88
231.3
171.6
49
39.4
29.2
09
87.5
64.9
69
135.7
100.7
29
183.9
136.4
89
232.1
172.2
50
51
40.2
29.8
10
88.4
65. 5
70
136.5
101.3
30
184.7
137.0
90
232.9
172.8
41.0
30.4
111
89.2
66.1
171
137.3
101.9
231
185.5
137.6
291
233.7
173.3
52
41.8 31.0
12
90.0
66.7
72
138.2
102. 5
32
186.3
138.2
92
234. 5
173.9
53
42.6
31.6
13
90.8
67.3
73
139.
103.1
,33
187.1
138.8
93
235.3
174.5
54
43.4
32.2
14
91.6
67.9
74
139.8
103.7
34
188.0
139.4
94
236.1
175. 1
55
44.2
32.8
15
92.4
68.5
75
140.6
104.2
35
188.8
140.0
95
236.9
175.7
56
45.0
33.4
16
93.2
69.1
76
141.4
104.8
36
189.6
140.6
96
237.7
176.3
57
45.8
34.0
17
94.0
69.7
77
142.2
105.4
37
190.4
141.2
97
238.6
176.9
58
46.6
34.6
18
94.8
70.3
78
143.0
106.0
38
191.2
141.8
98
239.4
177. 5
59
47.4
35.1
19
95.6
70.9
79
143.8
106.6
39
192.0
142.4
99
240.2
178.1
60
48.2
35.7
20
96.4
71.5
80
144.6
107.2
40
192.8
143.0
300
241.0
178.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
NE. f E.
SE. i E.
X\
V. f W.
SW. i \V.
[For 4i Po
ints.
Page 628]
TABLE 1.
Difference of Latitude and Departure for 3} Points.
NE. i N.
NW
. JN.
SE. i S.
SW. i S
Dist.
Lnt.
Dop.
0.6
Dist.
Lilt.
Dep
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
61
47.2
38.7
121
93.5
76.8
181
139.9
114.8
241
186.3
152. 9
2
1.5
1.3
62
47.9
39. 3
22
94.3
77.4
82
140.7
115.5
42
187. 1
153. 5
3
2.3
1.9
63
48.7
40.0
23
95.1
78.0
83
141.5
116.1
43
187.8
154. 2
4
3.1
2.5
64
49.5
40.6
24
95.9
78.7
84
142.2
116.7
44
188.6
154.8
5
3.9
3.2
65
50.2
41.2
25
96.6
79.3
85 i 143.0
117.4
45
189.4
155.4
6
4.6
3.8
66
51.0
41.9
26
97.4
79.9
86
143.8
118.0
46
190.2
156.1
7
5.4
4.4
67
51.8
42.5
27
98.2
80.6
87
144.6
118.6
47
190.9
156.7
8
6.2
5.1
68
52.6
43.1
28
98.9
81.2
88
145. 3
119.3
48
191.7
157.3
9
7.0
5.7
69
53.3
43.8
29 i 99.7
81.8
89
146.1
119.9
49
192. 5
158.0
10
11
7.7
8.5
6.3
70
54.1
44.4
30
100.5
82.5
83.1
90
191
146.9
147.6
120.5
50
193. 3
158. 6
159. 2
7.0
71
54.9
45.0
131
101. 3
121. 2
251
194.0
12
9.3
7.6
72
55.7
45.7
32
102.0
83.7
92
148.4
121.8
52
194.8
159.9
13
10.0
8.2
73
56.4
46.3
33
102.8
84.4
93
149.2
122.4
53
195. 6
160.5
14
10.8
8.9
74
57.2
46.9
34
103. 6
85.0
94
150.0
123.1
54
196.3
161.1
15
11.6
9.5
75
58.0
47.6
35
104.4
85.6
95 1 150.7
123. 7
55
197. 1
161.8
16
12.4
10.2
76
58.7
48.2
36
105.1
86.3
96 ! 151.5
124.3
56
197.9
162.4
17
13.1
10.8
77
59.5
48.8
37
105.9
86.9
97 152.3
125.0
57
198.7
163.0
18
13.9
11.4
78
60.3
49.5
38
106.7
87.5
98 ! 153.1
125.6
58
199.4
163.7
19
14.7
12.1
79
61.1
50.1
39
107.4
88.2
99 1 153.8
126.2
59
200.2
164. 3
20
15.5
12.7
80
61.8
50.8
51.4
40
108.2
88.8
200 ! 154.6
126.9
60
201.0
20r. 8
164.9
165.6
21
16.2
13.3
81
62.6
141
109.0
89.4
201 1 155.4
127.5
261
22
17.0
14.0
82
63.4
52.0
42
109.8
90.1
02 1 156.1
128.1
62
202. 5
166.2
23
17.8
14.6
83
64.2
52.7
43
110. 5
90.7
03 i 156.9
128.8
63
203.3
166. 8
24
18.6
15.2
84
64.9
53.3
44
111.3
91.4
04 ' 157.7
129.4
64
204.1
167. 5
25
19.3
15.9
85
65.7
53.9
45
112.1
92.0
05 158.5
130.1
65
204.8
168. 1
26
20.1
16.5
86
66.5
54.6
46
112.9
92.6
06 159.2
130.7
66
205. 6
168.7
27
20.9
17.1
87
67.3
55.2
47
113.6
93.3
07 1 160.0
131.3
67
206.4
169.4
28
21.6
17.8
88
68.0
55.8
48
114.4
93.9
08
160. 8
132.0
68
207.2
170.0
29
22.4
18.4
89
68.8
56.5
49
115.2
94.5
09
161.6
132.6
69
207. 9
170.7
30
31
23.2
19.0
90
69.6
57.1
57.7
50
151
116.0
95.2
95. 8"
10
211
162. 3
133.2
70
208.7
171.3
24.0
19.7
91
70.3
116.7
163. 1
133.9
271
209.5
171.9
32
24.7
20.3
92
71.1
,58.4
52
117.5
96.4
12
163.9
134.5
72
210. 3
172.6
33
25.5
20.9
93
71.9
59.0
53
118.3
97.1
13
164.7
135.1
73
211.0
173.2
34
26.3
21.6
94
72.7
59.6
54
119.0
97.7
14
165. 4
135.8
74
211.8
173.8
35
27.1
22.2
95
73.4
60. 3
55
119.8
98.3
15
166.2
136.4
75
212.6
174. 5
36
27.8
22.8
96
74.2
60.9
56
120.6
99.0
16
167.0
137.0
76
213.4
175. 1
37
28.6
23.5
97
75.0
61.5
57
121.4
99.6
17
167.7
137.7
77
214.1
175. 7
38
29.4
24.1
98
75.8
62.2
58
122.1
100. 2
18
168.5
138.3
78
214.9
176.4
39
30.1
24.7
99
76.5
62.8
59
122.9
100.9
19
169.3
138.9
79
215. 7
177.0
40
41
30.9
25.4
100
77. 3
63.4
60
123.7
124.5
101.5
l02. 1
20
170.1
170.8
139.6
80
216.4
177.6
31.7
26.0
101
78.1
64.1
161
221
140. 2
281
217.2
178.3
42
32.5
26.6
02
78.8
64.7
62
125.2
102.8
22
171.6
140.8
82
218.
178.9
43
33.2
27.3
03
79.6
65.3
63
126.0
103. 4
23
172.4
141.5
83
218.8
179.5
44
34.0
27.9
04
80.4
66.0
64
126. 8
104.0
24
173.2
142.1
84
219.5
180.2
45
34.8
28.5
05
81.2
66.6
65
127. 5
104.7
25
173.9
142.7
85
220.3
180.8
46
35.6
29.2
06
81.9
67.2
66
128. 3
105. 3
26
174.7
143.4
86
221.1
181.4
47
36.3
29.8
07
82.7
67.9
67
129.1
105.9
27
175.5
144.0
87
221.9
182.1
48
37.1
30.5
08
83.5
68.5
68
129.9
106.6
28
176.2
144.6
88
222.6
182.7
49
37.9
31.1
09
84.3
69.1
69
130.6
107.2
29
177.0
145. 3
89
223.4
183. 3
50
38.7
31.7
10
85.0
69.8
70
131.4
107.8
30
177.8
145.9
90
224.2
184.0
51
39.4
32.4
111
85.8
70.4
171
132. 2
108.5
231
178.6
146. 5
291
224.9
184.6
52
40.2
33.0
12
86.6
71.1
72
133.0
109.1
32
179.3
147.2
92
225. 7
185.2
53
41.0
33.6
13
87.4
71.7
73
133.7
109.8
33
180. 1
147.8
93
226.5
185.9
54
41.7
34.3
14
88.1
72.3
74
134. 5
110.4
34
180.9
148.4
94
227.3
186.5
55
42.5
34.9
15
88.9
73.0
75
135. 3
111.0
35
181.7
149. 1
95
228.0
187.1
56
43.3
35.5
16
89.7
73.6
76
136.0
111.7
36
182.4
149. 7
96
228.8
187.8
57
44.1
36.2
17
90.4
74.2
77
136. 8
112. 3
37
183.2
150.4
97
229.6
188.4
58
44.8
36.8
18
91.2
74.9
78
137, 6
112.9
38
184.0
151.0
98
230.4
189.0
59
45.6
37.4
19
92.0
75.5
79
138.4
113.6
39
184.7
151.6
99
231.1
189.7
60
46.4
38.1
20
92.8
76.1
80
139.1
114.2
40
185.5
152.3
300
231.9
190.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
NE. }
E.
SE. JE
NM^ i ^
sw. i ^
V.
[F
ir 4J Points. 1
r
TABLE 1.
-
[Page 529
Difference of Latitude and Departure for 3i Points.
NE. i N.
NW.
iN.
SE. i S.
SW. } s.
Dist.
Lat. 1 Dup.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. 1 Lat.
Dep.
Dist.
Lat.
Dep.
161.8
1
0.7
0.7
61
45.2
41.0
121
89.7
81.3
181
134.1
121.6
241
178.6
9
1.5
1.3
62
45.9
41.6
22
90.4
"81.9
82
134.9
122.2
42
179.3
162.5
3
2.2
2.0
63
46.7
42.3
23
91.1
82.6
83
135. 6
122.9
43
180.1
163.2
4
3.0
2.7
64
47.4
43.0
24
91.9
83.3
84
136. 3
123.6
44
180.8
163. 9
5
3.7
3.4
65
48.2
43.7
25
92.6
83.9
85
137.1
124.2
45
181.5
164.5
6
4.4
4.0
66
48.9
44.3
26
93.4
84.6
86
137.8
124.9
46
182.3
165.2
7
5.2
4.7
67
49.6
4.5.0
27
94.1
85.3
87
138.6
125. 6
47
183.0
165.9
8
5.9
5.4
68
50.4
45.7
28
94.8
86.0
88
139.3
126.3
48
183.8
166.5
9
6.7
6.0
69
51.1
46.3
29
95.6
86.6
89
140.0
126.9
49
184.5
167.2
10
7.4
6.7
70
51.9
47.0
30
96.3
87.3
90
140. 8 1 127. 6
50
185. 2 1 167. 9 1
11
8.2
7.4
71
52.6
47.7
131
97.1
88.0
191
141.5
128.3
251
186.0
168.6
12
8.9
8.1
72
53.3
48.4
32
97.8
88.6
92
142.8
128.9
52
186.7
169.2
13
9.6
8.7
73
54.1
49.0
33
98.5
89.3
93
143.0
129.6
53
187.5
169.9
14
10.4
9.4
74
54.8
49.7
34
99.3
90.0
94
143.7
130.3
54
188. 2
170.6
15
11.1
10.1
75
55.6
50.4
35
100.0
90.7
95
144.5
131.0
55
188.9
171.2
16
11.9
10.7
76
56.3
51.0
36
100.8
91.3
96
145.2
131.6
56
189.7
171.9
17
12.6
11.4
. 77
57.1
51.7
37
101.5
92.0
97
146.0
132.3
57
190.4
172.6
18
13.3
•12.1
78
57.8
52.4
38
102. 3
92.7
98
146.7
133.0
58
191.2
173. 3
19
14.1
12.8
79
58. 5 i 53. 1
39
103.0
93.3
99
147.4
133.6
59
191.9
173.9
20
14.8
13.4
80
59. 3 1 53. 7
40
103.7
104.5
94.0
' 94. 7
200
148.2
134.3
60
192.6
174.6
21
15.6
14.1
81
60.0
54.4
141
201
148.9
135.0
261
193.4
175. 3
22
16.3
14.8
82
60.8
5.5.1
42
105.2
95.4
02
149.7
135.7
62
194.1
175.9
23
17.0
1.5.4
83
61.5
5.5.7
43
106.0
96.0
03
1.50. 4
136.3
63
194.9
176.6
24
17.8
16. 1
84
62.2
56.4
44
106. 7
96.7
04
151.2
137.0
64
195. 6
177.3
25
18.5
16.8
85
63.0
.57.1
45
107.4
97.4
05
151.9
137.7
65
196.4
178.0
26
19.3
17.5
86
63.7
57.8
46
108.2
9.8.0
06
152. 6
138.3
66
197.1
178.6
27
20.0
18.1
87
64.5
58.4
47
108.9
98.7
07
153.4
139.0
67
197.8
179.3
28
20.7
18.8
88
6.5.2
59.1
48
109.7
99.4
08
154.1
139.7
68
198. 6 180.
29
21.5
19.5
89
65.9
59.8
49
110.4
100.1
09
154.9
140.4
69
199. 3 180. 6
30
22.2
20.1
90
66.7
60.4
50
111.1
100.7
101.4
10
211
155.6
141.0
70
200.1
200.8
181.3
31
23.0
20.8
91
67.4
61.1
151
111.9
156.3
141.7
271
182.0
32
23.7
21.5
92
68.2
61.8
52
112.6
102.1
12
157. 1
142.4
72
201. 5 182. 7
33
24.5
22 ^
93
68.9
62.0
53
11,3. 4
102.7
13
157.8
143.0
73
202. 3 183. 3
34
25.2
22.8
94
69.6
63.1
54
114.1
103.4
14
158.6
143.7
74
203.0 1 184.0
35
25.9
23.5
95
70.4
63.8
55
114.8
104.1
15
159.3
144.4
75
203.8 : 184.7
36
26.7
24.2
96
71.1
64.5
56
115.6
104.8
16
160.0
145. 1
76
204.5 185.4
37
27.4
24.8
97
71.9
&5.1
57
116. 3
105.4
17
160.8
145.7
/ /
205.2 186.0
38
28.2
2.5.5
98
72.6
65.8
58
117.1
106.1
18
161. 5
146.4
78
206.0 1 186.7
39
28.9
26.2
99
73.4
66.5
59
117.8
106. 8
19
162.3
147.1
79
206.7 i 187.4
40
41
29.6
30.4
26.9
27.5
100
101
74.1
67.2
60
118. 6
n9.3
107.4
20
163.0
147.7
80
207.5 188.0
74.8
67.8
161
108. 1
221
163.8
148.4
281
208. 2 i 188. 7
42
31.1
28.2
02
75.6
68.5
62
120.0
108.8
22
164.5
149.1
82
208. 9 1 189. 4
43
31.9
28.9
03
76.3
69.2
63
120.8 109.5
23
165.2
149.8
83
209.7 ' 190.1
44
32.6
29.5
04
77.1
69.8
64
121.5 110.1
24
166.
150.4
84
210. 4 190. 7
45
33.3
.30.2
05
77.8
70.5
65
122.3
110.8
25
166.7
151.1
,85
211.2 191.4
46
34.1
.30.9
06
78.5
71.2
66
12.3.0
111.5
26
167.5
151.8
86
211.9 192.1
47
34.8
31.6
07
79.3
71.9
67
123.7
112.2
27
168.2
152.4
87
212. 7 192. 7
48
35.6
32.2
08
80.0
72.5
68
124.5
112.8
28
168.9
1.53. 1
88
213.4 193.4
49
36.3
.32.9
09
80.8
73.2
69
125. 2
113. 5
29
169.7
1.53. 8
.89
214. 1 194. 1
50
37.0
33.6
34.2
10
81.5
73.9
70
126.0
114.2
30
170.4
1.54. 5
155. f
90
214. 9 194. 8
51
37.8
111
82.2
74.5
171
126.7
114.8
231
171.2
291
215.6 195.4
52
.38.5
34.9
12
83.0
7.5.2
72
127.4
115.5
32
171.9
1.55. 8
92
216. 4 , 196. 1
53
39.3
35. 6
.13
83.7
75.9
73
128.2
116.2
33
172.6
156. 5
93
217. 1 1 196. 8
54
40.0
36.3
14
84.5
76.6
74 i 128.9
116.9
34
173.4
157.1
94
217.8 : 197.4
00
40.8
36.9
15
85.2
77.2
75 i 129. 7
117.5
:«
174.1
157.8
95
218. 6 ! 198. 1
56
41.5
37.6
16
86.0
77.9
76 ! 130.4
118.2
36
174.9
158.5
96
219.3 i 198.8
57
42.2
.38.3
17
86.7
78.6
77 1 131. 1
118.9
37
175. 6
1.59. 2
97
220. 1 i 199. 5
58
43.0
39.0
18
87.4
79.2
78 1,31.9
119. 5
38
176. 3
159.8
98
220. 8 200. 1
59
43.7
39.6
19
88.2
79.9
79 132. 6
120.2
39
177.1
160.5
99
221. 5 200. 8
60
44.5
40.3
20
88.9
80.6
80 133. 4
120.9
40
177.8
161.2
300
222. 3 201. 5
i
Duit.
Dep.
Lat.
Dist.
Dep. 1 Lat. |
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. j Lat.
tfE. \ K.
S
E. }E.
XW. ] AV.
S\V. i AV.
[For 4,t Points. 1
24972°- 12-
-24
Page 530]
TABLE 1.
Difference of Ijdtitude and
Depart
lire for 4 Points.
NE.
my.
SE.
SW.
Dist.
Lat.
1 Dep-
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
1
0.7
61
43.1
43.1
121
. 85.6
85.6
181
128.0
128.0
241
170.4
170.4
2
1.4
1.4
62
43.8
43.8
22
86.3
86.3
82
128.7
128.7
42
171.1
171.1
3
, 2.1
2.1
63
44.5
44.6
23
87.0
87.0
83
129.4
129.4
43
171.8
171.8
4
2.8
2.8
64
45.3
46.3
24
87.7
87.7
84
130.1
130.1
44
172.6
172.5
5
3.5
3.5
65
46.0
46.0
25
88.4
88.4
85
130.8
130.8
45
173.2
173.2
6
4.2
4.2
66
46.7
46.7
26
89.1
89.1
86
131.5
131.5
46
173.9
173.9
7
4.9
4.9
67
47.4
47.4
27
89. 8
89.8
87
132.2
132.2
47
174.7
174.7
8
5.7
5.7
68
48.1
48.1
28 90. 5
90.5
88
132.9
132.9
48
175.4
175.4
9
6.4
6.4
69
48.8
48.8
29 91. 2
91.2
89
133.6
133.6
49
176.1
176.1
10
7.1
7.1
70
49.5
49.5
30 91.9
91.9
92.6
90
191
134.4
134.4
"issfi
50
176.8
176.8
11
7.8
7.8
71
50.2
50.2
131
92.6
135.1
261
177.5
177.6
12
8.5
8.5
72
50.0
50.9
32
93.3
93.3
92
135.8
13.5.8
62
178.2
178.2
13
9.2
9.2
73
51.6
51.6
33
94.0
94.0
93
136.5
136.5
63
178.9
178.9
14
9.9
9.9
74
52.3
52.3
34
94.8
94.8
94
137.2
137.2
64
179.6
179.6
15
10.6
10.6
75
53.0
53.0
35
95.5
96.5
95
137.9
137.9
66
180.3
180.3
16
11.3
11.3
76
53.7
53.7
36
96.2
96.2
96
138.6
138.6
56
181.0
181.0
17
12.0
12.0
77
54.4
54.4
37
96.9
96.9
97
139. 3
139.3
57
181.7
181.7
18
12.7
12.7
78
55.2
55.2
38
97.6
97.6
98
140.0
140.0
.58 ' 182.4
182.4
19
13.4
13.4
•79
55.9
55.9
39
98.3
98.3
99
140.7
140.7
59 183.1 1 183.1
20
14.1
14.1
80
56.6
56.6
40
99.0
99.0
200
141.4
141.4
60 183.8 1 183.8
21
14.8
14.8
81
57.3
57.3
141
99.7
99.7
201
142.1
142.1
261 184.6 ! 184.6
22
15.6
15.6
82
58.0
58.0
42
100.4
100.4
02
142.8
142.8
62 185. 3
186.3
23
16.3
16.3
83
58.7
68.7
43
101.1
101.1
03
143.5
143.5
63 186.
186.0
24
17.0
17.0
84
59.4
69.4
44
101.8
101.8
04
144.2
144.2
64 186. 7
186.7
26
17.7
17.7-
85
60.1
60.1
45
102.5
102.5
05
145.0
145.0
65 187.4
187.4
26
18.4
18.4
86
60.8
60.8
46
103.2
103.2
06
145.7
146.7
66
188.1
188.1
27
19.1
19.1
87
61.5
61.5
47
103.9
103.9
07
146.4
146.4
67
188.8
188.8
28
19.8
1-9.8
88
62.2
62.2
48
104.7
104.7
08
147.1
147.1
68
189.5
189.5
29
20.5
20.5
89
62.9
62.9
49
105.4
105.4
09
147. 8
147.8
69
190.2
190.2
30
21.2
21.9
21.2
21.9
90
63.6
63.6
50
106.1
106.1
10
148.6
148.6
70
271
190.9
190.9
31
91
64.3
64.3
161
106.8
106.8
211
149.2
149.2
191.6
191.6
32
22.6
22.6
92
65.1
65.1
52
107. 6
107.6
12
149. 9
149.9
72
192.3
192.3
33
23.3
23.3
93
66.8
65.8
63
108.2
108.2
13
150.6
160.6
73
193.0
193.0
34
24.0
24.0
94
66.5
66.5
64
108.9
108.9
14
151.3
161.3
74
193.7
193.7
35
24.7
24.7
95
67.2
67.2
65
"109.6
109.6
15
152.0
152.0
76
194.5
194.5
36
25.5
25.5
96
67.9
67.9
66 110. 3
110.3
16
152.7
152.7
76
195.2
195.2
37
26.2
26.2
97
68.6
68.6
67
111.0
111.0
17
163.4
153.4
77
195.9
195.9
38
26.9
26.9
98
69.3
69.3
58
111.7
111.7
18
154.1
154.1
78
196.6
196.6
39
27.6
27.6
99
70.0
70.0
59
112.4
112.4
19
164.9
154.9
79
197.3
197.3
40
28.3
28.3
100
101
70.7
70.7
60
113. 1
113.1
20
166.6
155.6
80
198.0
198.0
41
29.0
29.0
71.4
71.4
161
113.8
113.8
221
166.3
156.3
281
198.7
198.7
42
29.7
29.7
02
72.1
72.1
62
114.6
114.6
22
167.0
157.0
82
199.4
199.4
43
30.4
30.4
03
72.8
72.8
63
116. 3
115.3
23
157.7
157.7
83
200.1
200.1
44
31.1
31.1
04
73.5
73.6
64
116.0
116.0
24
158.4
158.4
84
200.8
200.8
45
31.8
31.8
05
74.2
74.2
65
116.7
116.7
25
159.1
159.1
85
201.5
201.5
46
32.5
32.5
06
75.0
75.0
66
117.4
117.4
26
159.8
159.8
86
202.2
202.2
47
33.2
33.2
07
75.7
76.7
67
118.1
118.1
27
160.5
160.5
87
202.9
202.9
48
33.9
33.9
08
76.4
76.4
68
118.8
118.8
28
161.2
161.2
88
203.6
203.6
49
34.6
34.6
09
77.1
77.1
69
119.5
119.6
29
161.9
161.9
89
204.4
204.4
50
35.4
35.4
10
77.8
77.8
70
120.2
120.2
30
162.6
162.6
90
205.1
205.1
51
36.1
36.1
111
78.5
78.5
171
120.9
120.9
231
163.3
163.3
291
205.8
'205.8
52
36.8
36.8
12
79.2
79.2
72
121.6
121.6
32
164.0
164.0
92
206.5
206.5
53
37.5
37.5
13
79.9
79.9
73
122.3
122.3
33
164.8
164. a
93
207.2
207.2
54
38.2
38.2
14
80.6
80.6
74
123.0
123.0
34
165.6
165.5
94
207.9
207.9
55
38.9
38.9
15
81.3
81.3
75
123.7
123.7
35
166.2
166.2
96
208.6
208.6
56
39.6
39.6
16
82.0
82.0
76
124. 5
124.5
36
166.9
166.9
96
209.3
209.3
57
40.3
40.3
17
82.7
82.7
77
125.2
126.2
37
167.6
167.6
97
210.0
210.0
58
41.0
41.0
18
83.4
83.4
78
125.9
126.9
38
168.3
168.3
98
210.7
210.7
59
41.7
41.7
19
84.1
84.1
79
126.6
126.6
39
169.0
169.0
99
211.4
211.4
60
42.4
42.4
20
84.9
84.9
80
127.3
127.3
40
169.7
169.7
300
212.1
212.1
Dist.
Dep.
L»t.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. .
Lat.
NE.
NW.
SE.
SW
•
[For 4 Points. 1
y //)
v/
^^-jo^y^i^^h^-^
^.
r/-^
^
?-■
TABLE 2.
[Page 531
Difference of Latitude anc
Deimrture for 1° (179°, 181
\ 359°
).
Diet.
Lat.
Dip.
Dist,
Lat.
Dep.
Dist.
Lat. j Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.0
61
61.0
1.1
121
121.0
2.1
181
181.0
3.2
241
241.0
4.2
2
2.0
0.0
62
62.0
1.1
22
122.0
2.1
82
182.0
3.2
42
242.
4.2
3
.3.0
0.1
63
63.0
1.1
23
123.0
2.1
83
183.0
3.2
43
243.0
4.2
4
4.0
0.1
64
64.0
1.1
24
124.0
2.2
84
184.0
S.2
44
244.0
4.3
5
5.0
0.1
65
65.0
1.1
25
125.0
2.2
85
185.0
.3.2
45
245.0
4.3
6
6.0
0.1
66
66.0
1.2
26
126.0
2.2
86
186.0
3.2
46
246.0
4.3
7
7.0
0.1
67
67.0
1.2
27
127.0
2.2
87
187.0
3.3
47
247.0
4.3
8
8.0
0.1
68
68.0
1.2
28
128.0
2.2
88
188.0
3.3
48
248.0
4.3
9
9.0
0.2
69
69.0
1.2
29
129.0
2.3
89
189.0
3.3
49
249.0
4.3
10
10.0
0.2
70
70.0
1.2
30
130.0
2.3
90
191
190.0
3.3
50
250.0
4.4
11
11.0
0.2
71
71.0
1.2
131
131.0
2.3
191.0
3.3
251
251.
4.4
12
12.0
0.2
72
72.0
1.3
32
132.0
2.3
92
192.0
3.4
52
252.
4.4
13
13.0
0.2
73
73.0
1.3
33
133.0
2.3
93
193.0
3.4
53
253.0
4.4
14
14.0
0.2
74
74.0
1.3
34
134.0
2.3
94
194.0
3.4
54
254.0
4.4
15
15.0
0.3
75
75.0
1.3
35
135.0
2.4
95
195.0
3.4
55
255.
4.5
16
16.0
0.3
76
76.0
1.3
36
136.0
2.4
96
196.0
3.4
56
256.0
4.5
17
17.0
0.3
77
V7.
1.3
37
137.0
2.4
97
197.0
3.4
57
257.0
4.5
18
18..
0.3
78
78.0
1.4
38
138.0
2.4
98
198.0
3.5
58
258.0
4.5
19
19.0
0.3
79
79.0
1.4
39
139.0
2.4
99
199.0
3.5
59
259.0
4.5
20
20.0
21.0'
0.3
80
80.0
1.4
40
140.0
141.0
2.4
200
200.0
3.5
60
260.0
261.0
4.5
4.6
21
0.4
81
81.0
1.4
141
275
201
201.0
3.5
261
22
22.0
0.4
82
82.0
1.4
42
142.0
2.5
02
202.0
3.5
62
262.0
4.6
23
23.0
0.4
83
83.0
1.4
43
14,3.0
2.5
03
203.0
3.5
63
263.0
4.6
24
24.0
0.4
84
84.0
1.5
44
144.0
2.5
04
204.0
3.6
64
264.0
4.6
25
25.0
0.4
85
85.0
1.5
45
145.0
2.5
05
205.0
3.6
65
2ft5.0
4.6
26
26.0
0.5
86
86.0
1.5
46
146.0
2.5
06
206.0
3.6
66
266.0
4.6
27
27.0
0.5
87
87.0
1.5
47
147.0
2.6
07
207.0
3.6
67
267.
4.7
28
28.0
0.5
88
88.0
1.5
48
148.0
2.6
08
208.0
3.6
68
268.0
4.7
29
29.0
0.5
89
89.0
1.6
49
149.0
2.6
09
209.0
3.6
69
269.0
4.7
30
31
30.0
0.5
90
91
90.0
91.0
1.6
.50
150.0
2.6
10
210.0
3.7
3.7
70
271
270.0
271.
4.7
31.0
0.5
1.6
1.51
151.0
2.6
211
211.0
4.7
32
32.0
0.6
92
92.0
1.6
52
152.0
2. 7
12
212.0
3.7
. 72
272.0
4.7
33
3.3.0
0.6
93
93.0
1.6
.53
1.53.
2. 7
13
213.0
.3.7
73
273.0
4.8
34
.34.0
0.6
94
94.0
1.6
.54
154.0
2. 7
14
214.0
3.7
74
274.0
4.8
35
3.5.0
0.6
95
95.0
1.7
.55
1.55.
') 7
15
215.0
3.8
75
275.0
4.8
36
36.0
0.6
96
96.0
1.7
56
156.0
2. 7
16
216.0
3.8
76
276.0
4.8
37
37.0
0.6
97
97.0
1.7
57
1.57.
2! 7
17
217.0
3.8
77
277.0
4.8
38
38.0
0.7
98
98.0
1.7
58
158.0
2.8
18
218.0
3.8
78
278.0
4.9
39
39.0
0.7
99
99.0
1.7
59
159.0
2.8
19
219.0
,3.8
79
279.0
4.9
40
40.0
0.7
0.7
100
lOO-.O
1.7
60
161
160.0
161.0
2.8
2.8
20
221
220.0
3.8
80
280.0
281.0
4.9
4.9
41
41.0
101
101.0
1.8
221.0
3.9
281
42
42.0
0.7
02
102.0
1.8
62
162.0
2:8
22
222.0
3.9
82
282.0
4.9
43
43.0
0.8
03
103.
1.8
63
163.0
2.8
23
223.0
3.9
83
283.0
4.9
44
44.0
0.8
04
104.0
1.8
64
164.0
2.9
24
224.0
3.9
84
284.0
.5.0
45
45.0
0.8
05
105.
1.8
65
165.
2.9
25
225.
3.9
85
285.
.5.0
46
46.0
0.8
06
106.0
1.8
66
166.0
2.9
26
226.0
3.9
86
286.0
.5.0
47
47.0
0.8
07
107.0
1.9
67
167.0
2.9
27
227.0
4.0
87
287.0
5.0
48
48.0
0.8
08
108.0
1.9
68
168.0
2.9
28
228.0
4.0
88
288.0
.5.0
49
49.0
0.9
09
109.0
1.9
69
169.0
2.9
29
229.0
4.0
89
289.0
.5.0
50
51
50.0
0.9
10
110.0
1.9
70
170.0
.3.0
30
230.0
4.0
4.0
90
291
290.0
5.1
.51.0
0.9
111
111.0
1.9
171
171.0
3.0
231
231.0
291.0
5.1
52
52.0
0.9
12
112.0
2.0
72
172.0
3.0
32
232.0
4.0
92
292.0
5.1
53
.53.0
0.9
13
11.3.0
2.0
73
173.
3.0
.33
233.0
4.1
93
293.0
.5.1
54
54.0
0.9
14
114.0
2.0
74
174.0
3.0
34
234.0
4.1
94
294.0
.5.1
55
.55.0
1.0
15
11.5.
2.0
75
175.0
.3.1
.35
235.0
4.1
95
295.0
•5.1
56
56.0
1.0
16
116.0
2.0
76
176.0
.3.1
36
236.
4.1
96
296.0
.5.2
57
.57.0
1.0
17
117.0
2.0
77
177.0
.3.1
37
237.0
4.1
97
297.0
5.2
58
.58.0
1.0
18
118.0
2.1
78
178.0
3.1
.38
238.
4.2
98
298.0
5.2
59
59.0
1.0
19
119.0
2.1
79
179.0
3.1
.39
239.0
4.2
99
299.0
,5.2
60
60.0
1.0
20
120.0
2.1
80
180.0
3.1
40
240.0
4.2
300
300.0
5.2
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
ijit.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
89° (<
n°, 269°, 271°
.
Page 532]
TABLE 2.
Difference of Latitude and Departure for 1° (179°, 181'
, 359°]
.
Dist.
Lat. 1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
301.0
5.3
361
360.9
6.3
421
420.9
7.3
481
480.9
8.4
541
540.9
9.5
02
302.0
5.3
62
361.9
6.3
22
421.9
7.4
82
481.9
8.4
42
541.9
9.5
03
303.0
5.3
63
362. 9
e.3
23
422.9
7.4
83
482.9
8.5
43
542.9
9.5
04
304.0
5.3
64
363.9
6.4
24
423.9
7.4
84
483.9
8.5
44
543.9
9.5
05
305.
5.3
65
364. 9
6.4
25
424.9
7.4
85
484.9
8.5
45
544.9
9.5
06
306.0
5.3
66
365.9
6.4
26
425.9
7.4
86
485.9
8.5
46
545.9
9.5
07
307.0
5.4
67
366.9
6.4
27
426.9
7.4
87
486.9
8.5
47
546.9
9.6
08
308.0
5.4
68
.367. 9
6.4
28
427.9
7.5
88
487.9
8.6
48
547.9
9.6
09
309.0
5.4
69
368. 9
6.4
29
428.9
7.5
89
488.9
8.6
49
548.9
9.6
10
310.0
5.4
70
369.9
370.9
6.5
30
429.9
7.5
90
489.9
8.6
50
549.9
9.6
311
311.0
5.4
371
6.5
431
430.9
7.5
491
490.9
8.6
551
550.9
9.6
12
312.0
5.4
72
371.9
6.5
32
431.9
7.5
92
491.9
8.6
52
551.9
9.6
13
313.0
5.5
73
372.9
6.5
33
432. 9
7.5
93
492.9
8.7
53
552.9
9.7
14
314.0
5.5
74
373.9
6.5
34
433.9
7.6
94
493.9
8.7
54
553.9
9.7
15
315.0
5.5
75
374.9
6.5
35
434.9
7.6
95
494.9
8.7
55
554.9
9.7
16
316.0
.5.5
76
375.9
6.6
36
435. 9
7.6
96
495.9
8.7
56
555. 9
9.7
17
317.0
5.5
77
376.9
6.6
37
436.9
7.6
97
496.9
8.7
57
556.9
9.7
18
318.0
5.5
78
377.9
6.6
38
437.9
7.6
98
497.9
8.7
58
557.9
9.7
19
319.0
5.6
79
378.9
6.6
39
438.9
7. 7
99
498.9
8.8
59
558.9
9.8
20
320.0
5.6
80
379.9
6.6
40
441
439. 9
440.9
7.7
500
501
499.9
8.8
60
559.9
560. 9
9.8
9.8
321
321.
•5.6
381
380.9
6.7
500.9
8.8
561
22
322.0
5.6
82
381.9
6.7
42
441.9
7.7
02
501.9
8.8
62
561.9
9.8
23
323.0
5.6
83
382. 9
6.7
43
442.9
7.7
03
502.9
8.8
63
562.9
9.8
24
324.0
.5.6
84
383. 9
6.7
44
443.9
(. 1
04
503.9
8.8
64
563.9
9.8
25
325.0
5.7
85
384.9
6.7
45
444.9
7.8
05
504.9
8.8
65
564.9
9.9
26
326.0
.5.7
86
385. 9
6.7
46
445.9
7.8
06
505.9
8.9
66
565.9
9.9
27
327.0
5. 7
87
386.9
6.8
47
446.9
7.8
07
506.9
8.9
67
566.9
9.9
28
328.0
5.7
88
387.9
6.8
48
447.9
7.8
08
507.9
8.9
68
567.9
9.9
29
329.0
5. 7
89
.388. 9
6.8
49
448.9
7.8
09
.508. 9
8.9
69
568.9
9.9
30
331
330.0
331.0
.5.8
90
389.9
6.8
50
449.9
450.9
7.8
10
509.9
8.9
70
569. 9
9.9
5.8
391
390.9
6.8
451
7.9
511
510.9
9.0
571
570.9
10.0
32
332.0
5.8,
92
391.9
6.8
52
451.9
7.9
12
511.9
9.0
72
571.9
10.0
33
333.0
5.8
93
392. 9
6.9
53
452.9
7.9
13
512.9
9.0
73
572. 9
10.0
34
333.9
5.8
94
393.9
6.9
54
453.9
7.9
14
513.9
9.0
74
573.9
10.0
35
334.9
5.8
95
394.9
6.9
55
454. 9
7.9
15
514.9
9.0
75
574. 9
10.0
36
335.9
.5.9
96
395.9
6.9
56
455.9
8.0
16
515.9
9.0
76
575. 9
10.0
37
336.9
.5.9
97
396.9
6.9
57
4.56. 9
8.0
17
516.9
9.1
77
576. 9
10.1
38
337.9
5.9
98
397.9
6.9
58
457. 9
8.0
18
517.9
9.1
78
577. 9
10.1
39
338.9
5.9
99
398.9
7.0
59
458.9
8.0
19
518.9
9.1
79
578.9
10.1
40
341
339.9
.5.9
400
399.9
7.0
60
461
459.9
8.0
20
519,9
9.1
80
579.9
10.1 .
340.9
6.0
401
400.9
7.0
460.9
8.0
521
520.9
•9.1
581
580. 9
10.1
42
341. 9
6.0
02
401.9
7.0
62
461.9
8.1
22
521.9
9.1
82
581.9
10.1
43
342.9
6.0
03
402.9
7.0
63
4(i2. 9
8.1
23
522. 9
9.2
83
582.9
10.2
44
343. 9
6.0
04
403.9
7. 1
64
463. 9
8.1
24
523.9
9.2
84
583. 9
10.2
45
344.9
6.0
05
404.9
7. 1
65
464.9
8.1
25
524. 9
9.2
85
584.9
10.2
46
345.9
6.0
06
405.9
7. 1
66
465.9
8.1
26
525.9
9.2
86
585. 9
10.2
47
346. 9
6.1
07
406.9
7. 1
67
466.9
8.1
27
526.9
9.2
87
586. 9
10.2
48
347.9
6.1
08
407.9
7, 1
68
467.9
8.2
28
527.9
9.2
88
587.9
10.2
49
348. 9
6.1
09
408.9
7. 1
69
468.9
8.2
29
528.9
9.3
89
588. 9
10.3
50
349. 9
350.9
6.1
6.1
10
411
409.9
410.9
7.2
7.2
70
471
469.9
8.2
8.2
30
531
529.9
9.3
90
589.9
590.9
10.3
10.3
351
470.9
530.9
9.3
591
52
351.9
6.1
12
411.9
7.2
72
471.9
8.2
32
531.9
9.3
92-
591.9
10.3
53
352.9
6.2
13
412.9
7.2
73
472.9
8.2
33
532.9
9.3
93
592.9
10.3
54
353.9
6.2
14
413.9
7.2
74
473.9
8.3
34
533.9
9.3
94
593.9
10.3
55
354.9
6.2
15
414.9
7.2
75
474.9
8.3
35
534.9
9.4
95
594.9
10.4
56
355. 9
6.2
16
415.9
7.3
76
475.9
8.3
36
535.9
9.4
96
595.9
10.4
57
356.9
6.2
17
416.9
7.3
77
476.9
8.3
37
536.9
9.4
97
596.9
10.4
58
357.9
6.2
18
417. 9
7.3
78
477.9
8.3
38
537.9
9.4
98
597.9
10.4
59
358.9
6.3
19
418.9
7.3
79
478.9
8.4
39
538.9
9.4
99
598.9
10.4
60
359.9
6.3
Lat.
20
Dist.
419.9
7.3
80
479.9
8.4
40
539.9
9.4
600
599.9
10.5
Dlst.
Dep.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
89° (91°, 269°
, 271°).
TABLE 2.
[Page 533
Difference of Latitude and Departure for 2° (178°, 182
°, 358°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.0
61
61.0
2.1
121
120.9
4.2
181
180.9
6.3
241
240.9
8.4
2
2.0
0.1
62
62.0
2.2
22
121.9
4.3
82
181.9
6.4
42
241.9
8.4
3
.3.0
0.1
63
63.0
2. 2
23
122.9
4.3
83
182.9
6.4
43
242.9
8.5
4
4.0
0.1
64
64.0
2.2
24
123.9
4.3
84
183.9
6.4
44
243.9
8.5
S
5.0
0.2
65
65.0
2.3
25
124.9
4.4
Sb
184. 9
6.5
45
244.9
8.6
6
6.0
0.2
66
66.0
2.3
26
125.9
4.4
86
185.9
6.5
46
245. 9
8.6
7
7.0
0.2
67
67.0
2.3
27
126.9 i 4.4
87
186.9
6.5
47
246. 8
8.6
8
8.0
0.3
68
68.0
2.4
28
127.9 1 4.5
88
187.9
6.6
48
247.8
.S.7
9
9.0
0.3
69
69.0
2.4
29
128.9
4.5
89 188. 9
6.6
49
248.8
8.7
10
10.0
0.3
70
70.0
2.4
30
129.9
4.5
90 ; 189.9
191 190.9
6.6
50
249.8
8.7
11
11.0
0.4
71
71.0
2.5
131
130.9
4.6
6.7
251
250.8
8.8
12
12.0
0.4
72
72.0
2.5
,32
131.9
4.6
92 ! 191.9
6.7
52
251.8
8.8
13
13.0
0.5
73
73.0
2.5
33
1.32.9
4.6
93 1 192.9
6.7
53
252.8
8.8
14
14.0
0.5
74
74.0
2.6
.34
ia3.9
4.7
94
193.9
6.8
54
253.8
8.9
15
15.0
0.5
75
75.0
2.6
35
134. 9
4.7
95
194.9
6.8
55
254.8
8.9
16
16.0
0.6
76
76.0
2.7
36
135.9
4.7
96
195.9
6.8
56
255.8
8.9
17
17.0
0.6
77
77.0
2.7
37
136.9
4.8
97
196.9
6.9
57
256.8
9.0
18
18.0
0.6
78
78.0
2.7
.38
137.9
4.8
98
197.9
6.9
58
257.8
9.0
19
19.0
0.7
79
79.0
2.8
,39
138.9
4.9
99
198.9
6.9
59
258.8
9.0
20
21
20.0
0.7
80
80.0
2.8
40
139.9
4.9
200
199.9
7.0
7.0
60
2.59. 8
9.1
21.0
0.7
81
81.0
2.8
141
140.9
4.9
201
200. 9
261
260.8
9.1
22
22.0
0.8
82
82.0
2.9
42
141.9
5.0
02
201.9
7.0
62
261.8
9.1
23
23.0
0.8
83
82.9
2.9
43
142. 9
.5.0
03
202.9
7.1
63
262.8
9.2
24
24.0
0.8
84
83.9
2.9
44
143.9
5.0
04
203. 9
7.1
64
263.8
9.2
25
25.0
0.9
85
84.9
3.0
45
144.9
.5.1
05
204.9
7.2
65
264.8
9.2
26
26.0
0.9
86
85.9
3.0
46
145.9
5.1
06
205.9
7.2
66
265.8
9.3
27
27.0
0.9
87
86.9
.3.0
47
146.9
5.1
07
206.9
7.2
67
266.8
9.3
28
28.0
1.0
88
87.9
3.1
48
147.9
5.2
08
207.9
7.3
68
267.8
9.4
29
29.0
1.0
89
88.9
3.1
49
148.9
5.2
09
208.9
7.3
69
268.8
9.4
30
30.0
1.0
90
89.9
3.1
50
149.9
5.2
10
211
209.9
7.3
70
269.8
9.4
31
31.0
1.1
91
90.9
3.2
151
150.9
.5.3
210.9
7.4
,271
270.8
9.5
32
32.0
1.1
92
91.9
3.2
52
151.9
5.3
12
211.9
7.4
72
271.8
9.5
33
33.0
1.2
93
92.9
3.2
53
152.9
5.3
13
212.9
7.4
73
272.8
9.5
34
34.0
1.2
94
93.9
3.3
.54
153. 9
5.4
14
213.9
7.5
74
273.8
9.6
35
35.0
1.2
95
94.9
3.3
55
154.9
5.4
15
214.9
7.5
75
274.8
9.6
36
36.0
1.3
96
95.9
3.4
.56
155. 9
.5.4
16
215.9
7.5
76
275.8
9.6
37
37.0
1.3
97
96.9
3.4
57
156.9
.5.5
17
216.9
7.6
77
276.8
9.7
38
38.0
1.3
98
97.9
3.4
bS
1.57. 9
5.5
18
217.9
7.6
78
277.8
9.7
39
39.0
1.4
99
98.9
3.5
59
158.9
.5.5
19
218.9
7.6
79
278.8
9.7
40
40.0
1.4
100
99.9
3.5
60
159.9
5.6
5.6
20
221
219. 9
7.7
80
279.8
9.8
41
41.0
1.4
101
100.9
3.5
161
160.9
220.9
7.7
281
280.8
9.8
42
42.0
1.5
02
101.9
3.6
62
161.9
5. 7
22
221.9
7.7
82
281.8
9.8
43
43.0
1.5
03
102.9
3.6
63
162.9
5. 7
23
222.9
7.8
83
282.8
9.9
44
44.0
1.5
04
103.9
3.6
64
163.9
.5.7
24
223. 9
7.8
84
283. 8
9.9
45
45.0
1.6
05
104.9
,3.7
65
164.9
.5.8
25
224.9
7.9
85
284.8
9.9
46
46.0
1.6
06
105. 9
3.7
66
165. 9
.5.8
26
225.9
7.9
86
285.8
10.0
47
47.0
1.6
07
106.9
3.7
67
166. 9
.5.8
27
226.9
7.9
87
286.8
10.0
48
48.0
1.7
08
107.9
3.8
68
167.9
.5.9
28
227.9
8.0
88
287.8
10.1
49
49.0
1.7
09
108.9
3.8
69
168.9
.5.9
29
228.9
8.0
89
288.8
10.1
50
51
50.0
1.7
10
109.9
110.9
3.8
3.9
70
171
169.9
170.9
.5.9
30
229.9
2.30. 9
8.0
8.1
90
291
289.8
290.8
10.1
10.2
51.0
1.8
111
6.0
231
52
52.0
1.8
12
111.9
3.9
72
171.9
6.0
32
231.9
8.1
92
291.8
10.2
53
53.0
1.8
13
112.9
,3.9
73
172.9
6.0
33
232.9
8.1
93
292.8
10.2
54
54.0
1.9
14
11.3.9
4.0
74
173.9
6.1
34
233.9
8.2
94
293.8
10.3
55
55.0
1.9
15
114.9
4.0
75
174. 9
6.1
.35
234.9
8.2
95
294.8
10.3
56
56.0
2.0
16
115.9
4.0
76
175.9
6.1
36
235.9
8.2
96
295.8
10.3
57
57.0
2.0
17
116.9
4.1
( i
176.9
6.2
37
236.9
8.3
97
296.8
10.4
58
58.0
2.0
18
117.9
4.1
78
177.9
6.2
38
237.9
8.3
98
297.8
10.4
59
59.0
2.1
19
118.9
4.2
79
178.9
6.2
39
238.9
8.3
99
298.8
10.4
60
60.0
2.1
20
119.9
4.2
80
179.9
6.3
40
239.9
8.4
300
299.8
10.5
Dist.
Dep.
Lat.
Dist.
Dep.
I^t.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
88° (9
2°, 268°, 272°)
Page 534]
TABLE 2.
Difference of Latituc
le and Departure for 2° (178°, 182
°, 358°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
1 Dep.
Dist.
Lat.
Dep.
301
300.8
10.5
361
360.8
12.6
421
420.8
14.7
481
480.7
16.8
541
540.7
18.9
02
301.8
10.5
62
361.8
12.6
22
421.8
14.7
82
481.7
16.8
42
541.7
18.9
03
302.8
10.6
63
362.8
12.7
23
422.8
14.7
83
482.7
16.8
43
542.7
18.9
04
303. 8
10.6
64
363.8
12.7
24
423.8
14.8
84
483.7
16.9
44
543.7
19.0
05
304.8
10.6
65
364.8
12.7
25
424.8
14.8
85
484.7
16.9
45
544.7
19.0
06
305.8
10.7
66
365.8
12.8
26
425.7
14.9
86
485.7
16.9
46
545.7
19.0
07
306.8
10.7
67
366.8
12.8
27
426.7
14.9
87
486.7
17.0
47
546. 7
19.1
08
307.8
10.7
68
367.8
12.8
28
427.7
14.9
88
487.7
17.0
48
547.7
19.1
09
308.8
10.8
69
368.8
12.9
29
428.7
15.0
89
488.7
17.0
49
548.7
19.1
10
309.8
10.8
70
369.8
12.9
30
429.7
15.0
90
489.7
17.1
50
549.7
550.7
19.2
311
310.8
10. 8
371
370.8
12. 9
431
430.7
15.0
491
490.7
17.1
551
19.2
12
311.8
10.9
72
371.8
13.0
32
431.7
15.1
92
491. 7
17.1
52
551.7
19.2
13
312.8
10.9
73
372.8
13.0
33
432.7
15.1
93
492.7
17.2
53
552.7
19.3
14
313.8
10.9
74
373.8
13.0
34
433.7
15.1
94
493.7
17.2
54 ' 553. 7
19.3
15
314.8
11.0
75
374.8
13.1
35
434.7
15.2
95
494.7
17.2
55
554.7
19.3
16
315.8
11.0
76
375.8
13.1
36
435. 7
15.2
96
495.7
17.3
56
555.7
19.4
17
316.8
11.0
77
376.8
13.1
37
436.7
15.2
97
496.7
17.3
57 556. 7
19.4
18
317.8
11.1
78
377.8
13.2
38
437.7
15.3
98
497. 7.
17.3
58 557. 7
19.4
19
318.8
11.1
79
378.8
13.2
39
438.7
15.3
99
498.7
17.4
59 558. 7
19.5
20
321
319.8
11.2
80
379.8
13.2
40
439.7
15.3
500
499.7
17.4
60 559. 7
19.5
320.8
11.2
381
380.8
13.3
441 440. 7
15.4
501
500.7
17.5
561 ; 560. 7
19.5
22
321.8
11.2
82
381.8
13.3
42 441. 7
15.4
02
501.7
17.5
62 1 561. 7
19.6
23
322.8
11.3
83
382.8
13.3
43
442.7
15.4
03
502.7
17.5
63
562. 7
19.6
24
323.8
11.3
84
383.8
13.4
44
443.7
15.5
04
503.7
17.6
64
563.7
19.6
25
324.8
11.3
85
384.8
13.4
45
444.7
15.5
05
504.7
17.6
65
564.7
19.7
26
325.8
11.4
86
385.8
13.5
46
445.7
15.6
06
505.7
17.6
66
565.7
19.7
27
326.8
11.4
87
386.8
13.5
47
446.7
15.6
07
506.7
17.7
67
566.7
19.7
28
327.8
U.4
88
387. 8
13.5
48
447.7
15.6
08
507.7
17.7
68
567.7
19.8
29
328.8
11.5
89
388.8
13.6
49
448.7
15.7
09
508.7
17.7
69
568.7
19.8
30
331
329.8
11.5
90
389.8
13.6
50
449.7
15.7
10
509.7
17.8
70
569.7
19.9
330.8
11.5
391
390.8
13.6
451
450.7
15.7
511
510.7
17.8
571
570.7
19.9
32
331.8
11.6
92
391.8
13.7
52
451.7
15.8
12
511.7
17.8
72
571.7
19.9
33
"S32.8
11.6
93
392. 8
13.7
53
452.7
15.8
13
512.7
17.9
73
572.7
20.0
34
333.8
11.6
94
393.8
13.7
54
453.7
15.8
14
513.7
17.9
74
573.6
20.0
35
334.8
11.7
95
394.8
13.8
55
454.7
15.9
15
514.7
17.9
75
574.6
20.0
36
335.8
11.7
96
395. 8
13.8
56
455. 7
15.9
16
515. 7
18.0
76
575.6
20.1
37
336.8
11.7
97
396.8
13.8
57
456.7
15.9
17
516.7
18.0
77
576.6
20.1
38
337.8
11.8
98
397.8
13.9
58
457. 7
16.0
18
517.7
18.1
78
577.6
20.1
39
338.8
11.8
99
398.8
13.9
59
458. 7
16.0
19
518.7
18.1
79
578.6
20.2
40
341
339.8
11.9
400
399.8
13.9
60
459.7
16.0
20
519.7
520.7
18.1
80
579.6
20.2
340.8
11.9
401
400.8
14.0
461
460.7
16.1
521
18.2
581
580.6
20.2
42
341.8
11.9
02
401.8
14.0
62
461.7
16.1
22
521. 7
18.2
82
581.6
20.3
43
342.8
12.0
03
402.8
14.0
63
462.7
16.1
23
522.7
18.2
83
582.6
20.3
44
343.8
12.0
04
403.8
14.1
64
463. 7
16.2
24
523.7
18.3
84
583.6
20.3
45
344.8
12.0
05
404.8
14.1
65
464.7
16.2
25
524.7
18.3
85
584.6
20.4
46
345.8
12.1
06
405.8
14.2
66
465.7
16.2
26
525.7
18.4
86
585.6
20.4
47
346.8
12.1
07
406.8
14.2
67
466.7
16.3
27
526.7
18.4
87
586.6
20.4
48
347. 8
12.1
08
407.8
14.2
68
467.7
16.3
28
527.7
18.4
88
587.6
20.5
49
348.8
12.2
09 1 408. 8
14.3
69
468.7
16.4
29
528.7
18.5
89
588.6
20.5
50
349.8
12.2
10
409.8
14.3
70
471
469.7
470.7
16.4
30
529. 7
18.5
90
589.6
20.5
351
350.8
12.2
411
410.8
14.3
16.4
531
530.7
18.5
591
590.6
20.6
52
351.8
12.3
12
411.8
14.4
72
471. 7
16.5
32
531.7
18.6
92
591.6
20.6
53
352.8
12.3
13
412.8
14.4
73
472.7
16.5
33
532.7
18.6
93
592.6
20.6
54
353.8
12.3
14
413.8
14.4
74
473.7
16.5
34
533.7
18.6
94
593.6
20.7
55
354.8
12.4
15
414.8
14.5
V5
474.7
16.6
35
534.7
18.7
95
594.6
20.7
56
355.8
12.4
16
415.8
14.5
76
475.7
16.6
36
535.7
18.7
96
595.6
20.7
57
356.8
12.4
17
416.8
14.5
77
476.7
16.6
37
536.7
18.7
97
596.6
20.8
58
357.8
12.5
18
417.8
14.6
78
477.7
16.7
38
537. 7
18.8
98
597. 6
20.8
59
358.8
12.5
19
418.8
14.6
79
478.7
16.7
39
5.38. 7
18.8
99
598.6
20.8
60
359.8
12.5
20
419.8
14.6
80 479. 7 16. 7
40
539. 7
18.8
600
599.6
20.9
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep. j Lat. |
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
88° (92°, 268°, 272°).
TABLE
■2.
[Page 535
Difference of Latitude and Departure for 3° (177°, 183
=,357°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Diet.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.9
3.2
121
120.8
6.3
181
180.8
9.5
241
240.7
12.6
2
2.0
0.1
62
61.9
3.2
22
121.8
6.4
82
181.8
9.5
42
241.7
12.7
3
3.0
0.2
63
62.9
3.3
23
122.8
6.4
83
182.7
9.6
43
242.7
12.7
4
4.0
0.2
64
63.9
3.3
24
123.8
6.5
84
183.7
9.6
44
243.7
12.8
5
5.0
0.3
65
64.9
3.4
25
124.8
6.5
85
184.7
9.7
45
244.7
12.8
6
6.0
0.3
66
65.9
3.5
26
125.8
6.6
86
185.7
9.7
46
245.7
12.9
7
7.0
0.4
67
66.9
3.5
27
126.8
6.6
87
186.7
9.8
47
246.7
12.9
8
8.0
0.4
68
67.9
3.6
28
127.8
6.7
88
187.7
9.8
48
247.7
13.0
9
9.0
0.5
69
68.9
3.6
29
128.8
6.8
89
188.7
9.9
49
248.7
13.0
10
11
10.0
0.5
0.6
70
71
69.9
3.7
30
129.8
130.8
6.8
90
189.7
190.7
9.9
50
2"51
249.7
250.7
13.1
13.1
11.0
70.9
3.7
131
6.9
191
10.0
12
12.0
0.6
72
71.9
3.8
32
131.8
6.9
92
191.7
10.0
52
251.7
13.2
13
13.0
0.7
73
72.9
3.8
33
132.8
7.0
93
192.7
10.1
53
252.7
13.2
14
14.0
0.7
74
73.9
3.9
34
133.8
7.0
94
193.7
10.2
54
253.7
13.3
15
15.0
0.8
75
74.9
3.9
35
134.8
7.1
95
194.7
10.2
55
254. 7
13.3
16
16.0
0.8
76
75.9
4.0
36
135.8
7.1
96
195.7
10.3
56
255.6
13.4
17
17.0
0.9
77
76.9
4.0
37
136. 8
7.2
97
196.7
10.3
57
256.6
13.5
18
18.0
0.9
78
77.9
4.1
38
137.8
7.2
98
197.7
10.4
58
257.6
13.5
19
19.0
1.0
79
78.9
4.1
39
138.8
7.3
99 198. 7
10.4
59
258.6
13.6
20
20.0
1.0
1.1
80
81
79.9
4.2
4.2
40
141
139.8
140.8
7.3
200 199. 7
10.5
60
259.6
13.6
21
21.0
80.9
7.4
201
200.7
10.5
261
260.6
13.7
22
22.0
1.2
82
81.9
4.3
42
141.8
7.4
02
201.7
10.6
62
261.6
13.7
23
23.0
1.2
83
82.9
4.3
43
142.8
7.5
03
202. 7
10.6
63
262.6
13.8
24
24.0
1.3
84
83.9
4.4
44
143.8
7.5
04
203.7
10.7
64
263.6
13.8
25
25.0
1.3
85
84.9
4.4
45
144.8
7.6
05
204.7
10.7
65
264.6
13.9
26
26.0
1.4
86
85.9
4.5
46
145.8
7.6
06
205.7
10.8
66
265. 6
13.9
27
27.0
1.4
87
86.9
4.6
47
146.8
7. 7
07
206.7
10.8
67
266.6
14.0
28
28.0
1.5
88
87.9
4.6
48
147.8
7.7
08
207.7
10.9
68
267.6
14.0
29
29.0
1.5
89
88.9
4.7
49
148.8
7.8
09
208.7
10.9
69
268. 6
14.1
30
30.0
1.6
90
89.9
4.7
50
149.8
7.9
10
209.7
11.0
70
269.6
14.1
31
31.0
1.6
91
90.9
4.8
151
150.8
7.9
211
210.7
11.0
271
270.6
14.2
32
32.0
1.7
92
91.9
4.8
52
151.8
8.0
12
211.7
11.1
72
271.6
14.2
33
33.0
1.7
93
92.9
4.9
53
152.8
8.0
13
212.7
11.1
73
272.6
14.3
34
34.0
1.8
94
93.9
4.9
54
153. 8
8.1
14
213.7
11.2
74
273.6
14.3
35
35.0
1.8
95
94.9
5.0
55
154. 8
8.1
15
214.7
11.3
75
274.6
14.4
36
36.0
1.9
96
95.9
5.0
56
155. 8
8.2
16
215.7
11.3
76
275. 6
14.4
37
36.9
1.9
97
96.9
5.1
57
156.8
8.2
17
216.7
11.4
77
276.6
14.5
38
37.9
2.0
98
97.9
5.1
58
157.8
8.3
18
217.7
11.4
78
277.6
14.5
39
38.9
2.0
99
98.9
5.2
59
158.8
8.3
19
218.7
11.5
79
278.6
14.6
40
39.9
2.1
100
99.9
5.2
60
159.8
8.4
20
219.7
220.7
11.5
80
279.6
14.7
41
40.9
2.1
101
100.9
5.3'
161
160.8
8.4
221
11.6
281
280. 6
14.7
42
41.9
2.2
02
101.9
5.3
62
161.8
8.5
22
221.7
11.6
82
281.6
14.8
43
42.9
2.3
03
102.9
5.4
63
162.8
8.5
23
222.7
11.7
83
282.6
14.8
44
43.9
2.3
04
103.9
5.4
64
163.8
8.6
24
223.7
11.7
84
283. 6
14.9
45
44.9
2.4
05
104.9
5.5
65
164.8
8.6
25
224.7
11.8
85
284.6
14.9
46
45.9
2.4
06
105.9
5.5
66
165.8
8.7
26
225.7
11.8
86
285.6
15.0
47
46.9
2.5
07
106.9
5.6
67
166.8
8.7
27
226.7
11.9
87
286.6
15.0
48
47.9
2.5
08
107.9
5.7
68
167.8
8.8
28
227.7
11.9
88
287.6
15.1
49
48.9
2.6
09
108.9
5. 7
69
168.8
8.8
29
228.7
12.0
89
288.6
15.1
50
49.9
2.6
2.7
10
109.8
5.8
70
169.8
8.9
30
229.7
230.7
12.0
90
289.6
15.2
51
50.9
111
110.8
5.8
171
170.8
8.9
231
12.1
291
290.6
15.2
52
.51.9
2.7
12
111.8
5.9
72
171.8
9.0
32
231.7
12.1
92
291.6
15.3
53
52.9
2.8
13
112.8
5.9
73
172.8
9.1
33
232.7
12.2
93
292.6
15.3
54
53.9
2.8
14
113.8
6.0
74
173.8
9.1
34
233.7
12.2
94
293.6
15.4
55
54.9
2.9
15
114.8
6.0
75
174.8
9.2
S6
234.7
12.3
95
294.6
15.4
56
55.9
2.9
16
115.8
6.1
76
175.8
9.2
36
235. 7
12.4
96
295.6
15.5
67
56.9
3.0
17
116.8
6.1
77
176.8
9.3
37
236.7
12.4
97
296.6
15.5
58
57.9
3.0
18
117.8
6.2
78
177.8
9.3
38
237.7
12.5
98
297.6
15.6
59
58.9
3.1
19
118.8
6.2
79
178.8
9.4
39
238.7
12.5
99
298.6
15.6
60
59.9
3.1
20
119.8
6.3
80
179.8
9.4
40
239.7
12.6
300
299.6
15.7
Diat.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. 1 Dep.
Lat.
Dist.
Dep.
Lat.
87° (
93°, 267
^ 273°
)■
Page 536]
TABLE -2.
Difference of Latitude and Departure for
3° (177°, 183
°, 357°
).
Dist. 1 Lat.
Dep.
Di.st.
Lat.
Dep.
Dist. : Lut.
Dep.
Dist.
Lat,
Dep.
Dist.
Lat.
Dep.
301 300.6
1.5.7
361
360.5
18.9
421 '. 420.4
22.0
481
480.3
25.2
,541
540.2
28.3
02 : 301. 6
15.8
62
361.5
19.0
22 421.4
22.1
82
481.3
25.2
42
541.2
28.4
03 i 302. 6
15.9
63
362.5
19.0
23 422. 4
22.2
83
482.3
25.3
43
542.2
28.4
04 303.5
1.5.9
64
363.5
19.1
24 423. 4
22.2
84
483.3
25.3
44
543.2
28.5
05 ' 304.5
16.0
65
364. 5
19.1
25 , 424.4
22.3
85
484.3
25.4
45
544.2
28.5
06 305. 5
16.0
66
365.5
19.2
26 , 425.4
22.3
86
485.3
25.4
46
545.2
28.6
07 : 306.5
16.1
67
366.5
19.2
27 426.4
22.4
87
486.3
25.5
47
546.2
28.6
08 : 307.5
16.1
68
367. 5
19.3
28 427. 4
22.4
88
487.3
2.5.5
48
547.2
28.7
09 : 308.5
16.2
69
368.5
19.3
29 428. 4
22.5
89
488.3
25.6
49
548.2
28.7
10 j 309.5
16.2
70
369.5
19.4
30 429.4
22.5
90
489..>
v^5. 6
50
549.2
28.8
311 1 310.5
16.3
371
370.5
19.4
431 430. 4
22.6
491
490.?
25.7
551
550.2
28.8
12 1 311.5
16.3
72
371.5
19.5
32 431. 4
22.6
92
491.3
25.7
52
551.2
28.9
13 ! 312.5
16.4
73
372. 5
19.5
33 432. 4
22.7
93
492.3
25.8
53
552.2
28.9
14
313.5
16.4
74
373.5
19.6
34
433. 4
22.7
94
493.3
25.9
54
553.2
29.0
15
314. 5
16.5
75
374.5
19.6
35
434.4
22.8
95
494.3
25.9
55
554.2
29.1
16
315.5
16.6
76
375.5
19.7
36
435.4
22.8
96
495.3
26.0
56
555.2
29.1
17
316.5
16.6
77
376.5
19.8
37
436.4
22.9
97
496.3
26.0
57
556.2
29.2
18
317.5
16.7
78
377.4
19.8
38 437.4
22.9
98
497.3
26.1
58
557.2
29.2
19
318.5
16.7
79
378.4
19.9
39 ! 438.4
23.0
99
498.3
26.1
59
558.2
29.3
20
319.5
16.8
80
381
379.4
380.4
19.9
40 ' 439. 4
23.0
500
501
499.3
500.3
26.2
60
559.2
29.3
29. 4
321
320. 5
16.8
20.0
441 ; 440.4
23.1
26.2
,561
560.2
22
321.5
16.9
82
381.4
20.0
42 441.4
23.1
02
501.3
26.3
62
561.2
29.4
23
322. 5
16.9
83
382.4
20.1
43 : 442.4
23.2
03
502.3
26.3
63
562.2
29.5
24
323.5
17.0
84
383.4
20.1
44 : 443.4
23.3
04
503.3
26.4
64
563.2
29.5
25
324. 5
17.0
85
384.4
20.2
45 1 444.4
23.3
05
504.3
26.4
65
564.2
29.6
26
325.5
17.1
86
385.4
20.2
46
445. 4
23.4
06
505. 3
26.5
66
565.2
29.6
27
326.5
17.1
87
386.4
20.3
47
446.4
23.4
07
506.3
26.5
67
566.2
29.7
28
327.5
17.2
88
387.4
20.3
48
447.4
2.3.5
08
507.3
26.6
68
567.2
29.7
29
,328. 5
17.2
89
388.4
20.4
49
448.4
23.5
09
508. 3
26.6
69
568.2
29.8
30
329.5
17.3
90
389.4
20.4
20.5
50
449.3
450.3
23.6
10
509.3
26.7
70
569.2
29.8
29. 9
331
330.5
17.3
391
390.4
451
23.6
511
510.3
26.7
571
570.2
32
331. 5
17.4
92
391.4
20.5
52 451.3
23.7
12
.511. 3
26.8
72
571.2
29.9
33
332.5
17.5
93
392.4
20.6
53
452. 3
23.7
13
512. 3
26.8
73
572.2
30.0
34
333. 5
17.5
94
393.4
20.6
54
453. 3
23.8
14
513.3
26.9
74
573.2
30.0
35
334.5
17.6
95
394.4
20.7
55
4.54. 3
23.8
15
514.3
27.0
75
574. 2
30.1
36
335.5
17.6
96
395.4
20.7
56
455. 3
23.9
16
515.3
27.0
76
575. 2
30.1
37
336.5
17.7
97
396.4
20.8
57
456. 3
23.9
17
516.3
27.1
77
576. 2
30. 2
38
337. 5
17.7
98
397.4
20.8
58
457. 3
24.0
18
517.3
27.1
78
577.2
30.2
39
338. 5
17.8
99
398.4
20.9
59
4.58. 3
24.0
19 518.3
27.2
79
578.2
30.3
40
339. 5
17.8
400
399.4
20.9
60
4.59. 3
24.1
20 519.3
27.2
80
579.2
30.3
341
340. 5
17.9
401
400.4
21.0
461
460.3
24.1
521
520. 3
27.3
.581
580. 2
30.4
42
341.5
17.9
02
401.4
21.1
62
461.3
24.2
22
521.3
27.3
82
581.2
30.4
43
342.5
18.0
03
402.4
21.1
63
462. 3
24.2
23
522.3
27.4
83
582.2
30.5
44
343.5
18.0
04
403.4
21.2
64
463.3
24.3
24
523. 3
27.4
84
583.2
30.5
45
344.5
18.1
05
404.4
21.2
65
464.3
24.4
25
524.3
27.5
85
584.2
30.6
46
345.5
18.1
06
405.4
21.3
66
465.3
24.4
26
525.3
27.5
86
585.2
30.6
47
346.5
18.2
07
406.4
21.3
67
466. 3
24.5
27
526.3
27.6
87
586.2
30.7
48
347.5
18.2
08
407.4
21.4
68
467.3
24.5
28
527.3
27.6
88
587.2
30.7
49
348.5
18.3
09
408.4
21.4
69
468.3
24.6
29
528.3
27.7
89
588.2
,30.8
50
349.5
350. 5
18.3
18:4
10
409.4
21.5
21.5
70
471
469.3
24.6
30
529.3
530.3
27.7
90
589.2
30.9
351
411
410.4
470.3
24.7
531
27.8
591
590. 2
30.9
52
351 5
18.4
12
411.4
21.6
• 72
471.3
24.7
32
531.3
27.8
92
591.2
31.0
53
352.5
18.5
13
412.4
21.6
73
472.3
24.8
33
532.3
27.9
93
592.2
31.0
54
353. 5
18.5
14
413.4
21.7
74
473.3
24.8
34
533.3
27.9
94
593.2
31.1
55
354.5
18. 6
15
414.4
21.7
75
474.3
24.9
35
534.3
28.0
95
594.2
31.1
56
a55.5
18.6
16
415.4
21.8
76
475.3
24.9
36
535.3
28.1
96
595.2
31.2
57
356. 5
18.7
17
416.4
21.8
77
476. 3
25.0
87
536.3
28.1'
97
596.2
31.2 .
58
357. 5
18.8
18
417.4
21.9
78
477.3
25.0
38
537.3
28.2
98
,597. 2
31.3
59
358.5
18.8
19
418.4
21.9
79
478.3
25.1
,39
538. 3
28.2
99
598.2
31.3
60
359.5
18.9
20
419.4
22.0
80
479. 3
25.1
40
539.3
28.3
600
599.2
.31.4
Dist.
Dep.
Lat.
DLst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
87° (93°, 267°, 273°). j
TABLE 2.
[Page 537 |
Difference of Latitude and Depart
are for 4° (176°, 184
°, 356°
).
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.9
4.3
121
120.7
8.4
181
180.6
12.6
241
240.4
16.8
2
2.0
0.1
62
61.8
4.3
22
121.7
8.5
82
181.6
12.7
42
241.4
16.9
3
3.0
0.2
63
62.8
4.4
23
122.7
8.6
83
182.6
12.8
43
242.4
17.0
4
4.0
0.3
64
63.8
•4.5
24
123.7
8.6
84
183.6
12.8
44
243.4
17.0
»
5.0
0.3
65
64.8
4.5
25 ! 124. 7
8.7
85
184.5
12.9
45
244.4
17.1
6
6.0
0.4
66
65.8
4.6
26
125.7
8.8
86
185. 5
13.0
46
245.4
17.2
7
7.0
0.5
67
66.8
4.7
27
126.7
8.9
87
186.5
13.0
47
246.4
17.2
8
8.0
0.6
68
67.8
4.7
28
127.7
8.9
88
187.5
13.1
48
247.4
17.3
9
9.0
0.6
69
68.8
4.8
29
128.7
9.0
89
188. 5
1.3.2
49
248.4
17.4
10
10.0
0.7
70
7X8
4.9
30
129.7
9.1
90
189. 5
13.3
50
249.4
17.4
11
11.0
0.8
71
5.0
131
130.7
9.1
191
190.5
13.3
251
250.4
17.5
12
12.0
0.8
72
71.8
.5.0
32
131.7
9.2
92
191.5
13.4
52
251.4
17.6
13
13.0
0.9
73
72.8
5.1
33
132.7
9.3
93
192.5
13.5
53
252.4
17.6
14
14.0
1.0
74
73.8
5.2
34
133.7
9.3
94
193. 5
13.5
54
253.4
17.7
15
15.0
1.0
75
74.8
.5.2
35
134.7
9.4
95
194.5
1,3.6
55
254.4
17.8
16
16.0
1.1
76
75.8
.5.3
36
135.7
9.5
96
195.5
13.7
56
255.4
17.9
17
17.0
1.2
M
76.8
5.4
37
136.7
9.6
97
196.5
13.7
57
256.4
17.9
18
18.0
1.3
78
77.8
5.4
.38
137.7
9.6
98
197.5
13.8
58
257.4
18.0
19
19.0
1.3
79
78.8
5.5
39
138.7
9.7
99
198.5
13.9
59
258.4
18.1
20
21
20.0
1.4
175
80
79.8
8b. 8
5.6
40
139. 7
9.8
200
199.5
14.0
60
259. 4
18.1
20.9
81
5.7
14r
140.7
9.8
201
200.5
14.0
261
260.4
18.2
22
21.9
1.5
82
81.8
5. 7
42
141.7
9.9
02
201.5
14.1
62
261.4
18.3
23
22.9
1.6
83
82.8
5.8
43
142.7
10.0
03
202. 5
14.2
63
262.4
18.3
24
23.9
1.7
84
83.8
5.9
44
143.6
10.0
04
203.5
14.2
64
26.3.4
18.4
25
24.9
1.7
85
84.8
5.9
45
144.6
10.1
05
204.5
14.3
65
264.4
18.5
26
25.9
1.8
86
85.8
6.0
46
145.6
10.2
06
205. 5
14.4
66
265.4
18.6
27
26.9
1.9
87
86.8
6.1
47
146.6
10.3
07
206. 5
14.4
67
266. 3
18.6
28
27.9
2.0
88
87.8
6.1
48
147.6
10.3
08
207.5
14.5
68
267.3
18.7
29
28.9
2.0
89
88.8
6.2
49
148.6
10.4
09
208.5
14.6
69
268.3
18.8
30
29.9
2.1
90
89.8
6.3
50
149.6
10.5
10
209.5
14.6
70
269.3
18.8
18.9
31
30.9
2.2
91
90.8
6.3
151
150.6
10.5
211
210.5
14.7
271
270.3
32
31.9
2.2
92
91.8
6.4
52
1.51. 6
10.6
12
211.5
14.8
72
271.3
19.0
33
32.9
2.3
93
92.8
6.5
53
152.6
10.7
13
212. 5
14.9
73
272.3
19.0
34
33.9
2.4
94
93.8
6.6
54
153.6
10.7
14
21.3. 5
14.9
74
273.3
19.1
35
34.9
2.4
95
94.8
6.6
55
154.6
10.8
15
214.5
15.0
75
274.3
19.2
36
35.9
2.5
96
95.8
6.7
56
155.6
10.9
16
21.5. 5
1.5.1
76
275.3
19.3
37
36.9
2.6
97
96.8
6.8
57
156.6
11.0
17
216.5
15.1
77
276.3
19.3
38
37.9
2.7
98
97.8
6.8
58
1.57. 6
11.0
18
217. 5
1.5.2
78
277.3
19.4
39
38.9
2.7
99
98.8
6.9
59
158.6
11.1
19
218. 5
15.3
79
278. 3
19.5
40
39.9
2.8
100
99.8
7.0
60
1.59. 6
160.6
11.2
20
219. 5
15.3
1.5.4
80
279.3
19.5
41
40.9
2.9
101
100.8
7.0
161
11.2
221
220. 5
281
280.3
19.6
42
41.9
2.9
02
101.8
7.1
62
161.6
11.3
22
221.5
15.5
82
281.3
19.7
43
42.9
3.0
03
102.7
7.2
63 ; 162. 6
11.4
23
222.5
1,5.6
83
282.3
19.7
44
43.9
3.1
04
103.7
7.3
64
163.6
11.4
24
223.5
15.6
84
283. 3
19.8
45
44.9
3.1
05
104.7
7.3
65
164.6
11.5
25
224.5
1,5.7
85
284.3
19.9
46
45.9
3.2
06
105.7
7.4
66
165.6
11.6
26
225.4
15.8
86
285. 3
20.0
47
46.9
3.3
07
106.7
7.5
67 ; 166.6
11.6
27
226.4
1,5.8
87
286. 3
20.0
48
47.9
3.3
OS
107.7
7.5
68 : 167.6
11.7
28
227.4
15.9
88
287. 3
20.1
49
48.9
.3.4
09
108.7
7.6
69 1 168.6
11.8
29
228.4
16.0
89
288.3
20.2
50
49.9
3.5
10
109.7
7. 7
70 I 169. 6
11.9
1179
30
229.4
16.0
90
289.3
20.2
51
50.9
3.6
111
110.7
7.7
171 , 170.6
231
230.4
16.1
291
290.3
20.3
52
51.9
,3.6
12
111.7
7.8
72 ' 171.6
12.0
32
231.4
16.2
92
291.3
20.4
53
.52.9
3.7
13
112.7
7.9
73
172.6
12.1
33
232.4
16.3
93
292.3
20.4
54
53.9
3.8
14
113.7
8.0
74
173.6
12.1
34
233.4
16.3
94
293.3
20.5
55
54.9
3.8
15
114.7
8.0
75
174.6
12.2
35
234.4
16.4
95
294.3
20.6
56
55.9
.3.9
16
115.7
8.1
76
175.6
12.3
36
235.4
16.5
96
295. 3
20.6
57
56.9
4.0
17
116.7
8.2
77
176.6
12.3
37
236. 4
16.5
97
296.3
20.7
58
57.9
4.0
18
117.7
8.2
78
177.6
12.4
38
237. 4
16.6
98
297.3
20.8
59
58.9
4.1
19
118.7
8.3
79
'178. 6
12.5
39
238.4
16.7
99-
298.3
20.9
60
59.9
4.2
20
119.7
8.4
80
179.6
12.6
40
239.4
16.7
300
299.3
20.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
I/at.
f
6°; (94°, 266
°, 274°).
Page 538]
TABLE 2.
Difference of Latitude and
Departure for
4° (176°, 184
°, 356°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat
Dep.
301
300.3
21.0
361
360.1
25.2
421
420.0
29.4
481
479.8
33.5
541
5.39. 7
37.7
02
301.3
21.1
62
361.1
25.2
22
421.0
29.4
82
480.8
33.6
42
540.7
37.8
03
302.2
21.1
63
362. 1
25.3
23
422.0
29.5
83
481.8
33.7
43
541.7
37.9
04
303.2
21.2
64
363.1
25.4
24
423.0
29.6
84
482.8
33.7
44
542.7
37.9
05 i 304.2
21.3
65
364.1
25.5
25
424.0
29.6
85
483.8
33.8
45
543.7
38.0
06 i 305. 2
21.3
66
365.1
25.5
26
424.9
29.7
86
484.8
33.9
46
544.7
38.1
07 306. 2
21.4
67
366.1
25.6
27
425.9
29.8
87
485.8
33.9
47
545.7
38.1
08 307. 2
21.5
68
367.1
25.7
28
426.9
29.9
88
486.8
34.0
48
546.7
38.2
09 308. 2
21.6
69
368.1
25.7
29
427.9
29.9
89
487.8
34.1
49
547.7
38.3
10 ( 309.2
21.6
70
369.1
370.1
25.8
30
428.9
30.0
90
488.8
34.2
50
548.7
38.3
311 [ 310.2
21.7
371
25.9
431
429.9
30.1
491
489.8
34.2
551
549.7
38.4
12 311.2
21.8
72
371.1
25.9
32
430.9
30.1
92
490.8
34.3
52
550.7
38.5
13 312. 2
21.8
73
372.1
26.0
33
431.9
30.2
93
491.8
34.4
53
551.7
38.5
14
313.2
21.9
74
373.1
26.1
34
432.9
.30.3
94
492.8
34.4
54
552.7
38.6
15
314.2
22.0
75
374.1
2&2
35
433, 9
30.3
95
493.8
34.5
55
553. 6
38.7
16
315. 2
22.1
76
375.1
26.2
36
434.9
30.4
96
494.8
34.6
56
554.6
38.7
17
316.2
22.1
77
376. 1
26.3
37
435.9
30.5
97
495.8
34.6
57
555.6
38.8
18
317.2
22.2
78
377.1
26.4
38
436.9
30.6
98
496.8
34.7
58
556.6
38.9
19
318.2
22.3
79
378.1
26.4
39
437.9
30.6
99
497.8
34.8
59
557.6
38.9
20
319.2
22.3
80
379. 1
26.5
26.6
40
441
438.9
30.7
30.8
500
501
498.8
34.8
60
558.6
39.0
321 320. 2
22.4
381
380.1
439.9
499.8
34.9
561
559.6
39.1
22
321.2
22.5
82
381.1
26.6
42
440.9
30.8
02
500.8
35.0
62
560. 6
39.2
23
322. 2
22.5
83
382.1
26.7
43
441.9
30.9
03
501.8
35.
63
561.6
39.2
24
323. 2
22.6
84
383.1
26.8
44
442.9
31.0
04
502.8
35.1
64
562.6
39.3
25
324.2
22.7
85
384.0
26.9
45
443.9
31.0
05
503. 8
35.2
65
563.6
39.4
26
325.2
22.7
86
385.0
26.9
46
444.9
31.1
06
504.8
35.2
66
564.6
39.4
27
326.2
22.8
87
386.0
27.0
47
445.9
31.2
07
505.8
35.3
67
565.6
39.5
28
327.2
22.9
88
387.0
27.1
48
446.9
31.2
08
506.8
35.4
68
566.6
39.6
29
328.2
23.0
89
388.0
27.1
49
447.9
31.3
09
507.8
35.5
69
567.6
39.7
30
329.2
23.0
90
389.
390.
27.2
50
448.9
31.4
10
511
508.8
35.6
70
568. 6
39.8
331
330.2
23.1
391
27.3
451
449. 9
31.5
509.8
35.6
571
569.6
39.8
32
331.2
23.2
92
391.0
27.3
52
450.9
31.5
12
510.8
35.7
72
570.6
39.9
33
332.2
23.2
93
392.0
27.4
53
451. 9
31.6
13
511.8
35.8
73
571.6
40.0
34
333.2
23.3
94
393.0
27.5
54
452.9
31.7
14
512.7
35.8
74
572. 6
40.0
35
334.2
23.4
95
394.0
27.6
55
453.9
31.7
15
513.7
35.9
75
573.6
40.1
36
335.2
23.4
96
395.0
27.6
56
454.9
31.8
16
514.7
36.0
76
574.6
40.2
37
336. 2
23.5
97
396.0
27.7
57
4.55. 9
31.9
17
515. 7
36.0
77
575.6
40.2
38
337.2
23.6
98
397.0
27.8
58
456.9
31.9
18
516.7
36.1
78
576.6
40.3
39
338.2
23.6
99
398.
27.8
59
457.9
32.0
19
517.7
36.2
79
577.6
40.4'
40
339.2
23.7
400
399.0
27.9
60
458.9
32.1
20
518.7
36.2
80
581
578.6
40.5
341
340.2
23.8
401
400.0
28.0
461
459. 9.
32.2
521
519.7
36.3
579.6
40.5
42
341.2
23.9
02
401.0
28.0
62
460. 9
32.2
22
520.7
36.4
82
580.6
40.6
43
342.2
23.9
03
402.0
28.1
63
461.9
32.3
23
521.7
36.4
83
581.6
40.7
44
343.1
24.0
04
403.0
28.2
64
462.9
32.4
24
522.7
36.5
84
582.6
40.7
45
344.1
24.1
05
404.0
28.2
65
463. 9
32.4
25
523.7
36.6
85
583.6
40.8
46
345.1
24.1
06
405.
28.3
66
4(>4.9
,32.5
26
524. 7
36.7
86
584.6
40.9
47
346.1
24.2
07
406.0
28.4
67
465. 8
32.6
27
525.7
36.8
87
585.6
40.9
48
347.1
24.3
08
407.0
28.5
68
466.8
32.6
28
526.7
36.8
88
586.6
41.0
49
348.1
24.3
09
408.0
28.5
69
467.8
32.7
29
527.7
36.9
89
587. 6
41.1
50
349.1
24.4
10
409.0
28.6
70
468.8
32.8
30
528.7
529.7
37.0
90
588.6
589.6
41.2
351
350.1
24.5
411
410.0
28.7
471
469.8
32.9
531
37.0
591
41.3
52
351.1
24.6
12
411.0
28.7
72
470.8
32.9
32
530.7
37.1
92
590.6
41.3
53
352.1
24.6
13
412.0
28.8
73
471.8
33.0
33
531. 7
37.2
93
591.6
41.4
54
353.1
24.7
14
413.0
28.9
74
472.8
33.1
34
532.7
37.2
94
592.6
41.5
55
354.1
24.8
15
414.0
28.9
75
473.8
33.1
35
533.7
37.3
95
593.6
41.5
56
355.1
24.8
16
415.0
29.0
76
474.8
33.2
36 : 534. 7
37.4
96
594.6
41.6
57
356.1
24.9
17
416.0
29.1
77
475. 8
33.3
37 ' 535. 7
37.5
97
595. 6
41.7
58
357.1
25.0
18
417.0
29.2-
78
476.8
33.3
38 ' 536. 7
37. 5
98
596.6
41.7
59
358.1
25.0
19
418.0
29.2
79
477.8
.33.4
39 j 537. 7
37.6
99
597.6
41.8-
60
359,1
25.1
20.
419.0
29.3
80
478.8
35.5
40 ! 538. 7
1
37.7
600
598.6
41.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. 1 Dep.
Lat.
Dist.
Dep.
Lat
;
m"; (
94°, 266°, 274°
.
TABLE 2.
[Page 539 |
Difference of Latitude and Departure for 5° (175°, 185
=,355°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dlst. Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.8
5.3
121
120.5
10.5
181
180.3
15.8
241
240.1
21.0
2
2.0
0.2
62
61.8
5.4
22
121. 5
10.6
82
181.3
15.9
42
241.1
21.1
3
3.0
0.3
63
62.8
5.5
23
122.5
10.7
83
182.3
15.9
43
242.1
21.2
4
4.0
0.3
64
63.8
5.6
24
123.5
10.8
84
183.3
16.0
44
243.1
21.3
5
5.0
0.4
&5
64.8
5.7
25
124.5
10.9
85
184.3
16.1
45
244.1-
21.4
6
6.0
0.5
66
65.7
5.8
26
125. 5
11.0
86
185.3
16.2
46
245.1
21.4
7
7.0
0.6
67
66.7
5.8
27
126.5
11.1
87
186.3
16.3
47
246.1
21.5
8
8.0
0.7
68
67.7
.5.9
28
127. 5
11.2
88
187.3
16.4
48
247.1
21.6
9
9.0
0.8
69
68.7
6.0
29
128. 5
11.2
89
188.3
16.5
49
248.1
21.7
10
10.0
0.9
1.0
70
69.7
70.7
6.1
30
129. 5
11.3
90
189.3
16.6
50
249.0
21.8
11
11.0
71
6.2
131
130.5
11.4
191
190.3
16.6
251
250.0
21.9
12
12.0
1.0
72
71.7
6.3
32
131. 5
11.5
92
191.3
16.7
52
251.
22.0
13
13.0
1.1
73
72.7
6.4
33
132. 5
11.6
93
192.3
16.8
53
252.
22.1
14
13.9
1.2
74
73.7
6.4
34
1,33. 5
11.7
94
193.3
16.9
54
253.0
22.1
15
14.9
1.3
75
74.7
6.5
35
134.5
11.8
95
194. 3
17.0
55
254.0
22.2
16
15.9
1.4
76
75.7
6.6
36
135.5
11.9
96
195.3
17.1
56
255.0
22.3
17
16.9
1.5
77
76.7
6.7
37
136.5
11.9
97
196.3
17.2
57
256.0
22.4
18
17.9
1.6
78
77.7
6.8
38
137. 5
12.0
98
197.2
17.3
58
257.0
22.5
19
18.9
1.7
79
78.7
6.9
39
138.5
12.1
99
198.2
17.3
59
2,58.
22.6
20
19.9
1.7
80
81
79.7
7.0
40
139.5
12.2
200
199.2
17.4
60
259.0
22.7
22.7
21
20.9
1.8
80.7
7.1
141
140.5
12.3
201
200.2
17.5
261
260.0
22
21.9
1.9
82
81.7
7.1
42
141.5
12.4
02
201.2
17.6
62
261.0
22.8
23
22.9
2.0
83
82.7
7.2
43
142.5
12.5
03
202.2
17.7
63
262.0
22.9
24
23.9
2.1
84
83.7
7.3
44
143.5
12.6
04
203.2
17.8
64
263.0
23.0
25
24. 9
2.2
85
84.7
7.4
45
144.4
12.6
05
204.2
17.9
65
264.0
23.1
26
25.9
2.3
86
85.7
7.5
46
145.4
12.7
06
205.2
18.0
66
26.5.0
23.2
27
26.9
2.4
87
86.7
7.6
47
146.4
12.8
07
206.2
18.0
67
266.0
23.3
28
27.9
2.4
88
87.7
7. 7
48
147.4
12.9
08
207.2
18.1
68
267.0
23.4
29
28.9
2.5
89
88.7
7.8
49
148.4
l.S.O
09
208.2
18.2
69
268.0
23.4
30
31
29.9
2.6
90
89.7
7.8
50
149.4
1.50. 4
13.1
10
211
209.2
18.3
70
269.0
23.5
23.6
30.9
2.7
91
90.7
7.9
151
13.2
210.2
18.4
271
270.0
32
31.9
2.8
92
91.6
8.0
52
151. 4
13.2
12
211.2
18.5
72
271.0
23.7
33
32.9
2.9
93
92.6
8.1
53
152.4
1,3.3
13
212.2
18.6
73
272.0
2.3.8
34
33.9
3.0
94
93.6
8.2
54
153. 4
13.4
14
213.2
18.7
74
273.
2,3.9
35
34.9
.3.1
95
94.6
8.3
.55
1.54. 4
13.5
15
214.2
18.7
75
274.0
24.0
36
35.9
3.1
96
9.5.6
8.4
56
1.5.5.4
13.6
16
215.2
18.8
76
274.9
24.1
37
36.9
3.2
97
96.6
8.5
57
1.56. 4
13.7
17
216.2
18.9
77
275.9
24.1
38
37.9
3.3
98
97.6
8.5
.58
1.57. 4
13.8
18
217.2
19.0
78
276.9
24.2
39
38.9
3.4
99
98.6
8.6
59
1.58. 4
13.9
19
218.2
19.1
79
277.9
24.3
40
41
39.8
3.5
100
99.6
8.7
60
159. 4
160. 4
13.9
20
219.2
19.2
80
278.9
24.4
40.8
3.6
101
100.6
8.8
161
14.0
221
220.2
19.3
281
279.9
24.5
42
41.8
3.7
02
101.6
8.9
62
161.4
14.1
22
221.2
19.3
82
280.9
24.6
48
42.8
3.7
03
102.6
9.0
63
162.4
14.2
23
222.2
19.4
83
281.9
24.7
44
43.8
3.8
04
103.6
9.1
64
16.3.4
14.3
24
223.1
19.5
84
282.9
24.8
45
44.8
3.9
05
104.6
9.2
65
164.4
14.4
25
224.1
19.6
85
283. 9
24.8
46
45.8
4.0
06
105.6
9.2
66
16.5.4
14.5
26
225. 1
19.7
86
284. 9
24.9
47
46.8
4.1
07
106.6
9.3
67
166.4
14.6
27
226.1
19.8
87
285.9
2,5.0
48
47.8
4.2
08
107.6
9.4
68
167.4
14.6
28
227.1
19.9
88
286.9
25.1
49
48.8
4.3
09
108.6
9.5
69
168.4
14.7
29
228.1
20.0
89
287.9
25.2
50
49.8
4.4
10
109.6
9.6
70
169.4
14.8
30
229.1
20.0
90
288.9
25.3
51
50.8
4.4
111
110.6
9.7
171
170.3
14.9
231
230.1
20.1
291
289.9
25.4
52
51.8
4.5
12
111.6
9.8
72
171.3
15.0
32
231.1
20.2
92
290.9
25.4
53
52.8
4.6
13
112.6
9.8
73
172.3
15.1
.33
232.1
20.3
93
291.9
25.5
54
53.8
4.7
14
113.6
9.9
74
173.3
15.2
34
233.1
20.4
94
292.9
25.6
55
54.8
4.8
15
114.6
10.0
75
. 174. 3
15.3
35
234. 1
20.5
95
293.9
25.7
56
55.8
4.9
16
115.6
10.1
76
175.3
15.3
36
235.1
20.6
96
294.9
2.5.8
57
56.8
5.0
17
116.6
10.2
77
176.3
15.4
37
2.36. 1
20.7
97
295.9
25.9
58
57.8
5.1
18
117.6
10.3
78
177.3
15.5
38
237. 1
20.7
98
296.9
26.0
59
58.8
5.1
19
118.5
10.4
79
178.3
1.5.6
,39
238.1
20.8
99
297.9
26.1
60
69.8
5.2
20
119.5
10.5
80
179.3
15.7
40
239.1
20.9
300
298.9
26.1
Lat.
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
85° (95°, 265°, 275°
.
Page 540]
TABLE -2.
Difference of Latitude and Departure foi
0° (175°, 185
°, 355°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
1 Lat.
Dep.
301
299.9
j 26.2
361
359.6
31.5
421
419.4
36.7
481
479.2
41.9
541
, ,538.9
47.2
02
300. 8
26.3
62
360.6
31.6
22
420.4
36.8
82
480.2
42.0
42
,539,9
47.3
03
301. 8
' 26.4
63
361.6
31.6
23
421. 4 I 36. 9
83
481.2
42.1
43
540,9
47.4
04
302.8
26.5
64
362.6
31.7
24
422.4
37.0
84
482.2
42.2
44
541.9
47.5
05
303.8
26.6
65
363.6
31.8
25
423.4
37.1
85
483.2
42.3
45
542.9
47.6
06
304.8
26.7
66 i 364.6
31.9
26
424.4
37.1
86
484.1
42.4
46
543.9
47.7
07
305. 8
26.8
67 ! 365.6
32.0
27
425.4
37.2
87
485. 1
42.4
47
544. 9 , 47. 7
08
306.8
26.9
68
366. 6
32.1
28
426.4
37.3
88
486. 1
42.5
48
545.9 : 47.8
09
307. 8
26.9
69
367. 6
32.2
29
427.4
37.4
89
487.1
42.6
49
,546.9 47.9
10
308.8
27.0
70
368.6
32.3
30
428.4
37.5
90
488.1
42.7
50
547. 9 : 48.
311
309.8
27.1
371
369. 6
32.3
431
429.4
37.6
491
489.1
42.8
551
548. 9 - 48. 1
12
310.8
27.2
72 ; 370. 6
32.4
32
430.4
37.7
92
490.1
42.9
52
549.9 : 48.2
13
311.8
27.3
73
371.6
32.5
33
431.3
37.7
93
491.1
43.0
53
550.9 I 48.3
. 14
312.8
27.4
74
372. 6
32.6
34
4,32. 3
37.8
94
492.1
43.1
,54
551.9 . 48.4
15
313.8
27.5
75
373.6
32.7
35
433. 3
37.9
95
493.1
43.1
55
552. 9 ' 48. 4
16
314.8
27.5
76
374.6
32.8
36
434.3
38.0
96
494.1
43.2
56
553. 9 : 48. 5
17
315.8
27.6
77
375.6
32.9
37
435.3
38.1
97
495.1
4.3.3
57
5.54.9 1 48.6
18
316.8
27.7
78
376.6
33.0
.38
436. 3
38. 2
98
496.1
43.4
58
555. 9 I 48. 7
19
317.8
27.8
79
377.6
33.0
39
437. 3
,38.3
99
497.1
43.5
59
556.9 ; 48.8
20
318.8
27.9
80
378. 6
33.1
40
438.3
38.4
500
498.1
43.6
60
561
557. 9 ; 48. 8
321
319.8
28.0
381
379.5
33.2
441
439.3
38.4
501
499.1
43.7
,558.8 ; 48,9
22
320.8
28.1
82
380.5
33.3
42
440.3
.38.5
02 ; 500. 1
43.8
62
559. 8 i 49.
23
321.8
28.2
83
381.5
3.3.4
43
441.3
.38.6
03 i 501. 1
43.8
63
560.8
49.1
24
322. 8
28.2
84
382.5
33.5
44
442. 3
,38.7
04
502.1
43.9
64
561.8
49.2
25
323.8
28.3
85
383. 5
33.6
45
443. 3 38. 8
05
503. 1
44.0
65
562.8
49.3
26
324.8
28.4
86
384. 5
.33.7
46
444. 3 38. 9
06
504. 1
44.1
66
563.8
49.4
27
325.8
28.5
87
385.5
33.7
47
445.3 1 39.0
07
505. 1
44.2
67
564.8
49.5
28
326.7
28.6
88
386.5
3.3.8
48
446. 3 ! 39. 1
08
506. 1
44.3
68
565. 8
49.6
29
.327. 7
28.7
89
387.5
33. 9
49
447. 3 i 39. 1
09
507.1
44.4
69
566.8
49.7
30
328.7
28.8
90
388.5
389.5
34.0
50
448. 3 t 39. 2
10
508.1
44.5
70
567. 8
568. 8
49.7
49.8
331
329.7
28.9
391
34.1
451
449.3 1 39.3
511
509.0
44.5
571
32
330.7
28.9
92
390.5
.34.2
52 450.3 1 39.4
12
510.0
44.6
72
569.8
49.9
33
331. 7
29.0
93
391. 5
34.3
53 i 451.3 39.5
13
511.0
44.7
73
570. 8
.50.0
34
332. 7
29.1
94
392.5
,34. 3
54 i 452. 3 : 39. 6
14
512.0
44.8
74
,571. 8
.50. 1
35
333. 7
29.2
95
393. 5
34.4
55
453. 3 39. 7
15
513.
44.9
75
572.8
.50. 2
36
334. 7
29.3
96
394. 5
34.0
56
454. 3 39. 8
16
514.
45.0
76
573. 8
,50.3
37
335. 7
29.4
97
395.5
34.6
57
4.55.3 i 39.8
17
515.
45.1
77
574.8
50.4
38
336. 7
29.5
98
.396. 5
.34.7
58 456.3 1 39.9
18
516.0
45.2
78
575.8
50.4
39
337.7
29.6
99
397.5
34.8
59 457.3 i 40.0
19
517.0
4,5.2
79
576.8 1 ,50.5
40
338.7
29.6
400
398.5 1
34.9
60 458. 2 j 40. 1
20
518.0
45.3
80
577. 8 j .50. 6
341
339.7
29.7
401
399.5
35.0
461 ! 459. 2 1 40. 2
521
519.0
45.4
581
578. 8 ! ,50. 7
42
340.7
29.8
02
400.5 '
35.0
62 ' 460.2 1 40.3
22
520.
45.5
82
579. 8 i .50. 8
43 341. 7
29.9
03
401.5 ;
35.1
63 ! 461.2
40.4
23
521,
45. 6
83
580.8
.50.9
44
.342. 7
30.0
04
402.5
35.2
64 462. 2
40.4
24
522.
45.7
84
581.8
50. 9
45
343. 7
30.1
05
403.5
35.3
65 463. 2
40.5
25
523.0
45.8
85
582. 8
51.0
46
344.7
30.2
06
404. 5 ;
35.4
66 464. 2
40.6
26
524.
45.9
86
583. 8
51.1
47
345. 7
30.3
07 1 405. 4 I
35.5
67
465.2
40.7
27
525.
45.9
87
584.8
5] . 2
48
346. 7
30.3
08 1 406. 4 1
35.6
68
466.2
40.8
28
526.
46.0
88
.585, 8
51.3
49
347.7
30.4
09 t 407. 4
35.7
69
467.2
40.9
29
527.0
46.1
89
586, 8
51.4
50
351
348.7
349. 7
30.5
10 1 408.4
35.7
70
468.2
41.0
30
528.0
46.2
90
587.8
51.5
30.6
411
409.4
.35. 8
471
469.2
41.1
531
529.0
46.3
591
588.7
51.6
52
350.7
30.7
12
410.4 :
35.9
72
470.2
41.1
32
530.
46.4
92
589.7
51.6
53
351.7
30.8
13
411.4
36.0
73
471.2
41.2
33
531.0
46.5
93
,590.7
51.7
54
352.6
.30.9
14
412. 4
36.1
74
472.2
41.3
34
532.0
46.6
94
.591,7
51.8
55
353. 6
30.9
15
41,3.4
.36.2
75
473. 2
41.4
35
533.
46.6
95
592, 7
.51.9
56
354.6
31.0
16
414.4
36.3
76
474.2
41.5
,36
.533. 9
46.7
96
,593. 7
52.0
57
355.6
31.1
17
415.4
36.4
77
475.2
41.6
37
534. 9
46.8
97
594, 7
,52.1
58
356. 6
31.2
18
416.4
36.4
78
476.2
41.7
38
535. 9
46.9
98
595, 7
52.2
59
357. 6
31.3
19
417.4
36.5
79
477.2
41.8
39
536.9
47.0
99
596, 7
52.3
60
358.6
31.4
20
418.4
36.6
80
478.2
41.8
40
537.9
47.1
600
597.7
52.3
Dist.
Dep.
Lat.
Dist.
Dep. j
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
i
55° (95°, 265°, 275°)
1
TABLE 2.
[Page 541
Difference of Latitude and Departure for 6° (174°, 186
°, 354°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.7
6.4
121
120.3
12.6
181
180.0
18.9
241
239.7
25.2
2
2.0
0.2
62
61.7
6.5
22
121.3
12.8
82
181.0
19.0
42
240.7
25.3
3
3.0
0.3
63
62.7
6.6
23
122. 3
12.9
83
182.0
19.1
43
241.7
25.4
4
4.0
0.4
64
63.6
6.7
24
123. 3
13.0
84
183.0
19.2
44
242.7
25.5
5
5.0
0.5
65
64.6
6.8
25
124. 3
13.1
85
184.0
19.3
45
243.7
25.6
6
6.0
0.6
66
65.6
6.9
26
125. 3
13.2
86
185.
19.4
46
244.7
25.7
/
7.0
0.7
67
66.6
7.0
27
126.3
13.3
87
186.0
19.5
47
245. 6
25.8
8
8.0
0.8
68
67.6
7.1
28
127.3
13.4
88
187.0
19.7
48
246.6
25.9
9
9.0
0.9
69
68.6
7.2
29
128.3
13.5
89
188.0
19.8
49
247.6
26.0
10
11
9.9
10.9
1.0
70
69.6
7.3
30
129.3
130.3
13.6
90
189.0
190.0
19.9
50
248.6
26.1
26.2
1.1
71
70.6
7.4
131
13.7
191
20.0
251
249.6
12
11.9
1.3
72
71.6
7.5
32
131.3
13.8
92 ; 190.9
20.1
52
250.6
26.3
13
12.9
1.4
73
72.6
7.6
33
132.3
13.9
93 191.9
20.2
53
251.6
26.4
14
13.9
1.5
74
73.6
7. 7
34
133.3
14.0
94 192. 9
20.3
54
2.52. 6
26.6
15
14.9
1.6
75
74.6
7.8
35
134.3
14.1
95 193. 9
20.4
55
253.6
26.7
16
15.9
1.7
76
75.6
7.9
36
135.3
14.2
96 194.9
20.5
56
254.6
26.8
17
16.9
1.8
77
76.6
8.0
37
136.2
14.3
97
195.9
20.6
57
255. 6
26.9
18
17.9
1.9
78
77.6
8.2
38
137.2
14.4
98
196.9
20.7
58
256.6
27.0
19
18.9
2.0
79
78.6
8.3
39
138.2
14.5
99
197.9
20.8
59
257. 6
27.1
20
19.9
2.1
80
79.6
8.4
40
139. 2
140.2
14.6
200
201
198.9
20.9
60
258.6
259.6
27.2
21
20.9
2.2
81
80.6
8.5
141
14.7
199.9
21.0
261
27.3
22
21.9
2.3
82
81.6
8.6
42
141.2
14.8
02
200.9
21.1
62
260.6
27.4
23
22.9
2.4
83
82.5
8.7
43
142.2
14.9
03
201.9
21.2
63
261.6
27.5
24
23.9
2.5
84
83.5
8.8
44
143.2
15.1
04
202. 9
21.3
64
262.6
27.6
25
24.9
2.6
85
84.5
8.9
45
]44.2
15.2
05
203. 9
21.4
65
263.5
27.7
26
25.9
2.7
86
85.5
9.0
46
145.2
1.5.3
06
204.9
21.5
66
264.5
27.8
27
26.9
2.8
87
86.5
9.1
47
146.2
15.4
07
205.9
21.6
67
265. 5
27.9
28
27.8
2.9
88
87.5
9.2
48
147.2
15.5
08
206.9
21.7
68
266. 5
28.0
29
28.8
3.0
89
88.5
9.3
49
148.2
15.6
09
207.9
21.8
69
267.5
28.1
30
31
29.8
3.1
90
89.5
9.4
50
151
149.2
150. 2
15.7
15. 8'
10
208.8
22.0
70
268.5
28.2
3.2
91
90.5
9. 5
211
209.8
22. 1
27\
269. 5
28.3
32
31.8
3.3
92
91.5
9.6
.52-
151.2
1.5.9
12
210.8
22! 2
72
270. 5
28.4
33 1 32.8
3.4
93
92.5
9.7
53
1.52. 2
16.0
13
211.8
22.3
73
271.5
28.5
34 1 33.8
3.6
94
93.5
9.8
54
1.53.2
16.1
14
212.8
22.4
74
272. 5
28.6
35
34.8
3.7
95
94.5
9.9
55
1.54. 2
16.2
15
213. 8
22. 5
75
273. 5
28.7
36
;».8
3.8
96
9.5.5
10.0
56
155. 1
16.3
16
214.8
22.6
76
274. 5
28.8
37
36.8
3.9
97
96.5
10.1
57
156.1
16.4
17
21.5.8
22.7
77
275. 5
29.0
38
37.8
4.0
98
97.5
10.2
58
1.57. 1
16.5
18
216.8
22.8
78
276. 5
29.1
39
38.8
4.1
99
98.5
10.3
.59
158. 1
16.6
19
217.8
22.9
79
277. 5
29.2
40
39.8
4.2
100
99.5
10.5
10.6
60
161
159. 1
16.7
16.8
20
221
218.8
219.8
23.0
23. 1
80
281
278. 5
279. 5'
29.3
29.4'
41 40. 8
4.3
101
100.4
160.1
42 41.8
4.4
02
101.4
10.7
62
161.1
16.9
22
220.8
23.2
82
280. 5
29.5
43 j 42.8
4.5
03
102.4
10.8
63
162.1
17.0
23
221.8
23. 3
83
281.4
29.6
44 i 43.8
4.6
04
103. 4
10.9
64
163. 1
17.1
24
222.8
2.3.4
84
282. 4 29. 7
45 ! 44.8
4.7
05
104.4
11.0
65
164.1
17.2
25
223. 8
23. 5
85
283. 4 29. 8
46 i 45. 7
4.8
06
105.4
11.1
66
165. 1
17.4
26
224.8
23. 6
86
284.4 29.9
47 i 46. 7
4.9
07
106.4
11.2
67
166. 1
17.5
27
225. 8
23.7
87
285. 4 30.
48 . 47.7
5.0
08
107.4
11.3
68
167.1
17.6
28
226.8
23.8
88
286.4
30.1
49 48. 7
5.1
09
108.4
11.4
69
168.1
17.7
29
227.7
23.9
89
287.4
30.2
50 i 49. 7
5.2
10
109.4
11.5
70
169.1
17.8
30
228.7
229. 7'
24.0
90
288.4
30.3
51 1 50.7
5.3
111
110.4
11.6
171
170.1
17.9
231
24.1
291 1 289. 4
30.4
52 ! 51. 7
5.4
12
111.4
11.7
72
171.1
18.0
32
230. 7
24.3
92 290.4
30.5
53 j 52.7
5.5
13
112.4
11.8
73
172.1
18.1
33
231.7
24.4
93 291.4 30.6
54 i 53.7
5.6
14
113.4
11.9
74
173.0
18.2
34
232. 7
24.5
94 1 292. 4 30. 7
55 i 54.7
5.7
15
114.4
12.0
75
174.0
18.3
35
2.33. 7
24.6
95 1 293.4 1 ,30.8
56 1 55. 7
5.9
16
115.4
12.1
76
175.0 1 18.4
36 234.7
24.7
96 294.4 i 30.9
57 56.7
6.0
17
116.4
12.2
77
176.0
18.5
37 ; 235.7
24.8
97 i 295.4 1 31.0
58 : 57.7
6.1
18
117.4
12.3
78
177.0
18.6
38 j 236.7
24.9
98 ' 296.4 1 .31.1
59 58. 7
6.2
19
118.3
12.4
79
178.0
18.7
39 : 237.7
2.5.0
99 i 297.4 ! 31.3
60 ; 59. 7
1
6.3
20
119.3
12.5
80
179.0
18.8
40 1 238. 7
25.1
300
298.4
31.4
Diet. Dep.
Lat.
Diet.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. ' Dep.
Lat.
Dist.
Dep.
Lat.
84° [i
•6°, 264°, 276° 1
.
1
Page 542]
TABLE 2.
Difference of Latitude and Departure for 6° (174°, 186°, 354°).
Dist.
Lat.
Dep.
DiBt.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
lilt.
Dep.
301
299.3
31.5
361
359.0
37.7
421
418.7
44.0
481
478.4
50.3
541
538.0
56.5
02
300.3
31.6
62
360.0
37.8
22
419.7
44.1
82
479.4
50.4
42
539.0
56.6
03
301.3
31.7
63
361.0
37.9
23
420.7
44.2
83
480.4
50.5
43
540.0
56.7
04
302.3
31.8
64
362.0
38.0
24
421.7
44.3
84
481.3
50.6
44
541.0
56.8
05
303. 3
31.9
65
363.
38.1
25
422.7
44.4
85
482.3
50.7
45
542.0
56.9
06
304. 3
32.0
66
364.0
38.3
26
423.7
44.5
86
483. 3
50.8
46
543.0
57.0
07
305. 3
32.1
67
365.0
38.4
27
424.7
44.6
87
484.3
50.9
47
544.0
57.1
08
306.3
32.2
68
366.0
38.5
28
425. 7
44.7
88
485.3
51.0
48
545.0
57.2
09
307.3
32.3
69
367.0
38.6
29
426. 6
44.8
89
486. 3
51.1
49
546.0
57.3
10
308.3
309.3
32.4
70
368.0
38.7
30
427.6
428.6
44.9
'45.
90
487.3
488. 3
51.2
51.3
50
547.0
548.0
57.4
57.5
311
32.5
371
369.0
38.8
431
491
551
12
310.3
32.6
72
370.
38.9
32
429.6
45.2
92
489. 3
51.4
52
549.0
57.6
13
311.3
32.7
73
371.0
39.0
33
430. 6
45.3
93
490.3
51.5
53
550.0
57. 7
14
312.3
32.8
74
371.9
39.1
34
431.6
45.4
94
491. 3
51.6
54
551.0
57.9
15
313.3
32.9
75
372.9
39.2
35
4.32. 6
45.5
95
492.3
51.7
55
552.0
58.0
16
314. 3
33.0
76
373.9
39.3
36
433.6
45.6
96
493.3
51.8
56
553.0
58.1
17
315.3
33.1
77
374.9
39.4
37
434.6
45.7
97
494.3
51.9
57
554.
58.2
18
316.3
33.2
78
375.9
39.5
38
435.6
45.8
98
495.3
52.0
58
555.
58.3
19
317.3
33.3
79
376.9
39.6
39
436. 6
45.9
99
496.3
52.1
59
556.0
58.4
20
318.2
33.4
80
381
377.9
39.7
40
437. 6
46.0
500
497.3
52.3
60
556. 9
58. 5
321
319. 2
33.6
378.9
39.8
441
438.6
46.1
501
498.3
52.4
561
557.9
58.6
22
320.2
33.7
82
379.9
39.9
42
439.6
46.2
02
499.3
52.5
62
558.9
58.7
23
321.2
33.8
83
380.9
40.0
43
440.6
46.3
03
500.2
52.6
63
559.9
58.8
24
322.2
33.9
84
381.9
40.1
44
441.6
46.4
04
501.2
52.7
64
560.9
59.0
25
323.2
34.0
85
382.9
40.2
45
442.6
46.5
05
502.2
52.8
65
561.9
59.1
26
324.2
34.1
86
383.9
40.3
46
443.6
46.6
06
503.2
52. 9
66
562.9
59.2
27
325. 2
34.2
87
384.9
40.5
47
444.5
46.7
07
504.2
53.0
67
563.9
59.3
28
326.2
34.3
88
385.9
40.6
48
445.5
46.8
08
505.2
53.1
68
564.9
59.4
29
327.2
34.4
89
386.9
40.7
49
446.5
46.9
09
506.2
53.2
69
565.9
59. 5
30
328.2
34.5
34.6
90
391
387.9
388.9
40.8
50
447.5
47.0
10
511
507.2
508.2
53.3
70
566.9
59.6
331
329.2
40.9
451
448.5
47.1
53.4
571
567.9
59.7
32
330. 2
34.7
92
389. 9
41.0
52
449. 5
47.2
12
509.2
53.5
72
568.9
59.8
33
331.2
34.8
93
390. 8
41.1
53
450. 5
47.3
13
510.2
53.6
73
569.9
59.9
34
332. 2
34.9
94
391.8
41.2
54
451.5
47.5
14
511.2
53.7
74
570.9
60.0
35
333. 2
35.0
95
392.8
41.3
55
452.5
47.6
15
512.2
53.8
75
571.9
60.1
36
334. 2
35.1
96
393.8
41.4
56
453.5
47.7
16
513.2
53.9
76
572.9
60.2
37
335.2
35.2
97
394.8
41.5
57
454.5
47.8
17
514. 2
54.0
77
573. 9
60. 3
38
336. 1
35.3
98
395. 8
41.6
58
455.5
47.9
18
515. 2
54.1
78
574.9
60.4
39
337.1
35.4
99
396.8
41.7
59
456.5
48.0
19
516. 2
54.2
79
575. 8
60.5
40
341
338.1
339.1
35.5
400
397.8
398.8
41.8
60
457.5
48.1
20
517.2
54.3
80
576.8
60.6
35.6
401
41.9
461
458. 5
48.2
521
518.1
54.5
581
577.8
60.7
42
340.1
35.7
02
399.8
42.0
62
459.5
48.3
22
519. 1
54.6
82
578.8
60.8
43
341.1
35.8
03
400.8
42.1
63
460. 5
48.4
23
520.1
54.7
83
579.8
60.9
44
342.1
36.0
04
401.8
42.2
64
461.5
48.5
24
521.1
54.8
84
580.8
61.1
45
343.1
36.1
05
402.8
42.3
65
462.5
48.6
25
522.1
54.9
So
581.8
61.2
46
344.1
36.2
06
403.8
42.4
66
463.4
48.7
26
523.1
55.0
86
582.8
61.3
47
345.1
36.3
07
404.8
42.5
67
464.4
48.8
27
524.1
55.1
87
583.8
61.4
48
346.1
36.4
08
405.8
42.6
68
465. 4
48.9
28
525. 1
55.2
88
584.8
61.5
49
347. 1
36.5
09
406.8
42.7
69
466.4
49.0
29
526.1
55.3
89
585.8
61.6
50
351
348. 1
349.1
36.6
10
411
407.8
42.9
43.0
70
471
467.4
468.4
49.1
30
527.1
528.1
55.4
55.5
90
586.8
61.7
61.8
36:7
408.7
49.2
531
591
587.8
52
350.1
36.8
12
409.7
43.1
72
469.4
49.3
32
529.1
55.6
92
588.8
61.9
53
351.1
36.9
13
410.7
43.2
73
470.4
49.4
33
530.1
55.7
93
589.8
62.0
54
352.1
37.0
14
411.7
43.3
74
471.4
49.5
34
531.1
55.8
94
590.8
62.1
55
353.1
37.1
15
412.7
43.4
75
472.4
49.6
35
532.1
55.9
95
591.8
62.2
56
354.0
37.2
16
413.7
43.5
76
473.4
49.8
36
533.1
56.0
96
592.8
62.3
57
355.0
37.3
17
414.7
43.6
77
474.4
49.9
37
534.1
56.1
97
593. 8
62.4
58
356.0
37.4
18
415.7
43.7
78
475.4
50.0
38
535. 1
56.2
98
594.7
62.5
59
357.0
37.5
19
416.7
43.8
79
476.4
50.1
39
536.1
56.3
99
595. 7
62.6
60
358.0
37.6
20
417.7
43.9
80
477.4
50.2
40
537.1
56.4
600
596.7
62.7
Diet.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
84° (96°, 264°, 276°). 1
TABLE 2.
[Page 543
Difference of Latitude and Departure for 7° (173°, 187°, 353°)
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.5
7.4
121
120.1
14.7
181
179.7
22.1
241
239.2
29.4
2
2.0
0.2
62
61.5
7.6
22
121.1
14.9
82
180.6
22.2
42
240.2
29.5
3
3.0
0.4
63
62.5
7.7
23
122.1
1.5.0
83
181.6
22.3
43
241.2
29.6
4
4.0
0.5
64
63. 5
7.8
24
123.1
15.1
84
182.6
22.4
44
242.2
29.7
5
5.0
0.6
65
64.5
7.9
25
124.1
15.2
85
183.6
22.5
45
243. 2
29.9
6
6.0
0.7
66
65.5
8.0
26
125. 1
15.4
86
184.6
22.7
46
244.2
30.0
7
6.9
0.9
67
66.5
8.2
27
126.1
15.5
87
185.6
22.8
47
245.2
30.1
8
7.9
1.0
68
67.5
8.3
28
127.0
1.5.6
88
186.6
22.9
48
246.2
30.2
9
8.9
1.1
69
68.5
8.4
29
128.0
1.5.7
89
187.6
23.0
49
247.1
30.3
10
9.9
1.2
70
69.5
8.5
30
129.0
15.8
90
188.6
23.2
50
248.1
30.5
11
10.9
1.3
71
70.5
8.7
131
130.0
16.0
191
189.6
23.3
251
249.1
30.6
12
11.9
1.5
72
71.5
8.8
32
131.0
16.1
92
190.6
23.4
52
250.1
30.7
13
12.9
1.6
73
72.5
8.9
33
132.0
16.2
93
191.6
23.5
53
251.1 30.8
14
13.9
1.7
74
73.4
9.0
34
133.0
16.3
94
192.6
23.6
54
252.1 31.0
15
14.9
1.8
75
74.4
9.1
35
134.0
16.5
95
193.5
23.8
55
253. 1 31. 1
16
15.9
1.9
76
75.4
9.3
36
135.0
16.6
96
194.5
23.9
56
254. 1 31. 2
17
16.9
2.1
77
76.4
9.4
37
136.0
16.7
97
195.5
24.0
57
2.55.1 , 31.3
18'
17.9
2.2
78
77.4
9.5
38
137.0
16.8
98
196.5
24.1
58
256.1 , 31.4
19
18.9
2.3
79
78.4
9.6
39
138.0
16.9
99
197.5
24.3
59
257.1 31.6
20
19.9
20.8
2.4
80
79.4
9.7
40
139.0
17.1
200
198.5
24.4
60-
258. 1 i 31. 7
259.1 i 31.8
21
2.6
81
80.4
9.9
141
139.9
17.2
201
199.5
24.5
261
22
21.8
2.7
82
81.4
10.0
42
140.9
17.3
02
200.5
24.6
62
260.0 1 31.9
23
22.8
2.8
83
82.4
10.1
43
141.9
17.4
03
201.5
24.7
63
261.0 : 32.1
24
23.8
2.9
84
83.4
10.2
44
142.9
17.5
04
202.5
24.9
64
262.0
32.2
25
24.8
3.0
85
84.4
10.4
45
143.9
17.7
05
203.5
25.0
65
263.0
32.3
26
25.8
3.2
86
85.4
10.5
46
144.9
17.8
06
204.5
25.1
66
264.0
32. 4
27
26.8
3.3
87
86.4
10.6
47
145,9
17.9
07
205.5
2.5.2
67
265.0
32.5
28
27.8
3.4
88
87.3
10.7
48
146.9
18.0
08
206.4
25.3
68
266.0
32.7
29
28.8
3.5
89
88.3
10.8
49
147.9
18.2
09
207.4
2.5.5
69
267.0
.32.8
30
29.8
3.7
90
91
89.3
90.3
11.0
11.1
50
151
148.9
18.3
18.4
10
208.4
25.6
70
271
268.0
32.9
31
30.8
3.8
149.9
211
209.4
2.5.7
269.0
33.0
32
31.8
3.9
92
91.3
11.2
52
150.9
18.5
12
210.4
25.8
72
270.0
,33.1
33
32.8
4.0
93
92.3
11.3
53
151.9
18.6
13
211.4
26.0
73
271.0
33. 3
34
33. 7
4.1
94
93.3
11.5
54
152. 9
18.8
14
212.4
26.1
74
272.0
33.4
35
34.7
4.3
95
94.3
11.6
55
153.8
18.9
15
213.4
26.2
75
273.0
33.5
36
35.7
4.4
96
95.3
11.7
56
154.8
19.0
16
214.4
26.3
76
273.9
3,3.6
37
36.7
4.5
97
96.3
11.8
57
155.8
19.1
17
215. 4
26.4
77
274.9
33.8
38
37.7
4.6
98
97.3
11.9
58
156.8
19.3
18
216.4
26.6
78
275.9
33.9
39
38.7
4.8
99
98.3
12.1
59
1.57. 8
19.4
19
217.4
26.7
79
276.9
34.0
40
41
39.7
40.7
4.9
100
99-. 3
12.2
60
158.8
19.5
20
218.4
26.8
80
277.9
,34.1
5.0
101
100.2
12.3
161
159. 8
19.6
221
219.4
26.9
281
278.9
,34. 2
42
41.7
5.1
02
101.2
12.4
62
160.8
19.7
22
220.3
27.1
82
279.9
34.4
43
42.7
5.2
03
102. 2
12.6
63
161.8
19.9
23
221.3
27.2
83
280.9
34.5
44
43.7
5.4
04
103.2
12.7
64
162.8
20.0
24
222.3
27.3
84
281.9
34.6
45
44.7
5.5
05
104.2
12.8
65
163.8
20.1
25
223.3
27.4
85
282.9
34.7
46
45.7
5.6
06
105.2
12.9
66
164.8
20.2
26
224, 3
27.5
86
283.9
34.9
47
46.6
5.7
07
106.2
13.0
67
165.8
20.4
27
225.3
27.7
87
284.9
35.0
48
47.6
5.8
08
107.2
13.2
68
166.7
20.5
28
226.3
27.8
88
285.9
35.1
49
48.6
6.0
09
108.2
13.3
69
167.7
20.6
29
227.3
27.9
89
286.8
35.2
50
49.6
6.1
10
109.2
13.4
70
168.7
20.7
30
228.3
28.0
90
287.8
35.3
51
50.6
6.2
111
110.2
13.5
171
169.7
20.8
231
229.3
28.2
291
288.8
35.5
52
51.6
6.3
12
111.2
13.6
72
170.7
21.0
32
230.3
28.3
92
289.8
35.6
53
52.6
6.5
13
112.2
13.8
73
171.7
21.1
33
231.3
28.4
93
290.8
35.7
54
53.6
6.6
14
113.2
13.9
74
172.7
21.2
34
232.3
28.5
94
291.8
35.8
55
54.6
6.7
15
114.1
14.0
75
173.7
21.3
35
233.2
28.6
95
292.8
36.0
56
55.6
6.8
16
115. 1
14.1
76
174.7
21.4
36
234.2
28.8
96
293.8
36.1
57
56.6
6.9
17
116.1
14.3
77
175.7
21.6
37
235.2
28.9
97
294.8
.36.2
58
57.6
7.1
18
117.1
14.4
78
176.7
21.7
38.
236.2
29.0
98
295.8
36.3
59
58.6
7.2
19
118.1
14.5
79
177.7
21.8
39
237.2
29.1
99
296.8
.36.4
60
59.6
7.3
20
119.1
14.6
80
178.7
21.9
40
238.2
29.2
300
297.8
36.6
Diat.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat. JDist.
Dep.
Lat.
Dist.
Dep.
Lat.
83° (97°, 263°, 277°).
1
Page 544]
TABLE 2.
Difference of Latitude and Departure for
7° (173°, 187
°, 353°
)■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. 1 Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
298.7
36.7
361
358.3
44.0
421 417.9
51.3
481
477.4
.58.6
541
537.
65.9
02
299.7
36.8
62
359.3
44.1
22 i 418.8
51.4
82
478.4
58.7
42
537.9
66.0
03
300.7
36.9
63
360.3
44.2
23 419. 8
51.5
83
479.4
58.8
43
538.9
66.2
04
301.7
37.0
64
361.3
44.4
24
420.8
51.7
84
480.4
59.0
44
539. 9
66.3
05
302.7
37.2
65
362.3
44.5
25
421.8
51.8
85
481.4
59.1
45
540.9
66.4
06
303.7
37.3
66
363.3
44.6
26
422.8
51.9
. 86
482.4
59.2
46
541.9
66.6
07
304.7
37.4
67
364. 3
44.7
27
423.8
52.0
87
483.4
59.4
47
542. 9
66.7
08
305.7
37.5
68
365.2
44.8
28
424.8
52.2
88
484.3
59.5
48
543. 9
66.8
09
306.7
37.7
69
366.2
45.0
29
425.8
52.3
89
485. 3
59.6
49
544.9
66.9
10
307.7
37.8
70
367.2
45.1
30
426.8
52.4
'90
486.3
487.3
59.7
59.8
50
.545. 9
67.0
311
308.7
37.9
371
368.2
4.5.2
431
427.8
52.5
491
551
546. 9
67.1
12
309.7
38.0
72
369. 2
45.3
32 : 428.8
52.6
92
488.3
59.9
52
547.9
67.2
13
310.7
38.1
73
370.2
45. 5
33 ! 429.8
52.8
93
489. 3
60.1
53
548. 9
67.4
14
311.7
38.3
74
371.2
45. 6
34
430.8
52.9
94
490.3
60.2
54
549.9
67.5
15
312.6
38.4
75
372.2
4.5.7
35
431.7
53.0
95
491. 3
60.3
55
5.50. 8
67.6
16
313.6
38.5
76
373.2
45.8
36
432.7
53.1
96
492.3
60.5
"56
551.8
67.8
17
314.6
38.6
77
374.2
45.9
37
433.7
53.3
97
493. 3
60.6
57
552.8
67.9
18
315.6
38.7
78
375.2
46.1
38
434.7
53.4
98
494.3
60.7
58
553.8
68.0
19
316.6
38.9
79
376.2
46.2
39
435.7
53.5
99
495.3
60.8
59
554.8
68.1
20
317.6
39.0
80
377.2
46.3
40
436.7
53.6
500
496.3
61.0
60
555.8
68.3
321
318.6
39.1
381
378.1
46.4
441
437.7
53.7
501
497.2
61.1
561
556.8
68.4
22
319.6
39.2
82
379.1
46.5
42 i 438. 7
53.9
02
498.2
61.2
62
557.8
68.5
23
320.6
39.4
83
380.1
46.7
43 ' 439. 7
54.0
03
499.2
61.3
63
558.8
68.6
24
321.6
39.5
84
381.1
46.8
44 ' 440. 7
54.1
04
500. 2
61.4
64
559. 8
68.7
25
322.6
39.6
85
382.1
46.9
45 441. 7
54.2
05
501.2
61.5
65
560.8
68. 9
26
323.6
39.7
86
383.1
47.0
46 , 442.7
54.3
06
502.2
61. ()
66
561.8
69.0
27
324.6
39.8
87
384.1
47.2
47 443. 7
54.5
07
503.2
61,8
67
562.8
69.1
28
325.5
40.0
88
385.1
47.3
48 : 444. 7
54.6
08
504.2
61.0
68
563.8
69.2
29
326. 5
40.1
89
386.1
47.4
49 445.6
54.7
09
505.2
62.
69
564.8
69.3
30
327.5
40.2
90
387.1
47.5
50 446.6
54.8
10
506.2
62.1
70
"571
565.8
69.4
331
328.5
40.3
391
388.1
47.6
451 i 447.6
55.0
511
507.2
62. 3"
566.7
69.6
32
329.5
40.5
92
389.1
47.8
52 i 448.6
55.1
12
508.2
62.4
72
567.7
69.7
33
330.5
40.6
93
390.1
47.9
53 449.6
55.2
13
509.2
62.5
73
568.7
69.8
34
331.5
40.7
94
391.1
48.0
.54 ' 450.6
55. 3
14
510.2
62.6
74
569.7
69.9
35
332.5
40.8
95
392.0
48.1
55 : 451.6
55.4
15
511.1
62.7
75
570. 7
70.1
36
333.5
40.9
96
393.0
48.3
56 : 452.6
55.6
16
512.1
62. 9
76
571.7
70.2
37
334.5
41.1
97
394.0
48.4
57 4.53. 6
55.7
17
513.1
63.0
77
572.7
70.3
38
335.5
41.2
98
395.
48.5
58 454. 6
5.5.8
18
514.1
63.1
78
573.;
70.4
39
336. 5
41.3
99
396.0
48.6
59 455.6
55.9
19
515.1
63.2
79
574,7
7(1.5
40
341
337.5
41.4
400
397
48.7
60 1 456.6
56.1
20
516.-1
63.4
80
575. 7
70.7
70. 8
338.4
41.6
401
398.0
48.9
461 i 457.6
56.2
521
517.1
63.5
581
576.7
42
339.4
41.7
02
399.0
49.0
62 : 458.5
.56.3
22
518.1
63.6
82
577. 6
70.9
43
340.4
41.8
03
400.0
49.1
63
4.59. 5
.56.4
23
519.1
63.7
83
578. 6
71.0
44
341.4
41.9
04
401.0
49.2
04
460. 5
56.5
24
520. 1
63.8
84
579. 6
71.2
45
342.4
42.0
05
402.0
49.4
65
461.5
.56.7
25
521.1
64.0
85
580. 6
71. 3
46
343. 4
42.2
06
403.0
49.5
66
462.5
56.8
26
522.1
64. 1
86
531.6
71.4
47
344.4
42.3
07
404.0
49.6
67
463.0
56.9
27
523.1
64.2
87
582.6
71.5
48
345.4
42.4
08
405.0
49.7
68
464.5
57.0
28
524.1
64.3
88
583. 6
71.6
49
346.4
42.5
09
405.9
49.8
69
465.5
57.2
29
525.
64.5
89
584. 6
71.8
50
347.4
42.6
10
406.9
50.0
70
471
466.5
57.3
30
531
526.0
527.0
64.6
90
585. 6
58(i. (i
71.9
7L'.
351
348.4
42.8
411
407.9
50.1
467.5
57.4
64.7
591
52
349.4
42.9
12
408.9
50.2
72
468. 5
57.5
32
528.0
64.8
92
587. li
7-'. 1
53
350.4
43.0
13
409.9
50.3
/ b
469. 5
57.6
33
529.0
64.9
93
588. 6
72. 2
54
351.4
43.1
14
410.9
50.4
74 ' 470.5
57.8
34
530.0
65.1
94
589. 6
72.4
55
352.3
43.3
15
411.9
50.6
75 \ 471.5
57.9
35
531.
6.5.2
95
590. 6
72.5
56
353.3
43.4
16
412.9
50.7
76 ; 472.4
58.0
36
532.
65.3
96
591.5
72. 6
57
354.3
43.5
17
413.9
50.8
77 ! 473.4
58.1
37
533.0
65.4
97
592. 5
72.7
58
355.3
43.6
18
414.9
50.9
78 1 474.4
58.2
38
534.
65.6
98
593.5
72.9
59
356.3
43.7
19
415.9
51.1
79
475.4
58.4
39
535.0
65.7
99
594.5
73.0
60
357.3
43.9
20
416.9
51.2
80
476.4
58.5
40
536.0
65.8
600
595.5
73.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat,
83° (97°, 263°, 277°
•
TABLE -i.
[Page 545
Difference of Latitude and Departure for 8° (172", 188°, 352=
.
DUt.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.1
61
60.4
8.5
121
119.8
16.8
181
179.2
25.2
241
238.7
33.5
f.
2.0
0.3
62
61.4
8.6
22
120.8
17.0
■82
180.2
25.3
42
239.6
.33.7 1
3
3.0
0.4
63
62.4
8.8
23
121.8
17.1
83
181.2 25.5
43
240.6 .33.8
4
4.0
0.6
64
63.4
8.9
24
122.8
17.3
84
182.2 : 25.6
44
241.6 : 34.0
5
5.0
0.7
65
64.4
9.0
25
123. 8
17.4
85
183. 2 1 25. 7
45
242. 6 34. 1
6
5.9
0.8
66
65.4
9.2
26
124. 8
17.5
86
184.2 ; 25.9
46
243.6 \ 34.2
7
6.9
1.0
67
66.3
9.3
27
125.8
17.7
87
185.2 26.0
47
244.6 , 34.4
8
7.9
1.1
68
67.3
9.5
28
126.8
17.8
88
186. 2 : 26. 2
48
245.6 ! 34.5
9
8.9
1.3
69
68.3
9.6
29
127.7
18.0
89
187. 2 : 26. 3
49
246.6 1 34.7
10
9.9
1.4
70
69.3
9.7
30
128.7
18.1
90
188.2 i 26.4
50
247.6 ' 34.8
11
10.9
1.5
71
70.3
9.9
131
129.7
18.2
191
189. 1 1 26. 6
251
248.6 34.9
1?
11.9
1.7
72
71.3
10.0
32
130.7
18.4
92
190.1 1 26.7
52
249. 5 35. 1
13
12.9
1.8
73
72.3
10.2
33
131.7
18.5
93
191. 1 ! 26. 9
53
250. 5 35. 2
14
13.9
1.9
74
73.3
10.3
34
132.7
18.6
94
192. 1 1 27.
54
251.5 35.3
15
14.9
2.1
75
74.3
10.4
;55
133. 7
18.8
95
193. 1 ' 27. 1
55
252. 5
35.5
16
15.8
2.2
76
75.3
10.6
36
134.7
18.9
96
194. 1 27. 3
56
253.5
35.6
17
16.8
2.4
77
76.3
10.7
37
135.7
19.1
97
195.1
27.4
57
2.54. 5
35.8
18
17.8
2.5
78
77.2
10.9
38
1.36. 7
19.2
98
196.1
27.6
58
255. 5
35.9
19
18.8
2.6
79
78.2
11.0
39
137.7
19.3
99
197.1
27.7
59
256.5
36.0
20
19.8
2.8
80
79:2
11.1
40
141
138.6
139. 6
19.5
200
198.1
27.8
60
257.5
36.2
!^1
20.8
2.9
81
80.2
11.3
19.6
201
199.0
28.0
261
258.5
36.3
!^i?
21.8
3.1
82
81.2
11.4
42
140.6
19.8
02
200.0
28.1
62
259.5
36.5
23
22.8
3.2
83
82.2
11.6
43
141.6
19.9
03
201.0 28.3
63
260.4
36.6
24
23.8
3.3
84
83.2
11.7
44
142.6 ! 20.0
04
202.0 i 28.4
64
261.4
36.7
25
24.8
3.5
85
84.2
11.8
45
143.6 j 20.2
05
203.0 \ 28.5
65
262.4
36.9
2fi
25.7
3.6
86
85.2
12.0
46
144.6 i 20.3
06
204. ' 28. 7
66
263.4
37.0
27
26.7
3.8
87
86.2.
12.1
47
145.6 i 20.5
07
205. I 28. 8
67
264.4
37.2
28
27.7
3.9
88
87.1
12.2
48
146.6 ' 20.6
08
206.0 28.9
68
265. 4
37.3
29
28.7
4.0
89
88.1
12.4
49
147. 5 '•■ 20. 7
09
207. 29. 1
69
266.4
37.4
30
29.7
4.2
90
89.1
12.5
50
148.5 20.9
10
208. 29. 2
70
267.4
37.6
31
30.7
4.3
91
90.1
12.7
151
149.5 21.0
211
208.9 ! 29.4
2V1
268.4
37.7
32
.31.7
4.5
92
91.1
12.8
52
150.5 21.2
12
209.9 29.5
72
269. 4
37.9
33
32.7
4.6
93
92.1
12.9
53
151.5 ! 21.3
13
210. 9 29. 6
73
270. 3
38.0
34
33.7
4.7
94
93.1
13.1
54
152.5 21.4
14
211.9 ( 29.8
74
271.3
38.1
35
34.7
4.9
95
94.1
13.2
.55
153.5 21.6
15
212.9
29.9
75
272.3
38.3
36
35.6
.5.0
96
95.1
13.4
56
154. 5 ! 21. 7
16
213.9
30.1
76
273. 3
38.4
37
36.6
.5.1
97
96.1
13.5
57
15.5.5 21.9
17
214.9
30.2
77
274.3
38.6
38
.37.6
5.3
98
97.0
13.6
58
156. 5 22.
18
215. 9
30.3
78
275.3
38.7
39
38.6
5.4
99
98.0
1.3.8
59
157.5 22.1
19
216.9
30.5
79
276.3
38.8
40
39.6
5.6
100
99.0
13.9
60
158.4 1 22.3
20
217.9
30.6
80
277.3
39.0
41
40.6
5.7
101
100.0
14.1
161
1.59. 4
22.4
221
218.8
30.8
281
278.3
39.1
42
41.6
5.8
02
101.0
14.2
62
160.4
22.5
22
219.8
30.9
82
279.3
39.2
43
42.6
6.0
03
102.0
14.3
63
161.4
22.7
23
220.8
31.0
83
280.2
39.4
44
43.6
6.1
04
103.0
14.5
64
162.4
22.8
24
221.8
31.2
84
281.2
39.5
45
44.6
6.3
05
104.0
14.6
65
163. 4
23.0
25
222.8
31.3
85
282.2
39.7
46
45.6
6.4
06
105.0
14.8
66
164.4
23.1
26
223.8
31.5
86 1 283. 2
39.8
47
46.5
6.5
07
106.0
14.9
67
165. 4
23.2
27
224.8
31.6
87 1 284.2
.39. 9
48
47.5-
6.7
08
106.9
15.0
68
166.4 ! 23.4
28
225.8
31.7
88 1 285. 2
40.1
49
48.5
6.8
09
107.9
15.2
69
167. 4 1 23. 5
29
226.8
31.9
89 286. 2
40.2
50
49.5
7.0
10
108.9
15.3
15.4
70
168. 3
169.3
23.7
30
227.8
32.0
90 287. 2
40.4
40.'5
51
50.5
7.1
111
109.9
171
2.3.8
231
228.8
32.1
291 ' 288.2
52
51.5
7.2
12
110.9
15.6
72
170.3 i 23.9
32
229.7
32.3
92 1 289.2
40.6
53
52.5
7.4
13
111.9
1.5.7
73
171. 3 24. 1
33
230.7
32.4
93 i 290. 1
40.8
54
53.5
7.5
14
112.9
15.9
74
172. 3 i 24. 2
34
231.7
32.6
94 i 291. 1
40.9
55
54.5
7.7
15
113.9
16.0
75
17.3.3 1 24.4
35
232.7
32.7
95
292.1
41.1
56
55.5
7.8
16
114.9
16.1
76
174.3 1 24.5
36
233.7
32.8
96
293.1
41.2
57
56.4
7.9
17
115.9
16.3
77
175. 3
24.6
37
234.7
33.0
97
294.1
41.3
58
57.4
8.1
18
116.9
16.4
78
176. 3
24.8
38
235.7
33.1
98
295.1
41.5
59
.58.4
8.2
19
117.8
16.6
79
177.3
24.9
39
236. 7
33.3
99
296.1
41.6
60
59.4
8.4
20
118.8
16.7
80
178.2
25.1
40
237.7
33.4
300
297.1
41.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
DLst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
82° (<
)8°; 262°, 278°
)■
1
24972°— 12-
Page 546]
TABLE 2.
Difference of Latitude and Departure for 8° (172°, 188°, 352'
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
298.0
41.9
361
357.5
50.2
421
416.9
58.6
481
476.3
66.9
541
535.7
75.2
02
299.0
42.0
62
358.5
50.4
22
417.9
58.7
82
477.3
67.1
42
536.7
.75.4
03
300.0
42.2
63
859. 4
50.5
23
418.9
58.9
83
478.3
67.2
43
537. 7
75. 5
04
301.0
42.3
64
360.4
50.7
24
419.8
59.0
84
479.3
67.4
44
538.7
75.7
05
302.0
42.5
65
361.4
50.8
25
420.8
59.2
85
480.3
67.5
45
539. 7
7.5.8
06
303.0
42.6
66
362.4
50.9
26
421.8
59.3
86
481.2
67.6
46
540.6
75.9
07
304.0
42.7
67
363.4
51.1
27
422.8
59.4
87
482.2
67.8
47
541.6
76.1
08
.305.0
42.9
68
364.4
51.2
28
423.8
59.6
88
483.2
67.9
48
542.6
76.2
09 306.
43.0
69
365. 4
51.4
29
424.8
59.7
89
484.2
68.1
49
,543. 6
76.4
10
307.0
43.1
70
366.4
367.4
51.5
30
425.8
426.8
59.8
90
485.2
68.2
50
544.6
76.5
311
307.9
43.3
371
51.6
431
60.0
491
486.2
68.3
551
545.6
76.6
12 i 308.9
43.4
72
368.4
51.8
32
427.8
60.1
92
487.2
68.5
52
546.6
76.8
13 309. 9
43.6
73
369.3
51.9
33
428.8
60.3
93
488.2
68.6
53
547.6
76.9
14
310.9
43.7
74
370.3
52.1
34
429.8
60.4
94
489.2
68.8
54
548.- 6
77.1
15
311.9
43.8
75
371.3
52.2
35
430.7
60.5
95
490.2
68.9
55
549.6
77.2
16
312.9
44.0
76
372.3
52.3
36
431.7
60.7
96
491.2
69.0
56
550.6
77.4
17
313.9
44.1
77
373.3
52.5
37
432.7
60.8
97
492.1
69.2
57
,551.5
77.5
18
314.9
44.3
78
374.3
52.6
38
433. 7
61.0
98
493.1
69.3
58
552. 5
77.6
19
315.9
44.4
79
375. 3
52.7
39
434.7
61.1
99
494.1
69.5
59
553.5
77.8
20
321
316.9
44.5
80
376.3
52.9
40
435.7
61.2
500
495.1
69.6
60
554.5
77.9
317.9
44.7
381
377.3
53.0
441
436.7
61.4
501
496. 1
69.7
561
555.5
78.1
, 22
318.8
44.8
82
378. 3
53.2
42
437.7
61.5
02
497.1
69. 9
62
556.5
78.2
23
319.8
45.0
83
379.2
53.3
43
438.7
61.7
03
498.1
70.0
63
557.5
78.3
24
320.8
45.1
84
380.2
53.4
44
439.7
61.8
04
499.1
70.2
64
558.5
78.5
25
321.8
45.2
85
381.2
53.6
45
440.6
61.9
05
500.1
70.3
65
559.5
78.6
26
322.8
45.4
86
382.2
53.7
46
441.6
62.1
06
501.0
70.4
66
560.5
78.8
27
323.8
45.5
87
383.2
53.9
47
442.6
62.2
07
502.0
70.6
67
561. 5
78.9
28
324. 8
45.7
88
384.2
54.0
48
443.6
62.4
08
503.0
70.7
68
562. 5
79.0
29
325.8
45.8
89
385.2
54.1
49
444.6
62.5
09
504.0
70.8
69
563.5
79.1
30
326.8
45.9
90
386.2
54.3
50
445.6
62.6
10
505.0
70.9
70
564.5
79.3
79.4
331
327.8
46.1
391
387.2
54.4
451
446.6
62.8
511
506.0
71.1
571
565.4
32
328.7
46.2
92
388.2
54.6
52
447.6
62.9
12
507.0
71.2
72
566.4
79.6
33
329.7
46.3
93
389.1
54.7
53
448.6
63.0
13
508.0
71.4
73
,567. 4
79.7
34
330.7
46.5
94
390.1
54.8
54
449.6
63.2
14
509.
71.5
74
568. 4
79.8
35
331.7
46.6
95
391.1
55.0
55
450.5
63.3
15
510.0
71.6
75
569.4
80.0
36
332.7
46.8
96
392.1
55.1
56
451.5
63.5
16
510.9
71.8
76
570.4
80.1
37
333. 7
46.9
97
393.1
55.3
57
452.5
63.6
17
511.9
71.9
77
571.4
80.2
38
334.7
47.0
98
394. 1
55.4
58
453.5
63.7
18
512.9
72.0
78
572.4
80.4 •
39
335.7
47.2
99
395.1
55.5
59
454.5
63.9
19
513.9
72.2
79
573.4
80.5
40
.336.7
47.3
47.5
400
401
396.1
55.7
60
455.5
64.0
20
514.9
72.3
80
574.4
80.6
341
337.7
397.1
55.8
461
456.5
64.2
521
515.9
72.4
581
575. 4
80.8
42
338.6
47.6
02
398.1
56.0
62
457.5
64.3
22
516.9
72.6
82
576.4
80.9
43
339.6
47.7
03
399.1
56.1
63
458.5
64.4
23
517.9
72.8
83
577.4
81.1
44
340.6
47.9
04
400.0
56.2
64
459.5
64.6
24
518.9
73.0
84
578.4
81.3
45
341. 6
48.0
05
401.0
56.4
65
460.4
64.7
25
5)9.9
73.1
85
579.4
81.4
46
342.6
48.2
06
402.0
56.5
66
461.4
64.9
26
520.9
73.2
86
580.3
81.6
47
343.6
48.3
07
403.0
56.6
67
462.4
65.0
27
521.8
7,3.4
87
581.3
81.7
48
344. 6
48.4
08
404.0
56.8
68
463.4
65.1
28
522.8
73. 5
88
582. 3
81.8
49
345.6
48.6
09
405.0
56.9
69
464.4
65.3
29
523.8
73.7
89
583. 3
82.0
50
346.6
48.7
10
406.0
407.0
57.1
70
465.4
65.4
30
524.8
73.8
90
584. 3
82.1
351
347.6
48.9
411
57.2
471
466.4
65.6
531
525.8
73.9
591
585.3
82.2
52
348.5
49.0
12
408.0
57.3
72
467.4
65.7
32
526.8
74.1
92
586.3
82.4
53
349.5
49.1
13
409.0
57.5
73
468.4
65.8
33
527.8
74.2
93
587.3
82.5
54
350.5
49.3
14
409.9
57.6
74
469.4
66.0
34
528.8
74.3
94
588.3
82.6
55
351.5
49.4
15
410.9
57.8
75
470.4
66.1
35
529.8
74.5
95
589.3
82.8
56
352.5
49.5
16
411.9
57.9
76
471.3
66.2
36
530.8
74.6
96
590. 3
8,3.0
57
353.5
49.7
17
412.9
58.0
77
472.3
66.4
37
531. 7
74.7
97
591.2
83.1
58
354.5
49.8
18
413.9
58.2
78
473.3
66.5
38
532.7
74.9
98
592.2
83.2
59
355.5
50.0
19
4)4.9
58.3
79
474.3
66.7
,39
533.7
7.5.0
99
593.2
83.3
60
356.5
50.1
20
415.9
58.5
80
475.3
66.8
40
534.7
75.1
600
594.2
83.5
Dlst. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
82° (98°, 262°, 278°). 1
TABLE 2.
[Page 647
Difference of Latitude and Departure for 9° (171°, 189'
,351°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Ijit.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
60.2
9.5
121
119.5
18.9
181
178.8
28.3
241
238.0
37.7
2
2.0
0.3
62
61.2
9.7
22
120.5
19.1
82
179.8
28.5
42
239.
.37.9
3
3.0
0.5
63
62.2
9.9
23
121.5
19.2
83
180.7
28.6
43
240.0
38.0
4
4.0
0.6
64
63.2
10.0
24
122.5
19.4
84
181.7
28.8
44
241.0
38.2
5
4.9
0.8
65
64.2
10.2
25
123.5
19.6
85
182.7
28.9
45
242.0
38.3
6
5.9
0.9
66
65.2
10.3
26
124.4
19.7
86
183.7
29.1
46
243.0
38.5
7
6.9
1.1
67
66.2
10.5
27
125.4
19.9
87
184.7
29.3
47
244.0
38.6
8
7.9
1.3
68
67.2
10.6
28
126.4
20.0
88
185.7
29.4
48
244.9
38.8
9
8.9
1.4
69
68.2
10.8
29
127.4
20.2
89
186.7
29.6
49
245.9
39.0
10
11
9.9
1.6
70
69.1
11.0
30
128.4
20.3
2a6
90
187.7
29.7
50
246.9
247.9
39.1
10.9
1.7
71
70.1
11.1
131
129.4
191
188.6
29.9
251
39.3
12
11.9
1.9
72
71.1
11.3
32
130.4
20.6
92
189.6
30.0
52
248.9
39.4
13
12.8
2.0
73
72.1
11.4
33
131.4
20.8
93
190.6
30.2
53
249.9
39.6
14
13.8
2.2
74
73.1
11.6
34
1.32. 4
21.0
94
191.6
30.3
54
250.9
39. 7
15
14.8
2.3
75
74.1
11.7
35
133. 3
21.1
95
192.6
30.5
55
251.9
39.9
16
15.8
2.5
76
75.1
11.9
36
134.3
21.3
96
193.6
30.7
56
252.8
40.0
17
16.8
2.7
77
76.1
12.0
37
135. 3
21.4
97
194.6
30.8
57
253.8
40.2
18
17.8
2.8
78
77.0
12.2
38
136.3
21.6
98
195.6
31.0
58
254.8
40.4
19
18.8
3.0
79
78.0
12.4
39
137.3
21.7
99
196.5
31.1
59
255. 8
40.5
20
19.8
3.1
80
79.0
12.5
40
138.3
139.3
21.9
200
197.5
31.3
60
256.8
257.8
40.7
40.8
21
20.7
3.3
81
80.0
12.7
141
22.1
201
198.5
31.4
261
22
21.7
3.4
82
81.0
12.8
42
140.3
22.2
02
199.5
31.6
62
258. 8
41.0
23
22.7
3.6
83
82.0
13.0
43
141.2
22.4
03
200.5
31.8
63
259.8
41.1
24
23.7
3.8
84
83.0
13.1
44
142.2
22.5
04
201.5
31.9
64
260.7
41.3
25
24.7
3.9
85
84.0
13.3
45
143.2
22.7
05
202.5
32.1
65
261.7
41.5
26
25.7
4.1
86
84.9
13.5
46
144.2
22.8
06
203.5
32.2
66
262.7
41.6
27
26.7
4.2
87
85.9
13.6
47
145.2
23.0
07
204.5
32.4
67
263.7
41.8
28
27.7
4.4
88
86.9
13.8
48
146.2
23.2
08
205.4
32.5
68
264.7
41.9
29
28.6
4.5
89
87.9
13.9
49
147.2
23.3
09
206.4
32.7
69
265.7
42.1
30
29.6
4.7
4.8
90
88.9
14.1
50
148.2
23.5
10
207.4
32.9
70
266.7
267.7
42.2
42.4
31
30.6
91
89.9
14.2
151
149.1
23.6
211
20s. 4
33.0
271
32
31.6
5.0
92
90.9
14.4
52
150. 1
2.3.8
12
209.4
33.2
72
268.7
42.6
33
32.6
. 5.2
93
91.9
14.5
53
151.1
23.9
13
210.4
33.3
73
269.6
42.7
34
33.6
5.3
94
92.8
14.7
54
1.52.1
24.1
14
211.4
33.5
74
270.6
42.9
35
34.6
5.5
95
93.8
14.9
55
153.1
24. 2
15
212.4
33.6
75
271.6
43.0
36
35.6
5.6
96
94.8
15.0
56
154.1
24! 4
16
213.3
33.8
76
272.6
43.2
37
36.5
5.8
97
95.8
15.2
57
155. 1
24.6
17
214.3
33.9
77
273.6
43.3
38
37.5
5.9
98
96.8
15.3
58
156.1
24.7
18
215.3
34.1
78
274.6
43.5
39
38.5
6.1
99
97.8
15.5.
59
157.0
24.9
19
216.3
34.3
79
275.6
43.6
40
39.5
6.3
6.4
100
98.8
15.6
15.8
60
158.0
25.0
20
221
217.3
34.4
80
276.6
277.5
43.8
44.0
41
40.5
101
99.8
161
159.0
25.2
218.3
34.6
281
42
41.5
6.6
02
100.7
16.0
62
160.0
25.3
22
219.3
34.7
82
278.5
44.1
43
42.5
6; 7
03
101.7
16.1
63
161.0
25.5
23
220.3
34.9
83
279.5
44.3
44
43.5
6.9
04
102.7
16.3
64
162.0
25.7
24
221.2
35.0
84
280.5
44.4
45
44.4
7.0
05
103.7
16.4
65
163.0
25.8
25
222.2
.35.2
85
281.5
44.6
46
45.4
7.2
06
104.7
16.6
66
164.0
26.0
26
223.2
35.4
86
282.5
44.7
47
46.4
7.4
07
105.7
16.7
67
164.9
26.1
27
224.2
35.5
87
283.5
44.9
48
47.4
7.5
08
106.7
16.9
68
165. 9
26.3
28
225. 2
35.7
88
284.5
45.1
49
48.4
7.7
09
107.7
17.1
69
166.9
26.4
29
226.2
35.8
89
285.4
45.2
50
51
49.4
7.8
10
108.6
17.2
70
167.9
168.9
26.6
26.8
30
231
227.2
228.2
36.0
90
286.4
45.4
60.4
8.0
111
109.6
17.4
171
36.1
291
287.4
45.5
52
51.4
8.1
12
110.6
17.5
72
169.9
26.9
32
229.1
36.3
92
288.4
45.7
53
52.3
8.3
13
111.6
17.7
73
170.9
27.1
33
230.1
36.4
93
289.4
45.8
54
53.3
8.4
14
112.6
17.8
74
171.9
27.2
34
231. 1
36.6
94
290.4
46.0
55
54.3
8.6
15
113.6
18.0
75
172.8
27.4
35
232. 1
36.8
95
291.4
46.1
56
55.3
8.8
16
114.6
18.1
76
173.8
27.5
36
233.1
36.9
96
292.4
46.3
57
56.3
8.9
17
115.6
18.3
77 i 174. 8
27.7
37
234.1
37.1
97
293.3
46.5
58
57.3
9.1
18
116.5
18.5
78
175.8
27.8
38
235.1
37.2
98
294.3
46.6
59
58.3
9.2
19
117.5
18.6
79
176.8
28.0
.39
236.1
37.4
99
295. 3
46.8
60
59.3
9.4
20
118.5
18.8
80
177.8
28.2
40
237.0
37.5
300
296.3
46.9
bist.
Dep.
Lat.
Di3t.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
81° (99°, 261°, 279°
)•
Page 548]
TABLE 2.
Difference of Latitude and Departure for 9° (171°, 189
^ 351°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
301
297.3
47.1
361
.356. 6
56.5
421 i 415.8
65.9
481
475.1
75.2
541
534. 4 U4. 6
02
298.3
47.2
62
357.5
56.7
22 : 416.8
66.0
82
476.1
75.3
42
535. 4 i 84. 7
03
299.3
47.4
63
358.5
56.8
23 j 417.8
66.2
83
477.1
75. 5
43
536.3 i 84.9
04
300.3
47.6
64
3.59. 5
56.9
24 : 418. 8
66.3
84
478.0
75.6
44
5.37.3 ; 85.1
05
301.2
47.7
65
360.5
57.1
25 I 419.8
66.5
85
479.0
75.8
45
538.3 1 85.3
06
302.2
47.9
66
361.5
57.3
26
420.8
66.6
86
480.0
75.9
46
539.3 i 85.4
07
303.2
48.0
67
362.5
57.4
27
421.7
66. 8
87
481.0
76.1
47
540. 3
85.6
08
304.2
48.2
68
363.5
57.6
28
422.7
67.0
88
482.0
76.2
48
541.3
85.7
09
305.2
48.3
69
364.5
57.7
29
423.7
67.1
89
483.0
76.4
49
.542. 3
85.9
10
306.2
48.5
70
365.4
57.9
30
424.7
67.3
90
484.0
76.5
50
543.3
86.0
311
307.2
48.7
371
366.4
58.1
431
425. 7
67.4
491
485.0
76.7
551
544.3
86.2
12
308.2
48.8
72
367.4
58.2
32
426.7
67.6
92
485.9
76.8
52
545. 2
86.3
13
309.1
49.0
73
368.4
58.4
33
427.7
67.7
93
486.9
77.0
53
546.2
86.5
14
310.1
49.1
74
369.4
58.5
34
428.7
67.9
&4
487.9
77.1
54
547. 2
86.6
15
311.1
49.3
75
370.4
58.7
35
429.6
68.1
95
488.9
77.3
55
548.2
86.8
16
312. 1
49.4
76
371.4
58.8
36
430.6
68.2
96
489.9
77.5
56
549.2
87.0
17
313.1
49.6
77
372.4
59.0
37
431.6
68.4
97
490.9
77. 7
57
5.50. 2
87.1
18
314.1
49.8
78
373.3
59.1
38
432. 6
68.5
98
491.9
77.9
58
551. 2
87.3
19
315. 1
49.9
79
374.3
59.3
39
433.6
68.7
99
492.9
78.0
59
552.2
87.4
20
316. 1
50.1
80
375.3
59.5
40
434.6
68.8
500
501
493.8
78.2
60
553.1
87.6
321
317.
50.2
381
376. 3
59.6
441
435.6
69.0
494.8
78.4
561
554.1
87.7
22
318.
50.4
82
377. 3
59.8
42
436.6
69.1
02
495.8
78.5
62
555.1
87.9
23
319.0
50. 5
83
378.3
59.9
43
437.5
69.3
03
496.8
78. 7
63
556.1
88.0
24
320.0
50.7
84
379.3
60.1
44
438.5
69.5
04
497.8
78.8
64
557.1
88.2
25
321.
50.8
85
380.3
60.2
45
439.5
69.6
05
498.8
79.0
65
558.1
88.3
26
322.0
51.0
86
381.2
60.4
46
440.5
69.8
06
499.8
79.1
66
559. 1
88.5
27
323.0
51.2
87
382.2
60.5
47
441.5
69.9
07
500.8
79.2
67
560.1
88.6
28
324.0
51.3
88
383.2
60.7
48
442. 5
70.1
08
501.7
79.4
68
561.0
88.8
29
324. 9
51.5
89
384.2
60.9
49
443.5
70.2
09
502. 7
79.5
69
562.
88.9
30
325.9
51.7
90
385.2
386.2
61.0
50
444.5
445.4
70.4
10
511
503. 7
79.7
70
563. i 89. 1 1
331
326.9
51.8
391
61.2
451
70.6
504.7
79.8
571
564.0
89.2
32
327.9
51.9
92
387.2
61.3
52
446.4
70.7
12
505. 7
80.1
72
565.0
89.4
33
328.9
52.1
93
388.2
61.5
53
447.4
70.9
13
506.7
80.2
73
.566.0
89.5
34
329.9
52.3
94
389.1
61.6
54
448.4
71.0
14
507.7
80.3
74
567.0
89.7
35
330. 9
52.4
95
390.1
61.8
55
449.4
71.2
15
508. 7
80.5
75
568.0
89.9
36
331.9
52.6
96
391. 1
62.0
56
450. 4
71.3
16
509.6
80.6
76
568. 9
90.1
37
332. 8
52.7
97
392.1
62.1
57
451.4
71.5
17
510. 6
80.8
77
56,9. 9
90.2
38
.333.8
52.9
98
393.1
62.3
58
452.4
71.7
18
511.6
80.9
78
570.9
90.3
39
334. 8
53.0
99
394.1
62.4
59
4.53. 3
71.8
.19
512. 6
81.1
79
571.9
90.5
40
335. 8
53.2
400
395. 1
62.6
60
454. 3
72.0
72.1
20
52i
513.6
81.3
80
581
572.9
573.9
90.7
341
336. 8
53.3
401
396.1
62.7
461
455.3
514.6
81.4
90.9
42
337. 8
53.5
02
397.0
62.9
62
456. 3
72.3
22
515.6
81.6
82
574.9
91.0
43
338.8
53.7
03
398.0
63.0
63
457.3
72.4
23
516. 6
81.8
83
575.9
91.2
44
339.8
53.8
04
399.0
63.2
64
458.3
72.6
24
517.6
81.9
84
576.9
91.3
45 1 340.8
54.0
05
400.0
63.4
65
4.59. 3
72.7
25
518.6
82.1
85
577.9
91.5
46 341. 7
54.1
06
401.0
63.5
66
460.3
72.9
26
519.5
82.3
86
578.8
91.7
47 342. 7
54.3
07
402.0
63.7
67
461.2
73.1
27
520. 5
82.4
87
579.8
91.8
48 i 343. 7
54.4
08
403.0
63.8
68
462.2
73.2
28
521.5
82.6
88
580.8
92.0
49 344.7
54.6
09
404.0
64.0
69
463.2
73.4
29
522.5
82.7
89
581.8
92.1
50 345. 7
54.8
10
405.0
64.1
70
464.2
73.5
30
523.5
82.9
90
582.8
92.2
351 i 346. 7
54.9
411
405.9
64.3
471
465.2
73.7
531
524. 5
83.1
591
583.8
92.4
52 • 347. 7
55.1
12
406.9
.64.5
72
466.2
73.8
32
525. 5
83.2
92
584.8
92.5
53
348.7
55.2
13
407.9
64.6
73
467.2
74.0
33
526.5
83.4
93
585.7
92.7
54
349.6
55.4
14
408.9
64.8
74
468.2
74.2
34
527.5
83.5
94
586.7
92.9
55
350.6
55.5
15
409.9
64.9
75
469.2
74.3
35
528.4
83.7
95
587.7
93.1
56
351. 6
55.7
16
410.9
65.1
76
470.1
74.5
36
529.4
83.8
96
588.7
93.2
57
352.6
5.5.9
17
411.9
65.2
77
471.1
74.6
37
530.4
84.0
97
589.7
93.4
58
353. 6
56.0
18
412.9
65.4
78
472.1
74.8
38
531. 4
84.1
98
590.7
93.5
59
354.0
56.2
19
413.8
65.6
79
473.1
74.9
39
532.4
84.3
99
591.7
93.7
60
355.6
56.3
20
414.8
65.7
80-
474.1
75.0
40
533.4
84.4
600
592.6
93.8
DIst.
Dep.
LiU.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
pist.
Dep.
Lat.
Dist.
Dep.
Lat.
81° (99°, 261°, 279°).
TABLE
2.
[Page 549
Difference of Latitude and Departure for 10° (170°, 190
°, 350°
)■
Dist.
Lat.
Dep.
Dist.
Lat. i Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
60.1
10.6
121
119.2
21.0
181
178.3
31.4
241
237.3
41.8
2
2.0
0.3
62
61.1
10.8
22
120.1
21.2
82
179.2
31.6
42
238. 3
42.0
3
3.0
0.5
63
62.0
10.9
23
121.1
21.4
83
180.2
31.8
43
239.3
42.2
4
3.9
0.7
64
63.0
11.1
24
122.1
21.5
84
181.2
32.0
44
240.3
42.4
5
4.9
0.9
65
64.0
11.3
25
123.1
21.7
85
182.2
32.1
45
241.3
42.5
6
5.9
1.0
66
65.0
11.5
26
124.1
21.9
86
183. 2
32.3
46
242.3
42.7
7
6.9
1.2
67
66.0
11.6
27
125.1
22.1
87
184.2
32.5
47
243.2
42.9
8
7.9
1.4
68
67.0
11.8
28
12a 1
22.2
88
185.1
32.6
48
244.2
43.1
9
8.9
1.6
69
68.0
12.0
29
127.0
22.4
s9
186.1
32.8
49
245. 2
43.2
10
9.8
1.7
70
68.9
12.2
30
128.0
129.0
22.6
90
187.1
33.0
50
246.2
43.4
43.6
11
10.8
1.9
71
69.9
12.3
131
22.7
191
188.1
33.2
251
247.2
12
11 8
2.1
72
70.9
12.5
32
130.0
22.9
92
189.1
33.3
52
248.2
43.8
13
12.8
2.3
73
71.9
12.7
33
131.0
23.1
93
190.1
33.5
53
249.2
43.9
14
13.8
2.4
74
72.9
12.8
34
132.0
23.3
94
191.1
33.7
54
250.1
44.1
15
14.8
2.6
75
73.9
13.0
35
132.9
23.4
95
192.0
33.9
.55
251.1
44.3
16
15.8
2.8
76
74.8
13.2
36
133.9
23.6
96
193.0
34.0
56
252.1
44.5
17
16.7
3.0
it
75.8
13.4
37
134.9
23.8
97
194.0
,34.2
57
253.1
44.6
18
17.7
3.1
78
76.8
13.5
38
135.9
24.0
98
195.0
34.4
58
254.1
44.8
19
18.7
3.3
79
77.8
13.7
39
136.9
24.1
99
196.0
34.6
59
2,55. 1
4.5.0
20
19.7
3.5
80
78.8
13.9
40
137.9
138. 9
24.3
200
201
197.0
34.7
60
256.1
45.1
21
20.7
3.6
81
79.8
14.1
141
24.5
197.9
,34.9
261
257.0
45.3
22
21.7
3.8
82
80.8
14.2
42
139.8
24.7
02
198.9
35.1
62
258.0
45.5
23
22.7
4.0
83
81.7
14.4
43
140.8
24.8
03
199.9
35.3
63
259.0
4,5.7
24
23.6
4.2
84
82.7
14.6
44
141.8
25.0
04
200.9
35.4
64
260.0
45.8
25
24.6
4.3
85
83.7
14.8
45
142.8
25.2
05
201.9
35.6
65
261.0
46.0
26
25.6
4.5
86
84.7
14.9
46
143.8
25.4
06
202.9
35.8
66
262.0
46.2
27
26.6
4.7
87
85.7
15.1
47
144.8
25. 5
07
203.9
35.9
67
262.9
46.4
28
27.6
4.9
88
86.7
15.3
48
145. 8
25.7
08
204.8
36.1
68
263.9
46.5
29
28.6
■5.0
89
87.6
15.5
49
146. 7
25. 9
09
205. 8
36.3
69
264.9
46.7
30
29.5
5.2
90
88.6
15.6
50
147.7
26.0
26.2
10
206.8
36.5
70
265.9
46.9
31
30.5
5.4
91
89.6
15.8
151
148.7
211
207.8
36.6
271
266.9
47.1
32
31.5
5.6
92
90.6
16.0
52
149.7
26.4
12
208.8
36.8
72
267.9
47.2
33
32.5
5.7
93
91.6
16.1
53
150.7
26.6
13
209.8
-37.0
73
268.9
47.4
34
33.5
5.9
94
92.6
16.3
54
151.7
26.7
14
210..7
37.2
74
269.8
47.6
35
34.5
6.1
95
93.6
16.5
55
152. 6
26.9
15
211.7
37.3
75
270.8
47.8
36
35.5
6.3
96
94.5
16.7
56
153.6
27.1
16
212.7
37.5
76
271.8
47.9
37
36.4
6.4
97
95.5
16.8
57
154.6
27.3
17
213. 7
37.7
77
272. 8
48.1
38
37.4
6.6
98
96.5
17.0
58
155. 6
27.4
18
214.7
,37.9
78
273.8
48.3
39
38.4
6.8
99
97.5
17.2
59
156. 6
27.6
19
215.7
38.0
79
274.8
48.4
40
41
39.4
40.4
6.9
100
98.5
17.4
17.5
60
161
157. 6
158.6
27.8
28.0
20
221
216.7
38.2
80
275.7
276.7
48.6
7.1
101
99.5
217.6
38.4
281
48.8
42
41.4
7.3
02
100.5
17.7
62
159.5
28.1
22
218.6
,38.5
82
277.7
49.0
43
42.3
7.5
03
101.4
17.9
63
160.5
28.3
23
219.6
38.7
83
278.7
49.1
44
43.3
7.6
04
102.4
18.1
64
161.5
28.5
24
220.6
38.9
84
279.7
49.3
45
44.3
7.8
05
103.4
18.2
65
162.5
28.7
25
221.6
,39.1
85
280.7
49. 5
46
45.3
8.0
06
104.4
18.4
66
163. 5
28.8
26
222.6
39.2
86
281.7
49.7
47
46.3
8.2
07
105.4
18.6
67
164.5
29.0
27
223.6
39.4
87
282.6
49.8
48
47.3
8.3
08
106.4
18.8
68
1&5.4
29.2
28
224.5
39.6
88
283. 6
.50.
49
48.3
8.5
09
107.3
18.9
69
166.4
29.3
29
225.5
39.8
89
284.6
50.2
50
49.2
8.7
10
108.3
19.1
70
167.4
29.5
30
226.5
39.9
90
291
285.6
.50.4
51
50.2
8.9
111
109.3
19.3
171
168.4
29.7
231
227.5
40.1
286.6
50.5
52
51.2
9.0
12
110.3
19.4
72
169.4
29.9
32
'228. 5
40.3
92
287.6
50.7
53
52.2
9.2
13
111.3
19.6
73
170.4
30.0
33
229.5
40.5
93
288.5
50.9
54
53.2
9.4
14
112. 3
19.8
74
171.4
30.2
34
230.4
40.6
94
289.5
51.1
55
54.2
9.6
15
113.3
20.0
75
172.3
,30.4
35
231.4
40.8
95
290. 5
51.2
56
55.1
9.7
16
114.2
20.1
76
173.3
30.6
36
232. 4
41.0
96
291.5
51.4
57
56.1
9.9
17
115. 2
20.3
77
174.3
30.7
37 1 233.4
41.2
97
292.5
51.6
58
57.1
10.1
18
116.2
20.5
78
175. 3
30. 9
38
234.4
41.3
98
293.5
51.7
59
58.1
10.2
19
117.2
20.7
79
176.3
31.1
39
2.35.4
41.5
99
294.5
51.9
60
59.1
10.4
20
118.2
20.8
80
177.3
31.3
40
236.4
41.7
300
295.4
62.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
80° (1
00°, 260
°, 280°).
1
Page 550]
TABLE 2.
Difference of Latitude and Departure fur 10° (170°, 19C
°, 350°)
Dist.
I^t.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
296.4
52.3
361
355. 5
62.7
421
414.6
73.1
481
473.7
83.5
541
532.8
93.9
02
297.4
52.5
62
356.5
62.9
22
415. 6
73.3
82
474.7
83.7
42
533.8
94.1
03
298.4
62.6
63
357. 5
63.0
23
416.6
73.5
83
475. 7
83.9
43
534.8
94.3
04
299.4
52.8
64
358.5
63.2
24
417.6
73.6
84
476.6
84.1
44
535. 7
94.5
05
300.4
53.0
65
359. 5
63.4
25
418.5
73.8
85
477.6
84.2
45
536.7
94.6
06
301.4
53.1
66
360. 4
63.6
26
419.5
74.0
86
478.6
84.4
46
537. 7
94.8
07
302. 3
53.3
67
361.4
63.7
27
420.5
74.2
87
479.6
84.6
47
538. 7
95.0
08
303.3
53. 5
68
,362. 4
63.9
28
421.5
74.3
88
480.6
84.7
48
539. 7
95.1
09
,S04. 3
53.7
69
363.4
64.1
29
422. 5
74.5
89
481.6
84.9
49
540. 7
95.3
10
311
305. 3
53.8
70
364. 4
64.3
30
423.5
74.7
.90
482.6
85.1
50
541.6
9.5.5
306.3
.54.0
371
365. 4
64.4
431
424.5
74.9
491
483.5
85.2
551
542.6
9.5.6
12
307. 3
54.2
72
366. 4
64.6
32
425. 4
75.0
92
484.5
85.4
52
543.6
95.8
13
308. 2
54.3
73
367.3
64.8
33
426.4
75.2
93
485.5
85.6
53
544.6
96.0
14
309.2
54.5
74
368.3
65.0
34
427.4
75.4
94
486.5
8.5.8
54
545.6
96.2
15
310.2
54.7
75
369.3
65.1
35
428.4
75.5
95
487.5
85.9
55
546.6
96.3
16
311.2
54.9
76
370.3
65.3
36
429.4
75. 7
96
488.5
86.1
56
547.5
96.5
17
312.2
55.1
77
371.3
65.5
37
430.4
75.9
97
489.4
86.3
57
548.5
96.7
18
313.2
55.2
78
372.3
65.6
38
431.3
76.1
98
490.4
86.5
58
549.5
96.9
19
314.2
55.4
79
373.2
65.8
39
432.3
76.2
99
491.4
86.6
59
550.5
97.0
20
321
315.1
55.6
80
374.2
66.0
40
433.3
76.4
500
492.4
86.8
60
551.5
97.2
316.1
55.8
381
375.2
66.2
441
434.3
76.6
501
493.4
87.0
561
552. 5
97.4
22
317.1
55.9
82
376.2
66.3
42
435.3
76.8
02
494.4
87.2
62
553.5
97.6
23
318.1
56.1
83
377.2
66.5
43
436.3
76.9
03
495. 3
87.3
63
554.4
97.7
24
319.1
56.3
84
378.2
66.7
44
437.3
77.1
04
496. 3
87.5
64
555. 4
97.9
25
320.1
56.4
85
379.2
66.9
45
4.38. 2
77.3
05
497.3
87.7
65
556.4
98.1
26
321.0
56.6
86
380.1
67.0
46
439.2
77.5
06
498. 3
87.9
66
557.4
98.3
27
322.0
56.8
87
381.1
67.2
47
440.2
77.6
07
499. 3
88.0
67
558.4
98.4
28
323.0
57.0
88
.382. 1
67.4
48
441.2
77.8
08
500.3
88.2
68
559.4
98.6
29
324.0
57.1
89
383. 1
67.6
49
442.2
78.0
09
501.3
88.4
69
560. 3
98.8
30
325.
57.3
90
384. 1
67.7
67.9
50
443. 2
78.2
10
502.2
88.6
70
561.3
99.0
331
326.0
57.5
391
385. 1
451
444.2
78.3
511
503.2
88.7
571
562. 3
99. 1
32 327.
57.7
92
386.
68.1
52
445.1
78.5
12
504.2
88.9
72
563. S
99.3
33 , 327.9
57.8
93
387.0
68.2
53
446.1
78.7
13
505.2
89.1
73
564.3
99.5
34
328.9
58.0
94
388.
68.4
54
447.1
78.8
14
506.2
89.2
74
565. 3
99.6
35
329. 9
58.2
95
389.
68.6
55
448.1
79.0
15
507.2
89.4
75
566. 3
^ 99.8
36
330.9
58.4
96
390.0
68.8
56
449.1
79.2
16
508.2
89.6
76
567.2
100.0
37
331.9
58.5
97
391.0
68.9
57
450.1
79.4
17
509.1
89.8
77
568.2
100.2
38
3,32. 9
58.7
98
392.0
69.1
58
451.0
79.5
18
510.1
89.9
78
569.2
100.3
39
333.9
58.9
99
392.9
69.3
59
452.0
79.7
19
511.1
90.1
79
570.2
100.5
40
.334. 8
59.1
400
393.9
69.5
60
461
453.0
454.0
79.9
20
521"
512.1
90.3
90.5
80
581
571.2
572. 2
100.7
341
335. 8
59.2
401
394.9
69.6
80.1
513.1
UX).9
42
336.8
59.4
02
395.9
69.8
62
455.0
80.2
22
514.1
90.6
82
573.2
101.0
43
337.8
59.6
03
396.9
70.0
63
456.0
80.4
23
515.1
90.8
83
574.1
101.2
44
338.8
59.8
04
397.9
70.2
64
457.0
80.6
24
516.0
91.0
84
575.1
101.4
45
339.8
59.9
05
398.9
70.3
65
457.9
80.8
25
517.0
91.2
85
576.1
101.6
46
340.7
60.1
06
399.8
70.5
66
458.9
80.9
26
518.0
91.3
86
577.1
101.7
47
341.7
60.3
07
400.8
70.7
67
459. 9
81.1
27
519.0
91.5
87
578.1
101.9
48
342.7
60.4
08
401.8
70.9
68
460.9
81.3
28
520.0
91.7
88
579.1
102.1
49
343.7
60.6
09
402.8
71.0
69
461.9
81.5
29
521.0
91.9
89
580.0
102.3
50
344.7
60.8
10
403.8
71.2
70
462.9
81.6
30
521.9
92.0
90
581.0
102.4
351
345.7
61.0
411
404.8
71.4
471
463.8
81.8
531
522.9
92.2
591
582.0
102.6
52
346.7
61.1
12
405.7
71.6
72
464.8
82.0
32
523.9
92.4
92
583.0
102.8
53
347.6
61.3
13
406.7
71.7
73
465. 8
82.1
33
524.9
92.5
93
584.0
102.9
54
348.6
61.5
14
407.7
71.9
74
466.8
82.3
34
525.9
92.7
94
585.0
103.1
55
349.6
61.7
15
408.7
72.1
75
467.8
82.5
35
526.9
92.9
95
586.0
103.3
56
350.6
61.8
16
409.7
72.2
76
468.8
82.7
36
527.9
93.1
96
586.9
103.5
57
351.6
62.0
17
410.7
72.4
77
469.8
82.8
37
528.8
93.2
97
587.9
103.6
58
352.6
62.2
18
411.7
72.6
78
470.7
83.0
38
529.8
93.4
98
588.9
103.8
59
353.5
62 4
19
412.6
72.8
79
471.7
83.2
39
530.8
93.6
99
589.9
104.0
60
354.5
62.5
20
413.6
72.9
80
472.7
83.4
40
531.8
93.8
600
590.9
104.2
01st.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
80° (1
00°, 260
°, 280°
)•
TABLE 2.
[Page 551
Difference of Latitude and Departure for
11° (169°, 191
°, 349°).
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. Dep.
1
1.0
0.2
61
59.9
11.6
121
118.8
23.1
181
177.7
34.5
241
236.6
46.0
2
2.0
0.4
62
60.9
11.8
22
119.8.
23.3
82
178.7
34.7
42
237.6
46.2
3
2 9
0.6
63
61.8
12.0
23
120.7
23.5
83
179.6
34.9
43
238.5
46.4
4
3.9
0.8
64
62.8
12.2
24
121.7
23.7
84
180.6
35.1
44
239.5
46.6
5
4.9
1.0
65
63.8
12.4
25
122. 7
23.9
85
181.6
35.3
45
240.5
46.7
6
5.9
1.1
66-
64.8
12.6
26
123.7
24.0
86
182.6
35.5
46
241.5
46.9
7
6.9
1.3
67
65.8
12.8
27
124.7
24.2
87
183.6
3.5.7
47
242.5
47.1
8
7.9
1.5
68
66.8
13.0
28
125.6
24.4
88
184. 5 .
35.9
48
243.4
47.3
9
8.8
1.7
69
67.7
13.2
29
126.6
24.6
89
185.5
36.1
49
244.4
47.5
10
9.8
1.9
70
68.7
13.4
30
127.6
128. 6'
24.8
90
186.5
.36.3
50
245.4
47.7
11
10.8
2.1
71
69.7
13.5
131
25.0
191
187.5
36.4
251
246.4 47.9 |
12
11.8
2.3
72
70.7
13.7
32
129.6
25.2
92
188.5
36.6
52
247.4
48.1
13
12.8
2.5
73
71.7
13.9
33
130.6
25.4
93
189.5
36.8
53
248.4
48.3
14
13.7
2.7
74
72.6
14.1
34
131.5
25.6
94
190.4
37.0
54
249.3
48.5
15
14.7
2.9
75
73.6
14.3
35
132.5
2,5.8
95
191.4
37.2
55
250.3
48.7
16
15.7
3.1
76
74.6
14.5
36
1,33. 5
26.0
96
192.4
37.4
56
251.3
48.8
17
16.7
3.2
77
75.6
14.7
37
134.5
26.1
97
193.4
37.6
57
252.3
49.0
18
17.7
3.4
78
76.6
14.9
38
1,35. 5
26.3
98
194.4
37.8
58
253.3
49.2
19
18.7
3.6
79
77.5
15.1
39
136.4
26.5
99
195.3
38.0
59
254.2
49.4
20
21
19.6
20.6
3.8
4.0
80
78.5
15.3
40
137.4
26.7
200
196.3
38.2
60
255.2
49.6
81
79.5
1.5.5
141
1.38. 4
26.9
201
197.3
38.4
261
256.2
49.8
22
21.6
4.2
82
80.5
1.5.6
42
1,39. 4
27.1
02
198.3
38.5
62
257.2
50.0
23
22.6
4.4
83
81.5
15.8
43
140.4
27.3
03
199.3
38.7
63
258.2
50.2
24
23.6
4.6
84
82.5
16.0
44
141 4
27.5
04
200.3
,38,9
64
259.1
,50.4
25
24.5
4.8
85
83.4
16.2
45
142.3
27.7
05
201.2
39.1
65
260. 1 ; 50. 6 |
26
25.5
5.0
86
84.4
16.4
46
143.3
27.9
06
202.2
39.3
m
261.1
50.8
27
26.5
5.2
87
8.5.4
16.6
47
144.3
28.0
07
203.2
39.5
67
262.1
50.9
28
27.5
5.3
88
86.4
16.8
48
145. 3
28.2
08
204.2
39.7
68
263.1
51.1
29
28.5
5.5
89
87.4
17.0
49
146.3
28.4
09
205.2
39.9
69
264.1
51.3
-30
29.4
5.7
90
88.3
17.2
50
147.2
28.6
10
206.1
40.1
70
265.0
51.5
31
30.4
5.9
91
89.3
17.4
151
148. 2
28.8
211
207.1
40.3
271
266.0
»51.7
32
31.4
6.1
92
90.3
17.6
52
149.2
29.0
12
208.1
40.5
72
267.0
51.9
33
32.4
6.3
93
91.3
17.7
53
150.2
29.2
13
209.1
40.6
73
268.0
52.1
34
,33.4
6.5
94
92.3
17.9
54
151. 2
29.4
14
210.1
40.8
74
269.0
52.3
35
34.4
6.7
95
93.3
18.1
55
152.2
29.6
15
211.0
41.0
75
269.9
52.5
36
:».3
6.9
96
94.2
18.3
56
153.1
29.8
If)
212.0
41.2
76
270.9
52.7
37
36.3
7.1
97
95.2
18.5
57
154.1
30.0
17
213.
41.4
77
271.9
52.9
38
37.3
7.3
98
96.2
18.7
58
155.1
30.1
18
214.0
41.6
78
272.9
53.0
39
.38.3
7.4
99
97.2
18.9
59
156.1
30.3
19
215.0
41.8
79
273.9
53.2
40
39.3
7.6
100
98.2
19.1
60
157.1
158.0
30.5
20
216.0
42.0
80
274.9
53.4
41
40.2
7.8
101
99.1
19.3
161
30.7
221
216.9
42.2
281
275.8
53.6
42
41.2
8.0
02
100.1
19.5
62
159.0
,30.9
22
217.9
42.4
82
276.8
53.8
43
42.2
8.2
03
101.1
19.7
63
160.0
31.1
23
218.9
42.6
83
277.8
54.0
44
43.2
8.4
04
102.1
19.8
64
161.0
31.3
24
219.9
42.7
84
278.8
54.2
45
44.2
8.6
05
103. 1
20.0
6.5
162.0
31.5
25
220.9
42.9
85
279.8
.54.4
46
4.5.2
8.8
06
104.1
20.2
66
163.0
31.7
26
221.8
4,3.1
86
280.7
54.6
47
46.1
9.0
07
105.
20.4
67
163. 9
31.9
27
222.8
43.3
87
281.7
54.8
48
47.1
9.2
08
106.0
20.6
68
164.9
32.1
28
223.8
43.5
88
282.7
5.5.0
49
48.1
9.3
09
107.0
20.8
69
165.9
32.2
29
224.8
43.7
89
283. 7 i 55. 1 1
50
49.1
9.5
10
108.0
21.0
70
166.9
167.9
32.4
32.6
30
231
225.8
43.9
90
284.7
285.7
,55.3
51
50.1
9.7
111
109.0
21.2
171
226.8
44.1
291
55.5
52
51.0
9.9
12
109.9
21.4
72
168.8
32.8
32
227.7
44.3
92
286 6 55. 7
53
52.0
10.1
13
110.9
21.6
73
169.8
3.3.0
33
228.7
44.5
93
287.6 : 55.9
54
53.0
10.3
14
111.9
21.8
74
170.8
33.2
34
229.7
44.6
94
288.6 56.1
55
54.0
10.5
15
112.9
21.9
75
171.8
3,3.4
35
230.7
44.8
95
289. 6 1 56. 3
56
55.0
10.7
16
113.9
22.1
76
172.8
33.6
36
231.7
4.5.0
96
290.6 ! 56.5
57
56.0
10.9
17
114.9
22.3
77
173.7
33.8
37
232. 6
4,5.2
97
291.5 i 56.7
58
56.9
11.1
18
115.8
22.5
78
174.7
34.0
38
233.6
4.5.4
98
292.5 ! 56.9
59
57.9
11.3
19
116.8
22.7
79
175. 7
34.2
39
234.6
45.6
99
293.5
57.1
60
58.9
11.4
20
117.8
22.9
80
176.7
34.3
40
235.6
45.8
300
294.5
57.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dop.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
79° (1
01°, 259
", 281°
)•
1
Page 552]
TABLE 2.
Difference of Latitude and Departure for 11° (169°, 191
°, 349°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
295.4
57.4
361
354.3
68.9
421
413.2
80.3
481
472.1
91.8
541
531.0
103.2
02
296.4
57.6
62
355.3
69.1
22
414.2
80.5
82
473.1
92.0
42
532.0
103. 4
03
297.4
57.8
63
356.3
69.3
23
415.2
80.7
83
474.1
92.2
43
533.0
103.6
04
298.4
58.0
64
357.3
69.5
24
416.2
80.9
84
475.1
92.4
44
534.
103.8
05
299.4
58.2
65
358.3
69.6
25
417.2
81.1
85
476.1
92.6
45
535.0
104.0
06
300.3
58.4
66
359. 2
69.8
26
418.1 : 81.3
86
477.0
92.8
46
535. 9
104.2
07
301. 3
58.6
67
360.2
70.0
27
419.1 ' 81.5
87
478.0
93.0
47
536. 9
104. 4
08
302.3
58.8
68
361.2
70.2
28
420.1 : 81.7
88
479.0
93.2
48
537. 9
104.6
09
303.3
59.0
69
362.2
70.4
29
421.1 ! 81.9
89
480.0
93.3
49
538.9
104.8
10
304.3
59.2
70
363. 2
70.6
30
422.1 1 82.1
90
481.0
93.5
50
539. 9
105.
311
305.3
59.3
371
364.1
70.8
431
423.0
82.2
491
481. 9^ '"^.6
551
540. 8~
105. 1
12
306.2
59.5
72
365.1
71.0
32
424.0
82.4
92
482.9
93.8
52
541.8
105. 3
13
307.2
59.7
73
366.1
71.2
33
425.
82.6
93
483.9
94.0
53
542. 8
105.. 5
14
308.2
59.9
74
367.1
71.4
34
426.0
82.8
94
484.9
94.2
54
543.8
105. 7
15
309.2
60.1
75
368.1
71.6
35
427.0
83.0
95
485.9
94.4
55
544.8
10.5.9
16
310.2
60.3
76
369.1
71.7
36
428.0
83.2
96
486.9
94.6
56
545.8
106. 1
K-
311.1
60.5
77
370.0
71.9
37
428.9
83.4
97
487.8
94.8
57
546.7
106. 3
18
312.1
60.7
78
371.0
72.1
38
429.9
83.6
98
488.8
95.0
58
547.7
106.5
19
313.1
60.9
79
372.0
72.3
39
430.9
83.8
99
489.8
95.2
59
548.7
106.7
20
314.1
61.1
80
373.0
72.5
40
431.9
432.9
84.0
84.1
500
490.8
491.8
95.4
60
549.7
550. 7
106.9
321
315.1
61.3
381
374.0
72.7
441
501
95.6
561
107.1
22
316.1
61.4
82
374.9
72.9
42
433.8
84.3
02
492.7
95.8
62
.551.6
107.2
23
317.0
61.6
83
375.9
73.1
43
434.8
84.5
03
493.7
96.0
63
552. 6
107.4
24
318.0
61.8
84
376.9
73.3
44
435.8
84.7
04
494.7
96.2
64
553. 6
107.6
25
319.0
62.0
85
377.9
73.5
45
436.8
84.9
05
495.7
96.4
65
5.54. 6
107.8
26
320.0
62.2
86
378.9
73.7
46
437.8
85.1
06
496.7
96.6
66
555. 6
108.0
27
321.0
62.4
87
379.9
73.8
47
438. 8
85.3
07
497.7
96.8
67
556.6
108.2
28
321.9
62.6
88
380.8
74.0
48
439.7
85.5
08
498.6
97.0
68
557. 6
108.4
29
322.9
62.8
89
381.8
74.2
49
440.7
85.7
09
499.6
97.2
69
558. 6
108.6
30
323.9
63.0
90
382.8
74.4
50
441.7
85.9
10
500.6
97.3
70
559. 5
560. 5
108.8
109.
331
1(24.9
63.2
391
383.8
74.6
451
442.7
86.1
511
501.6
97.5
571
32
325.9
63.4
92
384.8
74.8
52
443.7
86.2
12
502.6
97.6
72
561. 5
109.1
33
326.8
63.5
93
385. 7
75.0
53
444.6
86.4
13
503.5
97.8
73
562. 5
109.3
34
327. 8
63.7
94
386.7
7.5.2
54
445.6
86.6
14
504. 5
98.0
74
563. 5
109.5
35
328.8
63.9
95
387.7
75.4
55
446.6
86. 8
15
505.5
98.2
75
564. 5
109.7
36
329.8
64.1
96
388. 7
75,6
56
447.6
87.0
16
506.5
98.4
76
565.4
109.9
37
330.8
64.3
97
389.7
75.8
57
448.6
87.2
17
507.5
98.6
77
566.4
110.1
38
331.8
64.5
98
390.7
75.9
58
449.6
87.4
18
508. 5
98.8
78
567.4
110.3
39
332.7
64.7
99
391.6
76.1
59
450.5
87.6
19
509.4
99.0
79
568.3
110.5
40
333. 7
64.9
400
392.6
76.3
60
451.5
87.8
20
510. 4
511.4
99.2
80
569. 3
110.7
341
334.7
65.1
401
393.6
76.5
46]
452.5
88.0
521
99.4
581
570. 3
110.9
42
335.7
65.3
02
394.6
76.7
62
453.5
88.2
22
512.4
99.6
82
.571.3
111.1
43
336.7
65.5
03
395.6
76.9
63
454. 5
88.3
23
513.4
99.8
83
572.3
111.3
44
337.6
65.6
04
396.5
77.1
64
4.55. 4
88.5
24
514. 3
100.0
84
573. 2
111.5
45
338. 6
65.8
05
397.5
77.3
65
456. 4
88.7
25
515. 3
100.2
85
574. 2
111.7
46
339.6
66.0
06
398.5
77.5
66
457.4
88.9
26
516.3
100.4
86
575.2
111.8
47
340.6
66.2
07
399.5
77. 7
67
458.4
89.1
27
517.3
100.6
87
576.2
112.1
48
341.6
66.4
08
400.5
77.9
68
459. 4
89.3
28
518.3
100.8
88
577.2
112.3
49
342.6
66.6
09
401.5
78.1
69
460.4
89.5
29
519. 3
101.0
89
578.2
112.4
50
343. 5
66.8
10
402.4
78.2
70
461. 3
462.3
89.7
30
520. 2
101.2
90
579.1
112.6
351
344.5
67.0
411
403.4
78.4
471
89.9
531
.521. 2
101.4
591
580.1
112.8
52
345.5
67.2
12
404.4
78.6
72
463.3
90.1
32
522.2
101.6
92
581.1
113.0
53
346.5
67.4
13
405.4
78.8
73
464.3
90.3
33
523. 2
101.7
93
582.1
113.2
54
347.5
67.5
14
406.4
79.0
74
465. 3
90.4
34
524.2
101.8
94
583.1
113.3
55
348.4
67.7
15
407.3
79.2
75
466.2
90.6
35
525.1
102.0
95
584.0
113.5
56
349.4
67.9
16
408.3
79.4
76
467.2
90.8
36
526. 1
102.2
96
585.
11.3.7
57
350.4
68.1
17
409.3
79.6
77
468.2
91.0
37
527.1
102.4
97
586.0
113.9
58
351.4
68.3
18
410.3
79.8
78
469.2
91.2
38
528.1
102.6
98
587.0
114.1
59
352.4
68.5
19
411.3
80.0
79
470.2
91.4
39
529.1
102.8
99
588.
114.3
60
353.4
68.7
20
412.3
80.1
80
471.1
91.6
40
530. 1
103.0
600
589.0
114.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dift.
Dep.
Lat.
79° (1
01°, 259°, 281°
)•
.TABLE 2.
[Page 663
Difference of Latitude and Departure for 12°
(168°, 192°, 348°).
Dlst.
Lat.
Dep
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.7
12.7
121
118.4
25.2
181
177.0
37.6
241
235.7
50.1
2
2.0
0.4
62
60.6
12.9
22
119. 3
25.4
82
178.0
37.8
42
236.7
50.3
3
2.9
0.6
63
61.6
13.1
23
120.3
25.6
83
179.0
38.0
43
237.7
50.5
4
3.9
0.8
64
62.6
13.3
24
121.3
25.8
84
180.0
38.3
44
238.7
50.7
5
4.9
].0
65
63.6
13.5
25
122.3
26.0
85
181.0
38.5
45
239.6
50.9
6
5.9
1.2
66
64.6
13.7
26
123.2
26.2
86
181.9
38.7
46
240.6
51.1
7
6,8
1.5
67
65.5
13.9
27
124.2
26.4
87
182.9
38.9
47
241.6
51.4
8
7.8
1.7
68
66.5
14.1
28
125.2
26.6
88
183.9
39.1
48
242.6
51.6
9
8.8
1.9
69
67.5
14.3
29
126.2
26.8
89
184.9
39.3
49
243.6
51.8
10
11
9.8
2.1
70
14.6
30
127.2
27.0
90
185.8
39.5
50
244.5
52.0
10.8
2."3
71
"•^4
14.8
131
128.1
27.2
191
186.8
39.7
251
245.5
52.2.
12
11.7
2.5
72
70.4
15.0
32
129.1
27.4
92
187.8
39.9
52
246.5
.52.4
13
12.7'
2.7
73
71.4
15.2
33
130.1
27.7
93
188.8
40.1
53
247.5
52.6
14
13.7
2.9
74
72.4
15.4
34
131.1
27.9
94
189.8
40.3
54
248.4
52.8
15
14.7
3.1
75
73.4
15.6
35
132.0
28.1
95
190.7
40.5
55
249.4
53.0
16
15.7
3.3
76
74.3
15.8
36
133. 28. 3
96
191.7
40.8
56
250.4
53.2
17
16.6
3.5
77
75.3
16.0
37
134.0 28.5
97
192.7
41.0
57
251.4
53.4
18
17.6
3.7
78
76.3
16.2
38
135. : 28. 7
98
193.7
41.2
58
252.4
53.6
19
18.6
4.0
79
77.3
16.4
39
136.0 ; 28.9
99
194.7
41.4
59
253.3
53.8
20
19.6
4.2
80
78.3
16.6
40
136.9
29.1
200
195.6
41.6
60
254.3
255.3
54.1
21
20.5
4.4
81
79.2
16.8
141
137.9
29. 3
201
196.6
41.8
261
54.3
22
21.5
4.6
82
80.2
17.0
42
138.9
29.5
02
197.6
42.0
62
256.3
54.5
23
22.5
4.8
83
81.2
17.3
43
139.9
29. 7
03
198.6
42.2
63
257.3
54.7
24
2.3. 5.
5.0
84
82.2
17.5
44
140.9
29.9
04
199.5
42.4
64
258.2
54.9
25
24.5
5.2
85
83.1
17.7
45
141.8
30.1
05
200.5
42.6
65
259.2
5.5.1
26
25.4
5.4
86
84.1
17.9
46
142.8
30.4
06
201.5
42.8
66
260.2
55. 3
27
26.4
5.6
87
85.1
18.1
47
143.8
30.6
07
202.5
43.0
67
261.2
55. 5
28
27.4
.5.8
88
86.1
18.3
48
144.8
30.8
08
203.5
43.2
68
262.1
55. 7
29
28.4
6.0
89
87.1
18.5
49
145.7
31.0
09
204.4
43.5
69
263. 1 ; 55. 9
30
31
29.3
30.3
6.2
90
88.0
18.7
50
146.7
31.2
10
205.4
206.4
43.7
70
264. 1 ' 56. 1
674
91
89.0
18.9
151
147.7
31.4
211
43.9
271
265.1
56. 3
32
31.3
6.7
92
90.0
19.1
52
148.7
31.6
12
207.4
44.1
72
266.1
56.6
33
32.3
6.9
93
91.0
19.3
53
•149.7
31.8
13
208.3
44.3
73
267.0
56.8
34
33.3
7.1
94
91.9
19.5
54
150.6
32.0
14
209.3
44.5
74
268.0
57.0
35
34.2
7.3
95
92.9
19.8
55
151.6
32.2
15
210.3
44.7
75
269.0
57.2
36
35.2
7.5
96
93.9
20.0
56
152.6
32.4
16
211.3
44.9
76
270.0
57.4
37
36.2
7. 7
97
94.9
20.2
57
153. 6
32.6
17
212.3
45.1
77
270.9
57.6
38
37.2
7.9
98
95.9
20.4
58
154. 5
32.9
18
213.2
45.3
78
271.9
57. 8
39
38.1
8.1
99
96.8
20.6
59
155. 5
33.1
19
214.2
45.5
79
272.9
58.0
40
39.1
8.3
100
97.8
20.8
60
156.5
33. 3
33. 5
20
215.2
45.7
80
273.9
58.2
41
40.1
8.5
101
98.8
21.0
161
157.5
221
216.2
45.9
281
274.9
58.4
42
41.1
8.7
02
99.8
21.2
62
158.5
33.7
22
217.1
46.2
82
275.8
58.6
43
42.1
8.9
03
100.7
21.4
63
159.4
33.9
23
218.1
46.4
83
276.8
58.8
44
43.0
9.1
04
101.7
21.6
64
160.4
34.1
24
219.1
46.6
84
277.8
.59.
45
44.0
9.4
05
102.7
21.8
65
161.4
34.3
25
220.1
46.8
85
278.8
59.3
46
45.0
9.6
06
103. 7
22.0
66
162.4
34.5
26
221.1
47.0
86
279.8
59. 5
47
46.0
9.8
07
104.7
22.2
67
163.4
34.7
27
222.0
47.2
87
280.7
59.7
48
47.0
10.0
08
105. 7
22.5
68
164.3
.34.9
28
223.0
47.4
88
281.7
59. 9
49
47.9
10.2
09
106.6
22.7
69
165.3
35.1
29
224.
47.6
89
282.7
60.1
50
48.9
10.4
10
107.6
22.9
70
166.3
35.3
35:6
30
225.0
47.8
90
283.7
60.3
51
49.9
10.6
111
108.6
23.1
171
167.3
231
226.0
48.0
291
284.6
60. 5
52
50.9
10.8
12
109.6
23.3
72
168.2
35.8
32
226.9
48.2
92
285.6
60.7
53
51.8
11.0
13
110.5
23.5
73
169.2
36.0
33
227.9
48.4
93
286. 6
60.9
54
52.8
11.2
14
111.5
23.7
74
170.2
36.2
34
228.9
48.7
94
287.6
61.1
55
53.8
11.4
15
112.5
23.9
75
171.2
36.4
35
229.9
48.9
95
288. 6
61.3
56
54.8
11.6
16
113.5
24.1
76
172.2
36.6
36
230.8
49.1
96
289.5
61.5
57
55.8
11.9
17
114.4
24.3
77
173.1
36.8
37
231.8
49.3
97
290.5
61.7
58
56.7
12.1
18
115. 4
24.5
78
174.1
.37.0
38
232.8
49.5
98
291.5
62.0
59
57.7
12.3
19
116.4
24.7
79
175. 1
37.2
39
233. 8
49.7
99
292.5
62.2
60
58.7
12.5
20
117.4
24.9
80
176.1
37.4
40
234.8
49.9
300
293.4
62.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lut.
Dist.
Dep.
Lat.
78° (102°, 258°, 282°
)•
Page 564]
TABLE 2.
Difference of Latitude and Departure for 12° (168°, 192°, 348
°)-
Dlst.
I^t.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
294.4
62.6
361
353.1
75.0
421
411.8
87.5
481
470.5
100.0
541
529.2
112.5
02
295.4
62.8
62
354.1
75.2
22
412.8
87.7
82
471.5
100.2
42
530.2
112.7
03
296.4
63.0
63
355.1
75.4
23
413.8
87.9
83
472.5
100.4
43
531. 1
112.9
04
297.4
63.2
64
356.0
75. 7
24
414.7
88.1
84
473.4
100.6
44
532. 1
113.1
05
298.3
63.4
65
357.0
75.9
25
415.7
88.3
85
474.4
100.8
45
533. 1
113.3
06
299.3
63.6
66
358.0
76.1
26
416.7
88.6
86
475.4
101.0
46
534.1
113.5
07
300.3
63.8
67
359.0
76.3
27
417.7
88.8
87
476.4
101.2
47
535.1
113.7
08
301.3
64.0
68
360.0
76.5
28
418.6
89.0
88
477.3
101.4
48
536.*0
113.9
09
302.2
64.2
69
360.9
76.7
29
419.6
89.2
89
478.3
101.6
49
537.0
114.1
10
303. 2
64.4
70
361.9
76.9
30
420.6
89.4
90
479.3
101.9
50
538.0
114.4
311
304. 2
64.6
371
362.9
77.1
431
421.6
89.6
491
480.3
102.1
551
538.9
114.6
12
305.2
64.8
72
363.9
77.3
32
422.6
89.8
92
481.2
102.3
52
539.9
114.8
13
306. 2
65.1
73
364.8
77.5
33
423.5
90.0
93
482.2
102.5
53
540. 9
115.0
14
307. 1
65.3
74
365. 8
77. 7
34
424.5
90.2
94
483.2
102.7
54
541.9
115.2
15
308.1
65.5
75
366.8
77.9
35
425.5
90.4
95
484.2
102.9
55
542.9
115.4
16
309.1
65.7
76
367.8
78.2
36
426. 5
90.6
96
485. 2
103.1
56
543.8
115.6
17
310.1
65.9
77
368.8
78.4
37
427.5
90.8
97
486.1
103.3
57
544.8
115. 8
18
311.1
66.1
78
369.7
78.6
38
428.4
91.0
98
487.1
103.5
58
545. 8
116.0
19
312.0
66.3
79
370.7
78.8
39
429.4
91.3
99
488.1
103.8
59
546.8
116.2
20
321
313.
66.5
80
371.7
79.0
40
430.4
91.5
91.7
500
489.1
104.0
- 60
547.8
116.4
314.0
66.7
381
372.7
79.2
441
431.4
501
490.0
104.2
56 f
548.7
'116.6
22
315.0
66.9
82
373.7
79.4
42
432.3
91.9
02
491.0
104.4
62
549.7
116.8
23
315.9
67.1
83
374.6
79.6
43
433. 3
92.1
03
492.0
104.6
63
550.7
117.0
24
316.9
67.3
84
375.6
79.8
44
434.3
92.3
04
493.0
104.8
64
551.7
117.2
25
317.9
67.6
85
376.6
80.0
45
435.3
92.5
05
494.0
105.
6.5
552.7
117.4
26
318.9
67.8
86
377.6
80.2
46
436.3
92.7
06
495.
105.2
66
553.7
117.6
27
319.9
68.0
87
378.5
80.4
47
437.2
92.9
07
495.9
105.4
67
554.6
117.8
28
320.8
68.2
88
379.5
80.7
48
438.2
93.1
08
496.9
105. 6
68
555. 6
118.0
29
321.8
68.4
89
380. 5
80.9
49
439.2
93.3
09
497.9
105.8
69
556. 6
118.2
30
331
322.8
68.6
90
381.5
81.1
50
440.2
93.5
10
498.9
106.0
70
557. 5
118.5
323.8
68.8
391
382.5
81.3
451
441.1
93.7
511
499.8
106.2
571
558.5
118.7
32
324.7
69.0
92
383.4
81.5
52
442.1
93.9
12
500.8
106.4
72
559. 5
118.9
33
325. 7
69.2
93
384.4
81.7
53
443.1
94.1
13
501.8
106.6
73
560.5
119.1
34
326.7
69.4
94
385.4
81.9
54
444.1
94.4
14
502.8
106. 8
74
561.5
119.3
35
327.7
69.6
95
386.4
82.1
55
445.1
94.6
15
503.7
107.0
75
562.4
119.5
36
328.7
69.8
96
387. 3
82.3
56
446.0
94.8
16
504.7
107.2
76
563.4
119.7
37
329. 6
70.0
97
388.3
82.5
57
447.0
95.0
17
505.7
107.4
77
564.4
119.9
38
330. 6
70.3
98
389.3
82.7
58
448.0
95.2
18
506.7
107.6
78
565.4
120.1
39
331. 6
70.5
99
390.3
82.9
59
449.
95.4
19
507.7
107.8
79
566.4
120.3
40
332.6
70.7
400
391.3
83.1
60
450.-0
95.6
95. 8
20
508.7
108.1
80
567.4
568.3
120.6
120.8
341
333. 5
70.9
401
392.2
83.4
461 1 450.9
521
509.6
108.3
581
42
334.5
71.1
02
393.2
83.6
62
451.9
96.0
22
510.6
108.5
82
569.3
121.0
43
335.5
71.3
03
394. 2
83.8
63
452.9
96.2
23
511.6
108.7
83
570.3
121.2
44
336.5
71.5
04
395.2
84.0
64
453. 9
96.5
24
512.5
108.9
84
571.2
121.4
45
337.5
71.7
05
396.2
84.2
65
454.8
96.7
25
513.5
109.2
85
572.2
121.6
46
338.4
71.9
06
397.1
84.4
66
455. 8
96.9
26
514.5
109.4
86
573.2
121.8
47
339.4
72.1
07
398.1
84.6
67
456.8
97.1
27
515. 5
109.6
87
574.2
122.0
48
340.4
72.3
08
399.1
84.8
68
457.8
97.3
28
516.5
109.8
88
575.2
122.2
49
341.4
72.5
09
400.1
85.0
69
458.8
97.5
29
517.5
110.0
89
576.2
122.4
50
342.4
72.7
10
401.0
85.2
85.4
70
471
459.7
97.7
30
518.4
110.2
90
577.1
122.6
351
343.3
73.0
411
402.0
460. 7
97.9
531
519.4
110.4
591
578.1
122.8
52
344.3
73.2
12
403.0
85.6
72
461.7
98.1
32
520.4
110.6
92
579.1
123.0
53
345.3
73.4
13
404.0
8.5.8
73 1 462. 7
98.3
33
521. 3
110.8
93
580.0
123; 2
54
346.3
73.6
14
405.0
86.1
74
463.6
98.5
34
522.3
111.0
94
581.0
123.4
55
347.2
73.8
15
405.9
86.3
75
464.6
98.7
35
523.3
111.2
95
582.0
123.6
56
348.2
74.0
16
406.9
86.5
76
465.6
98.9
36
524.3
111.4
96
583.0
123.9
57
349.2
74.2
17
407.9
86.7
77
466.6
99.1
37
525.3
111.6
97
584.0
124.1
58
350. 2
74.4
18
408.9
86.9
78
467.6
99.4
38
526.2
111.8
98
584.9
124.3
59
351.2
74.6
19
409.8
87.1
79
468.5
99.6
39
527.2
112.0
99
585.9
124.5
60
352.1
74.8
20
410.8
87.3
80
469.5
99.8
40
528.2
112.3
600
586.9
124.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
7
8° (102°, 258°, 282°).
TABLE 2.
[Page
555
Difference of Latitude and Departure for 13° (167°, 193
°, 347°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.2
61
59.4
13.7
121
117.9
27.2
181
176.4
40.7
241
234.8
54.2
2
1.9
0.4
62
60.4
13.9
22
118.9
27.4
82
177.3
40.9
42
335.8
54.4
3
2.9
0.7
63
61.4
14.2
23
119.8
27.7
83
178.3
41.2
43
236.8
54.7
4
3.9
0.9
64
62.4
14.4
24
120.8
27.9
84
179.3
41.4
44
237.7
54.9
5
4.9
1.1
65
63.3
14.6
25
121.8
28.1
85
180.3
41.6
45
238.7
55.1
6
5.8
1.3
66
64.3
14.8
26
122.8
28.3
86
181.2
41.8
46
• 239. 7
55.3
7
6.8
1.6
67
65.3
15.1
27
123.7
28.6
87
182.2
42.1
47
240.7
55.6
8
7.8
1.8
68.
66.3
15.3
28
124.7
28.8
88
183.2
42.3
48
241.6
55.8
9
8.8
2.0
69
67.2
15.5
29
125.7
29.0
89
. 184. 2
42.5
49
242.6
56.0
10
9.7
2.2
70
68.2
15.7
30
126.7
29.2
90
191
185.1
42.7
50
243.6
.56.2
11
10.7
2.5
71
69.2
16.0
131
127.6
29.5
186.1
43.0
251
244.6
56.5
12
11.7
2.7
72
70.2
16.2
32
128.6
29.7
92
187.1
43.2
52
245.5
56.7
13
12.7
2.9
73
71.1
16.4
33
129.6
29.9
93
188.1
43.4
53
246.5
56.9
14
13.6
3.1
74
72.1
16.6
34
130.6
30.1
94
189.0
43.6
54
247.5
57.1
15
14.6
3.4
75
73.1
16.9
35
131.5
30.4
95
190.0
43.9
55
248.5
57.4
16
15.6
3.6
76
74.1
17.1
36
132.5
30.6
96
191.0
44,1
56
249.4
57.6
17
16.6
3.8
77
75.0
17.3
3f
133.5
30.8
97
192.0
44.3
57
2.50. 4
57.8
18
17.5
4.0
78
76.0
17.5
38
134.5
31.0
98
192.9
44.5
58
251.4 1 58.0 1
19
18.5
4.3
79
77.0
17.8
39
135. 4
31.3
99
193.9
44.8
59
252.4
58.3
20
19.5
4.5
80
77.9
18.0
40
136.4
31.5
200
194.9
45.0
60
253.3
58.5
58.7
21
20.5
4.7
81
78.9
18.2
141
137.4
31.7
201
195.8
45.2
261
254.3
22
21.4
4.9
82
79.9
18.4
42
138.4
31.9
02
196.8
45.4
62
255.3
58.9
23
22.4
5.2
83
80.9
18.7
43
139.3
32.2
03
197.8
45.7
63
256.3
59.2
24
23.4
5.4
84
81.8
18.9
44
140.3
32.4
04
198.8
45.9
64
257.2
59.4
25
24.4
5.6
85
82.8
19.1
45
141.3
32.6
05
199.7
46.1
65
258.2
59.6
26
25.3
5.8
86
83.8
19.3
46
142.3
.32.8
06
200.7
46.3
66
259.2
59.8
27
26.3
6.1
87
84.8
19.6
47
143.2
33.1
07
201.7
46.6
67
260.2
60.1
28
27.3
6.3
88
85.7
19.8
48
144.2
33. 3
08
202.7
46.8
68
261.1
60.3
29
28.3
6.5
89
86.7
20.0
49
145.2
3.3.5
09
203. 6
47.0
69
262.1
60.5
30
29.2
6.7
90
87.7
20.2
50
146.2
33.7
10
211
204.6
205.6
47.2
70
263.1
60.7
31
30.2
7.0
91
88.7
20.5
151
147.1
34.0
47.5
271
264.1
61.0
32
31.2
7.2
92
89.6
20.7
52
148.1
34.2
12
206.6
47.7
72
265.0
61.2
33
32.2
7.4
93
90.6
20.9
53
149.1
34.4
13
207.5
47.9
73
266.0
61.4
34
33.1
7.6
94
91.6
21.1
54
1.50. 1
34.6
14
208.5
48.1
74
267.0
61.6
35
34.1
7.9
95
92.6
21.4
55
151.0
34.9
15
209.5
48.4
75
268.0
61.9
36
35.1
8.1
96
93.5
21.6
56
1.52.
3.5.1
16
210. 5
48.6
76
268.9
62.1
37
36.1
8.3
97
94.5
21.8
57
153.0
35.3
17
211.4
48.8
77
269.9
62.3
38
37.0
8.5
98
95.5
22.0
58
1.54.
35.5
18
212.4
49.0
78
270.9
62.5
39
38.0
8.8
99
96.5
22.3
59
154.9
35.8
19
213.4
49.3
79
271.8
62.8
40
39.0
9.0
100
97.4
22.5
60
155.9
36.0
20
221
214.4
215.3
49.5
80
272.8
63.0
41
39.9
9.2
101
98.4
22.7
161
156.9
36.2
49.7
281
273.8
63.2
42
40.9
9.4
02
99.4
22.9
62
157.8
36.4
22
216.3
49.9
82
274.8
63.4
43
41.9
9.7
03
100.4
23.2
63
158.8
36.7
23
217.3
50.2
83
275.7
63.7
44
42.9
9.9
04
101.3
23.4
64
159.8
36.9
24
218.3
50.4
84
276.7
63.9
45
43.8
10.1
05
102.3
23.6
65
160.8
37.1
25
219.2
50.6
85
277.7
64.1
46
44.8
10.3
06
103.3
23.8
66
161.7
37.3
26
220.2
50.8
86
278.7
64.3
47
4.5.8
10.6
07
104.3
24.1
67
162.7
37.6
27
221.2
51.1
87
279.6
64.6
48
46.8
10.8
08
105. 2
24.3
68
163.7
37.8
28
222.2
51.3
88
280.6
64.8
49
47.7
11.0
09
106.2
24.5
69
164.7
38.0
29
223.1
51.5
89
281.6
65.0
50
51
48.7
11.2
10
107.2
108.2
24.7
70
165.6
.38.2
30
224.1
51.7
90
282.6
65.2
49.7
11.5
111
2.5.0
171
166.6
38.5
281
225.1
52.0
291
283.5
65.5
52
50.7
11.7
12
109.1
25.2
72
167.6
38.7
32
226. 1
52.2
92
284.5
65.7
53
51.6
11.9
13
110.1
25.4
73
168.6
38.9
33
227.0
52.4
93
285.5
65.9
54
52.6
12.1
14
111.1
2.5.6
74
169.5
39.1
34
228.0
52.6
94
286.5
66.1
55
53.6
12.4
15
112.1
2.5.9
75
170.5
39.4
35
229.0
52.9
95
287.4
66.4
56
54.6
12.6
16
113.0
26.1
76
171.5
39.6
36
230.0
53.1
96
288.4
66.6
57
55.5
12.8
17
114.0
26.3
77
172.5
39.8
37
230.9
53.3
97
289.4
66.8
58
56.5
13.0
18
115.0
26.5
78
173.4
40.0
38
231.9
53.5
98
290.4
67.0
59
57.5
13.3
19
116.0
26.8
79
174.4
40.3
39
232.9
53.8
99
291.3
67.3
60
58.5
13.5
20
116.9
27.0
80
175.4
40.5
40
233.8
54.0
300
292.3
67.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
-7°(1
03°, 257°, 283°).
Page 556]
TABLE 2.
■-
Difference of Latitude and Departure for 13° (167°, 193°, 347°
)■
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301 1 293.3
67.7
361
351.8
81.2
421
410.2
94.7
481
468.7
108.2
541
527.2
121.7
02 1 294.3
67.9
62
352.7
81.4
22
411.2
94.9
82
469.7
108.4
42
528.1
121.9
03 295.2
68.1
63
353.7
81.6
23
412.2
95.1
83
470. 6 ' 108. 6
43
529.1
122. 1
04 296.2
68.4
64
354.7
81.9
24
413.1
95.3
84
471.6 ,108.8
44
530. 1
122.3
05 297.2
68.6
65
355.6
82.1
25
414.1
95.6
85
472. 6 I 109.
45
531.1
122. 5
06 ! 298.2
68.8
66
356. 6
82.3
26
415.1
95.8
86
473. 6 109. 3
46
532.0
122.8
07 : 299. 1
69.0
67
357.6
82.5
27
416.1
96.0
87
474. 5 1 109. 5
47
533.
123.0
08 i 300. 1
69.3
68
358.6
82.8
28
417.0
96.2
88
475. 5 1 109. 7
48
534.0
123.2
09 301.1
69.5
69
359.5
83.0
29
418.0
96.5
89
476. 5 1 109. 9
49
535.0
123. 4
10 302.1
69.7
70
360.5
83.2
30
419.0
96.7
90
477.5 1 110.1
50
535.9
123.7
311 1 303.0
69.9
371
361.5
83.4
431
420.0
96.9
491
478.4 110.4
551
536. 9
123.9
12 i 304.0
70.2
72
362.5
83.7
32
420.9
97.1
92
479.4 110.6
52
537.9
124.1
13 1 305.0
70.4
73
363. 4
83.9
33
421.9
97.4
93
480.4
110.9
53
538.9
124.4
14 i 306.0
70.6
74
364.4
84.1
34
422.9
97.6
94
481.4
111.1
54
539.8
124. 6
15
306.9
70.8
75
365.4
84.3
35
423.9
97.8
95
482.3
111.3
55
540.8
124. 9
16
307.9
71.1
76
366.4
84.6
36
424.8
98.0
96
483.3
111.5
56
541.8
125. 1
17
308.9
71.3
77
367.3
84.8
37
425.8
98.3
97
484. 3
111.8
57
542.8
125. 3
18
309.9
71.5
78
368.3
85.0
38
426.8
98.5
98
485.3
112.
58
543.7
125.5
19
310.8
71.7
79
369.3
85.2
39
427.8
98.7
99
486.2
112.2
59
544.7
125. 8
20
311. 8
72.0
80
370. 3
85.5
40
428.7
98.9
500
487.2
112.4
60
545.7
126.0
321
312.8
72.2
381
371.2
85.7
441
429.7
99.2
501
488.2
112.6
561
546.7
126.2
22
313.8
72.4
82
372.2
85.9
42
430.7
99.4
02
489.2
112.9
62
547.6
126.4
23
314.7
72.6
83
373.2
86.1
43
431.6
99.6
03
490.1
113.1
63
548.6
126.7
24
315.7
72.9
84
374.2
86.4
44
432.6
99.8
04
491.1
113.3
64
549.6
126.9
25
316.7
73.1
85
375.1
86.6
45
433.6
100.1
05
492.1
113.5
65
550.6
127.1
26
317.6
73.3
86
376.1
86.8
46
434.6
100.3
06
493.1
113.8
66
551.5
127.3
27
318. 6
73.5
87
377. 1
87.0
47 435. 5
100.5
07
494.0
114.0
67
552.5
127. 6
28
319.6
73.8
88
378. 1
87.3
48
436.5
100.7
08
495.0
114.2
68
553. 5
127.8
29
320.6
74.0
89
379.0
87.5
49
437. 5
101.0
09
496.0
114. 5
69
554. 5
128.0
30
321.5
74.2
90
380.0
87.7
50
451
438.5
101.2
10
511
496.9 ;114.7
497.9 |114.9
70
571
555.4
556.4
128.3
331
322.5
74.4
391
381.0
87.9
439. 4
101.4
128.5
32
323.5
74.7
92
382.0
88.2
52
440.4
101.6
12
498.9
115.1
72
557.4
128.7
33
324.5
74.9
93
382.9
88.4
53
441.4
101.9
13
499.9
115.4
73
558.4
128.9
34
325.4
75.1
94
383.9
88.6
54
442.4
102.1
14
500.8
115.6
74
559.3
129.2
35
326.4
75.3
95
384.9
88.8
55
443. 3
102.3
15
501.8
115.8
75
560.3
129.4
36
327.4
75.6
96
385.9
89.1
56
444.3
102.5
16
502.8
116.0
76
561.3
129.6
37
328.4
75.8
97
386. 8
89.3
57 i 445. 3
102.8
17
503.8
116.3
77
562.3
129.8
38
329. 3
76.0
98
387.8
89.5
58 1 446. 3
103.0
18
504. 7
116.5
78
563. 2
1.30.
39
330.3
76.2
99
388.8
89.7
59 : 447. 2
103.2
19
505. 7
116. 7
79
564. 2
130.2
40
331.3
"332. 3
76.5
400
389.8
90.0
60
448.2
103.4
103.7
20
506.7 ! 116.9
80
565.2
566.2
130.4
341
76.7
401
390.7
90.2
461
449.2
521
507.7 117.2
581
130.7
42
333. 2
76.9
02
391.7
90.4
62
450.2
103.9
22
508.6 117.5
82
567. 1
131.0
43
334.2
77.1
03
392.7
90.6
63
451.1
104.1
23
509.6 117.7
83
568.1
131.2
44
335.2
77.4
04
393.6
90.8
64
452. 1
104. 3
24
510.6
117.9
84
569. 1
131.4
45
336.2
77.6
05
394. 6
91.1
65
453. 1
104.6
25
511.6
118.1
85
570.1
131.6
46
337.1
77.8
06
395.6
91.3
66
454.1
104.8
26
512. 5
118.3
86
571.0
1.31.8
47
338.1
78.0
07
396. 6
91.5
67
455.
105.0
27
513.5
118.5
87
572.0
1.32.
48
3.39. 1
78.3
08
397.5
91.7
68
456.0
105. 2
28
514.5
118.7
88
573.
132.3
49
340. 1
78.5
09
398.5
92.0
69
457.0
105. 5
29
515.5
119.0
89
573. 9
132.5
50
341.
78.7
10
.399. 5
92.2
70
458.
458.9
105.7
30
516. 4
517.4
119.2
119.4
90
574. 9
575.9
132. 8
351
342.0
78.9
411
400.5
92.4
471
105.9
531
591
1.33.
52
343.
79.2
12
401.4
92.6
72
459.9
106.1
32
518.4
119.6
92
576.9
133.2
53
344.0
79.4
13
402.4
92.9
73
460.9
106.4
.33
519.4
119.9
93
577.8
133.4
54
344.9
79.6
14
403.4
93.1
74
461.9
106.6
34
520.3
120.1
94
578.8
1.33. 6
55
345. 9
79.8
15
404.4
93.3
75
462. 8
106.8
35
521. 3
120.3
95
579.8
133. 8
56
346. 9
80.1
16
405. 3
93.5
76
463.8
107.0
36
522. 3
120.5
96
580.8
134.
57
347.9
80.3
17
406.3
93.8
77
464.8
107.3
37
523.3
120.8
97
581.7
1.34. 3
58
348. 8
80.5
18
407.3
94.0
78
465. 8
107.5
38
524.2
121.0
98
582.7
134.5
59
349.8
80.7
19
408.3
94.2
79
466.7
107.7
39
525.2
121.2
99
583.7
134. 8
60
350.8
81.0
20
409.2
94.4
80
467.7
107.9
40
526.2
121.5
600
584.6
135.
Dist.
Dep.
Lat.
Dist
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
"7° (103°, 257
°, 283°
)■
TABLE 2.
[Page 557
Difference of Latitude and Departure for 14° (166°, 194
°, 346°
)■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1
0.2
61
59.2
14.8
121
117.4
29.3
181
175.6
43.8
241
233.8
58.3
2
1.9
0.5
62
60.2
15.0
22
118.4
29.5
82
176.6
44.0
42
234.8
58.5
3
2.9
0.7
63
61.1
15.2
23
119.3
29.8
83
177.6
44.3
43
235.8
58.8
4
3.9
1.0
64
62.1
15.5
24
120.3
30.0
84
178.5
44.5
44
236.8
59.0
5
4.9
1.2
65
63.1
15.7
25
121.3
30.2
85
179.5
44.8
45
237.7
59.3
6
5.8
1.5
66
64.0
16.0
26
122.3
30.5
86
180.5
45.0
46
238.7
59.5
7
6.8
1.7
67
65.0
16.2
27
123.2
30.7
87
181.4
45.2
47
239.7
59.8
8
7.8
1.9
68
66.0
16.5
28
124.2
31.0
88
182.4
45. 5
48
240.6
60.0
9
8.7
2.2
69
67.0
16.7
29
125.2
31.2
89
183.4
45.7
49
241.6
60.2
10
9.7
2.4
2.7
70
71
67.9
16.9
30
126.1
31.4
90
184.4
46.0
50
242.6
60.5
11
10.7
68.9
17.2
131
127.1
31.7
191
185.3
46.2
251
243.5
60.7
12
11.6
2.9
72
69.9
17.4
32
128.1
31.9
92
186.3
46.4
52
244.5
61.0
13
12.6
3.1
73
70.8
17.7
33
129.0
32.2
93
187.3
46.7
53
245.5
61.2
14
13.6
3.4
74
71.8
17.9
-34
130.0
32.4
94
188.2
46.9
54
246.5
61.4
35
14.6
3.6
75
72.8
18.1
35
131.
32.7
95
189.2
47.2
55
247.4
61.7
16
15.5
3.9
76
73.7
18.4
36
132.0
32.9
96
190.2
47.4
56
248.4
61.9
17
16.5
4.1
77
74.7
18.6
37
132.9
33.1
97
191.1
47.7
57
249.4
62.2
18
17.5
4.4
78
75.7
18.9
38
133.9
33.4
98
192.1
47.9
58
250.3
62.4
19
18.4
4.6
79
76.7
19.1
39
134.9
33.6
99
193.1
48.1
59
251.3
62.7
20
19.4
4.8
80
77.6
19.4
40
135.8
33.9
200
194.1
48.4
60
252.3
62.9
21
20.4
5.1
81
78.6
19.6
141
136.8
34.1
201
195.0
48.6
261
253.2
63.1
22
21.3
5.3
82
79.6
19.8
42
137.8
34.4
02
196.0
48.9
62
254. 2
63.4
23
22.3
5.6
83
80.5
20.1
43
138.8
34.6
03
197.0
49.1
63
255. 2
63.6
24
23.3
5.8
84
81.5
20.3
44
139.7
34.8
04
197.9
49.4
64
256.2
63.9
25
24.3
6.0
85
82.5
20.6
45
140.7
35.1
05
198.9
49.6
65
257.1
64.1
26
25.2
6.3
86
83.4
20.8
46
141.7
35.3
06
199.9
49.8
66
258.1
64.4
27
26.2
6.5
87
84.4
21.0
47
142. 6
35. 6
07
200.9
50.1
67
259. 1
64.6
28
27.2
6.8
88
85.4
21.3
48
143.6
35.8
08
201.8
50.3
68
260.0
64.8
29
28.1
7.0
89
86.4
21.5
49
144.6
36.0
09
202.8
50.6
69
261.0
65.1
30
29.1
7.3
90
91
87.3
21.8
50
145. 5
36. 3
10
203.8
50.8
70
262.0
65.3
31
30.1
7.5
88.3
22.0
151
146.5
36. 5
211
204.7
51.0
271
263.0
6.5.6
32
31.0
7.7
92
89.3
22.3
52
147.5
;i6.8
12
205.7
51.3
72
263.9
6.5.8
33
32.0
8.0
93
90.2
22.5
53
148. 5
37.0
13
206.7
51.5
73
264.9
66.0
34
33.0
8.2
94
91.2
22.7
54
149.4
37.3
14
207.6
51.8
74
265.9
66.3
35
34.0
8.5
95
92.2
23.0
55
150.4
37.5
15
208.6
52.
75
266.8
66.5
36
34.9
8.7
96
93. 1 23. 2
56
151.4
37.7
16
209.6
52.3
76
267.8
66.8
37
35.9
9.0
97
94.1
23.5
57
152.3
38.0
17
210.6
52.5
77
268.8
67.0
38
36.9
9.2
98
95.1
23.7
58
153. 3
38.2
18
211.5
52.7
78
269.7
67.3
39
37.8
9.4
99
96.1
24.0
59
154.3
38.5
19
212.5
53.0
79
270.7
67.5
40
41
.38.8
39.8
9.7
9.9
100
97.0
24.2
60
155.2
38.7
20
213.5
53. 2
80
271.7
67.7
101
98.0
24.4
161
156.2
38.9
221
214.4
53.5
281
272.7
68.0
42
40.8
10.2
02
99.0
24.7
62
157.2
39.2
22
215.4
53.7
82
273.6
68.2
43
41.7
10.4
03
99.9
24.9
63
158.2
39.4
23
216.4
5.3.9
83
274.6
68.5
44
42.7
10.6
04
100.9
25.2
64
159.1
39.7
24
217.3
54.2
84
275. 6
68.7
45
43.7
10.9
05
101.9
25.4
65
160.1
39.9
25
218. 3
54.4
85
276.5
68.9
46
44.6
11.1
06
102.9
25.6
66
161.1
40.2
26
219.3
54.7
86
277.5
69.2
47
45.6
11.4
07
103.8
25.9
67
162.0
40.4
27
220.3
54.9
87
278.5
69.4
48
46.6
11.6
08
104.8
26.1
68
163.0
40.6
28
221.2
55.2
88
279.4
69.7
49
47.5
11.9
09
105.8
26.4
69
164.0
40.9
29
222.2
55. 4
89
280.4
69.9
50
48.5
12.1
10
106.7
26.6
70
165.0
41.1
30
223.2
55.6
90
281.4
70.2
51
49.5
12.3
111
107.7
26.9
171
165.9
41.4
231
224.1
55.9
291
282.4
70.4
52
50.5
12.6
12-
108.7
27.1
72
166.9
41.6
32
225. 1
56.1
92
283.3
70.6
53
51.4
12.8
13
109.6
27.3
73
167.9
41.9
33
226.1
56.4
93
284. 3
70.9
54
52.4
13.1
14
110.6
27.6
74
168.8
42.1
34
227.0
56.6
94
285.3
71.1
65
53.4
13.3
15
111.6
27.8
75
169.8
42.3
35
228.0
56.9
95
286.2
71.4
56
54.3
13.5
16
112.6
28.1
76
170.8
42.6
36
229.0
57.1
96
287.2
71.6
57
55.3
13.8
17
113.5
28.3
77
171.7
42.8
37
230.0
57.3
97
288.2
71.9
58
56.3
14.0
18
114.5
28.5
78
172.7
43.1
38
230. 9
57. 6
98
289.1
72.1
59
57.2
14.3
19
115.5
28.8
79
173.7
43.3
39
231.9
57.8
99
290.1
72.3
60
58.2
14.5
20
116.4
29.0
80
174.7
43.5
40
232.9
58.1
300
291.1
72.6
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
■6° (1
04°, 256°, 284°
).
Page 558]
TABLE
2.
*
Difference of Latitude and Departure for 14° (166°, 194°, 346°
)■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
292.0
72.8
361
350.2
87.3
421
408.5
101.8
481
466.7
116.3
541
525.
130.9
02
293.0
73.0
62
351.2
87.6
22
409.4
102.1
82
467.7
116.6
42
525. 9
131.2
03
294.0
73.3
63
352.2
87.8
23
410.4
102.3
83
468.6
116.8
43
526. 9
1.31. 4
04
294.9
73.5
64
353.2
88.0
24
411.4
102.6
84
469.6
117.1
44
527.9
131.6
05
295. 9
73.8
65
354.1
88.3
25
412.3
102.8
85
470.6
117.3
45
528. 8
131.9
06
296.9
74.0
66
355.1
88.5
26
413.3
103.0
86
471.5
117.6
46
529. 8
132. 1
07
297.8
74.2
67
356.1
88.8
27
414.3
103.3
87
472.5
117.8
47
530.8
132.3
08
298.8
74.5
68
357.0
89.0
28
415. 3
103.5
88
473. 5
118.0
48
531.7
132.6
09
299.8
74.7
69
358.0
89.2
29
416.2
103.8
89
474.5
118.3
49
532.7
132.8
10
300.8
75.0
70
359.0
89.5
30
417.2
104.0
90
475.4
118.5
50
533.7
534.6
133.0
311
301.7
75.2
371
359.9
89.7
431
418.2
104.2
491
476.4
118.8
551
133.3
12
302.7
75.5
72
360.9
90.0
32
419.1
104.5
92
477. 4
119.0
52
535.6
133.6
13
303.7
75.7
73
361. 9
90.2
33
420.1
104.7
93
478.3
119.2
53
536.6
133.8
14
304.6
75.9
74
362.9
90.5
34
421.1
105.0
94
479.3
119. 5
54
537. 5
134.0
15
305.6
76.2
75
363.8
90.7
35
422.0
105. 2
95
480.3
119.7
55
538.5
134.3
16
306.6
76.4
76
364.8
90.9
36
423.0
105.5
96
481.3
120.0
56
539. 5
134. 5
17
307.6
76.7
77
365.8
91.2
37
424.0
105.7
97
482.2
120.2
57
540. 5
134.8
18
308.5
76.9
78
366.7
91.4
38
425.0
105.9
98
483.2
120.4
58
541.4
135.
19
309.5
77.2
79
367.7
91.7
39
425.9
106.2
99
484.2
120.7
59
542.4
135.2 .
20
310.5
77.4
80
381
368.7
91.9
40
426.9
106.4
500
485.1
121.
60
543.4
544. 3
135. 5
135. 7
321
311.4
77.6
369.6
92.2
441
427.9
106.7
501
486.1
121.2
561
22
312.4
77.9
82
370.6
92.4
42
428.8
106.9
02
487.1
121.4
62
545. 3
135.9
23
313.4
78.1
83
371.6
92.6
43
429.8
107.1
03
488.0
121.7
63
546.3
136.2
24
314.3
78.4
84
372.6
92.9
44
430.8
107.4
04
489.0
122.0
64
547.2
136.5
25
315.3
78.6
85
373.5
93.1
45
431.7
107.6
05
490.0
122.1
65
548. 2-
136.6
26
316.3
78.8
86
374. 5
93.4
46
432.7
107.9
06
491.0
122.4
66
549.2
136.9
27
317.3
79.1
87
375.5
93.6
47
433.7
108.1
07
491.9
122.6
67
550.1
1.37. 1
28
318.2
79.3
88
376.4
93.8
48
434. 7
108.4
08
492.9
122.9
68
551.1
137.4
29
319.2
79.6
89
377.4
94.1
49
435. 6
108.6
09
493.9
123.1
69
552.1
137.6
30
331
320.2
79.8
90
378.4
94.3
50
436.6
108.8
10
494.9
123.4
70
553.1
137.9
138.1
321.1
80.1
391
379.4
94.6
451
437.6
109. 1
511
495.-8
123.6
571
554.0
32
322.1
80.3
92
380.3
94.8
52
438.5
109.3
12
496.8
123. 8
72
555.
138.3
33
323.1
80.5
93
381.3
95.1
53
439.5
109.6
13
497.8
124.1
73
556.
138. 6
34
324.0
80.8
94
382.3
95.3
54
440.5
109.8
14
498.7
124. 3
74
557.0
138.8
35
325.0
81.0
95
383.2
95.5
55
441.5
110.1
15
499.7
124.6
75
557.9
139.1
36
326.0
81.3
96
384. 2
95.8
56
442.4
110.3
16
500.7
124.8
76
558.9
139. 3
37
327.0
81.5
97
385.2
96.0
57
443.4
110.5
17
501.7
125.0
77
559.9
139. 5
38
327.9
81.7
98
386.1
96.3
58
444. 4
110.8
18
502.6
125.3
78
• 560. 9
139.8
39
328.9
82.0
99
387.1
96.5
59
445.3
111.0
19
503.6
125.6
79
561.8
140.0
40
329.9
82.2
400
388.1
96.7
60
446.3
111.3
20
504.6
125. 8
80
562.8
140.3
341
330.8
82.5
401
389.1
97.0
461
447.3
111.5
521
505.5
126.0
581
563.8
140.5
42
331.8
82.7
02
390.0
97.2
62
448.2
111.7
22
506.5
126.2
82
564. 7
140.8
43
332.8
83.0
03
391.0
97.5
63
449.2
112.0
23
.507.5
126.5
83
565.7
141.0
44
333.7
83.2
04
392.0
97.7
64
450.2
112.2
24
508.4
126. 8
84
566. 7
141.3
45
334.7
83.4
05
392.9
98.0
65
451. 2
112.5
25
509.4
127.0
85
567.6
141.5
46
335.7
83.7
06
393.9
98.2
66
452. 1
112.7
26
510.4
127.2
86
568.6
141.8
47
336.7
83.9
07
394.9
98.4
67
453.1
113.0
27
511.4
127.5
87
569.6
142.0
48
337. 6
84.2
08
395.8
98.7
68
454.1
113.2
28
512.3
127.8
88
570.6
142.3
49
338.6
84.4
09
396.8
98.9
69
455.0
113.4
29
513. 3
128.0
89
571.5
142.5
50
339.6
84.7
10
397.8
99.2
70
456.0
113.7
30
514.3
128.2
128. 5
90
572. 5
573.5
142.8
351
340.5
84.9
411
398.8
99.4
471
457.0
113.9
531
515.3
591
143.0
52
341.5
85.1
12
399.7
99.7
72
457.9
114.2
32
516.2
128.8
92
574.4
143.3
53
342.5
85.4
13
400.7
99.9
73
458.9
114.4
33
517.2
129.0
93
575. 4
143.5
54
343.5
85.6
14
401.7
100.1
74
459.9
114.6
34
518.2
129.2
94
576.4
143.8
55
344.4
85.9
15
402.6
100.4
75
460.9
114.9
35
519.1
129.4
95
577. 3
144.0
56
345.4
86.1
16
403.6
100.6
76
461.8
115.1
36
520.1
129.7
96
578. 3
144.2
57
346. 4
86.3
17
404.6
100.9
77
462.8
115.4
37
521.1
129.9
97
579. 3
144.5
58
347.3
86.6
18
405.5
101.1
78
463.8
115.6
38
522.1
130. 2
98
580.3
144.7
59
348.3
86.8
19
406. 5
101. 3
79
464.- 7
115. 9
39
523.0
130.4
99
581.2
144.9
60
349.3
87.1
20
407.5
101.6
80
465.7
116.1
40
524.0
130.6
600
582.2
145. 1
Cist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
76° (104°, 2.56
°, 284°
)•
TABLE
2.
[Page 559 |
Dist.
Difference of Latitude and Departure for 15° (165°, 195°
, 345°)
Lat.
D«p.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.9
15.8
121
116.9
31.3
181
174.8
46.8
241
232.8
62.4
2
1.9
0.5
62
59.9
16.0
22
117.8
31.6
82
175.8
47.1
42
233.8
62.6
3
2.9
0.8
63
60.9
16.3
23
118.8
31.8
83
176.8
47.4
43
234.7
62.9
4
3.9
1.0
64
61.8
16.6
24
119.8
32.1
84
177.7
47.6
44
235.7
63.2
5
4.8
1.3
65
62.8
16.8
25
120.7
32.4
85
178.7
47.9
45
236.7
63.4
6
5.8
1.6
66
63.8
17.1
26
121.7
32.6
86
179.7
48.1
46
237.6
63.7
7
6.8
1.8
67
64.7
17.3
27
122.7
32.9
87
180.6
48.4
47
238.6
63.9
8
7.7
2.1
68
65.7
17.6
28
123.6
33.1
88
181.6
48.7
48
239.5
64.2
9
8.7
2.3
69
66.6
17.9
29
124.6
33.4
89
182.6
48.9
49
240.5
64.4
10
9.7
2.6
70
67.6
18.1
30
125.6
33.6
90
183.5
49.2
. 50
241.5
64.7
11
10.6
2.8
71
68.6
18.4
131
126.5
33.9
191
"184.5
49.4
251
242.4
65.0
12
11.6
3.1
72
69.5
18.6
32
127.5
34.2
92
185.5
49.7
52
243.4
65.2
13
.12.6
3.4
73
70.5
18.9
33
128.5
34.4
93
186.4
50.0
53
244.4
65.5
14
13.5
3.6
74
71.5
19.2
34
129.4
34.7
94
187.4
50.2
54
245.3
65.7
15
14.5
3.9
75
72.4
19.4
35
130.4
34.9
95
188.4
50.5
55
246.3
66.0
16
15.5
4.1
76
73.4
19.7
36
131.4
35.2
96
189.3
50.7
56
247.3
66.3
17
16.4
4.4
77
74.4
19.9
37
132.3
35.5
'97
190.3
51.0
57
248.2
66.5
18
17.4
4.7
78
75.3
20.2
38
133.3
35.7
98
191.3
51.2
58
249.2
66.8
19
18.4
4.9
79
76.3
20.4
39
134.3
36.0
99
192.2
51.5
59
250.2
67.0
20
19.3
5.2
80
77.3
78.2
20.7
40
135.2
36.2
200
193.2
51.8
60
251.1
252.1
67.3 .
67.6
21
20.3
5.4
81
21.0
141
136.2
36.5
201
194.2
52.0
261
22
21.3
5.7
82
79.2
21.2
42
137.2
36.8
02
195.1
52.3
62
253.1
67.8
23
22.2
6.0
83
80.2
21.5
43
1,38. 1
37.0
03
196.1
52.5
63
254.0
68.1
24
23.2
6.2
84
81.1
21.7
44
139.1
37.3
04
197.0
52.8
64
255.0
68.3
25
24. 1
6.5
85
82.1
22.0
45
140.1
37.5
05
198.0
53.1
65
256.0
68.6
26
25. 1
6.7
86
83.1
22.3
46
141.0
37.8
06
199.0
53.3
66
256.9
68.8
27
26.1
7.0
87
84.0
22.5
47
142.0
38.0
07
199.9
53.6
67
257.9
69.1
28
27.0
7.2
88
85.0
22.8
48
143.0
38.3
08
200.9
53.8
68
258.9
69.4
29
28.0
7.5
89*
86.0
23.0
49
143.9
38.6
09
201.9
54.1
69
259.8
69.6
30
29.0
7.8
90
86.9
23.3
50
144.9
38.8
10
211
202.8
54.4
70
260.8
69.9
31
29.9
8.0
91
87.9
23.6
151
145.9
39.1
203.8
54.6
271
261.8
70.1
32
30.9
8.3
92
88.9
23.8
52
146.8
39.3
12
204.8
54.9
72
262.7
70.4
33
31.9
8.5
93
89.8
24.1
53
147.8
39.6
13
20,5.7
55.1
73
263.7
70.7
34
32.8
8.8
94
90.8
24.3
54
148.8
39.9
14
206.7
,55.4
74
264.7
70.9
35
33.8
9.1
95
91.8
24.6
55
149.7
40.1
15
207.7
55.6
75
265. 6
71.2
36
34.8
9.3
96
92.7
24.8
56
150.7
40.4
16
208.6
55.9
76
266.6
71.4
37
35.7
9.6
97
93.7
2.5.1
57
151.7
40.6
17
209.6
56.2
77
267.6
71.7
38
36.7
9.8
98
94.7
25.4
58
152.6
40.9
18
210.6
56.4
78
268.5
72.0
39
37.7
10.1
99
95.6
25.6
59
153.6
41.2
19
211.5
56.7
79
269.5
72.2
40
38.6
10.4
10.6
100
96.6
25.9
60
161
154.5
155.5
41.4
20-
221
212.5
56.9
80
270. 5
72.5
72.7
41
39.6
101
97.6
26.1
41.7
213.5
57.2
2^
271.4
42
40.6
10.9
02
98.5
26.4
62
156.5
41.9
22
214.4
57.5
82
272.4
73.0
43
41.5
11.1
03
99.5
26.7
63
157.4
42.2
23
215.4
57.7
83
273.4
73.2
44
42.5
11.4
04
100.5
26.9
64
158.4
42.4
24
216.4
58.0
84
274.3
73.5
45
43.5
11.6
05
101.4
27.2
65
159.4
42.7
25
217.3
58.2
85
275.3
73.8
46
44.4
11.9
06
102.4
27.4
66
160.3
43.0
26
218.3
58.5
86
276.3
74.0
47
45.4
12.2
07
103.4
27.7
67
161.3
43.2
27
219.3
58.8
87
277.2
74.3
48
46.4
12.4
08
104.3
28.0
68
162.3
43.5
28
220.2
59.0
88
278.2
74.5
49
47.3
12.7
09
105.3
28.2
69
163.2
43.7
29
221.2
59.3
89
279.2
74.8
50
51
48.3
49.3
12.9
13.2
10
111
106.3
28.5
70
164.2
44.0
30
222.2
59.5
90
280.1
75.1
107.2
28.7
171
16,5.2
44.3
231
223.1
59.8
291
281.1
7.5.3
52
50.2
13.5
12
108.2
29.0
72
166.1
44.5
32
224.1
60.0
92
282.1
75.6
53
51.2
13.7
13
109.1
29.2
73
167.1
44.8
33
225.1
60.3
93
283.0
7.5.8
54
52.2
14.0
14
110.1
29.5
74
168.1
45.0
34
226.0
60.6
94
284.0
76.1
55
53.1
14.2
15
111.1
29.8
75
169.0
45.3
35
227.0
60.8
95
28i.9
76.4
56
54.1
14.5
16
112.0
30.0
76
170.0
45.6
36
228.0
61.1
96
285.9
76.6
57
55.1
14.8
17
113.0
30.3
77
171.0
45.8
37
228.9
61.3
97
286.9
76.9
58
56.0
15.0
18
114.0
30.5
78
171.9
46.1
38
229.9
61.6
98
287.8
77.1
59
57.0
15.3
19
114.9
.30.8
79
172.9
46.3
39
230.9
61.9
99
288'. 8
77.4
60
58.0
15.5
20
115.9
31.1
80
173.9
46.6
40
231.8
62.1
300
289.8
77.6
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
75° (105°, 25,
)°, 285<
')•
Page 560]
TABLE 2.
Difference of Latitude and Departure for 15° (165°, 195°, 345°
)•
,
Diit.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
140.0
301
290.7
77.9
361
348.7
93.4
421
406.6
109.0
481
464.6
124.5
541
522.6
02
291.7
78.2
62
349.6
93.7
22
407.6
109.2
82
465.6
124.8
42
523.5
140.3
03
292.7
78.4
63
350.6
94.0
23
408.6
109.5
83
466.5
125.0
43
524.5
140.5
04
293. 6
78.7
64
351.6
94.2
24
409. 5
109.7
84
467.5
125. 3
44
525.5
140.8
05
294.6
78.9
65
352.5
94.5
25
410.5
110.0
86
468.5
125. 6
45
526.4
141.1
06
295.6
79.2
66
353.5
94.7
26
411.5
110.3
86
469.4
125.8
46
527.4
141.4
07
296.5
79.5
67
354.5
95.0
27
412.4
110.5
87
470.4
126.1
47
528.4
141.6
08
297.5
79.7
68
355.4
95.3
28
413.4
110.8
88
471.4
126.4
48
529. 3
141.9
09
298.4
80.0
69
356.4
95.5
29
414.4
111.0
89
472.3
126.6
49
530.3
142.1
10
299.4
80.2
70
357.4
95.8
30
415.3
111.3
90
473.3
126.9
50
531. 3
142.4
311
300.4
80.5
371
358.3
96.0
431
416.3
111.6
491
474. 3
127.1
551
532.2
142.6
12
301.3
80.8
72
359.3
9(5.3
32
417.3
111.8
92
475.2
127.4
52
533.2
142.9
13
302. 3
81.0
73
360.3
96.5
33
418.2
112.1
93
476.2
127.6
53
5.34. 2
143.1
14
303.3
81.3
74
361.2
96.8
34
419.2
112.3
94
477.2
127.9
54
535.1
143.4
15
304. 2
81.5
75
362.2
97.1
35
420.2
112.6
95
478.1
128.1
55
536.1
143.7
16
305.2
81.8
76
363.2
97.3
36
421.1
112.9
96
479.1
128.4
56
537.1
143.9
17
306.2
82.1
77
364.1
97.6
37
422.1
113. 1
97
480.1
128.6
57
538.0
144.2
18
307. 1
82.3
78
365.1
97.8
38
423. 1
113.4
98
481.0
128.9
58
539.0
144.4
19
308.1
82.6
79
366.1
98.1
39
424.0
113.6
99
482.0
129.1
59
540.0
144.7
20
309. 1
82.8
80
367.0
98.4
40
425,0
113.9
500
483.0
483.9
129.4
129. 7
60
540.9
144.9
321
310.0
83.1
381
368.0
98.6
441
426.0
114.1
501
561
541.9
145.2
22
311.0
83.3
82
369.0
98.9
42
426.9
114.4
02
484.9
129.9
62
542.9
145.4
23
312.0
83.6
83
369.9
99.1
43
427.9
114.7
03
485.9
130.2
63
543.8
145.7
24 1 312.9
83.9
84
370.9
99.4
44
428.8
114.9
04
486.8
130.4
64
544.8
146.0
25 ! 313.9
84.1
85
371.9
99.6
45
429.8
115.2
05
487.8
130.7
65
545.8
146.2
26 1 314.9
84.4
86
372.8
99.9
46
430.8
115.4
06
488.8
131.0
66
546.7
146.5
27 1 315.8
84.6
87
373.8
100.2
47
431.7
115.7
07
489.7
131.2
67
547.7
146.7
28 1 316.8
84.9
88
374.8
100.4
48
432.7
116.0
08
490.7
131.5
68
548.7
147.0
29
317.8
8.5.1
89
375.7
100.7
49
433.7
116.2
09
491.7
131.7
69
549.6
147.2
30
318.7
85.4
90
376.7
100.9
50
434.6
435.6
116.5
lie. 7
10
492.6
132.0
70
550.6
147.5
331
319.7
8.5.7
391
377.7
101.2
451
511
493.6
132.3
571
551.6
147.8
32
320. 7
85.9
92
378.6
101.5
52
436.6
117.0
12
494.5
132.5
72
552.5
148.0
33
321.6
86.2
93
379.6
101.7
53
437. 5
117.3
13
495.5
132.8
73
553.5
148.3
34
322.6
86.5
94
380.6
102.0
.54
438. 5
117.5
14
496.5
133.0
74
554.4
148.5
35
323.6
86.7
95
381.5
102.2
55
439.5
117.8
15
497.4
133.3
75
555.4
148.8
36
324.5
87.0
96
382. 5
102.5
56
440.4
118.0
16
498.4
13,3.5
76
556.4
149.0
37
325. 5
87.2
97
383.4
102.8
57
441.4
118.3
17
499.4
133. 8
77
557.3
149.3
38
326.5
87.5
98
384.4
103.0
58
442.4
118.5
18
.500. 3
134.0
78
558.3
149.5
39
327.4
87.7
99
385.4
103. 3
59
443.3
118.8
19
.501. 3
134. 3
79
559.3
149.8
40
328.4
88.0
400
386. 3
103.5
103. 8
60
444.3
119.1
20
502. 3
134.6
80
560.2
150.1
150. 3
341
329. 4
88.3
401
387.3
461
445. 3
119.3
521
50.3.2 134.8
581
561.2
42
330.3
88.5
02
388.3
104.1
62
446.2
119.6
22
504.2 135.1
82
562.2
150.6
43
331.3
88.8
03
389.2
104.3
63
447.2
119.8
23
505.2 13.5.3
83
563.1
150.8
44
,332. 3
89.0
04
390.2
104.6
64
448.2
120.1
24
506. 1 ! 135. 6
84
564.1
1.51. 1
45
333.2
89.3
05
391. 2
104.8
65
449.1
120.4
25
507. 1 ! 135. 9
85
565.1
151.4
46
334. 2
89.6
06
392.1
105. 1
66
450.1
120.6
26
508. 1 1 136. 1
86
566.0
151.6
47
335. 2
89.8
07
393.1
105.3
67
451. 1
120.9
27
509. i 136. 4
87
567.0
151.9
48
336.1
90.1
08
394.1
105.6
68
452.
121.1
28
510. ! 136. 6
88
568.0
152.2
49
337.1
90.3
09
395.0
105.9
69
453.0
121.4
29
511.0 136.9
89
568.9
152.4
50
351
.338. 1
90.6
10
396.0
106.1
70
454.0
121-. 7
30
511.9
137.2
90
569.9
152.7
339.
90.9
411
397.0
106.4
471
454.9
121.9
531
512.9
137.4
591
570.9
153.0
52
340.0
91.1
12
397.9
106.6
72
455.9
122.2
32
513.9
137.7
92
571.8
153.2
53
340.9
91.4
13
398.9
106.9
73
456.9
122.4
33
514.8
137.9
93
572. 8
153.5
54
341.9
91.6
14
399.9
107.2
74
457.8
122.7
34
515.8
138.2
94
573.8
153.7
55
342.9
91.9
15
400.8
107.4
75
458.8
122.9
35
516.8
138.4
95
574.7
154.0
56
343.8
92.1
16
401.8
107.7
76
459.8
123.2
36
517. 7
138. 7
96
575.7
154.2
57
344.8
92.4
17
402.8
107.9
77
460.7
123. 5
37
518.7
139.
97
576.7
154.5
58
345.8
92.7
18
403.7
108.2
78
461.7
123.7
38
519.7
139.2
98
577. 6
154.8
59
346. V
92.9
19
404.7
108.5
79
462.7
124.0
39
520.6
139.5
99
578.6
155.0
60
347.7
93.2
20
405.7
108.7
80
463.6
124.2
40
521.6
139.7
600
579.5
155.3
Dist.
Dep.
Lav.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
^5° (1
05°, 255°, 285°
.
TABLE 2.
[Page 561
Difference of Latitude and Departure for
16° (164°, 196°, 344=
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.6
16.8
121
116.3
33.4
181
174.0
49.9
241
231.7
66.4
2
1.9
0.6
62
59.6
17.1
22
117.3
33.6
82
174.9
50.2
42
232.6
66.7
3
2.9
0.8
63
60.6
17.4
23
118.2
33.9
83
175.9
50.4
43
233.6
67.0
4
3.8
1.1
64
61.5
17.6
24
119.2
34.2
84
176.9
50.7
44
234.5
67.3
5
4.8
1.4
65
62.5
17.9
25
120.2
34.5
85
177.8
51.0
45
235.5
67.5
6
5.8
1.7
66
63.4
18.2
26
121.1
34.7
86
178.8
51.3
46
236.5
67.8
7
6.7
1.9
67
64.4
18.5
27
122. 1
35.0
87
179.8
51.5
47
237.4
68.1
8
7.7
2.2
68
65.4
18.7
28
123.0
35.3
88
180.7
51.8
48
238.4
68.4
9
8.7
2.5
69
66.3
19.0
29
124.0
.35.6
89
181.7
52.1
49
239.4
68.6
10
9.6
2.8
70
67.3
19.3
30
131
125.0
125.9
35.8
90
182.6
52.4
50
240.3
68.9
11
10.6
3.0
71
68.2
19.6
36.1
191
183.6
52.6
251
241.3
69.2
12
11.5
3.3
72
69.2
19.8
32
126.9
36.4
92
184.6
.52.9
52
242.2
69.5
13
12.5
3.6
73
70.2
20.1
33
127.8
36.7
93
185.5
53.2
53
243.2
69.7
14
13.5
3.9
74
71.1
20.4
34
128.8
36.9
94
186.5
53.5
54
244.2
70.0
15
14.4
4.1
75
72.1
20.7
35
129.8
37.2
95
187.4
.53.7
55
245. 1
70.3
16
15.4
4.4
76
73.1
20.9
36
130.7
37.5
96
188.4
54.0
56
246.1
70.6
17
16.3
4.7
77
74.0
21.2
37
131.7
37.8
97
189.4
54.3
57
247.0
70.8
18
17.3
5.0
78
75.0
21.5
38
132.7
38.0
98
190.3
54.6
58
248.0
71.1
19
18.3
6.2
79
75.9
21.8
39
133.6
38. 3
99
191.3
54.9
59
249.0
71.4
20
19.2
5.5
80
76.9
22.1
40
134.6
38.6
38.9'
200
201
192.3
55.1
60
249.9
250.9
71.7 •
21
20.2
5.8
81
77.9
22.3
141
135.5
193. 2
55.4
261
71.9
22
21.1
6.1
82
78.8
22.6
42
136.5
39.1
02
194.2
55.7
62
251.9
72.2
23
22.1
6.3
83
79.8
22.9
43
137.5
39.4
03
195.1
56.0
63
252.8
72.5
24
23.1
6.6
84
80.7
23.2
44
138.4
39.7
04
196.1
.56.2
64
253.8
72.8
25
■24.0
6.9
85
81.7
23.4
45
139.4
40.0
05
197.1
56.5
65
254.7
73.0
26
25.0
7.2
86
82.7
23.7
46
140.3
40.2
06
198.0
56.8
66
255. 7
73.3
27
26.0
7.4
87
83.6
24.0
47
141.3
40.5
07
199.0
57.1
67
256.7
73.6
28
26.9
7.7
88
84.6
24.3
48
142. 3
40.8
08
199.9
57.3
68
257.6
73.9
29
27.9
8.0
89
85.6
24.5
49
143. 2
41.1
09
200.9
57.6
69
258.6
74.1
30
31
28.8
8.3
90
86.5
24.8
50
144.2
145.2
41.3
41.6
10
201.9
57.9
70
259.5
74.4
29.8
8.5
91
87.5
25.1
151
211
202.8
.58.2
271
260.5
74.7
32
30.8
8.8
92
88.4
25.4
52
146.1
41.9
12
203.8
.58.4
72
261.5
75.0
33
31.7
9.1
93
89.4
25.6
53
147.1
42.2
13
204.7
58.7
73
262.4
75.2
34
32.7
9.4
94
90.4
2.5.9
54
148.0
42.4
14
205.7
.59.0
74
263.4
75.5
35
33.6
9.6
95
91.3
26.2
.55
149.0
42.7
15
206.7
59.3
75
264.3
75.8
36
34.6
9.9
96
92.3
26.5
56
150.0
43.0
16
207.6
59.5
76
265.3
76.1
37
35.6
10.2
97
93.2
26.7
57
150. 9
43.3
17
208.6
.59.8
77
266.3
76.4
38
36.5
10.5
98
94.2
27.0
58
151.9
43. 6
18
209.6
60.1
78
267.2
76.6
39
37.5
10.7
99
95.2
27.3
59
152. 8
4.3.8
19
210. 5
60.4
79
268.2
76.9
40
41
38.5
11.0
100
96.1
27.6
60
161
153. 8
154.8
44.1
20
211.5
60.6
80
269.2
77.2
39.4
11.3
101
97.1
27.8
44.4
221
212.4
60.9
281
270. 1
77.5
42
40.4
11.6
02
98.0
28.1
62
155. 7
44.7
22
213. 4
61.2
82
271.1
77.7
43
41.3
11.9
03
99.0
28.4
63
156.7
44.9
23
214. 4
61.5
83
272.0
78.0
44
42.3
12.1
04
100.0
28.7
64
157. 6
45.2
24
215. 3
61.7
84
273.0
78.3
45
43.3
12.4
05
100.9
28.9
65
158. 6
45.5
25
216.3
62.0
85
274.0
78.6
46
44.2
12.7
06
101.9
29.2
66
159. 6
4.5.8
26
217.2
62.3
86
274.9
78.8
47
45.2
13.0
07
102.9
29.5
67
160. 5
46.0
27
218.2
62.6
87
275.9
79.1
48
46.1
13.2
08
103.8
29.8
68
161.5
46.3
28
219.2
62.8
88
276.8
79.4
49
47.1
13.5
09
104.8
30.0
69
162. 5
.46.6
29
220.1
63.1
89
277.8
79.7
50
48.1
13.8
10
105.7
30.3
70
163.4
164.4
46.9
30
221.1
63.4
90
278.8
79.9
51
49.0
14.1
111
106.7
30.6
171
47.1
231
222. 1
63.7
291
279.7
80.2
52
50.0
14.3
12
107.7
30.9
72
165.3
47.4
32
223.0
6.3.9
92
280.7
80.5
53
.50.9
14.6
13
108.6
31.1
73
166. 3
47.7
33
224.0
64.2
93
281.6
80.8
54
51.9
14.9
14
109.6
31.4
74
167.3
48.0
34
224.9
64.5
94
282.6
81.0
55
52.9
15.2
15
110.5
31.7
75
168.2
48.2
35
225.9
64.8
95
283.6
81.3
56
53.8
15.4
16
111.5
.32.0
76
169.2
48.5
36
226.9
a5. 1
96
284.5
81.6
57
54.8
15.7
17
112.5
32.2
77
170.1
48.8
37
227.8
6.5.3
97
285.5
81.9
58
55.8
16.0
18
113.4
32.5
78
171.1
49.1
38
228. 8
6.5.6
98
286.5
82.1
59
56.7
16.3
19
114.4
32.8
79
172.1
49.3
39
229.7
6.5.9
99
287.4
82.4
60
57.7
16.5
20
115.4
33.1
80
173.0
49.6
40
230.7
66.2
300
288.4
82.7
Diet.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
74° (1
06°, 254
°, 286°
)•
24972°— 12 26
Page 562]
TABLE 2.
Difference of Latitude and Departure for 16° (164°, 196°, 344=
)■
Diet.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
289.3
82.9
361
347.0
99.5
421
404.7
116.0
481
462.4
132.5
541
520.1
149.1
02
290.3
83.2
62
348.0
99.7
22
405.6
116.3
82
463.3
132.8
42
521.0
149.4
03
291.2
83.5
63
348.9
100.0
23
406.6
116.6
83
464.3
133.1
43
522.0
149.7
04
292.2
83.8
64
349. 9
100.3
24
407.6
116.8
84
465. 2
133.4
44
523.0
150.0
05
293.2
84.0
65
350.8
100.6
25
408.5
117.1
85
466.2
133.6
45
523.9
150.2
06
294.1
84.3
66
351.8
100.8
26
409.5
117.4
86
467.2
133.9
46
524. 9
150.4
07
295.1
84.6
67
352.8
101.1
27
410.4
117.7
87
468.1
134.2
47
525.9
150.7
08
296.0
84.9
68
353.7
101.4
28
411.4
117.9
88
469.1
134.5
48
526.8
151.0
09
297.0
8.5.1
69
354.7
101.7
29
412.4
118.2
89
470.1
134.8
49
527.8
151.3
10
298.0
85.4
70
355.6
101.9
30
413.3
118.5
90
471.0
135.0
50
528.7
151.6
311
298.9
85.7
371
72
356.6
102.2
431
414.3
118.8
491
472.0
135.3
551
529.7
151.9
12
299.9
86.0
357.6
102.5
32
415.2
119.0
92
472.9
1,35. 6
52
530.6
152.2
13
300.9
86.2
73
358.5
102.8
33
416.2
119.3
93
473.9
135.9
53
531.6
152.5
14
301.8
86.5
74
359.5
103.1
34 1 417. 2
119.6
94
474.9
136.2
54
532.6
152.8
15
302. 8
86.8
75
360. 4
103.3
35 i 418. 1
119. 9
95
475. 8
136.4
55
533. 5
153.0
16
303.7
87.1
76
361.4
103.6
36 ; 419. 1
120.1
96
476.8
136.7
56
534. 5
153.2
17
304.7
87.3
77
362.4
103.9
37
420.0
120.4
97
477.7
137.0
57
535.4
153.5
18
305.7
87.6
78
363.3
104.2
38
421.0
120.7
98
478.7
137.3
58
536.4
153.8
19
306.6
87.9
79
364.3
104.4
39
422.0
121.0
99
479.7
137.5
59
537.4
154,1
20
321
307.6
88.2
80
365.3
104.7
40
422.9
121.2
500
5bi
480.6
137.8
60
538.3
154.4
308.5
88.4
381
366.2
105.0
441
423.9
121.5
481.6
138.1
561
539.3
154.7
22
309.5
88.7
82
367.2
105.3
42
424.9
121.8
02
482.6
138.3
62
540.3
154.9
23
310.5
89.0
83
368.1
105.5
43
425.8
122.1
03
483.5
138.6
63
541.2
155.2
24
311.4
89.3
84
369.1
105.8
44
426.8
122.3
04
484.5
138.9
64
542.2
155.4
25
312.4
89.5
85
370. 1
106.1
45
427.7
122.6
05
485.4
139. 2
65
543.1
155.7
26
313.3
89.8
86
371.
106.4
46
428.7
122.9
06
486.4
139.4
66
544.1
156.0
27
314.3
90.1
87
372.
106.6
47
429.7
123.2
07
487.3
139.7
67
545.1
156. 3
28
315.3
90.4
88
372.9
106.9
48
430.6
123.4
08
488.3
140.0
68
546.0
156.6
29
316.2
90.6
89
373.9
107.2
49
431.6
123.7
09
489.3
140.3
69 547.
156.9
30
331
317.2
90.9
90
374.9
375.8
107.5
50
432.6
124.0
10
490.2
491.2
140.6
70 547. 9
157.1
318.2
91.2
391
107.7
451
433.5
124.3
511
140.8
571
548.9
157.3
32
319.1
91.5
92
376.8
108.0
52
434.5
124.6
12
492.1
141.1
72
549.8
157.6
33
320.1
91.8
93
377.8
108.3
53
435.4
124.8
13
493.1
141.4
141.7
73
550.8
157.9
34
321.0
92.0
94
378.7
108.6
54
436.4
125. 1
14
494.1
74
551.8
158.2
35
322.0
92.3
95
379.7
108.8
55
437.4
125.4
15
495.0
141.9
75
552.7
158.4
36
323.0
92.6
96
380.6
109.1
56
438.3
125.7
16
496.0
142.2
76
553.7
158.7
37
323.9
92.9
97
381.6
109.4
57
439.3
125.9
17
496.9
142.5
77
554.6
1.59.
38
324.9
93.1
98
382.6
109.7
58
440.2
126.2
18
497.9
142.8
78
5.55. 6
159.3
39
325.8
93.4
99
383.5
109.9
.59
441.2
126.5
19
498.9
143.0
79
556.5
159.5
40
326.8
93.7
400
384.5
110.2
60
442.2
126.8
l27.
20
521
499.8
143.3
80
557.5
159.8
341
327.8
94.0
401
385.4
110.5
461
443.1
500.8
143. 6
581
558.4
160.1
42
328. 7
94.2
02
386.4
110.8
62
444.1
127.3
22
501.7
143. 9
82 1 559.4
160.4
43
329.7
94.5
03
387.4
111.0
63
445.0
127.6
23
502.7
144.1
83 560. 4
160.6
44
330.7
94.8
04
388.3
111.3
64
446.0
127.9
24
503.7
144.4
84
561.3
161.0
45
331.6
95.1
05
389.3
111.6
65
447.0
128.1
25
504.6
144.7
85
562.3
161.3
46
332.6
95.3
06
390.2
111.9
66
447.9
128.4
26
505.6
145.0
86
563. 2
161.6
47
333.5
95.6
07
391.2
112.1
67
448.9
128.7
27
506.6
145.3
87
564.2
161.8
48
334.5
95.9
08
392.2
112.4
68
449.8
129.0
28
507.5
145.6
88
565. 2
162.1
49
335. 5
96.2
09
393.1
112.7
69
450.8
129.2
29
508. 5
145.8
89
566. 1
162.4
50
336.4
96.4
10
394.1
113.0
70
451.8
452:7
129.5
30
509.4
146.1
146. 4
90
567.1
162.7
351
337. 4
96.7
411
395.1
113.3
471
129.8
531
510.4
591
568.1
162.9
52
338. 3
97.0
12
396.0
113.5
72
453.7
130.1
32
511.4
146.7
92
569.0
163.2
53
339.3
97.3
13
397.0
113.8
73
454.7
130.3
33
512.3
146. 9
93
570.0
163.5
54
340.3
97.5
14
397.9
114.1
74
455.6
130.6
34
513.3
147.2
94
571.0
163.8
55
341.2
97.8
15
398.9
114.4
75
456.6
1.30. 9
35
514. 3
147.5
95
571.9
164.0
56
342.2
98.1
16
399.9
114.6
76
457.5
131.2
36
515.2
147.8
96
572.9
164.3
57
343.1
98.4
17
400.8
114.9
77
458.5
1,31.4
37
516.2
148.0
97
573.9
164.6
58
344.1
98.6
18
401.8
115.2
78
459.5
131.7
38
517.2
148.2
98
574.8
164.9
59
34.5.1
98.9
19
402.7
115.5
79
460.4
132.0
39
518. 1
148.5
99
575.8
165.1
60
346.0
99.2
20
403.7
115.8
80
461.4
132.3
40
519.1
148.8
600
576.8
165.4
Dist.
Dep. j Lat. ]
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
•4° (106°, 2.54°, 28(1°).
TABLE 2.
[Page 663
Difference of Latitude and Departure for 17° (163°, 197
°, 343°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.3
17.8
121
115.7
35.4
181
173.1
52.9
241
230.5
70.5
2
1.9
0.6
62
59.3
18.1
22
116.7
35.7
82
174.0
53.2
42
231.4
70.8
3
2.9
0.9
63
60. 2
18.4
23
117.6
36.0
83
175.0
53.5
43
232.4
71.0
4
3.8
1.2
64
61.2
18.7
24
118.6
36.3
84
176.0
53.8
44
233.3
71.3
5
4.8
1.5
65
62.2
19.0
25
119.5
36.5
85
176.9
.54.1
45
234.3
71.6
6
5.7
1.8
66
63.1
19.3
26
120.5
36.8
86
177.9
54.4
46
235.3
71.9
7
6.7
2.0
67
64.1
19.6
27
121.5
37.1
87
178.8
54.7
47
236.2
72.2
8
7.7
2.3
68
65.0
19.9
28
122.4
37.4
88
179.8
5.5.0
48
237.2
72.5
9
8.6
2.6
69
66.0
20.2
29
123.4
37.7
89
180.7
55.3
49
238.1
72.8
10
11
9.6
2.9
70
66.9
20.5
20.8
30
124.3
38.0
90
181.7
55.6
50
239.1
73.1
10.5
3.2
71
67.9
131
125.3
38.3
191
182.7
55.8
251
240.0
73.4
12
11.5
3.5
72
68.9
21.1
32
126.2
38.6
92
183. 6
56.1
52
241.0
73.7
13
12.4
3.8
73
69.8
21.3
33
127.2
38.9
93
184.6
56.4
53
241.9
74.0
14
13.4
4.1
74
70.8
21.6
34
128.1
39.2
94
185.5
56.7
54
242.9
74.3
15
14.3
4.4
75
71.7
21.9
35
129.1
39.5
95
186.5
57.0
55
243. 9
74.6
16
15.3
4.7
76
72.7
22.2
36
130.1
39.8
96
187.4
57.3
56
244.8
74.8
17
16.3
5.0
77
73.6
22.5
37
131.0
40.1
97
188.4
57.6
57
245.8
75.1
18
17.2
5.3
78
74.6
22.8
38
132.0
40.3
98
189.3
57.9
58
246.7
75.4
19
18.2
5.6
79
75.5
23.1
39
132.9
40.6
99
190.3
58.2
59
247.7
75.7
20
19.1
5.8
80
76.5
23.4
40
133.9
40.9
200
191. 3
.58.5
58.8
60
261
248.6
76.0
21
20.1
6.1
81
77.5
23.7
141
134.8
41.2
201
192.2
249.6
76.3
22
21.0
6.4
82
78.4
24.0
42
135. 8
41.5
02
193.2
.59.1
62
250. 6
76.6
23
22.0
6.7
83
79.4
24.3
43
136.8
41.8
03
194.1
59.4
63
251.5
76.9
24
23.0
7.0
84
80.3
24.6
44
137.7
42.1
04
195.1
59.6
64
252.5
77.2
25
23.9
7.3
85
81.3
24.9
45
138.7
42.4
05
196.0
59.9
65
253.4
77.5
26
24.9
7.6
86
82.2
25.1
46
139.6
42.7
06
197.0
60.2
66
254. 4
77.8
27
25.8
7.9
87
83.2
25.4
47
140.6
43.0
07
198.0
60.5
67
255.3
78.1
28
26.8
8.2
88
84.2
25.7
48
141.5
43.3
08
198.9
60.8
68
256.3
78.4
29
27.7
8.5
89
85.1
26.0
49
142.5
43.6
09
199.9
61.1
69
257.2
78.6
30
28.7
8.8
90
86.1
26.3
50
143.4
144.4
43.9
10
200.8
61.4
70
258.2
78.9
31
29.6
9.1
91
87.0
26.6
151
44.1
211
201.8
61.7
271
259.2
79.2
32
30.6
9.4
92
88.0
26.9
52
145.4
44.4
12
202.7
62.0
72
260.1
79.5
33
31.6
9.6
93
88.9
27.2
53
146.3
44.7
13
203.7
62.3
73
261.1
79.8
34
32.5
9.9
94
89.9
27.5
54
147. 3
45.0
14
204.6
62.6
74
262.0
80.1
35
33.5
10.2
95
90.8
27.8
55
148.2
45.3
15
205.6
62.9
75
263.0
80.4
36
34.4
10.5
96
91.8
28.1
56
149.2
45.6
16
206.6
63.2
76
263.9
80.7
37
,35.4
10.8
97
92.8
28.4
57
150.1
45.9
17
207.5
63.4
77
264.9
81.0
38
36.3
11.1
98
93.7
28.7
58
151.1
46.2
18
208.5
63.7
78
265.9
81.3
39
37.3
11.4
99
94.7
28.9
59
152.1
46.5
19
209.4
64.0
79
266.8
81.6
40
38.3
11.7
100
101
95.6
29.2
60
153.0
"154.
46.8
20
210.4
64.3
80
267.8
81.9
41
39.2
12.0
96.6
29.5
161
47.1
221
211.3
64.6
281
268.7
82.2
42
40.2
12.3
02
97.5
29.8
62
154.9
47.4
22
212.3
64.9
82
269.7
82.4
43
41.1
12.6
03
98.5
.30.1
63
155. 9
47.7
23
213.3
65.2
83
270.6
82.7
44
42.1
12.9
04
99.5
30.4
64
156.8
47.9
24
214.2
65.5
84
271.6
83.0
45
43.0
13.2
05
100.4
30.7
65
157.8
48.2
25
215. 2
65.8
85
272.5
83.3
46
44.0
13.4
06
101.4
31.0
66
158.7
48.5
26
216.1
66.1
86
273. 5
83.6
47
44.9
13.7
07
102.3
31.3
67
159.7
48.8
27
217.1
66.4
87
274.5
83.9
48
45.9
14.0
08
103. 3
31.6
68
160.7
49.1
28
218.0
66.7
88
275.4
84.2
49
46.9
14.3
09
104.2
31.9
69
161.6
49.4
29
219.0
67.0
89
276.4
84.5
50
51
47.8
14.6
10
105.2
.32.2
70
162.6
49.7
30
220.0
67.2
67.5
90
291
277.3
84.8
48.8
14.9
111
106.1
32.5
171
163.5
50.0
231
220.9
278.3
85.1
52
49.7
15.2
12
107.1
32.7
72
164.5
50.3
32
221.9
67.8
92
279.2
85.4
53
50.7
15.5
13
108.1
33.0
73
165.4
50.6
33
222.8
68.1
93
280.2
85.7
54
51.6
15.8
14
109.0
.33.3
74
166.4
50.9
.34
223.8
68.4
94
281.2
86.0
55
52.6
16.1
15
110.0
33.6
75
167.4
51.2
35
224.7
68.7
95
282.1
86.2
56
53.6
16.4
16
110.9
33.9
76
168.3
51. 5
36
225.7
69.0
96
283.1
86.5
57
54.5
16.7
17
111.9
34.2
77
169.3
51.7
37
226.6
69.3
97
284.0
86.8
58
55.5
17.0
18
112.8
34.5
78
170.2
52.0
38
227.6
69.6
98
285.
87.1
59
56.4
17.2
19
113.8
34.8
79
171.2
52.3
39
228.6
69.9
99
285.9
87.4
60
57.4
17.5
20
114.8
35.1
80
172.1
52.6
40
229.5
70.2
300
286.9
87.7
Dist.
Dep.
Lat.
Dist.
Dep.
I,at.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat. 1
73° (1
07°, 253°, 287°
)•
Page 564]
TABLE -2.
Difference of Latitude and Departure for 17° (163°, 197°, 34J
°)-
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
301
287.8
88.0
361
345. 2
105. 5
421
402.6
123.1
481 - 460.0
140.6
541
517.3
158.2
02
288.8
88.3
62
346.1
105.8
22
403.5
123.4
82
460. 9
140.9
42
.518.3
158.5
03
289.7
88.6
63
347.1
106.1
23
404.5
123.7
83
461.9
141.2
43
519.2
158.8
04
290.7
88.9
64
348.1
106.4
24
405.4
124.0
84
462.8
141.5
44
520.2
159.1
05
291.6
89.2
65
349.0
106.7
25
406.4
124.3
85
463.8
141.8
45
521.2
159.3
06
292.6
89.5
66
3.50.
107.0
26
407. 3
124.6
86
464.7
142. 1
46
522.1
159.6
07
293.5
89.8
67
350. 9
107.3
27
408. 3
124.8
87
465. 7
142. 3
47
523. 1
1.59. 9
08
294.5
90.1
68
351. 9
107.6
28
409.3
125. 1
88
466.7
142. 6
48
524.0
160.2
09
295. 5
90.3
69
3.52. 8
107.9
29
410.2
125.4
89
467.6
142.9
49
525.0
160.5
10
296. 4
90.6
70
353.8
108.2
30
411.2
125.7
90
491
468.6
469. 5
143. 2
50
526.0
160.8
311
297.4
90.9
371
354.8
108.5
431
412.1
126.0
143. 5
551
526.9
161.1
12
298.3
91.2
72
355.7
108.8
32
413.1
126.3
92
470. 5
143. 8
52
527.9
161.4
13
299.3
91.5
73
356.7
109.1
33
414.0
126.6
93
471.4
144.1
53
528.8
161.7
14
300.2
91.8
74
357. 6
109.4
34
415.0
126. 9
94
472. 4
144.4
54
529.8
162.0
15
301.2
92.1
75
358.6
109.6
35
416.0
127.2
95
473.4
144.7
55
530.8
162.3
16
302.2
92.4
76
359.5
109.9
36
416.9
127.5
96
474.3
145.
56
531.7
162.6
17
303.1
92.7
77
360.5
110.2
37
417.9
127.8
97
475.3
145. 3
57
532.7
162.9
18
304.1
93.0
78
361.4
110.5
38
418.8
128.1
98
476. 2
145. 6
58
533.6
163. 2
19
305.0
93.3
79
362.4
110.8
39
419.8
128.4
99
477.2
145. 9
59 i 534.6
163.5
20
306.0
306.9
93.6
80
,363. 4
364.3
111.1
40
420.7
128. 6
500
478.1
146. 2
60
535. 5
536.5
163.8
321
93.9
381
111.4
441
421.7
128.9
501
479.1
146.5
561
164.1
22
307.9
94.1
82
365. 3
111.7
42
422.7
129.2
02
480.1
146.8
62 ' 537.5
164.4
23
308.8
94.4
83
366. 2
112.0
43
423.6
129. 5
03
481.0
147.1
63
538.4
164.6
24
309.8
94.7
84
367.2
112.3
44
424.6
129.8
04
482.
147.4
64
539.4
164.8
25
310. 8
95.0
85
368.1
112.6
45
425. 5
130.1
05
482.9
147.7
65
540.3
165. 1
26
311.7
95.3
86
369.1
112.9
46
426.5
130.4
06
483.9
148.
66
541.3
165. 4
27
312.7
95.6
87
370.1
113.2
47
427.4
130.7
07
484.8
148.3
67
542.2
165.7
28
313.6
95.9
88
371.0
113.4
48
428.4
131.0
08
485.8
148. 6
68
543.2
166.0
29
314.6
96.2
89
372.0
113.7
49
429.3
131.3
09
486.7
148. 9
69
544.1
166.4
30
315.5
96.5
90
372.9
114.0
50
430.3
131.6
10
511
487.7
488.7
149.1
70
545. 1
166.7
331
316.5
96.8
391
373.9
114.3
451
431.3
131.9
149.4
571
546.1
167.0
32
317.5
97.1
92
374.8
114.6
52
432.2
132.2
12
489.6
149.7
72
547.0
167.2
33
318.4
97.4
93
375. 8
114.9
53
433.2
132.4
13
490.6
1.50.
73
548.0
167.5
34
319. 4
97.7
94
376.7
115.2
54
434.1
132.7
14
491.5
150. 2
74
548. 9
167. 8
35
320.3
97.9
95
377. 7
115.5
55
435. 1
133.0
15
492.5
1.50. 5
75
549.9
168.1
36
321.3
98.2
96
378. 7
115.8
.56
436.0
133. 3
16
493.4
150.8
76
550.8
168.4
37
322.2
98.5
97
379.6
116.1
57
437.0
133.6
17
494.4
151. 1
77
551. 8
168.7
38
323.2
98.8
98
380.6
116.4
58
438.0
133.9
18
495. 3
151.4
78
552.7
169.
39
324.2
99.1
99
381. 5
116.7
■59
438.9
134.2
19
496.3
151.7
79
553.7
169.3
40
325.1
99.4
99. 7
400
382. 5
383.4
117.0
60
439.9
440.8
134.5
20
497.2
152.0
80
554.6
169.6
341
326.1
401
117.2
461
134.8
521
498.2
152.3
581
555.6
169.9
42
327.0
100.0
02
384.4
117. 5
62
441.8
135.1
22
499.2
152.6
82
556.5
170.2
43
328.
100.3
03
385.4
117.8
63
442. 7
135.4
23
500.1
152.9
83
557.5
170.5
44
328. 9
100.6
04
386. 3
118.1
64
443.7
135.7
24
501.1
153. 2
84
558.4
170.8
45
329.9
100.9
05
387.3
118.4
65
444.6
136.0
25
.502.
1.53. 5
a5
559. 4
171.1
46
330.8
101.2
06
388. 2
118.7
66 445. 6
136.2
26
503.
153. 8
86
560.4
171. 3
47
331.8
101.5
07
389.2
119.0
67 446. 6
136.5
27
503.9
154. 1
87
561.3
171.6
48
332.8
101.8
08
390.1
119.3
68 447. 5
136.8
28
504. 9
154.4
88
562.3
171.9
49
333.7
102.0
09
391.1
119.6
69 448. 5
137.1
29
505. 9
154. 7
89
563.2
172.2
50
334.7
102.3
10
392.0
393.0
119.9
70
449.4
137.4
30
.506. 8
1.55.
90
591
564.2
565. 1
172.5
a51
335.6
102.6
411
120.2
471
450.4
137.7
531
507.8
1,55. 3
172.8
52
336.6
102.9
12
394.
120.5
72
451. 3
138.0
32
508.7
1.55. 6
92
566. 1
173.1
53
337.5
103.2
13
394.9
120.8
73
452. 3
138.3
33
509. 7
1.55. 9
93
567.1
173.4
54
338.5
103.5
14
395. 9
121.0
74 1 453. 3
138.6
34
510.6
1.56 2
94
568.0
173.7
55
339.5
103.8
15
396. 8
121.3
75
454. 2
138.9
35
511.6
156.5
95
569.
174.0
56
340.4
104.1
16
397.8
121.6
76
455.2
139.2
36
512.6
156. 8
96
569. 9
174.3
57
341.4
104.4
17
398. 7
121.9
77
456. 1
139.5
37
513. 5
1.57. 1
97
570.9
174.6
58
342.3
104.7
18
399.7
122.2
78
457.1
139.8
38
514.5
157. 3
98
571.8
174.9
59
.343. 3
105.
19
400.7
122.5
79
458.0
140.0
39
51.5. 4
1.57.6
99
572.8
175. 2
60
344.2
105.3
20
401.6
122.8
80
459.
140.3
40
516.4
157. 9
600
573.8
175.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
""
•3° (107°, 253°, 287°
.
TABLE 2.
[Page 565
Difference of Latitude and Departure for 18° (162°, 198°, 342°
)-
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
1.0
0.3
61
58.0
18.9
121
115.1
37.4
181
172.1
56.9
241
229.2
74.6
2
1.9
0.6
62
59.0
19.2
22
116.0
37.7
82
17.3.1
56.2
42
230.2
74.8
3
2.9
0.9
63
,59.9
19. 5
23
117.0
38.
83
174.0
56.6
43
231.1
75.1
4
3.8
1.2
64
60.9
19.8
24
117.9
.38. 3
84
175.
.56. 9
44
232.1
75.4
5
4.8
1.5
65
61.8
20.1
25
118.9
38.6
85
175. 9
57.2
45
233.0
75.7
6
5.7
1.9
66
62.8
20.4
26
119.8
38.9
86
176.9
57. 5
46
234.
76.0
7
6.7
2.2
67
63.7
20.7
27
120.8
.39.2
87
177.8
57.8
47
234.9
76.3
8
7.6
2.5
68
64.7
21.0
28 i 121.7
39.6
88
178.8
58.1
48
235. 9
76.6
9
8.6
2.8
69
65. 6
21.3
29 1 122. 7
39.9
89
179.7
58.4
49
236.8
76.9
10
9.5
10.5
3.1
70
66.6
21.6
21.9
30 ! 123.6
40.2
90
180. 7 ! 58. 7
50
237.8
238.7
77.3
77.6
11
3.4
71
67.5
131 i 124.6
40.5
191
181.7 ; 59.0
251
12
11.4
3.7
72
68.5
22.2
32
125.5
40.8
92
182.6
59.3
62
239.7
77.9
13
12.4
4.0
73
69. 4
22.6
33
126.5
41.1
93
183.6
59.6
53
240.6
78. 2
14
13.3
4.3
74
70.4
22.9
34
127.4
41.4
94
184. 5
59.9
54
241.6
78.5
15
14.3
4.6
75
71.3
23.2
35
128.4
41.7
95
185. 5
60.3
55
242.5
78.8
16
15.2
4.9
76
72.3
23.5
36
129. 3
42.0
96
186.4
60.6
56
243. 5
79.1
17
16.2
5.3
77
73.2
23.8
37
130. 3
42.3
97
187.4
60.9
57
244.4
79.4
18
17.1
5.6
78
74.2
24.1
38
131.2
42.6
98
188. 3
61.2
58
245.4
79.7
19
18.1
5.9
79
75.1
24.4
39
132. 2
43.0
99
189.3
61.5
59
246.3
80.0
20
19.0
6.2
80
76.1
24.7
40
'133. 1
4.3.3
200
190.2
61.8
62.1
60
261
247.3
248.2
80.3
80.7
21
20.0
6.5
81
77.0
25.0
141
134.1
43.6
201
191.2
22
20.9
6.8
82
78.0
25. 3
42
135. 1
43.9
02
192.1
62.4
62
249.2
81.0
23
21.9
7.1
83
78.9
25. 6
43
136.0
44.2
03
193. 1
62.7
63
250. 1
81.3
24
22.8
7.4
84
79.9
26.0
44
137.0
44.5
04
194.0
63.0
64
251. 1
81.6
25
23.8
7. 7
85
80.8
26.3
45
137.9
44.8
05
195.
63. 3
65
252.
81.9
26
24.7
8.0
86
81.8
26.6
46
138. 9
4.5.1
06
195. 9
63. 7
66
253.
82.2
27
2.5.7
8.3
87
82.7
26.9
47
139.8
4.5.4
07
196. 9
64.0
67
253. 9
82.6
28
26.6
8.7
88
83.7
27.2
48
140.8
45.7
08
197.8
64.3
68
254. 9
82.8
29
27.6
9.0
89
84.6
27.5
49
141.7
46.0
09
198.8
64.6
69
255. 8
83.1
30
28.5
9.3
90
85.6
27.8
50
142.7
46.4
10
199.7
200.7
64.9
70
256.8
83.4
83.7
31
29.5
9.6
91
86.5
28.1
■151
143. 6 ! 46. 7
211
65.2
271
267. 7
32
30.4
9.9
92
87.5
28.4
52
144. 6
47.0
12
201.6
65.5
72
268.7
84.1
33
31.4
10.2
93
88.4
28.7
53
145. 5
47.3
13
202. 6
65.8
73
259. 6
84.4
34
32.3
10.5
94
89.4
29.0
54
146. 5
47. 6
14
203. 5
66.1
74
260.6
84.7
35
33.3
10.8
95
90.4
29.4
55
147.4
47.9
15
204. 5
66.4
75
261.5
85.
36
34.2
11.1
96
91.3
29.7
56
148.4
48.2
16
205. 4
66.7
76
262. 5
85.3
37
35.2
11.4
97
92. 3
30.0
57
149. 3
48.5
17
206.4
67.1
77
263. 4
8.5.6
38
36.1
11.7
98
93.2
30.3
58
1.50. 3
48.8
18
207. 3
67.4
78
264.4
85.9
39
37.1
12.1
99
94.2
30.6
59
161.2
49.1
19
208.3
67.7
79
265. 3
86.2
40
41
38.0
39.0
12.4
100
95.1
30.9
60
152. 2
49.4
20
209.2
210. 2
68.0
80
266. 3
86. 5
'86.8
12.7
101
96.1
31. 2
161
163.r
49.8
221
68.3
281
26772
42
39.9
13.0
02
97.0
31.5
62
1.54. 1
50.1
22
211.1
68.6
82
268.2
87.1
43
40.9
13.3
03
98.0
31.8
63
1.55.
50.4
23
212.1
68.9
83
269.1
87.6
44
41.8
13.6
04
98.9
32.1
64
1.56.0
.50.7
24
213.0
69.2
84
270.1
87.8
45
42.8
13.9
05
99.9
.32.4
65
1.56. 9
51.0
25
214.0
69.5
85
271.1
88.1
46
43.7
14.2
06
100.8
32.8
66
157.9
.51.3
26
214. 9
69.8
86
272.0
88.4
47
44.7
14.5
07
101.8
33.1
67
1.58. 8
51.6
27
215. 9
70.1
87
273.0
88.7
48
45.7
14.8
08
102.7
33.4
68
159. 8
51.9
28
216.8
70. 5
88
273.9
89.0
49
46.6
15.1
09
103. 7
33.7
69
160.7
52.2
29
217.8
70.8
89
274.9
89.3
50
47.6
15.5
10
104.6
10.5:6'
34.0
70
161.7
62.5
30
218.7
71.1
71.4
90
276.8
89.6
51
48.5
15.8
111
34.3
171
162.6
52.8
231
219.7
291
276.8
89.9
52
49.5
16.1
12
106. 5
34.6
72
163.6
53. 2
32
220.6
71.7
92
277.7
90.2
53
50.4
16.4
13
107. 5
34.9
73
164. 5
.53. 5
33
221.6
72.0
93
278.7
90.6
54
51.4
16.7
14
108.4
3.5.2
74
ia5.5
.53.8
34
222. 5
72.3
94
279.6
90.9
55
52. 3
17.0
15
109.4
.36.5
75
166.4
54.1
35
223. 6
72.6
95
280.6
91.2
56
53.3
17.3
16
110.3
35.8
76
167.4
54.4
36
224.4
72.9
96
281.5
91.6
57
54.2
17.6
17
111.3
36.2
77
168. 3
.54.7
37
225.4
73.2
97
282.6
91.8
58
5.5.2
17.9
18
112.2
36.5
78
169. 3
55.0
38
226.4
73. 5
98
283. 4
92.1
59
56.1
18.2
19
113.2
36.8
79
170.2
65.3
39
227. 3
73.9
99
284.4
92.4
60
67.1
J8.5
20
114.1
37.1
80
171.2
56.6
40
228. 3
74.2
300
285.3
92.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
'"
2°'(108°, 252°, 288°).
Page 666]
TABLE 2.
Difference of Latitude and Departure for 18° (
162°, 198°, 342=
)•
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
DLst.
l.dt.
I'ep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
286.3
93.0
361 \ 343.3
111.6
421
400.4
130.1
481
457.5
148.6
541
514.5
167.2
02
287.2
93.3
62
344.3
111.9
22
401.4
130.4
82
458. 5
148.9
42
515.5
167.5
03
288.2
93.7
63
345.2
112.2
23
402.3
130.7
83
459.4
149.3
43
516. 4
167.9
04
289.1
94.0
64
346.2
112.5
24
403. 3
131.0
84
460.4
149.6
44
517.4
168.2
Or,
290.1
94.3
65
347.1
112.8
25
404.2
131.3
85
461.3
149.9
45
518.3
168.5
06
291.0
94.6
66
348.1
113.1
26
405.2
131.7
86
462.3
150.2
46
519.3
168.8
07
292.0
94.9
67
349.0
113.4
27
406.1
132.0
87
463. 2
150. 5
47
520. 2
169.1
08
292.9
95.2
68
350.0
113.7
28
407.1
132.3
88
464.2
150.8
48
521.2
169.4
09
293.9
95.5
69
350. 9
114.0
29
408.0
132.6
89
465. 1
151.1
49
522. 1
169.7
10
294.8
95.8
96.1
70
351.9
114.3
30
409.0
409.9
132.9
133.2
90
491
466.1
467.0
151.4
15 1. 7
50
551
523.1
524.0
170.0
311
295.8
371
352.9
114.7
431
170.3
12
296.7
96.4
72
353.8
115.0
32
410.9
133. 5
92
468.0
152.0
52
525.0
170.6
13
297.7
96.7
73
354.8
115.3
33
411.8
133. 8
93
468.9
152. 3
53
525. 9
170. 9
14
298.6
97.0
74
355.7
115.6
34
412.8
134.1
94
469.8
1.52. 6
54
526.9
171.2
15
299.6
97.4
75
356.7
115.9
•35
413.7
134. 4
95
470.8
153.
55
527.8
171.5
16
300. 5
97.7
76
357.6
116.2
36
414.7
1,34. 7
96
471.7
153.3
56
528.8
171.8
17
.301.5
98.0
77
358. 6
116.5
37
415.6
1.35. 1
97
472.7
153. 6
57
529.7
172.1
18
302.4
98.3
78
359.5
116.8
38
416.6
135.4
98
473.6
1.53. 9
58
530.7
172.4
19
303.4
98.6
79
360.5
117.1
39
417.5
135.7
99
474.6
154.2
.59
531.6
172.7
20
304.3
98.9
80
361.4
117.4
40
418.5
136.0
500
475.5
154.5
60
532.6
173.0
321
305.3
99.2
381
362.4
117.7
441
419.4
136.3
501
476.5
154.8
561
533.5
173.3
22
306.2
99.5
82
363.3
118.1
42
420.4
136.6
02
477.4
1.55. 1
62
534.5
173.6
23
307.2
99.8
83
364.3
118.4
43
421.3
136.9
03
478.4
155. 4
63
535.4
173.9
24
308.2
100.1
84
365.2
118.7
44
422.3
137.2
04
479.3
155.7
64
536.4
174.2
25
309.1
100.4
85
366.2
119.0
45
423.2
137.5
05
480.3
156.1
65
537.3
174.6
26
310.1
100.7
86
367.1
119.3
46
424.2
137.8
06
481.2
156.4
66
538.3
174.9
27
311.0
101.1
87
368.1
119.6
47
425. 1
138.1
07
482.2
156.7
67
539.2
175.2
28
312.0
101.4
88
369.0
119.9
48
426.1
138.4
08
483.2
157.
68
540.2
175.5
29
312.9
101.7
89
370.0
120.2
49
427.0
138.8
09
484.1
157.3
69
.541.1
175.8
30
313. 9
102.
102.3
90
391
370.9
120.5
50
428.0
428.9
139.1
10
485.1
157.6
70
542.1
176.1
331
314.8
371.9
120.8
451
1.39. 4
511
486.0
157.9
571
543.0
176.4
32
315.8
102.6
92
372.8
121.1
52
429.9
139.7
12
487.0
158.2
72
544.0
176.7
33
316.7
102.9
93
373. 8
121.5
53
430.8
140.0
13
487.9
158.5
73
544.9
177.0
34
317.7
103. 2
94
374.7
121.8
54
431.8
140.3
14
488.9
158. 8
74
545.9
177.3
35
318.6
103. 5
95
375.7 i 122.1
55
432.7
140. 6
15
489. 8
159. 1
75
546.8
177.6
36
319. 6
103. 8
96
376. 6 : 122. 4
56
433.7 140.9
16
490.8
159.4
76
547. 8
178.0
37
320.5
104.1
97
377. 6 i 122. 7
57
4S4. 6
141.2
17
491.7
159.7
1 1
548.7
178.3
38
321.5
104.5
98
378. 5 1 123.
58
435. 6
141.5
18
492.7
160.0
78
549.7
178.6
39
322.4
104.8
99
379. 5 ! 123. 3
- 59
436.5
141.8
19
493.6
160.3
79
550.6
178.9
40
323.4
105.1
400
380. 4 1 123. 6
60
437. 5
142.2
20
494.6
160.7
80
551.6
552. 5
179.2
179.5
341
324.3
105.4
401
381.4
123.9
461
438.4
142.5
521
495.5
161.0
581
42
325.3
105.7
02
382.3
124.2
62
439.4
142.8
22
496. 5
161.3
82
553. 5
179.8
43
326.2
106.0
03
383.3
124.5
63
440.3
143. 1
23
497.4
161.6
83
554.4
180.1
44
327.2
106.3
04
384.2
124.9
64
441. 3
143.4
24
498.4
161.9
84
555.4
180.4
45
328.1
106.6
05
385.2
125.2
65
442.2
143. 7
25
499. 3
162.2
85
556.3
180.7
46 - 329. 1
106.9
06
386.1
125.5
66
443.2
144.0
26
500.3
162.5
86
557.3
181.1
47 1 330.0
107.2
07
387.1
125. 8
67
444.2
144.3
27
501.2
162.9
87
558.2
181.4
48 331.0
107.5
08
388.0
126.1
68
445.1
144.6
28
502. 2
163. 2
88
559.2
181.7
49
331.9
107.9
09
389.0
126.4
69
446.1
144.9
29
503.1
163.5
89
560.1
182.0
50
332.9
108.2
10
389.9
390.9
126.7
70
447.0
145. 2
30
504.1
163.8
90
561.1
182.3
351
333.8
108.5
411
127.0
471
448.0
145.6
531
505.0
164.1
591
562.0
182.7
52
334.8
108.8
12
391.8
127.3
72
448.9
145.9
32
506.0
164.4
92
563.0
183.0
53
335. 7
109.1
13
392.8
127.6
73
449.9
146.2
,33
506.9
164.7
93
563.9
183.3
54
336.7
109.4
14
393.7
127.9
74
450.8
146. 5
,34
.507. 9
ia5.o
94
564.9
183.6
55
337. 6
109.7
15
394.7
128.3
75
451.8
146.8
.35
508. 8
165. 3
95
565. 8
183.9
56
338. 6
110.0
16
395.6
128.6
76
452.7
147.1
36
509. 8
165. 6
96
566. 8
184.2
57
339. 5
110.3
17
396.6
128.9
77
453. 7
147.4
37
510.7
165.9
97
567.7
184.5
58
340.5
110.6
18
397.5
129.2
78
454.6
147.7
38
511.7
166.2
98
568.7
184.8
59
341.4
110.9
19
398.5
129.5
79
455.6
148.0
39
512.6
166.5
99
569.6
185.1
60
342.4
111.3
20
399.5
129.8
80
456.5
148.3
40
513.6
166.9
600
570.6
185.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
72° (108, 252°, 28J?°
).
TABLE 2.
[Page
567
Difference of Latitude and Departure for 19° (161°, 199
°, 341°
)■
Diet.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.3
61
57.7
19.9
121
114.4
39.4
181
171.1
58.9
241
227.9
78.5
2
1.9
0.7
62
58.6
20.2
22
115.4
39.7
82
172.1
59.3
42
228.8
78.8
3
2.8
1.0
63
59.6
20.5
23
116.3
40.0
83
173.0
59.6
43
229.8
79.1
4
3.8
1.3
64
60.5
20.8
24
117.2
40.4
84
174.0
59.9
44
230.7
79.4
5
4.7
1.6
65
61.5
21.2
25
118.2
40.7
85
174.9
60.2
45
231.7
79.8
6
5.7
2.0
66
62.4
21.5
26
119.1
41.0
86
175.9
60.6
46
232.6
80.1
7
6.6
2.3
67
63.3
21.8
27
120.1
41.3
87
176.8
60.9
47
233.5
80.4
8
7.6
2.6
68
64.3
22.1
28
121.0
41.7
88
177.8
61.2
48
234.5
80.7
9
8.5
2.9
69
65.2
22.5
29
122.0
42.0
89
178.7
61.5
49
235.4
81.1
10
9.5
3.3
70
66.2
22.8
30
122.9
42.3
90
179.6
61.9
50
236.4
81.4
11
10.4
3.6
71
67.1
23.1
131 ; 123.9
42.6
191
180.6
62.2
251
237.3
81.7
12
11.3
3.9
72
68.1
23.4
32 1 124.8
43.0
92
181.5
62.5
52
238.3
82.0
13
12.3
4.2
73
69.0
23.8
33
125. 8
43.3
93
182.5
62.8
53
239.2
82.4
14
13.2
4.6
74
70.0
24.1
34
126.7
43.6
94
183.4
63.2
54
240.2
82.7
15
14.2
4.9
75
70.9
24.4
35
127.6
44.0
95
184.4
6.3.5
55
241.1
83.0
16
15.1
5.2
76
71.9
24.7
36
128.6
44.3
96
185.3
63.8
56
242.1
83.3
17
16.1
5.5
77
72.8
25.1
37
129.5
44.6
97
186.3
64.1
57
243.0
83.7
18
17.0
"5.9
78
73.8
25.4
38
130.5
44.9
98
187.2
64.5
58
243.9
84.0
19
18.0
6.2
79
74.7
25.7
39
131.4
45.3
99
188.2
64.8
59
244.9
84.3
20
18.9
6.5
80
75.6
26.0
40
132.4
133.3
45.6
200
189.1
65.1
60
245.8
84.6
21
19.9
6.8
81
76.6
26.4
141
45.9
201
190.0
65.4
261
246.8
85.0
22
20.8
7.2
82
77.5
26.7
42
134.3
46.2
02
191.0
6.5.8
62
247.7
85.3
23
21.7
7.5
83
78.5
27.0
43
135.2
46.6
03
191.9
66.1
63
248.7
85.6
24
22.7
7.8
84
79.4
27.3
44
136.2
46.9
04
192.9
66.4
64
249.6
86.0
25
23.6
8.1
85
80.4
27.7
45
137.1
47.2
05
193.8
66.7
65
250.6
86.3
26
24.6
8.5
86
81.3
28.0
46
138.0
47.5
06
194.8
67.1
66
251.5
86.6
27
25.5
8.8
87
82.3
28.3
47
139.0
47.9
07
195.7
67.4
67
252.5
86.9
28
26.5
9.1
88
83.2
28.7
48
139.9
48.2
08
196.7
67.7
68
253. 4
87.3
29
27.4
9.4
89
84.2
29.0
49
140.9
48.5
09
197.6
68.0
69
254.3
87.6
30
28.4
29.3
9.8
90
85.1
29.3
50
141.8
48.8
10
198.6
68.4
70
255.3
87.9
31
10.1
91
86.0
29.6
151
142.8
49.2
211
199.5
68.7
271
256.2
88.2
32
30.3
10.4
92
87.0
30.0
52
143.7
49.5
12
200.4
69.0
72
257.2
88.6
33
31.2
10.7
93
87.9
30.3
53
144.7
49.8
13
201.4
69.3
73
258.1
88.9
34
32.1
11.1
94
88.9
30.6
54
145.6
50.1
14
202.3
69.7
74
259.1
89.2
35
33.1
11.4
95
89.8
30.9
55
146.6
50.5
15
203.3
70.0
75
260.0
89.5
36
34.0
11.7
96
90.8
31.3
56
147.5
50.8
16
204.2
70.3
76
261.0
89.9
37
35.0
12.0
97
91.7
31.6
57
148.4
51.1
17
205.2
70.6
77
261.9
90.2
38
35.9
12.4
98
92.7
31.9
58
149.4
51.4
18
206.1
71.0
78
262.9
90.5
39
36.9
12.7
99
93.6
32.2
59
150.3
51.8
19
207.1
71.3
79
263.8
90.8
40
37.8
13.0
100
94.6
32.6
60
151.3
52.1
20
208.0
209.0
71.6
80
264.7
91.2
41
38.8
13.3
101
95.5
32.9
161
152.2
52.4
221
72.0
281
265.7
91.5
42
.39.7
13.7
02
96.4
33.2
62
153. 2
52.7
22
209.9
72.3
82
266.6
91.8
43
40.7
14.0
03-
97.4
33.5
63
1,54. 1
5.3.1
23
210.9
72.6
83
267.6
92.1
44
41.6
14.3
04
98.3
,33.9
64
155.1
.53.4
24
2U.8
72.9
84
268.5
92.5
45
42.5
14.7
05
99.3
34.2
65
156.0
53.7
25
212.7
73.3
85
269.5
92.8
46
43.5
15.0
06
100.2
34.5
66
157.0
54.0
26
213. 7
73.6
86
270.4
93.1
47
44.4
15.3
07
101.2
34.8
67
157.9
54.4
27
214.6
73.9
87
271.4
93.4
48
45.4
15.6
08
102.1
35.2
68
158.8
.54.7
28
215.6
74.2
88
272.3
93.8
49
46.3
16.0
09
103.1
35.5
69
1.59. 8
55.0
29
216.5
74.6
89
273.3
94.1
50
47.3
16.3
10
104.0
35.8
70
160.7
161.7
55.3
30
217.5
218.4
74.9
75.2
90
291
274.2
94.4
51
48.2
16.6
111
105.
36.1
171
55. 7
231
275. 1
94.7
52
49.2
16.9
12
105.9
36.5
72
162.6
56.0
32
219.4
75.5
92
276.1
95.1
53
.50.1
17.3
13
106.8
36.8
73
163.6
56. 3
.33
220.3
75.9
93
277.0
95.4
54
.51.1
17.6
14
107.8
37.1
74
164.5
.56.6
34
221.3
76.2
94
278.0
95.7
55
52.0
17.9
15
108.7
37.4
75 ; 165.5
57.0
.35
222.2
76.5
95
278.9
96.0
56
52.9
18.2
16
109.7
37.8
76
166.4
57.3
36
223.1
76.8
96
279.9
96.4
57
.53.9
18.6
17
110.6
38.1
77
167.4
.57.6
37
224.1
77.2
97
280.8
96.7
58
54.8
18.9
18
111.6
.38.4
78
168.3
58.0
38
225.0
77. 5
98
281.8
97.0
59
.55.8
19.2
19
112.5
38.7
79
169.2
58.3
39
226.0
77.8
99
282.7
97.3
60
56.7
19.5
20
113.5
39.1
80
170.2
58.6
40
226.9
78.1
300
283.7
97.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
■1° (109°, 2.51
°, 289°
)■
Page 568]
TABLE 2.
Difference of Latitude and Departure for 19* (161°, 199°, 341°
)•
Dist.
301
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
284.6
98.0
361
341.3
117.5
421
398. 1
137.0
481
454.8
156.6
541
511.5
176.1
02
285.5
98.3
62
342.3
117.8
22
399.0
137.4
82
455. 7
1.56. 9
42
512.4
176.4
03
286.5
98.6
63
343.2
118.2
23
400.0
137.7
83
456.7
157.2
43
513.4
176.8
04
287.4
99.0
64
344.2
118.5
24
400.9
138.0
84
457.6
157. 6
44
514.3
177.1
05
288.4
99.3
65
345.1
118.8
25
401.8
138. 4
85
458.6
157.9
45
515. 3
177.4
06
289.3
99.6
66
346.1
119.1
26
402. 8
1.38. 7
86
459. 5
158.2
46
516.2
177.7
07
290.3
99.9
67
347.0
119.5
27
403.7
139.0
87
460.5
158.5
47
517. 2
178.1
08
291.2
100.3
68
348.
119.8
28
404.7
139.3
88
461.4
158.9
48
518.1
178.4
09
292.2
100.6
69
348.9
120.1
29
405. 6
139.7
89
462.4
159.2
49
519.1
178.7
10
311
293.1
100.9
70
349.8
120.4
30
406.6
140.0
90
463.3
159.5
50
520.0
179.0
179.4
294. 1
101.2
371
350.8
120.8
431
407.5
140.3
491
464. 3t^
keg. 8
551
521.0
12
295.0
101.6
72
351.7
121.1
32
408.5
140.6
92
465. 2
160.2
52
521.9
179.7
13
295.9
101.9
73
352. 7
121.4
33
409.4
141.0
93
466. 1
160. 5
53
522. 8
180.0
14
296.9
102.2
74
353.6
121.7
34
410.4
141.3
94
467.1
160.8
54
523.8
180. 3
15
297.8
102.5
75
354. 6
122. 1
35
411.3
141.6
95
468.0
161. 1
55
524.7
180.7
• 16
298.8
102.9
76
355. 5
122.4
36
412.2
141.9
96
469.0
161.5
56
525. 7
181.0
17
299.7
103.2
77
356.5
122.7
37
413.2
142.3
97
469.9
161.8
57
526.6
181.3
18
300.7
103.5
78
357. 4
123.0
38
414.1
142.6
98
470.9
162.1
58
•527.6
181.6
19
301.6
103.8
79
358.4
123.4
39
415.1
142.9
99
471.8
162.4
59
528. 5
182.0
20
302.6
104.2
80
359. 3
123. 7
40
416.0
143.2
500
472.8
162.8
60
529.5
530.4
182. 3
182.6
321
303. 5
104.5
381
360. 2
124.0
441
417.0
143.6
501
473.7
163.1
561
22
304.5
104.8
82
361.2
124.4
42
417.9
143.9
02
474.7
163.4
62
531.4
182.9
23
305. 4
105.1
83
362.1
124.7
43
418.9
144.2
03
475.6
163.7
63
532. 3
183.3
24
306.3
105.5
84
363. 1
125.0
44
419.8
144.5
04
476.5
164.1
64
533.2
183.6
25
307.3
105.8
85
364.0
125. 3
45
420.8
144.9
05
477.5
164.4
65
534.2
183.9
26
308.2
106.1
86
365.0
125.7
46
421.7
145.2
06
478.4
164.7
66
535. 1
184.2
27
309. 2
106.4
87
365. 9
126.
47
422.6
145.5
07
479.4
165.
67
536.1
184.6
28
310.1
106.8
88
366. 9
126.3
48
423.6
145.8
08
480.3
165.4
68
537.0
184.9
29
311.1
107.1
89
367.8
126.6
49
424. 5
146.2
09
481.2
165.7
69
538.
185.2
30
312.0
107.4
90
368.8
127.0
50
425.5
146.5
10
482. 2
483.1
166.1
70
538.9
185.6
185.9
331
313.0
107.7
391
369.7
127.3
451
426.4
146.8
511
166.4
571
539.9
32
313. 9
108.1
92
370.6
127.6
52
427.4
147.1
12
484.1
166.7
72
540. 8
186.2
33
314.9
108.4
93
371.6
127.9
53
428.3
147.5
13
485.0
167.0
73
541.7
186.5
34
31.5. 8
108.7
94
372. 5
128.3
54
429. 3
147.8
14
486.0
167.4
74
542.7
186.9
35
316.7
109.1
95
373.5
128. 6
55
430. 2
148.1
15
486.9
167.7
75
543.6
187.2
36
317.7
109.4
96
374.4
128.9
56
431.2
148.4
16
487.9
168.0
76
.544. 6
187.5
37
318.6
109.7
97
375.4
129.2
57
432.1
148.8
17
488.8
168.3
77
545.5
187.8
38
319.6
110.0
98
376.3
129.6
58
433.0
149.1
18
489.7
168.7
78
546.5
188.2
39
320.5
110.4
99
377. 3
129.9
59
434.
149.4
19
490.7
169.0
79
547.4
188.5
40
321.5
110.7
400
378.2
130.2
60
434.9
149.7
20
491.6
169.3
80
548.4
188.8
341
322.4
111.0
401
379.2
130.5
461
4.35. 9
150.1
521
492.6
169.6
581
549.3
189.1
42
323.4
111.3
02
380.1
130.9
62
436.8
150.4
22
493. 5
170.0
82
550.3
189.5
43
324.3
111.7
03
381.0
131.2
63
437.8
150.7
23
494.5
170.3
83
551.2
189.8
44
325.3
112.0
04
382.0
131.5
64
438.7
151.0
24
495.4
170.6
84
552.2
190.1
45
326.2
112.3
05
382.9
131.8
65
439.7
151.4
25
496.4
170.9
85
553. 1
190.4
46
327.1
112. 6
06
383.9
132.2
66
440.6
151.7
26
497.3
171.2
86
554.1
190.8
47
328.1
113.0
07
384.8
132.5
67
441.6
152.0
27
498.3
171.6
87
555.
191.1
48
329.0
113.3
08
385.8
132.8
68
442. 5
152.4
28
499.2 ;171.9
88
555. 9
191.4
49
330.0
113.6
09
386.7
133. 1
69
443.4
152.7
29
500.1
172.2
89
556. 9
191.7
50
330.9
113.9
10
387.7
133.5
70
444.4
153.
30
501.1
172. 5
90
557.8
558.8
192.1
192.4
351
331.9
114.3
411
388.6
133.8
471
445.3
153.3
531
502.
172.9
591
52
332.8
114.6
12
389.6
134.1
72
446.3
153.7
,32
503.0
173.2
92
559.7
192.7
53
333. 8
114.9
13
390.5
134.4
73
447.2
154.0
33
503.9
173.5
93
560. 7
193.0
54
334.7
115. 2
14
391.4
134.8
74
448.2
154.3
34
504.9
173.8
94
561.6
193.4
55
335.7
115.6
15
392.4
135.1
75
449.1
154.6
35
505.8
174.2
95
562.6
193.7
56
336.6
115.9
16
393.3
135.4
76
450.1
155.
36
506. 8
174.5
96
563. 5
194.0
57
337. 5
116.2
17
394.3
135.7
77
451.0
155.3
37
507. 7
174.8
97
564.5
194.3
58
338.5
116.5
18
395.2
136.1
78
452.0
155.6
38
508.7
175.1
98
565. 4
194.7
59
339.4
116.9
19
396.2
136.4
79
452.9
155.9
39
.509.6
175. 5
99
566.4
195.0
60
340.4
117.2
20
397.1
136.7
80
453.8
156.3
40
510.6
175.8
600
567. 3
195. 3
Dist.
Dep.
Lat.
Dist. ^
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
ri° (1
09°, 251
°, 289°
)■
TABLE 2.
[Page 569 |
Difference of Latitude and Departure for 20° (160°, 20C
°, 340°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.3
61
57.3
20.9
121
113.7
41.4
181
170.1
61.9
241
226. 5
82.4
2
1.9
0.7
62
58.3
21.2
22
114.6
41.7
82
171.0
62.2
42
227.4
82.8
3
2.8
1.0
63
59.2
21.5
23
115.6
42.1
83
172.0
62.6
43
228.3
83.1
4
3.8
1.4
64
60.1
21.9
24
116.5
42.4
84
172.9
62.9
44
229. 3
83. 5
5
4.7
1.7
65
61.1
22.2
25
117.5
42.8
85
173.8
63.3
45
230.2
83.8
6
5.6
2.1
66
62.0
22.6
26
118.4
43.1
86
174.8
63.6
46
231.2
84.1
7
6.6
2.4
67
63.0
22.9
27
119.3
43.4
87
175.7
64.0
47
232.1
84.5
8
7.5
2.7
68
63.9
23.3
28
120. 3
43.8
88
176.7
64.3
48
233.0
84.8
9
8.5
3.1
69
64.8
23.6
29
, 121.2
44.1
89
177.6
64.6
49
234.0
85. 2
10
9.4
10.3
3.4
70
65.8
23.9
30
122.2
123.1
44.5
90
178.5
65.0
50
234.9
8.5.5
85.8
11
3.8
71
9^.7
24.3
131
44.8
191
179.5
65.3
251
235.9
12
11.3
4.1
72
67.7
24.6
32
124.0
45.1
92
180.4
65.7
52
236.8
86.2
13
12.2
4.4
73
68.6
2.5.0
33
125.0
45.5
93
181.4
66.0
53
237.7
86.5
14
13.2
4.8
74
69.5
25.3
34
125.9
45.8
94
182.3
66.4
54
238.7
86.9
15
14.1
5.1
75
70.5
25.7
35
126.9
46.2
95
183.2
66.7
55
239.6
87.2
16
15.0
.5.5
76
71.4
26.0
36
127.8
46.5
96
184.2
67.0
56
240.6
87.6
17
16.0
5.8
77
72.4
26.3
37
128.7
46.9
97
185.1
67.4
57
241.5
87.9
18
16.9
6.2
78
7.3.3
26.7
38
129.7
47.2
98
186.1
67.7
58
242.4
88.2
19
17.9
6.5
79
74.2
27.0
39
130.6
47.5
99
187.0
68.1
59
243.4
88.6
20
18.8
19.7
6.8
80
75.2
27.4
40
141
131. 6
132.5
47.9
200
187.9
68.4
60
244.3
88.9
89.3
21
7.2
81
76.1
27.7
48.2
201
188.9
68.7
261
245.3
22
20.7
7.5
82
77.1
28.0
42
133. 4
48.6
02
189.8
69.1
62
246.2
89.6
23
21.6
7.9
83
78.0
28.4
43
134.4
48.9
03
190.8
69.4
63
247.1
90.0
24
22.6
8.2
84
78.9
28.7
44
135.3
49.3
04
191.7
69.8
64
248.1
90. 3
25
23.5
8.6
85
79.9
29.1
45
136. 3
49.6
05
192.6
70.1
65
249.0
90. 6
26
24.4
8.9
86
80.8
29.4
46
137. 2
49.9
06
193.6
70.5
66
250.0
91.0
27
25.4
9.2
87
81.8
29.8
47
1.38. 1
.50. 3
07
194.5
70.8
67
250.9
91.3
28
26.3
9.6
88
82.7
30.1
48
139.1
50. 6
08
195. 5
71.1
68
251.8
91.7
29
27.3
9.9
89
83.6
30.4
49
140.0
51.0
09
196.4
71.5
69
252.8
92.0
30
28.2
10.3
90
84.6
30.8
50
140.9
51.3
10
197.3
71.8
70
253.7
92.3
92.7
31
29.1
10.6
91
85.5
31.1
151
141.9 1 .51.6
211
198.3
72.2
271
254.7
32
30.1
10.9
92
86.5
31.5
52
142.8 1 .52.0
12
199.2
72.5
72
255.6
93.0
33
31.0
11.3
93
87.4
31.8
53
143.8 ' .52.3
13
200.2
72.9
73
256.5
93.4
34
31.9
11.6
94
«8.3
32.1
54
144. 7 ; 52. 7
14
201.1
73.2
74
257.5
93.7
35
32.9
12.0
95
89.3
.32.5
55
145. 7 ; 53.
15
202.0
73.5
75
258.4
94.1
36
33.8
12.3
96
90.2
32.8
56
146.6 53.4
16
203.
73.9
76
259.4
94.4
37
34.8
12.7
97
91.2
33.2
57
147. 5 j 53. 7
17
203.9
74.2
77
260.3
94.7
38
35.7
13.0
98
92.1
33.5
58
148. 5 1 54.
18
204.9
74.6
78
261.2
95.1
39
36.6
1.3.3
99
9,3.0
33.9
59
149.4
54.4
19
205.8
74.9
79
262.2
95.4
40
37.6
13.7
100
101
94.0
34.2
60
161
150. 4
151. 3
54.7
20
206.7
75.2
80
263.1
95.8
41
38.5
14.0
94.9
34.5
55.1
221
207.7
75.6
281
264.1
96.1
42
39.5
14.4
02
95.8
34.9
62
152.2
55.4
22
208.6
75.9
82
265.
96.4
43
40.4
14.7
03
96.8
35.2
63
153. 2
55.7
23
209.6
76.3
83
265.9
96.8
44
41.3
15.0
04
97.7
35. 6
64
154.1
56.1
24
210.5
76.6
84
266.9
97.1
45
42.3
15.4
05
98.7
35.9
65
155.
56.4
25
211.4
77.0
85
267.8
97.5
46
43.2
15.7
06
99.6
36.3
66
156.0
.56.8
26
212.4
77.3
86
268.8
97.8
47
44.2
16.1
07
100.5
36.6
67
156.9
57.1
27
213.3
77.6
87
269.7
98.2
48
45.1
16.4
08
101.5
36.9
68
157.9
57.5
28
214.2
78.0
88
270.6
98.5
49
46.0
16.8
09
102.4
37.3
69
158.8
57.8
29
215.2
78.3
89
271.6
98.8
50
47.0
47.9
17.1
10
103.4
37.6
70
159.7
58.1
30
231
216.1
78.7
90
272.5
99.2
51
17.4
111
104.3
38.0
171
160.7
58.5
217.1
79.0
291
273.5
99.5
52
48.9
17.8
12
105.2
38.3
72
161.6
58.8
32
218.0
79.3
92
274.4
99.9
53
49.8
18.1
13
106.2
38.6
73
162.6
59.2
33
218.9
79.7
93
275.3
100.2
54
50.7
18.5
14
107.1
39.0
74
163.5
59.5
34
219.9
80.0
94
276.3
100. 6
55
51.7
18.8
15
108.1
39.3
75
164.4
59.9
35
220.8
80.4
95
277.2
100.9
56
52.6
19.2
16
109.0
39.7
76
16.5.4
60.2
36
221.8
80.7
96
278.1
101.2
57
53.6
19.5
17
109.9
40.0
77
166.3
60.5
37
222.7
81.1
97
279.1
101.6
58
54.5
19.8
18
110.9
40.4
78
167.3
60.9
38
223.6
81.4
98
280.0
101.9
59
55.4
20.2
19
111.8
40.7
79
168.2
61.2
39
224.6
81.7
99
281.0
102.3
60
56.4
20.5
20
112.8
41.0
80
169.1
61.6
40
225.5
82.1
300
281.9
102.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
t
0° (110°, 250°, 290°
)•
Page 670]
TABLE 2.
Difference of Latitude anc
Depart
ure for 20° (
160°, 200°, 340
')■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
282.9
103.0
361
339.2
123.5
421
395.6
144.0
481
452.0
164.5
541
508.4
185.0
02
283.8
103.3
62
340.2
123.8
22
396.6
144.3
82
453.
164.8
42
509.3
185. 4
03
284.7
103.6
63
341.1
124.2
23
397. 5
144.7
83
453.9
165.2
43
510.3
185.7
04
285.7
104.0
64
342.1
124.5
24
398.4
145.0
84
454.8
165.5
44
511.2
186.0
05
286.6
104.3
65
343.0
124.8
25
399. 4
145.4
85
455.8
165.9
45
512.1
186.4
06
287.6
104.7
66
343.9
125.2
26
400.3
145.7
86
456.7
166.3
46
513.1
186.8
07
288.5
105.0
67
344.9
125.5
27
401.3
146.1
87
457.7
166.6
47
514.0
187.1
08
289.4
105.4
68
345.8
125. 9
28
402.2
146.4
88
458.6
166.9
48
515.
187.4
09
290.4
105. 7
69
346.8
126.2
29
403. 1 •
146.7
89
459.5
167.3
49
515.9
187.8
10
291.3
106.0
70
347.7
126.6
30
404.1
147.1
90
460.5
167.7
50
516. 8
188.2
311
292.3
106.4
371
348.6
126.9
431
405.0
147.4
491
461.4
168.0
551
517.8
188. 5
12
293.2
106.7
72
349.6
127.2
32
406.0
147.8
92
462.4
168.3
52
518.7
188.8
13
294.1
107.1
73
350.5
127.6
33
406.9
148.1
93
463.3
168.6
53
519.7
189.1
14
295.1
107.4
74
351.5
127.9
34
407.8
148.4
94
464.2
168.9
54
520.6
189.4
15
296.0
107.7
75
352.4
128.3
35
408.8
148.8
95
465. 2
169.3
55
521.5
189.8
16
297.0
108.1
76
353.3
128.6
36
409.7
149.1
96
466.1
169.6
56
522. 5
190.2
17
297.9
108.4
77
354.3
129.0
37
410.7
149.5
97
467.0
170.0
57
523. 4
190. 5
18
298.8
108.8
78
355. 2
129.3
38
411.6
149.8
98
468.0
170.3
58
524. 4
190.8
19
299.8
109.1
79
356.2
129.6
39
412.5
150.2
99
468.9
170.7
59
525.3
191.2
20
300.7
109. 5
80
357.1
130.0
40
413.5
414.4
150.5
500
469.9
171.0
60
526.2
191.6
321
301.6
109.8
381
358.0
130.3
441
150.8
501
470.8
171.3
561
527.2
191.9
22
302.6
110.1
82
359.0
130.7
42
415.4
151. 2
02
471.7
171.7
62
528.1
192.2
23
303. 5
110.5
83
359.9
131.0
43
416.3
151.5
03
472.7
172.0
63
529.0
192.5
24
304.5
110.8
84
360.8
131.3
44
417.2
151.9
04
473.6
172.4
64
5.30.
192.9
25
305. 4
111.2
85
361.8
131.7
45
418.2
152.2
05
474.5
172.7
65
530. 9
193.2
26
306.3
111.5
86
362.7
132.
46
419.1
152.5
06
475. 4
173.0
66
531. 8
193. 6
27
307.3
111.8
87
363.7
132.4
47
420.0
152.9
07
476.4
173.4
67
532. 8
193.9
28
308.2
112.2
88
364.6
132.7
48
421.0
153.2
08
477.3
173.7
68
533. 7
194.2
29
309.2
112.5
89
365. 5
133.1
49
421.9
153.6
09
478.3
174.1
69
534.7
194.6
30
310.1
112.9
113.2
90
366.5
133.4
50
422.9
153.9
10
479.2
174.4
70
535. 6
195.0
331
311.0
391
367.4
133.7
451
423.8
154.3
511
480.2
174.8
571
536.6
195.3
32
312.0
113.6
92
368.4
134.1
52
424.7
154.6
12
481.1
175.1
72
537.5
195.6
33
312.9
113. 9
93
369.3
134.4
53
425.7
154.9
13
482.1
175.4
73
538.5
195. 9
34
313.9
114.2
94
370.2
134.8
54
426.6
155.3
14
483.0
•175. 8
74
539.4
196.3
35
314.8
114.6
95
371.2
135.1
55
427.6
155. 6
15
484.0
176.1
75
540. 3
196.6
36
315.7
114.9
96
372.1
135.4
56
428.5
156.0
16
484.9
176.5
76
541.3
197.0
37
316.7
115.3
97
373.1
135.8
57
429.4
156. 3
17
4a5.8
176.8
77
542.2
197.3
38
317.6
115.6
98
374.0
136.1
58
430.4
156.7
18
486.8
177.2
78
543.2
197.7
39
318.6
116.0
99
374.9
136.5
59
431.3
157.0
19
487.7
177.5
79
544.1
198.0
40
319.5
116.3
400
401
375.9
136.8
60
432.3
157.4
20
488.7
177.9
80
545.0
198.4
341
320.4
116.6
376.8
137.2
461
433.2
157. 7
521
489.6
178.2
581
546.0
198.7
42
321.4
117.0
02
377.8
137.5
62
434.1
158.0
22
490.5
178.5
82
546.9
199.0
43
322.3
117.3
03
378.7
137.8
63
435.1
158.4
23
491. 5
178.9
83
547.9
199.4
44
323.3
117. 7.
04
379.6
138.2
64
436.0
158. 7
24
492.4
179.2
84
548.8
199.8
45
324.2
118.0
05
380. 6
138.5
65
437.
159.0
25
493."4
179.6
85
549. 8
200.1
46
325;l
118.4
06
381.5
138.9
66
437.9
159. 4
26
494.3
179.9
86
550.7
200.4
47
326.1
118.7
07
382.5
139.2
67
438. 8
159. 7
27
495.3
180.2
87
551.7
200.8
48
327.0
119.0
08
383.4
139.6
68
439.8
160.1
28
496.2
180.6
88
552.6
201.2
49
328.0
119.4
09
384.3
139.9
69
440.7
160.4
29
497.1
181.0
89
553. 5
201.5
50
351
328.9
119.7
10
385.3
140.2
70
441.7
160.8
30
498.1
181.3
90
554.4
201.8
202.1
329.8
120.1
411
386.2
140.6
471
442.6
161.1
531
499.0
181.6
591
555.4
52
330.8
120.4
12
387.2
140.9
72
443.5
161.4
32
499.9
181.9
92
556.3
202.4
53
331.7
120.7
13
388.1
141.3
73
444.5
161.8
33
500.9
182.3
93
557.3
202.8
54
332.7
121.1
14
389.0
141.6
74
445.4
162.1
34
501.8
182.6
94
558.2
203.2
55
333.6
121.4
15
390.0
141.9
75
446.4
162. 5
35
502.7
183.0
95
559.1
203. 5
56
334.5
121.8
16
390.9
142.3
76
447.3
162.8
36
503.7
183.3
96
560.0
203.8
57
335.5
122.1
17
391.9
142.6
77
448.2
163. 2
37
504.6
183.7
97
561.0
204.2
58
336. 4
122.5
18
392.8
143.0
78
449.2
163. 5
38
505. 5
184.0
98
561. 9
204. 6
59
337.4
122.8
19
393.7
143.3
79
450.1
163. 8
39
506.5
184.3
99
562.9
204.9
60
338.3
123.1
20
394.7
143.7
80
451.1
164.2
40
507.4
184.7
600
563.8
205.2
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
■0° (1
10°, 25C
°, 290°
)•
.
•
TABLE 2.
[Page
671
Difference of Latitude and Departure for 21° (159°, 201
°, 339°
).
Dist
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
,1
0.9
0.4
61
56.9
21.9
121
113.0
43.4
181
169.0
64.9
241
225.0
86.4
2
1.9
0.7
62
57.9
22.2
22
113.9
43.7
82
169.9
65.2
42
225.9
86.7
3
2.8
1.1
63
58.8
22.6
23
114.8
44.1
83
170.8
65.6
43
226.9
87.1
4
3.7
1.4
64
59.7
22.9
24
115.8
44.4
84
171.8
6.5.9
44
227.8
87.4
5
4.7
1.8
65
60.7
23.3
25
116.7
44.8
85
172.7
66.3
45
228.7
87.8
6
5.6
2.2
66
61.6
23.7
26
117.6
45.2
86
173.6
66.7
46
229.7
88.2
7
6.5
2.5
67
62.5
24.0
27
118.6
45.5
87
174.6
67.0
47
230.6
88.5
8
7.5
2.9
68
63.5
24.4
28
119.5
45.9
88
175.5
67.4
48
231.5
88.9
9
8.4
3.2
69
64.4
24.7
29
120.4
46.2
89
176.4
67.7
49
232.5
89.2
10
9.3
10.3
3.6
70
65.4
25.1
30
121.4
46.6
90
177.4
68.1
50
233.4
89.6
11
3.9
71
66.3
25.4
131
122.3
46.9
191
178.3
68.4
251
234.3
90.0
12
11.2
4.3
72
67.2
25.8
32
123.2
47.3
92
179.2
68.8
52
235.3
90.3
13
12.1
4.7
73
68.2
26.2
33
124.2
47.7
93
180.2
69.2
53
236. 2
90.7
14
13.1
5.0
74
69.1
26.5
34
125.1
48.0
94
181.1
69.5
54
237.1
91.0
15
14.0
5.4
75
70.0
26.9
35
126.0
48.4
95
182.0
69.9
55
238.1
91.4
16
14.9
5.7
76
71.0
27.2
36
127.0
48.7
96
183.0
70.2
56
239.0
91.7
17
15.9
6.1
77
71.9
27.6
37
127.9
49.1
97
183. 9
70.6
57
239.9
92.1
18
16.8
6.5
78
72.8
28.0
38
128.8
49.5
98
184.8
71.0
58
240.9
92.5
19
17.7
6.8
79
73.8
28.3
39
129.8
49.8
99
185.8
71.3
59
241.8
92.8
20
18.7
7.2
80
74.7
28.7
40
130.7
50.2
200
186.7
71.7
60
242.7
93.2
21
19.6
7.5
81
75.6
29.0
141
131.6
50.5
201
187.6
72.0
261
243.7
93.5
22
20.5
7.9
82
76.6
2^.4
42
132.6
50.9
02
188.6
72.4
62
244. 6
93.9
23
21.5
8.2
83
77.5
29.7
43
133.5
51.2
03
189.5
72.7
63
245.5
94.3
24
22 4
8.6
84
78.4
30.1
44
134.4
51.6
04
190.5
73.1
64
246.5
94.6
25
23! 3
9.0
85
79.4
30.5
45
135.4
52.0
05
191.4
73.5
65
247.4
95.0
26
24.3
9.3
86
80.3
30.8
46
136.3
52.3
06
192.3
73.8
66
248.3
95.3
27
2.5.2
9.7
87
81.2
31.2
47
137.2
52.7
07
193.3
74.2
67
249.3
95.7
28
26.1
10.0
88
82.2
31.5
48
138.2
53.0
08
194.2
74.5
68
250.2
96.0
29
27.1
10.4
89
83.1
3U9
49
139.1
53.4
09
195.1
74.9
69
251.1
96.4
30
31
28.0
10.8
90
84.0
32.3
50
140. [ 53. 8
10
196.1
75.3
"75. 6
70
271
252.1
96.8
28.9
11.1
91
85.0
32.6
151
141.0
54.1
211
197.0
253.
97.1
32
29.9
11.5
92
85.9
33.0
52
141.9
54.5
12
197.9
76.0
72
253.9
97.5
33
30.8
11.8
93
86.8
,33. 3
53
142.8
.54.8
13
198.9
76.3
73
254.9
97.8
34
31.7
12.2
94
87.8
33.7
54
143. 8
55.2
14
199.8
76.7
74
255.8
98.2'
35
32.7
12.5
95
88.7
34.0
55
144.7
55. 5
15
200.7
77.0
75
256.7
98.6
36
33.6
12.9
96
89.6
34.4
56
145.6
55. 9
16
201.7
77.4
76
257.7
98.9
37
34.5
13.3
97
90.6
34.8
57
146.6
56.3
17
202.6
77.8
77
258.6
99.3
38
35.5
1.3.6
98
91.5
35. 1
58
147.5
56.6
18
203.5
78.1
78
259.5
99.6
39
.36.4
14.0
99
92.4
35.5
59
148.4
57.0
19
204.5
78.5
79
26a 5
100.0
40
37.3
14.3
100
93.4
35.8
60
149.4
57.3
20
205.4
78.8
80
281
261.4
100.3
41
38.3
14.7
101
94.3
36.2
161
150.3
57.7
221
206.3
79.2
262.3
100.7
42
39.2
15.1
02
9.5.2
36.6
62
151.2
58.1
22
207.3
79.6
82
263. 3
101.1
43
40.1
15.4
03
96.2
36.9
63
152.2
.58.4
23
208.2
79.9
83
264.2
101.4
44
41.1
15.8
04
97.1
37. 3
64
153. 1
58.8
24
209.1
80.3
84
265.1
101.8
45
42.0
16.1
05
98.0
37.6
65
154.
59.1
25
210.1
80.6
85
266.1
102.1
46
42.9
16.5
06
99.0
38.0
66
155.0
59.5
26
211.0
81.0
86
267.0
102. 5
47
43.9
16.8
07
99.9
38.3
67
155. 9
59.8
27
211.9
81.3
87
267.9
102.9
48
44.8
17.2
08
100.8
38.7
68
156.8
60.2
28
212.9
81.7
88
268.9
103.2
49
45.7
17.6
09
101.8
39.1
69
157.8
60.6
29
213.8
82.1
89
269.8
103. 6
50
46.7
17.9
10
102.7
39.4
70
158.7
60.9
30
214.7
215. 7
82.4
82.8
90
270.7
103.9
104.3
51
47.6
18.3
111
103.6
39.8
171
159.6
61.3
231
291
271.7
52
48.5
18.6
12
104.6
40.1
72
160.6
61.6
32
216.6
83.1
92
272.6
104.6
53
49.5
19.0
13
105. 5
40.5
73
161.5
62.0
33
217.5
83. 5
93
273.5
105.
54
50.4
19.4
14
106.4
40.9
74
162.4
62.4
34
218.5
83.9
94
274.5
105.4
55
51.3
19.7
15
107.4
41.2
75
163.4
62.7
35
219.4
84.2
95
275.4
105. 7
56
52.3
20.1
16
108. 3
41.6
76
164.3
63.1
36
220.3
84.6
96
276.3
106.1
57
53.2
20.4
17
109.2
41.9
77
165. 2
63.4
37
221.3
84.9
97
277.3
106.4
58
54.1
20.8
18
110.2
42.3
78
166.2
63.8
38
222.2
85.3
98
278.2
106.8
59
.55.1
21.1
19
111.1
42.6
79
167.1
64.1
39
233.1
85.6
99
279.1
107.2
60
56.0
21.5
20
112.0
43.0
80
168.0
64.5
40
224.1
86.0
300
280.1
107.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
69° (
111°, 249°, 291
°)-
Page 672]
TABLE 2.
Difference of Latitude and Departure for 21° (159°, 201°, 339
°)-
Dist.
Lat. 1 Dep.
Dist. ! Lat.
Dep.
Dist. 1 Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
301
281. ! 107. 9
361
337.0
129.4
421 I 393.0
150.9
481
449.0
172.4
541 505. 1
193. 9
02
281.9 1108.2
62
337.9
129.7
22
394.0
151.2
82
450.0
172.7
42 : 506.0
194.2
03
282.9
108.6
63
338.9
130.1
23
394.9
151.6
83
450. 9
173.1
43
507.0
194.6
04
283.8
108.9
64
339.8
130.4
24
395.8
152.0
84
451. 8
173.5
44
507. 9
195.
05
284.7
109.3
65
340. 7
130.8
25
396.8
152.3
85
452.8
173.8
45
508. 8
195.3
06
285.7
109.7
66
341.7
131.2
26
397.7
152.7
86
453. 7
174.2
46
509.8
195. 7
07
236.6
110.0
67
342.6
131.5
27
398.6
153.
87
454.6
174.5
47
510.7
196.0
08
287.5
110.4
68
343. 5
131.9
28
399. 6
153. 4
88
455.6
174.9
48
511.6
196. 4
09
288.5
110.7
79
344.5
132. 2
29
400.5
153.7
89
456.5
175.2
49
512.6
196. 8
10
289.4
111.1
70
345.4
132.6
30
431
401.4
154.1
90
457. 4
175.6
50
513.5
197.1
311
290.3
111.5
371
346.3
133.0
402.4
154. 5
491
458. 4
176.0
551
514.4
197.5
12
291.3
111.8
72
347.3
133.3
32
403. 3
154.8
92
459.3
176.3
52
515.4
197.8
13
292.2
112.2
73
348. 2
133.7
33
404.2
155. 2
93
460.2
176.7
53
516.3
198. 2
14
293.1
112.5
74
349.1
134.0
34
405.2
155. 5
94
461.2
177.0
54
517. 2
198.6
15
294.1
112.9
75
350. 1 1 1.34. 4
.35
406.1
155.9
95
462.1
177.4
55
518.2
198.9
16
295.0
113. 2
76
351.0
134.7
36
407.0
156.3
96
463.0
177.8
56
519.1
199.3
17
295.9
113.6
77
351.9
135.1
37
408.0
156.6
97
464.0
178.1
57
520.0
199.6
18
296.9
114.0
78
352.9
135.5
38
408.9
157.0
98
464.9
178.5
58
521.0
200.0
19
297.8
114.3
79
353.8
135.8
39
409.8
157.3
99
465.8
178.8
59
521.9
200.3
20
321
298.7
114.7
80
354.7
136.2
40
410.8
157.7
500
466. 8
179.2
60
522.8
200.7
299.7
115.0
381
355.7
136.5
441
411.7
158.0
501
467.7
179.5
561 ; 523.8
201.
22
300.6'
115.4
82
356.6
136.9
42
412.6
158.4
02
468.6
179.9
62 1 524. 7
201.4
23
301.5
115.8
83
357. 5
137.3
43
413.6
158. 8
03
469.6
180.3
63 i 525. 6
201.8
24
302.5
116.1
84
358. 5
137.6
44
414. 5
159.1
04 1 470.5
180.6
64 1 526.6
202.1
25
303.4
116.5
85
359.4
138.0
45
415.4
159.5
05
471.5
181.0
65
527. 5
202.5
26
304.3 1116.8
86
360.3
138.3
46
416.4
159.8
06
472.4
181.3
66
528.4
202.8
27
305.3
117.2
87
361.3
138.7
47
417.3
160.2
07
473.3
181.7
67
529.4
203. 2
28
306.2
117.5
88
362.2
139. 1
48
418.2
160.5
08
474. 3
182.0
68 ! 530.3
203. 5
29
307.1
117.9
89
363.1
139.4
49
419. 2
160. 9
09-
475.2
182.4
69 ; 531. 2
203.9
30
308.1
118.3
90
364.1
1.39. 8
50
420.1
161.3
10
476.1
182.8
70 i 532. 2
204.3
331
309.0
118.6
391
365.0
140. 1
451
421.0
161.6
511
477.1
183. 1
571
533.1
204.6
32
309.9
119.0
92 i 365. 9
140.5
52
422.0
162.0
12
478.0
183. 5
72
534.0
205.
33
310.9
119.3
93
366.9
140.8
53
422.9
162.3
13
478.9
183. 8
73
535.
205. 4
34
311.8
119.7
94
367.8
141.2
54
423.8
162.7
14
479.9
184. 2
74
535.9
205. 7
35
312.7
120.1
95
368.7
141.6
55
424.8
163.1
15
480.8
184.6
75
536.8
206.1
36
313.7
120.4
96
369.7
141.9
56
425.7
163. 4
16
481.7
184.9
76
537.8
206.4
37
314. 6
120.8
97
370.6
142.3
57
426.6
163.8
17
482.7
185.3
77
538.7
206.8
38
315.5
121.1
98
371. 5
142.6
58
427.6
164.1
18
483.6
185.6
78
539.6
207.1
39
316.5
121.5
99
372.5
143.0
59
428.5
164.5
19
484.5
186.0
79
540.6
207. 5
40
341
317.4
121.8
400
373.4
143.4
143.7
60
429.4
164.9
20
485.5
186.4
80
581
541.5
542.4
207.9
318.3
122.2
401
374.3
461
430.4
165.2
521
486.4
186.7
208. t
42
319.3
122.6
02
375.3
144.1
02
431. 3
165.6
22
487.3
187.1
82
543.4
208.6
43
320.2
122.9
03
376.2
144.4
63
432.2
165. 9
23
488.3
187.4
83
544. 3
208.9
44
321.1
123.2
04
377.1
144.8
64
433. 2
166.3
24
489.2
187.8
84
545. 2
209. 3
45
322.1
123.6
05
378.1
145.1
65
434.1
166.6
25
490.1
188.1
85
546.2
209.6
46
323.0
124.0
06
379.0
145.5
66
435.0
167.0
26
491.1
188.5
86
547.1
210.0
47
323.9
124.4
07
379.9
145.9
67
436.0
167.4
27
492.0
188.9
87
548.0
210.4
48
324.9
124.7
08
380.9
146.2
68
436.9
167.7
28
492.9
189.2
88
549.0
210.7
49
325.8
125.1
09
381.8
146.6
69
437.8
168.1
29
493.9
189.6
89
549.9
211.1
50
326.7
125.4
10
382.7
146.9
70
438.8
168.4
30
494.8
189.9
90
550.8
211.4
211.8
351
327.7
125. 8
411
383.7
147.3
471
439.7
168.8
531
495.7
190.3
591
551.8
52
328.6
126.1
12
384.6
147.7
72
440.6
169.2
32
496.7
190.7
92
552. 7
212.2
53
329.5
126.5
13
385.5
148.0
73
441.6
169.5
33
497.6
191.0
93
553.6
212.5
54
330.5
126.9
14
.386. 5
148.4
74
442.5
169.9
34
498.5
191.4
94
554.6
212.9
55
331.4
127.2
15
387.4
148.7
75
443.4
170.2
35
499.5
191.7
95
555.5
213. 2
56
332.3
127.6
16
388.4
149.1
76
444.4
170.6
36
500.4
192.1
96
556.4
213.6
57
333.3
127.9
17
389. 3
149.4
77
445.3
170.9
37
501.3
192.4
97
557.4
213.9
58
334.2
128.3
18
390.2
149.8
78
446.2
171.3
38
502.3
192.8
98
558.2
214.3
59
3a5.1
128.7
19
391.2
150.2
79
447.2
171.7
39
503.2
193.2
99
559. 2
214.7
60
336.1
129.0
20
392.1
150.5
80
448.1
172.0
40
504.1
193.5
600
560.1
215.
*
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
6
9° (111°, 249°, 291°
)■
TABLE 2.
[Page
673
Difference of Latitude and Departure for 22° (158°, 202, 338°,
.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.6
22.9
121
112.2
45. 3
181
167.8
67.8
241
223. 5
90.3
90.7
2
1.9
0.7
62
57.5
23.2
22
113. 1
45.7
82
168.7
68.2
42
224.4
3
2.8
1.1
63
58.4
23.6
23
114.0
46. 1
83
169.7
68.6
43
225.3
91.0
4
3.7
1.5
64
59.3
24.0
24
115.0
46.5
84
170. 6
68.9
44
226.2
91.4
5
4.6
1.9
65
60.3
24.3
25
115.9
46.8
85
171.5
69.3
45
227.2
91.8
6
5.6
2.2
66
61.2
24.7
26
116.8
47.2
86
172.5
69.7
46
228.1
92.2
7
6.5
2.6
67
62.1
25.1
27
117.8
47.6
87
173.4
70.1
47
229.0
92.5
8
7.4
3.0
68
63.0
25.5
28
118.7
47.9
88
174.3
70.4
48
229.9
92.9
9'
8.3
3.4
69
64.0
25.8
29
119.6
48.3
89
175. 2
70.8
49
230.9
93.3
10
9.3
3.7
70
64.9
26.2
30
120.5
48.7
90
176.2
71.2
50
231.8
232.7
93.7
94.0
11
10.2
4.1
71
65.8
26.6
131
121.5
49.1
191
177.1-
71.5
251
12
11.1
4.5
72
66.8
27.0
32
122.4
49.4
92
178.0
71.9
52
233.7
94.4
13
12.1
4.9
73
67. 7
27.3
33
123.3
49.8
93
178.9
72.3
53
234.6
94.8
14
13.0
5.2
74
68.6
27.7
34
124.2
50.2
94
179.9
72.7
54
235.5
95.2
15
13.9
5.6
75
69.5
28.1
35
125.2
50.6
95
180.8
73.0
55
236.4
95.5
16
14.8
6.0
76
70.5
28.5
36
126.1
50.9
96
181.7
73.4
56
237.4
95.9
17
15.8
6.4
77
71.4
28.8
37
127.0
51.3
97
182.7
73.8
57
238. 3
96.3
18
16.7
6.7
78
72.3
29.2
38
128.0
51.7
98
183.6
74.2
58
239.2
96.6
19
17.6
7.1
79
73.2
29.6
39
128.9
52.1
99
184,5
74.5
59
240.1
97.0
20
18.5
7.5
80
74.2
30.0
30. 3
40
141
129.8
52.4
200
201
185.4
74.9
60
261
241.1
242.0
97.4
21
19.5
7.9
81
75.1
130.7
52.8
186.4
75.3
97.8
22
20.4
8.2
82
76.0
30.7
42
131.7
53. 2
02
187.3
75.7
62
242.9
98.1
23
21.3
8.6
83
77.0
31.1
43
132.6
53.6
03
188.2
76.0
63
243.8
98.5
24
22.3
9.0
84
77.9
31.5
44
133. 5
53.9
04
189.1
76.4
64
244.8
98.9
25
23.2
9.4
85-
78.8
31.8
45
134.4
54. 3
05
190.1
76.8
65
245. 7
99.3
26
24.1
9.7
86
79.7
32.2
46
135.4
54.7
06
191.0
77.2
66
246.6
99.6
27
25.0
10.1
87
80.7
32.6
47
136. 3
5.5.1
07
191.9
77.5
67
247.6
100.0
28
26.0
10.5
88
81.6
33.0
48
137. 2
55. 4
08
192.9
77.9
68
248. 5
100.4
29
26.9
10.9
89
82.5
33.3
49
138. 2
.55. 8
09
193.8
78.3
69
249.4
100.8
30
27.8
11.2
90
83.4
33.7
50
139. 1 j 56. 2
10
194.7
78.7
70
250.3
101.1
31
28.7
li. 6
91
84.4
34.1
151
140.
56. 6
2ii
195.6
79.0
271
251.3
101.5
32
29.7
12.0
92
85.3
34.5
52
140.9
56. 9
12
196.6
79.4
72
252.2
101.9
33
30.6
12.4
93
86.2
34.8
53
141.9
57.3
13
197.5
79.8
73
253.1
102. 3
34
31.5
12.7
94
87.2
35.2
54
142.8
.57.7
14
198.4
80.2
74
254.0
102. 6
35
32.5
13.1
95
88.1
35.6
55
143. 7
.58.1
15
199.3
80.5
75
2.55.
103.0
36
33.4
13.5
96
89.0
36.0
56
144.6
58. 4
16
200.3
80.9
76
255.9
103.4
37
34.3
13.9
97
89.9
36.3
57
145.6
58.8
17
201.2
81.3
77
256.8
103. 8
38
35.2
14.2
98
90.9
36.7
58
146.5
59.2
18
202. 1
81.7
78
257.8
104.1
39
36.2
14.6
99
91.8
37.1
59
147.4
.59.6
19
203. 1
82.0
79
258.7
104.5
40
37.1
15.0
100
92.7
37.5
60
148.3
149.3
59.9
60. 3
20
221
204.0
204.9
82.4
80
259.6
104.9
41
38.0
15.4
101
93.6
37.8
161
82.8
281
260.5
105.3
42
38.9
15.7
02
94.6
38.2
62
1.50. 2
60. 7
22
205. 8
83.2
82
261.5
105.6
43
39.9
16.1
03
95.5
38.6
63
151. 1
61.1
23
206.8
83.5
83
262.4
106.0
44
40.8
16.5
04
96.4
39.0
64
152.1
61.4
24
207.7
83.9
84
263.3
106.4
45
41.7
16.9
05
97.4
39.3
65
153.0
61.8
25
208. 6
84.3
85
264.2
106.8
46
42.7
17.2
06
98.3
39.7
66
153. 9
62.2
26
209. 5
84.7
86
265.2
107.1
47
43.6
17.6
07
99.2
40.1
67
154.8
62.6
27
210.5
85.0
87
266.1
107.5
48
44.5
18.0
08
100.1
40.5
68
155.8
62.9
28
211.4
85.4
88
267.0
107.9
49
45.4
18.4
09
101.1
40.8
69
156.7
63. 3
29
212.3
85.8
89
268.0
108.3
50
46.4
47.3
18.7
19.1
10
102.0
41.2
70
157. 6
63.7
30
213.3
86.2
90
268.9
108.6
51
lU
102.9
41.6
171
158.5
64.1
231
214.2
86.5
291
269.8
109.0
52
48.2
19.5
12
103.8
42.0
72
159.5
64.4
32
215.1
86.9
92
270.7
109.4
53
49.1
19.9
13
104.8
42.3
73
160.4
64.8
33
216.0
87.3
93
271.7
109.8
54
50.1
20.2
14
105.7
42.7
74
161.3
6.5.2
34
217.0
87.7
94
272.6
UO.l
55
51.0
20.6
15
106.6
43.1
75
162.3
6.5.6
35
217.9
88.0
95
273.5
110. 5
56
51.9
21.0
16
107.6
43.5
76 i 163.2
6.5.9
36
218.8
88.4
96
274.4
110.9
57
52.8
21.4
17
108.5
43.8
77 i 164. 1
66. 3
37
219.7
88.8
97
275.4
111.3
58
53.8
21.7
18
109.4
44.2
78 i 165.0
66.7
.38
220.7
89.2
98
276.3
111.6
59
54.7
22.1
19
110.3
44.6
79
166.0
67.1
39
221.6
89.5
99
277.2
112.0
60
55.6
22.5
20
111.3
45.0
80
166.9
67.4
40
222.5
89.9
300
278.2
112.4
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
68° (112°, 248°, 292°).
Page 574]
TABLE 2.
Difference of Latitude and Departure for 22° (158°, 202
°, 338=
)•
Dist.
Lat.
Dep.
Dist. ] Lat.
Dep.
Di.st.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
279.1
112.7
361
334.7
135.2
421
390.3
157.7
481
446.0
180.2
541
501.6
202.7
02
280.0
113.1
62
335. 6
135.6
22
391.3
158.1
82
446.9
180.6
42
502.5
203.1
03
280.9
113.5
63
336.6
136.0
23
392.2
158.4
83
447.8
180.9
43
503.4
203. 5
04
281.9
113.9
64
337.5
136.3
24
393. 1
158.8
84
448.8
181.3
44
504.4
203.8
05
282.8
114.2
65
338.4
136.7
25
394.1
159.2
85
449.7
181.7
45
505. 3
204.2
06
283.7
114.6
66
339.3
137.1
26
395.0
159.6
86
450.6
182.1
46
506.2
204.6
07
284.6
115.0
67
340.3
137.5
27
395.9
159.9
87
451.6
182.4
47
507.2
205.
08
285.6
115.4
68
341.2
137.8
28
.396. 8
160.3
88
452.5
182.8
48
508.1
205. 3
09
286.5
115.7
69
342.1
138.2
29
397.8
160.7
89
453.4
183.2
49
509.
205. 7
10
311
287.4
116.1
70
343. 1
138.6
30
398. 7
161.1
90
454.3
183.6
50
510.0
510.9
206. 1
. 288. 4
116.5
371
344.0
139.
431
399. 6
161.4
491
455.3
184.0
551
206.5
12
289.3
116.8
72
344.9
139.3
32
400.5
161.8
92
456.2
184.3
52
511.8
206.8
13
290.2
117.2
73
345.8
139.7
33
401.5
162.2
93
457.1
184.7
53
512.7
207.2
14
291.1
117.6
74
346.8
140.1
34
402.4
162.6
94
458.0
185.1
54
513.6
207.6
15
292.1
118.0
75
347.7
140.5
35
403. 3
162.9
95
459.0
185.4
55
514.6
208.0
16
293.0
118.3
76
348.6
140.8
36
404.3
163. 3
96
459.9
185.8
56
515.5
208.3
17
293.9
118.7
77
349.5
141.2
37
405.2
163.7
97
460.8
186.2
57
516.4
208.7
18
294.8
119.1
78
350.5
141.6
38
406.1
164.1
98
461.8
186.6
58
517.4
209.1
19
295.8
119.5
79
351.4
141.9
39
407.0
164.4
99
462.7
186.9
59
518.3
209.4
20
•296.7
119.8
80
352.3
142.3
40
408.0
164.8
500
463.6
187.3
60
519.2
209.8
321
297.6
120.2
381
353.3
142.7
441
408.9
165.2
501
464.5
187.7
561
520.1
210. 2
22
298.6
120.6
82
354.2
143.1
42
409.8
165.5
02
465.4
188.0
62
521.0
210.5
23
299.5
121.0
83
355. 1
143.4
43
410.7
165.9
03
466.4
188.4
63
522.0
210.9
. 24
300.4
121.3
84
356.0
143.8
44
411.7
166.3
04
467.3
188.8
64
522.9
211.3
25
301.3
121.7
85
357.0
144.2
45
412.6
166.7
05
468.2
189.2
65
523.8
211.7
26
302.3
122.1
86
357.9
144.6
46
413.5
167.0
06
469.2
189.5
66
524.8
212.0
27
303.2
122.5
87
358.8
144.9
47
414.5
167.4
07
470.1
189.9
67
525.7
212.4
28
304.1
122.8
88
359.7
145.3
48
415.4
167.8
08
471.0
190.3
68
526.6
212.8
29
305.0
123.2
89
360.7
145.7
49
416.3
168.2
09
471.9
190.7
69
527. 5
213.2
30
306.0
123.6
90
361.6
146.1
50
451
417.2
418.2
168.5
10
472.9
473.8
191.1
70
528. 5
213.5
331
306.9
124.0
391
362.5
146.4
168.9
511
191.4
571
529.4
213.9
32
307.8
124.3
92
363.5
146.8
52
419.1
169.3
12
474.7
191.8
72
530.3
214.3
33
308.8
124.7
93
364.4
147.2
53
420.0
169.7
13
475.6
192.2
73
531.2
214.7
34
309.7
125. 1
94
365. 3
147.6
54
420.9
170.0
14
476.6
192.5
74
532.2
215.0
35
310.6
125.5
95
366.2
147.9
55
421.9
170.4
15
477.5
192.9
75
533.1
215. 4
36
311.5
125.8
96
367.2
148.3
56
422.8
170.8
16
478.4
193.3
76
534.0
215.8
37
312.5
126.2
97
368. 1
148.7
57
423.7
171.2
17
479. 3
193.7
77
534.9
216.2
38
313.4
126.6
98
369.0
149.1
58
424.6
171.5
18
480.3
194.0
78
535.9
216.5
39
314.3
127.0
99
369.9
149.4
59
425.6
171.9
19
481.2
194.4
79
536.8
216.9
40
315.2
127.3
400
370.9
149.8
60
426.5
427.4
172.3
20
482.1
194.8
80
537.7
217.3
341
316.2
127.7
401
371. if
150.2
461
172.7
521
483.0
195.2
581
538.6
217.7
42
317.1
128.1
02
372.7
150.6
62
428.4
173.0
22
484.0
195.5
82
539.6
218.0
43
318.
128.5
03
373.7
150.9
63
429.3
173.4
23
484.9
195.9
83
540.5
218.4
44
319.0
128.8
04
374.6
151.3
64
4,30. 2
173.8
24
485.8
196.3
84
541.4
218.8
45
319.9
129.2
05
375.5
151.7
65
431.1
174.2
25
486.7
196.7
85
542.4
219.2
46
320.8
129.6
06
376.4
152.1
66
432.1
174.5
26
487.7
197.0
86
543.3
219.5
47
321.7
130.0
07
377.4
152.4
67
433.0
174.9
27
488.6
197.4
87
544.2
219.9
48
322.7
130.3
08
378.3
152.8
68
433.9
175.3
28
489.5
197.8
88
545.1
220.3
49
323.6
130.7
09
379.2
153.2
69
434.8
175. 7
29
490.4
198.2
89
546.1
220.7
50
351
324. 5 i 131. 1
10
380.1
153.6
70
435.8
176.0
30
491.4
198.5
90
547.0
221.0
325. 4
131.5
411
381.1
153.9
47L
436.7
176.4
531
492.3
198.9
591
547.9
221.4
52
326.4
131.8
12
382.0
154.3
72
437.6
176.8
32
493.2
199.3
92
548.9
221.8
53
327.3
132.2
13
382.9
154.7
73
438.6
177.2
33
494.2
199.7
93
549.8
222.2
54
328.2
132.6
14
383.9
155.1
74
439.5
177.5
34
495.1
200.0
94
550.7
222.5
55
329.2
133.0
15
384.8
155.4
75
440.4
177.9
35
496.0
200.4
95
551.7
222.9
56
330.1
133.3
16
385.7
155.8
76
441.3
178.3
36
496.9
200.8
96
552.6
223. 3
57
331.0
133.7
17
386.6
156.2
77
442.3
178.7
37
497.9
201.2
97
553.5
223.7
68
332.0
134.1
18
387.6
156.6
78
443.2
179.0
38
498.8
201.5
98
554.4
224.0
59
332.9
134.5
19
388.5
156.9
79
444.1
179.4
39
499.7
201.9
99
555.4
224.4
60
333.8
134.8
20
389.4
157.3
80
445.0
179.8
40
500.7
202.3
600
556.3
224.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
i
8° (112°, 248
\ 292°
)•
TABLE
2.
[Page 576
Difference of Latitude and Departure for 23° (157°, 203°, 337°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
56.2
23.8
121
111.4
47.3
181
166.6
70.7
241
221.8
94.2
2
1.8
0.8
62
57.1
24.2
22
112.3
47.7
82
167. 5
71.1
42
222.8
94.6
3
2.8
1.2
63
58.0
24.6
23
113.2
48.1
83
168.5
71.5
43
223.7
94.9
4
3.7
1.6
64
58.9
25.0
24
114.1
48.5
84
169.4
71.9
44
224.6
95.3
5
4.6
2.0
65
59.8
25.4
25
115.1
48.8
85
170.3
72.3
45
225.5
95.7
6
5.5
2.3
66
60.8
25.8
26
116.0
49.2
86
171.2
72.7
46
226.4
96.1
7
6.4
2.7
67
61.7
26.2
27
116.9
49.6
87
172.1
73.1
47
227.4
96.5
8
7.4
3.1
68
62.6
26.6
28
117.8
50.0
88
173.1
73.5
48
228.3
96.9
9
8.3
3.5
69
63.5
27.0
29
118.7
.50.4
89
174.0
73.8
49
229.2
97.3
10
9.2
3.9
70
64.4
27.4
30
119.7
120.6
50.8
51.2
90
174.9
74.2
50
230.1
97.7
11
10.1
4.3
71
65.4
27.7
131
191
175.8
74.6
251
231.0
98.1
12
11.0
4.7
72
66.3
28.1
32
121.5
51.6
92
176.7
75.0
52
232.
98.5
13
12.0
5.1
73
67.2
28.5
33
122.4
52.0
93
177.7
75.4
53
232.9
98.9
14
12.9
5.5
74
68.1
28.9
34
123.3
52.4
94
178.6
75.8
54
233.8-
99.2
15
13.8
5.9
75
69.0
29.3
35
124.3
52.7
95
179.5
76.2
55
234.7
99.6
16
14.7
6.3
76
70.0
29.7
36
125.2
53.1
96
180.4
76.6
56
235.6
100.0
17
15.6
6.6
77
70.9
30.1
37
126.1
53.5
97
181.3
77.0
57
236.6
100.4
18
16.6
7.0
78
71.8
30.5
38
127.0
53.9
98
182.3
77.4
58
237.5
100.8
19
17.5
7.4
79
72.7
30.9
39
128.0
54.3
99
183.2
77.8
59
238.4
101.2
20
18.4
7.8
80
73.6
31.3
40
128.9
54.7
200
184.1
78.1
60
239.3
101.6
21
19.3
8.2
81
74.6
31.6
141
129.8
55.1
201
185.0
78.5
261
240.3
102.0
22
20.3
8.6
82
75.5
32.0
42
130.7
55.5
02
185.9
78.9
62
241.2
102.4
23
21.2
9.0
83
76.4
32.4
43
131.6
5,5.9
03
186.9
79.3
63
242.1
102.8
24
22.1
9.4
84
77.3
32.8
44
132.6
56.3
04
187.8
79.7
64
243.0
103.2
25
23.0
9.8
85
78.2
33.2
45
133.5
56.7
05
188.7
80.1
65
243.9
103.5
26
23.9
10.2
86
79.2
33.6
46
134.4
57.0
06
189.6
80.5
66
244.9
103. 9
27
24.9
10.5
87
80.1
,34.0
47
135.3
57.4
07
19a 5
80.9
67
245.8
104.3
28
25.8
10.9
88
81.0
34.4
48
136.2
57.8
08
191.5
81.3
68
246.7
104.7
29
26.7
11.3
89
81.9
34.8
49
137.2
58.2
09
192.4
81.7
69
247.6
105.1
30
31
27.6
28.5
11.7
90
82.8
35.2
50
138. 1
58.6
10
193.3
82.1
70
248.5
105.5
105.9
12.1
91
83.8
35.6
151
139.0
59.0
211
194.2
82.4
271
249.5
32
29.5
12.5
92
84.7
35.9
52
139.9
59.4
12
195.1
82.8
72
250.4
106.3
33
30.4
12.9
93
85.6
36.3
53
140.8
59.8
13
196.1
83.2
73
251.3
106.7
34
31.3
n.3
94
86.5
36.7
54
141.8
60.2
14
197.0
83.6
74
252.2
107.1
35
32.2
13.7
95
87.4
37.1
55
142.7
60.6
15
197.9
84.0
75
253.1
107.5
36
33.1
14.1
96
88.4
37.5
56
143.6
61.0
16
198.8
84.4
76
254.1
107.8
37
34.1
14.5
97
89.3
37.9
57
144.5
61.3
17
199.7
84.8
77
255.0
108.2
38
35.0
14.8
98
90.2
38.3
58
145.4
61.7
18
200.7
85.2
78
255.9
108.6
39
35.9
15.2
99
91.1
38.7
59
146.4
62.1
19
201.6
a5.6
79
256.8
109.0
40
36.8
15.6
100
101
92.1
93.0
39.1
60
147.3
62.5
20
202.5
203.4
86.0
80
257.7
258.7
109.4
109.8
41
37.' 7
16.0
39.5
161
148.2
62.9
221
86.4
281
42
38.7
16.4
02
93.9
39.9
62
149.1
63.3
22
204.4
86.7
82
259.6
110.2
43
39.6
16.8
03
94.8
40.2
63
150.0
63.7
23
205.3
87.1
83
260. 5
110.6
44
40.5
17.2
04
95.7
40.6
64
151.0
64.1
24
206.2
87.5
84
261.4
111.0
45
41.4
17.6
05
96.7
41.0
65
151.9
64.5
25
207.1
87.9
85
262.3
111.4
46
42.3
18.0
06
97.6
41.4
66
152. 8
64.9
26
208.0
88.3
86
263.3
111.7
47
43.3
18.4
07
98.5
41.8
67
153.7
65.3
27
209.0
88.7
87
264.2
112.1
48
44.2
18.8
08
99.4
42.2
68
154.6
65.6
28
209.9
89.1
88
265.1
112.5
49
45.1
19.1
09
100.3
42.6
69
155. 6
66.0
29
210.8
89.5
89
266.0
112.9
50
46.0
19.5
10
101.3
43.0
70
156. 5
66.4
30
231
211.7
89.9
90
266.9
267.9
113.3
51
46.9
19.9
111
102.2
43.4
171
157.4
66.8
212.6
90.3
291
113.7
52
47.9
20.3
12
103.1
43.8
72
158.3
67.2
32
213.6
90.6
92
268.8
114.1
53
48.8
20.7
13
104.0
44.2
73
159.2
67.6
,33
214.5
91.0
93
269.7
114.5
54
49.7
21.1
14
104.9
44.5
74
160.2
68.0
34
215.4
91.4
94
270.6
114.9
55
50.6
21.5
15
105.9
44.9
75
161.1
68.4
35
216.3
91.8
95
271.5
11,5.3
56
51.5
21.9
16
106.8
45.3
76
162.0
68.8
36
217.2
92.2
96
272.5
115.7
57
52.5
22.3
17
107.7
4.5.7
77
162.9
69.2
37
218.2
92.6
97
273.4
116.0
58
53.4
22.7
18
108.6
46.1
78
163.8
69.6
38
219.1
93.0
98
274.3
116.4
59
54.3
23.1
19
109.5
46.5
79
164.8
69.9
39
220.0
93.4
99
275.2
116.8
60
55.2
23.4
20
110.5
46.9
80
70.3
40
220.9
93.8
300
276.2
117.2
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
67° (1
113°, 24-
1°, 293
= ).
Page 676]
TABLE 2.
Difference of Latitude and Departure for
23° (157°, 203°, 337"^
)•
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
277.1
117.6
361
332.3
141.1
421
387.5
164.5
481
442.7
188.0
541
498.0
211.4
02
278.0
118.0
62
333.2
141. 5
22
388. 5
164.9
82
443.7
188.4
42
498.9
211.8
03
278.9
118.4
63
334.1
141.8
23
389.4
165.3
83
444.6
188.8
43
499.8
212.2
04
279.8
118.8
64
335. 1
142.2
24
390.3
166.7
84
445. 5
189. 2
44
500.7
212.6
05
280.8
119.2
65
336.0
142.6
25
391.2
166.1
85
446.4
189.5
45
501.7
213.0
06
281.7
119. 6
66
336.9
143.0
26
392.1
166.5
86
447.3
189.9
46
502. 6
213.4
07
282.6
120.0
67
337.8
143.4
27
393. 1
166.8
87
448.3
190.2
47
503. 5
213.8
08
283. 5
120.4
68
338. 7
143.8
28
394.0
167.2
88
449.2
190.6
48
504.4
214.2
09
284.4
120.8
69
339.7
144.2
29
394.9
167.6
89
450.1
191.0
49
505.3
214.6
10
285. 4
121.2
70
340. 6
144.6
T45.
30
395.8
168.0
90
451.0
191.4
50
506.3
507.2
215.0
215. 3
311
286.3
121.6
371
341.5
431
396.7
168.4
491
451.9
191.8
551
12
287.2
121.9
72
342. 4
145. 4
32
397.7
168.8
92
452.9
192.2
52
508.1
215.6
13
288.1
122.3
73
343. 4
145. 7
33
398.6
169. 2
93
453.8
192.6
53
509.0
216.0
14
289.
122.7
74
344.3
146.1
34
399.5
169.6
94
454.7
193.
54
509.9
216.4
15
290.0
123. 1
75
345.2
146.5
35
400.4
170.0
95
455.6
193.4
55
510.9
216.8
16
290.9
123.5
76
346.1
146.9
36
401.3
170.4
96
456.6
193.8
56
511.8
217.2
17
291.8
123.9
77
347.0
147.3
37
402.3
170.8
97
457.5
194.2
57
512.7
217.6
18
292.7
124.3
78
348.0
147.7
38
403.2
171.1
98
458.4
194.6
58
513.6
218.0
19
293.6
124.6
79
348.9
148.1
39
404.1
171. 5
99
459.3
195.0
59
514.5
218.4
20
321
294.6
125.0
80
349.8
148.5
40
405.0
405.9
171.9
500
460.2
195.4
60
515. 5
516. 4
218.8
219.2
295. 5
125.4
381
350.7
148.9
441
172.3
501
461.2
195.8
561
22
296.4
125.8
82
351.6
149.3
42
406.9
172.7
02
462.1
196.2
62
517. 3
219.6
23
297.3
126.2
83
352.6
149.7
43
407.8
173.1
03
463.0
196.6
63
518.2
220.0
24
298.2
126. 6
84
353.5
1.50.0
44
408.7
173.5
04
463.9
197.0
64
519.2
220.4
25
299.2
127.0
85
354.4
150. 4
45
409.6
173.9
05
464.9
197.4
65
520.1
220.8
26
300.1
127.4
86
355.3
150. 8
46
410.5
174.3
06
465.8
197.8
66
521.0
221. 2
27
301.0
127.8
87
356.2
151.2
47
411.5
174.7
07
466.7
198. 1
67
521.9
221.6
28
301.9
128.2
88
357.2
151.6
48
412.4
175.1
08
467.6
198.5
68
522.8
222.0
29
302.8
128.6
89
358.1
152.0
49
413. 3
175.4
09
468.5
198.8
69
523.8
222.3
30
331
303.8
128.9
90
359.0
152.4
50
414.2
415. 2
175.8
10
469.5
470.4
199.3
70
524.7
222.7
223.1
304.7
129.3
391
359.9
152.8
451
176.2
511
199.7
571
525.6
32
305.6
129.7
92
360.8
1.53. 2
52
416.1
176.6
12
471.3
200.0
72
526.5
223.4
33
306.5
130.1
93
361.8
1.53. 6
53
417.0
177.0
13
472.2
200.4
73
527.4
223.8
34
307.5
130.5
94
362.7
154.0
54
417.9
177.4
14
473.1
200.8
74
528.4
224.2
35
308.4
130.9
95
363.6
154.3
55
418.8
177.8
15
474.0
201.2
75
529.3
224.6
36
309.3
131.3
96
364. 5
1.54. 7
56
419.8
178.2
16
475.0
201.6
76
530.2
225.
37
310.2
131.7
97
365.4
1.55. 1
57
420.7
178.6
17
475.9
202.0
77
531.1
225.4
38
311. 1
132.1
98
366.4
155.5
58
421.6
179.0
18
476.8
202.4
78
532.0
225. 8
39
312.1
132.5
99
367.3
155. 9
59
422.5
179.4
19
477.7
202.8
79
533.
226.2
40
313.0
132.9
400
368.2
156.3
60
461
423.4
424. 4
179.7
20
478.6
479. 6
203.2
80
533.9
226.6
341
313.9
133.2
401
369.1
156.7
180.1
521
203.6
581
534.8
227.0
42
314.8
133.6
02
370.0
157.1
62
425.3
180.5
22
480. 5
204.0
82
535. 7
227.4
43
315.7
134.0
03
371.0
157.5
63
426.2
180.9
23
481.4
204.4
83
536.6
227.8
44
316.7
134.4
04
371.9
157.9
64
427.1
181.3
24
482.3
204.8
84
537.6
228.2
45
317.6
134.8
05
372.8
158. 3
65
428.0
181.7
25
483.2
205. 2
85
538.5
228.6
46
318.5
135.2
06
373. 7
158.6
66
429.0
182.1
26
484.2
205. 5
86
539.4
229.0
47
319.4
135.6
07
374. 6-
159.0
67
429.9
182.5
27
485. 1
205.9
87
540.3
229.4
48
320.3
136.0
08
375. 6
159.4
68
430.8
182.9
28
486.0
206.3
88
541.2
229.8
49
321.3
136.4
09
376.5
159. 8
69
431.7
183.3
29
486.9
206.7
89
542.2
230.2
50
322.2
136.8
10
377. 4
378.3
160.2
160.6
70
471
432.6
183.7
30
487.8
488. 8
207. 1
90
543. 1
544.0"
230.6
351
323.1
137.2
411
433.6
184.0
531
207.4
591
231.0
52
324.0
137.5
12
379. 3
161.0
72
434.5
184.4
32
489.7
207.8
92
544.9
231.3
53
324.9
137.9
13
380.2
161.4
73
435. 4
184.8
33
490. 6
208.2
93
545.8
231.7
54
325.9
138.3
14
,381. 1
161.8
74
436.3
185.2
34
491.5
208.6
94
546.8
232.0
55
326.8
138.7
15
382. 0'
162.2
75
437.2
18.5.6
35
492.5
209.0
95
547.7
232.4
56
327.7
139.1
16
382.9
162.5
76
438. 2
186.0
36
493.4
209.4
96
548. 6
232.8
57
328. 6
139.5
17
383.9
162.9
77
4.39. 1
186.4
37
494.3
209.8
97
549. 5
233. 2
58
329.5
139.9
18
384.8
163.3
78
440.0
186.8
38
495. 2
210. 2
98
550. 4
233.6
59
330. 5
140.3
19
385.7
163.7
79
440.9
187.2
39
496.1
210.6
99
551. 3
234.0
60
331.4
140.7
20
386.6
164.1
80
441.8
187.6
40
497.1
211.0
600
552.3
234.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
57°(11
3°, 247=
, 293°
.
TABLE 2.
[Page 577 j
Difference of Latitude and Departure for 24° ( 156
°, 204°, 336°).
Dist.
1
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
0.9
0.4
61
55.7
24.8
121
110.5
49.2
181
165.4
73.6
241
220.2
98.0
2
1.8
0.8
62
56.6
25.2
22
111.5
49.6
82
166. 3
74.0
42
221. 1
98.4
3
2.7
1.2
63
57.6
25.6
23
112.4
50.0
83
167.2
74.4
43
222.0
98.8
4
3.7
1.6
64
58.5
26.0
24
113.3
50.4
84
168.1
74.8
44
222.9
99.2
5
4.6
2.0
65
59.4
26.4
25
114.2
50.8
85
169.0
75.2
45
223. 8
99.7
6
5.5
2.4
66
60.3
26.8
26
115.1
51.2
86
169.9
75. 7
46
224.7
100.1
7
6.4
2.8
67
61.2
27.3
27
116.0
51.7
87
170.8
76.1
47
225. 6
100.5
8
7.3
3.3
68
62.1
27.7
28
116.9
52.1
88
171.7
76.5
48
226.6
100.9
9
8.2
3.7
69
63.0
28.1
29
117.8
52.5
89
172.7
76.9
49
227.5
101.3
10
9.1
4.1
4.5
70
63.9
28.5
30
118.8
119.7
52.9
53. 3
90
173.6
77.3
50
228.4
101.7
102. 1
11
10.0
71
64.9
28.9
131
191
174.5
77.7
251
229.3
12
11.0
4.9
72
65.8
29.3
32
120.6
53.7
92
175.4
78.1
52
230.2
102.5
13
11.9
5.3
73
66.7
29.7
33
121. 5
54.1
93
176.3
78.5
53
231.1
102.9
14
12.8
5.7
74
67.6
30.1
34
122.4
54.5
.94
177.2
78.9
54
232.
103.3
15
13.7
6.1
75
68.5
30.5
35
123.3
54.9
95
178.1
79.3
55
233.
103.7
16.
14.6
6.5
76
69.4
30.9
36
124.2
55.3
96
179.1
79.7
56
233.9
104.1
17
15.5
6.9
77
70.3
31.3
37
125.2
55.7
97
180.0
80.1
57
234.8
104.5
18
16.4
7.3
78
71.3
31.7
38
126.1
56.1
98
180.9
80.5
58
235.7
104.9
19
17.4
7.7
79
72.2
32.1
39
127.0
56.5
99
181.8
80.9
59
236.6
105.3
20
18.3
19.2
8.1
80
73.1
32.5
3279
40
127.9
128.8
56.9
200
182.7
183. 6
81.3
60
237. 5
105.8
106:2
21
8.5
81
74.0
141
57.3
201
81.8
2(31
238.4
22
20.1
8.9
82
74.9
33.4
42
129.7
57.8
02
184.5
82.2
62
239.3
106.6
23
21.0
9.4
83
75.8
33.8
43
130.6
58.2
03
185. 4
82.6
63
240.3
107.0
24
21.9
9.8
84
76.7
34.2
44
131.6
58.6
04
186.4
83.0
64
241.2
107.4
25
22.8
10.2
85
77.7
34.6
45
132.5
59.0
05
187.3
83.4
65
212. 1
107.8
26
23.8
10.6
86
78.6
35.0
46
133.4
59.4
06
188.2
83.8
66
243.0
108.2
27
24.7
11.0
87
79.5
35.4
47
134.3
■59.8
07
189.1
84.2
67
243.9
108. 6
28
25.6
11.4
88
80.4
35.8
48
135.2
60.2
08
190.0
84.6
68
244.8
109.
29
26.5
11.8
89
81.3
36.2
49
136.1
60.6
09
190.9
85.0
69
245.7
109.4
30
27.4
28.3
12.2
12.6
90
82.2
m.e
50
137.0
61.0
10
191.8
192. 8
85.4
70
246.7
109.8
31
91
83.1
37.0
151
137.9
61.4
211
85.8
271
247.6
110.2
32
29.2
13.0
92
84.0
37.4
52
138. 9 1 61. 8
12
193.7
86.2
72
248.5
110.6
33
30.1
13.4
93
85.0
.37.8
53
139. 8 : 62. 2
13
194.6
86.6
73
249. 4
111.0
34
31.1
13.8
94
85.9
38.2
54
140. 7 62. 6
14
195. 5
87.0
74
250. 3
111.4
35
32.0
14.2
95
86.8
38.6
55
141.6 I 63.0
15
196.4
87.4
75
251.2
111.9
36
32.9
14.6
96
87.7
39.0
56
142. 5 : 63. 5
16
197.3
87.9
76
252. 1
112. 3
37
33.8
15.0
97
88.6
39.5
57
143.4 63.9
17
198.2
88.3
77
253.1
112.7
38
34.7
15.5
98
89.5
39.9
58
144. 3 i 64. 3
18
199.2
88.7
78
254.
113.1
39
35.6
15.9
99
90.4
40.3
59
145. 3 i 64. 7
19
200.1
89.1
79
254. 9
113.5
40
36.5
37.5
16.3
16.7
100
91.4
40.7
60
146.2
147. 1
65.1
20
201.0
201.9
89.5
80
255. 8
2.56. 7
11.3.9
114.3
41
101
92.3
41.1
161
65.5
221
89.9
281
42
38.4
17.1
02
93.2
41.5
62
148.0 1 65.9
22
202.8
90.3
82
257.6
114.7
43
39.3
17.5
03
94.1
41.9
63
148. 9 ! 66. 3
23
203.7
90.7
83
258. 5
116.1
44
40.2
17.9
04
95.0
42.3
64
149. 8 1 66. 7
24
204.6
91.1
84
259.4
115.5
45
41.1
18.3
05
95.9
42.7
65
150. 7
67.1
25
205. 5
91.5
85
260.4
115.9
46
42.0
18.7
06
96.8
43.1
66
151.6
67.5
26'
206.5
91.9
86
261.3
116. 3
47
42.9
19.1
07
97.7
43.5
67
1.52. 6
67.9
27
207.4
92.3
87
262.2
116.7
48
43.9
19.5
08
98.7
43.9
68
153.5
68.3
28
208.3
92.7
88
263.1
117.1
49
44.8
19.9
09
99.6
44.3
69
154.4
68.7
29
209.2
93.1
89
264.0
117.5
50
45.7
20.3
10
100.5
44.7
70
155.3
69.1
69.6
30
231
210.1
93.5
90
264.9
118.0
51
46.6
20.7
111
101.4
45.1
171
156. 2
211.0
94.0
291
265.8
118.4
52
47.5
21.2
12
102.3
45.6
72
157. 1 70.
32
211.9
94.4
92
266.8
118.8
53
48.4
21.6
13
103.2
46.0
73
158.0 70.4
33
212.9
94.8
93
267.7
119.2
54
49.3
22.0
14
104.1
46.4
74
159. ! 70. 8
34
213. 8
95.2
94
268.6
119.6
55
50.2
22.4
15
105. 1
46.8
75
159. 9
71.2
35
214.7
95.6
95
269.5
120.0
56
51.2
22.8
16
106.0
47.2
76
160.8
71.6
.36
215.6
96.0
96
270.4
120.4
57
52.1
23.2
17
106.9
47.6
77
161.7
72.0
37
216.5
96.4
97
271.3
120.8
58
53.0
23.6
18
107.8
48.0
78
162. 6
72.4
38
217.4
96.8
98
272. 2
121.2
59
53.9
24.0
19
108.7
48.4
79
163. 5
72.8
38
218.3
97.2
99
273^2
121.6
60
54.8
24.4
20
109.6
48.8
80
164.4
73.2
40
219.3
97.6
300
274.1
122.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
f
6° (1
i", 24<)°, 294°
)•
_,
24972
12 27
Page 578]
TABLE 2.
Difference of Latitude and Departure for 24° (156°, 204°, 336°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
275.0
122.4
361
329.8
146.8
421
384.6
171.2
481
439.4
195.6
541 494. 2
220.0
02 1 275. 9
122.8
62
330.7
147.2
22
385. 5
171.6
82
440.3
196.0
42
495.1
220.4
03
276.8
123.2
63
331.6
147.6
23
386.4
172.1
83
441.2
196.5
43
496.0
220.9
04
277.7
123. 7
64
332.5
148.1
24
387.3
172.5
84
442.1
196.9
44
496.9
221.3
05
278.6
124.1
65
333.4
148.5
25
388.2
172.9
85
443.0
197.3
45
497.8
221.7
06
279.5
124.5
66
334.3
148.9
26
389.2
173.3
86
444.0
197.7
46
498.8
222.1
07
280.4
124.9
67
335. 3
149.3
27
390.1
173.7
87
444.9
198.1
47
499.7
222.5
08
281.4
125. 3
68
336.2
149.7
28
391.0
174.1
88
445.8
198.5
48
500.6
222.9
09
282.3
125.7
69
,337. 1
150. 1
29
391.9
174.5
89
446.7
198.9
49
501.5
223.3
10
283.2
126.1
70
338.0
150.5
30
392.8
174.9
90
447.6
199.3
50
502.4
503. 4
223.7
311
284.1
126.5
371
338.9
150.9
431
393.7
175.3
491
448.6
199.7
551
224.1
12
285.0
126.9
72
.339. 8 ; 151. 3
32
394. 6
175.7
92
449.5
200.1
52
504.3
224.5
13
285.9
127.3
73
340.7
151.7
33
395.6
176.1
93
450.4
200.5
53
505.2
224.9
14
286.8
127.7
74
341.7
152.1
34
396. 5
176.5
94
451.3
200.9
54
506.1
225. 3
15
287.8
128.1
75
342.6
152.5
35
397.4
176.9
95
452.2
201.3
55
507.0
225.7
16
288.7
128.5
76
343. 5
152.9
36
398.3
177.3
96
453.1
201.7
56
507.9
226.1
17
289.6
128.9
77
344.4
1.53. 3
37
399.2
177.7
97
454.0
202.2
57
508.8
226.6
18
290.5
129.3
78
345. 3 : 153. 7
38 400. 1
178.2
98
454.9
202.6
58
509.7
227.0
19
291.4
129.8
79
346. 2 1 154. 2
39 1 401.
178.6
99
455.8
203.0
59
510.6
227.4
20
292.3
130.2
80
347.1
348.1
154.6
40 1 402.0.
179.0
500
456.8
203.4
60
511.6
227.8
321
293.2
130.6
381
1-55.
441 ; 402.9
179.4
501
457.7
203.8
561
512.5
228. 2
22
294,2
131.0
82
349.0
155.4
42 403. 8
179.8
02
458.6
204.2
62
513.4
228.6
23
295.1
131.4
83
349.9
155.8
43 404. 7
180.2
03
459.5
204.6
63
514.3
229.0
24
296.0
131.8
84
350.8
156.2
44 ! 405. 6
180.6
04
460.4
205.0
64
515.2
229.4
25
296.9
132.2
85
351.7
156.6
45 1 40C.5
181.0
05
461.3
205.4
65
516.1
229.8
26
297.8
132.6
86
352.6
157.0
46 1 407.4
181.4
06
462. 2
205.8
66
517.0
230.2
27
298.7
133.0
87
353.5
157. 4
47 1 408.3
181.8
07
463.2
206.2
67
518.0
230.6
28
299.6
133.4
88
354.4
157.8
48 : 409. 3
182.2
08
464.1
206.6
68
518.9
231.0
29
300.5
133.8
89
355.4
158.2
49 410. 2
182.6
09
465.0
207.0
69
519.8
231. 4
30
301.5
134.2
90
356.3
1.58. 6
50
411.1
412.0
183.0
183. 4
10
511
465.9
207.4
70
520. 7
231.8
331
302.4
134.6
391
357. 2 i 159.
451
466.8
207.8
571
521.6
232.2
32
303.3
135.0
92
358.1
159.4
52 : 412.9
183. 8
12
467.7
208.2
72
522.5
232.7
33
304.2
135.4
93
359.0
159.8
.53 413.8
184.3
13
468.6 208.7
73
523.4
233.1
34
305.1
135.9
94
359.9
160.3
,54 414. 7
184.7
14
469.5
209.1
74
524.3
233.5
35
,306.
136.3
95
360.8
160.7
55
415.7
185.1
15
470. 5
209.5
75
525.3
233. 9
36
,306. 9
136.7
96
361.8
161.1
56
416.6
185. 5
16
471.4
209.9
76
526.2
234.3
37
307.9
137.1
97
362.7
161.5
57
417.5
185.9
17
472.3
210.3
77
527.1
234.7
38
308.8
137.5
98
363.6
161.9
58
418.4
186.3
18
473.2
210.7
78
528.
235. 1
39
309.7
137.9
99
364.5
162.3
59
419.3
186.7
19
474.1
211.1
79
528.9
235. 5
40
310.6
311.5
138.3
400
365.4
'366. 3
162.7
60
420.2
187.1
20
475.0
211.5
80
529.8
235.9
2.36. 3
341
138.7
401
163.1
461
421.1
187.5
521
475.9
211.9
581
530.8
42
312. 4
139.1
02
367.2
163.5
62
422.0
187.9
22
476.8
212.3
82
531.7
236. 7
43
313.3
139.5
03
368.2
163.9
63
423.0
188.3
23
477.8
212.7
83
532.6
237.1
44
314.3
139.9
04
369.1
164.3
64
423.9
188.7
24
478.7
213.1
84
533.5
237. 5
45
315. 2
140.3
05
370.0
164.7
65
424.8
189.1
25
479.6
213.5
85
534.4
237. 9
46
316. 1
140.7
06
370.9
165.1
66
425.7
189.5
26
480.5
213.9
86
535.3
238.3
47
317.0
141.1
07
371.8
165.5
67
426.6
189.9
27
481.4
214.4
87
5.36. 2
238.8
48
317.9
141.5
08
372.7
165.9
68
427.5
190.4
28
482.3
214.8
88
537.1
2.39. 2
49
318.8
142.0
09
373.6
166.4
69
428.4
190.8
29
483.2
215.2
89
538.0
239. 6
50
319. 7
142.4
10
374.5
166.8
70
429.4
191.2
30
484.2
215. 6
90
539.0
240.0
351
320.6
142.8
411
375.5
167.2
471
430.3
191.6
531
485.1
216.0
591
539.9
240.4
52
321.6
143.2
12
376.4
167.6
72
431.2
192.0
32
486.0
216.4
92
540.8
240.8
53
322.5
143.6
13
377.3
168.0
73
432.1
192.4
33
486.9
216.8
93
541.7
241.2
54
323.4
144.0
14
378.2
168.4
74
433.
192.8
34
487.8
217.2
94
542.6
241.6
55
324.3
144.4
15
379.1
168.8
75
433.9
193.2
35
488.7
217.6
95
543.5
242.0
56
325.2
144.8
16
380.0
169.2
76
434.8
193.6
36
489.6
218.0
96
544.4
242.4
57
326.1
145.2
17
380.9
169.6
77
435.8
194.0
37
490.6
218.4
97
545.4
242.8
58
327.0
145.6
18
381.9
170.0
78
436.7
194.4
38
491.5
218.8
98
546. 3
243.2
59
328.0
146.0
19
382.8
170.4
79
437.6
194.8
39
492.4
219.2
99
547.2
243.6
60
328.9
146.4
20
383.7
170.8
80
438.5
195. 2 40
493.3
219.6
600
548.1
244,0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat. Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
66° (114°, 246°, 294°).
TABLE
2.
[Page
679
Difference of Latitude and Departure for 25° (155°, 205°, 335°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
55.3
25.8
121
109.7
51.1
181
164.0
76.5
241
218.4
101.9
2
1.8
0.8
62
56.2
26.2
22
110.6
51.6
82
164.9
76.9
42
219.3
102. 3
3
2.7
1.3
63
57.1
26.6
23
111.5
52.0
83
165.9
77.3
43
220.2
102.7
4
3.6
1.7
64
58.0
27.0
24
112.4
52.4
84
166.8
77.8
44
221.1
103.1
5
4.5
2.1
65
58.9
27.5
25
113.3
52.8
85
167.7
78.2
45
222.0
103. 5
6
5.4
2.5
66
59.8
27.9
26
114.2
53.2
86
168.6
78.6
46
223.
104.0
7
6.3
3.0
67
60.7
28.3
27
115.1
53.7
87
169.5
79.0
47
223. 9
104.4
8
7.3
3.4
68
61.6
28.7
28
116.0
54.1
88
170.4
79.5
48
224.8
104.8
9
8.2
3.8
69
62.5
29.2
29
116.9
.54.5
89
171.3
79.9
49
225.7
105.2
10
9.1
4.2
70
63.4
29.6
30
117.8
54. 9
90
172.2
80.3
50
226.6
105. 7
11
10.0
4.6
71
64.3
30.0
131
118.7
55.4
191
173.1
80.7
251
227.5
106.1
12
10.9
5.1
72
65.3
30.4
32
119.6
55.8
92
174.0
81.1
52
228.4
106.5
13
11.8
5.5
73
66.2
30.9
.33
120.5
56.2
93
174.9
81.6
53
229.3
106.9
14
12.7
5.9
74
67.1
31.3
.34
121.4
56.6
94
175.8
82.0
54
230.2
107.3
15
13.6
6.3
75
68.0
31.7
35
122.4
.57.1
95
176.7
82.4
55
231.1
107.8
16
14.5
6.8
76
68.9
32.1
36
123.3
57.5
96
177.6
82.8
56
232.0
108.2
17
15,4
7.2
77
69.8
32. 5
37
124.2
57.9
97
178.5
83.3
57
232.9
108.6
18
16.3
7.6
78
70.7
33.0
38
125. 1
.58.3
98
179.4
83.7
58
233. 8
109.0
19
17.2
8.0
79
71.6
33.4
39
126.0
58.7
99
180.4
84.1
59
234.7
109.5
20
18.1
19.0
8.5
80
72.5
33.8
34.2
40
126.9
127.8
59.2
59.6
200
181.3
84.5
60
235.6
109.9
21
8.9
81
73.4
141
201
182. '2~
84.9
261
236.5
110.3
22
19.9
9.3
82
74.3
34.7
42
128.7
60.0
02
183.1
85.4
62
237.5
110.7
23
20.8
9.7
83
75.2
35.1
43
129.6
60.4
03
184.0
85.8
63
238.4
111.1
24
21.8
10.1
84
76.1
35.5
44
130.5
60.9
04
184.9
86.2
64
239.3
111.6
25
22.7
10.6
85
77.0
.35. 9
45
131.4
61.3
05
185.8
86.6
65
240.2
112.0
26
23.6
n.o
86
77.9
36.3
46
132.3
61.7
06
186.7
87.1
66
241.1
112.4
27
24.5
11.4
87
78.8
36.8
47
133.2
62.1
07
187.6
87.5
67
242.0
112.8
28
25.4
11.8
88
79.8
37.2
48
134.1
62.5
08
188.5
87.9
68
242.9
113.3
' 29
26.3
12.3
89
80.7
.37.6
49
135.0
63.0
09
189.4
88.3
69
243.8
113.7
30
27.2
12.7
90
81.6
38.0
38."5
50
151
135.9
63.4
10
190. 3
88.7
70
244.7
114.1
31
28.1
13.1
91
82.5
136.9
63.8
211
191.2
89.2
271
245.6
114.5
32
29.0
13.5
92
as. 4
38.9
52
137.8
64.2
12
192.1
89.6
72
246.5
115.0
33
29.9
13.9
93
84.3
39.3
53
138.7
64.7
13
193.
90.0
73
247.4
115. 4
34
30.8
14.4
94
85.2
39.7
54
139.6
65.1
14
193.9
90.4
74
248.3
115.8
35
31.7
14.8
95
86.1
40.1
55
140.5
65.5
15
194.9
90.9
75
249.2
116.2
36
32.6
15.2
96
87.0
40.6
56
141.4
65.9
16
195.8
91.3
76
250.1
116.6
37
33.5
15.6
97
87.9
41.0
57
142.3
66.4
17
196.7
91.7
77
251.0
117.1
38
34.4
16.1
98
88.8
41.4
58
143.2
66.8
18
197.6
92.1
78
252.0
117.5
39
35.3
16.5
99
89.7
41.8
59
144.1
67.2
19
198.5
92.6
79
252.9
117.9
40
36.3
16.9
100
90.6
42.3
60
145.0
67.6
20
221
199.4
200.3
93.0
80
253.8
118.3
41
37.2
17.3
101
91.5
42.7
161
145.9
68.0
93.4
281
254.7
118.8
42
38.1
17.7
02
92.4
43.1
62
146.8
68.5
22
201.2
93.8
82
255. 6
119. 2
43
39.0
18.2
03
93.3
43.5
63
147.7
68.9
23
202.1
94.2
83
2.56. 5
119.6
44
39.9
18.6
04
94.3
44.0
64
148.6
69.3
24
203.0
94.7
84
257.4
120.0
45
40.8
19.0
05
95.2
44.4
65
149.5
69.7
25
203.9
95.1
85
258.3
120.4
46
41.7
19.4
06
96.1
44.8
66
150. 4
70.2
26
204.8
95.5
86
259.2
120.9
47
42.6
19.9
07
97.0
45.2
67
151.4
70.6
27
205.7
95.9
87
260.1
121. 3
48
43.5
20.3
08
97.9
45.6
68
1.52. 3
71.0
28
206.6
96.4
88
261.0
121.7
49
44.4
20.7
09
98.8
46.1
69
153.2
71.4
29
207.5
96.8
89
261.9
122.1
50
45.3
21.1
10
ill
99.7
46.5
70
in
154.1
71.8
30
208.5
97.2
'97.6
90
262.8
263.7
122.6
123.0
51
46.2
21.6
100.6
46.9
155.0
72.3
231
209.4
291
52
47.1
22.0
12
101. 5
47.3
72
155.9
72.7
32
210.3
98.0
92
264.6
123.4
53
48.0
22.4
13
102.4
47.8
73
156. 8
73.1
.33
211.2
98.5
93
265. 5
123. 8
54
48.9
22.8
14
103. 3
48.2
74
157.7
73.5
34
212.1
98.9
94
266.5
124.2
55
49.8
23.2
15
104.2
48.6
75
158.6
74.0
35
213.0
99.3
95
267.4
124.7
56
50.8
23.7
16
105. 1
49.0
76
159.5
74.4
36
213. 9
99.7
96
268. 3.
125. 1
57
51.7
24.1
17
106.0
49.4
77
160.4
74.8
37
214.8
100.2
97
269.2
125. 5
58
52.6
24.5
18
106.9
49.9
78
161.3
75.2
38
215. 7
100.6
98
270.1
12.5.9
•59
53.5
24.9
19
107.9
50.3
79
162.2
75.6
39
216.6
101.0
99
271.0
126.4
60
54.4
25.4
20
108.8
50.7
80
163.1
76.1
40
217.5
101.4
300
271.9
126.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
35° (115°, 245
°, 295°
)•
Page 680]
TABLE -2.
Difference of Latitude and Departure for 25° (155°, 205°, 335°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
272.8
127.2
361
327.1
152.5
421
381.5
177.9
481
435.9
203.3
541
490.3
228. 6
02
273.7
127.6
62
328.0
153.0
22
382.4
178.3
82
436.8
203.7
42
491.2
229.0
03
274.6
128.0
63
329.0
153.4
23
383.3
178.7
83
437.7
204.1
43
492.1
229. 4
04
275.5
128.4
64
329.9
153. 8
24
384.2
179.2
84
438.6
204. 5
44
493.0
229.9
05
276.4
128. 9
65
330. 8
154.2
25
385. 1
179.6
85
439.5
204.9
45
493.9
230.3
06
277.3
129.3
66
331.7
1.54. 6
2()
386.0
180.0
86
440.4
205. 4
46
494.8
2.30. 7
07
278.2
129.7
67
332.6
155.1
27
387.0
180. 4
87
441.3
205.8
47
495.7
231.1
08
279.1
130.1
68
333. 5
155.5
28
387. 9
180.9
88
442.2
206.2
48
496.6
231.6
09
280.0
130.6
69
334. 4
155.9
29
388.8
181.3
89
443.1
206.6
49
497. 6
232.
10
280.9
131.0
70
335.3
156.3
30
389.7
181.7
90
444.0
207.1
50
498.4
232.4
311
281.8
131.4
371
336.2
156. 8
431
390.6
182. 1
491
444.9
207. 5
551
499. 3
232. 8
12
282.7
131.8
72
337.1
157.2
32
391. 5
182.5
92
445.9
207.9
52
500.2
233. 2
13
283.6
132.2
73
338.0
157.6
33
392.4
183.0
93
446. 8
208. 3
53
501.1
233. 7
14
284.5
132. 7
74
338.9
158.0
34
393.3
183.4
94
447.7
208.7
54
502.0
234.1
15
285.4
133. 1
75
339.8
158. 5
35
394.2
183. 8
95
448. 6 i 209. 1
55
503.0
234.5
16
286.4
133.5
76
340.7
158.9
36
395. 1
184.2
96
449.5
209. 6
56
503.9
235.
17
287.3
133.9
77
341.6
1.59. 3
37
396. 1 184. 7
97
450. 4
210.
57
504.8
235.4
18
288.2
134.4
78
342.5
159.7
38
396. 9 1 185. 1
98
451.3
210.4
58
505.7
2a5.8
19
289. 1 1 134. 8
79
343.5
160.1
39
397. 8 • 185. 5
99
452.2
210.9
.59
506.6
2.36. 2
20
290. i 135. 2
80
344. 4
160.6
40
398.7 118.5.9
.500
.501
453.1 211.3
60
507.5
2.36. 6
321
290. 9 \ 135. 6
381
345.3
161.0
441
399.6 186.3
454.0 211.7
.561
508.4
237.1
22
291. 8 1 136. 1
82
346.2
161.4
42
400.6 186.8
02
454. 9 ! 212. 1
62
509.3
237. 5
23
292. 7 136. 5
83
347.1
161.8
43
401.5 187.2
03
4.55.8 212.5
63
510.2
237. 9
24
293. 6 1 136. 9
84
348.0
162.3
44
402.4 187.6
04
456.7 213.0
64
511.1
238.3
g5
294. 5 ! 137. 3
85
348. 9
162.7
45
403.3 188.0
05
457.7 213.4
65
512.0
238.7
26
295.4
137.7
86
349; 8
163.1
46
404. 2 1 188. 5
06
458.6 213.8
66
512.9
239.2
27
296.3
138.2
87
350.7
163.5
47
405.1 1188.9
07
459.5 1214.2
67
513.8
239.6
28
297.2
138.6
88
351.6
163. 9
48
406. 1 189. 3
08
460.4 1214.7
68
514.8
240.1
29
298.1
139.0
89
352.5
164.4
49
406. 9 1 189. 7
09
461.3
215.1
69
515.7
240. 5
30
331
299.0
30070"
139.4
90
353.4
164.8
50
407.8
190.1
10
462.2
215.5
215. 9
70
516.6
517. 5"
240.9
139. 9
391
354.3
165.2
451
408.7
190.6
511
463.1
571
241. S
32
300.9
140.3
92
355.2
165. 6
52
409.6
191.0
12
464.0
216.4
72
518. 4
241.7
33
301.8
140.7
93
356.1
166.1
53
410.5
191.4
13
464.9
216.8
73
519.3
242. 1
34
302.7
141.1
94
357.
166.5
54
411.4
191.8
14
465. 8
217. 2
74
520.2
242. 6
35
303.6
141.5
95
358.0
166.9
55
412. 3
192.3
15
466.7
217.7
75
521.1
243.
36
304.5
142.0
96
358. 9
167.3
56
413.2
192.7
16
467.6
218.1
76
522.0
243. 4
37
305.4
142.4
97
359.8
167.7
57
414.1
193. 1
17
468.5
218.5
77
522.9
243. 8
38
306.3
142.8
98
360.7
168.2
58
415.1
193.5
18
469.4
218.9
78
.523. 8
244. 3
39
307.2
143.2
99
361.6
168.6
59
416.0
194.0
19
470.3
219.3
79
524.7
244.7
40
341"
308.1
143.7
400
362.5
363.4
169.0
169. 4
60
416.9
194.4
20
471.2
219.8
80
52&.6
245. 1
"245.5
309.0
144. 1
401
461
417.8
194.8
521
472.2
220.2
581
526.5
42
309.9
144. 5
02
364.3
169.9
62
418.7
195.2
22
473. 1
220.6
82
527.4
246.
43
310.8
144.9
03
365.2
170. 3
63
419.6
195. 6
23
474.0
221.0
83
528.3
246. 4
44
311.7
145.4
04
366.1
170. 7
64
420.5
196.1
24
474.9
221. 4
84
529. 3
246.8
45
312.6
145.8
05
367.0
171.1
65
421.4
196. 5
25
475.8
221. 9
85
530.2
247.2
46
313.5
146.2
06
367.9
171.6
66
422.3
196.9
26
476.7
222.3
86
531. 1
247.7
47
314.5
146.6
07
368.8
172.0
67
423.2
197.3
27
477.6
222.7
87
532.
248.1
48
315.4
147.0
08
369.7
172. 4
68
424.1
197.8
28
478.5
223.2
88
532.9
248. 5
49
316.3
147. 5
09
370.6
172.8
69
425.0
198.2
29
479.4
223.6
89
533.8
248.9
50
317.2
147.9
10
371.5
173. 2
70
425.9
198.6
30
480.3
224.0
90
534.7
249.4
351
318.1
148.3
411
372.5
173. 7
471
426.8
199.0
531
481.2
224.4
.591
535.6
249.8
52
319.0
148.7
12
373.4
174.1
72
427.7
199.4
32
482.1
224.8
92
536.5
250.2
53
319.9
149.2
13
374.3
174.5
73
428.6
199.9
33
483.0
225. 3
93
537. 4
250. 6
54
320.8
149.6
14
375. 2
174. 9
74
429.6
200.3
34
483.9
225.7
94
538.3
251.1
55
321.7
150.
15
376.1
175. 4
75
430. 5
200.7
35
484.8
226.1
95
539.2
251.5
56
322.6
150. 4
16
377.0
175. 8
76
431.4
201.1
36
485. 7
226. 5
96
540.1
251.9
57
323.5
150. 8
17
377.9
176.2
77
432. 3
201.6
37
486.7
226.9
97
541.0
252.3
58
324.4
151. 3
18
378.8
176. 6
78
433.2
202.0
38
487. 6
227.4
98
541.9
252.7
59
325. 3
151.7
19
379.7
177.0
79
434.1
202. 4
39
488.5
227.8
99
542.8
253. 1
60
326.2
152.1
20
380.6
Dep.
177.5
80
435.
202.8
40
489.4
228.2
600
543.8
253. 6
Dist.
Dep.
Lat.
Dist.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
\
<
55° (1
15°, 245°, 295°
.
TABLE 2.
[Page 581
Difference of Latitude and Departure for 26° (154°, 206°, 334°
)•
Dist.
Lat.
Dep.
Dist.
Lat,
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.4
61
54.8
26.7
121
108.8
53.0
181
162.7
79.3
241
216.6
105.6
2
1.8-
0.9
62
.55. 7
27.2
22
109.7
5,3.5
82
163.6
79.8
42
217.5
106.1
3
2.7
1.3
63
56.6
27.6
23
110.6
53.9
83
164.5
80.2
43
218. 4,
106.5
4
3.6
1.8
64
57.5
28.1
24
111.5
54.4
84
165.4
80.7
44
219.3
107.0
5
4.5
2.2
65
58.4
28.5
25
112.3-
54.8
86
166.3 81.1
45
220.2
107.4 .
6
5.4
2.6
66
59.3
28.9
26
113.2
55.2
86
167.2 81.5
46
221.1
107.8
7
6.8
3.1
67
60.2
29.4
27 ' 114. 1
55.7
87
168.1 1 82.0
47
222.0
108. 3
8
7.2
3.5
68
61.1
29.8
28 : 115.0
56.1
88
169.0 1 82.4
48
222.9
108.7
9
8.1
3.9
69
62.0
30.2
29 115.9
56.5
89
169.9 1 82.9
49
223.8
109.2
10
9.0
4.4
70
62.9
30.7
30 ; 116.8
57.0
90
170.8
171.7
83.3
50
224.7
225.6
109. 6
11
9.9
4.8
71
63.8
31.1
131 1 117.7
57.4
191
83:7
251
110.0
12
10.8
5.3
72
64.7
31.6
32 ! 118.6
57.9
92
172.6
84.2
52
226.5
110.5
13
11.7
5.7
73
65.6
32.0
,33 I 119.5
58.3
93
173.5
84.6
53.
227.4
110.9
14
12.6
6.1
74
66.5
32.4
34 \ 120.4
58.7
94
174.4
8,5.0
54
228.3
111.3
15
13.5
6.6
K 75
67.4
32.9
35
121.3
59.2
95
175.3
8.5.5
55
229.2
111.8
16
14.4
7.0
76
68.3
,33. 3
36
122.2
59.6
96
176.2
85.9
56
230.1
112.2
17
15.3
7.5
77
69.2
33.8
37
123.1
60.1
97
177.1
86.4
57
231.0
112.7
18
16.2
7.9
78
70.1
34.2
38
124.0
60.5
98
178.0
86.8
58
231.9
113.1
19
17.1
8.3
79
71.0
34.6
,39
124.9
60.9
99
178.9
87.2
59
232.8
113. 5
20
18.0
18.9
8.8
9.2
80
71.9
3.5.1
40
125. 8
126.7
61.4
61.8
200
201
179.8
87.7
60
233.7
114.0
114.4
21
81
72.8
3.5.5
141
180.7
88.1
261
234. 6
22
19.8
9.6
82
73.7
3.5.9
42
127.6
62.2
02
181.6
88.6
62
236.5
114.9
23
20.7
10.1
S3
74.6
36.4
43
128.5
62.7
03
182. 5
89.0
63
2,36. 4
115.3
24
21.6
10.5
84
75.5
36.8
44
129.4
63.1
04
183.4
89.4
64
237. 3
115.7
25
22.5
11.0
85
76.4
37.3
45
1.30. 3
63.6
05
184.3
89.9
65
2,38. 2
116.2
26
2.3.4
n.4
86
77.3
37.7
46
1,31.2
64.0
06
185.2
90. 3
66
239. 1
116. 6
27
24.3
11.8
87
78.2
,38.1
47
132. 1
64. 4
07
186.1
90.7
67
.240.0
117.0
28
25.2
12.3
88
79.1
38.6
48
133.0
64.9
08
186.9
91.2
68
240.9
117.5
29
26.1
12.7
89
80.0
39.
49
1.33.9 ! 6,5.3
09 i 187.8
91.6
69
241.8
117.9
30
27.0
13.2
90
80.9
39.5
"39. 9
50
151
1,34. 8 1 65. 8
10 j 188. 7
92.1
70
242.7
243.6
118.4
118.8'
31
27.9
13.6
91
81.8
Ki6. 7
66.2
211
189.6
92. 5
271
32
28.8
14.0
92
82.7
40.3
52
136.6
66.6
12
190.5
92.9
72
244.5
119.2
33
29.7
14.5
93
83.6
40.8
53
137.5
67.1
13
191.4
93.4
73
245. 4
119.7
34
.30.6
14.9
94
84.5
41.2
54
138.4
67.5
14
192.3
93.8
74
246.3
120. 1
35
31.5
15.3
95
85.4
41.6
55
139.3
67.9
15 ' 193.2
94.2
10
247.2
120.6
36
32.4
15.8
96
86.3
42.1
56
140.2 i 68.4
16 . 194. 1
94.7
76
248.1
121.
37
33.3
16.2
97
87.2
42.5
57
141.1
68.8
17 ! 19.5.0
95.1
77
249.
121.4
38
,34.2
16.7
98
88.1
43.0
58
142.0
69.3
18
195.9
95.6
78
249.9
121.9
39
35.1
17.1
i19
89.0
43.4
59
142.9
69.7
19
196.8
96.0
79
2.50. 8
122.3
40
41
36.0
3t>. 9
17.5
100
101
89.9
90.8
43.8
60
143.8
144.7
70.1
20
197.7
96.4
80
251.7
122. 7
18.0
44.3
161
70.6
221 ! 198.6
96.9
281
252.6
123. 2
42
37.7
18.4
02
91.7
44.7
62
145.6
71.0
22
199.5
97.3
82
253. 6
123.6
43
38.6
18.8
03
92.6
45.2
63
146.5
71.5
23
200.4
97.8
83
254. 4
124. 1
44
39.5
19.3
04
93.5
45.6
64
147.4
71.9
24
201.3
98.2
84
255. 3
124. 5
45
40.4
19.7
05
94.4
46.0
65
148.3
72.3
25
202.2
98.6
85
2.56. 2
124.9
46
41.3
20.2
06
95.3
46.5
66
149. 2
72.8
26 ! 203. 1
99.1
86
257. 1
12,5.4
47
42.2
20.6
07
96.2
46.9
67
1.50.1
7,3.2
27 204.0
99.5
87
258.0
125. 8
48
43.1
21.0
08
97.1
47.3
68
151.0
7,3.6
28 204. 9
99.9
88
258. 9
126.3
49
44.0
21.5
09
98.0
47.8
69
151.9
74.1
29 205. 8
100.4
89
259.8
126.7
50
44.9
21.9
22.4
10
98.9
48.2
70
152.8
74.5
30 206. 7
100.8
90
260.7
127.1
51
45.8
111
99.8
48.7
171
153.7
7.5.0
231 i 207.6
101.3
291
261.5
127.6
52
46.7
22.8
12
100.7
49.1
72
1.54. 6
75.4
32
208.5
101.7
92
262.4
128.0
53
47.6
23.2
13
101.6
49.5
73
155. 5
75.8
33
209.4
102.1
93
263. 3
128.4
54
48.5
23.7
14
102. 5
50.0
74
156.4
76.3
34
210. 3
102.6
94
264.2
128.9
55
49.4
24.1
15
103.4
50.4
75
157.3
76.7
35 1 211.2
103.
95
265.1
129.3
56
50.3
24.5
16
104.3
.50. 9
76
158.2
77.2
36 j 212. 1
103. 5
96
266.0
129.8
57
51.2
25.0
17
105.2
51.3
77
159.1
77.6
37 1 213.0
103. 9
97
266.9
130. 2
58
52.1
2.5.4
18
106.1
51.7
78
160.0
78.0
,38
213.9
104. 3
98
267.8
130.6
59
53.0
25.9
19
107.0
52.2
79
160.9
78.5
39
214.8
104.8
99
268.7
131.1
60
53.9
26.3
20
107.9
52.6
80
161.8
78.9
40
215.7
105.2
300
269.6
131.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. I Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
64° (116°, 244°, 296°
)•
Pa
ge 582]
TABLE 2.
Difference of Latitude and Departure for 26° (154°, 206°, 334).
Dist.
Lat. i Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
270. 5 ' 132.
361
324. 5
158. 3
421
378. 4
184.6
481
432.3
210.9
641
486.2
237.2
02
271.4 :132.4
62
325. 4
158. 7
• 22
379. 3
185.
82
433. 2
211.3
42
487.1
237.6
03
272.3
132. 8
63
326.3
159.1
23
.380. 2
18,5.4
83
434. 1 211. 7
43
488.0
238.0
04
273.2
133. 3
64
327.2
159. 6
24
381.1
185. 9
84
435.0 212.2
44
488.9
238. 5
05
274.1
133. 7
65
328.1
160.0
25
382.0
186. 3
85
435.9 212.6
45
489.8
238.9
06
275.
134.1
66
329.0
160.4
26
.382. 9
186.7
86
436.8
213.0
46
490.7
2.39. 3
07
275.9
134.6
67
329.9
160.9
27
383.8
187.2
87
437.7
213.5
47
491. 6
2.39. 8
08
276.8
136.0
68
330.8
161.3
28
384. 7
187.6
88
438. 6
213.9
48
492.6
240.2
09
277. 7
135. 5
69
331.7
161.8
29
385. 6
188.1
89
439.5
214.4
49
493.4
240.7
10
278.6
135.9
70
332.6
162.2
30
431
386.5
387.4
188. 5
90
440. 4 j 214. 8
441. 3 , 215. 2
50
651
494.3
495.2
241.1
311
279.5
136.3
371
333. 5
162.6
188. 9
491
241.5
12
280.4
136.8
72
334.4
163.1
32
388.3
189.4
92
442. 2 \ 215. 7
52
496.1
242.0
13
281.3
137.2
73
335.3
163.5
33
389.2
189.8
93
443.1 j 216.1
53
497.
242.4
14
282.2
137.7
74
336.2
164.0
34
390.1
190. 3
94
444.0
216.6
54
497.9
242.9
15
283.1
138.1
75
337.1
164.4
35
391.0
190. 7
95
444.9
217.0
55
498.8
243. 3
16
284.0
138.5
76
338.
164.8
36
391 .9
191.1
96
445.8
217.4
56
499.7
243.7
17
284.9
139.0
77
338. 9
165.3
37
392.8
191.6
97
446.7
217.9
57
500.6
244.2
18
285.8
139.4
78
339.8
165.7
38
393.7
192.0
98
447.6
218.3
58
501. 5
244.6
19
286.7
13,9.8
79
340.7
166.2
39
394.6
192.4
99
448.5
218.7
59
502.4
245.0
20
287.6
140.3
80
341.5
166. 6
167.
40
395. 5
1^2.9
193. 3"
500
449.4
219.2
60
66r
503. 3
604.2
246.5
321
288. 5 i 140. 7
381
342.4
441
396.4
501
450.3
219.6
245. 9
22
289. 4 \ 141. 2
82
343.3
167. 5
42
397.3
193. 8
02
451. 2 j 220. 1
62
606. 1
246.4
23
290.3
141.6
83
344.2
167.9
43
398.2
194.2
03
452.1 i220.5
63
506.0
246.8
24
291.2
142.0
84
345. 1
168. 3
44
399. 1
194. 7
04
453.0 i 221.0
64
506.9
247.3
25
292.1
142. 5
85
346.0
168.8
45
400.0
195. 1
05
4.53.9 221.4
65
■507. 8
247.7
26
293.0
142.9
86
.346. 9
169.2
46
400.9
195.5
06
454. 8 : 221. 8
66
508.7
248.1
27
293.9
14.3. 4
87
347.8
169.7
47
401.8
196.0
07
4.55.7 I222.3
67
509.6
248.6
28
294.8
143.8
88
348. 7
170.1
48
402.7
196.4
08
456. 6 i 222. 7
68
510. 5
249.
29
295.7
144.2
89
349.6
170.5
49
403. 6
196.8
09
457.5
223.1
69
511.4
249.4
30
296.6
144.7
145. 1
90
.350. 5
171.0
50
404.5
197.3
197.7
10
458.4
223.6
70
512.3
249.9
331
297.5
391
351.4
171.4
451
405. 4
511
459. 3
224.0
571
513.2
2.50. 3
32
298.4
145. 6
92
352. 3
171.8
52
406.3
198.1
12
460.2
224.4
72
514. 1
250.8
33
299.3
146.0
93
353. 2
172. 3
53
407.2
198.6
13
461.1
224.9
73
51.5.
251. 2
34
300.2
146.4
94
354. 1
172.7
54
408.1
199.0
14
462.
225. 3
74
515.9
251.6
35
301.1
146.9
95
355.0
173. 2
55
409.0
199.5
15
462. 9 1 225. 8
75
516.8
252.1
36
302.0
147. 3
96
355. 9
173.6
56
409.9
199.9
16
463. 8 : 226. 2
76
517.7
262. 6
37
302.9
147.7
97
356.8
174.0
57
410.8
200. 3
17
464. 7 ' 226. 6
77
518.6
252. 9
38
303.8
148.2
98
357.7
174. 5
58
411.7
200.8
18
465. 6 1 227. 1
78
519. 5
253.4
39
304.7
148.6
99
358.6
174.9
59
412.6
201.2
19
466. 5 ! 227. 5
79
520.4
253.8
40
305.6
306.5
149.0
149. 5
400
401
359.5
175.4
60
413.5
201.7
20
467. 4 ' 228.
80
521.3
254.3
341
360.4
175.8
461
414.4
202. 1
521
468. 3 ! 228. 4
581
522.2
254.7
42
307.4
149.9
02
361.3
176.2
62
415. 2
202. 5
22
469. 2 '' 228. 8
82
523.1
256.1
43
308.3
150.4
03
362.2
176.7
63
416.1
203.0
23
470. 1 i 229. 3
83
524.0
255.6
44
309.2
150. 8
04
363.1
177.1
64
417.0
203.4
24
471. i 229. 7
84
524.9
2.56.
45
310.1
151. 2
05
364.0
177. 5
65
417.9
203.8
25
471.9
230.1
85
525. 8
256.4
46
311.0
151.7
06
364.9
178.0
66
418.8
204.3
26
472.8
230.6
86
526.7
256.9
47
311.9
152.1
07
365.8
178.4
67
419.7
204.7
27
473.7
231.0
87
527.6
257.3
48
312.8
152.6
08
366.7
178.9
68
420.6
205. 2
28
474.6
231.5
88
528.5
257.8
49
313. 7
153.
09
367.6
179.3
69
421.5
205.6
29
475.5
231.9
89
529.4
258.2
50
351
314.6
315.5
153.4
10
368. -5
179.7
70
422.4
206.0
30
476.4
232.3
90
530.3
258.6
259.1
153.9
411
369.4
180.2
471
423. 3
206.5
531
477.3
232.8
591
531.2
52
316.4
154. 3
12
370.3
180.6
72
424.2
206.9
32
478.2
233.2
92
532. 1
269.6,
53
317.3
154. 7
13
371.2
181.1
73
425.1
207.3
33
479.1
233.6
93
633.0
259.9
54
318.2
155. 2
14
372.1
181.5
74
426.0
207.8
34
480.0
234.1
94
633.9
260.4
55
319.1
1.55. 6
15
373.0
181.9
75
426.9
208.2
35
480.9
234.5
95
534.8
260.8
56
320.0
156.1
16
373.9
182.4
76
427.8
208.7
36
481.8
235.
96
635.7
261. 3
57
320.9
156.5
17
374.8
182.8
77 1 428. 7
209.1
37
482.7
2.35. 4
97
536.6
261.7
58
321.8
156.9
18
375.7
183.2
78 i 429.6
209.5
38
483.6
235.8
98
537.5
262.1
59
322.7
157.4
19
376.6
183.7
79
430.5
210.0
39
484.5
236.3
90
538.4
262.6
60
323.6
157.8
20
377.5
184.1
80
431.4
210.4
40
486.3
236.7
600
539.3
263.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
64°
(116°, 244°, 296°).
TABLE 2.
[Page 583
Difference of Latitude and Departure for
27° (153°, 207
°, 333°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
54.4
27.7
121
107.8
54.9
181
161.3
82.2
241
214.7
109.4
2
1.8
0.9
62
55.2
28.1
22
108.7
55.4
82
162.2
82.6
42 i 215.6
109.9
3
2.7
1.4
63
56.1
28.6
23
109.6
55.8
83
163.1
83.1
43 j 216.5
110.3
4
3.6
1.8
64
57.0
29.1
24
110.5
56.3
84
163.9
83.5
44 217.4
110.8
5
4.5
2.3
65
57. 9
29.5
25
111.4 i 56.7
85
164.8
84.0
45
218.3
111.2
6
5.3
2.7
66
58.8
30.0
26
112. 3 ! 57. 2
86
165.7
84.4
46
219.2
111.7
7
6.2
3.2
67
.59.7
30.4
27
113. 2 ! 57. 7
87
166.6
84.9
47
220.1
112.1
8
7.1
3.6
68
60.6
30.9
28
114.0 i 58.1
88
167.5
85.4
48
221.0
112.6
9
8.0
4.1
69
61.5
31.3
29
114.9 ' 58. 6
89
168.4
85.8
49
221.9
113.0
10
8.9
4.5
570
70
62.4
31.8
30
115.8 ' 59.0
116.7 1 59.5
90
169.3
170.2
86.3
86.7
50
222.8
113.5
114.0
11
9.8
71
63.3
32.2
131
191
251
22376"
12
10.7
5.4
72
64.2
32.7
32
117.6 i 59.9
92
171.1
87.2
52 224. 5
114.4
13
11.6
5.9
73
65.0
33.1
33
118.5 ; 60.4
93
172.0
87.6
53 i 225. 4
114.9
14
12.5
6.4
74
65.9
33.6
34
119.4 : 60.8
94
172.9
88.1
54 1 226. 3
115.3
15
13.4
6.8
75
66.8
34.0
35
120. 3 ; 61. 3
95
173.7
88.5
55 227.2
115.8
16
14.3
7.3
76
67.7
34.5
36
121.2 61.7
96
174.6
89.0
56 j 228. 1
116.2
17
15.1
7. 7
77
68.6
35.0
37
122.1
62.2
97
175.5
89.4
.57 1 229.0
116.7
18
16.0
8.2
78
69.5
35.4
38
123.0
62.7
98
176.4
89.9
.58 ; 229.9
117.1
19
16.9
8.6
79
70.4
35.9
39
123. 8
63.1
99
177.3
90.3
.59 1 230.8
117.6
20
17.8
9.1
9.5
80
81
71.3
36.3
40
124.7
1!>5.6
63.6
200
178.2
90.8
60 1 231.7
118.0
118.5
21
18.7
72.2
36.8
141
64.0
201
179.1
91.3
261 ! 2.32.6
22
19.6
10.0
82
73.1
37.2
42
126.5
64.5
02
180.
91.7
62 233. 4
118.9
23
20.5
10.4
83
74.0
37.7
43
127.4
64.9
03
180.9
92.2
63 234.3
119.4
24
21.4
10.9
84
74.8
38.1
44
128.3
65.4
04
181.8
92.6
64 ' 235. 2
119.9
25
22.3
11.3
85
75.7
38.6
45
129.2
6.5.8
05
182. 7
93.1
65 236. 1
120.3
26
23.2
11.8
86
76.6
39.0
46
130.1
66.3
06
183. 5
93.5
66 ': 237.
120.8
27
24.1
12.3
87
77.5
39.5
47
131.0
66. 7
07
184.4
94.0
67
237.9
121.2
28
24.9
12.7
88
78.4
40.0
48
131.9
67.2
08
185. 3
94.4
68
238.8
121.7
29
2.5.8
13.2
89
79.3
40.4
49
132.8
67.6
09
186.2
94.9
69
239.7
122.1
30
26.7
13.6
90
80.2
40.9
50
133.7
68.1
10
187.1
■95.3
70
240.6
122.6
31
27.6
14.1
91
81.1
41.3
151
134.5 1 68.6
211
188.0
95.8
271
241.5
123.0
32
28.5
14.5
92
82.0
41.8
52
135.4 69.0
12
188.9
96.2
72
242.4
123.5
33
29.4
15.0
93
82.9
42.2
53
136.3 ! 69.5
13
189.8
96.7
73
243.2
123.9
34
30.3
1.5.4
94
83.8
42.7
54
137. 2 1 69. 9
14
190.7
97.2
74
244.1
124.4
35
31.2
15.9
95
84.6
43.1
.55
138. 1 1 70. 4
15
191.6
97.6
75
245.0
124.8
36
32.1
16.3
96
85.5
43.6
56
139.0 i 70.8
16
192.5
98.1
76 ! 245.9
125.3
37
33.0
16.8
97
86.4
44.0
57
139.9 ! 71.3
17
193.3
98.5
77
246.8
125.8
38
33.9
17.3
98
87.3
44.5
58
140.8 j 71.7
18
194.2
99.0
78
247.7
126.2
39
34.7
17.7
99
88.2
44.9
59
141.7 i 72.2
19
195.1
99.4
79
248.6
126.7
40
35.6
18.2
18.6
100
89.1
45.4
60
142.6
143.5
72.6
20
196.0
99.9
80
249.5
250.4
127.1
41
36.5
101
90.0
45.9
161
73.1
221
196.9
100.3
281
127.6
42
37.4
19.1
02
90.9
46.3
62
144.3
73. 5
22
197.8
100.8
82
251.3
128.0
43
38.3
19.5
03
91.8
46.8
63
145.2
74.0
23
198.7
101.2
83
252.2
128.5
44
39.2
20.0
04
92.7
47.2
64
146.1
74.5
24
199.6
101.7
84
253.0
128.9
45
40.1
20.4
05
93.6
47.7
65
147.0
74.9
25
200.5
102.1
85
253. 9
129.4
46
41.0
20.9
06
94.4
48.1
66
147.9
7.5.4
26
201.4
102.6
86
254.8
129.8
47
41.9
21.3
07
95.3
48.6
67
148.8
75.8
27
202.3
103.1
87
255.7
130. 3
48
42.8
21.8
08
96.2
49.0
68
149.7
76.3
28
203.1
103.5
88
256.6
130.7
49
43.7
22.2
09
97.1
49.5
69
150.6
76.7
29
204.0
104.0
89
257.5
131.2
50
51
44.6
22.7
10
98.0
49.9
70
151.5
77.2
30
2M.9
104.4
90
258.4
131.7
45.4
23.2
HI
98.9
50.4
171
152.4
77.6
231
205.8
104.9
291
259.3
132.1
52
46.3
23.6
12
99.8
50.8
72
1.53. 3
78.1
32
206.7
105.3
92
260.2
132.6
53
47.2
24.1
13
100.7
51.3
73
154.1
78.5
33
207.6
105.8
93
261.1
133.0
54
48.1
24.5
14
101.6
51.8
74
155.
79.0
34
208. 5
106.2
94
262.0
133.5
55
49.0
25.0
15
102.5
52.2
75
155.9
79.4
35
209.4
106.7
95
262.8
133.9
56
49.9
25.4
16
103.4
52.7
76
156.8
79.9
36
210. 3
107.1
96
263.7
134.4
57
50.8
25.9
17'
104.2
53.1
77
157.7
80.4
37
211.2
107.6
97
264.6
134.8
58
51.7
26.3
18
105.1
53.6
78
158.6
80.8
38
212.1
108.0
98
265.5
135. 3
59
52.6
26.8
19
106.0
54.0
79
159.5
81.3
39
213.0
108.5
99
266.4
135.7
60
53.5
27.2
20
106.9
54.5
80
160.4
81.7
40
213.8
109.0
300
267.3
136.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
63° (1
17°, 243°, 297°
)•
Page 584]
TABLE 2.
Difference of Latitude and Departure for 27° (153°, 207
°, 333°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
268.2
136.7
361
321.7
163.9
421 375. 1
191.1
481
428.6
218.3
•541
482.0
245. 6
02
269. 1
137.1
62
322.5
164.4
22 : 376.0
191.6
82
429.4
218.8
42
482.9
246.1
03
270.0
137.6
63
323.4
164.8
23 j 376.9
192.0
83
430.3
219.2
43
483.8
246.5
04
270.9
138.0
64
324.3
165. 3
24 377.8
192.5
84
431.2
219.7
44
484.7
247.0
05
271.8
138.5
65
325.2
165.7
25 378. 7
193.0
85
432.1
220.1
45
485.6
247.4
06
272. 7
138.9
66
326.1
166.2
26 379.6
193.4
86
433.0
220. 6
46
486.4
247. 9
07
273.5
139.4
67
327.0
166.6
27 ' 380.5
193.9
87
433.9
221.1
47
487.3
248.4
08
274.4
1.39. 8
68
327.9
167.1
28 .381.4
194.3
88
434.8
221.5
48
488.2
248.8
09
275.3
140.3
69
328. 8
167. 5
29 382. 2
194.8
89
435.7
222.0
49
489.1
249.2
10
311
276.2
277.1
140.7
70
329. 7
168.0
30 383. 1
431 ! 384.0
195.2
195. 7
90
436.6
437.'5-.
222.4
"222"."9
50
551
490.0
249.7
141.2
371
330. 6
168.4
491
490.9
250.1
12
278.0
141.7
72
331.0
168.9
32 ' 384. 9 i 196. 1
92
438.3
223.3
52
491.8
250.6
13
278.9
142.1
73
332.3
169.3
33 385. 8 1 196. 6
93
439.2
223.8
53
492.7
251.0
14
279.8
142.6
74
333. 2
169.8
34 1 386.7 : 197.0
94
440. 1
224.2
54
493. 6
251.5
15
280.7
143.0
75
334.1
170.3
35 ; 387. 6 - 197. 5
95
441.0
224.7
55
494.5
252.0
16
281.6
143. 5
76
335.0
170.7
36 1 388. 5 ' 197. 9
96
441.9
225.2
56
495.4
252.4
17
282.5
143.9
77
335. 9
171.2
37 ! 389. 4 198. 4
97
442.8
225.6
57
496.3
252.9
18
283.3
144.4
78
336. 8
171.6
38 1 390. 3 198. 9
98
443.7
226.1
58
497.2
253. 3
19
284.2
144.8
79
337.7
172.1
39 ; 391.2 1199.3
99
444.6
226.5
59
498.1
253. 8
20
285.1
145. 3
80
338.6
172.5
40
392. ' 199. 8
500
445.5
227.0
60
499.0
2.54. 2
321
286.0
145.7
381
339. 5
173.
441
392. 9 2"00. 2
501 1 446. 4
227.5
561
499.8
254.7
22
286.9
146.2
82
340.4
173.4
42
393. 8 : 200. 7
02 ' 447. 3
227.9
62
500.7
2.55. 1
23
287.8
146.6
. 83
341.3
173.9
43
394. 7 i 201. 1
03 i 448.2
228.4
63
.501. 6
2.55. 6
24
288.7
147.1
84
342.1
174.3
44
395.6 1201.6
04
449.0
228.8
64
502.5
256.0
25
289.6
147.6
85
343.0
174.8
45
396.5
202.0
05
449.9
229.3
65
503. 4
256.5
26
290.5
148.
86
343.9
175.2
46
397.4
202.5
06
450. 8
229.8
66
.504. 3
257.
27
291.4
148.5
87
344.8
175.7
47
398.3
202.9
07
451.7
230.2
67
505. 2
257. 4
28
292.3
148.9
88
345.7
176.2
48
399. 2
203.4
08
452.6
230.6
68
506.1
257. 9
29
293.2
149.4
89
346.6
176.6
49
400.1 1203.8
09
453.5
231.0
69
507.0
258.3
30
294.0
149.8
150.3
90
.347. 5
34874"
177.1
177:5
50
401.0 L204.3
10
454.4
231.5
70
507.9
258. 8
259. 2
331
294. 9
391
451
401.8
204.7
511
455.3
231.9
571
508.7
32
295.8
150. 7
92
349. 3
178.0
52
402.7
205.2
12
456.2
232.4
72
509. 6
259.7
33
296.7
151.2
93
350.2
178.4
53
403. 6
205. 7
13
457.1
232.9
73
510.5
260.1
34
297.6
151.6
94
351.1
178.9
54
404.5
206.1
14
458.
233. 3
74
511.4
260.6
35
298.5
152.1
95
352.
179.3
55
405. 4
206.6
15
458.8
233.8
75
512.3
261.1
36
299.4
152. 5
96
352.8
179.8
56
406.3
207.0
16
459.7
234.2
76
513. 2
261.5
37
300.3
153.0
97
353.7
180.2
57
407.2
207.5
17
460.6
234.7
77
514.1
262.
38
301.2
153.5
98
354.6
180.7
58
408. 1
207.9
18
461.5
235. 2
78
515.0
262.4
39
302.1
153.9
99
355. 5
181.2
59
409.0
208.4
19
462.4
235.7
79
515. 9
262.9
40
341
302.9
154.4
"154. 8
400
356.4
"357. 3
181.6
60
461
409.9
.208. 8
209.3
20
521
463.3
464.2"
236. 1
80
516. 8
263.4
303. 8
401
182. 1
410.8
236.6
581
517.7
263. 8
42
304.7
155. 3
02
358.2
182.
62
411.6
209. 8
22
465.1
237.0
82
518.5
264.3
43
305.6
155.7
03
359. 1 183.
63
412.5
210.2
23
466.0
237.5
83
519. 4
264.7
44
306.5
156.2
04
360. 183. 4
64
•413.4
210.7
24
466.9
237.9
84
520. 3
265.2
45
307. 4
156.6
05
360. 9 183. 9
65
414. 3
211.1
25
467.8
238.4
85
.521.2
265.6
46
308.3
157.1
06
361. 8 184. 3
66
415.2
211.6
26
468.7
238.8
86
522.1
266.0
47
309.2
157.5
07
362. 6 184. 8
67
416.1
212.0
27
469.5
239.3
87
523.0
266.5
48
310.1
1.58.0
08
363.5 185.2
68
417.0
212.5
28
470.4
239. 7
88
523. 9
267.0
49
311.0
158.5
09
364.4 185.7
69
417.9
212.9
29
471.3
240.2
89
524. 8
267.4
50
311. 9
158.9
10
365. 3 186. 1
70
418.8
213.4
30
531
472.2
240.6
90
525.7
267.9
351
312.7
159.4
411
366. 2 186. 6
471
419.7
213.8
473.1
241.1
591
526.6
268."3"
52
313.6
159.8
12
367.1 187.1
72
420.6
214.3
32
474.0
241.5
92
527.5
268.8
53
314. 5
160.3
13
368.0
187.5
73
421.4
214.7
33
474.9
242.0
93
528. 4
269.2
54
315.4
160.7
14
368.9
188.0
74
422.3
215. 2
.34
475.8
242.4
94
529. 3
269. 7
55
316.3
161.2
15
369.8
188. 4
75
423.2
215.7
35
476.7
242.9
95
530. 1
270.1
56
317. 2
161.6
16
370.7
188.9
76
424.1
216.1
36
477. 6
243.4
96
.531.
270.6
57
318.1
162.1
17
371.6
189.3
77
425.0
216.6
37
478.4
243.8
97
531.9
271.1
58
319.0
162.5
18
372.4
189.8
78
425.9
217.0
38
479. 3
244.3
98
532. 8
271.5
59
319.9
163.0
19
373.3
190.2
79
426.8
217.5
39
480.2
244.7
99
533. 7
272.0
60
320.8
163.4
20
374.2
190.7
80
427.7
217.9
40
481.1
245.2
600
534.6
272.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat
(
33° (117°, 243°, 297°
.
TABLE 2.
[Page 585 j
Difference of Latitude and Departure for
28° (152°, 208°, 332°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
53.9
28.6
121
106.8
56.8
181
159.8
85.0
241
212.8
113.1
2
1.8
0.9
62
54.7
29.1
22
107.7
57.3
82
160.7
85.4
42
213. 7
113.6
3
2.6
1.4
63
.55.6
29.6
23
108.6
57.7
83
161.6
85.9
43
214. 6
114.1
4
3.5
1.9
64
.56.5
30.0
24
109.5
58.2
84
162.0
86.4
44
215.4
114.6
5
4.4
2.3
65
57.4
30.5
25
110.4
.58.7
85
163.3
86.9
45
216.3
115.0
()
5.3
2.8
66
.58.3
31.0
26
111.3
59.2
86
164.2
87.3
46
217.2
115.5
7
6.2
3.3
67
59.2
31.5
27
112.1
.59. 6
87
165.1
87.8
47
218.1
116.0
8
7.1
3.8
68
60.0
31.9
28
113.0
60.1
88
166.0
88.3
48
219.0
116.4
9
7.9
4.2
69
60.9
32.4
29
113.9
60.6
89
166.9
88.7
49
219.9
116. 9
10
8.8
4.7
70
61. 8
32.9
30
114.8
61.0
61.5
90
167.8
89.2
50
220.7
221.6
117.4
11
9.7
5.2
71
62?3-
33.3
131
115.7
191
168.6
89.7
251
117.8
12
10.6
.5.6
72
63.6
33.8
32
116.5
62.
92
169.5
90.1
52
222.5
118.3
13
11.5
6.1
73
64.5
34.3
33
117.4
62.4
93
170.4
90.6
53
223.4
118.8
14
12.4
6.6
74
65. 3
34.7
34
118.3
62.9
94
171.3
91.1
.54
224.3
119.2
15
13.2
7.0
75
66.2
35. 2
35
119.2
63.4
95
172.2
91.5
55
225.2
119.7
16
14.1
7.5
76
67. 1
35.7
36
120.1
63.8
96
173.1
92.0
56
226.0
120.2
17
15.0
8.0
77
68.0
36. 1
37
121.0
64.3
97
173.9
92.5
57
226.9
120.7
18
15.9
8.5
78
68.9
,36.6
38
121.8
64.8
98
174.8
93.0
58
227.8
121.1
19
16.8
8.9
79
69.8
37.1
39
122.7
65.3
99
175.7
93.4
59
228.7
121.6
20
17.7
9.4
80
70.6
37.6
38.0
40
123.6
65.7
200
176.6
177.5
93.9
60
229.6
122.1
21
18.5
9.9
81
71.5
141
124.5
66.2
201
94.4
261
230.4
122.5
22
19.4
10.3
82
72.4
38.5
42
125.4
66. 7
02
178.4
94.8
62
231.3
123.0
23
20.3
10.8
83
73.3
39.0
43
126.3
67.1
03
179.2
95.3
63
232.2
123. 5
24
21.2
11.3
84
74.2
39.4
44
127.1
67.6
04
180.1
95.8
64
233.1
123. 9
25
22.1
11.7
85
7.5.1
39.9
45
128.0
68.1
05
181.0
96.2
65
234.0
124.4
26
23.0
12 2
86
75.9
40.4
46
128.9
68.5
06
181.9
96.7
66
234.9
124.9
27
23.8
li;?
87
76.8
40.8
47
129.8
69.0
07
182. 8
97.2
67
235. 7
125.3
28
24.7
1.3.1
88
77. 7
41.3
48
130.7
69. 5
08
183. 7
97.7
68
236.6
125.8
29
25.6
1,3.6
89
78.6
41.8
49
131. 6
70.0
09
184.5
98.1
69
237.5
126. 3
30
3f
26.5
14.1
90
79.5
42.3
42.7
50
151
132.4
133.3
70.4
10
185.4
98.6
70
271
238.4
126.8
27.4
14.6
91
80.3
70.9
211
186.3
99.1
239.3
127.2
32
28.3
15.0
92
81.2
43.2
52
134.2
71.4
12
187.2
99.5
72
240.2
127.7
33
29.1
1.5. 5
93
82.1
43.7
53
135.1
71.8
13
188.1
100.0
73
241.0
128.2
34
30.0
16.0
94
83.0
44.1
.54
136.0
72.3
14
189.
100.5
74
241.9
128. 6
35
30.9
16.4
95
83.9
44.6
55
136.9
72.8
15
189.8
100.9
75
242.8
129.1
36
31.8
16.9
96
84.8
4,5.1
56
137. 7
73.2
16
190.7
101.4
76
243.7
129.6
37
32.7
17.4
97
85.6
4,5.5
57
138.6
73.7
17
191.6
101.9
77
244.6
130.0
38
33. 6
17.8
98
86.5
46.0
,58
139.5
74.2
18
192. 5
102.3
78
245.5
130. 5
39
34.4
18.3
99
87.4
46.5
59
140.4
74.6
19
193.4
102.8
79
246.3
131.0
40
41
35. 3
36.2
18.8
100
88.3
46.9
60
141.3
75.1
75.6
20
221
194.2
195. 1
103.3
103.8
80
247.2
248. 1
131.5
131.9
19.2
101
89.2
47.4
161
142.2
281
42
37. 1
19.7
02
90.1
47.9
62
143.0
76.1
22
196.0
104.2
82
249.0
1.32.4
43
38.0
20.2
03
90.9
48.4
63
143.9
76.5
23
196. 9
104.7
83
249.9
1,32. 9
44
38.8
20.7
04
91.8
48.8
64
144.8
77.0
24
197.8
105.2
84
2.50. 8
133. 3
45
39.7
21.1
05
92.7
49.3
&5
145.7
77.5
25
198.7
105.6
85
251.6
1,33. 8
46
40.6
21.6
06
93.6
49.8
66
146.6
77.9
26
199. 5
106. 1
86
252. 5
134.3
47
41.5
22.1
07
94.5
50.2
67
147.5
78.4
27
200.4
106.6
87
253.4
134. 7
48
42.4
22.5
08
95.4
50.7
68
148.3
78.9
28
201. 3
107.0
88
254.3
135.2
49
43.3
23.0
09
96.2
51.2
69
149.2
79.3
29
202.2
107.5
89
255.2
ia5.7
50
51
44.1
23.5
10
97.1
51.6
70
150.1
79.8
30
203.1
204.0
108.0
108.4
90
291
256.1
256. 9"
1.36. 1
45:0
23.9
111
98.0
,52.1
171
1,51.0
80.3
231
136. 6
52
45.9
24.4
12
98.9
52.6
72
151.9
80.7
32
204.8
108.9
92
257.8
137.1
53
46.8
24.9
13
99.8
.53.1
73
152.7
81.2
33
205. 7
109.4
93
258.7
137.6
54
47.7
25.4
14
100.7
,53.5
74
153.6
81.7
34
206.6
109.9
94
259.6
138.0
55
48.6
25.8
15
101.5
54.0
75
154. 5
82.2
35
207. 5
110.3
95
260.5
138. 5
56
49.4
26.3
16
102.4
54.5
76
155.4
82.6
,36
208.4
110.8
96
261.4
139.
57
50. 3
26.8
17
103. 3
,54.9
77
156.3
83.1
37
209.3
111.3
97
262.2
139. 4
58
51.2
27.2
18
104.2
,55. 4
78
157.2
83.6
38
210.1
111.7
98
263.1
139. 9
59
52.1
27.7
19
105.1
55.9
79
1,58.
84.0
39
211.0
112.2
99
264.0
140.4
60
53.0
28.2
20
106.0
56.3
80
158.9
84.5
40
.211.9
112.7
300
264.9
140.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
I^t.
82° (1
18°, 242°, 298°
)•
!
Page 586]
TABLE 2.
Difference of Latitude and Departure for 28° (152°, 208°, 332
")•
Dist.
Lat. 1 Dep.
1
Dist. i Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
265.7 !l41.3
361 318. 7
169.5
421
371.7
197.7
481
424.7
225.8
541
477.7
254.0
02
266.6
141.8
62
319.6
170.
22
372.6
198.1
82
425. 6
226.3
42
478.6
254.5
03
267.5
142. 3
63
320.5
170.4
23
373. 5
198.6
83
426.5
226.8
43
479.4
255.
04
268.4
142.7
64
321.4
170.9
24
374.3
199.1
84
427.4
227.3
44
480.3
2.55. 5
05
269.3
143.2
65
322.2
171.4
25
375.2
199.5
85
428.3
227.7
45
481.1
255.9
06
270.2
143.7
66
323.1
171.8
26
376.1
200.0
86
429. 2
228.2
46
.482.
256.4
07
271.0
144.1
67
324.0
172.3
27
377.0
200.5
87
430.1
228.6
47
482.9
256.9
08
271.9
144.6
68
324.9
172.8
28
377.9
200.9
88
430.9
229.1
48
483.8
257. 3
09
272.8
145.1
69
325.8
173.2
29
378.8
201.4
89
431.8
229.6
49
484.7
257.8
10
311
273.7
274.6
145. 5
70
326.7
173.7
30
431
379. 6
380. 5
201.9
90
491
432. 6
230.0
230.5
50
485.6
258.2
146.0
371'
327.5
174.2
202.3
433.5
551
486.5
258.7
12
275.5
146.5
72
328.4
174.6
32
381.4
202.8
92
434.4
231.0
52
487.4
259.1
13
276.3
146.9
73
329.3
175.1
33
382. 3
203. 3
93
435. 3
231.4
53
488.3
259.6
14
277.2
147.4
74
330.2
175.6
34
383.2
203. 8
94
4.36. 2
231.9
54
489.2
260.1
15
278.1
147.9
75
331.1
176.1
35
384.1
204. 2
95
437. 1
2.32. 4
55
490.1
260.6
16
279.0
148.4
76
332.0
176.5
36
384. 9
204.7
96
437.9
232.9
56
490.9
261.0
17
279.9
148.8
77
332.8
177.0
37
385.8
205. 2
97
4.38. 8
233.4
57
491.8
261.5
18
280.7
149.3
78
333.7
177.5
38
386.7
205.6
98
439.7
233. 8
58
492.7
262.0
19
281.6
149.8
79
334.6
177.9
39
387.6
206.1
99
440.6
234.3
59
493.5
262.5
20
282.5
150.2
80
385.5
178.4
40
388.5
206.6
500
441.5
442. 3
234.7
235.2
60
494.4
262.9
321
283.4
150.7
381 ! 336.4
178.9
441 i 389.4
207.0
501
561
495.3
263.4
22
284.3
151.2
82
337.3
179.3
42
390.2
207.5
02
443. 2
235. 6
62
496.2
263.8
23
285.2
151.6
83
338.1
179.8
43
391.1
208.0
03
444.1
236.1
63
497.1
264.3
24
286.0
152.1
84
3.39.
180.3
44
392.
208.4
04
445.0
236.6
64
498.0
264. 7
25
286.9
152.6
85 I 339.9
180.8
45
392.9
208.9
05
445.9
237.1
65
498.9
265.2
26
287.8
153. 1
86
340.8
181.2
46
393.8
209.4
06
446.8
237.5
66
499.8
265.7
27
288.7
153.5
87
341.7
181.7
47
394.6
209.9
07
447.6
238.0
67
500.7
266.2
28 ; 289.6
154.0
88
342.6
182.2
48
395.5
210.3
08
448.5
238.5
68
501.6
266.6
29 1 290.5
154.5
89
343.4
182.6
49
396.4
210.8
09
449.4
239.0
69 1 502.4
267.1
30 1 291.3
154.9
90 i 344. 3
183.1
50
397.3
398.2
211.3
10
450. 3
239.4
70 1 503.3
267.6
268.0
331 1 292.2
155.4
391 345. 2
183.6
451
211.7
511
451.2
239.9
571 I 504.2
32 1 293. 1
155.9
92 346. 1
184.0
52
399.1
212.2
12
452.1
240.4
72
505.1
268.5
33 ; 294.0
156.3
93 347.
184.5
53
399.9
212.7
13
452.9
240.8
73
505.9
269.0
34 1 294.9
156. 8
94
347.9
185.0
54
400.8
213. 1
14
453.8
241.3
74
506.8
269.4
35 : 295. 8
157.3
95
348.7
185. 4
55
401.7
213.6
15
454.7
241.8
75
507.7
269. 9
36 ' 296.6
157.7
96
349.6
185.9
56
402.6
214. 1
16
455.6
242.2
76
508.6
270.4
37 : 297.5
158.2
97
350.5
186.4
57
403. 5
214.6
17
456.4
242.7
77
509.4
270.9
38 '< 298.4
158.7
98
351.4
186.9
58
404.4
215.0
18
457.3
243.2
78
510.3
271.3
39 299.3
159. 2
99
352.3
187.3
59
405.2
215.5
19
458.2
243. 7
79
511.2
271.8
40 300. 2
159.6
400
353. 1
187.8
60
406.1
407.0
216.0
20
459.1
244.1
80
512.1
272.3
272.7
341 301.
160.1
401
354.0
188.3
461
216. 4
521
460.0
244.6
581
513.
42
301.9
160.6
02
354.9
188.7
62
407.9
216.9
22
460.9
245.
82
513. 9
273. 2
43
302.8
161.0
03
355.8
189.2
63
408.8
217.4
23
461.8
245.5
83
514.8
273.7
44
303.7
161.5
04
356.7
189.7
64
409.7
217.8
24
462.7
246.0
84
515.7
274.2
45
304.6
162.0
05
357.6
190.1
65
410.5
218.3
25
463.5
246.5
85
516.5
274.7
46
305.5
162.4
06
358.4
190. 6
66
411.4
218.8
26
464.4
246.9
86
517.4
275.1
47
■306.4
162.9
07
359.3
191.1
67
412.3
219.2
27
465.3
247.4
87
518.3
275.5
48
307.2
163.4
08
360.2
191.5
68
413.2
219.7
28
466.2
247.9
88
519.2
276.0
49
308.1
163.8
09
361.1
192.0
69
414.1
220.2
29
467.1
248.3
89
520.1
276.5
50 1 309.0
351 1 309.9
164.3
10
362.0
362.9
192.5
70
415.0
220.7
30
468.0
248.8
90
521.0
277.0
164.8
411
193.
471
415.8
221.1
531
468.9
249.3
591
521.8
277.4
52 1 310. 8
165.3
12
363.7
193.4
72
416.7
221.6
82
469.8
249.8
92
522.6
277.9
53 i 311. 7
165.7
13
364.6
193. 9
73
417.6
222.1
33
470.7
250.2
93
523.5
278.4
54
312.5
166.2
14
365.5
194.4
74
418.5
222. 5
34
471.5
250.7
94
524.4
278.8
55
313.4
166.7
15
366.4
194.8
75
419.4
223.0
35
472.4
251.1
95
525.3
279.3
56
314.3
167.1
16
367. 3
195.3
76
420. 3
223. 5
36
473.3
251.6
96
526.2
279.8
57
315.2
167.6
17
368.2
195.8
77
421.1
223. 9
37
474.2
252.1
97
527.1
280.3
58
316.1
168.1
18
369.0
196.2
78
422.0
224.4
.38
475.1
252. 6
98
528.0
280.8
59
316.9
168.5
19
369.9
196.7
79
422.9
224.9
39
476.0
253. 1
99
528.9
281.3
60
317.8
169.0
20
370.8
197.2
80
423.8
225. 3
40
476.8
253.6
600
529.8
281.7
Dist.
Dep.
Lat. Dist.
Dep.
Lat.
Dist.
Dep.
Lat. Dist. 1
Dep.
Lat.
Dist.
Dep.
Lat.
6
2° (118°, 242'
', 298°).
TABLE 2.
[Page 687 |
Difference of Latitude and
Departure for 29° (151°, 209°, 331
")■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
53.4
29.6
121
105.8
58.7
181
158.3
87.8
241
210.8
116.8
2
1.7
1.0
62
54.2
30.1
22
106.7
59.1
82
159.2
88.2
42
211.7
117.3
3
2.6
1.5
63
55.1
30.5
23
107.6
59.6
83
160.1
88.7
43
212.5
117.8
4
3.5
1.9
64
56.0
31.0
24
108.5
60.1
84
160.9
89.2
44
213.4
118.3
5
4.4
2.4
65
56.9
31.5
25
109.3
60.6
85
161.8
89.7
45
214. 3
118.8
6
5.2
2.9
66
57.7.
32.0
26
110.2
61.1
86
162.7
90.2
46
215. 2
119.3
7
6.1
3.4
67
58.6
32.5
27
111.1
61.6
87
163.6
90.7
47
216.0
119.7
8
7.0
3.9
68
59.5
33.0
28
112.0
62.1
88
164.4
91.1
48
216.9
120.2
9
7.9
4.4
69
60.3
33.5
29
112.8
62.5
89
165.3
91.6
49
217.8
120.7
10
8.7
4.8
70
61.2
33.9
30
113.7
63.0
90
166.2
92.1
50
218.7
219.5
121.2
11
9.6
5.3
71
62.1
34.4
131
114.6
63.5
191
167.1
92.6
251
121.7
12
10.5
5.8
72
63.0
34.9
32
115.4
64.0
92
167.9
93.1
52
220.4
122.2
13
11.4
6.3
73
63.8
35.4
33
116.3
64.5
93
168.8
93.6
53
221.3
122.7
14
12.2
6.8
74
64.7
35.9
34
117.2
65.0
94
169.7
94.1
.54
222.2
123.1
15
13.1
7.3
75
65.6
36.4
35
118.1
65.4
95
170.6
94.5
55
223.0
123.6
16
14.0
7.8
76
66.5
36.8
36
118.9
65.9
96
171.4
95.0
56
223.9
124.1
17
14.9
8.2
77
67.3
37.3
37
119.8
66.4
97
172.3
95.0
57
224.8
124.6
18
15.7
8.7
78
68.2
37.8
38
120.7
66.9
98
173.2
96.0
58
225.7
125.1
19
16.6
9.2
79
69.1
38.3
39
121.6
67.4
99
174.0
96.5
59
226.5
125.6
20
17.5
9.7
80
70.0
38.8
40
122.4
67.9
200
174.9
97.0
60
227.4
126.1
21
18.4
10.2
81
70.8
39.3
141
123.3
68.4
201
175.8
97.4
261
228.3
126. 5
22
19.2
10.7
82
71.7
39.8
42
124.2
68.8
02
176.7
97.9
62
229.2
127.0
23
20.1
11.2
83
72.6
40.2
43
125.1
69.3
03
177.5
98.4
63
230.0
127.5
24
21.0
11.6
84
73.5
40.7
44
125.9
69.8
04
178.4
98.9
64
230.9
128.0
25
21.9
12.1
85
74.3
41.2
45
126.8
70.3
05
179.3
99.4
65
231.8
128.5
26
22.7
12.6
86
75.2
41.7
46
127.7
70.8
06
180.2
99.9
66
232.6
129.0
27
23.6
13.1
87
76.1
42.2
47
128.6
71.3
07
181.0
100.4
67
233.5
129.4
28
24.5
13.6
88
77.0
42.7
48
129.4
71.8
08 ! 181.9
100.8
68
234.4
129.9
29
25.4
14.1
89
77.8
43.1
49
130. 3
72.2
09 ! 182.8
101.3
69
235. 3
130. 4
30
31
26.2
14.5
90
78.7
43.6
50
131.2
72.7
10
211
183.7
101.8
70
236.1
237.0
130.9
27.1
15.0
91
79.6
44.1
151
132.1
73.2
184. 5
102.3
271
131.4
32
28.0
15.5
92
80.5
44.6
.52
132.9
73.7
12 : 185.4
102.8
72
237.9
131.9
33
28.9
16.0
93
81.3
45.1
53
133.8
74.2
13
186.3
103. 3
73
238.8
132.4
34
29.7
16.5
94
82.2
45.6
54
134.7
74.7
14
187.2
103.7
74
239.6
132.8
35
30.6
17.0
95
83.1
46.1
55
135. 6
75.1
15
188.0
104.2
75
240.5
133.3
36
31.5
17.5
96
84.0
46.5
56
136.4
75.6
16
188.9
104.7
76
241.4
133.8
37
32.4
17.9
97
84.8
47.0
57
137. 3
76.1
17
189.8
105. 2
77
242.3
134. 3
38
33.2
18.4
98
85.7
47.5
58
138.2
76.6
18
190.7
105. 7
78
243.1
134.8
39
34.1
18.9
99
86.6
48.0
59
139.1
77.1
19
191.5
106.2
79
244.0
135. 3
40
35.0
19.4
19.9
100
101
87.5
88. 3
48.5
60
139.9
77.6
20
221
192.4
193. 3
106.7
80
244.9
135.7
41
35.9
49.0
161
140.8
78.1
107.1
281
245. 8
136.2
42
36.7
20.4
02
89.2
49.5
62
141.7
78.5
22
194.2
107.6
82
246.6
136.7
43
37.6
20.8
03
90.1
49.9
63
142.6
79.0
23
195.0
108.1
83
247.5
137.2
44
38.5
21.3
04
91.0
.50.4
64
143. 4
79.5
24
195.9
108.6
84
248.4
137.7
45
39.4
21.8
05
91.8
50.9
65
144.3
80.0
25
196.8
109.1
85
249.3
138.2
46
40.2
22.3
06
92.7
51.4
66.
145.2
80.5
26
197.7
109.6
86
250.1
138.7
47
41.1
22.8
07
93.6
51.9
67
146.1
81.0
27
198.5
110.1
87 I 251.0
139.1
48
42.0
23.3
08
94.5
52.4
68
146.9
81.4
28
199.4
110.5
88 1 251.9
139.6
49
42.9
23.8
09
95.3
52.8
69
147.8
81.9
29
200.3
111.0
89 252.8
140.1
50
51
43.7
24.2
10
96.2
53.3
70
148.7
82.4
.30
201.2
111.5
90
253.6
254. 5
140.6
44.6
24.7
111
97.1
53.8
171
149.6
82.9
231
202.0
112.
291
141.1
52
45.5
25.2
12
98.0
54.3
72
150.4
83.4
32
202.9
112.5
92 255. 4
141.6
53
46.4
25.7
13
98.8
54.8
73
151.3
83.9
33
203.8
113.
93
256.3
142.0
54
47.2
26.2
14
99.7
55.3
74
152.2
84.4
34
204.7
113.4
94
257.1
142.5
55
48.1
26.7
15
100.6
55.8
75
153.1
84.8
,35
205.5
113.9
95
258.0
143.0
56
49.0
27.1
16
101.5
56.2
76
153.9
85.3
36
206.4
114.4
96
258.9
143.5
57
49.9
27.6
17
102.3
56.7
77
154.8
85.8
37
207. 3
114.9
97
259.8
144.0
58
50.7
28.1
18
103. 2
57.2
78
155.7
86.3
38
208.2
115.4
98
260.6
144.5
59
51.6
28.6
19
104.1
57.7
79
156.6
86.8
39
209.0
115.9
99
261.5
145.0
60
52.5
29.1
20
105.0
58.2
80
157.4
87.3
40
209.9
116.4
300
262.4
145. 4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
61° (1
19°, 241°, 299°
).
Page 588]
TABLE 2.
Difference of Latitude and Departure for 29° (151°, 209°, 331=
)•
Dist. 1 l,at.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
263.2
145.9
361
315.7
175.0
421
368.2
204.1
481
420.7
233.2
541
473.2
262.3
02
264.1
146.4
62
316.6
175.5
22
369.1
204.6
82
421. 5
233.7
42
474.0
262.8
03
265.0
146.9
63
317.5
176.0
23
369. 9
205.1
83
422.4
234.2
43
474.9
263. 2
04
265.9
147.4
64
318.3
176.5
24
370.8
205. 6
84
423.3
234.6
44
475.8
263. 7
05
266.7
147.9
65
319.2
177.0
25 1 371. 7
206.0
85
424.2
235.1
45
476.6
264. 2
06 267. 6
148.4
66
320.1
177.4
26 i 372. 6
206.5
86
425.0
235. 6
46
477.5
264.7
07 268. 5
148.8
67
321.0
177.9
27
373.4
207.0
87
425.9
2,36. 1
47
478.4
265. 2
08 269. 4
149.3
68
321.8
178.4
28
374. 3
207.5
88
426.8
236. 6
48
479.3
265. 7
09 ! 270.2
149.8
69
322.7
178.9
29
375.2
208.0
89
427.7
237.1
49
480.1
266.2
10
271.1
150.3
70
323.6
179.4
30
376.1
208.5
90
428.5
237.6
50
481.0
266. 6
267.1
311
1 272.0
150.8
371
324.5
179.9
431
376.9
209.0
491
429.4
238.0
551
481.9
12 ; 272.9
151. 3
72
325.3
180.4
32
377.8
209.4
92
430.3
238.5
52
482.8
267. 6
13 273. 7
151.7
73
326.2
180.8
33
378.7
209.9
93
431.2
239.0
53
483.6
268. 1
14 274.6
152.2
74
327.1
181.3
34
379.6
210.4
94
432.0
239.5
54
484.5
268. 6
15 275. 5
1.52. 7
75
328. 1 181. 8
35
380.4
210.9
95
432.9
240.0
55
485.4
269. 1
16 : 276.3
153. 2
7.6
328. 8 : 182. 3
36
381.3
211.4
96
433.8
240. 5
56
486.3
269. 5
17 ' 277.2
153.7
77
329.7
182.8
37
382.2
211.9
97
434.7
240. 9
57
487.1
270.0
18 1 278. 1
154.2
78
330.6
183. 3
38
383.1
212.3
98
435. 5
241.4
58
488.0
270.5
19 : 279.0
154.7
79
331.4
183.7
39
383.9
212.8
99
436.4
241.9
59
488.9
271.0
20 279. 8
155.1
80
332.3
184.2
40
384.8
213. 3
500
437. 3
242.4
60
489.8
271. 5
321 280. 7
155.6
381
333.2
184.7
441
385. 7 i 213. 8
501
438.2
242.9
561
490.6
272.
22 , 281.6
156.1
82
334.1
185.2
42
386.6 214.3
02
439.0
243.4
62
491.5
272. 5
23 ! 282.5
156. 6
83
334.9
185.7
43
387. 4 : 214. 8
03
439.9
243.9
63
492.4
272.9
24 283. 3
157.1
84
335.8
186.2
44 1 388.3
215.3
04
440.8
244.3
64
493.2
273. 4
25 284. 2
157.6
85
336.7
186.7
45
389.2
215. 7
05
441.6
244. 8
65
494.1
273. 9
26 285. 1
158. 1
86
337.6
187.1
46
390.0 !216.2
06
442.5
245.3
66
495.
274,4
27 286.
158.5
87
338. 4
187.6
47
390. 9 ! 216. 7
07
443. 4
245. 8
67
495. 9
274.9
28 286. 8
159.
88
339. 3
188.1
48
391.8 217.2
08
444.3
246. 3
68
496.8
275. 4
29 ': 287.7
159.5
89
340. 2
188.6
49
392.7 217.7
09
445. 2
246.8
69
497.7
275. 9
30
288,6
160.0
90
341.1
341. 9
189.1
189.6
50
451
393.5
218.2
2l8. 7
10
446.1
247.3
70
498.5
276. 3
31
289.5
160.5
391
394.4
511
447.0
247.8
571
499.4
276.8
32 290. 3
161.0
92
342.8
190.0
52
395.3
219.1
12
447.8
248.2
72
500.3
277.3
33 291.2
161.4
93
343.7
190. 5
53
396.2
219.6
13
448.6
248.7
73
501.1
277.8
34 i 292. 1
161. 9
94
344.6
191.0
54
397.0
220.1
14
449.5
249. 2
74
502.0
278.3
35 i 293.0
162.4
95
345.4
191.5
55
397.9
220. 6
15
450. 4
249.7
75
502. 9
27S. 8
36 , 293.8
162.9
96
346.3
192.0
56
398.8
221.1
16
451.3
250. 2
76
503.7
279.2
37 ! 294.7
163. 4
97
347.2
192.5
57
399. 7
221.6
17
452.2
250.6
77
504.6
279. 7
38 ! 295.6
163.9
98
348.1
193.0
58
400.5
222.0
18
453.1
251. 1
78
505.5
280.2
39
296.5
164.4
99
348.9 193.4
59
401.4
222. 5
19
453.9
251.6
79
506.4
280.7
40
297.3
164.8
400
349. 8 i 193. 9
60
402.3
223.0
20
454.8
252. 1
80
507.2
281.2
281.7
341
298.2
165.3
401
350.7 ;194.4
461
403.2
223. 5
521
455. 6
252. 6
581
508.1
42
299.1
165.8
02
351.6
194.9
62
404.0
224.0
22
456.5
253. 1
82
509.0
282.2
43
300.0
166.3
03
352.4
195.4
63
404.9
224.5
23
457.4
253.6
83
509.9
282.7
44
300.8
166.8
04
353.3
195.9
64
405.8
225.0
24
458.3
254.0
84
.510.7
283.2
45
301. 7
167.3
05
354.2
196.3
65
406.7
225. 4
25
459. 1
254.5
85
511.6
283. 6
46
302.6
167.7
06
355.1
196.8
66
407.5
225.9
,26
460.0
255.0
86
512.5
284.1
47
303.5
168.2
07
355. 9 i 197. 3
67
408.4
226.4
27
460.9 ! 255.51
87
513.4
284.6
48
304.3
168.7
08
356. 8 i 197. 8
68
409.3
226.9
28
461.8
256.0
88
514.3
285.
49
305.2
169.2
09
357. 7 : 198. 3
69
410.2
227.4
29
462.6
256.5
89
515.1
285. 5
50
306.1
169.7
10
358.6 t
198.8
70
411.0
227.9
30
531
463.5
256.9
90
516.0
286.0
351
307.0
170.2
411
359.4
199.3
471
411.9
228.3
464.4
257.4
591
516.9
286. 5
52
307.8
170.7
12
360.3
199.7
72
412.8
228.8
32
465. 3
257.9
92
517.7
287.0
53
308.7
171.1
13
361.2
200.2
73
413.7
229.3
33
466.1
258.4
93
518.6
287.5
54
309.6
171.6
14
362.1
200.7
74
414.5
229.8
34
467.0
258.9
94
519.5
288.0
55
310.5
172.1
15
362.9
201.2
75
415.4
230.3
35
467.9
259.4
95
520.4
288.5
56
311.3
172.6
16
363.8
201.7
76
416.3
230.8
36
468.8
259.9
96
521.2
288.9
57
312.2
173.1
17
364.7
202.2
77
417. 2
231.3
37
469.6
260. 3
97
522.1
289.4
58
313.1
173.6
18
365. 6
202.7
78
418.0
231.7
38
470.5
260.8
98
523.0
289.9
59
314.0
174.0
19
366.4
203. 1
79
418.9
232.2
39
471.4
261. 3
99
523.9
290.4
60
314.8
174.5
20
367.3
203.6
80
419.8
232.7
40
472.3
261.8
600
524.8
290.9
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
6
1° (119°, 241°, 299°)
TABLE 2.
[Page
589
Difierence of Latitude and Departure for 30° (150°, 210°, 330°
)•
Dist.
Lat.
Dep.
Dist.
I^t.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
52.8
30.5
121
104.8
60.5
181
156.8
90.5
241
208.7
120.5
o
1.7
1.0
62
53.7
31.0
22
105. 7
61.0
82
157.6 1 91.0
42
209.6
121.0
3
2.6
1.5
63
54.6
31.5
23
106.5
61.5
83
1.58.5 ! 91.5
43
210.4
121.5
4
3.5
2.0
64
55.4
32.0
24
107.4
62.0
84
159.3 ! 92.0
44
211.3
122.
5
4.3
2.5
65
56.3
32.5
25
108.3
62.5
85
160.2 ' 92.5
45
212.2
122.5
6
5.2
3.0
66
57.2
33.0
26
109.1
63.0
86
161. 1 93.
46
213.0
123.0
7
6.1
3.5
67
58.0
33.5
27
110.0
63.5
87
161. 9 93. 5
47
213.9
123.5
8
6.9
4.0
68
58.9
34.0
28
110.9
64.0
88
162. 8 94.
48
214.8
124.0
9
7.8
4.5
69
59.8
34.5
29
111.7
64.5
89
163. 7 94. 5
49
215.6
124.5
10
a
8.7
9.5
5.0
70
60.6
35.0
30
112.6
65.0
90
164.5
95.0
50
216.5
125.0
5.5
71
61.5
35.5
131
113.4
65.5
191
165.4
95.5
251
217.4
125.5
12
10.4
6.0
72
62.4
36.0
32
114.3
66.0
92
166.3
96.0
52
218.2
126.0
13
11.3
6.5
73
63.2
36.5
33
115. 2
66.5
93
167.1
96.5
53
219.1
126.5
14
12.1
7.0
74
(34.1
37.0
34
116.0
67.0
94
168.0
97.0
54
220.0
127.0
15
13.0
7.5
75
6.5.0
37.5
35
116.9
67.5
95
168.9
97.5
55
220. 8
127.5
16
13.9
8.0
76
65.8
38.0
36
117.8
68.0
96
169.7
98..0
56
221.7
128.0
17
14.7
8.5
77
66.7
38. 5
37
118.6
68.5
97
170.6
98.5
57
222.6
128.5
18
15.6
9.0
78
67. 5
39.
38
119.5
69.0
98
171. 5
99.0
58
223. 4
129.0
19
16.5
9.5
79
68.4
39. 5
39
120. 4
69.5
99
172.3
99.5
59
224. 3
129. 5
20
21
17.3
18.2
10.0
10.5
80
81
69.3
7d."i"
40.0
40. h
40
141
121.2
122.1
70.0
70.5
200
201
173.2
100.0
60
225.2
130.0
130.5
174.1
100.5
261
226.0
22
19.1
11.0
82
71.0
41.0
42
123.
71.0
02
174.9
101.
62
226.9
131.0
23-
19.9
11.5
83
71.9
41.5
43
123. 8
71.5
03
175. 8
101.5
63
227.8
131. 5
24
20.8
12.0
84
72.7
42.0
44
124.7
72.0
04
176.7
102.0
64
228.6
132.0
25
21.7
12.5
85
73.6
42. 5
45
125. 6
72.5
05
177.5
102.5
65
229. 5
132.5
26
22.5
13.0
86
74.5
43.0
46
126.4
73.0
06
178.4
103.0
66
230. 4
133.0
27
23.4
13.5
87
75.3
43.5
47
127. 3
73.5
07
179.3
103. 5
67
231.2
133. 5
28
24. 2
14.0
88
76.2
44.0
48
128.2
74.0
08
180.1
104.0
68
232. 1
134.0
29
h'.i
14.5
89
77.1
44.5
49
129.
74.5
09
181.0
104. 5
69
233.
134. 5
30
31
26.0
15.0
90
77.9
4.5.0
50
129.9
130. 8
75.0
75.5
10
211
181.9
182.7
105.
70
233.8
135.
135.5
26.8
15. 5
91
78.8
4.5.5
151
105. 5
271
234.7
32
27.7
16.0
92
79.7
46.0
52
131.6
76.0
12
183. 6
106.0
72
235. 6
136.0
33
28.6
16.5
93
80.5
46.5
53
132.5
76.5
13
184.5
106.5
73
236.4
1.36. 5
34
29.4
17.0
94
81.4
47.0
54
133. 4
77.0
14
185.3
107.0
74
237.3
137.
35
30.3
17.5
95
82.3
47.5
55
1.34. 2
77.5
15
186. 2
107. 5
75
238.2
137.5
36
31.2
18.0
96
83.1
48.0
56
135.1
78.0
16
187.1
108.0
76
239.0
138.
37
32.0
18.5
97
84.0
48.5
57
136.0
78.5
17
187. 9
108. 5
77
239. 9
138. 5
38
32.9
19.0
98
84.9
49.0
58
136.8
79.0
18
188.8
109.0
78
240.8
139.
39
33.8
19.5
99
85.7
49.5
59
137.7
79.5
19
189.7
109.5
79
241.6
139. 5
40
41
34.6
35.5
20.0
100
86.6
50.0
60
138.6
139.4
80.0
80.5
20
190. 5
110.0
80
242.5
140.0
140.5
20.5
101
87.5
50.5
161
221
191.4
110.5
281
243. 4
42
36.4
21.0
02
88.3
51.0
62
140.3
81.0
22
192. 3
111.0
82
244.2
141.0
43
37.2
21.5
03
89.2
51.5
63
141.2
81.5
23
193.1
111.5
83
245. 1
141.5
44
38.1
22.0
04
90.1
52.
64
142.0
82.
24
194.0
112.0
84
246.
142.0
45
39.0
22.5
05
90. 9
52. 5
65
142. 9
82. 5
25
194.9
112. 5
85
246. 8
142. 5
46
39.8
23.0
06
91.8
.53.
66
143. 8
83.
26
195. 7
113.0
86
247.7
143.0
47
40.7
23. 5
07
92.7
53. 5
67
144.6
83. 5
27
196. 6
113.5
87
248.5
143.5
48
41.6
24.0
08
93. 5
54.0
68
145. 5
84.
28
197.5
114.0
88
249.4
144.0
49
42.4
24.5
09
94.4
.54.5
69
146. 4
84. 5
29
198.3
114.5
89
2.50. 3
144. 5
50
51
4,3.3
44.2
25.0
10
95.3
55.
70
171
147.2
148. r
85.
30
199.2
115.0
90
251.1
145.
145. 5
25.5
111
96.1
.55. 5
8.5.5
231
200.1
115.5
291
252.
52
45.0
26.0
12
97.0
56.0
72
149.0
86.0
32
200.9
116.0
92
252.9
146.0
53
4.5.9
26.5
13
97.9
56.5
73
149.8
86. 5
33
201.8
116.5
93
2.53. 7
146. 5
54
46.8
27.0
14
98.7
.57.0
74
1.50. 7
87.0
34
202. 6
117.0
94
254. 6
147.0
55
47.6
27.5
15
99.6
57. 5
75
151.6
87.5
35
203. 5
117.5
95
255. 5
147. 5
56
48.5
28.0
16
100. 5
58.0
76
1.52. 4
88.0
36
204.4
118.0
96
256. 3
148.0
57
49.4
28.5
17
101.3
58. 5
77
1.53. 3
88. 5
37
205. 2
118.5
97
257. 2
148. 5
58
50.2
29.0
18
102.2
59.0
78
154. 2
89.0
38
206. 1
119.0
98
258. 1
149.0
59
51.1
29.5
19
103. 1
59.5
79
155.
89.5
89
207.0
119.5
99
258. 9
149. 5
60
52.0
30.0
20
103.9
60.0
80
155. 9
90.0
40
207.8
120.
300
259.8
150.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
60° (1
20°, 240
°, 300°
)■
Page 590]
TABLE 2.
Difference of Latitude and Departure for 30
° (150
°, 210°, 330°).
Dist.
Lat.
Dcp.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
260.7
150.5
361
312.6
180.5
421
364.6
210.5
481
416.6
240.5
541
468.5
270.5
02
261.5
151.0
62
313.5
181.0
22
365.5
211.0
82
417.4
241.0
42
469.4
271.0
03
262.4
151.5
63
314.4
181.5
23
366.3
211.5
83
418.3
241.5
43
470.3
271.5
04
263.3
152.0
64
315.2
182.0
24
367.2
212.0
84
419.2
242.0
44
471.1
272.
05
264.1
152.5
65
316.1
182. 5
25
368.1
212.5
85
420.0
242.5
45
472.0
272.5
06
265.
153.
66
317.0
183.0
26
368. 9
213.0
86
420.9
243.0
46
472.9
273.0
07
265. 9
153.5
67
317.8
183. 5
27
369.8
213.5
87
421.8
243.5
47
473.7
273.5
08
266. 7
154.0
68
318.7
184.0
28
370.7
214.0
88
422.6
244.0
48
474.6
274.0
09
267. 6
154.5
69
319.6
184.5
29
.371. 5
214.5
89
423.5
244.5
49
475.5
274. 5
10
268.5
269.3
155.0
70
320.4
185.0
30
372.4
373.3
215.0
90
491
424.4
245.0
50
476.3
477.2
275.0
275. 5
311
155. 5
371
321.3
185.5
431
215.5
425.2
245.5
551
12
270.2
156.
72
322.2
186.0
32
374. 1
216.0
92
426.1
246.0
52
478.1
276.0
13
271.1
156. 5
73
323.0
186.5
33
375.0
216.5
93
426.9
246.5
53
478.9
276.5
14
271.9
157.0
74
323.9
187.0
34
375.9
217.0
94
427.8
247.0
54
479.8
277.0
15
272.8
157.5
75
324. 8
187.5
35
376. 7
217.5
95
428. 7
247.5
55
480.7
277.5
16
273.7
158.0
76
325.6
188.0
36
377.6
218.0
96
429.6
248.0
56
481.5
278.0
17
274.5
158.5
77
326.5
188.5
37
378.5
218.5
97
430.4
248.5
57
482.4
278. 5
18
275.4
159.0
78
327.4
189.0
38
379.3
219.0
98
431.3
249.0
58
483.3
279.0
19
276.3
159.5
79
328.2
189.5
39
380.2
219.5
99
432.2
249.5
59
484.1
279.5
20
277.1
160.0
80
329.1
330.
190.0
190. 5
40
381.1
220.0
500
433.0
250.0
250. 5
60
485.0
280.0
321
278.0
160.5
381
441
381.9
220.5
501
433. 9
561
485.9
280.5
22
278.9
161.0
82
330.8
191.0
42
382.8
221.0
02
434.8
251.0
62
486.7
281.0
23
279.7
161.5
83
331.7
191. 5
43
383.7
221. 5
03
435. 6
251. 5
63
487.6
281.5
24
280.6
162.0
84
332.6
192.
44
384.5
222.0
04
436. 5
252.
64
488.5
282.
25
281.5
162.5
85
333.4
192.5
45
385.4
222.5
05
437.4
252.5
65
489.3
282. 5
26
282.3
163.0
86
334.3
193.0
46
386. 3
223.0
06
438.2
253.0
66
490.2
283.0
27
283.2
163.5
87
335.2
193.5
47
387.1
223.5
07
439.1
253.5
67
491.1
283. 5
28
284.1
164.0
88
336.0
194.0
48
388.0
224.0
08
440.0
254.0
68
491.9
284.0
29
284.9
164.5
89
336.9
194.5
49
388.9
224.5
09
440.8
254.5
69
492.8
284.5
30
285.8
165.0
90
337.8
195.0
50
389.7
390.6
225.0
10
441.7
255.0
255.5
70
• 493. 6
494.5
285.
331
286.7
165.5
391
338.6
195.5
451
225.5
511
442.6
571
285. 5
32
287.5
166.0
92
339.5
196.0
52
391.5
226.0
12
443.4
256.0
72
495.4
286.0
33
288.4
166.5
93
340.4
196.5
53
392. 3
226.5
13
444.3
256. 5
73
496.3
286. 5
34
289.3
167.0
94
341.2
197.0
54
393.2
227.0
14
445.2
257.0
74
497.1
287.0
35
290.1
167.5
95
342.1
197.5
55
394. 1 227. 5
15
446.0
257.5
lO
497.9
287.5
36
291.0
168.0
96
343.0
198.0
56
394. 9 ! 228.
16
446. 9
258.0
76
498.8
288.0
37
291.9
168.5
97
343.8
198. 5
57
395.8
228.5
17
447.8
258. 5
77
499. 7
288. 5
38
292.7
169.0
98
344.7
199.0
58
396. 6
229.0
18
448.6
259.
78
500.5
289.
39
293.6
169.5
99
345.6
199.5
59
397.5
229. 5
19
449.4
259. 5
79
501. 3
289.5
40
294. 5
170.0
400
346.4
200.0
60
398.4
230.0
20
450.3
451.2
260.0
80
502. 2
503.1
290.0
290.5
341 295.3
170.5
401
347. 3
200.5
461
399. 2
230.5
521
260.5
581
42 i 296. 2
171.0
02
348.1
201.0
62
400.1
231.0
22
452.1
261.0
82
504.0
291.0
43
297.1
171.5
03
349.0
201.5
63
401.0
231.5
23
452.9 '261.5
83
504.9
291.5
44
297.9
172.0
04
349.9
202.0
64
401.8
232.0
24
453.8
262.0
84
505.8
292.0
45
298.8
172.5
05
350.7
202.5
65
402.7
232.5
25
454.7
262.5
85
506.6
292.5
46
299.7
173.0
06
351.6
203.
66
403. 6
233.0
26
455.5
263.0
86
507.5
293.0
47
300.5
173. 5
07
352. 5
203.5
67
404.4
233.5
27
456.4
263.5
87
508.4
293. 5
48
301.4
174.0
08
353.3
204.0
68
405. 3
234:0
28
457. 3
264.0
88
.509. 2
294,0
49
302.3
174. 5
09
354.2
204.5
69
406.2
234.5
29
458.1
264.5
89
510.1
294. 5
50
351
303.1
175.0
10
355.1
205.0
70
471
407.0
235.0
30
459.
265.0
90
511.0
295.
304.0
175.5
411
355. 9
205.5
407.9
235. 5
531
459.9
265. 5
591
511.8
295.5
52
304.8
176.0
12
356.8
206.0
72
408.8
236.0
32
460.7
266.
92
512.7
296.
53
305.7
176.5
13
357.7
206.5
73
409.6
236.5
33
461.6
266. 5
93
513.6
296. 5
54
306.6
177.0
14
358.5
207.0
74
410.5
237.0
34
462.5
267.0
94
514.4
297.0
55
307.4
177.5
15
359.4
207.5
75
411.4
237.5
35
463.3
267.5
95
515.5
297.5
56
308.3
178.0
16
360.3
208.0
76
412.2
238.0
36
464.2
268.0
96
516.2
298.0
57
309.2
178.5
17
361.1
208.5
77
413.1
238.5
37
465. 1
268.5
97
517.0
298.5
58
310.0
179.0
18
362.0
209.0
78
414.0
239.0
38
465.9
269.0
98
517.9
299.0
59
310.9
179.5
19
362.9
209.5
79
414.8
239.5
39
466.8
269.5
99
518.8
299.5
60
311.8
180.0
20
363.7
210.0
80
415.7
240.0
40
467.7
270.0
600
519.6
300.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
60° (1
20°, 240°, 300°
)•
TABLE 2.
[Page 591 |
Difference of Latitude and Departure for 31° (149°, 21]°, 329'
)•
Dist.
Lat.
Dep.
DLst.
I-at.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.9
0.5
61
52.3
31.4
121
103.7
62.3
181
155.1
93.2
241
206.6
124.1
2
1.7
1.0
62
53.1
31.9
22
104.6
62.8
82
156.0
93.7
42
207.4
124.6
3
2.6
1.5
63
54
32.4
23
105.4
63.3
83
156.9
94.3
43
208.3
125. 2
4
3.4
2.1
64
54.9
33.0
24
106.3
63.9
84
157.7
94.8
44
209.1
125.7
5
4.3
2.6
65
55.7
33.5
25
107.1
64.4
85
158.6
95.3
45
210.0
126.2
6
5.1
3.1
66
56.6
34.0
26
108.0
64.9
86
159.4
95.8
46
210.9
126.7
7
6.0
3.6
67
57.4
34.5
27
108.9
65.4
87
160.3
96.3
47
211.7
127.2
8
6.9
4.1
68
58.3
35.0
28
109.7
65.9
88
161.1
96.8
48
212.6
127.7
9
7.7
4.6
69
59.1
35.5
29
110.6
66.4
89
162.0
97.3
49
213.4
128.2
10
8.6
5.2
70
60.0
36.1
30
111.4
67.0
90
162.9
97.9
50
214.3
128.8
11
9.4
5.7
71
60.9
36.6
131
112.3
67.5
191
163.7
98.4
251
215.1
129.3
12
10.3
6.2
72
61.7
37.1
32
113.1
68.0
92
164.6
98.9
52
216.0
129.8
13
11.1
6.7
73
62.6
37.6
33
114.0
68.5
93
165.4
99.4
53
216.9
130.3
-14
12.0
7.2
74
63.4
38.1
34
114.9
69.0
94
166.3
99.9
54
217.7
130.8
15
12.9
7.7
75
64.3
38.6
35
115. 7
69.5
95
167.1
100.4
55
218.6
131.3
16
13.7
8.2
76
65.1
39.1
36
116.6
70.0
96
168.0
100.9
56
219.4
131.8
17
14.6
8.8
77
66.0
39.7
37
117.4
70.6
97
168.9
101.5
57
220.3
132.4
18
15.4
9.3
78
66.9
40.2
38
118.3
71.1
98
169.7
102.0
58
221.1
132.9
19
16.3
9.8
79
67.7
40.7
39
119.1
71.6
99
170.6
102.5
59
222.0
133.4
20
21
17.1
10.3
80
68.6
41.2
40
120.0
72.1
200
171.4
103.0
60
222.9
223.7
133.9
134.4
18.0
10.8
81
69.4
41.7
141
120. 9
72.6
201
172.3
103.5
261
22
18.9
11.3
82
70.3
42.2
42
121.7
73.1
02
173.1
104.0
62
224.6
1.34.9
23
19.7
11.8
83
71.1
42.7
43
122. 6
73.7
03
174.0
104.6
63
225.4
135.5
24
20.6
12.4
84
72.0
43.3
44
123.4
74.2
04
174.9
105.1
64
226.3
136.0
25
21.4
12.9
85
72.9
43.8
45
124.3
74.7
05
175.7
105.6
65
227.1
136.5
26
22.3
13.4
86
73.7
44.3
46
125.1
75.2
06
176.6
106.1
66
228.0
137.0
27
23.1
13.9
87
74.6
44.8
47
126.0
75. 7
07
177.4
106.6
67
228.9
137.5
28
24.0
14.4
88
75.4
45.3
48
126.9
76.2
08
178.3
107.1
68
229.7
138.0
29
24.9
14.9
•89
76.3
45.8
49
127.7
76.7
09
179.1
107.6
69
230.6
138.5
30
25.7
15.5
90
91
77.1
46.4
50
128.6
77.3
77.8
10
211
180.0
108.2
"108. 7
70
231.4
139. 1
31
26.6
16.0
78.0
46.9
151
129.4
180.9
271
232. 3
139. 6
32
27.4
16.5
92
78.9
47.4
52
130.3
78.3
12
181.7
109.2
72
233.1
140.1
33
28.3
17.0
93
79.7
47.9
53
131.1
78.8
13
182.6
109.7
73
234
140.6
34
29.1
17.5
94
80.6
48.4
54
132.0
79.3
14
183. 4
110.2
74
234. 9
141.1
36
30.0
18.0
95
81.4
48.9
55
132.9
79.8
15
184.3
110.7
75
235.7
141.6
36
30.9
18.5
96
82.3
49.4
56
133.7
80.3
16
185.1
111.2
76
336.6
142. 2
37
31.7
19.1
97
83.1
50.0
57
134.6
80.9
17
186.0
111.8
77
237.4
142.7
38
32.6
19.6
98
84.0
50.5
58
135.4
81.4
18
186.9
112.3
78
238.3
143. 2
39
33.4
20.1
99
84.9
51.0
59
136. 3
81.9
19
187.7
112.8
79
239. 1
143. 7
40
41
34.3
35.1
20.6
21. 1
100
85.7.
51.5
60
137.1
82.4
20
188.6
113.3
80
240.0
144.2
144.7
101
86.6
52.0
161
138.
82.9
22r
189.4
113.8
281
240.9
42
36.0
21.6
02
,87. 4
52.5
62
1.38. 9
83.4
22
190. 3
114.3
82
241.7
145.2
43
36.9
22.1
03
88.3
53.0
63
139.7
84.0
23
191.1
114.9
83
242.6
145.8
44
37.7
22.7
04
89.1
53.6
64
140.6
84.5
24
192.0
115.4
84
243.4
146. 3
45
38.6
23.2
05
90.0
54.1
65
141.4
85.0
25
192. 9
115.9
85
244.3
146.8
46
39.4
23.7
06
90.9
54.6
66
142.3
85.5
26
193.7
116.4
86
245.1
147. 3
47
40.3
24.2
07
91.7
55.1
67
143.1
86.0
27
194.6
116.9
87
246.0
147. 8
48
41.1
24.7
08
92.6
55.6
68
144.0
86.5
28
195.4
117.4
88
246.9
148. 3
49
42.0
25.2
09
93.4
56.1
69
144.9
87.0
29
196.3
117.9
89
247.7
148.8
50
51
42.9
2.5.8
10
94.3
56.7
70
145.7
87.6
30
197.1
118. 5
90
248.6
149.4
43.7
26.3
111
95.1
57.2
171
146.6
88.1
231
198.0
119.0
291
249.4
149. 9
52
44.6
26.8
12
96.0
57.7
72
147.4
88.6
32
198.9
119.5
92
250.3
1.50. 4
53
45.4
27.3
13
96.9
58.2
73
148.3
89.1
.33
199.7
120.0
93
251.2
150. 9
54
46.3
27.8
14
97.7
58.7
74
149.1
89.6
34
200.6
120.5
94
252.0
151.4
55
47.1
28.3
15
98.6
59.2
75
150.0
90.1
35
201.4
121.0
95
252.9
151.9
56
48.0
28.8
16
99.4
59.7
76
150.9
90.6
36
202.3
121.5
96
253.7
1.52. 5
57
48.9
29.4
17
100.3
60.3
77
151.7
91.2
37
203.1
122.1
97
254.6
153.0
58
49.7
29.9
18
101.1
60.8
78
152.6
91.7
38
204.0
122.6
98
255. 4
153. 5
59
50.6
30.4
19
102.0
61.3
79
153.4
92.2
39
204.9
123.1
99
256.3
154.
60
51.4
.
30.9
20
102.9
61.8
80
154.3
92.7
40
205.7
123.6
300
257. 1
154.5
Lat.
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
59° (1
21°, 239
°, 301°
)•
Page 592]
TABLE 2.
Difference of Latitude and Departure for
31° (149°, 211
°, 329°
)■
Dist.
Lai.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.>
Dep.
Dist.
. Lat.
Dep.
Dist.
Lat.
Dep.
301
258.
1.55.0
.361
309.4
185.9
421
,360. 9
216. 8
481
412.3
247.7
541
463. 7
278.6
02
258.
155. 5
62
310. 3
186. 4
22
361. 7
217.3
82
413. 2
248.2
42
464. 6
279.1
03
259. 7
156.1
63
311.2
187.0
23
362. 6
217.9
83
414.0
248.8
43
465.4
279.7
04
260.6
156.6
64
312.0
187 5
24
,363. 4
21,S. 4
84
414.9
249.3
44
466.3
280.2
05
261. 4
157.1
65
312. 9
188.0
25
364. 3
218.9
85
415.7
249.8
45
467.2
280.7
00
262.3
157.6
66
313.7
188. 5
26
365.2
219. 4
86
416.6
250.3
46
408.0
281.2
07
263.2
1.58. 1
67
314.6
189.
27
:!60-.
219.9
87
417.4
250.8
47
408,9
281.7
08
264.0
158.6
68
315.4
189. 5
28
306. 9
220. 4
88
418. 3
251. 3
48
409.7
282.3
09
264. 9
159. 2
69
316. 3
190. 1
29
367. 7
221.0
89
419.2
251.9
49
470.6
282.8
]0
31 r
265. 7
266.6
159.7
70
317. 2
190.0
191.1
30
431
368.
369.4^
221.5
222.
90
420.0
252. 4
50
471.4
472.3
283. 3
283. 8
160.2
371
318.0
491
420.9
252.9
551
12
267.4
160.7
72
318. 9
191.0
32
370. 3
222.5
92
421.7
253.4
52
473.2
284.3
13
268. 3
161.2
73
319. 7
192. 1
33
371.2
223.
93
422.6
253.9
53
474.0
284. 8
14
269.2
161.7
74
320.6
192.
34
372.
223. 5
94
423.4
254.4
54
474.9
285. 3
15
270.0
162.2
75
,321. 4
193.1
35
372.9
224.0
95
424.3
254.9
55
475. 7
285.8
16
270. 9
162.8
76
322. 3
193. 7
36
373.7
224.6
96
425. 2
255.5
50
476.6
286.4
17
271.7
163.3
77
323. 2
194. 2
37
374.6
225. 1
97
426.0
256.0
57-
477.4
286.9
18
272.6
163.8
78
324.0
194.7
38
375.4
225.6
98
426.9
256. 5
58
478.3
287.4
19
273.4
164.3
79
324. 9
195.2
39
376.3
226.1
99
427.7
257.0
59
479.2
287.9
20
274.3
164.8
165. 3
80
381
325.7
326. 6
195. 7
Y96."2
40
441
377.2
378.
226.6
500
428.6
257. 5
60
480.0
288.4
321
27o:2~
227. 1
501
429.4
258.
561
480.9
288.9
22
276.0
105.8
82
327. 4
196. 7
42
378.9
227.7
02
430. 3
258. 6
62
481.7
289.5
23
276.9
166.4
83
328.3
197. 3
43
379.7
228.2
03
431. 2
259.1
63
482.6
290.
24
277.7
166.9
84
329. 2
197.8
44
380.6
228.7
04
432.0
259.6
64
483.4
290.5
25
278.6
167.4
85
3.30.
198. 3
45
381.4
229.2
05
432. 9
260.1
65
484.3
291.0
26
279.4
167.9
86
330. 9
198.8
46
382. 3
229.7
06
433.7
260.6
66
485. 2
291. 5
27
280.3
168. 4
87
331.7
199.3
47
383.2
230.2
07
434.6
261.1
67
486.0
292.0
28
281.2
168.9
88
332. 6
199. 8
48
384.0
230.7
08
435.4
261.6
262.2
68
486.9
292.5
29
282.0
169.5
89
333.4
200. 4
49
384. 9
231.3
09
430. 3
69
487.7
293.1
30
282 9
170.0
90
334.3
335.2
200. 9
50
385.7
386.6
231.8
232. 3
10
511
437.2
262.7
70
488.6
293.6
331
283.7
170.5
391
201. 4
451
438.0
263.2
571
489.4
294. 1
32
284.6
171.0
92
336.
201.9
52
387.4
232.8
12
438.9
203.7
72
490.3
294. 6
33
285.4
171.5
93
330. 9
202.4
53
388. 3
233.3
13
439. 7
204.2
73
491.2
295. 1
34
286.3
172.0
94
337.7
202. 9
54
389. 2
233. 8
14
440.6
204.7
74
492.0
295. 6
35
287.2
172.5
95
338.6
203. 4
55
390.
234. 3
15
441.4
205.2
75
492.9
296. 1
36
288.0-
173.1
96
339.4
204.0
56
390. 9
2.34. 9
10
442. 3
205.8
76
493.7
296.7
37
288.9
173.6
97
340.3
204.5
57
391.7
235. 4
17
443. 2
266. 3
77
494.6
297. 2
38
289.7
174.1
98
341.2
205.
58
392.6
235.9
18
444.0
266.8
78
495.4
297.7
39
290. 6
174.6
99
,342.
205. 5
59
393.4
236.4
19
444.9
267. 3
79
496.3
298.2
40
291.4
175.1
400
342.9
200.0
20675
60
401
394. 3
,395. 2
236. 9
237."4
20
445.7
267.8
80
497.2
298.7
341
292.3
175.6
401
343.7
521
440.6
268.3
581
498.0
299.2
42
293.2
176.1
02
344.6
207.0
02
396.0
238.
22
447. 4
268.9
82
498.9
299. 8
43
294.0
176.7
03
345.4
207.6
03
390.9
238.5
23
448.3
269.4
83
499.7
300.3
44
294.9
177.2
04
346.3
208. 1
64
397. 7
239.0
24
449.2
269.9
84
500.6
300. 8
45
295.7
177.7
05
347.2
208.6
65
398.0
239.5
25
4.50.
270.4
85
501.4
301. 3
46
296.6
178.2
06
348.0
209.1
66
399.4
240.0
26
450.9
270.9
86
502.3
301.8
47
297.4
178.7
07
348.9
209.6
67
400.3
240.5
27
451.7
271.4
87
503. 2
302. 3
48
298.3
179.2
08
349.7
210.1
68
401.2
241.0
28
452.6
271.9
88
.504.
302. 8
49
299.2
179.8
09
350. 6
210.7
69
402.0
241.5
29
453.4
272.4
89
504. 9
303. 3
50
300.0
180.3
10
351. 4
211.2
211. 7"
70
471
402.9
403.7
242.1
30
4.54. 3
273.0
90
505.7
506.6
.303. 9
351
300.9
180.8
411
352: 3'
242.6
531
455.2
273.5
591
304.4
52
301.7
181.3
12
353.2
212.2
72
404.6
243.1
32
456.0
274.0
92
507.4
304.9
53
302.6
181.8
13
354.0
212.7
73
405. 4
243.0
33
456. 9
274.5
93
508.3
305.4
54
303.4
182.3
14
3.54.9
213. 2
74
400.3
244.1
34
457.7
275.
94
509.2
3a5.9
55
.304. 3
182.8
15
355.7
213.7
75
407.2
244.
35
458. 6
275. 5
95
510.0
306.4
56
305.2
183.4
16
356.6
214.3
76
408.0
245.2
36
459.4
276.1
96
510.9
307.0
57
306.0
183.9
17
357.4
214.8
77
408.9
245. 7
37
400. 3
276. 6
97
511. 7
307.5
58
306.9
184.4
18
358.3
215. 3
78
409.7
246.2
38
461. 2
277.1
98
512.6
308.0
59
307.7
184.9
19
359.2
215.8
79
410. 6
246. 7
.39
462.0
277.
99
513.4
308.5
60
308.6
185.4
20
360.0
216.3
80
411.4
247. 2
40
462.9
278. 1
600
514.3
309.
Dist.
Dep.
Lat.
DLst.
Dep.
Lat.
Dist.
Dep.
Lat,
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
)9° (121°, 239°, 301°
)•
TABLE 2.
[Page
693
Difference of Latitude and Departure for 32° (148°, 212°, 328°
)■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. j Lat.
Dep.
Dist. !
Lat.
Dep.
1
0.8
0.5
61
51.7
32.3
121
102.6
64.1
181 153.5
95.9
241
204.4
127.7
o
1.7
1.1
62
52.6
32.9
22
103. 5
64.7
82 154. 3
96.4
42 i
205. 2
128.2
3
2.5
1.6
63
53.4
33.4
23
104. 3
6.5.2
8:i
1.55.2 i 97.0
43
206.1
128. 8
4
3.4
2.1
64
54.3
33.9
24
105.2
65.7
84
1.56.0 : 97. 5 1
44
206.9
129.3
5
4.2
2.6
65
55.1
34.4
25
106.0
66.2
85
156. 9
98.0
45
207.8
129.8
6
5.1
3.2
66
56.0
3.5.0
26
106.9
66.8
86
157. 7
98.6
46
208.6
130.4
i
5.9
3.7
67
56.8
35.5
27
107.7
67.3
87
1.58. 6
99.1
47
209.5
130.9
H
6.8
4.2
68
57.7
36.0
28
108.6
67.8
88
1.59. 4
99.6
48
210.3
131.4
.9
7.6
4.8
69
58.5
36.6
29
109.4
68.4
89
160. 3
100.2
49
211.2
131.9
10
8.5
.5.3
70
.59.4
37.1
30
110.2
68.9
90
161.1
100.7
50
212.0
132.5
n
9.3
5.8
71
60.2
37.6
131
111.1
69.4
191
162.
101.2
2.')1
212. 9
133.0
^•2
10.2
6.4
72
61.1
38.2
32
111.9
69.9
92
162. 8
101.7
52
213.7
133.5
13
11.0
6.9
73
61.9
38.7
33 112.8
70.5
93
163. 7
102. 3
53
214.6
134.1
14
11.9
7.4
74
62.8
39.2
34 113.6
71.0
94
164.5
102.8
54
215.4
134.6
15
12.7
7.9
75
63.6
39.7
35 i 114.5
71.5
95
165.4
103. 3
55
216.3
135.1
Ifi
13.6
8.5
76
64.5
40.3
36 j 115.3
72.1
96
166. 2
103.9
.56
217.1
135.7
17
14.4
9.0
77
65.8
40.8
■37 ! 116.2
72.6
97
167.1
104.4
57
217.9
136.2
18
15.3
9.5
78
66.1
41.3
38 117.0
73.1
98
167.9
104. 9
58
218.8
136.7
19
16.1
10.1
79
67.0
41.9
39 i 117.9
73.7
99
168.8
105. 5
59
219.6
1.37. 2
20
21
17.0
10.6
80
67.8
68.7
42.4
40 ' 118. 7
74.2
200
169.6
170. .5
106.0
60
220. 5
221.3
137.8
17.8
11.1
81
42.9
141
119.6
74.7
201
106.5
261
138.3
22
18.7
11.7
82
69.5
43. 5
42
120.4
7.5.2
02
171.3
107.
62
222.2
138.8
23
19.5
12.2
83
70.4 1 44.0
43
121.3
75.8
03
172.2
107. 6
63
223.0
139. 4
24
20.4
12.7
84
71. 2 ' 44. 5
44
122.1
76.3
04
173.
108. 1
64
223.9
139.9
25
21.2
13.2
85
72. 1 45.
45
123.0
76.8
05
173.8
108.6
65
224.7
140.4
26
22.0
13.8
86
72.9 45.6
46
123.8
77.4
06
174.7
109. 2
66
225. 6
141.0
27
22.9
14.3
87
73. 8 i 46. 1
47
124.7
77.9
07
175. 5
109.7
67
226.4
141.5
28
23.7
14.8
88
74.6 1 46.6
48
125.5
78.4
08
176.4
110.2
68
227.3
142.0
29
24.6
1.5.4
89
75. 5 1 47. 2
49
126.4
79.0
09
177. 2
110.8
69
228.1
142.5
30
31
25.4
15.9
1674
90
76. 3 47. 7
50
127.2
79.5
10
211
178.1
111.3
70
229.0
229.8
143.1
26.3
91
77.2
48.2
151
128.1
80.0
178. 9
111.8
271
143.6
32
27.1
17.0
92
78.0
48.8
52
128.9
80.5
12
179.8 112.3
72
230.7
144.1
33
28.0
17.5
93
78.9
49.3
53 ; 129.8
81.1
13
180.6 112.9
73
231.5
144.7
34
28.8
18.0
94
79.7
49.8
■54
130.6
81.6
14
181.5 113.4
74
232.4
145. 2
35
29.7
18.5
95
80.6
.50. 3
.55
131.4
82.1
15
182.3 113.9
75
233. 2
145. 7
36
.30.5
19.1
96
81.4
50.9
56
132.3
82.7
16
183. 2 ; 114. 5
76
234.1
146. 3
37
31.4
19. B
97
82.3
51.4
57
133.1
83.2
17
184.0
11.5.
( t
234. 9
146.8
38
32.2
20.1
98
83.1
51.9
58
134.0
83.7
18
184.9
11.5.5
78
2.35. 8
147.3
39
33.1
20.7
99
84.0
52. 5
59
134. 8
84.3
19
185.7
116.1
79
236. 6
147.8
40
33.9
21.2
21.7
100
101
84.8
85.7
53.0
60
135.7
84.8
20
186.6
187. 4'
116.6
80
237. 5
23873
148.4
41
.34.8
53.5
161
136.5
8.5.3
221
117.1
281
148.9
42
3.5.6
22.3
02
86.5
54.1
62
137.4
a5.8
22
188.3
117.6
82
239.1
149.4
43
36.5
22.8
03
87.3
54.6
63
138.2
86.4
23
189.1
118.2
83
240.0
1.50.0
44
37.3
23.3
04
88.2
55.1
64
139.1
86.9
24
190.0
118.7
84
240.8
1.50. 5
45
38.2
23.8
05
89.0
55.6
65
1,39. 9
87.4
25
190.8
119.2
85
241.7
151.0
46
39.0
24.4
06
89.9
56.2
66
140.8
88.0
26
191.7
119.8
86
242. 5
151.6
47
39.9
24.9
07
90.7
56.7
67
141.6
88.5
27
192. 5
120. 3
87
243. 4
152. 1
48
40.7
25.4
08
91.6
57.2
68
142. 5
89.0
28
193.4
120.8
88
244.2
152. 6
49
41.6
26.0
09
92.4
57.8
69
143. 3
89.6
29
194.2
121.4
89
245. 1
1.53. 1
50
42.4
26.5
27.0
10
111
93. 3
94.1
58. 3
70
144.2
90.1
30
195. 1
195.9
121.9
90
245.9
246.8
153. 7
1.54. 2
51
43.3
.58.8
171
145.0
90.6
231
122. 4
291
52
44.1
27.6
12
95.0
59.4
72
145.9
91.1
32
196.7
122.9
92
247.6
154.7
53
44.9
28.1
13
95.8
.59.9
73
146.7
91.7
33
197.6
123. 5
93
248.5
155.3
54
45.8
28.6
14
96.7
60.4
74
147.6
92.2
34
198.4
124.0
94
249.3
155.8
55
46.6
29.1
15
97.5
60.9
75
148.4
92.7
35
199. 3
124.5
95
2.50. 2
1.56. 3
56
47.5
29.7
16
98.4
61.5
76 i 149.3
93.3
3()
200. 1
125.1
96
251.
1.56. 9
57
48.3
30.2
17
99.2
62.0
77
150.1
93.8
37
201.0
125.6
97
251.9
157.4
58
49.2
30.7
18
100.1
62.5
78
151.
94.3
38
201.8
126.1
98
252.7
157. 9
59
50.0
31.3
19
100.9
63.1
79
1.51. 8
94.9
39
202.7
126.7
99
253.6
1.58. 4
60
50.9
31.8
20
101.8
63.6
80
152.6
95.4
40
203.5
127.2
300
254.4
159.0
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
1 Lat.
58° (122°, 238°, ,302'
)•
24972°— 12 28
Page 694]
TABLE 2.
Difference- of latitude and Departure for 32° (148°, 2JS
°, 328=
)•
IDist
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
255. 3
1.59. 5
361
.306. 2
191. 3
421
357.0
223.1
481
407.9
2.54. 9
541
458.8
286.7
02
256.1
160.0
62
.307.
191.8
192.3
02
357. 9
223.6
82
408.8
255. 4
42
459. 6
287.2
03
257.
160. 5
63
.307. 9
23
358. 7
224.1
83
409.6
2.55. 9
43
460. 5
287.7
04
257. 8
161.1
64
308.7
192.9
24
359. 6
224.7
84
410. 5
256. 5
44
461.3
288.3
05
258. 7
161.6
65
309.5
193.4
25
360. 4
225.2
,85
411.3
257.
45
462.2
288. 8
06
259. 5
162.1
66
310. 4
193. 9
26
.361. 3
225. 7
86
412.2
257. 5
46
463.0
289. 3
07
260.4
162.7
67
311.2
194. 5
27
362.1
226. 3
87
41.3.
258. 1
47
463.9
289. 9
08
261.2
163.2
68
312. 1
195.
28
363.
226. 8
88
413.9
258. 6
48
464.7
290. 1
09
262.1
163.7
69
312. 9
195. 5
29
363. 8
227. 3
89
414.7
259. 1
49
465.6
290.9
10
262.9
164.3
70
371
313.8
314.6
196.0
196. 6
30
4.31
.364. 7
227.8
90
415.6
259. 6
50
466.4
291.5
311
263. 8
164.8
365. 5
228.4
491
416.4
260.2
5.51
467.3
292.0
12
264.6
165.3
72
315. 5
197.1
32
366. 4
228.9
92
417. 3
260.7
52
468.1
292. 5
13
265. 4
165.8
73
316.3
197.6
33
367. 2
229. 4
93
418.1
261. 2
53
469.0
293.0
• 14
266. 3
166.4
74
.317. 2
198.2
34
368. 1
230.
94
419.0
261.8
54
469.8
293.6
15
267.1
166.9
75
.318.
198.7
35
368.9
230.5
95
419.8
262.3
55
470.7
294.1
16
268.0
167.4
76
318.9
199.2
36
369.8
231.0
96
420.6
262.8
56
471.5
294.0
17
268. 8
168.0
77
319.7
199.8
37
370.6
231.6
97
421. 5
263. 4
57
472.4
295. 2
'18
269. 7
168. 5
78
320. 6
200.3
38
371.5
232.1
98
422.3
263.9
58
473.2
295.7
19
270. 5
169.0
79
321.4
200.8
39
372.3
232. 6
99
423. 2
264.4
59
474.1
296.2
20
271.4
169.6
80
322.3
201.3
40
373.2
233. 1
500
424.0
265.0
60
474.9
296.7
321
272 2
170.1
381
323.1
201.9
441
374.0
233. 7
,501
424. 9
265. 5
.561
475. 8
297.3
22
27311
170.6
82
324.
202. 4
42
374.8
234.2
02
425. 7
266.0
62
476.6
297.8
23
273.9
171.1
83
324.8
202.9
43
375. 7
234. 7
03
426.6
266. 5
63
477. 5
298.3
24
274.8
171.7
84
325. 7
203. 5
44
376. 5
235. 3
04
427.4
267.1
64
478.3
298.9
25
275.6
172.2
85
326.5
204.0
45
377. 4
235. 8
05
428.3
267.6
65
479.2
299.4
26
276.5 !172.7
86
327.4
204. 5
46
378.2
236. 3
06
429.1
268.1
66
480.0
299. 9
27
277.3 173.3
87
328. 2
205. 1
47
379.1
236.9
07
430.
268.7
67
480.9
.300. 5
28
278.2
173.8
88
329. 1
205.6
48
379.9
237.4
08
430.8
269.2
, 68
481.7
301.0
29
279.0
174.3
89
329.9
206. 1
49
380.8
237.9
09
431.7
269.7
69
482. 6
301. 5
30
279.9
174.9
90
330.8
206.6
50
381. 6
238.4
10
432.5
270.3
70
483.4
,302. 1
331
280.7
17.5.4
391
331.6
207.2
451
382. 5
239.0
511
433. 4
270.8
571
484.3
302.6
32
281.6
175. 9
92
332. 5
207.7
52
383. 3
239.5
12
434.2
271.4
72
485.1
303.2
33
282.4
176.4
93
333. 3
208. 2
53
384. 2
240.0
13
435.1
271.9
73
486.0
.303. 7
34
283.3
177.0
94
334. 2
208.8
54
385.
240.6
14
435. 9
272.4
74
486.8
,304. 2
35
284.1
177. 5
95
335.
209.3
55
385. 9
241.1
15
436.8
272.9
.75
487.7
304.7
36
285.
178.0
96
335. 8
209.8
56
386. 7
241.6
16
437.6
273.5
76
488.5
,305. 3
37
285. 8
178.6
97
336. 7
210.4
57
387.6
242.2
17
4,38. 5
274.0
77
489.4
305. 8
38
286.7
179.1
98
337.5
210. 9
58
388.4
242.7
18
439. 3
274. 5
78
490.2
306. 3
39
287.5
179.6
99
.338. 4
211.4
59
389. 3
243.2
19
440.2
275.0
79
491.1
306. 8
40
288.3
180.2
400
339.2
211.9
60
,390. 1
391.0
243.8
20
441.0
275.6
80
491. 9
307.4
307.9
341
289.2
180.7
401
340. 1
212. 5
461
244.3
521
441.9
276.1
581
492.8
42
290.0
181.2
02
340. 9
213.
62
391.8
244.8
22
442.7
276.6
82
493. 6
308. 4
43
290.9
181.7
03
341.8
213.5
63
392.7
245. 4
23
443.6
277.2
83
494.5
309.
44
291.7
182.3
04
342. 6
214.1
64
393. 5
245. 9
24
444.4
277.7
84
495.3
309. 5
45
292.6
182.8
05
343.5
214.6
65
394.4
246.4
25
445. 3
278.2
85
496.2
310.
46
293.4
183.3
06
344.3
21.5. 1
66
395. 2
246.9
26
446.1
278.7
86
497.0
310. 5
47
294.3
183.9
07
345.2
215. 7
67
396.0
247.5
27
446.9
279.3
87
497.8
311. 1
48
295.1
184. 4
08
,346.
216.2
68
396.9
248.0
28
447.8
279.8
88
498.7
311.6
49
296.0
184.9
09
346.9
216.7
69
397.7
248.5
29
448.6
280.3
89
499. 5
312.1
50
296.8
185.4
10
347.7
217.2
70
471
398.6
399.4
249.0
30
449.5
280.9
90
500.3
312. 6
351
297.7
186.0
411
348.6
217.8
249.6
531
450.3
281.4
591
501.2
313. 2
52
298.5
186.5
12
349.4
218.3
• 72
400.3
2.50. 1
32
451. 1
281.9
92
502.0
313.7
53
299.4
187.0
13
350.3
218.8
73
401.1
250.6
33
452.0
282.4
93
,502. 9
314.2
54
.300. 2
187.6
14
351.1
219.4
74
402.0
251.2
34
452.8
283.0
94
,503. 7
314. 8
55
301.1
188.1
15
352.0
219.9
75
402.8
251.7
35
453.7
283.5
95
504.6
315.3
56
.301.9
188.6
16
352.8
220.4
76
403.7
252.2
36
4.54. 5
284.0
96
505.4
315. 8
57
.302. 8
189.2
17
.353. 6
221.0
77
404.5
252.8
37
455.4
284.6
97
506.2
316. 4
58
,303. 6
189.7
18
354.5
221.5
78
40,5.4
253.3
38
456.2
285.1
98
,507. 1
316. 9
59
.304. 5
190.2
19
355.3
222.0
79
406.2
253.8
39
457.1
285.6
99
508.0
.317. 4
60
305. 3
190.8
20
356. 2
222.5
80
407.1
2.54. 3
40
457.9
286.2
600
508.8
318.0
Diet.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
5
8° (1
22°, 238°, .302°
)■
•
TABLE 2.
[Page 595
Difference of Latitude and Departure for
33° (147°, 213
°, 327°
)•
Dist.
Lat.
Dep.
Plst.
Lat.
Dep.
Dist,
Lat,
Dep.
Dist,
Lat,
Dep,
Dist.
Lat.
Dep,
i
0.8
0.5
61
.51.2
,33.2
121
101, 5
65.9
181
• 1.51. 8
98,6
241
202.1
131,3
2
1.7
1.1
62
.52.0
33.8
22
102,3
66,4
82
1.52, 6
99,1
42
203.0
131,8
3
2.5
1.6
63
52. 8
34.3
23
103,2
67,0
83
153. 5
99,7
43
203. 8
132, 3
4
S.4
2.2
64
53.7
34,9
24
104.0
67, 5
84
154, 3
100,2
44
204.6
132.9
5
4.2
2.7
65
.54.5
35,4
25
104.8
68,1
85
1.5.5. 2
100,8
45
205. 5
133.4
6
5.0
8.3
66
55.4
3.5,9
26
105.7
68,6
86
1.56,
101,3
• 46
206,3
134.0
7
5.9
3.8
67
56.2
36.5
27
106.5
69,2
87
156,8
101,8
47
207,2
134.5
8
6.7
4.4
68
57.0
37.0
28
107. 3
69,7
88
157, 7
102,4
48
208,0
135. 1
9
7.5
4.9
69
57.9
.37,6
29
108.2
70,3
89
158,5
102,9
49
208, 8
135. 6
10
8.4
5.4
70
58.7
38,1
30
109.0
70,8
90
1.59, 3
103,5
50
209, 7
210,5
136, 2
11
9.2
6.0
71
59.5
,38,7
131
109.9
71,3
191
160,2
104,0
251
136,7
12
10.1
6.5
72
60.4
39.2
32
110.7
71,9
92
161,0
104,6
52
211,3
137,2
13
10.9
7.1
73
61.2
39.8
33
111.5
72.4
93
161, 9
105,1
53
212, 2
137,8
14
11.7
7.6
74
62.1
40.3
34
112.4
73,0
94
162, 7
105, 7
54
213,0
138,3
15
12.6
8.2
75
62.9
40.8
.35
113.2
73,5
95
163, 5
106,2
55
213,9
138.9
16
13.4
8.7
76
63.7
41.4
.36
114.1
74,1
96
164,4
106,7
56
214.7
139.4
17
14.3
9.3
77
64.6
41.9
37
114.9
74,6
97
165, 2
107,3
57
215. 5
140.0
18
15.1
9.8
78
65.4
■42,5
38
115.7
75, 2
98
166.1
107,8
58
216.4
140.5
19
15.9
10.3
79
6(5.3
43,0
39
116.6
75, 7
99
166,9
108.4
59
217.2
141.1
20
16.8
10.9
80
67.1
43.6
40
117.4
76,2
200
167.7
168,6
108.9
60
218.1
218,9
141.6
21
17.6
11.4
81
67. 9
44.1
141
118. 3
76.8
201
109.5
261
142.2
22
18.5
12.0
82
68.8
44.7
42
119.1
77.3
02
169. 4
110,0
62
219,7
142.7
23
19.3
12.5
83
69.6
4.5.2
43
119.9
77.9
03
170.3
110,6
63
220,6
143.2
24
20.1
13.1
84
70.4
4.5,7
44
120.8
78.4
04
171,1
111,1
64
221.4
143.8
25
21.0
13.6
85
71.3
46.3
45
121.6
79.0
05
171.9
111,7
65
222, 2
144.3
26
21.8
14.2
86
72.1
46.8
46
122.4
79.5
06
172,8
112,2
66
223.1
144,9
27
22.6
14.7
87
73.0
47.4
47
12.3,3
80.1
07
17,3.6
112,7
67
223. 9
145,4
28
23.5
15.2
88
73.8
47.9
48
124,1
80. 6
08
174.4
U3,3
68
224.8
146,
29
24.3
15.8
89
74.6
48.5
49
125,0
81.2
09
175. 3
113.8
69
225. 6
146,5
30
31
25.2
26.0
16.3
90
75. 5
49.0
50
125, 8
81.7
10
176.1
177.0
114.4
70
226.4
147.1
147.6
16.9
91
76.3
49.6
151
126,6
82.2
211
114.9
271
227.3
32
26.8
17.4
92
77.2
.50.1
52
127,5
82.8
12
177.8
115.5
72
228.1
148,1
33
27.7
18.0
93
78.0
.50.7
53
128,3
8.3.3
13
178.6
116.0
73
229,0
148,7
34
28.5
18.5
94
78.8
51,2
54
129,2
a3.9
14
179. 5
116,6
74
229,8
149,2
35
29.4
19.1
95
79.7
51.7
55
130,0
84.4
15
180, 3
117,1
75
230,6
149, 8
36
30.2
19.6
96
80.5
.52.3
.56
130.8
85.0
16
181,2
117,6
76
231,5
1.50, 3
37
31.0
20.2
97
81.4
.52.8
57
131.7
85.5
17
182,0
118,2
77
232.3
150, 9
38
31.9
20.7
98
82.2
.53. 4
58
132.5
86.1
18
182,8
118,7
78
233.2
151.4
39
32,7
21.2
99
83.0
.53.9
.59
133.3
86.6
19
183, 7
119,3
79
234.0
1.52.
40
33.5
21.8
100
• 83.9
.54, 5
60
134.2
135,
87.1
20
221
184,5
119,8
80
234.8
235,7
152. 5
41
34.4
22.3
101
84.7
55.0
161
87.7
185, 3
120,4
281
153.0
43
35.2
22.9
02
85. 5
5.5.6
62
135,9
88,2
22
186, 2
120,9
82
236,5
153.6
43
36.1
23.4
03
86.4
56.1
63
1,36, 7
88.8
23
187,0
121.5
S3
237,3
1.54. 1
44
.36. (t
24.0
04
87.2
.56,6
64
137,5
89.3
24
187,9
122,0
84
238, 2
1.54, 7
45
.37.7
24.5
05
88.1
■57,2
65
1.38. 4
89.9
25
188,7
122.5
85
239,0
155.2
46
.38.6
25.1
06
88.9
57, 7
66
139. 2
90.4
26
189,5
123. 1
86
239,9
155.8
47
39.4
25.6
07
89.7
.58. 3
67
140.1
91,0
27
190,4
•123.6
87
240,7
156.3
48
40. 3
26.1
08
90.6
.58.8
68
140,9
91.5
28
191,2
124.2
88
241.5
156. 9
49
41.1
26.7
09
91.4
59.4
m
141,7
92.0
29
192,1
124.7
89
242,4
1.57. 4
50
51
41.9
42.^8
27.2
27.8
10
111
92. 3
93.1
59. 9
60:5
70
171
142,6
143, 4
92.6
30
192,9
193.7
125.3
90
243,2
157. 9
9.3,1
231
125. 8
291
244,1
1,58. 5
52
48.6
28.3
12
93.9
61.0
72
144.3
93.7
32
194,6
126.4
92
244,9
159.0
53
44.4
28.9
13
94.8
61.5
73
145. 1
94.2
33
195, 4
126 9
93
245,7
1.59. 6
54
45.3
29.4
14
9.5.6
62. 1
74
145. 9
94.8
34
196,2
127.4
94
246, 6
160.1
55
46.1
30.0
15
96.4
62. 6
75
146. 8
95.3
35
197,1
128.0
95
247.4
160.7
56
47.0
30.5
16
97. 3
6.3.2
76
147.6
9.5.9
36
197,9
128.5
96
248.2
161.2
57
47.8
31.0
17
98.1
6.3.7
77
148.4
96.4
37
198,8
129.1
97
249,1
161.8
58
48.6
31.6
18
99.0
64. 3
78
149.3
96,9
,38
199, 6
129.6
98
249.9
162.3
59
49.5
32.1
19
99.8
64.8
79
150.1
97,5
39
200,4
130.2
99
250,8
162.8
60
50.3
32.7
20
100.6
65.4
80
151.0
98,0
40
201.3
130.7
300
251.6
163.4
Dist,
Dep.
Lat
Dist.
Dep.
Lat.
Dist.
Dep.
Lat,
Dist,
Dep,
I.at.
Dist.
Dep.
Lat.
7° (123°, 2,37°, 303°
.
Page 596J
TABLP] 2.
Difference of Latitude and Departure for 33° (147°, 213
327°
)■
Dlst.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
252.4
16.3.9
.361
.302. 8
196.6
421
353.1
229.3
481
403. 4
262.
541
453.7
294.6
OS
253. 3
164. 4
62
303. 6
197.1
22
353. 9
229.8
82
404. 2
262. 5
42
454. 6
295.2
03
254.1
165.0
63
304. 4
197.7
23
354.7
230.4
83
405. 1
263. 1
43
455.4
295.7
04
255.0
165.5
64
305. 3
198.2
24
355.6
230.9
84
405. 9
203. 6
44
456. 2
296.2
05
255. 8
166.1
ens
306. 1
198.8
25
356. 4
231.4
85
406.7
264.1
45
457. 1
296.8
Oti
256. 6
166.6
66
307.0
199.3
26
.357. 3
232.
86
407.6
264.7
46
4.57. 9
297. 3
07
257. 5
167. 2
67
307.8
199.8
27
.358. 1
232. 5
87
408.4
265.2
47
458.8
297.9
08
258. 3
167. 7
68
308.6
200.4
28
359.0
233. 1
88
409. 3
265.8
48
459.6
298.4
09
259.2
168. 3
69
309. 5
200.9
29
359. 8
233. 6
89
410.1
266.3
49
460.4
299.0
10
260.0
168.8
70
310. 3
311.2
201. 5
.30
360.6
361.5
234.2
90
411.
411.8
266.8
50
461.3
299.5
311
260.8
169.3
371
202.0
431
234. 7
491
267.4
551
462. 1
300.1
)?.
261.7
169. 9
72
312.
202.6
32
362.3
235. 2
92
412. 6
267.9
52
463.0
300.6
13
262.5
170.4
73
312.8
203.1
33
363.1
235.8
93
413. 5
268. 5
53
463.8
301.2
14
263.3
171.0
74
313. 7
203.7
34
364.
236. 3
94
414.3
269.0
54
464.6
301.7
15
264.2
171.5
75
314. 5
204.2
35
304.8
2.36. 9
95
415. 1
269.6
55
465.5
302.3
Ifi
265.0
172.1
76
315. 3
204.7
36
365. 7
237. 4
96
416.0
270.1
56
466.3
302.9
17
265.9
172.6
77
316. 2
205. 3
37
3()6. 5
238.
97
416.8
270.7
57
467.2
303. 4
18
266.7
173.2
78
317.0
205.8
38
367. 3
238. 5
98
417. 6
271.2
58
468.0
303.9
19
267. 5
173.7
79
317.9
206.4
39
368. 2
239.1
99
418. 5
271.8
.59
468.8
304.5
20
321
268.4
269.2
174.2
174.8
80
318.7
206.9
40
369.0
369. 9
239. 6
5C0
•501
419. 3
272.3
60
469.7
470. 5
305.0
381
319.5
207.5
441
240.1
420.2
272.8
561
305. 5
09
270.1
175. 3
82
320. 4
208.0
42
370.7
240.7
02
421.0
273.4
62
471.3
306.1
23
270.9
175.9
83
321.2
208.6
43
371.5
241 . 2
03
421.9
273.9
63
472.2
306.6
24
271.7
176.4
84
322.1
209.1
44
372. 4
241.8
04
422.7
274.5
64
473.0
307. 2
25
272.6
177.0
85
322.9
209.6
45
373. 2
242. 3
05
423. 5
275.
65
473. 8
307.7
26
273.4
177.5
86
323. 7
210.2
46
374. 1
242. 9
06
424.4
275. 6
66
474.7
308. 3
27
274.2
178.1
87
324.6
210.7
47
374.9
243. 4
07
425. 2
276. 1
67
475. 5
308.8
28
275.1
178.6
88
325. 4
211.3
48
375. 7
244.0
08
426.0
276. 7
68
476.4
309.4
29
275. 9
179.1
89
32(). 2
211.8
49
376. 6
244. 5
09
426.9
277. 2
69
477.2
309.9
30
331
276.8
277.6
179. 7
180.2
90
327. 1
212.4
212.9
50
451
377.4
378. 2
245. 1
245. 6
10
511
427.7
277.8
70
478.0
478.9
310.4
311.0
391
327.9
428.5
278.3
571
32
278.4
180.8
92
328.8
213. 5
52
379.1
246. 1
12
429.4
278.8
72
479.7
311.5
33
279.3
181.3
93
329.6
214.0
53
379. 9
246.7
13
430.2
279.4
73
480.6
312.0
34
280.1
181.9
94
330.4
214.0
54
380.8
247. 2
14
431.1
279.9
74
481.4
312.6
35
281.0
182.4
95
331.3
215.1
55
381.6
247. 8
15
431.9
280.4
75
482.2
313. 1
36
281.8
183.
96
332.1
215.6
56
.382. 4
248. 3
16
432. 7
281.0
76
483. 1
313. 7
37
282.6
183.5
97
333.
216.2
57
383.3
248.9
17
433.6
281.5
i i
483. 9
314. 2
38
283.5
184.1
98
333.8
216.7
58
384.1
249.4
18
434.4
282.1
78
484.7
314.8
39
284.3
184.6
99
334.6
217.3
59
385.0
2.50.
19
435. 3
282.6
79
485. 6
315. 3
40
341
285.2
185. 1
400
33.5.5
217.8
60
,385.8
250. 5
20
436. 1 ^
283. 2
80
486.4
487.2
315. 9
316.4
286.0
lai. 7
401
336.3
218.4
461
386.6
251.
521
436.9
283.7
581
42
286.8
186.2
02
337.1
218.9
62
387. 5
251.6
22
437.8
284.3
82
488.1
317.0
43
287.7
186.8
03
338.0
219. 5
63
388.3
252. 1
23
438.6
284.8
83
488.9
.317. 5
44
288. 5
187.3
04
338.8
220.0
64
389. 1
252. 7
24
439.4
285.4
84
489.8
318.1
45
289.3
187.9
05
339.7
220. 5
65
390.0
253. 2
25
440. 3
285.9
85
490.6
318. 6
46
290.2
188.4
06
340.5
221.1
66
390. 8
2.53. 8
26
441.1
286.5
86
491.5
319. 2
47
291.0
189.0
07
.341. 3
221.6
67
391.7
254. 3
27
442.0
287.0
87
492.3
319. 7
48
291.9
189. 5
08
342.2
222. 2
68 ; 392.5
2.54. 9
28
442.8
287.5
88
493.1
320.2
49
292.7
190.0
09
343.0
222.7
69 i 393.3
255. 4
29
443.6
288.1
89
494.0
320.8
50
293.5
294.4
190.6
10
343.9
223.3
70
394.2
255. 9
30
531
444.5
288.6
90
494.8
321.3
351
191.1
411
344.7
223.8
471
395.
256.5
44.5.3
289.2
591
495.7
321.9
52
295.2
191.7
12
345. 5
224.4
72
395.8
257.0
32
446. 1
289.7
92
496.5
322.4
53
296.1
192.2
13
346.4
224.9
73
.396. 7
257. 6
33
447.0
290.3
93
497.3
322.9
54
296.9
192.8
14
347.2
225. 4
74
397.5
258. 1
34
447.8
290.8
94
498.1
323.5
55
297.7
193. 3
15
348.1
226.0
75
398.3
258.7
35
448.7
291.4
95
499.0
324.1
56
298.6
193. 9
16
348.9
226.5
76
399.2
259. 2
36
449.5
291.9
96
499.8
324.6
57
299.4
194.4
17
349.7
227.1
77
400.0
259.8
37
450.3
292.5
97
500.6
325. 1.
58
300.2
194.9
18
350.6
227.6
78
400.9
260. 3
38
451.2
293.0
98
501.5
325.7
59
301.1
195.5
19
.351.4
228.2
79
401.7
260.9
.39
452.0
29.3.6
99
502.3
326.2
60
301.9
196.0
20
352.2
228.7
80
402.6
261.4
40
452.9
294.1
600
503.2
326.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
)7° (123°, 237°, 303°
)•
TABLE ±
[Page 697
Difference of Latitude and Departure for 34° (146°, 214°, 326°
)■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
.50.6
34.1
121
100.3
67.7
181
150.1
101.2
241
199.8
134.8
2
1.7
1.1
62
51.4
34.7
22
101.1
68.2
82
150.9
101.8
42
200.6
135. 3
3
2.5
1.7
63
52.2
35.2
23
102.0
68.8
•83
151.7
102.3
43
201.5
135.9
4
3.3
2.2
64
53.1
3.5.8
24
102.8
69.3
84
152.5
102.9
44
202.3
136.4
5
4.1
2.8
65
53.9
36.3
25
103. 6
69.9
85
153. 4
103. 5
45
203.1
137.0
6
5.0
3.4
66
54.7
36.9
26
104.5
70.5
86
154.2
104.0
46
203.9
137.6
7
5.8
3.9
67
55.5
37.5
27
105. 3
71.0
87
1.55.
104.6
47
204.8
138.1
8
6.6
4.5
68
56.4
38.0
28
106.1
71.6
88
155. 9
105. 1
48
205.6
138.7
9
7.5
5.0
69
57.2
38.6
29
106.9
72.1
89
1.56. 7
105. 7
49
206.4
139.2
10
8.3
5.6
70
58.0
58.9
39.1
30
107.8
72.7
90
157.5
106.2
50
207.3
139.8
11
9.1
6.2
71
39.7
131
108.6
73.3
191
158.3
106.8
251
208.1
140.4
12
9.9
6.7
72
.59.7
40.3
32
109.4
7.3.8
92
159.2
107.4
52
208.9
140.9
13
10.8
7.3
73
60. 5
40.8
33
110.3
74.4
93
160.0
107.9
53
209.7
141. 5
14
11.6
7.8
74
61.3
41.4
34
111.1
74.9
94
160.8
108.5
.54
210.6
142.0
15
12.4
8.4
75
62.2
41.9
35
111.9
75.5
95
161.7
109.0
55
211.4
142.6
16
13.3
8.9
76
63.0
42.5
36
112.7
76.1
96
162.5 109.6
.56
212.2
143.2
17
14.1
9.5
77
63.8
43.1
37
113.6
76.6
97
163.3
110.2
57
213.1
143.7
18
14.9
10.1
78
64.7
43.6
38
114.4
77.2
98
164.1
110.7
58
213.9
144.3
19
15.8
10.6
79
65.5
44.2
.39
115.2
77. 7
99
165.0
111.3
.59
214.7
144.8
20
16.6
11.2
11.7
80
66.3
44.7
40
116.1
78.3
200
165.8 111.8
60
215.5
145.4
145. 9
21
17.4
81
67.2
45.3
141
116.9
78.8
201
166.6 112.4
261
216.4
22
18.2
12.3
82
68.0
4.5.9
42
117.7
79.4
02
167.5 113.0
62
217.2
146. 5
23
19.1
12.9
83
68.8
46.4
43
118.6
80.0
03
168.3 113.5
63
218.0
147.1
24
19.9
1.3.4
84
69.6
47.0
44
119.4
80.5
04
169.1
114.1
64
218.9
147.6
25
20.7
14.0
85
70.5
47.5
45
120.2
81.1
05
170.0
114.6
65
219.7
148.2
26
21.6
14.5
86
71.3
48.1
46
121.0
81.6
06
170.8
11.5.2
66
220.5
148.7
27
22.4
15.1
87
72.1
48.6
47
121.9
82.2
07
171.6
115. 8
67
221.4
149.3
28
23.2
15.7
88
73.0
49.2
48
122.7
82.8
08
172.4
116.3
68
222. 2
149.9
29
24.0
16.2
89
73.8
49.8
49
123.5
83.3
09
173.3
116.9
69
223.0
150.4
30
31
24.9
16.8
90
74.6
50.3
50
124.4
83.9
10
174.1
117.4
118.0
70
271
223.8
151.0
25.7
17.3
91
75.4
50.9
1.51
125.2
84.4
211
174.9
224.7
151. 5
32
26.5
17.9
92
76.3
51.4
52
126.0
8.5.0
12
175.8
118. 5
72
225.5
152. 1
33
27.4
18.5
93
77.1
52.0
53
126.8
a5.6
13
176.6
119.1
73
226. 3
152. 7
34
28.2
19.0
94
77.9
.52.6
.54
127.7
86.1
14
177.4
119.7
74
227.2
153.2
35
29.0
19.6
95
78.8
53.1
.55
128.5
86.7
15
178.2
120.2
75
228.0
153.8
36
29.8
20.1
96
79.6
53.7
56
129.3
87.2
16
179.1
120.8
76
228.8
154. 3
37
30.7
20.7
97
80.4
54.2
57
130. 2
87.8
17
179.9
121.3
77
229.6
1.54.9
38
31.5
21.2
98
81.2
54.8
58
131.0
88.4
18
180.7
121.9
78
230. 5
155. 5
39
32.3
21.8
99
82.1
55. 4
.59 : 131. 8
88.9
19
181.6
122. 5
79
231.3
1.56.0
40
41
33.2
34.0
22.4
22.9
100
82.9
55.9
60
161
132.6
89.5
20
182.4
123.0
80
232.1
1.56.6
157.1
101
83.7
56. 5
133.5
90.0
221
183. 2
123.6
281
233.0
42
,34.8
23.5
02
84.6
57.0
62 i 134.3
90.6
22
184.0
124.1
82
233.8
1.57. 7
43
35.6
24.0
03
85.4
.57.6
63 i 135. 1
91.1
23
184.9
124.7
83
234.6
158. 3
44
36.5
24.6
04
86.2
.58.2
64
136.0
91.7
24
185.7
125.3
84
235.4
158. 8
45
37.3
25.2
05
87.0
58.7
65
136.8
92.3
25
186.5
125.8
85
236.3
159.4
46
38.1
25.7
06
87.9
59.3
66
137.6
92.8
26
187.4
126.4
86
237.1
159. 9
47
39.0
26.3
07
88.7
59.8
67 ! 138.4
93.4
27
188.2
126.9
87
237. 9
160. 5
48
39.8
26.8
08
89.5
60.4
68 1 139.3
93.9
28
189.0
127.5
88
238. 8
161.0
49
40.6
27.4
09
90.4
61.0
69
140.1
94.5
29
189.8
128.1
89
239.6
161.6
50
41.5
28.0
10
91.2
61.5
70
140.9
95.1
30
190.7
128.6
129. 2
90
29r
240.4
162.2
162. 7
51
42.3
28.5
111
92.0
62.1
171
141.8
95.6
231
191.5
241.2
52
43.1
29.1
12
92.9
62.6
72
142.6
96.2
32
192.3
129.7
92
242.1
163. 3
53
43.9
29.6
13
93.7
63.2
73
143.4
96.7
33
193.2
130.3
93
242.9
163.8
54
44.8
30.2
14
94.5
63.7
74
144.3
97.3
34
194.0
130.9
94
243.7
164. 4
55
45.6
30.8
15
95.3
64.3
75
145.1
97.9
35
194.8
131.4
95
244.6
ia5.
56
. 46.4
31.3
16
96.2
64.9
76
145.9
98.4
36
195. 7
1.32.
96
245.4
165. 5
57
47.3
31.9
17
97.0
65.4
77
146.7
99.0
37
196.5
132.5
97
246.2
166.1
58
48.1
32.4
18
97.8
66.0
78
147.6
99.5
38
197.3
13.3.1
98
247.1
166.6
59
48.9
33.0
19
. 98.7
66.5
79
148.4
100.1
39
198.1
133. 6
99
247.9
167.2
60
49.7
33.6
20
99.5
67.1
80
149.2
100.7
40
199.0
134.2
300
248.7
167.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist
Dep.
Lat.
56° (124°, 236
°, .304°
)•
Page 698]
TABLE 2.
Difference of Latitude and Esparture for 34° (146°, 214
°, 326°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
249.5
168.3
361
299.3
201.9
421
349.0
235.4
481
398.8
269.0
541
448.5
302. 5
02 , 250.4
168.9
62
300.1
202.4
22
349.9
236.0
82
399.6
269.5
42
449.4
303.1
as
251.2
169.4
63
300.9
203.0
23
350.7
236.5
83
400.4
270.1
43
450. 2
303.6
04
252.0
170.0
64
301.8
203. 5
24
351.5
237.1
84
401.3
270.6
44
451.0
304. 2
05
252.9
170.6
65
302. 6
204.1
25
352. 3
237.7
85
402.1
271.2
45
451.8
304.8
06
253.7
171.1
66
303.4
204.7
26
353.2
238.2
86
402.9
271.8
46
452. 6
305. 3
07
254.5
171.7
67
304. 3
205.2
27
354.0
238.8
87
403.8
272.3
47
453. 5
305.9
08
255.3
172.2
68
305.1
205. 8
28
354.8
239.3
88
404.6
272.8
48
454. 3
306.4
09
256.2
172.8
69
305.9
206.3
29
355.7
239.9
89
405.4
273.4
49
4.55. 2
307.0
10
257.0
173.3
70
306.7
206.9
30
356.5
357.3
240.4
90
406.2
274.0
50
456.
307.5
311
257.8
173.9
371
307.6
207.5
431
241.0
491
407.1
274.6
551
456.8
308.1
12
258.7
174.5
72
308.4
208.0
32
358.1
241.6
92
407.9
275.1
52
457.6
308.7
13
259.5
175.0
73
309.2
208.6
33
359.0
242.1
93
408.7
275. 7
53
458. 4
309.2
14
260.3
175.6
74
310.1
209.1
34
359.8
242.7
94
409.5
276.2
54
4,59. 3
309.8
15
261.2
176.1
75
310.9
209. 7
35
360.6
243.2
95
410.4
276.8
55
460.1
310.3
16
262.0
176.7
76
311.7
210.3
36
361.5
243.8
96
411.2
277.4
56
460.9
310.9
17
262.8
177.3
77
312.6
210.8
37
362.3
244.4
97
412.0
277.9
57
461.7
311.5
18
263.7
177.8
78
313.4
211.4
38
363.1
244.9
98
412.8
278.4
58
462.6
312.0
19
264.5
178.4
79
314.2
211.9
39
364.0
245.5
99
413.7
279.0
59
463.4
312.6
20
265. 3
266.1
178.9
80
315.0
212. 5
40
364.8
365.6
246.0
500
414.5
279.6
60
464.2
313.1
321
179. 5
381
315.9
213.0
441
246.6
501
415.3
280.1
561
465. 1
313.7
22
267.0
180.1
82
316.7
213.6
42
366.4
247.2
02
416.2
280.7
62
465.9
314.3
23
267.8
180.6
83
317. 5
214.2
43
367. 3
247.7
03
417.0
281.3
63
466. 8
314.8
24
268.6
181.2
84
318.4
214.7
44
368.1
248.3
04
417.8
281.8
64
467.6
315. 4
25
269.5
181.7
85
319. 2
215.3
45
368.9
248.8
05
418.6
282.4
65
468. 4
315. 9
26
270.3
182.3
86
320.0
215.8
46
369.8
249. 4
06
419.4
282.9
66
469.2
.316. 5
27
271.1
182.9
87
320. 8
216.4
47
370.6
250.0
07
420.3
283.5
67
470.1
317.1
28
271.9
183.4
88
.321. 7
217.0
48
371.4
250.5
08
421.1
284.1
68
470.9
.317. 6
29 i 272. 8
184.0
89
322.5
217.5
49
372.2
251.1
09
421.9
284.6
69
471.7
318.2
30 ' 273. 6
331 , 274.4
184. 5
90
323.3
218.1
50
373.1
251.6
252."2
10
511
422.8
285.2
70
472.6
318. 7
319. 3
185.1
391
324.2
218.6
451
373.9
423.6
285.8
571
473. 4
32 ; 275. 2
185. 6
92
325.0
219.2
52
374.7
252.8
12
424.4
286.3
72
474.2
319.9
.33
276.1
186.2
93
325.8
219.8
53
375.6
253.3
13
425.3
286.9
73
475.
320.4
34
276.9
186.8
94
326.6
220.3
54
376.4
253.9
14
426.1
287.4
74
475. 9
321.0
35
277.7
187.3
95
.327. 5
220.9
55
377. 2
254.4
15
426.9
288.0
75
476.7
321.5
36
278.6
187.9
96
328.3
221.4
56
378.0
255.0
16
427.8
288.5
76
477. 5
322.1
37
279.4
188.4
97
329.1
222.0
57
378.9
255.5
17
428.6
289.1
77
478.3
322.7
38
280.2
189.0
98
.330.
222.6
58
379.7
256.1
18
429.4
289.6
78
479.2
323.2
39
281.0
189.6
99
330.8
223.1
59
380. 5
256. 7
19
430.3
290.2
79
480.0
323.8
40
281.9
282.7
190.1
400
331.6
223.7
60
381.3
257.2
20
431.1
431.9
290.8
80
480.8
324. 3
341
190.7
401
332.4
224.2
461
382.2
257.8
521
291.3
581
481.6
324. 9
42
283.5
191.2
02
333.3
224.8
62
383.0
258.3
22
432.8
291.9
82
482. 5
325.4
43
284.4
191.8
03
334. 1
225.4
63
383.8
258.9
23
433.6
292.5
83
483. 3
326.0
44
285. 2
192.4
04
334.9
225.9
64
384.7
259. 5
24
434.4
293.0
84
484.1
326. 6
45
286.0
192.9
05
335.8
226.5
65
385.5
260.0
25
435.3
293.6
85
485.0
327.2
46
286.9
193.5
06
336.6
227.0
66
386.3
260. 6
26
436.1
294.1
86
485.8
327.7
47
287.7
194.0
07
337.4
227.6
67
387.2
261.1
27
436.9
294.7
87
486.6
328.2
48
288.5
194.6
08
338.3
228.1
68
388.0
261.7
28
437.8
295.3
88
487. 5
328.8
49
289.3
195.2
09
339.1
228. 7
69
388.8
262.3
29
438.6
295.8
89
488. 3
329.4
50
290.2
195.7
10
339.9
229.3
70
389.7
262.8
30
439.4
296.4
90
489.2
329.9
330. 5
351
291.0
196.3
411
340.7
229.8
471
390.5
263.4
531
440.3
296.9
591
490.
52
291.8
196.8
12
341.6
230.4
72
391.3
263.9
32
441.1
297.4
92
490.8
331.0
53
292.7
197.4
13
342.4
230.9
73
392.1
264.5
33
441.9
298.0
93
491.6
331.6
.54
293.5
198.0
14
343.2
231.5
74
393.0
265.0
34
442.7
298.6
94
492. 5
332.2
55
294.3
198.5
15
344.1
232.1
75
393.8
265. 6
35
443.6
299.1
95
493. 3
332.7
56
295.1
199.1
16
344.9
232.6
76
.394. 6
266. 2
36
444.4
299.7
96
494.1
333.3
57
296.0
199.6
17
345.7
233.2
77
395.5
266.7
37
445.3
300.2
97
494.9
333.8
58
296.8
200.2
18
346.5
233.7
78
396.3
267.3
38
446.1
300.8
98
495; 8
334.4
59
297.6
200.7
19
347.4
234.3
79
397. 1
267.9
39
446.9
301.4
99
496.6
334. 9
60
298.5
201.3
20
348.2
234.9
80
397.9
268.4
40
447.7
302.0
600
497.4
335.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
56° (1
24°, 236°, 304°
)•
r
TABLE 2.
[Page 699 |
Difference of Latitude and
Departure for 35° (145°, 215
°, 325°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
50.0
35.0
121
99.1
69.4
181
148.3
103.8
241
197.4
138.2
2
1.6
1.1
62
50.8
35.6
22
9.9.9
70.0
82
149.1
104.4
42
198.2
138.8
3
2.5
1.7
63
51.6
36.1
23
100.8
70.5
83
149.9
105.0
43
199.1
139.4
4
3.3
2.3
64
52.4
36.7
24
101.6
71.1
84
150.7
105.5
44
199.9
140.0
5
4.1
2.9
65
53.2
37.3
25
102.4
71.7
85
151.5
106.1
45
200.7
140.5
6
4.9
3.4
66
54.1
37.9
26
103.2
72.3
86
153.4
106.7
46
201.5
141.1
7
5.7
4.0
67
54.9
38.4
27
104.0
72.8
87
153. 2
107.3
47
202.3
141.7
8
6.6
4.6
68
55.7
39.0
28
104.9
73.4
88
154.
107.8
48
203.1
142.2
9
7.4
5.2
69
56.5
39.6
29
105.7
74.0
89
154.8
108.4
49
204.0
142.8
10
8.2
5.7
70
57.3
58.2
40.2
30
106.5
74.6
90
155.6
109.0
50
204.8
205.6
143.4
11
9.0
6.3
71
40.7
131
107.3
75.1
191
156.5
109. H
251
144.0
12
9.8
6.9
72
59.0
41.3
32
108.1
75.7
92
157.3
110.1
52
206.4
144.5
13
10.6
7.5
73
59.8
41.9
33
108.9
76.3
93
158.1
110.7
53
207.2
145.1
14
11.5
8.0
74
60.6
42.4
34
109.8
76.9
94
158.9
111.3
.54
208.1
145.7
15
12.3
8.6
75
61.4
43.0
35
110.6
77.4
95
159.7
111.8
55
208.9
146.3
16
13.1
9.2
76
62.3
43.6
36
111.4
78.0
96
160.6
112.4
56
209.7
146.8
17
13.9
9.8
77
63.1
44.2
37
112.2
78.6
97
161.4
113.0
57
210.5
147.4
18
14.7
10.3
78
63.9
44.7
38
113.0
79.2
98
162.2
113.6
58
211.3
148.0
19
15.6
10.9
79
64.7
45.3
39
113.9
79.7
99
163.0
114.1
59
212.2
148.6
20
16.4
11.5
80
65.5
45.9
40
114.7
80.3
200
163.8
114.7
60
213.0
149.1
21
17.2
12.0
81
66.4
46.5
141
115.5
80.9
201
164.6
115.3
261
213.8
149.7
22
18.0
12.6
82
67.2
47.0
42
116.3
81.4
02
165.5
115.9
62
214.6
150.3
23
18.8
13.2
83
68.0
47.6
43
117.1
82.0
03
166.3
116.4
63
215. 4
150.9
24
19.7
13.8
84
68.8
48.2
44
118.0
82.6
04
167.1
117.0
64
216.3
151.4
25
20.5
14.3
85
69.6
48.8
45
118.8
83.2
05
167.9
117.6
65
217.1
152.0
26
21.3
14.9
86
70.4
49.3
46
119.6
83.7
06
168.7
118.2
66
217.9
152.6
27
22.1
1.5.5
87
71.3
49.9
47
120.4
84.3
07
169.6
118.7
67
218.7
153.1
28
22.9
16.1
88
72.1
50.5
48
121.2
84.9
08
170.4
119.3
68
219.5
153.7
29
23.8
16.6
89
72.9
51.0
49
122.1
85.5
09
171.2
119.9
69
220.4
154. 3
30
24.6
17.2
90
73.7
51.6
50
122.9
123.7
86.0
• 10
172.0
120. 5
70
221.2
154. 9
31
25.4
17.8
91
74.5
52.2
151
86.6
211
172.8
121.0
271
222.0
155.4
32
26.2
18.4
92
75.4
52.8
52
124.5
87.2
12
173.7
121.6
72
222.8
156.0
33
27.0
18.9
93
76.2
53.3
53
125.3
87.8
13
174.5
122.2
73
223.6
1.56. 6
34
27.9
19.5
94
77.0
53.9
54
126.1
88.3
14
175.3
122.7
74
224.4
157.2
35
28.7
20.1
95
77.8
54.5
55
127.0
88.9
15
176.1
123.3
75
225.3
157. 7
36
29.5
20.6
96
78.6
55.1
56
127.8
89.5
16
176.9
123.9
76
226.1
158.3
37
30.3
21.2
97
79.5
55.6
57
128.6
90.1
17
177.8
124.5
77
226.9
158.9
38
31.1
21.8
98
80.3
56.2
58
129.4
90.6
18
178.6
125.0
78
227.7
159. 5
39
31.9
22.4
99
81.1
56.8
59
130.2
91.2
19
179.4
125.6
79
228.5
160.0
40
32.8
22.9
100
81.9
57.4
60
131.1
91.8
20
180.2
126.2
80
229.4
160.6
41
33.6
23.5
101
82.7
57.9
161
131.9
92.3
221
181.0
126.8
281
230.2
161.2
42
34.4
24.1
02
83.6
58.5
62
132.7
92.9
22
181.9
127.3
82
231.0
161.7
43
35.2
24.7
03
84.4
59.1
63
133.5
93.5
23
182.7
127.9
83
231.8
162.3
44
36.0
25.2
04
85.2
59.7
64
134.3
94.1
24
183.5
128. 5
84
232.6
162.9
45
36.9
25.8
05
86.0
60.2
65
135.2
94.6
25
184.3
129.1
85
233.5
163.5
46
37.7
26.4
06
86.8
60.8
66
136.0
95.2
26
185.1
129.6
86
234.3
164.0
47
38.5
27.0
07
87.6
61.4
67
136.8
95.8
27
185.9
130.2
87
235.1
164.6
48
39.3
27.5
08
88.5
61.9
68
137.6
96.4
28
186.8
130.8
88
235.9
165. 2
49
40.1
28.1
09
89.3
62.5
69
138.4
96.9
29
187.6
131.3
89
236. 7
165.8
50
41.0
28.7
10
90.1
63.1
70
139.3
97.5
30
188.4
131.9
90
237.6
166.3
51
41.8
29.3
111
90.9
63.7
171
140.1
98.1
231
189.2
132. 5
291
238.4
166.9
52
42.6
29.8
12
91.7
64.2
72
140.9
98.7
32
190.0
133.1
92
239.2
167.5
53
43.4
30.4
13
92.6
64.8
73
141.7
99.2
33
190.9
133.6
93
240.0
168.1
54
44.2
31.0
14
93.4
6.5.4
74
142.5
99.8
34
191.7
134.2
94
240.8
168.6
55
45.1
31.5
15
94.2
66.0
75
143.4
100.4
35
192.5
134.8
95
241.6
169.2
56
45.9
32.1
16
95.0
66.5
76
144.2
100.9
36
193.3
135.4
96
242.5
169.8
57
46.7
32.7
17
95.8
67.1
77
145.0
101. 5
37
194.1
135. 9
97
243.3
170.4
58
47.5
33.3
18
96.7
67.7
78
145. 8
102.1
38
195.0
136. 5
98
244.1
170.9
59
48.3
33.8
19
97.5
68.3
79
146.6
102.7
39
195.8
137.1
99
244.9
171.5
60
49.1
34.4
20
98.3
68.8
80
147.4
103.2
40
196.6
137.7
300
245.7
172.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
<
)0° (1
25°, 2:55
°, .305°
)•
Page 600]
TABLE 2.
Difference of Latitude and Departure for 35° (145°, 215°, 325°).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
246.6
172.6
361
295.7
207.0
421
344.9
241.5
481
394.0
275.9
541
443.2
310.3
02
247.4
173.2
62
296.5
207.6
22
345. 7.
242.0
82
394. 8
276.4
42
444.0
310. 9
03
248.2
173.8
63
297.4
208.2
23
.346. 5
242.6
83
395.7
277.0
43
444.8
311.4
04
249.0
174.3
64
298.2
208.8
24
347. 3
243. 2
84
396. 5
277.6
44
445.6
312.0
Go
249.9
174.9
65
299.0
209.3
25
348.1
243. 8
85
397.3
278.2
45
446.4
312.6
06
250.7
175.0
66
299.8
209.9
26
349.0
244. 3
86
398.1
278.7
46
447.3
313. 2
07
251.5
176.1
67
300.6
210. 5
27
349. 8
244.9
87
398.9
279.3
47
448.1
313. 7
08
252.3
176.6
68
301.5
211.1
28
350. 6
245. 5
88
399.8
279.9
48
448.9
314.3
09
253. 1
177.2
69
302.3
211.6
29
351.4
246.0
89
400.6
280.5
49
449.7
314.9
10
253.9
177.8
70
303.1
212.2
30
352.2
353. 1
246.6
90
401.4
402.^2
281.0
50
450.5
315. 4
311
254.8
178.4
371
303.9
212.8
431
247.2
491
281.6
551
451.4
316.0
12
255.6
178.9
72
304.7
213.4
32
353.9
247.8
92
403.0
282.2
52
452.2
316. 6
13
256.4
179.5
73
305. 6
21,3. 9
33
354. 7
248.3
93
403. 9
282.8
53
453.
317.2
14
257.2
180.1
74
306.4
214.5
34
355.5
248.9
94
404.7
283.3
64
453.8
317. 7
15
258.
180.7
75
307.2
215. 1
35
*56. 3
249.5
95
405. 5
283.9
55
454.6
318. 3
16
258. 9
181.2
76
308.0
215. 6
.36
.357. 2
250.1
96
406.3
284.5
56
455. 5
318. 9
17
259.7
181.8
77
308.8
216.2
37
358.0
250.6
97
407.1
285.1
57
456.3
319. 5
18
260.5
182.4
78
309.6
216.8
38
358. 8
251.2
98
408.0
285.6
58
457.1
320.0
19
261.3
183.0
79
310.5
217.4
39
359. 6
251.8
99
408.8
286.2
59
457.9
320.6
20
262.1
183.5
80
311.3
217.9
40
360.4
252.4
500
409.6
286.8
60
458. 7
.321. 2
321.8
321
263.0
184.1
381
312.1
218.5
441
361.3
252.9
501
410.4
287.4
561
459. 6
22
263.8
184.7
82
312.9
219.1
42
362.1
253.5
02
411.2
287.9
62
460.4
322.3
23
264.6
185.2
83
313.7
219.7
43
362.9
254.1
03
412.1
288.5
63
461.2
322.9
24
265.4
185.8
84
314.6
220. 2
44
363.7
254.7
04
412.9
289. 1
64
462.0
323. 5
25
266.2
186.4
85
315.4
22o!8
45
364. 5
255. 2
05
413.7
289.7
Go
462.8
324. 1
26
267.1
187.0
86
316.2
221.4
46
365.4
255. 8
06
414.5
290.2
66
463. 7
324.6
27
267.9
187.5
87
317.0
222.0
47
366. 2
256.4
07
415. 3
290.8
67
464. 5
325. 2
28
268.7
188.1
88
317.8
222.5
48
367.0
256. 9
08
416.1 1291.4
68
465. 3
325. 8
29
269.5
188.7
89
318.7
223.1
49
367.8
257. 5
09
417.0
291.9
69
466.1
326. 4
30
270.3
189.3
90
319.5
223.7
50
368.6
369.4
258.1
10
417.8
292.5
70
466.9
326. 9
327.5
331
271.1
189.8
391
320.3
224.3
451
258.7
511
418.6
293.1
571
467. 8
32
272.0
190.4
92
321.1
224.8
52
370. 3
259.2
12
419.4
293.7
72
468.6
.328. 1
33
272.8
191.0
93
.321. 9
225. 4
53
371.1
259. 8
13
420.2
294.2
73
469.4
328. 7
34
273.6
191.6
94
322.8
226.0
54
371. 9
260.4
14
421.1
294.8
74
470.2
329. 2
35
274.4
192.1
95
323.6
226.5
55
372. 7
261.0
15
421.9
295.4
75
471.0
329. 8
36
275.2
192.7
96
324. 4
227.1
56
373. 5
261.5
16
422.7
296.0
76
471.9
330. 4
37
276. 1
193.3
97
325.2
227.7
57
374. 4
262.1
17
423. 5
296.5
77
472.7
331.0
38
276.9
193.9
98
326.0
228. 3
58
375. 2
262. 7
18
424.3
297.1
78
473. 5
331. 5
39
277.7
194.4
99
326.9
228.8
59
376.
263. 3
19
425.2
297.7
79
474.3
332. 1
40
278.5
279.3
195.0
400
327.7
229.4
60
376.8
263.8
20
426.0
298.3
80
581
475.1
476.
332. 7
333. 3
341
195.6
401
328.5
230.
461
377.6
264.4
521
426.8
298.8
42
280.2
196.1
02
329.3
230.6
62
378.5
265.
22
427.6
299.4
82
476. 8
333.8
43
281.0
196.7
03
330.1
231. 1
63
379. 3
26.5.5
23
428.4
300.0
83
477.6
334. 4
44
281.8
197.3
04
330.9
231.7
64
380. 1
266.1
24
429.3
300.5
84
478.4
335.
45
282.6
197.9
05
331.8
232. 3
65
380. 9
266.7
25
430.1
301.1
85
479. 2
335. 6
46
283.4
198.4
06
332.6
232.9
66
381.7
267.3
26
430.9
301.7
86
480.1
336. 1
47
284.3
199.0
07
333.4
233.4
67
382.6
267.8
27
431.7
302.3
87
480.9
336. 7
48
285.1
199.6
08
334.2
234.0
68
383.4
268.4
28
432.5
302.8
88
481.7
337. 3
49
285.9
200.2
09
335.0
234.6
69
384.2
269.0
29
433.4
303.4
89
482.5
337.9
50
286.7
200.7
10
335.9
336.7
235.1
235.7
70
471
385.0
269.6
30
434.2
435.0
304.0
90
483.3
338. 4
351
287.5
201.3
411
385.8
270.1
531
304.5
591
484.2
339.
52
288. 3
201.9
12
337.5
236.3
72
386.6
270.7
32
435.8
305.1
92
485.0
339.6
53
289.2
202.5
13
338.3
236.9
73
387.5
271.3
33
436.6
305.7
93
485. 8
340.2
54
290.0
203.0
14
339.1
237. 4
74
388.3
271.9
34
437.5
306.3
94
486.6
340.7
55
290.8
203.6
15
340.0
238.0
75
389.1
272.4
35
438.3
306.8
95
487.4
341.3
56
291.6
204.2
16
340. 8
238.6
76
389.9
273.0
36
439 1
307.4
96
488.3
341.9
57
292.4
204.7
17
341.6
239.2
77
390.7
273.6
37
439.9
308.0
97
489.1
342.5
58
293.3
205.3
18
342.4
239.7
78
391.6
274.2
38
440.7
308.6
98
489.9
343.0
59
294.1
205.9
19
343.2
240. 3
79
392.4
274.7
.39
441.5
309.1
99
490.7
.343. 6
60
294.9
206.5
20
344.1
240.9
80
393.2
275. 3
40
442.3
309.7
600
491.5
344.1
Dirt.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
55° (1
25°, 235
°, 305°
).
TABLE 2.
[Page 601
Difference of Latitude and Depart
jre for 36° (144°, 216°, 324'
)■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
49.4
35.9
121
97.9
71.1
181
146.4
106.4
241
195.0
141.7
2
1.6
1.2
62
50.2
36.4
22
98.7
71.7
82
147. 2
107.0
42
195.8
142.2
3
2.4
1.8
63
.51.0
37.0
23
99.5
72.3
83
148.1
107.6
43
196.6
142.8
4
3.2
2.4
64
51.8
37.6
24
100.3
72.9
84
148. 9
108.2
44
197.4
143.4
5
4.0
2.9
65
52.6
38.2
25
101.1
73.5
85
149.7
108.7
45
198.2
144.0
6
4.9
3.5
m
53.4
38.8
26
101.9
74.1
86
1.50. 5
109.3
46
199.0
144.6
7
5. 7
4.1
67
54.2
39.4
27
102.7
74.6
87
151.3
109.9
47
199.8
145. 2
8
6.5
4.7
68
55.0
40.0
28
103. 6
75.2
88
152.1
110.5
48
200.6
145.8
9
7.3
5.3
69
5.5.8
40.6
29
104.4
7.5.8
89
152.9
111.1
49
201.4
146.4
10
11
8.1
5.9
70
56.6
57,4
41.1
30
105.2
76.4
90
153.7
111.7
50
202.3
146.9
8.9
6.5
71
41.7
131
106.0
77.0
191
1.54. 5
112.3
251
203.1
147. 5
12
9.7
7.1
72
58.2
42.3
32
106.8
77.6
92
155.3
112.9
52
203.9
148.1
13
10.5
7.6
73
59.1
42.9
33
107.6
78.2
93
1.56.1
113.4
53
204.7
148.7
14
11.3
8.2
74
.59.9
4.3.5
34
108.4
78.8
94
156. 9
114.0
54
205.5
149.3
15
12.1
8.8
75
60.7
44.1
35
109.2
79.4
95
157. 8
114.6
55
206.3
149.9
16
12.9
9.4
76
61.5
44.7
36
110.0
79.9
96
158.6
115.2
56
207.1
1.50. 5
17
13.8
10.0
77
62.3
4.5.3
37
110.8
80.5
97
1.59. 4
115.8
57
207. 9
151.1
18
14.6
10.6
78
63.1
45.8
38
111.6
81.1
98
160.2
116.4
58
208.7
151.6
19
15.4
n.2
79
63.9
46.4
39
112.5
81.7
99
161.0
117.0
59
209.5
152.2
20
16.2
11.8
80
64.7
47.0
40
113.3
82.3
200
161.8
162.6
117.6
60
210. 3
152.8
21
17.0
12.3
81
65.5
47.6
141
114.1
82.9
201
118.1
261
211.2
1.53. 4
22
17.8
12.9
82
66.3
48.2
42
114.9
83.5
02
163.4
118.7
62
212.0
1.54.
23
18.6
13.0
83
67.1
48.8
43
115.7
84.1
03
164.2
119.3
63
212.8
154.6
24
19.4
14.1
84
68.0
49.4
44
116.5
84.6
04
165.0
119.9
64
213.6
1.55. 2
25
20.2
14.7
85
68.8
50.0
45
117.3
85.2
05
165.8
120.5
65
214.4
1.55. 8
26
21.0
1.5. 3
86
69.6
50.5
46
118.1
8.5.8
06 166.7
121.1
66
215.2
156.4
27
21.8
15.9
87
70.4
51.1
47
118.9
86.4
07 167. 5
121.7
67
216.0
1.56.9
28
22. 7
16.5
88
71.2
51.7
48
119.7
87.0
08 168. 3
122.3
68
216.8
157. 5
29
23! 5
17.0
89
72.0
52.3
49
120.5
87.6
09 169. 1
122.8
69
217.6
1.58. 1
30
31
24.3
17.6
90
72.8
52.9
50
121.4
88.2
10 1 169.9
123.4
70
218.4
1.58. 7
159.3"
25.1
18.2
91
73.6
53.5
151
122.2
88.8
211
170.7
124.0
271
219.2
32
25.9
18.8
92
74.4
54.1
52
123.0
89.3
12
171.5
124.6
72
220.1
1.59. 9
33
26.7
19.4
93
75.2
54.7
53
123.8
89.9
13
172.3
125.2
73
220.9
1(>0. 5
34
27.5
20.0
94
76.0
55.3
54
124.6
90.5
14
173.1
125.8
74
221.7
161.1
35
28.3
20.6
95
76.9
.55. 8
55
125. 4
91.1
15
173. 9
126.4
75
222. 5
161.6
36
29.1
21.2
96
77.7
56.4
56
126.2
91.7
16
174.7
127.0
76
223.3
162.2
37
29.9
21.7
97
78.5
57.0
57
127.0
92.3
17
175.6
127.5
77
224.1
162. 8
38
30.7
22.3
98
79.3
57.6
58
127.8
92.9
18
176.4
128.1
78
224. 9
163. 4
39
31.6
22.9
99
80.1
58.2
59
128.6
93.5
19
177.2
128.7
79
225.7
164.0
40
41
32.4
33.2"
23.5
24.1
100
80.9
58.8
60
129.4
130.3
94.0
20
178.0
129.3
129.9
80
281
226.5
227.3
164.6
165.2
101
81.7
59.4
161
94.6
221
178.8
42
34.0
24.7
02
82.5
60.0
62
131.1
95.2
22
179. 6
130.5
82
228.1
165. 8
43
34.8
25.3
03
83.3
60.5
63
131.9
95. 8
23
180.-4
131.1
83
229.0
166. 3
44
.35. 6
25.9
04
84.1
61.1
64
132.7
96.4
24
181 2
131.7
84
229. 8
166. 9
45
36.4
26.5
05
84.9
61.7
65
133. 5
97.0
25
182.0
132.3
85
2,30. 6
167. 5
46
37.2
27.0
06
a5.8
62.3
66
134.3
97.6
26
182.8
132.8
86
231.4
168.1
47
38.0
27.6
07
86.6
62.9
67
135.1
98.2
27
183.6
133.4
87
232.2
168. 7
48
38.8
28.2
08
87.4
63.5
68
1.35. 9
98. 7
28
184.5
134.0
88
233.0
169. 3
49
39.6
28.8
09
88.2
64.1
69
1.36. 7
99.3
29
185.3
134.6
89
2.33. 8
169.9
50
40.5
29.4
30.0
10
89.0
64.7
70
137.5
138.3
99.9
30-
186.1
135.2
135. 8
90
291
234. 6
170.5
51
41.3
111
89.8
65.2
171
100.5
231
186.9
235.4
171.0
52
42.1
.30.6
12
90.6
a5.8
72
139. 2
101.1
32
187.7
136.4
92
236.2
171.6
53
42.9
31.2
13
91.4
66.4
73
140.0
101.7
33
■188. 5
137.0
93
237.
172.2
54
43.7
31.7
14
92.2
67.0
74
140.8
102.3
34
189.3
137. 5
94
237. 9
172.8
55
44.5
32.3
15
93.0
67.6
75
141.6
102. 9
:»
190.1
138.1
95
238.7
173. 4
56
45.3
32.9
16
93.8
68.2
76
142.4
103. 5
36
190.9
138.7
96
239. 5
174.0
57
46.1
33.5
17
94.7
68.8
77
143.2
104.0
37
191.7
139.3
97
240. 3
174.6
58
46.9
34.1
18
95.5
69.4
78
144.0
104. 6
38
192. 5
139.9
98
241.1
175. 2
59
47.7
,34.7
19
96.3
69.9
79
144.8
105. 2
39
193.4
140. 5
99
241.9
175. 7
60
48.5
35.3
20
97.1
70.5
80
145.6
105. 8
40
194.2
141.1
300
242.7
176.3
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
W.?t.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
14" (1
26°, 234
°, ,306°
).
Page 602]
TABLE 2.
1
Difference of Latitude and Departure for 36° (144°, 216°, 324=
)■
Diet. , Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
243.5
176.9
361
292.1
212.2
421
340.6
247.5
481
389.1
282.7
541
437.7
318.0
02
244.3
177.5
62
292.9
212.8
22
341.4
248.1
82
390.0
283. 3
42
438.5
318.6
03
245. 1
178.1
63
293.7
213. 4
23
342.2
248.6
83
390. 8
283.9
43
439.3
319.1
04
246.0
178.7
64
294.5
214.0
24
343.
249. 2
84
391.6
284.5
44
440.2
319.7
05
246.8
179.3
65
295.3
214.6
25
343.8
249.8
85
392.4
285.1
45
441.0
320.3
06
247.6
179.9
66
296.1
215.1
26
344.7
250. 4
86
393.2
2&5.6
46
441.8
320.9
07
248.4
180.5
67
296.9
215.7
27
345.5
251.0
87
394.0
286.2
47
442.6
321.5
08
249.2
181.1
68
297.7
216.3
28
346. 3
251.6
88
394.8
286.8
48
443.4
322.1
09
250.0
181.6
69
298.5
216.9
29
347.1
252.2
89
395.6
287.4
49
444.2
322.7
10
311
250.8
182.2
70
299.3
217.5
30
347. 9
252.8
90
396.4
288.0
50
445.0
323.3
251.6
182.8
371
300.2
218.1.
431
348.7
253.3
491
397.3
288.6
551
445.8
323. 8
12
252.4
183. 4
72
301.0
218.7
32
349.5
253.9
92
398.1
289.2
52
446.6
324.4
13
253.2
184.0
73
301. 8
219.3
33
350.3
254.5
93
398.9
289.8
53
447.4
325.0
14
2.54.
184.6
74
302.6
219.8
34
351.1
255.1
94
399.7
290.3
54
448.2
325. 6
15
254.9
18.5. 2
75
303.4
220.4
35
351.9
255.7
95
400.5
290.9
55
449.0
326.2
16
255.7
185.8
76
304.2
221.0
36
352.7
256. 3
96
401.3
291.5
56
449.8
326.8
17
256. 5
186.4
77
305.
221.6
37
353.6
256.9
97
402.1
292.1
57
450.7
327.4
18
257.3
186.9
78
305.8
222.2
38
354.4
257.5
98
402.9
292.7
58
451.5
328.0
19
2.58. 1
187.5
79
306.6
222.8
39
355. 2
258.0
99
403. 7
293.3
59
452.3
328.5
20
321
258.9
259.7
188.1
80
307.4
223.4
40
356.0
258.6
500
404.5
293. 9
60
453.1
329,1
188.7
381
308.2
224.0
441
356.8
259. 2
501
40^5. 3
294.5
561
453. 9
329.7
22
260.5
189.3
82
309.1
224.5
42
357.6
259.8
02
406.1
295.0
62
454.7
330. 3
23
261.3
189.9
83
309.9
225.1
43
358.4
260.4
03
407.0
295.6
63
455. 5
330.9
24
262.1
190.5
84
310.7
225. 7
44
359. 2
261.0
04
407.8
296.2
64
456.3
331.5
25
262.9
191.0
85
311.5
226.3
45
360.0
261.6
05
408.6
296.8
65
457. 1
332.1
26
263.7
191.6
86
312.3
226.9
46
360.8
262.2
06
409.4
297.4
66
457.9
332.7
27
264.6
192.2
87
313. 1
227.5
47
361.6
262. 8
07
410.2
298.0
67
458.7
333.3
28
265.4
192.8
88
313.9
228.1
48
362.4
263. 3
08
411.0
298.6
68
459.5
333.8
29
266.2
193.4
89
314.7
228.7
49
363.3
263.9
09
411.8
299. 2
69
460.3
334.4
30
267.0
194.0
90
315.5
229.2
50
364.1
364.9
264.5
10
412.6
299.8
70
461.1
335.0
331
267.8
194.6
391
316.3
229.8
451
265.1
511
413.4
300.3
571
462.0
335. 6
32
268.6
195.2
92
317.1
230.4
52
3&5. 7
265.7
12
414.2
300.9
72
462.8
336.2
33
269.4
195. 7
93
318.0
231.0
53
366.5
266.3
13
415.1
.301. 5
73
463.6
336.8
34
270.2
196.3
94
318.8
231.6
54
367. 3
266.9
14
415.9
302. 1
74
464.4
337. 4
35
271.0
196.9
95
319.6
232.2
55
368.1
267. 5
15
416.7
302.7
75
465.2
338.
36
271.8
197.5
96
320.4
232.8
56
.368. 9
268.0
16
417.5
303. 3
76
466.0
338. 5
37
272. 6
198.1
97
321.2
233.4
57
369.7
268.6
17
418.3
303. 9
77
466.8
339.1
38
273.5
198.7
98
322.0
233. 9
58
,370.5 269.2
18
419.1
304.4
78
467.6
339.7
39
274.3
199. 3
99
322.8
234.5
59
371.3
269. 8
19
419.9
305.
79
468.4
340. 3
40
275.1
199.9
400
323.6
235. 1
60
372. 2
270.4
20
420.7
.305. 6
80
469.3
340. 9
341
275.9
200. 4
401
324.4
235. 7
461
373.0
271. 0^
521
421.5
306. 2
581
470.1
341. 5
42
276.7
201.0
02
325.2
236. 3
62
373.8
271.6
22
422.3
306.8
82
470.9
342. 1
43
277.5
201.6
03
326.
236.9
63
374.6
272.2
23
423.1
307.4
83
471.7
342.7
44
278.3
202.2
04
326.9
237.5
64
375.4
272.7
24
423.9
308.0
84
472.5
343.2
45
279. 1
202.8
05
327.7
238.1
65
376.2
273.3
25
424.7
308. 6
85
473.3
343.8
46
279.9
203. 4
06
328. 5
238.7
66
377.0
273.9
26
425. 5
309.2
86
474.1
344.4
47
280.7
204.0
07
329. 3
239.2
67
377.8
274. 5
27
426.4
309. 7
87
474.9
345.0
48
281.5
204.6
08
3.30. 1
239.8
68
378. 6
275.1
28
427.2
310.3
88
475. 7
345. 6
49
282.4
205.1
09
330.9
240.4
69
379.4
275.7
29
428.0
310.9
89
476.5
.346. 2
50
283.2
205.7
10
331.7
241.0
70
380.2
276.3
30
428.8
311.5
90
477. 3
478.2
346. 8
351
284.0
206.3
411
332.5
241.6
471
381.1
276.9
531
429.6
312. 1
591
347.4
52
284.8
206.9
12
333. 3
242.2
72
381. 9
277.4
32
430.4
312.7
92
479.0
.347. 9
53
285. 6
207.5
13
334.1
242.8
73
382.7
278.0
33
431. 2
313.3
93
479.8
348. 5
54
286. 4
208.1
14
334.9
243. 4
74
383.5
278.6
34
432.0
313.9
94
480.6
349. 1
55
287.2
208.7
15
335. 8
243.9
75
384.3
279.2
35
432.9
314.4
95
481.4
349.7
56
288.0
209.3
16
336.6
244.5
76
385.1
279. 8
36
433. 7
315.
96
482. 2
350.3
57
288.8
209.8
17
337. 4
245.1
77
385.9
280.4
37
434. 5
3i.5.6
97
483.0
350.9
58
289.6
210.4
18
338. 2
245. 7
78
386.7
281.0
38
435. 3
316. 2
98
483.8
351.5
59
290.4
211.0
19
339.0
246.3
79
387.5
281.6
39
436.1
316. 8
99
484.6
352.1
60
291.3
211.6
20
339.8
246.9
80
388.3
282.1
40
436.9
317.4
600
485.4
352.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
DLst.
Dep.
Lat.
Dist.
Dep.
Lat.
Diat. Dep.
Lat.
54° (126°, 234°, 306°
)•
TABLE 2.
[Page
603
Difference of Latitude and Departure for 37° (143°, 217°, 823°]
.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
48.7
36.7
121
96.6
72.8
181
144.6
108.9
241
192.5
145.0
2
1.6
1.2
62
49.5
37.3
22
97.4
73.4
82
145. 4
109.5
42
193.3
145.6
3
2.4
1.8
63
50.3
37.9
23
98.2
74.0
83
146.2
110.1
43
194.1
146.2
4
3.2
2.4
64
51.1
38.5
24
99.0
74.6
84
146.9
110.7
44
194.9
146.8
5
4.0
3.0
65
51.9
39.1
25
99.8
75.2
85
147.7
111.3
45
195.7
•147. 4
6
4.8
3.6
66
52.7
39.7
26
100.6
75.8
86
148.5
111.9
46
196.5
148.0
7
5.6
4.2
67
53.5
40.3
27
101.4
76.4
87
149.3
112.5
47
197.3
148.6
8
6.4
4.8
68
54.3
40.9
28
102.2
77.0
88
150.1
113.1
48
198.1
149.3
9
7.2
5.4
69
55.1
41.5
29
103.0
77.6
89
150.9
113.7
49
198.9
149.9
10
8.0
6.0
70
55.9
42.1
42.7
30
103.8
78.2
90
151.7
114.3
50
199.7
150.5
11
8.8
6.6
71
56.7
131
104.6
78.8
191
152.5
114.9
251
200.5
151.1
12
9.6
7.2
72
57.5
4.3.3
32
105.4
79.4
92
153.3
115.5
52
201.3
151.7
13
10.4
7.8
73
.58.3
43.9
33
106.2
80.0
93
154.1
116.2
53
202.1
152.3
14
11.2
8.4
74
59.1
44.5
34
107.0
80.6
94
1.54.9
116.8
54
202.9
152. 9
15
12.0
9.0
75
59.9
45.1
35
107.8
81.2
95
155.7
117.4
55
203.7
1-53. 5
16
12.8
9.6
76
60.7
45.7
36
108.6
81.8
96
156.5
118.0
56
204.5
154. 1
17
13.6
10.2
77
61.5
46.3
37
109.4
82.4
97
157.3
118.6
57
205.2
154. 7
18
14.4
10.8
78
62.3
46.9
38
110.2
83.1
98
158.1
119.2
58
206.0
1.55. 3
19
15.2
11.4
79
63.1
47.5
39
111.0
83.7
99
158.9
119.8
59
206.8
155. 9
20
21
16.0
16.8
12.0
12.6
80
81
63.9
48.1
40
111.8
112.6
84.3
200
159.7
120. 4
60
261
207. 6
156.5
64.7
48.7
141
84.9
201
160.5
121.0
208.4
157. 1
22
17.6
13.2
82
65.5
49.3
42
113.4
85.5
02
161.3
121.6
62
209.2
157. 7
23
18.4
13.8
83
66.3
.50.0
43
114.2
86.1
03
162.1
122.2
63
210.0
1,58. 3
24
19.2
14.4
84
67.1
50.6
44
115.0
86.7
04
162.9
122.8
64
210.8
158. 9
25
20.0
1.5.0
85
67.9
51.2
45
115.8
87.3
05
163.7
123.4
65
211.6
159.5
26
20.8
15.6
86
68.7
51.8
46
116.6
87.9
06
164.5
124.0
66
212.4
160.1
27
21.6
16.2
87
69.5
52. 4
47
117.4
88.5
07
165.3
124.6
67
213.2
160.7
28
22.4
16.9
88
70.3
53.0
48
118.2
89.1
08
166.1
125.2
68
214.0
161.3
29
23.2
17.5
89
71.1
53.6
49
119.0
89.7
09
166.9
125.8
69
214.8
161. 9
30
24.0
18.1
90
71.9
54.2
50
119.8
90.3
10
167.7
126.4
127.0
70
21.5. 6
162.5
31
24.8
18.7
91
72.7
54.8
151
120.6
90.9
211
168.5
271
216.4
163.1
32
25.6
19.3
92
73.5
55.4
52
121.4
91.5
12
169.3
127.6
72
217.2
163.7
33
26.4
19.9
93
74.3
56.0
53
122.2
92.1
13
170.1
128.2
73
218.0
164. 3
34
27.2
20.5
94
75.1
56.6
54
123.0
92.7
14
170.9
128.8
74
218.8
164.9
35
28.0
21.1
95
75.9
.57.2
55
123. 8
93.3
15
171.7
129.4
75
219.6
165. 5
36
28.8
21.7
9(5
76.7
57.8
56
124. 6
93.9
16
172. 5
130.0
76
220.4
166.1
37
29.5
22.3
97
77.5
.58.4
57
125. 4
94.5
17
173. 3
130. 6
77
221.2
166. 7
38
30.3
22.9
98
78.3
59.0
58
126. 2
95.1
18
174.1
131.2
78
222.0
167. 3
39
31.1
23.5
99
79.1
59.6
59
127.0
95.7
19
174.9
131.8
79
222.8
167. 9
40
41
31.9
24.1
100
79.9
80.7
60.2
60
161
127.8
96.3
20
175.7
132. 4
133.0
80
223.6
168. 5
169. 1
32.7
24.7
101
60.8
128.6
96.9
221
176.5
281
224.4
42
33. 5
25.3
02
81.5
61.4
62
129.4
97.5
22
177. 3
133.6
82
225.2
169. 7
43
34.3
25.9
03
82.3
62.0
63
130.2
98.1
23
178.1
134.2
83
226.0
170.3
44
35.1
26.5
04
83.1
62.6
64
131.0
98.7
24
178.9
134.8
84
226.8
170.9
45
35.9
27.1
05
as. 9
63.2
65
131.8
99.3
25
179.7
135. 4
85
227.6
171.5
46
36.7
27.7
06
84.7
63. 8
66
132. 6
99.9
26
180.5
1,36.
86
228.4
172.1
47
37.5
28.3
07
85.5
64.4
67
133. 4
100.5
27
181. 3
1,36. 6
87
229.2
172.7
48
38.3
28.9
08
86.3
65.
68
134. 2
101.1
28
182.1
137. 2
88
230.
173.3
49
39.1
29.5
09
87.1
65.6
69
135.0
101.7
29
182.9
137. 8
89
230.8
173.9
50
39.9
30.1
10
87.8
66.2
70
135. 8
136.6
102. 3
102.9
30
231
183.7
138.4
90
231.6
174.5
175.1
51
40.7
30.7
111
88.6
68.8
171
184.5
139.
291
232.4
52
41.5
31.3
12
89.4
67.4
72
137. 4
103. f
32
186.3
139.6
92
233.2
175.7
53
42.3
.31.9
13
90.2
68.0
73
138.2
104.1
33
186.1
140.2
93
2.34.0
176. 3
54
43.1
32.5
14
91.0
68.6
74
139.0
104.7
34
186.9
140.8
94
234. 8
176.9
55
43.9
33.1
15
91.8
69.2
75
1.39. 8
105. 3
35
187.7
141.4
95
2a5.6
177.5
56
44.7
33.7
16
92.6
69.8
76
140.6
105. 9
36
188.5
142.0
96
236.4
178.1
57
45.5
34.3
17
93.4
70.4
77
141.4
106.5
37
189.3
142.6
97
237. 2
178.7
58
46.3
34.9
18
94.2
71.0
78
142.2
107.1
38
190.1
143. 2
98
238.0
179.3
59
47.1
35.5
19
95.0
71.6
79
143.0
107.7
39
190.9
143.8
99
238.8
179.9
60
47.9
36.1
20
95.8
72.2.
80
143.8
108.3
40
191.7
144.4
300
239.6
180.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
53° (
27°, 23;
?°, 307'
')•
Page 604]
TABLE 2.
Difference of Latitude and Departure for 37° (143°, 217°, 323'
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
240.4
181.1
361
288.3
217.3
421
336.2
253.4
481
384.1
289.5
541
432.0
325. 6
02
241.2
181.7
62
289.1
217.9
22
337.0
254.0
82
384. 9
290.0
42
432.8
326. 2
03
242.0
182.4
63
289.9
218.5
23
337.8
254.6
83
385. 7
290.6
43
433.6
326. 8
04
242. 7
183.0
64
290.7
219.1
24
338.6
255. 2
84
386. 5
291.2
44
434.4
327. 3
05
543.5
183.6
65
291.5
219.7
25
339.4
255.8
85
387.3
291.8
45
435.2
327. 9
06
244.3
184.2
66
292.3
220.3
26
340. 2
256.4
86
388.1
292.4
46
436.0
328. 5
07
245.1
184.8
67
293.1
220.9
27
341.
257.
87
388.9
293.0
47
436.8
329. 1
08
245. 9
185.4
68
293.9
221.5
28
341.8
257.6
88
389. 7
293.6
48
437.6
329. 7
09
246.7
186.0
69
294.7
222.1
29
342.6
258. 2
89
390. 5
294.2
49
438.4
330. 3
10
247.5
186.6
70
295.5
222.7
30
343.4
258.8
259. 4
90
491
.391. 3
392. 1
294.8
50
439.2
330.9
331. 5
311
248.3
187. 2
371
296.3
223.3
431
344.2
295.4
551
440.0
12
249.1
187.8
72
297.1
223.9
32
345.
260.0
92
392.9
296.0
52
440.8
332.1
13
249.9
188.4
73
297.9
224. 5
33
345. 8
260. 6
93
393.7
296.6
53
441.6
332.7
14
250.7
189.0
74
298.7
225. 1
34
346. 6
261.2
94
394. 5
297.2
54
442.4
333. 3
15
251.5
189.6
75
299.5
225.7
35
347. 4
261.8
95
395. 3
297. 8
55
443.2
333. 9
16
252. 3
190.2
76
300.3
226.3
36
348.2
262. 4
96 i 396.1
298. 5
56
444.0
3.34. 6
17
253.1
190. 8
77
301.1
226.9
37
349.0
263.
97
396. 9
299. 1
57
444.8
235. 2
18
253. 9
191.4
78
301.8
227. 5
38
349.8
263. 6
98
397.7
399.7
58
445.6
335. 8
19
254.7
192.0
79
302.6
228.1
39
350. 6
2tM.2
99
398.5
300.3
59
446.4
336.4
20
321
255.5
256.3
192.6
193. 2
80
381
303.4
304. 2
228.7
40
351.4
352.2
264.8
500
399. 3
300.9
60
447.2
337.0
229.3
441
265.4
501
400.1
301.5
561
448.0
337.6
22
257.1
193.8
82
305.0
229.9
42
353.
266.0
02
400.9
302.1
62
448.8
338.2
23
257.9
194.4
83
305.8
230. 5
43
353.8
266.6
03
401.7
302.7
63
449.6
338. 8
24
258.7
195.
84
306.6
231.1
44
354.6
267. 2
04
402. 5
303. 3
64
450.4
339.4
25
259.5
195.6
85
307.4
231.7
45
355.4
267. 8
05
403. 3
303. 9
65
451.2
340.0
26
260.3
196.2
86
308.2
232.3
46
356.2
268.4
06
404.1
304.5
66
452.0
340.6
27
261.1
196.8
87
309.
232.9
47
357.
269.0
07
404.9
305.1
67
452.8
341.2
28
261.9
197.4
88
309.8
233.5
48
357. 8
269.6
08
405.7
305.7
68
453.6
,341. 8
29
262.7
198.0
89
310.6
234.1
49
358. 6
270.2
09
406.5
306.3
69
454.4
342. 4
30
331
263. 5
2f)4.3
198.6
90
311.4
234.7
50
359.4
270.8
10
407.3
306.9
70
455. 2
343.0
199.2
391
312.2
235.3
451
360.1
271.4
511 1 408.1
307.5
571
456.0
343. 6
32
265. 1
199.8
92
313.0
235.9
52
360.9
272.0
12 j 408.9
.308. 2
72
456.8
344. 3
33
265. 9
200.4
93
313.8
236.5
53
361.7
272.6
13
409.7
.308. 8
73
457.6
344.9
34
266.7
201.0
94
314.6
237.1
54
362. 5
273. 2
14
410.5
309.4
74
458.4
345. 5
35
267. 5
201. 6
95
315.4
237.7
55
363. 3
273. 8
15
411.3
310.
75
459.2
34t>. 1
36
268.3
202.2
96
316.2
238. 3
56
364.1
274. 4
16
412.1
310. 6
76
460.0
346.7
37
269.1
202.8
97
317.0
238. 9
57
364. 9
275.
17
412.9
311.2
77
460.8
,347. 3
38
269. 9
203.4
98
317.8
239. 5
58
365. 7
275. 6
18
413.7
311. 8
78
461.6
,347. 9
39
270.7
204.0
. 99
318. 6
240.1
59
366. 5
276.2
19
414.5
312.4
79
462.4
348. 5
40
341
271.5
204.6
400
319.4
240.7
241.3
60
461
367. 3
368. 1
276. 8
'277.4
20
"521
415.3
313.
80
463.2
349.1
272.3
205. 2
401
320.2
"4i6ri
313.6
581
464.0
349. 7
42
273.1
205.8
02
321.0
241. 9
62
368. 9
278.0
22
416.9
314. 2
82
464.8
350. 3
43
273. 9
206.4
03
321.8
242. 5
63
369. 7
278.6
23
417.7
314.8
83
465.6
350. 9
44
274.7
207.0
(4
322. 6
243. 1
64
370. 5
279.2
24
418.5
315. 4
84
466.4
351.5
45
275.5
207. 6
05
323. 4
243.7
65
371.3
279. 8
25
419. 3
316.
85
467.2
352.1
46
276.3
208. 2
06
324. 2
244. 3
66
372.1
280.4
26
420.1
316.6
86
468.0
X,-2. 7
47
277.1
208.8
07
325.
244.9
67
372. 9
281.0
27
420.9
317.2
87
468.8
.353. 3
48
277.9
209.4
08
325.8
245. 5
68
373. 7
281.6
28
421.7
.317. 8
88
469. 6
353. 9
49
278.7
210.0
09
326. 6
246. 1
69
374.5
282.3
29
422.5
318. 4
89
470.4
354. 5
50
279.5
210.6
10
327. 4
246.7
247.3
70
375.3
376. 1
282.9
30
423. 3
319.0
90
471.2
355. 1
355. 7
351
280.3
211.2
411
328. 2
471
28375^
531
424.1
319. 6
591
472.0
52
281.1
211.8
12
329.0
247.9
*r2
376.9
284.1
32
424. 9
320.2
92
472.8
356. 3
53
281.9
212.4
13
329.8
248. 5
73
377. 7
284.7
33
425.7
320.8
93
473.6
356. 9
54
282.7
213.0
14
330.6
249.2
74
378.5
285. 3
34
426.5
.321. 4
94
474.4
357. 5
55
283.5
213.6
15
331.4
249. 8
75
379.3
285. 9
35
427. 3
322.0
95
475.2
358. 1
•56
284.3
214.2
16
332.2
2,50. 4
76
380. 1
286.5
.36
428.1
322.6
96
476.
358. 7
57
285.1
214.8
17
333.0
251.0
77
380. 9
287.1
37
428.9
323.2
97
476.8
359. 3
58
285. 9
215.4
18
333.8
251.6
78
381.7
287.7
38
429. 7
323. 8
98
477.6
3,59. 9
59
286.7
216.1
19
334.6
252. 2
79
382. 5
288.3
.39
430. 5
324. 4
99
478.4
360. 5
60
287.5
216.7
20
335. 4
252.8
80
383. 3
288.9
40
431.3
325.0
600
479.2
361.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat,
3° (127°, 233°, .307°
)•
-
TABLE 2.
[Page
605
Difference of Latitude and Departure for 38° (142°, 216
°, 322'
)■
Dist.
Lat.
De|..
Dist.
Lat.
Dep.
Dist. : Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.6
61
48.1
37.6
121
95.3
74.5
181
142.6
111., 4
241
189.9
148.4
2
1.6
1.2
62
48.9
38.2
22
96.1
75.1
82
143.4
112. 1
42
190.7
149.0
3
2.4
1.8
63
49.6
38.8
23
96.9
75.7
83
144.2
112.7
43
191.5
149.6
4
3.2
2.5
64
50.4
39.4
24
97.7
76.3
84
145.
113. 3
44
192.3
150.2
5
8.9
3.1
65
51.2
40.0
25
98.5
77.0
85
145.8
113.9
45
193.1
150.8
6
4.7
3.7
66
52.0
40.6
26
99.3
77.6
86
146. 6
114.5
46
193.9
151.5
7
5.5
4.3
67
52.8
41.2
27
100.1
78.2
87
147.4
115.1
47
194.6
152.1
8
6.3
4.9
68
53.6
41.9
28
100. 9
78.8
88
148.1
115.7
48
195. 4
152.7
9
7.1
5.5
69
54.4
42.5
29
101.7
79.4
89
148.9
116.4
49
196.2
153.3
10
7.9
6.2
70
55.2
43.1
30
102.4
80.0
90
149.7
117.0
50
197.0
153.9
11
8.7
6.8
71
55.9
43.7
131 j 103.2
80.7
191
150.5
117.6
251
197.8
154.5
12
9.5
7.4
72
56.7
44.3
32 i 104.0
81.3
92
151.3
118.2
52
198. 6
155.1
13
10.2
8.0
73
57.5
44.9
33 104. 8
81.9
93
152.1
118.8
53
199.4
155. 8
14
11.0
8.6
74
58.3
45.6
34 : 105. 6
82.5
94
152.9
119.4
54
200.2
156.4
15
11.8
9.2
75
59.1
46.2
35 ; 106.4
83.1
95
153. 7
120.1
55
200.9
157.0
16
12.6
9.9
76
59.9
46.8
36 107. 2
83.7
96
154. 5
120.7
56
201.7
157.6
17
13.4
10.5
77
60.7
47.4
37 108.0
84.3
97
155. 2
121.3
57
202.5
158.2
18
14.2
11.1
78
61.5
48.0
38 108. 7
85.0
98
156.
121.9
58
203. 3
158.8
19
15.0
11.7
79
62.3
48.6
39 1 109.5
85.6
99
156. 8
122. 5
59
204.1
159.5
20
15.8
12.3
12. 9
80
63.0
49.3
49.9
40
141
110.3
86.2
200
157.6
123. 1
60
261
204.9
205.7
160.1
21
16.5
81
63.8
111.1
86.8
201
158. 4
123.7
160.7
22
17.3
13.5
82
64.6
50.5
42 i 111.9
87.4
02
159. 2
124.4
62
206. 5
161.3
23
18.1
14.2
83
65.4
51.1
43 112. 7
88.0
03
160.0
125.
63
207.2
161.9
24
18.9
14.8
84
66.2
51.7
44 113.5
88.7
04
160.8
125.6
()4
208.0
162. 5
25
19.7
15.4
85
67.0
52.3
45 ' 114.3
89.3
05
161.5
126. 2
65
208.8
163.2
26
20.5
16.0
86
67.8
52.9
46 115.0
89.9
06
162. 3
126.8
66
209.6
163. 8
27
21.3
16.6
87
68.6
53.6
47 1 115.8
90.5
07
163.1
127.4
67
210.4
164.4
28
22.1
17.2
88
69.3
54.2
48 i 116.6
91.1
08
163. 9
128.1
68
211.2
165.0
29
22.9
17.9
89
70.1
54.8
49 117.4
91.7
09
164.7
128.7
69
212.0
165.6
30
23.6
18.5
90
70.9
55.4
50 118.2
92.3
10
165. 5
l66:'3
129.3
70
212.8
166.2
166.8
31
24.4
19.1
91
71.7
56.
151 119.0
93.0
211
129.9
271
213. 6
32
25.2
19.7
92
72.5
56. 6
52 119. 8
93.6
12
167.1
130. 5
72
214.3
167. 5
33
26.0
20.3
93
73.3
57. 3
53 120. 6
94.2
13
167.8
131.1
73
215.1
168.1
34
26.8
20.9
94
74.1
57.9
54 121.4
94.8
14
168.6
131.8
74
215.9
168.7
35
27.6
21.5-
95
74.9
58.5
55 122. 1
95.4
15
169. 4
132. 4
75
216. 7
169. 3
36
28.4
22. 2
96
75.6
59.1
56 ' 122.9
96.0
16
170.2
1.33.
76
217. 5
169.9
37
29.2
22! 8
97
76.4
59.7
57 123. 7
96.7
17
171.0
133.6
77
218.3
170.5
38
29.9
23.4
98
77.2
60.3
58 ; 124.5
97.3
18
171.8
134.2
78
219.1
171.2
39
30.7
24.0
99
78.0
61.0
59 j 125.3
97.9
19
172. 6
134.8
79
219.9
171.8
40
41
31.5
24.6
100
78.8
61.6
60
126.1
126.9"
98.5
99.1
20
221
173. 4
135.4
80
220. (i
172.4
173.0
.32.3
25.2
101
79.6
62.2
161
174.2
136. 1
281
221.4
42
33.1
25.9
02
80.4
62.8
62 127. 7
99.7
22
174.9
136. 7
82
222. 2
173.6
43
33.9
26. 5
03
81.2
63.4
63 128. 4
100.4
23
175.7
137. 3
83
223!
174.2
44
34.7
27.1
04
82.0
64.0
64
129. 2
101.0
24
176.5
137. 9
84
223. 8
174.8
45
35. 5
27.7
05
82.7
64.6
65
130.
101.6
25
177.3
138.5
85
224. 6
175.5
46
36.2
28.3
06
83.5
65.3
66
130. 8
102.2
2(>
178.1
139. 1
86
225.4
176.1
47
37.0
28.9
07
84.3
a5.9
67
131.6
102.8
27
178.9
1.39. 8
87
226. 2
176.7
48
37.8
29. 6
08
85.1
66.5
68
132. 4
103.4
28
179.7
140. 4
88
226.9
177.3
49
38.6
30.2
09
85.9
67.1
69
133. 2
104.0
29
180. 5
141.0
89
227.7
177.9
50
51
39.4
40.2
:«).8
31.4
10
86.7
87.5
67.7
70
171
134.0
134. 7
104.7
"10573
30
181.2
182.0
141.6
142.2
90
291
228.5
178.5
111
68.3
231
229. 3
179.2
52
41.0
32.0
12
88.3
69.0
72
135. 5
105. 9
32
182.8
142.8
92
230. 1
179.8
53
41.8
32.6
13
89.0
69.6
73
136.3
106.5
33
183. 6
143.4
93
230. 9
180.4
54
42.6
33. 2
14
89.8
70.2
74
137. 1
107.1
34
184.4
144.1
94
231.7
181.0
55
43.3
33. 9
15
90.6
70.8
75
137.9
107.7
35
185. 2
144.7
95
232. ■&
181.6
56
44.1
34. 5
16
91.4
71.4
76
138. 7
108.4
36
186.0
145. 3
9(i
233. 3
182.2
57
44.9
35. 1
17
92.2
72.0
77
139. 5
109.0
37
186. 8
145. 9
97
234.
182.9
58
4.5.7
35. 7
18
93.0
72.6
78
140.3
109.6
38
187. 5
146. 5
98
234. 8
183. 5
59
46.5
.36.3
'19
93.8
73.3
79
141.1
110.2
39
188. 3
147.1
99
■£i5. 6
184.1
60
47.3
36. 9
20
94.6
73.9
80
141.8
110.8
40
189.1
147.8
30<1
236. 4
184.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
52
' (128°, 232°,
308°).
Page 606]
TABLE 2.
Difference of Latitude and Departure for
^8° (142°, 218°, 322°
)■
Dist.
Lat. 1 Dep.
Dist.
Lat. 1 Dep.
Dist. Lat. 1 Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
237.2
185.3
361
284.5
222.8
421
331. 8 j 259. 2
481
379.
296.2
.541
426.3
333.1
02
238.0
185.9
62
285.3
222.9
22
332. 5
259.8
82
379.8
296.8
42
427.1
333.7
03
238.8
186.6
63
286.0
223.5
23
333.3
260.4
88
380.6
297.4
43
427.9
334. 8
04
239.6 187.2
64
286.8
224.1
24
334. 1
261.0
84
381.4
298.0
44
428.7
335.
05
240.3
187.8
65
287.6
224. 7
25
334. 9 1 261. 7
85
382.2
298.6
45
429.5
335. 6
•06
241.1
188.4
66
288.4
225. 3
26
335. 7 : 262. 3
86
383.0
299.2
46
430.8
3.36. 2
07
241.9
189.0
67
289.2
226.0
27
336. 5 ; 262. 9
87
383.8
299.8
47
431.0
336. 8
08
242.7
189.6
68
290.0
226.6
28
337.3 263.5
88
384.5
300.4
48
431.8
337.4
09
243.5
190.2
69
290.8
227.2
29
338.1 264.1
89
385.3
301.1
49
432.6
338.0
10
244.3
190.9
70
291.6
227.8
30
338.8 264.7
90
386.1
386.9
801.7
50
433.4
338.6
339.3
311
245.1
191.5
371
292. 4 i 228. 4
431
389.6
265. 4
491
302.3
551
484.2
12
245.9
192.1
72
293.1
229.0
32
340. 4
266.
92
387.7
302.9
52
48.5.0
339.9
13
246.6
192.7
73
293.9
229.6
33
341.2
266.6
98
388. 5
808.5
53
435.8
340. 5
14
247.4
193.3
74
294.7
230.3
34
342.0
267.2
94
389.8
304.2
54
436.6
341. 1
15
248.2
193.9
10
295.5
230.9
35
342.8
267.8
95
390. 1
304.8
55
437. 4
341. 7
16
249.0
194.6
76
296.3
231.5
36
343.6
268.4
96
390.9
.305. 4
56
488.1
342.3
17
249.8
195.2
77
297.1
232.1
37
344. 4 1 269. 1
97
391.6
306.0
0(
488.9
343.
18
250.6
195.8
78
297.9
232.7
38
345. 2 ; 269. 7
98
392.4
306.6
58
439.7
343. 6
19
251.4
196.4
79
298.7
233.3
.39
845. 9 1 270. 3
99
.393. 2
307.2
59
440.5
344.2
20
252.2
197.0
197.6
80
299.4
234.0
40
846. 7 ! 270. 9
500
.394.
307.8
60
441.3
344. 8
345. 4
821 253.
381
300. 2 i 234. 6
441
347.5 1271.5
501
394. 8 : 308. 4
.561
442.1
22 253. 7
198.2
82
301.0
235.2
42
348. 3 i 272. 1
02
395.6
309.1
62
442.9
346.
23 254. 5
198.9
83
301.8
235.8
48
349.1 :272. 7
08
396.4
309.7
63
443.7
346. 6
24 255.3
199.5
84
302.6
236.4
44
349.9 273.4
04
397. 2
310.8
64
444.4
347. 2
25 ; 2.56. 1
200.1
85
303.4
237.0
45
350.7 274.0
05
397. 9
310.9
65
445.2
347. 8
26 256.9
200.7
86
304. 2
237.7
46
351.5 1274.6
06
398. 7
811.6
66
446.0
348. 5
27 257. 7
201.3
87
305.
238.8
47
352. 2 ' 275. 2
07
399.5
812.2
67
446.8
349. 1
28 258. 5
201.9
88
305.7
238.9
48
353.0 275.8
08
400.8
312.8
68
447.6
349. 7
29 259. 3
202.6
89
306. 5 239. 5
49
353.8 276.4
09
401.1
818.4
69
448.4
350. 3
30 260.0
331 i 260.8
203.2
203. 8
90
307. 3 ! 240. 1
50
354. 6 277. 1
10
401.9
314.
70
449.2
3.50. 9
391
308.1 i240.7
451 1 355. 4 I 277. 7
511
402.7
314. 6
571
4.50.
351.6
32 261.6
204.4
92
308.9 241.3
52 356. 2 278. 3
12
403.5
315.2
72
4.50. 7
352. 2
33 262. 4
205.
93
309.7 242.0
53 a57.0 278.9
13
404.2
315.8
73
4.51.5
352. 8
34 i 263.2
205.6
94
310.5 242.6
54 , 357.8 279.5
14
405.0
316.4
74
452.8
353. 4
35 j 264.0
206.3
95
311.3 243.2
55 ; 358. 5 280. 1
15
405. 8
317.1
75
453.1
354.
36 ; 264.8
206.9
96
312.1 243.8
56 359. 3 280. 7
16
406.6
317.7
76
453.9
354. 6
37 1 265.6
207. 5
97
312. 8 244. 4
57 1 360.1 281.4
17
407. 4.
318. 3
77
454.7
355. 2
38 ' 266.3
208.1
98
313.6 245.0
58 ; 360. 9 282.
18
408.2
318.9
78
455. 5
;»5.8
39 267.1
208. 7
99
314. 4 ! 245. 7
59 i 361. 7 282. 6
19
409.0
319.5
79
456.3
456. 4
40
267.9
209. 3
400
315. 2 ; 246. 3
60
362. 5 288. 2
363. 3 283. 8
20
409.8
320.2
80
581
457.1
457.8
357. 1
341
268.7
209.9
401
316.0 246.9
461
521
410.6
820.8
357. 7
42
269.5
210.6
02
316,8 :247.5
62 i 364. 1 1 284. 4
22
411.8
821.4
82
458.6
358. 3
43
270.3
211.2
03
317.6 1248.1
68
364. 9 1 285. 1
23
412.1
822.0
83
459.4
358. 9
44
271. 1
211.8
04
318. 4 j 248. 7
64
365. 6 • 285. 7
24
412.9
322.6
84
460.2
359. 5
45
271.9
212.4
05
319.1 249.3
65
366. 4 i 286. 3
25
418.7
828.2
85
461.0
360.2
46
272.7
213.
06
819.9 250.0
66
367. 2 , 286. 9
26
414.5
323.8
86
461.8
360.8
47
273.4
213.6
07
320. 7 ' 250. 6
67
368.0
287.5
27
415.8
324.5
87
462.6
361.4
48
274.2
214.3
08
321.5 1251.2
68
368.8
288. 1
28
416.1
325.1
88
468.3
362.0
49
275. j 214. 9
09
322. 3 j 251. 8
69
369.6
288.7
29
416.9
325.7
89
464.1
362.6
50
275.8 215.5
10
828. 1 ' 252. 4
70
370.4
289.3
30
417.6
826.8
90
464.9
368.2
351
276.6 216.1
411
328. 9 1 253.
471
371.2
290.0
581
418. 4 1 326. 9
.591
465.7
363.8
52
277.4 216.7
12
324. 7 i 253. 7
72
371. 9
290.6
32
419.2 |327.5
92
466.5
,364.4
53
278.2
217.3
13
325. 5 ; 254. 3
78
372.7
291.2
38
420.0
328.2
98
467.3
.365.1
54
279.0
218.0
14
326.2 254.9
74
373.5
291.8
84
420.8
328.8
94
468.1
365. 7
55
279:7
218.6
15
327.0 255.5
75
374.3
292.4
35
421.6
329.4
95
468.9
366. 3
56
280.5
219.2
16
327. 8 ; 256. 1
76
375.1
293.1
36
422.4
330.0
96
469.7
366.9
57 1 281.3
219.8
17
828. 6 ' 256. 7
77
375.9
293.7
37
423.2
.3.30. 6
97
470.5
367.5
58 i 282. 1
220.4
18
329. 4 j 257. 4
78
376.7
294. 3
38
424.0
831.2
98
471.2
368.1
59
282.9
221.0
19
380.2
258.0
79
377. 5
294.9
39
424.7
381.8
99
472.0
.368. 7
60
283.7
221.6
20
831.0
258.6
80
878.2
295.5
40
425.5
832.5
600
472.8
869.4
Dist. [ Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep. I>at.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
52° (128°, 232°, 308°
)•
TABLE
[Page
607
Difference of Latiti d.
and Departure for 39° (141°, 219°, 321°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep,
Dist.
Lat,
Dep.
Dist.
Lat.
Dep.
1
0.8
^0.6
61
47.4
38.4
121
94.0
76.1
181
140.7
113.9
241
187.3
151.7
2
1.6
1.3
62
48.2
39.0
22
94.8
76.8
82
141.4
114.5
42
188.1
1,52.3
3
2.3
1.9
63
49.0
39.6
23
95.6
77.4
83
142.2
115.2
43
188.8
152.9
4
3.1
2.5
64
49.7
40.3
24
96.4
78.0
84
143.0
115.8
44
189. 6
1,53. 6
5
3.9
3.1
65
.50.5
40.9
25
97.1
78.7
85
143.8
116.4
45
190.4
1,54, 2
6
4.7
3.8
66
51.3
41.5
26
97.9
79.3
86
144.5
117.1
46
191.2
1,54.8
7
5.4
4.4
67
52.1
42.2
27
98.7
79.9
87
145.3
117.7
47
192.0
1.55. 4
8
6.2
5.0
68
52.8
42.8
28
99.5
80.6
88
146.1
118.3
48
192.7
156.1
9
7.0
5.7
69
53.6
43.4
29
100.3
81.2
89
146.9
118.9
49
193.5
156.7
10
7.8
6.3
70
54.4
44.1
30
101.0
81.8
90
147.7
119.6
50
194.3
157.3
11
8.5
6.9
71
.55.2
44.7
131
101.8
82.4
191
148.4
120.2
251
195.1
158.0
12
9.3
7.6
72
56.0
45.3
32
102.6
83.1
92
149.2
120.8
52
195.8
158.6
13
10.1
8.2
73
56.7
45.9
33
103.4
83.7
93
150.0
121.5
53
196.6
159.2
14
10.9
8.8
74
57.5
46.6
34
104.1
84.3
94
150.8
122,1
.54
197.4
159.8
15
11.7
9.4
75
58.3
47.2
35
104.9
85.0
95
151.5
122.7
55
198.2
160.5
16
12.4
10.1
76
59.1
47.8
36
105.7
85.6
96
152.3
123.3
56
198,9
161.1
17
13.2
10.7
77
.59.8
48.5
37
106.5
86.2
97
153.1
124.0
57
199.7
161.7
18
14.0
11.3
78
60.6
49.1
38
107.2
86.8
98
153.9
124.6
58
200.5
162.4
19
14.8
12.0
79
61.4
49.7
39
108.0
87.5
99
154.7
125.2
59
201.3
163.0
20
15.5
16.3
12.6
13.2
80
62.2
50.3
40
108.8
88.1
200
155.4
125.9
60
202.1
163.6
164.3
21
81
62.9
51.0
141
109.6
88.7
201
156.2
126.5
261
202.8
22
17.1
13.8
82
63.7
51-6
42
110.4
89.4
02
157.
127.1
62
203.6
164.9
23
17.9
14.5
83
64.5
52.2
43
111.1
90.0
03
157.8
127.8
63
204,4
165.5
24
18.7
15.1
84
65. 3
52.9
44
111.9
90.6
04
158.5
128.4
64
205.2
166. 1
25
19.4
15.7
85
66.1
.53.5
45
112.7
91.3
05
159. 3
129.0
65
205.9
166. 8
26
20.2
16.4
86
66.8
54.1
46
113.5
91.9
06
160.1
129.6
66
206.7
167.4
27
21.0
17.0
87
67.6
54.8
47
114.2
92.5
07
160.9
1,30. 3
67
207.5
168.0
28
21.8
17.6
88
68.4
.55. 4
48
115.0
93.1
08
161.6
130.9
68
208.3
168.7
29
22.5
18.3
89
69.2
56.0
49
115.8
93.8
09
162.4
131.5
69
209.1
169.3
30
31
23.3
24.1
18.9
i9V5'
90
69.9
56.6
50
116.6
94.4
10
163.2
132.2
70
209.8
169.9
91
70.7
57.3
151
117.3
95.0
211
164.0
132.8
271
210.6
170.5
32
24.9
20.1
92
71.5
57.9
52
118.1
95.7
12
164.8
133.4
72
211.4
171.2
33
25.
20.8
93
72.3
58.5
53
118.9
96.3
13
165.5
134.
73
212.2
171.8
34
26.4
21.4
94
73.1
59.2
.54
119.7
96.9
14
166.3
1.34. 7
74
212.9
172.4
35
27.2
22.0
95
73.8
59.8
.55
120.5
97.5
15
167.1
135.3
75
213.7
173.1
36
28.0
22.7
96
74.6
60.4
.56
121.2
98.2
16
167.9
135.9
76
214.5
173.7
37
28.8
23.3
97
75.4
61.0
57
122.0
98.8
17
168.6
136.6
77
215.3
174.3
38
39
29.5
23.9
98
76.2
61.7
58
122.8
99.4
18
169.4
137.2
78
216.0
175.0
30.3
24.5
99
76.9
62.3
59
123.6
100.1
19
170.2
137.8
79
216. 8
175. 6
40
31.1
25.2
100
77.7
62.9
60
T61
124.3
125.1
100.7
20
171.0
1.38. 5
80
217.6
176.2
41
31.9
25.8
101
78.5
63.6
101.3
221
171.7
139.1
281
218.4
176.8
42
32.6
26.4
02
79.3
64.2
62
125.9
101.9
22
172.5
139.7
82
219.2
177.5
43
33.4
27.1
03
80.0
64.8
63
126.7
102.6
23
173.3
140. 3
83
219.9
178.1
44
34.2
27.7
04
80.8
65.4
64
127. 5
103.2
24
174.1
141.0
84
220.7
178.7
45
,35.
28.3
05
81.6
66.1
65
128.2
103.8
25
174.9
141.6
85
221.5
179.4
46
35.7
28.9
06
82.4
66.7
66
129.0
104.5
26
175.6
142.2
86
222.3
180.0
47
36.5
•29.6
07
8.3.2
67. '3
67
129.8
105.1
27
176.4
142.9
87
223.0
180.6
48
37.3
30.2
08
83.9
68.0
68
130.6
105.7
28
177.2
143. 5
88
223. 8
181.2
49
.38.1
30.8
09
84.7
68.6
69
131.3
106.4
29
178.0
144.1
89
224.6
181.9
50
38.9
31.5
10
85.5
69.2
70
132.1
107.0
30
178.7
179.5
144.7
90
225.4
182.- 5
51
39.6
32.1
111
86.3
69. 9
171
1S2.9
107.6
231
145. 4
291
226.1
183.1
52
40.4
32.7
12
87.0
70.5
72
133.7
108.2
32
180. 3
146.0
92
226.9
183.8
53
41.2
.33.4
13
87.8
71.1
73
134.4
108.9
33
181.1
146.6
93
227.7
184.4
54
42.0
.34.0
14
88.6
71.7
74
.135.2
109.5
34
181.9
147.3
94
228.5
185.
55
42.7
34.6
15
89.4
72.4
75
136.0
110.1
35
182.6
147.9
95
229.3
185.6
56
43.5
.35. 2
16
90.1
73.0
76
136.8
110.8
36
183.4
148.5
96
230.0
186.3
57
44.3
35.9
17
90.9
73.6
77
137.6
111.4
37
184.2
149.1
97
230.8
186.9
58
45.1
36.5
18
91.7
74.3
78
138.3
112.0
.38
185.0
149.8
98
231.6
187.5
59
45.9
37.1
19
92.5
74.9
79
139.1
112.6
39
185.7
150.4
99
232.4
188. 2
60
46.6
37.8
20
93.3
75.5
80
139.9
113.3
40
186.5
151.0
300
233.1
188.8
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
51° (129°, 23
1°, 309
')•
Page 608J
TABLE -2.
Difference of Latitude ami Departure for
39° (141°, 219°, 321°
)•
Dist. 1 Lat.
Dep.
Dist.
Lat.
Dep.
Dist. Lat.
Dep.
Dist.
Lat
Dep.
Dist.
Lat.
Dep.
301
1 233.9
189.4
361
280.6
227.1
421 327.2
264. 9
481
373. 8
302. 6
541
420.4
340.4
02
1 234.7
190.
62
281.3
227.8
22 j 328.0
265.5
82
374. 6
303. 3
42
421.2
341.0
03
235.5
190.6
63
282.1
228. 4
23
328. 7
266. 2
83
375. 4
303. 9
43
422.0
341.7
04
236. 3
191.3
64
282. 9
229.0
24
329.5
266. 8
84
376. 1
304. 5
44
422.7
342.3
05 237.
191.9
65
283.7
229.7
25
3.30. 3
267.4
85
376.9
305. 2
45
423.5
342.9
0« 237. 8
192.5
66
284.4
230. 3
2()
331.1
268.0
86
377. 7
305. 8
46
424. 3
343.6
07 238. 6
193. 2
67
285.2
230. 9
27
.331.9
268.7
87
378.5
306.4
47
425. 1
344.2
08 239. 4
193.8
68
286.0
231. 5
28
332.6
269. 3
88
379. 3
307.1
48
425. 9
344.8
09 240. 1
194.4
69
286.8
232. 2
29 333. 4
269. 9
89
380.0
307.7
49
426.6
345:5
10 240. 9
311 : 241.7
195.0
70
287.6
232.8
233. 4
30 334. 2
270.6
271.2
90
491
380.8
381.6
308.3
308. 9
50
427.4
346.1
195. 7
371
288. 3
431 1 3;».o
551
428. 2
346.7
12 242. 5
196.3
72
289.1
234. 1
32
335. 7
271.8
92
382.4
309. 6
52
429.0
.347. 4
13 243. 3
196.9
73
289.9
234.7
33
336. 5
272. 5
93
383.1
310.2
53
429.7
348.0
14 244.0
197. 6
74
290.7
235.3
34
337. 3
273. 1
94
383. 9
310.8
54
430. 5
348.6
15 244.8
198.2
75
291.4
236.0
35
338.1
273.7
95
384.7
311.5
55
431. 3
:349.2
16 245. 6
198. 8
76
292.2
236.6
36
338.8
274. 3
9t>
385. 5
312.1
56
432.1
349.9
17 246.4
199.5
77
293.0
237.2
37
339. 6
275.
97
386. 2
312. 7
57
432. 8
,350. 5
18 247. 1
200. 1
78
293.8
237.8
38
340. 4
275. 6
98
387.0
313. 3
58
433. 6
351. 1
19 247. 9 i 200. 7
79
294.5
238.5
39
341.2
276.2
99
387.8
314.
59
434.4
351.7
20
248.7
201.3
202.
80
295.3
296.1
239. 1
239.7
40
342.
342. 7
276.9
500
388. 6
389. 4
314.7
60
435. 2
435.9
352. 4
321
249. 5
381
441
277.5
501
315. 3
561
353.0
22 250.3
202.6
82
296.9
240.4
42
343. 5
278.1
02
390.1
315. 9
62
436.7
.353. 6
23 ! 251-.0
203.2
83
297.7
241.0
43
344. 3
278. 7
03
390. 9
316.5
63
437. 5
354. 3
24 251.8
203.9
84
298.4
241.6
44
345. 1
279.4
04
391.7
317.1
64
438. 3
354. 9
25 252. 6
204. 5
85
299. 2
242.2
45
345. 8
280.0
05
392. 5
317.8
65
439.1
355. 5
26 253. 4
205.1
86
300.0
242. 9
46
346.6
280. 6
06
393. 2
318.4
66
439. 8
356. 2
27
254.1
205.7
87
300.8
243.5
47
347.4
281.3
07
394.0
319.0
67
440. 6
356. 8
28
254.9
206.4
88
301. 5
244.1
48
348. 2
281.9
08
394. 8
319.6
68
441.4
357. 4
29
255.7
207.0
89
302. 3
244. 8
49
349.0
282.5
09
395. (i
320.3
69
442.2
3.58. 1
30
256.5
257.2
207. 6
90
303.1
245. 4
246.
50
451
349.7
283.2
10
396.3
320.9
70
443.0
"44377"
358.7
331
208.3
391
303. 9
3.50. 5
283.8
511
397.1
321.6
571
.359. 3
32
258.0
208.9
92
304.7
246.7
52
351.3
284.4
12
397. 9
322.2
72
444. 5
359. 9
33
258.8
209.5
93
305.4
247.3
53
352. 1
285.
13
398.7
322. 8
73
445. 3
360.6
34
259.6
210.2
94
306.2
247.9
54
352. 8
285. 7
14
399. 4
323. 4
74
446.1
361.2
,35
260.4
210.8
95
307.0
248.5
00
353. 6
286.3
15
400.2
324. 1
iO
446.9
361.8
36
261.1
211.4
96
307.8
249.2
56
.354. 4
286.9
16
401.0
324.7
76
447. 6
362. 4
37
261.9
212.0
97
308. 5
249.8
0/
355. 2
287.6
17
401.8
325. 3
77
448.4
363. 1
38
262.7
212.7
98
309.3
250.4
58
355. 9
288.2
18
402. 5
325. 9
78
449.2
363.7
39
263.5
213. 3
99
310.1
251.1
59
3.56. 7
288.8
19
403.3
326. 6
79
4.50.
364. 3
40
341
264.2
213.9
400
310. 9
251. 7
60
357. 5
289.4
"290.1
20
404.1
,327. 2
80
450.7
365.0
265.0
214.6
401
311.6
252.3
461
358.3
521
404.9
327.8
581
451.5
365. 6
42
265.8
215.2
02
312. 4
252.9
62
359.1
290.7
22
405.7
328. 5
82
452.3
366.2
43
266.6
215. 8
03
313.2
2.53. 6
63
359. 8
291.3
23
406.4
329.1
83
453. 1
366.9
44
267.3
216.4
04
314.0
254.2
64
360. 6
292.0
24
407.2
329.7
84
453.9
367.5
45
268.1
217.1
05
314.8
254. 8
65
361.4
292.6
25
408.0
330.4
85
4.54. 6
368.1
46
268.9
217.7
06
315. 5
255.5
66
362.2
293.2
26
408.8
331.0
86
455. 4
368.8
47
269.7
218.3
07
316. 3
2.56. 1
67
362. 9
293. 8
27
409.5
331.6
87
456. 2
369.4
48
270. 5
219.0
08
317.1
256.7
68
363. 7
294.5
28
410. 3
332.3
88
457.
370.0
49
271.2
219.6
09
317.9
257. 3
69
364. 5
295.1
29
411.1
332.9
89
457.8
370. 6
50
272.0
220.2
10
411
318.6
258.0
70
365.3
295. 7
30
411.9
333.5
90
458. 5
371.3
351
272.8
220.8
319.4
258. 6
471
366.
296.4
531
412.6
334.1
591
459.3
371.9
52
273.6
221.5
12
320.2
259. 2
72
366. 8
297.0
32
413.4
334.8
92
460.1
372. 5
53
274.3
222.1
13
321.0
259.9
7.)
367. 6
297.6
33
414.2
335.4
93
460.9
373.2
54
275.1
222.7
14
321.8
260.5
74
368.4
298.3
34
415.0
336.1
94
461.6
373.8
55
275.9
223.4
15
322. 5
261.1
75
369.2
298.9
35
415. 8
336. 7
95
462.4
374.4
56
276.7
224.0
16
323. 3
261.8
76
369.9
299. 5
.36
416. 5
337. 3
96
463.2
375.1
57
277.5
224.6
17
324.1
262.4
77
370.7
300.1
37
417.3
337. 9
97
464.0
375.7
58
278.2
225. 3
18
324.9
263.
78
371.5
300.8
38
418. 1
338.5
98
464.8
376.3
59
279.0
225.9
19
325. 6
263.6
79
372. 3
301.4
39
418.9
339.1
99
465. 5
376.9
60
279.8
226.5
20
326.4
264.3
80
373.0
302.0
40
419.6
339.8
600
466.3
377.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist. Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
c
)1° (129°, 231°, 309°
)■
TABLE 2.
[Page
609
Difference of Latitude and Departure for 40° (140°, 220°, 320°
)■
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist. 1 Lat. j Dep.
' 1
Dist.
Lat.
Dep.
1
0.8
0.6
61
46.7
39.2
121
92.7
77.8
181
138.7
116.3
241
184.6
154.9
2
1.5
1.3
62
47.5
39.9
22
93.5
78.4
82
139.4
117.0
42
185.4
155. 6
3
2.3
1.9
63
48.3
40.5
23
94.2
79.1
83
140.2
117.6
43
186.1
156.2
4
3.1
2.6
64
49.0
41.1
24
95.0
79.7
84
141.0
118. 3
44
186.9
156.8
5
3.8
3.2
65
49.8
41.8
25
95.8
80.3
85
141.7
118.9
45
187.7
157.5
6
4.6
3.9
66
50.6
42.4
26
96.5
81.0
86
142.0
119.6
46
188.4
158.1
7
5.4
4.5
67
51.3
43.1
27
97.3
81.6
87
143.3
120.2
47
189.2
158.8
8
6.1
5.1
68
52.1
43.7
28
98.1
82.3
88
144.0
120.8
48
190.0
159.4
9
6.9
.5.8
69
52.9
44.4
29
98.8
82.9
89
144.8
121.5
49
190.7
160.1
10
11
7. 7
6.4
70
53.6
45.0
30
99.6
83.6
90
145.0
122.1
50
191.5
160.7
8.4
7.1
71
54.4
45.6
131
100.4
84.2
191
146.3
122.8
251
192.3
161.3
12
9.2
7. 7
72
55.2
46.3
32
101.1
84.8
92
147.1
123.4
52
193.0
162.0
13
10.0
8.4
73
55.9
46.9
33
iOl.9
85.5
93
147.8
124.1
53
193.8
162.6
14
10.7
9.0
74
56.7
47.6
34
102.6
86.1
94
148.6
124.7
54
194.6
163.3
15
11.5
9.6
75
57.5
48.2
35
103.4
86.8
95
149.4
125.3
55
195.3
163.9
16
12.3
10.3
76
58.2
48.9
36
104.2
87.4
96
150.1
126.0
56
196.1
164.6
17
13.0
10.9
77
59.0
49.5
37
104.9
88.1
97
150.9
126.6
57
196.9
165.2
18
13.8
11.6
78
59.8
50.1
38
105. 7
88.7
98
151.7
127.3
58
197.6
165.8
19
14.6
12.2
79
60.5
50.8
39
106. 5
89.3
99
152. 4
127.9
59
198.4
166. 5
20
15.3
12.9
80
61.3
51.4
40
107.2
108.0
90.0
90.6
200
201
153.2
128.6
60
199.2
167.1
21
16.1
13.5
81
62.0
52.1
141
154.
129.2
261
199. 9
167.8
22
16.9
14.1
82
62.8
52.7
42
108.8
91.3
02
154.7
129.8
62
200.7
168.4
23
17.6
14.8
83
63.6
53.4
43
109.5
91.9
03
155.5
130. 5
63
201.5
169.1
24
18.4
15.4
84
64.3
54.0
44
110.3
92.6
04
156. 3
131.1
64
202.2
169. 7
25
19.2
16.1
85
65.1
54.6
45
111.1
93. 2
05
157.0
131.8
65
203.0
170.3
26
19.9
16.7
86
65.9
55.3
46
111.8
93.8
06
157.8
132.4
66
203.8
171.0
27
20.7
17.4
87
66.6
55.9
47
112.6
94.5
07
158.6
133.1
67
204.5
171.6
28
21.4
18.0
88
67.4
.56.6
48
113.4
95.1
08
159.3
133.7
68
205. 3
172.3
29
22. 2
18.6
89
68.2
57.2
49
114.1
95.8
09
160.1
134.3
69
206.1
172.9
30
23!
19.3
90
68.9
57.9
50
114.9
96.4
.10
160.9
135.0
70
206. 8
207.6
173.6
31
23.7
19.9
91
69.7
58.5
151
115.7
97.1
211
161.6
135.6
271
174.2
32
24.5
20.6
92
70.5
59.1
52
116.4
97.7
12
162.4
136.3
72
208.4
174.8
33
25.3
21.2
93
71.2
59.8
53
117.2
98.3
13
163.2
136.9
73
209.1
175.5
34
26.0
21.9
94
72.0
60.4
54
118.0
99.
14
163.9
137. 6
74
209.9
176. 1
35
26.8
22.5
95
72.8
61.1
55
118.7
99.6
15
164.7
138.2
75
210.7
176.8
36
27.6
23.1
96
73.5
61.7
56
119. 5
UK). 3
16
166.5
138.8
76
211.4
177.4
37
28.3
23.8
97
74.3
62.4
57
120. 3
100.9
17
166.2
139. 5
77
212.2
178.1
38
29.1
24.4
98
75.1
63.0
58
121.0
101.6
18
167.0
140.1
78
213.0
178.7
39
29.9
25.1
99
75.8
63.6
.59
121.8
102.2
19
167.8
140.8
79
213.7
179.3
40
30.6
25.7
26. 4
100
76.6
64.3
60
122.6
102.8
20
168.5
141.4
80
214.5
180.0
41
31.4
101
77.4
64.9
161
123. 3
103. 5
221
169.3
142.1
281
215.3
180.6
42
32.2
27.0
02
78.1
65.6
62
124.1
104.1
22
170.1
142.7
82
216.0
181.3
43
32.9
27.6
03
78.9
66.2
63
124. 9
104.8
23
170.8
143.3
83
216.8
181.9
44
33.7
28.3
04
79.7
66.8
64
125. 6
105.4
24
171.6
144.0
84
217.6
182.6
45
34.5
28.9
05
80.4
67.5
65
126.4
106.1
25
172.4
144.6
85
218.3
183.2
46
35.2
29.6
06
81.2
68.1
66
127.2
106.7
26
173.1
145.3
86
219.1
183.8
47
36.0
30. 2
07
82.0
68.8
67
127.9
107.3
27
173.9
145.9
87
219.9
184.5
48
36.8
30.9
08
82.7
69.4
68
128.7
108.0
28
174.7
146.6
88
220.6
185. 1
49
37.5
31.5
09
83.5
70.1
69
129. 5
108. 6
29
175.4
147.2
89
221.4
185.8
50
38.3
32.1
10
84.3
70.7
70
130.2
109.3
30
176.2
147.8
90
222.2
186.4
187.1
51
39.1
32.8
111
85.0
71.3
171
131.0
109.9
231
177.0
148.5
291
222. 9
52
39.8
33.4
12
85.8
72.0
72
131.8
110.6
32
177.7
149.1
92
223.7
187.7
53
40.6
34.1
13
86.6
72.6
73
132.5
111.2
33
178.5
149.8
93
224.5
188.3
54
41.4
34.7
14
87.3
73. 3
74
133. 3
111.8
34
179.3
150.4
94
225. 2
189.0
55
42.1
35.4
15
88.1
73.9
75
134.1
112.5
35
180.0
151. 1
95
226.0
189.6
56
42.9
36.0
16
88.9
74.6
76
134.8
113.1
36
180.8
151.7
96
226.7
190.3
57
43. 7 .36. 6 1
17
89.6
75.2
77
135.6
113.8
37
181.6
152.3
97
227.5
190.9
58
44.4
37.3
18
90.4
75.8
78
136.4
114.4
38
182.3
153.
98
228. 3
191.6
59
45.2
37.9
19
91.2
76.5
79
.137.1
115.1
39
183.1
153.6
99
229.0
192.2
60
46.0
38.6
20
91.9
77.1
80
137.9
115.7
40
183.9
154.3
300
229.8
192.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
5
0° (1.30°, 230=
, 310°
.
24972°— 12-
-29
Page 610]
TABLE 2.
Difference of latitude and Departure for 40° (140°, 220
°, 320°
).
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
230.6
193.5
361
276.5
232.1
421
322.5
270.6
481
368.5
309.2
541
414.4
347.7
02
231.3
194.1
62
277.3
232.7
22
323.3
271.3
82
369.2
309.8
42
415.2
348.4
03
232.1
194.8
63
278.1
233.3
23
324.0
271.9
83
370.0
310.5
43
416.0
349.0
04
232.9
195.4
64
278.8
234.0
24
324.8
272.6
84
370. 8
311.1
44
416.7
349.7
05
233.6
196.1
65
279.6
234.6
25
325. 6
273.2
85
371.5
311.7
45
417.5
350. 3
06
234.4
196.7
66
280.4
235.3
26
326.3
273.8
86
372.3
312. 4
46
418. 3
351.0
07
235.2
197.3
67
281.1
235.9
27
327.1
274.5
87
373.1
313.0
47
419.0
351.6
08
235.9
198.0
68
281.9
236.6
28
327.9
275. 1
88
373.8
313.6
48
419.8
352. 2
09
236.7
198.6
69
282.7
237. 2
29
328.6
275.8
89
374.6
314.3
49
420.6
352. 9
10
237.5
199.3
70
283.4
237. 8
30
329.4
276.4
90
375.4
314.9
50
421. 3
353. 5
354. 2
311
238.2
199.9
371
284.2
238.5
431
330.2
277.1
491
376.1
315.6
551
422.1
12
239.0
200.6
72
285.0
239.1
32
330. 9
277.7
92
376. 9
316.2
52
422.9
354. 8
13
239.8
201.2
73
285.7
239.7
33
331.7
278. 3
93
377.7
316.9
53
423.6
355. 5
14
240.5
201.8
74
286.5
240.4
34
332.5
279.0
94
378.4
317.5
54
424.4
356. 1
15
241.3
202.5
75
287.3
241.0
35
333. 2
279.6
95
379. 2
318.2
55
425.2
3.56. 8
16
242.1
203. 1
76
288.0
241.7
36
334.0
280.3
96
380.0
318.8
56
425.9
357.4
17
242.8
203.8
77
288. 8'
242.3
37
334.8
280.9
97
380.7
319.5
57
426.7
358.0
18
243. 6
204.4
78
289.6
243.0
38
335.5
281.6
98
381.5
320.1
58
427.5
358.7
19
244.4
205.1
79
290.3
243.6
39
336. 3
282.2
99
382. 3
320.8
59
428.2
359.3
20
321
245. 1
205.7
80
291.1
244.3
40
337.1
282.8
500
383.0
383. 8
321.4
60
429.0
360.
360.6
245.9
206.3
381
291.9
244.9
441
337.8
283.5
501
322.0
561
429.8
22
246.7
207.0
82
292.6
245.6
42
338.6
284.1
02
384.6
322.7
62
430.5
361.2
23
247.4
207.6
83
293.4
246.2
43
339.4
284.8
03
385. 3
323.3
63
431.3
361.9
24
248.2
208.3
84
294.2
246.8
44
340.1
285.4
04
386.1
324.0
64
432.1
362.5
25
249.0
208.9
85
294.9
247.5
45
340.9
286.0
05
386.8
324.6
65
432.8
363.2
26
249.7
209.6
86
295.7
248.1
46
341.7
286.7
06
387. 6
325.2
66
433.6
363.8
27
250.5
210.2
87
296.5
248. 8
47
342.4
287.3
07
388.4
325.9
67
434.3
364.5
28
251.3
210.8
88
297.2
249.4
48
343.2
288.0
08
389.2
326.5
68
435.1
365.1
29
252.
211.5
89
298.0
250.1
49
344.0
288.6
09
389.9
327. 1
o9
435.9
365.8
30
252.8
212.1
90
298.8
250. 7
50
344.7
289.3
10
390.7
391.5
327.8
70
436.6
366.4
331
253. 6
212.8
391
299.5
251.3
451
345.5
289. 9
511
328.4
571
437.4
367.0
32
254.3
213.4
92
300.3
252.0
52
346.3
290.5
12
392.2
329.1
72
438.2
367.7
33
255.1
214.1
93
301.1
252.6
53
.347.0
291.2
13
393.0
329.7
73
438.9
368.3
34
255.9
214.7
94
301.8
253.3
54
347.8
291.8
14
393. 8
330.4
74
439.7
369.0
35
256.6
215.3
95
302.6
253.9
55
348.6
292.5
15
394.5
331.0
75
440.5
369.6
36
257.4
216.0
96
303.4
254.6
56
349.3
293. 1
16
395.3
331.6
76
441.2
370.2
37
258.2
216.6
97
304.1
255.2
57
350.1
293.8
17
396. 1
332.3
77
442.0
370.9
38
258.9
217.3
98
304.9
255.8
58
350.8
294.4
18
396. 8
332.9
78
442.8
371.5
39
259.7
217.9
99
305.7
256.5
59
351.6
295.0
19
397.6
333.6
79
443.5
372.2
40
260.5
218.6
400
306.4
257.1
60
352.4
295.7
20
398.3
334.2
80
444.3
372.8
341
261.2
219.2
401
307.2
257.8
461
353.1
296. 3
521
399. 1
334.9
581
445.1
373.5
42
262.0
219.8
02
308.0
258.4
62
353.9
297.0
22
399.9
335. 5
82
445.8
374.1
43
262.8
220. 5
03
308.7
259.1
63
354.7
297.6
23
400.6
336.1
83
446.6
374.8
44
263.5
221.1
04
309.5
259.7
64
355.4
298.3
24
401.4
336.8
84
447.4
375.4
45
264.3
221.8
05
310.2
260.3
65
356.2
298.9
25
402.2
337.4
85
448.1
376.0
46
265.1
222.4
06
311.0
261.0
66
357.0
299.5
26
402.9
338.1
86
448.9
376.7
47
265.8
223.1
07
311.8
261.6
67
357.7
300.2
27
403.7
338.7
87
449.7
377.3
48
266.6
223.7
08
312.5
262.3
68
358.5
300.8
28
404.5
339.4
88
450.4
378.0
49
267.4
224.3
09
313. 3
262.9
69
359.3
301.5
29
405.2
340.0
89
451.2
378.6
50
268.1 1 225.0
10
314.1
263.6
70
360.0
302.1
30
406.0
406.8
340.6
90
591
452.0
379.2
351
268.9
225.6
411
314.8
264.2
471
360.8
302. 8
531
341.3
452.7
379.9
52
269.6
226.3
12
315.6
264.8
72
361.6
303.4
32
407.5
341.9
92
453.5
380.5
53
270.4
226.9
13
316.4
265.5
73
362.3
304.0
33
408.3
342.6
93
454.3
381.2
54
271.2
227.6
14
317.1
266.1
74
363. 1
304.7
34
409.1
343.2
94
455.0
381.8
55
271.9
228.2
15
317.9
266.8
75
363. 9
305.3
35
409.8
343.9
95
455.8
382. 4
56
272.7
228.8
16
318.7
267.4
76
364.6
306.0
36
410.6
344.5
96
456.6
383.1
57
273.5
229.5
17
319.4
268.1
77
365.4
306.6
37
411.4
345.2
97
457.3
383. 7
58
274.2
230.1
18
320.2
268.7
78
366.2
307.3
38
412.1
345.8
98
458.1
384.4
59
275.0
230.8
19
321.0
269.3
79
366.9
307. 9
39
412.9
346.4
99
458.9
385.0
60
275.8
231.4
20
321.7
270.0
80
367.7
308.5
40
413.7
347.1
600
459.6
385.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
50° (1
30°, 230
°, 310°
)■
TABLE 2.
[Page 611
Difference of Latitude and Departure for 41° (139°, 221°, 319°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.8
0.7
61
46.0
40.0
121
91.3
79.4
181
136.6
118.7
241
181.9
158. 1
2
1.5
1.3
62
46.8
40.7
22
92.1
80.0
82
137.4
119.4
42
182.6
158.8
3
2.3
2.0
63
47.5
41.3
23
92.8
80.7
83
138.1 120.1
43
183.4
1.59. 4
4
3.0
2.6
64
48.3
42.0
24
93.6
81.4
84
138. 9 120. 7
44
184.1
160. 1
5
3.8
3.3
65
49.1
42.6
25
94.3
82.0
85
139.6 121.4
45
184.9
160. 7
6
4.5
3.9
66
49.8
43.3
26
95.1
82.7
86
140.4
122.0
46
185.7
161.4
7
5.3
4.6
67
50.6
44.0
27
95.8
83.3
87
141.1
122.7
47
186.4
162.0
8
6.0
5.2
68
51.3
44.6
28
96.6
84.0
88
141.9
123.3
48
187.2
162.7
9
6.8
5.9
69
52.1
45.3
29
97.4
84.6
89
142.6
124.0
49
187.9
163.4
10
7.5
6.6
70
52.8
45.9
30
98.1
85.3
90
143.4
124.7
50
188.7
164.0
11
8.3
7.2
71
53.6
46.6
131
98.9
85.9
191
144.1
125.3
251
189.4
164.7
12
•9.1
. 7.9
72
54.3
47.2
32
99.6
86.6
92
144.9
126.0
52
190.2
165.3
13
9.8
8.5
73
55.1
47.9
33
100.4
87.3
93
145.7
126.6
53
190.9
166.0
14
10.6
9.2
74
55.8
48.5
34
101.1
87.9
94
146.4
127. 3
54
191.7
166.6
15
11.3
9.8
75
56.6
49.2
35
101.9
88.6
95
147.2
127.9
55
192.5
167.3
16
12.1
10.5
76
57.4
49.9
36
102.6
89.2
96
147.9
128.6
56
193.2
168.0
17
12.8
11.2
77
58.1
50.5
37
103.4
89.9
97
148.7
129.2
57
194.0
168.6
18
13.6
11.8
78
58.9
51.2
38
104.1
90.5
98
149.4
129.9
58
194.7
169.3
19
14.3
12.5
79
59.6
51.8
39
104.9
91.2
99
150.2
130.6
59
195.5
169.9
20
15.1
13.1
80
'60.4
52.5
40
105.7
106.4
91.8
92. 5
200
'201"
150.9
151.7
131.2
60
196.2
170.6
171.2
21
15.8
13.8
81
61.1
53.1
141
131. 9
261
197.0
22
16.6
14.4
82
61.9
53.8
42
107. 2
93. 2
02
152.5
132.5
62
197.7
171.9
23
17.4
1.5.1
83
62.6
54. 5
43
107.9
93.8
03
153. 2
133. 2
63
198.5
172.5
24
18.1
15.7
84
63.4
55.1
44
108.7
94.5
04
154.
133.8
64
199.2
173.2
25
18.9
16.4
85
64.2
55.8
45
109.4
9.5.1
05
154.7
134.5
65
200.0
173.9
26
19.6
17.1
86
64.9
56.4
46
110.2
95.8
06
155.0
135.1
66
200.8
174.5
27
20.4
17.7
87
65.7
57.1
47
110.9
96.4
07
156.2
ia5.8
67
201.5
175.2
28
21.1
18.4
88
66.4
57.7
48
111.7
97.1
08
157.0
136.5
68
202.3
175.8
29
21.9
19.0
89
67.2
58.4
49
112.5
97.8
09
157.7
137.1
69
203.0
176.5
30
22.6
19.7
90
67.9
59.0
50
151
113.2
114.0
98.4
10
211
158.5
159. 2
137.8
138. 4
70
271
203.8
204.5
177.1
177.8
31
23.4
20.3
91
68.7
59.7
99.1
32
24.2
21.0
92
69.4
60.4
52
114.7
99.7
12
160.0
139.1
72
205.3
178.4
33
24.9
21.6
93
70.2
61.0
53
115. 5
100.4
13
160.8
139.7
73
206.0
179.1
34
25.7
22.3
94
70.9
61.7
54
116.2
101.0
14
161.5
140.4
74
206.8
179.8
35
26.4
23.0
95
71.7
62.3
55
117.0
101.7
15
162.3
141.1
75
207.5
180.4
36
27.2
23.6
96
72.5
63.0
56
117.7
102.3
16
163.
141.7
76
208.3
181.1
37
27.9
24.3
97
73.2
63.6
57
118. 5
103.0
17
163.8
142.4
77
209.1
181.7
38
28.7
24.9
98
74.0
64.3
58
119.2
103. 7
18
164.5
143.
78
209.8
182.4
39
29.4
25.6
99
74.7
64.9
59
120.0
104.3
19
165. 3
143.7
79
210.6
183.0
40
30.2
26.2
100
75.5
6.5.6
60
120.8
121. 5
1(15.0
20
166.0
144.3
80
211.3
183.7
41
30.9
26.9
101
76.2
66.3
161
105.6
221
166.8
145.0
281
212.1
184.4
42
31.7
27.6
02
77.0
66.9
62
122.3
106.3
22
167.5
145. 6
82
212.8
185.
43
32.5
28.2
03
77.7
67.6
63
123.0
106.9
23
168.3
146.3
83
213.6
185.7
44
33.2
28.9
04
78.5
68.2
64
123. 8
107.6
24
169.1
147.0
84
214.3
186. 3
45
34.0
29.5
05
79.2
68.9
65
12jl.5
108.2
25
169.8
147.6
85
215.1
187.0
46
34.7
30.2
06
80.0
69.5
66
125.3
108.9
26
170.6
148.3
86
215.8
187.6
47
35.5
30.8
07
80.8
70.2
67
126.0
109.6
27
171. 3
148.9
87
216.6
188.3
48
36.2
31.5
08
81.5
70.9
68
126.8
110.2
28
172.1
149.6
88
217.4
188.9
49
37.0
32.1
09
82.3
71.5
69
127.5
110.9
29
172.8
150.2
89
218.1
189.6
50
37.7
32.8
10
83.0
83.8
72.2
70
128.3
111.5
112.2
30
173.6
150.9
90
218.9
190.3
190.9
51
38.5
33.5
111
72.8
171
129.1
231
174.3
151.5
291
219.6
52
39.2
34.1
12
84.5
73.5
72
129.8
112.8
32
175. 1
152.2
92
220.4
191.6
53
40.0
34.8
13
85.3
74.1
73
1.30. 6
113.5
33
175.8
152.9
93
221.1
■192. 2
54
40.8
35.4
14
86.0
74.8
74
131.3
114.2
34
176.6
153.5
94
221.9
192.9
55
41.5
36.1
15
86.8
75.4
75
132.1
114.8
35
177.4
154.2
95
222.6
193.5
56
42.3
36.7
16
87.5
76.1
76
132.8
115.5
36
178.1
154.8
96
223.4
194.2
57
43.0
37.4
17
88.3
76.8
77
133.6
116.1
37
178.9
155.5
97
224.1
194.8
58
43.8
38.1
18
89.1
77.4
78
134. 3
116.8
38
179.6
156.1
98
224.9
195.5
59
44.5
38.7
19
89.8
78.1
79
135.1
117.4
39
180.4
156.8
99
225.7
196.2
60
45.3
39.4
20
90.6
78.7
80
135.8
118.1
40
181.1
157.5
300
226.4
196.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Diet.
Dep.
Lat.
Dist.
Dep.
Lat.
49° (1
31°, 228
°, 311°
)•
Page 612]
TABLE 2.
Difference of Latitude and Departure for 41° (139°, 221°, 319°
)•
Dist.
301
Lat.
Dep.
Dist.
hat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
227.2
197.5
361
272.5
236.9
421
317.7
276.2
481
363.0
315.6
541
408.3
354.9
02
227.9
198.1
62
273.2
237.5
22
318.5
276.9
82
363.8
316.2
42
409.0
355. 6
03
228.7
198.8
63
274.0
238.2
23
319.2
277.5
83
364.5
316.9
43
409.8
356.2
04
229.4
199. 4
64
274.7
238. 8
24
320.0
278.2
84
365.3
317.5
44
410.6
356.9
05
230.2
200.1
65
275.5
239.5
25
320.8
278.8
85
366.0
318. 2
45
411.3
357.5
06
230.9
200.8
66
276.2
240.1
26
321.5
279.5
86
366.8
318.8
46
412.1
358.2
07
231.7
201.4
67
277.0
240.8
27
322.3
280.1
87
367.5
319.5
47
412.8
358.8
08
232.5
202.1
68
277.7
241.4
28
323.0
280.8
88
368.3
320.1
48
413.6
359.5
09
233.2
202.7
69
278.5
242.1
29
323.8
281.5
89
369.0
320.8
49
414.3
360.2
10
234.0
203.4
70
279.2
242.7
30
324. 5
282.1
90
369.8
321.5
50
415.1
360.8
311
234.7
204.0
371
280.0
243.4
431
325.3
282.8
491
370.6
322.1
551
415.8
361.5
12
235.5 204.7
72
280.8
244.1
32
326.0
283.4
92
371.3
322.8
52
416.6.
362.1
13
236.2 205.4
73
281.5
244.7
33
326.8
284.1
93
372.1
323.4
53
417.3
362.8
14
237.0
206.0
74
282.3
245.4
34
327.5
284.7
94
372.8
324.1
54
418.1
363.4
15
237.7
206.7
75
283.0
246.0
35
328.3
285.4
95
373.6
324.7
55
418.9
364.1
16
238.5
207.3
76
283.8
246.7
36
329.1
286ro
96
374.3
325.4
56
419.6
364.8
17
239.2
208.0
77
284.5
247.3
37
329.8
286.7
97
375.1
326.0
57
420.4
365.4
18
240.0
208.6
78
285.3
248.0
38
330.6
287.4
98
375.8
326.7
58
421.1
366.1
19
240.8
209. 3
79
286.
248.7
39
331. 3
288.0
99
376.6
327.4
59
421.9
366.7
20
241.5
209.9
80
286.8
249.3
40
332.1
332. 8
288.7
500
377.3
328.
60
422.6
367.4
321
242.3
210.6
381
287.5
250.0
441
289.3
501
378.1
328.7
561
423.4
368.0
22
243.0
211.3
82
288.3
250.6
42
3.33. 6
290.0
02
378.9
329.3
62
424.1
368.7
23
243.8
211.9
83
289.1
251.3
43
334.3
290.6
03
379.6
330.
63
424.9
369.4
24
244.5
212.6
84
289.8
251.9
44
335.1
291.3
04
380. 4 ; 330. 6
64
425.7
370,0
25
245.3
213.2
85
290.6
252.6
45
335. 8
292.0
05
381.1 1331.3
65
426.4
370.7
26
246.0
213.9
86
291.3
253.2
46
336. 6
292.6
06
381.9
332.0
66
427.2
371.3
27
246.8
214.5
87
292.1
253.9
47
337.4
293.3
07
382.6
332.6
67
427.9
372.0
28
247.5
215.2
88
292.8
254.6
48
338.1
293.9
08
383.4
3.33. 3
68
428.7
372.6
29
248.3
215.9
89
293.6
255. 2
49
338.9
294.6
09
384.1
333.9
69
429.4
373.3
30
331
249.1
216.5
90
294.3
255.9
50
339.6
295.2
10
384.9
334.6
70
430.2
374.0
249.8
217. 2
391
295.1
256. 5
451
340.4
295.9
511
385.7
335.2
571
430.9
374.6
32
250.6
217.8
92
295.8
257.2
52
341.1
296.5
12
386.4
335. 9
72
431.7
375.3
33
251. 3
218.5
93
296.6
257. 8
53
341.9
297.2
13
387.2
336.5
73
432.4
375.9
34
252.1
219.1
94
297.4
258.5
54
342.6
297.9
14
387.9
337.2
74
433.2
376.6
35
252.8
219.8
95
298.1
259. 2
55
343. 4
298.5
15
388.7
337.9
75
434.
377. 2
36
253.6
220.4
96
298. 9
259.8
56
344.1
299.2
16
389.4
338. 5
76
434.7
377.9
37
254. 3
221.1
97
299.6
260. 5
57
344.9
299.8
17
390.2
339.2
77
435. 5
378. 5
38
255.1
221.8
98
300.4
261.1
58
345.7
300.5
18
390.9
339.8
78
436.2
379.2
39
255.8
222.4
99
301.1
261.8
59
346.4
301.1
19
391.7
340.5
79
437.0
379. 8
40
341
256.6
"257. 4
223.1
400
301.9
262.4
60
347.2
301.8
20
521
392.4
393.2
341.1
80
437.7
438. 5
380.5
223.7
401
302.6
263.1
461
347.9
302.5
341.8
581
381.2
42
258. 1
224.4
02
303. 4
263. 7
62
348.7
303.1
22
394.0
342.5
82
439.2
381.8
43
258.9
225.0
03
304. 2
264.4
63
349.4
303.8
23
394.7
343. 1
83
440.0
382. 5
44
259.6
225.7
04
304. 9
265. 1
64
350.2
304.4
24
395.5
343. 8
84
440.7
383.2
45
260.4
226.3
05
305.7
265. 7
65
350.9
305.1
25
396.2
344.4
85
441.5
383. 8
46
261.1
227.0
06
306.4
266.4
66
351.7
305.7
26
397.0
345. 1
86
442.3
384.5
47
261.9
227.7
07
307. 2
267.0
67
352. 5
306.4
27
397.7
345. 7
87
443.0
385. 1
48
262.6
228.3
08
307. 9
267. 7
68
353. 2
307.0
28
398. 5
346.4
88
443.8
385.8
49
263. 4
229.0
09
308.7
268.3
69
3.54.
307.7
29
399.2
347.0
89
444.5
386.4
50
351
264.2
229.6
10
309.4
IjIO. 2
269.0
269. 6
70
471
354. 7
355. 5
308.4
30
400.0
347.7
90
445.3
387.1
264.9
2.30. 3
411
309.0
531
400. 7"
348.4
591
446.0
387.7
52
265.7
230.9
12
310. 9
270. 3
72
356. 2
309.7
32
401.5
349.
92
446.8
388.4
53
■266. 4
231.6
13
311.7
271.0
73
357.0
310.3
33
402.2
349. 7
93
447.5
389. 1
54
267.2
232.3
14
312.5
271.6
74
357.7
311.0
34
403.0
350.3
94
448. 3
389.7
55
267.9
232.9
15
313.2
272.3
75
358. 5
311.6
35
403.8
.351.0
95
449.1
390.4
56
268.7
233.6
16
314.
272.9
76
359. 2
312.3
36
404.5
351.6
96
449.8
391.0
57
269.4
234.2
17
314.7
273.6
77
360.0
312.9
37
405.3
352. 3
97
450.6
391.7
58
270. 2
234.9
18
315.5
274. 2
78
360.8
313.6
38
406.0
352.9
98
451. 3
.392. 3
59
270.9
235.5
19
316.2
274.9
79
361.5
314.3
39
406.8
353. 6
99
452.1
393.0
60
271.7
236.2
20
317.0
275.6
80
362.3
314.9
40
407.5
354.3
600
452.8
393.6
Dist.
Dcp.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
49° (1
31°, 229°, 311°
)■
TABLE 2.
[Page 613 |
Difference of Latitude and Departure for 42° (138°, 222°, 318°
.
Dist.
Lai.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat. [
Dep.
1
0.7
0.7
61
45.3
40.8
121
89.9
81.0
181
134.5
121.1
241
179.1
161. 3
2
1.5
1.3
62
46.1
41.5
22
90.7
81.6
82
135.3
121.8
42
179.8
161.9
3
2.2
2.0
63
46.8
42.2
23
91.4
82.3
83
136.0
122.5
43
180.6
162. 6
4
3.0
2.7
64
47.6
42.8
24
92. 1
83.0
84
136.7
123.1
44
181.3
163.3
5
3.7
3.3
65
48.3
43.5
25
92.9
83.6
85
137.5
123.8
45
182.1
163.9
6
4.5
4.0
66
49.0
44.2
26
93.6
84.3
86
138. 2
124.5
46
182.8
164.6
7
5.2
4.7
67
49.8
44.8
27
94.4
85.0
87
139.0
125. 1
47
183.6
165.3
8
5.9
5.4
68
50.5
45. 5
28
95.1
85.6
88
139.7
125.8
48
184.3
165.9
9
6.7
6.0
69
51.3
46.2
29
95.9
86.3
89
140.5
126.5
49-
185.0
166.6
10
7.4
6.7
70
52.0
46.8
30
96.6
87.0
90
141.2
127.1
50
185.8
167.3
11
8.2
7.4
71
52.8
47.5
131
97.4
87.7
191
141.9
127.8
251
186.5
168.0
12
8.9
8.0
72
53.5
48.2
32
98.1
88.3
92
142.7
128.5
52
187.3
168.6
13
9.7
8.7
73
54.2
48.8
33
98.8
89.0
93
143.4
129.1
53
188.0
169.3
14
10.4
9.4
74
55.0
49.0
34
99.6
89.7
94
144.2
129.8
54
188.8
170.0
15
11.1
10.0
75
55.7
50.2
35
100.3
90.3
95
144.9
130.5
55
189.5
170.6
16
11.9
10.7
76
56.5
50.9
36
101.1
91.0
96
145.7 1131.1
56
190.2
171.3
17
12.6
11.4
77
57.2
51.5
37
101.8
91.7
97
146.4
131.8
57
191.0
172.0
18
13.4
12.0
78
58.0
52.2
38
102.6
92.3
98
147.1
132.5
58
191.7
172.6
19
14.1
12.7
79
58.7
52.9
39
103. 3
93.0
99
147.9
133.2
59
192.5
173.3
20
14.9
13.4
80
59.5
53.5
40
104.0
93.7
200
148.6
133.8
60
193.2
174.0
21
15.6
14.1
81
60.2
54.2
141
104.8
94.3
201
149.4
134. 5
261
194.0
"l74. 6
22
16.3
14.7
82
60.9
54.9
42
105.5
95.
02
150. 1 ! 135. 2
62
194.7
175. 3
23
17.1
15.4
83
61.7
55.5
43
106.3
95. 7
03
150.9 135.8
63
195.4
176.
24
17.8
16.1
84
62.4
56.2
44
107.0 : 96.4
04
151.6
136.5
64
196. 2
176.7
25
18.6
16.7
85
63.2
56.9
45
107. 8
97.0
05
152.3
137.2
65
196. 9
177. 3
26
19.3
17.4
86
63.9
57.5
46
108.5
97.7
06
153.1
137.8
66
197. 7
178.0
27
20.1
18.1
87
64.7
58.2
47
109. 2
98.4
07
153.8
138.5
67
198.4
178.7
- 28
20.8
18.7
88
65.4
58.9
48
110.0 ; 99.0
08
154.6
139.2
68
199.2
179. 3
29
21.6
19.4
89
66.1
59.6
49
no. 7 99.7
09
155. 3
139.8
69
199. 9
180.0
30
22.3
20.1
90
66.9
60.2
50
111.5 100.4
10
156.1
140.5
70
200.6
180.7
31
23.0
20.7
91
67.6
60.9
151
112.2 101.0
211
156.8
141.2
271
201.4
181.3
32
23.8
21.4
92
68.4
61.6
52
113.0 101.7
12
157.5
141.9
72
202.1
182.0
33
24.5
22.1
93
69.1
62.2
53
113.7 102.4
13
1.58. 3
142. 5
73
202.9
182.7
34
25.3
22.8
94
69.9
62.9
54
114.4 103.0
14
159.0
143.2
74
203.6
183. 3
35
26.0
23.4
95
70.6
63.6
55
115.2 '103.7
15
159.8
143.9
75
204.4
184.0
36
26.8
24.1
96
71.3
64.2
56
115.9 104.4
16
160.5
144. 5
76
205.1
184.7
37
27.5
24.8
97
72.1
64.9
57
116.7 ! 105.1
17
161.3
145. 2
77
205.9
185.3
38
28.2
25.4
98
72.8
65.6
58
117.4 1105.7
18
162.0
145.9
78
206.6
186.0
39
29.0
26.1
99
73.6
66.2
59
118.2 106.4
19
162.7
146.5
79
207.3
186.7
40
41
29.7
26.8
100
74.3
66.9
60
118.9 107.1
20
163. 5
147.2
80
'281
208.1
208.8
187.4
188.
30.5
27.4
101
75.1
67.6
161
119.6
107.7
221
164.2
147.9
42
31.2
28.1
02
75.8
68.3
62
120.4
108.4
22
165.0
148.5
82
209.6
188.7
43
32.0
28.8
03
76.5
68.9
63
121.1
109.1
23
165.7
149.2
83
210.3
189.4
44
32.7
29.4
04
77.3
69.6
64
121.9
109.7
24
166.5
149.9
84
211.1
190.0
45
33.4
30.1
05
78.0
70.3
65
122.6
110.4
25
167.2
150.6
85
211.8
190.7
46
34.2
30.8
06
78.8
70.9
66
123. 4
111.1
26
168.0
151.2
86
212.5
191.4
47
34.9
31.4
07
79.5
71.6
67
124.1
111.7
27
168.7
151.9
87
213.3
192.0
48
35.7
32.1
08
80.3
72.3
68
124.8
112.4
28
169.4
152.6
88
214.0
192.7
49
36.4
32.8
09
81.0
72.9
69
125.6 113.1
29
170.2
153. 2
89
214.8
193.4
50
37.2
37.9
33.5
10
81.7
73.6
70
126.3
113.8
114.4
30
231
170.9
153.9
90
215.5
194.0
194.7
51
34.1
111
82.5
74.3
171
127.1
171.7
154.6
291
216.3
52
38.6
34.8'
12
83.2
74.9
72
127.8 1115.1
32
172.4
155.2
92
217.0
195. 4
53
39.4
35.5
13
84.0
75. 6
73
128.6 ill5.8
33
173.2
155.9
93
217.7
196.1
64
40.1
36.1
14
84.7
76.3
74
129.3 i 116.4
34
173.9
156.6
94
218.5
196.7
55
40.9
36.8
15
85.5
77.0
75
130.1
117.1
35
174.6
15'. 2
95
219.2
197.4
56
41.6
37.5
16
86.2
77.6
76
130.8
117.8
36
175.4
157. 9
96
220.0
198. 1
57
42.4
38.1
17
86.9
78.3
77
131.5
118.4
37
176.1
158. 6
97
220.7
198.7
58
43.1
38.8
18
87.7
79.0
78
132.3
119.1
38
176.9
159. 3
98
221.5
199. 4
59
43.8
39.5
19
88.4
79.6
79
133.0
119.8
39
177.6
159. 9
99
222. 2
200. 1
60
44.6
40.1
20
89.2
80.3
80
133.8
120.4
40
178.4
160.6
300
222^9
200.7
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
t8° (1
^2°, 228°, 312).
Page 614]
TABLE 2.
Difference of Latitude and Departure for
12° (138°, 222
°, 318°
)•
Dist.
Lat. Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
ijit.
Dep.
301
223.7
201.4
361
268.3
241.6
421
312.9
281.7
481
357. 5
321. 9
541
402.1
362.0
02
224.4
202.1
62
269.0
242.2
22
313.6
282.4
82
358.2
322.5
42
402.8
362.7
03
225.2
202.8
63
269.8
242.9
23
314. 4
283.0
83
358.9
323.2
43
403.5
363. 3
04
225.9
203.4
64
270. 5
243.6
24
315.1
283.7
84
359.7
323.9
44
404.3
364.0
05
226.6
204.1
65
271.2
244.2
25
315.8
284.4
85
360.4
324.6
45
405.0
364. 7
06
227.4
204.8
66
272.0
244. 9
26
316.6
285.1
86
361.2
325. 2
46
405.8
365.4
07
228.1
205.4
67
272.7
245. 6
27
317. 3
285.7
87
361.9
325.9
47
406.5
366.
08
228.9
206.1
68
273. 5
246.2
48
318.1
286.4
88
362. 7
326.6
48
407.2
366.7
09
229.6
206.8
69
274.2
246. 9
29
318.8
287.1
89
363.4
327.2
49
408.0
367.4
10
230.4
207.4
70
275.0
247.6
30
319.6
287.7
90
,364. 1
327.9
50
408.7
.368.
311 1 231. 1
208.1
371
275.7
248. 3
431
320. 3
288.4
491
364.9
328.6
551
409.5
368.7
12
231.9
208.8
72
276. 5
248. 9
32
321.0
289.1
92
365. 6
329.2
52
410.2
369. 4
13
232.6
209.4
73
277.2
249. 6
33
321.8
289.7
93
366. 4
329. 9
53
411.0
370.0
14
233. 3
210.1
74
277.9
2.50. 3
34
322. 5
290. 4
94
367.1
330.6
54
411.7
370.7
15
234. 1
210.8
75
278.7
250. 9
35
323. 3
291.1
95
367.9
331.3
55
412.4
371.4
16
234.8
211.5
76
279.4
251.6
36
324.0
291.7
96
368.6
331.9
56
413. 2
372.0
17
235.6
212.1
77
280.2
252.3
37
324.8
292.4
97
369.3
332.6
57
41.3. 9
372.7
18
236. 3
212.8
78
280.9
252.9
38
325. 5
293.1
98
370.1
333.3
58
414.7
373. 4
19 237. 1
213.5
79
281.7
253. 6
39
326.2
293.8
99
370.8
3,33. 9
59
415. 4
374. 1
20
237.8
214.1
80
282.4
254.3
40
327.0
294.4
500
371. 6
334. 6
60
416.2
374.7
321
238.6
214.8
381
283.1
254.9
441
327.7
295.1
501
372. 3
335.3
561
416.9
375.4
22 239. 3
215.5
82
283.9
255.6
42
328.5
295. 8
02
373.1
335.9
62
417.6
376.1
23 240.0
216.1
83
284.6
256. 3
43
329.2
296.4
03
373.8
336.6
63
418.4
376.7
24 240.8
216.8
84
285.4
257.0
44
330.0
297.1
04
374.5
337.2
64
419.1
377. 4
25 ; 241.5
217.5
85
286.1
257.6
45
330.7
297.8
05
375.3
337.9
65
419.9
378.1
26 242. 3
218.1
86
286.9
258. 3
46
331.4
298.4
06
376.0
338.6
66
420.6
378.7
27 243.0
218.8
87
287.6
259.0
47
332.2
299.1
07
376.8
3,39. 3
67
421.4
379.4
28 243. 8
219.5
88
288.3
259. 6
48
332.9
299.8
08
377.5
339.9
68
422.1
380.1
29 244.5
220.1
89
289.1
260.3
49
333. 7
300.4
09
378.3
340.6
69
422.8
380.7
30
245.2
220.8
90
289.8
261.0
50
334.4
335.2'
301.1
10
379.0
341.3
70
423. 6
424.3
381.4
331
246.0
221.5
391
290.6
261.6
451
301.8
511
379.7
341.9
571
382. 1
32 246. 7
222.2
92
291.3
262.3
52
335.9
302. 5
12
380.5
342.6
72
425.1
382.8
33 247. 5
222.8
93
292.1
263.0
53
336. 6
.303. 1
13
,381.2
,343. 3
73
425.8
383.4
34 : 248.2
223.5
94
292.8
263. 6
54
337.4
303.8
14
382.0
343. 9
74
426.6
384. 1
35 1 249.0
224.2
95
293. 5
264.3
55
338.1
304.5
15
382.7
344.6
75
427.3
384.8
36 1 249.7
224.8
96
294.3
265.0
56
338.9
305. 1
16
383.5
345.3
76
428.0
385.4
37 1 250.4
225.5
97
295.
265.7
57
339.6
305. 8
17
384.2
346.0
77
428.8
386.1
3S 1 251.2
226.2
98
295.8
266.3
58
340.4
306. 5
18
384.9
346.6
78
429.5
386.8
39 : 251.9
226.8
99
296.5
267.0
59
341.1
.307. 1
19
385.7
347.3
79
430.3
387.4
40"
252. 7
227.5
400
297. 3
267.7
60
341. 8
342.6
307.8
20
386.4
387.2
348.0
80
431.0
388.1
341
253.4
228.2
401
298.0
268.3
461
308. 5
521
348.6
581
431.8
388.8
42
254.2
228.8
02
298.7
269.0
62
343.3
309. 1
22
387.9
349.3
82
432.5
,389. 4 >.
43
254.9
229.5
03
299.5
269.7
63
344.1
.309.8
23
388.7
350.0
83
433.2
390.1
44
255.6
230.2
04
300.2
270. 3
64
,344. 8
310. 5
24
389.4
350. 6
84
434.0
390.8
45
256.4
230.9
05
301.0
271.0
65
345. 6
,311.2
25
390.1
351.3
85
434.7
391.4
46
.257.1
231.5
06
301. 7
271.7
66
346.3
311.8
26
390.9
352.0
86
435.5
392.1
47
257. 9
232.2
07
302.5
272. 3
67
347.
312.5
27
391.6
352.6
87
436.2
392.8
48
258. 6
232.9
08
303.2
273.0
68
347.8
313. 2
28
392.4
353.3
88
437.0
393. 4
49
259. 4
233. 5
09
.303. 9
273.7
69
348.5
313.8
29
393.1
354.0
89
437.7
394.1
50
260.1
234.2
10
304. 7
274.3
70
349.3
350.0
314.5
.30
393.9
394.6
354.6
90
438.4
394.8
351
260.8
234.9
411
305. 4
275.0
471
31,5. 2
531
355.3
591
439.2
395.4
52
261.6
235.5
12
306.2
275.7
72
350.8
315.8
32
395.3
356.0
92
440.0
396.1
53
262.3
236.2
13
306.9
276.4
73
351.5
316. 5
33
396.1
356.6
93
440.7
396.8
54
263.1
236.9
14
307.7
277.0
74
352.3
317.2
34
396.8
357.3
94
441.4
397.5
55
263.8
237.5
15
308.4
277.7
75
353.0
317.8
35
397.6
358.0
95
442.2
398.1
56
264.6
238.2
16
309.1
278.4
76
353.7
318. 5
36
398.3
358.6
96
442.9
398.8
57
265. 3
238.9
17
309.9
279.0
77
354.5
319.2
37
399.1
359.3
97
443.7
399.5
58
266.0
239.6
18
310. 6
279.7
78
355. 2
319.9
38
399.8
360.0
98
444.4
400.1
59
266.8
240.2
19
311.4
280.4
79
356.0
320. 5
,39
400.6
360.6
99
445.2
400.8
60
267.6
240.9
20
312.1
281.0
80
356.7
321.2
40
401.3
361.3
600
445.9
401.5
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
18° (1
,32°, 228
°, 312°
)•
TABLE 2.
[Page 615
Difference of Latitude and Departure for 43° (137°, 223
°, 317°
)•
Diet.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
44.6
41.6
121
88.5
82.5
181
132.4
123.4
241
176.3
164.4
2
1.5
1.4
62
45.3
42.3
22
89.2
83.2
82
133.1
124.1
42
177.0
165.0
3
2.2
2.0
63
46.1
43.0
23
90.0
83.9
83
133.8
124.8
43
177.7
165.7
4
2.9
2.7
64
46.8
43.6
24
90.7
84.6
84
134.6
125. 5
44
178.5
166.4
5
3.7
3.4
65
47.5
44.3
25
91.4
85.2
85
135.3
126.2
45
179.2
167.1
6
4.4
4.1
66
48.3
45.0
26
92.2
85.9
86
136.0
126.9
46
179.9
167.8
7
5.1
4.8
67
49.0
45.7
27
92.9
86.6
87
136.8
127.5
47
180.6
168.5
8
5.9
5.5
68
49.7
46.4
28
93.6
87.3
88
137.5
128.2
48
181.4
169.1
9
6.6
6.1
69
50.5
47.1
29
94.3
88.0
89
138.2
128.9
49
182.1
169.8
10
7.3
6.8
70
51.2
47.7
30
95.1
88.7
89.3
90
139.0
129.6
50
182.8
170.5
11
8.0
7.5
71
51.9
48.4
131
95.8
191
139.7
130.3
251
183.6
171.2
12
8.8
8.2
72
52.7
49.1
32
96.5
90.0
92
140.4
130.9
52
181.3
171.9
13
9.5
8.9
73
53.4
49.8
33
97.3
90.7
93
141.2
131.6
53
185.0
172.5
14
10.2
9.5
74
54.1
50.5
34
98.0
91.4
94
141.9
132.3
54
185.8
173.2
15
11.0
10.2
75
54.9
51.1
35
98.7
92.1
95
142.6
133.0
55
186.5
173.9
16
11.7
10.9
76
55.6
51.8
36
99.5
92.8
96
143.3
133.7
56
187.2 174.6
17
12.4
11.6
77
56.3
52.5
37
100.2
93.4
97
144.1
134.4
57
188.0 175.3
18
13.2
12.3
78
57.0
53.2
38
100.9
94.1
98
144.8
135.0
58
188.7
176.0
19
13.9
13.0
79
57.8
53.9
39
101.7
94.8
99
145,. 5
135.7
59
189.4
176.6
20
21
14.6
15.4
13.6
80
58.5
54.6
40
102.4
103. 1
95.5
96.2
200
146.3
136.4
60
190.2
190.9
177.3
178.0
14.3
81
59.2
55.2
141
201
147.0
137.1
261
22
16.1
15.0
82
60.0
55.9
42
103.9
96.8
02
147.7
137.8
62
191.6
178.7
23
16.8
15.7
83
60.7
56.6
43
104.6
97.5
03
148. 5
138.4
63
192.3
179.4
24
17.6
16.4
84
61.4
57.3
44
105.3
98.2
04
149.2
139.1
64
193.1
180.0
25
18.3
17.0
85
62.2
58.0
45
106.0
98.9
05
149.9
139.8
65
193.8
180.7
26
19.0
17.7
86
62.9
58.7
46
106.8
99.6
06
150.7
140.5
66
194.5 i 181.4
27
19.7
18.4
87
63.6
59.3
47
107.5
100.3
07
151.4
141.2
67
195. 3 182. 1
28
20.5
19.1
88
64.4
60.0
48
108.2
100.9
08
152.1
141.9
68
196.0 i 182.8
29
21.2
19.8
89
65.1
60.7
49
109.0
101.6
09
152.9
142.5
69
196.7
183.5
30
31
21.9
20.5
90
65.8
61.4
50
109.7
102.3
10
153.6
143.2
70
197.5
184.1
22.7
21.1
91
66.6
62.1
151
110.4
103.0
211
154.3
143.9
271
198.2
184.8
32
23.4
21.8
92
67.3
62.7
52
111.2
103.7
12
155.0
144.6
72
198.9
185.5
33
24.1
22.5
93
68.0
63.4
53
111.9
104.3
13
155.8
145.3
73
199.7 1 186.2
34
24.9
23.2
94
68.7
64.1
54
112.6
105.0
14
156.5
145.9
74
200.4 ; 186.9
35
25.6
23.9
95
69.5
64.8
55
113.4
105.7
15
157.2
146.6
75
201.1 187.5
36
26.3
24.6
96
70.2
65.5
56
114.1
106.4
16
158.0
147.3
76
201.9 i 188.2
37
27.1
25.2
97
70.9
66.2
57
114.8
107.1
17
158.7
148.0
77
202.6
188.9
38
27.8
25.9
98
71.7
66.8
58
115.6
107.8
18
159.4
148.7
78
203.3
189.6
39
28.5
26.6
99
72.4
67.5
59
116.3
108.4
19
160.2
149.4
79
204.0
190.3
40
29.3
27.3
100
101
73.1
68.2
60
117.0
109.1
20
160.9
150.0
80
281
204.8
205:5
191.0
191.6
41
SOA)
28.0
73.9
68.9
161
117.7
109.8
221
161.6
150.7
42
30.7
28.6
02
74.6
69.6
62
118.5
110.5
22
162.4
151.4
82
206.2 ' 192.3
43
31.4
29.3
03
75.3
70.2
63
119.2
111.2
23
163.1
152.1
83
207. 193.
44
32.2
30.0
04
76.1
70.9
64
119.9
111.8
24
163.8
152.8
84
207. 7 193. 7
45
32.9
30.7
05
76.8
71.6
65
120.7
112. 5
25
164.6
153.4
85
208. 4 194. 4
46
33.6
31.4
06
77.5
72.3
66
121.4
113.2
26
165.3
154.1
86
209. 2 . 1^. 1
47
34.4
32.1
07
78.3
73.0
67
122.1
113.9
27
166.0
154.8
87
209. 9 195. 7
48
35.1
32.7
08
79.0
73.7
68
122. 9
114.6
28
166.7
155.5
88
210. 6 196. 4
49
35.8
33.4
09
79.7
74.3
69
123. 6
115.3
29
167.5
156.2
89
211.4 197.1
50
36.6
34.1
10
80.4
75.0
70
171
124. 3
115.9
30
168.2
168.9
156.9
90
212. 1 i 197. 8
51
37.3
34.8
111
81.2
75.7
125.1
116.6
231
157.5
291
212.8
198.5
52
38.0
a5.5
12
81.9
76.4
72
125.8
117. 3
32
169.7
158.2
92
213.6
199.1
53
38.8
36.1
13
82.6
77.1
73
126. 5
118.0
33
170.4
158.9
93
214.3
199.8
54
39.5
36.8
14
83.4
77.7
74
127. 3
118.7
34
171.1
159.6
94
215.0
200.5
55
40.2
37.5
15
84.1
78.4
75
128.0
119.3
35
171.9
160.3
95
215.7
201.2
56
41.0
38.2
16
84.8
79.1
76
128.7
120.0
36
172.6
161.0
96
216.5
201.9
57
41.7
38.9
17
85.6
79,8
77
129.4
120.7
37
173.3
161.6
97
217.2
202.6
58
42.4
39.6
18
86.3
80.5
78
130.2
121.4
38
174.1
162.3
98
217.9
203.2
59
43.1
40.2
19
87.0
81.2
79
130.9
122.1
39
174.8
163.0
99
218.7
203.9
60
43.9
40.9
20
87.8
81.8
80
131. 6
122.8
40
175. 5
163.7
300
219.4
204.6
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
i7° (1
33°, 227°, 313°
).
1
Page 616]
TABLE 2.
Difference of Latitude and Departure for 43° (137°, 223
°, 317°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
220.1
205. 3
361
264.0
246.2
421
307.9
287.1
481
351.8
328.1
541
395.7
369.0
02
220 9
206.0
62
264.8
246.9
22
308.6
287.8
82
352. 5
328.7
42
396.4
369.7
03
221.6
206.7
63
265.5
247.6
23
309.4
288.5
83
353. 2
329. 4
43
397. 1
370.3
04
222.3
207.3
64
266.2
248.3
24
310.1
289.2
84
354.
330.1
44
397.9
371.0
05
223.1
208.0
65
267.0
248.9
25
310.8
289. 9
85
354.7
330.8
45
398.6
371.7
06
223.8
208.7
66
267.7
249.6
26
311.6
290.5
86
355.4
331.4
46
399.3
372.4
07
224.5
209.4
67
268.4
250.3
27
312.3
291.2
87
356. 2
332. 1
47
400.1
373.1
08
225.3
210.1
68
269.1
251.0
28
313.
291.9
88
356.9
332.8
48
400.8
373.7
09
226.0
210.7
69
269.9
251.7
29
313.8
292.6
89
357.7
333.5
49
401.5
374. 4
10
311
226.7
211.4
70
270.6
252. 3
30
314.5
293.3
90
358.4
334.2
50
402.2
375.1
227.5
212.1
371
271.3
253.0
431
315.2
293.9
491
359.1
fsst- ^
551
403.
375.8
12
228.2
212.8
72
272.1
253.7
32
316.0
294.6
92
359.8
335. 5
52
403.7
376.5
13
228.9
213.5
73
272.8
254.4
33
316.7
295.3
93
360.6
336.2
53
404.4
377.1
14
229.7
214.2
74
273.5
255. 1
34
317.4
296.0
94
361.3
336.9
54
405.2
377.8
15
230.4
214.8
75
274.3
255.8
35
318.1
296.7
95
362.0
337.6
55
405.9
378.5
16
231.1
215.5
76
275.0
256.4
36
318.9
297.4
96
362.8
338.3
56
406.6
379.2
17
231.8
216.2
77
275. 7
257.1
37
319.6
298.0
97
?63. 5
338.9
57
407. 4
379. 9
18
232.6
216.9
78
276.5
257.8
38
320.3
298.7
98
364.2
339.6
58
408.1
380.6
19
233.3
217.6
79
277.2
258.5
39
321.1
299.4
99
364. 9
340.3
59
408.8
381. 2
20
321
234.0
218.2
80
277.9
259.2
40
321.8
300.1
500
365. 7
341.0
60
409.6
381.9
382.6
234.8
218.9
381
278.7
259.8
441
322.5
300.8
501
366.4
341.7
561
410. 3
22
2.35. 5
219.6
82
279.4
260.5
42
323.3
301.4
02
367.1
342.4
62
411.0
383.3
23
236.2
220.3
83
280.1
261.2
43
324.0
302.1
03
367.8
343.0
63
411.8
384.0
24
237.0
221.0
84
280.8
261.9
44
324.7
302.8
04
368.6
343.7
64
412.5
384.6
25
237.7
221.7
85
281.6
262.6
45
325.5
303.5
05
369.3
344.4
65
413.2
385. 3
26
238.4
222.3
86
282.3
263.3
46
326.2
304.2
06
370.0
345.1
66
414.0
386.0
27
239.2
223.0
87
283.0
263.9
47
326.9
304.9
07
370. 8
345.8
67
414.7
386.7
28
239.9
223.7
88
283.7
264.6
48
327.7
305.5
08
371.5
346.5
68
415.4
387.4
29
240.6
224.4
89
284.5
265.3
49
328.4
306.2
09
372.3
347.1
69
416.2
388.1
30
241. 4
225.1
90
285.2
266.0
50
329.1
306. 9
10
373.
373.8
347.8
70
416.9
388.7
331
242.1
225.7
391
286.0
266.7
451
329.9
307.6
511
348.5
571
417. 6
389.4
32
242.8
226.4
92
286.7
267.3
52
330. j6
308.3
12
374.5
349.2
72
418.3
390. 1 ,
33
243. 5
227.1
93
287.4
268.0
53
331.3
309.
13
375.2
349.9
73
419.1
390.8
34
244.3
227.8
94
288.2
268.7
54
332.1
309.6
14
376.0
350.5
74
419.8
391. 5
35
245.
228.5
95
288.9
269.4
55
332.8
310.3
15
376.6
351.2
75
420.5
392.2
36
245.7
229.2
96
289.6
270.1
56
333.5
311.0
16
377.4
351.9
76
421.3
392.8
37
246.5
229.8
97
290.4
270.8
57
334.3
311.7
17
378.2
352.6
77
422.0
393.5
38
247.2
230. 5
98
291.1
271.4
58
335.0
312.4
18
378.9
353.3
78
422.7
394.2
39
247.9
231.2
99
291.8
272.1
59
335.7
313.0
19
379.6
354.0
79
423.5
394. 9
40
248.7
231.9
400
292.6
272.8
60
336. 5
313.7
20
380.3
354.6
80
424.2
424.9
395.6
341
249.4
232. 6
401
293.3
273. 5
461
337.2
314.4
521
381.1
355. 3
581
396.2
42
250.1
233. 2
02
294.0
274.2
62
337. 9
315.1
22
381.8
356.0
82
425. 7
396.9
43
250.9
233.9
03
294.7
274.9
63
338.7
315.8
23
382.6
356.7
83
426.4
397.6
44
251.6
234. 6
04
295.5
275.5
64
339. 4
316.5
24
383.3
357.4
84
427.1
398.3
45
252.3
235.3
05
296.2
276.2
65
340.1
317.1
25
384.0
358.1
85
427.9
399.0
i9
353.1
236.0
06
296.9
276.9
66
340.8
317.8
26
384.7
358.7
86
428.6
399. 6
47
253.8
236.7
07
297.7
277.6
67
341.6
318.5
27
385. 5
359.4
87
429. 3
400.3
48
254.5
237.3
08
298.4
278.3
68
342.3
319.2
28
386.2
360.1
88
430. 1
401.0
49
255.3
238.0
09
299.1
278.9
69
343.0
319.9
29
386.9
360.8
89
430. 8
401.7
50
256.0
238.7
10
299.9
279.6
70
343.7
320.5
30
387.6
361.5
362. r
90
431. 5
402.4
351
256.7
239.4
411
300.6
280.3
471
344.5
321.2
531
388.4
591
432.3
403.1
52
257.4
240.1
12
301.3
281.0
72
345.2
321.9
32
389.1
362.8
92
433.0
403.7
53
258.2
240.8
13
302.1
281.7
73
345.9
322.6
33
389.9
363.5
93
433.7
404.4
54
258.9
241.4
14
302.8
282.4
74
346.7
323.3
34
390.6
364.2
94
434.5
405.1
55
259.6
242.1
15
303.5
283.0
75
347.4
324.0
35
391.3
364.9
95
435.2
405.8
56
260.4
242.8
16
304.3
283.7
76
348.1
324.6
36
392.
365.5
96
435.9
406.5
57
261.1
243.5
17
305.0
284.4
77
348.9
325. 3
37
392.8
366.2
97
436.7
407.2
58
261.8
244.2
18
305.7
285.1
78
349.6
326.0
38
393. 5
366.9
98
437.4
407.8
59
262.6
244.8
19
306.4
285.8
79
350.3
326.7
39
394.2
367.6
99
438.1
408.5
60
263.3
245.5
20
307.2
286.4
80
351.1
327.4
40
394.9
368.3
600
438.8
409.2
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
4
7° (1
33°, 227
°, 313°
)•
TABLE 2.
[Page 617
Difference of Latitude and Departure for 44° (136°, 224°, 316'
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
43.9
42.4
121
87.0
84.1
181
130.2
125.7
241
173.4
167.4
2
1.4
1.4
62
44.6
43.1
22
87.8
84.7
82
130.9
126.4
42
174.1
168.1
3
2.2
2.1
63
45.3
43.8
23
88.5
85.4
83
131.6
127.1
43
174.8
168.8
4
2.9
2.8
64
46.0
44.5
24
89.2
86.1
84
132.4
127.8
44
175.5
169.5
5
3.6
3.5
65
46.8
45.2
25
89.9
86.8
85
133.1
128.5
45
176.2
170.2
6
4.3
4.2
66
47.5
45.8
26
90.6
87.5
86
133.8
129.2
46
177.0
170.9
7
5.0
4.9
67
48.2
46.5
27
91.4
88.2
87
134.5
129.9
47
177.7
171.6
8
5.8
5.6
68
48.9
47.2
28
92.1
88.9
88
135.2
130. 6
48
178.4
172.3
9
6.5
6.3
69
49.6
47.9
29
92.8
89.6
89
136.0
131.3
49
179.1
173.0
10
7.2
6.9
70
50.4
48.6
30
93.5
94.2
90.3
90
136.7
132.0
50
179.8
173.7
174.4
11
7.9
7.6
71
51>1
49.3
131
91.0
191
137.4
132.7
251
180.6
12
8.6
8.3
72
51.8
50.0
32
95.0
91.7
92
138.1
133.4
52
181.3
175.1
13
9.4
9.0
73
52.5
50.7
33
95.7
92.4
93
138. 8
134.1
53
182.0
175.7
14
10.1
9.7
74
53.2
51.4
34
96.4
93.1
94
139.6
134.8
54
182.7
176. 4
15
10.8
10.4
75
54.0
52.1
35
97.1
93.8
95
140.3
135. 5
55
183.4
177.1
16
11.5
11.1
76
54.7
52.8
36
97.8
94.5
96
141.0
136.2
56
184.2
177.8
17
12.2
11.8
77
55.4
53.5
37
98.5
95.2
97
141.7
136.8
57
184.9
178.5
18
12.9
12.5
78
56.1
54.2
38
99.3
95. 9
98
142.4
137.5
58
185.6
179.2
19
13.7
13.2
79
56.8
54.9
39
100.0
96.6
99
143.1
138.2
59
186.3
179.9
20
14.4
13.9
80
57.5
55.6
40
100.7
97.3
200
143.9
138.9
60
187.0
180.6
21
15.1
14.6
81
58.3
56.3
141
101.4
97. 9
201
144.6
139.6
261
187.7
181.3
22
15.8
15.3
• 82
59.0
57.0
42
102.1
98.6
02
145. 3
140.3
62
188.5
182.0
23
16.5
16.0
83
59.7
57.7
43
102.9
99. 3
03
146.0
141.0
63
189.2
182.7
24
17.3
16.7
84
60.4
58.4
44
103. 6
100.0
04
146. 7
141.7
64
189.9
183. 4
25
18.0
17.4
85
61.1
59.0
45
104.3
100.7
05
147.5
142.4
65
190.6
184.1
26
18.7
18.1
86
61.9
59.7
46
105.
101.4
06
148.2
143.1
66
191.3
184.8
27
19.4
18.8
87
62.6
60.4
47
105.7
102.1
07
148.9
143.8
67
192.1
185.5
28
20.1
19.5
88
63.3
61.1
48
106.5
102.8
08
149.6
144.5
68
192.8
186.2
29
20.9
20.1
89
64.0
61.8
49
107.2
103. 5
09
150.3
145.2
69
193.5
186.9
30
21.6
20.8
90
64.7
62.5
50
107.9
104.2
10
151.1
145. 9
70
194.2
187.6
31
22.3
21.5
91
65.5
63.2
151
108.6
104.9
211
151.8
146.6
271
194.9
188.3
32
23.0
22.2
92
66.2
6.3.9
52
109.3
105. 6
12
152.5
147.3
72
195.7
188.9
33
23.7
22.9
93
66.9
64.6
53
110.1
106.3
13
153.2
148.0
73
196.4
189.6
34
24.5
23.6
94
67.6
65. 3
54
110.8
107.0
14
153. 9
148.7
74
197.1
190.3
35
25.2
24.3
95
68.3
66.0
55
111.5
107. 7
15
154.7
149.4
75
197.8
191.0
36
25.9
25.0
96
69.1
66.7
56
112.2
108.4
16
155.4
150.0
76
198.5
191.7
37
26.6
25.7
97
69.8
67.4
57
112.9
109. 1
17
156.1
150.7
77
199.3
192.4
38
27.3
26.4
98
70.5
68.1
58
113.7
109.8
18
156.8
151.4
78
200.0
193.1
39
28.1
27.1
99
71.2
68.8
59
114.4
110.5
19
157.5
152. 1
79
200.7
193.8
40
28.8
27.8
100
71.9
69.5
60
115. 1
115.8
111.1
iii:8
20
221
158.3
152.8
80
201.4
194.5
195.2
41
29.5
28.5
101
72.7
70.2
161
159.0
•153.5
281
202. 1
42
30.2
29.2
02
73.4
70.9
62
116.5
112.5
22
159.7
154.2
82
202.9
195.9
43
30.9
29.9
03
74.1
71.5
63
117.3
113.2
23
160.4
154.9
83
203.6
196.6
44
31.7
30.6
04
74.8
72.2
64
118.0
113.9
24
161.1
155.6
84
204. 3
197.3
45
32.4
31.3
05
75.5
72.9
65
118.7
114.6
25
161.9
156.3
85
205.0
198.0
46
33.1
32.0
06
76.3
73.6
66
119.4
115.3
26
162.6
157.0
86
205.7
198.7
47
33.8
32.6
07
77.0
74.3
67
120.1
116.0
27
163.3
157.7
87
206.5
199.4
48
34.5
33.3
08
77.7
75.0
68
120.8
116.7
28
164.0
158.4
88
207.2
200.1
49
35.2
34.0
09
78.4
75.7
69
121.6
117.4
29
164.7
159.1
89
207.9
200.8
50
36.0
34.7
10
111
79.1
79.8
76.4
70
122.3
118.1
30
165.4
159.8
90
208.6
201.5
51
36.7
35.4
77.1
171
123.0
118.8
231
166.2
160.5
291
209.3
202.1
52
37.4
36.1
12
80.6
77.8
72
123.7
119. 5
32
166.9
161.2
92
210.0
202.8
53
38.1
36.8
13
81.3
78.5
73
124.4
120.2
33
167.6
161.9
93
210.8
203. 5
54
38.8
37.5
14
82.0
79.2
74
125.2
120.9
34
168.3
162.6
94
211.5
204.2
55
39.6
38.2
15
82.7
79.9
75
125.9
121.6
35
169.0
163. 2
95
212.2
204.9
56
40.3
38.9
16
83.4
80.6
76
126.6
122.3
36
169.8
163.9
96
212.9
205. 6
57
41.0
39.6
17
84.2
81.3
77
127.3
123.0
37
170.5
164.6
97
213.6
206.3
58
41.7
40.3
18
84.9
82.0
78
128.0
123.6
38
171.2
165. 3
98
214.4
207.0
59
42.4
41.0
19
85.6
82.7
79
128.8
124. 3
39
171.9
166.0
99
215.1
207.7
60
43.2
41.7
20
86.3
83.4
80
129.5
125.0
40
172.6
166.7
300
215.8
208.4
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
16° (1
34°, 226
', 314°
)•
Page 618]
TABLE 2.
Difference of Latitude and Departure for 44° (136°, 224°, 316
')•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
301
216.5
209.1
361
259.7
250.8
421
302.8
292.5
481
346.0
334.1
541
389.2
375.8
02
217.2
209.8
62
260.4
251.5
22
303.6
293.2
82
346.7
334. 8
42
389.9
376. 5
03
218.0
210.5
63
261.1
252.2
23
304.3
293.8
83
347.4
335.5
43
390.6
377.2
04
218.7
211.2
64
261.8
252.9
24
.305.
294.5
84
348.2
336.2
44
391.3
377.9
05
219.4
211.9
65
262.6
253. 6
25
305.7
295. 2
85
348.9
336.9
45
392.0
378.6
06
220.1
212.6
66
263.3
254.3
26
306.4
295.9
86
.349. 6
337. 6
46
392.8
379.3
07
220.8
213.3
67
264.0
254.9
27
307.2
296.6
87
350.3
338.3
47
393.5
380.0
08
221.6
214.0
68
264.7
255.6
28
307.9
297.3
88
351.0
339.0
48
394.2
380. 7
09
222.3
214.7
69
265.4
256. 3
29
308.6
298.0
89
351.7
339.7
49
394.9
.381.4
10
223.0
215.4
70
266.2
266.9
257.0
30
309. 3
310.0
298.7
90
352.5
340.4
50
395.6
382.1
311
223.7
216.0
371
257. 7
431
299.4
491
353.2
341.1
551
396.4
382.7
12
224.4
216.7
72
267.6
258. 4
32
310.8
300.1
92
353.9
341.8
52
397.1
383.4
13
225.2
217.4
73
268.3
259.1
33
311.5
300.8
93
354. 6
342.5
53
397.8
384.1
14
225.9
218.1
74
269.0
259.8
34
312.2
301.5
94
355.3
343.2
54
398. 5
384.8
15
226.6
218.8
75
269.8
260.5
35
312.9
302.2
95
356. 1
343. 9
55
399.2
385.5
16
227.3
219.5
76
270.5
261.2
36
313.6
302. 9
96
356. 8
344.6
56
400.0 i 386.2
17 i 228.0
220.2
77
271.2
261.9
37
314.4
303.6
97
357.5
345.2
57
400.7
386.9
18 228. 8
220.9
78
271.9
262.6
38
315.1
304.3
98
358.2
345.9
58
401.4
387.6
19 229. 5
221.6
79
272.6
263. 3
39
315.8
305.0
99
358.9
346. 6
59
402.1
388.3
20
230.2
222.3
80
273.4
264.0
40
316.5
305.7
500
359.7
360.4
347.3
60
402.8
389.0
321
230.9
223.0
381
274.1
264.7
441
317.2
306.4
501
348.0
561
403.6
389.7
22
231.6
223.7
82
274.8
265.4
42
318.0
307.0
02
361.1
348.7
62
404. 3 i 390. 4
23
232.3
224.4
83
275.5
266.1
43
318.7
307.7
03
361.8
349.4
63
405.0 i 391.1
24
233.1
225.1
84
276.2
266.8
44
319.4
308.4
04
362.5
350.1
64
405.7
391.8
25
233.8
225.8
85
276.9
267.5
45
320.1
309.1
05
363.3
350.8
65
406.4
392.5
26 1 234.5
226.5
86
277.7
268.1
46
320. 8
309.8
06
364.0
351. 5
66
407.2
393.2
27 235. 2
227.2
87
278.4
268.8
47
321.5
310.5
07
364. 7 i 352. 2
67
407.9
393.9
28 235. 9
227.9
88
279.1
269.5
48
322. 3
311.2
08
365. 4 ! 352. 9
68
408.6
394.6
29 236. 7
228.6
89
279.8
270.2
49
323.0
311.9
09
366.1 |353.6
69
409.3
395.3
30 : 237.4
229.2
90
280.5
270.9
50
323.7
312.6
10
366. 9 1 354. 3
70
410.0
396.0
331 : 238. 1
229.9
391
281.3
271.6
451
324.4
313.3
511
367. 6 I 355.
571
410.7
396.7
32 238.8
230.6
92
282.0
272.3
52
325.2
314.0
12
368. 3 i 355. 7
72
411.5
397.3
33 i 239.5
231.3
93
282.7
273.0
53
325.9
314.7
13
369. 1 3.56. 4
73
412.2
398.0
34 240. 3
232.0
94
283.4
273.7
54
326.6
315.4
14
369. 7 i 357. 1
74
412.9
398.7
35 241.
232.7
95
284.1
274.4
55
327.3
316.1
15
370.5 1357.8
75
413.6 1 399.4
36 i 241. 7
233.4
96
284.9
275.1
56
328.0
316. 8
16
371.2 i358.4
76
414. 3 i 400. 1
37 ; 242.4
234.1
97
285.6
275.8
57
328.7
317.5
17
371. 9 1 3.59. 1
77
415.1 i 400.8
38 1 243.1
2.S4. 8
98
286.3
276.5
58
329.5 1318. 2
18
372.6
359.8
78
415.8
401.5
39 i 243.9
235. 5
99
287.0
277.2
59
330.2
318.9
19
373.3
360.5
79
416.5
402.2
40
244.6
236. 2
400
287.7
277.9
60
330.9
319.6
20
374.1
361.2
80
417.2
402.9
403.6
341
245.3
236.9
401
288.5
278.6
461
331.6
320.2
521
374.8
361.9
581
417.9
42
246.0
237.6
02
289.2
279.3
62
332.3
320.9
22
375.5
362.6
82
418.7
404.3
43
246.7
238.3
03
289.9
280.0
63
333.1
321.6
23
376.2 .363.3
83
419.4
405.0
44
247.5
239.0
04
290.6
280.7
64
333.8
322.3
24
376. 9
364.0
84
420.1
405.7
45
248.2
239.7
05
291.3
281.3
65
334.5
323.0
25
377.7
364.7
85
420.8
406.4
46
248.9
240.4
06
292.1
282.0
66
335.2
323.7
26
378.4
365.4
86
421.5
407.1
47
249.6
241.1
07
292.8
282.7
67
335.9
324.4
27 1 379. 1
366.1
87
422.3
407.8
48
250.3
241.7
08
293. 5
283.4
68
336.7
325.1
28
379.8
366.8
88
423.0
408.5
49
251.1
242.4
09
294.2
284.1
69
337.4
325.8
29
380.5
367.5
89
423.7
409.1
50
251.8
243.1
10
294.9
284.8
70
338.1
326.5
30
381.2
368.2
90
424.4
409.9
351
252.5
243.8
411
295.7
285.5
471
338.8
327.2
531
382.0
368.9
591
425. 1
410.5
52
253.2
244.5
12
296.4
286.2
72
339.5
327.9
32
382.7
369.6
92
425.9
411.2
53
253.9
245.2
13
297.1
286. 9
73
340.3
328.6
33
383.4
370.3
93
426.6
411.9
54
254.6
245.9
14
297.8
287.6
74
341.0
329.3
34
384.1
371.0
94
427.3
412.6
55
255.4
246.6
15
298.5
288.3
75
341.7
330.0
35
384.8
371.7
95
428.0
413.3
56
256.1
247.3
16
299.2
289.0
76
342.4
330.7
36
385.6
372.4
96
428.7
414.0
57
256.8
248.0
17
300.0
289.7
77
343.1
331.4
37
386.3
373.1
97
429. 5
414.7
58
257.5
248.7
18
300.7
290.4
78
343.8
332.1
38
387.0
373.7
98
430.2
415.4
59
258.2
249.4
19
301.4
291.1
79
344.6
332.7
39
387.7
374.4
99
430.9
416.1
60
259.0
250.1
20
302.1
291.8
80
345.3
333.4
40
388.4
375.1
600
431.6
416.8
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
4
6° (134°, 226°, 314°)
TABLE 2.
[Pa-e 619
Difference of Latitude and Departure for 45° (135°, 225°, 315°
)•
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
Dist.
Lat.
Dep.
1
0.7
0.7
61
43.1
43.1
121
85.6
85.6
181
128.0
128.0
241
170.4
170.4
2
1.4
1.4
62
43.8
43.8
22
86.3
86.3
82
128.7
128.7
42
171.1
171.1
3
2.1
2.1
63
44.5
44.5
23
87.0
87.0
83
129.4
129.4
43
171.8
171.8
4
2.8
2.8
64
45.3
45.3
24
87.7
87.7
84
130.1
130.1
44
172.5
172.5
5
3.5
3.5
65
46.0
46.0
25
88.4
88.4
85
130.8
130.8
45
173.2
173. 2
6
4.2
4.2
66
46.7
46.7
26
89.1
89.1
86
131.5
131.5
46
173.9
173.9
7
4.9
4.9
67
47.4
47.4
27
89.8
89.8
87
132.2
132.2
47
174.7
174.7
8
5.7
5.7
68
48.1
48.1
28
90.5
90.5
88
132.9
132.9
48
175.4
175. 4
9
6.4
6.4
69
48.8
48.8
29
91.2
91.2
89
133.6
133.6
49
176.1
176.1
10
7.1
7.1
70
49.5
49.5
30
91.9
91.9
90
134.4
134.4
135. 1
50
176.8
176.8
11
7.8
7.8
71
50.2
50.2
131
92.6
92.6
191
135.1
251
177.5
177.5
12
8.5
8.5
72
50.9
50.9
32
93.3
93.3
92
135.8
135.'8
52
178.2
178.2
13
9.2
9.2
73
51.6
51.6
33
94.0
94.0
93
136.5
136.5
53
178.9
178.9
14
9.9
9.9
74
52.3
52.3
34
94.8
94.8
94
137.2
137.2
54
179.6
179.6
15
10.6
10.6
75
53.0
53.0
35
95.5
95.5
95
137.9
137.9
55
180.3
180.3
16
11.3
11.3
76
53.7
53.7
36
96.2
96.2
96
138.6
138.6
56
181.0
181.0
17
12.0
12.0
77
54.4
54.4
37
96.9
96.9
97
139.3
139.3
57
181.7
181.7
18
12.7
12.7
78
55.2
55.2
38
97.6
97.6
98
140.0
140.0
58
182.4
182.4
19
13.4
13.4
79
55.9
55.9
39
98.3
98.3
99
140.7
140.7
59
183.1
183.1
20
21
14.1
14.8
14.1
80
56.6
56.6
40
99.0
99.0
200
201
141.4
142.1
141.4
142. 1
60
183.8
183.8
14.8
81
57.3
57.3
141
99.7
99.7
261
184.6
184.6
22
15.6
15.6
82
58.0
.58.0
42
100.4
100.4
02
142.8
142.8
62
185.3
185.3
23
16.3
16.3
83
58.7
58.7
43
101.1
101.1
03
143.5
143.5
63
186.0
186.0
24
17.0
17.0
84
59.4
59.4
44
101.8
101.8
04
144.2
144.2
64
186.7
186.7
25
17.7
17.7
85
60.1
60.1
45
102.5
102.5
05
145.0
145.0
65
187.4
187.4
26
18.4
18.4
86
60.8
60.8
46
103. 2
103. 2
06
145.7
145.7
66
188.1
188.1
27
19.1
19.1
87
61.5
61.5
47
103. 9
103.9
07
146.4
146.4
67
188.8
188.8
28
19.8
19.8
88
62.2
62.2
48
104.7
104.7
08
147.1
147.1
68
189.5
189.5
29
20.5
20.5
89
62.9
62.9
49
105. 4
105.4
09
147.8
147.8
69
190.2
190.2
30
21.2
21.2
90
63.6
63.6
50
106.1
106.8
106.1
10
148.5
148.5
70
190.9
190.9
31
21.9
21.9
91
64.3
64.3
151
106.8
211
149.2
149. 2
271
191.6
191.6
32
22.6
22.6
92
65.1
65.1
52
107.5
107.5
12
149. 9 i 149. 9
72
192.3
192.3
33
23.3
23.3
93
a5.8
65.8
53
108.2
108.2
13
150. 6 j 150. 6
73
193.0
193.0
34
24.0
24.0
94
66.5
66.5
54
108.9
108.9
14
151.3
151.3
74
193.7
193.7
35
24.7
24.7
95
67.2
67.2
55
109.6
109.6
15
152.0
152.
75
194.5
194. 5
36
25.5
25.5
96
67.9
67.9
56
110.3
110.3
16
152. 7 ; 152. 7
76
195.2
195.2
37
26.2
26.2
97
68.6
68.6
57
111.0
111.0
17
153. 4
153.4
77
195.9
195.9
38
26.9
26.9
98
69.3
69.3
58
111.7
111.7
18
154.1
154.1
78
196.6
196.6
39
27.6
27.6
99
70.0
70.0
59
112.4
112.4
19
154.9
154.9
79
197.3
197.3
40
28.3
28.3
100
70.7
70.7
60
113.1
113.8
113.1
20
155.6
155. 6
80
198.0
198.0
41
29.0
29.0
101
71.4
71.4
161
113.8
221
156.3
156. 3
281
198.7
198.7
42
29.7
29.7
02
72.1
72.1
62
114.6
114.6
22
157.0
157.0
82
199.4
199.4
43
30.4
30.4
03
72.8
72.8
63
115.3
11.5. 3
23
157.7
157.7
83
200.1
200.1
44
31.1
31.1
04
73.5
73.5
64
116.0
116.0
24
158. 4
158.4
84
200.8
200.8
45
31.8
31.8
05
74.2
74.2
Ck)
116.7
116.7
25
159.1
1.59. 1
85
201.5
201. 5
46
32.5
32.5
06
75.0
75.0
66
117.4
117.4
26
159. 8 1 1.59. 8
86
202.2
202.2
47
33.2
33.2
07
75.7
75.7
67
118.1
118.1
27
160.5 160.5
87
202.9
202.9
48
33.9
33.9
08
76.4
76.4
68
118.8
118.8
28
161.2 161.2
88
203.6
203. (.
49
34.6
34.6
09
77.1
77.1
69
119.5
119.5
29
161.9 !l61.9
89
204.4
204.4
50
51
35.4
35.4
10
77.8
78.5
77.8
78.5
70
171
120.2
120.9
120.2
30
162.6
162. 6
90
205. 1
205. 1
36.1
36.1
111
120. 9
231
163. 3
163. 3
291
205. 8
205. >•
52
36.8
36.8
12
79.2
79.2
72
121.6
121.6
32
164.0
164.
92
206.5
206.5
53
37.5
37.5
13
79.9
79.9
73
122.3
122.3
33
164.8
164. 8
93
207.2
207.2
54
38.2
38.2
14
80.6
80.6
74
123.0
123.
34
ia5.5
165. 5
94
207.9
207.9
55
38.9
38.9
15
81.3
81.3
75
123.7
123.7
35
166.2
166. 2
95
208.6
208.6
56
39.6
39.6
16
82.0
82.0
76
124.5
124.5
36
166.9
166.9
96
209.3
209.3
57
40.3
40.3
17
82.7
82.7
77
125.2
125:2
37
167.6
167.6
97
210.0
210.0
58
41.0
41.0
18
83.4
8.3.4
78
125. 9
125.9
38
168.3
168. 3
98
210.7
210.7
59
41.7
41.7
■19
84.1
84.1
79
126.6
126.6
39
169.0
169.
99
211.4
211.4
60
42.4
42.4
20
84.9
84.9
80
127.3
127.3
40
169.7
169.7
300
212.1
212.1
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
4
15° (1
J5°, 225
^ 315°
)•
Page 620]
TABLE 2.
Difference of Latitude and Depart
ure for 45° (135°, 225°, 315
°)-
Dist.
Lat.
Dep.
Dist.
Lat. j Dep.
Dist.
Lat.
Dep.
Dist.
l^at.
Dep.
Dist.
Lat.
Dep.
301
212.8
212.8
361
255.3 255.3
421
297.7
297.7
481
340.1
340.1
541
382.5
382.5
02
213.5
213.5
62
256.0 256.0
22
298.4
298.4
82
340.8
340.8
42
383.2
383.2
03
214.3
214.3
63
256. 7 i 256. 7
23
299.1
299.1
83
341.5
341.5
43
383. 9
383.9
04
215.0
215.0
64
257.4 257.4
24
299.8
299.8
84 1 342.2
342.2
44
384.7
384.7
06
215.7
215.7
65
258.1
258.1
25
300.5
300. 5
85
342. 9 1 342. 9
45
385.4
385. 4
06
216.4
216.4
66
258.8
258.8
26
301.2
301.2
86
343.6 [343.6
46
386.1
386. 1
07
217.1
217.1
67
259.5
259. 5
27
301. 9
301.9
87
344.3
344.3
47
386.8
386.8
08
217.8
217.8
68
260.2
260.2
28
302. 6
302.6
88
345. 1
345.1
48
387.5
387.5
09
218.5
218.5
69
260.9
260.9
29
303. 4
303.4
89
345.8
345.8
49
388.2
388. 2
10
311
219.2
219.9
219.2
70
261. 6 i 261. 6
30
304. 1
304.1
90
346.5
346.5
50
388.9
388.9
219. 9
371
262.3
262.3
431
304.8
304.8
491
347. 2 1 347. 2
551
389.6
389. 6
12
220.6
220.6
72
263.0
263.
32
305. 5
305. 5
92
347. 9
347.9
.52
390.3
390. 3
13
221.3
221.3
73
263.8
263.8
33
.306. 2
306.2
93
348. 6
348.6
53
391.0
391.
14
222.0
222.0
74
264.5
264.5
34
306.9
306.9
94
349.3
349.3
54
391. 7
391.7
15
222.7
222.7
75
265.2
265.2
35
307.6
307. 6
95
350. < 350.
55
392.4
392.4
16
223.4
223.4
76
265. 9
265.9
36
308.3
308.3
96
350.7 1350.7
56
393.1
,393. 1
17
224.2
224.2
77
266.6
266.6
37
309.0
309.0
97
351.4 ;351.4
57
393.9
393. 9
18
224.9
224.9
78
267.3
267.3
38
309.7
309.7
98
352.1 1352.1
58
394.6
394.6
19
225.6
225.6
79
268.0
268.0
39
310.4
310.4
99
352. 8 ! 352. 8
,59
395.3
395. 3
20
226.3
226.3
80
268.7 1268.7
40
311.1
311.1
311.8
500
353. 5 1 353. 5
60
396.0
396.7
396.0
321 1 227.0
227.0
381
269.4 1269.4
441
311.8
501
354.3
354.3
,561
396. 7
22 i 227. 7
227.7
82
270.1 270.1
42
312. 5
312.5
02
355.0
355.0
62
397.4
397.4
23 ! 228.4
228.4
83
270. 8 270. 8
43
313.3
313.3
03
355.7
355.7
63
398.1
398.1
24 ! 229.1
229.1
84
271.5 ;271.5
44
314.0
314.0
04
356.4
356.4
64
398. 8
398.8
25 ! 229. 8
229.8
85
272. 2 • 272. 2
45
314.7
314.7
05
357.1
357.1
a5
399.5
399.5
26
230.5
230.5
86
272. 9 ' 272. 9
46
315. 4 1 315. 4
06
357.8
357.8
66
400.2
400.2
27
231.2
231.2
87
273. 7 < 273. 7
47
316.1
316.1
07
358.5
358.5
67
400.9
400.9
28
231.9
231.9
88
274. 4 i 274. 4
48 1 316. 8
316.8
08
359.2
359.2
68
401.6
401 . 6
29
232.6
232.6
89
275.1 1275.1
49 1 317.5
317.5
09
359.9
359. 9
69
402. 3
403. 3
30
233.3
233.3
90
275. 8 1 275. 8
50 i 318. 2
318.2
10
360.6
360.6
70
403.0
403.
331
234.1
234.1
391
276.5
276.5
451 ! 318.9
318.9
511
361.3
361.3
571
403.8
403.8
32
234.8
234.8
92
277.2
277.2
52
319.6
319.6
12
362.0
362.
72
404.5
404.5
33
235.5
235. 5
93
277.9
277.9
53
320.3
320.3
13
362.7
362.7
73
405. 2
405.2
34
236.2
236.2
94
278.6
278.6
54
321.0
321.0
14
363.5
363.5
74
405. 9
405. 9
35
236.9
236.9
95
279.3
279.3
55
321.7
321. 7
15
364.2
364.2
75
406. 6
406.6
36
237.6
237.6
96
280.0
280.0
56
322.4
.322. 4
16
364.9
364. 9
76
407. 3
407.3
37
238.3
238.3
97
280.7
280.7
57
323.2
323.2
17
365. 6
365.6
77
408.0
408.0
38
239.0
239.0
98
281.4 1281.4
58
323.9
,323. 9
18
366.3
366.3
78
408.7
408.7
39
239.7
239.7
99
282.1 1282.1
59
324.6
324.6
19
367.0
367.0
79
409.4
409.4
40
240.4
241.1
240.4
400
282.8 1282.8
60
325.3
326.0
325.3
326.
20
521
367.7
367.7
80
581
410.1
410.1
341
241.1
401
283.6 1283.6
461
368.4
368.4
410.8
410.8
42
241.8
241.8
02
284'. 3 1284.3
62
326.7
326. 7
22
369.1
369.1
82
411.5
411. 5
43
242.5
242.5
03
285. i 285.
63
327.4
327. 4
23
369.8
369.8
83
412.2
412. 2
44
243.2
243.2
04
285.7 '285.7
64
328.1
328.1
24
370.5
370.5
84
412.9
412.9
45
244.0
244.0
05
286. 4 ; 286. 4
65
328.8
328.8
25
371.2
371.2
85
413.7
413.7
46
244.7
244.7
06
287.1 1287.1
66 1 329. 5
329.5
26
371.9
371.9
86
414.4
414.4
47
245.4
245.4
07
287. 8 287. 8
67 : 330.2
330.2
27
372.6
372.6
87
415.1
415.1
48
246.1
246.1
08
288.5 '288.5
68 i 330.9
330.9
28
373.4
373.4
88
415.8
415. 8
49
246.8
246.8
09
289. 2 i 289. 2
69 i 331.6
331.6
29
374.1
374.1
89
416.5
416.5
50
247.5
248.2
247.5
10
289.9
290.6
289.9
70 ! 332.3
332.3
30
374.8 374.8
90
417.2
417.2
351
248.2
411
290.6
471 333. 1
333. 1
531
375.5
375.5
.591
417.9
417.9
52
248.9
248.9
12
291. 3 ' 291. 3
72
333.8
333.8
32
376.2
376. 2
92
418.6
418.6
53
249.6
249.6
13
292. 1 292.
73
3.34. 5
334.5
33
376.9
376.9
93
419.3
419.3
54
250.3
250.3
14
292. 7 1 292. 7
74
33.5.2
335.2
34
377.6
377.6
94
420.0
420.
55
251.0
251.0
15
293. 5 1 293. 5
75
3.35. 9
335.9
35
378. 3
378.3
95
420.7
420.7
56
251.7
251.7
16
294. 2 ' 294. 2
76 ! 336.6
336.6
.36
379.0
379.0
96
421.4
421.4
57
252.4
252.4
17
294. 9 ; 294. 9
77 ! 337.3
337.3
37
379.7
379.7
97
422.1
422.1
58
253.1
253.1
18
295. 6 295. 6
78 i 338.0
338.0
38
380.4
380.4
98
422.8
422.8
59
253.9
253.9
19
296. 3 1 296. 3
79
338.7
338.7
39
381.1
381.1
99
423.6
423.6
60
254.6
254.6
20
297.0
297.0
80
339.4
339.4
40
381.8
381.8
600
424.3
424.3
Dlst.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
Dist.
Dep.
Lat.
45° (135°, 22E
°, 315°
)■
Hh.
< a-Vo^
^^.
■y
TABLE 3.
y
[Page 621
Meri(flonal Parts, or
Increased Latitudes.
Comp
1
293.465
M.
0°
1°
go
3°
4°
5°
V>
70
8°
V
M.
0.0
59.6
119.2
178.9
238.6
298.3
358.2
418.2
478.3
538.6
1
1.0
60.6
20.2
79.9
39.6
99.3
59.2
19.2
79.3
39.6
1
2
2.0
61.6
21.2
80.8
40.6
300.3
60.2
20.2
80.3
40.6
2
3
3.0
62.6
22.2
81.8
41.6
01.3
61.2
21.2
81.3
41.6
3
4
4.0
63.6
23.2
82.8
42.5
02.3
62.2
22.2
82.3
42.6
4
5
5.0
64.6
124.2
183.8
243.5
303.3
363.2
423.2
483.3
543.6
5
6
6.0
65.6
25.2
84.8
44.5
04.3
64.2
24.2
84.3
44.6
6
7
7.0
66.5
26.2
85.8
45.5
05.3
65.2
25.2
85.3
45.6
7
8
7.9
67.5
27.2
86.8
46.5
06.3
66.2
26.2
86.3
46.6
8
9
8.9
68.5
28.2
87.8
47.5
07.3
67.2
368.2
27.2
87.3
47.6
548.6
9
10
10
9.9
69.5
129.1
188.8
248.5
308.3
428.2
488.3
11
10.9
70.5
30.1
89.8
49.5
09.3
69.2
29.2
89.3
49.6
11
12
11.9
71.5
31.1
90.8
50.5
10.3
70.2
30.2
90.4
50.6
12
13
12.9
72.5
32.1
91.8
51.5
11.3
VI. 2
31.2
91.4
51.7
13
14
13.9
73.5
33.1
92.8
52.5
12.3
T2.2
32.2
92.4
52.7
14
15
14.9
74.5
134.1
193.8
253.5
313.3
373.2
433.2
493.4
553.7
15
16
15.9
75.5
35.1
94.8
54.5
14.3
74.2
34.2
94.4
54.7
16
17
16.9
76.5
36.1
95.8
55.5
15.3
75.2
35.2
95.4
55.7
17
18
17.9
77.5
37.1
96.8
56.5
16.3
76.2
36.2
96.4
56.7
18
19
18.9
78.5
38.1
97.8
57.5
17.3
77.2
37.2
97.4
57.7
19
20
19.9
79.5
139.1
198.8
258.5
318.3
378. 2
438.2
498.4
558.7
20
21
20.9
80.5
40.1
99.7
59.5
19.3
79.2
39.2
99.4
59.7
21
22
21.9
81.5
41.1
200.7
60.5
20.3
80.2
40.2
500.4
60.7
22
23
22.8
82.4
42.1
01.7
61.5
21.3
81.2
41.2
01.4
61.7
23
24
23.8
83.4
43.1
02.7
62.5
22.3
82.2
42.2
02.4
62.7
24
25
24.8
• 84.4
144.1
203.7
263.5
323.3
383.2
443.2
503.4
563.7
25
26
25.8
85.4
45.1
04.7
64.5
24.3
84.2
44.2
04.4
64.7
26
27
26.8
86.4
46.0
05.7
65.5
25.3
85.2
45.2
05.4
65.7
27
28
27.8
87.4
47.0
06.7
66.5
26.3
86.2
46.2
06.4
66.8
28
29
28.8
88.4
48.0
07.7
67.4
27.3
87.2
47.2
07.4
67.8
29
30
29.8
89.4
149.0
208.7
268.4
328.3
388.2
448.2
508.4
568.8
30
31
30.8
90.4
50.0
09.7
69.4
29.3
89.2
49.2
09.4
69.8
31
32
31.8
91.4
51.0
10.7
70.4
30.3
90.2
50.2
10.4
70.8
32
33
32.8
92.4
52.0
11.7
71.4
31.3
91.2
51.2
11.4
71.8
33
34
33.8
93.4
53.0
12.7
72.4
32.3
92.2
52.2
12.4
72.8
34
35
34.8
94.4
154.0
213.7
273.4
333. 3
393.2
453.2
513.4
573.8
35
36
35.8
95.4
55.0
14.7
74.4
34.3
94.2
54.3
14.5
74.8
36
37
36.7
96.4
56.0
15.7
75.4
35.3
95.2
55.3
15.5
75.8
37
38
37.7
97.3
57.0
16.7
76.4
36.2
96.2
56.3
16.5
76.8
38
39
38.7
98.3
58.0
17.7
77.4
37.2
97.2
57.3
17.5
77.8
39
40
39.7
99.3
159.0
218.7
278.4
338.2
398.2
458.3
518.5
578.8
40
41
40.7
100.3
60.0
19.7
79.4
39.2
99.2
59.3
19.5
79.9
41
42
41.7
01.3
61.0
20.6
80.4
40.2
400.2
60.3
20.5
80.9
42
43
42.7
02.3
62.0
21.6
81.4
41.2
01.2
61.3
21.5
81.9
43
44
43.7
03.3
63.0
22.6
82.4
42.2
02.2
62.3
22.5
82.9
44
45
44.7
104.3
164.0
223.6
283.4
343.2
403.2
463.3
523.5
583.9
45
46
45.7
05.3
65.0
24.6
84.4
44.2
04.2
64.3
24.5
84.9
46
47
46.7
06.3
66.0
25.6
85.4
45.2
05.2
65.3
25.5
85.9
47
48
47.7
07.3
67.0
26.6
86.4
46.2
06.2
66.3
26.5
86.9
48
49
48.7
08.3
68.0
27.6
87.4
47.2
07.2
67.3
27.5
87.9
49
50
49.7
109.3
168.9
228.6
288.4
348.2
408.2
468.3
528.5
588.9
50
51
50.7
10.3
69.9
29.6
89.4
49.2
09.2
69.3
29.5
89.9
51
52
51.6
11.3
70.9
30.6
90.4
50.2
10.2
70.3
30.5
90.9
52
53
52.6
12.3
71.9
31.6
91.4
51.2
11.2
71.3
31.5
91.9
53
54
53.6
13.2
72.9
32.6
92.4
52.2
12.2
72.3
32.5
93.0
54
55
54.6
114.2
173.9
233.6
293.4
353.2
413.2
473.3
533.5
594.0
55
56
55.6
15.2
74.9
34.6
94.4
54.2
14.2
74.3
34.6
95.0
56
57
56.6
16.2
75.9
35.6
95.4
55.2
15.2
75.3
.35.6
96.0
57
58
57.6
17.2
76.9
36.6
96.3
56.2
16.2
76.3
36.6
97.0
58
59
68.6
18.2
77.9
37.6
97.3
57.2
17.2
77.3
37.6
98.0
59
M.
0°
10
2o
S"
4°
5°
6°
JO
8°
9°
M.
Page 6221
TABLE 3.
Meridional Parts, or
Increased Latitttdes.
Comp
1
263.465
M.
10°
11°
12°
13°
14°
15°
16°
i;°
18°
19°
M,
599.0
659.6
720.5
78i;5
842.8
. 904.4
966.3
1028. 5
1091.0
1153. 9
1
600.0
60.6
21.5
82.5
43.9
05.4
67.3
29.5
92.0
54.9
1
2
01.0
61.7
22.5
83.6
44.9
06.5
68.3
30.5
93.1
56.0
2
3
02.0
62.7
23.5
84.6
45.9
07.5
69.4
31.6
94.1
57.0
3
4
03.0
63.7
24.5
85.6
46.9
08.5
70.4
32.6
95.2
58.1
4
5
604.1
664.7
725.5
786.6
847.9
909.6
971.4
1033. 7
1096. 2
1159. 1
5
6
05.1
65.7
26.6
87.6
49.0
10.6
72.5
34.7
97.3
60.2
6
7
06.1
66.7
27.6
88.7
50.0
11.6
73.5
35.7
98.3
61.2
7
8
07.1
67.7
28.6
89.7
51.0
12.6
74.6
36.8
99.4
62.3
8
9
08.1
68.7
29.6
90.7
52.0
13.7
75.6
37.8
1100. 4
63.3
9
10
609.1
669.8
730.6
791.7
853.1
914.7
976.6
1038. 9
1101.4
1164. 4
10
11
10.1
70.8
31.6
92.7
54.1
15.7
77.7
39.9
02.5
65.4
11
12
11.1
71.8
32.7
93.8
55.1
16.8
78.7
40.9
03.5
66.5
12
13
12.1
72.8
33.7
94.8
56.1
17.8
79.7
42.0
04.6
67.5
13
14
13.1
73.8
34.7
95.8
57.2
18.8
80.8
43.0
05.6
68.6
14
15
15
614.1
674.8
735.7
796.8
858.2
919.8
981.8
1044. 1
1106. 7
1169. 7
16
15.2
75.8
36.7
97.8
59.2
20.9
82.8
45.1
07.7
70.7
16
17
16.2
76.8
37.7
98.9
60.2
21.9
83.9
46.1
08.8
71.8
17
18
17.2
77.9
38.8
99.9
61.3
22.9
84.9
47.2
09.8
72.8
18
1 19
18.2
78.9
39.8
800.9
62.3
24.0
85.9
48.2
10.9
73.9
19
20
619.2
679.9
740.8
801.9
863.3
925.0
987.0
1049.3
1111.9
1174. 9
20
21
20.2
80.9
41.8
02.9
64.3
26.0
88.0
50.3
13.0
76.0
21
22
21.2
81.9
42.8
04.0
65.4
27.1
89.0
51.3
14.0
77.0
22
23
22.2
82.9
43.8
05.0
66.4
28.1
90.1
52.4
15.0
78.1
23
24
23.2
83.9
44.9
06.0
67.4
29.1
91.1
53.4
16.1
79.1
24
25
624.2
684.9
745.9
807.0
868.5
930.1
992.1
1054. 5
1117.1
1180. 2
25
26
25.3
86.0
46.9
08.1
69.5
31.2
93.2
5.5.5
18.2
81.2
26
27
26.3
87.0
47.9
09.1
70.5
32.2
94.2
56.6
19.2
82.3
27
28
27.3
88.0
48.9
10.1
71.5
33.2
95.3
57.6
20.3
83.3
28
29
28.3
89.0
49.9
11.1
72.6
34.3
96.3
58.6
21.3
84.4
29
30
629.3
690.0
751.0
812.1
873.6
935.3
997.3
1059. 7
1122. 4
1185. 5
30
31
30.3
91.0
52.0
13.2
74.6
36.3
98.4
60.7
23.4
86.5
31
32
31.3
92.0
53.0
14.2
75.6
37.4
99.4
61.8
24.5
87.6
32
33
32.3
93.1
54.0
15.2
76.7
38.4
1000.4
62.8
25.5
88.6
33
34
33.3
94.1
55.0
16.2
77.7
39.4
01.5
63.9
1064. 9
26.6
89.7
34
35
634.3
695.1
756.0
817.3
878.7
940.5
1002.5
1127.6
1190. 7
35
36
35.4
96.1
57.1
18.3
79.7
41.5
03.6
65.9
28.7
91.8
36
37
36.4
97.1
58.1
19.3
80.8
42.5
04.6
67.0
29.7
92.8
37
38
37.4
98.1
59.1
20.3
81.8
43.6
05.6
68.0
30.8
93.9
38
39
38.4
99.1
60.1
21.3
82.8
44.6
06.7
69.1
31.8
95.0
39
40
639.4
700.2
761.1
822.4
883.8
945.6
1007.7
1070. 1
1132. 9
1196.
40
41
40.4
01.2
62.2
23.4
84.9
46.7
08.7
71.2
• 3.{. 9
97.1
41
42
41.4
02.2
63.2
24.4
85.9
47.7
09.8
72.2
35.0
98.1
42
43
42.4
03.2
64.2
25.4
86.9
48.7
10.8
73.2
36.0
99.2
43
44
43.4
04.2
65.2
26.5
88.0
49.7
11.8
74.3
37.1
1200.2
44
45
644.5
705.2
766.2
827.5
889.0
950.8
1012.9
1075. 3
1138. 1
1201. 3
45
46
45.5
06.2
67.3
28.5
90.0
51.8
13.9
76.4
39.2
02.3
46
47
46.5
07.3
68.3
29.5
91.0
52.8
15.0
77.4
40.2
03.4
47
48
47.5
08.3
69.3
30.5
92.1
53.9
16.0
78.5
41.3
04.5
48
49
48.5
09.3
70.3
31.6
93.1
54.9
17.0
1018. 1
79.5
42.3
05.5
49
50
649.5
710.3
771.3
832.6
894.1
955.9
1080. 5
1143. 4
1206. 6
50
51
50.5
11.3
72.3
33.6
95.2
57.0
19.1
81.6
44.4
07.6
51
52
51.5
12.3
73.4
34.6
96.2
58.0
20.2
82.6
45.5
08.7
52
53
52.5
13.4
74.4
35.7
97.2
59.0
21.2
83.7
46.5
09.7
53
54
53.6
14.4
75.4
36.7
98.2
60.1
22.2
84.7
47.6
10.8
54
55
654.6
715.4
776.4
837.7
899.3
961.1
1023. 3
1085. 8
1148. 6
1211.8
55
56
55.6
16.4
77.4
38.7
900.3
62.1
24.3
86.8
49.7
12.9
56
57
56.6
17.4
78.5
39.8
01.3
63.2
25.3
87.9
50.7
14.0
57
58
57.6
18.4
79.5
40.8
02.3
64.2
26.4
88.9
51.8
15.0
58
59
58.6
19.4
80.5
41.8
03.4
65.2
27.4
89.9
52.8
16.1
59
M.
10°
11°
12°
1S°
14°
15°
10°
17°
18°
19°
M.
TABLE 3.
[Page
623
Meridional Parts, or Increased Latitudes.
l^ouip. 293.466
M.
20°
21°
22°
28°
24°
25°
26°
27°
28°
29°
M.
1217. 1
1280. 8
1344.9
1409.5
1474. 5
1540. 1
1606.2
1672. 9
1740. 2
1808. 1
1
18.2
81.9
46.0
10.6
75.6
41.2
07.3
74.0
41.3
09.2
1
2
19.3
82.9
47.1
11.6
76.7
42.3
08.4
75.1
42.4
10.4
2
3
20.3
84.0
48.1
12.7
77.8
43.4
09.5
76.2
43.6
11.5
3
4
21.4
85.1
1286. 1
49.2
13.8
78.9
44.5
10.6
77.4
44.7
12.6
4
1222. 4
1350.3
1414. 9
1480.0
1545.6
1611.7
1678. 5
1745. 8
1813.8
6
23.5
87.2
51.4
16.0
81.1
46.7
12.9
79.6
46.9
14.9
6
7
24.5
88.3
52.4
17.1
82.2
47.8
14.0
80.7
48.1
16.1
7
8
25.6
89.3
53.5
18.1
83.3
48.9
15.1
81.8
49.2
17.2
8
9
26.7
90.4
54.6
19.2
84.3
50.0
16.2
82.9
50.3
18.3
9
10
1227. 7
1291.5
1355.7
1420.3
1485.4
1551. 1
1617. 3
1684.1
1751. 5
1819. 5
10
11
28.8
92.5
56.7
21.4
86.5
52.2
18.4
85.2
52.6
20.6
11
12
29.8
93.6
57.8
22.5
87.6
53.3
19.5
86.3
53.7
21.8
12
13
30.9
94.7
58.9
23.5
88.7
54.4
20.6
87.4
54.8
22.9
13
14
32.0
95.7
59.9
24.6
89.8
55.5
21.7
88.5
56.0
24.0
14
15
1233.
1296.8
1361.0
1425. 7
1490.9
1556. 6
1622.8
1689. 7
1757. 1
1825. 2
15
16
34.1
97.9
62.1
26.8
92.0
57.7
23.9
90.8
58.2
26.3
16
17
35.1
98.9
63.2
27.9
93.1
58.8
25.0
91.9
59.4
27.5
17
18
36.2
1300.0
64.2
29.0
94.2
59.9
26.2
93.0
60.5
28.6
18
19
37.3
01.1
65.3
30.0
95.2
61.0
27.3
94.1
61.6
29.7
19
20
1238.3
1302.1
1366.4
1431. 1
1496. 3
1562. 1
1628. 4
1695. 3
1762. 7
1830. 9
20
21
39.4
03.2
67.5
32.2
97.4
63.2
29.5
96.4
63.9
32.0
21
22
40.4
04.3
68.5
33.3
98.5
64.3
30.6
97.5
65.0
33.2
22
23
41.5
05.3
69.6
34.4
99. 6 65. 4
31.7
98.6
66.1
34.3
23
24
42.6
06.4
70.7
35.4
1500.7
66.5
32.8
99.7
67.3
1768.4
35.4
24
25
1243. 6
1307. 5
1371.8
1436. 5
1501. 8
1567.6
1633. 9
1700.9
1836. 6
25
26
44.7
08.5
72.8
37.6
02.9
68.7
35.0
02.0
69.5
37.7
26
27
45.7
09.6
73.9
38.7
04.0
69.8
36.1
03.1
70.7
38.9
27
28
46.8
10.7
75.0
39.8
05.1
70.9
37.3
04.2
71.8
40.0
28
29
47.9
11.7
76.1
1377. 1
40.9
06.2
72.0
38.4
05.3
72.9
41.2
29
30
1248. 9
1312. 8
1442.0
1507.3 1 1573.1
1639. 5
1706.5
1774. 1
1842.3
30
31
50.0
13.9
78.2
43.0
08.4
74.2
40.6
07.6
75.2
43.4
31
32
51.0
14.9
79.3
44.1
09.4
75.3
41.7
08.7
76.3
44.6
32.
33
52.1
16.0
80.4
45.2
10.5
76.4
42.8
09.8
77.4
45.7
33
34
53.2
17.1
81.5
46.3
11.6
77.5
43.9
10.9
. 78.6
46.9
34
35
1254. 2
1318. 2
1382. 5
1447.4
1512.7
1578. 6
1645.0
1712. 1
1779. 7
1848.
35
36
55.3
19.2
83.6
48.5
13.8
79.7
46.2
13.2
80.8
49.2
36
37
56.4
20.3
84.7
49.5
14.9
80.8
47.3
14.3
82.0
50.3
37
38
57.4
21.4
85.8
50.6
16.0
81.9
48.4
15.4
83.1
51.4
38
39
58.5
22.4
86.8
51.7
17.1
83.0
49.5
16.6
84.2
52.6
39
40
1259. 5
1323. 5
1387. 9
1452. 8
1518.2
1584. 1
1650.6
1717. 7
1785.4
1853.7
40
41
60.6
24.6
89.0
53.9
19.3
85.2
51.7
18.8
86.5
54.9
41
42
61.7
25.6
90.1
55.0
20.4
86.3
52.8
19.9
87.6
56.0
42
43
62.7
26.7
91.1
56.1
21.5
87.4
53.9
21.1
88.8
57.2
43
44
63.8
27.8
92.2
57.1
22.6
88.5
55.1
22.2
89.9
58.3
44
45
1264.9
1328. 9
1393. 3
1458. 2
1523. 7
1589. 6
1656.2
1723. 3
1791. 1
1859.5
45
46
65.9
29.9
94.4
59.3
24.8
90.7
57.3
24.4
92.2
60.6
46
47
67.0
31.0
95.5
60.4
25.9
91.8
58.4
25.5
93.3
61.8
47
48
68.0
32.1
96.5
61.5
27.0
92.9
59.5
26.7
94.5
. 62.9
48
49
69.1
33.1
97.6
62.6
28.0
94.1
60.6
27.8
95.6
64.0
49
60
1270. 2
1334. 2
1398. 7
1463.7
1529.1
1595. 2
1661.7
1728. 9
1796. 7
1865. 2
50
51
71.2
35.3
99.8
64.8
30.2
96.3
62.9
30.0
97.9
66.3
51
52
72.3
36.3
1400.9
65.8
31.3
97.4
64.0
31.2
99.0
67.5
52
53
73.4
37.4
01.9
66.9
32.4
98.5
65.1
32.3
1800.1
68.6
53
54
74.4
38.5
03.0
68.0
33.5
99.6
66.2
33.4
01.3
69.8
54
55
1275. 5
1339. 6
1404. 1
1469. 1
1534.6
1600.7
1667.3
1734.5
1802. 4
1870. 9
55
56
76.6
40.6
05.2
70.2
35.7
01.8
68.4
35.7
03.5
72.1
56
57
77.6
41.7
06.2
71.3
36.8
02.9
69.5
36.8
04.7
73.2
57
58
78.7
42.8
07.3
72.4
37.9
04.0
70.7
37.9
05.8
74.4
58
59
79.7
43.8
08.4
73.5
39.0
05.1
71.8
39.1
07.0
75.5
59
M.
20°
21°
22°
23°
24°
25°
26°
27°
28°
29°
M.
Page 624]
TABLE 3.
Meridional Parts, or
Increased Latitudes.
Coinp.
1
293.465
M.
80°
81°
82°
33°
84°
35°
86°
87°
38°
89°
M.
1876. 7
1946.
2016.
2086. 8
2158. 4
2230. 9
2304. 2
2378. 5
2453. 8
2530. 2
1
77.8
47.1
17.2
88.0
59.6
32.1
05.5
79.8
55.1
31.5
1
2
79.0
48.3
18.3
89.2
60.8
33.3
06.7
81.0
56.4
32.8
2
3
80.1
49.4
19.5
90.3
62.0
34.5
07.9
82.3
57.6
34.0
3
4
81.3
50.6
20.7
91.5
63.2
35.7
09.2
83.5
58.9
35.3
4
5
1882. 4
1951. 8
2021. 9
2092. 7
2164.4
2236. 9
2310. 4
2384. 8
2460.2
2536. 6
5
6
83.6
52.9
23.0
93.9
65.6
38.2
11.6
86.0
61.4
37.9
6
7
84.7
54.1
24.2
95.1
66.8
39.4
12.9
87.3
62.7
.39.2
7
8
85.9
55.3
25.4
96.3
68.0
40.6
14.1
88.5
64.0
40.5
8
9
87.0
56.4
26.6
97.5
69.2
41.8
15.3
89.8
65.2
41.7
9
10
10
1888. 2
1957. 6
2027. 7
2098.7
2170. 4
2243.
2316. 5
2391.
2466. 5
2543.
11
89.3
58.7
28.9
99.8
71.6
44.2
17.8
92. 3
67.8
44.3
11
12
90.5
59.9
30.1
2101.0
72.8
45.5
19.0
93.5
69.0
45.6
12
13
91.6
61.1
31.3
02.2
74.0
46.7
20.3
94.8
70.3
46.9
13
14
92.8
62.2
32.4
03.4
75.2
47.9
21.5
96.0
71.6
48.2
14
15
1893. 9
1963. 4
2033. 6
2104. 6
2176. 4
2249: 1
2322. 7
2397. 3
2472. 8
2549. 5
15
16
95.1
64.6
34.8
05.8
77.6
50.3
24.0
98.5
74.1
50.7
16
17
96.2
65.7
36.0
07.0
78.8
51.6
25.2
99.8
75.4
52.0
17
18
97.4
66.9
37.1
08.2
80.0
52.8
26.4
2401.0
76.6
53.3
18
19
98.5
68.1
38.3
09.4
81.2
54.0
27.7
02.3
77.9
54.6
19
20
1899. 7
1969. 2
2039. 5
2110. 6
2182. 5
2255.2
2328. 9
2403. 5
2479. 2
2555. 9
20
21
1900.8
70.4
40.7
11.8
83.7
56.4
30.1
04.8
80.4
57.2
21
22
02.0
71.5
41.8
12.9
84.9
57.7
31.4
06.0
81.7
58.5
22
23
03.1
72.7
43.0
14.1
86.1
58.9
32.6
07.3
83.0
59.8
23
24
04.3
73.9
44.2
15.3
87.3
60.1
33.8
08.5
84.3
61.0
24
25
1905. 5
1975.
2045.4
2116.5
2188. 5
2261. 3
2335. 1
2409. 8
2485. 5
2562. 3
25
26
06.6
76.2
46.6
17.7
89.7
62.5
36.3
11.1
86.8
63.6
26
27
07.8
77.4
47.7
18.9
90.9
63.8
37.6
12.3
88.1
64.9
27
28
08.9
78.5
48.9
20.1
92.1
65.0
38.8
13.6
89.3
66.2
28
29
10.1
79.7
50.1
21.3
93.3
66.2
40.0
14.8
90.6
67.5
29
30
1911.2
1980.9
2051. 3
2122. 5
2194. 5
2267. 4
2341. 3
2416. 1
2491. 9
2568. 8
30
31
12.4
82.0
52.5
23.7
95.7
68.7
42.5
17.3
93.2
70.1
31
32
13.5
83.2
53.6
24.9
96.9
69.9
43.7
18.6
94.4
71.4
32
33
14.7
84.4
54.8
26.1
98.1
71.1
45.0
19.8
95.7
72.7
33
34
15.8
85.5
56.0
27.3
99.4
72.3
46.2
21.1
97.0
73.9
34
35
1917.
1986. 7
2057. 2
2128. 5
2200.6
2273. 5
2347. 5
2422. 3 : 2498. 3
2575. 2
35
36
18.2
87.9
58.4
29.6
01.8
74.8
48.7
23. 6 . 99. 5
76.5
36
37
19.3
89.1
59.5
30.8
03.0
76.0
49.9
24.9
2500. 8
77.8
37
38
20.5
90.2
60.7
32.0
04.2
77.2
51.2
26.1
02.1
79.1
38
39
21.6
91.4
61.9
33.2
05.4
78.4
52.4
27.4
03.4
80.4
39
40
1922. 8
1992. 6
2063. 1
2134. 4
2206. 6
2279. 7
2353.7
2428. 6
2504. 6
2581.7
40
41
23.9
93.7
64.3
35.6
07.8
80.9
54.9
29.9 i 05.9
83.0
41
42
25.1
94.9
65.5
36.8
09.0
82.1
56.1
31.2 j 07.2
84.3
42
43
26.3
96.1
66.6
38.0
10.2
, 83.3
57.4
32. 4 1 08. 5
85.6
43
44
27.4
97.2
67.8
39.2
11.5
84.6
58.6
33. 7 1 09. 7
86.9
44
45
1928. 6
1998. 4
2069.
2140.4
2212. 7
2285. 8
2359.9
2434.9 i 2511.0
2588. 2
45
46
29.7
99.6
70.2
41.6
13.9
87.0
61.1
36.2
12.3
89.5
46
47
30.9
2000.7
71. 4 ' 42. 8
15.1
88.3
62.4
37.4
13.6
90.8
47
48
32.0
01.9
72.6
44.0
16.3
89.5
63.6
38.7
14.8
92.1
48
49
33.2
03.1
73.7
45.2
17.5
90.7
64.8
40. : 16. 1
93.4
49
50
1934. 4
2004.3
2074. 9
2146. 4
2218. 7
2291. 9
2366. 1
2441. 2 i 2517. 4
2594. 7
50
51
35.5
05.4
76.1
47.6
19.9
93.2
67.3
42.5 18.7
96.0
51
52
36.7
06.6
77.3
48.8
21.1
94.4
68.6
43. 7 i 20.
97.3
52
53
37.8
07.8
78.5
50.0
22.4
95.6
69.8
45. j 21. 2
98.5
53
54
39.0
08.9
79.7
51.2
23.6
96.9
71.1
46. 3 22. 5
2447.5 ! 2523.8
99.8
54
55
1940.2
2010. 1
2080. 8
2152. 4
2224. 8
2298. 1
2372. 3
2601.1
55
56
41.3
11.3
82.0
53.6
26.0
99.3
73.6
48.8
25.1
02.4
56
57
42.5
12.5
83.2
54.8
27.2
2300.5
74.8
50.1
26.4
03.7
57
58
43.6
13.6
84.4
56.0
28.4
01.8
76.1
51.3
27.6
05.0
58
59
44.8
14.8
85.6
57.2
29.6
03.0
77.3
52.3
28.9
06.3
59
M.
80°
81°
82°
33°
34°
85°
86°
87°
88°
89°
M.
TABLE 3.
[Page
625
Meridional Parts, or
Increased Latitudes.
Comp
1
293.465
M.
40°
41°
42°
48°
44°
45°
46°
47°
48°
49°
M.
2607. 6
2686. 2
2766.
2847.1
2929.5
3013. 4
3098.7
3185. 6
3274. 1
3364. 4
1
08.9
87.6
67.4
48.5
30.9
14.8
3100.1
87.1
75.6
65.9
1
2
10.2
88.9
68.7
49.9
32.3
16.2
01.6
88.5
77.1
67.4
2
3
11.5
90.2
70.1
51.2
33.7
17.6
03.0
90.0
78.6
69.0
3
4
12.8
91.5
71.4
52.6
35.1
19.0
04.4
91.4
80.1
70.5
3372.
4
5
2614. 1
2692. 8
2772. 8
2853.9
2936.5
3020. 4
3105.9
3192. 9
3281. 6
5
6
15.4
94.2
74.1
55.3
37.9
21.8
07.3
94.4
83.1
73.5
6
16.8
95.5
75.4
56.7
39.3
23.3
08.8
95.8
84.6
75.1
7
8
18.1
96.8
76.8
58.0
40.6
24.7
10.2
97.3
86.1
76.6
8
9
19.4
98.1
78.1
59.4
42.0
26.1
11.6
98.8
87.6
78.1
9
10
2620.7
2699.5
2779.5
2860.8
2943.4
3027. 5
3U3.1
3200.2
3289.
3379. 6
10
11
22.0
2700.8
80.8
62.1
44.8
28.9
14.5
01.7
90.5
81.2
11
12
23.3
02.1
82.2
63.5
46.2
30.3
16.0
03.2
92.0
82.7
12
13
24.6
03.4
83.5
64.9
47.6
31.7
17.4
04.6
93.5
84.2
13
14
25.9
04.8
84.8
66.2
49.0
33.2
18.8
06.1
95.0
85.7
14
15
2627. 2
2706.1
2786. 2
2867. 6
2950.4
3034. 6
3120. 3
3207. 6
3296.5
3387. 3
15
16
28.5
07.4
87.5
69.0
51.8
36.0
21.7
09.0
98.0
88.8
16
17
29.8
08.7
88.9
70.3
53.2
37.4
23.2
10.5
99.5
90.3
17
18
31.1
10.1
90.2
71.7
54.5
38.8
24.6
12.0
3301.0
91.8
18
19
20
32.4
11.4
91.6
73.1
55.9
40.2
26.0
13.4
02.5
93.4
19
2633. 7
2712. 7
2792. 9
2874. 4
2957. 3
3041. 7
3127. 5
3214. 9
3304.
3394. 9
20
21
35.0
14.0
94.3
75.8
58.7
43.1
28.9
16.4
05.5
96.4
21
22
36.3
15.4
95.6
77.2
60.1
44.5
30.4
17.9
07.0
98.0
22
23
37.6
16.7
97.0
78.6
61.5
45.9
31.8
19.3
08.5
99.5
23
24
38.9
18.0
98.3
79.9
62.9
47.3
33.3
20.8
10.0
3401.
24
25
2640.2
2719. 3
2799.7
2881. 3
2964.3
3048. 7
3134. 7
3222. 3
3311.5
3402. 6
25
26
41.6
20.7
2801.0
82.7
65.7
50.2
36.2
23.7
13.0
04.1
26
27
42.9
22.0
02.4
84.0
67.1
51.6
37.6
25.2
14.5
05.6
27
28
44.2
23.3
03.7
85.4
68.5
53.0
39.0
26.7
16.0
07.2
28
29
45.5
24.7
05.1
86.8
69.9
54.4
40.5
28.2
17.5
08.7
29
30
2646.8
2726.
2806.4
2888. 2
2971. 3
3055.9
3141. 9
3229.6
3319.
3410. 2
30
31
48.1
27.3
07.8
89.5
72.7
57.3
43.4
31.1
20.5
11.8
31
32
49.4
28.6
09.1
90.9
74.1
58.7
44.8
32.6
22.1
13.3
32
33
50.7
30.0
10.5
92.3
75.5
60.1
46.3
34.1
23.6
14.8
33
34
35
52.0
31.3
11.8
93.7
76.9
61.5
47.7
35.6
25.1
16.4
34
2653.3
2732. 6
2813. 2
2895.
2978.3
3063.0
3149. 2
3237.
3326. 6
3417. 9
35
36
54.7
34.0
14.5
96.4
79.7
64.4
50.6
38.5
28.1
19.5
36
37
56.0
35.3
15.9
97.8
81.1
65.8
52.1
40.0
29.6
21.0
37
38
57.3
36.6
17.2
99.2
82.5
67.2
53.5
41.5
31.1
22.5
38
39
58.6
38.0
18.6
2820.
2900.5
83.9
68.7
55.0
42.9
32.6
24.1
39
40
2659.9
2739. 3
2901.9
2985.3
3070. 1
3156. 4
3244. 4
3334. 1
3425. 6
40
41
61.2
40.6
21.3
03.3
86.7
71.5
57.9
45.9
35.6
27.2
41
42
62.5
42.0
22.7
04.7
88.1
72.9
59.4
47.4
37.1
28.7
42
43
63.9
43.3
24.0
06.1
89.5
74.4
60.8
48.9
38.6
30.2
43
44
45
65.2
44.6
25. '4
07.4
90.9
75.8
62.3
50.3
40.2
31.8
44
2666. 5
2746.0
282S. 7
2908.8
2992. 3
3077. 2
3163. 7
3251. 8
3341. 7
3433. 3
45
46
67.8
47.3
28.1
10.2
93.7
78.7
65.2
53.3
43.2
34.9
46
47
69.1
48.6
29.4
11.6
95.1
80.1
66.6
54.8
44.7
36.4
47
48
70.4
50.0
30.8
13.0
96.5
81.5
68.1
56.3
46.2
38.0
48
49
71.7
51.3
32.2
14.3
97.9
82.9
69.5
57.8
47.7
39.5
49
50
2673. 1
2752. 7
2833.5
2915. 7
2999. 3
3084.4
3171.0
3259. 3
3349.2
3441.0
50
51
74.4
54.0
34.9
17.1
3000.7
85.8
72.5
60.7
50.8
42.6
51
52
75.7
55.3
36.2
18.5
02.1
87.2
73.9
62.2
52.3
44.1
52
53
77.0
56.7
37.6
19.9
03.5
88.7
75.4
63.7
53.8
45.7
53
54
78.3
58.0
39.0
21.2
04.9
90.1
76.8
65.2
55.3
47.2
54
55
55
2679. 6
2759. 3
2840. 3
2922.6
3006.3
3091.5
3178. 3
3266. 7
3356.8
3448.8
56
81.0
60.7
41.7
24.0
07.7
93.0
79.7
68.2
58.3
50.3
56
57
82.3
62.0
43.0
25.4
09.2
94.4
81.2
69.7
59.9
51.9
57
58
83.6
63.4
44.4
26.8
10.6
95.8
82.7
71.1
61.4
53.4
58
59
84.9
64.7
45.8
28.2
12.0
97.3
84.1
72.6
62.9
55.0
59
M.
40°
41°
42°
48°
44°
46°
46°
47°
48°
49°
M.
24972°— 12-
-30
Page 626]
TABLE 3.
Meridional Parts, or
Increased Latitudes.
Comp.
1
293.465
M.
50°
51°
52°
68°
54°
55°
56°
57°
58°
69°
M.
3456. 5
3550. 6
3646. 7
3745. 1
3845. 7
3948. 8
4054.5
4163.
4274. 4
4389. 1
1
58.1
52.2
48.4
46.7
47.4
50.5
56.3
64.8
76.3
91.0
1
2
59.6
53.8
50.0
48.4
49.1
52.3
58.1
66.6
78.2
92.9
2
3
61.2
55.4
51.6
50.0
50.8
54.0
59.8
68.5
80.1
94.9
3
4
62.7
56.9
53.2
51.7
52.5
55.7
61.6
70.3
82.0
96.8
4
5
3464.3
3558.5
3654.8
3753. 4
3854.2
3957. 5
4063. 4
4172. 1
4283. 9
4398. 8-
5
6
65.9
60.1
56.5
55.0
55.9
59.2
65.2
74.0
85.7
4400.7
6
7
67.4
61.7
58.1
56.7
57.6
61.0
67.0
75.8
87.6
02.6
7
8
69.0
63.3
59.7
58.3
59.3
62.7
68.8
77.7
89.5
04.6
8
9
70.5
64.9
61.3
60.0
61.0
64.5
70.6
79.5
91.4
06.5
9
10
3472. 1
3566.5
3663.0
3761. 7
3862. 7
3966. 2
4072.4
4181. 3
4293.3
4408. 5
10
11
73.6
68.1
64.6
63.3
64.4
68.0
74.2
83.2
95.2
10.4
11
12
75.2
69.7
66.2
65.0
66.1
69.7
76.0
85.0
97.1
12.4
12
13
76.7
71.3
67.9
66.7
67.8
71.5
77.7
86.9
99.0
14.3
13
14
78.3
72.8
69.5
68.3
69.5
73.2
79.5
88.7
4300; 9
16.3
14
15
3479. 9
3574. 4
3671. 1
3770.
3871.2
3975.0
4081'. 3
4190. 6
4302. 8
4418.2
15
16
81.4
76.0
72.7
71.7
72.9
76.7
83.1
92.4
04.7
20.2
16
17
83.0
77.6
74.4
73.3
74.6
78.5
84.9
94.2
06.6
22.1
17
18
84.5
79.2
76.0
75.0
76.3
80.2
86.7
96.1
08.5
24.1
18
19
86.1
80.8
77.6
76.7
78.1
82.0
88.5
97.9
10.4
26.1
19
20
3487. 7
3582. 4
3679. 3
3778. 3
3879. 8
3983. 7
4090. 3
4199. 8
4312. 3
4428.
20
21
89.2
84.0
80.9
80.0
81.5
85.5
92.1
4201. 6
14.2
30.0
21
22
90.8
85.6
82.5
81.7
83.2
87.2
93.9
03.5
16.1
31.9
22
23
92.4
87.2
84.2
83.3
84.9
89.0
95.7
05.3
18.0
33.9
23.
24
93.9
88.8
85.8
3687. 4
85.0
86.6
90.7
97.5
07.2
19.9
35.8
24
25
3495.5
3590.4
3786. 7
3888. 3
3992. 5
4099.3
4209.0
4321. 8
4437. 8
25
26
97.1
92.0
89.1
88.4
90.0
94.3
4101. 1
10.9
23.7
39.8
26
27
98.6
93.6
90.7
90.0
91.8
96.0
02.9
12.8
25.6
41.7
27
28
3500.2
95.2
92.3
91.7
93.5
97.8
04.8
14.6
27.5
43.7
28
29
01.8
96.8
94.0
93.4
9l2
3896. 9
99.5
06.6
16.5
29.4
45.7
29
30
3503.3
3598. 4
3695.6
3795. 1
4001.3
4108. 4
4218. 3
4331.3
4447.6
30
31
04.9
3600.0
97.3
96.8
98.6
03.1
10.2
20.2
33.2
49.6
31
32
06.5
01.6
'98.9
98.4
3900. 4
04.8
12.0
22.0
35.2
51.6
32
33
08.0
03.2
3700. 5
3800.1
02.1
06.6
13.8
23.9
37.1
53.5
33
34
09.6
04.8
02.2
01.8
03.8
08.3
15.6
25.8
39.0
55.5
34
35
3511.2
3606.4
3703. 8
3803. 5
3905. 5
4010. 1
4117.4
4227. 6
4340.9
4457. 5
35
36
12.7
08.0
05.5
05.1
07.2
11.9
19.2
29.5
42.8
59.4
36
37
14.3
09.6
07.1
06.8
09.0
13.6
21.0
31.3
44.7
61.4
37
38
15.9
11.2
08.7
08.5
10.7
15.4
22.9
33.2
46.6
63.4
38
39
17.5
12.8
10.4
10.2
12.4
17.2
24.7
35.1
48.6
65.4
39
40
3519.
3614. 5
3712.
3811. 9
3914. 1
4018.9
4126. 5
4236. 9
4350.5
4467. 3
40
41
20.6
16.1
13.7
13.6
15.9
20.7
28.3
38.8
52.4
69.3
41
42
22.2
17.7
15.3
15.2
17.6
22.5
30.1
40.7
54.3
71.3
42
43
23.7
19.3
17.0
17.0
19.3
24.3
31.9
42.5
56.2
73.3
43
44
25.3
20.9
18.6
18.6
21.0
26.0
33.8
44.4
58.2
75.3
44
45
3526. 9
3622. 5
3720. 3
3820. 3
3922. 8
4027. 8
4135.6
42tt6.3
4360. 1
4477.2
45
46
28.5
24.1
21.9
22.0
24.5
29.6
37.4
48.1
62.0
79.2
46
47
30.1
25.7
23.6
23.7
26.2
31.4
39.2
50.0
63.9
81.2
47
48
31.6
27.3
25.2
25.4
28.0
33.1
41.0
51.9
65.9
83.2
48
49
33.2
29.0
26.9
27.1
29.7
34.9
42.9
53.8
67.8
85.2
49
50
3534.8
3630. 6
3728. 5
3828. 7
3931. 4
4036. 7
4144. 7
4255. 6
4369. 7
4487.2
50
51
36.4
32.2
30.2
30.4
33.2
38.5
46.5
57.5
71.7
89.1
51
52
37.9
33.8
31.8
32.1
34.9
40.2
48.3
59.4
73.6
91.1
52
53
39.5
35.4
33.5
33.8
36.6
42.0
50.2
61.3
75.5
93.1
53
54
41.1
37.0
3638. 6"
35.1
35.5
38.4
43.8
52.0
63.1
77.4
95.1
4497.1
54
55
55
3542.7
3736. 8
3837. 2
3940.1
4045. 6
4153. 8
4265.0
4379. 4
56
44.3
40.3
38.4
38.9
41.8
47.4
55.7
66.9
81.3
99.1
56
57
45.9
41.9
40.1
40.6
43.6
49.1
57.5
68.8
83.2
4501. 1
57
58
47.4
43.5
41.7
42.3
45.3
50.9
59.3
70.7
85.2
03.1
58
59
49.0
45.1
43.4
45.0
47.0
52.7
61.1
72.5
87.1
05.1
59
M.
60°
61°
52°
58°
54°
56°
56°
57°
58°
69°
M.
TABLE 3.
[Page
627
Meridional Parts, oi
Increased Latitudes.
Comp
293.465
M.
60°
61°
62°
68°
64°
65°
66°
67°
68°
69°
M.
4507.1
4628. 7
4754. 3
4884.1
5018. 4
5157. 6
5302. 1
5452. 4
5609.1
5772. 7
1
09.1
30.8
56.4
86.3
-20.6
59.9
04.6
55.0
11.8
75.5
1
2
11.1
32.9
58.6
88.5
22.9
62.3
07.0
57.6
14.4
78.3
2
3
13.1
34.9
60.7
90.7
25.2
64.7
09.5
60.1
17.1
81.1
3
4
15.1
37.0
62.8
92.9
27.5
67.0
11.9
62.7
19.8
83.8
4
5
4517. 1
4639.
4764. 9
4895. 1
5029.8
5169. 4
5314. 4
5465.2
5622. 4
5786. 6
5
6
19.1
41.1
67.1
97.3
32.1
71.8
16.9
67.8
25.1
89.4
6
7
21.1
43.2
69.2
99.5
34.3
74.2
19.3
70.4
27.8
92.2
i
8
23.1
45.2
71.3
4901. 7
36.6
76.5
21.8
72.9
30.5
95.1
8
9
2.5.1
47.3
73.5
03.9
38.9
78.9
24.3
75.5
33.2
97.9
5800.7
' 9
10
10
4527. 1
4649.4
4775. 6
4906.1
5041. 2
5181.3
5326. 7
5477.1
5635.9
11
29.1
51.5
77.8
08.3
43.5
83.7
29.2
80.7
38.5
03.5
11
12
31.1
53.5
79.9
10.5
45.8
86.0
31.7
83.2
41.2
06.3
12
13
33.1
55.6
82.0
12.8
48.1
88.4
34.2
85.8
43.9
09.1
13
14
35.1
57.7
84.2
15.0
50.4
90.8
36.6
88.4
46.6
11.9
14
15
4537.1
4659.7
4786. 3
4917. 2
5052.7
5193. 2
5339. 1
5491.0
5649. 3
5814. 7
' 15
16
39.2
61.8
88.5
19.4
55.0
9.5.6
41.6
93.6
52.0
17.6
16
17
41.2
63.9
90.6
21.6
57.3
98.0
44.1
96.2
54.7
20.4
17
18
43.2
66.0
92.8
23.9
59.6
5200.4
46.6
98.7
57.4
23.2
18
19
20
45.2
68.1
94.9
26.1
61.9
02.7
49.1
.5501. 3
60.1
26.0
19
20
4547. 2
4670. 1
4797. 1
4928. 3
.5064.2
5205. 1
5351.5
5503. 9
5662. 8
5828. 9
21
49.2
72.2
99.2
30.5
66.5
07.5
54.0
06.5
65.5
31.7
21
22
51.3
74.3
4801. 4
32.8
68.8
09.9
56.5
09.1
68.2
34.5
22
23
53.3
76.4
03. 5
35.0
71.1
12.3
59.0
11.7
70.9
37.4
23
24
25
55.3
78.5
05.7
37.2
73.4
14.7
61.5
14.3
73.7
40:2
24
4.557. 3
4680. 6
4807. 8
4939. 4
5075. 7
5217. 1
5364.0
5516. 9
5676. 4
5843.
25
26
59.3
82.6
10.0
41.7
78.1
19.5
66.5
19.5
79.1
45.9
26
27
61.4
84.7
12.1
43.9
80.4
21.9
69.0
22.1
81.8
48.7
27
28
63.4
86.8
14.3
46.1
82.7
24.3
71.5
24.7
84.5
51.6
28
29
65.4
88.9
16.5
48.4
85.0
•26.7
74.0
27.3
87.3
54.4
29
30
4567.4
4691.
4818. 6
4950.6
5087.3
5229.1
5376.5
5529.9
5690.0
5857.3
30
31
69.5
93.1
20.8
52.9
89.6
-31.6
79.0
32.5
92.7
60.1
31
82
71.5
95.2
23.0
.55.1
92.0
34.0
81.5
35.2
95.4
63.0
32
33
73.5
97.3
25.1
57.3
94.3
36.4
84.0
37.8
98.2
65.9
33
34
75.6
99.4.
27.3
59.6
96.6
38.8
86.5
40.4
5700.9
68.7
34
35
4577. 6
4701. 5
4829.5
4961. 8
5098.9
5241. 2
5389. I
5543.0
5703. 6
5871.6
35
36
79.6
03.6
.31.6
64.1
5101.3
43.6
91.6
45.6
06.4
74.4
36
37
81.7
05.7
.33.8
66.3
03.6
46.0
94.1
48.3
09.1
77.3
37
38
83.7
07.8
36.0
68.6
05.9
48.5
96.6
50.9
11.9
80.2
38
39
85.7
09.9
38.1
70.8
08.3
50.9
99.1
53.5
14.6
83.1
39
40
4587. 8
4712.0
4840. 3
4973. 1
5110. 6
5253. 3
5401.6
5556. 1
5717.3
5885.9
40
41
89.8
14.1
42.5
75.3
12.9
55.7
04.2
58.8
20.1
88.8
41
42
91.8
16.2
44.7
77.6-
15.3
58.2
06.7
61.4
22.8
91.7
42
43
93.9
18.3
46.8
79.8
17.6
60.6
09.2
64.0
25.6
94.6
43
44
45
■95.9
20.4
49.0
82.1
19.9
63.0
11.8
66.7
28.3
97.4
44
4598.
4722. 5
4851. 2
4984.3
5122. 3
5265.4
5414.3
5569.3
5731. 1
5900.3
45
46
4600.0
24.6
53.4
86.6
24.6
67.9
16.8
71.9
33.9
03.2
46
47
02.1
26.7
55. 6
88.9
27.0
70.3
19.3
74.6
36.6
06.1
47
48
04.1
28.9
57.8
91.1
29.3
72.8
21.9
77.2
39.4
09.0
48
49
06.1
31.0
59.9
93.4
31.7
75.2
24.4
79.9
42.1
11.9
49
50
4608. 2
4733. 1
4862.1
4995. 6
5134.
5277. 6
5427.
5582. 5
5744.9
5914. 8
50
51
10.2
35.2
64.3
97.9
36.4
80.1
.29.5
85.2
47.7
17.7
51
52
12.3
37.3
66.5
5000.2
38.7
82.5
32.0
87.8
50.4
20.6
52
53
W.3
39.4
68.7
02.4
41.1
85.0
34.6
90.5
53.2
23.5
53
54
16.4
41.6
70.9
04.7
43.4
87.4
37.1
93.1
56.0
26.4
54
55
4618. 5
4743. 7
4873. 1
5007.0
5145. 8
5289. 8
5439. 7
5595. 8
5758. 8
5929.3
55
56
20.5
45.8
75.3
09.3
48.1
92.3
42.2
98.4
61.5
32.2
56
57
22.6
47.9
77.5
11.5
50.5
94.7
44.8
.5601. 1
64.3
35.1
57
58
24.6
50.0
79.7
13.8
52.8
97.2
47.3
03.8
67.1
38.1
58
59
26.7
52.2
81.9
16.1
55.2
99.7
49.9
06.4
69.9
41.0
59
il.
60°
Cl°
02°
68°
64°
65°
66°
6!°
•68°
69°
M.
Page 628]
TABLE 3.
Meridional Parts, or
Increased Latitudes.
Comp.
1
293.465
M.
70°
71°
72°
78°
74°
75°
76°
77°
78°
7»°
M.
5943. 9
6123. 5
6312.5
6512.0
6723. 2
6947. 7
7187. 3
7444.4
7721. 6
8022. 7
1
46.8
26.6
15.8
15.4
26.8
51.6
91.5
48.8
26.4
27.9
1
2
49.7
29.7
19.0
18.9
30.5
55.4
95.6
53.3
1 31.3
33.2
2
3
52.7
32.8
22.3
22.3
34.1
59.3
99.7
57.7
36.1
38.5
3
4
55.6
35.8
25.5
25.7
37.7
63.2
7203. 9
62.2
40.9
43.7
4
5
5958. 5
6138.9
6328. 8
6529.1
6741.4
6967. 1
7208.
7466. 7
7745.8
8049.0
5
6
61.5
42.0
32.0
32.6
45.0
70.9
12.2
71.1
50.6
54.3
6
7
64.4
45.1
35.3
36.0
48.7
74.8
16.4
75.6
55.5
59.6
7
8
67.3
48.2
38.5
39.5
52.3
78.7
20.5
80.1
60.3
64.9
8
9
70.3
51.3
41.8
42.9
56.0
82.6
24.7
84.6
65.2
70.2
9
10
5973. 2
6154. 4
6345.
6546. 4
6759. 7
6986. 5
7228. 9
7489. 1
7770. 1
8075. 5
10
11
76.2
57.5
48.3
49.8
63.3
90.4
33.1
93.6
74.9
80.8
11
12
79.1
60.6
51.6
53.3
67.0
94.3
37.3
98.1
79.8
86.1
12
13
82.1
63.7
54.8
56.7
70.7
98.3
41.5
7502.6
84.7
91.5
13
14
85.0
66.8
58.1
60.2
74.3
7002.2
45.7
07.1
89.6
96.8
14
15
5988.
6169. 9
6361. 4
6563.7
6778.
7006.1
7249. 9
7511. 7
7794. 5
8102. 2
15
16
90.9
73.0
64.7
67.1
81.7
10.0
54.1
16.2
99.4
07.5
16
17
93.9
76.1
67.9
70.6
85.4
14.0
58.3
20.7
7804. 3
12.9
17
18
96.9
79.2
71.2
74.1
89.1
17.9
62.5
25.3
09.3
18.3
18
19
99.8
82.3
74.5
77.6
92.8
21.8
66.7
29.8
14.2
23.7
19
20
6002.8
6185. 5
6377. 8
6581.0
6796. 5
7025. 8
7270. 9
7534.4
7819. 1
8129. 1
20
21
05.8
88.6
81.1
84.5
6800. 2
29.7
75.2
38.9
24.1
34.5
21
22
08.7
91.7
84.4
88.0
03.9
33.7
79.4
43.5
29.0
39.9
22
23
11.7
94.8
87.7
91.5
07.6
37.7
83.7
48.1
34.0
45.3
23
24
14.7
98.0
91.0
95.0
11.3
41.6
87.9
52.7
39.0
50.8
24
25
6017.7
6201.1
6394. 3
6598. 5
6815.
7045.6
7292.2
7557. 3
7844.0
8156. 2
25
26
20.7
04.2
97.6
6602.
18.8
49.6
96.4
61.8
48.9
61.6
26
27
23.6
07.4
6400.9
05.5
22.5
53.5
7300.7
66.4
53.9
67.1
27
28
26.6
10.5
04.3
09.0
26.2
57.5
05.0
71.0
58.9
72.6
28
29
29.6
13.7
07.6
12.5
30.0
61.5
09.2
75.7
63.9
78.0
29
80
6032.6
6216. 8
6410.9
6616.1
6833. 7
7065.5
7313. 5
7580. 3
7868.9
8183.5
30
31
35.6
20.0
14.2
19.6
37.4
69.5
17.8
84.9
74.0
89.0
31
32
38.6
23.1
17.6
23.1
41.2
73.5
22.1
89.5
79.0
94.5
32
33
41.6
26.3
20.9
26.6
44.9
77.5
26.4
94.2
84.0
8200.0
33
34
44.6
29.4
24.2
30.2
48.7
81.5
30.7
98.8
89.1
05.5
34
35
6047.6
6232. 6
6427.6
6633.7
6852. 4
7085.5
7335.0
7603.4
7894. 1
8211. 1
35
36
50.6
35.8
30.9
37.2
56.2
89.5
39.3
08.1
99.2
16.6
36
37
53.6
38.9
34.2
40.8
60.0
93.5
43.6
12.8
7904.2
22.1
37
38
56.6
42.1
37.6
44.3
63.7
97.6
47.9
17.4
09.3
27.7
38
39
59.7
45.3
40.9
47.9
67.5
7101.6
52.3
22.1
14.4
33.3
39
40
6062.7
6248. 4
6444.3
6651.4
6871. 3
7105. 6
7356. 6
7626. 8
7919.4
8238. 8
40
41
65.7
51.6
47.6
55.0
75.1
09.7
60.9
31.4
24.5
44.4
41
42
68.7
54.8
51.0
58.5
78.9
13.7
65.3
36.1
29.6
50.0
42
43
71.7
58.0
54.4
62.1
82.6
17.8
69.6
40.8
34.7
55.6
43
44
74.8
61.2
57.7
65.7
86.4
21.8
74.0
45.5
39.9
61.2
44
45
6077. 8
6264.4
6461. 1
6669. 2
6890. 2
7125. 9
7378. 3
7650. 2
7945.
8266. 8
45
46
80.8
67.6
64.5
72.8
94.0
29.9
82.7
55.0
50.1
72.4
46
47
83.9
70.8
67.8
76.4
97.8
34.0
87.1
59.7
55.2
78.1
47
48
86.9
74.0
71.2
80.0
6901.7
38.1
91.4
64.4
60.4
83.7
48
49
89.9
77.2
74.6
83.5
05.5
42.2
95.8
69.1
65.5
89.3
49
50
6093.0
6280. 4
6478.
6687. 1
6909.3
7146. 2
7400.2
7673.9
7970. 7
8295.0
50
51
96.0
83.6
81.4
90,7
13.1
50.3
04.6
78.6
75.9
8300.7
51
52
99.1
86.8
84.8
94.3
16.9
54.4
09.0
83.4
81.0
06.4
52
53
6102. 1
90.0
88.2
97.9
20.8
58.5
13.4
88.1
86.2
12.0
53
54
05.2
93.2
91.6
6701. 5
24.6
62.6
17.8
92.9
91.4
17.7
54
55
6108. 2
6296.4
6495.0
6705. 1
6928. 4
7166. 7
7422. 2
7697. 7
7996. 6
8323. 4
55
56
11.3
99.6
98.4
08.7
32.3
70.8
26.6
7702. 5
8001.8
29.2
56
57
14.3
6302. 9
6.501. 8
12.4
36.1
75.0
31.1
07.2
07.0
34.9
57
58
17.4
06.1
05.2
16.0
40.0
79.1
35.5
12.0
12.2
40.6
58
59
20.5
09.3
08.6
19.6
43.8
83.2
39.9
16.8
17.5
46.4
59
M.
70°
71"
72°
78°
74°
75°
76°
77°
78°
79°'
M.
TABLE 4.
[Page 629 |
Length of
a Degree in Latitude and
Liongitude.
Degree of Long.
Degree of Lat.
Lat.
Lat.
Naut. miles.
Statute miles.
Meters.
Naut. miles.
Statute miles.
Meters.
o
60.068
69. 172
Ill 321
59. 661
68.704
110 567
o
1
0.059
9.162
1 304
.661
.704
568
1
2
0.031
9.130
1 253
.662
.705
569
2
3
59. 986
9.078
1 169
.663
.706
570
3
4
9.922
9.005
1 051
.664
.708
68. 710
573
4
5
. 59. 840
68.911
110 900
59. 666
110 576
5
6
9.741
8.795
715
.668
.712
580
6
7
9.622
8.660
497
.670
.715
584
7
8
9.487
8.504
245
.673
.718
589
8
9
9.333
8.326
109 959
.676
.721
595
9
10
59. 161
68.129
109 641
59. 680
68. 725
110 601
10
11
8.971
7.910
9 289
.684
.730
608
11
12
8.764
7.670
8 904
.687
.734
616
12
13
8.538
7.410
8 486
.692
.739
624
13
14
8.295
7.131
8 036
.697
.744
633
14
15
58.034
66.830
107 553
59. 702.
68. 751
110 643
15
16
7.756
6.510
7 036
.707
.757
653
16
17
7.459
6.169
6 487
.713
.764
663
17
18
7.146
5.808
5 906
.719
.771
675
18
19
6.816
5.427
5 294
.725
.778
686
19
20
56. 468
65.026
104 649
59. 732
68. 786
110 699
20
21
6.102
4.606
3 972
.739
.794
712
21
22
5.720
4.166
3 264
.746
.802
725
22
23
5.321
3.706
2 524
.754
.811
739
23
24
4.905
3.228
1 754
.761
.820
753
24
25
26
54. 473
4.024
62.729
2.212
100 952
119
59. 769
.777
68.829
.839
110 768
783
25
26
27
3.558
1.676
99 257
.786
.848
799
27
28
3.076
1.122
8 364
.795
.858
815
28
29
2.578
0.548
7 441
.804
.869
832
29
30
52.064
59.956
96 488
59. 813
68. 879
110 849
30
31
1.534
9.345
5 506
.822
.890
866
31
32
0.989
8.716
4 495
.831
.901
883
32
33
0.428
8.071
3 455
.841
.912
901
33
34
49. 851
7.407
2 387
.851
.923
919
34
35
49. 259
56. 725
91 290
59. 861
68. 935
110 938
35
36
8.653
6.027
166
.871
.946
956
36
37
8.031
5.311
89 014
.881
.958
975
37
38
7. 395
4.579
7 835
.891
.969
994
38
39
6.744
3.829
6 629
.902
.981
111 013
39
40
46. 079
53.063
85 396
59.912
68.993
111 033
40
41
» 5.899
2.281
4 137
.923
69.006
052
41
42
, 4.706
1.483
2 853
.933
.018
072
42
43
4.000
0.669
1 543
.944
.030
091
43
44
3.280
49. 840
208
.954
. .042
111
44
45
2.546
8.995
78 849
.965
.054
131
45
Page 630]
TABLE 4.
Length of a Degree in Latitude and Longitude.
Lat.
45
46
47
46
49
50
51
52
53
64
Degree of Long.
Naut. miles. Statute miles.
42. 546
1.801
1.041
0.268
39.484
38. 688
7.880
7.060
6.229
5.386
48.995
8.136
7.261
6.372
5.469
44.552
3.621
2.676
1.719
0.749
Meters.
78 849
7 466
6 058
4 628
3 174
71 698
200
68 680
7 140
5 578
Degree of Lat.'
Naut. miles. Statute miles.
59.965
.976
.987
.997
60. 008
60. 019
.029
.039
.050
.060
69.054
.066
.079
.091
.103
69. 115
.127
.139
.151
.163
Meters.
Ill 131
151
170
190
210
111 229
249
268
287
306
Lat.
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
34. 532
3.668
2.794
1.909
1.015
39. 766
8.771
7.764
6.745
5. 716.
63 996
2 395
774
59 135
7 478
60. 070
.080
.090
.100
.109
9.175
.086
.197
.209
.220
111 325
343
362
380
397
55
56
57
58
59
60
61
62
63
64
30. 110
29.197
8.275
7.344
6.404
34.674
3.623
2.560
1.488
0.406
55 802
4 110
2 400
675
48 934
60. 118
.128
.137
.145
.154
69. 230
.241
.251
.261
.271
111 415
432
448
464
480
60
61
62
63
64
65
66
67
68
25.456
4.501
3.538
2.567
1.590
29. 315
8.215
7.106
5.988
4.862
47 177
5 407
3 622
1 823
012
60.162
.170
.178
.186
.193
69. 281
.290
.299
.308
.316
111 496
511
525
539
553
65
66
67
68
69
70
71
72
73
74
20.606
19. 616
8.619
7.617
6.609
23. 729
2.589
1.441
0.287
19. 127
38 188
6 353
4 506
2 648
781
60.200
.207
.213
.220
.225
69. 324
.332
.340
.347
.354
111 566
578
590
602
613
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
15. 596
4.578
3.556
2.529
1.499
10.465
9.428
8.388
7.345
6.300
17. 960
6.788
5.611
4.428
3.242
12. 051
10. 857
9.659
8.458
7. 255
28 903
7 017
5 123
3 220
1 311
60. 231
.236
.241
.246
.250
69. 360
.366
.372
.377
.382
19 394
7 472
5 545
3 612
1 675
60. 254
.257
.260
.263
.265
.386
.390
.394
.397
.400
111 623
633
642
650
658
111 665
671
677
682
687
75
76
77
78
79
80
81
82
83
84
85
5.253
86
4.205
87
3.154
88
2.103
89
1.052
90
6.049
4.842
3.632
2.422
1.211
o'
9 735
7 792
5 846
3 898
1 949
60.268
.269
.270
.271
.272
.272
.402
.404
.405
.407
.407
.407
111 691
694
696
698
699
699
85
86
87
88
89
90
TABLE 5A.
[Pag
e631
Distance of an Object by Two Bearings.
Difference
between
the course
Difference between the course and first bearing, in points.
and second
bearing, in
points.
2
2^
S'A
2K
3
»y^
85^ I
3
1.96
1.09
3i
1.57
0.94
2.19
1.31
3
1.32
0.84
1.76
1.12
2.42
1.53
3|
1.14
0.76
1.47
0.99
1.94
1.30
2.64
1.77
4
1.00
0.71
1.27
0.90
1.62
1.15
2.12
1.50
2.85
2.01
4i
0.90
0.66
1.12
0.83
1.40
1.04
1.77
1.31
2.29
1.69
3.05
2.26
4J
0.81
0.63
1.00
0.77
1.23
0.95
1.53
1.18
1.91
1.48
2.45
1.90
3.25
2.51
4i
0.74
0.60
0.91
0.73
1.10
0.89
1.34
1.08
1.65
1.32
2.05
1.65
2.61
2.10
5
0.69
0.57
0.83
0.69
1.00
0.83
1.20
1.00
1.45
1.21
1.77
1.47
2.19
1.82
5i
0.64
0.55
0.77
0.66
0.92
0.79
1.09
0.94
1.30
1.11
1.56
1.34
1.88
1.62
5J
0.60
0.53
0.72
0.63
0.85
0.75
1.00
0.88
1.18
1.04
1.39
1.23
1.66
1.46
5}
0.57
0.52
0.68
0.61
0.79
0.72
0.93
0.84
1.08
0.98
1.26 : 1.14
1.48
1.34
6
0.54
0.50
0.64
0.59
0.74
0.69
0.86
0.80
1.00
0.92
1.16
1.07
1.35
1.24
6i
0.52
0.49
0.60
0.57
0.70
0.66
0.81
0.76
0.93
0.88
1.07
1.01
1.23
1.16
6i
0.50
0.47
0.58
0.55
0.67
0.64
0.77
0.73
0.88
0.84
1.00
0.96
1.14
1.09
6|
0.48
0.46
0.55
0.54
0.64
0.62
0.73
0.71
0.83
0.80
0.94
0.91
1.06
1.03
7
0.46
0.45
0.53
0.52
0.61
0.60
0.69
0.68
0.79
0.77
0.89
0.87
1.00
0.98
7i
0.45
0.44
0.51
0.51
0.59
0.58
0.67
0.66
0.75
0.74
0.84
0.83
0.94
0.93
7i
0.43
0.43
0.50
0.50
0.57
0.56
0.64
0.64
0.72
0.72
0.80
0.80
0.90
0.89
7J
0.42
0.42
0.48
0.48
0.55
0. 55
0.62
0.62
0.69
0.69
0.77
0.77
0.86
0.86
8
0.41
0.41
0.47
0.47
0.53
0.53
0.60
0.60
0.67
0.67
0.74
0.74
0.82
0.82
8i
0.41
0.41
0.46
0.46
0.52
0.52
0.58
0.58
0.65
0.65
0.72
0.72
0.79
0.79
8i
0.40
0.40
0.45
0.45
0.51
0.51
0.57
0.57
0.63
0.63
0.69
0.69
0.76
0.76
8J
0,39
0.39
0.45
0.44
0.50
0.50
0.56
0.55
0.61
0.61
0.68
0.67
0.74
0.73
9
0.39
0.38
0.44
0.43
0.49
0.48
0.55
0.54
0.60
0.59
0.66
0.65
0.72
0.71
9i
0.39
0.38
0.44
0.42
0.49
0.47
0.54
0.52
0.59
0.57
0.64
0.63
0.70
0.68
9i
0.38
0.37
0.43
0.41
0.48
0.46
0.53
0.51
0.58
0.56
0.63 : 0.61
0.69
0.66
9i
0.38
0.36
0.43
0.40
0.48
0.45
0..52
0.49
0.57
0.54
0.62 I 0.59
0.67
0.63
10
0.38
0.35
0.43
0.40
0.47
0.44
0..52
0.48
0.57
0.52
0.61 ; 0.57
0.66
0.61
lot
0.38
0.35
0.43
0.39
0.47
0.43
0.52
0.47
0.56
0.51
0.61 1 0.55
0.65
0.59
lOJ
0.38
0.34
0.43
0.38
0.47
0.42
0.51
0.45
0.56
0.49
0.60 ; 0.53
0.65
0.57
lOi
0.39
0.33
0.43
0.37
0.47
0.40
0.51
0.44
0.56
0.48
0.60 i 0.51
0.64
0.55
11
0.39
0.32
0.43
0.36
0.47
0.39
0.51
0.43
0.56
0.46
0.60 : 0.50
0.64
0.53
lit
0.39
0.31
0.44
0.35
0.48
0.38
0.52
0.41
0.56
0.45
0. 60 0. 48
0.64
0.51
llj
0.40
0.31
0.44
0..34
0.48
0.37
0.52
0.40
0.56
0.43
0.60
0.46
0.63
0.49
llj
0.41
0.30
0.45
0.33
0.49
0.36
0.52
0..39
0.56
0.42
0.60
0.44
0.64
0.47
12
0.41
0.29
0.45
0.32
0.49
0. 35
0.53
0.37
0.57
0.10
0.60
0.43
0.64
0.45
m
0.42
0.28
0.46
0.31
0.50
0.34
0.54
0.36
0.57
0.38
0.61
0.41
0.64
0.42
12J
0.43
0.28
0.47
0.30
0.51
0.32
0. 55
0.35
0.58
0.37
0.61
0.39
0.65
0.41
12i
0.45
0.27
0.48
0.29
0.52
0.31
0.56
0.33
0.59
0.35
0.62
0.37
0.65
0.39
13
0.46
0.26
0.50
0.28
0.53
0.30
0.57
0.32
0.60
0.33
0.63
0.35
0.66
0.37
13}
0.48
0.24
0.51
0.26
0.55
0.28
0.58
0.30
0.61
0.32
0.64
0.33
0.67
0.35
13i
0.50
0.23
0.53
0.25
0.57
0.27
0.60
0.28
0.63
0.30
0.66
0.31
0.69
0.32
13J
0.52
0.22
0. 55
0.24
0.59
0.25
0.62
0.26
0. 65
0. 28 0. 68
0.29
0.70
0.30
14
0.54
0.21 0.58
0.22
0.61
0.23
0.64
0.24
0.67
0. 26 0. 69
0.27
0.72
0.28
Page
B32] TABLE
5A.
Distance of an Object by Two Bearings.
Difference
between
the course
Difference between the course and first bearing, in points.
and second
bearing, in
points.
SH
4
*M.
4M
4K
5
w, 1
4|
3.44
2.76
5
2.76
2.30
3.62
3.01
5i
2.31.
1.98
2.91
2.50
3.80
3.26
5J
1.99
1.76
2.44
2.15
3.05
2.69
3.96
3.49
5}
1.75
1.59
2.10
1.90
2.55
2.31
3.18
2.88
4.12
3.72
6
1.57
1.45
1.85
1.71
2.20
2.03
2.66
2.46
3.31
3.05
4.26
3.94
6i
1.42
1.34
1.65
1.56
1.94
1.82
2.29
2.16
2.77
2.61
^.f.
3.22
4.40
4.14
«i
1.31
1.25
1.50
1.44
1.73
1.66
2.02
1.93
2.38
2.28
2.74
3.53
3.38
6f
1.21
1.17
1.38
1.33
1.57
1.52
1.81
1.75
2.10
2.04
2.47
2.39
2.95
2.87
7
1.13
1.11
1.27
1.25
1.44
1.41
1.64
1.61
1.88
1.84
2.17
2.13
2.55
2.50
n
1.06
1.05
1.19
1.17
1.33
1.32
1.50
1.49
1.70
1.69
1.94
1.92
2.24
2.22
7J
1.00
1.00
1.11
1.11
1.24
1.24
1.39
1.38
1.56
1.55
1.76
1.76
2.01
2.00
7|
0.95
0.95
1.05
1.05
1.17
1.17
1.30
1.30
1.45
1.44
1.62
1. 62
1.82
1.82
8
0.91
0.91
1.00
1.00
1.10
1.10
1.22
1.22
1.35
1.35
1.50
1.50
1.67
1.67
81-
0.87
0.87
0.95
0.95
1.05
1.05
1.15
1.15
1.27
1.26
1.40
1.39
1.54
1.54
8J
0.84
0.83
0.91
0.91
1.00
1.00
1.09
1.09
1.20
1.19
1.31
1.30
1.44
1.43
8f
0.81
0.80
0.88
0.87
0.96
0.95
1.04
1.03
1.14
1.12
1.24
1.22
1.35
1.34
9
0.78
0.77
0.85
0.83
0.92
0.90
1.00
0.98
1.08
1.06
1.18
1.15
1.28
1.25
9i
0.76
0.74
0.82
0.80
0.89
0.86
0.96
0.93
1.04
1.01
1.12
1.09
1.21
1.18
9J
0.74
0.71
0.80
0.77
0.86
0.83
0.93
0.89
1.00
0.96
1.08
1.03
1.16
1.11
9i
0.73
0.68
0.78
0.74
0.84
0.79
0.90
0.85
0.97
0.91
1.04
0.97
1.11
1.04
10
0.71
0.66
0.77
0.71
0.82
0.76
0.88
0.81
0.94
0.87
1.00
0.92
1.07
0.99
10}
0.70
0.63
0.75
0.68
0.80
0.72
0.86
0.77
0.91
0.82
0.97
0.88
1.03
0.93
lOi
0.69
0.61
0.74
0.65
0.79
0.69
0.84
0.74
0.89
0.78
0.94
0.83
1.00
0.88
10}
0.68
0.59
0.73
0.63
0.77
0.66
0.82
0.70
0.87
0.75
0.92
0.79
0.97
0.83
11
0.68
0.56
0.72
0.60
0.76
0.64
0.81
0.67
0.85
0.71
0.90
0.75
0.95
0.79
Hi
0.67
0.54
0.71
0.57
0.76
0.61
0.80
0.64
0.84
0.67
0.88
0.71
0.93
0.75
Hi
0.67
0.52
0.71
0.55
0.75
0.58
0.79
0.61
0.83
0.64
0.87
0.67
0.91
0.70
11}
0.67
0.50
0.71
0.52
0.74
0.55
0.78
0.58
0.82
0.61
0.86
0.64
0.90
0.66
12
0.67
0.48
0.71
0.50
0.74
0.52
0.78
0.55
0.81
0.57
0.85
0.60
0.88
0.63
12}
0.67
0.45
0.71
0.48
0.74
0.50
0.77
0.52
0.81
0.54
0.84
0.56
0.87
0.59
12i
0.68
0.43
0.71
0.45
0.74
0.47
0.77
0.49
0.80
0.51
0.84
0.53
0.87
0.55
12|
0.68
0.41
0.71
0.43
0.74
0.44
0.77
0.46
0.80
0.48
0.83
0.50
0.86
0.51
13
0.69
0.38
0.72
0.40
0.75
0.42
0.78
0.43
0.80
0.45
0.83
0.46
0.86
0.48
13}
0.70
0.36
0.73
0.37
0.76
0.39
0.78
0.40
0.81
0.41
0.83
0.43
0.86
0.44
13i
0.71
0.34
0.74
0.35
0.76
0.36
0.79
0.37
0.81
0.38
0.84
0.39
0.86
0.41
13}
0.73
0.31
0.75
0.32
0.77
0.33
0.80
0.34
0.82
0.35
0.84
0.36
0.86
0.37
14
.0.74
0.28
0.77
0.29
0.79
0.30
0.81
0.31
0.83
0.32
0.85
0.32
0.87
0.33
5^
5Ji
6
65i
6%
6K
' 1
6J
4.52
4.33
6}
3.63
3.52
4.63
4.49
7
3.04
2.98
3.72
3.65
4.74
4.64
7}
2.62
2.59
3.11
3.08
3.80
3.76
4.83
4.77
7J
2.30
2.29
2.68
2.67
3.18
3.17
3.87
3.86
4.91
4.88
7}
2.06
2.06
2.36
2.36
2.74
2.74
3.24
3.24
3.94
3.93
4.97
4.97
8
1.87
1.87
2.11
2.11
2.41
2.41
2.79
2.79
3.30
3.30
3.99
3.99
5.03
5.03
8}
1.72
1.71
1.92
1.92
2.16
2.16
2.46
2.46
2.84
2.84
3.34
3.34
4.04
4.03
8J
1.59
1.58
1.76
1.75
1.96
1.95
2.20
2.19
2.50
2.49
2.88
2.87
3.38
3.36
8}
1.48
1.46
1.63
1.61
1.80
1.78
2.00
1.98
2.24
2.21
2.53
2.51
2.91
2.88
9
1.39
1.36
1.52
1.49
1.66
1.63
1.83
1.80
2.03
1.99
2.27
2.23
2.56
2.51
9}
1.31
1.27
1.42
1.38
1.55
1.50
1.69
1.64
1.86
1.81
2.06
2.00
2.29
2.23
9i
1.25
1.19
1.35
1.29
1.46
1.39
1.58
1.51
1.72
1.65
1.89
1.81
2.08
1.99
91
1.19
1.12
1.28
1.20
1.38
1.30
1.48
1.40
1.61
1.51
1.75
1.64
1.91
1.80
10
1.14
1.05
1.22
1.13
1.31
1.21
1.40
1.30
1.51
1.39
1.62
1.50
1.77
1.63
10}
1.10
0.99
1.17
1.06
1.25
1.13
1.33
1.20
1.42
1.29
1.53
1.38
1.65
1.49
lOJ
1.06
0.94
1.13
0.99
1.20
1.05
1.27
1.12
1.35
1.19
1.44
1.27
1.55
1.36
lOf
1.03
0.88
1.09
0.93
1.15
0.99
1.22
1.04
1.29
1.11
1.37
1.18
1.46
1.25
11
1.00
0.83
1.05
0.88
1.11
0.92
1.17
0.97
1.24
1.03
1.31
1.09
1.39
1.15
11}
0.98
0.78
1.03
0.82
1.08
0.87
1.13
0.91
1.19
0.96
1.25
1.01
1.32
1.06
llj
0.95
0.73
1.00
0.77
1.05
0.81
1.10
0.85
1.15
0.89
1.21
0.93
1.27
0.98
11}
0.94
0.69
0.98
0.72
1.02
0.76
1.07
0.79
1.12
0.83
1.17
0.86
1.22
0.90
12
0.92
0.65
0.96
0.68
1.00
0.71
1.04
0.73
1.09
0.77
1.13
0.80
1.18
0.83
12}
0.91
0.61
0.94
0.63
0.98
0.66
1.02
0.68
1.06
0.71
1.10
0.74
1.14
0.77
12i
0.90
0.57
0.93
0.59
0.97
0.61
1.00
0.63
1.04
0.66
1.07
0.68
1.11
0.71
12}
0.89
0.53
0.92
0.55
0.95
0.57
0.98
0.59
1.02
0.61
1.05
0.63
1.08
0.65
13
0.89
0.49
0.91
0.51
0.94
0.52
0.97
0.54
1.00
0.56
1.03
0.57
1.06
0.59
13}
0.88
0.45
0.91
0.47
0.93
0.48
0.96
0.49
0.99
0.51
1.01
0.52
1.04
0.54
13J
0.88
0.42
0.91
0.43
0.93
0.44
0.95
0.45
0.98
0.46
1.00
0.47
1.02
0.48
13}
0.88
0.38
0.90
0.39
0.92
0.40
0.95
0.41
0.97
0.41
0.99
0.42
1.01
0.43
ii
n BQ
n 9A
n a^
n rtK
n QO
n 'X^
n Qj.
n Qft
n Qfi
(\ 37
n Q8
n .S8
1 n(>
n .'^a
TABLE 5A. [Page 638
Distance of an Object by Two Bearings.
Difference
between
Difference between the course and first bearing, in points.
the course
and second
bearing, in
points.
7}i
■•%
m
8
SH
8}i
m
9
»i
5.07
5.06
8i
4.07
4.05
5.10
5.08
8i
3.41
3.37
4.10
4.06
5.12
5.06
9
2.94
2.88
3.43
3.36
4.11
4.03
5.13
5.03
9i
2..58
2.51
2.95
2.87
3.44
3.34
4.12
3.39
5.12
4.97
^
2.31
2.21
2.60
2.49
2.96
2.84
3.44
3.30
4.11
3.93
5.10
4.88
9i
10
2.10
1.98
2.33
"2.19
2.61
2.46
2.97
2.79
3.44
3.24
4.10
3.86
5.07
4.77
1.92
1.78
2.11
1.95
2.34
2.16
2.61
2.41
2.96
2.74
3.43
3.17
4.07
3.76
5.03
4.64
lOJ
1.78
1.61
1.93
1.75
2.12
1.92
2.34
2.11
2.61
2.36
2.95
2.67
3.41
3.08
4.04
3.65
lOJ
1.66
1.46
1.79
1.58
1.94
1.71
2.12
1.87
2.34
2.06
2.60
2.29
2.94
2.59
3.38
2.98
10|
1.56
1.34
1.67
1.43
1.80
1.54
L95
1.67
2.12
1.82
2.33
2.00
2.58
2.22
2.91
2.50
11
1.47
1.22
1.57
1.30
1.68
1.39
1.80
1.50
1.94
1.62
2.11
1.76
2.31
1.92
2.56
2.13
Hi
1.40
1.12
1.48
1.19
1.57
1.26
1.68
l.,35
1.80
1.44
1.93
1.55
2.10
1.69
2.29
1.84
llj
1.34
1.03
1.41
1.09
1.49
1.15
1.58
1.22
1.68
1.30
1.79
1.38
1.92
1.49
2.08
1.61
111
1.28
0.95
1.34
1.00
1.41
1.05
1.49
LIO
1.57
1.17
1.67
1.24
1.78
1.32
1.91
1.41
12
1.23
0.87
1.29
0.91
1.35
0.95
1.41
1.00
1.49
1.05
1.57
1.11
1.66
1.17
1.77
1.25
12i
1.19
0.80
1.24
0.83
1.29
0.87
1.35
0.91
1.41
0.95
1.48
1.00
1.56
1.05
1.65
1.11
12J
1.15
0.73
1.20
0.76
1.24
0.79
1.29
0.82
1.35
0.86
1.41
0.89
1.47
0.93
1.55
0.98
12}
1.12
0.67
1.16
0.69
1.20
0.72
1.25
0.74
1.29
0.77
1.34
0.80
1.40
0.83
1.46
0.87
13
1.09
0.61
1.13
0.63
1.16
0.65
1.20
0.67
1.24
0.69
1.29
0.72
1.34
0.74
1.39
0.77
13i
1.07
0.55
1.10
0.57
1.13
0.58
1.17
0.60
1.20
0.62
1.24
0.64
1.28
0.66
1.32
0.68
13J
1.05
0..50
1.08
0.51
1.10
0.52
1.13
0.53
1.16
0.55
1.20
0.-56
1.23
0.58
1.27
0.60
13J
1.03
0.44
1.06
0.45
1.08
0.46
1.11
0.47
1.13
0.48
1.16
0.50
1.19
0.51
1.22
0.52
14
1.02
0.39
1.04
0.40
1.06
0.41
1.08
0.41
1.10
0.42
1.13
0.43
1.15
0.44
1.18
0.45
»'/
9;^
»K
10
lO'A
105^
lOK
" 1
lOi
4.97
4.50
•
lOJ
3.99
3.52
4.91
4.33
10|
3.34
2.87
3.94
3.38
4.83
4.14
11
2.88
2.39
3.30
2.74
3.87
3.22
4.74
3.94
m
2.53
2.04
2.84
2.28
3.24
2.61
3.80
3.05
4.63
3.72
lu
2.27
1.75
2.50
1.93
2.79
2.16
.3.18
2.46
3.72
2.88
4.52
3.49
11}
2.06
1..52
2.24
1.66
2.46
1.82
2.74
2.03
3.11
2.31
3.63
2.69
4.40
3.20
12
1.89
1.33
2.03
1.44
2.20
1.56
2.41
1.71
2.68
1.90
3.04
2.15
3.53
2.50
4.26
3.01
12}
1.75
1.18
1.86
1.25
2.00
1.34
2.16
1.45
2.36
1.59
2.62
1.76
2.95
1.98
3.42
2.30
12i
1.62
1.03
1.72
1.09
1.83
1.16
1.96
1.24
2.11
1.34
2.30
1.46
2.55
1.62
2.86
1.82
12}
1.53
0.91
1.61
0.96
1.69
1.01
1.80
1.07
1.92
1.14
2.06
1.23
2.24
1.34
2.47
1.47
13
1.44
0.80
1.51
0.84
1.58
0.88
1.66
0.92
1.76
0.98
1.87
1.04
2.01
1.11
2.17
1.21
13i
1.37
0.71
1.42
0.73
1.48
0.76
1.55
0.80
1.63
0.84
1.72
0.88
1.82
0.94
1.94
1.00
13J
1.31
0.62
1..35 : 0.64
1.40
0.66
1.46
0.69
1.52
0.72
1.59
0.75
1.67
0.79
1.76
0.83
13}
1.25
0.54
1.29 i 0.55
1.33
0.57
1.38
0..59
1.42
0.61
1.48
0.63
1.54
0.66
1.62
0.69
14
1.21
0.46
1.24 0.47
1.27
0.49
1.31
0..50
1..S5
0.52
1..39
0.53
1.44
0.55
1.50
0.57
llJi
115^
"K
12
UH
is^
liH
18 1
12i
4.12
2.77
12i
3.31
2.10
3.96
2.51
12}
2.77
1.65
3.18
1.90
3.80
2.26
13
2.38
1.32
2.66
1.48
3.05
1.69
3.62
2.01
13}
2.10
1.08
2.29
1.18
2.55
1.31
2.91
1.50
3.44
1.77
13J
1.88
0.89
2.02
0.95
2.20
1.04
2.44
1.15
2.76
1.30
3.25
1.53
13}
1.70
0.73
1.81
0.77
1.94
0.83
2.10
0.90
2.31
0.99
2.61
1.12
3.05
1.31
14
1.56
0.60
1.64
0.63
1.73
0.66
1.85
0.71
1.99
0.76
2.19
0.84
2.45
0.94
2.85
1.09
Page 634]
TABLE 6B.
Distance
of an Object by Two Bearings.
Difference
between
the course
and second
bearing.
Difference between the course and first bearing.
20°
22°
24°
26°
28°
so°
a
2°
30°
1.97
0.98
32
1.64
0.87
2.16
1.14
34
1.41
0.79
1.80
1.01
2.34
1.31
36
1.24
0.73
1.55
0.91
1.96
1.15
2.52
1.48
38
1.11
0.68
1.36
0.84
1.68
1.04
2.11
1.30
2.70
1.66
40
1.00
0.64
1.21
0.78
1.48
0.95
1.81
1.16
2.26
1.45
2.88
1.85
42
0.91
0.61
1.10
0.73
1.32
0.88
1.59
1.06
1.94
1.30
2.40
1.61
3.05
2.04
44
0.84
0.58
1.00
0.69
1.19
0.83
1.42
0.98
1.70
1.18
2.07
1.44
2.55
1.77
46
0.78
0.56
0.92
0.66
1.09
0.78
1.28
0.92
1.52
1.09
1.81
1.30
2.19
1.58
48
0.73
0.54
0.85
0.64
1.00
0.74
1.17
0.87
1.37
1.02
1.62
1.20
1.92
1.43
50
0. 68 0. 52
0.80
0.61
0.93
0.71
1.08
0.83
1.25
0.96
1.46
1.12
1.71
1.31
52
0.65 0.51
0.75
0.59
0.87
0.68
1.00
0.79
1.15
0.91
1.33
1.05
1.55
1.22
54
0.61 0.49
0.71
0.57
0.81
0.66
0.93
0.76
1.07
0.87
1.23
0.99
1.41
1.14
56
0.58 0.48
0.67
0.56
0.77
0.64
0.88
0.73
1.00
0.83
1.14
0.95
1.30
1.08
58
0. 56 0. 47
0.64
0.54
0.73
0.62
0.83
0.70
0.94
0.80
1.07
0.90
1.21
1.03
60
0.53 0.46
0.61
0.53
0.69
0.60
0.78
0.68
0.89
0.77
1.00
0.87
1.13
0.98
62
0. 51 0. 45
0.58
0.51
0.66
0.58
0.75
0.66
0.84
0.74
0.94
0.83
1.06
0.94
64
0.49 0.44
0.56
0.50
0.63
0.57
0.71
0.64
0.80
0.72
0.89
0.80
1.00
0.90
66
0.48:0.43
0.54
0.49
0.61
0.56
0.68
0.62
0.76
0.70
0.85
0.78
0. 95
0.87
68
0. 46 0. 43
0.52
0.48
0.59
0.54
0.66
0.61
0.73
0.68
0.81
0.75
0.90
0.84
70
0.45 0.42
0.50
0.47
0.57
0.53
0.63
0.59
0.70
0.66
0.78
0.73
0.86
0.81
72
0. 43 0. 41
0.49
0.47
0.55
0.52
0.61
0.58
0.68
0.64
0.75
0.71
0.82
0.78
74
0. 42 i 0. 41
0.48
0.46
0.53
0.51
0.59
0.57
0.65
0.63
0.72
0.69
0.79
0.76
76
0. 41 ! 0. 40
0.46
0.45
0.52
0.50
0.57
0.56
0.63
0.61
0.70
0.67
0.76
0.74
78
0. 40 0. 39
0.45
0.44
0.50
0.49
0.56
0.54
0.61
0.60
0.67
0.66
0.74
0.72
80
0. 39 0. 39
0.44
0.44
0.49
0.48
0.54
0. 53
0.60
0.59
0.65
0.64
0.71
0.70
82
0. 39 i 0. 38
0.43
0.43
0.48
0.47
0.53
0.52
0.58
0..57
0.63
0.63
0.69
0.69
84
0.38-0.38
0.42
0.42
0.47
0.47
0.52
0.51
0.57
0.56
0.62
0.61
0.67
0.67
86
0.37
0.37
0.42
0.42
0.46
0.46
0.51
0.51
0.55
0.55
0.60
0.60
0.66
0.65
88
0.37
0.37
0.41
0.41
0.45
0.45
0.50
0.50
0.54
0.54
0.59
0.59
0.64
0.64
90
0.36
0.36
0.40
0.40
0.45
0.45
0.49
0.49
0.53
0.53
0.58
0.58
0.62
0.62
92
0.36
0.36
0.40
0.40
0.44
0.44
0.48
0.48
0.52
0.52
0.57
0.57
0.61
0.61
94
0.36
0. 35
0.39
0.39
0.43
0.43
0.47
0.47
0.51
0.51
0.56
0.55
0.60
0.60
96
0.35
0.35
0.39
0.39
0.43
0.43
0.47
0.46
0.51
0.50
0.55
0.54
0.59
0.59
98
0.35
0.35
0.39
0.38
0.42
0.42
0.46
0.46
0.50
0.50
0.54
0.53
0.58
0.57
100
0.35
0.34
0.38
0.38
0.42
0.41
0.46
0.45
0.49
0.49
0.53
0.52
0.57
0.56
102
0.35
0.34
0.38
0.37
0.42
0.41
0.45
0.44
0.49
0.48
0.53
0.51
0.56
0.55
104
0.34
0.33
0.38
0.37
0.41
0.40
0.45
0.43
0.48
0.47
0.52
0.50
0.56
0.54
106
0.34
0.33
0.38
0.36
0.41
0.39
0.45
0.43
0.48
0.46
0.52
0.50
0.55
0.53
108
0.34
0.32
0.38
0.36
0.41
0.39
0.44
0.42
0.48
0.45
0.51
0.49
0.55
0.52
110
0.34
0.32
0.37
0.35
0.41
0.38
0.44
0.41
0.47
0.44
0.51
0.48
0.54
0.51
112
0.34
0.32
0.37
0.35
0.41
0.38
0.44
0.41
0.47
0.44
0.50
0.47
0.54
0.50
114
0.34
0.31
0.37
0.34
0.41
0.37
0.44
0.40
0.47
0.43
0.50
0.46
0.54
0.49
116
0.34
0.31
0.38
0.34
0.41
0.37
0.44
0.39
0.47
0.42
0.50
0.45
0.53
0.48
118
0.35
0.31
0.38
0.33
0.41
0.36
0.44
0.39
0.47
0.41
0.50
0.44
0.53
0.47
120
0.35
0.30
0.38
0.33
0.41
0.36
0.44
0.38
0.47
0.41
0.50
0.43
0.53
0.46
122
0.35
0.30
0.38
0.32
0.41
0.35
0.44
0.37
0.47
0.40
0.50
0.42
0.53
0.46
124
0.35
0.29
0.38
0.32
0.41
0.34
0.44
0.37
0.47
0.39
0.50
0.42
0.53
0.44
126
0.36
0.29
0.39
0.31
0.42
0.34
0.45
0.36
0.47
0.38
0.50
0.41
0.53
0.43
128
0.36
0.28
0.39
0.31
0.42
0.33
0.45
0.35
0.48
0.38
0.50
0.40
0.53
0.42
130
0.36
0.28
0.39
0.30
0.42
0.32
0.45
0.35
0.48
0.37
0.51
0.39
0.54
0.41
132
0.37
0.27
0.40
0.30
0.43
0.32
0.46
0.34
0.48
0.36
0.51
0.38
0.54
0.40
134
0.37
0.27
0.40
0.29
0.43
0.31
0.46
0.33
0.49
0.35
0.52
0.37
0.54
0.39
136
0.38
0.26
0.41
0.28
0.44
0.30
0.47
0.32
0.49
0.34
0.52
0.36
0.55
0.38
138
0.39
0.26
0.42
0.28
0.45
0.30
0.47
0.32
0.50
0.33
0.53
0.35
0.55
0.37
140.
0.39
0.25
0.42
0.27
0.45
0.29
0.48
0.31
0.51
0.33
0.53
0.34
0.56
0.36
142
0.40
0.25
0.43
0.27
0.46
0.28
0.49
0.30
0. 51
0.32
0.54
0.33
0.56
0.35
144
0.41
0.24
0.44
0.26
0.47
0.28
0.50
0.29
0.52
0.31
0.55
0.32
0.57
0.34
146
0.42
0.24
0.45
0.25
0.48
0.27
0.51
0.28
0.53
0.30
0.56
0.31
0.58
0.32
148
0.43
23
0.46
0.25
0.49
0.26
0.52
0.27
0.54
0.29
0.57
0.30
0.59
0.31
150
0.45
0.22
0.48
0.24
0.50
0.25
0.53
0.26
0.55
0.28
0.58
0.29
0.60
0.30
152
0.46
0.22
0.49
0.23
0.52
0.24
0.54
0.25
0.57
0.27
0.59
0.28
0.61
0.29
154
0.48
0.21
0.50
0.22
0.53
0.23
0.56
0.24
0.58
0.25
0.60
26
0.62
0.27
156
0.49
0.20
0.52
0.21
0.55
0.22
0.57
0.23
0.60
0.24
0.62
25
0.64
0.26
158
0.51
0.19
0.54
0.20
0.57
0.21
0.59
0.22
0.61
0.23
0.63
0.24
0.66
0.25
160
0.53
0.18
0.56
0.19
0.59
0.20
0.61
0.21
0.63
0.22
0.65
0.22
0.67
0.23
TABLE 5B. [Page 635 |
Distance of an Object by Two Bearings.
Diflerence
Difference between the course and first bearing.
between
the course
ind second
84°
86°
88°
40°
4«°
44°
46° 1
bearing.
44°
3.22
2.24
46
2.69
1.93
3.39
2.43
48
2.31
1.72
2.83
2.10
3.65
2.63
50
2.03
1.55
2.43
1.86
2.96
2.27
3.70
2.84
52
1.81
1.43
2.13
1.68
2.54
2.01
3.09
2.44
3.85
3.04
54
1.63 1.32
1.90
1.54
2.23
1.81
2.66
2.16
3.22
2.60
4.00
3.24
56
1.49
1.24
1.72
1.42
1.99
1.66
2.33
1.93
2.77
2.29
3.34
2.77
4.14
3.43
58
1.37
1.17
1.57
1.33
1.80
1.53
2.08
1.76
2.43
2.06
2.87
2.44
3.46
2.93
60
1.28
1.10
1.45
1.25
1.64
1.42
1.88
1.63
2.17
1.88
2.62
2.18
2.97
2.57
62
1.19
1.05
1.34
1.18
1.51
1.34
1.72
1.62
1.96
1.73
2.25
1.98
2.61
2.30
64
1.12
1.01
1.25
1.13
1.40 1.26
1.58
1.42
1.79
1.61
2.03
1.83
2.33
2.09
66
1.06
0.96
1.18
1.07
1.31
1.20
1.47
1.34
1.66
1.51
1.85
1.69
2.10
1.92
68
1.00
0.93
1.11
1.03
1.23
1.14
1.37
1.27
1.63
1.42
1.71
1.68
1.92
1.78
70
0.95 0.89
1.05
0.99
1.16
1.09
1.29
1.21
1.43
1.34
1.58
1.49
1.77
1.66
72
0. 91 i 0. 86
1.00
0.95
1.10
i.a5
1.21
1.15
1.34
1.27
1.48
1.41
1.64
1.66
74
0.87
0.84
0.95
0.92
1.05
1.01
1.15
1.10
1.26
1.21
1.39
1.34
1.53
1.47
76
0.84
0.81
0.91
0.89
1.00
0.97
1.09
1.06
1.20
1.16
1.31
1.27
1.44
1.40
78
0.80
0.79
0.88
0.86
0.96
0.94
1.04
1.02
1.14
1.11
1.24
1.22
1.36
1.33
80
0.78
0.77
0.85
0.83
0.92
0.91
1.00
0.98
1.09
1.07
1.18
1.16
1.28
1.27
82
0.75
0.75
0.82
0.81
0.89
0.88
0.96
0.95
1.04
1.03
1.13
1.12
1.22
1.21
84
0.73
0.73
0.79
0.79
0.86
0.85
0.93
0.92
1.00
0.99
1.08
1.07
1.17
1.16
86
0.71
0.71
0.77
0.77
0.83
0.83
0.89
0.89
0.96
0.96
1.04
1.04
1.12
1.12
88
0.69
0.69
0.75
0.76
0.80
0.80
0.86
0.86
0.93
0.93
1.00
1.00
1.08
1.07
90
0.67
0.67
0.73
0.73
0.78
0.78
0.84
0.84
0.90
0.90
0.97
0.97
1.04
1.04
92
0.66
0.66
0.71
0.71
0.76
0.76
0.82
0.82
0.87
0.87
0.93
0.93
1.00
1.00
94
0.66
0.64
0.69
0.69
0.74
0.74
0.79
0.79
0.85
0.86
0.91
0.90
0.97
0.97
96
0.63
0.63
0.68
0.67
0.73
0.72
■0.78
0.77
0.83
0.82
0.88
0.88
0.94
0.93
98
0.62
0.62
0.67
0.66
0.71
0.70
0.76
0.75
0.81
0.80
0.86
0.85
0.91
0.90
100
0.61
0.60
0.65
0.64
0.70
0.69
0.74
0.73
0.79
0.78
0.84
0.83
0.89
0.88
102
0.60
0.59
0.64
0.63
0.68
0.67
0.73
0.71
0.77
0.76
0.82
0.80
0.87
0.85
104
0.60
0.58
0.63
0.61
0.67
0. 65
0.72
0.69
0.76
0.74
0.80
0.78
0.85
0.82
106
0.59
0.57
0.63
0.60
0.66
0.64
0.70
0.68
0.74
0.72
0.79
0.76
0.83
0.80
108
0. 58 : 0. 55.
0.62
0.59
0.66
0.62
0.69
0.66
0.73
0.70
0.77
0.74
0.81
0.77
110
0. 58 ! 0. 54
0.61
0.57
0.65
0.61
0.68
0.64
0.72
0.68
0.76
0.71
0.80
0.75
112
0.57
0. 53
0.61
0.56
0.64
0.59
0.68
0.63
0.71
0.66
0.76
0.69
0.79
0.73
114
0.57
0.52
0.60
0.66
0.63
0.68
0.67
0.61
0.70
0.64
0.74
0.68
0.78
0.71
116
0.56
0.51
0.60
0.64
0.63
0.57
0.66
0.60
0.70
0.63
0.73
0. 66
0.77
0.69
118
0.56
0.50
0.59
0.52
0.63
0.55
0.66
0.58
0.69
0.61
0.72
0.64
0.76
0.67
120
0.56
0.49
0.59
0.51
0.62
0. 54
0.65
0.67
0.68
0.59
0.72
0.62
0.75
0.66
122
0.56
0.47
0.59
0.50
0.62
0. 53
0.65
0.55
0.68
0.58
0.71
a. 60
0.74
0.63
124
0.56
0.46
0.59
0.49
0.62
0.51
0.65
0.54
0.68
0.66
0.71
0.58
0.74
0.61
126
0.56
0.45
0.59
0.48
0.62
0.50
0.64
0.52
0.67
0.54
0.70
0.57
0.73
0.59
128
0.56
0.44
0.59
0.46
0.62
0.49
0.64
0.61
0.67
0.53
0.70
0.55
0.73
0.57
130
0.56
0.43
0.59
0.45
0.62
0.47
0.64
0.49
0.67
0.51
0.70
0.63
0.72
0.55
132
0.56
0.42
0.69
0.44
0.62
0.46
0.64
0.48
0.67
0.50
0.70
0.62
0.72
0.64
134
0.57
0.41
0.69
0.43
0.62
0.45
0.64
0.46
0.67
0.48
0.69
0.50
0.72
0.62
136
0.57
0.40
0.60
0.41
0.62
0.43
0.65
0.45
0.67
0.47
0.70
0.48
0.72
0.60
138
0.58
0.39
0.60
0.40
0.63
0.42
0.'65
0.43
0.67
0.46
0.70
0.47
0.72
0.48
140
0.58
0.37
0.61
0.39
0.63
0.40
0.65
0.42
0.68
0.43
0.70
0.45
0.72
0.46
142
0.59
0.36
0.61
0..S8
0.63
0.39
0.66
0.41
0.68
0.42
0.70
0.43
0.72
0.46
144
0.60
0.35
0.62
0.36
0.64
0.38
0.66
0.39
0.68
0.40
0.71
0.41
0.73
0.43
146
0.60
0.34
0.63
0.35
0.65
0.36
0.67
0.37
0.69
0.39
0.71
0.40
0.73
0.41
148
0.61
0.32
0.63
0.34
0.66
0..35
0.68
0.36
0.70
0.37
0.72
0.38
0.74
0.39
150
0.62
0.31
0.64
0.32
0.66
0.33
0.68
0.34
0.70
0.36
0.72
0.36
0.74
0.37
152
0.63
0.30
0.65
0.31
0.67
0.32
0.69
0.33
0.71
0.33
0.73
0.34
0.75
0.35
154
0.65
0.28
0.67
0.29
0.68
0.30
0.70
0.31
0.72
0.32
0.74
0.32
0.76
0.33
156
0.66
0.27
0.68
0.28
0.70
0.28
0.72
0.29
0.73
0.30
0.75
0.30
0.77
0.31
158
0.67
0.25
0.69
0.26
0.71
0.27
0.73
0.27
0.74
0.28
0.76
0.28
0.78
0.29
160
0.69
0.24
0.71
0.24
0.73
0.25
0.74
0.25
0.76
0.26
0.77
0.26
0.79
0.27
Page 636]
TABLE 5B.
Distance of an Object by Two Bearings.
Difference
between
DifEerence between the course and first bearing. " 1
Liie cuui»e
and second
bearing.
48°
50°
52°
64°
56°
58°
60°
58°
4.28
3.63
60
3.57
3.10
4.41
3.82
62
3.07
2.71
3.68
3.25
4.54
4.01
64
2.70
2.42
3.17
2.85
3.79
3.41
4.66
4.19
66
2.40
2.20
2.78
2.54
3.26
2.98
3.89
3.55
4.77
4.36
68
2.17
2.01
2.48
2.30
2.86
2.65
3.34
3.10
3.99
3.71
4.88
4.53
70
1.98
1.86
2.24
2.10
2.55
2.39
2.94
2.76
3.43
3.22
4.08
3.83
4.99
4.69
72
1.83
1.74
2.04
1.94
2.30
2.19
2.62
2.49
3.01
2.86
3.51
3.33
4.17
3.96
74
1.70
1.63
1.88
1.81
2.10
2.02
2.37
2.27
2.68
2.58
3.08
2.96
3.58
3.44
76
1.58
1.54
1.75
1.70
1.94
1.88
2.16
2.10
2.42
2.35
2.74
2.66
3.14
3.05
78
1.49
1.45
1.63
1.60
1.80
1.76
1.99
1.95
2.21
2.16
2.48
2.43
2.80
2.74
80
1.40
1.38
1.53
1.51
1.68
1.65
1.85
1.82
2.04
2.01
2.26
2.23
2.53
2.49
82
1.33
1.32
1.45
1.43
1.58
1.56
1.72
1.71
1.89
1.87
2.08
2.06
2.31
2.29
84
1.26
1.26
1.37
1.36
1.49
1.48
1.62
1. 61
1.77
1.76
1.93
1.92
2.13
2.12
86
1.21
1.20
1.30
1.30
1.41
1.41
1.53
1.52
1.66
1.65
1.81
1.80
1.98
1.97
88
1.16
1.16
1.24
1.24
1.34
1.34
1.45
1.45
1.56
1.56
1.70
1.70
1.84
1.84
90
1.11
1.11
1.19! 1.19
1.28
1.28
1.38
1.38
1.48
1.48
1.60
1.60
1.73
1.73
92
1.07
1.07
1.14 1.14
1.23
1.23
1.31
1.31
1.41
1.41
1.52
1.52
1.63
1.63
94
1.03
1.03
1.10^ 1.10
1.18
1.17
1.26
1.26
1.35
1.34
1.44
1.44
1.55
1.54
96
1.00
0.99
1. 06 1 1. 06
1.13
1.13
1.21
1.20
1.29
1.28
1.38
1.37
1.47
1.47
98
0.97
0.96
1. 03 ' 1. 02
1.10
1.08
1.16
1.15
1.24
1.23
1.32
1.31
1.41
1.39
100
0.94
0.93
1. 00 ! 0. 98
1.06
1.04
1.12
1.11
1.19
1.18
1.27
1.25
1.35
1.33
102
0.92
0.90
0. 97 ; 0. 95
1.03
1.01
1.09
1.06
1.15
1.13
1.22
1.19
1.29
1.27
104
0.90
0.87
0. 95 0. 92
1.00
0.97
1.06
1.02
1.12
1.08
1.18
1.14
1.25
1.21
106
0.88
0.84
0.92
0.89
0.97
0.94
1.03
0.99
1.09
1.04
1.14
1.10
1.20
1.16
108
0.86
0.82
0.90
0.86
0.95
0.90
1.00
0.95
1.05
1.00
1.11
.1.05
1.17
1.11
110
0.84
0.79
0.88
0.83
0.93
0.87
0.98
0.92
1.02
0.96
1.08
1.01
1. 13
1.06
112
0.83
0.77
0.87
0.80
0.91
0.84
0.95
0.88
1.00
0.93
1.05
0.97
1.10
1.02
114
0.81
0.74
0.85
0.78
0.89
0.82
0.93
0.85
0.98
0.89
1.02
0.93
1.07
0.98
116
0.80
0.72
0.84
0.75
0.88
0.79
0.92
0.82
0.96
0.85
1.00
0.90
1.04
0.94
118
0.79
0.70
0.83
0.73
0.86
0.76
0.90
0.79
0.94
0.83
0.98
0.86
1.02
0.90
120
0.78
0.68
0.82
0.71
0.85
0.74
0.89
0.77
0.91
0.80
0.96
0.83
1.00
0.87
122
0.77
0.66
0.81
0.68
0.84
0.71
0.87
0.74
0.90
0.77
0.95
0.80
0.98
0.83
124
0.77
0.63
0.80
0.66
0.83
0.69
0.86
0.71
0.90
0.74
0.93
0.77
0.96
0.80
126
0.76
0.61
0.79
0.64
0.82
0.66
0.85
0.69
0.88
0.71
0.91
0.74
0.95
0.77
128
0.75
0.59
0.78
0.62
0.81
0.64
0.84
0.66
0.87
0.69
0.90
0.71
0.93
0.74
130
0.75
0.57
0.78
0.60
0.81
0.62
0.83
0.64
0.86
0.66
0.89
0.68
0.92
0.71
132
0.75
0.56
0.77
0.57
0.80
0.59
0.83
0.61
0.85
0.64
0.88
0.66
0.91
0.68
134
0.74
0.54
0.77
0.55
0.80
0.57
0.82
0.59
0.85
0.61
0.87
0.63
0.90
0.65
136
0.74
0.52
0.77
0.53
0.80
0.55
0.82
0.57
0.84
0.58
0.87
0.60
0.89
0.62
138
0.74
0.50
0.77
0.51
0.79
0.53
0.81
0.54
0.84
0.56
0.86
0.58
0.89
0.59
140
0.74
0.48
0.77
0.49
0.79
0.51
0.81
0.52
0.83
0.54
0.86
0.55
0.88
0.57
142
0.74
0.46
0.77
0.47
0.79
0.49
0.81
0.50
0.83
0.51
0.85
0.52
0.87
0. 54
144
0.75
0.44
0.77
0.45
0.79
0.46
0.81
0.48
0.83
0.49
0.85
0.50
0.87
0.51
146
0.75
0.42
0.77
0.43
0.79
0.44
0.81
0. 45
0.83
0.46
0.85
0.47
0.87
0.49
148
0.76
0.40
0.77
0.41
0.79
0.42
0.81
0.43
0.83
0.44
0.85
0.45
0.87
0.46
150
0.76
0.38
0.78
0.39
0.80
0.40
0.81
0.41
0.83
0.42
0.85
0.42
0.87
0.43
152
0.77
0.36
0.78
0.37
0.80
0.38
0.82
0.38
0.83
0.39
0.85
0.40
0.87
0.41
154
0.77
0.34
0.79
0.35
0.81
0.35
0.82
0.36
0.84
0.37
0.85
0.37
0.87
0.38
156
0.78
0.32
0.80
0.32
0.81
0.33
0.83
0.34
0.84
0.34
0.86
0.35
0.87
0.35
158
0.79
0.30
0.81
0.30
0.82
0.31
0.83
0.31
0.85
0.32
0.86
0.32
0.87
0.33
160
0.80
0.27
0.82
0.28
0.83
0.28
0.84
0.29
0.85
0.29
0.86
0.30
0.88
0.30
TABLE 5B. [Page 637
Distance of an Object by Two Bearings.
Difference
between
the course
Difference between the course and first bearing.
and second
bearing.
62°
64°
66°
68°
70°
73°
74"
76°
72°
5.08
4.84
74
4.25
4.08
5.18
4.98
76
3.65
3.54
4.32
4.19
5.26
5.10
78
3.20
3.13
3.72
3.63
4.39
4.30
5.34
5.22
80
2.86
2.81
3.26
3.21
3.78
3. 72
4.46
4.39
5.41
5.33
82
2.58
2.56
2.91
2.88
3.31
3.28
3.83
3.80
4.52
4.48
5.48
5.42
84
2.36
2.34
2.63
2.61
2.96
2.94
3. 36
3.35
3.88
3.86
4.57
4.55
5.54
5.51
86
2.17
2.17
2.40
2.39
2.67
2.66
3.00
2.99
3.41
3.40
3.93
3.92
4.62
4.61
5.59
5.57
88
2.01
2.01
2.21
2.21
2.44
2.44
2.71
2.71
3.04
3.04
3.45
3.45
3.97
3.97
4.67
4.66
90
1.88
1.88
2.05
2.05
2.25
2.25
2.48
2.48
2.75
2.75
3.08
3.08
3.49
3.49
4.01
4.01
92
1.77
1.76
1.91
1.91
2.08
2.08
2.28
2.28
2.51
2.51
2.78
2.78
3.11
3.11
3.52
3.52
94
1.67
1.66
1.80
1.79
1.95
1.94
2.12
2.11
2.31
2.30
2.54
2.53
2.81
2.80
3.14
3.13
96
1.58
1.57
1.70
1.69
1.83
1.82
1.97
1.96
2.14
2.13
2.34
2.33
2.57
2.55
2.84
2.82
98
1.50
1.49
1.61
1.59
1.72
1.71
1.85
1.84
2.00
1.98
2.17
2.15
2.36
2.34
2.59
2.56
100
1.43
1.41
1.53
1.51
1.63
1.61
1.75
1.72
1.88
1.85
2.03
2.00
2.19
2.16
2.39
2.35
102
1.37
1.34
1.46
1.43
1.55
1.52
1.66
1.62
1.77
1.73
1.90
1. 86
2.05
2.00
2.21
2.16
104
1.32
1.28
1.40
i.36
1.48
1.44
1.58
1.53
1.68
1. 63
1.79
1.74
1.92
1.87
2.07
2.01
106
1.27
1.22
1.34
1.29
1.42
1.37
1.51
1.45
1.60
1.54
1.70
1.63
1.81
1.74
1.94
1.87
108
1.23
1.17
1.29
1.23
1..37
1.30
1.44
1.37
1.53
1.45
1.62
1.54
1.72
1.63
1.83
1.74
110
1.19
1.12
1.25
1.17
1.32
1.24
1.39
1. 30
1.46
1.37
1.54
1.45
1.64
1.54
1.74
1.63
112
1.15
1.07
1.21
1.12
1.27
1.18
1.33
1.24
1.40
1.30
1.48
1.37
1.56
1.45
1.65
1.53
114
1.12
1.02
1.17
1.07
1.23
1.12
1.29
1.18
1.35
1.24
1.42
1.30
1.50
1.37
1.58
1.44
116
1.09
0.98
1.14
1.03
1.19
1.07
1.25
1.12
1.31
1.17
1.37
1.23
1.44
1.29
1.51
1.36
118
1.07
0.94
1.11
0.98
1.16
1.02
1.21
1.07
1.26
1.12
1.32
1.17
1.38
1.22
1.45
1.28
120
1.04
0.90
1.08
0.94
1.13
0.98
1.18
1.02
1.23
1.0<)
1.28
1.11
1.34
1.16
1.40
1.21
122
1.02
0.86
1.06
0.90
1.10
0.93
1.15
0.97
1.19
1.01
1.24
1.05
1.29
1.10
1.35
1.14
124
1.00
0.83
1.04
0.86
1.08
0.89
1.12
0.93
1.16
0.96
1.21
1.00
1.25
1.04
1.31
1.08
126
0.98
0.79
1.02
0.82
1.05
0.85
1.09
0.88
1.13
0.92
1.18
0.95
1.22
0.99
1.27
1.02
128
0.97
0. 76
1.00
0.79
1.03
0.82
1.07
0.84
1.11
0.87
1.15
0.90
1.19
0.94
1.23
0.97
130
0.95
0.73
0.98
0.75
1.02
0.78
1.05
0.80
1.09
0.83
1.12
0.86
1.16
0.89
1.20
0.92
132
0.94
0.70
0.97
0.72
1.00
0.74
1.03
0.77
1.06
0.79
1.10
0.82
1.13
0.84
1.17
0.87
134
0.93
0.67
0. 96
0.69
0.99
0.7]
1.01
0.73
1.04
0.75
1.08
0.77
1.11
0.80
1.14
0.82
136
0.92
0.64
0.95
0.66
0.97
0.68
1.00
0.69
1.03
0.71
1.06
0.74
1.09
0.76
1.12
0.78
138
0.91
0.61
0.94
0.63
0.96
0.64
0.99
0.66
1.01
0.68
1.04
0.70
1.07
0.72
l.M)
0.74
140
0.90
0.58
0.93
0.60
0.95
0.61
0.97
0. 63
1.00
0.64
1.03
0.66
1.05
0.68
1.08
0.70
142
0.90
0.55
0.92
0.57
0.94
0.58
0.96
0.59
0.99
0,61
1.01
0.62
1.04
0.64
1.06
0.65
144
0.89
0.52
0.91
0.54
0.93
0.55
0.96
0. 56
0.98
0.57
1.00
0.59
1.02
0.60
1.05
0.62
146
0.89
0.50
0.91
0.51
0.93
0.52
0.95
0. 53
0.97
0. 54
0.99
0. 55
1.01
0.57
1.03
0.58
148
0.89
0.47
0.90
0.48
0.92
0.49
0.94
0.50
0. 96
0.51
0.98
0.52
1.00
0.53
1.02
0.54
150
0.88
0.44
0.90
0.45
0.92
0.46
0.94
0.47
0.95
0.48
0.97
0.49
0.99
0.50
1.01
0.50
152
0.88
0.41
0.90
0.42
0.92
0.43
0.93
0.44
0.95
0.45
0.97
0.45
0.98
0.46
1.00
0.47
154
0.88
0.39
0.90
0.39
0.91
0.40
0.93
0.41
0.94
0.41
0.96
0.42
0.98
0.43
0.99
0.43
156
0.89
0. .36
0.90
0.37
0.91
0.37
0.93
0.38
0.94
0..38
0.96
0.39
0.97
0.39
0.99
0.40
158
0.89
0. 33
0.90
0..34
0.91
0.34
0.93
0.35
0.94
0.35
0.95
0. 36
0.97
0.36
0.98
0.37
160
0.89 0.30
1
0.90
0.31
0.91
0.31
0.93
0.32
0.94
0.32
0.95
0.33
0.96
0.33
0.98
0.33
Page 638] TABLE oB. |
Distance of an Object by Two Bearings.
Difference
Difference between the course and first bearing.
between
the course
and second
78°
80°
82°
84°
86°
88°
90°
92°
bearing.
88°
5.63
5.63
90
4.70
4.70
5.67
5.67
92
4.04
4.04
4.74
4.73
5.70
5.70
94
3.55
3.54
4.07
4.06
4.76
4.75
5.73
5.71
96
3.17
3.15
3.57
3.55
4.09
4.07
4.78
4.76
5.74
5.71
98
2.86
2.83
3.19
3.16
3.c;d
3.56
4.11
4.07
4.80
4.75
5.76
5.70
100
2.61
2.57
2.88
2.84
3.20
3.16
.3.61
3.55
4.12
4.06
4.81
4.73
5.76
5.67
102
2.40
2.35
2.63
2.57
2.90
2.83
3.22
3.15
3.62
3.54
4.13
4.04
4.81
4.70
5.76
5.63
104
2.23
2.16
2.42
2.35
2.64
2.56
2.91
2.82
3.23
3.13
3.63
.3.52
4.13
4.01
4.81
4.66
106
2.08
2.00
2.25
2.16
2.43
2.34
2.65
2.55
2.92
2.80
3.23
.3.11
3.63
3.49
4.13
3.97
108
1.96
1.86
2.10
2.00
2.26
2.15
2.45
2.33
2.66
2.53
2.92
2.78
3.24
3. 08
3.63
3.45
110
1.85
1.73
1.97
1.85
2.11
1.98
2.27
2.13
2.45
2.31
2.67
2.51
2.92
2.75
3.23
3.04
112
1.75
1.62
1.86
1.72
1.98
1.83
2.12
1.96
2.28
2.11
2.46
2.28
2.67
2.48
2.92
2.71
114
1.66
1.52
1.76
1.61
1.87
1.71
1.99
1.82
2.12
1.94
2.28
2.08
2.46
2.25
2.67
2.44
116
1.59
1.43
1.68
1.51
1.77
1.59
1.88
1.69
2.00
1.79
2.13
1.91
2.28
2.05
2.46
2.21
118
1.52
1.34
1.60
1.41
1.68
1.49
1.78
1.57
1.88
1.66
2.00
1.76
2.13
1.88
2.28
2.01
120
1.46
1.27
1.53
1.33
1.61
1.39
1.69
1.47
1.78
1.54
1.89
1.63
2.00
1.73
2.13
1.84
122
1.41
1.19
1.47
1.25
1.54
1.31
1.62
1.37
1.70
1.44
1.79
1.52
1.89
1.60
2.00
1.70
124
1.36
1.13
1.42
1.18
1.48
1.23
1.55
1.28
1.62
1.34
1.70
1.41
1.79
1.48
1.89
1.56
126
1.32
1.06
1.37
1.11
1.43
1.15
1.48
1.20
1.55
1.26
1.62
1.31
1.70
1..38 1.79
1.45
128
1.28
1.01
1.33
1.04
1.38
1.08
1.43
1.13
1.49
1.17
1.55
1.23
1.62
1.28
1.70
1.34
130
1.24
0.95
1.29
0.98
1.33
1.02
1.38
1.06
1.44
1.10
1.49
1.14
1.56
1.19
1.62
1.24
132
1.21
0.90
1.25
0.93
1.29
0.96
1.34
0.99
1.39
1.03
1.44
1.07
1.49
1.11
1.55
1.16
134
1.18
0.85
1. 22
0.88
1.26
0.90
1.30
0. 93
1.34
0.97
l.,39
1.00
1.44
1.04
1.49
1.07
136
1.15
0.80
l!l9
0.83
1.22
0.85
1.26
0.88
1.30
0.90
1.34
0.93
1.39
•0.97
1.44
1.00
138
1.13
0.76
1.16
0.78
1.19
0.80
1.23
0.82
1.27
0.85
1.30
0.87
1.35
0.90
1..S9
0.93
140
1.11
0.71
1.14
0.73
1.17
0.75
1.20
0.77
1.23
0.79
1.27
0.82
l.,31
0.84
1.34
0.86
142
1.09
0.67
1.12
0.69
1.14
0.70
1.17
0.72
1.20
0.74
1.24
0.76
1.27
0.78
1..30
0.80
144
1.07
0.63
1.10
0.64
1.12
0.66
1.15
0.67
1.18
0.69
1.21
0.71
1.24
0.73
1.27
0.75
146
1.05
0.59
1.08
0.60
1.10
0.62
1.13
0.63
1.15
0.64
1.18
0.66
1.21
0.67
1.24
0.69
148
1.04
0. 55
1.06
0.56
1.08
0.57
1.11
0.59
1.13
0.60
1.15
0.61
1.18
0.62
1.21
0.64
150
1.03
0.51
1.05
0.52
1.07
0.53
1.09
0.54
1.11
0.55
1.13
0.57
1.15
0.58
1.18
0.59
152
1.02
0.48
1.04
0.49
1.05
0.49
1.07
0.50
1.09
0.51
1.11
0.52
1.13
0. .53
1.15
0.54
154
1.01
0.44
1.02
0.45
1.04
0.46
1.06
0.46
1.08
0.47
1.09
0.48
1.11
0.49
1.13
0.50
156
1.00
0.41
1.01
0.41
1.03
0.42
1.05
0.43
1.06
0.43
1.08
0.44
1.09
0.45
1.11
0.45
158
0.99
0.37
1.01
0.38
1.02
0.38
1.03
0.39
1.05
0.39
1.06
0.40
1.08
0.40
1.09
0.41
160
0.99
0.34
1.00
0.34
1.01
0.35
1.02
0.35
1.04
0.35
1.05
0.36
1.06
r
0.36
1.08
0.37
94°
96°
98°
100°
102°
104°
106°
108° 1
104°
5.74
5.57
106
4.80
4.61
5.78
5.51
108
4.12
3.92
4.78
4.55
5.70
5.42
110
3.62
3.40
4.11
3.86
4.76
4.48
5.67
5.33
112
3.23
2.99
3.61
3.35
4.09
3.80
4.74
4.40
5.63
5.22
114
2.92
2.66
3.22
2.94
3.59
3.28
4.07
3.72
4.70
4.30
5.59
5.10
116
2.66
2.39
2.91
2.61
3.20
2.88
3.57
3.21
4.04
3.63
4.67
4.19
5.54
4.98
118
2.45
2.17
2.65
2.34
2.90
2.56
3.19
2.81
3.55
3.13
4.01
3.54
4.62
4.08
5.48
4.84
120
2.28
1.97
2.45
2.12
2.64
2.29
2.88
2.49
3.17
2.74
3.52
3.05
3.97
3.44
4. .57
3.96
122
2.12
1.80
2.27
1.92
2.43
2.06
2.63
2.23
2.86
2.43
3.14
2.66
3.49
2.96
3.93
3.33
124
2.00
1.65
2.12
1.76
2.26
1.87
2.42
2.01
2.61
2.16
2.84
2.35
3.11
2.58
3.45
2.86
126
1.88
1.52
1.99
1.61
2.11
1.71
2.25
1.82
2.40
1.95
2.59
2.10
2.81
2.27
3.08
2.49
128
1.78
1.41
1.88
1.48
1.98
1.56
2.10
1.65
2.23
1.76
2.39
1.88
2.57
2.02
2.78
2.19
130
1.70
1.30
1.78
1.36
1.87
1.43
1.97
1.51
2.08
1.60
2.21
1.70
2.36
1.81
2.54
1.94
132 '
1.62
1.20
1.69
1.26
1.77
1.32
1.86
1.38
1.96
1.45
2.07
1.54
2.19
1.63
2.34
1.74
134
1.55
1.12
1.62
1.16
1.68
1.21
1.76
1.27
1.85
1.33
1.94
1.40
2.0511.47
2.17
1.56
136
1.49
1.04
1.55
1.07
1.61
1.12
1.68
1.16
1.75
1.22
1.83
1.27
1.92
1.34
2.03
1.41
138
1.44
0.96
1.49
0.99
1.54
1.03
1.60
1.07
1.66
1.11
1.74
1.16
1.81
1.21
1.90
1.27
140
1.39
0.89
1.43
0.92
1.48
0.95
1.53
0.98
1. 59
1.02
1.65
1.06
1.72
1.10
1.79
1.15
142
1.34
0.83
1.38
0.85
1.43
0.88
1.47
0.91
1.52
0.94
1.58
0.97
1.64
1.01
1.70
1.05
144
1.30
0.77
1.34
0.79
1.38
0.81
1.42
0.83
1.46
0.86
1.51
0.89
1.56
0.92
1.62
0.95
146
1.27
0.71
1.30
0.73
1.33
0.75
1.37
0.77
1.41
0.79
1.45
0.81
1.50
0.84
1.54
0.86
148
1.23
0.65
1. 26 ; 0. 67
1.29
0.69
1.33
0.70
1.36
0.72
1.40
0.74
1.44
0.76
1.48
0.78
150
1.20
0.60
1.23
0.61
1.26
0.63
1.29
0.64
1.32
0.66
1.35
0.67
1.38
0.69
1.42
0.71
152
1.18
0.55
1.20
0.56
1.22
0.57
1.25
0.59
1.28
0.60
1.31
0.61
1.34
0.63
1.37
0.64
154
1.15
0.50
1.17
0.51
1.19
0.52
1.22
0.53
1.24
0.54
1.27
0.56
1.29
0.57
1.32
0.58
156
1.13
0.46
1.15
0.47
1.17
0.47
1.19
0.48
1.21
0.49
1.23
0.50
1.25
0.51
1.28
0.52
158
1.11
0.42
1.13
0.42
1.14
0.43
1.16
0.44
1.18
0.44
1.20
0.45
1.22
0.46
1.24
0.47
160
1.09
0.37
1.11
0.38
1.12
0.38
1.14
0.39
1.15
0.39
1.17
0.40
1.19
0.41
1.21
0.41
TABLE 5B. [Page 639
Distance of an Object by Two Bearings.
Difference
between
the course
and second
bearing.
Difference between the course and first bearing.
110°
112°
114°
116°
118°
120°
122°
120°
122
124
126
128
130
132
134
136
138
140
142
144
146
148
150
152
154
156
158
160
5.41
4.52
3.88
3.41
3.04
2.75
2.51
2.31
2.14
2.00
1.88
1.77
1.68
1.60
1.53
1.46
1.40
1.35
1.31
1.26
1.23
4.69
3.83
3.22
2.76
2.40
2.10
1.86
1.66
1.49
1.34
1.21
1.09
0.99
0.89
0.81
0.73
0.66
0.59
0.53
0.47
0.42
5.34
4.46
3.83
3.36
3.00
2.71
2.48
2.28
2. 12
l!97
1.85
1.75
1.66
1.58
1.51
1.44
1.39
1.33
1.29
1.25
4.53
3.70
3.10
2.65
2.30
2.01
1.78
1.58
1.42
1.27
1.14
1.03
0.93
0.84
0.75
0.68
0.61
0.54
0.48
0.43
5.26
4.39
3.78
3.31
2.96
2.67
2.44
2.25
2.08
1.95
1.83
1.72
1.63
1.55
1.48
1.42
1.37
1.32
1.27
4.36
3.55
2.98
2.54
2.20
1.92
1.69
1.50
1.34
1.20
1.07
0.96
0.87
0.78
0.70
0.62
0.56
0.49
0.43
5.18
4.32
3.72
3.26
2.91
2.63
2.40
2.21
2.05
1.91
1.80
1.70
1.61
1.53
1.46
1.40
1.34
1.29
4.19
3.41
2.85
2.42
2.09
1.83
1.61
1.42
1.26
1.13
1.01
0.90
0.80
0.72
0.64
0.57
0.50
0.44
5.08
4.25
3.65
3.20
2.86
2.58
2.36
2.17
2.01
1.88
1.77
1.67
1.58
1.50
1.43
1.37
1.32
4.01
3.25
2.71
2.30
1.98
1.73
1.52
1.34
1.18
1.05
0.94
0.83
0.74
0.66
0.58
0.51
0.45
4.99
4.17
3.58
3.14
2.80
2.53
2.31
2.13
1.98
1.84
1.73
1.63
1.55
1.47
1.41
1.35
3.82
3.10
2.57
2.18
1.88
1.63
1.42
1.25
1.10
0.98
0.87
0.77
0.68
0.60
0.53
0.46
4.88
4.08
3.51
3.08
2.74
2.48
2.26
2.08
1.93
1.81
1.70
1.60
1.52
1.44
1.38
3.63
2.93
2.44
2.06
1.76
1.53
1.33
1.17
1.03
0.90
0.80
0.70
0.62
0.54
0.47
124°
126°
128°
130°
182°
184°
136° 1
134°
136
138
140
142
144
146
148
150
152
154
156
158
160
4.77
3.99
3.43
3.01
2.68
2.42
2.21
2.04
1.89
1.77
1.66
1.56
1.48
1.41
3.43
2.77
2.29
1.93
1.65
1.42
1.24
1.08
0.95
0.83
0.73
0.64
0.56
0.48
4.66
3.89
3.34
2.94
2.62
2.37
2.16
1.99
1.85
1.72
1.62
1.53
1.45
3.23
2.60
2.15
1.81
1.54
1.32
1.14
0.99
0.87
0.76
0.66
0.57
0.49
4.54
3.79
3.26
2.86
2.55
2.30
2.10
1.94
1.80
1.68
1.58
].49
3.04
2.44
2.01
1.68
1.43
1.22
1.05
0.91
0.79
0.68
0.59
0.51
4.41
3.6S
3.17
2.78
2.48
2.24
2.04
1.88
1.75
1.63
1.53
2.84
2.27
1.86
1.55
1.31
1.12
0.96
0.83
0.71
0.61
0.52
4.28
3.57
3.07
2.70
2.40
2.17
1.98
1.83
1.70
1.58
2.63
2.10
1.72
1.43
1.20
1.02
0.87
0.74
0.64
0.54
4.14
3.46
2.97
2.61
2.33
2.10
1.92
1.77
1.64
2.43
1.93
1.58
1.30
1.09
0.92
0.78
0.66
0.56
4.00
3.34
2.87,
2.52
2.25
2.03
1.85
1.71
2.24
1.77
1.44
1.18
0.99
0.83
0.69
0.58
148°
150
152
154
156
158
160
188°
140°
142°
144°
146°
148°
150° 1
3.85
8.22
2.77
2.43
2.17
1.96
1.79
2.04
1.61
1.30
1.06
0.88
0.73
0.61
3.70
3.09
2.66
2.33
2.08
1.88
1.85
1.45
1.16
0.95
0.78
0.64
3.55
2.96
2.54
2.23
1.99
1.66
1.30
1.04
0.84
0.68
3.38
2.83
2.43
2.13
1.48
1.15
0.91
0.73
3.22
2.69
2.31
1.31
1.01
0.79
3.05
2.55
1.14
0.87
2.88
0.98
Page 640]
TABLE 6.
Distance of Visibility of Objects at Sea.
Height,
Nautical
Statute
Height,
Nautical
Statute
Height,
Nautical
Statute
«•
feet.
miles.
miles.
feet.
miles.
miles.
feet.
miles.
miles.
1
1.1
1.3
100
11.5
13.2
760
31.6
36.4
2
1.7
1.9
105
11.7
13.5
780
32.0
36.9
3
2.0
2.3
110
12.0
13.8
800
32.4
37.3
4
2.3
2.6
115
12.3
14.1
820
32.8
37.8
5
2.5
2.9
120
12.6
14.0
840
33.2
38.3
6
2.8
3.2
125
12.9
14.8
860
33.6
38.7
7
2.9
3.5
130
13.1
15.1
880
34.0
39.2
8
3.1
3.7
135
13.3
15.3
900
34.4
39.6
9
3.5
4.0
140
13.6
15.8
920
34.7
40.0
10
3.6
4.2
145
13.8
15.9
940
35.2
40.5
11
3.8
4.4
150
14.1
16.2
960
35.5
40.9
12
4.0
4.6
160
14.5
16.7
980
35.9
41.3
13
4.2
4.8
170
14.9
17.2
1,000
36.2
41.7
14
4.3
4.9
180
15.4
17.7
1,100
38.0
43.8
15
4.4
5.1
190
15.8
18.2
1,200
39.6
45.6
16
4.6
5.3
200
16.2
18.7
1,300
41.3
47.6
17
4.7
5.4
210
16.6
19.1
1,400
42.9
49.4
18
4.9
5.6
220
17.0
19.6
1,500
44.4
51.1
19
5.0
5.8
230
17.4
20.0
1,600
45.8
52.8
20
5.1
5.9
240
17.7
20.4
1,700
47.2
54.4
21
5.3
6.1
250
18.2
20.9
1,800
48.6
56.0
22
5.4
6.2
260
18.5
21.3
1,900
49.9
57.5
23
5.5
6.3
270
18.9
21.7
2,000
51.2
59.0
24
5.6
6.5
280
19.2
22.1
2,100
52.5
60.5
25
5.7
6.6
290
19.6
22.5
2,200
53.8
61.9
26
5.8
6.7
300
19.9
22.9
2,300
55.0
63.3
27
6.0
6.9
310
20.1
23.2
2,400
56.2
64.7
28
6.1
7.0
320
20.5
23.6
2,500
57.!?
66.0
29
6.2
7.1
330
20.8
24.0
2,600
58.5
67.3
30
6.3
7.2
340
21.1
24.3
2,700
59.6
68.6
31
6.4
7.3
350
21.5
24.7
2,800
60.6
69.8
32
6.5
7.5
360
21.7
25.0
2,900
61.8
71.1
33
6.6
7.6
370
22.1
25.4
3,000
62.8
72.3
34
6.7
7.7
380
22.3
25.7
3,100
63.8
73.5
35
6.8
7.8
390
22.7
26.1
3,200
64.9
74.7
36
6.9
7.9
400
22.9
26.4
3,300
65.9
75.9
37
6.9
8.0
410
23.2
26.7
3,400
66.9
77.0
38
7.0
8.1
420
23.5
27.1
3,500
67.8
78.1
39
7.1
8.2
430
23.8
27.4
3,600
68.8
79.2
40
7.2
8.3
440
24.1
27.7
3,700
69.7
80.3
41
7.3
8.4
450
24.3
28.0
3, 800
70.7
81.4
42
7.4
8.5
460
24.6
28.3
3,900
71.6
82.4
-43
7.5
8.7
470
24.8
28.6
4,000
72.5
83.5
44
7.6
8.8
480
25.1
28.9
4,100
73.4
84.5
45
7.7
8.9
490
25.4
29.2
4,200
74.3
85.6
46
7.8
9.0
500
25.6
29.5
4,300
75.2
86.6
47
7.9
9.0
520
26.1
30.1
4,400
76.1
87.6
48
7.9
9.1
540
26.7
30.7
4, .500
76.9
88.5
49
8.0
9.2
560
27.1
31.2
4,600
77.7
89.5
50
8.1
9.3
580
27.6
31.8
4,700
78.6
90.5
55
8.5
9.8
600
28.0
32.3
4,800
79.4
91.4
60
8.9
10.2
620
28.6
32.9
4,900
80.2
92.4
65
9.2
10.6
640
29.0
33.4
5,000
81.0
93.3
70
9.6
11.0
660
29.4
33.9
6,000
88.8
102.2
75
9.9
11.4
680
29.9
34.4
7,000
96.0
110.5
80
10.3
11.8
700
30.3
34.9
8,000
102.6
118.1
85
10.6
12.2
720
30.7
35.4
9,000
108.7
125.2
90
10.9
12.5
740
31.1
35.9
10,000
114.6
132.0
95
11.2
12.9
If
TABLE 7
[Page 641 |
For converting Arc into Time,
and the reverse.
o
H. M.
O
H. M.
O
H. M.
o
H. M.
H. M.
O
H. M.
t
M. S.
/
M. s.
f
M. S.
'
M. s.
'
M. S.
t
M. S.
It
S. A
"
S. A
tl
S. aV
"
s. A
"
s. ^
tl
s. A
1
4
31
4 4
121
8 4
181
12 4
241
16 4
301
20 4
2
8
62
4 8
122
8 8
182
12 8
242
16 8
302
20 8
3
12
63
4 12
123
8 12
183
12 12
243
16 12
303
20 12
4
16
64
4 16
124
8 16
184
12 16
244
16 16
304
20 16
5
20
65
4 20
125
8 20
185
12 20
245
16 20
305
20 20
6
24
66
4 24
126
8 24
186
12 24
246
16 24
306
20 24
7
28
67
4 28
127
8 28
187
12 28
247
16 28
307
20 28
8
32
68
4 32
128
8 32
188
12 32
248
16 32
308
20 32
9
36
69
4 36
129
8 36
189
12 36
249
16 36
309
20 36
10
40
70
4 40
130
8 40
190
12 40
250
16 40
310
20 40
11
44
71
4 44
131
8 44
191
12 44
'251
16 44
311
20 44
12
48
72
4 48
132
8 48
192
12 48
252
16 48
312
20 48
13
52
73
. 4 52
133
8 52
193
12 52
253
16 52
313
20 52
14
56
TT
4 56
134
8 56
194
12 56
254
16 56
314
20 56
15
1
75
5
135
9
195
13
255
17
315
21
16
1 4
76
5 4
136
9 4
196
13 4
256
17 4
316
21 4
17
1 8
77
5 8
137
9 8
197
13 8
257
17 8
317
21 8
18
1 12
78
5 12
138
9 12
198
13 12
258
17 12
318
21 12
19
1 16
79
5 16
139
9 16
199
13 16
259
17 16
319
21 16
20
120
80
5 20
140
9 20
200
13 20
260
17 20
320
21 20
21
1 24
81
5 24
141
9 24
201
13 24
261
17 24
321
21 24
22
1 28
82
5 28
142
9 28
202
13 28
262
17 28
322
21 28
23
1 32
83
5 32
143
9 32
203
13 32
263
17 32
323
21 32
24
1 36
84
5 36
144
9 36
204
13 36
264
17 36
324
21 36
25
1 40
85
5 40
145
9 40
205
13 40
265
17 40
325
21 40
26
1 44
86
5 44
146
9 44
206
13 44
266
17 44
326
21 44
27
1 48
87'
5 48
147
9 48
207
13 48
267
17 48
327
21 48
28
1 52
88
5 52
148
9 52
208
13 52
268
17 52
328
21 52
29
1 56
89
5 56
149
9 56
209
13 56
269
17 56
329
21 56
30
2
90
6
150
10
210
14
270
18
330
22
31
2 4
91
6 4
151
10 4
211
14 4
271
18 4
331
22 4
32
2 8
92
6 8
152
10 8
212
14 8
272
18 8
332
22 8
33
2 12
93
6 12
153
10 12
213
14 12
273
18 12
333
22 12
34
2 16
94
6 16
154
10 16
214
14 16
274
18 16
334
22 16
35
2 20
95
6 20
155
10 20
215
14 20
275
18 20
335
22 20
36
2 24
96
6 24
156
10 24
216
14 24
276
18 24
336
22 24
37
2 28
97
6 28
157
IP 28
217
14 28
277
18 28
337
22 28
38
2 32
98
6 32
158
10 32
218
14 32
278
18 32
338
22 32
39
2 36
99
6 36
159
10 36
219
14 36
279
18 36
339
22 36
40
2 40
100
6 40
160
161
10 40
220
221
14 40
14 44
280
18 40
340
22 40
41
2 44
101
6 44
10 44
281
18 44
341
22 44
42
2 48
102
6 48
162
10 48
222
14 48
282
18 48
342
22 48
43
2 52
103
6 52
163
10 52
223
14 52
283
18 52
343
22 52
44
2 56
104
6 56
164
10 56
224
14 56
284
18 56
344
22 56
45
3
105
7
165
11
225
15
285
19
345
23
46
3 4
106
7 4
166
11 4
226
15 4
286
19 4
346
23 4,
47
3 8
107
7 8
167
11 8
227
15 8
287
19 8
347
23 8
48
3 12
108
7 12
168
11 12
228
15 12
288
19 12
348
23 12
49
3 16
109
7 16
169
11 16
229
15 16
289
19 16
349
23 16
50
51
3 20
110
7 20
170
171
11 20
230
15 20
290
19 20
350
23 20
3 24
111
7 24
U 24
231
15 24
291
19 24
;i51
23 24
52
3 28
112
7 28
172
11 28
232
15 28
292
19 28
352
23 28
53
3 32
113
7 32
173
11 32
233
15 32
293
19 32
353
23 32
54
3 36
114
7 36
174
11 36
234
15 36
294
19 36
354
23 36
55
3 40
115
7 40
175
11 40
235
15 40
295
19 40
355
23 40
56
3 44
116
7 44
176
n 44
236
15 44
296
19 44
356
23 44
57
3 48
117
7 48
177
11 48
237
15 48
297
19 48
357
23 48
58
3 52
118
7 52
178
11 52
238
15 52
298
19 52
358
23 52
59
3 56
119
7 56
179
11 56
239
15 56
299
19 56
359
23 56
60
4
120
8
180
12
240
16
300
20
360
24
Note. — When turniiiK seconds oi arc into timo, and vice vcrwi, it should be remembered that the fraetiona are sixtieths:
thus, the value in time of 42" is not 2'.4S, but 2" jg-2«.8.
2497
-12-
-31
Page 642] TABLE 8.
Sidereal into Mean Solar Time.
To be subtracted from a sidereal time interval.
0»
1'
Oh
3h
4k
«!■
6'
!»
Forseconds.
TO.
1
2
3
4
TO. e.
0.000
0.164
0. 328
0. 491
0.655
m. «.
9.830
9.993
10. 157
10. 321
10.485
m. e.
19.659
19. 823
19. 987
20. 151
20. 314
m. 8.
29. 489
29. 653
29. 816
29. 980
30. 144
TO. 8.
39. 318
39. 482
39. 646
39. 810
39. 974
TO. «.
49. 148
49. 312
49. 475
49. 639
49. 803
TO. «.
58. 977
59. 141
59. 305
59. 469
59. 633
m. e.
1 8.807
1 8.971
1 9.135
1 9.298
1 9. 462
«.
1
2
3
4
0.003
.005
.008
.011
5
6
7
8
9
0. 819
0. 983
1. 147
1.311
1. 474
10.649
10. 813
10. 976
11.140
11. 304
20. 478
20. 642
20. 806
20. 970
21. 134
30. 308
30. 472
30. 635
30. 799
30. 963
40. 137
40. 301
40. 465
40. 629
40. 793
49. 967
50. 131
50. 295
50. 458
50. 622
50. "786
50. 950
51.114
51. 278
51.441
59. 796
59. 960
1 0.124
1 0. 288
1 0.452
1 9. 626
1 9.790
1 9. 954
1 10. 118
1 10.281
5
6
7
8
9
.014
.016
.019
.022
.025
10
11
12
13
14
1.638
1. 802
1.966
2. 130
2.294
11.468
11. 632
11. 795
11.959
12. 123
21. 297
21. 461
21. 625
21. 789
21. 953
31. 127
31.291
31. 455
31. 618
31. 782
40. 956
41. 120
41. 284
41. 448
41.612
1 0.616
1 0.779
1 0.943
1 1.107
1 1.271
1 10.445
1 10.609
1 10.773
1 10.937
1 11.100
10 . 027
11 . 030
12; .033
131 .035
14 1 .038
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
2. 457
2. 621
2. 785
2. 949
3. 113
12.287
12. 451
12.615
12. 778
12.942
22. 117
22. 280
22.444
22. 608
22. 772
22.936
23. 099
23. 263
23. 427
23. 591
31. 946 ! 41. 776
32.110 41.939
32. 274 42. 103
32. 438 . 42. 267
32. 601 1 42. 431
51.605
51. 769
51 .-933
52. 097
52. 260
1 1.435
1 1. 599
1 1. 762
1 1. 926
1 2.090
1 11.264
1 11.428
1 11.592
1 11. 756
1 11.920
15
16
17
18
19
.041
.044
.046
.049
.052
3. 277
3. 440
3.604
3. 768
3. 932
13. 106
13. 270
13.434
13.598
13. 761
32. 765
32. 929
33. 093
33. 257
33. 420
42. 595
42. 759
42. 922
43. 086
43. 250
43. 414
43. 578
43. 742
43. 905
44. 069
52. 424
52. 588
52. 752
52. 916
53. 080
1 2.254
1 2.418
1 2.582
1 2. 745
1 2.909
1 s.ofs
1 3. 237
1 3.401
1 3.564
1 3. 728
1 3. 892
1 4. 0.56
1 4. 220
1 4.384
1 4.547
1 12.083
1 12.247
1 12.411
1 12.575
1 12.739
1 12.903
1 13.066
1 13.230
1 13.394
1 13.558
20
21
22
23
24
.055
.057
.060
.063
.066
4. 096
4. 259
4. 423
4. 587
4. 751
13. 925
14.089
14. 253
14.417
14. 581
23. 755
23. 919
24. 082
24. 246
24. 410
33. 584
33. 748
33. 912
,34. 076
34. 240
53. 243
53. 407
53. 571
53. 735
53. 899
54. 063
54. 226
54. 390
54. 554
54. 718
54. 882
55. 046
55. 209
55. 373
55. 537
25; .068
26: .071
27 i .074
28: .076
29' .079
30 i .082
311 .085
32! .087
33 i .090
34' .093
30
31
32
33
34
4.915
5. 079
5. 242
5.406
5.570
14. 744
14. 908
15. 072
15.236
15. 400
24. 574
24. 738
24. 902
25.065
25. 229
34. 403
34. .567
34. 731
34. 895
35. 059
44. 233
44. 397
44. 561
44. 724
44. 888
1 13.722
1 13.886
1 14.049
1 14.213
1 14.377
35
36
37
38
39
5. 734
5. 898
6. 062
6. 225
6. 389
15. 563
15. 727
15. 891
16.055
16. 219
16.383
16. 546
16. 710
16. 874
17. 038
25. 393
25. 557
25. 721
25. 885
26. 048
26. 212
26. 376
26. 540
26. 704
26. 867
35. 223
35. 386
35. 550
35. 714
35. 878
45. 052
45. 216
45. 380
45. .544
45. 707
1 4.711
1 4.875
1 5.039
1 5.203
1 5. 367
1 14.541
1 14.705
1 14.868
1 15.032
1 15. 196
35
36
37
38
,39
.096
.098
.101
.104
.106
40
41
42
43
44
6. .553
6. 717
6.881
7. 045
7. 208
36. 042
36. 206
.36. 369
36. 533
36. 697
36. 861
37. 025
37.188
37. 352
37. 516
45. 871
46. 035
46. 199
46. 363
46. 527
55. 701
55. 865
56. 028
56. 192
56. 356
1 5.530
1 5.694
1 5.858
1 6. 022
1 6. 186
1 15.360
1 15.524
1 1.5.688
1 1.5.851
1 16.015
1 16.179
1 16. .343
1 16. .507
1 16.671
1 16.834
40
41
42
43
44
.109
.112
.115
.117
.120
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
7. 372
7.536
7.700
7. 864
8. 027
8. 191
8.355
8. 519
8. 683
8. 847
17.202
17. 366
17. 529
17. 693
17. 857
27. 031
27. 195
27. 359
27. 523
27. 687
46. 690
46. 854
47.018
47. 182
47. 346
56. 520
56. 684
56. 848
57. Oil
57. 175
1 6.350
1 6. 513
1 6.677
1 6.841
1 7.005
45
46
47
48
49
50
51
52
53
54
.123
.126
.128
.131
.134
.137
.139
.142
.145
.147
18.021
18. 185
18.349
18. 512
18. 676
27. 850
28. 014
28. 178
28. 342
28.506
37. 680
37.844
38. 008
38. 171
38. 335
47.510
47. 673
47. 837
48. 001
48. 165
57. 339
57. 503
57. 667
57. 831
57. 994
1 7. 169
1 7. 332
1 7. 496
1 7. 660
1 7.824
1 16.998
1 17. 162
1 17.326
1 17.490
1 17.654
9. 010
9.174
9. 338
9. 502
9. 666
18. 840
19.004
19. 168
19. 331
19. 495
28. 670
28. 833
28. 997
29. 161
29. 325
38. 499
38. 663
38. 827
38. 991
39. 154
48. 329
48. 492
48. 656
48. 820
•0 48. 984
58. 158
58. 322
58. 486
58.650
58. 814
1 7. 988
1 8.152
1 8. 315
1 8.479
1 8.643
1 17.817
1 17.981
1 18.145
1 18.309
1 18.473
55
56
57
58
59
.150
.1.53
.156
.158
0.161
TABLE 8.
Sidereal into Mean Solar Time.
[Page 643
a
1
To be subtracted from a sidereal time interval.
8i>
9»
10i>
111.
12b
18'
14k
lo'
For seconds. 1
m.
1
2
3
4
m. t.
1 18.636
1 18.800
1 18.964
1 19.128
1 19.292
m. «.
1 28.466
1 28.630
1 28. 794
1 28.958
1 29. 121
m. 8.
1 38.296
1 38.4.59
1 38.623
1 38. 787
1 38.951
m. a.
1 48. 125
1 48. 289
1 48.453
1 48. 617
1 48. 780
m. «.
1 57.955
1 58. 119
1 58. 282
1 58.446
1 58.610
m. li.
2 7.784
2 7.948
2 8.112
2 8.276
2 8.440
m. 8.
2 17.614
2 17. 778
2 17. 941
2 18. 105
2 18. 269
m. 8.
2 27.443
2 27. 607
2 27. 771
2 27. 9,35
2 28. 099
«.
1
2
3
4
«.
0.003
.005
.008
.011
5
6
7
8
9
1 19.456 1 1 29.285
1 19.619 1 29.449
1 19. 783 1 29. 613
1 19. 947 1 29. 777
1 20.111 1 29.940
1 39. 115
1 39. 279
1 39.442
1 39.606
1 39.770
1 48.944
1 49. 108
1 49. 272
1 49.436
1 49.600
1 58.774
1 58.938
1 59. 101
1 59.265
1 59.429
2 8.603
2 8.767
2 8.931
2 9.095
2 9.259
2 18. 433
2 18. .597
2 18. 761
2 18.924
2 19. 088
2 28. 263
2 28. 426
2 28. 590
2 28. 754
2 28. 918
5
6
7
8
9
.014
.016
.019
.022
.025
.027
.030
. 033
.035
.038
.041
.044
.046
.049
.052
.055
.057
.060
.063
.066
.068
.071
.074
.076
.079
:082
.085
.087
.090
.093
.096
.098
.101
.104
.106
.109
.112
.115
.117
.120
.123
.126
.128
.131
.134
10
11
12
13
14
1 20. 275 1 30. 104 1 39. 934
1 20.439 1 30.268 1 40.098
1 20. 602 1 30. 432 1 40. 261
1 20. 766 1 30. 596 1 40. 425
1 20. 930 1 30. 760 1 40. 589
1 49. 763
1 49.927
1 50.091
1 50. 255
1 50.419
1
1
1
2
2
59. 593
59. 757
59. 921
0.084
0.248
2 9. 423
2 9.586
2 9.750
2 9.914
2 10.078
2 19.252
2 19.416
2 19. 580
2 19. 744
2 19.907
2 20.071
2 20. 235
2 20. 399
2 20. 563
2 20. 727
2 20. 890
2 2T. 054
2 21. 218
2 21. 382
2 21.546
2 21. 709
2 21. 873
2 22.037
2 22. 201
2 22. 365
2 22. 529
2 22. 692
2 22. 856
2 23. 020
2 23. 184
2 29. 082
2 29. 245
2 29. 409
2 29. 573
2 29. 737
10
11
12
13
14
15 1 21.094 1 30.923 1 40.753
16! 1 21.258 1 31.087 1 40.917
17 i 21.422 1 31.251 1 41.081
18 1 21.585 1 31.415 1 41.244
19 1 21.749 1 31.579 1 41.408
1 50.583
1 50. 746
1 50. 910
1 51.074
1 51. 238
2
2
2
2
2
0.412
0. 576
0.740
0.904
1.067
2 10.242
2 10.405
2 10.569
2 10. 733
2 10. 897
2 11. 061
2 11. 225
2 11. 388
2 11.5.52
2 11. 716
2 11.880
2 12.044
2 12. 208
2 12. 371
2 12. 535
2 12.699
2 12. 863
2 13. 027
2 1.3. 191
2 13.354
2 13.518
2 13. 682
2 13. 846
2 14.010
2 14. 173
2 29.901
2 30. 065
2 .30. 228
2 30. 392
2 30. 556
2 30. 720
2 .30. 884
2 31.048
2 31.211
2 31. 375
2 31.539
2 31. 703
2 31.867
2 32. 031
2 .32. 194
2 32. 358
2 32. 522
2 32. 686
2 32. 850
2 33.013
15
16
17
18
19
20
21
22
23
24
.25
26
27
28
29
30
31
32
33
84
35
36
37
38
39
20 1 21.913 1 31.743 1 41. .572 ' 1 51.402
211 1 22.077 1 31.906 1 41.736 1 51.565
22 122.241 1.32.070 141.900 151.729
23 1 22. 404 1 32. 234 1 42. 064 1 51. 893
24 1 22.568 1 32. .398 1 42.227 1 52.057
2
2
2
2
2
1.231
1.395
1.559
1.723
1.887
25 1 22. 732 1 32. 562
26 1 22. 896 1 32. 726
27 1 23. 060 1 32. 889
28 1 23. 224 1 33. 053
29 1 23. 387' 1 33. 217
1 42. 391 1 52. 221
1 42. .555 1 52. 385
1 42. 719 1 52. 548
1 42. 883 ' 1 52. 712
1 43. 047 1 52. 876
2
2
2
2
2
2.050
. 2. 214
2.378
2.542
2.706
30
31
32
33
34
1 23.551 1 33.381
1 23.715 1 33. .545
1 23. 879 1 33. 708
1 24.043 1 33.872
1 24.207 1 ;«.036
1 43. 210 1 53. 040
1 43. 374 i 1 53. 2(M
1 43. .538 ' 1 53.368
1 43. 702 i 1 53. 531
1 43.866 ! 1 53.695
2
2
2
2
2.869
3.033
3.197
3.361
3. 525
35
36
37
38
39
1 24. 370 1 34. 200 ! 1 44. 029 i 1 53. 859
1 24. .534 j 1 34. .364 i 1 44. 193 1 1 54. 023
1 24. 698 . 1 34. 528 S 1 44. 357 1 54. 187
1 24.862 : 1 .34.691 ; 1 44. 521 , 1 54.351
1 25. 026 1 1 34. 855 j 1 44. 685 [ 1 of. 514
2
9
2
2
2
3.689
3.a52
4.016
4.180
4.344
2 23. 348
2 23. 512
2 23. 675
2 23. 839
2 24. 003
2 24. 167
2 24. .331
2 24.495
2 24. 658
2 24. 822
2 24. 986
2 25. 150
2 25. 314
2 25. 477
2 25. 641
2 33. 177
2 33. 341
2 33. 505
2 33. 669
2 33. 833
40
41
42
43
44
45
46
47
48
49
1 25. 190
1 2.5.353
1 25.517
1 25. 681
1 25.845
1 26.009
1 26. 172
1 26. 336
1 26.500
1 26.664
1 :«.019
1 3o. 183
1 35.347
1 35.511
1 35.674
1 35. 8.38
1 36.002
1 36. 166
1 36.330
1 36.493
1 36.657
1 36.821
1 36.985
1 37.149
1 .37.313
1 37. 476
1 37. 640
1 37. 804
1 .37.968
1 38. 132
1 44.849
1 45.012
1 45.176
1 4.5.340
1 4.5.504
1 45. 668"
1 45.832
1 45.995
1 46. 159
1 46.323
1 54. 678
1 .54.842
1 55.006
1 55.170
1 55.:«3
1 55.497
1 55. 661
1 55. 825
1 55. 989
1 56. 153
2
2
2
2
2
2
2
2
2
2
4.508
4.672
4.835
4.999
5. 163
5.327
5.491
.5.655
5.818
5. 982
2 14. 337
2 14. .501
2 14.665
2 14. 829
2 14. 993
2 15. 156
2 1.5.320
2 15.484
2 15.648
2 15. 812
2 33. 996
2 34. 160
2 34. 324
2 .34. 488
2 34.652
2 34.816
2 34. 979
2 35. 143
2 3.5. .307
2 35.471
2 35. 635
2 a5. 798
2 35. 962
2 36. 126
2 36. 290
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
1 26.828
1 26.992
1 27. 156
1 27. .319
1 27.483
1 27.647
1 27.811
1 27.975
1 28. 138
1 28.302
1 46.487
1 46.651
1 46.815
1 46.978
1 47. 142
1 56.316
1 .56.480
1 .56.644
1 56.808
1 56.972
2
2
2
2
2
6.146
6.310
6.474
6.637
6.801
2 15.976
2 16. 139
2 16. ;W3
2 16.467
2 16.631
2 25. 805
2 25. 969
2 26. 133
2 26. 297
2 26. 460
50
51
52
53
54
.137
.139
.142
.145
.147
1 47.306
1 47.470
1 47.634
1 47. 797
1 47.961
1 57. 136
1 57.299
1 57. 463
1 57. 627
1 57. 791
2
2
2
2
2
6.965
7.129
7.293
7.457
7.620
2 16. 795
2 16. 959
2 17.122
2 17. 286
2 17. 4.50
2 26. 624
2 26. 788
2 26. 9.52
2 27.116
2 27. 280
2 36. 454
2 36. 618
2 36. 781
2 36. 945
2 37. 109
55
56
57
58
59
.1.50
.153
.156
.158
0.161
Page 644]
TABLE s.
Sidereal into Mean Solar Time.
1
■2
To be subtracted from a sidereal time interval.
16^
17"
18'
lOb
20i>
ail"
221"
ask
For aeconds.l
in.
1
2
3
4
m. 8.
2 37. 273
2 37. 437
2 37. 601
2 37. 764
2 37. 928
2 47. 102
2 47. 266
2 47. 430
2 47. .594
2 47. 758
7J1, ».
2 56. 932
2 57. 096
2 57. 260
2 57. 424
2 57. 587
2 57. 751
2 57. 915
2 58. 079
2 58. 243
2 58. 406
m. «.
3 6.762
3 6.925
3 7. 089
3 7. 253
3 7.417
3 7.581
3 7.745
3 7.908
3 8.072
3 8.236
m. «.
3 16.591
3 16. 755
3 16.919
3 17.083
3 17.246
3 17.410
3 17. 574
3 17. 738
3 17.902
3 18. 066
m. s.
3 26.421
3 26. 585
3 26. 748
3 26. 912
3 27. 076
3 27. 240
3 27. 404
3 27. 568
3 27. 731
3 27. 895
7H. S.
3 36. 250
3 36. 414
3 36. 578
3 36. 742
3 36. 906
m. 8.
3 46. 080
3 46. 244
3 46. 407
3 46.571
3 46. 735
1
2
3
4
5
6
7
8
9
10
11
12
13
14
0. 003
.005
.008
.011
.014
.016
. 019
.022
.025
.027
.030
.033
.035
.038
5
6
7
8
9
10
11
12
13
14
2 38. 092
2 38. 256
2 38. 420
2 38. 584
2 38. 747
2 47. 922
2 48. 085
2 48. 249
2 48. 413
2 48. 577
3 37. 069
3 37. 233
3 37. 397
3 37.561
3 37. 725
3 46. 899
3 47. 063
3 47. 227
3 47. 390
3 47. 5.54
2 38. 911
2 39. 075
2 39. 239
2 .39. 403
2 39. 566
2 48. 741
2 48. 905
2 49.068
2 49. 232
2 49. 396
2 58. 570
2 58. 734
2 58. 898
2 59. 062
2 .59. 226
3 8.400
3 8.564
3 8.728
3 8.891
3 9.055
3 18.229
3 18.393
3 18.557
3 18. 721
3 18. 885
3 19.049
3 19.212
3 19.376
3 19.540
3 19. 704
3 28. 059
S 28. 223
3 28. 387
3 28. .550
3 28. 714
3 28. 878
3 29. 042
3 29. 206
3 29. 370
3 29. 533
3 37. 889
3 38. 052
3 38.216
3 38. 380
3 38. 544
3 47. 718
3 47. 882
3 48. 046
3 48. 210
3 48. 373
15
16
17
18
19
20
21
22
23
24
2 39. 730
2 39. 894
2 40. 058
2 40. 222
2 40. 386
2 49. 560
2 49. 724
2 49. 888
2 50. 051
2 50. 215
2 59. 389
2 59. .553
2 59. 717
2 .59. 881
3 0.045
3 9.219
3 9.383
3 9.547
3 9.710
3 9.874
3 38. 708
3 38. 871
3 39. 0;35
3 39. 199
3 39. .363
3 48. 537
3 48. 701
3 48. 86;5
3 49. 029
3 49. 193
15
16
17
•18
19
.041
.044
.046
.049
.052
2 40. 549
2 40. 713
2 40. 877
2 41.041
2 41.205
2 50. 379
2 50. 543
2 50. 707
2 50. 870
2 51.034
3
3-
3
3
3
0. 209
0.372
0. 536
0.700
0.864
3 10.038
3 10.202
3 10. 366
3 10.530
3 10.693
3 19. 868
3 20.032
3 20. 195
3 20. 359
3 20. 523
3 29. 697
3 29. 861
3 30. 025
3 30. 189
3 30. 353
3 39. 527
3 39. 691
3 39. 854
3 40.018
3 40. 182
3 49. 356
3 49. 520
3 49. 684
3 49. 848
3 50.012
20
21
22
2,3
24
. 055
.0,57
. 060
.063
.066
25
26
27
28
29
2 41.369
2 41. 532
2 41.696
2 41. 860
2 42. 024
2 51. 198
2 51. 362
2 51. 526
2 51. 690
2 51.853
3
3
3
3
3
1.028
1.192
1.355
1.519
1.683
,3 10.857
3 11.021
3 11. 185
3 11.349
3 11.513
3 20. 687
3 20. 851
3 21.014
3 21.178
3 21.342
3 30. 516
3 30. 680
3 30. 844
3 31.008
3 31. 172
3 40. 346
3 40. 510
3 40. 674
3 40. 837
3 41.001
3 50. 175
3 50. 339
3 50. .503
3 50. 667
3 50. 831
25
26
27
28
29
.068
.071
.074
.076
.079
30
31
32
33
34
35
36
37
38
39
2 42. 188
2 42. 352
2 42. 515
2 42. 679
2 42. -843
2 52. 017
2 52. 181
2 52. 345
2 52. 509
2 52. 673
3
3
3
3
3
1.847
2.011
2.174
2.338
2.502
3 11. 676
3 11. 840
3 12.(X)4
3 12. 168
3 12. 332
3 12. 496
3 12.659
3 12. 823
3 12.987
3 13. 151
3 13.315
3 1.3.478
3 13.642
3 13.806
3 13.970
3 21. 506
3 21. 670
3 21.834
3 21.997
3 22. 161
3 22. 325
3 22. 489
3 22. 653
3 22.817
3 22. 980
3 31. 3,36
3 31. 499
3 31. 663
3 31.827
3 31. 991
3 41. 165
3 41. 329
3 41. 493
3 41. 657
3 41. 820
3 50. 995
3 51. 158
3 51. 322
3 51. 486
3 .51.650
30
31
32
33
34
.082
.085
.087
.090
.093
2 43. 007
2 43. 171
2 43. 334
2 43. 498
2 43. 662
2 52. 836
2 .53. 000
2 53. 164
2 53. 328
2 53. 492
3
3
3
3
3
2.666
2.830
2.994
3. 157
3.321
3 32. 155
3 32. 318
3 32. 482
3 32. 646
3 32. 810
3 41. 984
3 42. 148
3 42. 312
3 42. 476
3 42. 639
3 51.814
3 51. 978
3 52. 141
3 52. 305
3 52. 469
35
36
37
38
39
40
41
42
43
44
. 096
.098
.101
.104
.106
.109
.112
.115
.117
.120
40
41
42
43
44
2 43. 826
2 43. 990
2 44. 154
2 44.317
2 44. 481
2 53. 656
2 53. 819
2 53. 983
2 54. 147
2 54. 311
3
3
3
3
3
3. 485
3. 649
3.813
3.977
4.140
3 23. 144
3 23. 308
3 23. 472
3 23. 6;W
3 23.800
3 32. 974
3 33. 138
3 33. 301
3 33. 466
3 33. 629
3 42. 803
3 42. 967
3 43. 131
3 43. 295
3 43. 459
3 52. 633
3 52. 797
3 52. 961
3 63. 124
3 53. 288
3 53. 452
3 53.616
3 53. 780
3 53. 943
3 54. 107
3 54. 271
3 54. 435
3 54. 599
3 54. 763
3 54. 926
3 55. 090
3 55. 254
3 5.5.418
3 55. 582
3 55. 746
45
46
47
48
49
2 44.645
2 44.809
2 44. 973
2 45. 137
2 45. 300
2 54. 475
2 .54. 638
2 54. 802
2 54. 966
2 55. 130
3
3
3
3
3
4.304
4. 468
4.632
4.796
4.960
3 14. 134
3 14.298
3 14.461
3 14.625
3 14. 789
3 23. 963
3 24.127
3 24.291
3 24. 4.55
3 24. 619
3 33. 793
3 33. 957
3 34. 121
3 34. 284
3 34.448
3 34.612
3 34. 776
3 34.940
3 35. 104
3 35. 267
3 43. 622
3 43. 786
3 43. 950
3 44.114
3 44. 278
3 44. 442
3 44.605
3 44. 769
3 44. 933
3 45. 097
4b
46
47
48
49
50
51
52
53
64
65
56
57
58
59
. 123
.126
.128
.131
.134
.137
.139
.142
. 145
.147
.150
. 1.53
.156
.1.58
0.161
50
51
52
53
54
55
56
57
58
59
2 45. 464
2 45. 628
2 45. 792
2 45. 956
2 46. 120
2 46. 283
2 46. 447
2 46.611
2 46. 755
2 46. 939
2 55. 294
2 55. 458
2 55. 621
2 55. 785
2 55. 949
3
3
3
3
3
5. 123
5.287
5. 451
5. 615
5.779
3 14.953
3 15. 117
3 IS. 281
3 15. 444
3 15.608
3 24. 782
3 24.946
3 25. 110
3 25. 274
3 25. 438
2 56. 113
2 56. 277
2 56. 441
2 56. 604
2 56. 768
3
3
3
1 3
5.942
6.106
6. 270
6. 434
6. .598
3 15.772
3 15.936
3 16. 100
3 16. 264
3 16. 427
3 25.602
3 25. 765
3 25. 929
3 26. 093
3 26. 257
3 35. 431
3 35. .595
3 35. 759
3 35. 923
3 36. 086
3 45. 261
3 45. 425
3 45. 588
3 45. 752
3 45. 916
TABLE 9.
Meaii Solar into Sidereal Time,
To be added to a mean time interval.
3i>
41"
0.000
0.164
0.329
0.493
0. 657
5
6
7
8
^
10
11
12
13
14
0.821
0.986
1.150
1.314
1.478
1.643
1.807
1.971
2.136
2.300
15
16
17
18
19
'20
21
22
23
24
25
26
27
28
29
2.464
2.628
2.793
2. 957
3.121
9.856
10.021
10. 185
10.349
10^5J4_
10.678
10.842
11.006
11.171
11.335
11.499
11.663
11.828
11.992
12. 156^
012. 321
12.485
12.649
12. 813
12.978
3.285
3.450
3.614
3.778
3.943
4. 107
4.271
4.435
4.600
4.764
4.928
5.093
5.257
5.421
5.585
5.750
5.914
6.078
6.242
6.407
13. 142
13.306
13.471
13. 635
13.799
13. 963
14. 128
14. 292
14.456
14.620
OH. 785
14.949
15. 113
15. 278
15.442
19. 713
19. 877
20.041
20. 206
20. 370
20. .534
20.699
20. 863
21. 027
21. 19 1
21.356
21. 520
21.684
21.819
22.013
22. 177
22. 341-
22. 506
22. 670
22. 834
29. 569
29. 734
29. 898
30.062
30. 227
7. 392
7.557
7.721
7.885
8. 049
8.214
8. 378
8. 542
8.707
_8^71^
9. o:»
9.199
9. 364
9. 528
9.692
15.606
15.770
15.935
16.099
16.^6.3
16.427
16.592
16. 756
16.920
17.085
17.249
l"!. 413
17.577
17. 742
17.906^
18.070
18.234
18. 399
18. .563
18. 727
18.892
19.056
19.220
19.384
19. .549
22. 998
23. 163
23. 327
\ 23.491
23^a56
i'O 2.3. 820^
23. 984
24. 148
24.313
24. 477
24. 641"
24. 805
24. 970
i 25! 134
I 25. 298
I 25. 463
25. 627
25. 791
25. 955
< 26.120
' 26. 284
' 26. 448
! 26. 612
; 26. 777
! 2 6. 941
i 2
30. 391
30. 555
30. 719
30. 884
31.048
31. 212"
31. 376
31.541
31.705
31. 869
32.034
32. 198
32. 362
32. 526
3 2. 69 1_
32. 855
33. 019
33. 183
33. 348
J) 33^512
33. 676"
33. 841
34. 005
34. 169
; OJR 333
I 34.498"
34. 662
I 34. 826
I 34.990
1 35. 155
39.426
39.590
39. 754
39.919
40. 083
4a 247
40.412
40. 576
40. 740
40. 904
41.069
41. 233
41. 397
41.561
41.726
! 35. 319
! 35. 483
36. 648
35.812
I 35. 976
105
27. 270
27. 434
27.598
27^762^
27.927
28. 091
28. 255
28. 420
28. 584
"0 28. 748
28.912
29. 077
29. 241
29. 405
36. 140
36. 305
36.469
36. 633
.36.798
"O" 36". 962"
37. 126
37.290
37. 455
37.619
377783
37. 947
38. 112
38. 276
,38.440
38.605
38. 769
38. 933
39. 097
39. 262
41.890
42. 054
42. 219
42. 383
42. 547
42.711
42. 876
43. 040
43. 204
0^3. 368
43:5.33
43. 697
43. 861
44. 026
<0 44. 190
44.354
44. 518
44. 683
44. 847
45. Oil
m. 8.
49. 282
49. 447
49.611
49. 775
0Jr9. 939
50." 104
50. 268
10. 432
.50. 597
50. 7 61
50. 925
51. 089
51. 254
51.418
51. 582
51. 746
51.911
52. 075
52. 239
52.404
"52; 568
52. 732
52. 896
53. 061
53.225
45. 176
45. .340
45. 504
45. 668
45. 833
45. 997
46. 161
46. 325
46. 490
46. 654
46. 818
46. 983
47. 147
47.311
47. 475
47. 640
47. 804
47. 968
48. 132
048. 297_
48. 461
48. 625
48. 790
48. 954
49. 118
55. 032
55. 196
55. 361
55. 525
55.6 89
55. 853
56.018
56. 182
56. 346
0J6.M0
'0 56. 675
56. 839
57. 003
57. 168
0_57. 332
57.496
57.660
57. 825
57. 989
0_58. 153
"0 58. 31 7"
58. 482
58. 646
58.810
58. 975
Page 646]
TABLE y.
Mean Solar into Sidereal Time.
To be added to a mean time interval.
8'
1
2
3
_4
5
6
7
8
_9
10
11
12
13
U
15
16
17
18
19
20
21
24
25
2(1
27
28
20
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
1 18.852
1 19.016
1 19.180
1 19.345
jl_19. 509
1 r9.'673
1 19.837
1 20. 002
1 20. 166-
1 20.330
1 20. 495
1 20.659
1 20.823
1 20.987
1 21^1.52
1 21.316
1 21.480
1 21.644
1 21.809
1 21.973
22. 137
22. .302
22. 466
22. 630
22.794
22. 959"
23. 123
23. 287
23. 451
23. 616
23. 780
23. 944
24. 109
24. 273
24^37_
24. 601
24.766
24. 9,30
25. 094
25. 259
25. 423
25. 587
25. 751
25.916
26. 080
26.244
26.408
26. 573
26. 737
26.901
27. 066
27. 2.30
27. 394
27. 558
27. 723
»''
27. 887
28. 051
28. 215
28. 380
28. 544
1 28.708
1 28.873
1 29.037
1 29.201
1 29.365
1 29.530'
1 29.694
1 29.858
1 .30.022
1_30.J87^
"l 30.351
1 30.515
1 30.680
1 30.844
1 31.008
1 31.172
1 31.337
1 31.501
1 31.665
1 31.829
1 31.994
1 32.158
1 32. .322
1 32.487
132. 651
1 i52. 815
1 ,32.979
1 33. 144
1 ,33.308
1 3.3.472
1 38.5ft5
1 38.729
1 38.893
1 39.0.58
1 39.222
1 39.386
1 39.5.50
1 39.715
1 .39.879
1 40.043
1 40. 207
1 40.372
1 40. .536
1 40. 700
jl_40^865
1 41.029
1 41. 193
1 41.3,57
1 41.. 522
1 41.686
1 3.3.637
1 3,3.801
1 33.965
1 34. 129
1 34. 294
1 34.458
1 34.622
1 34. 786
1 34.951
1 35.115
1 3-5.279
1 35.444
1 .35.608
1 35. 772
1 35.936
1 36. 101
1 .36.265
1 36.429
1 36.593
1 36. 758
1 36.922
1 37.086
1 ,37.251
1 37.415
1 37.579
1 37. 743
1 37.908
1 38.072
1 38.236
1 38.400
1 41. 850
1 42.015
1 42. 179
1 42.343
1 42^ 507
1 42. 672
1 42.8,36
1 43.000
1 43.164
1 43.329
1 43.493
1 43.657
1 43.822
1 43.986
1 44. 150
1 44. 314
1 44.479
1 44.643
1 44.807
1 44.971
1 45. 136'
1 45. 300
1 4.5.464
1 45. 629
1 45. 793
111'
1 48.421
1 48.585
1 48. 7.50
1 48.914
1 49.078
1 45. 957
1 46.121
1 46.286
1 46.450
1 46.614
1 46. 778
1 46.943
1 47. 107
1 47.271
1 47.436
1 47.600
1 47. 764
1 47.928
1 48.093
1 48.257
1 49.243
1 49.407
1 49.571
1 49. 735
1 49^900
1 50. 064'
1 .50.228
1 .50.393
1 50. ,557
1 50^721
I 50.885
1 51.050
1 51.214
I 51.. 378
1 51. .542
1 51. 707
1 51.871
1 ,52.035
1 .52.200
1 52. 364
1 .52.-528
1 .52.692
1 ,52.857
1 53.021
1 ,5.3. ia5
1 53. 349
1 ,53.514
1 ,53.678
1 53.842
1 54.007
1 54. 171
1 54.335
1 .54.499
1 54. 664
J_54.828
1 54.992
1 55. 1.56
1 55. 321
1 55. 4a5
1 .55. 649
1 .55.814
1 55.978
1 ,56. 142
1 56.306
1 56. 471
12"
1 .56. 6,35
1 ,56. 799
1 ,56.964
1 57.128
1 57.292
1 57. 456
1 ,57.621
1 57. 785
1 57. 949
1 58. 113
1 ,58.278
1 58.442
1 58.606
1 58. 771
1 58. 935
IS'
59. 099 ' 2
59. 263 i 2
59. 428
59. 592
59. 756
1 59.920
2 0. 085
2 0. 249
2 0. 413
2 0. 578
'2 0.742'
0. 906
1.070
1.2,35
h399_
1 . 563
1.727
1.892
2.056
2.22
2. 385'
2. .549
2. 713
2.877
_3^,Q42
3. 206
3. 370
3. 534
3. 699
3. 863
8.134
8.298
8. 463
8.627
8.791
8. 9,56
9.120
9.284
9.448
9. 613
2 9.777
2 9. 941
2 10. 105
2 10. 270
2 10.434
2 10.598
2 10. 763
2 10.927
2 11.091
2 11.2.55
2 11.420
2 11.. 584
2 11. 748
2 11.912
212. 077
2 12.241
2 12.405
2 12. ,570
2 12.734
2 12.898
4.027
4.192
4. 3,56
4. 520
4.684
4.849
5. 013
,5. 177
5. 342
5^506
5.670
5. 834
5. 999
6.163
6.327
6.491'
6.&56
6.820
6.984
7.149
2 13.062
2 13.227
2 1.3.391
2 13. ,5,55
2 13. 720
I 2 13.884
I 2 14.048
i 2 14.212
2 14.377
2J4^541
2 14.70,5
2 14.869
2 1.5.0.34
2 15. 198
2 15. 362
7. 313
7.477
7.641
7.806
7.970
2 15. ,527
2 1,5.691
2 15.8.55
2 16.019
2 16. 184
2 16.348
2 16. ,512
2 16. 676
2 16. 841
2 17.005
2 17. 169
2 17.3,34
2 17.498
2 17.662
2 17.826
17.991
18. 1.55
18. 319
18. 483
18. 648
2 18.812
2 18.976
2 19.141
2 19.305
2J9^469
"2 19.633
2 19. 798
2 19.962
2 20. 126
2 20.290
2 20.4.55
2 20.619
2 20. 783
2 20. 948
2 21.112
2 21.276
2 21.440
2 21.605
2 21. 769
2 2 1. 933
2 22. 098
2 22. 262
2 22. 426
2 22. ,590
2^22. 755^
2 22.919
2 23.083
2 23. 247
2 23. 412
2 2,3. .576
2 23. 740
2 23. 905
2 24. 069
2 24. 233
2 24. 397
2 24. .562
2 24. 726
2 24. 890
2 25.054
2 25.219
2 25. 383
2 2.5.547
2 25. 712
2 25. 876
2 26.040
2 26.204
2 26. 369
2 26. 5,33
2 26.697
2 26. 861
2 27.026
2 27. 190
2 27. 354
2 27.519
2 27.683
27.847
28.011
28. 176
28. 340
28.504
2 28.668
2 28. 833
2 28. 997
2 29. 161
2 29.326
2 29.490
2 29. 654
2 29. 818
2 29.983
2 .30. 147
2 30.311
2 30. 476
2 30. 640
2 ,30. 804
2 .30. 968
2 31. 133
2 31.297
2 31. 461
2 31. 625
2 31. 790
2 31. 954
2 .32. 118
2 32. 283
2 32. 447
2 32. 611
2 .32. 775
2 32. 940
2 33. 104
2 33. 268
2 ,33 . 432
2 33:'597
2 33. 761
2 33. 925
2 ,34.090
2J4.254
2 34.418
2 34. ,582
2 34. 747
2 34.911
235. 075
2 35. 239
2 -35. 404
2 35. 568
2 .35. 732
2_35^897
'2 36.061
2 36. 225
2 36. 389
2 36. 554
2 36. 718
2 36. 882
2 37. 047
2 37. 211
2 37. 375
2 37. 539
For seconds,
0.003
.005
.008
.011
.014
.016
.019
.022
. 02 5
. 027"
.030
. 033
.036
.038
.041
.044
.047
.049
.0.5 2
. 055'
.0.57
.060
.•063
.06 6
.068'
.071
.074
.077
07 9
.082'
.085
.088
.090
.093
.096
.099
.101
.104
.107
. 110
.112
.115
.118
.120
. 123
.126
.129
.1.31
.134
.137
.140
.142
.145
148
.151
.153
.156
.159
0.162
TABLE !t. [Page 647
Mean Solar into Sidereal time.
To be added to a mean time interval.
IS"
i;!-
ISi
19h
SO''
21h
vt. «.
3 26. 986
3 27. 150
3 27. 315
3 27. 479
3 27. 643
22h
23k
For seconds.
m.
1
2
3
4
m. s,
2 37. 704
2 37. 868
2 38. 032
2 38. 196
2 38. 361
2 47. 560
2 47. 724
2 47. 889
j 2 48. 053
1 2 48. 217
m. 8.
2 57.417
2 57. 581
2 57. 745
2 57. f)09
2 58. 074
2 58. 238
2 58. 402
2 58. 566
2 58. 731
2 58. 895
2 59. 059
2 59. 224
2 59. 388
2 59. 552
2 59. 716
2 59. 881
3 0.045
3 0.209
3 0.373
3 0.538
m. s.
3 7.273
3 7. 437
3 7. 602
3 7.766
3 7.930
3 8. 094
3 8.259
3 8.423
3 8.587
3 8.751
3 8.916
3 9.080
3 9.244
3 9.409
3 9.573
3 9.737
3 9.901
3 10.066
3 10.230
3 10.394
VI. 8.
3 17. 129
3 17.294
3 17.458
3 17.622
3 17. 787
in. s.
3 36. 842
3 37. 007
3 37.171
3 37. 335
3 37. 500
m. it.
3 46. 699
3 46.863
3 47.027
3 47.192.
3 47. 356
». 8.
1 : 0. 003
2| .005
3! .008
4! .011
5, .014
6' .016
7 .019
8 .022
9 .025
5
6
7
8
9
10
11
12
13
14
2 38. 525 1 2 48. 381
2 38. 689 i 2 48. 546
2 38. 854 1 2 48. 710
2 39. 018 : 2 48. 874
2 39. 182 1 2 49. 039
3 17.951
3 18. 115
3 18. 279
3 18.444
3 18.608
3 18. 772
3 18.937
3 19.101
3 19.265
3 19.429
3 27.807
3 27. 972
3 28. 136
3 28. 300
3 28. 464
3 37. 664
3 37. 828
3 37. 992
3 38. 157
3 38. 321
3 47. 520
3 47. 685
3 47. 849
3 48.013
3 48. 177
2 39. 346
2 39. 511
2 39. 675
2 39. 839
2 40.003
2 49.203
2 49. .367
2 49. 531
2 49. 696
2 49. 860
3 28. 629
3 28. 793
3 28. 957
3 29. 122
3 29. 286
3 29. 4.50
3 29. 614
3 29. 779
3 29.943
3 30. 107
3 30. 271
3 30. 436
3 .30. 600
3 30. 764
3 30.929
3 38. 485
3 38. 649
3 38. 814
3 38.978
3 39. 142
3 39.'307
3 39. 471
3 39. 635
3 39. 799
3 39. 964
3 40. 128
3 40. 292
3 40. 456
3 40. 621
3 40. 785
3 48. 342
3 48. .506
3 48. 670
3 48. 834
3 48. 999
3 49. 163
3 49. 327
3 49. 492
3 49. 656
3 49. 820
'3 49. 984"
3 .50. 149
3 .50.313
3 .50. 477
3 50. 642
3 50.80(>
3 .50. 970
3 51. i;m
3 51. 299
3 51.463
10 . 027
U .030
12 . 033
13 . 036
14 .038
15
16
17
18
19
2 40. 168
2 40. 332
2 40. 496
2 40. 661
2 40. 825
2 50. 024
1 2 50. 188
2 50. 353
2 50. 517
2 50. 681
2 50:846
2 51.010
2 51.174
2 51.338
2 51.503
3 19.594
3 19. 758
3 19.922
3 20. 086
3 20. 251
15 . 041
16 . 044
17 . 047
18 .049
19: .0.52
20
21
22
23
24
25
26
27
28
29
30
31
32
.33
34
35
36
37
.38
39
40
41
42
43
44
2 40. 989
2 41. 153
2 41.318
2 41.482
2 41. 646
3 0.702
3 0.866
3 1.031
3 1. 195
3 1.359
3 10.559
3 10.723
3 10.887
3 11.051
3 11.216
3 20. 415
3 20.579
3 20. 744
3 20.908
3 21.072
20
21
22
23
24
25
26
27
28
29
. 0.55
.0.57
.060
.063
.066
2 41.810
2 41.975
2 42. 139
2 42. 303
2 42. 468
2 51.667 3 1.523
2 51.831 3 1.688
2 51. 995 1 3 1. 852
2 52. 160 i 3 2. 016
2 52. 324 3 2. 181
3 11.380
3 11. .544
3 11. 708
3 11.873
3 12.037
3 21. 236
3 21.401
3 21. 565
3 21. 729
3 21.893
3 31.093
3 31.257
3 31.421
3 31.586
3 31. 750
3 40. 949
3 41.114
3 41. 278
3 41.442
3 41.606
.068
.071
.074
.077
.079
2 42. 632
2 42. 796
2 42.960
2 43. 125
2 43.289
2 52. 488
2 52. 653
2 52. 817
2 52. 981
2 53. 145
2 53. 310
2 53. 474
2 53. 638
2 53. 803
2 53. 967
2 .54. 131
2 54. 295
2 54. 460
2 54. 624
2 54. 788
3 2.345
3 2. .509
3 2.673
3 2.838
3 3.002
3 3.166
3 3.330
3 3.495
3 3.659
3 3.823
3 12. 201
3 12.366
3 12.530
3 12.694
3 12.858
3 13.023
3 13. 187
3 13.351
3 13.515
3 13.680
3 22.058
3 22. 222
3 22.' 386
3 22. .551
3 22. 715
3 31.914
3 32. 078
3 32. 243
3 32. 407
3 .32. 571
3 41.771
3 41. 935
3 42. 099
3 42. 264
3 42. 428
3 51.627
3 .51. 791
3 51. 9.56
3 .52. 120
3 52. 284
30
31
32
33
34
. 082
' .085
.088
.090
.093
2 43. 453
2 43. 617
2 43. 782
2 43. 946
2 44. no
2 44. 275
2 44. 439
2 44.603
2 44. 767
2 44. 932
3 22.879
3 23.043
3 23. 208
3 23. 372
3 23. 536
3 32. 736
3 32. 900
3 33. 064
3 33. 228
3 33. 393
3 42. 592
3 42. 756
3 42. 921
3 43. 085
3 43. 249
3 .52.449
3 52. 613
3 52. 777
3 52. 941
3 53. 106
35! .096
36 ' . 099
371 .101
38 1 .104
39: .107
3 3.988
3 4.152
3 4.316
3 4.480
3 4.645
3 13.844
3 14.008
3 14.173
3 14. .337
3 14.501
3 23. 700
3 23. 86.5
3 24.029
3 24. 193
3 24. a58
3 33. .557
3 33. 721
3 33. 886
3 34.0.50
3 34. 214
3 43. 413
3 43.578
3 43. 742
3 43. 906
3 44. 071
3 53. 270
3 .53.434
3 .53. 598
3 53. 763
3 53. 927
3 54. 091
3 54. 256
3 54. 420
3 54. 584
3 54. 748
40 .110
41: .112
42 i .115
43! .118
44} .120
45
46
47
48
49
50
51
52
53
54
55"
56
57
58
59
2 45.096
2 45. 260
2 45. 425
2 45. 589
2 45. 753
2 54. 952
2 55.117
2 55. 281
2 55. 445
2 55. 610
3 4.809
3 4.973
3 5.137
3 5.302
3 5.466
3 14.665
3 14.830
3 14.994
3 15. 1.58
3 15.322
3 24.522
3 24. 686
3 24. 850
3 25. 015
3 25. 179
3 34. 378
3 34. 543
3 34. 707
3 34. 871
3 35. 0*5
3 3!). 200
3 35. 364
3 35. 528
3 35. 693
3 :«. 857
3 44. 2*5
3 44. 399
3 44. .563
3 44. 728
3 44. 892
45
46
47
48
49
.123
.126
.129
.131
.134
2 45. 917
2 46. 082
2 46. 246
2 46. 410
2 46. 574
2 55. 774
2 55. 938
2 56. 102
2 56. 267
2 56. 431
3 5.630
3 5.795
3 5.959
3 6.123
3 6.287
3 15. 487
3 15. mi
3 15.815
3 15.980
3 16. 144
3 25. 343
3 25. 508
3 25. 672
3 25. 836
3 26.000
3 45. 056
3 45. 220
3 45. 385
3 45. 549
3 45. 713
3 54. 913
3 55. 077
3 55. 241
3 55. 405
3 55. 570
50
51
52
53
.54
.137
.140
.142
.145
.148
2 46. 739
2 46. 903
2 47. 067
2 47. 232
2 47. 396
2 56. 595
2 56. 759
2 .56. 924
2 57. 088
2 57. 252
3 6.452
3 6.616
3 6.780
3 6. 944
3 7. 109
3 16.308
3 16.472
3 16.637
3 16.801
3 16.965
3 26. 165
3 26. 329
3 26. 493
3 26. 657
3 26. 822
3 36. 021
3 36. 185
3 36. :i50
3 36. 514
3 36. 678
3 45. 878
3 46. 042
3 46. 206
3 46. 370
3 46.-5.35
3 55. 734
3 55. 898
3 56. 063
3 56. 227
3 .56. 391
55
56
57
58
59
.151
.153
.156
.159
0.162
Page 648]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
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TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 649
1)
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Page 650]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
•9
S Ia
l6 >0 iS lA
l-J
o
in ''^
T3
3
5
o
n
■xoiddy
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1 eo c^c^c^ -N c
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■— - - - - -- rH rti-H 'iic^ oicc r^ cc 0^i2
■^r-Tfi^'^i--'s<f-*t^!Mi-EOXcoxeoxcox;co30cox«xeoxccx
rHi-HXiO'^QOt-iWI^'n
■^t-cot^coxcoxecx
coxMXcoxcoxeox
S-raixosoiot^oM
P5XCOXCOCCOTXCCX
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^ -^ t^ -T t- -v r- -ri* f i^
c)coi-iecwMOTj«c5'*
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S533SS385S
r*'«j<r-coi-«xcox
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1- !D 1> I-*
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to to to to to to to to to to
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to to to to to
to to to to to
tti CO tf CO OJ ui tf X oi en
tAkOinin loinioin^
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 651
7
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to m CD
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in CD in CD
Page 652]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
s §
8
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TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 653
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Page 654]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
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TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 655
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Page 656]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
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TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 657
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Page 658]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
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[Page 659
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g'-vwto^xqCi-itpiocoitp^oiaoMiCiCWapOs'rtiOiCMaooQiMTtOQ
M,--ii-i.-HrHOC^OMOMOC4»OCCiCMiCeC'*l"-V'V'V'*^TOiCeCl'3CO
SS828S§SSSSS
tre CO -J" CO ■* ■'T -v
(-■OCOJIplOXCJQlCrHM
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wiflc^ic?iioec^eo-v
t^Mi-'Oi-finXJJMQC
rt^'^cC'^CO'^eOiC?!
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S38
l> "<*'X
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0i tA tC 9^ O lA t^
— ' O '-H O ^H .-I c
X'V X ^Xt
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r-*l-lO— I OMlf
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X ""CX-^X
X'^X
8COiOXO»^T
X M X CO XC
tOia.-l,~(U5
fH-HriOlO
TfX-^X-^
COM OiiO
cSocNiS
x-^xco
in eoifflSS'fl"
ccxeoxeo
cMiCCJioco-vw-^-^eo
xeoxcoxcoxeoxco
tooic^eoos
(MTJ'CO'^CO
xeoxeox
ccxeoxeo
eccoeo
X eoxeox
c5io^oo
eoxeooieo
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253838
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Page 660]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
O .-* N
r1 rf
o
c o 1 ad V
sa
|2i
tf oatfccpjcyieJaQp^aJ 05 so 0? ai C^ go S:5 m a^' m rt g^ SJ co Ctj cd oI cc P3 cd
O tH (N CO
rtMOiiCOit-t^QOiOOCOM'?)
■^ iCi '-O ^ 'S '-Ci '•£ '-O '-O '-D 1.^ ! 'i it^ '-O lA ".i 11^ ^ iC- 'O lO "-O iC to lO to lO CO iC :0 lO
123 X i3 X 2i X 2i X 2i X 2; yi
•^iC'-oiotoicotctoio-oin
^iC^'CtOiC'-D^OO'C
,c*ifstoiCtoif2iraiCic*.oic
oiooiooooi;
"O lO ^ lO O 1^ to i-O CO iC jo lO O lO ^ lO — m -O lO fO 10 to lO to lI to iC to lO to 10
to us to ic to i;
SiCtOL": tOiCtOiOtOiffltOiJ^tDiffl tOtOtomtOu^tomtOiCtOO
■m,_— lanOCCt^tOOliC OCC?^MC0Oi0^tCl— 'Xtoai-:tHr-*MCOr-'M'CTitOOOOCtOO'I''-<COCO'--l'^3l
a ic o tS S) 25 iS ic <c u: If; Sicinooioo-^o-T- o ■* o -f >-i -:i- ^ -f ,-( co t-. «5 .-h co m co -m ;o m co m f 1
,^ictoiniCicic»OiCi^i(i oif;toif;toictoic;oic,tootoiotointoictoifDj'.ootoictoifltOifrtoii5toiC
^iCtOiCi-OiCiCiOiCiCiO iCifitDiCOiCtOintOiC.tOi/StOiCtOiOtOiCtOiC itOiOtOiCtOiiTtOi^tOifStOiO
SicoSifiiSiraiciSioui
^lOtoidCiniOiCiftiOic
iOii55ioii'COii5orr|5'TO-a'0'4r-.-^r-i'W
iftlOtOiOtOiCtDinaSiCltOifltOiOtOlOtDiOtOini
«crnOxtotoxica)cg--cj
to >n to it3 to i^ to o to lo to ic
gu5o>Ai.oiS335iOic>ciaioooo.f:oioO'5',o^O"^o-5'0-
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•^'.■^oiCiomiCiomioiCjiootciCtoictoictoo toictoictoiotoiatoic toictoirttDiotoi-ttoiCtoiffl
tOOtOiOtOw^tOirttOiOtOiiO
SiCOiAioSBiSiCiCira StSoiCoS&vfsSS o-^O'^o-s'S-fi"^'
i^iOtOiCi^iOifltOi-OiOin lOiOtOiCtOiOtOiOtOiC tOiCtOiCtOiCtOifJtOiO
psCOi— "rfOKJffltOOCH— t- XltOQifjTH^-^SOCSC-I 3'i-iif;OtOCT>f-r-5CtO,^00'9'inMCOC-l'*OiOCTi
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-J■«"C^lC^-Htoo^•»o>GOoo»r^OtOlHl5I^-T:CMh^c^"^'HO©t'•aiXX5?^-oto■-^-^
^>o;o»otoif:toij^iciOi-':ootoiotOL'ttoiCtoiojtoiotoictoi-'^touitoi.'r'tointoif;toii:t;toiOtovctoi^
f^ -H oi \o i-* •■o o t^ <^ cc a ' O' cc ot-' ^ 'S ^ ^'^ ^ f ■'2-2 'S "H •■2.':: '£ "^'^ '^
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SiCOiSiiiSOiCOiftiniCicOiOOOO'SOiOCiiCOiCOiCOiCOO
^ lO to lO to ic '.o ic to If;' xo icvcs toiOtoif;' toif; "-Oic Itoif; to if; toic to i^ toif: jtoio to ic toif; too too to L-t
»xa>t^otO'"OJ^'*?^M
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^ o to o to iC to o to o to
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to i-t to O to O tp O to o
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p^otootootootooto tototototototototoo
SSSSSSSSSS'SSSSSSSSggSg
o o to o to o to o to o to o to o to O to o to o to o
S'l^OX-^Oi'^'OiWOCO
0000000000
^OtOOtOOtOOtOtOtO
SMi-iMT-ii-ny<--MO
iioijoooooo
to to to to to to to to to to
CCOl-fOl-fCCOCOOI-- tOt^^cpr-tOXiQXI'O-r
0000000000 000000000000
to o to O to O to o to o to o to o to o to o to O to o
-i'xtpxosioai-fO'*' OMi~ic3!-*2'53iJi':2
S0000 00000;0000000000
^ O to o to o to O to to to j to to to to to to to to to to
cc T-i CO o g" o -t" Ci o OS '-c X to CO to X r- 1^ !;■ to X to
■0000000000 lO 000000 00000
to to to -o to to to iC to O ; to O to »C to o to o to o to o
SSSg88S8SS8|3SS3gS8SS§
rtSOtOOtOtOtOtOtOtOtO'tOtOtOtOtOtOtOtOtOtO
totototototototototo
SooooSooooo
^totototototototototo
aOx^x>-ix^t-i~Ht:-
50000000000
jtotototototototototo
Sggggggggg
totototototototototo
to to to to to to to to to to
ggggSSSSBSSS
tototototototootootoo
COOCO-9''3'"*-*«OM
0000000000
^tototototototototo
OMOiM»!?1tOfHtOi--tI--i-(
000000000000
OtOtOtOtOtOtOtOtOtOtOtO
C0t0C0OT5<OTr^'*'S'O'3'O^O*J'OC0t0C0t0«
ooooooooooioooooooooooo
to to to to to to to to to to to to to to to to to to to to to to
500
jtOtOtOtOtOtOtOtCtOtC
totototototototototo
0000000000
to to to to to to to to to to
gggggggggggg
tOtOtOtOtOtOtOtOtOtOtOtO
SSSSSSSSSSS
jtotototototototototo
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to to to to to to to to to to
to to to to to to to to to to
^-OtOtOtOtOtOtOtOtOtO
(COOCOOMOCCOMO
jOWOi-HOTHOiHOrH
'tototototototototoco
■«0.-HO--lO— tO»H
totototototototototo
i to to to to to to to to to to
S--* S3 "^ 22 "t! J2 n! 25 ::!
.HC5iHOfHOr-lOT-l
totototototototototo
03 CO ft- 03 Oi IX CtJ 02 P5 CC 55 02 aj O) ftj CO a; CO Oh CO
7^'
totototototototototo
ojcofticopija^ftjcoojw
totootototototototototo
SSSSSSSSoSSS
tOtOtOtOtOtOtOtOtOtOtOtO
totototototototototototo
ft^coft^coftjcoaSc^ftScopjco
»
fN
1
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t— ,
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^
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^
^
1
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h<^
OS
3
O
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 661
S^
■a(i)p
xojddy
S i3 a S 8 s s
ojcoBS'teaJMaJKcSx axpjx!jjccasa;«te «»3BSto«aiBJtorta3 aSoJoiccaJaiKcoMco
t-'^r-"V£-^t-'fl*r»'^
gSS3i;a?2SS SS88S83S83 SSSS3!;S3S5
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^toi/ji^otoio^iccci.- '^ictoicxiii^tou^tcio tcre^oiCtoiaca^'ef
f- ■^ r* ■* r-
J3
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rH^i-lCOl-tCCi— ICCOC
« I 5
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3S32
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tOtC^tO^<OCOtO<0^ to (D to to
(£COU
TOT iC OS 1/
3&;0&<:
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3-
Page 662]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
a
3
o
oj
■^
3
3
d
s
n
■s
0)
a
o
»
^ai^^AXaic^a^Q^ca dcACc^aJo^ccaJinaicQ
rf;l>'T"t--I'l>Tt"i^<^t*-j<
n -f "> ^ lO r- OJ -f M O
-< w 6i CO T) c^ c) c-i ^ n
ojcoC^cofi^iQQB^'ccQ^cQ ci!x:^:iic:^c€sia^oi
-fC-lTT-HiOr-iiOOOO OOO'Ct-i-rOl^tMCO
Ht--^r-'*i---j*t>.r
00^COCO0O«00CO30W
i>.Tft^<ij<i>'»j'r--
O lO -f ?1 W GC C-) "Tf. to o
KuMCOMCQi-H-^rH-T-r-i
'OOOiSO'Oi-'Ti-i-HCO
fODMoocoaocococo
3iO if^ >— I o (p lo i-i o m
.^-^C^-j-oorococoaoco
xoooocococoaocooict
XCOXCOOOCOOOCOXM
xcccoMXMoorsx:^
[-'■*i>.-rt^-t"I--'*i-^-TC i^-^OTj"t-
-COX«:XCOXP300COXeO»CO
SiCiQiCiOO'^ri-iT'i— coc^eo
rt-rot-rooocoxcOQOCOooco
J I- -f i^ -f i:^ -r 1-
--i?a>-(C»^?IC0'M7-tC^'n MC^MMCOt-f^.-1-rO lOO'StOOi.lO'Tr-iM
«r--*oo>'^T-(.-f-r^'POl5i-rcii-
g '^ f -O "^ I* •*■ t- -1* t^ -1" I- -f t> -
t OC X lO --' ri
-t TO r-i M M M
■- f t^ -t* t* -f
rt ?1 c^ cl n c-i :o -^ CO ^ .-r o -^^ O o lO 2 lA d) -^
[~-^t--fI^TC*^t^**l>'Vt-'7'I-COl^CCXr3
s^o-^o>ftoiOOu'tolinoiOiOoioo'00'vlO"5i-^-rf-i'^i-i?5c^co
STj'.-i-Tf-.-jj'O'JO'So
rf* ^ iC ^ iC'O O « »0 '.D iC
« ifl 'O O :ii u-D to •»* 1-- •«»" : I-' •»• t- ■* i^ 't I* T
•t^M<t--3'I>-Tt^rrt>"rJ<
ji -X. r- X O S =C 1-1 1-- C^ iHl
^ -o iC o in « o ^ 1(3 ro >o
^ -^ ic '^ ic'-o lo o lO «o k;
2; -v eg c>i r- o 01 go r-i tp ?o ■ai iQ c-1 CO o o X c-1 1.'; o !^l X o .-. t^ ■»»■ -T t^ .-4
■Vr-CTpFHTIHi-CiS^OlOOlOOlCOlOOOiOOlOOOOinr-l-S'^-.Tft-l-r
■-DiO':3iCOiOOiOOK5 '-3iO«iO^ire'-0iCSif5'-O-*'t~-**'l>'*
seocoxc'iMi>icoc^Mc5eoc')coc^coc^'VrH'^rHl'*<i-HTri-^'VrH'fT-Mioo[iOoooioooi^
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s?Jco?ieo5icoMcocoso eo C4 co c^ c»5 m cc c-i co c5 -* 6) ■^?i tji .-iti. ,-i ^ r-4 1-^ rnis — uSOic omo
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^ to iC *^ i« to O -O O -^ u3
CN|COCNCOO<«NCO?)M
;DiOtOiO(DiO;oir:oiO
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-^ m CJ ^^ CO .-I -fi o 1:5 X 1
ccccM eocccoeoco M M :
•^ ift itf iT* ^ iC'-O lO itf L'i CO lO tD ifHD m ^ tO '-3 iC
; --O u*; -^ I* « ir; :s iC --0 lO
toiOtomtoio^inom^icoiT^om'-Oi-t^i.': coifttoi-'ioi^-^iffoio
-i --O.^ r-i-it^QXQXOl aixovxQi-'^r-^ys
^ -O u*; -.0 iC-^ lO O 1-1 -J ift to o o o *o lO to 1/5 O iQ
fi 1.0 CO g" -* « lO CO "^ T^
S"coi5*»'ira'*"^-»f"riC-r irsMtoco's-Mi-c^t^-—
^to>ceoin«»o'^icoio oiO(o>n--oift(OiotDic
; '-O rS) -O '-O iC -^ iC '.O lO
-^ iC to in to
lO to 1.0 to lO
.-■ i?5 .-^ .ft r-. -r c^ •* c^j tj'
to ^ to lO to it; to in to ift
r-i-ixooia>oxi-<to
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to lO to u3 ^o »s to in -^ lO
.— I— Mr-cctOfj-iOiC-*
to m to o to in to ic to in
2;g
toin^o
tpm too in to in
in to ^ to in --0 <n
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to in to in to in to o to in
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^ to to to to to to to to to to
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^ to to tD to to to to to to to
^?JM'r)c^iMC^?jco'>»«o
SO-HOi-«0>-'CSrHO.-.
■si to to to to to to to to to to
ftJaJOSoDPSMipSMaHoi
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sssss
to to to to to
C^5> CO ^54
to to to to to
5I>0£;q-jo=;^-^
to to to
to to to to to to to
000 !
to to to to to f
gggggggg
stotoototocoto
i-iT-.-i,-<^QC^QC>I3i
r-iOi-iOrHOi-'Oi-'in
to to to to to to to o to in
to X to X to 1^ to i^ to t^
0000000000
OtOtOtOtOtOtOtOtOtO
to to to to to
to to to to to
tOtOtOtOtOtOOtOtOtO
I to to to to to to to to to to
CKlxPduSticcCiicoadcn s^ccaSu^tfccoJcncxicclBicnc^ccatcfiC^iiotfcc
■^^ 5 ^^^^ ? "§" S S? "g"^iri"S^ K "^ITT'
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 663
a.
c
3
7
-s
>
T!
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1— 1
o
5
0)
3
■H
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lA <w r» 00 o>
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X030iS«!'.OX^CO'Ot00^3Ci:OX--pX-.OX!OQOO
ift lO lO in lO u^ is i-o lO ic ,ia lA o lO lO i^ ic ifl lO lO ift >o
ij!50i5i(5ift'OSireiOiS SisSiSiOiKiAiSireioIiSiB
su5 2S lo >o oS ic So S lO o lO is in ift lO lO tO iffl
^ir;oiaoiOioi£5ifl»Oift lOinoiooioiOiowsio
iTS ifs ic lO lO lO ifc iffl o i5 iff ic itt ift irt lO iCiS ira »n lo o
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jiOiOiOiCiCiOiOiOiOiO
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ii5i3io»oi5ioioi?5t?SS !»5 iSioiSinicioifE«io«oi-';
taioooiaiOiAi^oic 'iaoo>f:oiA>n>cot20in
giOOiftOirtOOOiOO lO OiOiOifli^OioiOuS Oirt lOiOiraiOiOiOiOiOySi^i-'DiCiCiCiftiCOiraOiO
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laoiOifSioooou'roiooicoiooiftOio
|»/5ioomi«idomtoi.'; .-oiA'SiAOiAOiotoiAtoiA
§i5o>c5&i?5ou5oiOo ioo3o3io»oio
^lOtootoiotoirt -ooto iiA'.oo^iQ>aioia
iHomoifflOiSoiOjOi.'ioifsoinovooiooio
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to to to to to to to to t;
J [3 S b Jn S S o o o lA
: !to in to o to m to m to o
to I?; to ift to I-': to m to o to m
^lOtoin
bSciSooi>|i>i>oi'3SSot5u::
to to to to to to to |to to to to to to to to to in
ioSoinoino*SK5
, to in to tn to in to -s to m
Oin^-^rt^M-i-r-H-^fO
i-Hin •-^ini-4in^Hin^^'n^^in
'.omtointomtOtntomtoin
^lO to to
sssssss
to to to to to to to
S33
to to to
to to to to to t;
I 1— xxr-ai'-oto^-'in
: o>nOinoini— (inrHio
' to>ntoiotointointoin
riTCOCO-fiMin'—'tO 0t03l
^inii-.io.-iinr-iin.— Oi-i-r
-J m to la -^ o to m -o in to o
S8S3
^tOtOtO
to to to to to to to
jooo
I to to to
OOOOO
to to to to to
to in
Sojooo^i^wtoMun
iC'^'ini— <in'~'ini— 'in
to in to .n to in to in to in
rfT-inMtO--)I^--X05l3»
r-<in<-<inrHinr-<ini— .in^^-T*
■o in to in to in to in to in to in
SSSo
^ to to to
Sg88833
to to to to to to to
388
to to to
SoSSS
--0 to to to to
to in
o X ^ r^ CI to M in -f -r
— lOi-Hini— iiCr-tin^-ift
to >n to in to in to in to in
in«itOtNXi-l3iQOOa^X
winf-iinr-(iOT->in'M"*c*i^
o in to in to in to in to m to m
SOOO
- to to to
88S3S3S
to to to to to o to
to to to
SSSS8
to to to to to
O 3)
T-*in ;
to in '
■— liSErHiOJ^i3r^if5'— 'O
to in to in to in to in to in
i--c2X!MO»opa>cixeot»
^itSr-.iOf-iinci'viM-T'M'*
tointomtointointoictoin
s'sss
^ to to to
•»< t-- lO to tp >n I
oooooo <
to to to to to to to ]■■
SSSSSS;
3 to to to ■£> to ti
tcx-fr-intoto-fi'.jc'c
rHiQi-HinT— tini— 'lO'— 'in n
to in to in to in to in to ic •:
•i to in to in to ic to u-ti
-• o to to
X ^ h- in to to in
ooooooo
to to to to «5 to to
83S
to to to
8SS«S?
to to to to to ti
■^rxint;;toinx'xo»^
to in to »n to lO to in to tn
■mn c-iin
to in to in
to m to m to in to in
^ to to to
5> m x to to i^ in
to to to to to to to
S3S
to to to
8::332S;
to --o to to to ti
to in to in
.^ to to to
ggggggg
to to to to to to to
8S2
to to to
to to to to to
tom toin toin
C-l 1^ C-" —
tomtom
'M-J'CI-r C4T
tomtomtomtom
tor- 1^ in
i-H m i-iio
:o m to m
1-1 o ^ m c^ m
tomtomtom
to m to m
tomtomtomtom
SSSS
^ to to to
Sm r^ r- to x -IT* , t
oooooo,.
to to to to X to to t
5 to to to -.o m ti
> to m to ic
torn torn torn 'C
IS to m to m to m to m
■»^Bp ;
•xojddy i
5'^"
^ to to to
. — CI3i-T"X
'Or-«m— im
to to to to to to to to to to to to m to m
it-inxM
i tomtom
S ft 4^ m ?5 ^ 1 c
tc m to m to m t
■iXMQ(NOJO?3QQ
istomtomtomtom
^ to to to
Sooo
to to to to to to to
ggggggggggS
^* to to to t:
3 to to to to to to to
to to to
jss
.to to to
83S
to to m to m
2S,
torn'
^mi-tm
to m to m
torn torn tom
torn torn
to m to m to m to m
3 = 333
m to lO to m
ii-im
, to m to m
to m torn to m It
301X— ■t^MmmM
■jtomtomtomtom
i o ooooom
: to to to to to to m
omo
'torn to
m to m to in
.m oir- r»
•-I T ■-■ -TT
torn -o m
tfoDtfxajQQoiUQjeo Pi^tuX^X^Oi^X^
to m to m to m , to m to m
■XtOQ"*C^C^-^Q
CJcowcocococoeo
to m to m to m to m
Page 664]
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
^ I
B
S
p.
O
e
7
o
3
w
•«!
dJ
T3
H
3
■■3
o
•xojdd V
tf «j oi X oi ix' tf x a; tc 'a; CO p; a,' a; CO cfl IX :i iX'
CiSxK5xKx25ccP5x alxccaitfxpcjcccdx
L
lC ^ lO tr
ire ift icicic
if;iCiC*CiC'>CiCi!^iCiitiOiflifliftif5
lOiCiCiftiOiCidOiOiO
iCtd-liOirtiCidCiOirt
g* to iC (D ifJ *P 'f^ '-P "^ r* ■^ I
iSiretSiftiSiCiC'Ai-tiC ,1
ss
ire S S lO ic lo Its
lO lA ift ift lO lO iK lO lO iC
iCcotooo^rotocQ^oio
i-TiCutiCiCiOtSiCiCiC
u^itioiOiOinicmiiSic
1/3101010 lis jiOiOiCiOiOiOiOuTiCiO iCiCOiftOi-COif; Sic
lit: lO lO iC lO lO lO >^ iC 'O lO iC lO iC lO tO lO (S '."t CC If; to i.T ^ lO
^iOiOiCiCioio>.oif:^tCic
O lO o "■
sin^cic^io^Dirt^if
OiCOiCOioOiOOiO
tO>CiOiO(D>CnoiCOiC
tOiOtOiC(DiCtO»CAOlO
to lO --D i.o cc lO to L*: '-o ic
^tOiOtCUt'Oi'ttCi'^tOiC tD»C^iCtOiC(OiCtC»C tOiCtOiOtOiC'-O'CtOi.'; ".OiCtOiO^iCtOif-tOiO
^ to l"; -^ ic tc lO to >.': '-o >o ^ to ic to lO to i<; to lO ^ ic to lO to ic to lt to lO to lo to lO to itt x o so »o to lO
-aQCn-<ffl>w«QOQ--oi!— QOCJi»«i--.eotC'<t"i»iiCicire-*'tocoi-»eoaocs ooi-iaiooO'— cc^co
SOiCOiOO"Si— Its'—I^!!— iTTi— -^f— ^i-i-r^H-*j',i-iT-,—rTj'r-lTM~-^t-i-r '—■'I''— (■^?J-7'ClCOC-»W
^tOiOtOiratOiCtOiOtOiC ■'BiCtCiOtOiOtOifltOiOtOiOtOiOtOi-ttOu^'dC tOiOtCiOtOiOtOifttCiO
S'r-'-J'-'QC-lOiCOcriMX ■^I^iCI-'iCtOtOiOt— lO
^toioxiotoictoiotoic toiotoictoitrtoifftoic
so O to iC to iC to iC ^ X:
ft .— 3t T-i -9" ^ -ri — f — f — -T >-H — • f- "tf .-. T? J5 -j«
-:toiotoioto»otoir:toic toiotoioton^toiOtoio
tOiOtOiOtOiOtOiCtOiiO
tOiCtOiCtOiOtOiOtOiO
to >?: to ic to "O to 1-t to 1(5
^ (O lO to ic to ic to 1^' to >c -to >t: to lO to lO to lO to lO
tOifftOiOtOiOtOiCtOiO tOiOtOiCtOiCSOi^tO'O
S r-l -f r-l -^ T-< -V C^ f C^ -^ MT C5"^N-^M"«'CJC0
^toictoiotoictoirrtoic toiftxiotomtoiotoif;
M w cc CO CO :4 co.eo
to »e to lO to ic to ic to >c
coccccmeccocofNccw
to O to lO to O to tO' to iC
S'OXrHt^MtOCC-^-fCC
^tOuttOiCtOiOtOiOtOiC
^tOiCtOiOtOiCtOiOtOut
inCItOr-tt-OOQiTjpX
to lO to lO to iC to lO to iC
CO ^ O Q Q
:to ift to If? to
CO CO CO CO CO
ifS to O to iC
t-itoc^icco-s"incotoi->
CO CO CO CO « coco CO CO CO
tOiOtOiCtOiOtOtCtDiO
eOcOcOeOcocococoM'M
■tOiOtOiOtOiCtOiCtOiO
1^ W ' W V S— ' I'- r.'J ;ij trj ■•T'
COCOCOC^TrC-I-^Cl-^M
to lO to lO to lO to lO to lO
tciOtoiotoictootom
j£"*tDif5iOtococcoiOiOOOst->xeor-"'q'i(
S(M^N-»J'C^-7'C-l"*C-l"VC0C0eOC0C0COCOC
^ to lO to lO to lO to ic to i(t ito lo to lO to ift to i;
I CO CO
to lO
COMTOCO'^C
to >o to tC to it
f CS ■* CI "^ CI "
I to iC to lO to tC to >C to lO
_^CDiOtDiCtOiOtO>(;tD»0
'CO CO so CO TO
I to into in to
eoeo
lO to in to in
j-veo'i" C4
to in to in to
in to in to in
■X s-i Q o M Oi •* t- to in
■^ 6) in ?i in i-iin i-H in rH
to in to in to in to in to in
sags
^ tom to
-" CI CO CO CO
m to m to m to in
?tot^ino2eoO'-'<No
COCOCOCOCO'1'CO'^CO
sintointcintDintoic
CO CO in 1^ t-
toin to in to
in toift toin
iin
5 to in to
to X -r Q ci
.-.in — i25iH
m to in i> m
^tointcintointointom tomtointointoic-tous
to in tons to
Sco"*cococccocoMcoeO;'»j'ecTco'v?^'*M'VW
^tointointointointoin tomtointointointoin
cJiOClSi-i
m to into in
sss
tOiOt*
COCJ O ^JOp
in t^ m t* m
to >n to in to
in to 'O to in t
1 Ori o
; r-inr-
SSBSS
in t* ic I" in
- to CO CO C"
jj to in to ir
to in to li
•V CO
to in
tointointointointomitoiintotn
SS3S2
in to in i> m
I— m i-- in t'-
in o CO fj o
O—i Oi—O
in i^ in i> in
; CO CO CO CI
^ to in to if
oeo??
3 in ton
;38
to»n
toincocoO'—c^OJ ■*t*toino>ec.-n-<cooi into
"VN-^c-nTSMm— ini-(in>~<in— iOt-.oooo
to in to in to ic to m 'to in to in to in r* in t-* m-t^ in
SS2
t^int*
— co Oiin to
D — in.-.ic
scorteO
C^ O O d XT
jtointoiOtointomtoin m
CO -r CO"V c^ •*
jtcintointomtoin
mr-iinr-iOOOOOO
tointoint^int^int^in'i
•I .-( QCO
■:i>int~
•xojddv
ftcoeococ^"'j"(M-*c-i-tc^.-j'CJ
^ to in to m to in^ to in to in to in
|tox
to in
a^X'-jtoMM'iniM
to in to in to in to in
in — ' o o o
to in 1- ic t-
lOt^iOt-m 'i
! o r* ^5 in to
> rH in f— in r-
I- to -t; Oi Ci
■V r- T W*
c^a> ffjcito
- -lrf■^^"fl•
- — t^ ■*
8SSS8S;
^tomtotOtointo
3 to m !
Xincjeocji-Hinc»
to in to in to in toin
88Sg
tom r-int-
tf CO tf CO ficj X 02 X Pj CO tf X CtH X 02 CO SCl CO PJ CO
'T"T'¥^ ?5-
in r» ■»fr>" ^
;S2
02to02xtfcoC£Hy503x'
eo CO CO <S
D X o> .n o) cs
-< -^ — " -T c* •*
- -T< I-" ■V 1^ ■^
OHXOicCCl^xtfxtfoQ
TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 665
a
a,
XI
I
•- ,2
1
S
3
o
•aj«p
•xojddv
•ajBp
■xojad
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^iftiCiOiOiAiOiOiOiOiC
5vC lOiffliC
iOiOidCiC»fSiC»'5i/3>f
iiCiOiniomvc>c»nkdoire>cmiOic«o»o^
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f i-tiO^ to OI^
53|T-H«i-(M.HM'--t«?IC0|C-lCCC^C0OlCOC^«-^c5
•iStcuctoiotoic^iOtcic -.ciotciiC'^ic^cut^iit koiotoiOfOiC«om'.oic
SOOOiaiCiOXf-tI^C^tC|NiOCO-rTfeOiQM«5>-'
rHMr-iCOC^COMSCWCOC^COMMCJTOC-lcONeO
^toi^5dn!Oia^iiDt©ioteia*.oiC5Di05oicoiC
vD m ?D lO <o o to ic -js u»
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8S8SS§5SSS5?5{3S«8«S§SSSiS2SSSSSSSSJggSS£S2S2g
ESSSS2S33SS:SS8Sg883oS
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rf»r-irei^iret-irer">ret>ic ■r"-^t^-i'r-^r*^r»v
ar-twMOirer^X'^i-'C^Tffr»r--j|©coeo?»r-«
»re c^ >-' -£i '.o <
CJ ift W iC i-i <
::8SS
■vxeoxeo
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' CO CO eo :o -v ec
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,SSS?!32S§3Sg;8S
'xcoxMXeoxco
SQOcoi—— (-u-xt-ireQc-i TOxt^ireO'-i-j'XQC-T*
T-(ireNire(N"V!NTjtci5-j'iKcoco«^c(3"V?i'vc»
HreSift
't^ -^ t- -1* X
SSSSc
X -V X T
XDi
XCOXCOXCOXCO
^ t^ "* i>- "* r
iCOi-iO-ttDIXM— tOi
. Tt" t^ -J* t* -f t^
ic ire o> ^ rt h
-J- c^ 'T' c* ire F-
t- -V I^ ■* t- T
gCOC^X I-
^5)0©
t^ -J" X -^ X
ccMXxeo'rft-o—d^-r
'^ — irei-iireoi-j'Si'wrt
rfXMXcOXeOXCOX
Mxcoxeo
t^ "J" r- "W t~ -t i^-tr"!"
OiXCO -f X o
-t rH ifS r-( S i-H
r-Tft* Tf t- -w
SSS8S
X'VX'TX
coxecxc
|CCMC
XMCi
rt eo CI ire r-i (p
j'ciirei-ioo
C- CO X M ai M
dV
r- ■* t-'ft*
SS38g8
OStcOiaipHMC^oitf oj WoDoiaiftJaiftJtcaJai oJcrioixftSaaftJcooJai aJccajxpiaopiaiK'iM
S8SIS2
X -^ X eo X
COX COXffl
XCOX
cox COCiM
'TT'
?" s ^'i"^'3~lF,"W s""s"'s"^
Page 666]
TABLE 10.
Mean Time of Sun's Visible Risinf; and Setting.
R a
3
I
3
O
W
2
OS
'xoaddv
H
s
p4 cc C^ od Ph 'A P^ 00 pc; CO
^ O « O ^ O — 1.-5 O ifl «
tfoipicociiaipi^'aiaix MxsixPSMoiaioSco piaipJaiQixsJxaixo^ai
if:oi.t50irt«io«ico
irt CO ift "O m 50 ic ^ m to |»o ;o lO (O lO ^ lO o uo ^ lO o
^ iC lO lo lO ic o in to ic o uo o li^ o ic ^o ic « lO « lis to i^ -o lO to ir:; -o L*^ -o o ^ o CO o "s iQ --o L- :o o to
^iCucoiooiciOinic^ L':toujtoiotoictoi-i(o
lOtOiC'^iOtOiOiBintO ifltOiCtOiC'-OxntOOtOOtO
S*^o<Mco<-ii5astpxiac toonoi-noeow'^o'o'oQr-t^ijiiooi'c^MTf
rfjioioioiOinifliffli.'ridc tCiCtf;oi/ti;oictoicto irsoio^iatoictointo
initointoi/5'.oi^toic^oto
^iCiC'OiCiCinOiffiCiCiCirtiniOiOtOiCtOiOtO.iCtOi.'lOiOtDiCtOiOcOiOtOiOtOiaoinoifiOiOtD
g".— 'OQi— lO^r-MtOiA ^tpcOr-CJOiOOOi?!
■VT" ^ »0 CO i« CO in CO lO WOCOincOOMOf) o
^tf5Lt»CiCi.TiC>OiOiOif3 lOOiddnifliC^OintO
■^•^:oiosoiceoocoi-'5;coiocoiScoii5coiO?io
,r5tOiQtD»atO>0'.OiCtO iiOtOiC^OiO'-OOtOiOtOiftO
t^>HtOCOif;-fCOiS^r»-QQO!riOI— ^tOCOf'I'COtO
»c o u*; to lO 'O lO to lO to iio to »c to i^ -j lO to ir; -o in to
^■^-*co'vSocoineooicoiSe?iScoSsSSS'c^oc^oc5oc-iOfio^oc^Or4S^I^2^Sr
,^icinmi.':»niCioimnirt|iniOinii!;iCinminoift|>otDictoic<ointOiOtoif3i:ointoin-ointou';tomt;
■*-TWTCOi?;MinMiOiMiCcoiAco>Scoin?ii3r*oc-ioc-iOTio?Jo MOc^ocio>-iOi-i^X;i-
^lOutmidniomininiolicmininiomiCinmo inioictoiotointointo in-oo^>nwOtoo-.oif:"o
2 O t^ 3- 31 QO o
.^icininiCiciniOiniOin |in>nininiftiOiOi(;inin 'iftioinicio^oictovnto ic toic to lo^ in to u~ '.o li to
i O CO 31 31 X c
3i3iXQt^.-Htoc'iUncO'*'-fcoio«tOr-r-Q»oaoixoi^«--'to^inco-t'*'C'jirat--'tocjt--oia^
M-Tco3«iOcouDrfocoiAo325coSMincOi?5fginc»5-^ciM&:^sSo?Jc35^5§io2^
■^»i:MninininminmiCiO|inininiooiOinKti>ooininioininto»ntointoictointoiotointoin-ointo
jSOo03:^XCil^OtO--'OMineO**»rcOiQ'NtoL-Ht^QG©OiOiXOt^<HitD5JincO"^-»'T^
fe^Tt>M'^m'^C'?uOK'inj:oinM>ncoiocoiScoiS,coinco3fiinc^oc~io:r4 0CNOc^oc'io*JSc
^»fflOinin>nininininin|moinmininiCinininiciOiniOinininto>ntointointooto>;:tomtoif
» O X O 31 3^ 31 X O I--. 1-1 -J? ?l to M '^ -^ -r in CO '-P '?1 ^ ^ l-~ Q X 31 3a X O t^ — ' to Ol O "1 'T' -r -^ 1- --1 to
S'T-v-^-'t'co-TJoincoinjiooMincou'iobifJfOin.coinr^inSi-ri.cc-^
gininininmoiCioifflio inininicicmirainmto <ninin'inininininmto intointointomtoinooto
* rfsioiCiOininmininiCiC
tocoin«incoiacoin|COtSeoincoinD5in«o,'riO'^ioc-io?io^iocio
lomininmimommio.imoinmmininintnoin^intootoiotointoiCto
b;^ m m m in ic o iC' >o mm
-:ciQ.-(0— I _ ,.
ft -^ o Tf in -^ ic -I" m ri< li; «
^»nioinintCin>niniOiOinin>niniominininin
S«t^WI-"q'tOiniQtO;-1'^«t:^fOX(M(^-H3lOOOw3JC-]XC-lt*!OI^-f
incoiocoineoiocoiSroincoinco»nco"Ocoin coocooc-ioc^oc-ioc^o
intnininininininminiinininicmmoimnin inoinootointointotn'-o
to to li? t — f I- CO X ^^ gi
coincgineoincoineoin
inioininioiooininic
S^m^i?5^in^in-^in|^oeoScoincOiccoui coiSsoiOMincoocoS M*ncoincoScoocoocoS
^ininininioiomininin-inocoinininiOintnin ininmmmmininioin »3mminintootomtoin--o
~ '.o in '-0 in to in to
fi*2':?2!i'i^'7;^'i:?3^*^^Q^'^T'3^T^>5K=P'^"-5i*r'^t^'-Px'>nxinci'*3i-T'OMO'*i—
S-*tn-*iO-vo"^o-^un;-T'iO"^in'TrincoincoinMOcoJScoin«ocoin,coSc^in
^lOiciCininiOiniCiom inininiOiOin»nmmin|intnin»noiOiOininin ininu-mintnLntomtoineo
jj'^'Cg-^fN-I'tMCO'MCOMlMCOC^'S'r-CT-^inOiCi
fti^ic-vinTi«i.n*i'm'^iO'vm'^io-vic-9'»C"Vin
■sjinininoinininioinminiomoininicininin
'Otoo>'-oo>[*aoi--oooo
TincoiScoincoiocoo
iSintninictOinininin
-XI- a
3 in Mir
in in in in in in li
m in to lO to
-^ ■* '^» -T --I -f (M -^ CO -f CO "0 m TO -f CI -f M i.n 1-1 in
ft-^ic -Tio^m'^iO'^inNi'io-fin^iA^in-^in
^iCininminininininif5'in>ninininininiOicin
to 1-1 to o -o o I- o t-
in^iO-Tin-nn^in
in in in in in in in in in in '
o in CO o « I n CO in ?
S'lncoocoincom-t'in^i-r-f-ff'fincovnMin
■^m^ioTinTfio-T-ic^oM'in'irinfic^in
^ininiCininiCinininin jininooinininioioin
'cO to iM to OJ to iM 1* M t-
,'ij'in'rin-fl'i5-i< un-rm
■lauoinmiOininininm
i-'t-WXOXOX
■^ in -*■ lo T in -r in
1^ lO in in 1^
03J 301
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TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
[Page 667
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Page 668]
TABLE 10.
Mean Time of Sun's Visiljle Rising and Setting.
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Page 670]
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TABLE 10.
Mean Time of Sun's Visible Rising and Setting.
O CJ c3 M W N
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TABLE 10..
]Mean Time of Sun's Visible Rising and Setting.
[Page 671
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Pag
e672]
a^ABLE 11 ;
For reducing the Time of the Moon's passage over the Meridian of Greenwich to the Time of its
pass-
age
over any other Meridian. The numbers taken from this Table are to be added to the Time at 1
Greenwich in West Longitude, subtracted in
East Longitude.
Longi-
Daily variation of the
moon's passing the meridian.
Longi-
tude.
tude.
40»
42m
44n
46"
48»
50"
52»
54"
56"
58"
60"
62" I
64"
66"
o
m.
m.
m.
m.
■m.
m.
m.
m.
m.
m.
m.
m.
m.
m.
o
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
10
1
1
1
1
1
1
1
1
2
2
2
2
2
2
10
15
2
2
2
3
2
2
2
2
2
2
2
3
3
3
15
20
2
2
2
2
3
3
3
3
3
3
3
3
4
4
20
25
3
3
3
3
3
3
4
4
4
4
4
4
4
5
25
30
3
3
4
4
4
4
4
4
5'
5
5
5
5
5
30
35
4
4
4
4
5
5
5
5
5
6
6
6
6
6
35
40
4
5
5
5
6
6
6
6
6
6
7
7
7
7
40
45
5
5
5
6
6
6
6
7
i
7
7
8
8
8
45
50
6
6
6
6
7
7
7
7
8
8
8
9
9
9
50
55
6
6
7
7
7
8
8
8
9
9
9
9
10
10
55
60
7
7
7
8
8
8
9
9
9
10
10
10
11
11
60
65
7
8
8
8
9
9
9
10
10
10
11
11
12
12
65
70
8
8
9
9
9
10
10
10
11
11
12
12
12
13
70
75
8
9
9
10
10
10
11
11
12
12
12
13
13
14
75
80
9
9
10
10
11
11
12
12
12
13
13
14
14
15
80
85
9
10
10
11
11 12
12
13
13
14
14
15
15
16
85
90
10
10
11
11
12
12
13
13
14
14
15
15
16
16
90
95
11
11
12
12
13
13
14
14
15
15
16
16
17
17
95
100
11
12
12
13
13
14
14
15
16
16
17
17
18
18
100
105
12
12
13
13
14
15
15
16
16
17
17
18
19
19
105
110
12
13
13
14
15
15
16
16
17
18
18
19
20
20
110
115
13
13
14
15
15
16
17
17
18
19
19
20
20
21
115
120
13
14
15
15
16
17
17
18
19
19
20
21
21
22
120
125
14
15
15
16
17
17
18
19
19
20
21
22
22
23
125
130
14
15
16
17
17
18
19
19
20
21
22
22
23
24
130
135
15
16
16
17
18
19
19
20
21
22
22
23
24
25
135
140
16
16
17
18
19
19
20
21
22
23
23
24
25
26
140
145
16
17
IS
19
19
20
21
22
23
23
24
25
26
27
145
150
17
17
18
19
20
21
22
22
23
24
25
26
27
27
150
155
17
18
19
20
21
21
22
22
23
24
25
26
27
28
28
155
160
18
19
20
20
22
23
24
25
. 26
27
28
28
29
160
165
18
19
20
21
22
23
24
25
26
27
27
28
29
30
165
170
19
20
21
22
23
24
25
25
26
! 27
28
29
30
31
170
175
19
20
21
22
23
24
25
26
27
1 28
29
30
31
32
175
180
20
21
22
23
24
25
26
27
28
i ^
30
31
32
33
180
40"
42m
44»
46-
48»
50"
52"
54"
56"
58"
60"
62"
64»
66"
(j^rl^U^ /)U^
TABLE 12. [Page 673
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Dechnation or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
1"
2"
8"
4"
5"
6"
7" 8"
9"
10"
11"
12"
18"
14"
15"
16"
17"
18"
19"
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
2
2
2
2
'2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
2
2
2
2
2
3
3
2
2
2
2
2
3
3
3
1
1
1
1
2
2
2
2
1
1
1
1
2
2
• 2
2
1
1
1
1
2
2
2
2
3
1
1
1
1
2
2
2
2
3
1
1
1
1
1
1
1
2
1
1
1
2
1
2
3
4
5
6
7
8
9
10
2
2
2
3
3
2
2
2
3
3
2
2
3
3
3
2
3
3
3
3
3
3
3
3
4
3
3
3
4
4
3
3
3
4
4
3
3
4
4
4
I
4
4
5
3
4
4
4
5
11
12
13
14
15
16
17
18
19
20
-1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
2
3
3
3
3
3
3
3
3
3
3
3
3
3
4
3
3
4
t
3
4
4
4
4
4
4
4
4
5
4
4
5
5
5
4
5
5
5
5
5
5
5
5
6
5
5
5
6
6
5
5
6
6
6
16
17
18
19
20
21
22
23
24
25
2
2
2
2
2
2
2
2
2
2
2
2
3
I
3
3
3
3
3
3
3
4
4
4
4
4
4
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
5
6
3
3
3
3
3
3
4
4
4
4
4
4
4
5
5
5
5
5
5
5
3
3
3
4
4
4
4
4
4
5
5
5
5
5
5
5
6
6
6
6
4
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
6
7
7
4
4
4
4
6
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
4
4
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
8
8
8
5
5
5
5
5
6
6
6
6
7
7
7
7
7
8
8
8
8
8
9
5
5
5
6
6
6
6
7
7
7
7
7
8
8
8
8
9
9
9
9
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
9
10
10
10
6
6
6
6
7
7
7
7
8
8
8
9
9
9
9
10
10
10
10
11
6
6
7
7
7
7
8
8
8
9
6
7
7
7
8
7
7
7
8
8
21
22
23
24
25
26
27
28
29
30
26
27
28
29
30
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
8
8
8
9
9
8
9
9
9
10
31
32
33
34
35
36
37
38
39
40
9
9
9
10
10
10
10
11
11
11
12
12
12
12
13
9
10
10
10
11
11
11
11
12
12
10
10
10
11
11
31
32
33
34
35
11
12
12
12
13
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
.2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
3
4
4
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
6
6
6
6
6
5
5
5
5
5
5
5
6
6
6
6
6
6
6
6
7
7
7
7
7
5
6
6
6
6
6
6
6
7
7
7
7
7
7
7
7
8
8
8
8
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
8
9
9
9
9
7
7
7
7
8
8
8
8
'8
8
9
9
9
9
9
9
10
10
10
10
8
8
8
8
8
8
9
9
9
9
9
10
10
10
10
10
10
11
11
11
8
8
9
9
9
9
9
10
10
10
10
10
11
11
11
11
11
12
12
12
9
9
9
10
10
10
10
10
11
11
11
11
11
12
12
12
12
13
13
13
10
10
10
10
11
11
11
11
11
12
12
12
12
13
13
13
13
14
14
14
10
11
11
11
11
11
11
11
12
12
12
13
13
13
14
13
13
14
14
14
41
42
43
44
45
12
12
12
12
13
12
13
13
13
13
13
13
14
14
14
14
14
14
15
15
15
15
15
16
16
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
13
13
13
14
14
14
14
15
15
15
14
14
14
14
15
15
15
15
16
16
14
15
15
15
16
16
16
16
17
17
15
16
16
16
17
16
16
17
17
17
17
17
17
18
18
18
18
18
19
19
24972°— 12-
-33
Page 674]
TABLE 12
,
1
For finding the Variation of the Sun's
Right
Ascension or Declination, or
of the Equation of Time, in 1
any number of minutes of time
the Horary Motion being given
it the
top of the page in seconds, 1
and the number of minutes of time in the side column.
Also
for finding
the Variation of the 1
Moon's
Declination or Eight Ascension in
seconds of time.
the motion
in one minute being given 1
at the top, and the numbers in
the side column being taken for seconds
.
1
Horary motion
M.
20"
21"
22"
28"
24"
25"
28"
27"
28"
29"
SO"
81"
82"
88"
84"
86"
86"
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
4
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
4
5
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
5
6
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
6
7
2
2
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
7
8
3
3
3
3
3
3
3
4
4
4
4
4
4
4
5
5
5
8
9
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
5
5
9
10
3
4
4
4
4
4
4
5
4
5
5
5
5
5
5
6
6
6
6
10
11
11
4
4
4
4
5
5
5
6
6
6
6
6
6
7
12
4
4
4
5
5
5
5
5
6
6
6
6
6
7
7
7
/
12
13
4
5
5
5
5
5
6
6
6
6
7
7
7
7
7
8
8
13
14
5
5
5
5
6
6
6
6
7
7
7
7
7
8
8
8
8
14
15
5
5
6
6
6
6
7
7
7
7
8
8
8
8
9
9
9
15
16
5
6
6
6
6
7
7
7
7
8
8
8
9
9
9
9
10
16
17
6
6
6
7
7
7
7
8
8
8
9
9
9
9
10
10
10
17
18
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
18
19
6
7
7
7
8
8
8
9
9
9
10
10
10
10
11
11
11
19
20
7
7
7
8
8
8
9
9
9
10
10
10
11
11
11
12
12
20
21
7
7
8
8
8
9
9
9
10
10
11
11
11
12
12
12
13
21
22
7
8
8
8
9
9
10
10
10
11
11
11
12
12
12
13
13
22
23
8
8
8
9
9
10
10
10
11
11
12
12
12
13
13
13
14
23
24
8
8
9
9
10
10
10
11
11
12
12
12
13
13
14
14
14
24
25
8
9
9
9
9
10
10
10
10
10
10
11
11
12
12
13
13
13
14
14
15
15
25
26
11
11
12
12
13
13
13
14
14
15
15
16
26
27
9
9
10
10
11
11
12
12
13
13
14
14
14
15
15
16
16
27
28
9
10
10
11
11
12
12
13
13
14
14
14
15
15
16
16
17
28
29
10
10
11
11
12
12
13
13
14
14
15
15
15
16
16
17
17
29
30
10
11
11
12
12
12
13
13
14
14
15
15
16
16
17
17
18
18
30
31
10
11
11
12
13
13
14
14
15
16
16
17
17
18
18
19
31
32
11
n
12
12
13
13
14
14
15
15
16
17
17
18
18
19
19
32
33
n
12
12
13
13
14
14
15
15
16
17
17
18
18
19
19
20
33
34
11
12
12
13
14
14
15
15
16
16
17
18
18
19
19
20
20
34
35
12
12
13
13
13
14
15
15
16
16
17
17
18
18
19
19
20
20
21
36
36
12
13
14
14
15
16
16
17
18
19
19
20
20
21
22
36
37
12
13
14
14
15
15
16
17
17
18
19
19
20
20
21
22
22
37
38
13
13
14
15
15
16
16
17
18
18
19
20
20
21
22
22
23
38
39
13
14
14
15
16
16
17
18
18
19
20
20
21
21
22
23
23
39
40
13
14
15
15
15
16
17
17
18
19
19
20
21
21
22
23
23
24
40
41
14
14
16
16
17
18
18
19
20
21
21
22
23
23
24
25
41
42
14
15
15
16
17
18
18
19
20
20
21
22
22
23
24
25
25
42
43
14
15
16
16
17
18
19
19
20
21
22
22
23
24
24
25
26
43
44
15
15
16
17
18
18
19
20
21
21
22
23
23
24
25
26
26
44
45
46
15
15
16
16
17
17
17
18
18
19
20
20
21
22
23
23
24
25
26
26
27
45
46
18
19
20
21
21
22
23
24
25
25
26
27
28
47
16
16
17
18
19
20
20
21
22
23
24
24
25
26
27
27
28
47
48
16
17
18
18
19
20
21
22
22
23
24
25
26
26
27
28
29
48
49
16
17
18
19
20
20
21
22
23
^4
25
25
26
27
28
29
29
49
50
51
17
17
18
18
18
19
19
20
20
20
21
21
22
22
23
23
23
24
25
26
27
28
28
29
30
50
24
25
26
26
27
28
29
30
31
51
52
17
18
19
20
21
22
23
23
24
25
26
27
28
29
29
30
31
52
53
18
19
19
20
21
22
23
24
25
26
27
27
28
29
30
31
32
53
54
18
19
20
21
22
23
23
24
25
26
27
28
29
30
31
32
32
54
55
18
19
20
20
21
21
21
22
23
24
25
26
26
27
28
28
29
30
31
32
33
55
56
19
22
23
24
25
27
28
29
30
31
32
33
34
56
57
19
20
21
22
23
24
25
26
27
28
29
29
30
31
32
33
34
57
58
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
58
59
20
21
22
23
24
25
26
27
28
29
30
30
31
32
33
34
35
59
60
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
60
TABLE 12. [Page_676
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
87"
88"
89" 40"
41"
42"
48"
44"
46"
46"
47"
48"
49"
50"
61" 52"
68"
1
2
3
4
5
1
1
2
2
3
1
1
2
3
3
1
1
2
3
3
1
1
2
3
3
1
1
2
3
3
1
1
2
3
4
1
1
2
3
4
1
1
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
2
3
4
1
2
3
3
4
1
2
3
3
4
1
2
3
3
4
1
2
3
4
4
I
2
3
4
5
6
7
8
9
10
4
4
5
6
6
4
4
5
6
6
4
5
5
6
7
4
5
5
6
7
4
5
5
6
7
4
5
6
6
7
8
8
9
10
11
11
12
13
13
14
15
15
16
17
18
18
19
20
20
21
22
22
23
24
25
4
5
6
6
7
4
5
6
7
7
5
5
6
7
8
5
5
6
7
8
5
6
6
7
8
5
6
6
7
8
5
6
7
7
8
5
6
7
8
8
5
6
7
8
9
5
6
7
8
9
5
6
7
8
9
10
11
11
12
13
6
7
8
9
10
11
12
13
14
15
7
7
8
9
9
7
8
8
9
10
7
8
8
■9
10
10
11
12
12
13
14
14
15
16
16
17
18
18
19
20
20
21
21
22
23
7
8
9
9
10
11
11
12
13
13
14
lo
16
17
17
18
19
19
20
21
21
22
23
23
8
8
9
10
10
11
12
12
13
14
14
15
16
16
17
18
18
19
20
21
21
22
23
23
24
8
9
9
10
11
11
12
13
14
14
15
16
16
17
18
19
19
20
21
22
22
23
24
24
25
26
27
27
28
29
8
9
10
10
11
8
9
10
11
11
8
9
10
11
12
9
9
10
11
12
9
10
10
11
12
9
10
11
11
12
9
10
11
12
13
9
10
11
12
13
10
10
11
12
13
11
12
13
14
15
16
17
18
19
20
10
10
11
12
12
10
11
11
12
13
13
14
15
15
16
"16
17
18
18
19
20
20
21
22
22
23
23
24
25
25
26
27
27
28
29
29
30
30
31
32
32
33
34
34
35
35
36
37
37
38
12
12
13
14
15
15
16
17
18
18
12
13
14
14
15
12
13
14
15
15
13
13
14
15
16
13
14
14
15
16
13
14
15
16
16
13
14
15
16
17
14
14
15
16
17
'14
15
16
16
17
14
15
16
17
18
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
13
14
14
15
15
16
17
17
18
19
19
20
20
21
22
16
17
17
18
19
16
17
18
18
19
16
17
18
19
20
17
18
18
19
20
17
18
19
20
20
18
18
19
20
21
18
19
20
20
21
18
19
20
21
22
23
23
24
25
26
19
19
20
21
22
21
22
23
24
25
19
20
21
21
22
20
20
21
22
23
20
21
21
22
23
20
21
22
23
24
21
22
22
23
24
21
22
23
24
25
22
23
23
24
25
22
23
24
25
26
23
24
25
26
27
26
27
28
29
30
31
32
33
34
35
23
23
24
25
26
23
24
25
26
26
24
25
25
26
27
28
28
29
30
31
24
25
26
27
27
25
26
26
27
28
25
26
27
28
29
26
27
28
28
29
26
27
28
29
30
31
31
32
33
34
27
28
29
29
30
27
28
29
30
31
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
22
23
23
24
25
25
26
27
27
28
28
29
30
30
31
31
32
33
33
34
35
35
36
36
37
23
24
25
25
26
27
27
28
29
29
30
31
31
32
33
"33
34
34
35
36
36
37
38
38
39
24
25
25
26
27
27
28
29
29
30
31
31
32
33
.33
34
35
35
36
37
37
38
39
39
40
25
25
26
27
27
28
29
29
30
31
31
32
33
33
34
35
36
36
37
38
38
39
40
40
41
25
26
27
27
28
29
29
30
31
32
32"^
33
34
34
35
36
36
37
38
39
39
40
41
41
42
26
27
28
29
29
27
28
29
29
30
28
29
30
31
31
29
30
30
31
32
29
30
31
32
33
30
31
32
33
33
31
32
33
34
35
32
33
34
34
35
36
37
38
39
40
29
30
31
32
32
33
34
34
35
36
37
37
38
39
39
40
41
42
42
43
30
31
32
32
33
31
32
32
33
34
31
32
33
34
35
32
33
34
34
35
33
34
34
35
36
33
34
35
36
37
34
35
36
37
38
35
36
37
37
38
36
36
37
38
39
36
37
38
39
40
41
42
43
44
45
34
34
35
36
37
35
35
36
37
38
35
36
37
38
38
36
37
38
38
39
37
38
38
39
40
38
38
39
40
41
38
39
40
41
42
39
40
41
42
43
40
41
42
42
43
41
42
42
43
44
46
47
48
49
50
37
38
39
40
40
38
39
40
41
41
39
40
41
41
42
40
41
42
42
43
41
42
42
43
•44
42
42
43
44
45
43
43
44
45
46
43
44
45
46
47
44
45
46
47
48
45
46
47
48
49
49
50
51
52
53
51
52
53
54
55
56
57
58
59
60
41
42
43
43
44
42
43
44
44
45
43
44
44
45
46
44
45
45
46
47
45
46
46
47
48
46
47
47
48
49
47
48
48
49
50
48
48
49
50
51
49
49
50
51
52
Page 676] TABLE 12.
For finding the Variation of the Sun'a Eight Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Eight Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
54"
56"
66"
57"
68"
69"
60"
61"
62"
63"
64"
65"
66"
67"
68"
69"
70"
1
2
3
4
5
1
2
3
4
5
5
6
7
8
9
1
2
3
4
5
6
6
7
8
9
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
6
1
2
3
4
6
1
2
3
5
6
1
2
3
5
6
1
2
4
5
6
1
2
3
4
5
6
7
8
9
10
6
7
7
8
9
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
10
6
7
8
9
11
6
7
9
10
11
7
8
9
10
11
7
8
9
10
11
7
8
9
11
7
8
9
10
11
7
8
9
10
12
7
8
9
11
12
6
7
8
9
10
11
12
13
14
15
10
11
12
13
14
10
11
12
13
14
10
11
12
13
14
15
16
17
18
19
20
21
21
22
23
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
11
12
13
14
15
15
16
17
18
19
20
21
22
23
24
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
11
12
13
14
15
11
12
13
14
15
11
12
13
14
16
12
13
14
15
16
12
13
14
15
16
12
13
14
15
16
12
13
14
15
17
12
13
15
16
17
12
14
15
16
17
13
14
15
16
17
13
14
15
16
18
11
12
13
14
15
16
17
18
19
20
14
15
16
17
18
15
16
17
17
18
19
20
21
22
23
16
17
18
19
20
16
17
18
19
20
17
18
19
20
21
17
18
19
20
21
17
18
19
20
21
17
18
20
21
22
18
19
20
21
22
18
19
20
21
22
18
19
20
22
23
18
20
21
22
23
19
20
21
22
23
16
17
18
19
20
21
22
23
24
25
19
20
21
22
23
21
22
23
24
25
21
22
23
24
25
22
23
24
25
26
22
23
24
25
26
22
23
25
26
27
23
24
25
26
27
23
24
25
26
28
23
25
26
27
28
24
25
26
27
28
24
25
26
28
29
25
26
27
28
29
21
22
23
24
25
26
27
28
29
30
23
24
25
26
27
24
25
26
27
28
28
29
30
31
32
33
34
35
36
37
38
39
39
40
41
24
25
26
27
28
29
30
31
32
33
34
35
35
36
37
38
39
40
41
42
25
26
27
28
29
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
i6
27
28
29
30
30
31
32
33
34
26
27
28
29
30
31
32
33
34
35
26
27
28
29
31
27
28
29
30
31
27
28
29
30
32
28
29
30
31
32
28
29
30
31
33
29
30
31
32
33
29
bO
31
32
34
29
31
32
33
34
30
31
32
33
35
30
32
33
34
35
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
28
29
30
31
32
32
33
.34
35
36
37
38
39
40
41
32
33
34
35
36
37
38
39
40
41
32
33
34
35
36
33
34
35
36
37
33
34
35
36
37
34
35
36
37
38
34
35
36
37
39
35
36
37
38
39
35
36
37
39
40
36
37
38
39
40
36
37
39
40
41
31
32
33
34
35
35
36
37
38
39
36
37
38
39
40
41
42
43
44
45
37
38
39
40
41
38
39
40
41
42
43
44
45
46
47
38
39
41
42
43
39
40
41
42
43
40
41"
42
43
44
40
41
42
44
45
46
47
48
49
50
41
42
43
44
45
41
43
44
45
46
42
43
44
46
47
36
37
38
39
40
41
42
43
44
45
41
42
43
44
45
40
41
42
43
44
40
41
42
43
44
42
43
44
45
46
42
43
44
45
47
44
45
46
47
48
44
46
47
48
49
45
46
47
48
50
46
48
49
50
51
47
48
49
51
52
48
49
50
51
53
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
41
42
43
44
45
46
47
48
49
50
50
51
52
53
54
42
43
44
45
46
47
48
49
50
50
51
52
53
54
55
43
44
45
'46
47
48
49
49
50
51
52
53
54
55
56
44
45
46
47
48
48
49
50
51
52
53
54
55
56
57
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
46
47
48
49
50
51
52
53
54
55
47
48
49
50
51
48
49
50
51
52
48
49
50
51
53
49
50
51
52
53
50
51
52
53
54
51
52
53
54
65
51
52
54
55
56
52
53
54
56
57
53
54
55
56
58
54
55
56
57
58
60
61
62
63
64
65
67
68
69
70
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
52
53
54
55
56
53
54
55
56
57
54
55
56
57
58
59
60
61
62
63
54
55
57
58
59
60
61
62
63
64
55
56
57
59
60
56
57
58
59
61
57
58
59
60
61
58
59
60
61
62
59
60
61
62
63
56
57
58
59
60
57
58
59
60
61
58
59
60
61
62
61
62
63
64
65
62
63
64
65
66
63
64
65
66
67
63
65
66
67
68
64
66
67
68
69
TABLE 12. [Page 677
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
Jl"
72"
78"
74"
75" 76" 77" 78"
79"
80"
81"
82"
88"
84"
•85"
86"
87"
1
2
3
4
5
1
2
4
5
6
1
2
4
5
6
7
8
10
11
12
1
2
4
5
6
7
9
10
11
12
13
15
16
17
18
19
21
22
23
24
26
27
28
29
30
32
33
34
35
37
38
39
40
41
43
44
45
46
47
49
50
51
52
54
55
'56
57
58
60
61
62
63
64
66
67
68
69
71
72
73
1
2
4
.5
6
7
9
10
11
12
14
15
16
17
19
20
21
22
23
25
1
3
4
5
6
8
9
10
11
13
14
15
16
18
19
20
21
23
24
25
1
3
4
5
6
8
9
10
11
13
14
15
16
18
19
20
22
23
24
25
1
3
4
5
6
8
9
10
12
13
1
3
4
5
7
1
3
4
5
7
1
3
4
5
7
1
3
4
5
7
1
3
4
5
7
1
3
4
6
7
1
3
4
6
7
1
3
4
6
7
1
3
4
6
7
1
3
4
6
7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
7
8
9
11
12
8
9
10
12
13
8
9
11
12
13
8
9
11
12
13
8
9
11
12
14
8
10
11
12
14
8
10
11
12
14
8
10
11
13
14
9
10
11
13
14
16
17
18
20
21
9
10
11
13
14
16
17
19
20
22
9
10
12
13
15
6
7
8
9
10
13
14
15
17
18
13
14
16
17
18
19
20
22
23
24
25
26
28
29
30
31
32
34
35
36
37
38
40
41
42
43
44
46
47
48
49
50
52
53
54
55
56
58
59
60
61
62
64
65
66
67
68
70
71
72
14
15
17
18
19
21
22
23
24
26
14
16
17
18
20
14
16
17
18
20
21
22
24
25
26
15
16
17
19
20
21
23
24
25
27
15
16
18
19
20
22"
23
24
26
27
15
16
18
19
21
15
17
18
19
21
15
17
18
20
21
16
17
19
20
22
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
19
20
21
22
24
25
26
27
28
30
31
32
33
34
36
21
22
23
25
26
22
23
25
26
27
22
24
25
26
28
22
24
25
27
28
23
24
26
27
28
23
24
26
27
29
23
25
26
28
29
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
26
27
28
30
31
32
33
35
36
37
38
39
41
42
43
44
46
47
48
49
51
52
53
54
56
57
58
69
60
62
63
64
65
67
68
69
70
72
73
74
26
28
29
30
31
27
28
29
30
32
27
28
30
31
32
27
29
30
31
33
28
29
30
32
33
28
29
31
32
33
35
36
37
39
40
28
30
31
32
34
35
36
38
39
41
42
43
45
46
47
29
30-
31
33
34
29
30
32
33
35
29
31
32
34
35
30
31
33
34
35
30
32
33
34
36
30
32
33
34
36
38
39
41
42
44
45
46
48
49
51
52
54
55
57
58
33
34
35
36
38
33
34
35
37
38
33 34
35 35
36 36
37 38
39 39
34
36
37
38
40
36
37
38
40
41
36
37
39
40
42
36
38
39
41
42
37
38
40
41
43
37
39
40
42
43
44
46
47
49
50
52
53
54
56
57
59
60
62
63
65
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
37
38
39
40
41
43
44
45
46
47
49"
50
51
52
53
54
56
57
58
59
60
62
63
64
65
'66
67
69
70
71
39
40
41
43
44
45
46
48
49
50
51
53
54
55
56
58
59
60
61
63
64
65
66
68
69
70
71
73
74
75
39
41
42
43
44
46
47
48
49
51
52
53
54
56
57
58
60
61
62
63
65
66
67
68
70
40
41
42
44
45
40
42
43
44
46
41
42
43
45
46
41
43
44
45
47
42
44
45
46
48
43
44
46
47
48
43
45
46
48
49
44
45
47
48
50
46
47
49
50
51
47
48
49
51
52
47
49
50
51
53
48
49
51
52
53
55
56
57
59
60
61
63
64
65
67
68
69
71
72
73
75
76
77
79
80
49
50
51
53
64
49
51
52
53
55
50
51
53
54
55
50
52
53
55
56
51
52
54
55
57
53
54
55
56
58
59
60
62
63
64
65
67
68
69
71
53
55
56
57
59
54
55
57
58
59
55
57
58
59
61
56
57
59
60
62
57
58
59
61
62
57
59
60
62
63
58
60
61
62
64
59
61
62
64
65
41
42
43
44
45
60
61
62
64
65
66
68
69
70
72
61
62
63
65
66
67
68
70
71
72
74
75
76
78
79
62
63
65
66
68
63
64
66
67
68
64
65
66
68
69
64
66
67
69
70
65
67
68
69
71
66
67
69
70
72
67
68
70
71
73
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
69
70
72
73
74
76
77
78
80
81
70
71
72
74
75
71
72
73
75
76
71
73
74
76
77
72
74
75
77
78
73
75
76
77
79
74
75
77
78
80
71
72
73
75
76
72
73
74
76
77
73
74
75
77
78
77
78
79
81
82
77
79
80
82
83
78
80
81
83
84
79
81
82
84
85
80
82
83
85
86
81
83
84
86
87
Page 678] TABLE 12.
For finding the Variation of the Sun's Eight Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Eight Ascension, in seconds of time, the motion in one minute being given
at the top and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
88"
89"
90"
.91"
92"
98"
94"
95"
96"
9!"
98"
99"
100"
101"
102"
108"
104"
1
2
3
4
5
1
3
4
6
7
1
3
4
6
7
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
6
8
2
3
5
7
8
2
3
5
7
8
2
3
5
7
8
2
3
5
7
8
2
3
5
7
9
2
3
5
7
9
2
3
5
7
9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
9
10
12
13
15
16
18
19
21
22
23
25
26
28
29
31
32
34
35
37
38
40
41
43
44
9
10
12
13
15
16
18
19
21
22
24
25
27
28
30
31
33
34
36
37
39
40
42
43
45
9
11
12
14
15
17
18
20
21
23
24
26
27
29
30
32
33
35
36
38
39
41
42
44
45
9
11
12
14
15
17
18
20
21
23
24
26
27
29
30
32
33
35
36
38
9
11
12
14
15
17
18
20
21
23
25
26
28
29
31
9
11
12
14
16
9
11
13
14
16
10
11
13
14
16
10
11
13
14
16
10
11
13
15
16
10
11
13
15
16
10
12
13
15
17
10
12
13
15
17
10
12
13
15
17
10
12
14
15
17
10
12
14
15
17
19
21
22
24
26
27
29
31
33
34
10
12
14
16
17
6
7
8
9
10
17
19
20
22
23
17
19
20
22
24
17
19
21
22
24
18
19'
21
22
24
18
19
21
23
24
18
20
21
23
25
18
20
21
23
25
18
20
22
23
25
19
20
22
24
25
19
20
22
24
26
19
21
23
24
26
11
12
13
14
15
25
26
28
29
31
25
27
28
30
31
25
27
29
30
32
26
27
29
30
32
26
27
29
31
32
26
28
29
31
33
26
28
30
31
33
27
28
30
32
33
27
29
30
32
34
27
29
31
32
34
28
29
31
33
35
16
17
18
19
20
32
34
35
37
38
33
34
36
37
39
33
34
36
38
39
33
35
36
38
40
34
35
37
38
40
34
36
37
39
40
34
36
38
39
41
35
36
38
40
41
35
37
38
40
42
35
37
39
40
42
36
37
39
41
43
36
38
39
41
43
36
38
40
42
43
21
22
23
24
25
39
41
42
44
46
40
41
43
44
46
40
42
43
45
47
41
42
44
45
47
41
43
44
46
48,
42
43
45
46
48
42
44
45
47
49
42
44
46
47
49
43
45
46
48
50
43
45
47
48
50
44
45
47
49
51
44
46
48
49
51
45
46
48
50
52
53
55
57
58
60
45
47
49
50
52
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
45
47
48
50
51
53
54
56
57
59
60
62
63
65
66
67
69
70
72
73
75
76
78
79
81
82
84
85
87
88
46
47
49
50
52
53
55
56
58
59
61
62
64
65
67
68
11
73
74
47
48
50
51
53
54
56
57
59
60
62
63
65
66
68
69
71
72
74
75
47
49
50
52
53
55
56
58
59
61
62
64
65
67
68
70
71
73
74
76
48
49
51
52
54
48
50
51
53
54
49
50
52
53
55
49
51
52
54
55
50
51
53
54
56
50
52
53
55
57
51
52
54
56
57
51
53
54
56
58
52
53
55
57
58
52
54
56
57
59
53
54
56
58
60
54
55
57
59
61
62
64
66
68
69
55
57
58
60
61
56
57
59
60
62
56
58
60
61
63
57
59
60
62
63
58
59
61
62
64
58
60
61
63
65
59
60
62
64
65
59
61
63
64
66
60
62
63
65
67
61
62
64
66
67
61
63
65
66
68
62
64
65
67
69
63
64
66
67
69
71
72
74
75
77
64
65
67
68
70
64
•66
67
69
71
65
67
68
70
71
66
67
69
70
72
66
68
70
71
78
67
69
70
72
74
68
69
71
73
74
68
70
72
73
75
69
71
72
74
76
70
71
73
75
77
70
72
74
76
77
71
73
75
76
78
80
81
83
85
87
41
42
43
44
45
71
73
74
76
78
72
74
75
77
78
73
74
76
78
79
74
75
77
78
80
74
76
78
79
81
75
77
78
80
82
76
78
79
81
83
77
78
80
82
83
85
87
88
90
92
77
79
81
82
84
"86
88
89
91
93
78
80
82
83
85
79
81
82
84
86
46
47
48
49
50
76
77
79
80
82
83
85
86
88
89
77
78
80
81
83
84
86
87
89
90
77
79
80
82
83
85
86
88
90
91
78
80
81
83
84
86
87
89
90
92
79
81
82
84
85
80
81
83
85
86
81
82
84
86
87
82
83
85
86
88
82
84
86
87
89
83
85
87
88
90
84
86
87
89
91
87
88
90
92
94
88
89
91
93
94
96
98
100
101
103
88
90
92
94
95
97
99
101
102
104
51
52
53
54
55
56
57
58
59
60
87
88
90
91
93
88
89
91
92
94
89
90
92
93
95
90
91
93
94
96
91
92
94
95
97
91
93
95
96
98
92
94
96
97
99
93
95
97
98
100
94
96
98
99
101
95
97
99
100
102
TABLE 12.
i
[Page 679
For finding the Variation of the Sun's Right Ascension
or Declination, or of the Equation of Tjme, in 1
anv number of minutes of time,
;he Horary Motion being given at the top of the page
in seconds, 1
anj the number of minutes of time in the side column.
Also for finding the Variatior of the |
Moon's
Declination or Eight Ascension
, in seconds of time,
the motion in one minute
being given
at the top and the numbers in the side column being
taken for seconds.
M.
1
Horary motion.
M.
105"
106"
107"
108"
109"
110"
111"
112"
118"
114"
115"
116"
iij"
118"
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
2
4
4
4
, 4
4
4
4
4
4
4
4
4
4
4
2
3
5
5
5
5
5
6
6
6
6
6
6
6
6
6
3
4
7
7
7
7
.7
7
7
7
8
8
8
8
8
8
4
5
6
9
9
9
9
9
9
9
9
9
10
10
10
10
10
5
11
11
11
11
11
11
11
11
11
11
12
12
12
12
6
7
12
12
12
13
13
13
13
13
13
13
13
14
14
14
I
8
14
14
14
14
15
15
15
15
15
15
15
15
16
16
8
9
16
16
16
16
16
17
17
17
17
17
17
17
18
18
9
10
11
18
18
18
18
18
18
19
19
19
19
19
19
20
20
10
19
19
20
20
20
20
20
21
21
21
21
21
21
22
11
^?.
21
21
21
22
22
22
22
22
23
23
23
23
23
24
12
13
23
23
23
23
24
24
24
24
24
25
25
25
25
26
13
14
25
25
25
25
25
26
26
26
26
27
27
27
27
28
14
15
26
27
27
27
27
28
28
28
28
29
29
29
29
30
15
16
28
28
29
29
29
29
30
30
30
30
31
31
31
31
16
17
30
30
30
31
31
31
31
32
32
32
33
33
33
33
17
18
32
32
32
32
33
33
33
34
34
34
35
35
35
35
18
19
33
34
34
34
35
35
35
35
36
36
36
37
37
37
19
20
35
35
36
36
36
37
37
37
38
38
38
39
39
39
20
21
37
37
37
38
38
39
39
39
40
40
40
41
41
41
21
22
39
39
39
40
40
40
41
41
41
42
42
43
43
43
22
23
40
41
41
41
42
42
43
43
43
44
44
44
45
45
23
24
42
42
43
43
44
44
44
45
45
46
46
46
47
47
24
25
44
44
45
45
45
46
46
47
47
48
48
48
49
49
25
26
46
46
46
47
47
48
48
49
49
49
50
50
51
51
26
27
47
48
48
49
49
50
50
50
51
51
52
52
53
53
27
28
49
49
50
50
51
51
52
52
53
53
54
54
55
55
28
29
51
51
52
52
53
53
54
54
55
55
56
56
57
57
29
30
53
53
54
54
55
65
56
56
57
57
58
58
59
59
30
31
31
54
55
55
56
56
57
57
58
58
59
59
60
60
61
32
56
57
57
58
58
59
59
60
60
61
61
62
62
63
32
33
58
58
59
59
60
61
61
62
62
63
63
64
64
65
33
34
60
60
61
61
62
62
63
63
64
65
65
66
66
67
34
35
61
62
62
63
64
64
65
65
66
67
67
68
68
69
35
36
36
63
64
64
65
65
66
67
67
68
68
69
70
70
71
37
a5
65
66
67
67
68
68
69
70
70
71
72
72
73
37
38
67
67
68
68
69
70
70
71
72
72
73
73
74
75
38
39
68
69
70
70
71
72
72
73
73
74
75
75
76
77
39
40
70
71-
71
72
73
73
74
75
75
76
77
77
78
79
40
41
72
72
73
74
74
75
76
77
77
78
79
79
80
81
41
42
74
74
75
76
76
77
78
78
79
80
81
81
82
83
42
43
75
76
77
77
78
79
80
80
81
• 82
82
83
84
85
43
44
77
78
78
79
80
81
81
82
83
84
84
85
86
87
44
45
79
80
80
81
82
83
83
84
85
86
86
87
88
89
45
46
46
81
81
82
83
84
84
85
86
87
87
88
89
90
90
47
82
83
84
85
85
86
87
88
89
89
90
91
92
92
47
48
84
sa
86
86
87
88
89
90
90
91
92
93
94
94
48
49
86
87
87
88
89
90
91
91
92
93
94
95
96
96
49
50
88
89"
88
90
89
90
91
92
93
93
94
95
96
97
98
98
50
51
51
91
92
93
94
94
95
96
97
98
99
99
100
52
91
92
93
94
94
95
96
97
98
99
100
101
101
102
52
63
93
94
95
95
96
97
98
99
100
101
102
102
103
104
53
54
95
95
96
97
98
99
100
101
102
103
104
104
105
106
54
55
96
97
98
99
100
101
102
103
104
105
105
106
107
108
55
56
98
99
100
101
102
103
104
105
105
106
107
108
109
110
56
57
100
101
102
103
104
105
105
106
107
108
109
110
111
112
57
58
102
102
103
104
105
106
107
108
109
110
111
112
113
114
58
59
103
104
105
106
107
108
109
110
HI
112
113
114
115
116
59
60
105
106
107
108
109
110
111
112
113
114
115
116
117
118
60
Page 680] - TABLE 12.
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
119"
120"
121"
122"
128"
124"
126"
126"
127"
128"
129"
180"
181"
182"
1
2
3
4
5
2
4
6
8
10
2
4
6
8
10
2
4
. 6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
10
2
4
6
8
11
2
4
6
8
11
2
4
6
9.
11
2
4
6
9
11
2
'^
9
11
2
4
7
9
11
2
4
7
9
11
1
2
3
4
5
6
7
8
9
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
12
14
16
18
21
12
14
17
19
21
13
15
17
19
21
13
15
17
19
21
13
15
17
19
21
13
15
17
19
21
;>8
15
17
19
22
13
15
17
20
22
13
15
17
20
22
13
15
18
20
22
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
11
12
13
14
15
.22
24
26
28
30
22
24
26
28
30
22
24
26
28
30
22
24
26
28
31
23
25
27
29
31
23
25
27
29
31
23
25
27
29
31
23
25
27
29
32
23
25
28
30
32
23
26
28
30
32
34
36
38
41
43
24
26
28
30
32
24
26
28
30
33
24
26
28
31
33
24
26
29
31
33
16
17
18
19
20
32
34
36
38
40
32
34
36
38
40
32
84
36
38
40
33
35
37
39
41
33
35
37
39
41
33
35
37
39
41
33
35
38
40
42
34
36
38
40
42
34
36
38
40
42
34
37
39
41
43
35
37
39
41
43
35
37
39
41
44
35
37
40
42
44
21
22
23
24
25
42
44
46
48
50
42
44
46
48
50
42
44
46
48
50
43
45
47
49
51
43
45
47
49
51
43
45
48
50
52
44
46
48
50
52
44
46
48
50
53
44
47
49
51
53
45
47
49
51
53
45
47
49
52
54
46
48
50
52
54
46
48
50
52
55
46
48
51
53
55
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
52
54
56
58
60
52
54
56
58
60
52
54
56
58
61
53
55
57
59
61
53
55
57
59
62
54
56
58
60
62
54
56
58
60
63
55
57
59
61
63
55
57
59
61
64
55
58
60
62
64
56
58
60
62
65
56
59
61
63
65
57
59
61
63
66
57
59
62
64
66
26
27
28
29
30
61
63
65
67
69
71
73
75
77
79
62
64
66
68
70
63
65
67
69
71
63
65
67
69
71
64
66
68
70
72
64
66
68
70
72
65
67
69
71
73
65
67
69
71
74
66
68
70
72
74
66
68
70
73
75
67
69
71
73
75
67
69
72
74
76
68
70
72
74
76
68
70
73
75
77
31
32
33
34
35
72
74
76
78
80
73
75.
77
79
81
73
75
77
79
81
74
76
78
80
82
74
76
79
81
83
75
77
79
81
83
76
78
80
82
84
76
78
80
83
85
77
79
81
83
85
77
80
82
84
86
• 78
80
82
85
87
79
81
83
85
- 87
79
81
84
86
88
36
37
38
39
40
41
42
43
44
45
81
83
85
87
89
82
84
86
88
90
83
85
87
89
91
83
85
87
89
92
84
86
88
90
92
85
87
• 89
91
93
85
88
90
92
94
86
88
90
92
95
87
89
91
93
95
87
90
92
94
96
88
90
92
95
97
89
91
93
95
98
90
92
94
96
98
90
92
95
97
99
41
42
43
44
45
46
47
48
49
50
46
47
48
49
50
51
52
53
54
55
91
93
95
97
99
101
103
105
107
109
92
94
96
98
100
93
95
97
99
101
94
96
98
100
102
94
96
98
100
103
95
97
99
101
103
96
98
100
102
104
97
99
101
103
105
97
99
102
104
106
98
100
102
105
107
99
101
103
105
108
100
102
104
106
108
100
103
105
107
109
101
103
106
108
110
102
104
106
108
110
103
105
107
109
111
104
106
108
110
112
105
107
109
111'
113
105
107
110
' 112
114
106
108
110
113
115
107
109
111
113
116
108
110
112
114
116
119'
121
123
125
127
109
111
113
115
117
110
112
114
116
118
111
113
115
117
119
111
114
.116
118
120
112
114
117
119
121
51
52
53
54
55
56
57
58
59
GO
111
113
115
117
119
112
114
116
118
120
113
115
117
119
121
114
116
118
120
122
115
117
119
121
123
116
118
120
122
124
117
119
121
123
125
118
120
122
124
126
119
122
124
126
128
120
123
125
127
129
121
124
126
128
130
122
124
127
129
131
123
125
128
130
132
56
57
58
59
60
TABLE 12. :Page 681
For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Righo Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
138"
134"
185"
186"
183"
188"
139"
140"
141"
142"
148"
144"
145"
148"
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
9
4
7
9
11
2
4
7
9
11
13
16
18
20
22
25
27
29
31
34
36
38
40
42
45
2
5
7
9
11
2
5
7
9
11
2
5
7
9
11
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
9
12
2
5
7
10
12
2
5
7
10
12
2
5
7
10
12
2
5
7
10
12
1
2
3
4
5
13
16
18
20
22
14
16
V
20
23
14-
16
18
20
23
14
16
18
21
23
14
16
18
21
23
14
16
19
21
23
14
16
19
21
23
14
16
19
21
24
14
17
19
21
24
14
17
19
21
24
14
17
19
22
24
15
17
19
22
24
15
17
19
22
24
t>
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
24
27
29
31
33
35
38
40
42
44
25
27
29
32
34
25
27
29
32
34
25
27
30
32
34
25
28
30
32
35
25
28
30
32
35
26
28
30
. 33
35
26
28
31
33
35
26
28
31
33
36
26
29
31
33
36
26
29
31
34
36
27
29
31
34
36
27
29
32
34
37
39
41
44
46
49
51
54
56
58
61
36
38
41
43
45
36
39
41
43
45
37
39
41
43
46
37
39
41
44
46
37
39
42
44
46
37
40
42
44
47
38
40
42
45
47
38
40
43
45
47
38
41
43
45
48
38
41
43
46
48
39
41
44
46
48
47
49
51
53
55
47
49
51
54
56
47
50
52
54
56
48
50
52
54
57
48
50
53
55
57
48
51
53
55
58
49
51
53
56
58
49
51
54
56
58
49
52
54
56
59
50
52
54
57
59
50
52
55
57
60
50
53
55
58
60
51
53
56
58
60
58
60
62
64
67
58
60
63
65
67
59
61
63
65
68
59
61
63
66
68
59
62
64
66
69
60
62
64
67
69
60
63
65
67
70
61
63
65
68
70
61
63
66
68
71
62
64
66
69
71
62
64
67
69
72
62
05
67
70
72
63
65
68
70
73
63
66
68
71
73
26
>>-
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51'
52
53
54
55
69
71
73
75
78
69
71
74
76
78
70
72
74
77
79
70
73
75
77
79
71
73
75
78
80
71
74
76
78
81
72
74
76
79
81
72
75
77
79
82
73
75
78
80
82
73
76
78
80
83
74
76
79
81
83
74
77
79
82
84
75
77
80
82
85
75
78
80
83
86
31
32
33
34
35
80
82
84
86
89
80
83
85
87
89
81
83
86
88
90
82
84
86
88
91
82
84
87
89
91
83
85
87
90
92
83
86
88
90
93
84
86
89
91
93
85
87
89
92
94
85
88
90
92
95
86
88
91
93
95
86
89
91
94
96
87
89
92
94
97
88
90
92
95
97
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
91
93
95
98
100
102
104
106
109
HI
92
94
96
98
101
92
95
97
99
101
93
95
. 97
100
102
94
96
98
100
103
94
97
99
101
104
95
97
100
102
104
96
98
100
103
105
96
99
101
103
106
97
99
102
104
107
98
100
102
105
107
98
101
103
106
108
99
102
104
106
109
100
102
105
107
110
112
114
117
119
122
103
105
107
109
112
104
106
108
110
113
104
107
109
111
113
105
107
110
112
114
106
108
110
113
115
107
109
111
114
116
107
110
112
114
117
108
110
113
115
118
109
111
114
116
118
110
112
114
117
119
110
113
115
118
120
111
114
116
118
121
113
115
117
120
122
114
116
118
121
123
115
117
119
122
124
116
118
120
122
125
116
119
121
123
126
117
120
122
124
127
118
120
123
125
127
119
121
124
126
128
120
122
125
127
129
"132
134
136
139
141
121
123
125
128
130
133
135
137
140
142
122
124
126
129
131
122
125
127
130
132
123
126
128
131
133
124
127
129
131
134
51
52
53
54
55
56
57
58
59
60
56
57
58
59
60
124
126
129
131
133
125
127
130
132
134
126
128
131
133
135
127
129
131
1.34
136
128
130
132
135
1.37
129
131
133
136
138
130
132
134
137
139
131
133
135
138
140
133
136
138
141
143
134
137
139
142
144
135
138
140
143
145
136
139
141
144
146
Page 682] TABLE 12.
For finding the Variation of the Sun's Eight Ascension, or Declination, or of the Equation of Time in
any number of minutes of time, the Horary Motion being given at the top of the page in seconds,
and the number of minutes of time in the side column. Also for finding the Variation of the
Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given
at the top, and the numbers in the side column being taken for seconds.
M.
Horary motion.
M.
147"
148"
149"
160"
151"
152"
158"
154"
155"
156"
167"
158"
159"
160"
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2
5
7
10
12
2
5
7
10
12
2
5
7
10
12
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
5
8
10
13
3
6
8
10
13
3
5
8
11
13
3
5
8
11
13
3
5
8
11
13
1
2
3
4
6
15
17
20
'22
25
16
17
20
22
25
15
17
20
22
25
15
18
20
23
25
15
18
20
23
25
15
18
20
23
25
15
18
20
23
26
15
18
21
23
26
16
18
21
23
26
16
18
21
23
26
16
18
21
24
26
16
18
21
24
26
16
19
21
24
27
16
19
21
24
27
6
7
8
9
10
27
29
32
34
37
39
42
44
47
49
27
30
32
35
37
27
30
32
35
37
28
30
33
35
38
28
30
33
35
38
28
30
33
35
38
28
31
33
36
38
28
31
33
-36
39
28
31
34
36
39
29
31
34
36
39
29
31
34
37
39
29
32
34
37
40
29
32
34
37
40
29
32
35
37
40
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
.30
31
32
33
34
35
39
42
44
47
49
40
42
45
47
50
40
43
45
48
50
40
43
45
48
50
41
43
46
48
51
41
43
46
48
51
41
44
46
49
51
41
44
47
49
52
42
44
47
49
52
42
44
47
50
52
42
45
47
50
53
42
45
48
50
53
43-
45
48
51
53
21
22
23
24
25
26
27
28
29
30
51
54
56
59
61
64
66
69
71
74
52
54
57
59
62
52
55
57
60
62
53
55
58
60
63
53
55
58
60
63
53
56
58
61
63
54
56
59
61
64
54
56
59
62
64
54
57
59
62
65
65
67
60
62
65
55
58
60
63
65
65
68
61
63
66
56
58
61
64
66
59
61
64
67
64
67
69
72
74
65
67
70
72
75
65
68
70
73
75
65
68
70
73
76
66
68
71
73
76
66
69
71
74
77
67
69
72
74
77
67
70
72
76
78
68
70
73
75
78
68
71
73
76
79
68
71
74
76
79
69
72
74
77
80
69
72
75
77
80
31
32
33
34
35
36
37
38
39
40
76
78
81
83
86
76
79
81
84
86
77
79
82
84
87
78
80
83
85
88
78
81
83
86
88
79
81
84
86
89
79
82
84
87
89
80
82
85
87
90
80
83
85
88
90
81
83
86
88
91
81'
84
86
89
92
82
84
87
90
92
82
85
87
90
93
83
85
88
91
93
88
91
93
96
98
89
91
94
96
99
89
92
94
97
99
90
93
95
98
100
91
93
96
98
101
103
106
108
111
113
91
94
96
99
101
92
94
97
99
102
92
95
98
100
103
93
96
98
101
103
94
96
99
101
104
94
97
99
102
105.
95
97
100
103
105
95
98
101
103
106
96
99
101
104
107
36
37
38
39
40
41
42
43
44
46
41
42
43
44
45
100
103
105
108
110
101
104
106
109
111
102
104
107
109
112
103
105
108
110
113
104
106
109
111
114
105
107
110
112
115
105
108
110
113
116
106
109
111
114
116
107
109
112
114
117
107
110
113
115
118
108
111
113
116
119
109
111
114
117
119
109
112
115
117
120
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
113
115
118
120
123
113
116
118
121
123
114
117
119
122
124
115
118
120
123
125
116
118
121
123
126
117
119
122
124
127
117
120
122
125
128
118
121
123
126
128
119
121
124
127
129
120
122
125
127
• 130
120
123
126
128
131
121
124
126
129
132
122
125
127
130
133
123
125
128
131
133
46
47
48
49
50
61
52
53
64
56
125
127
130
132
1.35
126
128
131
133
136
127
129
132
134
137
128
130
133
135
138
128
131
133
136
138
129
132
134
137
139
130
133
135
138
140
131
133
136
139
141
132
134
137
140
142
133
135
138
140
143
133
136
139
141
144
134
137
140
142
145
135
138
140
143
146
136
139
141
144
147
137
140
142
145
147
138
141
143
146
148
139
142
144
147
149
140
143
145
148
150
141
143
146
148
151
142
144
147
149
1.52
143
145
148
150
1.53
144
146
149
151
1.54
145
147
1.50
1.52
155
146
148
151
1.53
156
147
149
162
164
1.57
147
150
153
155
158
148
151
1.54
156
159
149
152
155
157
160
66
67
58
59
60
TABLE 13.
[Page
683
For finding
the Sun's change of Eight Ascension for any given number of hours.
Hourly
Number of hours.
Uourly
tion.
1
2
3
4
6
6
7
8
9
10
11
1£
tion.
«.
8.
s.
8.
s.
8.
8.
8.
8.
8.
8.
8.
8.
8.
8.50
8.5
17.0
25.5
34.0
42.5
51.0
59.5
68.0
76.5
85.0
93.5
102.0
8.50
8.55
8.6
17.1
25.7
34.2
42.8
51.3
59.9
68.4
77.0
85.5
94.1
102.6
8.55
8.60
8.6
17.2
25.8
34.4
43.0
51.6
60.2
68.8
77.4
86.0
94.6
103.2
8.60
8.65
8.7
17.3
26.0
34.6
43.3
51.9
60.6
69.2
77.9
86.5
95.2
103.8
8.65
8.70
8.7
17.4
17.5
26.1
34.8
43.5
52.2
60.9
69.6
78.3
87.0
87.5
95.7
104.4
105.0
8.70
8.75
8.8
26.3
35.0
43.8
52.5
61.3
70.0
78.8
96.3
8.75
8.80
8.8
17.6
26.4
35.2
44.0
52.8
61.6
70.4
79.2
88.0
96.8
105.6
8.80
8.85
8.9
17.7
26.6
35.4
44.3
53.1
62.0
70.8
79.7
88.5
97.4
106.2
8.a5
8.90
8.9
17.8
26.7
35.6
44.5
53.4
62.3
71.2
80.1
89.0
97.9
106.8
8.90
8.95
9.0
17.9
26.9
27.0
35.8
36.0
44.8
53.7
62.7
71.6
80.6
89.5
98.5
99.0
107.4
108.0
8.95
9.00
9.0
18.0
45.0
54.0
63.0
72.0
81.0
90.0
9.00
9.05
9.1
18.1
27.2
36.2
45.3
54.3
63.4
72.4
81.5
90.5
99.6
108.6
9.05
9.10
9.1
18.2
27.3
36.4
45.5
54.6
63.7
72.8
81.9
91.0
100.1
109.2
9.10
9.15
9.2
18.3
27.5
36.6
45.8
54.9
64.1
73.2
82.4
91.5
100.7
109.8
9.15
9.20
9.2
18.4
27.6
36.8
46.0
46.3
55.2
64.4
73.6
82.8
92.0
101.2
110.4
9.20
9.25
9.3
18.5
27.8
37.0
55.5
64.8
74.0
83.3
92.5
101.8
111.0
9.25
9.30
9.3
18.6
27.9
37.2
46.5
55.8
65.1
74.4
83.7
93.0
102.3
111.6
9.30
9.35
9.4
18.7
28.1
37.4
46.8
56.1
65.5
74.8
84.2
93.5
102.9
112.2
9.35
9.40
9.4
18.8
28.2
37.6
47.0
56.4
65.8
75.2
84.6
94.0
103.4
112.8
9.40
9.45
9.5
18.9
28.4
37.8
47.3
56.7
66.2
75.6
85.1
94.5
104.0
104.5
113.4
9.45
9.50
9.5
19.0
28.5
38.0
47.5
57.0
66.5
76.0
85.5
95.0
114.0
9.50
9.55
9.6
19.1
28.7
38.2
47.8
57.3
66.9
76.4
86.0
95.5
105.1
114.6
9.55
9.60
9.6
19.2
28.8
38.4
48.0
57.6
67.2
76.8
86.4
96.0
105.6
115.2
9.60
9.65
9.7
19.3
29.0
38.6
48.3
57.9
67.6
77.2
86.9
96.5
106.2
115.8
9.65
9.70
9.7
19.4
29.1
29.3
38.8
48.5
48.8
58.2
67.9
77.6
87.3
97.0
106.7
116.4
9.70
9.75
9.8
19.5
39.0
58.5
68.3
78.0
87.8
97.5
107.3
117.0
9.75
9.80
9.8
19.6
29.4
39.2
49.0
58.8
68.6
78.4
88.2
98.0
107.8
117.6
9.80
9.85
9.9
19.7
29.6
39.4
49.3
59.1
69.0
78.8
88.7
98.5
108.4
118.2
9.85
9.90
9.9
19.8
29.7
39.6
49.5
59.4
,69.3
79.2
89.1
99.0
108.9
118.8
9.90
9.95
10.0
10.0
19.9
29.9
;!0.0
39.8
40.0
49.8
50.0
59.7
69.7
70.0
79.6
80.0
89.6
99.5
100.0
109.5
119.4
9.95
10.00
20.0
60.0
90.0
110.0
120.0
10.00
10.05
10.1
20.1
30.2
40.2
50.3
60.3
70.4
80.4
90.5
100.5
110.6
120.6
10.05
10.10
10.1
20.2
30.3
40.4
50.5
60.6
70.7
80.8
90.9
101.0
111.1
121.2
10.10
10.15
10.2
20.3
30. 5
40.6
50.8
60.9
71.1
81.2
91.4
101.5
111.7
121.8
10.15
10.20
10.2
20.4
;50.6
40.8
51.0
61.2
71.4
71.8
81.6
82.0
91.8
92.3
102.0
102.5"
112.2
112.8
122.4
10.20
10.25
10.3
20.5
30.8
41.0
51.3
61.5
123.0
10.25
10.30
10.3
20.6
30.9
41.2
51.5
61.8
72.1
82.4
92.7
103.0
113.3
123.6
10.30
10.35
10.4
20.7
31. 1
41.4
51.8
62.1
72.5
82.8
93.2
103.5
113.9
124.2
10.35
10.40
10.4
20.8
31.2
41.6
52.0
62.4
72.8
83.2
93.6
104.0
114.4
124.8
10.40
10.45
10.50
10.5
10.5
20.9
31.4
31. 5
41.8
52.3
62.7
73.2
83.6
94.1
104.5
115.0
125.4
126.
10.45
2L0
42.0
52.5
63.0
73.5
84.0
94.5
105.0
115.5
10.50
10. .55
10.6
21.1
31.7
42.2
52.8
63.3
73.9
84.4
95.0
105.5
116.1
126.6
10.55
10.60
10.6
21.2
31.8
42.4
53.0
63.6
74.2
84.8
95.4
106.0
116.6
127.2
10.60
10.65
10.7
21.3
32.0
42.6
53.3
63.9
74.6
85.2
95.9
106.5
117.2
127.8
10.65
10.70
10.75
10.7
10.8
21.4
21.5
32.1
42.8
53.5
53.8
64.2
64.5
74.9
75.3
85.6
86.0
96.3
107.0
117.7
118.3
128.4
129. O'
10.70
10.75
32.3
43.0
96.8
107.5
10.80
10.8
21.6
32.4
43.2
54.0
64.8
75.6
86.4
97.2
108.0
118.8
129.6
10.80
10.85
10.9
21. y
32.6
43.4
54.3
65.1
76.0
86.8
97.7
108.5
119.4
130. 2
10.85
10.90
10.9
21.8
32.7
43.6
54.5
65.4
76.3
87.2
98.1
109.0
119.9
1,30. 8
10.90
10.95
11.0
11.0
21.9
22.0
32.9
43.8
44.0
54.8
65.7
66.0
76.7
87.6
88.0
98.6
109. 5
120.5
131. 4
132.
10.95
11. (X)
33.0
55.0
77.0
99.0
110.0
121.0
11.00
11.05
11.1
22.1
33.2
44.2
55.3
66.3
77.4
88.4
99.5
110.5
121.6
132.6
11.05
11.10
11.1
22.2
33.3
44.4
55.5
66.6
77.7
88.8
99.9
111.0
122.1
133. 2
11.10
11.15
11.2
22.3
33.5
44.6
55.8
66.9
78.1
89.2
100.4
111.5
122.7
133.8
11.15
11.20
11.2
11.3
22.4
33.6
33.8
44.8
56.0
56.3
67.2
67.5
78.4
89.6
100.8
101.3
112.0
112.5
123. 2
1.34. 4
11.20
11.25
22.5
45.0
78.8
90.0
123.8
13.5.0
11.25
11.. 30
11.3
22.6
33.9
45.2
56.5
67.8
79.1
90.4
101.7
113.0
124.3
ia5.6
11.30
11.35
11.4
22.7
34.1
45.4
56.8
68.1
79.5
90.8
102.2
113.5
124.9
136. 2
11.35
11.40
11.4
22.8
34.2
45.6
57.0
68.4
79.8
91.2
102.6
114.0
125.4
136. 8
11.40
11.45
11.5
22.9
34.4
45.8
57.3
68.7
80.2
91.6
103.1
114.5
126.0
137.4
11.45
Page 684] TABLE 13.
For finding the Sun's change of Right Ascension for any given number of hours.
Hourly
varia'
tion.
Number of hours.
Hourly
varia-
tion.
IS
14
15
16,
17
18
19
20
21
22
23
21
8.' 50
110. 5
119.
127. 5
136.
144. 5
153.0
161. 5
170.
178. 5
187.
195. 5
204.
8. .50
8.55
111.2
119.7
128.3
136.8
145.4
153.9
162.5
171.0
179.6
188.1
196.7
205.2
8.55
8.60
111.8
120.4
129.0
137.6
146.2
154.8
163.4
172.0
180. 6
189.2
197.8
206.4
8.60
8.65
112.5
121.1
129.8
138.4
147.1
155.7
164.4
173.0
181.7
190.3
199.0
207.6
8.65
8.70
113.1
121.8
130.5
139.2
147.9
156.6
157.5
165.3
166.3
174.0
175.
182.7
191.4
200.1
208.8
8.70
8.75
113.8
122.5
131.3
140.0
148.8
183.8
192.5
201.3
210.0
8.75
8.80
114.4
123.2
132.0
140.8
149.6
158.4
167.2
176.
184.8
193.6
202.4
211.2
8.80
8.85
115. 1
123.9
132.8
141.6
150.5
159.3
168.2
177.0
185.9
194.7
203.6
212.4
8.85
8.90
115. 7
124.6
133. 5
142.4
151.3
160.2
169.1
178.0
186.9
195.8
204.7
213.6
8.90
8.95
116.4
117.0
125.3
134.3
143.2
152.2
161.1
162.0
170.1
179.0
180.0
188.0
196.9
205.9
214.8
8.95
9.00
126.0
135.
144.0
153.0
171.0
189.
198.0
207.0
216.0
9.00
9.05
117.7
126.7
135.8
144.8
153.9
162.9
172.0
181.0
190.1
199.1
208.2
217.2
9.05
9.10
118.3
127.4
136.5
145.6
154.7
163.8
172.9
182.0
191.1
200.2
209.3
218.4
9.10
9.15
119.0
128.1
137.3
146.4
155. 6
164.7
173.9
183.0
192.2
201.3
210.5
219.6
9.15
9.20
119.6
128.8
129.5
138.0
147.2
148.0
156. 4 S 165. 6
157. 3 ! 166. 5
174.8
184.0
193.2
202.4
203.5
2H.6
220.8
9.20
9.25
120.3
138.8
175.8
185.0
194.3
212.8
222.0
9.25
9.30
120.9
130.2
139.5
148.8
158. 1 ' 167. 4
176.7
186.0
195.3
204.6
213.9
223.2
9.30
9.35
121.6
130. 9
140.3
149. 6
159. i 168. 3
177.7
187.0
196.4
205.7
215.1
224.4
9.35
9.40
122.2
131.6
141.0
150.4
159.8
169.2
178.6
188.0
197.4
206.8
216.2
225.6
9. 40
9.45
122.9
132.3
141.8
151.2
160.7
16"i.5
170.1
171.0
179.6
180.5
189.0
198. 5
l99. 5
207.9
217.4
218.5
226.8
9.45
9.50
123.5
133.0
142.5
152.
190.
209.0
228.0
9. 50
9.55
124.2
13.3. 7
143.3
152.8
162.4
171.9
181.5
191.0
200.6
210.1
219.7
229 2
9.55
9.60
124.8
134.4
144.0
153.6
163.2
172.8
182.4
192.0
201. 6
211.2
220.8
230. 4
9.60
9,65
125.5
135.1
144.8
154.4
164.1
173.7
183.4
193.
202.7
212.3
222.0
231.6
9.65
9.70
126.1
135.8
136.5
145.5
155. 2
164.9
165. 8
174.6
184.3
194.0
195.0
203.7
204.8
213.4
223. 1
232.8
9.70
9.75
126.8
146.3
156.0
175.5
185.3
214.5
224.3
234.
9. 75
9.80
127.4
137.2
147.0
156. 8
166.6
176.4
186.2
196.0
205.8
■215.6
225.4
235.2
9.80
9.85
128.1
137.9
147.-8
1.57. 6
167.5
177.3
187.2
197.0
206.9
216.7
226.6
238. 4
9.85
9.90
128.7
138.6
148.5
158.4
168.3
178.2
188.1
198.0
207.9
217.8
227.7
237.6
9.90
9.95
129.4
139.3
149.3
159. 2
169.2
179.1
189.1
199.0
200.0
209.0
210.0
218.9
228.9
230.0
238. 8
9.95
10.00
130.0
140.0
150.0
160.0
170.0
180.0
190.0
220.0
240.0
10.00
10.05
130.7
140.7
150.8
160.8
170.9
180.9
191.0
201.0
211.1
221.1
231.2
241.2
10.05
10.10
131.3
141.4
151.5
161.6
171.7
181.8
191.9
202.0
212.1
222.2
232. 3
242.4
10.10
10.15
132.0
142.1
152.3
162.4
172.6
182.7
192.9
203.0
213.2
223.3
233. 5
243.6
10.15
10.20
132.6
142.8
153.0
163.2
173.4
183.6
184.5
193.8
204.0
214.2
224.4
234.6
235.8
244.8
10.20
10.25
133.3
143.5
153.8
164.0
174.3
194. 8
205.0
215.3
225.5
246.
10.25
10.30
133.9
144.2
154.5
164.8
175.1
185.4
195.7
206.0
216.3
226. 6
236.9
247.2
10.30
10.35
134.6
144.9
155.3
165.6
176.0
186. 3
196.7
207.0
217.4
227.7
238.1
248.4
10.35
10.40
135.2
145.6
156.0
166.4
176.8
187.2
197.6
208.0
218.4
228.8
239.2
249.6
10. 40
10.45
135.9
146.3
156.8
167.2
177.7
188.1
198.6
209.0
219.5
229.9
231. 0^
240.4
241.5
250.8
252.0
10.45
10.50
136.5
147.0
157.5
168.0
178.5
189.0
199.5
210.0
220.5
10.50
10.55
137.2
147.7
158.3
168.8
179.4
189.9
200.5
211.0
221.6
232.1
242.7
253.2
10.55
10.60
137.8
148.4
159.0
169.6
180.2
190.8
201.4
212.0
222.6
233.2
243.8
254.4
10. 60
10.65
138.5
149.1
159.8
170.4
181.1
191.7
202.4
213.0
223.7
234.3
245.0
255.6
10. 65
10.70
139.1
149.8
160.5
171.2
181.9
192.6
203. 3
204.3
214.0
224.7
235.4
246.1
256.8
10.70
10.75
139.8
150.5
161.3
172.0
182.8
193.5
215.0
225.8
236.5
247.3
258.0
10. 75
10.80
140.4
151.2
162.0
172.8
183.6
194.4
205.2
216.0
226.8
237.6
248.4
259.2
10.80
• 10.85
141.1
151.9
162.8
173.6
184.5
195.3
206.2
217.0
227.9
238.7
249.6
260.4
10. 85
10.90
141.7
152.6
163.5
174.4
185.3
196.2
207.1
218.0
228.9
239.8
250.7
261.6
10. 90
10.95
142.4
153.3
164.3
175.2
186.2
197.1
198.0
208.1
219.0
230.0
231.0
240.9
242.0
251.9
262.8
10.95
1 1 . 00
11.00
143.0
154.0
165.0
176.0
187.0
209.0
220.0
253.0
264.
11.05
143.7
154.7
165. 8
176.8
187.9
198. 9
210.0
221.0
232.1
243.1
254.2
265.2
11.05
11.10
144.3
155.4
166.5
177.6
188.7
199.8
210.9
222.0
233. 1
244.2
255.3
266. 4
11.10
11.15
145.0
156.1
167.3
178.4
189.6
200.7
211.9
223.0
234.2
245. 3
256.5
267.6
11.15
11.20
145.6
156.8
168.0
179.2
190.4
201.6
212.8
213. 8
224.0
235.2
236. 3
246.4
257.6
268. 8
27070
11.20
"11.25
11.25
146. 3
157.5
168.8
180.0
191.3
202.5
225.0
247. 5
258.8
11.30
146.9
158.2
169.5
180.8
192.1
203.4
214.7
226.0
237.3
248.6
259. 9
271.2
11.30
11.35
147.6
158.9
170.3
181.6
193.0
204.3
215.7
227.0
238.4
249.7
261.1
272. 4 1
11.35
11.40
148.2
159.6
171.0
182.4
193.8
205.2
216.6
228.0
239.4
250.8
262.2
273.6
11.40
11.45
148.9
160.3
171.8
183.2
194.7
206.1
217.6
240.5
251.9
263.4
274.8
11.45
TABLES U, 15, 16. [Page 685
TABLE 14.
TABLE 15.
Dip of the Sea
Horizon.
Dip of the Sea at different Distances from the Observer.
Dist. of
Land in
5ea Miles.
Height of the Eye above the Sea in Feet.
Height of 1 Dip of the
the Eye. 1 Horizon.
6
10
15
so
25
SO
35
40
Feet. ' "
^
,
f
,
,
,
,
,
1 59
i
11
23
34
45
57
68
79
91
2 ; 1 23
i
6
12
17
23
28
34
40
45
3 j 1 42
4 i 1 58
5 2 11
6 : 2 24
7 ! 2 36
1
4
8
12
15
19
23
27
30
1
3
6
9
12
15
17
20
23
li
3
5
7
10
12
14
16
19
1*
3
4
6
8
10
12
14
16
8 ' 2 46
9 2 56
10 3 06
2
2
4
5
7
8
9
11
12
2i
2
3
4
6
7
8
9
10
3
2
3
4
5
6
(
8
9
11 '' 3 15
3i
2
3
4
5
6
6
7
8
12 • 3 24
13 3 32
14 i 3 40
4
5
2
2
3
4
4
5
4
5
5
6
6
7
6
7
7
i
6
2
3
4
4
5
5
6
6
15 ! 3 48
16 3 55
17 4 02
18 4 09
19 4 16
20 4 23
Note to Table 15. — The numbers of this Table below the black lines
are the same as are given in Table 14, the visible horizon corresponding
to those heights not being so far distant as the land.
21 4 29
22 4 36
23 4 42
24 1 4 48
25 4 54
26 5 00
27 5 06
28
5 11
29
5 17
30
31
5 22
5 27
32
5 33
TABLE 16.
33 j 5 38
The Sun's Parallax
34 5 43
in Altitude.
35 5 48
36 5 53
Altitude.
Parallax.
37 5 58
38 6 02
o
//
39
6 07
9
40
6 12
10
9
45
6 36
20
8
50
6 56
30
8
55
7 16
40
7
60
7 35
50
6
65
7 54
55
5
70
8 12
60
4
75
8 29
65
4
80
8 46
70
3
85
9 02
75
2
90
9 18
80
2
95
9 33
85
1
100
9 48
90
Page 686]
TABLE 17.
Parallax in Altitude of a Planet.
■epniniY
3»
050iCO<:D(riiC"*CC(M(M^0050Dt^CD'£>U5iCl"*COCOC^rHi-(0
00C0t^C0iOTt*C0C0<NTHOO0500t^«0C0irS'<l*-*WC0<Mr-lT-lO
b-b-i:OiC'^COC-lC<I)-l0005COt^l:^CDlCW'*-^CCC^<NT-Hi-lO
cOCOiC-^COWfMi-IOOOSaOODt^COlClft-^'^COCOCq WrHrHO
lClC-^C0C^T-li-lOO050i00t^t^CDlClC-^"<*<C0CCWC^rHrHO
-1*-<J<eO'Mi-i.-iOOOS05CCI:^t^<©iO"5"<*<'^COCOC^(Mi-ii-iOO
C0C0(M.-lT-iOO0i0500 t^ >- COCOlC'^'^-^COCCC^Wi-HrHOO
'MlMr-iOO0i05 0D0Dr^l>C0:0l0i0'*'*C<tC0(NC^C^rHi-IOO
T-HrHOOOjaOGOOOl— t^CDtOlClO"«*<^COCCCOC^C^C<»tHi-IOO
OO0t0500G0I:^t^l-^':C'<r'i0iC'*M'e0C0e0C^MC^i-ii-ii-iOO
05a)00001r^t-t-C0»C0iOiO'<**'^Tfe»500NNC^<Ni-<i-«r-(OO
oooooot-t-cD'^xnuswswS'^'^'^cocoNeqwwi-HrH.-ii-Hoo
t>.t:^t^c0cDiCi0ifii0-^M'-^«C0CCC<lNC^C^r-tr-i.-ii-(OOO
COC&5C'lClOlO"*-*'*'<*COCOMCOC^C^C'^C^T
lOiOlOTh'*-^"*t<CCCCCO«00N©^C<IC^lMT
■^■^•^WOOOOCCCOCOC^MNNIMNt
coeocccoc^ie^NC^wNC^fi^iT
^ ooooo
C^ (N (N IM (M (N T
^oooooooo
HOOOOOOOOOOOOOO
■opminv
....
TABLES Ife
, 19.
[Page 687
TABLE 18.
TABLE 19.
Augmentation of the Moon's Semidiameter.
Augmentation of the Moon's
- Horizontal Parallax.
■s >p
Ji'sSemi<
£2
p.oi o
<:
J '8
Hor. Parallax. |
J
5'
1A'
17'
3=-
53'
67'
61'
30"
0"
80"
0"
80"
0"
o
//
ft
1)
//
tt
ft
o
tf
ft
'/
0.1
0.1
0.1
0.1
0.2
0.2
0.0
.0.0
0.0
2
0.6
0.6
0.7
0.7
0.8
0.8
2
0.0
0.0
0.0
4
1.0
1.1
1.2
1.3
1.4
1.5
4
0.1
0.1
0.1
b
1.5
1.6
1.7
1.9
2.0
2.1
6
0.1
0.1
0.1
8
2.0
2.1
2.3
2.4
2.6
2.7
8
0.2
0.2
0.2
10
2.4
2.6'
2.8
3.0
3.2
3.4
10
0.3
0.3
0.4
12
2.9
3.1
3.3
3.6
3.8
4.0
12
0.5
0.5
0.5
14
3.4
3.6
3.9
1.1
4.4
4.7
14
0.6
0.7
0.7
16
3.8
4.1
4.4
4.7
5.0
5.3
16
0.8
0.9
0.9
18
4.3
4.6
4.9
5.2
5.6
5.9
18
1.0
1.1
1.1
20
4.7
5.1
5.4
5.8
6.1
6.5
20
1.2
1.3
1.4
22
5.2
5.5
5.9
6.3
6.7
7.1
22
1.5
1.6
1.7
24
5.6
6.0
6.4
6.8
7.3
t. 1
24
1.7
1.9
2.0
26
6.0
6.5
6.9
7.4
7.8
8.3
26
2.0
2.2
2.3
28
6.5
6.9
7.4
7.9
8.4
8.9
28
2.3
2.5
2.6
30
6.9
7.3
7.9
8.4
8.9
9.5
30
2.6
2.8
3.0
32
7.3
7.8
8.3
8.9
9.4
10.0
32
2.9
3.1
3.4
34
7.7
8.2
8.8
9.4
10.0
10.6
34
3.3
3.5
3.8
36
8.1
8.6
9.2
9.8
10.5
11.1
36
3.6
3.9
4.1
38
8.4
9.0
9.7
10.3
10.9
11.6
38
4.0
4.3
4.6
40
8.8
9.4
10.1
10.7
11.4
12.1
40
4.3
4.6
5.0
42
9.2
9.8
10.5
11.2
11.9
12.6
42
4.7
5.0
5.4
44
9.5
10.2
10.9
11.6
12.3
13.1
44
5.0
5.4
5.8
46
9.8
10.5
11.3
12.0
12.8
13.6
46
5.4
5.8
6.2
48
10.2
10.9
11.6
12.4
13.2
14.0
48
5.8
6.2
6.6
50
10.5
11.2
12.0
12.8
13.6
14.4
50
6.1
6.6
7.1
52
10.8
11.5
12.3
13.1
14.0
14.9
52
6.5
7.0
7.5
54
11.1
11.8
12.7
13.5
14.4
15.3
54
6.8
7.4
7.9
56
11.3
12.1
13.0
13.8
14.7
15.6
56
7.2
7.7
8.3
58
11.6
12.4
13.3
14.1
15.1
16.0
58
7.5
8.1
8.6
60
11.8
12.7
13.5
14.4
15.4
16.3
60
7.8
8.4
9.0
62
12.1
12.9
13.8
14.7
15.7
16.6
62
8.1
8.8
9.4
64
12.3
13.2
14.1
15.0
16.0
16.9
64
8.4
9.1
9.7
66
12.5
13.4
14.3
15.2
16.2
17.2
66
8.7
9.4
10.0
68
12.7
13.6
14.5
15.5
16.5
17.5
68
9.0
9.7
10.3
70
12.9
13.8
14.7
15.7
16.7
17.7
70
9.2
9.9
10.6
72
13.0
13.9
14.9
15.9
16.9
17.9
72
9.5
10.2
10.9
74
13.1
14.1
15.0
16.0
17.1
18.1
74
9.7
10.4
11.1
76
13.3
14.2
15.2
16.2
17.2
18.3
76
9.8
10.6
11.3
78
13.4
14.3
15.3
16.3
17.4
18.4
78
10.0
10.8
11.5
80
13.5
14.4
15.4
16.4
17.5
18.6
80
10.1
10.9
11.7
82
13.5
14.5
15.5
16.5
17.6
18.7
82
10.3
11.0
11.8
84
13.6
14.6
15.6
16.6
17.6
18.7
84
10.3
11.1
11.9
86
13.6
14.6
15.6
16.6
17.7
18.8
86
10.4
11.2
12.0
88
13.7
14.6
15.6
16.7
17.7
18.8
88
10.4
11.2
12.0
90
13.7
14.6
15.6
16.7
17.7
18.8
90
10.5
11.3
12.0
Page 688]
TABLE 20A.
Mean Eefraction.
[Barometer, 30 inches. Fahrenheit's Thermometer,
50°.J
Apparent
Altitude.
Mean Re-
Apparent
Mean Re-
Apparent
Mean Re-
Apparent
Mean Re-
Apparent
Altitude.
Mean Re-
fraction.
Altitude.
fraction.
Altitude.
fraction.
Altitude.
fraction.
fraction.
o /
/
o /
9 30
5 35.1
o t
15 00
3 34. 1
o /
25 00
2 4.4
/
42 00
1 04.7
00
36 29.4
35
5 32.4
10
3 31.7
10
2 3.4
20
1 03.9
1 00
24 53. 6
40
5 29.6
20
3 29. 4
20
2 2.5
40
1 03.2
2 00
18 25. 5
45
5 27.0
30
3 27.1
30
2 1.6
43 00
1 02.4
3 00
14 25. 1
50
5 24.3
40
3 24.8
40
2 0.7
20
1 01.7
4 00
11 44.4
55
5 21.7
50
3 22.6
^0
1 59.8
40
1 01.0
5 00
9 52.0
10 00
5 19.2
16 00
3 20.5
26 00
1 58.9
44 00
1 00.3
05
9 44.0
05
5 16.7
10
3 18. 4
10
1 58.1
20
59.6
10
9 36.2
10
5 14.2
20
3 16.3
20
1 57.2
40
58.9
15
9 28.6
15
5 11.7
30
3 14.2
30
1 56.4
45 00
58.2
20
9 21.2
20
5 9.3
40
3 12.2
40
1 55.5
20
57.6
25
9 14.0
25
5 6.9
50
3 10.3
50
1 54.7
40
56.9
5 30
9 7.0
10 30
5 4.6
17 00
3 8.3
27 00
1 53.9
46 00
56.2
35
9 0.1
35
5 2.3
10
3 -6.4
10
1 53.1
20
55.6
40
8 53.4
40
5 0.0
20
3 4.6
20
1 52.3
40
55.0
45
8 46.8
45
4 57.8
30
3 2.8
30
1 51.5
47 00
54. 3
50
8 40.4
50
4 55.6
40
3 1.0
40
1 50.7
20
53.7
55
8 34.2
55
4 53.4
50
2 59.2
50
1 50.0
40
53.1
6 00
8 28.0
11 00
4 51.2
18 00
2 57.5
28 00
1 49.2
48 00
52.5
05
8 22.1
05
4 49.1
10
2 55.8
20
1 47.7
49 00
50.6
10
8 16.2
10
4 47.0
20
2 54. 1
40
1 46.2
50 00
48.9
15
8 10.5
15
4 44.9
30
2 52.4
29 00
1 44.8
51 00
47.2
20
8 4.8
20
4 42.9
40
2 50.8
20
1 43.4
52 00
45.5
25
7 59.3
25
4 40.9
50
2 49.2
40
1 42.0
53 00
43.9
6 30
7 53.9
11 30
4 38. 9
19 00
2 47.7
30 00
1 40.6
54 00
42.3
35
7 48.7
35
4 36.9
10
2 46.1
20
1 39.3
55 00
40.8
40
7 43.5
40
4 35.0
20
2 44.6
40
1 38.0
56 00
39.3
45
7 38. 4
45
4 33.1
30
2 43. 1
31 00
1 36.7
57 00
37.8
50
7 33.5
50
4 31.2
40
2 41.6
20
1 35.5
58 00
36.4
55
7 28.6
55
4 29.4
50
2 40.2
40
1 34.2
59 00
35.0
7 00
7 23.8
12 00
4 27.5
20 00
2 38.8
32 00
1 33.0
60 00
33.6
05
7 19.2
05
4 25.7
10
2 37.4
20
1 31.8
61 00
32.3
10
7 14.6
10
4 23.9
20
2 36.0
40
1 30.7
62 00
31.0
15
7 10.1
15
4 22.2
30
2 34.6
33 00
1 29.5
63 00
29.7
20
7 5.7
20
4 20.4
40
2 33. 3
20
1 28.4
64 00
28.4
25
7 1.4
25
4 18.7
50
2 32.0
40
1 27.3
65 00
27.2
7 30
6 57.1
• 12 30
4 17.0
21 00
2 30.7
34 00
1 26.2
66 00
25.9
35
6 53.0
35
4 15.3
10
2 29.4
20
1 25.1
67 00
24.7
40
6 48.9
40
4 13.6
20
2 28.1
40
1 24.1
68 00
23.6
45
6 44.9
45
4 12.0
30
2 26.9
35 00
1 23. 1
69 00
22.4
50
6 41.0
50
4 10.4
40
2 25.7
20
1 22.0
70 00
21.2
55
6 37.1
55
4 8.8
50
2 24.5
40
1 21.0
71 00
72 00'
20.1
8 00
6 33.3
13 00
4 7.2
22 00
2 23.3
36 00
1 20.1
18.9
05
6 29.6
05
4 5.6
10
2 22.1
20
1 19.1
73 00
17.8
10
6 25.9
10
4 4.1
20
2 20.9
40
1 18.2
74 00
16.7
15
6 22.3
15
4 2.6
30
2 19.8
37 00
1 17.2
75 00
15.6
20
6 18.8
20
4 1.0
40
2 18.7
20
1 16.3
76 00
14.5
25
6 15.3
25
3 59.6
50
2 17.5
40
1 15.4
77 00
13.5
8 30
6 11.9
13 30
3 58.1
23 00
2 16.4
38 00
1 14.5
78 00
12.4
35
6 8.5
35
3 56. 6
10
2 15.4
20
1 13.6
79 00
11.3
40
6 5.2
40
3 55.2
20
2 14.3
40
1 12.7
80 00
10.3
45
6 2.0
45
3 53.7
30
2 13.3
39 00
1 11.9
81 00
9.2
50
5 58.8
50
3 52.3
40
2 12.2
20
1 11.0
82 00
8.2
55
5 55.7
55
3 50.9
50
2 11.2
40
1 10.2
83 00
7.2
6.1
9 00
5 52.6
14 00
3 49.5
24 00
2 10.2
40 00
1 9.4
84 00
05
5 49.6
10
3 46.8
10
2 9.2
20
1 8.6
85 00
5.1
10
5 46.6
20
3 44.2
^0
2 8.2
40
1 7.8
86 00
4.1
15
5 43.6
30
3 41.6
30
2 7.2
41 00
1 7.0
87 00
3.1
20
5 40.7
40
3 39.0
40
2 6.2
20
1 6.2
88 00
2.0
25
5 37.9
50
3 36.5
50
2 5.3
40
1 5.4
89 00
1.0
9 30
5 35.1
15 00
3 34.1
25 00
2 4.4
42 00
1 4.7
90 00
0.0
TABLE SOB.
[Page 689
Correction of the Sun's Apparent Altitude for Refraction and Parallax.
[Barometer, 30 Inches. Fahrenheit's Thermometer,
80°.]
Apparent
Altitude,
Mean Re-
fraction anf
Parallax 0.
Apparent
Altitude.
Mean Re-
fraction and
Parallax 0.
Apparent
Altitude.
Mean Re-
fraction and
Parallax 0.
Apparent
Altitude.
Mean Re-
fraction and
Parallax ©.
Apparent
Altitude.
Mean Re-
fraction and
Parallax 0.
o /
/ //
'
/ //
O '
/ tr
o t
t 11
o /
/ V
9 30
5 26
15 00
3 25
25 00
1 56
42 00
58
00
36 20
35
5 23
10
3 24
10
1 55
20
57
1 00
24 45
40
5 21
20
3 21
20
1 55
40
56
2 00
18 17
45
5 18
30
3 19
.30
1 54
43 00
55
3 00
14 16
50
5 15
40
3 17
40
1 53
20
55
4 00
11 35
55
5 13
50
3 15
50
1 52
40
54
5 00
9 43
10 00
5 10
16 00
3 13
26 00
1 51
44 00
53
05
9 35
05
5 8
10
3 10
10
1 50
20
53
10
9 27
10
5 5
20
3 8
20
1 49
40
52
15
9 20
15
5 3
30
3 6
30
1 48
45 00
52
20
9 12
20
5
40
3 4
40
1 48
20
52
25
9 5
25
4 58
50
3 2
50
1 47
40
51
5 30
8 58
10 30
4 56
17 00
3
27 00
1 46
46 00
50
35
8 51
35
4 53
10
2 58
10
1 45
20
50
40
8 44
40
4 51
20
2 57
20
1 44
40
49
45
8 38
45
4 49
30
2 55
30
1 44
47 00
48
50
8 31
50
4 47
40
2 53
40
1 43
20
48
55
8 25
55
4 44
50
2 51
50
1 42
40
47
6 00
8 19
11 00
4 42
18 00
2 50
28 00
1 41
48 00
47
05
8 13
05
4 40
10
2 48
20
1 40
49 00
45
10
8 7
10
4 38
20
2 46
40
1 38
50 00
43
15
8 2
15
4 36
30
2 44
29 00
1 37
51 00
41
20
7 56
20
4 34
40
2 43
20
1 35
52 00
40
25
7 50
25
4 32
50
2 41
40
1 34
53 00
39
6 30
7 45
11 30
4 30
19 00
2 40
30 00
1 33
54 00
37
35
7 40
35
4 28
10
2 38
20
1 31
55 00
36
40
7 35
40
4 26
20
2 37
40
1 30
56 00
34
45
7 29
45
4 24
30
2 35
31 00
1 29
57 00
33
50
7 25
50
4 22
40
2 34
20
1 28
58 00
32
55
7 20
55
4 20
50
2 32
40
1 26
59 00
31
7 00
7 15
12 00
4 19
20 00
2 31
32 00
1 25
60 00
30
05
7 10
05
4 17
10
2 29
20
1 24
61 00
28
10
7 6
10
4 15
20
2 28
40
1 23
62 00
27
15
7 1
15
4 13
30
2 27
33 00
1 22
63 00
26
20
6 57
20
4 11
40
2 25
20
1 20
64 00
24
25
6 52
25
4 10
50
2 24
40
1 19
65 00
23
7 30
6 48
12 30
4 8
21 00
2 23
34 00
1 18
66 00
22
35
6 44
35
4 6
10
2 21
20
1 17
67 00
21
40
6 40
40
4 5
20
2 20
40
1 16
68 00
21
45
6 36
45
4 3
30
2 19
35 00
1 15
69 00
19
50
6 32
50
4 1
40
2 18
20
1 15
70 00
18
55
6 28
55
4
50
2 17
40
1 14
71 00
17
8 00
6 24
13 00
3 58
22 00
2 15
36 00
1 13
72 00
16
05
6 21
05
3 57
10
2 14
20
1 12
73 00
16
10
6 17
10
3 55
20
2 13
40
1 11
74 00
15
15
6 13
15
3 54
30
2 12
37 00
1 10
75 00
14
20
6 10
20
3 52
40
2 11
20
1 9
76 00
13
25
6 6
25
3 51
50
2 10
40
1 8
77 00
12
8 30
6 3
13 30
3 49
23 00
2 8
38 00
1 8
78 00
10
35
6
35
3 48
10
2 7
20
1 7
79 00
9
40
5 56
40
3 46
20
2 6
40
1 6
80 00
8
45
5 53
45
3 45
30
2 5
39 00
1 5
81 00
7
50
5 50
50
3 43
40
2 4
20
1 4
82 00
6
55
5 47
55
3 42
50
2 3
40
1 3
83 00
6
9 00
5 44
14 00
3 41
24 00
2 2
40 00
1 2
84 00
5
05
5 41
10
3 38
10
2 1
20
1 2
85 00
4
10
5 38
20
3 35
20
• 2
40
1 1
86 00
3
15
5 35
30
3 33
30
1 59
41 00
1
87 00
2
20
5 32
40
3 30
40
1 58
20
59
88 00
2
25
5 29
5 26
50
3 28
3 25
50
1 57
40
58
89 00
1
9 30
15 00
25 00
1 56
42 00
58
90 00 1
1
24972°— 12-
-34
Page 690]
TABLE 21, 1
Correction of the Mean Refraction for the Height of the Barometer. 1
Barom.
Mean refraction.
Barom.
Add.
0'
1'
2'
8'
V
5'
«'
7'
8'
9' 10'
0"
30"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0" 80" 0"
tr
,f
„
II
*/
n
„
„
„
„
n
//
II
II
//
„
„
„
//
„
„
27. 50
2
5
7
10
12
15
17
20
23
25
28
30
33
35
38
40
43
45
48
51
27.55
2
5
7
10
12
15
17
20
22
25
27
30
32
35
37
40
42
45
47 50 1
27.60
2
5
7
10
12
14
17
19
22
24
27
29
31
34
36
39
41
44
46
49
27.65
2
5
7
9
12
14
16
19
21
24
26
28
31
33
36
38
40
43
45
48
27.70
2
2
5
4
7
7
9
9
11
11
14
13
.16
16
18
18
21
20
23
23
25
25
28
27
30
29
32
32
35
34
37
36
39
42
44
47
27.75
39
41
43
46
27.80
2
4
7
9
11
13
15
18
20
22
24
27
29
31
33
35
38
40
42
45
27.85
2
4
6
9
11
13
15
17
19
22
24
26
28
30
32
35
37
39
41
44
27.90
2
4
6
8
10
13
15
17
19
21
23
25
27
30
32
34
36
38
40
43
27.95
28.00
2
2
4
4
6
6
8
8
10
10
12
12
14
14
16
16
18
18
21
20
23 |25
27
26
29
28
31
30
33
32
35
34
37
36
39
38
42
22
24
41
28.05
2
4
6
8
10
12
14
16
18
20
22
24
25
27
29
31
33
35
37
39
28.10
2
4
6
8
9
11
13
15
17
19
21
23
25
27
29
31
33
34
36
38
28.15
2
4
6
7
9
11
13
15
17
19
20
22
24
26
28
30
32
34
36
37
28.20
"0"
2
2
4
3
5
5
7
7
9
9
11
10
13
12
14
14
16
16
18
18
20
19
22
21
24
23
25
25
27
26
29
28
31
30
33
32
35
36
28.25
34135
28. 30
2
3
5
7
8
10
12
14
15
17
19
21
22
24
26
27
29
31
33
34
28. 35
2
3
5
7
8
10
12
13
15
17
18
20
22
23
25
27
28
30
32
33
28.40
2
3
5
6
8
10
11
13
14
16
18
19
21
23
24
26
27
29
31
32
28.45
2
3
3
5
4
6
6
8
7
9
9
11
10
12
12
14
14
16
15
17
17
19
18
20
20
22
21
23
23
25
24
27
26
28
27
30
29
31
30
28.50
31. 50
28,55
3
4
6
7
9
10
12
13
15
16
17
19
20
22
23
25
26
28l29
31.45
28.60
1
3
4
6
7
8
10
11
13
14
15
17
18
20
21
23
24
25
27:28
31.40
28.65
3
4
5
7
8
9
11
12
14
15
16
18
19
20
22
23
25
26127
31.35
28.70
3
4
5
6
8
9
10
12
13
14
16
15
17
18
20
21
22
24
25 1 26
31.30
28.75
2
4
5
6
7
9
10
11
13
14
16
18
19
20
21
23
24
25
31. 25
28.80
2
4
5
6
7
8
10
11
12
13
14
16
17
18
19
21
22
28
24
31.20
28.85
2
3
5
6
7
8
9
10
12
13
14
15
16
17
19
20
21
22
23
31.15
28.90
2
3
4
■5
7
8
9
10
11
12
13
14
16
17
18
19
20
21
22
31.10
28.95
2
3
4
4
5
5
6
6
7
7
8
8
9
9
11
10
12
11
13
12
14
13
15
14
16
15
17
16
18
17
19
18
20
19
21
20
31.05
29.00
2
3
31.00
29.05
2
3
4
5
6
7
8
9
10
11
11
12
13
14
15
16
17
18
19
30.95
29.10
2
3
4
4
5
6
7
8
9
10
11
12
13
14
15
15
16
17
18
30.90
29.15
2
3
3
4
5
6
7
8
9
9
10
11
12
13
14
15
15
16
17
.30. 85
29.20
2
2
3
4
5
6
6
7
8
8
9
8
10
9
10
10
11
11
12
11
13
12
14
13
15
14
15
14
16
15
30.80
29.25
2
3
4
4
5
6
7
30.7?"
29.30
2
3
3
4
5
6
6
7
8
8
9
10
11
11
12
13
13
14
30. 70
29.35
2
3
3
4
5
5
6
7
7
8
9
9
10
10
11
12
13
13
30. 65
29. 40
2
2
3
4
4
5
5
6
7
7
8
8
9
10
10
11
12
12
30.60
29.45
2
2
3
3
4
4
5
6
6
7
7
8
8
9
9
10
11
11
30.55
29.50
2
2
3
3
4
5
5
6
6
7
7
8
8
9
9
10
10
30.50
29.55
2
2
3
3
4
4
5
5
5
6
6
7
7
8
8
9
9
30.45
29.60
2
2
2
3
3
4
4
4
5
5
6
6
6
7
7
8
8
30.40
29.65
2
2
2
3
3
4
4
4
5
5
5
6
6
6
7
t
30.35
29.70
1
2
2
2
3
3
3
4
4
4
5
5
5
5
6
6
30.30
29.75
1
1
2
2
2
3
3
3
3
4
4
4
4
5
5
5
30.25
29.80
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
30.20
29.85
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
30. 15
29.90
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
30.10
29.95
1
1
1
1
1
1
1
1
1
1
1
30.05
30.00
80"
0"
80"
0"
80"
0"
30.00
Bubtract.
0"
80"
0"
80" 0"
80"
0"
80"
0" 80"
0"
80"
0"
80"
0"
Add.
0'
V
2'
8'
♦' j 5' i 6' 1 V
8'
9'
10'
_
1
klean refraction.
TABLE 22.
[Page
691
Correction of the Mean Refraction for the Height of the Thermometer.
Mean refraction.
Ther.
Add.
Ther.
Add.
0'
I' 1
2'
3'
4'
5' 6'
J'
8'
9'
10'
0"
SO"
0"
30"
0"
80"
0"
30"
0"
30"
0"
30"
0'
II
SO"
0"
80"
0"
SO"
0"
SO"
0"
o
It
It
//
//
II
It
II
ft
It
II
II
II
II
II
n
//
n
II
II
ft
o
—10
4
8
12
16
20
24
28
33
37
41
46
50
55
60
65
70
75
80
85
90
—10
— 8
4
8
12
15
19
23
27
31
36
40
44
48
53
58
62
67
72
77
82
87
— 8
— 6
4
7
n
15
19
22
26
30
34
38
42
47
51
55
60
64
69
74
79
84
- 6
— 4
4
7
n
14
18
22
25
29
33
37
41 !45
49
53
57
62
66
71
76
80
— 4
— 2
3
7
10
14
17
16
21
20"
24
23
28
27
31
30
35
34
39
37
43
41
47
45
51
49
55
53
59
57
64
61
68
65
72
69
77
74
- 2
3
7
10
13
2
3
6
9
12
16
19
22
25
29
32
36
39
43
47
50
54
58
62
66
70
2
4
3
6
9
12
15
18
21
24
28
31
34 |37
41
44
48
52
55
69
63
67
4
6
3
6
8
11
14
17
20
23
26
29
32 136
39
42
46
49
53
56
60
64
6
8
3
5
8
11
14
16
19
22
25
28
31
34
37
40
43
47
50
54
57
61
8
10
•3
5
8
10
13
15
18
21'
24
26
29
32
35
38
41
44
48
51
54
58
10
11
2
5.
7
10
13
15
18
20
23
26
28
31
34
37
40
43
46
49
53
56
11
12
2
5
7
10
12
15
17
20
22
25
28
30
33
36
39
42
45
48
51
54
12
13
2
5
7
9
12
14
17
19
22
24
27
30
32
35
38
41
44
47
50
53
13
14
2
5
7
9
11
14
16
19
21
24
26
29
31
34
37
40
42
45
48
51
14
15
2
4
7
9
11
13
16
18
20
23
25
28
30
33
36
38
41
44
47
50
15
16
2
4
6
9
11
13
15
18
20
22
25
27
29
32
35
37
40
43
45
48
16
17
2
4
6
8
10
13
15
17
19
21
24
26
29
31
33
36
39
41
44
47
17
18
2
4
6
8
10
12
14
16
19
21
23
25
28
30
32
35
37
40
43
45
18
19
20
2
2
4
4
6
6
8
8
10
9
12
11
14
13
16
15
18
17
20
19
22
22
24
24
27
26
29
28
31
30
34
33
36
35
39
37
41
40
44
42
19
20
21
2
4
5
7
9
11
13
15
17
19
21
23
25
27
29
31
34
36
38
41
21
22
2
3
5
7
9
11
12
14
16
18
20
22
24
26
28
30
32
35
37
39
22
23
2
3
5
7
8
10
12
14
15
17
19
21
23
25
27
29
31
33
36
38
23
24
2
3
5
6
8
10
11
13
15
17
18
18
20
19
22
21
24
23
26
25
28
27
30
29
32
31
34
33
36
35
24
25
25
2
3
5
6
8
9
11
13
14
16
26
3
4
6
7
9
n
12
14
15
17
19
20
22
24
26
28
29
31
33
26
27
3
4
6
7
9
10
12
13
15
16
18
19
21
23
25
26
28
30
32
27
28
3
4
5
7
8
10
11
12
14
n>
17
19
20
22
23
25
27
29
30
28
29
3
4
5
6
8
9
11
12
13
15
16
18
19
21
22
24
26
27
29
29
30
2
4
5
6
7
9
10
11
13
14
15
17
18
20
21
23
24
26
28
30
31
2
3
5
6
7
8
9
11
12
13
15
16
17
19
20
22
23
25
26
31
32
2
3
4
6
7
8
9
10
11
13
14
15
16
18
19
20
22-
23
25
32
33
2
3
4
5
6
7
8
10
11
12
13
14
15
17
18
19
21
22
23
33
34
2
3
4
5
6
7
8
9
10
11
12
13
14
16
17
18
19
21
22
34
35
2
3
4
5
6
6
7
8
9
10
11
13
14
15
16
17
18
19
20
35
36
2
3
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
36
37
2
2
3
4
5
6
6
7
8
9
10
11
12
13
14
15
16
17
18
37
38
2
3
4
4
5
6
7
8
9
10
11
12
13
13
14
15
16
38
39
2
3
3
4
5
5
6
7
8
8
9
10
11
11
12
13
14
15
39
40
2
2
3
4
4
5
6
6
7
8
8
9
10
10
11
12
13
13
40
41
2
2
3
3
4
4
5
6
6
7
7
8
9
o
10
11
11
12
41
. 42
2
2
3
3
4
4
5
5
6
7
7
8
8
9
S
10
11
42
43
2
2
3
3
3
4
4
5
5
6
6
7
7
8
8
9
9
43
44
1
2
2
3
3
3
4
4
4
5
5
6
6
7
7
8
8
44
45
1
1
2
2
2
3
3
3
4
4
4
5
5
6
6
6
7
45
46
1
1
1
2
2
2
2
2
3
3
4
4
4
4
5
5
5
46
47
1
1
1
1
1
2
2
2
2
2
3
3
3
3
4
4
4
47
48
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
48
49
1
1
1
1
1
1
1
1
1
1
1
1
49
50
50
Add.
Ther.
0"
30"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
Add.
Ther.
c
1'
2'
8'
V
a'
6'
J'
8'
9'
10'
Mean refraction.
Page 692]
TABLE 22.
Correction of the Mean Befraction for the Height of the Thermometer.
Mean refraction.
Ther.
Ther.
0'
T'
2'
3'
4'
5'
8'
!'
8' 1 9'
10'
Subt.
Subt.
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
SO"
0"
80"
0"
80"
0"
o
//
II
//
II
//
//
II
It
//
II
//
//
//
II
//
II
//
II
II
II
II
50
50
51
1
1
1
1
1
1
1
1
1
1
1
1
51
52
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
3
52
53
1
1
1
1
1
2
2
2
2
2
2
3
3
3
3
4
4
53
54
55
1
1
1
1
1
2
2
2
2
2
2
3
2
3
3
3
3
4
3
4
3
4
4
5
4
5
4
5
5
6
5
6
5
54
6
55
56
1
2
2
2
3
3
4
4
4
5
5
6
6
6
7
7
8
56
57
2
2
2
3
3
4
4
5
5
6
6
6
7
8
8
8
9
57
58
2
2
3
3
4
4
5
5
6
6
7
7
8
9
9 j 10
10
58
59
2
2
3
3
4
4
5
5
6
6
7
8
8
9
10
10 i 11
12
59
60
2
2
3
3
4
5
5
6
7
7
8
9
9
10
11
11 i 12
13
60
61
2
3
3
4
4
5
6
7
7
8
9
9
10
11
12
12 13
14
61
62
2
3
3
4
5
6
6
7
8
9
9
10
11
12
13
14 1 15
15
62
63
2
3
4
5i 5
6
7
8
8
9
10
11
12
13
14
15 j 16
17
63
64
2
2
3
4
5i 6
7
7
8
9
10
11
12
13
14
15
16 1 17
18
64
65
2
3
3
4
5| 6
7
8
9
10
11
12
13
14
15
16 j 17 ! 18
19
65
66
2
3
4
5
6 6
(
8
9
10
11
12
14
15
16
17 18 19
20
66
67
2
3
4
5
6 7
8
9
10
11
12
13
14
16
17
18
19 20
22
67
68
2
o
4
5
6 7
8
9
11
11
13
14
15
16
18
19
20 22
23
68
69
2
3
4
5
7 8
9
10
10
11
12
12
12
13
14
15
16
16
17
17
19
20
21
21 : 23
22 24
24
25
69
70
2
3
5
6
7 8
9
18 120
70
71
2
4
5
6
7 8
10
11
12
13
15
16
18
19 120
22
23 ! 25
27
71
72
2
4
5
6
8 9
10
11
13
14
16
17
18
20
21
23
25 : 26
28
72
73
3
4
5
7
8 9
11
12
13
14
16
18
19
21
22
24
26 1 27
29
73
74
3
3
4
4
5
6
7
7
8i 10
8 10
11
11
12
13
14
14
15
16
17
18
18
19
20
21
22
23
25
26
27 1 28
28 ; 29
30
31
74
75
22 '24
75
76
3
4
6
7
9 10
12
13
15
16
18
20
22
23
25
27
29 j 31
32
76
77
3
5
6
8
9 11
12
14
16
17
19
21
22
24
26
28
30 32
34
77
78
2
3
5
6
8
9i 11
13
14
16
18
20
21
23
25
27
29
31 t 33
35
78
79
2
3
5
6
8
10' 11
13
15
17
18
20
22
24
26
28
30
32
34
36
79
80
2
3
5
7
8
10 12
14
15
17
19
21
23
25
27
29'
31
33
35
37
80
81
2
3
5
7
9
10 12
14
16
18
20
21
24
26
28
30
32
34
36
38
81
82
2
4
5
7
9
11 13
14
16
18
20
22
24
26
28
31
33
35
37
40
82
83
2
4
5
7
9
11 13
15
17
19
21
23
25
27
29 31
34
36
38
41
83
84
2
4
6
8
9
11: 13
15
17
19
21
23
26
28
30 i32
35
37
39
42
84
85
2
4
6
8
10
12} 14
16
18
20
22
24
26
29
31
33
36
38
40
43
85
86
2
4
6
8
10
12 t 14
16
18
20
23
25
27
29
32
34
37
39
42
44
86
87
2
4
6
8
10
12; 14
17
19
21
23
25
28
30
32
35
38
40
43
45
87
88
2
4
6
8
10
13 15
17
19
21
24
26
28
31
33
36
38
41
44
46
88
89
2
4
6
9
11
13 15
17
20
20
22
23
24
25
27
27
29
30
32
32
34
35
37
38
39
40
42
43
45
46
48
49
89
90
2
4
7
9
11
13 16
18
90
91
2
4
7
9
11
14 16
18
21
23
25
28
31
33
36 '39
41
44
47
50
91
92
2
5
7
9
11
14 16
19
21
24
26
29
31
34
37 39
42
45 48
51
92-
93
2
5
7
9
12
14 17
19
22
24
27
29
32
35
37 40
43 1 46
49
52
93
94
. 2
5
7
10
10
12
12
14 17
15 17
19
20
22
22
25
25
27
28
30
30
33
33
35
36
38 Ul
44 1 47
50
51
53
54
94
95
2
5
7
39
42
45
48
95
96
2
5
7
10
12
15 18
20
23
26
28
31
34
37
40
43
46
49
52
55
96
97
3
5
8
10
13
15 18
21
23
26
29
32
35
38
41
44
47
50
53
56
97
98
3
5
8
10
13
16 18
21
24
27
29
32
35
38
41
44
48
51
54
58
98
99
3
3
5
5
8
8
11
11
13
13
16, 19
16 1 19
21
22
24
25
27
28
30
31
33
34
36
37
39
40
42
43
45
46
49
50
52
55
59
99
100
53
56
60
100
Subt.
Ther.
0"
80"
0"
80"
0"
80"
0" i 80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
80"
0"
Subt.
Ther.
0'
1'
2'
3'
I'
B'
6'
7'
8'
9'
10'
Mean refraction.
TABLES 23, 24.
[Page 693
TABLE 23.
Correction of the Moon's Altitude for parallax and re-
fraction corresponding to a mean
value of the hori-
zontal parallax, 57'
30".
Moon's
alt.
Corr.
Moon's
alt.
Corr.
Moon's
alt.
Corr.
Moon's
alt.
Corr.
o
/
o
f
o
1
O
,
10
51
31
48
51
35
71
18
11
52
32
47
52
35
72
17
12
52
33
47
53
34
73
17
13
52
34
46
54
33
74
16
14
52
35
46
55
32
75
15
15
52
36
45
56
32
76
14
16
52
37
45
57
31
77
13
17
52
38
44
58
30
78
12
18
52
39
44
59
29
79
11
.
19
52
40
43
60
28
80
10
20
51
[
21
51
41
42
61
27
81
9
22
51
42
42
62
26
82
8
23
51
43
41
63
26
83
7
24
50
44
40
64
25
84
6
25
50
45
40
65
24
85
5
26
50
46
39
66
23
86
4
27
49
47
38
67
22
87
3
28
49
48
38
68
21
88
2
29
49
49
37
69
20
89
1
30
48
50
36
70
19
90
TABLE 24.
Dorrecti
on of tl
[B.
le Mooi
irometer
I's App
30 inche
irent Altitude
s.— Fahrenheit's 1
or Par
rhermoc
allax and Refr
aeter, 50°.]
actio
n.
Moon's
H
orizonta
1 paralla:!
[.
55
Correction for seconds of
parallax.— Add.
Corr. for
app. alt.
64'
66'
56'
57'
68'
59'
60'
61'
1^
0"
8"
4"
6"
8"
of alt.
o /
/ //
/ tt
/ n
/ //
' //
/ //
/ //
/ w
//
//
II
II
It
II
5
43 56
44 56
45 56
46 56
47 56
48 55
49 55
50 55
2
4
6
8
10
44 11
45 11
46 11
47 11
48 11
49 10
50 10
5110
10
10
12
14
16
18
20
25
25
25
25
25
24
24
24
20
20
22
24
26
28
30
39
39
38
38
38
38
37
37
30
30
32
34
36
38
40
52
51
51
51
51
51
51
51
40
40
42
44
46
48
50
45 4
46 3
47 3
47 14
48 3
49 3
49 14
50 3
51 3
52 3
50
50 < 52
54
4
56
6
58
8
6
45 15
46 15
48 14
50 13
51 13
52 13
2
10
26
26
25
25
25
25
25
25
10
10
12
14
16
18
20
36
36
36
35
35
34
34
34
20
20
22
24
26
28
30
46
46
45
45
45
44
44
44
30
30
32
34
36
38
40
55
55
55
54
54
54
53
53
40
40
42
44
46
48
50
46 4
47 3
48 3
49 3
50 3
50 12
51 2
51 11
52 1
53 1
50
50
52
2
54
4
56
6
58
8
7
46 12
47 12
48 12
49 12
52 11
53 10
10
21
20
20
20
19
18
18
18
10
10
12
14
16
18
20
29
28
28
27
27
26
25
25
20
20
22
24
26
28
30
36
36
35
35
34
34
34
33
30
30
32
34
36
38
40
43
42
42
41
41
40
40
40
40
40
42
44
46
48
50
50
49
48
48 55
48
49 54
48
47
46
46
50
50
52
2
54
4
56
6
58
8
Add.
8
46 56
47 56
50 54
51 54
52 53
53 53
10
47 2
48 2
49 1
50
51
59
59
58
10
10
12
14
16
18
2 1
20
8
7
7
6
6
52 5
53 4
54 4
20
20
22
24
26
28
3 2
30
13
13
12
11
11
10
10
9
30
30
32
34
36
38
4 2
40
19
18
17
17
16
16
15
14
40
40
42
44
46
48
5 3
50
24
23
22
22
21
51 25
20
52 24
19
19
50
50
52
2
54
4
56
6
58
8
6 4
7 4
9
47 28
48 27
49 26
50 26
53 24
54 23
10
33
32
31
30
30
29
28
27
10
10
12
14
16
18
8 5
20
37
36
35
34
34
33
32
32
20
20
22
24
26
28
9 5
30
41
41
40
39
38
37
37
36
30
30
32
34
36
38
40
45
44
43
43
42
41
40
39
40
40
42
44
46
48
50
49
48
47
46
46
45
44
44
50
49
51
53
55
57
Page 694]
TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction. |
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Horizontal parallax.
li
Correction for seconds of
parallax. — Add.
Corr.
for
app. alt.
II
minutes
of alt.
64'
55'
66'
67'
58'
59'
60'
61'
0"
2"
4"
6"
8"
o /
' //
/ //
/ II
/ //
/ //
/ //
1 II
/ //
II
II
//
//
II
It
Add.
10
47 53
48 52
49 51
50 50
51 50
52 48
53 48
54 47
2
4
6
8
V 0"
10
56
55
54
53 52
51
50
50
10
10
12
14
16
18
2 1
20
59
58
57
56 55
55
54
53
20
20
22
24
26
28
3 1
30
48 2
49 1
50
59 58
57
56
55
30
29
31
33
35
37
4 1
40
5
4
2
51 2 i 52 1
53
59
58
40
39
41
43
45
47
5 2
50
7
6
5
4 i 4
2
54 1
55
50
49
51
2
53
4'
55
6
67
8
6 2
7 2
11
48 10
49 9
50 8
51 7 52 7
53 5
54 4
55 3
10
12
11
10
9 9
7
6
5
10
10
12
14
16
18
8 2
20
15
14
12
12 11
9
8
7
20
20
22
24
26
28
9 3
30
17
16
14
13 13
11
10
9
30
29
31
33
35
37
40
19
18
17
15 15
13
12
11
40
39
41
43
45
47
50
21
20
18
17
17
52 17
15
53 17
14
54 15
13
55 14
50
49
51
2
53
4
55
6
57
8
12
48 22
49 21
50 19
51 18
10
24
23
21
20 1 19
18
16
15
10
10
12
14
16
18
20
26
25
23
22
21
20
18
17
20
20
22
24
25
27
30
27
26
24
23
22
20
19
18
30
29
31
33
35
37
40
28
27
25
24
23
21
20
19
40
39
41
43
45
47
50
29
28
26
50 27
25
24
22
21
20
50
49
61
2
53
4
55
6
57
8
1
13
48 30
49 29
51 26
52 25
53 23
54 22
55 20
10
31
30
28
27
26
24
22
21
10
10
12
14
16
18
2
20
32
31
29
27
26
24
23
21
20
19
21
23
25
27
3
30
33
32
30
28
27
25
23
22
30
29
31
33
36
37
4
40
34
32
30
29
28
26
24
22
40
39
41
43
45
47
5
50
35
33
31
30
51 30
28
52 28
26
25
23
50
49
51
53
55
57
6
7
14
48 35
49 33
50 31
53 26
54 25
55 23
2
4
6
8
10
35
34
32
30
28
26
25
23
10
10
12
14
16
18
8
20
36
.34
32
30
29
27
25
24
20
19
21
23
25
27
9
30
36
34
32
30
29
27
25
23
30
29
31
33
35
37
40
36
34
32
30
29
27
25
23
40
39
41
43
45
47
50
36
34
32
30
29
27
25
54 25
23
55 23
50
49
51
2
53
4
55
6"
57
8
15
48 36
49 35
50 33
51 31
52 29
53 27
10
36
35
32
30
28
26
24
22
10
10
12
14
16
18
20
36
35
32
30
28
26
24
22
20
19
21
23
25
27
30
36
34
31
29
28
25
23
21
30
29
31
33
35
37
40
36
34
31
29
27
25
23
21
40
39
41
43
45
47
50
16
35
33
30
28
26
24
53 23
21
19
.50
49
51
2
53
4
55
6
57
8
48 35
49 32
50 29
51 27
52 25
54 20
55 18
10
34
32
29
27
25
23
20
18
10
10
12
13
15
17
20
34
32
29
27
25
22
20
17
20
19
21
23
25
27
30
33
31
28
26
24
21
19
16
30
29
31
33
35
36
40
33
31
28
25
23
21
18
16
40
38
40
42
44
46
50
32
30
27
50 26
24
51 23
22
20
17
15
55 13
50
48
50
2
52
4
54
6'
56
8
Sub.
V 0"
17
48 31
49 29
52 21
53 18
54 16
10
30
28
25
22
20
17
14
12
10
10
12
13
15
17
2
20
28
26
23
20
18
15
12
10
20
19
21
23
25
27
3
30
27
25
22
19
17
14
11
9
30
29
31
33
34
36
4
40
26
24
21
18
16
13
10
i
40
38
40
42
44
46
6 1
50
26
23
20
17
15
52 13
12
9
6
50
48
50
2
52
4
53
6
65
8
6 1
7 1
18
48 24
49 21
50 18
51 15
53 10
54 7
55 4
10
23
20
17
14
12
9
6
3
10
10
11
13
15
17
8 1
20
22
19
16
13
11
8
5
2
20
19
21
23
25
27
9 1
30
21
18
15
12
10
6
3
30
29
30
32
34
36
40
20
17
14
10
8
4
1
54 58
40
38
40
42
44
46
50
18
15
49 13
12
9
51 7
6
52 4
2
53
53 59
53 57
56
54 55
50
48
50
2
51
4
53
6
65
8
19
48 16
50 10
10
15
12
8
5
2
52 59
55
53
10
10
11
13
16
17
20
13
10
6
3
57
53
51
20
19
21
23
26
27
30
12
8
5
2
51 58
55
51
49
30
29
30
32
34
36
40
10
6
3
56
53
49
47
40
38
40
42
44
46
50
9
5
2
50 58
55
51
48
45
50
48
50
51
63
56
TABLE 2i.
[Page 696J
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 60°.]
Moon's
Horizontal parallax.
M
Correction for seconds of
parallax. — Add.
Corr.
for
app. alt.
minutes
o£ alt.
54'
55'
66'
57'
58'
59'
60'
61'
0"
2"
4"
6"
8"
o /
1 II
/ II
/ If
/ II
' //
/ 11
1 II
. n
II
//
II
II
//
II
Sub.
20
48 6
49 3
49 59
50 56
51 52
52 49
53 45
54 42
2
4
6
8
V
0"
10
5
2
58
55
51
47
43
40
10
9
11
13
15
17
2-
20
3
56
52
49
45
41
37
20
19
21
23
24
26
3
30
1
48 58
53
50
46
42
38
35
30
28
30
32
34
36
4
40
59
56
52
48
44
40
36
33
40
38
39
41
43
45
5
50
57
54
50
46
42
51 39
38
34
30
50
47
49
2
51
4
53
6
54
7
6
7
21
47 55
48 51
49 47
50 43
52 35
53 31
54 28
10
53
49
45
41
37
33
29
26
10
9
11
13
15
17
8
20
51
47
43
39
35
31
27
23
20
19
21
22
24
26
9
2
30
48
44
40
36
32
28
24
20
30
28
30
32
34
35
40
46
42
38
33
29
25
21
17
40
37
39
41
43
45
50
43
47 42
39
35
31
27
22
18
14
54 11
50
47
49
2
50
4
52
6
54
7
22
48 37
49 33
50 29
51 25
52 20
53 16
10
40
35
30
26
22
17
13
8
10
9
11
13
15
17
20
37
32
27
23
19
14
10
5
20
19
20
22
24
26
30
34
30
25
20
16
11
/
3
30
28
30
31
33
35
40
32
27
22
18
13
9
4
40
37
39
41
43
45
50
29
25
20
15
11
6
1
53 57
50
46
48
2
50
4
52
6
54
7
23
47 27
48 22
49 17
50 13
51 8
52 3
52 58
53 54
10
25
20
15
10
5
55
51
10
9
11
13
15
17
20
22
17
12
7
2
51 57
52
48
20
18
20
22
24
26
80
19
14
9
4
54
49
45
30
28
29
31
33
35
40
16
11
6
1
50 57
51
46
42
40
37
39
40
42
44
50
13
8
3
49 58
54
48
43
52 40
38
53 35
50
46
48
2
50
4
51
5
53
7
1
24
47 10
48 5
49
49 55
50 50
51 45
10
8
3
48 57
52
47
42
37
32
10
9
11
13
15
16
2
1
20
5
54
49
44
39
33
28
20
18
20
22
24
26
3
1
30
2
47 57
51
46
41
35
30
24
30
27
29
30
32
34
4
1
40
46 59
54
48
43
38
32
27
21
40
36
38
40
42
44
5
2
50
56
51
45
40
49 37
35
29
23
18
50
46
47
2
49
4
51
5^
53
7.
6
7
2
2
25
46 53
47 48
48 42
50 31
51 26
52 20
53 14
10
50
45
39
33
28
22
16
10
10
9
11
13
14
16
8
2
20
46
41
35
29
24
18
12
6
20-
18
20
22
24
25
9
3
30
43
38
32
26
20
14
8
3
30
27
29
31
33
34
40
40
34
28
23
17
11
5
52 59
40
36
38
40
42
43
50
37
31
25
19
49 16
14
7
1
56
50
45
47
2
49
4
51
5
52
7
26
46 34
47 28
48 22
50 10
51 4
51 58
52 52
10
31
25
19
13
7
1
54
48
10
9
11
13
14
16
20
27
21
15
9
3
50 57
50
44
20
18
20
22
23
25
30
24
18
12
6
49 59
53
46
40
.30
27
29
31
32
34
40
20
14
8
2
55
49
42
36
40
36
38
39
41
43
50
17
11
4
48 58
51
45
38
51 35
32
52 28
50
45
47
2
48
4
50
5
52
7
1
27
46 14
47 7
48 1
48 54
49 48
50 41
10
11
4
47 58
51
44
37
31
24
10
9
11
12
14
16
2
1
20
7
1
54
47
40
33
27
20
20
18
20
21
23
25
3
1
30
3
46 57
50
43
36
29
23
16
30
27
28
30
32
34
4
1
40
45 59
53
46
39
32
25
19
12
40
36
37
39
41
43
5
2
50
56
49
42
47 38
35
28
49 24
21
15
8
50
44
46
2
48
4
50
5
52
7
6
7
2
3
28
45 53
46 46
48 31
50 17
51 11
52 4
H)
49
42
34
27
20
13
6
5159
10
9
11
12
14
16
8
3
20
45
38
30
23
16
9
2
55
20
18
19
21
23
25
9
3
30
41
34
26
19
12
5
50 57
50
30
26
28
30
32
33
40
37
30
23
15
8
1
54
46
40
35
37
39
41
42
50
29
34
26
19
47 15
11
4
49 57
49
42
50
44
46
2
48
4
49
5
51
7
45 30
46 22
48 7
49
49 53
50 45
5138
10
26
18
11
3
48 56
49
40
34
10
9
10
12
14
16
20
22
14
7
47 59
52
44
36
29
20
17
19
21
23
24
30
18
10
2
55
47
39
31
24
30
26
28
30
31
33
40
14
6
46 58
51
43
35
27
20
40
35
37
38
40
42
50
11
3
55
47
39
31
23
15
50
ll
45
47
49
51
Page 696]
TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction. [
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
Horizontal parallax.
o c
1-
Correction for seconds of
parallax.— Add.
Corr.
for
app. alt.
minutes
of alt.
54'
55'
66'
67'
58'
59'
60'
61'
0"
2"
4"
It
6"
II
8"
o /
/ n
/ //
/ //
/ n
r II
/ II
/ //
/ //
n
//
//
II
Sub.
30
45 6
45 57
46 50
47 42
48 34
49 26
60 18
51 10
2
3
5
7
1' 0"
10
2
64
46
38
30
22
13
6
10
9
10
12
14
16
2 1
20
44 58
50
42
34
26
18
9
1
20
17
19
21
23
24
3 1
30
54
46
37
29
21
13
4
60 56
30
26
28
29
31
33
4 2
40
50
42
33
25
17
8
52
40
35
36
38
40
42
5 2
50
45
38
29
21
12
4
49 55
49 50
47
50 42
50
43
46
2
47
3
49
5
60
7
6 3
7 3
31
44 41
45 33
46 24
47 16
48 7
48 59
10
37
29
20
12
2
54
45
37
10
9
10
12
14
15
8 4
20
33
24
15
7
47 58
49
40
32
20
17
19
21
22
24
9 4
30
28
20
11
2
54
45
36
27
30
26
27.
29
31
32
40
24
16
7
46 58
49
40
31
22
40
34
36
38
39
41
50
20
11
2
53
44
35
26
17
60
43
44
2
46
3
48
5
50
7
32
44 15
45 7
45 58
46 49
47 40
48 31
49 22
50 13
10
11
3
53
44
35
26
17
8
10
8
10
12
14
15
20
7
44 58
48
39
30
21
11
2
20
17
19
20
22
24
30
3
53
44
34
25
16
6
49 57
30
26
27
29
30
32
40
43 58
48
39
29
20
. 11
1
52
40
34
35
37
39
41
50
54
44
34
24
15
6
48 56
47
50
42
44
2
46
3
47
5
49
7
1
33
43 48
44 39
45 29
46 19
47 10
48
48 50
49 41
10
44
34
25
15
5
47 55
45
36
10
8
10
12
13
15
2 1
20
40
30
20
10
50
40
31
20
17
18
20
22
23
3 1
30
35
29
15
5
46 55
45
35
26
30
25
27
28
30
32
4 2
40
30
20
10
50
40
30
20
40
33
36
37
38
40
5 2
50
25
15
5
45 55
45
36
24
14
50
42
43
2
45
3
47
5
48
7
6 3
7 3
34
43 21
44 11
45
45 50
46 40
47 30
48 19
49 9
10
16
6
44 55
45
34
24
14
3
10
8
10
12
13
15
8 4
20
11
1
50
40
29
19
9
48 58
20
17
18
20
21
23
9 4
30
6
43 56
45
35
24
13
3
52
30
25
26
28
30
31
40
1
51
40
30
19
8
47 58
47
40
33
36
36
38
40
50
42 56
46
35
24
14
3
52
47 47
42
48 36
50
41
43
2
44
3
46
5
48
7
35
42 52
43 41
44 30
45 19
46 9
46 58
10
47
36
25
14
3
52
41
30
10
8
10
11
13
15
20
42
31
20
9
45 58
47
36
25
20
16
18
20
21
23
30
37
26
15
3
52
41
30
19
30
24
26
28
29
31
40
32
21
10
44 58
47
36
25
14
40
33
34
36
38
39
50
27
16
4
53
42
30
19
8
50
41
42
2
44
3
46
5
47
6
36
42 22
43 11
43 59
44 48
45 37
46 26
47 14
48 2
10
17
5
54
42
31
19
8
47 56
10
8
10
11
13
14
1 1
20
12
48
37
25
14
2
60
20
16
18
19
21
23
2 1
30
7
42 55
43
31
20
8
46 56
44
30
24
26
27
29
31
3 2
40
1
50
38
26
14
2
50
39
40
32
34
35
37
39
4 2
50
41 56
44
32
20
8
45 56
44
33
47 27
60
40
42
2
43
3
45
5
47
6
5 3
6 3
37
41 51
42 39
43 27
44 15
45 3
45 51
46 39
10
46
34
21
9
44 57
45
33
21
10
8
10
11
13
14
7 4
20
41
29
16
4
52
40
27
15
20
16
17
19
21
22
8 4
30
35
23
11
43 58
46
34
21
9
30
24
26
27
29
30
9 6
40
30
18
5
53
40
28
15
3
40
32
33
35
37
38
50
25
12
42 59
47
34
22
45 16
9
46 3
46 57
50
40
41
2
43
3
45
5
46
6
38
41 19
42 7
42 54
43 41
44 29
46 51
10
14
2
49
36
23
10
45 57
45
10
8
9
11
13
14
20
8
41 56
43
30
17
4
51
38
20
16
17
19
20
22
30
3
51
38
24
12
44 68
45
32
30
23
25
27
28
30
40
40 58
45
32
18
6
52
39
26
40
31
33
35
36
38
50
52
39
26
13
46
33
20
.50
39
41
2
42
3
44
5
46
6
39
40 47
41 33
42 20
43 7
43 54
44 40
45 27
46 13
10
42
28
15
1
48
34
21
(
10
8
9
11
12
14
1 1
20
36
23
9
42 55
42
28
15
1
20
15
17
19
20
22
2 1
30
30
17
3
49
36
22
8
46 54
30
23
25
26
28
29
3 2
40
26
11
41 57
43
30
16
2
48
40
31
32
34
36
37
4 2
50
19
5
51
37
23
9
44 56
42
50
39
40
42
43
45
5 3
TABLE 24.
[Page 697
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Horizontal parallax.
li
Correction for seconds of
parallax. — Add.
Corr.
Moon's
app. alt.
Ss
for
minutes
54'
66'
66'
57'
58'
69'
60'
61'
la
0"
i"
4"
It
6"
8"
of alt.
o /
/ //
/ //
/ //
f II
/ //
1 It
/ II
/ 11
„
n
II
It
It
Sub.
40
40 14
41
41 46
42 32
43 18
44 4
44 50
45 36
2
3
5
6
6'
3"
10
8
40 54
39
25
11
43 57
43
29
10
8
9
11
12
14
7
4
20
2
48
33
19
5
50
36
22
20
15
17
18
20-
21
8
5
30
39 56
42
28
13
42 59
44
30
16
30
23
24
26
27
29
9
5
40
50
36
22
7
53
38
24
- 9
40
30
32
34
.35
37
50
45
30
16
1
47
32
18
3
50
38
40
2
41
3
43
5
44
6
41
39 39
40 24
41 10
41 55
42 41
43 26
44 11
44 56
10
33
18
4
49
34
19
4
49
10
8
9
11
12
14
,20
27
12
40 58
43
28
13
43 58
43
20
15
17
18
20
21
30
21
6
51
36
22
7
51
37
HO
23
24
26
27
29
40
16
45
30
16
45
30
40
30
32
.33
.35
.36
50
10
39 54
39
24
9
42 53
38
23
50
38
39
1
41
3
42
4
44
6
42
39 4
39 48
40 33
41 17
42 2
42 47
43 31
44 16
10
38 58
42
27
11
41 56
41
25
10
10
7
9
10
12
13
1
1
20
52
36
21
5
50
34
18
3
20
15
16
18
19
21
2
1
30
46
30
14
40 58
43
27
11
43 56
.30
22
24
25
27
28
3
2
40
40
24
8
52
36
21
49
40
30
31
3;^
34
.36
4
2
50
34
18
2
46
30
14
42 58
42
50
37
38
l"
40
3
41
4^
43
6
5
6
3
4
43
38 28
39 12
39 56
40 40
41 24
42 8
42 52
43 36
10
22
6
50
34
18
1
45
29
10
7
9
10
12
13
7
4
20
16
38 59
43
27
11
41 54
38
22
20
15
16
18
19
20
8
5
30
10
53
37
20
5
48
31
15
,30
22
23
25
26
28
9
5
40
4
47
30
14
40 58
41
24
8
40
29
31
32
34
.35
50
37 57
41
24
7
51
34
17
1
50
37
38
1
39
3
41
4
42
6
44
37 51
38 35
39 18
40 1
40 44
41 27
42 10
42 54
10
45
28
11
39 54
37
20
3
46
10
7
9
10
11
13
20
38
21
4
47
30
13
41 56
39
20
14
16
17
19
20
30
32
15
38 58
41
24
7
49
32
.30
21
23
24
26
27
40
26
9
51
34
17
42
25
40
29
30
31
33
.34
50
20
2
44
27
10
40 3
40 53
40 46
35
18
50
36
37
1
39
3
40
4
41
6
1
1
45
37 14
37 56
38 38
39 21
41 28
42' 11
10
7
49
31
14
39 56
39
21
3
10
7
8
10
11
13
2
1
20
43
25
7
49
32
14
41 56
20
14
15
17
18
20
3
2
30
36 54
37
18
1
43
25
' 7
49
.30
21
23
24
25
27
4
3
40
48
30
11
38 54
36
18
42
40
28
30
31
32
34
5
3
50
41
23
4
47
29
11
40 52
.34
50
35
37
1
38
3
39
. 4
41
6
6
7
4
5
4e
36 35
37 17
37 58
38 40
39 22
40 4
40 45
41 27
10
29
10
51
33
15
39 57
38
20
10
7
8
10
11
12
8
5
20
22
3
44
26
8
49
31
12
20
14
15
17
18
19
9
6
30
16
36 57
38
20
1
42
24
5
30
21
22
23
25
26
40
9
50
32
13
38 54
35
17
40 58
40
28
29
30
32
33
50
2
35 56
43
25
37 18
6
47
28
39 21
9
50
50
35
36
1
37
3'
39
4
40
5
47
36 37
37 59
38 40
40 2
40 43
10
49
30
11
52
34
14
39 55
36
10
7
8
10
11
12
20
42
23
4
45
26
6
47
28
20
14
15
16
18
19
30
36
17
36 57
.38
19
38 59
40
21
.30
20
22
23
24
26
40
30
10
50
31
12
52
32
13
40
27
29
.30
31
33
50
23
3
43
36 36
24
37 17
5
45
25
39 17"
5
50
34
35
1
37
3
38
4
39
5
1
1
48
35 16
35 56
37 57
38 37
39 58
10
10
50
30
10
50
30
10
50
10
7
8
9
11
12
2
1
20
3
43
23
2
43
22
2
42
20
13
15
16
17
19
3
2
30
34 56
36
16
36 55
35
15
38 55
34
,30
20
21
23
24
25
4
3
40
49
29
9
48
28
8
48
27
40
27
28
29
31
32
5
3
50
49
42
34 35
22
1
41
21
37 13
37 53
40
19
50
33
35
1
36
3
37
4
39
5
6
7
4
5
35 15
35 54
36 34
38 32
39 11
10
29
8
47
27
6
46
25
4
10
7
8
9
10
12
8
5
20
22
1
40
20
36 59
38
17
38 56
20
13
14
16
17
18
9
6
30
15
34 54
33
12
51
30
9
48
30
20
21
22
23
25
40
8
47
26
5
44
23
2
41
40
26
27
29
.30
31
50
1
40
19
35 58
36
15
37 54
33
50
33
34
35
36
38
Page 698]
TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches. — Fahrenheit's Thermometer 50°.] •
Horizontal parallax.
is 0)
Correction for seconds of
parallax. — Add.
Corr.
Moon's
%t
for
minutes
54'
56'
56'
57'
58'
59'
60'
61'
m
0"
•I"
4"
0"
8"
of alt.
O '
' It
' ft
/ n
' 11
/ tf
f It
' //
/ ff
It
//
It
//
II
It
50
33 54
34 33
35 11
35 50
36 29
37 8
37 46
38 25
1
3
4
5
10
47
26
4
43
21
38
17
10
6
8
9
10
12
20
40
19
34 57
36
14
36 53
31
9
20
13
14
15
17
18
30
33
11
49
28
6
45
23
1
30
19
20
22
23
24
40
26
4
42
20
35 58
37
15
37 53
40
26
27
28
29
31
50
19
33 57
35
13
51
35 44
29
7
45
37 37
50
32
33
1
35
3
36
4
37
5
Sub.
51
33 12
33 50
34 28
35 6
36 22
36 59
10
5
43
21
34 58
36
14
51
29
10
6
8
9
10
11
2 1
20
32 58
36
13
50
28
6
43
21
20
13
14
15
16
18
3 2
30
51
29
6
43
21
35 58
36
13
30
19
20
21
23
24
4 3
40
44
22
33 59
36
14
50
28
5
40
25
26
28
29
30
5 4
50
52
37
14
51
28
6
34 58
42
20
36 57
50
31
33
1
34
2
35
4
36
5
6 4
7 5
32 30
33 7
33 44
34 21
35 35
36 12
36 49
10
23
36
13
50
27
4
41
10
6
7
9
10
11
8 6
20
15
32 52
29
6
43
19
35 56
33
20
12
13
15
16
17
9 6
30
8
45
21
33 5^
35
11
48
24
30
18
20
21
22
23
40
1
38
14
50
27
3
40
16
40
24
26
27
28
29
50
31 54
31
7
43
19
34 11
34 55
32
8
50
31
32
r
33
2
34
4
35
5
53
31 47
32 23
32 59
33 35
34 47
35 24
36
10
39
15
51
27
3
39
15
35 51
10
6
7
8
10
11
20
32
8
44
20
33 56
31
7
43
20
12
13
14
16
17
30
25
36
12
48
23
34 59
35
.HO
18
19
20
22
23
40
17
31 53
28
4
40
15
51
27
40
24
25
26
28
29
. 50
10
46
21
32 57
32
7
43
34 35
19
50
30
31
32
2
34
4
.35
5
54
31 3
31 38
32 13
32 49
33 24
33 59
35 10
1
10
30 55
30
5
41
16
51
26
1
10
6
7
8
9
11
20
48
22
31 57
33
8
43
18
34 53
20
12
13
14
15
16
30
40
15
49
25
35
10
45
30
18
19
20
21
22
40
33
8
42
17
32 52
27
1
37
40
23
25
26
27
28
50
26
36
9
44
32 36
19
33 53
28
50
29
30
1
32
2
.33
3
34
5
55
30 18
30 52
31 27
32 1
33 10
33 45
34 19
10
10
45
19
31 53
28
2
36
11
10
6
(
8
9
10
20
3
38
12
46
20
32 54
28
3
20
11
13
14
15
16
30
29 55
30
4
38
12
46
20
33 54
30
17
18
19
20
22
40
48
- 22
30 56
30
4
37
11
45
40
23
24
25
26
27
50
40
14
48
22
31 14
31 55
29
3
37
50
28
30
1
31
2
32
3
33
4
56
29 33
30 7
30 40
31 47
32 21
32 55
33 28
10
25
29 59
32
6
39
13
46
20
10
6
7
8
9
10
20
18
51
24
30 58
31
4
37
11
20
11
12
13
14
16
30
10
43
16
50
23
31 56
29
2
30
17
18
19
20
21
1 1
40
3
36
9
42
15
48
21
32 54
40
22
23
24
25
27
2 2
50
28 55
28
29 20
1
34
7
40
12
45
50
28
29
1
30
2
31
3
32
4
3 2
4 3
57
28 47
29 53
30 25
30 58
31 31
32 3
32 36
10
39
12
45
17
50
22
31 55
27
10
5
6
7
9
10
5 4
20
32
5
37
9
42
14
47
19
20
11
12
13
14
15
6 5
30
24
28 57
29
1
33
6
38
10
30
16
17
18
19
21
7 5
40
17
49
21
29 53
25
30 57
29
1
40
22
23
24
25
26
8 6
50
58
9
41
13
45
17
49
21
3152
50
27
28
1
29
2
30
3
31
4
9 7
28 1
28 33
29 5
29 37
30 9
30 41
31 12
3144
10
27 53
25
28 57
28
32
4
35
10
5
6
7
8
9
20
45
17
49
20
29 52
23
30 55
26
20
10
12
13
14
15
30
38
9
41
12
44
15
46
17
30
16
17
18
19
20
40
30
1
33
4
35
6
38
9
40
21
22
23
24
25
50
22
27 53
24
28 55
27
29 58
29
50
26
27
1
28
2
29
3
30
4
59
27 14
27 45
28 16
28 47
29 18
29 49
30 20
30 51
10
6
37
7
38
9
40
11
42
10
5
6
7
8
9
20
26 58
29
27 59
30
1
31
2
33
20
10
11
12
13
14
30
51
21
51
22
28 53
23
29 54
24
30
15
16
17
18
19
40
43
13
43
14,
44
14
45
15
40
20
21
22
23
24
50 35
5
35
5
36
6
36
6
50
25
26
27 29
30
TABLE 24.
[Page 699
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
■3.2
Correction for seconds of
parallax.— Add.
Corr.
for
minutes
54'
55'
5«'
67'
58'
5«'
60'
61'
IS.
0"
•ill
4"
6"
8"
of alt.
o /
' II
/ II
' II
1 II
/ II
' II
' II
/ II
II
//
II
II
„
II
60
26 26
26 57
27 27
27 57
28 27
28 57
29 27
29 57
1
2
3
4
10
19
49
19
49
19
49
18
48
10
5
6
7
8
9
20
11
41
11
40
10
40
9
39
20
10
11
12
13
14
30
3
32
2
31
1
31
30
.SO
15
16
17
18
19
40
25 55
24
26 53
23
27 53
22
28 51
21
40
20
21
22
23
24
50
47
16
45
26 37
14
44
27 36
13
.42
12
50
25
26
1
27
2
28
3
29
4
61
25 39
26 8
27 6
28 5
28 34
29 3
10
31
29
26 58
27
27 56
25
28 54
10
5
6
7
8
9
20
23
25 52
20
49
18
47
16
45
20
10
11
12
12
13
30
15
43
12
40
10
38
7
35
.30
14
15
16
•17
18
40
7
35
4
32
1
29
27 58
26
40
19
20
21
22
23
50
24 59
27
25 55
24
26 52
20
49
27 40
17
50
24
25
1
26
2
27
3
28
4
62
24 50
25 19
25 47
26 15
26 43
27 11
28 8
10
42
10
38
6
34
2
30
27 58
10
5
6
6
7
8
20
34
2
29
25 57
25
26 53
21
49
20
9
10
11
12
12
30
26
24 54
21
49
17
45
12
40
30
14
15
16
17
18
40
18
46
13
41
8
36
3
31
40
19
19
20
21
22
50
10
37
4
32
25 59
25 51
27
26 54
21
50
23
24
25
2
26
3
27
4
63
24 2
24 29
24 56
25 23
26 18
26 45
27 12
1
10
23 54
21
48
15
42
9
36
3
10
4
5
6
7
8
20
46
13
39
6
33
27
26 54
20
9
10
11
12
13
30
37
4
31
24 58
24
25 51
18
45
30
13
14
15
16
17
40
29
23 55
22
49
15
42
8
35
40
18
19
20
21
22
50
64
20
47
13
40
6
33
25 59
26
50
22
23
1
24
2
25
26
23 12
23 39
24 5
24 32
24 58
25 24
25 50
26 17
3
3
10
4
31
23 57
23
49
15
41
8
10
4
5
6
7
8
20
22 56
22
48
14
40
6
32
25 58
20
9
10
10
11
12
30
47
13
39
5
31
24 57
22
48
30
13
14
15
16
16
40
39
5
30
23 56
22
48
13
39
40
17
18
19
20
21
50
31
22 23
22 57
22
23 13
48
13
39
4
30
50
22
23
1
23
2
24
2
25
3
Sub.
65
22 48
23 39
24 4
24 30
24 55
25 21
10
14
40
5
30
23 55
20
46
11
10
4
5
6
7
7
V 1"
20
6
31
22 56
21
46
11
36
• 1
20
8
9
10
11
12
2 2
30
21 58
23
48
13
37
2
27
24 52
30
13
13
14
15
16
3 3
40
49
14
39
4
28
23 53
18
43
40
17
18
18
19
20
4 4
50
41
6
30
22 55
19
44
8
33
50
21
22
r
23
2
23
2
24
3
5 5
6 5
66
21 32
21 57
22 21
22 46
23 10
23 35
23 59
24 23
10
24
48
12
37
1
25
49
14
10
4
5
6
7
7
7 6
20
15
39
3
28
22 52
15
40
4
20
8
9
10
n
11
8 7
30
7
31
21 55
19
43
6
31
23 55
.30
12
13
14
15
16
9 8
40
20 59
22
46
10
34
22 57
21
45
40
16
17
18
19
20
50
50
14
21 5
• 37
1
25
48
22 39
12
36
23 26
50
20
21
1
22
2
23
2
24
3
67
20 41
21 28
21 52
22 15
23 2
10
33
20 56
19
43
6
29
22 52
16
10
4
5
5
6
^
20
25
48
11
34
21 57
20
43
7
20
8
8
9
10
11
30
16
39
2
25
48
11
34
22 57
.30
12
12
13
14
15
40
8
30
20 53
16
39
2
24
47
40
15
16
17
18
18
50
19 59
21
44
7
30
21 52
21 43
15
37
50
19
20
1
21
1
22
2
22
3
68
19 50
20 13
20 35
20 58
21 21
22 5
22 28
10
42
4
27
49
12
34
21 56
19
10
4
4
5
6
7
20
33
19 56
18
40
2
24
47
9
20
7
8
9
9
10
30
25
47
9
31
20 53
15
37
21 59
.30
11
12
13
13
14
40
16
38
22
44
5
27
49
40
15
16
16
17
18
50
7
29
19 51
13
20 4
34
20 25
20 56
20 47
17
21 8
39
50
18
19
1
20
1
21
2
21
3
69
18 59
19 21
19 42
21 30
10
50
12
33
19 55
16
37
20 59
20
10
4
4
5
6
6
20
42
3
24
45
7
28
49
10
20
7
8
8
9
10
30
33
18 54
15
36
19 57
18
39
30
11
11
12
13
13
40
24
45
6
27
48
9
29
20 50
40
14
15
15
16
17
50
16
37
18 57
18
39
20
41
50
18
18
19
20
20
Page 700]
TABLE 24.
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer 30 inches.— Fahrenheit's Thermometer 50°.]
Moon's
Horizontal parallax.
5«
Correction for seconds of
parallax.— Add.
Corr.
for
app. alt.
og
minutes
of alt.
54'
55'
66'
67'
58'
59'
60'
61'
0"
2"
4"
II
6"
It
8"
It
O 1
/ //
t It
/ //
/ //
/ //
/ II
/ II
/ //
n
//
II
70
18 7
18 28
18 48
19 9
19 30
19 50
20 11
20 31
1
1
9,
3
10
17 58
19
39
20
41
1
21
10
3
4
5
5
6
20
50
10
30
18 50
11
31
19 51
11
20
7
7
8
9
9
30
41
1
21
41
1
21
41
1
30
10
11
11
12
13
40
32
17 53
12
32
18 52
12
32
19 52
40
13
14
15
15
18
50
24
17 15
44
17 35
3
23
43
3
22
19 12
42
50
17
17
1
18
1
19
19
3"
71
17 54
18 14
18 34
18 53
19 32
10
6
26
45
5
24
43
3
22
10
3
4
4
5
6
20
16 57
17
36
17 55
14
33
18 53
12
20
6
7
8
8
9
30
48
8
27
46
5
24
43
2
30
10
10
11
12
12
40
40
16 59
18
37
17 56
15
34
18 52
40
13
13
14
15
15
50
31
50
9
28
47
5
24
42
50
16
17
17
18
19
72
16 22
16 41
17
17 18 1 17 37
17 55
18 14
18 32
1
1
2
10
13
32
16 50
9
27
46
4
22
10
3
4
4
5
5
20
5
23
41
16 59
18
36
17 54
12
20
6
7
7
8
8
30
15 57
14
32
50
9
27
46
3
30
9
10
10
11
11
40
48
5
23
41
16 59
17
35
17 53
40
12
13
13
14
14
50
73
39
15 56
14
32
50
16 40
7
25
43
50
15
16
1
16
1
17
2
18
2
15 30
15 47
16 5
16 22
16 58
17 15
17 33
10
21
38
15 56
13
30
48
5
23
10
3
3
4
5
5
20
12
29
47
4
21
39
16 56
13
20
6 1 6
7
7
8
30
3
20
37
15 55
12
29
46
3
30
9 i 9
10
10
n
40
14 54
11
28
45
2
19
36
16 53
40
11
12
13
13
14
50
45
2
19
35
15 52
15 42
9
26
42
50
14
15
1
15
1
16
2
17
2
Sub.
74
14 36
14 53
15 9
15 26
15 59
16 16
16 32
10
28
44
17
33
49
6
22
10
3
3
4
4
5
V I"
20
19
35
14 51
8
24
40
15 56
12
20
5
6
6
7
8
2 '>
30
10
26
42
14 58
14
30
46
2
30
8
9
9
10
11
3 3
40
1
17
33
49
5
20
36
15 52
40
11
11
12
12
13
4 4
50
13 52
8
23
39
14 55
14 45
10
26
42
50
13 i 14
, 1
14
1
15
2
16
2
5 5
6 6
75
13 43
13 59
14 14
14 29
15 1
15 16
15 32
10
34
50
5
20
36
14 52
7
22
10
3 3
4
4
5
7 7
20
25
41
13 56
11
. 27
42
14 57
12
20
5
6
6
7
7
8 8
30
16
32
46
1
17
32
47
2
30
8
8
9
9
10
9 9
40
7
22
37
13 52
7
22
37
14 51
40
10
11
11
12
12
50
12 58
13
28
42
13 57
12
27
41
14 31
50
13
13
14
1
14
1
15
2
76
12 49
13 4
13 18
13 33
13 47
14 2
14 17
10
41
12 55
9
24
38
13 53
7
21
10
2
3
3
4
4
20
32
46
14
28
43
13 57
11
20
5
5
6
6
7
30
23
37
12 51
5
19
33
47
1
30
7
8
8
8
9
40
14
27
41
12 55
9
23
36
13 50
40
9
10
10
11
11
50
5
18
32
45
12 59
13
26
40
50
12
12
13
1
13
1
14
2
77
11 56
12 9
12 22
12 36
12 49
13 3
13 16
13 30
10
• 47
13
27
40
12 53
7
20
10
2
3
3
4
4
20
38
11 51
4
17
30
43
12 57
10
20
4
5
6
6
6
30
29
42
11 55
8
21
33
47
30
7
7
7
8
8
40
19
32
45
11 58
11
23
36
12 49
40
9
9
9
10
10
50
10
23
35
48
1
13
26
39
50
11
11
12
12
1
13
2
78
11 1
11 14
11 26
11 39
11 52
12 4
12 16
12 29
1
10
10 52
5
17
30
42
11 54
6
19
10
2
2
3
3
4
20
43
10 55
8
20
32
44
11 56
8
20
4
4
5
5
6
30
34
46
10 58
10
22
34
46
11 58
30
6
6
7
7
8
40
25
37
48
12
24
36
48
40
8
8
9
9
10
50
16
28
39
10 51
3
10 53
15
26
38
50
10
10
11
1
11
1
12
1
79
10 7
10 19
10 30
10 42
11 5
11 16
11 28
10
9 58
9
21
32
43
10 55
6
17
10
2
2
3
3
3
20
49
11
22
33
44
10 56
7
20
4
4
4
5
5
30
40
9 50
1
12
23
34
45
10 56
30
6
fi
6
7
7
40
31
41
9 52
3
13
24
35
46
40
7
8
8
8
9
50
22
32
43
9 54
4
15
25
36
50
9
10
10
10
11
FABLE 24.
[Page 701
Correction of the Moon's Apparent Altitude for Parallax and Refraction.
[Barometer
30 inche
.—Fahrenheit's Thermometer 50°.]
Moon's
app. alt.
Horizontal parallax.
Correction for Beconds of
parallax. — ^Add.
Corr.
for
minutes
54'
55'
66'
57'
58'
59'
w
61'
si g.
0"
2"
4"
«"
S"
of alt.
/
/ It
t It
/ It
/ 11
, „
r n
1 It
/ //
It
It
tl
It
II
11
80
9 13
9 23
9 34
9 44
9 55
10 5
10 15
10 26
1
1
1
10
3
14
24
34
45
9 55
5
15
10
2
2
2
3
3
20
8 54
4
14
24
35
45
9 55
5
20
3
4
4
4
5
30
45
8 55
5
15
25
35
45
9 54
30
5
6
6
6
40
36
46
8 55
5
15
25
35
44
40
7
7
7
8
8
50
27
37
8 27
46
8 37
8 56
6
15
25
34
50
8
9
9
1
9
1
10
1
81
8 18
8 46
8 56
9 5
9 14
9 24
10
9
18
27
36
46
8 55
4
13
10
1
2
2
2
3
20
7 59
8
17
26
36
45
8 54
3
20
3
3
4
4
4
30
50
7 59
8
17
26
35
44
8 52
30
4
5
5
5
6
40
41
50
7 59
8
17
25
34
42
40
6
6
6
7
7
50
32
41
7 31
49
7 58
7 48
7
15
24
32
50
7
8
8
1
8
1
9
1
82
7 23
7 40
7 57
8 5
8 13
8 22
10
14
22
30
38
47
7 55
3
11-
10
1
2
2
2
2
20
4
12
20
28
37
45
7 52
20
3
3
3
3
4
30
6 55
3
11
19
27
35
42
7 50
30
4
4
5
5
5
40
46
6 54
2
10
17
25
32
40
40
5
6
6
6
6
50
37
45
6 52
7
15
22
30
50
7
7
7
7
1
8
1
Sub.
83
6 28
6 35
6 43
6 50
6 57
7 5
7 12
7 20
10
19
26
33
40
47
6 54
2
9
10
1
1
2
2
2
V v
20
9
16
23
30
37
44
6 51
6 58
20
2
3
3
3
3
2 2
30
7
13
20
27
34
41
48
30
3
4
4
4
4
3 3
40
5 51
5 58
4
11
18
24
31
38
40
5
5
5
5
6
4 4
50
42
49
5 55
1
8
14
21
27
50
6
6
6
6
I
1
5 5
6 6
84
5 33
5 39
5 45
5 52
5 58
6 4
6 10
6 17
1
10
23
30
36
42
48
5 54
6
10
1
1
1
2
2
7 7
20
14
20
26
32
38
44
5 50
5 55
20
2
2
2
3
3
8 8
30
5
10
16
22
28
34
39
45
30
3
3
3
3
4
9 9
40
4 56
1
7
13
18
24
29
35
40
4
4
4
4
5
50
47
4 52
4 58
3
8
14
19
25
5 14
50
0~
5
5
5
5
6
1
85
4 37
4 43
4 48
4 53
4 58
5 4
5 9
10
28
33
38
43
48
4 53
4 58
3
10
1
1
1
1 1 1
20
18
24
28
33
38
43
48
4 53
20
2
2
2
2 1 2
30
9
14
19
23
28
33
38
43
30
2
3
3
3
3
40
5
10
14
19
23
28
33
40
3
3
4
4
4
50
3 51
3 42
3 56
3 46
5
9
13
18
22
50
4
4
4
5
5
1
86
3 50
3 55
3 59
4 3
4 7
4 11
10
33
37
41
45
49
3 53
3 57
1
10
1
1
1
1
1
20
23
27
31
35
39
43
46
3 50
20
1
1
2
2
2
30
14
18
21
25
29
33
36
40
30
2
2
2
2 i 2
40
5
9
12
16
19
23
26
30
40
3
3
3
3
3
50
2 56
2 59
2 50
3
6
9
13
16
19
50
3
3
3
4
4
87
2 47
2 53
2 56
2 59
3 2
3 5
3 9
10
37
40
43
46
49
2 52
2 55
2 58
10
1
1
1
1
20
28
31
33
36
39
42
45
47
20
1
1
1
1
1
30
19
21
24
26
29
32
34
37
30
1
1
2
2
2
40
10
12
15
17
19
22
24
27
40
2
2
2
2
2
50
88
1
3
5
7
1 57
9
1 59
12
14
2 4
16
50
2
2
2
3
3
1 51
1 53
1 55
2 2
2 6
10
42
43
45
47
49
1 51
1 53
1 55
10
20
32
34
36
38
39
41
43
44
20
1
1
1
1
1
30
23
25
26
28
29
31
32
34
30
1
1
1
1
1
40
14
15
16
19
20
21
22
24
40
1
1
1
1
1
50
5
6
* 7
9
10
1
11
1 1
12
1 2
13
50
1
1
1
2
2
89
56
57
58
59
1 3
10
46
47
48
49
50
51
51
52
10
20
37
37
38
39
40
40
41
42
20
30
28
28
28
29
30
30
31
31
30
40
19
19
19
19
20
20
21
21
40
50
9
10
10
10
10
10
10
10
50
1
1
1
1
1
Page 702]
TABLE 25.
Table showing the variation of the altitude of an object arising from a change of 100 seconds in
the
declination. Unmarked quantities in the Table are positive. If the change move the body toward 1
the elevated pole, apply the correction to the altitude with the signs in the Table; otherwise, |
change the signs.
•
1
B
<
latitude of same name as declination.
Latitude of different name from declination.
<
g
3
Q
70°
60°
50°
40°
30°
20°
10°
0°
10°
iW>
80°
40°
50°
60°
70°
„
It
II
II
„
„
„
II
„
,1
It
II
„
„
„
o
o
94
87
76
64
50
34
17
17
34
50
64
76
87
94
10
95
88
78
65
51
35
18
18
35
51
65
78
88
95
10
20
100
92
82
68
53
36
18
18
36
53
68
82
92
100
20
30
100
88
74
57
39
20
20
39
57
74
88
100
30
40
100
84
65
45
22
22
45
65
84
100
40
50
100
78
53
27
27
53
78
100
50
60
100
68
35
35
68
100
60
70
50
100
34
51
17
51
100
~9T
70
94
87
77
64
17
34
50
64
77
87
10
95
87
77
65
50
34
17
- 1
18
35
51
66
78
88
96
10
20
99
91
81
67
52.
35
17
- 1
•19
37
54
69
83.
93
101
20
30
107
98
87
73
56
38
18
- 2
22
41
59
76
90
102
30
2
40
111
98
82
63
42
20
- 2
25
47
68
86
102
40
2
50
116
97
74
50
24
- 3
.30
57
81
103
50
60
124
95
64
30
- 5
40
73
103
60
70
139
50
92
43
- 8
59
17
108
70
94 87
77
64
34
17
34
50
64
77
87
94
10
94 87
77
64
50
34
16
- 1
19
36
52
67
79
89
97
10
20
98
90
79
66
51
34
16
~ 3
21
39
56
71
84
95
103
20
30
105
96
86
70
54
36
16
- 4
24
44
62
78
93
104
30
4
40
107
94,
78
59
39
17
— 6
29
51
71
90
106
40
4
50
111
92
70
45
19
- 8
35
62
86
109
50
60
117
88
56
23
-12
47
81
112
60
70
127
81
32
~]
9
70
119
70
94 1 87
77
65
50
34
17
17
34
50
65
77
87
94
10
94
87
76
64
49
33
16
— 2-
20
37
53
67
80
90
98
10
20
97
89
78
65
50
33
15
- 4
22
40
57
73
86
96
104
20
30
103
94
83
69
52
34
14
- 6
26
46
64
81
95
107
,30
6
40
105
92
76
57
36
14
- 9
32
54
74
93
109
40
6
50
107
88
66
41
15
-13
40
66
91
113
50
60
111
82
51
17
-18
53
87
119
60
—
70
118
72
22
-29
80
129
70
95
87
77
65
50
35
18
18
35
50
^
77
87
95
10
94
86
76
63
49
33
15
- 3
20
38
54
68
81
91
99
10
20
96
88
77
64
49
32
14
- 5
24
40
59
74
- 87
98
106
20
30
101
93
81
67
50
32
12
- 8
28
48
66
83
97
109
30
8
40
102
89
73
54
33
11
-12
35
57
78
97
113
40
8
50
104
84
62
37
11
-17
44
70
95
118
50
60
105
77
45
11
-24
59
93
125
60
70
109
62
13
-39
90
140
70
95
88
78
65
51
35
18
18
35
51
65
78
88
95
10
94
86
75
63
48
32
15
- 3
21
38
55
69
82
92
100
10
20
95
87
76
63
48
31
12
- 6
25
43
60
76
89
100
20
30
100
91
80
65
49
30
10
-10
30
50
69
86
100
30
10
40
100
87
70
51
31
8
-15
38
60
81
100
40
10
50
100
81
58
33
6
-21
48
75
100
50
60
100
71
39
5
-31
66
100
60
70
100
53
35
3
18
-48
100
70
96
89
78
66
51
18
35
51
66
78
89
96
10
94
86
76
63
48
32
14
- 4
22
39
56
70
83
94
101
10
20
94
86
76
«2
47
29
11
- 8
27
45
62
78
91
102
20
30
99
90
78
64
47
28
8
-12
33
53
71
88
103
30
12
40
108
98
84
68
49
28
5
-18
41
63
85
104
40
12
50
112
97
77
54
29
2
-25
53
80
105
50
60
120
95
65
33
-1
-37
72
107
60
70
134
91
44
-6
-58
110
70
«
T3
3
70°
60°
60°
40=
80°
20°-
10°
0°
10°
20°
80°
40°
60°
60°
70°
•o
3
1
Latitude of same name as c
eclinat
ion.
Latitude of different name from declina
tion.
^_
<
<
Q
TABLE 25. [Page 703
Table showing the variation of the altitude of an object arising from a change of 100 seconds in
the
declination. Unmarked quantities in the Table are positive. If the change move the body toward
the elevated pole, apply the correction to the altitude with the signs in the Table; others
ise,
change the signs.
i
a
1
a5
1
<
Latitude of same name as declination.
Latitude of different name from declination.
<
.2
c
70°
60°
50°
40°
30°
20°
10°
0°
10°
20°
80°
40°
50°
60°
70°
o
o
ff
II
fl
II
II
It
II
„
ti
II
II
II
II
II
II
o
o
97
89
79
66
52
35
18
18
35
52
66
79
89
97
10
94
86
76
63
48
31
14
- 4
23
40
57
72
85
95
103
10
20
94
86
75
61
46
27
10
- 9
28
45
64
80
93
104
20
30
97
89
77
62
45
26
6
- 14
35
55
74
91
106
30
14
40
106
96
82
66
46
25
2
- 21
44
67
88
107
40
14
50
109
93
73
50
25
- 2
- 30
58
85
110
50
60
115
89
60
27
- 7
- 43
79
114-
60
70
125
82
35
-16
- 69
121
70
—
98
90
80
67
52
36
18
18
36
52
67
80
90
98
10
94
86
76
63
48
31
13
- 5
23
41
58
73
86
97
104
10
20
94
85
74
61
45
27
9
- 10
30
48
66
82
95
106
20
30
96
87
75
61
44
25
4
- 17
37
58
77
94
109
30
16
40
104
94
80
63
44
22
- 24
48
70
92
111
40
16
50
106
90
70
47
21
- 6
- ,S4
62
90
115
50
60
110
84
54
21
-14
- 50
86
121
60
70
117
73
25
-26
- 79
132
70
99
91
81
68
53
36
18
18
36
53
68
81
91
99
10
95
87
76
63
48
31
13
- 6
24
42
59
74
88
98
106
10
20
93
85
74
60
44
26
8
- 12
31
50
68
84
98
109
20
30
95
86
74
59
42
23
2
- 19
40
60
79
97
112
30
18
40
102
92
78
61
41
20
- 3
- 27
51
74
96
116
40
18
50
103
87
66
43
17
-10
- .S9
67
95
121
50
60
105
79
49
16
-20
- 56
93
128
60
70
108
64
16
-36
- 89
143
70
100
92
82
68
53
36
18
18
36
53
68
82
92
100
10
95
87
76
63
48
31
12
- 6
25
43
60
76
89
100
10
20
93
85
74
60
43
25
6
- 13
33
52
70
86
100
20
30
94
85
73
58
40
21
- 21
42
63
82
100
30
20
40
100
90
76
59
39
17
- 6
- 31
55
78
100
40
20
50
100
83
63
39
13
-15
- 43
72
100
50
60
100
74
43
10
-26
- 63
100
60
70
100
56
6
-46
-100
70
93
83
69
54
^7
19
19
37
54
69
83
93
101
10
96
88
77
63
48
30
12
— 7
26
45
62
78
91
102
10
20
93
85
73
59
43
25
5
- 15
35
54
72
88
103
20
30
94
85
72
57
39
19
- 2
- 23
45
66
86
103
30
22
40
98
88
74
57
36
14
- 9
- 34
58
82
104
40
22
50
110
97
80
60
36
9
-19
- 48
77
106
50
60
117
95
68
38
4
-33
- 70
107 \
60
70
131
92
70
47
55
- 3
-56
-111
70
95
84
37
19
19
37
55
70
84
95
103
10
97
88
77
64
48
30
11
- 8
27
46
63
79
93
104
10
20
93
85
73
59
42
24
4
- 16
36
56
74
91
105
20
30
93
84
71
56
38
18
— 4
- 26
48
69
89
107
30
,
24
40
97
86
72
54
34
12
-12
- 37
62
86
109
40
24
50
107
93
77
66
32
5
-23
- 53
83
111
50
60
112
91
64
32
- 2
-39
— 77
115
60
70
123
83
38
-13
-67
-122
70
96
85
72
56
38
19
19
38
56
■72
85
96
105
10
98
89
78
64
48
30
11
- 9
28 : 47
65
81
95
106
10
20
95
85
73
'59
41
23
3
- 18
38 1 58
77
94
108
20
30
93
83
70
54
36
16
- 6
- 28
50 72
92
111
30
26
40
96
85
70
52
32
9
-16
- 41
66
•91
114
40
26
50
105
92
74
53
28
1
-28
- 58
88
117
50
60
108
86
58
27
- 8
-46
- 84
123
60
70
115
75
29
-23
-78
-134
70
§
•c
a
6
t
•3
70°
60°
60°
40°
80°
20°
10°
0°
10°
.20°
80°
40°
50°
60°
70°
3
g
•a
1
"3
Latitude of Etame name as declination.
Latitude of different name from declination.
Q
<
"<
P
Page 704]
TABLE 26.
Variation of Altitude in one minute from meridian
passage
Declination of the
same name as the latitude;
npper transit; reduction addltlre.
Lati-
tude.
Lati-
tude.
0°
1°
2°
3°
4°
5°
6°
JO
8°
9°
10°
11°
o
,1
II
It
//
//
It
II
//
II
II
II
II
28.1
22.4
18.7
16.0
14.0
12.4
11.1
10.1
1
28.0
22.4
18.6
16.0
13.9
12.4
11.1
1
2
28.0
22.3
18.6
15.9
13.9
12.3
2
3
27.9
22.3
18.5
15.8
13.8
3
4
28.1
27.8
22.2
18.5
15.8
4
5
22.4
28.0
27.7
22.1
18.4
5
6
18.7
22.4
28.0
27.6
22.0
6
7
16.0
18.6
22.3
27.9
27.4
7
8
14.0
16.0
18.6
22.3
27.8
8
9
12.4
13.9
15.9
18.5
22.2
27.7
9
10
11.1
12.4
13.9
15.8
18.5
22.1
27.6
10
11
10.1
11.1
12.3
13.8
15.8
18.4
22.0
27.4
11
12
9.2
10.1
11.1
12.3
13.8
15.7
18.3
21.9
27.3
12
13
8.5
9.2
10.0
11.0
12.2
13.7
15.6
18.2
21.7
27.1
13
14
15
7.9
8.5
9.2
10.0
10.9
12.1
13.6
15.5
18.0
21.6
26.9
14
15
7.3
7.8
8.4
9.1
9.9
10.9
12.1
13.5
15.4
17.9
21.4
26.7
16
6.8
7.3
7.8
8.4
9.1
9.8
10.8
12.0
13.4
15.3
17.8
21.3
16
17
6.4
6.8
7.2
7.8
8.3
9.0
9.8
10.7
11.9
13.3
15.2
17.6
17
18
6.0
6.4
6.8
7.2
7.7
8.3
8.9
9.7
10.6
11.8
13.2
15.0
18
19
5.7
6.0
6.3
6.7
7.2
7.6
8.2
8.9
9.6
10.6
11.7
13.1
19
20
20
5.4
5.7
6.0
6.3
6.7
7.1
7.6
8.1
8.8
9.5
10.5
11.6
21
5.1
5.4
5.6
5.9
6.3
6.6
7.0
7.5
8.1
8.7
9.5
10.4
21
22
4.9
5.1
5.3
5.6
5.9
6.2
6.6
7.0
7.5
8.0
8.6
9.4
22
23
4.6
4.8
5.0
5.3
5.5
5.8
6.1
6.5
6.9
7.4
7.9
8.5
23
24
4.4
4.6
4.8
5.0
5.2
5.5
5.8
6.1
6.4
6.8
6.4
7.3
7.8
24
25
4.2
4.4
4.6
4.7
5.0
5.2
5.4
5.7
6.0
6; 8
7.2
25
26
4.0
4.2
4.3
4.5
4.7
4.9
5.1
5.4
5.7
6.0
6.3
6.7
26
27
3.9
4.0
4.1
4.3
4.5
4.7
4.9
5.1
5.3
5.6
5.9
6.2
27
28
3.7
3.8
4.0
4.1
4.3
4.4
4.6
4.8
5.0
5.3
5.5
5.8
28
29
3.5
3.7
3.8
3.9
4.1
4.2
4.4
4.6
4.7
5.0
5.2
4.9
5.5
29
30
3.4
3.5
3.6
3.7
3.9
4.0
4.2
4.3
4.5
4.7
5.1
30
31
3.3
3.4
3.5
3.6
3.7
3.8
4.0
4.1
4.3
4.4
4.6
4.8
31
32
3.1
3.2
3.3
3.4
3.5
3.7
3.8
3.9
4.1
4.2
4.4
4.6
32
33
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.9
4.0
4.2
4.3
33
34
2.9
3.0
3.1
3.2
3.2
3.3
3.2
3.4
3.6
3.7
3.8
3.9
4.1
34
35
2.8
2.9
3.0
3.0
3.1
3.3
3.4
3.5
3.6
3.7
3.9
35
36
2.7
2.8
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
36
37
2.6
2.7
2.7
2.8
2.9
2.9
3.0
3.1
3.2
3.3
3.4
3.5
37
38
2.5
2.6
2.6
2.7
2.8
2.8
2.9
3.0
3.0
3.2
3.2
3.3
38
39
2.4
2.5
2.5
2.6
2.7
2.7
2.8
2.9
2.9
3.0
2.9
3.1
3.2
39
40
2.3
2.4
2.4
2.5
2.6
2.6
2.7
2.7
2.8
3.0
3.0
40
41
2.3
2.3
2.4
2.4
2.5
2.5
2.6
2.6
2.7
2.8
2.8
2.9
41
42
2.2
2.2
2.3
2.3
2.4
2.4
2.5
2.5
2.6
2.6
2.7
2.8
42
43
2.1
2.1
2.2
2.2
2.3
2.3
2.4
2.4
2.5
2.5
2.6
2.7
43
44
2.0
2.1
2.1
2.1
2.2
2.2
2.3
2.3
2.4
2.4
2.5
2.4
2.5
2.4
44
45
2.0
2.0
2.0
2.1
2.1
2.2
2.2
2.2
2.3
2.3
45
46
1.9
1.9
2.0
2.0
2.0
2.1
2.1
2.2
2.2
2.2
2.3
2.3
46
47
1.8
1.9
1.9
1.9
2.0
2.0
2.0
2.1
2.1
2.1
2.2
2.2
47
48
1.8
1.8
1.8
1.9
1.9
1.9
2.0
2.0
2.0
2.1
2.1
2.1
48
49
1.7
1.7
1.8
1.8
1.8
1.8
1.9
1.9
1.9
2.0
2.0
2.1
49
50
1.6
1.7
1.7
1.7
1.8
1.8
1.8
1.8
1.9
1.9
1.9
2.0
50
51
1.6
1.6
1.6
1.7
1.7
1.7
1.7
1.8
1.8
1.8
1.9
1.9
51
52
1.5
1.6
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.8
1.8
1.8
52
53
1.5
1.5
1.5
1.5
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.7
53
54
1.4
1.4
1.5
1.5
1.5
1.5
1.5
1.6
1.6
1.6
1.6
1.6
1.7
54
55
1.4
1.4
1.4
1.4
1.5
1.5
1.5
1.5
1.5
1.6
1.6
55
56
1.3
1.3
1.4
1.4
1.4
• 1.4
1.4
1.4
1.5
1.5
1.5
1.5
56
57
1.3
1.3
1.3
1.3
1.3
1.4
1.4
1.4
1.4
1.4
1.4
1.5
57
58
1.2
1.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.4
1.4
1.4
58
59
1.2
1.2
1.2
1.2
1.2
1.3
1.3
1.3
1.3
1.3
1.3
1.3
59
60
1.1
1.1
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.3
1.3
60
0°
1°
go
8°
4°
5°
6"
JO
8°
9°
10°
11°
De
clinatio
1 of the
tame nan
le as the
latitude;
upper tra
Qsit; redu
ction add
Itlre.
TABLE 26.
[Page 705
Vaxiation of Altitude in one minute from meridian passage.
Lati-
tude.
Declination of the
same name as the latitude; upper transit
reduction addltlre.
Lati-
tude.
12°
1S°
14°
15°
16°
17°
18°
19°
20°
21°
22°
28°
24°
o
9.2
8.5
7.9
7.3
6.8
6.4
6.0
5.7
5.4
5.1
4.9
4.6
4.4
o
1
10.1
9.2
8.5
7.8
7.3
6.8
6.4
6.0
5.7
5.4
.5.1
4.8
4.6
1
2
11.1
10.0
9.2
8.4
7.8
7.- 2
6.8
6.3
6.0
5.6
5.3
5.0
4.8
2
3
12.3
11.0
10.0
9.1
8.4
7.8
7.2
6.7
6.3
5.9
5.6
5.3
5.0
3
4
13.8
12.2
10.9
9.9
9.1
8.3
7. 7
7.2
6.7
6.3
5.9
5.5
5.2
4
5
15.7
13.7
12.1
10.9
9.8
9.0
8.3
7.6
7.1
6.6
6.2
5.8
5.5
5
6
18.3
15.6
13.6
12.1
10.8
9.8
8.9
8.2
7.6
7.0
6.6
6.1
5.8
6
7
21.9
18.2
15.5
13.5
12.0
10.7
9.7
8.9
8.1
7.5
7.0
6.5
6.1
*
8
27.3
21.7
18.0
15.4
13.4
11.9
10.6
9.6
8.8
8.1
7.5
6.9
6.4
8
9
27.1
21.6
17.9
15.3
13.3
1.5.2
11.8
10.6
9.5
8.7
8.0
7.4
6.8
9
10
10
26.9
21.4
17.8
13.2
11.7
10.5
9.5
8.6
7.9
7.3
11
26.7
21.3
17.6
15.0
13.1
11.6
10.4
9.4
8.5
7.8
11
12
26.5
21.1
17.5
14.9
13.0
11.5
10.3
9.3
8.4
12
13
26.2
20.9
17.3
14.8
12.8
11.3
10.1
9.2
13
. 14
•
26.0
20.7
17.1
14.6
12.7
11.2
10.0
14
15
25.7
20.4
16.9
14.4
12.5
11.1
15
16
26.5
2-5.4
20.2
16.7
14.3
12.4
16
17
21.1
26.2
25.1
20.0
16.5
14.1
17
18
17.5
20.9
26.0
24.8
19.7
16.3
18
19
20
14.9
13.0
17.3
14.8
20.7
25.7
24.5
19.5
19
17.1
20.4
25.4
24.2
20
21
11.5
12.8
14.6
16.9
20.2
25.1
21
22
10.3
11.3
12.7
14.4
16.7
20.0
24.8
22
23
9.3
10.1
11.2
12.5
14.3
16.5
19.7
24.5
23
24
8.4
9.2
10.0
11.1
12.4
14.1
16.3
19.5
24.2
24
25
7.7
8.3
9.0
9.9
10.9
12.2
13.9
16.1
19.2
23.8
25
26
7.1
7.6
8.2
8.9
9.8
10.8
12.1
13.7
15.9
18.9
23.5
26
27
6.6
7.0
7.5
8.1
8.8
9.6
10.6
11.9
13. 5
1.5.6
18.6
23.1
27
28
6.2
6.5
7.0
7.4
8.0
8.7
9.5
10.5
11.7
13.3
1.5.4
18.3
22.7
28
29
5.7
6.1
6.4
6.9
7.3
6:8
7.9
8.6
9.4
8.4
10.3
11.5
13.1
15.1
18.0
29
30
5.4
5.7
6.0
6.4
7.2
7.8
9.2
10.1
11.3
12.8
14.9
30
31
5.1
5.3
5.6
5.9
6.3
6.7
7.1 7.7
8.3
9.0
10.0
11.1
12.6
31
32
4.8
5.0
5.2
5.5
5.8
6.2
6.5
7.0
7.5
8.1
8.9
9.8
10.9
32
33
4.5
4.7
4.9
5.1
5.4
5.7
6.1
6.4
6.9
7.4
8.0
8.7
9.6
33
34
35
4.3
4.4
4.6
4.8
5.1
4.7
5.3
5.6
5.9
5.5
6.3
5.8
6.8
6.2
7.3
6.6
7.8
7.1
8.6
,34
4.0
4.2
4.4
4.5
5.0
5.2
/. /
35
36
3.8
4.0
4.1
4.3
4.5
4.7
4.9
5.1
5.4
5.7
6.1
6.5
7.0
36
37
3.6
3.8
3.9
4.0
4.2
4.4
4.6
4.8
5.0
5.3
5.6
6.0
6.4
37
38
3.4
3.6
3.7
■3.8
4.0
4.1
4.3
4.5
4.7
4.9
5.2
6.5
5.8
38
39
3.3
3.4
3.5
3.6
3.8
3.9
4.0 1 4.2
4.4
4.6
4.8
5.1
5.4
39
40
3.1
3.2
3.3
3.4
3.6
3.7
3.8
4.0
4.1
4.3
4.5
4.7
5.0
40
41
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.9
4.0
4.2
4.4
4.6
41
42
2.9
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.7
3.8
4.0
4.1
4.3
42
43
2.7
2.8
2.9
3.0
3.0
3.1
3.2
3.3
3.5
3.6
3.7
3.9
4.0
43
44
45
2.6
2.7
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
3.6
3.8
44
2.5
2.6
2.6
2.7
2.8
2.8
2.9
3.0
3.1
3.2
3.3
3.4
3.5
45
46
2.4
2.4
2.5
2.6
2.6
2.7
2.8
2.8
2.9
S.O
3.1
3.2
3.3
46
47
2.3
2.3
2.4
2.4
2.5
2.6
2.6
2.7
2.8
2.9
2.9
3.0
3.1
47
48
2.2
2.2
2.3
2.3
2.4
2.4
2.5
2.6
2.6
2.7
2.8
2.9
.3.0
48
49
2.1
2.1
2.0
2.2
2.1
2.2
2.3
2.3
2.4
2.4
2.5
2.6
2.6
2.7
2.6
2.8
2.6
49
50
2.0
2.1
2.2
2.2
2.3
2.3
2.4
2.4
2.5
50
51
1.9
2.0
2.0
2.0
2.1
2.1
2.2
2.2
2.3
2.3
2.4
2.4
2.5
51
52
1.8
1.9
1.9
1.9
2.0
2.0
2.1
2.1
2.1
2.2
2.2
2.3
2.4
52
53
1.8
1.8
1.^8
1.9
1.9
1.9
2.0
2.0
2.0
2.1
2.1
2.2
2.2
53
54
1.7
1.7
1.7
1.8
1.8
1.8
1.9
1.9
1.9
2.0
2.0
2.1
2.1
54
55
55
1.6
1.6
1.7
1.7
1.7
1.8
1.8
1.8
1.9
1.9
1.9
2.0
2.0
56
1.5
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.8
1.8
1.8
1.9
1.9
56
57
1.5
1.5
1.5
1.5
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.8
1.8
57
58
1.4
1.4
1.5
1.5
1.5
1.5
1.5
1.6
1.6
1.6
1.6
1.7
1.7
58
59
1.4
1.4
1.4
1.4
1.4
1.5
1.5
1.5
1.5
1.5
1.6
1.6
1.6
59
60
1.3
1.3
1.3
1.3
1.4
1.4
1.4
1.4
1.4
1.5
1.5
1.6
1.6
60
12°
18°
14°
16°
ia°
17°
18°
19°
20°
21°
22°
28°
24°
De<
.llnatioi:
I of the s
ante nai
neaa th
1 latitude; upper
transit-
redueti
on addkl
Ire.
24972°— 12-
-35
Page 706_
TABLE
26.
Variation of Altitude in one minute from meridian passage.
Declination of the
»ame name as the latitude; npper transit
reduction additive.
Lati-
tude.
Lati-
tude.
25°
26°
2J°
28°
29°
80°
81°
82°
88°
84°
85°
86°
8J°
o
4.2
4.0
3.9
3.7
It
3.5
It
3.4
n
3.3
3.1
//
3.0
2.9
If
2.8
2.7
2.6
o
1
4.4
4.2
4.0
3.8
3.7
3.5
3.4
3.2
3.1
3.0
2.9
2.8
2.7
1
2
4.6
4.3
4.1
4.0
3.8
3.6
3.5
3.3
3.2
3.1
.3.0
2.8
2.7
2
3
4.7
4.5
4.3
4.1
3.9
3.7
3.6
3.4
3.3
3.2
3.0
2.9
2.8
3
4
5.0
4.7
4.5
4.3
4.1
3.9
3.7
3.5
3.4
.3.3
3.1
3.0
2.9
4
5
5.2
4.9
4.7
4.4
4.2
4.0
3.8
3.7
3.' 5
3.3
3.2
3.1
3.0
5
6
5.4
5.1
4.9
4.6
4.4
4.2
4.0
3.8
3.6
3.5
3.3
3.2
3.0
6
7
5.7
5.4
5.1
4.8
4.6
4.3
4.1
,3.9
3.7
3.6
3.4
3.3
3.1
7
8
6.0
5.7
5.3
5.0
4.8
4.5
4.3
4.1
3.9
3.7
3.5
3.4
3.2
8
9
6.4
6.0
5.6
5.3
5.0
4.7
4.4
4.2
4.0
3.8
3.6
3.5
3.3
9
10
6.8
6.3
5.9
5.5
5.2
4.9
4.6
4.4
4.2
3.9
3.8
3.6
3.4
10
11
7.2
6.7
6.2
5.8
6.5
5.1
4.8
4.6
4.3
4.1
3.9
3.7
3.5-
11
12
7.7
7.1
6.6
6.2
5.8
5.4
5.1
4.8
4.5
4.3
4.0
3.8
3.6
12
13
8.3
7.6
7.1
6.5
6.1
5.7
5.3
5.0
4.7
4.4
4.2
4.0
3.8
13
14
9.1
8.2
7.6
7.0
6.4
6.0
5.6
5.2
4.9
4.6
4.4
4.1
3.9
14
15
9.9
8.9
8.1
7.4
6.9
6.4
5.9
5.5
5.2
4.8
4.5
4.3
4.0
15
16
10.9
9.8
8.8
8.0
7.3
6.8
6.3
5.8
5.4
5.1
4.8
4.5
4.2
16
17
12.2
10.8
9.6
8.7
7.9
7.2
6.7
6.2
5.7
5.3
5.0
4.7
4.4
17
18
13.9
12.1
10.6
9.5
8.6
7.8
7.1
6.6
6.1
5.6
5.2
4.9
4.6
18
19
16.1
13.7
11.9
10.5
9.4
8.4
7.7
7.0
7.5
6.4
6.0
5.5
5.1
4.8
19
20
19.2
15.9
13.5
11.7
10.3
9.2
8.3
6.9
6.3
5.8
5.4
5.0
20
21
23.8
18.9
15.6
13.3
11.5
10.2
9.1
. 8.2
7.4
6.8
6.2
.5.7
5.3
21
22
23.5
18.6
15.4
13.1
11.3
10.0
8.9
8.0
7.3
6.6
6.1
5.6
22
23
23.1
18.3
15.1
12.8
11.1
9.8
8.7
7.9
7.1
6.5
6.0
23
24
22.7
18.0
14.9
12.6
10.9
9.6
8.6
7.7
7.0
6.4
24
25
22.3
17.7
14.6
12.4
10.7
9.4
8.4
7.5
6.8
25
26
21.9
17.4
14.3
12.1
10.5
9.2
8.2
7.4
26
27
21.5
17.0
14.0
11.9
10.3
9.1
8.1
27
28
21.1
16.7
13.8
11.7
10.1
8.9
28
29
22.3
20.6
16.3
13.5
11.4
9.9
29
30
17.7
21.9
20.2
16.0
13.2
11.1
:»
31
14.6
17.4
21.5
19.8
15.6
12.9
31
32
12.4
14.3
17.0
21.1
19.3
15.3
32
33
10.7
12.1
14.0
16.7
20.6
18.9
.33
34
9.4
10.5
11.9
13.8
16.3
20.2
34
35
8.4
9.2
10.3
11.7
13.5
16.0
19.8
35
36
7.5
8.2
9.1
10.1
11.4
13.2
15.6
19.3
36
37
6.8
7.4
8.1
8.9
9.9
11.1
12.9
15.3
18.9
■•
37
38
6.2
6.7
7.2
7.9
8.7
9.6
10.9
12.6
14.9
18.4
38
39
5.7
6.1
6.5
7.1
7.7
8.5
9.4
10.6
12.2
14.5
17.9
39
40
5.3
5.6
6.0
6.4
6.9
7.5
8.2
9.2
10.4
11.9
14.1
17.4
40
41
4.9
5.2
5.5
5.8
6.2
6.7
7.3
8.0
8.9
10.1
11.6
13.8
17.0
41
42
4.5
4.8
5.0
5.3
5.7
6.1
6.6
7.1
7.8
8.7
9.8
11.3
13.4
42
43
4.2
4.4
4.6
4.9
5.2
5.5
5.9
6.4
6.9
7.6
8.5
9.5
11.0
43
44
3.9
4.1
4.3
4.5
4.8
5.1
5.4
5.8
6.2
6.7
7.4
8.2
9.3
44
45
3.7
3.8
4.0
4.2
4.4
4.7
4.9
5.2
5.6
6.0
6.6
7.2
8.0
45
46
3.5
3.6
3.7
3.9'
4.1
4.3
4.5
4.8
5.1
5.4
5.9
6.4
7.0
4ti
47
3.3
3.4
3.5
3.6
3.8
4.0
4.2
4.4
4.6
4.9
5.3
5.7
6.2
47
48
3.1
3.2
3.3
3.4
3.5
3.7
3.9
4.0
4.3
4.5
4.8
5.1
5.5
4S
49
2.9
3.0
3.1
3.2
3.3
3.4
3.6
3.7
3.9
4.1
4.4
4.6
5.0
49
50
2.7
2.8
2.9
3.0
3.1
3.2
3.3
3.5
3.6
3.8
4.0
4.2
4.5
50
51
2.6
2.6
2.7
2.8
2.9
3.0
3.1
3.2
,3.4
3.5
3.7
.3.9
4.1
51
52
2.4
2.5
2.6
2.6
2.7
2.8
2.9
3.0
3.1
3.2
3.4
3.6
3.7
52
53
2.3
2.3
2.4
2.5
2.5
2.6
2.7
2.8
2.9
3.0
3.1
,3.3
3.4
53
54
2.2
2.2
2.3
2.3
2.4
2.5
2.5
2.6
2.7
2.8
2.9
3.0
3.2
54
55
2.0
2.1
2.1
2.2
2.3
2.3
2.4
2.4
2.5
2.6
2.7
2.8
2.9
.55
56
1.9
2.0
2.0
2.1
2.1
2-.2
2.2
2.3
2.4
2.4
2.5
2.6
2.7
56
57
1.8
1.9
1.9
2.0
2.0
2.0
2.1
2.2
2.2
2.3
2.3
2.4
2.5
57
58
1.7
1.8
1.8
1.8
1.9
1.9
2.0
2.0
2.1
2.1
2.2
2.3
2.3
58
59
1.6
1.7
1.7
1.7
1.8
1.8
1.9
1.9
1.9
2.0
2.0
2.1
2.2
.59
60
1.6
1.6
1.6
1.6
1.7
1.7
1.7
1.8
1.8
1.9
1.9
2.0
2.0
60
95°
26°
27°
28°
29°
80°
81°
82°
88°
84°
85°1
86°
87°
De<
!linatior
of the
iame na
me as th
e latitud
e; upp«
r transit
reduct
on addl
tlve.
TABLE 26.
[Page
707
Variation of Altitude in one minute from meridian passage.
Lati-
tude.
Declination of the
wme name as the latitude; upper transit
reduction addltlre.
Lati-
tude.
38°
8»°
40°
41°
42°
48°
44°
45°
46°
47°
48°
49°
50°
o
2.5
2.4
2.3
2.3
2.2
2.1
2.0
2.0
1.9
i:8
1.8
1.7
1.7
o
0.
1
2.6
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
1.9
1.8
1.7
1.7
1
'>
2.6
2.5
2.4
2.4
2.3
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
2
3
'>.7
2.6
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
1.9
1.8
1.7
3
4
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
2.0
1.9
1.8
1.8
4
5
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
1.9
1.8
5
6
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
2.0
1.9
1.8
6
7
3.0
2.9
2.7
2.6
2.5
2.4
2.3
2.2
2.2
2.1
2.0
1.9
1.8
/
8
3.1
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
1.9
8
9
3.2
3.0
2.9
2.8
2.7
2.5
2.4
2.3
2.2
2.2
2.1
2.1
2.0
1.9
9
10
3.3
3.1
3.0
2.8
2.7
2.6
2.5
2.4
2.3
2.2
2.0
1.9
10
11
3.4
3.2
3.1
2.9
2.8
2.7
2.6
2.4
2.3
2.2
2.1
. 2.1
2.0
11
12
3.5
3.3
3.1
3.0
2.9
2.7
2.6
2.5
2.4
2.3
2.2
2.1
2.0
12
13
3.6
.3.4
3.2
3.1
2.9
2.8
2.7.
2.6
2.4
2.3
2.2
2.1
2.0
13
14
3.7
3.5
3.3
3.2
3.0
2.9
2.7
2.6
2.5
2.4
2.3
2.2
2.1
14
15
3.8
3.6
3.4
3.3
3.1
3.0
2.8
2.7.
2.6
2.4
2.3
2.2
2.1
15
16
4.0
3.8
3.6
.3.4
3.2
3.0
2.9
2.8
2.6
2.5
2.4
2.3
2.2
16
17
4.1
3.9
3.7
3.5
3.3
3.1
3.0
2.8
2.7
2.6
2.4
2.3
2.2
17
18
4.3
4.1
3.8
3.6
3.4
3.2
3.1
2.9
2.8
2.6
2.5
2.4
2.3
18
19
20
4.5
4.2
4.0
3.7
3.5
3.3
3.2
3.0
3.1
2.8
2.9
2.7
2.8
2.6
2.4
2.3
19
20
4.7
4.4
4.1
3.9
3.7
.3.5
3.3
2.6
2.5
2.4
21
4.9
4.6
4.3
4.0
3.8
3.6
3.4
3.2
3.0
2.9
2.7
2.6
2.4
21
22
5.2
4.8
4.5
4.2
4.0
3.7
3.5
3.3
3.1
2.9
2.8
2.6
2.5
22
23
5.5
5.1
4.7
4.4
4.1
3.9
3. 6 3. 4
3.2
3.0
2.9
2.7
2.6
23
24
25
5.8
6.2
5.4
5.7
5.0
4.6
4.3
4.0
3.8 ^ .3.5
3.3
3.1
3.0
2.8
2.6
2.7
24
25
5.3
4.9
4.5
4.2
3. 9 1 3. 7
3.5
3.3
3.1
2.9
26
6.7
6.1
5.6
5.2
4.8
4.4
4.1 t 3.8
.3.6
3.4
3.2
,3.0
2.8
26
27
7.2
6.5
6.0
5.5
5.0
4.6
4.3 4.0
3.7
3.5
3.3
3.1
2.9
27
28
7.9
7.1
6.4
5.8
5.3
4.9
4. 5 4. 2
3.9
3.6
3.4
3.2
.3.0
28
29
8.7
7.7
8.5
6.9
7.5
6.2
6.7
5.7
6.1
5.2
4. 8 4. 4
4.1
.3.8
3.5
3.3
3.1
29
30
9.6
5.5
5.1 i 4.7
4.3
4.0
3.7
3.4
3.2
30
31
10.9
9.4
8.2
7.3
6.6
5.9
5.4
4.9
4.5
4.2
3.9
3.6
3.3
31
32
12.6
10.6
9.2
8.0
7.1
6.4
5.8
.5.2
4.8
4.4
4.0
.3.7
,3.5
32
33
14.9
12.2
10.4
8.9
7.8
6.9
6.2
5.6
5.1
4.6
4.3
3.9
3.6
33
34
18.4
14.5
11.9
14.1
10.1
8.7
7.6
6.7
6.0
.5.4
4.9
4.5
4.1
.3.8
34
35
35
17.9
11.6
9.8
8.5
7.4 I 6.6
.5.9
5.3
4.8
4.4
4.0
36
17.4
13.8
11.3
9.5
8.2
7.2
6.4
5.7
5.1
4.6
4.2
36
37
17.0
13.4
11.0
9.3
.8.0
7.0
6.2
5.5
.5.0
4.5
37
38
16.5
13.0
10.7
9.0
/. /
6.8
6.0
5.3
4.8
38
39
16.0
12.6
10.3
8.7
7.5
6.5
5.8
5.1
39
40
15.5
12.2
10.0
8.4
7.2
6.3
5.6
40
41
15.0
11.8
9.7
8.1
7.0
6.1
41
42
16.5
14.5
11.4
9.3
7.9
6.7
42
43
13.0
16.0
14.0
11.0
9.0
7.6
43
44
10.7
12.6
15.5
13.6
10.6
8.7
44
45
45
9.0
10.3
12.2
15.0
13.1
10.2
46
7.7
8.7
10.0
11.8
14.5
12. 6
46
47
6.8
7.5
8.4
9.7
11.4
14.0
47
48
6.0
6.5
7.2
8.1
9.3
11.0
13.6
48
49
5.3
5.8
5.1
6.3
7.0
7.9
9.0
10.6
8.7
13.1
49
50
50
4.8
5.6
6.1
6.7
7.6
10.2
12.6
51
4.3
4.6
5.0
.5.4
5.9
6.5
7.3
8.4
9.9
12.1
51
52
3.9
4.2
4.5
4.8
5.2
5.7
6.3
7.0
8.0
9.5
11.6
52
53
3.6
.3.8
4.0
4.3
4.6
5.0
5.4
6.0
6.7
1. 1
9.1
11.1
53
54
3.3
3.5
3.7
3.9
4.1
4.4
4.8
5.2
4.6
5.8
5.0
6.5
7.4
8.7
10.6
54
55
3.0
3.2
3.3
3.5
3.7
4.0
4.3
5.5
6.2
7.1
8.3
55
56
2.8
2.9
3.1
3.2
3.4
3.6
3.8
4.1
4.4
4.8
5.3
5.9
6."8
56
57
2.6
2.7
2.8
2.9
3.1
3.2
3.4
3.6
.3.9
4.2
4.6
5.0
5.6
57
58
2.4
2.5
2.6
2.7
2.8
2.9
3.1
3.3
3.5
3.7
4.0
4.4
4.8
58
59
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.0
3.1
3.3
3.6
3.8
4.2
59
60
2.1
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
3.0
3.2
3.4
3.6
60
S8°
89°
40°
41°
42°
48°
44°
45°
46°
47°
48°
49°
50°
De
■linatioi
1 of the
«aine na
Tieasth
e latitude; uppe
r transit
reduct
on addli
iTe.
TABLE 26.
[Page
709
Variation of Altitude in one minute from meridian
passage.
Lati-
tnde.
Declination of a different name from the latitude
; upper transit; reduction additive.
Lati-
tude.
0°
1°
2°
8°
V
5°
6°
JO
8°
9°
10°
no
o
a
tt
tt
tt
tt
n
n
//
It
//
ff
28.1
22.4
18.7
16.0
14.0
12.4
11.1
10.1
1
28.1
22.4
18.7
16.0
14.0
12.4
11.2
10.1
9.3
1
2
28.1
22.4
18.7
16.0
14.0
12.5
11.2
10.2
9.3
8.6
2
3
28.1
22.4
18.7
16.0
14.0
12.5
11.2
10.2
9.3
8.6
8.0
3
4
28.1
22.4
18.7
18.7
16.0
16.0
14.0
12.5
11.2
10.2
9.3
8.6
8.0
8.0
7.4
7.4
7.0
4
5
5
22.4
14.0
12.5
11.2
10.2
9.3
8.6
6
18.7
16.0
14.0
12.5
11.2
10.2
9.3
8.6
8.0
7.5
7.0
6.6
6
7
16.0
14.0
12.4
11.2
10.2
9.3
8.6
8.0
7.5
7.0
6.6
6.2
7
8
14.0
12.4
11.2
10.2
9.3
8.6
8.0
7.5
7.0
6.6
6.2
5.9
8
9
10
12.4
iiri
11.2
10.2
9.3
8.6
8.6
8.0
8.0
7.5
7.0
6.0
6.2
6.2
5.9
5.6
5.6
9
10.1
9.3
7.4
7.0
6.6
5.9
5.3
10
11
10.1
9.3
8.6
8.0
7.4
7.0
6.6
6.2
5.9
5.6
5.3
5.1
11
12
9.2
8.5
7.9
7.4
7.0
6.5
6.2
6.9
5.6
5.3
6.0
4.8
12
13
8.5
7.9
7.4
6.9
6.5
6.2
5.8
5.6
5.3
5.0
4.8
4.6
13
14
15
7.9
7.3
7.4
6.9
6.5
6.2
5.8
5.5
5.3
5.0
4.8
4.6
4.4
14
6.9
6.5
6.1
5.8
5.5
5.3
5.0
4.8
4.6
4.4
4.2
15
16
6.8
6.5
6.1
5.8
5.5
5.2
5.0
4.8
4.6
4.4
4.2
4.1
16
17
6.4
6.1
5.8
5.5
5.2
5.0
4.8
4.6
4.4
4.2
4.1
3.9
17
18
6.0
5.7
5.5
5.2
5.0
4.8
4.6
4.4
4.2
4.1
3.9
3.8
18
19
5.7
5.4
5.4
5.1
5.2
4.9
4.9
4.7
4.7
4.5
4.5
4.4
. 4.2
4.0
3.9
3.8
3.6
19
20
4.3
4.2
4.0
3.9
3.8
3.6
3.5
20
21
5.1
4.9
4.7
4.5
4.3
4.2
4.0
3.9
3.7
3.6
3.5
3.4
21
22
4.9
4.7
4.5
4.3
4.1
4.0
3.9
3.7
3.6
3.5
3.4
3.3
22
23
4.6
4.4
4.3
4.1
4.0
3.8
3.7
3.6
3.5
3.4
3.3
3.2
23
24
4.4
4.2
4.2
4.1
3.9
3.8
3.7
3.6
3.5
3.3
3.4
3.3
3.2
3.1
24
25
25
4.1
3.9
3.8
3.7
3.5
3.4
3.2
3.1
3.1
3.0
26
4.0
3.9
3.8
3.6
3.5
3.4
3.3
3.2
3.1
3.0
3.0
2.9
26
27
3.9
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.9
2.8
27
28
3.7
3.6
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.8
2.7
28
29
3.5
3.4
3.3
3.3
3.2
3.2
3.1
3.1
3.0
3.1
3.0
2.9
2.8
2.8
2.7
2.6
29
30
30
3.4
3.0
2.9
2.8
2.7
2.7
2.6
2.5
31
3.3
3.2
3.1
3.0
2.9
2.9
2.8
2.7
2.6
2.6
2.5
2.5
31
32
3.2
3.1
3.0
2.9
2.8
2.8
2.7
2.6
2.6
2.5
2.5
2.4
32
33
3.0
2.9
2.9
2.8
2.7
2.7
2.6
2.5
2.5
2.4
2.4
2.3
,33
34
2.9
2.8
2.8
2.7
2.6
2.6
2.5
2.5
2.4
2.4
2.3
2.3
.34
35
2.8
2.7
2.7
2.6
2.5
2.5
2.4
2.4
2.3
2.3
2. 2*
2.2
35
36
2.7
2.6
2.6
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
36
37
2.6
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.2
2.1
2.1
37
38
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.1
2.0
38
39
40
2.4
2:3
2.4
2.3
2.3
2.2
2.3
2.2
2.2
2.2
2.1
2.1
2.1
2.0
2.0
2.0
2.0
1.9
2.0
39
2.2
2.1
2.1
2.0
1.9
40
41
2.3
2.2
2.2
2.1
2.1
2.1
2.0
2.0
1.9
1.9
1.9
1.8
41
42
2.2
2.1
2.1
2.1
2.0
2.0
2.0
1.9
1.9
1.9
1.8
1.8
42
43
2.1
2.1
2.0
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.8
1.7
43
44
45
2.0
2.0
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
1.6
44
4.5
1.9
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
46
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
46
47
1.8
1.8
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.6
47
48
1.8
1.7
1.7
1.7
^1.7
1.6
1.6
1.6
1.6
1.6
1.5
1.5
48
49
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.5
49
50
1.6
1.6
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.5
1.4
1.4
50
51
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
51
52
1.5
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.3
52
53
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
53
54
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.3
1.3
54
55
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.2
1.2
55
56
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
56
57
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
57
58
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
58
59
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
59
60
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
J°
1.0
1
1.0
1.0
60
0°
1°
2°
S°
4°
5°
6°
8°
9°
10°
11°
Declin
fttion ol
a differ
■nt name
from th
; latitude
upper tr
an.sit; rec
uction addltlre.
1 Page 710]
TABLE
L't>.
Variation of Altitude in one minute from men
jian passage.
Lati-
tude.
Declination of a different name from the latitude; upper traasit; reduction addltlre. 1
Lati-
tude.
12°
13°
14°
1.5°
16°
17°
18°
19°
20°
21°
22°
23°
24°
c
//
f/
11
II
II
II
II
II
II
II
II
II
II
o
9.2
8.5
7.9
7.3
6.8
6.4
6.0
6.7
5.4
5.1
4.9
4.6
4.4
1
8.5
7.9
7.4
6.9
6.5
6.1
5.7
5.4
6.1
4.9
4.7
4.4
4.2
1
9
7.9
7.4
6.9
6.6
6.1
6.8
5.5
5.2
4.9
4.7
4.5
4.3
4.1
2
3
7.4
6.9
6.5
6.1
5.8
6.5
6.2
4.9
4.7
4.5
4.3
4.1
3.9
3
4
7.0
6.5
6.2
6.8
5.5
6.2
6.0
4.7
4.5
4.3
4.1
4.0
3.8
4
5
6.5
6.2
5.8
5.5
5.2
5.0
4.8
4.5
4.3
4.2
4.0
3.8
3.7
5
ti
6.2
5.8
5.5
5.3
5.0
4.8
4.6
4.4
4.2
4.0
3.9
3.7
3.6
6
5.9
5.6
5.3
5.0
4.8
4.6
4.4
4.2
4.0
3.9
3.7
3.6
3.6
7
8
5.6
5.3
5.0
4.8
4.6
4.4
4.2
4.0
3.9
3.7
3.6
3.5
3.4
8
9
5.3
5.0
4.8"
4.6
4.4
4.2
4.1
3.9
3.8
3.6
3.6
3.4
3.3
9
10
6.0
4.8
4.6
4.4
4.2
4.1
3.9
3.8
3.6
3.6
3.4
3.3
3.2
10
U
4.8
4.6
4.4
4.2
4.1
3.9
3.8
3.6
3.5
3.4
3.3
3.2
3.1
11
12
4.6
4.4
4.3
4.1
3.9
.3.8
3.7
3.5
3.4
3.3
3.2
3.1
,3.0
12
13
4.4
4.3
4.1
3.9
.3.8
3.7
3.5
3.4
3.3
3.2
3.1
3.0
2.9
13
14
4.2
4.1
3.9
3.8
3.7
3.6
3.4
3.3
3.2
3.1
3.0
2.9
2.8
14
15
15
4.1
3.9
3.8
3.7
3.5
3.4
3.3
.3.2
3.1
3.0
2.9
2.8
2.8
16
3.9
3.8
3.7
3.5
.3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.8
2.7
16
17
3.8
,3.7
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.8
2.7
2.6
17
18
3.7
3.5
3.4
3.3
.3.2
3.1
3.0
2.9
2.9
2.8
2.7
2.6
2.5
18
19
3.5
3.4
3.3
3.2
3.1
3.0
3.0
2.9
2.9
2.9
2.9
2.8
2.7
2.6
2.6
2.6
2.6
2.5
19
20
3.4
3.3
3.2
3.1
2.8
2.7
2.6
2.4
20
21
3.3
.3.2
3.1
3.0
2.9
2.8
2.8
2.7
2.6
2.6
2.6
2.4
2.4
21
•>■>
3.2
.3.1
3.0
2.9
2.8
2.8
2.7
2.6
2.6
2.6
2.4
2.4
2.3
22
23
3.1
3.0
2.9
2.8
2.8
2.7
2.6
2.6
2.6
2.4
2.4
2.3
2.3
23
24
3.0
2.9
2.8
2.8
2.7
2.6
2.5
2.6
2.4
2.4
2.3
2.3
2.2
24
26
25
2.9
2.8
2.7
2.7
2.6
2.6
2.5
2.4
2.4
2.3
2.3
2.2
2.2
26
2.8
2.7
2.7
2.6
2.5
2.6
2.4
2.4
2.3
2.3
2.2
2.1
2.1
2t>
27
2.7
2.7
2.6
2.5
2.5
2.4
2.4
2.3
2.2
2.2
2.1
2.1
2.1
27
28
2.6
2.6
2.5
2.5
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.1
2.0
28
29
2.6
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.0
2.0
2.0
2S
30
2.5
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.0
2.0
2.0
1.9
30
31
2.4
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.0
2.0
2.0
1.9
1.9
31
32
2.3
2.3
2.2
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.9
1.8
32
33
2.3
2.2
2.2
2.1
2.1
2.1
2.0
2.0
1.9
1.9
1.9
1.8
1.8
33
34
2.2
.2.2
2.1
2.1
2.0
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.8
34
35
2.2
2.1
2.1
2.0
2.0
2.0
1.9
1.9
1.8
1.8
1.8
1.7
1.7
35
36
2.1
2.1
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
.36
37
2.0
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
1.6
37
38
2.0
1.9
1.9
1.9
1.8
1.8
1.8
1.8
1.7
1.7
1.7
1.6
1.6
38
39
40'
1.9
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.6
1.6
39
1.9
1.8
1.8
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.5
40
41
1.8
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.6
1.5
1.5
41
42
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.6
1.5
1.6
1.5
42
43
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.5
1.6
1.5
1.5
1.4
1.4
43
44
45
1.7
1.6
1.6
1.6
1.6
1.6
1.5
1.6
1.5
1.5
1.6
1.5
1.6
1.5
1.5
1.6
1.5
1.4
1.4
1.4
1.4
44
46
1.6
1.4
1.4
1.4
1.4
46
1.6
1.6
1.5
1.5
1.6
1.6
1.4
1.4
1.4
1.4
1.4
1.3
1.3
46
47
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
47
48
1.6
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.3-
1.3
• 1.3
1.3
1.3
48
49
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
49
50
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
50
51
1.4
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
51
52
1.3
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.1
1.1
52
53
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
53
54
1.2
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
54
65
55
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
66
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1.0
1.0
56
57
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1.0
1.0
1.0
1.0
1.0
57
58
1.1
1.1
1.1
1.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
.58
59
1.1
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
59
60
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9
0.9
0.9
0.9
0.9
0.9
60
12°
18°
14°
16°
16°
17°
18°
19°
20°
21°
22°
28°
24°
Dec
ination
ofadiff
*reiit na
me from
the lati
tude; u[
per trui
sit; redi
ctiou ai
ditlve.
TABLE
L'ti.
[Page
711
Variation of
Altitude in one minute from meridian paasage.
Declinatfon of a different name from the latitude; upper transit; reduction addltlre.
tude.
Lati-
tude.
25°
26°
27°
28°
29°
80°
81°
82°
33°
34°
85°
86°
37°
c
w
rf
It
n
II
It
II
II
//
II
II
n
ft
o
4.2
4.0
3.9
3.7
3.5
3.4
3.3
3.1
3.0
2.9
2.8
2.7
2.6
1
4.1
3.9
3.7
3.6
3.4
3.3
3.2
3.1
2.9
2.8
2.7
2.6
2.6
1
9
3.9
3.8
3.6
3.5
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2
3
3.8
3.6
3.5
3.4
.3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
3
4
3.7
3.6
3.5
3.4
3.3
3.2
3.0
2.9
2.8
2.8
2.7
2.6
2.6
2.5
2.4
" 273
4
5
3.4
3.3
3.2
3.1
3.0
2.9
2.7
2.6
2.5
2.4
6
3.4
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.4
2.4
2.3
6
3.3
3.2
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.5
2.4
2.3
2.2
7
8
3.2
3.1
3.0
2.9
2.8
2.7
2.7
2.6
2.5
2.4
2.3
2.3
2.2
8
9
10
3.1
3.0
2.9
2.9
2.8
2.7
2.6
2.5
2.4
2.4
2.3
2.2
2.2
9
3.1
3.0
2.9
2.8
2.7
2.6
2.5
2.5
2.4
2.3
2.2
2.2
2.1
10
11
3.0
2.9
2.8
2.7
2.6
2.5
2.5
2.4
2.3
2.3
2.2
2.1
2.1
11
12
2.9
2.8
2.7
2.6
2.6
2.5
2.4
2.3
2.3
2.2
2.2
2.1
2.0
12
13
2.8
2.7
2.7
2.6
2.5
2.4
2.4
2.3
2.2
2.2
2.1
2.1
2.0
13
14
2.7
2.7
2.6
2.5
2.4
2.4
2.3
2.3
2.2
2.1
2.1
2.0
2.0
14
15
2.7
2.6
2.5
2.5
2.4
2.3
2.3
2.2
2.1
2.1
2.0
2.0
1.9
15
16
2.6
2.5
2.5
2.4
2.3
2.3
2.2
2.2
2.1
2.0
2.0
1.9
1.9
16
17
2.5
2.5
2.4
2.3
2.3
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
17
IS
2.5
2.4
2.4
2.3
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.8
18
IS
20"
2.4
2.4
2.3
2.2
2.2
2.1
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1.8
19
2.4
2.3
2.3
2.2
2.1
2.0
2.0
1.9
1.9
1.9
1.8
1.8
20
21
2.3
2.3
2.2
2.1
2.1
2.0
2.0
2.0
1.9
1.9
1.8
1.8
1.7
21
9'?
2.3
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1.7
1.7
22
23
2.2
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1.8
1.7
1.7
23
24
2.2
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.6
24
25
2.1
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1.8
1.7
1.7
1.6
1.6
25
26
2.1
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.7
1.7
1.7
1.6
1.6
. 26
27
2.0
2.0
1.9
1.9
1.9
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.6
27
28
2.0
1.9
1.9
1.9
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.6
1.5
28
29
30
1.9
1.9
1.9
1.9
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.5
29
1.8
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.6
1.5
30
31
1.8
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.5
31
32
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.4
32
33
1.8
1.7
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.4
1.4
33
34
1.7
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.4
1.4
1.4
34
35
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
35
36
1.6
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
1.3
36
37
1.6
1.6
1.6
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
1.3
1.3
37
38
1.6
1.5
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
1.3
1.3
1.3
38
39
1.5
1.5
1.5
1.5
1.4
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
39
40
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.2
40
41
1.5
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.2
1.2
41
42
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
42
43
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
43
44
1.4
1.4
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
44
45
1.3
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
45
46
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
46
47
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
47
48
1.2
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
1.1
48
49
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.1
49
50
1.2
1.2
1.2
1.1
1.1
1.1
1.1
1.1
50
51
1.2
1.1
1.1
1.1
1.1
1.1
1.1
1.1
1.0
51
52
1.1
1.1
1.1
1.1
1.1
1.1
1.0
1.0
52
53
1.1
1.1
1.1
1.1
1.0
1.0
1.0
53
54
1.1
1.0
1.0
1.0
1.0
1.0
54
55
1.0
1.0
1.0
1.0
1.0
55
56
1.0
1.0
1.0
1.0
56
57
1.0
1.0
1.0
57
58
59
60
1.0
0.9
0.9
58
59
60
6.8
0.8
0.8
25°
26°
27°
28°
2«°
80°
81°
82°
88°
84°
86°
86°
37°
Decl
ination
of the Bi
imenan
e as the
latitude
; lover
transit;
reducti<
m 8ubtri
tctlre.
Page 712]
TABLE 26.
Variation of Altitude in one minute from meridian passage.
Lati-
tude.
Declination of a (lllfprent name from the latitude; upper transit; reduction •»adltlTe. 1
Lati-
tude.
38°
39°
40°
41°
42°
4S°
44°
45°
46°
4JO
4!5°
49°
50°
o
//
II
II
II
II
II
II
tl
II
II
It
II
II
o
2.0
2.4
2.3
2.3
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1
2.5
2.4
2.3
2.2
2.1
2.1
2.0
1.9
1.9
1.8
1.7
1.7
1.6
1
2
2.4
2.3
2.3
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1.6
o
3
2.4
2.3
2.2
2.1
2.1
2.0
1.9
1.9
1.8
1.8
1.7
1.6
1.6
3
4
2.3
2.2
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1.6
1.6
4
5
2.3
2.2
2.1
2.1
2.0
1.9
1.9
1.8
1.8
1.7
1.6
1.6
1.5
5
6
2.2
2.2
2.1
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
6
7
2.2
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1.7
1.6
1.6
1.0
1.5
/
8
2.1
2.1
2.0
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.0
1.5
8
9
2.1
2.0
2.0
1.9
1.9
1.8
1.8
1.7
1.6
1.6
1.6
1.5
1.5
9
10
2.1
2.0
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
1.4
10
11
2.0
2.0
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
11
12
2.0
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
1.4
1.4
12
13
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
13
14
1.9
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
1.4
1.4
1.4
14
15
1.9
1.8
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.4
15
16
1.8
1.8
1.7
1.7
1.7
1.6
1.6
1.5
1.5
1.4
1.4
1.4
1.3
16
17
1.8
1.8
1.7
1.7
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
17
18
1.8
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.4
1.3
1.3
18
19
20
1.7
1.7
1.7
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
19
20
1.7
1.7
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
21
1.7
1.6
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
21
22
1.7
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
22
23
1.6
1.6
1.6
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.2
23
24
1.6
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
24
25
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
25
26
1.6
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
26
27
1.5
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.2
27
28
1.5
1.5
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.1
28
29
1.5
1.4
1.4
1.4
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
29
30
1.5
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
30
31
1.4
1.4
1.4
1.3
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
31
32
1.4
1.4
1.3
1.3
1.3
1.3
1.2
• 1.2
1.2
1.2
1.1
1.1
1.1
32
33
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
33
34
1.4
1.3
1.3
1.3
1.3
1. 2"
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
34
35
1.3
1.3
1.3
1..S
1.2
1.2
1.2
1.1
1.1
1.1
1.1
35
36
1.3
1.3
1.3
1.2
1.2
1.2
1.2
1.1
1.1
1.1
1.1
36
37
1.3
1.3
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
37
38
1.3
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
38
39
1.2
1.2
1.2
1.2
1.2
1.1
1.1
1.1
.39
40
1.2
1.2
1.2
1.2
1.1
1.1
1.1
40
41
1.2
1.2
1.2
1.1
1.1
1.1
41
42
1.2
1.2
1.1
1.1
1.1
42
43
1.2
1.1
1.1
1.1
4.S
44
1.1
1.1
1.1
44
4.5
46
45
46
1.1
1.1
1.1
0.9
47
48
49
0.9
0,9
0.9
0.9
0.9
0.8
47
48
49
0.9
0.9
0.9
50
51
52
53
54
0.9
0.9
0.9
0.8
0.8
0.9
0.9
0.8
0.8
0.8.
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
511
51
52
53
54
0.9
0.9
0.8
0.8
0.9
0.9
0.8
0.9
0.9
0.9
55
56
57
58
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.8
0.8
0.7
0.7
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
55
56
57
58
0.8
0.8
0.8
0.8
0.8
0.8
59
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
59
60
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
60
'38°
89°
40°
41°
42°
43°
44°
43°
48°
47°
48°
40°
50°
Dec
ination
of the 8
lunenan
le as the
latitude
; lower
transit;
reductio
n subtra
CtlTC.
TABLE
26.
[Page
713
V^ariation of Altitude in one minute from meridian passage.
Declination of a different name from the latitude: DDoer transit: reduction addltlre.
Lati-
tude.
Lati-
tude.
51°
52°
53°
54°
65°
56°
57°
58°
59°
60°
61°
62°
63°
o
ir
ft
„
tr
„
It
n
„
ff
n
//
If
„
o
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
1
1.6
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
1
2
1.0
1.5
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
2
3
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
3
4
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
4
5
1.5
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
1.0
5
6
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.0
1.0
1.0
6
7
1.4
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
0.9
/
8
1.4
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
0.9
8
9
1.4
1.4
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.0
1.0
1.0
0.9
9
10
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
10
11
1.4
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
11
12
1.4
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
0.9
0.9
12
13
1.3
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.0
1.0
1.0
0.9
0.9
13
14
1.3
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
14
15
15
1.3
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
16
1.3
1.3
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
16
17
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
17
18
1.3
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
18
19
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
1.0
0.9
0.9
0.9
19
20
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
0.8
20
21
1.2
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.9
0.8
21
22
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
1.0
0.9
0.9
0.9
22
23
1.2
1.2
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
0.-9
23
24
1.2
1.1
1.1
1.1
1.1
1.0
1.0
1.0
0.9
0.9
24
25
1.2
1.1
1.1
1.1
1.0
1.0
1.0
1.0
0.9
25
26
1.1
1.1
1.1
1.1
1.0
1.0
1.0
0.9
26
27
1.1
1.1
1.1
1.0
1.0
1.0
1.0
27
28
1.1
1.1
1.1
1.0
1.0
1.0
28
29
30
1.1
1.1
1.1
1.1
1.0
1.0
1.0
29
1.0
1.0
30
31
1.1
1.0
1.0
31
32
33
34
1.1
1.1
1.0
32
33
34
0.8
0.7
6.8
36
36
37
38
39
6.^
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
35
36
37
38
39
0.8
0.8
0.8
0.8
6.8
0.8
0.8
0.8
0.8
6.8
40
41
42
43
44
6.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
40
41
42
43
44
0.9
0.8
0.8
0.8
0.9
0.9
0.8
0.9
0.9
0.8
0.9
45
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
45
46
0.9
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
46
47
0.9
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.6
47
48
0.8
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.6
48
49
0.8
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
49
50
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.6
50
51
0.8
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
51
52
0.8
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
52
53
0.8
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
53
54
55
0.8
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
54
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
55
56
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
56
57
0.7
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
57
58
0.7
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
58
59
0.7
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.5
59
60
0.7
0.7
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.6
0.5
60
61°
52°
68°
54°
55°
56°
67°
58°
69°
60°
61°
62°
63°
D
eclinatic
n of the
same ne
ime as t
tie latitu
de; lows
r transit
; reduct
ion 80 bt
ractlfe.
Page 714]
TABLE
37.
Reduction to be applied
to Altitudes near the Meridian.
Var.
Imin.
(Table
Time from meridian passage.
Var.
1 min.
(Table
m. s.
m. s.
TO. s.
m. 8.
m. s.
m. 8.
m. e.
m. s.
m. s.
m. 8.
m. 8.
26.)
//
80
1
1 80
£
2 SO
3
3 SO
40
4 SO
5
5 30
6
8 30
26.)
1 If
t II
/ //
T It
/ //
t n
' tt
/ tl
/ rr
/ If
/ //
' //
' //
tl
0.1
1
1
1
2
2
2
3
4
4
0.1
0.2
1
1
2
3
3
4
5
6
7
8
0.2
0.3
1
1
2
3
4
5
6
7
9
11
13
0.3
0.4
1
2
2
4
5
6
8
10
12
14
17
21
0.4
0.5
1
2
3
4
6
8
10
12
15
18
0.5
0.6
1
1
2
4
5
7
10
12
15
18
22
25
0.6
0.7
1
2
3
4
6
9
11
14
17
21
25
30
0.7
0.8
1
2
3
5
7
10
13
16
20
24
29
34
0.8
0.9
1
2
4
6
8
11
14
18
22
27
32
38
0.9
1.0
00
1
2
4
6
9
12
16
20
25
30
36
42
1.0
2.0
2
4
8
12
18
24
32
41
50
1
1 12
1 24
2.0
3.0
1
3
7
12
19
27
37
48
1 1
1 15
1 31
1 48
2 6
.3.0
4.0
I
4
9
16
25
36
49
1 4
1 21
1 40
2 1
2 24
2 49
4.0
5.0
1
5
11
20
31
45
1 1
1 20
1 41
2 5
2 31
3
3 36
3 31
4 13
5.0
6.0
6.0
1
6
13
24
37
54
1 13
1 36
2 1
2 30
3 1
7.0
2
7
16
28
44
1 3
1 26
1 52
2 22
2 55
3 32
4 12
4 56
7.0
8.0
2
8
18
32
50
1 12
1 38
2 8
2 42
3 20
4 2
4 48
5 38
8.0
9.0
2
9
20
36
56
1 21
1 50
2 24
3 2
3 45
4 32
5 24
6 20
9.0
10.0
2
10
22
40
1 2
1 30
2 3
2 40
2 56
3 23
4 10
5 2
5 32
6
6 36
7 2
7 45
10.0
11.0
11.0
3
11
25
44
1 9
1 39
2 15
3 43
4 35
12.0
3
12
27
48
1 15
1 48
2 27
3 12
4 3
5
6 3
7 12
8 27
12.0
13.0
3
13
29
52
1 21
1 57
2 39
3 28
4 23
5 25
6 33
7 48
9 9
1.3.0
14.0
3
14
0-61
56
1 27
2 6
2 51
3 44
4 43
5 50
7 4
8 24
9 51
14.0
15.0
4
15
34
1
1 34
2 15
3 4
4
5 3
6 15
7 34
9
10 34
11 16
15.0
16.0
4
16
36
1 4
1 40
2 24
3 16
4 16
5 24
6 40
8 4
9 36
16.0
17.0
4
17
38
1 8
1 46
2 33
3 28
4 32
5 44
7 5
8 34
10 12
11 58
17.0
18.0
4
18
40
1 12
1 52
2 42
3 40
4 48
6 4
7 30
9 4
10 48
12 40
18.0
19.0
5
19
43
1 16
1 59
2 51
3 53
5 4
6 25
7 55
9 35
11 24
13 23
19.0
20.0
5
20
21
45
1 20
2 5
3
4 5
5 20
6 45
8 20
10 5
12
14 5
14 47
20.0
21.0
21.0
5
47
1 24
2 11
3 9
4 17
5 36
7 5
8 45
10 35
12 36
22.0
5
22
49
1 28
2 17
3 18
4 30
5 52
7 25
9 10
11 5
13 12
15 29
22.0
23.0
6
23
52
1 32
2 24
3 27
4 42
6 8
7 46
9 35
11 36
13 48
16 12
23.0
24.0
6
24
54
1 36
2 30
3 36
4 54
6 24
8 6
10
12 6
14 24
16 54
24.0
25.0
6
25
56
1 40
2 36
3 45
5 6
6 40
8 26
8 46
10 25
12 36
15
25.0
26.0
26.0
6
26
58
1 44
2 42
3 54
5 18
6 56
10 50
13 6
27.0
7
27
1 1
1 48
2 49
4 3
5 30
7 12
9 7
11 15
27.0
28.0
7
28
1 3
1 52
2 55
4 12
5 43
7 28
9 27
11 40
28.0
TABLE 27.
Reduction to be applied to Altitudes near the Meridian,
[Page 716
Var.
1 min.
^Table
26.)
Time from meridian passage.
Var.
1 min.
(Table
26.)
m. s.
7
70. S.
7 30
m. s.
8
VI. s.
» so
m. s.
9
m. s.
9 80
m. s.
10
m. s.
10 30
m. s.
11
in. s.
11 30
m. s.
\t
m. s.
12 30
VI. .«,
13
0.1
0.2
0.3
0.4
0^5'
0.6
0.7
0.8
0.9
/ //
5
10
15
20
/ //
6
11
17
23
/ rf
6
13
19
26
/ rf
7
14
22
29
1 It
8
16
24
32
9
18
27
36
/ //
10
20
30
40
/ ft
11
22
33
44
t n
12
24
36
48
f n
13
26
40
53
14
29
43
58
t t'
16
31
47
1 2
17
34
51
1 8
0.1
0.2
0.3
0.4
24
29
34
39
44
28
34
39
45
51
32
38
45
51
57
36
43
51
58
1 5
40
49
57
1 5
1 13
45
54
1 3
1 12
1 21
50
1
1 10
1 20
1 30
55
1 6
1 17
1 28
1 39
1
1 13
1 25
1 37
1 49
1 6
1 19
1 33
1 46
1 59
1 12
1 26
1 41
1 55
2 10
1 18
1 34
1 49
2 5
2 21
1 24
1 41
1 58
2 15
2 32
0.5
0.6
0.7
0.8
0.9
1.0
2.0
3.0
4.0
5.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
49
1 38
2 27
3 16
4 5
4 54
5 43
6 32
7 21
8 10
8 59
9 48
10 37
11 26
12 15
13 4
13 53
14 42
15 31
16 20
56
1 52
2 49
3 45
4 41
5 37
6 34
7 30
8 26
9 22
10 19
11 15
12 11
13 7
14 4
15
15 56
16 52
17 49
18 45
1 4
2 8
3 12
4 16
5 20
1 12
2 24
3 37
4 49
6 1
1 21
2 42
4 3
5 24
6 45
1 30
3
4 30
6 1
7 31
1 40
3 20
5
6 40
8 20
1 50
3 40
5 31
7 21
9 11
2 1
4 2
6 3
8 4
10 5
2 12
4 24
6 37
8 49
11 1
2 24
4 48
7 12
9 36
12
2 36
5 12
7 49
10 25
13 1
2 49
5 38
8 27
11 16
14 5
6 24
7 28
8 32
9 36
10 40
7 14
8 26
9 38
10 50
12 2
13 15
14 27
15 39
16 51
18 14
8 6
9 27
10 48
12 9
13 30
14 51
16 12
17 33
18 54
20 15
9 1
10 32
12 2
13 32
15 2
16 33
18 3
19 33
21 3
22 34
10
11 40
13 20
15
16 40
18 20
20
21 40
23 20
25
11 1
12 52
14 42
16 32
18 22
20 13
22 3
23 53
25 43
27 34
12 6
14 7
16 8
18 9
20 10
22 11
24 12
26 13
28 14
13 13
15 26
17 38
19 50
22 2
24 15
26 27
28 39
14 24
16 48
19 12
21 36
24
'26 24
28 48
15 37
18 14
20 50
23 26
26 2
16 54
19 43
22 32
25 21
28 10
6.0
7.0
8.0
9.0
10
11.0'
12.0
13.0
14.0
15.0
11.0
12,0
1.3.0
14,0
In.
11 44
12 48
13 52
14 56
16
28 39
16.0
17.0
18.0
19.0
20.0
17 4
18 8
19 12
20 16
19 16
20 28
21 40
21 36
22 57
24 18
24 4
25 34
26 40
16.0
17.0
18.0
19.0
20.0
21.0
17 9
21.0
Page 716]
TABLE 27.
Reduction to be applied
to Altitudes near the Meridian
Var.
1 min.
(Table
Time from meridian passage.
Var.
1 min.
(Table
m. s.
m. 8.
m. «.
m. s.
TO. S.
771. S.
m. 5.
TO. «.
m. s.
TO. S.
^26.)
18 30
14
14 80
15
15 80
16
16 80
17
17 SO
18
IS 30
19
19 30
26.)
u
/ //
/ It
t II
/ //
' II
/ //
/ //
f n
/ //
1 II
1 II
/ //
/ //
„
0.1
18
20
21
22
24
26
27
29
31
32
34
36
38
0.1
0.2
36
39
42
45
48
51
54
58
1 1
1 5
1 8
1 12
1 16
0.2
0.3
55
59
1 3
1 7
112
1 17
122
127
132
137
143
148
154
0.3
0.4
0.5
113
1 18 1 24
130
136
142
149
156
2 2
210
217
2 24
2 32
0.4
131
138
145
152
2
2 8
2 16
2 24
2 33
2 42
2 51
3 1
3 10
0.0
0.6
149
158
2 6
2 15
2 24
2 34
2 43
2 53
3 4
314
3 25
3 37
3 48
0.6
0.7
2 8
2 17 2 27
2 37
2 48
2 59
3 11
3 22
3 34
3 47
4
4 13
4 26
0.7
0.8
2 26
2 37 2 48
3
3 12
3 25
3 38
3 51
4 5
419
4 34
4 49
5 4
0.8
0.9
2 44
2 56
3 9
3 22
3 36
3 50
4 5
4 20
4 36
4 52
5 8
5 25
5 42
0.9
1.0
3 2
3 16
3 30
3 45
4
4 16
4 32
4 49 I 5 6
5 24
5 42
6 1
6 20
1.0
2.0
6 4
6 32
7
7 30
8
8 32
9 4
9 38 ' 10 12
10 48
1124
12 2
12 40
2.0
3.0
9 7
9 48
10 30
11 15
12 1
12 48
13 38
14 27
1519
16 12
17 7
18 3
19 1
.3.0
4.0
12 9
1314 14 1
15
16 1
17 4
18 9
19 16
20 25
2136
22 49
24 4
25 21
4.0
5.0
15 11
16 20
17 31
18 45
20 1
2120
22 41
24 5
25 31
27
28 31
5.0
6.0
18 13
19 36
21 2
82 30
24 1
25 36
27 13
6.0
7.0
21 16
22 52
24 32
2615
28 1
7.0
8.0
24 18
26 8
28 2
8.0
9.0
27 20
9.0
Var.
T
ime fror
nmerid
an passage.
Var.
1 min.
(Table
m. «.
m. 8.
m. s.
TO. S.
m, 8.
m. e.
TO. «.
m. «. ?«. s.
ra. s.
m. 8.
m. e.
m. s.
(Table
26.)
20
20 80
21
21 30
22
22 80
23
23 80 24
2130
25
25 30
26
. 26.)
//
1 It
/ //
/ //
' //
' II
1 II
1 II
1 II
/ //
t tl
/ //
/ //
/ //
ff
0.1
40
42
044
46
48
51
53
55
58
1
1 2
1 6
1 8
0.1
0.2
1 20
124
128
1 32
137
1 41
146
150
155
2
2 5
210
2 15
0.2
0.3
2
2 6
2 12
2 19
2 25
2 32
2 39
2 46
2 53
3
3 7
3 15
3 23
0.3
0.4
2 40
2 48
2 56
3 5
314
3 22
3 32
3 41 j 3 50
4
4 10
4 20
4 30
0.4
0.5
0.5
3 20
3 30
3 41
3 51
4 2
4 13
4 24
4 36
4 48
5
5 12
5 25
5 38
0.6
4
4 12
4 25
4 37
4 50
5 4
5 17
5 31
5 46
6
615
6 30
6 46
0.6
0.7
4 40
4 54
5 9
5 24
5 39
5 54
•610
6 27
6 43
7
717
7 35
7 53
0.7
0.8
5 20
5 36
5 53
6 10
6 27
6 45
7 3
7 22
7 41
8
8 20
8 40
9 1
0.8
0.9
6
618
6 37
6 56
7 16
7 36
7 56
817
8 38
9
9 22
9 45
10 50
10 8
1116
0.9
1.0
6 40
7
7 21
7 42
8 4
8 26
8 49
912
9 36
10
10 25
1.0
2.0
13 20
14
14 42
15 24
16 8
16 52
17 38
18 24
19 12
20
20 50
2140
22 32
2.0
3.0
20
21
22 3
23 7
2412
25 19
26 27
27 37
28 48
.SO
3.0
4.0
26 40
28 1
29 24
4.0
TABLE 28A.
For finding the Latitude of a place by Altitudea of Polaris.
[A— 1st correction. Argument, the star's hour angle (or 24'>— the star's hour angle).]
[Page 717
O"
S"
1
2
3
4
5
6
7
8
_9_
10
11
12
13
14
15
16
17
18
19
— 1
1 12 00.
1159.
1159.
1159.
1159.
1158,
1158,
1158,
1157.
1156,
1155,
1155
1154
1153.
1152.
1150.
1149.
1148,
1146,
1145
20
21
22
23
24
25
26
27
28
29
-1
1 11 43
1141
1140
1138,
11 36
1134,
1132.
1130
1127.
1125,
30
31
32
33
34
35
36
37
38
39
— 1
11 23.
1120
11 18,
11 15.
11 12
1109,
1106,
1103,
1100,
10 57,
40
41
42
43
44
45
46
47
48
49
-1 10 54
10 51,
10 47,
10 44,
10 40.
-1 10 37.
10 33.
10 29.
10 25.
10 21.
50 !-
51 '
52
53
54
55
56
57
58
59
60
-1 10 17
10 13
10 09
10 05
10 00,
-1 09 56,
09 51,
09 47,
09 42,
09 37.
-1 09 32.
1.0
i.i]
1.3;-
1.4
1.4'
1.5;
^■^,:
1.7
1.8;
2.0'
2.0
2.1
2.2;
2.2'
2.3j
2.4-
2.5"
2.6'
2.7|
2.7^
2.9
2.9
3.0'
3.0
3.2'
3.2|;
3.3
3.4'
3..5;
3.5;
3.7, ,
3.7'
3.8:
3.9'
3.9I
4.1'-
^
4.S!
4.3
4.5
4.5'
4.6
4.7
4.7
4.9
Ilk
-1 09 32,
09 27
09 22.
09 17
09 12.
-109 07
09 02
08 56
08 51
08 45
-1 08 40.
08 34
08 28
08 22
08 16.
-1 08 10
08 04,
07 58,
07 52
07 46
-1 07 39,
07 33,
07 26
07 19.
07 13,
-1 07 06
06 59,
06 52
06 4.5,
06 38.
-106 31,
06 24,
0616
06 09,
06 01.
-1 05 54,
05 46
05 38.
05 31,
__0523,
-1 05 15:
05 07,
04 59,
04 51.
04 42.
-1 04 34.
04 26.
04 17.
04 09.
04 00.
-1 03 52.
03 43.
03 34.
03 25.
03 16.
-1 03 07.
02 58.
02 49.
02 40.
02 30.
-1 02 21.
4.9
5.0|
5.2
5.3
5.3'
5.4'
5.4'
5.0
5.6
5.8-
5.8^
5.9;
5.9
6.0!
6.1'^
6.2
6.2
6.3
0.4
6.5"
6.6'
6.6'
6.8|
6.8
6.8'"
7.0;
7.0I
-;
7.2|-
7.2"
7.3'
7.4!
7.5
7.6'
-I
7.8|
7.8
I
.- 8.0|-
8.0"
8.0'
8.2'
8.2I
8.3;_
8.4'
8.4'
-1 02 21.
02 11.
02 02.
0152.
0143,
-1 01 33.
01 23.
01 13.
0103.
_(K)^3.
-1 00 43.
00 33.
00 23.
00 12.
00 02.
-0 59 52.
59 41.
59 31.
59 20.
_^5909.
-0 58 58:
58 48.
58 37.
58 26.
58 15.
-0 58 04.
57 52.
57 41.
57 30.
57 18.
-0 57 07;
56 56.
56 44.
56 32.
56 21.
-0 56 09.
55 57.
55 45.
55 33.
55 21.
I
9.5;-
9.6,
9.6
9.7,
9.7:_
9.81
9.9
1 10.0;
i 10.0'
T,-io.i!-
*^ 10.2:-
■0 50 54.
50 41.
50 28.
5014.
50 01.
-0 49 47.
49 33.
49 20.
49 06.
48 52.
13.3
13.4
13.5
13.5
13.6
13.'
13.7;
13.71
10.2
10.3
10.3'
10.5!
10.5' "
10.6!
10.6;
10.7i
^10,
8.5
8.6
8.7
8.7
8.8
8.9
9.0
9.0
9.0j
9.2
9.2
9.4I
9.4
-0 55 09,
54 57,
54 45.
54 32.
54 20.
-0 54 08.
53 55.
53 43.
53 30.
53 18.
lO"
-0 53 05
52 52
52 39
52 26
52 13
-0 52 00,
5147
5134
51 21,
5108.
-0 50 54.
10.9
10.9'
10.9'
u.il
11.1'
11.2'
11.2'
11.3'
11.4|
11.4
11.5;
11.6
ii.e'
11.7!
11.8,'
11.8
11.9;
12.0|
12.0
12.1'
12.1^
12.2'
12.3
12.3'
12.4;
12.5'
12.5!
12.6'
12.0'
12.7
12.8'
12.8!
12.9'
13.0
i
13.0j
13.0!
13.1
13.2
13.3
13.3;
-0 47 28.
47 14.
47 00.
46 45.
46 31.
-0 46 17.
46 02.
45 48.
45 33.
45 18.
-0 45 04.
44 49.
44 34.
44 19.
44 04.
-0 43 50.
43 35.
43 20.
43 05.
42 49.
-0 42 34.
42 19.
42 04.
4148.
4133.
-0 41 18.
41 02.
40 47.
40 31.
40 16.
-0 40 00.
39 44
39 28
39 13
38 5 7
-0 38 41
38 25,
38 09
37 53
37 37
-0 37 21,
37 05,
36 48
36 32,
36 16,
-0 36 00,
-0 48 38,
48 24,
48 10,
47 56.
47 42
.7
„ 13.81
/ I
^13.9j-
8 M~
t 14.0i
14.1!
14.1 _
14.2'
14.2|
14.3!
14.4!
-14.4-
14.6-
14.5
14.6
14.6
14.7|_
14.8-
14.9|
-14.9i-
15.0!"
]5.o'
lo.ol
15.1j
15.2;
15.2' '
15.3'
15.31
15.3J
-15.4!-
15.5
15.5'
15.6'
15.6
1.5.7! _
15.7!
15.7!
15.8'
15.8
-15.9';
15.9'
16.0
I6.0'
I6.1!
16.1
16.2;'
16.2
16.3
16.3
I6.3!
-0 36
35
35
35
34
-0 34
34
34
33
^33
-0 33
32
32
32
32
-0 31
31
31
31
30
-0 30
30
30
29
29
-0 29
28
28
28
27
00.0
43.7
27.3
10.9
54.5
38.1
21.6
05.0
48.4
31.7
15.0
58.2
41.4
24.6
07.8
50.9
34.0
27.1
10.1
53.0
36.0"
18.9
01.7
44.5
17.3
00.1
42.8
25.5
08.2
50.8
5^
-0 27
27
26
26
26
-0 26
25
25
25
24
33.4
16.0
58.5
41.0
23.5
05.9
48.3
30.7
13.1
55.4
-0 24
24
24
23
23
-0 23
22
22
22
21
37.7
20.0
02.2
44.4
26.6
08.8
50.9
33.0
15.1
57.2
-0 21
21
21
20
20
-0 20
19
19
19
18
018
39.2
21.2
03.2
45.2
27.1
09.0
50.9
32.8
14.6
56.4
38.2
16.3
16.4
16.4
16.4
16.4
16.5
16.6;
16.6
16.7!
I6.7!
le.sj
16.8J
16.8J
16.8
16.9J
16.9,
]6.9i
17.0J
17.11
17.o|
17.1!
17.2!
17.2!
17.2
17.2:
17.3'
17.3;
17.3,
17.4!
17.4
17.4
17.5'
17,0
17.5
17.6
17.6
17.6'
17.6
17.7
17.7!
17.7
17.8
17.8:
17.8'
17.8!
17.9
17.9
17.9!
17.9
18.0
18.0
18.0
18.0
18.1
18.1
18.1
18.1
18.2
18.2:
18.2j
-0 18 38.
18 20.
18 01.
17 43.
17 25.
-0 17 06,
16 48,
16 30
1611,
15 53,
-0 15 35,
15 16,
14 58,
14 39,
14 21,
-0 14 03,
13 44
13 26.
13 07,
12 48,
-0 12 30,
12 11
1153,
1134
1115,
-0 10 57,
10 38,
10 20
10 01,
09 42
18.2
18.2
18.3
18.3
18.3
18.3
-0 09 24,
09 05,
08 46,
08 27
08 09,
-0 07 50
07 31
07 12
06 54
06 35
.3
-0 06 16
05 57.
05 39.
05 20.
05 01.
-0 04 42.
04 23.
04 05.
03 46.
3 ^*-^
9 l«-^
5 ''■'
7 M
L 18.4'
^ 18.4
5 I
''•*
M
1 18.6
7r-18.6-
.7
18.6
18.6
18.6
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
18.6
I8.7!
-I8.7'-
I8.7!
18.7
18.7
.7
18.7
18.8
18.8:
40
39
.38
37
36
35
34
33
32
31_
30
29
28
27
26
25
24
23
22
21
1.6
03 27.4
— 03 08.5
02 49.7
02 30.9
02 12.0
01 53.2
-0 01 34.4
01 15.5
00 56.7
IS.i
4 ''■'
a 18-*!
^ 18.81
'' 18.8|
00 37.!
00 18.i
-0 00 00.(
18.9
18.8
18.8
18.9
18,8
18.9
18.9
18.9
gk
S"
Tk
S*
20
19
18
17
16
15
14
13
12
11
10
9
Change the sign to -t- when the argument is found at the bottom.
Page 718]
TABLE 28B.
For finding the Latitude of a place b
^ Altitudes of Polaris.
[B=the 2d correction. This
correction is alway.s additive.]
star's
Star's altitude. 1
Star's
hour
angle.
angle.
10°
16°
16°
17°
18°
19°
20°
21°
28°
28°
„
//
„
II
II
II
//
//
II
II
00
0.0
0.0
0.0
0.0
0.0
0.0.0
0.0
0.0
0.0
0.0
12 00
10
0.0 1
0.0 1
0.0 1
0.0 'i
0.0 •"
0.0 "
0.0 1
0.0 ■"
0.0 -,
0.0 -"
U .50
20
O.l'i
0.1
0.1 1
0.1-}
o.l'i
0.1 -1
0.1 2
0.1 ■„
O.l'i
0.1 -,
40
30
0.2',
0.2 J
0.2 'o
0.2 2
0.2-'
0-2:3
0.3 2
0.3 ■;
0.3 -:
0.3 -:
30
40
0.3i
0.3 2
0.4 •,
0.4-2
0.4-3
0.5 ,
0.5-3
0.5-;
0.6 -,
0.6 -,
20
50
0.4'
0.5,
0.6 -g
0.6-3
0-7 3
0.8
0.8-3
0-8 1
0.9-^
0.9-^
10
1 00
0.5 •'
0.8-
1-1 1
0.9'
0.9 ,
1.0'
1.3-
1-^
1-1 D
i.r,
1.2'
1.3-
00
10
o.--;
1-2 1
1-2 1
1.4-
1-4 1
1.5-^
1.6 •*
1- 7 "5
10 50
20
0.9"
1.4-
1.8,
2.2*
2.6,
3.0 ■"
3.5-
5.0?
1.5-3
1.6-4
I.7-,
1.8-5
1.9-5
2.0-5
2-1 6
2-2-„
2.8-
40
30
\S-\
2.0''
2.9'!
3.3,
3.6-^
4.0"
1.8-
2.3,
2.8-
3.2-
2.0 -"
2-1 1
2-6 -5
3.1 -,
3.6-^
4.2-
4.9-'
5.5-*
6.1 -*
6.7-
7.4-'
2.3-5
2.4-5
2.9-*
3.5 -g
4.1-
2-5 •«
3.1 -*
3.7-^
4.4-
.-»
40
12 1
-379-'
4-5 1
5.1-'
5.7-^
2.8-"
3.3 -g
3.9-
0.1 ,
5.8-'
6.4-?
3.2 -
.3.4 -g
4.0-
5.5-^
6-3 '«
7-1 1
7-9 -g
8-7 1
20
50
3.8-?
10
2 00
4.5''
00
10
3.7 ■«
4.3-
4-8 1
5.3 ■«
6.5 •«
7-0 •«
7-6 1
8-2 -5
8.7-^
9.2-^
4.8-1
5.4-
6.1-
6.8-'
8.3-'*
8.9-?
7.2-?
5.3 -»
6.0 -;
6.8-^
7-5 -g
9.1 -*
9.9-^
9 50
20
40
30
30
40
20
50
5.5-;
6.3 -g
6.9-
8.1 •'
8-6 1
9-8 1
7.1 -;
7.8-
7.9-1
8.7-*
10
3 00
6.0-'
00
10
4.3-^
6.6?
8.0 -•!
8.4-
9.1 •;
10.4 -?
9.4-'
10-4 '9
11.3 -;
12.1 -*
12.9-^
13.7 ■?
8 50
20
4.7-"
7. 1 •?
8.6-"
9.6 -1
10.4-^
11.0 -*
11. 7-'
10.2-^
10.9 -,
11.6 -:
10.7-^
11.5 -?
40
30
5.0-^
7.6-^
9.2-^
9.9-'
30
40
5.3-;^
8.1 •?
12.2 -'
20
50
5.7-"
8.6-^
10.5 •*
11.1-1
12.3 -'
13.0-?
10
4 00
6.0-
9.1 -^
9.7-^
10.4-'
10.9-^
11. 0-*
11.7-"
12.3-"
13.0 -J
13.0 •'
13.7 -'
14.4 -'
tx>
10
6.3-^
9.6';
10.2-^
11.6-^
12.2-;;
13.6 •?
14. 3-"
15.6 -'
15.7 -'
7 50
20
6.6-^
10.0 •"
10.7-^
11.3 -"
12.1 -?
12.8 -.
13.6-^
14.3 -;
14.9?
40
30
6.8-
10.4"
11.1"
11.7 •"
12.5-^
13.3''
14.0 -.
14.8-°
15.6-1
16.3-^
30
40
7.0-2
10.8-^
11.4 °
12.1 -"
13.0-;;
13.8 -•;
14.5 -?
15.3-^
16.1 ■?
16.9 -*
20
50
7.3-*
u.i-^
11.8"
12.5 •"
13.4 -"
14.2 -"
15.0-°
1.5.8 -'^
16.6-^
17.5 -*
10
5 00
7.5--
11.4 -^
12.1 -^
12.9"
13.7-^
14.5-^
15.4 -"
16.2 •"
17. 1-'
17.9 -"
00
10
7.6-^
11.6-J
12.4 i'
13.2-^
14.0-^
14.8 -^
15.7-^
16.5-^
17.4-^
18. 3-"
6 50
20
7.8 -f
n.7-
12.6 •?
13.4-2
14.2-2
15.1-^
16.0-^
16. 8 -'^
17.7-^
18.6-^
40
30
7.9-
11.9 •;
12.7-^
13.6 -*
14.4 -2
15.3-2
16.2-2
17.1 ■«
18.0 -J
18.9 -f
30
40
7.9 •»
12.0 •;
12.9-2
13.7 -J
14.6-2
15.5-2
16.4-2
17.3 --
18.1 -1
19.0 -1
20
50
7.9"
12.1 •'
13.0 -^
13.8 -J
14.7-1
15.6-1
16.5-1
17.3 -»
18.2-1
19.1 -1
10
6 00
7.9 •«
12.2-^
13.0 -"
13.9-^
14.7-''
15.6 -"
16.5-"
17.3-*'
18.3 -1
19.2-1
6 00
TABI
^E 28C
[
C=the 3d
correction. Hor. Arg., the star's
declinatio
n. Vett. Arg., B-the
2d correct
Ion.] ,
B.
88° 47'
88° 48'
88° 49' 1
20"
80"
40"
50"
0"
10"
20"
80"
40"
50"
0"
10"
20"
II
II
II
It
II
II
II
II
II
II
II
II
II
II
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
.0
0.0
.0.0
10
•+0.2
+0.1
+0.1
+0.0
0.0
-0.0
-0.1
-0.1
-0.2
-
-0.2
-0
.3
-0.4
-0.4
20
0.4
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
.6
0.7
0.8
30
0.6
0.5
0.3
0.1
0.0
0.1
0.3
0.5
0.6
0.7
.8
1.1
1.2
40
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1
.2
1.5
1.6
50
+1.0
+0.7
+0.5
+0.2
0. -0. 2
1
-0.5
i
-0.9
-1.0
-
-1.2
-1
.5
-1.7
-2.1
Mote.— Below 16° B is nearly proportional to the altitude.
TABLE 28B.
[Page 719
For finding the Latitude of a place by Altitudes of Polaris.
[B=the 2d correction. This correction is always additive.]
Star's
star's altitude.
star's
liour
angle.
24°
26°
26°
2J°
2S°
29°
80°
Sl°
82°
88°
angle.
A. m.
„
//
//
/; ' It
tt
//
It
It
//
h. III.
00
0.0 n
0.0 .1 0.0 „
0.0 „| 0.0
0.0 ": 0.0 -l
0.2 t; 0.2 •;
0.4 •: 0.4 -i
0.7 0.7 •
1.1 -^ 1.1 •*
1.5 -^l 1.6 -^
0.0 „
0.0 •"
0.2 l
0.4 i
0.7 •
1.7 ^
2.3 -^
2.9 •,
3.6 •;
0.0 ,
0.0 •"
0.2 'l
0.4 l
0.8 -^
1.2 f
1.7 •'
2.3 •'
3.0 •'
3.8 'l
4.7 •'
5.6 -9
6.5 •"
0.0 „
0.0 ■{
0.2 -l
0.5 l
0.8 -f
1.3-
1.8
0.0 „
0.0 ■"
0.2 l
0.5 'l
0.8 -^
1.3 'l
1.9 ■'*
0.0 .
12 00
10
0.0 •?
0.0 •?
0.0 •:;
0.0 •"
11 50
20
0.1 ■]
0.1 -l
0.2 ■;
0.2 ■;
40
30
0.3 -
0.3 •:
0.4 •:
0.5 l
.30
40
0.6 ■'.
0.6 J
1.0 *
0.7 •
1.1 *
0.9 -.
20
50
1.0 ■'
1.4 -l
1.9 ^
2.6 -l
3.4 -l
10
1 00
1.4 ••'
1.4 *
1.5 •'
00
10
20
1.8 -t
2.3 i
1.9 -l
2.4 -t
2.0 -:
2.5 -^
2.1 •«
7 •»
2.2 •"
2.8 ■%
3.5 'l
4.3 \
5.1 ■«
6.0 •"
2.4
3.2 'l
2.5 -"
3.3 -l
4.1 -«
10 50
40
30
2.9 -t
.3.1 •;
3.2 •'
3.4 •:
4.0 -l
4- 3,0
30
40
3.6 'l
3.8 •:
4.0 !
4.9 -^
4.5 l
5.3 l
6.2 ■•'
4.9 -l
5-0,n
5.3'-"
20
50
4.3 ■■:
4.^ •:
5.3 •"
4.7 ■;
^•**in
6.0 •"
6.2,-^
10
2 00
5.0 •'
5.5 •*
5.8 -^
6.8'"
7.0'-"
7.3'-'
00
10
5.8 •»
6.1 'l
6.4 -l
6.7 -^
7.0'"
7.2'"
7.5'-"
7.9'-'
8.2'-^
8.5'-?
9 50
20
6.6 i
7.0 i
7.3 l
7.6 •»
7- 9,!
8.3 •'
8.6 •'
8.9 •"
9.3'-
9.6?-'
40
30
7 5 ■'
7.9 i
8.2 -^
8.5 •»
8.9 ■«
9.3 •"
9.6 •"
10. „
10.4'-
10. 8 ,:;
30
40
8 3 •*
8 7 t
9.1 •'
9.5 ■«
10. '■'
10 4 •
10 8 •
11.2 -^
11.6 -■
12. '-,
20
50
9. 2
9,6 'l
10.0 -^
10.5 •
11.0
11.4
11.9 •
12.4 •
12.9,,
13. 3 \l
10
3 00
ib.o •*
10.5 •**
ii.oi"
11.5'°
12.0'-"
12.5'-'
13. 0'-'
13.6'-
14. 1 '•'
14.6'-^
00
10
10.9 ■'
11.4 •*
12. O^"
12.5'"
13.6'-?
13. 6 '•'
14. 2 ''2
14. 7 '•'
15.4'-^
16. O"
8 50
20
11.8 -^
10 4i.U
13.010
13.5'"
14.1"
14 7 •
15 3
1.5.9'-:
16.6,-;^
17.3 -^
40
30
12.6 ■'
1.3.3 -^
13.9 -9
14.5'°
15- 1 \l
15.8 ■'
16.4'-'
17. 1 '-^
17.8'-^
18.5 -^
30
40
13.5
14.2 'l
14.8 •«
15. 5'"
16.1 •
16.8 •"
17.5:-
18.2
19. 0'-',
19.7
20
50
14.3 *
15.0 ■'
15.7 i
16.4 -9
17.1 ■"
17.8 ■"
18.5 •"
19.4-2
20.1
20. 9 '-*
10
4 00
15.1 *
15.8 •*
16.6 •*
17.3 •»
18. 1 '■"
18.8'"
19.6'-'
20.4'-"
21.2'-'
22. 0'-'
00
10
15.9 -t
16.6 •*
17.3 ■*
18.1 -^
19.0 'l
19.7 l
20.6'"
21.4'-"
22. 3 '-'
23. 1 '■'
7 50
20
16.6 ■'
17.3 •!
18.1 -^
19.0 -l
19.8 t
20.6 •:
21.5 l
22.4'-"
23.2 l
24. 1 -"
40
30
17.2 ■;-
18.0 •'.
18.8 •'
19.7 ■'
20.5 •'
21.4 ■*
22.3 -l
23.2 -°
24.1 'l
25. 1 '-"
30
40
17.8 -^
18.6 •"
19.5 •'
20.3 t
21.2 i
22.1 •:
23.0 ■'
24.0 -f
24.9 -*
25.9 -°
20
50
18.3 -^
19.2 ■';
20.1 ■::■
21.0 ■'
21.9 •;
22.8 •'
23.7 •'
24.6 -l
25.7 -?
26.7 -?
10
5 00
18.8 •■■'
19.7 ■'
20.6 •»
21.5 •»
22.4 •■'
23.4 -^
24.4 •'
25.3 ■'
26.4 -'
27.4 -'
00
10
19.2 t
20.1 ■;;
21.1 •*
22.0 -^
22.9 ••'
23.9 -^
24.9 'l
25.8 ■]
27.0 -•;
28.0 -t
6 50
20
19.5 l
20.5 -t
21.4 -^
22.4 -^
23.3 X
24.3 l
2b A •*
26.2 •''
27.4 *
28.5 -°
40
.30
19.8 -^
20.7 -l
21.7 -^
22.6 •;
23. 6 -^
24.6 -^
25.7 -^
26.6 -^
27.8 ■*
28.8 -*
30
40
20.0 -^
20.9 ■■'
21.9 •;
22.8 -2
23.9 ••'
24.9 f
25.9 -2
26.9 -J
28.0 "•
29.1 l
20
50
20.1 -^
21.0 ■'
22.0 l
23.0 -2
24.0 •'
25.0 •'
26.0 •'
27.0 ■'
28.2 ■-
29.3 -^
10
6 00
20.2 ^
21.1 ■'
22.
23.1 •'
24.1 •'
25.1 •'
26.1 •'
27.1 •'
28.3 ■'
29.4 -'
6 00
TABLE 28C.
[C=tlie 3d correction. Hor. Arg.. tlie star's declination. Vert. Arg., B=the
2d correct
ion.]
B.
88° 47'
88° 48'
88^ 4»' 1
20"
80"
40"
o0»
0"
10"
20"
80"
40"
50"
0"
10" 20"
//
„
tt
ft
tt
It
It
It
tt
It
It
/
It 1'
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0 j 0.0
10
+0.2
+0.1
+0.1
+0.0
0.0
-0.0
-0.1
-0.1
-0.2
-0.2
-0
3
-0.4 1-0.4
20
0.4
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.4
0.5
6
0.7
0.8
:w
0.6
0.5
0.3
0.1
0.0
0.1
0.3
0.5
0.6
0.7
8
1.1
1.2
40
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
1
2
1.5
1.6
50
^1.0
+0.7
+0.5
+0.2
0.0
-0.2
-0.5
-0.7
-1.0
-1.2
-1
5
-1.7
-2.1
Page 720]
TABLE 28B.
For finding the Latitude of a place by Altitudes of Polaris.
[B = the 2d correction. Thi.s correction is always additive.]
star's
Star's altitude. 1
star's
hour
angle.
angle.
h. m.
00
84°
So°
86°
87°
88°
89°
40° 41°
42°
43°
0.0 ,
0.0 ,
0.0 ,
0.0 1
0.0 1
ti
0.0 1
// //
0. , 0. ,
0.0 ,
0.0 ,
h. m.
12 00
10
0.1
0.1
0.1
0.1 \
0.1 :-,
0.1 \
0.1 ■.,: 0.1 2
0.1 ■,
0.1 •.,
11 .50
20
0.2 ■„
0.2 -l
0.2 3
0.3 .3
0.3 ;-
0.3 .,
0.3 ; 0.3 ■,
0.3 ,
0.3 -,
40
30
0.5 4
0.5 ,
0.5 i
0.6 4
0.6 ...
0.6 ;.5
0.6 is: 0.7 :«
0.7 I
0.7 6
30
40
0.9 6
1.0 i
1.0 5
1.0 .6
1.1 ..5
1.1 .6
1.1 .7
1.2 .7
1.2 .7
1.3 \
20
50
1.5 i
1.5 -g
1.5 ■?
1.6 ;
1.6 ,
1.7 7
.1.8 7
1.9 8
1.9 •;
1.9 9
10
1 00
2.0
2.1
3.0 i
2.1
'.8
3.2
''■^
=^■5
'^■^
3. 7 1:1
^2i;
00
10" 50
10
2.8 ■«
2.8 'o
3.1
3.3,
3.4i;i
I 3.6, „
20
.3.6 9
3.7
3. 8 J Q
4.0 1:0
4.I1:,
4.3, „
4. 5 1.1: 4.6^;,
4.8;,
4.9 3
40
30
4.5 9
4.6i;o
4- 8 1.0
5. Oil
5- 2 1.1
5- 3 1.3
5. 6 12 •5. 8 12
e-Oo
6. 2 1.3
.30
40
5.4,,
5.61.1
5. 8 1 .,
6.1 10
6. 3 12
6.61.2
6.813 7.0,3
7- 3 1.4
7. '5 1.5
20
50
6.5
6. / 12
T.o,.-;
7.3,;.]
7. 5 1.3
7.8,4
8.1,4
8. 3 1.5
8- 7 1.5
9-0 1.5
10
2 00
10
8.81.2
9.2,,
9.5,i
9.8-
8.8i4
10.2 •
9.2,,
10.911
9.8,.
to;?
11. ' 1.7
12.1-
00
10.61:5
9 50
20
10.0,3
10. 5 1 2
10.813
11- 2 1.4
11. 7 1,4
12.1 1,5
12. 5 1.6
13.0, fi 13.4,7
13. 9 1 9
40
30
11. 3 1.3
11.7,,
12. 1 5
12.61..,
13.1 1.5
13.6,5
14.1,,,
14.6,:^ 15.1 1:7
15.6,0
30
40
12.6 ,
13.1 1.3
13.614
14.11..5
14.61.5
Ib.l,,
15. '1.6
16. 2 1.8
16.8,7
17.41,,
20
50
13.9 13
14. 4 1.6
15.0 1:4
15.6,4
16. 1 1.6
16. ' 1.6
17. 3 1.,
18.0 1.7
18. 5 1.8
19. 3 1.8
10
3 00
15.2^
15.9,^
17.9
17. (
I1.5
>i ^
19.2ir,
19.9 •
20.7i6
19. V^,
21.4i7
20.3
22.1 •
21-li8
22.9
00
.H 50
10
16. 61 3
17.3i3
18. f
20
17.9i3
18.6
19.314
20.0i.5
20.7 6
21.5
22.3 ,
23. 1 ig
23.9 ■;
24.8;-?
40
30
19.2 ,
19.9 3
20.713
21. 5 1.3
22.3 .4
23. 1 5
23.9 5
24.7,7! 25.6,7
26. 5 18
30
40
20. 5 , .,
21.2,.,
22.0
22. 8, .4
23. 7 1.4
24.6,5
25. 4 1.6
26. 4 1:5 127. 3 1.7
28. 3 1.7
20
50
21.7,,
22. 5 1.2
23.4,,
24. 2 1.4
25.1 1,4
26.1,4
27,0 1.4
27.9ibI 29.0 1.5
30. 1,7
10
4 00
^ii-8 1
23.7j„
24.6 •„
25. 6 ' ,
26. -S,
^^•^3
28.4 J,
29.5^^30.5^^
31.7,,
00
10
24.0,0
24.9
25.8,';
26. 8 , ,
27. 8 J'
28.8
29.9
30. 9, 'j 32.1 ,4
33.2
7 50
20
25. 1'l
26. Oj-,
27. Oj-
28. 0,':
29. Oj-
30.1 12
31.2-2
32.3 1'i .3.3.5,',
34.7i3
40
30
26.1
27.1
28.0 n
29. 1 lio
30. Im
31.3io
32.4 ,
33. 5 1:2
34. ' 1.3
36.0i;3
30
40
27.0 ■=
27.9 I
29.0 9
30.1 9
31.2io
32. 3 10
.33.5 „
34.7,1
.36.0io
37.3ii
20
50
27.8 'e
28.8 •
29.9 •
31.0
32.2 ,
33. 3 '9
34.4 9
35.8 ■„
37.0 10
38.4io
10
5 00
10
fe.4 ■'
29.1 5
29.6 ;
30.2
30.7 •'
31.3
31.8 -^
.32.5 5
33.0 •,
33.7 6
34.2 i
34.9 7
35.3
36.1 -,
36.7 •'
37.5 •
.38.0 ,
38.8 7
39. 4 \
00
() 50
40.2 -7
20
29.6
30.7 ■'
31.8 ■;
33.0 i
34.3 4
.35.6
.36.8 -5
38.2 ■;
39.5 \
40.9 V,
40
• 30
SO.O '3
31.1 3
32.3 3
33.5 4
34.7 4
36.0 4
37.3
38.6 4
40.0 4
41.5 4
30
40
30.3 ■,
31.4 •,
32.6 2
33.9 ■,
35.1 1
36.4 •,
37.6
39.0 3
40.4 3
41.9 ■,
20
50
30.5
31.6 7
32.8 ■,
.34.0 ■,
35.2 ■,
.36.5 •,
37.8 •,
39.3 1
40.7 \
42.1 -
10
6 00
30.5 '
31.7 ■'
32.9 "
34.1
35.3
36.6
37.9 •
39.4
40.8
42.2
t) 00
TABLE 28C.
(C
= the3de
orrection. Hor. Arg., the star's declination. Vert. Arg., B = the 2d correc
ion.]
B.
88° 47'
88° 48'
88° 49' 1
20"
80"
40"
50"
0"
10"
20"
80"
40"
50"
"
10"
20"
0.0
0.0
0.0
0.0
0.0
0.0
fi
0.0
//
0.0
0.0
0.0
.0
0.0
II
0.0
10
+0.2
+0.1
+0.1
+0.0 : 0.0
-0.0
-0.1
-0.1
-0.2
-0.2
-0
.3
-0.4
-0.4
20
0.4
0.3
0.2
0. 1 0.
0.1
0.2
0.3
0.4
0.5
.6
0.7
0.8
30
0.6
0.5
0.3
0. 1 1 0.
0.1
0.3
0.5
0.6
0.7
.8
1.1
1.2
40
0.8
0.6
0.4
0. 2 0.
0.2
0.4
0.6
0.8
1.0
1
.2
1.5
1.6
50
+1.0
+0.7
+0.5
+0.2 0.0
-0.2
-0.5
-0.7
-1.0
-1.2
-1
.5
-1.7
-2.1
24972
12 36
Page 722] TABLE 286.
For finding the Latitude of a
place by Altitudes of Polaris. 1
[B= the 2d correction. This correction is always additive.] 1
star's
Star's altitude. 1
Star's
htmr
angle.
augle.
63° 54°
55°
56°
57°
08°
59° 60°
h. VI.
00
1 tt > n
0. n 1 i 0. n 1
O.Ooi
0.
O.O02
0. 2
O.O0.2 O.O02
h. 1,1.
12 00
10
0.1 ol
0.1 04
0-1 04
0-2 0:3
0-2 0:3
0-2 0:4
0-2 0.4 0.2°4
11 50
20
f • ^ 0.5
0-5o5
0.5 0.6
0-5 0.6
0-5 0.7
0-6 0.6
0.60.7 0.60.7
40
30
1-0 0.8
1-0 0.8
1-1 0.8
i-io-9
1-2 0.9
i•^■0
J'qO.9^ oqI-"
:;o
40
1.810
1-8 1.1
1-9 1.1
2-0 1.1
rii-i
2. 2 1 „
2. 2 13; 2. 3i3
20
50
2.8 ° 2.9i3
=^-"1.3
\-W
3- 2 1.5
^•^■5
3- 5 1.5 3.61.,
10
1 00
4.0i^ -i-a,.
•I- =^16
4-^6
4-'iG
4-9i7
5-0l8^ '^-3l8
00
10
20
30
40
2-^:6
(.0, „
8.8
10.7.-^
15.0 -^
5. 6 J-;
7. 3 . „
9.1 •
ii.i2i
13-323
15.6"
5.81^
ll.o„„
13.823
16.1?-?
6.1,'°
7.9 •
11. 9 1
14-32 5
16.8^-
19. 3 ^'s
6.3^3
8-220
10-22 3
12. 5 1
14 8
17:4-
6.6,'
8.4^-^
10.6.;-
13-O25
15-52
18. 1 -^
6.8^2°^ 7.1^0
8.8:-° 9.1,4
11.0--^ 11.5;,
13.44 14-02 7
16.02^ 16.7;-;
18.8^- 19.6^-^
10 .50
40
30
20
50
2 00
10
00
10
17.324
I8.O25
mOjV
20. 1 2 8
020.83*;;
021.73-1 022.63",
9 50
20
19-7 2.5
20.5 2:6
21.3o'-
22-i;:8
22.929
23. 8 3
24.83.1
25. 8 33
40
30
22.22 6
23.1 2.6
24. or,
24.92.8
25. 8 3
26.831
27. 9 3 ,
29.183
30
40
24.82.6
25.72 7
26.7 2:8
27.7,9
28- 8 3
29.9 1
31. 1 3:2
32.43.1
20
50
27.4 2.7
28.42:7
29.5 2.8
30.62.9
31-83.0
33.0 32
'^- 3 3.3
35.834
10
3 00
.SO.I25
31-127
33.827
32.3
0.36.5^°
34-831
36.2_
37-^3
3?- 234
00
10
32.606
35. 1 2 8
37.93:0
039.43--
040.93:3
042.634
8 .50
20
35.2;-6
36.52 7
0/ . y ft
39. 4 1^
40.9 2.9
42- -^3
44.23.2
46.0 3.3
40
30
37.82.5
39- 2 2.6
40.7-:6
42-228
4o. g
45-63.0
47-43.1
49.333
30
40
40.324
■H-825
43.3,6
45.0.,-
46. 7 2 9
48.629
oO. 5 3
52.631
20
50
42.723
44.324
45.9,2.5
47-7^:6
49.62.6
51-5 2.8
53.529
55. 7 31
10
4 00
45-02
46.7„-3
48-^24
50.3
- 52-226
54-3„6
56- 4 ,8
58.8
00
10
47.22 1
49.07,
50.82,
052.823
54.8„,
56. 9 „fi
59.2 27
1 i-6i:8
7 50
20
49.32.0
51.12:0
53.1 It
55. l|^
57.22:3
59.42:4
1 1-9-2.4
1 4.4 2.5
40
30
51. 3 18
53. 1 1 "
55. 2i^
57.3i9
59.52.1
1 1-82.1
1 4.3 2.2
1 6.9 2.3
30
40
50
5 00
•53-l,:5
55.0 -^
56. 61,
5«-l'
59.4io
1 0.4 08
57.li,
58. 81;
1 0.3
59.2,8
1 1.0 -^
1 2.6
1 1.61 8
1 3.4^6
1 5.0
1 3.9 20
1 5.9i"
1 ^-6 '
1 6.5 20
1 8.5,8
-110-3 5
1 9.2„i
1 11. 3 --g
113.1
20
10
00
10
20
•57.3 0:9
58-2o8
1 1-6
1 2. 7 08
1 3.9
1 s.oj-;
1 6.4 1,
1 7.6 :"
1 9.012
1 10-2 :o
1 11-8 3
113.1 0:9
114.7 •
116.lJ:9
6 50
40
30
■5i'.Oo6
1 l-2o6
1 3.5^^
1 5- 907
1 8. 5 0.7
1 11- 2 0.6
1 14-0 0.8
\ Ji•^.8
30
40
50
59.9^-
1 0.0
! -;:
1 4. 5 „ 2
1 6-60.4
1 7.0(,i
1 9-2o4
1 9.6^t
1 11-804
1 12- 2 02
1 14-8o4
115.2°-*
1 17.804
118. 2 0:2
20
10
6 00
1 2.3"
1 4.7"'
1 7.1
1 9.7
1 12.4
1 15.4
1 18.4
6 00
TABL
E 28C.
[C = the 3d correction. Hor. Arg., the star's <
lecliuation.
Vert. Arg., B = the 2d correction.]
B.
88° 47; t
88° 4
8'
88° 49' 1
20"
• 80" ! 40"
50" 1 0" 10"
20"
80"
40"
50"
0"
10"
20"
30
It
+0.6
+0.5
+0.3
+0.1
0. 1 -0. 1
-0.3
0.5
-0.6
-0.7
-0.8
-1.1
-1.2
40
0.9
0.6
0.4
0.2
0.0 0.2
0.4
0.6
0.9
1.0
1.2
1.4
l.ti
50
1.0
0.7
0.5
0.2
0.0 0.2
0.5
0.7
1.0
1.2
1.5
1.7
2.0
60
1.2
0.9
0.6
0.2: 0.0 ! 0.2
0.6
0.9
1.2
1.5
1.8
2.1
2.5
70
1.5
1.1
0.7
0. 4 0. 0. 4
0.7
1.1
1.5
1.8
2.1
2.5
2.8
80
+1.6 +1.2
+0.8
+0.4 0.0 1 -0.4
-0.8
1.2
-1.6 -2.1
-2.5 -2.8
-3.3
TABLE 28D.
[Page 723
For finding the Latitude of a place by
Altitudes of Polaris. 1
[D=the 4th correction. (D has the same sign
as A when the Dec. <88°48', the opposite sign when the Dec. >88° 48'.)] 1
[Vertical Argument, A = the 1st correction. Horizontal Argument, the star
s declination.] 1
A.
Decimation, 88° ^7'
88° 48'
. Proportional parts. 1
20"
25"
SO"
35"
40"
46"
60"
55"
0"
5"
10"
15"
20"
25"
1"
2"
8"
4"
/
//
ff
tt
II
n
„
„
ft
//
tt
„
„
„
It
//
// .
,,
II
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2
1.1
1.0
0.8
0.7
0.6
0.4
0.2
0.1
0.0
0.1
0.2
0.4
0.6
t).7
0.0
0.0
0.1
0.1
4
2.2
1.9
1.7
1.4
1.1
0.8
0.6
0.3
0.0
0.3
0.6
0.8
1.1
1.4
0.1
0.1
0.2
0.2
6
3.3
2.9
2.5
2.1
1.7
1.2
0.8
0.4
0.0
0.4
0.8
1.2
1.7
2.1
0.1
0.2
0.2
0.3
8
10
4.4
3.9
3.3
2.8
2.2
1.7
1.1
1.4
0.6
0.7
0.0
0.0
0.6
0.7
1.1
1.7
2.2
2.8
0.1
0.2
0.3
0.3
0.4
0.4
0.6
.5.6
4.9
4.2
3.4
2.8
2.1
1.4
2.1
2.8
3.4
0.1
12
6.7
5.8
5.0
4.2
3.3
2.5
1.7
0.8
0.0
0.8
1.7
2.5
3.3
4.1
0.2
0.3
0.5
0.6
14
7.8
6.8
5.8; 4.9
3.9
2.9
1.9
1.0
0.0
1.0
1.9
2.9
3.9
4.9
0.2
0.4
0.6
0.8
16
8.9
7.8
6.7
5.5
4.4
5.0
3.3
3.8
2.2
2.5
1.1
1.2
■0.0
0.0
1.1
1.2
2.2
3.3
.3. 8
4.4
.5.0
5.5
0.2
0.2
0.4
0.5
0.7
0.7
0.9
1.0
18
10.0
8.8
7.5
6.2
2.5
6.2
20
11.1
9.7
8.3
6.9
5.5
4.2.
2.8
1.4
0.0
1.4
2.8
4.2
5.5
6.9
0.3
0.6
0.8
1.1
22
12.2
10.7
9.2
7.7
6.1
4.6
3.0
1.6
0.0
1.6
3.0
4.6
6.1
7.7
0.3
0.6
0.9
1.3
24
26
13.3
14.4
11.7
12.7
10.0
10.8
8.3
6.7
5.0
5.4
3.3
1.7
0.0
1.7
3.3
5.0
6.7
8.3
9.0
0.3
0.4
0.7
0.7
1.0
1.1
1.4
9.0
7.2
3.6
1.8
0.0
1.8
3.6
5.4
7.2
1.4
28
15.6
13.6
11.7
9.7
7.8
5.8
3.9
1.9
0.0
1.9
3.9
5.8
7.8
9.7
0.4
0.8
1.1
1.5
m
16.7
14.6
12.5
10.4
8.3
6.2
4.2
2.1
0.0
2.1
4.2
6.2
8.3
10.4
0.4
0.8
1.3
1.7
32
M
17.8
l8.9
15.6
16.6
13.3
11.1
8.9
6.7
4.4
4.7
2.2
2.3
0.0
0.0
2.2
4.4
6.7
8.9
11.1
0.4
0.9
1.3
1.8
14.2
11.8
9.4
7.1
2.3
4.7
7.1
9.4
11.8
0.5
0.9
1.4
1.9
36
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
2.5
5.0
7.5
10.0
12.5
0.5
1.0
1.5
2.0
38
21.1
18.4
15.8
1.3.2
10.6
7.9
5.3
2.7
0.0
2.7
5.3
7.9
10.6
13.2
0.5
1.1
1.6
2.1
40
42
22.2
23. sr
19.4
20.4
16.7
13.9
11.1
8.3
5.6
2.8
2.9
0.0
0.0
2.8
2.'9
5.6
8.3
11.1
13.9
0.6
0.6
1.1
1.2
1.7
1.7
2.2
17.6
14.6
11.7
8.8
5.8
5.8
8.8
11.7
14.6
2.3
44
24.4
21.4
18.3
15.3
12.2
9.2
6.1
3.0
0.0
3.0
6.1
9.2
12.2
15.3
0.6
1.2
1.8
2.4
46
25.6
22. 3
19.2
16.0
12.8
9.6
6.4
.3.2
0.0
.3.2
6.4
9.6
12.8
16.0
0.6
1.3
1.9
2.6
48
50
26.7
27.8"
23.3
24.3
20.0
16.7
13.3
10.0
6.7
6.9
3.3
3.4
0.0
0.0
3.3
3.4
6.7
6.9
10.0
13.3
16.7
0.7-
1.3
2.0
2.6
20.8
17.3
1.3.9
10.4
10.4
13.9
17.3
0.7
1.4
2.1
2.8
52
28.9
25. 3
21.7
18.0
14.4
10.8
7.2
3.6
0.0
3.6
7.2
10.8
14.4
18.0
0.7
1.4
2.2
2.9
54
30.0
26.2
22.5
18.8
15.0
11.2
7.5
3.8
0.0
3.8
7.5
11.2
15.0
18.8
0.7
1.5
2.2
3.0
56
31.1
.32.2
27.2
28.2
2.3.3
19.4
15.6
16. 1"
11.7
7.8
3.9
4.0
0.0
o."o
3.9
7.8
11.7
15. 6
16.1
19.4
20.1
0.8
0.8
1.6
1.6
2.3
2:4
3.1
3.2
58
24.2
20.1
12.1
8.0
4.0
8.0
12.1
60
33. 3
29.2
25.0
20.8
16.7
12.5
8.3
4.2
0.0
4.2
8.3
12.5
16.7
20.8
0.8
1.7
2.5
3.3
62
34.4
30.1
25.8
21.5
17.2
12.9
8.6
4.3
0.0
4.3
8.6
12.9
17.2
21.5
0.9
1.7
2.6
3.4
64
66
3.5.6
31.1
26.7
22.2
17.8
13.3
8.9
4.4
0.0
0.0
4.4
4.6
8.9
9.2
13.3
17.8
18.3
22.2
0.9
1.8
1.8'
2.7
2.8
3.6
.3.7
36.7
.32.1
27.5
22.9
18.3
1.3.8
9.2
4.6
13.8
22.9
0.9
68
37.8
33.
28.3
23.6
18.9
14.2
9.4
4.7
0.0
4.7
9.4
14.2
18.9
23.6
0.9
1.9
2.8
3.8
70
38.9
;m.o
29.2
24.3
19.4
14.6
9.7
4.9
0.0
4.9
9.7
14.6
19.4
24.3
1.0
1.9
2.9
3.9
72
' rr
40.0
35.0
30.0
25.0
20.0
15.0
10.0
5.0
0.0
5.0
10.0
15.0
20.0
25.0
1.0
2.0
3.0
4.0
Proportional parts.
„
„
„
„
//
ff
//
n
„
„
„
,f
„
„
20
0.2
0.2
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.1
0.1
0.1
40
0.4
0.3
0.3
0.2
0.2
0.1
0.0
0.0
0.0
0.0
0.0
0.1
0.2
0.2
1 00
0.6
0. 5 0. 4
0.4
0.3
0.2
0.1
0.1
0.0
0.1
0.1
0.2
0.3
0.4
1 20
0.7
0. 7 0. 5
0.5
0.4
0.2
0.1
0.1
0.0
0.1
0.1
0.2
0.4
0.5
1 40
0.9
0. 8 0. 7
0.6
0.5
0.3
0.2
0.1
0.0
0.1
0.2
0.3
0.5
0.6
2 00
1.1
1.0 0.8
0.7
0.6
0.4
0.2
0.1
0.0
0.1
0.2
0.4
0.6
0.7
Page 724]
TABLE 28D.
1
For finding the Latitude of a place by
Altitudes of Polaris. 1
rD=
he «h correction. ( D has the same sign
as A when the Dee. <8»^ 48', the opposite sign when the Dec. >88o 48'.)] 1
[Verti
wl Argument A = the 1st correction. Horizontal Argument, the star's declination.] 1
A.
Declination, 88° 48'
88° 49' ^ 1
Proportional parts. 1
80"
35"
40"
45"
50"
55"
0"
5"
10"
15"
20"
1"
2"
8"
4"
//
„
1'
^f
It
„
//
ft
If
II
If
//
It
II
ti
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
2
0.8
1.0
1.1
1.2
1.4
1.6
1.7
1.8
1.9
2.1
2.2
0.0
0.1
0.1
0.1
4
1.7
1.9
2.2
2.5
2.8
3.1
3.3
3.6
3.9
4.2
4.4
0.1
0.1
0.1
0.2
6
2.5
2.9
3.3
3.8
4.2
4.6
5.0
5.3
5.8
6.2
6.7
0.1
0.2
0.2
0.3
8
3.3
3.9
4.4
5.0
5.6
6.1
6.7
7.2
7.8
8.3
8.9
0.1
o:i
0.2
0.3
0.3
0.4
0.4
10
4.2
4.9
5.6
6.2
6.9
7.6
8.3
9.0
9.7
10.4
11.1
0.6
12
5.0
5.8
6.7
7.5
8.3
9.2
10.0
10.8
11.7
12.5
13.3
0.2
0.3
0.5
0.7
14
5.8
6.8
7.8
8.8
9.8
10.8
11.8
12.7
13.7
14.6
15.6
0.2
0.4
0.6
0.8
16
6.7
7.8
8.9
10.0
11.1
12.2
13.3
14.4
15.6
16.7
17.8
0.2
0.4
0.7
0.9
18
7.5
8.8
10.0
11.2
12.5
13.8
15.0
16.2
17.5
18.8
20.0
0.2
0.5
0.7
1.0
20
8.3
9.7
11.1
12.5
13.9
15.3
16.7
18.1
19.4
20.9
22.2
0.3
0.6
0.8
1.1
??
9.2
10.7
12.2
13.8
15.3
16.8
18.3
19.8
21.4
22.9
24.4
0.3
0.6
1.0
1.3
24
26"
10.0
11.7
13.3
15.0
16.7
18.4
20.0
21.7
23.3
25.0
26.7
0.3
0.4
0.7
1.0
1.4
10.8
12.7
14.4
16.2
18.0
19.9
21.7
23.5
25.3
27.1
28.9
0.7
1.1
1.4
m
11.7
13.6
15.6
17.5
19.4
21.4
23.3
25.3
27.2
29.2
31.1
0.4
0.8
1.2
1.6
so
12.5
14.6
16.7
18.8
20.8
22.9
25.0
27.1
29.2
31.2
33.3
0.4
0.8
1.2
1.6
32
13.3
15.6
16.6
17.8
20.0
22.2
24.4
26.7
28.9
31.1
33.3
"35.4"
35.5
0.4
0.9
1.3
1.8
U
14.2
18.9
21.2
23.6
26.0
28.4
30.7
33.1
37.8
0.5
0.9
1.4
1.9
86
15.0
17.5
20.0
22.5
25.0
27.5
30.0
32.5
35.0
37.5
40.0
0.5
1.0
1.5
2.0
88
15.8
18.4
21.1
23.8
26.4
29.0
31.6
.34.2
.37.0
39.6
42.2
0.5
1.1
1.6
2.2
40
42
16.7
19.4
22.2
25.0
27.8
.30.6
33.3
36.1
38.9
41.7
44.4
0.6
1.1
1.7
2.2
17.6
20.4
23.3
26.2
29.2
32.1
35.0
37.9
40.8
43.8
46.7
0.6
1.2
1.8
2.4
44
18.3
21.4
24.4
27.5
30.6
33.7
36.8
39.8
42.8
45.9
48.9
0.6
1.2
1.8
2.4
46
19.2
22.3
25.6
28.8
32.0
35.1
38.3
41.5
44.8
47.9
51.1
0.6
1.3
1.9
2.6
48
20.0
23.3
26.7
30.0
33.3
34.7
36.7
38. 2
40.0
43.3
46.7
50.0
52.1
53.3
0.7
1.3
2.0
2.7
50
20.8
24.3
27.8
31.2
41.7
45.1
48.6
55.5
0.7
1.4
2.1
2.8
52
21.7
25.3
28.9
.32.5
36.1
39.7
43.3
46.9
50.5
54.2
57.8
0.7
1.4
2.2
2.9
54
22.5
26.2
30.0
33.8
37.5
41.2
45.0
48.7
52.5
56.2
60.0
0.7
1.5
2.2
3.0
56
58'
23.3
24.2
27.2
31.1
35.0
38.9
42.8
44.3
46.7
50.5
52. 3
54.4
58.3
62.2
0.8
1.6
2.3
3.1
28.2
32.2
36.2
40.3
48.3
56.4
60.4
64.4
0.8
1.6
2.4
3.2
60
2.5.0
29.2
33.3
37. 5
41.7
45.9
50.0
54.2
58.3
62.5
66.7
0.8
1.7
2.5
3.3
62
25.8
30.1
34.4
38.8
43.0
47.3
51.7
56.0
60.3
64.6
68.9
0.9
1.7
2.6
3.4
64
66
26.7
31.1
35.6
40.0
44.4
48.9
53.3
57.8
62.2
66.7
71.1
0.9
1.8
1.8
2.7
2.7
3.6
3.6
27.5
32.1
36.7
41.2
45.8
50.4
55.0
59.6
64.2
68.8
73.3
0.9
68
28.3
33.0
.37.8
42.5
47.2
52.0
56.7
61.3
66.1
70.9
75.5
0.9
1.9
2.8
3.8
70
29.2
34.0
38.9
43.8
48.6
53.5
58.3
63.1
68.0
72.9
77.7
1.0
1.9
2.9
3.9
72
f It
30.0
35.0
40.0
45.
50.0
55.0
60.0
65.0
70.0
75.0
80.0
1.0
2.0
3.0
"
Proportional parts.
H
„
n
It
„
It
It
It
„
„
„
020
0.1
0.1
0.1
0.2
0.2
0.3
0.3
0.3
0.3
0.3
0.4
040
0.2
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.6
0.7
0.7
100
0.4
0.5
0.6
0.6
0.7
0.8
0.8
0.9
0.9
1.0
1.1
120
0.5
0.7
0.7
0.8
0.9
1.1
1.1
1.2
1.3
1.4
1.5
140
0.6
0.8
0.9
1.0
1.1
1.3
1.4
1.5
1.6
1.7
1.8
200
0.8
1.0
1.1
1.2
1.4
1.6
1.7
1.8
1.9
2.1
2. 2
TABLE 29.
[Page 725
Conversion Tables for Nautical and Statute Miles.
Natttical viiks into statute miies.
Siatide miles into nautical miles. 1
1 na<itical mile or knot -6,080 feet.
1 statute mile
= 5.280 feet. 1
1 statute mile =5,280 feet.
1 nautical mile or knot- 6,080 feet. 1
Nautical
Statute
Nautical
statute
Nautical
statute
statute
Nautical
statute
Nautical
statute
Nautical
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
miles.
1.00
1.151
8.75
10. 075
16.50
18.999
1.00
0.868
9.00
7.816
17.00
14.763
1.25
1.439
9.00
10. 363
16. 75
19. 287
1.25
1.085
9.26
8.032
17.25
14. 980
1.50
1.727
9.25
10.651
17.00
19. 575
1.60
1.302
9.60
8.249
17.50
15. 197
1.75
2.015
9.50
10. 939
17.25
19. 863
1.76
1.619
9.75
8.467
17.76
15.414
2.00
2.303
9.75
11. 227
17.50
20. 151
2.00
1.736
10.00
8.684
18.00
15. 632
2.25
2.590
10.00
11. 515
17.75
20.439
2.25
1.953
10. 25
8.901
18.25
15. 849
2.50
2.878
10.25
11. 803
18.00
20. 727
2.50
2.170
10.50
9.118
18.60
16. 066
2.76
8.166
10.50
12.090
18.25
21.015
2.75
2. 387
10.76
9.335
18.76
16. 283
3.00
3.454
10. 75
12. .378
18.50
21.. 303
3.00
2.604
11.00
9.552
19.00
16. .500
3.25
3.742
11.00
12.666
18.75
21.590
3.26
2.821
11.26
9. 769
19.26
16. 717
3.50
4.030
11.25
12. 954
19.00
21. 878
3.50
3.038
11.60
9.986
19.50
16.934
3.75
4.318
11.50
13. 242
19. 25
22. 166
3.76
3.256
11.76
10. 203
19.75
17.161
4.00
4.606
11.75
13.530
19.50
22.454
4.00
3.473
12.00
10.420
20.00
17. 369
4.25
4.893
12.00
13. 818
19.75
22. 742
4.26
3.690
12.25
10.638
20.26
17. 686
4.50
5.181
12.25
14.106
20.00
23. 030
4.60
3.907
12.50
10.855
20.60
17. 803
4.75
5.469
12.50
14. .393
20.25
23. 318
4.75
4.124
12.76
11.072
20.75
18. 020
5.00
5.757
12. 75
14. 681
20.50
2.3.606
5.00
4.:wi
13.00
11. 289
21.00
18. 2,37
5.25
6.045
13.00
14. 969
20.75
23. 893
5.25
4.569
13.25
11. 607
21. 25
18.454
5.50
6. 333
13.25
15. 257
21.00
24. 181
5.60
4.776
13.60
11. 724
21.50
18.671
5.75
6.621
13.50
15.545
21.25
24. 469
5.76
4.994
13.75
11.941
21.76
18. 888
6.00
6.909
13.75
15. 833
21.50
24. 757
6.00
6.211
14.00
12.158.
22.00
19. 106
6.25
7.196
14.00
16. 121
21.75
25.045
6.26
5.428
14.25
12. 376
22.25
19, 322
6.50
7.484
14.25
16.409
22.00
25. ,3.33
6.50
5.646
14.60
12. 693
22.50
19, 5,39
6.75
7.772
14.50
16. 696
22. 25
26. 621
6.75
5.862
14. 75
12. 810 i
22. 75
19, 756
7.00
8.060
14.75
16.984
22.50
25. 909
7.00
6.079
15.00
13.027 :
23.00
19. 973
7.25
8.348
15.00
17. 272
22.75
26. 196
7.26
6.296
16. 25
13.244 '
23.26
20. 191
7.50
8.636
15.25
17. 560
23.'00
26.484
7.60
6.613
16.50
13. 461
23.50
20. 408
7.75
8.924
15. 50
17.848
23. 50
27.060
7.76
6.730
16.76
13. 678
23. 75
20. 625
8.00
9.212
15. 75
18. 136
24.00
27. 636
8.00
6.947
16.00
13. 895
24.00
20. 842
8.25
9.500
16.00
18. 424
24.50
28. 212
8.25
7.164
16.26
14. 112
24.26
21.060
8.50
9.787
16.25
18. 712
25.00
28. 787
8.50
7.381
16.60
14.329
24.60
21.277
8.76
7.598
16.76
14.546
25.00
21.711
Page 726] TABLE 30.
Conversion Tables for Metric and English Limear Measure.
Metric to English.
Meters.
Feet.
Yards.
statute miles.
Nautical miles.
1
2
3
4
3. 280 833 3
6.561 666 7
9.842 500
13.123 333 3
1.093 611 1
2. 187 222 2
3.280 833 3
4.374 444 4
0.000 621 369
.001 242 738
. 001 864 106
.002 485 475
0.000 539 593
.001 079 185
.001 618 778
.002 158 370
5
6
7
8
9
16.404 166 7
19.685 000
22.965 833 3
26.246 666 7
29.527 500
5.468 055 6
6.561 666 7
7.6.55 277 8
8.748 888 9
9.842 500
.003 106 844
.003 728 213
.004 349 582
.004 970 950
.005 592 319
.002 697 963
.003 2.37 556
. 003 777 148
.004 .316 741
.004 856 333
English to metric.
No.
Feet to meters.
Yards to meters.
Statute miles to meters.
Nautical miles to meters.
1
2
3
4
0.304 800 6
0.609 601 2
0.914 401 8
1.219 202 4
0.914 401 8
1.828 803 7
2.743 205 5
3.657 607 3
1,609.35
3, 218. 70
4, 828. 05
6,437.40
1, 853. 25
3,706.50
5, 559. 75
7,413.00
5
6
7
8
9
1.524 003
1.828 803 7
2.133 604 3
•2. 438 404 9
3.743 205 5
4.572 009 1
5.486 411
6.400 812 8
7.315 214 6
8.229 616 5
8,046.75
9, 656. 10
11,265.45
12, 874. 80
14, 484. 15
9, 266. 25
11,119.50
12, 972. 75
14, 826. 00
16, 679. 25
TABLE 31. [Page 727 j
Conversion
Tables for Thermometer Scales.
£<i
[P°=Fahrenheit temperature; C°=Centigrade temperature; R°=Reaumur temperature.]
ntimimi temperatures— Fahr., Cent.
Rtau
R°=iC°=J(F°-
^32°).
C°=}R°=§ (F°
-32°).
r°.
1
C°.
R°.
F°.
C°.
R°.
-17.2
-13.8
51
+10.6
+ 8.4
2
16.7
13.3
52
11.1
8.9
Equivalent temperatures— Centiffrade and Fahrenheit.
3
4
16.1
15.6
12.9
12.4
53
54
11.7
12.2
9.3
9.8
Fo=8C°+32°.
5
6
7
15.0
14.4
13.9
12.0
11.6
11.1
55
56
57
12.8
13.3
13.9
10.2
10.7
11.1
C°.
F°.
C°.
.F°.
C°.
F°.
c°.
F°.
C°.
F°.
'
8
13.3
10.7
58
14.4
11.6
-10
14.0
32.0
10
50.0
20
68.0
30
86.0
9
. 12.8
10.2
59
15.0
12.0
- 9
15.8
1 1 33.8
11
51.8
21
69.8
31
87.8
10
12.2
9.8
60
15.6
12.4
- 8
17.6
2
35.6
12
53.6
22
71.6
32
89.6
11
11 7
9.3
61
16 1
12.9
— 7
19.4
3
37.4
13
55.4
23
73.4
33
91.4
12
U.l
8.9
62
16.7
13.3
- 6
21.2
4
39.2
14 ' 57. 2
24
75.2
34
93.2
13
10.6
8.4
63
17.2
13.8
- 5
23.0
5
41.0
15 j 59.0
25
77.0
35
95.0
14
10.0
8.0
64
17.8
14.2
- 4
24.8
6
42.8
16 60.8
26
78.8
36
96.8
15
9.4
7.6
65
18.3
14.7
- 3
26.6
7
44.6
17 i 62.6
27
80.6
.37
«8.6
16
8.9
7.1
66
18.9
15.1
- 2
28.4
8
46.4
18 64.4
28
82.4
38
100.4
17
8.3
6.7
67
19.4
15.6
- 1
30.2
9
48.2
19 66.2
29
84.2
39
102.2
18
19
7.8
7.2
6.2
5.8
68
69
20.0
20.6
16.0
16.4
20
6.7
5.3
70
21.1
16.9
21
6.1
4.9
71
21.7
17.3
22
5.6
4.4
72
22.2
17.8
23
5.0
4.0
73
22.8
18.2
24
4.4
3.6
74
23.3
18.7
25
3.9
.3.1
75
23.9
19.1
26
3.3
2.7
76
24.4
19.6
27
2.8
2.2
■77
25.0
20.0
Equivalent temperatures— Riaumur and Fahrenheit.
28
2.2
1.8
78
25.6
20.4
r°=| R°+32°.
29
30
1.7
1.1
1.3
0.9
79
80
26.1
26.7
20.9
21.3
R°.
F°.
R°.
F°.
R°.
F°.
R°.
F°.
31
32
— 0.6
0.0
-0.4
0.0
81
82
27.2
27.8
21.8
22.2
33
34
+ 0.6
1.1
+ 0.4
0.9
83
84
28.3
28.9
22.7
23.1
-10
- 9
9.5
11.8
1
32.0
34.2
10
11
54.5
56.8
20
21
77.0
79.2
85
1.7
1.3
85
29.4
23.6
— 8
14.0
2
36.5
12
59.0
22
81.5
36
2.2
1.8
86
30.0
24.0
— 7
16.2
3
38.8
13
61.2
23
83.8
37
2.8
2.2
87
30.6
24.4
— 6
18.5
4
41.0
14
63.5
24
86.0
38
3.3
2.7
88
31.1
24.9
- 5
20.8
5
43.2
15
65.8
25
88.2
39
3.9
3.1
89
31.7
25.3
— 4
23.0
6
45.5
16 68.0
26
90.5
40
4.4
3.6
90
32.2
25.8
— 3
25.2
7
47.8
17
70.2
27
92.8
41
5.0
4.0
91
32.8
26.2
— 2
27.5
8
50.0
18
72.5
28
95.0
42
5.6
4.4
92
3,3.3
26.7
— 1
29.8
9
52.2
19
74.8
29
97.2
43
44
6.1
6.7
4.9
5.3
93
94
33.9
34.4
27.1
27.6
45
■7.2
5.8
95
35.0
28.0
46
7.8
6.2
96
35.6
28.4
47
8.3
6.7
97
36.1
28.9
48
8.9
7.1
98
36.7
29.3
49
9.4
7.6
99
37.2
29.8
50
+10.0
+ 8.0
100
+37.8
+ 30.2
Page 728]
TABLE 32.
To obtain the True Force and Direction of the Wind from its Apparent Force and Direction on a
Moving Vessel.
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TABLE 33.
Distance by Vertical Angle.
[Page 729
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lO ^ ^ CO CO
ooooo
t- CO C^ •— L. ^ r- O O
ooooo
o r-eocJ.-H 1—w^oo ooooo
*■ CCi-d-HCO
O CC CO C-I i-M
r-tOiC-V*
HOOO
O 50 CO CJ Fi
»co wS
OOOOO
Hi-IOOO
MOOJOQt-
coco W04N
OOOOO
rtrtco«cS
OOOOO
ooooo o ooooo
0> 00 t^ to iQ
?m c^ CI 'N
ooooo
f5coT^Qoi;oC[>t^toireio
CS N i^ CI "-H :f-» i-H IM I— I 1-H ^H
ooooo 'o ooooo
^piQ-*eo
c5cS'NC4
ooooo
CO m S S CI
ooooo
Ci O CI c» o
ooooo
CJCICI w
ooooo
i^yj'^cc'N •H.-iooiOi
CKNCJCliN OC^Clr-t'-H
ooooo ooooo
coM«Wc3
ooooo
ooooo ooooo
?5?»c3ciw
ooooo
ooooo
OQO»OOCO,t**CiO'^CO
ooooo lo oooo
ooooooooooo
assss
ooooo
r-eom lO "*-«*"
oooooo
ooooo oooooo
ooooo
OCt-fOiOif
i-H iH tH 1— I 1— I
ooooo
O»0D0or-i-
ooooo
t£>tn-v eoco
ooooo
«c5cJc3ci
ooooo
«g^jHQa>ixi^t^tctCio-vcoeoc»
ooooo ooooo ooooo
ooooo ooooo
CO coco cicj
ooooo
Oio-^rrrtlAcoMSci
r-iOOOO 'ooooo
- 2g3S
Sio^-eom
1-IOOOO
ooooo
lO ^ ^ CO cc
ooooo
CO to "* CI p
cScicicicS
ooooo
M ^ cH « CI
ooooo
r-tctOiOin ■•j'eocici'-
ooooo ooooc
ooooo
tC lO lO -w ■«»•
ooooo
CCCJCI^O
ooooo
ooooo
cc 00 r^ to ic !•£ ■^ ^j" CO eo ' CI
ooooo ooooo o
O CJ ^ rH l-H
ooooo
^-';DlC■-^-*'^5eoc^cll-l
ooooo o o o o o
0>00l>«0 (OiC-^-VeO CIC»rH.-iO
ooooo ooooo ooooo
Oiopoepm ■w|-u'cocioli-'^ooo
ooooo ooooo ©oooo
o ■^ci'-"r-(|oooo© ©©©oo'ooo©© ooooo
•~ O O © Oil I©
oooo©©
_ to coior-
O CCi-HiH©
ooooo
cSOi->rHi-H
oo©©©
ictct-x© ©i-fNeov
J T ec CO d
^ I— I 1-1 .-I l-H
ooooo
>otor-oo©
-ooo
o©©oo
© © © CO 00
oo©©©
iotor»QO© <z> c* •»)> tc oo
T* CO CO C1 1-<
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CO CO CJ CI r-f .-I
oooooo
MC»CI«-i'-lO
©©o©o©
CIiH-H©0©
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OCl'^tOOOO
Page 730]
TABLE 33.
Distance by Vertical Angle.
s
s
c5c5c3^
X ■£ iC -* CC -1 — O O 3i ' ?* X X X t* ,t^ t- '-O -J -^
?J o ib S o
-.D lO M M —
lO ^ Q .-■ 5j iiO Q uo r» Q i05 ^* OS c-i r- r^ '?i •-' -^ CI M
C^O^'Mfej-^«<-l&l35lM.-(ii:>'^iM>-i&iO-<)"MCs|
xxi--t~t^ w w -.s ;3 ift 'iciftT-r -r .-r T :■: -TO N w
rf r-i X CO -»■ !C^ ■-" O O 3> |X X I* l^ to
f -O i-< .-. ' Ti« (N Jl M ^^ uO -M -*• t-
t- r- <o -^ -o
OOpX'-'IOilXi.'OtO
r-n-(?5eQOj«oSS.-(iO
XiN'QOiOCOi-lo|o>Xt*t-'C>
•■a '£ lO o uo
O •?• CO ?1 1-t
'.c i-'s i-*; 'O o
lO UO -J- -J- Tt*
r-l-M^r-iX 'SlfSl-'l^OXf-'
aBg?8
XXOC^vOCO
r-(OOOTt<SS
CO JO CO C-) (M M
■^ -*«"*•*• CO
CO 03 CO CO C4
S?5SSS
"V CO CI M 1-1
CO CO CO CO CO
to Q i50 CO i-H O O
'iC o t? ^ ^'
X t^ i^ -.o to
xr-oic^r-hr'^ir-i.-ici cO'toxtiia
COi-m3-^--l|,-lOin-fCO oirHOOO
i-'^-t<-fr)'l".j(-?'COCOCO MCOCOCOCJ
coao
MCOM i-i
"iJ'C'IOOi X
o a> lO i> c-i
co^i-<^Ci
t^ '-O to u-S iC
5?5f-Hr-l
N004XI>
f^TCO COCOCOCOCO COC-IC^CflCg
to iC lO ul "T
to X CO i-( OJ CO l^ to iC i.O -T -* -i*
c»?lco
-f CO CO CO
?3 COCOCO CJ
cgciWNOi
as t^ to lO "5
oit-iOt^C^xr-tor-ov
^^iScoc-ioiOf"eow
-*ccMco coc'lIMM■^^
CO CJ O !Q iC CUM t-i
r-ic-)M;soi-icg'Vi-<
xwoir-to>o-^-*f
tp>oaC"W"i-i
COMCO«iM
» ssss
Q to CO CI t^
OQCJMOl X
eo'^ocoo
to '^'4' CO CO
Q X 0> to "^
ino»eis^®i>apQcoc*
coioeoiHiohrco«c^t-i
rs
i-HingOCOOplcOOllOr-lt-
CMCl'NC^tfM i-<i-H(-<r-(rH
ss^as
Oi f '-' O'^
■*CO C»t-i o
C^ CI C-t C) CI
sssss
3S88B
C0(NC10lTHT-H.H.-fiHiH
MQt-Ot-
■"^rHOTt*
CO«fM<ni-H
SSS3S
OCOOU
iOtor*xc»
SSS28
Or-I(MCO'V
3B8S
8S8BS
-•ooo
rHOOOO
lO to I- go c3>
30 X Q CI lO
rHOOlO tf
CO CO CO CI CI
X cu~ ^ to
CO CO d CI 1-H
1 d CI CI CI
CI CI 71 M CI CI
r> o i-H -r ■!* -^ -o r-1 to CI
:i«ciwiooioo'*"<j<
i-ir-icoepo»eoxeo30"<»'C
codiHOiOto^-voScoe
CICICICIrHi-lt-HMT-t^r.
33SS?
230 tOMOJ
eococo c*Mi-H
-t xc
cocSc
Ot-'Vi-dX
COC*«CItH
»0 .4 u5 ij' -f
00000
^ ^ TJ" ^ CO
00000
00000
1(5 ^ ^ "^ tc
00000
00000
iCi eo I-* p* CO
— ■^■veoSS
00000
ir-«l— COQ
■(i-«000
t~COOt>iO
00000
CO CO cQ CO CO
00000
i^ -t .-( a> I- lo
000000
000000
000000
00000 00000 000000
00000
otcootcSS
00000
CO CO CO CO CO
00000
coi0 3;cgi-i
CO CO CO CO CO
00000
OiHdCO^ iO<Ot--XOi
dC4c36lSS
OOOOOO
CIQOQ*^'QI'!?WCI^OO»
cococicic<i;cic3cicicii-i
00000000000
■J CI CI CI
00000
0«'*t0 00
eoCli-ipOOQ
MClCldrHlH
OOOOOO
Od TfiOXO
TABLI
: 3i.
[Page 731 1
For finding the distance of an object by an
angle, measured from an elevated position, bet
ween the
object and the horizon l)eyond.
Dist.,
yards.
Height of the Eye Above the Level of the Sea, in
Feet.
Dist.,
yards.
20
30
40
50
60
70
80
»o
lOO
llO
130
o /
,
/
o /
o /
O /
o /
/
o /
o /
o /
100
3 44
5 37
7 29
9 21
11 11
13 00
14 47
16 34
18 16
19 58
21 37
100
200
1 50
2 46
3 43
4 39
5 35
6 31
7 27
8 23
9 18
10 13
11 08
200
300
1 12
1 49
2 26
3 04
3 41
4 19
4 56
5 33
6 11
6 48
7 25
300
400
52
1 21
1 48
2 16
2 44
3 n
3 40
4 08
4 3«
S 04
5 32
400
500
41
1 03
1 25
1 48
2 10
2 32
2 5J
3 17
3 39
4 01
4 24
500
600
34
52
1 10
1 29
1 47
2 05
2 24
2 42
3 01
3 20
3 38
600
700
28
44
1 01
1 15
1 31
1 46
2 01
2 18
2 34
2 50
3 05
700
800
24
38
51
1 05
1 18
1 32
1 46
2 00
2 13
2 27
2 41
800
900
21
33
45
57
1 09
1 22
1 33
1 45
1 57
2 10
2 22
900
1,000
18
29
40
50
1 01
1 12
1 23
1 15
1 34
1 45
1 56
1 44
2 07
1,000
1,100
16
26
35
45
55
1 05
1 24
1 34
1 54
1,100
1,200
15
23
32
41
50
59
1 08
1 17
1 26
1 35
1 44
1,200
1,300
13
21
29
37
45
53
1 02
1 10
1 18
1 27
1 35
1,300
1,400
12
19
27
34
41
49
57
1 04
1 12
1 20
1 27
1,400
1,500
11
18
24
31
38
45
52
59
1 07
1 14
1 21
1,500
1,600
10
16
22
29
35
42
48
55
1 02
1 08
1 15
1,600
1,700
15
21
27
33
39
45
51
58
1 04
1 10
1,700
1,800
14
19
25
31
36
42
48
54
1 00
1 06
1,800
1,900
13
18
23
29
34
39
45
50
56
1 02
1,900
2,000
12
17
22
27
. 32
37
42
47
53
58
2,000
2,100
11
16
20
25
30
35
40
45
50
55
2,100
2,200
10
15
19
24
28
33
38
42
47
52
2,200
2,300
14
18
22
27
31
36
40
45
49
2,300
2,400
13
17
21
25
29
34
38
42
47
2,400
2,500
12
16
20
24
28
32
36
40
44
2,500
2,600
11
15
19
23
26
30
34
38
42
2,600
2,700
11
14
18
22
25
29
33
36
40
2,700
2, 800
10
14
17
20
24
28
31
35
38
2,800
2,900
13
16
19
23
26
30
33
37
2,900
3,000
12
15
19
22
25
28
32
35
3,000
3,100
12
15
18
21
24
27
30
34
3,100
3,200
U
14
17
20
23
26
29
32
3,200
3,300
10
13
16
19
22
25
28
31
3,300
3,400
13
15
18
21
24
27
30
3,400
3,500
12
15
' 17
20
23
26
29
3,500
3,600
12
14
17
19
22
25
27
3,600
3,700
11
13
16
19
21
24
26
3,700
3,800
11
13
15
18
20
23
.25
■;, 800
3,900
10
12
15
17
20
22
25
3,900
4,000
12
14
16
19
21
24
4, ()(X)
4,100
11
14
16
18
20
23
4, 100
4,200
11
13
15
17
20
22
4, 200
4,300
10
13
15
17
19
21
4, 300
4,400
12
14
16
18
21
4,400
4,500
12
14
16
18
20
4, 5(X1
4,600
11
13
15
17
19
4,600
4,700
11
13
15
17
19
4,700
4,800
10
12
14
16
18
4,800
4,900
12
14
15
17
4,900
5,000
11
13
15
17
5,000
Page 732] TABLE 35.
Speed in knots per hour develoj)ed by a vessel traversing a measured nautical mile in anv given |
number of minutes and seconds
Kumber of mimites.
1
2
3
4
o
6
J
8
9
10
11
12
Knots.
Knots.
Knotf.
Knots.
Knots.
Knots.
A'«ote.
Knot.-i.
Knots.
Knots.
Knots.
Knot.".
60.000
30.000
20.000
15.000
12. 000
10.000
8.571
7.500
6.666
6.000
5.4,55
5. 000
1
59. 016
29. 752
19. 890
14. 938
11. 960
9.972
8.551
7.484
6.654
5.990
5.446
4. 993
1
2
58.065
29. 508
19. 780
14. 876
11.920
9.944
8.530
7.468
6.642
5.980
5. 438
4. 986
2
S
57. 143
29.268
19. 672
14. 815
]],880
9.917
8 510
7.453
6.629
5.970
5.429
4.979
3
4
5
56.250
55.'385
29. 032
19. 565
19.460
14.754
14. 694
11.841
11.803
9.890
9. 863
8.490
8. m
7.438
7.422
6.617
6.605
5.960
5.960
5.421
4.972
4.965
4
5
28.800
5. 413
6
54. 545
28. 571
19. 355
14.634
11.764
9.836
8.450
7.407
6.593
6.940
5.405
4. 9.58
6
7
53, 731
28. 346
19.251
14. 575
11.726
9.809
8. 430
7.392
6. ,581
5.930
5. .397
4. 951
7
8
52. 941
28. 125
19. 149
14.516
11.688
9.783
8.411
7. 377
6.569
5.921
5.-389
4. 945
8
9
10
52. 174
27.907
19.048
14. 458
11.650
9.756
8. .392
8.372
7.362
7.346
6.557
6. .546
5.911
5. 381
4.938
9
51.429
27. 692
18. 947
14.400
11.613
9.729
5.902
5. 373
4.932
10
n
50. 704
27. 481
18.848
14.342
11. 576
9.703
8.353
7.331
6.533
5.892
6.365
4. 924
n
12
50. (X)0
27. 273
18. 750
14. 286
11.538
9.677
8. 3.34
7.317
6.521
5.882
5.357
4.918
12
18
49. 315
27. 068
18. 652
14. 229
11.501
9.651
8. 315
7.302
6.609
5.872
5.349
4.911
13
14
15
48.649
26. 866
18. 556
14. 173
11.465
9.625
8.295
7.287
6.498
5.863
5.341
4.904
14
1,5"
48.000
26.667
18. 461
14. 118
11. 428
9.600
8.276
7.272
6.486
5.853
5.333
4.897
16
47. 368
26. 471
18. 367
14.063
11. ,392
9.574
8. 257
7.258
6.474
,5.844
5.325
4.891
16
17
46. 753
26. 277
18. 274
14.008
11.356
9.549
8.238
7.243
6.463
,5.834
5.317
4.884
17
18
46. 154
26. 087
18. 182
13. 953
11. 321
9.524
8.219
7.229
6.451
5.825
5.309
4.878
18
19
20'
45. 570
25. 899
18.090
13.900
11.285
9.499
8.200
8.181
7.214
6.440
5.815
6. 301
4.871
19
45.000
25. 714
18.000
13.846
11.250
9.473
7.200
6.428
6.806
5.294
4.865
20
21
44.444
25. 532
17. 910
13. 793
11. 214
9.448
8.163
7.186
6.417
6.797
6.286
4. 858
21
99
43.902
25. 362
17. 822
13. 740
11.180
9.424
8.144
7.171
6.405
5.787
5.278
4. 851
22
28
43. 373
25. 175
17.734
13. 688
11. 146
9. .399
8.126
7.167
6.394
6.778
5.270
4. 845
23
24
•2:i
42. 857
25.000
17.647
17. 560-
13. 636
11.111
11.077
9.376
8. 108 i 7. 142
6.383
6.769
5.263
4.838
24
42. 353
24. 828
13. 684
9.350
8.090
7.128
6.371
5.760
5. 2.56
4.832
25
26
41.860
24.658
17. 475 j 13. 6.33
11. 043
9.326
8.071
7.114
6.360
5.750
5.247
4. 825
26
27
41.379
24. 490
17.391 j 13. 483
11.009
9.302
8.053
7.100
6.349
5.741
5.240
4.819
27
28
40. 909
24. 324 117.307 113.433
10. 975
9.278
8.035
7.086
6.338
5. 7.32
5.232
4.812
28
29
30
40. 449
24. 161
17. 225
17. 143
13. 383
10. 942
9.254
8.017
7.072
6.327
6.315
5. 723
5.224
4.806
29
40.000
24.000
13. 333
10.909
9.2301 8.000
7.059
5.714
5.217
4.800
30
31
39.560
23. 841
17.061
13. 284
10. 876
9.207
7.982
7.045
6. .304
5. 705
5.210
4. 793
31
32
39. 130
23,684
16. 981
13. 235
10. 843
9.183
7.964
7.031
6.293
5.696
5.202
4.787
32
33
38. 710
23.529
16. 901
13. 186
10.810
9.1.60
7. 947
7.017
6.282
5.687
5. 196
4.780
33
34
35
38.298
37. 895
23. 377
16. 822
13.138
10. 778
9.137
7.929
7.004
6.271
6.678
6.187
4.774
4. 768
.34
35
23. 226
16.744
13.091
10. 746
9.113
7.912
6.990
6.260
5.669
5.179
36
3». 500
26.077
16. 667
13.043
10. 714
9.090
7.895
6.977
6.260
5.660
5.172
4.761
36
37
37. 113
22. 930
16. 590
12. 996
10. 682
9.068
7.877
6.963
6.239
5. 651
5.164
4. 7.55
37
38
36. 735
22. 785
16. 614
12.950
10. 661
9. 045
7.860
6.950
6.228
5.642
5.157
4.749
38
39
40'
36. 364
22.642
22. .500
16. 438
12. 903
10. 619
9.022
7.843
7. 826
6.936
6.923
6.217
6.207
5.633
5.150
4.743
39
36. 000
16. 363
12. 867
10. 588
9.000
5.625
6.143
4.737
40
41
:i5.644
22. .360 16.289
12. 811
10. .557
8.977
7.809
6.909
6. 196
5.616
5.135
4. 731
41
42
35. 294
22.222 16.216
12. 766
10. .526
8.956
7.792
6.896
6.185
5.607
5. 128
4.724
42
43
34. 951
22. 086
16. 143
12. 721
10.495
8. 933
7. 775
6.883
6.174
5.598
5. 121
4. 718
43
44
45
34. 615
21. 951
16. 071
16.000
12.676
12. 631
10. 465
lO; 4,34
8.911
8.889
7.758
7.741
6.870
6.857
6.164
6.690
5.114
4.712
44
45
34.286
21.818
6.153
6.581
5.106
4.706
46
33. 962
21.687
15.929
12. .587
10. 404
8.867
7.725
6.844
6.143
5.572
5.099
4.700
46
47
33. 645
21.557
15.859
12. ,543
10. 376
8.845
7.708
6.831
6.132
5. ,564
5.091
4.693
47
48
33. 333
21.429
15. 789
12. 500
10. 345
8. 823
7.692
6.818
6.122
5. .5.56
5.084
4.687
48
49
50
33. 028
21. 302
15. 721
15.652
12. 456
12.413
10. 315
8.801
7. 675
7.669
6.805
6. 792
6.112
5.547
5.538
5. 077
4.681
49
50
32. 727
21. 176
10. 286
8.780
6.101
5.070
4.675
51
32. 432
21. 053
15. 584
12. 371
10. 256
8.759
7.643
6.779
6.091
5.530
6.063
4.669
51
52
32. 143
20. 930
15.517
12.329
10. 227
8.737
7.627
6.766
6.081
5.521
5.056
4. 663
52
53
31.868
20.809
16. 450
12. 287
10. 198
8.716
7.611
6.754
6.071
5. 513
5.049
4.&57
53
54
55
31.579
20. 690
20. 571
15.384
15. 319
12.245
12. 203
10. 169
10. 140
8.695
7. 595
6.741
6.060
5.504
5.042
4. 651
4:64'6
54
65
31.304
8.675
7.579
6.739
6.050
5.496
5. 035
56
31.034
20. 455
15. 264
12.162
10.112
8.654
7.563
6.716
6.040
5.487
5.028
4. 6.39
66
57
30. 769
20. 3.39
15. 190
12. 121
10.084
8.633
7.647
6. 704
6.030
5. 479
5.020
4. 633
57
58
30. 508
20. 225
15. 126
12. 080
10. 055
8.612
7.531
6.691
6.020
6.471
5.013
4.627
58
59
30. 252
20. 112
15. 062
12.040
10. 027
8.591
7.516
6.679
6.010
6.463
5.006
4.621
,59
Sec.
Sec.
1
2
3
4
6
7
8
»
10
11
12
TABLE 36. ^ [Page 733
Reduction of Local Mean Time to Standard Meridian Time, and the reverse.
[If local meridian is east of standard meridian, subtract fromlocalmean time, oradd to standard meridian time. If local
meridian is west of standard meridian, add to local mean time, or subtract from standard meridian time.]
Difference of longitnde be-
Reduction to
be applied
to local mean
time.
DitTerence of longitude be-
Reduction to
be applied
to local mean
time.
tween Itx^al meridian and
tween local meridian and
standard meridian.
standard meridian.
O ' o /
MinuUs.
o / o /
Minutea.
00 to 07
7 23 to 7 37
30
08 to 22
1
7 38 to 7 52
31
23 to 37
2
7 53 to 8 07
32
38 to 52
3
8 08 to 8 22
33
53 to 1 07
4
8 23 to 8 37
34
1 08 to 1 22
5
8 38 to 8 52
35
1 23 to 1 37
6
8 53 to 9 07
36
. 1 38 to 1 52
7
9 08 to 9 22
37
1 53 to 2 07
8
9 23 to 9 37
38
2 08 to 2 22
9
9 38 to 9 52
39
2 23 to 2 37
10
9 53 to 10 07
40
2 38 to 2 52
11
10 08 to 10 22
41
>
2 53 to 3 07
12
10 23 to 10 37
42
3 08 to 3 22
13
10 38 to 10 52
43
3 23 to 3 37
14
10 53 to 11 07
44
3 38 to 3 52
15
11 08 toll 22
45-
3 53 to 4 07
16
11 23 to 11 37
46
4 08 to 4 22
17
11 38 to 11 52
47
4 23 to 4 37
18
11 53 to 12 07
48
4 38 to 4 52
19
12 08 to 12 22
49
4 53 to 5 07
20
12 23 to 12 37
50
5 08 to 5 22
21
12 38 to 12 52
51
5 23 to 5 37
22
12 53 to 13 07
52
5 38 to 5 52
23
13 08 to 13 22
53
5 53 to 6 07
24
13 23 to 13 37
54
« 08 to 6 22
25
13 38 to 13 52
55
6 23 to 6 37
26
13 53 to 14 07
56
6 38 to 6 52
27
14 08 to 14 22
57
6 53 to 7 07
28
14 23 to 14 37
58
7 08 to 7 22
29
14 38 to 14 52
59
Page 734]
TABLE 37.
Log. A and Log. B.
For Computing the Equation of Equal Altitudes. For Noon, A-; for Midnight, A+;
Argiiment=Elapsed Time.]
for Noon or Midnight
, B + .
1o
O'
Ik
2'
8'
4k
S
h
Log. A.
Log. B.
Log. A.
Log. B.
Ix>g. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log.B.
VI.
9. 40.59
9. 4059
9. 4072
9.4034
9.4109
9. 39.59
9. 4172
9. 3828
9.4260
9. 3635
9. 4374
9. ;-i369
1
.4059
.4059
.4072
.4034
. 4110
. 3957
.4173
. 3825
.4261
.3631
. 4376
. 33()4
2
.4059
.4059
.4073
. 4033
.4111
. 39.55
.4174
. 3822
.4263
.3627
.4378
. 3358
3
.4059
.4059
.4073
.4032
.4112
.3953
.4175
.3820
.4265
. .3624
.4380
. 3353
4
5
.4059
. 4059
.4074
.4031
9. 4030
. 4113
. 3952
.4177
9.4178
.3817
9. 3814
.4266
9. 4268
.3620
9. 3616
.4383
. 3.348
9.4059
9. 4059
9. 4074
9.4113
9. 39.50
9. 4385
9. 3343
6
.4060
.4059
.4074
.4029
.4114
. 3948
.4179
.3811
.4270
. .3612
.4387
. 3337
7
.4060
. 4059
.4075
. 4028
.4115
.3946
.4181
.3809
,4272
.3608
.4389
. 3.332
8
.4060
.4059
. 4075
.4027
.4116
.3944
.4182
. 3806
.4273
.3604
. 4391
. .3327
9
10
.4060
.4059
.4076
.4026
9. 4025
.4117
9. 4118
. 3943
9. 3941
.4183
.3803
9.3800
.4275
9. 4277
.3600
9. 3596
. 4393
9.4396
. 3221
9.3316
9.4060
9. 4059
9. 4076
9. 4184
11
.4060
. 4059
.4077
.4024
.4119
. 3939
.4186
.3797
. 4279
.3592
.4398
.3311
12
.4060
. 4058
.4077
. 4023
.4120
. 3937
.4187
. 3794
.4280
.:io88
.4400
. :!.305
13
.4060
. 4058
.4078
.4022
.4121
. 3935
.4188
.3792
.4282
.3584
.4402
. 3300
14
15
.4060
9. 4060
.4056
9. 4058
.4078
.4021
.4121
.3933
9: 393f
. 4190
9. 4191
. 3789
9;378([
.4284
9.4286
..3580
9.3.576
.4405
9. 4407
. 3294
9.3289'
9. 4079
9. 4020
9.4122
16
.4060
. 4058
.4079
.4019
.4123
. 3929
.4193
. 3783
.4288
.3572
.4409
. 3283
17
,4060
. 4057
. 4080
. 4018
. 4124
. 3927
.4194
. 3780
.4289
. 3.568
.4411
. 3278
18
.4061
.4057
. 4080
.4017
.4125
. 3925
.4195
. 3777
.4291
.3564
.4414
. 3272
19
20
.4061
. 4057
.4081
.4016
9. 4015
.4126
9.4127
. 3923
9. 3921
.4197
9. 4198
. 3774
9.3771
.4293
9.4295
.35.59
.4416
9. 4418'
. 3266
9.' 3261
9. 4061
9. 4057
9.4081
9. 3555
21
.4061
.4056
.4082
.4014
.4128
. 3919
.4199
. 3768
.4297
. .3551
.4420
. ■■y2r>r)
99
.4061
.4056
.4083
.4013
.4129
. 3917
.4201
. 3765
. 4299
. 3547
. 4423
. .3249
23
.4061
.4056
. 4083
.4012
.4130
. 3915
. 4202
. 3762
.4300
. 3542
.4425
. 3244
24
25
.4061
9. 4062
.4055
.4084
.4010
9.4009
.4131
9. 4132
. 3913
.4204
9. 4205
. 3759
9. 3756
.4302
. 3538
.4427
9. 44'30
. 32;i8
9.3232
9. 4055
9.4084
9. 3911
9. 4304
9.3534
26
.4062
. 4055
.4085
.4008
.4133
..3909
.4207
.3752
.4306
.3530
. 4432
. 3226
27
.4062
.4054
. 4086
.4007
.4134
. 3907
. 4208
. 3749
.4308
.3525
.4434
. 3220
28
.4062
.4054
. 4086
.4006
.4135
.3905
.4209
.3746
.4310
. 3521
. 4437
. 3214
29
3b"
.4062
9. 4062
.4054
.4087
9.4087
.4004
9. 4003
.4136
. .3903
.4211
.3743
.4312
. 3516
.4439
. 3208
^9. 320:!
9. 4053
9. 4137
9.3900
9. 4212
9. 3740
9. 4314
9. 3512
9. 4441
31
.4063
.4053
.4088
.4002
.4138
.3898
.4214
.3737
.4315
.3508
.4444
. 3197
32
.4063
.4052
.4089
.4001
.4139
.3896
. 4215
.3733
.4317
..3503
.4446
.3191
33
.4063
. 4052
.4089
.3999
.4140
.3894
.4217
.3730
.4319
.;«99
.4448
. 3185
34
35
.4063
.4051
.4090
.3998
.4141
.3892
9. ,3889
.4218
9. 4220
.3727
9:3723
.4321
9. 4323
.3494
9.3490
. 4451
. 3178
'9.3172
9.4064
9. 4051
9.4091
9. 3997
9. 4142
9. 4453
36
.4064
. 40.50
.4091
. 3995
.4144
. 3887
.4221
.3720
. 4325
. 3485
. 4456
. 3166
37
.4064
. 4050
.4092
.3994
. 4145
. .3885
.4223
.3717
.4327
.3480
. 4458
. 3160
38
.4064
.4049
.4093
. 3993
. 4146
. 3882
.4224
. 3713
.4329
.3476
. 4460
. 3154
39
40"
. 4065
.4049
9. 4048
.4093
. 3991
.'4147
9. 4148
.3880
9. 3878
.4226
.3710
9. 3707
.4331
9. 4333
.3471
.4463
. 3148
9.4065
9. 4094
9. 3990
9. 4227
9. 3467
9.4465
9. 3142
41
.4066
.4048
.4095
.3988
.4149
. 3875
.4229
. 3703
.4335
.3462
.4468
.3ia5
42
.4065
.4047
. 4095
. .3987
.4150
. 3873
. 4231
.3700
.4337
. 3457
. 4470
.3129
43
.4066
.4047
.4096
. 3985
.4151
.3871
.4232
.3696
.4339
. .3453
. 4473
. 3123
44
15'
»4066
.4046
.4097
.3984
.4152
9. 4154"
.3868
.4234
. 3693
.4341
9. 4.343
.3448
.4475
.3116
9:3110
9. 4066
9.4045
9.4097
9. 3982
9. 3866
9.4235
9.3690
9.3443
9. 4477
46
.4067
.4045
.4098
. 3981
.4155
.3863
. 4237
. 3686
. 4.345
. 3438
.4480
.3103
47
.4067
.4044
.4099
. 3979
.4156
.3861
.4238
.3683
. 4,347
. 3433
.4482
.3097
48
.4067
.4043
.4100
.3978
.4157
.3859
.4240
. 3679
.4349
, .3429
.4485
.3091
49
50
.4068
.4043
.4100
.3976
9.3975
.4158
.3856
9.3854
.4242
9. 4243
. 3675
9.3672
.4351
'9. 4353
.3424
.4487
.3084
9. :m»
9. 4068
9. 4042
9.4101
9. 4159
9. 3419
9.4490
51
.4068
.4041
.4102
. 3973
.4161
.3851
.4245
.3668
.4355
.3414
. 4492
. .3071
52
.4069
.4041
.4103
.3972
.4162
.3849
.4246
.3665
.4.357
..3409
.4494
. 3064
53
.4069
.4040
.4103
.3970
.4163
-.3846
.4248
.3661
. 4.359
..3404
.4497
. .3058
54
55'
.4069
.4039
9. 4038
.4104
9. 4105
.3969
.4164
.3843
973841
.4250
9. 4251
..3657
9. 3654'
.4361
9. 4363'
.3399
9.'3394
.4.500
. 3051
9. 4070
9. 3967
9. 4165
9. 4503
9. 3044
56
.4070
.4038
.4106
.3965
.4167
.3838
.4253
.3650
.4366
.3389
.4505
. 3038
57
.4071
.4037
.4107
.3964
.4168
.3836
. 4255
.3646
.4368
. 3384
. 4508
. 3031
58
.4071
. 4036
.4107
. .3962
.4169
. .38,33
. 4256
. .3643
. 4370
.3379
. 4510
. 3024
59
60
.4071
. 4035
9.4034
.4108
9. 4109
.3960
9. 3959
.4170
9.4172
. 38.30
.4258
. 3639
9. 36.35
.4372
9. 4374
. 3374
.4513
9.4515
.3017
9. 4072
9. 3828
9.4260
9. 3369
9. .3010
TABLE 37.
[Page 735
Log. A and Log. B.
For Computing the Equation of Equal Altitudes. For Noon, A—; for Midnight, A+;
for Noon or Midnight, B+. [
Argument=Elapsed Time.]
J
1.-
6
h
'
h
SI'
»i>
lOk
ii' 1
Log. A.
Log.E.
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log.B.
9. 4515
9. 3010
9.4685
9. 2530
9.4884
9. 1874
9.5115
9. 0943
9. 5379
8. 9509
9. 5680
8. 6837
]
.4518
.3003
.4688
. 2520
.4888
.1861
,5119
.0925
.5384
.9478
5685
,6770
2
.4521
. 2996
.4691
.2511
. 4893
.1848
.5123
.0906
. 5389
.9447
5691
,6701
S
.4523
.2989
.4694
. 2502
. 489i
.1835
.5127
.0887
.5393
.9416
,569€
. 6632
4
.4526
.2982
.4697
.2492
.4899
.1822
9.1809
.5132
9. 5136
.0867
9. 0848
.5398
.9384
.5701
9. 5707
. 6560
8,6488
9.4528
9. 2975
9. 4701
9. 2483
9. 4902
9. .5403
8.9352
fi
.4531
.2968
.4704
.2473
. 4906
. 1796
.5140
.0828
.5408
.9320
.5712
.6414
7
.4534
.2961
.4707
. 2463
.4910
.1782
.5144
.0809
. .5412
.9287
.5718
. 6339
s
.4536
.29.54
.4710
. 2454
.4913
.1769
.5148
.0789
..5417
. 9254
.5723
.6262
9
10
.4539
.2947
.4713
.2444
.4917
.1756
. 5153
.0769
.5422
9. 5427
. 9221
8.9187
.5728
.6183
9. 4542
9.2940
9. 4716
9. 24:i4
9. 4921
9. 1742
9. 5157
9. 0749
9.5734
8. 6103
n
.4544
. 2932
.4719
. 2425
.4924
.1728
. 5161
.0729
..5432
.9153
.5739
.6021
12
. 4.547
.2925
.4723
.2415
.4928
. 1715
. 5165
.0708
. 5436
.9118
. 5745
. ,5937
i:!
.4550
.2918
.4726
.2405
.4932
.1701
.,5169
.0688
. 5441
.9083
.5750
. 5852
1-i
15
. 4552
9. 4555
.2911
9. 2903
.4729
9. 4732
. 2395
.4935
9. 4939
.1687
.5174
.0667
.5446
.9048
. 5756
..5764
9.2385
9. 1673
9. 5178
9. 0646
9. 5551
8. 9013
O.STjI
8. 5674
16
. 4558
.2896
.4735
.2375
. 4943
.1659
.5182
.0625
. 5456
.8977
. 5767
. 5583
17
.4561
.2888
. 4738
. 23a5
.4946
.1645
.5186
.0604
. .5461
. 8940
. 5772
.5488
18
.4563
.2881
.4742
.2:555
.4950 .1630
. 5191
. 0583
. 5466
. 8903
.5778
. 5392
19
20
. 4.566
9. 4.569
.2873
'9. 28'66
.4745
.2344
.4954
.1616
9. 1602
. 5195
9.5199
.0561
9. 0.540
.5470
.8866
'8. 88'29"
.5783
..5293
8.5192
9. 4748
9. 2:i34
9. 4958
9. .5475
9. 5789
21
. 4572
.2858
.4751
. 2324
.4961
.1587
. 5204
. 0518
.5480
.8791
.5794
. 5088
22
. 4574
. 2850
. 47.55
. 2313
. 4965
. 1573
. 5208
. 0496
.5485
. 8752
.5800
.4981
2:!
. 4577
. 2843
. 4758
.2303
.4969
. 1558
.5212
.0474
. 5490
. 8713
.5806
.4871
24
25
.4.580
. 2835
.4761
9.4764
.2292
. 4973
. 1543
. 5217
9. 522f
. 0452
9.0429'
. 5495
.8674
8.8634
..5811
.4758
9.4583
9. 2827
9. 2282
9.4977 9.1528
9.5.500
9. 5817
8.4641
26
. 4585
.2819
.4768
.2271
. 4980 . 1513
. 5225
.0406
.5505
. 8,594
. .5822
.4521
27
. 4588
.2812
.4771
.2261
. 4984 . 1498
. 52.30
. 0383
. .5510
. 8,553
.5828
. 4397
28
. 4.591
.2804
.4774
.2250
. 4988 : . 1483
. 5234
. 0360
. .5515
.a5i2
.5834
. 4270
29
30
.4,594
9. 4597
.2796
9. 2788
.4778
. 2239
.49921 .1468
9. 4996 , 9. 1453
. 5238
9. 5243
. 0337
9. 0314
.5520
9. 5525'
.8470
.5839
. 4138
9. 4781
9. 2228
8. 8427
9. 5845
8. 4001
31
.4600
.2780
.4784
.2217
.,5000
. 1437
. 5247
.0290
. .5530
. 8384
. 5851
. 3860
32
.4602
. 2772
.4788
.2206
. 5003
.1422
. 5252
.0266
. 5535
. 8341
..5856
. 3713
33
. 4()05
.2764
.4791
.2195
.5007
.1406
.5256
.0242
. 5.540
.8297
. 5862
.,3561
34
35
. 4608
9.4611
. 27.56
9.2747
.4794
9.4798
. 2184
9. 2173
. .5011
.1390
5261
.0218
9. 0194
. 5545
'9. .55.50
.8253
.5868
. 3403
8. 3239
9. 5015
9. 1375
9. 5265
8. 8208
9. 5874
36
.4614
. 2739
.4801
.2162
.,5019
.1359
.5269
.0169
. .5555
.8162
.5879
. 3067
37
.4617
.2731
.4804
.2151
. .5023
.1343
.5274
.0144
. 5.560
.8115
. 5885
. 2888
38
.4620
.2723
.4808
.2140
.5027
.1327
. 5278
.0119
. 5.565
.8068
.5891
.2701
39
40
.4622
9. 4625
.2714
9. 2706
.4811
9.4815
.2128
.5031
.1310
9. 1294
. .5283
.0094
. 5570
9. .5576
.8020
. 5897
. 2505
8. 2299
9.2117
9. .50.35
9. 5287 i 9. 0069
8. 7972
9. ,5902
41
. 4628
. 2698
.4818
. 2105
. .5038
.1278
. 5292
.(X)43
. 5581
.7923
.5908
. 2082
42
. 4631
.2689
.4821
.2094
..5042
.1261
. 5296
.0017
. .5586
.7873
. .5914
. 1853
43
. 46.34
.2681
.4825
.2082
.5046
.1244
. 5301
8. 9991
. 5591
. 7823
.5920
. 1611
44
45
. 4637
9. 4640
.2672
.4828
.2070
9.2059
. ..5050
9. .50.54
.1228
. 5305
.9965
8. 9938
. ,5596
9. 5601
.7772
.5926
. 1.354
9.2(564
9. 4832
9. 1211
9. .5310
8. 7720
9. ,5931
8. 1080
46
.4643
.2655
. 48*5
.2047
.5058
.1194
.5315
. 9911
.5606
.7668
. 5937
.0786
47
.4(U6
.2646
. 4839
.2035
..5062
.1177
. 5319
.9884
.5612
.7614
.5943
.0470
48
.4649
.2638
.4842
.2023
..5066
.1159
.5324
.98.57
. ,5617
.7.560
.5949
.0128
49
50
. 4652
9. 46.55
.2629
9.2620
.4846
.2011
9."l9i>9
. .5070
.1142
. 5328
9.'.5333
.9830
8. 9802
.5622
9. .5627
.7.505
. .59.55
7. 9756
9.4849
9. 5074
9. 1125
8. 7449
9. 5961
7. 9348
51
.46.58
.2611
. 4853
.1987
. .5078
.1107
. 5337
.9774
.5632
.7392
. .5967
.8897
52
. 4661
.2602
.4856
.1974
.5082
.1089
. .5342
.9745
.5638
.7335
. ,5973
. 8391
53
.4664
. 2.593
.4860
.1962
.5086
.1072
.5347
.9717
.5643
.7276
.5979
.7817
54
.4667
.2.584
9. 2575
.4863
"9. 4867
. 19.50
9. 1937
.5091
.1054
.5^51
.9688
8.9659
..5648
9.'5654"
.7217
8. 71.56'
.,5985
.7154
55
9. 4670
9.5095
9. 1036
9.5356
9. ,5991
7.6368
56
. 4673
.2566
.4870
.1925
.5099
.1017
. ,5361
.9630
. .5659
.7094
.5997
.5405
57
.4676
. 2.557
.4874
.1912
.5103
.0999
.5365
.9600
. 5664
.7032
.6003
.4162
58
.4679
.2548
.4877
.1900
. 5107
.0981
.5370
.9570
. 5669
.6968
.6009
.2407
59
60
.4682
. 2539
.4881
.1887
.5111
.0962
. 5375
.9540
. ,5675
'9. .5680
.6903
8."6837
.6015
9.6021
6. 9591
Inf.
9. 4685
9. 2530
9. 4884
9. 1874
9.5115
9. 0943
9. .5379
8. 9.509
Page 736]
TABLE 37.
Log. A and Log. B.
[For Computing the Equation of Equal Altitudes. For Noon, A -; for Midnight, A +;
Argument = Elapsed Time.l
for Noon or Midnight, B - .
^:B
lat
IS"-
Ilk
loi-
IB'
i;!- 1
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log.B.
m.
9. 6021
Inf.
9.6406
8. 7563
9. 6841
9.0971
9. 7333
9. 3162
9. 7895
9. 4884
9. 8539
9. 6383
1
.6027
6. 9603
.6412
.7641
.6848
.1014
. 7342
.3194
.7905
.4911
.8550
.6407
.6033
7. 2431
.6419
.7718
.6856
.1057
. 7351
. 3225
.7915
.4937
.8562
.6431
8
.6039
.4198
.6426
.7794
.6864
.1099
. 7360
. 3256
. 7925
.4963
.8573
.6455
4
5
.6045
.5453
.6433
.7868
.6872
.1141
.7369
.3287
9.3319
.f935
9. 7945
.4990
.8585
'9. 8597
.6478
9. 6051
7.6428
9.6440
8. 7942
9. 6879
9. 1183
9. 7378
9. 5016
9. 6502
6
.6057
.7226
.6447
.8015
.6887
.1224
. 7386
.3350
.7955
.5042
.8608
.6526
7
.6063
.7902
.6454
.8087
.6895
.1265
. 7395
.3380
.7965
. 5068
.8620
.6550
S
.6069
.8488
.6461
.8158
. 6903
.1306
.7404
. 3411
.7975
.5094
.8632
.6573
9
10
.6075
.9005
.6467
. 8227
.6911
.1:347
.7413
.3442
9. U72
.7986
9.7996
.5120
.8644
.6597
9. 6621
9. 6082
7. 9469
9.6474
8. 8296
9. 6919
9. 1387
9. 7422
9. 5146
9. 8655
n
.6088
.9889
.6481
.8364
. ()926
.1428
. 7431
. .3503
.8006
. 5171
. 8667
.6644
V?
.6094
8. 0273
.6488
.8432
•. mu
.1468
.7440
.3533
.8016
.5197
.8679
.6668
v.\
.6100
.0627
.6495
.8498
.6942
.1507
.7449
. 3563
.8027
. 5223
.8691
.6691
14
15
.6106
.0955
.6502
.8564
8?8628
.6950
9. 6958
.1547
.7458
.3593
9. 3623
. 8037
'9. 8047
.5248
.8703
.6715
9. 67'38
9. 6112
8.1260
9.6509
9. 1586
9. 7467
9. 5274
9.8715
16
.6119
.1547
.6516
.8692
.6966
.1625
.7476
.3653
. 80.58
.5300
.8727
.6762
17
.6125
.1816
.6523
.8756
.6974
.1664
.7485
.3683
.8068
. 5325
.8739
.6785
1S
.6131
.2071
.6530
.8818
.6982
.1703
.7494
.3713
.8078
. 5351
. 8751
.6809
19
.6137
.2312
.6538
.8880
8. 8941
.6990
9^6998
.1741
. 7503
. 3742
9:3772"
.8089
9.8099
.5376
9. 5401
. 8763
9:8775'
.6832
9.6144
8. 2541
9. 6545
9. 1779
9. 7512
9. 6856
1>1
.6150
.2759
.6552
.9002
.7006
.1817
.7522
. 3801
.8110
.5427
.8787
.6879
•?:?.
. 6156
.2967
.6559
.9062
.70141 .1855
. 7531
.3831
. 8120
. .5452
. 8799
. 6903
S.S
.6163
.3166
.6566
.9121
.7022
. 1893
.7.540
. 3860
. 8131
.5477
.8812
.6926
24
.6169
.3357
.6573
9.6580
.9180
8. '9238
. 7030
9.7038
.1930
.7549
.3889
9: 3918
.8141
9. 8152
. 5502
9.5528
.8824
.6949
9: 6973
25
9. 6175
8.3540
9. 1967
9. 7558
9. 8836
26
.6182
.3717
.6588
.9295
.7047
.2004
.7568
.3947
.8162
.5553
.8848
.6996
27
.6188
.3887
.6595
. 9352
. 7055
.2041
. 7577
. 3976
.8173
.5578
.8861
.7019
28
.6194
.4051
.6602
.9408
. 7063
.2078
. 7.586
.4005
.8184
.,5603
. 8873
.7043
29
30
.6201
.4210
.6609
.9464
8. 9519
.7071
9.7079
.2114
9.2150
. 7595
9:7605
.4033
9. 4062
.8194
9.8205'
. 5628
.8885
.7066
9. 6207
8. 4363
9. 6616
9. 5653
9. 8898
9. 7089
31
.6214
. 4512
.6624
. 9573
. 7088
.2186
.7614
.4090
. 8216
.5677
.8910
.7112
32
.6220
.4657
.6631
. 9627
.7096! .2222
.7624
.4119
. 8227
.5702
. 8923
. 7136
33
.6226
.-479(1
. (5638
. 9681
.7104
.2258
.7633
.4147
.8237
.5727
. 89.35
.7159
34
,35
.6233
. 4i):',L'
. (liil.")
y. 6653
. 9734
8.9787
.7112
. 2293
.7642
.4175
9. 4204
.8248
'9:8259
.5752
.8948
9. 8961
.7182
9. 7205
9. 6239
8. 5064
9.7121
9. 2329
9. 7652
9. 5777
36
.6246
.5192
.6660
. 9839
.7129
.2.364
.7661
.4232
.8270
. 5801
. 8973
.7228
37
.6252
.5318
.6667
. 9891
. 7137
.2399
.7671
.4260
.8281
. 5826
. 8986
.7251
3H
.6259
.5440
.6675
.9942
.7146
. 24;«
.7680
.4288
.8292
.5850
.8999
.7275
39
40
.6265
. 5559
.6682
.9993
. 7154
.2468
.7690
.4316
.8303
'9:8314'
. 5875
.9011
.7298
9. 6272
8. 5675
9. 6690
9. 0043
9. 7162
9. 2503
9. 7699
9.4343
9. .5900
9. 9024
9. 7321
41
.62791 .5788
.6697
.0093
.7171
.2537
.7709
.4371
.8325
.5924
. 9037
.7344
42
. 6285 . 5899
.6704
.0142
.7179
.2571
.7718
.4399
.8336
.5948
. 90.50
.7367
43
.6292; .6008
.6712
.0191
.7187
.2605
.7728
.4426
.8347
.5973
. 9063
.7390
44
45
.6298
.6114
8. 6218
.6719
.0240
.7196
. 2639
'9. 2673
.7738
9. 7747
.4454
.8358
.5997
9:6022
. 9075
9. 9088
.7413
9. 7436
9. 6305
9. 6727
9. 0288
9. 7204
9.4481
9. 8369
46
.6311
. 6320
.6734
.0336
.7213
.2706
. 7757
.4.509
. 8380
.6046
.9101
.74.59
47
.6318
.6419
.6742
.0384
.7221
.2740
.7767
. 4536
. 8391
. ()070
.9114
.7482
48
.6325
.6.517
.6749
.0431
.7230
.2773
.7776
.4563
.8402
.6094
.9127
.7505
49
50
.6331
.6613
8. 6707
.6757
.0478
9. 0524
.7238
.2806
.7786
.4590
.8414
.6119
.9140
.7529
9. 6338
9. 6764
9. 7247
9. 2839
9. 7796
9. 4617
9.8425
9. 6143
9.9154
9. 7552
51
.6345
.6799
.6772
.0570
.7256
.2872
.7806
.4644
.8436
.6167
.9167
.7575
52
.6351
.6890
.6779
.0616
.7264
.2905
.7815
.4671
.8447
.6191
.9180
.7598
53
.6358
.6979
.6787
.0662
.7273
.2937
. 7825
.4698
.8459
.6215
.9193
.7621
54
55
.6365
9. 6372
.7067
8. 7153
.6795
.0707
.7281
.2970
.7835
.4725
.8470
. 62.39
.9206
.7644
9. 6802
9. 0752
9.7290
9. 3002
9.7845
9. 4752
9. 8481
9. 6263
9. 9220
9.7667
56
.6378
.7237
.6810
.0796
.7299
. 30.34
. 7855
.4778
. 8493
.6287
. 9233
.7690
57
.6385
.7321
.6818
.0840
. 7307
. 3066
.7865
.4805
.8504
.6311
.9246
.7713
58
. 6392
.7402
.6825
.0884
.7316
.3098
.7875
.4831
.8516
.6335
.9260
.7736
59
.6399
. 7483
.6833
.0928
.7324
. 3130
.7885
.4858
.8527
9.8539
. 6.359
9. 6383
. 9273
.7759
60
9.6406
8. 7563
9.6841
9.0971
9. 7333
9. 3162
9. 7895
9.4884
9. 9287
9. 7782
TABLE 37.
[Page 737
Log. A and Log. B.
[For Computing the Equation of Equal Altitudes. For Noon, A — ; for Midnight, A + ;
for Noon or Midnight, B ^. \
Argument => Elapsed Time.]
Is
IS*
19"
20'
21i>
22h
231. 1
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log.B.
0.0625
Log. A.
Log.B.
Log. A.
Log.B.
Log. A.
Log.B.
9. 9287
9. 7782
0. 0172
9. 9167
0. 1249
0. 2623
0. 2279
0. 4523
0. 4372
0. 7689
0.7652
1
.9300
.7804
.0188
.9190
.1269
.0650
.2649
. 2309
.4562
.4414
.7765
.7729
2
.9314
.7827
.0204
.9213
.1290
.0676
.2676
.2339
.4601
.4455
.7842
.7807
3
.9327
.7850
.0221
.9237
.1310
.0701
.2702
.2370
.4640
.4497
.7920
.7886
4
.9341
.7873
.0237
.9260
.1330
0.1351
.0727
0. 0753
.2729
.2401
.4680
.4540
0. 4582
.8000
.7967
5
9. 9355
9. 7896
0. 0253
9. 9284
0. 2756
0. 2431
0. 4720
0. 8081
0. 8049
6
.9368
.7919
.0270
.9307
.1371
.0779
.2783
.2462
.4761
.4625
.8163
.8133
7
.9382
.7942
.0286
.9331
.1392
.0805
.2810
.2493
.4801
.4668
.8247
.8218
8
.9396
.7965
.0303
.9355
.1412
.0830
.2838
.2524
.4842
.4711
.8333
.8305
9
.9410
.7988
.0319
.9378
9. 9402
.1433
.0856
0.0882
.2865
0. 2893
.2556
0. 2587
.4884
.4755
.8420
.8393
10
9. 9424
9. 8011
0. 0336
0. 1454
0. 4926
0.4799
0.8508
0.8483
11
.9437
.8034
. 0.353
.9426
.1475
.0909
.2921
.2619
.4968
.4844
.8599
.8574
12
.9451
.8057
.0370
.9449
.1496
.0935
.2949
.2650
.5010
.4889
.8691
.8667
13
.9465
.8080
.0386
.9473
.1517
.0961
.2977
.2682
.5053
.4934
.8786
.8763
14
.9479
.8103
. 0403
0.0420
.9497
.1538
0. 1559
.0987
.3005
.2714
0. 2746
.^097
0. 5140
.4980
.8882
0. 8980
.8860
15
9. 9493
9. 8126
9. 9520
0. 1013
0. 3034
0. 5026
0. 8959
16
.9508
.8149
.0437
.9544
.1581
.1040
.3063
.2778
.5184
.5072
.9080
.9060
17
.9522
.8172
.0454
.9568
.1602
.1066
.3091
.2811
.5229
.5118
.9183
.9164
18
.9536
.8195
.0472
.9592
.1623
.1093
.3120
.2843
.5274
.5165
.9288
.9270
19
20
.9550
9.9564
.8218
.0489
.9616
.1645
.1119
. 3150
.2876
0. 2909
.5319
.5213
.9396
.9378
9. 8241
0. 0506
9. 9640
0.1667
0. 1146
0. 3179
0. 5365
0. 5261
0.9506
0. 9489
21
. 9579
.8264
. 0523
.9664
.1689
.1173
.3208
.2942
.5411
.5309
.9618
.9603
22
. 9593
. 8287
.0541
.9687
.1711
.1200
.3238
.2975
. 5458
.5358
.9734
.9719
23
.9607
.8310
.0558
.9711
.1733
.1226
.3268
.3008
.5505
.5407
.9853
.9839
24
25
.9622
.8333
. 0576
. 9735
.1755
.1253
.3298
0. 3328
.3041
0. 3075
.5553
0.5601
.5457
.9975
.9961
9. 9636
9. 8356
0. 0593
9. 9760
0. 1777
0. 1280
0. 5507
1.0100
1.0087
26
.9651
. 8379
.0611
.9784
.1799
.1308
.3359
.3109
.5649
.5557
.0228
.0216
27
.9665
.8402
.0628
.9808
.1821
. 1335
. 3389
. 3143
. 5698
.5608
.0361
.0350
28
.9680
.8425
.0646
.9832
.1844
.1362
.3420
.3177
.5748
.5660
.0497
.0487
29
.9695
.8448
.0664
.9856
.1867
0. 1889
.1389
.3451
0.3482
.3211
0. 3245
.5798
"0;5848
.5712
0.5764
.0638
.0628
30
9.9709
9.8471
0.0682
9. 9880
0. 1417
1. 0783
1. 0774
31
.9724
.8494
.0700
.9904
.1912
.1444
.3514
.3280
. 5899
. 5817
.0934
.0925
32
.9739
.8517
.0718
.9929
.1935
.1472
.3545
. 3315
. 5951
.5871
.1089
. 1081
33
.9754
.8540
. 0736
.9953
.1958
.1499
.3577
.3350
.6003
.5925
.1250
.1242
34
35
.9769
.8563
.0754
0. 0772
.9977
.1981
.1527
.3609
0. 3641
. 3385
0.3420
.6056
0.6110
.5979
0. 6034
.1416
.1409
9.9784
9. 8586
0.0002
0.2004
0. 1555
1. 1590
1. 1583
36
.9798
.8609
.0790
.0026
.2028
.1582
.3674
.3456
.6164
.6090
.1770
.1764
37
.9813
.8632
.0809
.0051
.2051
.1610
.3706
.3491
.6218
.6147
.1958
.1952
38
.9829
.8655
.0827
.0075
.2075
.1638
.3739
.3527
.6273
.6204
.2154
.2149
39
.9844
.8678
.0845
.0100
.2098
6. 2122
.1667
.3772
0. 3805
.3563
0.3599
.6329
0.6386
.6261
o: 6319
.2359
.2354
40
9. 9859
9. 8701
0.0864
0. 0124
0. 1695
1. 2573
1. 2569
41
.9874
.8724
. 0883
.0149
.2146
. 1723
.3839
. 3636
.6443
. 6378
.2799
.2795
42
.9889
.8748
.0901
. 0173
.2170
.1751
. 3873
. 3673
.a50i
.6438
.3037
. 3033
43
.9904
.8771
. 0920
.0198
.2194
.1780
. 3907
.3710
.6560
.6498
.3288
.3285
44
45
.9920
9. 9935
.8794
9. 8817
.0939
0. 0958
.0223
.2218
0. 2243
.1808
. 3941
.3747
0. 3784
.6619
. 6559
.3554
. 3552
0. 0248
0. 1837
0. 3975
0. 6679
0. 6621
1. 3837
1. 3835
46
.9951
.8840
.0976
.0272
.2267
.1866
.4010
.3822
.6740
.6684
.4140
.4138
47
.9966
.8863
.0995
.0297
. 2292
.1895
.4045
. 3859
.6802
.6747
.4465
.4463
48
.9982
.8887
. 1015
.0322
.2316
.1924
.4080
.3897
.6865
. 6811
.4815
.4814
49
.9998
.8910
.1034
.0347
.2341
. 1953
.4115
0. 4151
. 3936
0. 3974
.6928
.6876
.5196
.5195
50
0.0013
9. 8933
0. 1053
0. 0372
0. 2366
0. 1982
0. 6993
0. 6942
1. 5613
1.5612
51
.0029
. 8956
.1072
. 0397
. 2.391
.2011
.4187
.4013
.7058
.7008
.6074
.6073
52
.0044
.8980
.1092
.0422
.2416
.2040
.4223
. 4052
.7124
.7076
.6588
.6587
53
.0060
.9003
.1111
.0447
.2442
.2070
.4260
.4091
.7191
.7144
.7171
.7171
54
55
.0076
0. 0092
.9026
.1131
.0473
.2467
0. 2493
.2099
.4297
.4130
0.4170
.7259
.7214
.7844
.7843
9. 9050
0. 1150
0.0498
0.2129
0. 4334
0. 7328
0. 7284
1. 8638
1.8638
56
.0108
.9073
.1170
. 0523
. 2518
.2159
.4371
.4210
.7398
. 7355
.9610
.9610
5V
.0124
.9096
.1190
.0548
.2544
.2189
.4408
.4250
.7469
.7428
2. 0863
2. 0863
58
.0140
.9120
.1209
. 0574
. 2570
. 2219
.4446
.4291
.7541
.7501
.2627
.2627
59
.0156
.9143
.1229
.0599
.2596
.2249
.4485
0.4523
.4331
.7615
.7576
2.5640
2.5640
60
0. 0172
9. 9167
0. 1249
0.0625
0. 2623
0. 2279
0.4372
0.7689
0.7652
Inf.
Inf.
24972°— 12-
-37
Page 738]
TABLE 37A.
Equal Altitudes near Noon.
Factor E=gjS'}
of numbers for LAT. and DEC. of |
Contrary
Same
>
ames.
Latitude.
Declination. 1
Lat.
N.
Lat.
N.
Lat.
N.
Lat.
N.
Lat.
N.
Dec.
N.
Dec.
N.
.000
12 22
.060
23 41
.120
33 21
.180
41 16
.240
.000
12 28
.060
12
.001
12 34
.061
23 52
.121
33 30
.181
41 23
.241
12
.001
12 40
.061
25
.002
12 46
.062
24 2
.122
33 39
.182
41 30
.242
25
.002
12 52
.062
38
.003
12 58
.063
24 13
.123
33 47
.183
41 37
.243
38
.003
13 4
.063
50
.004
13 10
.064
24 23
.124
33 56
.184
41 44
.244
50
"1 3
.004
.005
13 16
13 28
.064
.065
1 3
.005
13 22
.065
24 34
.125
34 4
.185
41 51
.245
1 15
..006
13 34
.066
24 44
.126
34 13
.186
41 58
.246
1 15
.006
13 40
.066
1 28
.007
13 46
.067
24 54
.127
34 22
.187
42 5
.247
1 28
.007
13 52
.067
1 41
.008
13 58
.068
25 5
.128
34 30
.188
42 12
.248
1 41
.008
14 4
.068
1 53
.009
14 10
.069
25 15
.129
34 39
.189
42 19
.249
1 54
.009
14 16
.069
2 6
.010
14 22
.070
25 25
.130
34 47"
. 190"
42 "26
. 250
2 7
.010
14 28
.070
2 18
.011
14 33
.071
25 36
.131
34 56
.191
42 33
.251
2 19
.011
14 39
.071
2 31
.012
14 45
.072
25 46
.132
35 4
.192
42 39
.252
2 32
.012
14 51
.072
2 43
.013
14 57
.073
25 56
.133
35 12
.193
42 46
.253
2 44
.013
15 3
.073
2 56
3" 8
.014
.0i5
15 8
15 20
.074
.075
26 6
26 16
.134
.135
35 21
35 29
.194
42 53
43 b
.254
.255
2 57
3 10
.014
.015
15 15
15 27
.074
.195
.075
3 21
.016
15 32
.076
26 26
.136
35 37
.196
43 6
.256
3 23
.016
15 39
.076
3 33
.017
15 43
.077
26 36
.137
35 46
.197
43 13
.257
3 35
.017
15 50
.077
3 46
.018
15 55
.078
26 46
.138
35 54
.198
43 20
.258
3 48
.018
16 2
.078
3 58
4 il
.019
.020
16 7
.079
.080
26 56
27 6
.139
.140
36 2
.199
.200
43 26
43 33"
.259
. 260
4
4 13
.019
.020
16 14
16 26
.079
16 18
36 11
.080
4 23
.021
16 30
.081
27 16
.141
36 19
.201
43 40
.261
4 25
.021
16 37
.081
4 36
.022
16 41
.082
27 26
.142
36 27
.202
43 46
.262
4 38
.022
16 48
.082
4 48
.023
16 53
.083
27 36
.143
36 35
.203
43 53
.263
4 51
.023
17
.083
5 1
5 13
.024
.025
17 4
17 16
.084
.085^
27 46
27 56
.144
"145
36 43
36 51
.204
.205
43 59
"44" 6
.264
. 265"
5 3
5 16
.024
". 025
17 11
.084
17 23
.085
5 26
.026
17 27
.086
28 6
.146
36 59
.206
44 12
.266
5 29
.026
17 35
.086
5 38
.027
17 39
.087
28 15
.147
37 7
.207
44 19
.267
6 41
.027
17 47
.087
5 51
.028
17 50
.088
28 25
.148
37 15
.208
44 25
.268
5 54
.028
17 58
.088
6 3
.029
18 1
.089
28 35
.149
37 23
.209
44 31
.269
6 7
.029
18 9
.089
6 16
.030
18 13
.090
"28^44"
.150
37 31
.210
44"38
.270
6 19
. 030
18 21
.090
6 28
.031
18 24
.091
28 54
.151
37 39
.211
44 44
.271
6 31
.031
18 32
.091
6 40
.032
18 35
.092
29 4
.152
37 47
.212
44 51
.272
6 43
.032
18 43
.092
6 53
.033
18 47
.093
29 13
.153
37 55
.213
44 57
.273
6 56
.033
18 55
.093
7 5
.034
18 58
19 9
.094
.095
29 23
29 32
.154
38 2
.214
.215
45 3
45" 9
.274
7 9
7 21
.034
19 6
.094
.095
7 17
.035
.155
38 10
.275
.035
19 17
7 30
.036
19 20
.096
29 42
.156
38 18
.216
45 16
.276
7 34
.036
19 28
.096
7 42
.037
19 32
.097
29 51
.157
38 26
.217
45 22
.277
7 46
•.037
19 40
.097
7 55
.038
19 43
.098
30 1
.158
38 33
.218
45 28
.278
7 59
.038
19 51
.098
8 7
.039
.040
19 54
20 5
.099
.100
30 10
30 20
.159
38 41
38 49 .
.219
45 34
.279
8 11
8 23
.039
.040
20 2
.099
8 19
.160
.220
45 40
.280
20 13
.100
8 32
.041
20 16
.101
30 29
.161
38 56
.221
45 46
.281
8 36
.041
20 24
.101
8 44
.042
20 27
.102
30 38
.162
39 4
.222
45 52
.282
8 48
.042
20 35
.102
8 56
.043
20 38
.103
30 48
.163
39 11
.223
45 58
.283
9
.043
20 46
.103
9 8
.044
.045
20 49
21
.104
. 105
30 57
31 6
.164
.165
39 19
39 26
.224
.225
46 5
46 11
.284
.285
9 12
9 25
.044
. 045
20 57
.104
9 21
21 8
.105
9 33
.046
21 11
.106
31 15
.166
39 34
.226
46 17
.286
9 37
.046
21 19
.106
9 45
.047
21 22
.107
31 24
.167
39 41
.227
46 23
.287
9 50
.047
21 30
.107
9 57 ! . 048
21 33
.108
31 34
.168
39 49
.228
46 29
.288
10 2
.048
21 41
.108
10 9 i .049
21 44
21 55
.109
. 110
31 43
"31 52
.169
39 56
40 4
.229
46 35
46 41
.289
10 14
.049
21 52
22 3
.109
.110
10 22
.050
.170
.230
.290
10 27
.050
10 34
.051
22 5
.111
32 1
.171
40 11
.231
46 46
.291
10 39
.051
22 13
.111
10 46
.052
22 16
.112
32 10
.172
40 18
.232
46 52
.292
10 51
.052
22 24
.112
10 58
.053
22 27
.113
32 19
.173
40 26
.233
46 58
.293
11 3
.053
22 35
.113
11 10
11 22
.054
.055
22 38
22 48
.114
.115
32 28
.174
40 33
.234
47 4
.294
11 15
1127"
.054
.055
22 46
2257
.114
32 37
.175
40 40
.235
47 10
.295
.115
11 34
.056
22 59
.116
32 46
.176
40 47
.236
47 16
.296
11 39
.056
23 8
.116
11 46
.057
23 10
.117
32 54
.177
40 55
.237
47 21
.297
11 51
.057
23 19
.117
11 58
.058
23 20
.118
33 3
.178
41 2
.238
47 27
.298
12 3
.058
23 29
.118
12 10
.059
23 31
.119
33 12
.179
41 9
.239
47 33
.299
12 16
.059
23 40
.119
12 22
.060
23 41
.120
33 21
.180
41 16
.240
47 39
.300
12 28
.060
23 50
.120
Eqiiation of E
qual Altitudes
(sec.)=EXreh
itive velority c
f Ship and Sun
(" per hour).
TABLE 38. [Page 139
Error in Longitude due to one minute Error of Latitude.
2
m
Latitude.
10
20
30
40
50
60
10
20
30
40
50
60
0°
5°
10°
15°
20°
25°
80°
85°
40°
45°
50°
65°
60°
65°
70°
75°
o
10
20
30
40
50
60
10
20
30
40
50
60
o
110
f
.4
.4
.4
.5
.7
.9
f
.4
.4
.5
.6
.9
.4
.5
.6
.8
1.2
.5
.6
.7
1.0
.5
.7
.9
1.3
.6
.8
1.1
. 7
1.0
1.5
/
.8
1.2
2.3
1
1.0
1.6
'
1.3
2.6
.9
1.6
1.8
1.2
2.7
2.9
1.8
3.0
1
t
o
110
105
.3
.3
.3
4
4
6
.3
.3
.4
.5
.6
.9
.3
.4
.6
.6
.8
.3
.4
.6
.7
1.2
.4
.5
.7
1.0
.4
.6
.8
1.3
.5
.7
1.1
.6
.9
1.5
.8
1.2
2.4
105
15
20
30
40
50
60
100
2
2
2
2
3
3
.2
.2
.3
.3
.4
.6
.2
.3
.3
.4
.6
.9
.3
.3
.4
.6
.8
.3
.4
.5
.7
1.2
.4
.5
.6
.9
.4
.5
.8
1.3
.5
. 7
1.1
2.1
.6
.9
1.5
.5
.6
1.0
2.1
.4
.7
1.3
.3
.5
.9
2.4
.6
.8
1.5
.6
1.0
2.2
.3
.7
1.3
1.1
1.6
.8
1.1
2.5
.7
1.5
.5
1.0
2.3
1.6
2.7
1.1
1.6
1.1
2.7
.7
1.5
2.9
1.7
2.8
1.6
3.0
3.0
100
15
20
30
40
50
60
35
20
30
40
50
60
95
2
.1
.1
.2
.2
.3
.3
.1
.2
.2
.3
.4
.6
.2
.2
.3
.4
.6
.9
.2
.3
.4
.5
.8
.3
.3
.5
.7
1.1
.3
.4
.6
.9
.4
.5
.8
1.3
.3
.5
.9
95
90
15
20
30
40
50
60
20
30
40
50
60
70
20
30
40
50
60
70
90
.0
.1
.1
.1
.2
.2
.1
.1
.2
.2
.3
.6
.1
.2
.3
.4
.5
1.1
.1
.2
.3
.5
.9
.2
.3
.5
.8
.2
.4
.6
1.1
20
30
40
50
60
70
85
1*
1*
1*
1*
2»
3*
.1*
.0
.0
.0
.0
.0
.0
.0
.0
.1
.1
.2
.0
.1
.1
.2
.3
.6
.0
.1
.2
.3
.5
1.1
.1
.2
.3
.5
.9
.1
.2
.4
.7
.2
.4
.6
1.1
1.0
2.7
1.6
3.1
85
20
30
40
50
60
70
20
30
40
50
60
70
20
30
40
50
60
70
20
30
40
50
60
70
80
75
70
J_
2*
2*
2*
3*
4*
6*
3*
3»
4*
4*
6*
2*
4*
4*
5*
6*
9*
.2*
.2*
.2*
.2*
.2*
.3*
.3*
.3*
.3*
.3*
.4*
.6*
.1*
.1*
.1*
.1*
.0
.0
.2*
.2*
.2*
.2*
.2*
.3*
.1*
.0
.0
.1
.1
.2
.1*
.0
.1
.2
.3
.6
.0
.1
.2
.3
.5
1.2
.0
.1
.3
.5
.9
.0
.2
.4
.7
.1»
.1
.2
.5
.9
.1
.3
.6
1.1
.1*
.1
.4
.7
.2*
.0
.2
.4
.9
.1
.4
.9
.0
.2
.5
1.1
T2*
.0
.3
.7
.2
.6
1.3
.0
.4
.8
.2*
.1
.5
1.1
.4
.9
2.4
.1
.6
1.3
.2*
.2
.8
.5
1.5
.2
.9
2.5
.2*
.6
1.3
.9
2.8
"73"
1.5
.2*
.8
2.6
1.5
.6
3.0
.2*
1.5
3.1
1.2
80
75
20
30
40
50
60
70
20
30
40
50
60
70
.2*
.2*
.1*
.1*
.1*
.0
.2*
.1*
.1*
.0
.1
.2
.1*
.1*
.0
.1
.3
.6
.1*
.0
.1
.3
.5
1.2
.4*
.4*
.4*
.5*
.6*
1.2*
.3*
.3*
.3*
.3*
.4*
.6*
.3*
.3*
.3*
.2*
.3*
.3*
.3*
.2*
.2*
.2*
.1*
.1*
.3*
.2*
.1*
.0
.1
.2
.2*
.1*
.0
.1
.2
.6
.2«
.1*
.1
.3
.5
1.2
.2*
3.1
70
20
30
40
50
60
70
'3 oi
'It
D
*
0°
5°
10°
16°
20°
26°
80°
85°
40°
46°
60°
66°
60°
66°
70°
75°
k
f
Latitude.
Page 740]
TABLE 39.
Amplitudes.
Declination.
Lati-
tude.
Lati-
tude.
©o.O
Oo.S
1°.0
10.5
2=.0
2°. 6
3°.0
3°. 5
i°.0
4°. 5
o°.0
5°. 5
6°.0
o
o
O
o
o
O
o
o
o
o
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
10
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.1
4.6
5.1
5.6
6.1
10
15
0.0
0.5
1.0
1.5
2.1
2.6
3.1
3.6
4.2
4.7
5.2
5.7
6.2
15
20
0.0
0.5
1.1
1.6
2.1
2.7
3.2
3.7
4.3
4.8
5.3
5.8
6.4
20
25
0.0
0.5
1.1
1.6
2.2
2.8
3.3
3.8
4.4
5.0
5.5
6.0
6.6
25
30
0.0
0.6
1.2
1.7
2.3
2.9
3.4
4.0
4.6
5.2
5.8
6.3
6.9
30
32
0.0
0.6
1.2
1.8
2.4
2.9
3.5
4.1
4.7
5.3
5.9
6.5
7.0
32
34
0.0
0.6
1.2
1.8
2.4
3.0
3.6
4.2
4.8
5.4
6.0
6.6
7.2
34
36
0.0
0.6
1.2
1.8
2.5
3.1
3.7
4.3
4.9
5.6
6.1
6.8
7.4
36
38
0.0
0.6
1.3
1.9
2.5
3.2
3.8
4.4
5.1
5.7
6.3
7.0
7.6
38
40
0.0
0.7
1.3
2.0
2.6
3.3
3.9
4.6
5.2
5.9
6.5
7.2
7.8
40
42
0.0
0.7
1.3
2.0
2.7
3.4
4.0
4.7
5.4
6.1
6.7
7.4
8.0
42
44
0.0
0.7
1.4
2.1
2.8
3.5
4.2
4.9
5.6
6.3
6.9
7.6
8.3
44
46
0.0
0.7
1.4
2.2
2.9
3.6
4.3
5.0
5.8
6.5
7.2
7.9
8.6
46
48
0.0
0.7
1.5
2.2
3.0
3.7
4.5
5.2
6.0
6.7
7.5
8.2
9.0
48
50
50
0.0
0.8
1.5
2.3
3.1
3.9
4.7
5.4
6.2
7.0
7.8
8.6
9.3
51
0.0
0.8
1.6
2.4
3.2
4.0
4.8
5.6
6.4
7.2
8.0
8.8
9.5
51
52
0.0
0.8
1.6
2.4
3.3
4.1
4.9
5.7
6.5
7.3
8.1
9.0
9.7
.52
53
0.0
0.8
1.6
2.5
3.3
4.2
5.0
5.8
6.7
7.5
8.3
9.2
10.0
53
54
0.0
0.9
1.7
2.5
3.4
4.3
5.1
6.0
6.8
7.7
8.5
9.4
0.2
54
55
0.0
0.9
1.7
2.6
3.5
4.4
5.2
6.1
7.0
7.9
8.7
9.6
10.5
55
56
0.0
0.9
1.8
2.7
3.6
4.5
5.4
6.3
7.2
8.1
9.0
9.9
0.8
56
57
0.0
0.9
1.8
2.7
3.7
4.6
5.5
6.4
7.4
8.3
9.2
10.1
1.1
57
58
0.0
0.9
1.9
2.8
3.8
4.7
5.7
6.6
7.6
8.5
9.5
0.4
1.4
58
59
60
0.0
0.0
1.0
1.9
2.9
3.9
4.9
5.8
6.8
7.8
8.8
9.7
0.7
1.7
59
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.1
60
61
0.0
1.0
2.1
3.1
4.1
5.2
.6.2
7.2
8.3
9.3
0.3
1.4
2.5
61
62
0.0
1.1
2.1
3.2
4.3
5.3
6.4
7.5
8.5
9.6
0.7
1.8
2.9
62
63
0.0
1.1
2.2
3.3
4.5
5.5
6.6
7.7
8.8
9.9
1.1
2.2
3.4
63
64
0.0
1.1
1.2
2.3
3.4
4.6
5.7
6.9
8.0
9.2
10.3
1.5
2.6
3.9
64
6.5.0
0.0
2.4
3.5
4.8
5.9
7.1
8.3
9.5
10.7
11.9
13.1
14.4
65.0
5.5
0.0
1.2
2.4
3.6
4.8
6.0
7.2
8.5
9.7
0.9
2.1
3.4
4.6
5.5
6.0
0.0
1.2
2.5
3.7
4.9
6.1
7.4
8.6
9.9
1.1
2.4
3.6
4.9
6.0
6.5
0.0
1.2
2.5
3.8
:
6.3
7.5
8.8
10.1
1.3
2.6
3.9
5.2
6.5
7.0
0.0
1.3
2.6
3.8
5.1
6.4
7.7
9.0
0.3
1.6
2.9
4.2
5.5
7.0
67.5
0.0
1.3
2.6
3.9
5.2
6.5
7.9
9.2
10.5
11.8
13.2
14.5
15.9
67.5
8.0
0.0
1.3
2.7
4.0
5.3
6.7
8.0
9.4
0.7
2.1
3.5
4.8
6.2
8.0
8.5
0.0
1.4
2.7
4.1
5.4
6.8
8.2
9.6
1.0
2.4
3.8
5.2
6.6
8.5
9.0
0.0
1.4
2.8
4.2
5.5
7.0
8.4
9.8
1.2
2.6
4.1
5.5
7.0
9.0
9.5
0.0
1.4
2.9
4.3
5.7
7.2
8.6
10.0
1.5
2.9
4.4
5.9
7.4
9.5
70.0
70.0
0.0
1.5
2.9
4.4
5.8
7.3
8.8
10.3
11.8
13.3
14.8
16.3
17.8
0.5
0.0
1.5
3.0
4.5
6.0
7.5
9.0
0.5
2.1
3.6
5.1
6.7
8.2
0.5
1.0
0.0
1.5
3.1
4.6
6.2
7.7
9.3
0.8
2.4
3.9
5.5
7.1
8.7
1.0
1.5
0.0
1.6
3.2
4.7
6.3
7.9
9.5
1.1
2.7
4.3
5.9
7.8
9.2
1.5
2.0
0.0
1.6
3.2
4.9
6.5
8.1
9.8
1.4
3.0
4.7
6.4
8.1
9.8
2.0
72.5
0.0
1.7
3.3
5.0
6.7
8.3
10.0
11.7
13.4
15.1
16.9
18.6
20.3
72.5
3.0
0.0
1.7
3.4
5.1
6.9
8.6
0.3
2.0
3.8
5.5
7.4
9.1
0.9
3.0
3.5
0.0
1.8
3.5
5.2
7.1
8.8
0.6
2.4
4.2
6.0
7.9
9.7
1.6
3.5
4.0
0.0
1.8
3.6
5.4
7.3
9.1
0.9
2.8
4.6
6.5
8.4
20.3
2.3
4.0
4.5
0.0
1.9
3.7
5.6
7.5
9.4
1.3
3.2
5.1
7.1
9.0
1.0
.3.0
4.5
75.0
0.0
1.9
3.8
5.8
7.7
9.7
11.7
13.6
15.6
17.7
19.7
21.7
28.8
75.0
5.5
0.0
2.0
3.9
6.0
8.0
10.0
2.1
4.1
6.2
8.3
20.4
2.5
4.7
5.5
6.0
0.0
2.1
4.0
6.2
8.3
0.4
2.5
4.6
6.8
8.9
1.1
3.3
5.6
6.0
6.5
0.0
2.1
4.2
6.4
8.6
0.8
3.0
5.2
7.4
9.6
1.9
4.2
6.6
6.5
7.0
0.0
2.2
4.4
6.6
8.9
1.2
3.5
5.8
8.1
20.4
2.8
5.2
7.7
7.0
TABLE 39.
[Page 741
Amplitudes.
Declination.
Lati-
tude.
Lati-
tude.
6°.0
6°.. 5
7°.0
7°. 5
8°.0
8°. 5
9°.0
9°. 6
10°.0
10°. 5
11°.0
11°. 5
1S°.0
o
o
°
O
O
o
o
o
o
o
o
o
6.0
6.5
7.0
7.5
8.0
8.5
9.0
9.5
10.0
10.5
11.0
11.5
12.0
10
6.1
6.6
7.1
7.6
8.1
8.6
9.1
9.7
0.1
0.7
1.2
1.7
2.2
10
15
6.2
6.7
7.2
7.8
8.3
8.8
9.3
9.8
0.4
0.9
1.4
1.9
2.5
15
20
6.4
6.9
7.4
8.0
8.5
9.1
9.6
10.1
0.7
1.2
1.7
2.3
2.8
20
25
6.6
7.1
7.7
8.3
8.8
9.4
9.9
0.5
1.1
1.6
2.2
2.8
3.3
25
30
30
6.9
7.5
8.1
8.7
9.3
9.8
10.4
11.0
11.5
12.1
12.7
13.3
13.9
32
7.0
7.7
8.3
8.8
9.5
10.0
0.6
1.2
1.8
2.4
3.0
3.6
4.2
32
34
7.2
7.8
8.5
9.0
9.7
0.3
0.8
1.5
2.1
2.7
3.3
8.9
4.5
34
36
7.4
8.0
8.7
9.3
9.9
0.5
1.1
1.8
2.4
3.0
3.6
4.3
4.9
36
38
7.6
8.2
8.9
9.5
10.2
0.8
1.4
2.1
2.7
3.4
4.0
4.7
5.3
38
40
7.8
8.5
9.1
9.8
10.5
11.1
11.7
12.4
13.1
13.8
14.4
15.1
15.7
40
42
8.0
8.8
9.4
10.1
0.8
1.5
2.1
2.8
3.5
4.2
4.8
5.6
6.2
42
44
8.3
9.1
9.7
0.5
1.1
1.9 i 2.5
3.3
4.0
4.7
5.3
6.1
6.8
44
46
8.6
9.4
10.1
0.8
1.5
2.3 1 3.0
3.8
4.5
5.2
5.9
6.7
7.4
46
48
9.0
9.7
0.5
1.2
2.0
2.8 I 3.5
4.3
5.0
5.8
6.6
7.3
8.1
48
50
9.3
10.1
10.9
11.7
12.5
13.3
14.1
14.9
15.7
16.5
17.3
18.1
18.9
50
51
9.5
0.4
1.2
2.0
2.8
3.6
4.4
5.2
6.0
6.8
7.7
8.5
9.3
51
52
9.7
0.6
1.4
2.2
3.1
3.9
4.7
5.6
6.4
7.2
8.1
8.9
9.7
52
53
10.0
0.8
1.7
2.5
3.4
4.2
5.1
5.9
6.8
7.6
8.5
9.4
20.2
53
54
0.2
1.1
2.0
2.8
3.7
4.6
5.4
6.3
7.2
8.1
8.9
9.8
0.7
54
55
10.5
11.4
12.3
13.1
14.0
14.9
15.8
16.7
17.6
18.5
19.4
20.3
21.2
55
56
0.8
1.7
2.6
3.5
4.4
5.3
6.2
7.2
8.1
9.0
9.9
0.9
1.8
56
57
1.1
2.0
2.9
3.9
4.8
5.8
6.7
7.7
8.6
9.6
20.5
1.5
2.4
57
58
1.4
2.3
3.3
4.3
5.2
6.2
7.2
8.2
9.1
20.1
1.1
2.1
3.1
58
59
1.7
2.7
3.7
4.7
5.7
6.7
7.7
8.7
9.7
20.3
0.7
1.7
2.8
3.8
59
60
60
12.1
13.1
14.1
15.1
16.2
17.2
18.2
19.3
21.4
22.4
23.5.
24.6
61
2.5
3.5
4.6
5.6
6.7
7.8
8.8
9.9
1.0
2.1
3.1
4.3
5.4
61
62
2.9
3.9
5.1
6.1
7.3
8.4
9.4
20.6
1.7
2.9
3.9
5.2
6.3
62
63
3.4
4.4
5.6
6.7
7.9
9.0
20.1
1.3
2.5
3.7
4.8
6.1
7.2
63
64
3.9
5.0
6.2
7.3
8.5
9.7
0.9
2.1
3.3
4.6
5.7
26.8
7.1
8.3
64
65.0
14.4
15.5
16.8
18.0
19.3
20.5
21.7
23.0
24.2
25.6
28.2
29.5
65.0
5.5
4.6
5.8
7.1
8.3
9.6
0.9
2.2
3.5
4.7
6.1
7.4
8.7
30.1
.5.5
6.0
4.9
6.2
7.4
8.7
20.0
1.3
2.6
3.9
5.3
6.6
8.0
9.3
0.7
6.0
6.5
5.2
6.5
7.8
9.1
0.4
1.8
3.1
4.4
5.8
7.2
8.6
30.0
1.4
6.5
7.0
5.5
6.8
8.2
9.5
0.9
2.2
3.6
5.0
6.4
7.8
9.2
0.7
2.1
7.0
67.5
15.9
17.2
18.6
19.9
21.3
22.7
24.1
25.5
27.0
28.4
29.9
31.4
32.9
67.5
8.0
6.2
7.6
9.0
20.4
1.8
3.2
4.7
6.1
7.6
9.1
30.6
2.2
3.7
8.0
8.5
6.6
8.0
9.4
0.9
2.3
3.8
5.3
6.8
8.3
9.8
1.4
3.0
4.6
8.5
9.0
7.0
8.4
9.9
1.4
2.8
4.4
5.9
7.4
9.0
30.6
2.2
3.8
5.5
9.0
9.5
7.4
8.9
20.4
1.9
3.4
5.0
6.5
8.1
9.7
1.4
3.0
4.7
6.4
9.5
70.0
17.8
19.3
20.9
22.4
24.0
25.6
27.2
28.8
30.5
32.2
33.9
35.7
37.4
70.0
0.5
8.2
9.8
1.4
3.0
4.6
6.3
7.9
9.6
1.3
3.1
4.9
6.7
8.5
0.5
1.0
8.7
20.3
2.0
3.6
5.3
7.0
8.7
30.5
2.2
4.0
5.9
7.8
9.7
1.0
1.5
9.2
0.9
2.6
4.3
6.0
7.8
9.5
1.4
3.2
5.0
7.0
8.9
40.9
1.5
2.0
9.8
1.5
3.2
5.0
6.8
8.6
30.4.
2.3
4.2
6.1
8.1
40.2
2.3
2.0
72.5
20.3
22.1
23.9
25.7
27.6
29.5
31.4
33.3
35.3
37.3
39.4
41.5
43.7
72.5
3.0
0.9
2.8
4.6
6.5
8.4
30.4
2.4
4.4
6.5
8.6
40.8
3.0
5.3
3.0
3.5
1.6
3.5
5.4
7.4
9.3
1.4
3.4
5.5
7.7
9.9
2.2
4.6
7.0
3.5
4.0
2.3
4.3
6.2
8.3
30.3
2.5
4.6
6.8
9.1
41^4
3.8
6.3
8.9
4.0
4.5
3.0
5.1
7.1
9.3
1.4
32.5
3.6
5.8
8.2
40.5
3.0
5.6
8.2
51.1
53.5
4.5
7.5.0
23.8
26.0
28.1
30.3
34.8
37.2
39.6
42.1
44.8
47.5
50.4
75.0
5.5
4.7
6.9
9.1
1.4
3.8
6.2
8.7
41.2
3.9
6.7
9.6
2.8
6.2
5.5
6.0
5.6
7.9
.30.2
2.6
5.1
7.7
40.3
3.0
5.9
8.9
52.1
5.5
9.3
6.0
6.5
6.6
9.0
1.4
4.0
6.6
9.3
2.1
5.0
8.1
51.3
4.8
8.7
63.0
6.5
7.0
7.7
30.2
2.8
5.5
8.2
41.1
4.1
7.2
50.5
4.1
8.0
62.4
7.6
7.0
Page 742
TABLE 39.
Amplitudes.
Lati-
tude.
Declination.
Lati-
tude.
12°.0
12°, 6
18°.
18°. 5
14°.0
14°. 5
15°.0
lo°.o
16°. \
16°. 5
i;°.o
17°. 5
18°.0
c
. o
O
o
o
O
o
o
o
O
o
o
12.0
12.5
13.0
13.5
14.0
14.5
15.0
15.5
16.0
16.5
17.0
17.5
18.0
10
2.2
2.7
3.2
3.7
4.2
4.7
5.3
5.8
6.3
6.8
7.3
7.9
8.3
10
15
2.5
2.9
3.5
4.0
4.5
5.0
5.6
6.1
6.6
7.1
7.7
8.2
8.7
15
20
2.8
3.3
3.8
4.4
4.9
5.5
6.0
6.5
7.1
7.6
8.1
8.7
9.2
20
25
3.3
3.8
4.4
4.9
5.5
6.1
6.6
7.1
7. 7
8.3
8.8
9.4
9.9
25
30
13.9
14.5
15.0
15.6
16.2
16.8
17.4
18.0
18.6
19.2
19.7
20.3
20.9
30
32
4.2
4.8
5.3
6.0
6.6
7.2
7.8
8.4
9.0
9.6
20.2
0.8
1.4
32
34
4.5
5.1
5.7
6.4
7.0
7.6
8.2
8.8
9.5
20.0
0.7
1.3
1.9
34
36
4.9
5.5
6.1
6.8
7.4
8.0
8.7
9.3
20.0
0.5
1.2
1.8
2.5
.36
38
5.3
6.0
6.6
7.2
7.9
8.5
9.2
9.8
20.4
0.5
1.1
1.8
2.4
3.1
38
40
15.7
16.4
17.1
17. «
18.4
19.1
19.7
21.1
21.8
22.4
23.1
23.8
40
41
6.0
6.7
7.3
8.0
8.7
9.4
20.0
0.8
1.4
2.1
2.8
3.5
4.2
41
42
6.2
6.9
7.6
8.3
9.0
9.7
0.4
1.1
1.8
2.5
3.2
3.9
4.6
42
43
6.5
7.2
7.9
8.6
9.3
20.0
0.7
1.4
2.2
2.9
3.6
4.3
5.0
43
44
6.8
7.5
8.2
8.9
9.6
0.4
1.1
1.8
2.6
3.3
4.0
4.7
5.4
44
45
17.1
17.8
18.5
19.3
20.0
20.7
21.5
22.2
23.0
23.7
24.4
25.2
25.9
45
46
7.4
8.2
8.9
9.6
0.4
1.1
1.9
2.6
3.4
4.1
4.9
5.7
6.4
46
47
7.7
8.5
9.3
20.0
0.8
1.5
2.3
3.1
3.8
4.6
5.4
6.2
6.9
47
48
8.1
8.9
9.7
0.4
1.2
2.0
2.8
3.6
4.3
5.1
5.9
6.7
7.5
48
49
8.5
9.3
20.1
0.8
1.6
2.4
3.2
4.1
4.9
5.7
6.5
7.3
8.1
49
50
18.9
19.7
20.5
21.3
22.1
22.9
23.7
24.6
25.4
26.2
27.0
27.9
28.7
50
51
9.3
20.1
0.9
1.8
2.6
3.5
4.3
5.1
6.0
6.8
7.6
8.5
9.4
51
52
9.7
0.6
1.4
2.3
3.1
4.0
4.9
5.7
6.6
7.5
8.3
9.2
30.1
52
53
20.2
1.1
1.9
2.8
,3.7
4.6
5.5
6.4
7.3
8.2
9.0
30.0
0.9
53
54
0.7
1.6
2.5
3.4
4.3
5.2
25.9
6.1
26.8
7.1
27.8
8.0
28.7
8.9
9.8
0.8
1.7
54
55
21.2
22.2
23.1
24.0
24.9
29.7
30.6
31.6
32.6
55
56
1.8
2.8
3.7
4.7
5.6
6.6
7.6
8.6
9.5
30.5
1.5
2.5
3.6
56
57
2.4
3.4
4.4
5.4
6.4
7.4
8.4
9.4
30.4
1.4
2.5
3.5
4.6
57
58
3.1
4.1
5.1
6.1
7.2
8.2
9.2
30.3
1.3
2.4
3.5
4.6
5.7
58
59
3.8
4.8
5.9
6.9
8.0
9.1
30.1
30.2
1.3
2.3
3.5
4.6
5.7
6.9
59
60
60
24.6
25.6
26.7
27.8
28.9
31.2
32. 3
33.4
34.6
35.8
36.9
38.2
61
5.4
6.5
7.6
8.8
9.9
1.1
2.2
3.5
4.6
5.8
7.1
8.3
9.6
61
62
6.3
7.5
8.6
9.8
31.0
2.2
3.4
4.7
5.9
7.2
8.5
9.8
41.2
62
63
7.2
8.5
9.7
31.0
2.2
3.*
4.7
6.1
7.4
8.7
40.1
41.5
2.9
63
64
8.3
9.6
30.9
2.2
3.5
4.8
6.2
7.6
39.2
9.0
40.4
1.8
3.3
4.8
64
65.0
29.5
30.8
32.2
33.5
34.9
36.3
37.8
40.7
42.2
43.8
45.4
47.0
65.0
5.5
30.1
1.5
2.9
4.3
5.7
7.1
8.6
40.1
1.6
3.2
4.8
6.5
8.2
5.5
6.0
0.7
2.2
3.6
5.0
6.5
8.0
9.5
1.1
2.7
4.3
5.9
7.7
9.4
6.0
6.5
1.4
2.9
4.3
5.8
7.3
8.9
40.5
2.1
3.8
5.4
7.1
8.9
50.8
6.5
7.0
67.5
2.1
3.6
5.1
6.7
8.2
9.8
1.5
3.2
4.9
6.6
8.4
50.3
2.3
7.0
32.9
34.4
36.0
37.6
39.2
40.8
42.6
44.3
46.1
47.9
49.8
51.8
53.9
67.5
8.0
3.7
5.3
6.9
8.6
40.2
1.9
3.7
5.5
7.4
9.3
51.3
3.4
5.6
8.0
8.5
4.6
6.2
7.9
9.6
1.3
3.1
4.9
6.8
8.8
50.8
2.9
5.1
7.5
8.5
9.0
5.5
7.2
8.9
40.7
2.5
4.3
6.2
8.2
50.3
2.4
4.6
7.0
9.6
9.0
9.5
6.4
8.2
40.0
1.8
3.7
5.6
7.6
9.7
1.9
4.2
6.5
9.1
61.9
9.5
70.0
37.4
39.3
41.1
43.0
45.0
47.0
49.2
51.4
53.7
56.1
58.7
61.5
64.6
70.0
0.5
8.5
40.4
2.4
4.4
6.4
8.6
50.8
3.2
5.7
8.3
61.1
4.3
7.8
0.5
1.0
9.7
1.7
3.7
5.8
8.0
50.3
2.6
5.2
7.9
60.7
3.9
7.5
71.7
1.0
1.5
40.9
3.0
5.1
7.4
9.7
2.1
4.6
7.4
60.3
3.5
7.1
71.4
6.9
1.5
2.0
2.3
4.4
6.7
fCl
51.5
4.1
6.9
59.4
9.9
3.1
6.8
71.1
6.7
90.0
2.0
72.5
43.7
46.0
48.4
50.9
53.6
56.4
62.7
66.4
70.9
76.5
90.0
72.5
3.0
5.3
7.7
50.3
3.0
5.9
8.9
62.2
6.1
70.6
6.3
90.0
3.0
.3.5
7.0
9.6
2.3
5.3 i 8.4
61.8
5.6
70.3
6.1
90.0
3.5
4.0
8-. 9
51.7
4.7
7.9 j 61.4
5.3
9.8
75.9
90.0
4.0
4.5
51.1
4.1
7.3
60.9 ' 4.9
9.5
75.5 1 90.0
'
4.5
TABLE 39. [Page 743
Amplitudes.
Lati-
tude.
Declination.
Lati-
tude.
18°.0
18°.5
19°.0
19°. 5
20°.
20°. 5
2I°.0
21°. 5
22°.
22°. 5
23°.
28°. 5
24°.0
o
10
15
20
25
30
32
34
36
38
O
18.0
8.3
8.7
9.2
9.9
20.9
1.4
1.9
2.5
3.1
o
18.5
8.8
9.2
9.7
20.5
21.5
2.0
2.5
3.1
3.8
o
19.0
9.3
9.7
20.3
1.1
22.1
2.6
3.1
3.7
4.4
o
19.5
9.8
20.2
0.8
1.6
o
20.0
0.3
0.7
1.4
2.2
o
20.5
0.8
1.3
1.9
2.7
o
21.0
1.3
1.8
2.4
3.3
o
21.5
1.8
2.3
3.0
3.9
o
22.0
2.3
2.8
3.5
4.4
o
22.5
2.9
3.3
4.0
5.0
o
23.0
3.4
3.9
4.6
5.5
o
23.5
3.9
4.4
5.1
6.1
24.0
4.4
4.9
5.7
6.7
o
10
15
20
25
22.7
3.2
3.8
4.4
5.1
23.3
3.8
4.4
5.0
5.7
23.8
4.4
5.0
5.7
6.4
24.4
5.0
5.6
6.3
7.0
25.0
5.6
6.2
6.9
7.7
25.6
6.2
6.9
7.6
8.4
26.2
6.8
7.5
8.2
9.1
26.8
7.4
8.1
8.9
9.7
27.4
8.0
8.7
9.5
30.4
28.0
8.7
9.4
30.2
1.1
30
32
34
36
38
40
41
42
43
44
23.9
4.2
4.6
5.0
5.4
24.4
4.8
5.3
5.7
6.2
25.1
5.5
6.0
6.4
6.9
25.8
6.2
6.7
7.2
7.7
26.5
6.9
7.4
7.9
8.4
27.2
7.7
8.1
8.6
9.1
27.9
8.3
8.8
9.3
9.8
28.6
9.1
9.6
30.1
0.6
29.3
9.8
30.3
0.8
1.4
30.0
0.5
1.0
1.6
2.2
30.7
1.2
1.7
2.3
2.9
31.3
1.8
2.4
3.0
3.6
32.1
2.6
3.2
3.8
4.4
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
25.9
6.4
6.9
7.5
8.1
28.7
9.4
30.1
0.9
1.7
26.7
7.2
7.7
8.3
8.9
27.4
7.9
8.5
9.1
9.7
28.2
8.7
9.3
9.9
.30.6
28.9
9.5
30.1
0.7
1.4
29.7
30.3
0.9
1.6
2.3
30.4
1.0
1.7
2.4
3.1
31.2
1.8
2.5
3.2
4.0
32.0
2.6
3.3
4.0
4.8
32.8
3.4
4.1
4.9
5.7
33.5
4.2
4.9
5.7
6.5
34.3
5.0
6.7
6.5
7.4
35.1
5.8
6.6
7.4
8.3
45
46
47
48
49
29.6
30.3
1.0
1.8
2.7
3g.4
1.1
1.9
2.7
3.6
31.3
2.0
2.8
3.7
4.6
32.1
2.9
3.7
4.6
5.6
33.0
3.8
4.7
5.6
6.6
33.9
4.7
5.6
6.6
7.6
34.8
5.6
6.5
7.5
8.6
35.6
6.5
7.5
8.5
9.6
36.5
7.4
8.4
9.5
40.6
37.4
8.4
9.4
40.5
1.7
38.3
9.3
40.3
1.4
2.6
39.2
40.2
1.3
2.5
3.8
50
51
52
53
54
55
56
57
58
59
32.6
3.6
4.6
5.7
6.9
33.6
4.6
5.6
6.8
8.0
34.6
5.6
6.7
7.9
9.2
35.6
6.7
7.8
9.1
40.4
36.6
7.7
8.9
40.2
1.6
37.6
8.8
40.0
1.4
2.8
38.7
9.8
41.1
2.5
4.1
39.7
41.0
2.3
3.8
5.4
40.8
2.1
3.5
5.0
6.7
48.6
9.6
50.6
1.7
2.9
54.2
5.6
7.1
8.7
60.5
62.5
4.7
7.1
70.0
3.5
41.9
3.2
4.6
6.2
8.0
42.9
4.3
5.8
7.5
9.3
44.0
5.4
7.0
8.8
50.7
45.2
6.7
8.3
50.1
2.2
55
56
57
58
59
60.0
0.5
1.0
1.5
2.0
38.2
8.9
9.6
40.4
1.2
39.4
40.1
0.9
1.7
2.5
40.6
1.4
2.2
3.0
3.9
41.9
2.7
3.5
4.4
5.3
43.2
4.0
4.9
5.8
6.8
44.5
5.4
6.3
7.3
8.3
45.8
6.7
7.7
8.7
9.8
47.2
8.1
9.1
50.2
1.3
49.9
51.0
2.1
3.3
4.6
51.4
2.5
3.7
5.0
6.3
52.9
4.1
5.3
6.7
8.1
54.4
5.7
7.0
8.5
60.0
60.0
0.5
1.0
1.5
2.0
62.5
3.0
3.5
4.0
•4.5
65.0
5.5
6.0
6.5
7.0
67.5
8.0
8.5
9.0
9.5
42.0
2.9
3.8
4.8
5.9
43.4
4.3
5.3
6.4
7.5
44.9
5.9
6.9
8.0
9.2
46.3
7.4
8.5
9.7
50.9
47.8
8.9
50.1
1.3
2.6
49.4
50.5
1.7
3.0
4.5
51.0
2.2
3.5
4.9
6.4
52.6
3.9
5.3
6.7
8.4
56.0
7.5
9.1
60.7
2.8
64.9
7.3
70.2
,3.7
8.3
57.8
9.4
61.1
3.0
5.2
59.7
61.4
3.4
5.5
7.8
61.7
3.6
5.7
8.1
70.9
62.5
3.0
3.5
4.0
4.5
47.0
8.2
9.4
50.8
2.3
48.7
50.0
1.3
2.7
4.3
50.4
1.8
3.2
4.7
6.4
52.2
3.6
5.1
6.8
8.7
54.0
5.6
7.3
9.1
61.1
56.0
7.6
9.4
61.4
3.7
66.2
9.2
72.8
7.7
90.0
58.0
9.8
61.8
4.0
6.5
60.2
2.2
4.4
6.8
9.8
73.3
8.1
90.0
67.6
70.4
3.8
8.4
90.0
70.6
4.1
8.6
90.0
74.4
8.9
90.0
65.0
.5.5
6.0
6.5
7.0
53.9
5.6
7.5
9.6
61.9
56.0
7.9
60.0
2.3
5.0
58.3
60.3
2.6
5.3
8.4
60.7
3.0
5.6
8.7
72.4
63.4
5.9
8.9
72.7
7.6
69.5
73.0
7.9
90.0
78.2
90.0
90.0
67.5
8.0
8.5
9.0
9.5
70.0
0.5
1.0
1.5
2.0
64.6
7.8
7r.7
6.9
90.0
69.1
71.9
7.1
90.0
72.2
7.2
90.0
77.4
90.0
90.0
70.0
0.5
1.0
1.5
2.0
Page 744]
TABLE 39.
Amplitudes.
Declination.
Lati-
tude.
Lati-
tude.
24°.
24°. 5
o
25°.
25°.5
26°.0
26°. 5
2J°.0
27°. 5
28°.
28°. 6
29°.0
29°.5
80°.
o
o
o
O
o
o
o
o
°
o
o
o
24.0
24.5
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
4
4.1
4.6
5.1
5.6
6.1
6.6
7.1
7.6
8.1
8.6
9.1
9.6
0.1
4
8
4.3
4.8
5.3
5.8
6.3
6.8
7.3
7.8
8.3
8.8
9.3
9.8
0.3
8
12
4.6
5.1
5.6
6.1
6.6
7.1
7.6
8.1
8.7
9.2
9.7
30.2
0.7
12
16
5.0
5.6
6.1
6.6
7.1
7.6
8.2
8.7
9.2
9.8
30.3
0.8
1.3
16
20
25.7
26.2
26.7
27.3
27.8
28.3
28.9
29.4
30.0
30.5
31.1
31.6
32.1
20
22
6.0
6.6
7.1
7.7
8.2
8.8
9.3
9.9
0.4
1.0
1.5
2.1
2.6
22
24
6.4
7.0
7.6
8.1
8.7
9.2
9.8
30.4
0.9
1.5
2.0
2.6
.3.2
24
26
6.9
7.5
8.1
8.6
9.2
9.7
30.3
0.9
1.5
2.1
2.6
3.2
3.8
26
28
7.4
8.0
8.6
9.2
2978
9.8
30.3
0.9
1.5
2.1
2.7
3.3
3.9
4.5
28
30
28.0
28.6
29.2
30.4
31.0
31.6
32.2
32.8
33.4
34.0
34.7
35.3
30
31
8.3
8.9
9.5
30.1
0.8
1.4
2.0
2.6
3.2
3.8
4.5
5.1
5.7
31
32
8.7
9.3
9.9
0.5
1.1
1.7
2.4
3.0
3.6
4.2
4.9
5.5
6.1
32
33
9.0
9.6
30.2
0.9
1.5
2.1
2.8
3.4
4.0
4.7
5.3
6.0
6,6
33
34
9.4
30.0
0.6
31.3
1.9
2.6
3.2
3.8
4.5
5.1
5.8
6.4
7.1
34
35
29.8
30.4
31.1
31.7
32.3
33.0
33.6
34.3
35.0
35.6
36.3
36.9
37.6
35
36
30.2
0.8
1.5
2.1
2.8
3.5
4.1
4.8
5.5
6.1
6.8
7.5
8.2
36
37
0.6
1.3
1.9
2.6
3.3
4.0
4.6
5.3
6.0
6.7
7.4
8.1
8.8
37
38
1.1
1.7
2.4
3.1
3.8
4.5
5.2
5.9
6.6
7.3
8.0
8.7
9.4
38
39
1.6
2.2
2.9
3.6
4.3
5.0
5.7
6.5
7.2
7.9
8.6
9.3
40.0
.39
40
32.1
32.8
33.5
34.2
34.9
35.6
36.3
37.1
37.8
38.5
39.3
40.0
40.7
40
41
2.6
3.3
4.1
4.8
5.5
6.2
7.0
7.7
8.5
9.2
40.0
0.7
1.5
41
42
3.2
3.9
4.7
5.4
6.1
6.9
7.7
8.4
9.2
9.9
0.7
1.5
2.3
42
43
3.8
4.5
5.3
6.1
6.8
7.6
8.4
9.2
9.9
40.7
1.5
2.3
3.1
43
44
4.4
5.2
6.0
6.8
7.5
8.3
9.1
40.0
40.7
1.6
2.4
3.2
4.0
44
45
35.1
35.9
36.7
37.5
38.3
39.1
39.9
40.8
41.6
42.5
43.3
44.1
45.0
45
46
5.8
6.6
7.5
8.3
9.1
40.0
40.8
1.7
2.5
3.4
4.3
5.1
6.0
46
47
6.6
7.4
8.3
9.1
40.0
0.9
1.7
2.6
3.5
4.4
5.3
6.2
7.1
47
48
7.4
8.3
9.2
40.0
0.9
1.8
2.7
3.6
4.6
5.5
6.4
7.4"
8.3
48
49
8.3
9.2
40.1
1.0
1.9
2.8
3.8
4.7
5.7
6.7
7.6
8.6
9.6
49
50
39.2
40.2
41.1
42.0
43.0
43.9
44.9
45.9
46.9
47.9
48.9
50.0
51.1
50
51
40.2
1.2
2.2
3.2
4.1
5.1
6.2
7.2
8.2
9.3
50.4
1.5
2.6
51
52
1.3
2.3
3.3
4.4
5.4
6.4
7.5
8.6
9.7
50.8
2.0
3.1
4.3
52
53
2.5
3.5
4.6
5.7
6.7
7.8
9.0
50.1
51.3
2.5
3.7
4.9
6.2
53
54
3.8
4.9
6.0
7.1
8.2
9.4
50.6
1.8
3.0
4.3
5.6
6.9
8.3
54
55.0
45.2
46.3
47.5
48.6
49.8
51.1
52.3
53.6
54.9
56.3
57.7
59.1
60.7
55.
5.5
5.9
7.1
8.3
9.5
50.7
2.0
3.3
4.6
6.0
7.4
8.9
60.4
2.0
5.5
6.0
6.7
7.9
9.1
50.4
1.6
2.9
4.3
5.7
7.1
8.6
60.1
1.7
.3.4
6.0
6.5
7.5
8.8
50.0
1.3
2.6
3.9
5.4
6.8
8.3
9.9
1.5
3.2
5.0
6.5
7.0
8.3
9.6
0.9
2.2
3.6
5.0
6.5
8.0
9.5
61.2
2.9
4.7
6.6
7.0
57.5
49.2
50.5
51.9
53.2
54.7
56.2
57.7
59.3
60.9
62.6
64.5
66.4
68.5
57.5
8.0
50.1
1.5
2.9
4.3
5.8
7.4
8.9
60.6
2.4
4.2
6.2
8.3
70.7
8.0
8.5
1.1
2.5
4.0
5.5
7.0
8.6
60.3
2.1
3.9
6.0
8.1
70.4
3.1
8.5
9.0
2.2
3.6
5.1
6.7
8.3
60.0
1.8
3.7
5.7
7.9
70.3
3.0
6.2
9.0
9.5
3.3
4.8
6.4
8.0
9.7
1.5
3.4
5.5
7.7
70.1
2.8
5.9
80.1
9.5
60.0
54.4
56.0
57.7
59.4
61.2
63.2
65.2
67.4
69.9
72.6
75.8
80.0
90.0
60.0
0.5
5.7
7.4
9.1
61.0
2.9
5.0
7.2
9.6
72.4
5.8
9.9
90.0
0.5
1.0
7.0
8.8
60.7
2.6
4.7
7.0
9.5
72.3
5.5
9.8
90.0
1.0
1.5
8.5
60.3
2.3
4.4
6.7
9.2
72.0
5.4
9.7
90.0
1.5
2.0
60.0
2.0
4.2
6.5
9.0
71.9
5.2
9.6
90.0
2.0
62.5
61.7
63.9
66.2
68.8
71.7
75.1
9.5
90.0
62.5
3.0
3.6
6.0
8.6
71.5
4.9
9.4
90.0
3.0
3.5
5.7
8.3
71.3
4.8
9.3
90.0
3.5
4.0
8.1
71.1
4.6
9.2
90.0
4.0
4.5
70.9
4.4
9.0
90.0
4.5
TABLE 40. [Page 745
Correction of the Amplitude as observed on the Apparent Horizon.
Lati-
tude.
Declination.
Lati-
tude.
0°
5°
10°
12°
14°
16°
18°
20°
22°
24°
26°
28°
30°
o
5
10
1.5
20
o
0.0
.1
.1
.2
.2
o
0.0
.1
.1
.2
.2
o
0.0
.1
.1
.2
.2
o
0.0
.1
.1
.2
.2
o
0.0
.1
.1
.2
.2
O
0.0
.1
.1
.2
.2
o
0.0
.1
.1
.2
.3
0.0
.1
.1
2
.3
o
0.0
.1
.1
.2
.3
0.0
.1
.1
.2
.3
0.0
.1
.1
.2
.3
O
0.0
.1
.1
.2
.3
0.0
.1
.1
.2
.3
o
5
:o
15
20
24
28
32
36
38
40
42
44
46
48
0.3
.3
.4
.5
.5
0.3
.4
.4
.5
.5
0.3
.4
.4
.5
.5
0.3
.4
.4
.5
.5
0.3
.4
.4
.5
.6
0.3
.4
.4
.5
.6
.4
.5
.6
0.3
.4
.5
.5
.6
0.3
.4
.5
.6
.6
0.3
.4
.5
.6
.6
0.3
.4
.5
.6
.6
0.4
.4
.5
.6
.7
0.4
.4
.5
.6
.7
24
28
32
36
38
0.6
.6
.6
.7
.7
0.6
.6
.6
.7
.8
0.6
.6
.7
.7
.8
0.6
.6
.7
.7
.8
0.6
.6
.7
.7
.8
0.6
.7
.7
.8
.8
0.6
. 7
.7
.8
.8
0.6
.7
.7
.8
.9
0.6
.7
.8
.8
.9
0.7
.7
.8
.9
1.0
0.7
.8
.8
.9
1.0.
0.7
.8
.9
.9
1.0
0.7
.8
.9
1.0
.1
40
42
44
46
48
50
52
54
56
58
0.8
.8
.9
1.0
.1
0.8
.9
.9
1.0
.1
0.8
.1
.2
0.8
.9
1.0
.1
.2
0.9
.9
1.0
.1
.2
0.9
1.0
.1
.2
.3
0.9
1.0
.1
.2
.3
0.9
1.0
.1
.2
.4
1.0
.1
.2
.3
.5
1.1
.2
.3
.5
.7
1.1
.2
.4
.6
.9
i;i
.3
.5
.8
2.3
1.3
.5
.8
2.2
3.2
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
1.2
.3
.4
.5
.6
1.8
2.0
.2
.6
3.1
1.2
.3
.4
.5
.7
1.9
2.1
.5
3.0
.6
1.3
.4
.5
.7
.9
1.3
.4
.5
.7
2.0
1.3
.4
.6
.9
2.2
1.4
.6
.8
2.0
.4
1.5
.7
.9
2.3
.9
1.6
.8
2.2
.8
4.0
1.7
2.1
.6
3.8
2.0
.5
3.7
2.4
3.5
3.4
60
62
64
66
68
2.1
.5
3.0
.8
5.7
2.3
.8
3.5
5.2
2.6
3.3
4.8
3.1
4.6
4.3
70
72
74
76
78
80
3.8
4.4
80
Page 746]
TABLE 41.
Natural Sines and Cosines.
Prop.
0°
1
3
2°
%°
4°
Prop.
parts
■29
()0
parts
2
2
M.
X. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
K! sine
N. COS.
00000
100000
01745
99985
0;5490
99939
05234
99863
06976
99756
1
00029
100000
01774
99984
03519
99938
05263
99861
07005
99754
59
2
1
2
00058
100000
01803
99984
03548
99937
05292
99860
07034
99752
58
2
1
8
00087
100000
01832
99983
03577
99936
05321
99858
07063
99750
57
2
2
4
00116
100000
•01862
99983
0360()
99935
05350
99857
07092
99748
56
2
2
5
00145
100000
01891
99982
03635
99934
05379
99855
07121
99746
55
2
3
6
00175
100000
01920
01949
99982
99981'
03664
99933
99932
05408
99854
07150
99744
54
53
2
2
3
7
00204
100000
03693
05437
99852
07179
99742
4
8
00233
100000
01978
99980
03723
99931
05466
99851
07208
99740
52
2
4
9
00262
100000
02007
99980
03752
99930
05495
99849
07237
99738
51
2
5
10
00291
100000
02036
99979
03781
99929
05524
99847
07266
99736
50
2
5
11
00320
99999
02065
99979
03810
99927
05553
99846
07295
99734
49
2
6
6
12
13
00349
99999
02094
99978
99977'
03839
99926
05582
99844
99842
07324
07353
99731
'99729
48
47
2
00378
99999
02123
03868
99925
05611
2
7
14
00407
99999
02152
99977
03897
99924
05640
99841
07382
99727
46
2
t
15
00436
99999
02181
99976
03926
99923
05669
99839
07411
99725
45
2
8
16
00465.
99999
02211
99976
03955
99922
05698
99838
07440
99723
44
8
17
00495
99999
02240
99975
03984
99921
05727
99836
07469
99721
43
9
18
19
00524
99999
02269
99974
99974
04013
99919
05756
99834
99833
07498
99719
42
9
00553
99998
02298
04042
99918
05785
07527
99716
41
10
20
00582
99998
02327
99973
04071 1 99917
05814
99831
07556
99714
40
10
21
00611
99998
02356
99972
04100 j 99916
05844
99829
07585
99712
39
11
22
00640
99998
02385
99972
04129 1 99915
05873
99827
07614
99710
38
11
23
00669
99998
02414
99971
04159
99913
05902
99826
07643
99708
37
12
12
24
25
00698
99998
02443
99970
99969
04188
99912
99911
05931
05960
99824
99822
07672
07701
99705
99703
36
35
00727
99997
02472
04217
13
26
00756
99997
02501
99969
04246
99910
05989
99821
07730
99701
34
13
27
00785
99997
02530
99968
04275
99909
06018
99819
07759
99699
33
14
28
00814
99997
02560
99967
04304
99907
06047
99817
07788
99696
32
14
29
00844
99996
02589
99966
04333
99906
06076
99815
07817
99694
31
15
15"
30
'31
00873
99996
02618
02647
99966
99965
04362
04391
99905
99904
06105
06134
99813
99812
07846
99692
30
29
00902
99996
07875
99689
15
32
00931
99996
02676
99964
04420
99902
06163
99810
07904
99687
28
16
33
00960
99995
02705
99903
04449
99901
06192
99808
07933
99685
27
16
34
00989
99995
027;M
99963
04478
99900
06221
99806
07962
99683
26
17
35
01018
99995
02763
99962
04507
99898
06250
99804
07991
99680
25
17
18
36
01047
99995
02792
99961
04536
04565
99897
99896
06279
99803
08020
08049
99678
99676'
24
23
37
01076
99994
02821
99960
06308
99801
18
38
01105
99994
02850
99959
04594
99894
06337
99799
08078
99673
22
19
39
01134
99994
02879
99959
04623
99893
06366
99797
08107
99671
21
19
40
01164
99993
02908
99958
04653
99892
06395
99795
08136
99668
20
20
41
01193
99993
02938
99957
04682
99890
06424
99793
08165
99666
19
20
21
42
43
01222
99993
02967
99956
99955
04711
99889
06453
06482
99792
99790
08194
99664
18
17
01251
99992
02996
04740 99888
08223
99661
21
44
01280
99992
03025
99954
04769
99886
06.511
99788
08252
99659
16
22
45
01309
99991
03054
99953
04798
99885
06540
99786
08281
99657
15
22
46
01338
99991
03083
99952
04827
99883
06569 ! 99784
08310
99654
14
23
47
01367
99991
03112
99952
04856
99882
06598 '■ 99782
08339
99652
13
23
48
01396
99990
03141
99951
04885 ; 99881
06627
99780
08368
99649
12
11
24
49
01425
99990
03170
99950
04914
99879
06656
99778
08397
99647
24
50
01454
99989
03199
99949
04943
99878
06685
99776
08426
99644
10
25
51
01483
99989
03228
99948
04972
99876
06714
99774
08455
99642
9
25
52
01513
99989
03257
99947
05001
99875
06743
99772
08484
99639
8
26
53
01542
99988
03286
99946
05030
99873
06773
99770
08513
99637
7
26
54
01571
99988
99987
03316
03345
99945
99944
05059
99872
06802
99768
99766
08542
08571
99635
6
27
55
01600
05088
99870
06831
99632
5
27
56
01629
99987
03374
99943
05117
99869
06860
99764
08600
99630
4
28
57
01658
99986
03403
99942
05146
99867
0(>889
99762
08629
99627
3
28
58
01687
99986
03432
99941
05175
998<i6
06918
99760
08658
99625
2
29
59
01716
99985
03461
99940
05205
99864
06947
99758
08687
99622
1
29
60
01745
99985
03490
99939
05234
99863
06976
99756
08716
99619
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. Sine.
N. COS.
N. sine.
M.
8
B°
88°
87°
86°
85°
TABLE il.
[Page 747
Natural Sines and Cosines.
Prop,
parts
20
5
o
6
5
JO
8°
9°
Prop.
M.
N.sine.
N. COS.
N. sine.
N. COS.
N.sine.
N.cos.
N. sine.
N. COS.
N. sine.
N. COS.
4
08716
99619
10453
99452
12187
99255
13917
99027
15643
98769
60
4
1
08745
99617
10482
99449
12216
99251
13946
99023
15672
98764
59
4
1
o
08774
99614
10511
99446
12245
99248
13975
99019
15701
98760
58
4
1
3
08803
99612
10540
99443
12274
99244
14004
99015
15730
98755
57
4
2
4
08831
99609
10569
99440
12302
99240
14033
99011
15758
98751
56
4
2
5
08860
99607
10597
99437
12331
99237
14061
99006
15787
98746
55
4
3
6
7
08889
99604
10626
99434
12360
12389
99233
99230'
14090
99002
15816
98741
54
53
4
4
3
08918
99602
10655
99431
14119
98998
15845
98737
4
8
08947
99599
10684
99428
12418
99226
14148
98994
15873
98732
52
3
4
9
08976
99596
10713
99424
12447
99222
14177
98990
15902
98728
51
3
5
10
09005
99594
10742
99421
12476
99219
14205
98986
15931
98723
50
3
5
11
09034
99591
10771
99418
12504
99215
14234
98982
15959
98718
49
3
6
6
12
13
09063
99588
10800
10829
99415
99412
12533
99211
14263
98978
15988
16017
98714
48
47
3
3
09092
99586
12562
99208
14292
98973
98709
7
14
09121
99583
10858
99409
12591
99204
14320
98969
16046
98704
46
3
7
15
09150
99580
10887
99406
12620
99200
14:549
98965
16074
98700
45
3
8
16
09179
99578
10916
99402
12649
99197
14378
98961
16103
98695
44
3
8
17
09208
99575
10945
99399
12678
99193
14407
98957
16132
98690
43
3
9
18
09237
99572
99570
10973
11002
99396
99393
12706
99189
14436
14464
98953
'98948
16160
16189
98686
42
3
9
19
09266
127*5
99186
98681
41
3
10 : 20
09295
99567
11031
99390
12764
99182
14493
98944
16218
98676
40
3
10 21
09324
99564
11060
99386
12793
99178
14522
98940
16246
98671
:59
3
11 22
09353
99562
11089
99383
12822
99175
14551
989:56
16275
98667
38
3
11 ! 23
09382
99559
11118
99380
12851
99171
14580
98931
16304
98662
37
2
12 24
12 ; 25
09411
09440
99556
11147
99377
12880
99167
99163
14608
98927
16333
98657
36
2
99553
11176
99374
12908
14637 1 98923
16361
98652
35
2
13 26
09469
99551
11205
99370
12937
99160
14666 1 98919
16390
98648
:54
2
13 : 27
09498
99548
11234
99367
12966
99156
14695 1 98914
16419
98643
33
2
14 : 28
09527
99545
11263
99364
12995 • 99152
14723 ; 98910
16447
98638
32
2
14 29
09556
99542
11291
99360
i:5024 i 99148
14752 , 9890(>
16476
98633
31
2
15
30
09585
99540
11320
99:557
1.3053
99144
99141
14781 1 98902
14810 I 98897
16505
165:5:5
98629
98624
30
29
2
15
31
09614
99537
11349
99:H54
i:«81
2
15 1 32
09642
995;W
11378
99351
13110
mn37
148:58 1 98893
16562
98619
28
2
16 1 33
09671
99531
11407
9S»:«7
131:59
991:53
14867 98889
16591
98614
27
2
16 i 34
09700
99528
11436
99344
13168
99129
14896 , 98884
16620
98609
26
2
17
35
09729
99526
11465
99341
13197
99125
14925
98880
16648
98604
25
2
17
18
36
37"
09758
99523
11494
99337
99334
13226
99122
14954
14982
98876
16677
98600
98595
24
23
2
09787
99520
11523
13254
99118
98871
16706
2
18
38
09816
99517
11552
99331
13283
99114
15011
98867
16734
98590
22
19
39
09845
99514
11580
99327
1:5312
99110
15040
98863
16763
98585
21
19 1 40
09874
99511
11609
99324
1:5341
99106
15069
98858
16792
98580
20
20 41
09903
99508
11638
99320
13370
99102
15097 1 98854
16820
98575
19
20 42
21 ; 43
09932
09961
99506
11667
99317
99314
13399
99098
99094
15126 1 98849
15155 i 98845
16849
16878
98570
18
99503
11696
13427
98565
17
21 i 44
09990
99500
11725
99310
i:5456
99091
15184 98841
16906
98561
16
22 45
10019
99497
11754
99307
1348.5
99087
15212 , 988:56
169:55
98556
15
22 46
10048
99494
11783
99303
1:5514
99083
15241 i 98832
16964
98551
14
23 ' 47
10077
99491
11812
99:500
1:5543
99079
15270 98827
16992
98546
13
23 ; 48
24 i'49
10106
99488
11840
99297
13572
99075
15299 i 98823
17021
17050
98541
12
11
10135
99485
11869
99293
13600
99071
15:527 ' 98818
98536
24 50
10164
99482
11898
99290
13629
99067
15356 i 98814
17078
98531
10
25 51
10192
99479
11927
99286
13658
99063
15385 1 98809
17107
98526
9
25 52
10221
99476
11956
99283
13687
99059
15414 ' 98805
17i:56
98521
8
26 53
10250
99473
11985
99279
13716
99055
15442 98800
17164
98516
7
26 : 54
27 55
10279
99470
12014
99276
13744
99051
15471 98796
17193
17222
98511
9^506
6
10308
99467
12043
99272
13773
99047
15500 98791
5
27 ' 56
10337
99464
12071
99269
13802
99043
15529 98787
17250
98501
4
28 ' 57
10366
99461
12100
99265
13831
990:59
15557 : 98782
17279
98496
3
28 ' 58
10395
99458
12129
99262
i;5860
990.35
15586 i 98778
17308
98491
2
29 i 59
10424
99455
12158
99258
13889
99031
15615
98773
17336
98486
1
29 : 60
i
10453
99452
12187
99255
13917
99027
15643
98769
17365
98481
N.cos.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
M.
s
[O
S3
°
82°
81°
s
D°
Page 748]
TABLE 41.
Natural Sines and Cosines.
Prop.
,0»
11
o
12°
18°
14°
Prop.
parts
28
parts
6
M.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
17365
98481
19081
98163
20791
97815
22495
97437
24192
97030
60
6
1
17393
98476
19109
98157
20820
97809
22523
97430
24220
97023
59
6
1
2
17422
98471
19138
98152
20848
97803
22552
97424
24249
97015
58
6
1
3
17451
98466
19167
98146
20877
97797
22580
97417
24277
97008
57
6
2
4
17479
98461
19195
98140
20905
97791
22608
97411
24305
97001
56
6
2
5
17508
98455
19224
98135
20933
97784
22637
97404
24333
96994
55
6
3
6
17537
98450
19252
98129
98124
20962
97778
22665
97398
24362
24390
96987
96980
54
53
5
5
3
1
17565
98445
19281
20990
97772
22693
97391
4
8
17594
98440
19309
98118
21019
97766
22722
97384
24418
96973
52
5
4
9
17623
98435
19338
98112
21047
97760
22750
97378
24446
96966
51
5
5
10
17651
98430
19366
98107
21076
97754
22778
97371
24474
96959
.50
5
5
11
17680
98425
19395
98101
21104
97748
22807
97365
24503
96952
49
5
6
12
17708
98420
19423
98096
98090"
21132
97742
22835
97358
24531
96945
48
47
5
5
6
13
17737
98414
19452
21161
97735
22863
97351
24559
96937
7
14
17766
98409
19481
98084
21189
97729
22892
97345
24587
96930
46
5
7
15
17794
98404
19509
98079
21218
97723
22920
97338
24615
96923
45
5
7
16
17823
98399
19538
98073
21246
97717
22948
97331
24644
96916
44
4
8
17
17852
98394
19566
98067
21275
97711
22977
97325
24672
96909
43
4
8
18
17880
98389
19595
98061
21303
97705
23005
97318
24700
24728
96902
42
4
9
19
17909
98383
19623
98056
21331
97698
2,3033
97311
96894
41
4
9
20
17937
98378
19652
98050
21360
97692
23062
97304
24756
96887
40
4
10
21
17966
98373
19680
98044
21388
97686
2.3090
97298
24784
96880
39
4
10
22
17995
98368
19709
98039
21417
97680
2.3118
97291
24813
96873
38
4
11
23
18023
98362
19737
98033
21445
97673
23146
97284
24841
96866
37
4
11
12
24
25
18052
98357
19766
19794
■98027
98b2r
21474
"21502"
97667
97661
23175
97278
24869
968.58
36
4
4
18081
98352
23203
97271
24897
96851
35
12
26
18109
98347
19823
98016
21530
97655
23231
97264
24925
96844
34
3
13
27
18338
98341
19851
98010
21559
97648
23260
97257
24954
96837
33
3
13
28
18166
98336
19880
98004
21587
97642
23288
97251
24982
96829
32
3
14
29
18195
98331
19908
97998
21616
97636
23316
97244
25010
96822
31
3
14
30
18224
98325
19937
97992
97987
21644
97630
23345
97237
97230
25038
96815
30
3
3
14
31
18252
98320
19965
21672
97623
23373
25066
96807
29
15
32
18281
98315
19994
97981
21701
97617
23401
97223
25094
96800
28
3
15
33
18309
98310
20022
97975
21729
97611
23429
97217
25122
96793
27
3
16
34
18338
98304
20051
97969
21758
97604
2.3458
97210
25151
96786
26
3
16
36
18367
98299
20079
97963
21786
97598
2.3486
97203
25179
96778
25
3
17
17
36
37
18395
98294
20108
97958
97952
21814
97592
23514
23542
97196
25207
96771
24
2
2
18424
98288
20136
21843
97585
97189
25235 1 96764
23
18
38
18452
98283
20165
97946
21871
97579
23571
97182
25263 j 96756
22
2
18
39
18481
98277
20193
97940
21899
97573
23599
97176
25291 ; 96749
21
2
19
40
18509
98272
20222
97934
21928
97566
23627
97169
25320
96742
20
2
19
41
18538
98267
20250
97928
21956
97560
23656
97162
25348
96734
19
2
20
20
42
43
18567
98261
20279
97922
97916
21985
97553
23684
97155
25376
96727
96719
18
17
2
18595
98256
20307
22013
97547
23712
97148
25404
2
21
44
18624
98250
20336
97910
22041
97541
23740
97141
25432
96712
16
2
21
45
18652
98245
20364
97905
22070
97534
23769
97134
2.5460
96705
15
2
21
46
18681
98240
20393
97899
22098
97528
23797
97127
25488
96697
14
22
47
18710
98234
20421
97893
22126
97521
23825
97120
25516
96690
13
22
48
18738
98229
20450
97887
22155
97515
23853
23882
97113
25545
25573
96682
12
23
49
18767
98223
20478
97881
22183
97508
97106
96676
11
23
50
18795
98218
20507
97875
22212
97502
23910
97100
25601
96667
10
24
51
18824
98212
20535
97869
22240
97496
23938
97093
25629
96660
9
24
52
18852
98207
20563
97863
22268
97489
23966
97086
25657
96653
8
25
53
18881
98201
20592
97857
22297
97483
23995
97079
25685
96645
t
25
54
18910
98196
20620
97851
97845
22325
"2235"3
97476
24023
24051
97072
97066
25713
96638
6
5
26
55
1S938
98190
20649
97470
26741
96630
26
56
18967
98185
20677
97839
22382
97463
24079
97058
26769
96623
4
27
57
18995
98179
20706
97833
22410
97457
24108
97051
26798
96615
3
27
58
19024
98174
20734
97827
22438
97450
24136
97044
25826
96608
2
28
59
19052
98168
20763
97821
22467
97444
24164
97037
258.54
96600
1
28
60
19081
98163
20791
97815
22495
97437
24192
97030
25882
96593
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
M.
79°
78°
77°
76°
76°
TABLE 41.
[Page 749
Katural Sines and Cosines.
Prop, j
lo=>
16°
17"
18°
19°
Prop.
parts
27
parts
9
M.
N.sine.
N.cos.
N. sine.
N. COS.
N.sine.
N.cos.
N.sine.
N.cos.
N.sine.
N.cos.
'<
25882
96593
27564
96126
29237
95630
30902
95106
32557
94552
60
9
Ol 1
25910
96585
27592
96118
29265
95622
30929
95097
32584
94542
59
9
1 2
25938
96578
27620
96110
29293
95613
30957
95088
32612
94533
58
9
1
3
25966
96570
27648
96102
29321
95605
30985
95079
32639
94523
57
9
2
4
25994
96562
27676
96094
29348
95596
31012
95070
32667
94514
56
8
2
5
26022
96555
27704
96086
29376
95588
31040
95061
32694
94504
55
8
3
6
26050
96547
27731
96078
29404
95579
95571
31068
95052
95043"
32722
94495
54
53
8
8
3
7
26079
96540
27759
96070
29432
31095
32749
94485
4
8
26107
96532
27787
96062
29460
95562
31123
95033
32777
94476
52
8
4
9
26135
96524
27815
96054
29487
9.55.54
31151
95024
32804
94466
51
8
5
10
26163
96517
27843
96046
29515
95545
31178
95015
32832
94457
50
8
5 11
26191
96509
27871
96037
29543
95536
31206
95006
32859
94447
49
7
5
12
13
26219
26247
96502
96494
27899
96029
29571
95528
31233
94997
32887
94438
48
47
7
7
6
27927
96021
29599
95519
31261
94988
32914
94428
6 14
26275
96486
27955
96013
29626
95511
31289
94979
32942
94418
46
7
7 15
26303
96479
27983
96005
29654
95.502
31316
94970
32969
94409
45
7
7 16
26331
96471
28011
95997
29682
95493
31344
94961
32997 \ 94399
44
7
8 i 17
26359
96463
28039
95989
29710
95485
31372
94952
3.3024 ! 94390
43
6
8 18
9 , 19
26387
96456
28067
95981
29737
9.5476
95467
31399
"31427
94943
94933
33051 < 94380
33079 . 94370
42
41
6
6
26415
96448
28095
95972
29765
9 20
26443
96440
28123
95964
29793
95459
31454
94924
33106 1 94361
40
6
9 21
26471
96433
28150
95956
29821
95450
31482
94915
33134
94351
39
6
10 22
26500
96425
28178
9.5948
29849
9.5441
31510
94906
33161
94342
38
6
10 23
26528
96417
28206
95940
29876
95433
31537
94897
,33189
94332
37
6
11
24
26556
96410
28234
95931
95923
29904
95424
95415
31565
94888
33216
94322
36
.35'
5
5
11
25
26584
96402
28262
29932
31593
94878
33244
94313
12 26
26612
96394
28290
95915
29960
95407
31620
94869
33271
94303
34
5
12 27
26640
96386
28318
95907
29987
95398
31648
94860
33298
94293
33
5
13 28
26668
96379
28346
95898
30015
95389
31675
94851
33326
94284
32
5
13 29
26696
96371
28374
95890
30043
95.380
31703
94842
33353
94274
31
5
14 30
14 31
26724
96363
28402
95882
30071
30098
95372
95363
31730
3175S
94832
94823
33381
33408"
94264
30
5
26752
96355
28429
95874
94254
29
4
14 32
26780
96347
28457
95865
30126
95354
31786
94814
33436 1 94245
28
4
15 1 33
26808
96340
28485
95857
30154
95345
31813
94805
33463 ! 94235
27
4
15 34
26836
90332
28513
95849
30182
95337
31841
94795
.33490
94225
26
4
16 : 35
26864
96324
28541
95841
30209
95328
31868
94786
3,3518
94215
25
4
16 i 36
17 37
26892
96316
28569
28597
95832
95824
30237
30265
95319
95310
31896
31923
94777
94768
33545
94206
24
23
4
3
26920
96308
3:i')73 94196
17 38
26948
96301
28625
95816
30292
95301
31951
94758
,33(500 94186
22
3
18 39
26976
96293
28652
95807
30320
952<J3
31979
94749
33627 94176
21
3
18 40
27004
96285
28680
95799
30348
95284
32006
94740
33655 94167
20
3
18 41
27032
96277
28708
95791
30376
95275
320,34
94730
33682
94157
19
3
19
42
43"
27060
27088
96269
28736
95782
95774
30403
30431
95266
95257
32061
94721
33710
33737
94147
94137
18
1'7"
3
3
19
96261
28764
32089
94712
20 44
27116
96253
28792
95766
30459
95248
32116
94702
33764
94127
16
2
20 45
27144
96246
28820
95757
30486
95240
32144
941)93
33792
94118
15
2
21 46
27172
96238
28847
95749
30514
95231
32171
94684
.33819
94108
14
2
21 47
27200
96230
28875
95740
30.542
95222
32199
94674
,33846
94098
13
2
22
48
27228
96222
28903
95732
95724
30570
30597
95213
95204
32227
32254
94665
94656"
33874
94088
12
2
22
49
27256
96214
28931
33901
94078
11
2
23 50
27284
96206
28959
95715
30625
95195
32282
94(i46
3,3929
94068
10
23 1 51
27312
96198
28987
95707
30653
95186
32309
94<;37
3.39.56
94058
9
23 52
27340
96190
29015
95698
30680
95177
32337
94«i27
33983
94049
8
24
53
27368
96182
29042
95690
30708
95168
32364
94618
34011
94039
7
24
25
54
55
27396
96174
96166
29070
29098
95681
95673
30736
30763
95159
95150
32.392
32419
94609
94.599
34038
94029
6
27424
34065
94019
5
25
56
27452
96158
29126
95664
30791 •
95142
32447
94.590
34093
94009
4
26
57
27480
96150
29154
95656
30819
95133
32474
94.580
34120
93999
3
26
58
27508
96142
29182
95647
30846
95124
32.502
94571
34147
93989
2
27
59
27536
96134
29209
95639
30874
95115
32529
94561
34175
93979
1
27
60
27564
96126
29237
95630
30902
95106
32557
94552
34202
93969
N.cos.
N.sine.
N.cos.
N. sine.
N.cos.
N.sine.
N.cos.
N.sine.
N. COS.
N.sine.
M.
7
1°
73
"
72°
71°
70°
Page 760]
TABLE 41.
Natural Sines and Cosines.
Prop.
parts
27
20
o
21
o
220
23°
24° 1
Prop.
parts
11
M.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N.cos.
N. sine.
N.cos.
34202
93969
35837
93358
37461
92718
39073
92050
40674
91355
60
11
1
34229
93959
35864
93348
37488
92707
39100
92039
40700
91343
59
11
1
2
34257
93949
35891
93337
37515
92697
39127
92028
40727
91331
58
11
1
3
34284
93939
35918
93327
37542
92686
39153
92016
40753
91319
57
10
2
4
34311
93929
35945
93316
37569
92675
39180
92005
40780
91307
56
10
2
5
34339
93919
35973
93306
37595
92664
39207
91994
40806
91295
55
10
3
6
7
34366
34393
93909
36000
93295
37622
92653
92642"
39234
91982
40833
91283
54
53
10
10
3
93899
36027
93285
37649
39260
91971
40860
91272
4
8
34421
93889
36054
93274
37676
92631
39287
91959
40886 91260
52
10
4
9
34448
93879
36081
93264
37703
92620
39314
91948
40913 : 91248
51
9
5
10
34475
93869
36108
93253
37730
92609
39341
91936
40939 ; 91236
50
9
5
n
34503
93859
36135
93243
37757
92598
39367
91925
40966 91224
49 9 1
5
12
34530
93849
36162
93232
37784
92587
39394
39421
91914
40992
91212
91200
48
47
9
9
fi
13
34557
93839
36190
93222
37811
92576
91902
41019
6
14
34584
93829
36217
93211
37838
92565
39448
91891
41045
91188
46
8
7
15
34612
93819
36244
93201
37865
92554
39474
91879
41072
91176
45
8
7
16
34639
93809
36271
93190
37892
92543
39501
91868
41098
91164
44 8 1
8
17
34666
93799
36298
93180
37919
92532
39528
91856
41125
91152
43 ; 8 1
8
18
34694
93789
36325
93169
37946
92521
39555
91845
41151
91140
91128
42
41
^
9
19
34721
93779
36352
93159
37973
92510
39581
91833
41178
8
9
20
34748
93769
36379
93148
37999
92499
39608
91822
41204
91116
40 1 7
9
21
34775
93759
36406
93137
38026
92488
39635
91810
41231
91104
39 ; 7
10
22
34803
93748
36434
93127
38053
92477
39661
91799
41257
91092
38 ; 7
10
23
34830
93738
36461
93116
38080
92466
39688
91787
41284
91080
37 ; 7
11
24
34857
93728
36488
93106
38107
38134"
92455
39715
91775
41310
91068
36
35
7
11
25
34884
93718
36515
93095
92444
39741
91764
41337
91056
6
12
26
34912
93708
36542
93084
38161
92432
39768
91752
41363
91044
34 6
12
27
34939
93698
36569
93074
38188
92421
39795
91741
41390
91032
33 6
13
28
34966
93688
36596
93063
38215
92410
39822
91729
41416
91020
32 6
13
29
34993
93677
36623
93052
38241
92399
39848
91718
41443
91008
31 6
14
30
35021
93667
36650
93042
38268
38295
92388
92377
39875
91706
91694
41469
90996
30
'
14
31
35048
93657
36677
93031
39902
41496
90984
29
b
14
32
35075
93647
36704
93020
38322
92366
39928
91683
41522
90972
28 ; 5
15
33
35102
93637
36731
93010
38349
92355
39955
91671
41549
90960
27 , 5
15
34
35130
93626
36758
92999
38376
92343
39982
91660
41575
90948
26 i 5
16
35
35157
93616
36785
92988
38403
92332
40008
91648
41602
90936
25 > 5
16
17
36
35184
93606
36812
92978
38430
38456
92321
40035
91636
41628
90924
24
^
37
35211
93596
36839
92967
92310
40062
91625
41655
90911
23
4
17
38
35239
93585
36867
. 92956
38483
92299
40088
91613
41681
90899
22 j 4
18
39
35266
93575
36894
92945
38510
92287
40115
91601
41707
90887
21 1 4
18
40
35293
93565
36921
92935
38537
92276
40141
91590
41734
90875
20 i 4
18
41
35320
93555
36948
92924
38564
92265
40168
91578
41760
90863
19 ! 3
19
19
42
43
35347
35375
93544
36975
92913
92902"
38591
38617"
92254
40195
40221
91566
41787
41813
90851
90839
18
17
3
93534
37002
92243
91555
3
20
44
35402
93524
37029
92892
38644
92231
40248
91.543
41840
90826
16
3
20
45
35429
93514
37056
92881
38671
92220
40275
91531
41866
90814
15
3
21
46
35456
93503
37083
92870
38698
92209
40301
91519
41892
90802
14
3
21
47
35484
93493
37110
92859
38725
92198
40328
91508
41919
90790
13
2
22
22
48
49
35511
93483
37137
92849
38752
92186
40355
91496
91484
41945
90778
12
2
35538
93472
37164
92838
38778
92175
40381
41972
90766
11
2
23
50
35565
93462
37191
92827
38805
92164
40408
91472
41998
90753
10
2
23
51
35592
93452
37218
92816
38832
92152
40434
91461
42024
90741
9
2
23
52
35619
93441
37245
92805
38859
92141
40461
91449
42051
90729
8
24
53
35647
93431
37272
92794
38886
92130
40488
91437
42077
90717
7
24
25
54
55
35674
93420
37299
92784
38912
38939"
92119
92107
40514
40541"
91425
42104
90704
6
35701
93410
37326
92773
91414
42130
90692
5
25
56
35728
93400
37353
92762
38966
92096
40567
91402
42156
90680
4
26
57
35755
93389
37380
92751
38993
92085
40594
91390
42183
90668
3
26
58
35782
93379
37407
92740
39020
92073
40621
91378
42209
90655
2
27
59
35810
93368
37434
92729
39046
92062
40647
91366
42235
90643
1
27
60
35837
93358
37461
92718
39073
92050
40674
91355
42262
90631
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
1
N.cos.
N. sine.
N. cos.
N. sine.
M.
6
»°
68°
67°
66°
65°
TABLE 41. [Page 751
Natural Sines and Cosines.
1
Prop.
parts
46
25°
26°
27°
28°
29°
Prop.
M.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
14
42262
90631
43837
89879
45399
89101
46947
88295
48481
87462
60
14
1
42288
• 90618
43863
89867
45425
89087
46973
88281
48506
87448
59
14
1
?.
42315
90606
43889
89854
45451 1 89074
46999
88267
48532
87434
.58
14
1
3
42341
90594
43916
89841
45477 ! 89061
47024
882.54
48557
87420
57
13
2
4
42367
90582
43942
89828
45503
89048
47050
•88240
48583
87406
56
13
2
5
42394
90569
43968
89816
45529
89035
47076
88226
48608
87391
0.1
13
3
6
42420
90557
43994
89803
45554
89021
47101
88213
88199"
48634
48659
87377
54
13
3
7
42446
90545
44020
89790
45580
89008
47127
87363
53
12
3
8
42473
90532
44046
89777
45606 ! 88995
47153
88185
48684
87349
52
12
4
9
42499
90520
44072
89764
45632 i 88981
47178
88172
48710
87335
51
12
4
10
42525
90507
44098
89752
45ft58 ; 88968
47204
88158
48735
87321
50
12
5
11
42552
90495
44124
89739
45684 1 88955
47229
88144
48761
87306
49
11
5
12
42578
90-183
44151
89726
45710 i ^8942
47255
88130
88117"
48786
87292
87278"
48
47
11
11
6
13
42604
90470
44177
89713
45736 1 88928
47281
48811
6
14
42631
90458
44203
89700
45762 i 88915
47306
88103
48837
87264
46
11
7
15
42657
90446
44229
89687
45787
88902
47332
88089
48862
87250
45
11
7
16
42683
90433
44255
89674
45813
88888
47358
88075
48888
87235
44
10
7
17
42709
90421
44281
89662
45839
88875
47383
88062
48913
87221
43
10
8
8
18
19
42736
42762
90408
90396
44307
89649
45865
88862
47409
474.34
88048
48938
87207
42
41
10
44333
89636
45891
88848
88034
48964
87193
10
9
20
42788
90383
44359
89623
45917 : 88835
47460
88020
48989
87178
40
9
9
21
42815
90371
44385
89610
45942 , 88822
47486
88006
49014 i 87164
39
9
10
22
42841
90358
44411
89597
45968 ' 88808
47511
87993
49040 i 87150
38
9
10
23
42867
90346
44437
89584
45994 i 88795
47.537
87979
49065
871.36
37
9
10
24
42894
90334
44464
89571
89558
46020 1 88782
47562
87965
49090
87121
87107
36
35
8
8
11
25
42920
90321
44490
46046
88768
47588
87951
49116
11
26
42946
90309
44516
89545
46072
88755
47614
87937
49141
87093
34
8
12
27
42972
90296
44542
89532
46097
88741
47639
87923
49166
87079
33
8
12
28
42999
90284
44568
89519
46123
88728
47665
87909
49192
87064
32
7
13
29
4;J025
90271
44594
89.506
46149
88715
47690
87896
49217
87050
31
7
13
13
30
31
43051
90259
90246
44620
89493
89480
46175
46201
88701
88688
47716
47741
87882
49242
87036
87021
30
29"
7
7
43077
44646
87868
49268
14
32
43104
90233
44672
89467
46226
88674
47767
87854
49293
87007
28
7
14
33
43130
90221
44698
89454
46252
88661
47793
87840
49318
86993
27
6
15
34
43156
90208
44724
89441
46278
88647
47818
87826
49344
86978
26
• 6
15
35
43182
90196
44750
89428
46304
88634
47844
87812
49369
86964
25
6
16
36
37
43209
43235
90183
44776
89415
89402
46.330
88620
47869
87798
49.394
49419
86949
24
6
16
90171
44802
46355
88607
47895
87784
86935
23
5
16
38
43261
90158
44828
89389
46381
88593
47920
87770
49445
86921
22
5
17
39
43287
90146
44854
89376
46407
88580
47946
87756
49470
86906
21
5
17
40
43313
90133
44880
89363
46433
88566
47971
87743
49495
86892
20 i 5
18
41
43340
90120
44906
89;»0
46458
88553
47997
87729
49521
86878
19 i 4
18
19
42
43
43366
90108
44932
89337
46484
46510
88539
8*526
48022
87715
87701
49546
49571
86863
86849
18 i 4
17 i "4
43392
90095
44958
89324
48048
19
44
43418
90082
44984
89311
46536
88512
48073
87687
49.596
868.34
16 : 4
20
45
43445
90070
45010
89298
46.561
88499
48099
87673
49622
86820
15 ; 4
20
46
43471
90057
45036
89285
46587
88485
48124
87659
49647
86805
14 3
20
47
43497
90045
45062
. 89272
46613
88472
481.50
87645
49672
86791
13 3
21
21
48
49
43523
90032
45088
89259
466.39
88458
8844.5"
48175
87631
49697
86777
12 3
Ti r"3~
43549
90019
45114
89245
46664
48201
87617
49723
86762
22
50
43575
90007
45140
89232
46690
88431
48226
87603
49748
86748
10 ; 2
22
51
43602
89994
45166
89219
46716
88417
48252
87589
49773
86733
9 ' 2
23
52
43628
89981
45192
89206
46742
88404
48277
87575
49798
86719
8 j 2
23
53
43654
89968
45218
89193
46767
88390
48303
87561
49824
86704
7 2
23
24
54
55
43680
43706
89956
45243
89180
46793
88377
88363
48328
"483.54
87546
87532
49849
49874
86690
86675
6 1 1
89943
45269
89167
46819
5
1
24
56
43733
89930
45295
89153
46844
88.349
48379
87518
49899
86661
4
1
25
57
43759
89918
45321
89140
46870
88,336
48405
87.504
49924
86646
3
1
25
58
43785
89905
45347
89127
46896
88.322
48430
87490
499.50
86632
• }
26
59
43811
89892
45373
89114
46921
88308
48456
87476
49975
86617
1
26
60
43837
89879
45399
89101
46947
88295
48481
87462
50000
86603
N. COS.
N. Bine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. cos.
N. sine.
M.
64
"
6S°
62°
61°
60°
Page 752] TABLE il.
Natural Sines and Cosines.
Prop,
parts.
25
80°
81°
82°
88°
84° 1
Prop.
parts.
16
il.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N.sine.
N. COS.
N. sine.
N. COS.
1
1
2
2
3
1
2
3
4
5
6
50000
50025
50050
50076
50101
50126
50151
86603
86588
86573
86559
86544
86530
86515
51504
51529
51554
51579
51604
51628
51653
85717
85702
85687
85672
85657
85642
85627
52992
53017
53041
53066
53091
53115
53140
53164
53189
53214
53238
53263
53288
84805
84789
84774
84759
84743
84728
84712
54464
54488
54513
54537
54561
54586
54610
83867
83851
83835
83819
83804
83788
83772
55919
55943
55968
55992
56016
56040
56064
82904
82887
82871
82855
82839
82822
82806
60
59
58
57
56
55
54
16
16
15
15
15
16
14
3
3
4-
4
5
5
/
8
9
10
11
12
50176
50201
50227
50252
50277
50302
86501
86486
86471
86457
86442
86427
86413
86398
86384
86369
86354
86340
86325
86310
86295
86281
86266
86251
51678
51703
51728
51753
51778
51803
85612
85597
85582
85567
85551
85536
84697
84681
84666
84650
84635
84619
84604
84588
84573
84557
84542
84526
54635
54659
54683
54708
54732
54756
83756
83740
83724
83708
83692
83676
56088
56112
56136
56160
56184
56208
82790
82773
82757
82741
82724
82708
53
52
51
50
49
48
14
14
14
13
13
13
5
6
6
7
7
8
13
14
15
16
17
18
50327
50352
50377
50403
50428
50453
50478
50503
50528
50553
50578
50603
51828
51852
51877
51902
51927
51952
85521
85506
85491
85476
85461
85446
53312
53337
53361
53386
53411
53435
53460
53484
53509
53534
53558
53583
54781
54805
54829
54854
54878
54902
83660
83645
83629
83613
83597
83581
56232
56256
56280
56305
56329
56353
82692
82675
82659
82643
82626
82610
47
46
45
44
43
42
41
40
39
38
37
36
36
34
33
32
31
30
13
12
12
12
11
11
11
11
10
10
10
10
9
9
9
9
8
8
8
8
9
9
10
10
19
20
21
22
23
24
51977
52002
52026
52051
52076
52101
85431
85416
85401
85385
85370
85355
85340
85325
85310
85294
85279
85264
85249
85234
85218
85203
85188
85173
84511
84495
84480
84464
84448
84433
54927
54951
54975
54999
55024
55048
83565
83549
83533
83517
83501
83485
56377
56401
56425
56449
56473
56497
82593
82577
82561
82544
82528
82511
10
11
11
12
12
13
25
26
27
28
29
30
50628
50654
50679
50704
50729
50754
86237
86222
86207
86192
86178
86163
52126
52151
52175
52200
52225
52250
53607
53632
53656
53681
53705
53730
84417
84402
84386
84370
84355
84339
55072
55097
55121
55145
55169
55194
83469
83453
83437
83421
83405
83389
56521
56545
56569
56593
56617
56641
82495
82478
82462
82446
82429
82413
13
13
14
14-
15
15
31
32
33
34
.35
36
50779
50804
50829
50854
50879
50904
50929
50954
50979
51004
51029
51054
86148
86133
86119
86104
86089
86074
86059
86045
86030
86015
86000
85985
85970
85956
85941
85926
85911
85896
52275
52299
52324
52349
52374
52399
53754
53779
53804
53828
53853
53877
84324
84308
84292
84277
84261
84245
55218
55242
55266
55291
55315
55339
83373
83356
83340
83324
83308
83292
566&5
.56689
.56713
56736
56760
56784
82396
82380
82363
82347
82330
82314
29
28
27
26
25
24
8
7
7
7
7
6
15
16
16
17
17
18
18
18
19
19
20
20
37
38
39
40
41
42
43
44
45
46
47
48
52423
52448
52473
52498
52522
52.547
85157
85142
85127
85112
85096
85081
53902
53926
53951
53975
54000
54024
54049
54073
54097
54122
54146
54171
84230
84214
84198
84182
84167
84151
55363
55388
55412
55436
55460
55484
83276
83260
83244
83228
83212
83195
56808
56832
56856
56880
56904
56928
82297
82281
82264
82248
82231
82214
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
6
6
6
5
5
5
5
4
4
4
3
3
51079
51104
51129
51154
51179
51204
52572
52597
52621
52646
52671
52696
85066
85051
85035
85020
85005
84989
84974
84959
84943
84928
84913
84897
84135
84120
84104
84088
84072
84057
84041
84025
84009
83994
83978
83962
55509
55533
55557
55581
55605
55630
83179
83163
83147
83131
83115
83098
56952
56976
57000
57024
57047
57071
57095
57119
57143
57167
57191
57215
57238
57262
57286
57310
57334
57358
82198
82181
82165
82148
82132
82115
82098
82082
82065
82048
82032
82015
81999
81982
81965
81949
81932
81915
20
21
21
22
22
23
23
23
24
24
25
25
49
.50
51
52
53
54
51229
51254
51279
51304
51329
51354
85881
85866
85851
85836
85821
85806
52720
52745
52770
52794
52819
52844
52869
52893
52918
52943
52967
52992
54195
54220
54244
54260
54293
54317
55654
55678
55702
55726
55750
55775
55799
55823
55847
55871
55895
55919
83082
83066
83050
83034
83017
83001
3
3
2
2
2
2
55
56
57
58
59
60
51379
51404
51429
§1454
51479
51504
85792
85777
85762
85747
86732
85717
84882
84866
84851
84836
84820
84805
54342
54366
54391
54415
54440
54464
83946
83930
83915
83899
83883
83867
82985
82969
82953
82936
82920
82904
1
1
1
1
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N. sine.
N. COS.
N.sine.
M.
59°
58°
57° 1 56°
55°
TABLE 41.
[Page 763
Natural Sines and Cosines.
Prop.
St
°
86
o
37°
Zi
°
39°
Prop.
parts
23
1
parts
18
M.
N. sine.
N.cos.
N. sine.
N.cos.
N. sine.
N.cos.
N. sine.
N. cos.
N. sine.
N. cos.
57358
81915
58779
80902
60182
79864
61566
78801
62932
77715
60
18
1
57.381
81899
58802
80885
60205
79846
61589
78783
62955
77696
59
18
1
2
57405
81882
58826
80867
60228
79829
61612
78765
62977
77678
58
17
1
O
57429
81865
58849
80850
60251
79811
61635
78747
63000
77660
57
17
2
4
57453
81848
58873
80833
60274
79793
61658
78729
63022
77641
56
17
2
5
57477
81832
58896
80816
60298
79776
61681
78711
63045
77623
55
17
2
3
6
7
57501
81815
58920
80799
80782
60321
79758
61704
78694
63068
63090"
77605
77586
54
16
57524
81798
58943
60:M4
79741
61726
78676
53
16
3
8
57548
81782
58967
80765
60367
79723
61749
78658
63113
77568
52
16
3
9
57572
81765
58990
80748
60390
79706
61772
78640
63135
77550
51
15
4
10
57596
81748
59014
80730
60414
79688
61795
78622
63158
77531
50
15
4
11
57619
81731
59037
80713
60437
79671
61818
78604
63180
77513
49
15
5
12
57643
81714
59061
80696
80679
60460
60483^
79653
79635
61841
61864
78586
63203
77494
48
14
S
13
57667
81698
59084
78568
63225
77476
47
14
5
14
57691
81681
59108
80662
60506
79618
61887
78550
63248
77458
46
14
6
15
57715
81664
59131
80644
60529
79600
619«)
78532
63271
77439
45
14
6
16
57738
81647
59154
80627
60553
79583
61932
78514
63293
77421
44
13
7
17
57762
81631
59178
80610
60576
79565
61955
78496
63316
77402
43
13
7
7
18
19
57786
57810
81614
59201
80593
80576
60599
60622
79547
61978
62001
78478
63338
63361
77384
42
13
81597
59225
79530
78460
77366
41
12
8
20
57833
81580
59248
80558
60645
79512
62024
78442
63383
77347
40
12
8
21
57857
81563
59272
80541
60668
79494
62046
78424
63406
77329
39
12'
8
22
57881
81546
59295
80524
60691
79477
62069
78405
63428
77310
38
11
9
23
57904
81530
59318
80507
60714
79459
62092
78387
63451
77292
37
11
9
24
57928
81513
59342
59365
80489
80472
60738
60761
79441
62115
62138
78369
78351
63473
77273
36
11
10
25
57952
81496
79424
63496
77255
35
11
10
26
57976
81479
59389
80455
60784
79406
62160
78333
63518
77236
34
10
10
27
57999
81462
59412
80438
60807
79388
62183
78315
63540
77218
33
10
11
28
58023
81445
59436
80420
60830
79371
62206
78297
63563
77199
32
10
11
29
58047
81428
59459
• 80403
60853
79353
62229
78279
63585
77181
31
9
12
12
30
31
58070
81412
59482
80386
80368
60876
60899"
79335
79318
62251
62274
78261
63608
77162
30
9
58094
81395
59506
78243
63630
77144
29
9
12
32
58118
81378
59529
80351
60922
79300
62297
78225
63653
77125
28
8
13
33
58141
81361
59552
803;M
60945
79282
62320
78206
63675
77107
27
8
13
34
58165
81344
59576
80316
60968
79264
62;}42
78188
63698
77088
26
8
13
35
58189
81327
59599
80299
60991
79247
62365
78170
63720
77070
25
8
14
36
58212
81310
59622
80282
80264
61015
61038
79229
62388
78152
78134
63742
63765
77051
77033
24
23
/
14
37
58236
81293
59646
79211
62411
7
15
38
58260
81276
59669
80247
61061
79193
62433
78116
63787
77014
22
/
15
39
58283
81259
59693
80230
61084
79176
62456
78098
63810
76996
21
6
15
40
58307
81242
59716
80212
61107
79158
62479
78079
63832
76977
20
6
16
41
58330
81225
59739
80195
61130
79140
62502
78061
63854
76959
19
6
16
42
58354
81208
59763
80178
61153
79122
62524
78043
78025
63877
"63899"
76940
"76921"
18
17
5
16
43
58378
81191
59786
80160
61176
79105
62547
5
17
44
58401
81174
59809
80143
61199
79087
62570
78007
63922
76903
16
5
17
45
58425
81157
59832
80125
61222
79069
62592
77988
63944
76884
15
18
46
58449
81140
59856
80108
61245 i 79051
62615
77970
63966
7()866
14
4
18
47
58472
81123
59879
80091
61268
79033
62638
779.52
63989
76847
13
4
18
19
48
49
58496
81106
59902
80073
80056
61291
61314
79016
78998
62660
62683
77934
77916
64011
76828
12
4
3
58519
81089
59926
64033
76810
11
19
50
58543
81072
59949
80038
61337
78980
62706
77897
64056
76791
10
3
20
51
58567
81055
59972
80021
61360
78962
62728
77879
64078
76772
9
3
20
52
58590
81038
59995
80003
61383
78944
62751
77861
64100
76754
8
2
20
53
58614
81021
60019
79986
61406
78926
62774
77843
64123
76735
7
2
21
54
55
58637
58661
81004
60042
79968
61429
614.51
78908
78891
62796
77824
77806
64145
64167
76717
76698
6
2
21
80987
60065
79951
62819
5
2
21
56
58684
80970
60089
79934
61474
78873
62842
77788
64190
76679
4
1
22
57
58708
80953
60112
79916
61497
78855
62864
77769
64212
76661
3
1
22
58
58731
80936
60135
79899
61520
78837
62887
77751
64234
76642
2
1
23
59
58755
80919
60158
79881
61543
78819
62909
77733
64256
76623
1
23
60
58779
80902
60182
79864
61566
78801
629.32
77715
64279
76604
N.cos.
N. sine.
N.cos.
N. sine.
N.cos.
N. sine.
N.cos.
N. sine.
N.cos.
N. sine.
M.
1
64°
53°
52"
5
1°
50°
24972°— 12-
-38
Page 764j
TABLE 41.
Natural Sines and Cosines.
Prop.
parts
22
40° 1
41
o
42° 1
48° 1
44
Prop.
parte
19
M.
N.sine.
N. COS.
N.sine.
N.cos.
N.sine.
N.cos.
N.sine.
N.cos.
N.sine.
N. cos.
64279
76604
65606
75471
66913
74314
68200
73135
69466
71934
60
19
1
64301
76586
65628
75452
66935
74295
68221
73116
69487
71914
.59
19
1
?.
64323
76567
65650
75433
66956
74276
68242'
73096
69508
71894
58
18
1
3
64346
76548
65672
75414
66978
74256
()8264
73076
()9529
71873
01
18
1
4
64368
76530
65694
75395
66999
74237
68285
73056
69549
71853
56
18
2
5
64390
76511
65716
75375
67021
74217
68306
73036
69570
71833
oa
17
2
6
64412
76492
65738
75356
67043
74198
74178
68327
73016
69591
71813
54
53
17
3
7
64435
76473
65759
75337
67064
68349
72996
69612
71792
17
3
8
64457
76455
65781
75318
67086
74159
68370
72976
69633
71772
52
16
3
9
64479
76436
65803
75299
67107
74139
68,391
72957
696.54
71752
51
16
4
10
64501
76417
65825
75280
67129
74120
68412
72937
t)9675
71732
50
16
4
11
64524
76398
65847
75261
67151
74100
68434
72917
69696
71711
49
16
4
ft
12
13
64546
64568
76380
65869
75241
67172
■67194"
74080
74061
68455
72897
69717
71691
71671'
48
47
15
76361
65891
75222
68476
72877
69737
15
ft
14
64590
76342
65913
75203
67215
74041
68497
72*57
69758
716.50
46
15
6
15
•64612
76323
65935
75184
67237
74022
6^518
72837
69779
71630
45
14
6
16
64635
76304
65956
75165
67258
74002
68539
72817
69800
71610
44
14
6
17
64657
76286
65978
75146
67280
73983
68561
72797
69821
71590
43
14
7
7
18
64679
76267
66000
66022
75126
75107
67301
73963
68582
72777
69842
69862
71569
71549
42
41
13
13
19
64701
76248
67323
73944
68603
72757
7
20
64723
76229
66044
75088
67344
73924
68624
72737
69883
71529
40
13
• 8
21
64746
76210
66066
75069
67366
73904
68645
72717
69904
71508
39
12
8
22
64768
76192
66088
75050
67387
73885
68666
72697
69925
71488
38
12
8
23
64790
76173
66109
75030
67409
73865
68688
72677
69946
71468
37
12
9
24
64812
76154
66131
75011
74992
67430
73846
68709
68730
72657
72637
69966
69987
71447
36
11
9
25
64834
76135
66153
67452
73826
71427
35
11
10
26
64856
76116
66175
74973
67473
73806
68751
72617
70008
71407
34
11
10
27
64878
76097
66197
74953
67495
73787
68772
72597
70029
71386
33
10
10
28
64901
76078
66218
74934
67516
73767
68793
72577
70049
71366
32
10
11
29
64923
76059
66240
74915
67538
73747
68814
72557
70070
71.345
31
10
11
30
31
64945
64967
76041
66262
74896
67559
73728
68835
72537
72517
70091
71325
30
10
9
11
76022
66284
74876
67580
73708
68857
70112
71305
29
12
•32
64989
76003
66306
74857
67602
73688
68878
72497
70132
71284
28
9
12
33
65011
75984
66327
74838
67623
73669
()8899
72477
70153
71264
27
9
12
34
65033
75965
66349
74818
67645
73649
68920
72457
70174
71243
26
8
13
35
65055
75946
66371
74799
67666
73629
68941
72437
70195
71223
25
8
13
36
65077
75927
66393
74780
67688
73610
68962
72417
72397
70215
71203
24
8
14
37
65100
75908
66414
74760
67709
7359Q
68983
70236
71182
23
7
14
38
65122
75889
66436
74741
67730
73570
69004
72377
70257
71162
22
7
14
39
65144
75870
66458
74722
67752
73551
69025
72357
70277
71141
21
7
15
40
65166
75851
66480
74703
67773
73531
69046
72337
70298
71121
20
6
15
41
65188
75832
66501
74683
67795
73511
69067
72317
70319
71100
19
6
15
42
65210
75813
66523
74664
67816
73491
73472
69088
69109
72297
70339
71080
18
17
6
5
16
43
05232
75794
66545
74644
67837
72277
70360
71059
16
44
65254
75775
66566
74625
67859
73452
69130
72257
70381
71039
16
17
45
65276
75756
66588
74606
67880
73432
69151
72236
70401
71019
15
17
46
65298
75738
66610
74586
67901
73413
69172
72216
70422
70998
14
4
17
47
65320
75719
66632
74567
67923
73393
69193
72196
70443
70978
13
4
18
18
48
49
65342
65364
75700
66653
74548
67944
73373
69214
69235
72176
72156
70463
. 70484
70957
12
4
75680
66675
74528
67965
73353
70937
a
•3
18
50
65386
75661
66697
74509
67987
73333
69256
72136
70505
70916
10
3
19
51
65408
75642
66718
74489
68008
73314
69277
72116
70525
70896
9
3
19
52
65430
75623
66740
74470
68029
73294
69298
1 72095
70546
70875
8
3
19
53
65452
75604
66762
74451
68051
73274
69319
72075
70567
70855
/
2
20
20
54
55
65474
.65496
75585
75566
66783
74431
68072
73254
69340
72055
70587
70608
70834
70813
6
5
2
2
66805
74412
68093
732;?4
69361
\ 72035
21
56
65518
75547
66827
74392
68115
73215
69382
72015
70628
70793
4
1
21
57
65540
75528
66848
74373
68136
73195
69403
71995
70649
70772
3
1
21
58
65562
75509
66870
74353
68157
73175
69424
71974
70670
70752
1
22
59
65584
75490
66891
74334
68179
73155
69445
71954
70690
70731
I
22
60
65606
75471
66913
74314
68200
73135
69466
71934
70711
70711
N.cos.
N.sine.
N. COS.
N.sine.
N.cos.
N. sine.
N.cos.
N. sine.
N.cos.
N.sine.
M.
49°
48°
4J°
46°
4o°
___
TABLE 42.
[Page 765
Logarith
ms of Numbers.
No.
1 100.
Log. 0.00000 2.00000. 1
No.
Log.
No.
Log.
No.
Log.
No.
Log.
No.
Log.
1
0.00000
21
1. 32222
41
1. 61278
61
1. 78533
81
1. 90849
2
0. 30103
22
1. 34242
42
1. 62325
62
1.79239
82
1.91.381
3
0.47712
23
1. 36173
43
1. 63347
63
1. 79934
83
1. 91908
4
0. 60206
24
1. 38021
44
1.64345
64
1.80618
84
1.92428
5
0. 69897
25
1. 39794
45
1. 65321
65
1. 81291
85
1.92942
6
0. 77815
26
1. 41497
46
1. 66276
66
1. 81954
86
1.93450
7
0. 84510
27
1. 43136
47
1. 67210
67
1. 82607
87
1.93952
8
0. 90309
28
1.44716
48
1. 68124
68
1. 83251
88
1. 94448
9
0. 95424
29
1. 46240
49
1.69020
69
1. 83885
89
1.94939
10
1.00000
30
1. 47712
50
1. 69897
70
1. 84510
90
1. 95424
11
1. 04139
31
1.49136
51
1. 70757
71
1. 85126
91
1.95904
12
1.07918
32
1.50515
52
1. 71600
72
1. 85733
92
1. 96379
13
1. 11394
33
1.51851
53
1. 72428
73
1. 86332
93
1. 96848
14
1. 14613
34
1. 53148
54
1. 73239
74
1. 86923
94
1. 97313
15
1. 17609
35
1.54407
55
1.74036
75
1. 87506
95
1. 97772
16
1. 20412
36
1. 55630
56
1. 74819
76
1. 88081
96
1. 98227
17
1. 23045
37
1. 56820
57
1. 75587
77
1. 88649
97
1. 98677
18
1. 25527
38
1.57978
58
1. 76343
78
1. 89209
98
1. 99123
19
1.27875
39
1. 59106
59
1. 77085
79
1. 89763
99
1.99564
20
1. 30103
40
1.60206
. 60
1. 77815
80
1. 90309
100
2. 00000
Page 766]
TABLE 42.
Logarithms of Numbers.
No.
100 1600
Log. 00000-
—20412. 1
No.
1
2
»
4
6
6
7
8
1
100
101
102
103
104
OOOOO
00432
00860
01284
01703
00043
00475
00903
01326
01745
02160
02572
02979
03383
03782
04179
04571
04961
05346
05729
00087
00518
00945
01368
01787
0O130
00561
00988
01410
01828
02243
02653
03060
03463
03862
04258
04650
05038
05423
05805
00173
00604
01030
01452
01870
02284
02694
03100
03503
03902
04297
04689
05077
05461
05843
00217
00647
01072
01494
01912
02325
02735
03141
03543
03941
00260
00689
01115
01536
0I9.">:i
02366
02776
03181
03583
03981
00303
00732
01157
01578
0199.1
02407
02816
03222
03623
04021
04415
04805
05192
05576
05956
00346
00775
01199
01620
020;!6
02449
02857
03262
03663
04060
00389
00817
01242
01662
02078
02490
02898
03302
03703
04100
04493
04883
05269
05652
06032
1
2
3
4
5
6
7
8
9
43
4
9
13
17
22
26
30
34
39
43
4
8.
13
17
21
25
29
34
38
105
106
107
108
109
110
111
112
113
114
02119
02531
02938
03342
03743
02202
02612
03019
03423
03822
04139
04532
04922
05308
05690
06070
0644H
06819
07188
07555
04218
04610
04999
05385
05767
04336
04727
05115
05500
05881
04376
04766
05154
05538
05918
04454
04844
05231
05614
05994
06371
06744
07115
07482
07846
2
3
4
5
6
7
8
9
41
4
8
12
16
21
25
29
33
37
40
4
8
12
16
20
24
28
32
36
115
116
117
118
119
06108
06483
06856
07225
07591
07954
08314
08672
09026
09377
09726
10072
10415
10755
11093
11428
11760
12090
12418
12743
06145
06521
06893
07262
07628
07990
08350
08707
09061
09412
09760
10106
10449
10789
11126
06183
06558
06930
07298
07664
08027
08386
08743
09096
09447
09795
10140
10483
10823
11160
06221
06595
06967
07335
07700
08063
08422
08778
09132
09482
09830
10175
10517
10857
11193
11528
11860
12189
12516
12840
13162
13481
13799
14114
14426
14737
15045
15351
15655
15957
16256
16554
16850
17143
17435
17725
18013
18298
18583
18865
19145
19424
19700
19976
20249
06258
06633
07004
07372
07737
08099
08458
08814
09167
09517
09864
10209
10551
10890
11227
06296
06670
07041
07408
07773
08135
08493
08849
09202
09552
09899
10243
10585
10924
11261
06333
06707
07078
07445
07809
06408
06781
07151
07518
07882
08243
08600
08955
09307
09656
10003
10346
10687
11025
11361
120
121
1.22
123
124
125
126
127
128
129
07918
08279
08636
08991
09342
09691
10037
10380
10721
11059
08171
08529
08884
09237
09587
08207
08565
08920
09272
09621
2
3
4
5
6
7
8
9
39
4
8
12
16
20
23
27
31
35
38
4
8
11
15
19
23
27
30
34
09934
10278
10619
10958
11294
09968
10312
10653
10992
11327
11661
11992
12320
12646
12969
130
131
132
133
134
135
136
137
138
139
11394
11727
12057
12385
12710
11461
11793
12123
12450
12775
11494
11826
12156
12483
12808
11561
11893
12222
12548
12872
11594
11926
12254
12581
12905
11628
11959
12287
12613
12937
11694
12024
12352
12678
13001
13322
13640
13956
14270
14582
14891
15198
15503
15806
16107
16406
16702
16997
17289
17580
17869
18156
18441
18724
19005
1 87
36
1
2
3
4
5
6
7
8
9
4
7
11
15
19
22
26
30
33
4
7
11
14
18
22
25
29
32
13033
13354
13672
13988
14301
13066
13386
13704
14019
14333
13098
13418
13735
14051
14364
13130
13450
13767
14082
14395
13194
13513
13830
14145
14457
14768
15076
15381
15685
15987
16286
16584
16879
17173
17464
17754
18041
18327
18611
18893
13226
13545
13862
14176
14489
13258
13577
13893
14208
14520
14829
15137
15442
15746
16047
16346
16643
16938
17231
17522
17811
18099
18384
18667
18949
13290
13609
13925
14239
14551
14860
15168
15473
15776
16077
16376
16673
16967
17260
17551
17840
18127
18412
18696
18977
19257
19535
19811
20085
20358
140
141
142
143
144
145
146
147
148
149
14613
14922
15229
15534
15836
14644
14953
15259
15564
15866
14675
14983
15290
15594
15897
14706
15014
15320
15625
15927
14799
15106
15412
15715
16017
16316
16613
16909
17202
17493
17782
18070
18355
18639
18921
So
34
1
2
3
4
5
6
7
8
9
4
7
11
14
18
21
25
28
32
3
7
10
14
17
20
24
27
31
16137
16435
16732
17026
17319
16167
16465
16761
17056
17348
16197
16495
16791
17085
17377
17667
17955
18241
18526
18808
16227
16524
16820
17114
17406
17696
17984
18270
18554
18837
19117
19396
19673
19948
20222
150
151
152
153
154
17609
17898
18184
18469
18752
19033
19312
19590
19866
20140
17638
17926
18213
18498
18780
T
2
3
4
5
6
7
8
9
33
3"
7
10
13
17
20
23
26
30
32
3
6
10
13
16
19
22
26
29
155
156
157
158
159
19061
19340
19618
19893
20167
19089
19368
19645
19921
20194
19173
19451
19728
20003
20276
19201
19479
19756
20030
20303
19229
19507
19783
20058
20330
19285
19562
19838
20112
20385
No.
1
2
3
4
6
6
J
8
9
TABLE 42.
Logarithms of Numbers.
[Page 757
No. 1600 2200.
Log. 20412—
-34242. 1
No.
1
2
3
4
5
6
7
8
9
160
161
162
163
164
20412
20683
20952
21219
21484
20439
20710
20978
21245
21511
20466
20737
21005
21272
21537
20493
20763
21032
21299
21564
20520
20790
'210.59
21325
21590
21854
22115
22376
22634
22891
20548
20817
21085
21352
21617
21880
22141
22401
22660
22917
23172
23426
23679
23930
24180
20575
20844
21112
21378
21643
21906
22167
22427
22686
22943
23198
23452
23704
23955
24204
20602
20871
21139
21405
21669
21932
22194
22453
22712
22968
23223
23477
23729
23980
24229
20629
20898
21165
21431
21696
21958
22220
22479
22737
22994
20656
20926
21192
21458
21722
21985
22246
22505
22763
23019
1
2
3
4
6
6
7
8
9
31
3
6
9
12
16
19
22
25
28
30
3
6
9
12
15
18
21
24
27
165
166
167
168
169
21748
22011
22272
22531
22789
21775
22037
22298
22557
22814
21801
22063
22324
22583
22840
21827
22089
22350
22608
22866
170
171
172
173
174
23045
23:300
23553
23805
24055
24304
24551
24797
25042
25285
23070
23325
23578
23830
24080
23096
23350
23603
23^53
24105
23121
23376
23629
23880
24130
23147
23401
23654
23905
241.55
23249
23602
23754
24005'
•24254
23274
23528
23779
24030
24279
1
2
3
4
5
6
7
8
9
29
3
6
9
12
15
17
20
23
26
28
3
6
8
11
14
17
20
22
25
175
176
177
178
179
24329
24576
24822
23066
25310
24353
24601
24846
25091
25334
25575
25816
26055
26293
26529
26764
26998
27231
27462
27692
27921
28149
28375
28601
28825
24378
24625
24871
25115
25358
25600"
24403
24650
24895
25139
25382
24428
24674
24920
25164
25406
24452
24699
24944
25188
25431
24477
24724
24969
25212
26465
25696
25936
26174
26411
26647
24602
24748
24993
25237
26479
24527
24773
25018
25261
25603
26744
180
181
182
183
184
25527
25768
26007
26245
26482
25551
25792
26031
26269
26505
26741
26975
27207
27439
27669
25624 ' 25648
25672
25912
26150
26387
26623
26a58
27091
27323
27554
27784
26720
25840 25864 ' 25888
26079 , 26102 I 26126
26316 26;«0 ' 26364
26553 26576 ' 26600
26788 26811 ! 26834
27021 27045 ': 27068
27254 27277 . 27300
27485 27508 1 27531
27715 27738 > 27761
27944 27967 ! 27989
28171 28194 ! 28217
28398 1 28421 28443
25959 ' 26983
26198 26221
26436 1 26458
26670 ; 26694
1
2
3
4
5
6
7
8
9
27
3
5
8
11
14
16
19
22
24
26
3
5
8
10
13
16
18
21
23
185
186
187
188
189
26717
26951
27184
27416
27646
26881
27114
27346
27577
27807
26905
27138
27370
27600
27830
28058
26928
27161
27393
27623
27852
190
191
192
193
194
27875
28103
28330
28556
28780
27898
28126
28353
2^578
28803
28012 : 28035
28240 i 28262
28466 28488
28081
28285 zsdvt
28611 i 28533
28735 ; 28758
28959 ' 28981
1
2
3
4
5
6
7
8
9
25
24
28623 ' 28646
28847 28870
28668
28892
29115
293,36
29557
29776
29994
28691
28914
28713
28937
29159
29380
29601
29820
,30038
3
6
8
10
13
16
18
20
23
2
6
7
10
12
14
17
19
22
195
196
197
198
199
29003
29226
29447
29667
29885
30103
30320
30535
30750
30963
29026
29248
29469
29688
29907
30125
30341
30557
30771
30984
29048
29270
29491
29710
29929
30146
30363
30578
30792
31006
29070 29092
29292 29314
29513 29535
29732 ' 29754
29951 29973
291.37
29^58
29579
29798
30016
29181
29403
29623
29842
30060
30276
29203
29425
29646
29863
.30081
200
201
202
203
204
30168 30190 i 30211
30384 30406 30428
30600 30621 ' 30643
30233 1 30255
30449 , 30471
30664 30685
30878 ,30899
31091 31112
30298
30707 ; 30728
1
2
3
4
5
6
7
8
9
28
2
6
7
9
12
14
16
18
21
22
30814
31027
308.35 1 30856
31048 i 31069
31260 i 31281
31471 1 31492
31681 31702
31890 31911
32098 32118
30920
31133
30942
31164
2
4
7
9
11
13
15
18
20
205
206
207
208
209
31175
31387
31597
31806
32015
31197
31408
31618
31827
32035
31218
31429
31639
31848
32056
31239
31450
31660
31869
32077
31302
31513
31723
31931
.321,39
31323
31634
31744
31962
32160
31345
31565
31765
31973
.32181
31366
31576
31785
31994
32201
32408
32613
32818
33021
33224
33425
3,3626
33826
340^5
34223
210
211
212
213
214
32222
32428
32634
32838
33041
32243
32449
32654
32858
33062
33264
33465
33(i6(i
33866
34064
32263
32469
32675
32879
33082
33284
;«486
33686
33885
;M084
32284 32305 , 32325
32490 32510 ; 32531
32346
32.562
32756
32960
33163
32,366
32572
32777
32980
.33183
33385"
,33586
33786
33985
34183
32387
32593
32797
33001
33203
33406
33606
33806
34005
34203
.32695 1 32715
32899 j 32919
33102 ; 33122
327.36
32940
33143
.33345
33546
33746
33946
34143
1
2
3
4
5
6
7
8
9
21
20
2
4
6
1?
13
15
17
2
4
6
8
10
12
14
16
215
216
217
218
219
33244
3,3445
33646
33846
34044
33304
3.3.506
33706
33905
34104
3.^325
3.3526
337f6
33925
UV2i
33365
33666
33766
33965
34163
No.
1
2
3
4
6
6
7
8
9
19
18
Page 758]
TABLE 42.
Logarithms
of Numbers.
No.
2200 2800.
Log. 34242-
44716.
No.
1
2
3
4
5
6
7
S
9
220
34242
34262
34282
34301
34321
34341
34361
34380
34400
34420
221
34439
34459
34479
34498
34518
34537
34557
34577
34596
34616
20
222
34635
34655
34674
34694
34713
34733
34753
34772
34792
34811
1
2
223
34830
34850
34869
34889
34908
34928
34947
34967
34986
35005
2
4
224
35025
35044
35238
36064
35083
35102
36122
35141
36160
35180
35199
35392
3
4
6
8
225
35218
35257
35276
35295
35315
35334
35353
35372
226
35411
35430
35449
35468
35488
35507
35526
35.545
35564
35583
5
10
227
35603
35622
35641
35660
;«679
36698
35717
35736
357,55 1 35774
6
12
228
35793
35813
35832
35851
35870
35889
36908
35927
35946
3596.5
7
14
229
35984
36003
36021
36040
36059
36078
36097
36116
36135
36154
8
9
16
18
230
36173
36192
36211
36229
36248
36267
36286
36305
36324
36342
231
36361
36380
36399
36418
36436
36455
36474
36493
36511
36530
X9
232
36549
36568
36586
36605
36624
36642
36661
36680
36698
,36717
I
2
233
36736
36754
36773
36791
36810
36829
36847
36866
36884
36903
2
4
234
235
36922
36940
36059
37144
36977
36996
37014
37033
37051
37070
37088
3
4
6
8
37107
37125
37162
37181
37199
37218
37236
37254
37273
236
37291
37310
37328
37346
37365
37383
37401
37420
37438
37457
5
10
237
37475
37493
37511
37530
37548
37566
37585
37603
37621
37639
6
11
238
37658
37676
37694
37712
37731
37749
37767
37785
37803
37822
7
13
239
37840
37858
37876
37894
37912
37931
37949
37967
37985
,38003
38184"
38364
8
9
15
17
240
241
38021
38202
38039
38220
38057
38238
38075
38256
38093
38274
38112
38292
38130
38310
38148
38328
38166
38346
18
242
38382
38399
38417
38435
38453
38471
38489
38507
38525
38543
243
38561
38578
38596
38614
38632
38650
38668
38686
38703
38721
1
2
3
4
5
6
2
244
38739
38757
38775
38792
38810
38828
38846
38863
39041
38881
39058
38899
39076
4
6
7
9
11
13
14
16
245
38917
38934
38952
38970
38987
39005
39023
246
39094
39111
39129
39146
39164
39182
39199
39217
39235
39252
247
39270
39287
39305
39322
39340
39358
39375
39393
39410
39428
248
.39445
39463
39480
39498
39515
39533
39650
39568
39585
.39602
249
39620
39637
39655
39672
39690
39707
39724
39742
39759
39933
39777
399.50
8
9
250
251
39794
39967
39811
39985
39829
40002
39846
40019
39863
40037
39881
40054
39898
40071
39915
40088
40106
40123
252
253
40140
40312
40157
40329
40175
40346
40192
40364
40209
40381
40226
40398
40243
40415
40261
40432
40278
40449
40295
40466
17
1
2
254
40483
40500
40518
40688
40535
40552
40569
40586
40756
40603
40773
40620
40790
40637
2
3
3
5
255
40654
40671
40705
40722
40739
40807
256
40824
40841
40858
40875
40892
40909
40926
40943
40960
40976
4
7
257
40993
41010
41027
41044
41061
41078
41095
41111
41128
41145
5
9
258
41162
41179
41196
41212
41229
41246
41263
41280
41296
41313
b
10
259
41330
41347
41363
41380
41397
41414
41430
41447
41464
41481
8
9
12
14
15
260
41497
41514
41531
41547
41564
41581
41597
41614
41631
41647
261
41664
41681
41697
41714
41731
41747
41764
41780
41797
41814
262
41830
41847
41863
41880
41896
41913
41929
41946
41963
41979
16
263
41996
42012
42029
42045
42062
42078
42095
42111
42127
42144
1
2
264
42160
42177
42193
42210
42226
42243
42259
42423
42275
424.39
42292
42308
2
3
3
5
265
42325
42341
42357
42374
42390
42406
42465
42472
266
42488
42504
42521
42537
42553
42570
42586
42602
42619
42635
4
6
267
42651
42667
42684
42700
42716
42732
42749
42765
42781
42797
5
8
268
42813
428.30
42846
42862
42878
42894
42911
42927
42943
42959
6
10
269
42975
42991
43008
43024
43040
43201
43056
43217
43072
43233
43088
43249^
43104
43120
7
8
11
13
270
43136
43152
43169
43185
43265
43281
271
272
43297
43457
43313
43473
43329
43489
43345
43505
43361
43621
4^377
43537
43393
43.563
43409
43569
43426
43684
43441
43600
9
14
15
273
43616
43632
43648
43664
43680
43696
43712
43727
43743
43759
1
2
274
43775
43791
43807
43823
43838
43854
44012
43870
44028
43886
44044
43902
44059
43917
2
3
3
5
275
43933
43949
43965
4;»81
43996
44075
276
44091
44107
44122
44138
44154
44170
44326
44185
44201
44217
44232
4
6
277
44248
44264
44279
44295
44311
44342
44358
44373
44389
5
8
278
44404
.44420
44436
44451
44467
44483
44498
44514
44529
44645
6
9
279
44560
44576
44592
44607
44623
44638
44654
44669
44685
44700
7
8
9
11
12
14
No.
1
2
s
4
5
6
7
8
9
TABLE 42.
Logarithms of Numbers.
[Page 769
No. 2800 3400.
Log. 14716 53148.
No.
1
2
3
4
5
6
7
8
9
1
280
281
282
283
284
44716
44871
45025
45179
45332
44731
44886
45040
45194
45347
44747
44902
45056
45209
45362
45515
45667
45818
45969
46120
44762
44917
45071
45225
45378
45530
45682
45834
45984
46135
44778
44932
45086
45240
45393
45545
45697
45849
46000
46150
44793
44948
45102
452.55
45408
45561
45712
45864
46015
46165
44809
44963
45117
45271
45423
45576
45728
45879
46030
46180
44824
44979
45133
45286
45439
45591
45743
45894
46045
46195
46345
46494
46642
46790
46938
44840
44994
45148
45301
45454
44855
45010
45163
45317
45469
16
1
2
3
4
5
6
7
8
9
2
3
5
6
8
10
11
13
14
285
286
287
288
289
45484
45637
45788
45939
46090
45500
45652
45803
45954
46105
45606
45758
45909
46060
46210
46359
45621
45773
45924
46075
46225
290
291
292
293
294
46240
46389
46538
46687
46835
46255
46404
46553
46702
46850
46270
46419
46668
46716
46864
46285
46434
46583
46731
46879
46300
46449
46598
46746
46894
46315
46464
46613
46761
46909
46330
46479
46627
46776
46923
46374
46509 46523
46657 ' 46672
46805 46820
46953 i 46967
1
15
1
2
3
4
5
6
7
8
9
2
3
5
6
8
9
11
12
14
295
296
297
298
299
46982
47129
47276
47422
47567
46997
47144
47290
47436
47582
47727
47871
48015
48159
48302
47012
47159
47305
47451
47596
47741
478*5
48029
48173
48316
47026
47173
47319
47465
47611
47041
47188
47334
47480
47625
47056
47202
47349
47494
47640
47070
47217
47363
47509
47654
47085
47232
47378
47524
47669
47100
47246
47392
47538
47683
47114
47261
47407
47553
47698
47842
47986
48130
48273
300
301
302
303
304
47712
47857
48001
48144
48287
47756
47900
48044
48187
48330
47770
47914
48058
48202
48344
47784
47929
48073
48216
48359
47799
47943
48087
48230
48373
48515
48657
48799
48940
49080
47813
47958
48101
48244
48387
48530
48671
48813
48954
49094
47828
47972
48116
48259
48401 ! 48416
48544 48558
48686 48700
48827 48841
48968 48982
49108 1 49122
49248 1 49262
49388 49402
49527 49541
49665 49679
49803 1 49817
49941 j 49955
50079 1 50092
.50215 ! 50229
50352 50365
50488 50501
1
305
306
307
308
309
48430
48572
48714
48855
48996
48444
48586
48728
48869
49010
48458
48601
48742
48883
49024
48473
48615
48756
48897
49038
48487
48629
48770
48911
49052
4*501
48643
487*5
48926
49066
1
2
3
4
5
6
7
8
9
14
1
3
4
6
7
8
10
11
13
310
311
312
313
314
49i;i6
49276
49415
49554
49693
491.50
49290
49429
49568
49707
49845
49982
50120
50256
50393
50529
50664
50799
50934
51068
49164
49304
49443
49582
49721
49178
49318
49457
49596
49734
49192
49332
49471
49610
49748
49206
49346
49485
49624
49762
49220
49360
49499
49638
49776
49234
49374
49513
49651
49790
49927
50065
50202
50338
50474
50610
50745
50880
51014
51148
315
316
317
318
319
49831
49969
50106
50243
50379
49859
49996
50133
50270
50406
49872
50010
50147
50284
50420
49886
50024
50161
50297
50433
5a569
50705
50840
50974
51108
49900
50037
50174
50311
50447
50583
50718
50853
50987
51121
49914
50051
50188
50325
50461
50596
.50732
50866
51001
51135
1
13
1
2
3
4
5
6
7
8
9
1
3
4
5
7
8
9
10
12
320
321
322
323
324
325
326
327
328
329
50515
50651
.50786
50920
51055
50542
50678
50813
50947
51081
50556
50691
50826
50961
51095
50623
50759
50893
51028
51162
50637
50772
50907
51041
51175
51188
51322
51455
51587
51720
51202
51335
51468
51601
51733
51215
51348
51481
51614
51746
51228
51362
51495
51627
51759
51242
51375
51508
51640
51772
51255
51388
51521
51654
51786
51268
51402
51534
51667
51799
51282
51415
51548
51680
51812
51943
52075
52205
52.336
52466
52595
52724
52853
52982
53110
51295
51428
51561
51693
51825
51957
52088
.52218
52.349
52479
52608
52737
52866
52994
53122
51308
51441
51574
51706
51838
1
330
.331
332
333
334
51851
51983
52114
52244
52375
51865
51996
52127
52257
52388
51878
52009
.52140
52270
52401
51891
52022
52153
52284
52414
51904
52035
52166
52297
52427
51917
52048
52179
52310
52440
51930
.52061
52192
52323
52453
51970
52101
52231
52362
52492
5262f
52750
52879
53007
53135
12
1
2
3
4
5
6
7
8
9
1
2
4
5
6
7
8
10
11
335
336
337
338
339
52504
52634
52763
52892
53020
52517
52647
52776
52905
53033
52530
52660
52789
52917
53046
52543
52673
52802
52930
53058
52556
52686
52815
52943
53071
52569
52699
52827
52956
53084
52582
52711
52840
52969
53097
No.
1
2
3
4
5
6
7
8
9
Page 760]
TABLE 42.
Logarithms of Numbers.
No.
S400 1000.
Log. 53148-
60206.
No.
1
2
3
4
5
6
;
8
9
340
341
342
343
344
53148
53275
53403
53529
53656
53161
53288
53415
53542
53668
53173
53301
53428
53555
53681
53186
53314
53441
53567
53694
53199
53326
53453
53580
53706
53832
53958
54083
54208
54332
53212
53339
53466
53593
53719
53224
53352
53479
53605
53732
53237
53364
53491
53618
53744
53870"
53995
54120
54245
54370
54494
54617
54741
54864
54986
53250
53377
53504
53631
53757
53263
53390
53517
53643
53769
63895
54020
54145
54270
54394
13
1
■>
i
5
6
8
9
1
3
4
5
7
8
9
10
12
12
345
346
347
348
349
53782
53908
54033
54158
54283
53794
53920
54045
54170
54295
53807
53933
54058
54183
54307
53820
53945
54070
54195
54320
53845
53970
54095
54220
54345
53857
53983
54108
54233
54357
53882
54008
54133
54258
54382
350
351
352
353
354
54407
54531
546.54
54777
54900
54419
54543
54667
54790
54913
54432
54555
54679
54802
54925
54444
54568
54691
54814
54937
54456
54580
54704
54827
54949
54469
54593
54716
54839
54962
54481
54605
54728
54851
54974
54506
54630
54753
54876
54998
54518
.54642
.54765
54888
55011
"55133
552.55
55376
55497
55618
55739
55859
55979
56098
56217
355
356
357
358
359
55023
55145
55267
55388
55509
55035
55157
55279
55400
55522
55047
55169
55291
55413
55534
55060
55182
55303
55425
55546
55072
55194
55315
55437
55558
55678
55799
55919
56038
56158
55084
55206
55328
55449
55570
55096
55218
55340
55461
55582
55108
55230
55352
55473
55594
55121
55242
55364
55485
55606
1
2
3
4
5
6
7
8
9
1
2
4
5
6
7
8
10
11
360
361
362
363
364
365
366
367
368
369
55630
55751
55871
55991
56110
" 56229
56348
56467
56585
56703
55642
55763
55883
56003
56122
55654
55775
55895
56015
56134
55666
55787
55907
56027
56146
55691
55811
55931
56050
56170
55703
55823
55943
56062
56182
55715
55835
55955
56074
56194
55727
55847
55967
56086
56205
56241
56360
56478
56597
56714
56253
56372
56490
56608
56726
56265
56384
56502
56620
56738
56277
56396
56514
56632
56750
56289
56407
56526
56644
56761
56301
56419
56538
56656
56773
56312
56431
56549
56667
56785
56902
57019
57136
57252
57368
56324
56443
56561
56679
56797
56336
.56455
56573
56691
56808
56926
57043
57159
57276
57392
57507"
57623
57738
57852
57967
370
371
372
373
374
375
376
377
378
379
56820
56937
57054
57171
57287
56832
56949
57066
57183
57299
56844
56961
57078
57194
57310
56855
56972
57089
57206
57322
56867
56984
57101
57217
57334
56879
56996
57113
57229
57345
56891
57008
57124
57241
57357
56914
57031
57148
57264
57380
11
1
2
3
4
5
6
7
8
9
1
2
3
4
6
7
8
9
10
57403
57519
57634
57749
57864
57415
57530
57646
57761
57875
57426
57542
57657
57772
57887
57438
57553
57669
57784
57898
58013
58127
58240
58354
58467
57449
57565
57680
57795
57910
57461
57576
57692
57807
57921
57473
57588
57703
57818
57933
57484
57600
57715
57830
57944
57496
57611
57726
57841
57955
380
381
382
383
384
"^385"
386
387
388
389
57978
58092
58206
58320
58433
57990
58104
58218
58331
58444
58001
58115
58229
58343
58456
58024
58138
58252
58365
58478
58035
58149
58263
58377
58490
58047
58161
58274
58388
58501
58614
58726
58838
58950
59062
58058
58172
58286
58399
58512
58070
58184
58297
58410
58524
58636
58749
58861
58973
59084
58081
58195
58309
58422
58535
5864"7"
58760
58872
58984
59095
58546
58659
58771
58883
58995
58557
58670
58782
58894
59006
58569
58681
58794
58906
59017
58580
58692
58805
58917
59028
58591
58704
58816
58928
59040
58602
58715
58827
58939
59051
58625
58737
58850
58961
59073
59184
59295
59406
59517
59627
10
390
391
392
393
394
59106
59218
59329
59439
59550
59118
59229
59340
59450
59561
59129
59240
59351
59461
59572
59140
5925J
59362
59472
59583
59151
59262
59373
59483
59594
59162
59273
59384
59494
59605
59173
59284
59395
59506
59616
59726
59835
59945
60054
60163
59195
59306
59417
59528
59638
59207
59318
59428
59539
59649
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
395
396
397
398
399
59660
59770
59879
59988
60097
59671
59780
59890
59999
60108
59682
59791
59901
60010
60119
59693
59802
59912
60021
60130
59704
59813
59923
60032
60141
59715
59824
59934
60043
60152
59737
59846
59956
60065
60173
59748
59857
59966
60076
60184
59759
59868
59977
60086
60195
No.
1
2
3
4
5
6
7
8
9
1
TABLE 42.
[Page 761
Logarithms of Numbers.
No.
4000 1600.
Log. 60206 66276. |
No.
1
.)
3
4
a
»
7
8
9
1
400
401
60206
60314
60217
60325
60228
60336
60239
60347
60249
60358
60260
60369
60271
60379
60282
60390
60293
60401
60304
60412
11
402
60423
60433
60444
60455
60466
60477
60487
60498
60509
60520
1
1
403
60531
60541
60552
60563
60574
60584
60595
60606
60617
60627
2
404
60638
60746
60649
60660
60670
60681
60692
60703
60713
60724
60831
60735
60842
3
4
3
4
6
V,
8
9
10
405
60756
60767
60778
60788
60799
60810
60821
406
60853
60863
60874
60885
60895
60906
60917
60927
60938
60949
6
407
60959
60970
60981
60991
61002
61013
61023
61034
61045
61055
408
61066
61077
61087
61098
, 61109
61119
61130
61140
61151
61162
8
9
409
410
61172
61278
61183
61194
61204
61215
61225
61236
61247
61257
61268
61289
61300
61310
61321
61331
61342
61352
61363
61374
411
61,384
61395
61405
61416
61426
61437
61448
61458
61469
61479
412
61490
61500
61511
61521
61532
61542
61553
61563
61574
61584
413
61595
61606
61616
61627
61637
«1648
61658
61669
61679
61690
414
61700
61711
61815
61721
61731
61742
61752
61857
61763
61868
61773
61784
61794
415
61805
61826
61836
61847
61878
61888
61899
416
61909
61920
61930
61941
61951
61962
61972
61982
61993
62003
417
62014
62024
62034
62045
62055
62066
62076
62086
62097
62107
418
62118
62128
62138
62149
62159
62170
62180
62190
62201
62211
419
62221
62232
62336
62242
62252
62263
62273
62284
62294
62304
62315
420
62325
62346
62356
62366
62377
62387
62397
62408
62418
421
62428
624,39
62449
62459
62469
62480
62490
62.500
62511
62521
422
62531
62.542
62552
62562
62572
62583
62593
62603
62613
62624
423
626.34
62644
62655
62665
62675
62685
62696 62706
62716
62726
424
62737
62747
62849
62757
6''8,59
62767
62870
62778
62880
6**890
<;L'7iis 62808
62'l00 *^^Qin
62818
62829
10
425
62839
62921
62931
426
62941
62951
62961
62972
62982
62992
63002
63012
63022
63033
1
2
3
4
5
1
2
3
4
5
427
63043
63053
63063
63073
63083
63094
63104
63114
63124
63134
428
63144
63155
63165
63175
63185
63195
63205
63215
63225
63236
429
430
63246
63347
63256
63^57"
63266
63367
63276
63286
63296
63397
63306
63317
63327
63428
63337
63377
63387
63407
63417
63438
431
63448
63458
63468
63478
63488
63498
63508
63518
63528
63538
6
6
432
63548
63558
63568
63579
63589
63599
63609
63619
63629
63639
7
4.33
63649
63659
63669
63679
63689
63699
63709
63719
63729
63739
8
8
434
63749
63759
638.59
63959
63769
63779
63789
63799
63809
63819
63829
63839
9
9
435
436
63849
63949
63869
63969
63879
63979
63889
63988
63899
63998
63909
64008
63919
64018
63929
64028
63939
64038
437
64048
64058
64068
64078
64088
64098
64108
64118
64128
64137
438
64147
64157
64167
64177
64187
64197
64207
64217
64227
64237
439
64246
642,56
643,55
64266
64365
64276
64375
64286
64296
64306
64316
64326
64335
440
64345
64385
64395
64404
64414
64424
64434
441
64444
64454
64464
64473
64483
64493
64503
64513
64523
64532
442
64542
64552
64562
64572
64582
64591
64601
64611
64621
64631
443
64640
64650
64660
64670
64680
64689
64699
64709
64719
64729
444
445
647.38
64748
64758
64768
64865
64777
64787
64797
64807
64816
64826
64836
64846
(H856
64875
64885
6t895
6*904
64914
64924
446
64933
64943
64953
64963
64972
64982
64992
65002
65011
65021
447
65031
65040
65050
65060
65070
65079
65089
65099
65108
65118
448
449
65128
65225
65137
65234
65147
65244
65341
65157
65254
65167
65263
65176
65273
65186
65283
65196
65292
65205
65302
65398
65215
65312
65408
9
450
65321
65331
65350
65360
a5369
65379
65389
451
65418
65427
65437
65447
65456
65466
65475
65485
65495
65504
1
1
452
65514
65523
65533
65543
65552
65562
65571
65581
65591
65600
2
2
453
65610
65619
65629
65639
65648
65658
65667
65677
65686
65696
3
3
454
65706
65715
65725
65820
65734
65744
65753
65763
65772
65782
65792
65887
4
5
4
5
455
65801
6.5811
65830
65839
65849
65858
65868
65877
456
65896
6.5906
65916
65925
65935
65944
65954
65963
65973
65982
6
5
457
65992
66001
66011
66020
66030
66039
66049
66058
66068
66077
7
6
458
66087'
66096
66106
66115
66124
66134
66143
66153
66162
66172
8
7
459
66181
66191
66200
66210
66219
66229
66238
66247
66257
66266
9
8
No.
1
2
3
4
5
6
!
8
e
1
Page 762]
TABLE 42.
Logarithms
of Numbers.
No.
4600 5200.
Log. 66'276-
71600.
No.
1
2
3
4
6
e
7
8
9
460
461
66276
66370
66285
66380
66295
66389
66304
66398
66314
66408
66323
66417
66332
66427
66342
66436
66351
66445
66361
66455
10
462
66464
66474
66483
66492
66502
66511
66521
66530
66539
66549
1
1
463
66558
66567
66577
66586
66596
66605
66614
66624
66633
66642
2
2
464
66652
66661
66671
66680
66773
66689
66783
66699
66792
66708
66801
66717
66811
66727
66820
66736
66829
3
4
5
6
7
8
9
3
4
5
6
7
8
9
465
66745
66755
66764
466
66839
66848
66857
66867
66876
66885
66894
66904
66913
66922
"467
66932
66941
66950
66960
66969
66978
66987
66997
67006
67015
468
67025
67034
67043
67052
67062
67071
67080
67089
67099
67108
469
470
67117
67210
67127
67219
67136
67228
67145
67237
67330
67154
67247
67339
67164
67256
67173
67265
67182
67274
67191
67201
67284
67293
471
67302
67311
67321
67348
67357
67367
67376
67385
472
67394
67403
67413
67422
67431
67440
67449
67459
67468
67477
473
67486
67495
67504
67514
67516
67532
67541
67550
67560
67569
474
67578
67587
67596
67688
67605
67614
67624
67633
67724
67642
67^51
67660
67752
476
67669
67679
67697
67706
67715
67733
67742
476
67761
67770
67779
67788
67797
67806
67815
67825
67834
67843
477
67852
67861
67870
67879
67888
67897
67906
67916
67925
67934
478
67943
67952
67961
67970
67979
67988
67997
68006
68015
68024
479
480
68034
68124
68043
68133
68052
68061
68151
68070
68079
68088
68178
68097
68106
68115
68205
68142
68160
68169
68187
68196
481
68215
68224
68233
68242
68251
68260
68269
68278
68287
68296
482
68305
68314
68323
68332
68341
68a50
68359
68368
68377
68386
483
484
68395
68485
68574"
68404
68494
68583
68413
68502
68422
68511
68431
68520
68440
68529
68449
68538
68628
68458
68547
68637
68467
68556
68476
68565
9
485
68592
68601
68610
68619
68646
68655
486
68664
68673
68681
68690
68699
68708
68717
68726
68735
68744
1
1
487
68753
68762
68771
68780
68789
68797
68806
68815
68824
68833
9
2
488
68842
68851
68860
68869
68878
68886
68895
68904
68913
68922
3
3
489
490
68931
69020
68940
69028
68949
69037
68958
68966
68975
68984
68993
69002
69011
4
5
4
5
69046
69055
69064
69073
69082
69090
69099
491
69108
69117
69126
69135
69144
69152
69161
69170
69179
69188
6
5
492
69197
69205
69214
69223
69232
69241
69249
69258
69267
69276
7
6
493
69285
69294
69302
69311
69320
69329
69338
69346
69355
693<)4
8
7
494
69373
69381
69390
69478
69566
69399
69408
69417
69425
69434
69443
69452
9
8
495
496
69461
69548
69469
69557
69487
69574
69496
69583
69504
69592
69513
69601
69522
69609
69531
69618
69539
69627
497
69636
69644
69653
69662
69671
69679
69688
69697
69705
69714
49g
69723
69732
69740
69749
69758
69767
69775
69784
69793
69801
499
500
69810
69897"^
69819
69827
69836
69845
699.32
69854
69862
69871
69958
69880
69966
69888
69906
69914
69923
69940
69949
69975
501
69984
69992
70001
70010
70018
70027
70036
70044
70053
70062
502
70070
70079
70088
70096
70105
70114
70122
70131
70140
70148
503
70157
70165
70174
70183
J0191
70200
70209
70217
70226
70234
504
70243
' 70329
70252
70260
70269
70278
70286
70295
70303
70389
70312
70321
505
70338
70346
70355
70364
70372
70381
70398
70406
506
70415
70424
70432
70441
70449
70458
70467
70475
70484
70492
507
70501
70509
70518
70526
70535
70544
70552
70561
70569
70578
508
509
70586
70672
"70757
70842
70595
70680
70603
70689
70612
70697
70(>21
70706
70629
70714
70638
70723
70646
70731
70655
70740
70825
70910
70663
70749
8
70766
70851
70774
70859
70783
70868
70791
70876
70800
70885
70808
70893
70817
70902
70834
70919
510
511
1
1
512
70927
70935
70944
70952
70961
70969
70978
70986
70995
71003
2
2
513
71012
71020
71029
71037
71046
71054
71063
71071
71079
71088
3
2
514
71096
71105
71189
71113
71122
71130
71139
71147
71231
71155
71164
71248
71172
4
5
3
4
515
71181
71198
71206
71214
71223
71240
71257
- 516
71265
71273
71282
71290
71299
71307
71315
71324
71332
71341
6
5
517
71349
71357
71366
71374
71383
71391
71399
71408
71416
71425
7
6
518
71433
71441
71450
71458
71466
71475
71483
71492
71500
71508
8
6
519
71517
71525
71533
71542
71550
71559
71567
71575
71584
71592
9
7
No.
1
2
3
4
6
6
J
8
9
1
TABLE 42.
Logarithms of Numbers.
[Page 763
Nj
.6200 5800.
Log. 71600 76343. 1
No.
1
2
3
4
6
6
t
8
9
1
520
521
522
523
524
71600
71684
71767
71850
71933
71609
71692
71775
71858
71941
71617
71700
71784
71867
71950
71625
71709
71792
71875
71958
71634
71717
71800
71883
71966
71642
71725
71809
71892
71975
71650
71734
71817
71900
71983
71659
71742
71825
71908
71991
71667
71750
71834
71917
71999
72082
72165
72247
72329
72411
72493
72575
72656
72738
72819
72900
72981
73062
73143
73223
73304
73384
73464
73544
73624
71675
71759
71842
71925
72008
72090
72173
i 72255
72337
72419
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
5.
6
7
8
525
526
527
528
529
72016
72099
72181
72263
72346
72024
72107
72189
72272
72354
72032
72115
72198
72280
72362
72041
72123
72206
72288
72370
72049
72132
72214
72296
72378
72057
72140
72222
72304
72387
72066
72148
i 72230
72313
72395
72074
72156
72239
72321
72403
530
531
532
533
534
535
536
537
538
539
540"
541
542
543
544
545
546
547
548
549
550
551
552
553
554
72428
72509
72591
72673
72754
72436
72518
72599
72681
72762
72444
72526
72607
72689
72770
72452
72534
72616
72697
72779
72460
72542
72624
72705
72787
72469
72550
72632
72713
72795
72477
72558
72640
72722
; 72803
72485
72567
72648
72730
72811
72501
72583
72665
j 72746
72827
72908
72989
73070
73151
73231
; 73312
73392
73472
73552
73632
72835
72916
72997
73078
73159
72843
72925
73006
73086
73167
72852
72933
73014
73094
73175
72860
72941
73022
73102
73183
72868
72949
73030
73111
73191
72876
72957
73038
73119
73199
: 72884
72965
73046
73127
73207
72892
72973
73054
73135
73215
73296
73376
73456
73636
73616
73239
73320
73400
73480
73560
73247
73328
73408
7.3488
73568
73255
73336
73416
73496
73576
73263
73344
73424
73504
73584
73272
73352
73432
73512
73592
73280
73360
73440
73520
73600
73288
73368
73448
73528
73608
8
7.3640
73719
73799
73878
73957
73648
73727
73807
73886
73965
73656
73735
73815
73894
73973
73664
73743
•73823
73902
73981
73672
73751
73830
73910
73989
73679
73759
73838
73918
73997
73687
73767
73846
73926
74005
73695
73775
73854
73933
74013
73703
73783
73862
73941
74020
73711
73791
73870
73949
74028
1
2
3
4
5
6
7
8
9
1
2
2
3
4
5
6
6
7
74036
74115
74194
74273
74351
74044
74123
74202
74280
74359
74052
74131
74210
74288
74367
74060
74139
74218
74296
74374
74068
74147
74225
74304
74382
74076
74155
74233
74312
74390
74084
74162
74241
74320
74398
74092
74170
74249
74327
74406
74099
74178
74257
74335
74414
74492
74570
74648
74726
74803
74107
74186
74265
74343
74421
ooo
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
74429
74507
74586
74663
74741
74437
74515
74.593
74671
74749
74445
74523
74601
74679
74757
74453
74531
74609
74687
74764
74461
74539
74617
74695
74772
74468
74547
74624
74702
74780
74476
74554
74632
74710
74788
74484
74562
74640
74718
74796
74500
74578
74656
74733
74811
74819
74896
74974
75051
75128
74827
74904
74981
75059
75136
74834
74912
74989
75066
75143
74842
74920
74997
75074
75151
74850
74927
75005
75082
75159
74858
74935
75012
75089
75166
74865
74943
75020
75097
75174
74873
74950
75028
75105
75182
74881
74958
75035
75113
75189
74889
74966
75043
75120
75197
75205
75282
75358
75435
75511
75213
75289
75366
75442
75519
75220
75297
75374
75450
75526
75228
75305
75381
75458
75534
75236
75312
75389
75465
75542
75618
75694
75770
75846
75921
75243
75320
75397
75473
75549
75626
75702
75778
75853
75929
75251
75328
75404
75481
75557
75259
75335
75412
75488
75565
75266
75343
75420
75496
75572
75648
75724
75800
75876
75952
75274
75351
75427
75504
7-5580
75656
75732
75808
75884
75959
76035
76110
76185
76260
76335
7
75587
75664
75740
75815
75891
75595
75671
75747
75823
75899
75603
75679
75755
75831
75906
75610
75686
75762
75838
75914
7563;f
75709
75785
75861
75937
75641
75717
75793
75868
75944
1
2
3
4
5
6 '
T i
8
9
1
1
2
3
4
4
5
6
6
575
576
577
578
579
75967
76042
76118
7619a
76268
75974
76050
76125
76200
76275
75982
76057
76133
76208
76283
75989
76065
76140
76215
76290
75997
76072
76148
76223
76298
76005
76080
76155
76230
76305
76012
76087
76163
76238
76313
76020
76095
76170
76245
76320
76027
76103
76178
76253
76328
Ko.
1
2
8
4
5
6
7
8
9
1
Page 764]
TABLE -12.
Logarithms
of Numbers.
No.
5800 6400.
Log. 76343 8061S. 1
No.
580
581
1
2
3
4
5
6
7
8
i)
1
76343
76418
76350
76425
76358
76433
76365
76440
76373
76448
76380
76455
76388
76462
76395
76470
76403
76477
76410
76485
8
582
76492
76500
76507
76515
76522
76530
76537
76545
76552
76559
i
1
583
76567
76574
76582
76589
76597
76604
76612
76619
76626
76634
2
584
76641
76649
76656
76664
76671
76678
76686
76760
76693
'76768
76701
76775
76708
76782
3
4
5
6
7
8
9
2
3
4
5
6
6
7
585
76716
76723
76730
76738
76745
76753
586
76790
76797
76805
76812
76819
76827
76834
76842
76849
76856
587
76864
76871
76879
76886
76893
76901
76908
76916
76923
76930
588
76938
76945
76953
76960
76967
76975
76982
76989
76997
77004
589
590
77012
77085
77019
77093
77026
77100
77034
77041
77048
77122
77056
77063
77070
77144
77078
77151
77107
77115
77129
77137
591
77159
77166
77173
77181
77188
77195
77203
77210
77217
77225
592
77232
77240
77247
77254
77262
77269
77276
77283
77291
77298
593
77305
77313
77320
77327
77335
77342
77349
77357
77364
77371
594
77379
77386
77393
77401
77408
77415
77422
77430
77437
77444
77517
595
77452
77459
77466
77474
77481
77488
77495
77503
77510
596
77525
77532
77539
77546
77554
77561
77568
77576
77583
77590
597
77597
77605
77612
77619
77627
77634
77641
77648
77656
77663
598
77670
77677
77685
77692
77699
77706
77714
77721
77728
77735
599
77743
77750
77757
77764
77772
77779
77786
77793
77801
77873
77808
77880
600
77815
77822
77830
77837
77844
77851
77859
77866
601
77887
77895
77902
77909
77916
77924
77931
77938
77945
77952
602
77960
77967
77974
77981
77988
77996
78003
78010
78017
78025
603
604
605
606
78032
78104
78039
78111
78183"
78254
78046
78118
78053
78125
78061
78132
78068
78140
78211
78283
78075
78147
78082
78154
78089
78161
78097
78168
7
78176
78247
78190
78262
78197
78269
78204
78276
78219
78290
78226
78297
78233
78305
78240
78312
1
9
1
1
607
78319
78326
78333
78340
78347
78355
78362
78369
78376
78383
608
78390
78398
78405
78412
78419
78426
78433
78440
78447
78455
3
4
5
609
78462
78469
78476
' 78547"
78483
•78490
78497
78504
78512
78519
78590
78526
3
4
610
78533
78540
78554
78561
78569
78576
78583
78597
611
78604
78611
78618
78625
78633
78640
78647
78654
78661
78668
6
4
612
78675
7i<682
78689
78696
78704
78711
78718
78725
78732
78739
7
5
613
78746
78753
78760
78767
78774
78781
78789
78796
78803
78810
8
6
614
78817
78824
78831
78838
78845
78852
78859
78866
78873
78880
78951
79021
9
6
615
616
78888
78958
78895
78965
78902
78972
78909
78979
78916
78986
78923
78993
78930
79000
78937
79007
78944
79014
617
79029
79036
79043
79050
79057
79064
79071
79078
79085
79092
618
79099
79106
79113
79120
79127
79134
79141
79148
79155
79162
619
79169
79176
79183
79190
79197
79267
79204
79211
79218
79225
79295
79232
620
79239
79246
79253
79260
79274
79281
79288
79302
621
79309
79316
79323
79330
79337
79344
79351
79358
79365
79372
622
79379
79386
79393
79400
79407
79414
79421
79428
79435
79442
623
79449
79456
79463
79470
79477
79484
79491
79498
79505
79511
624
79518
79525
79532
79539
79546
79553
79560
79567
79574
79581
625
79588
79595
79602
79609
79616
79623
79630
79637
79644
79650
626
79657
79664
79671
79678
79685
79692
79699
79706
79713
79720
627
79727
79734
79741
79748
79754
79761
79768
79775
79782
79789
628
629
630
79796
79865
79934
79803
79872
79810
79879
79817
79886
. 79955
79824
79893
79831
79900
79837
79906
79844
79913
79851
79920
79858
79927
6
79941
79948
79962
79969
79975
79982
79989
79996
631
80003
80010
80017
80024
80030
80037
80044
80051
80058
80065
1
1
632
80072
80079
80085
80092
80099
80106
80113
80120
80127
80134
2
1
633
80140
80147
80154
80161
80168
80175
80182
80188
80195
80202
3
2
634
80209
80216
80223
80229
80236
80243
80250
80318
,80257
80325
80264
80332
80271
4
5
2
3
635
80277
80284
80291
80298
80305
80312
80339
636
80346
80353
80359
80366
80373
80380
80387
80393
80400
80407
6
4
637
80414
80421
80428
80434
80441
80448
80455
80462
80468
80475
(
4
638
80482
80489
80496
80502
80509
80516
80523
80530
80536
80543
8
5
639
80550
80557
80564
80570
80577
80584
80591
80598
80604
80611
9
5
No.
1
2
»
4
5
6
7
8
9
, 1
TABLE 4->.
lPage766 1
Logarithms
of Numbers.
1
No
6400 7000.
Loff. 80618 84510. 1
No.
1
2
3
4
6
6
J
8
9
1
640
641
80618
80686
80625
80693
80632
80699
80638
80706
80645
80713
80652
80720
80659
80726
80665
80733
80672
80740
80679
80747
J
642
80754
80760
80767
80774
80781
80787
80794
80801
80808
80814
1
1
643
80821
80828
80835
80841
80848
80855
80862
80868
80875
80882
1
644
80889
80895
80902
80909
80916
80922
80929
80936
80943
80949
3
4
2
3.
4
4
5
6
6
645
80956
80963
80969
80976
80983
80990
80996
81003
81010
81017
646
81023
81030
81037
81043
81050
810.57
81064
81070
81077
81084
6
647
81090
81097
81104
81111
81117
81124
81131
81137
81144
81151
648
81158
81164
81171
81178
81184
81191
81198
81204
81211
81218
8
9
649
ft50
81224
81^31
81238
81245
81251
81318
81258
81325
81265
81271
81278
81285
81291
81298
81305
81311
81331
81338
81345
81351
6.51
81.358
81365
81371
81378
81385
81391
81398
81405
81411
81418
652
81425
81431
81438
81445
81451
81458
81465
81471
81478
81485
653
81491
81498
81505
81511
81518
81525
81531
81538
81544
81,551
654
655
81558
81624
81564
81571
81578
81584
81591
81598
81604
81611
81617
81684
81631
81637
81644
81651
81657
81664
81671
81677
656
81690
81697
81704
81710
81717
81723
81730
81737
81743
81750
a57
81757
81763
81770
81776
81783
81790
81796
81803
81809
81816
658
81823
81829
81836
81842
81849
81856
81862
81869
81875
81882
659
81889
81895
sutiir
81902
81968
81908
81915
81921
" 81987"
81928
81935
81941
82007
81948
82014
660
81954
81974
81981
81994
82000
661
82020
82027
82033
82040
82046
82053
82060
82066
82073
82079
662
82086
82092
82099
82105
82112
82119
82125
82132
82138
82145
663
82151
82158
82164
82171
82178
82184
82191
82197
82204
82210
664
66.5
82217
82223
82230
82236
82243
82249
82256
82263
82269
82276
82341
82282
82289
82295
82302
82308
82315
82321
82328
82334
666
82347
82354
82360
82367
82373
82.380
82387
82393
82400
82406
667
82413
82419
82426
82432
82439
82445
82452
82458
82465
82471
668
82478
82484
82491
82497
82504
82510
82517
82523
82530
82536
669
670
82543
82549
82614
82556
82562
82569
82575
82,582
82588
82653
82595
82659
82601
82666
82607
82620
82627
82633
82640
82646
671
82672
82679
82685
82692
82698
82705
82711
82718
82724
827:iO
672
82737
82743
827.50
82756
82763
82769
82776
82782
82789
82795
673
82802
82808
82814
82821
82827
82834
82840
82847
82853
82860
674
82866
82872
82879
82885
82892
82898
82963
82905
82969
82911
82975
82918
82982
82924
82988
675
82930
82937
82943
82950
82956
676
82995
83001
83008
83014
83020
83027
83033
83040
83046
83052
677
83059
83065
83072
8.3078
8.3085
83091
83097
83104
83110
83117
678
83123
mi99
83136
83142
83149
83155
83161
83168
83174
83181
679
680
8.3187
83193
8.3257
83200
83206
83213
83219
83225
83289
83232
8;iL'!l(>
S323S
,s;!:!0-'
S3245
,s:i.308
83251
83264
83270
83276
83283
681
83315
83321
83327
83334
8,3.340
8.3,347
83353
83359
83366
83372
682
83378
8,3385
83391
83,398
83404
8,3410
83417
83423
83429
8:M36
683
83442
83448
834,55
83461
83467
8.3474
83480
8,3487
83493
83499
684
685
83506
83569
83512
83575
83518
8,3525
83531
8*537
83(>dr
83544
83607
835.50
83613
835.^(1
83620
,S:!5(i3
8:!62(r
83582
83.588
83594
686
83632
83639
83645
83651
8.3658
83664
83670
83677
83683
83689
687
83696
83702
83708
83715
83721
83727
83734
83740
83746
83753
688
689
83759
83822
83765
83828
83771
83835
83778
83841
83784
83847
83790
83853
83797
83860
83803
83866
83809
83872
83816
83879
6
690
83885
8.3891
83897
83904
83910
83916
83923
83929
839,35
83942
691
83948
83954
83960
83967
83973
83979
83985
83992
83998
84004
1
1
692
84011
84017
84023
84029
84036
84042
84048
84055
84061
84067
9
1
693
84073
84080
84086
84092
84098
84105
84111
84117
84123
84130
3
2
694
84136
84142
84148
84155
84161
84167
84173
84180
84186
84192
84255
4
5
2
3
695
84198
84205
84211
84217
84223
84230
84236
84242
84248
696
84261
84267
84273
84280
84286
84292
84298
84305
84311
84317
6
4
697
84323
84.3.30
84336
84,342
84348
84354
84361
84367
84373
84379
7
4
698
84386
84392
84398
84404
84410
84417
84423
84429
84435
84442
8
5
699
84448
84454
84460
84466
84473
84479
84485
84491
84497
84504
9
5
No,
1
2
»
4
5
6
'
8
9
1
Page 766]
TABLE 42.
LogarithmB
of Numbers.
No
7000 7600.
Log. 84510 88081.
Ko.
- 1
2
3
4
5
6
7
8
9
1
700
701
84510
84572
84516
84578
84522
84584
84528
84590
84535
84597
84541
84603
84547
84609
84553
84615
84559
84621
84566
84628
I
702
84634
84640
84646
84652
84658
84665
84671
84677
84683
84689
1
1
703
84696
84702
84708
84714
84720
84726
84733
84739
84745
84751
1
704
84757
84819
84763
84770
84776
84782
84788
84794
84800
84807
84868
84813
84874
3
4
5
2
3
4
4
5
6
6
705
84825
84831
84837
84844
84850
84856
84862
706
84880
84887
84893
84899
84905
84911
84917
84924
84930
84936
707
84942
84948
84954
84960
84967
84973
84979
84985
84991
84997
6
708
85003
85009
85016
85022
85028
85034
85040
85046
85052
8.5058
8
9
709
85065
85071
85077
85083
85089
85095
85101
85107
85169
8511.4
85120
710
85126
85132
85138
85199
85144
85150
85156
85163
85175
85181
711
85187 .
85193
85205
85211
85217
85224
85230
85236
85242
712
85248
85254
85260
85266
85272
85278
85285
85291
85297
85303
713
85309
85315
85321
85327
85333
85339
85345
85352
85358
85364
714
85370
85376
85382
85388
85394
8.5400
85406
8.5467
85412
"8.5473
85418
85479
85425
715
85431
85437
85443
85449
85455
85461
85485
716
85491
85497
85503
85509
85516
85522
85528
85534
85540
85546
717
85552
85558
85564
85570
85576
85582
8.5588
85594
85600
85606
718
85612
85618
85625
85631
85637
85643
85649
85655
85661
- 85667
719
85673
85679
85739
85685
85691
85697
85703
85709
85715
85721
85781
85727
85788
720
85733
85745
85751
85757
85763
85769
85775
721
85794
85800
85806
85812
85818
85824
85830
85836
85842
85848
722
85854
85860
85866
85872
85878
85884
85890
85896
85902
85908
723
724
85914
85974
85920
85980
85926
85986
85932
85992
• 85938
85998
85944
86004
85950
86010
8.5956
86016
85962
86022
85968
86028
"86088
86147
(i
725
726
86034
86094
86040
86100
86046
86106
86052
86112
86058
86118
86064
86124
86070
86130
86076
86136
86082
86141
1
1
1
727
86153
86159
86165
86171
86177
86183
86189
86195
86201
86207
728
86213
86219
86225
86231
86237
86243
86249
86255
86261
86267
3
4
5
729
86273
86332
86279
86285
86291
86297
86303
86308
86314
86320
"86380
86326
86386
2
3
730
86338
86344
86350
86356
86362
86368
86374
731
86392
86398
86404
86410
86415
86421
86427
86433
86439 86445
6
4
732
86451
86457
86463
86469
86475
86481
86487
86493
86499 86504
4
733
86510
86516
86522
86528
86534
86540
86.546
86552
86558 86564
S
5
734
86570
86629"
86688
86576
86635
86694
86581
86641
86700
86587
86646"
86705
86593
86599
86605
86611
86670
86729
86617 86623
86676" 86682
86735 1 86741
9
5
735
736
86652
86711
86658
86717
86664
86723
737
86747
86753
86759
86764
86770
86776
86782
86788
86794 86800
738
86806
86812
86817
86823
86829
86835
86841
86847
86853 86^59
739
86864
86870
86929
86876
86882
86888
86894
86953
86900
86958
86906
"86964
86911 86917
86970 ! 86976
740
86923
86935
86941
86947
741
86982
86988
86994
86999
87005
87011
87017
87023
87029 ' 87035
742
87040
87046
87052
87058
87064
87070
87075
87081
87087
87093
743
87099
87105
87111
87116
87122
87128
87134
87140
87146
87151
744
87157
87163
87169
87175
87181
87186
87192
87198
87204
87210
745
87216
87221
87227
87233
87239
87245
87251
87256
87262 j 87268
746
87274
87280
87286
87291
87297
87303
87309
87315
87320 1 87326
747
87332
87338
87344
87349
87355
87361
87,367
87373
87379 1 87384
748
749
87390
87448
87396
87454
87402
87460
87408
87466
87413
87471
87419
87477
87425
87483
87541
87599
87431
87489
87547
87604
87437
87495
87552
87610
87442
87500
8755"8
87616
5
750
751
87506
87564
87512
87570
87518
87576
87523
87581
87529
87587
87535
87593
1
1
752
87622
87628
87633
87639
87645
87651
87656
87662
87668
87674
•>
1
753
87679
87685
87691
87697
87703
87708
87714
87720
87726
87731
3
2
754
87737
87743
87749
87754
87760
87766
87772
87829"
87777
87835"
87783
87841
87789
4
5
2
3
755
87795
87800
87806
87812
87818
87823
87846
756
87852
87858
87864
87869
87875
87881
87887
87892
87898
87904
6
3
757
87910
87915
87921
87927
87933
87938
87944
87950
87955
87961
4
4
758
87967
87973
87978
87984
87990
87996
88001
88007
88013
88018
s
4
759
88024
88030
88036
88041
88047
88053
88058
88064
88070
88076
9
No.
1
2
3
*
o
6
7
8
»
1
TABLE 42.
[Page 767
Logarithms
of Numbers.
No.
7600 8200.
Log. 88081 91381.
No.
1
2
3
1
6
6
7 .
8
9
760
761
88081
88138
88087
88144
88093
88150
88098
88156
88104
88161
88110
88167
88116
88173
88121
88178
88127
88184
88133
88190
«
762
88195
88201
88207
88213
88218
88224
88230
88235
88241
88247
i
1
763
88252
88258
88264
88270
88275
88281
88287
88292
88298
88304
1
764
88309
88315
88372
88321
88326
88332
883.38
88343
88349
88355
88360
3
4
2
2
3
765
88366
88377
88383
88389
88395
88400
88406
88412
88417
766
88423
88429
88434
88440
88446
88451
88457
88463
88468
88474
767
88480
88485
88491
88497
88502
88508
88513
88519
88525
88530
768
88536
88542
88547
88553
88559
88564
88570
88576
88581
88587
8
9
5
769
88593
88598
"88655"
88604
88610
88615
88621
88627
88632
88638
88694
88643
770
88649
88660
88666
88672
88677
88683
88689
88700
i
771
88705
88711
88717
88722
88728
88734
88739
88745
88750
88756
772
88762
88767
88773
88779
88784
88790
88795
88801
88807
88812
773
88818
88824
88829
88835
88840
88846
88852
88857
88863 ; 88868
774
775
88874
88880
88885
88891
88897
88902
88908
"88964
88913
"88969
88919 1 88925
88930
88936
88941
88947
88953
88958
88975 , 88981
776
88986
88992
88997
89003
89009
89014
89020
89025
89031
89037
777
89042
89048
89053
89059
89064
89070
89076
89081
89087
89092
778
89098
89104
89109
89115
89120
89126
89131
891,37
89143
89148
779
89154
89159
89165
89170
89176
89232
89182
89237
89187
89193
89248
89198
89254
89204
89260
780
89209
89215
89221
89226
89243
781
89265
89271
89276
89282
89287
89293
89298
89304
89310
89315
782
89321
89326
89332
89337
89343
89348
89354
89360
89365
89371
783
89376
89382
89387
89393
89398
89404
89409
89415
89421
89426
784
89432
89437
89443
89448
89454
89459
89465
89520
89470
89476
89481
785
89487
89492
89498
89504
89509
895ir.
89526
89531
89537
786
89542
89548
89553
89559
89564
89570
89575
89581
89586
89592
787
89597
89603
89609
89614
89620
89625
89631
89636
89642
89647
788
89653
89658
89664
89669
89675
89680
89686
89691
89697
89702
789
790"
89708
89763
89713
89768
89719
89774
89724
89730
89786
89735
89741
89746
89752
89757
89779
89790
89796
89801
89807 89812
791
89818
89823
89829
89834
89840
89845
89851
89856
89862 89867
792
89873
89878
89883
89889
89894
89900
89905
89911
89916 89922
793
89927
89933
89938
89944
89949
89955
89960
89966
89971
89977
794
89982
89988
89993
89998
90004
90009
90015
90020
90075
90026
90080
90031
90086
795
90037
90042
90048
90053
90059
90064
90069
796
90091
90097
90102
90108
90113
90119
90124
90129
90135
90140
797
90146
90151
90157
90162
90168
90173
90179
90184
S)0189
90195
798
90200
90206
90211
90217
90222
90227
90233
90238
90244
90249
799
90255
90309
90260
90266
90271
90276
90331
90282
90287
90.342
90293
90298
90.304
800
90314
90320
90325
90336
901347
90352
90358
801
90363
90369
90374
90380
90385
90390
90396
90401
90407
90412
802
90417
90423
90428
90434
90439
90445
90450
90455
90461
90466
803
90472
90477
90482
90488
90493
90499
90504
90509
90515
90520
804
90526
90531
90536
90542
90547
90553
90558
! 10563
9()()17~
90569
90623
90574
805
9ft580
90585
90590
90596
90601
90607
90612
90628
806
90634
90639
90644
90650
90655
90660
90666
90671
90677
90682
807
90687
90693
90698
90703
90709
90714
90720
90725
90730
90736
808
809
810
90741
90795
90747
90800
90752
90806
90757
90811
90763
90816
90768
90822
90875
90773
90827
90779
90832
90784
90838
90789
90843
9
90849
90854
90859
90865
90870
90881
90886
90891
90897
811
90902
90907
90913
90918
90924
90929
90934
90940
90945
909.50
^
1
812
90956
90961
90966
90972
90977
90982
90988
90993
90998
91004
?
1
813
91009
91014
91020
91025
91030
91036
91041
91046
91052
91057
3
2
814
91062
91068
91073
91078
91084
91089
91094
91100
91105
91110
4
5
2
3
815
91116
91121
91126
91132
91137
91142
91148
91153
91158
91164
816
91169
91174
91180
91185
91190
91196
91201
91206
91212
91217
6
3
817
91222
91228
91233
912.38
91243
91249
91254
91259
91265
91270
4
4
818
.91275
91281
91286
91291
91297
91302
91307
91312
91318
91323
8
4
819
91328
91334
91339
91344
91350
91355
91360
91365
91371
91376
9
5
No.
1
2
3
4
5
6
7
8
»
Page 768]
TABLE 42.
Logarithms
jf Numbers.
J
No.
8200 8800.
Ix)g. 91381 94448 1
No.
1
• 2
3
4
5
6
7
8
9
820
821
91381
91434
91387
91440
91392
91445
91397
91450
91403
91455
91408
91461
91413
91466
91418
91471
91424
91477
91429
91482
I 6
822
91487
91492
91498
91503
91508
91514
91519
91524
91529
91535
1 : 1
823
91540
91545
91551
91556
91561
91566
91572
91577
91582
91587
2 ! 1
824
91593
91598
91603
91609
91614
91619
91624
91630
91635
91640
3 ; 2
4 i 2
825
91645
91661
91656
91661
91666
91672
91677
91682
91687
91693
826
91698
91703
91709
91714
91719
91724
91730
91735
91740
91745
6
7
8
9
4
4
5
5
827
91751
91756
91761
91766
91772
91777
91782
91787
91793
91798
828
91803
91808
91814
91819
91824
91829
91834
91840
91845
91850
829
91855
91861
91866
91871
91876
91882
91887
91892
91897
91903
830
91908
91913
91918
91924
91929
91934
91939
91944
91950
91955
831
91960
91965
91971
91976
91981
91986
91991
91997
92002
92007
832
92012
92018
92023
92028
92033
92038
92044
92049
92054
92059
833
92065
92070
92075
92080
92085
92091
92096
92101
92106
92111
834
92117
92122
92127
92132
92137
92143
92148
92153
92158
92163
835
92169
92174
92179
92184
92189
92195
92200
92205
92210
92215
836
92221
92226
92231
92236
92241
92247
92252
92257
92262
92267
837
92273
92278
92283
92288
92293
92298
92304
92309
92314
92319
838
92324
92330
92335
92340
92345
92350
92355
92361
92366
92371
839
92376
92381
92387
92392
92397
92402
92407
92412
92418
92469
92423
92474
840
92428
92433
92438
92443
92449
92454
92459
92464
841
92480
92485
92490
92495
92500
92505
92511
92516
92521
92526
842
92531
92536
92542
92547
92552
92557
92562
92567
92572
92578
843
844
92583
92634
92588
92639
92593
92645
92598
92650
92603
92655
92609
92660
92711"
92763
92614
92665
92619
92670
92624
92675
92629
92681
9'2732
92783
6
845
846
92686
92737
92691
92742
92696
92747
92701
92752
92706
92758
92716
92768
92722
92773
92727
92778
1
9
1
1
2
2
3
847
92788
92793
92799
92804
92809
92814
92819
92824
92829
92834
848
92840
92845
92850
92855
92860
92865
92870
92875
92881
92886
3
4
5
849
92891
92896
92901
92906
92911
92916
92921
92927
92978
92932
92937
850
92942
92947
92952
92957
92962
92967
92973
92983
92988
851
92993
92998
93003
93008
93013
93018
93024
93029
93034
93039
6
3
852
93044
93049
93054
93059
93064
93069
93075
93080
93085
93090
7
4
853
93095
93100
93105
93110
93115
93120
93125
93131
93136
93141
8
4
854
855
856
93146
93151
93156
93161
93166
93171
93176
93181
93186
93192
9
5
93197
93247
93202
93252
93207
93258
93212
93263
93217
93268
93222
93273
93227
93278
93232
93283
93237
93288
93242
93293
857
93298
93303
93308
93313
93318
93323
93328
93334
93339
93344
858
93349
93354
93359
93364
93369
93374
93379
93384
93389
93394
859
93399
93404
93409
9-3414
93420
93425
93430
93480
93435
93440
93490
93445
860
93450
93455
93460
93465
93470
93475
93485
93495
861
93500
93505
93510
93515
93520
93526
93531
93536
93541
93546
862
93551
93556
93561
93566
93571
93576
93581
93586
93591
93596
863
93601
93606
93611
93616
93621
93626
93631
93636
93641
93646
864
93651
93656
93661
93666
93671
93676
93682
93687
93692
"93742
93697
"93747
865
93702
93707
93712
93717
93722
93727
93732
93737
866
93752
93757
93762
93767
93772
93777
93782
93787
93792
93797
867
93802
93807
93812
93817
93822
93827
93832
93837
93842
93847
868
869
93852
93902
93857
93907
93862
93912
93962
93867
93917
93967
93872
93922
93877
93927
93882
93932
93887
93937
93987
93892
93942
93992
93897
93947
93997
4
870
93952
93957
93972
93977
93982
871
94002
94007
94012
94017
94022
94027
94032
94037
94042
94047
1
872
94052
94057
94062
94067
94072
94077
94082
94086
94091
94096
2
1
873
94101
94106
94111
94116
94121
94126
94131
94136
94141
94146
3
1
874
94151
94156
94161
94211
94166
94171
94176
94181
94186
94191
94196
94245
4
5
2
2
875
94201
94206
94216
94221
94226
94231
94236
94240
876
94250
94255
94260
94265
94270
94275
94280
94285
94290
94295
6
2
877
94300
94305
94310
94315
94320
94325
94330
94335
94340
94345
7
3
878
94349
94354
94359
94364
94369
94374
94379
94384
94389
94394
8
3
879
94399
94404
94409
94414
94419
94424
94429
94433
94438
94443
9
4
No.
1
2
3
4
5
6
7
8
9
1
TABLE 42.
[Page 769
Logarithms
of Numbers.
No.
8800 9400.
Log. 94448 97313.
No.
1
2
3
4
3
6
7
8
9
880
881
94448
94498
94458
94503
94458
94507
94463
94512
94468
94517
94473
94522
94478
94527
94483
94488
94493
94542
»
94532 1 94537
882
94547
94552
94557
94562
94567
94571
94576
94581 j 94586
94591
1
i
883
94596
94601
94606
94611
94616
94621
94626
94630
94635
94640
2 ! i
884
94645
94650
94655
94660
"94709
94665
94714
94670
94675
94680
94729
94685
946S9
3 { 2
4 1 2
5 1 3
6 3
7 4
8 ' 4
9 5
885
94694
94699
94704
94719
94724
94734 i 94738
886
94743
94748
94753
94758
94763
94768
94773
94778
94783 ; 94787
887
94792
94797
94802
94807
94812
94817
94822 I 94827
94832
94836
888
94841
94846
94851
94856
94861
94866
94871 i 94876
94880
94885
889
890
94890
94895
94944
94900
94905
94910
94915
94919 '■ 94924 | 94929
94934
94983
94939
94949
94954
94959
94963
94968 94973
94978
891
94988
94993
94998
95002
95007
95012
95017 95022
95027
95032
892
95036
95041
95046
95051
95056
95061
95066 95071
95075
95080
893
95085
95090
95095
95100
95105
95109
95114 95119
95124
95129
894
95134
95139
95143
95148
95153
95158
95163 95168
95173
95177
895
95182
95187
95192
95197
95202
95207
95211 95216 i 95221 i 95226
896
95231
95236
95240
95245
95250
95255
95260 95265 | 95270
95274
897
95279
95284
95289
95294
95299
95303
95308 j 95313 i 95318
95323
898
95328
95332
95337
9bM2
95347
95352
95357 1 95361 i 95366
95371
899
900
95376
95381
95429
95386
95390
95395
95400
95405
95410 i 95415
95458 95463
9541!)
9o4(iS
95424
95434
95439
95444
95448
95453
901
95472
95477
95482
95487
95492
95497
95501 : 95506 95511
95516
902
95521
95525
95530
95535
95540
95545
95550 : 95554 95559
95564
903
95669
95574
95578
95583
95588
95593
95598 ! 95602 ' 95607
95612
904
95617
95622
95670
95626
95674
95631
95679
95636
95684
95641
95689
95646 ; 95650 i 95655
95694 95698 J 95703
95(i»iO
957(1S
905
95665
90<)
95713
95718
95722
95727
95732
95737
95742 : 95746 | 95751
957.^6
907
95761
95766
95770
95775
95780
95785
95789 i 95794 , 95799
95S()4
908
95809
95813
95818
95823
95828
95832
95837 1 95842 \ 95847
95852
909
95856
95861
95866
95871
95875
95923
95880
95928
95885 95890 ; 95895
95933 95938 j 95942
95K99
1)5947
910
95904
95909
95914
95918
911
95952
95957
95961
95966
95971
95976
95980 95985 95990
95995
912
95999
96004
96009
96014
9»K)19
96023
96028 ' 90)033 ' 96038
96042
913
96047
96052
96057
96061
9(i066
96071
96076 96080 \ 96085
96090
914
96095
96099
96104
96109
96114
96118
96123 96128 | 96133
96137
915
96142
96147
96152
96156
96161
96166
96171 : 96175
96180 1 96185
916
96190
96194
96199
96204
96209
96213
96218 i 96223
96227 { 96232
917
96237
96242
96246
96251
96256
96261
96265 96270
96275 1 962S0
918
96284
96289
96294
96298
96303
96308
96313 96317
96322 i 96327
919
96332
96336
96341
96388
96346
96350
96355
96360 96365
96369 1 96374
920
96379
96384
9^393
96398
96402
96407 96412
96417
96421
921
96426
96431
96435
96440
96445
96450
96454 96459
96464
96468
922
96473
96478
96483
96487
96492
96497
96501 96506
96511
96515
923
9a520
96525
96530
96534
96539
96544
96548 96553 1 96558
965(>2
924
925^
96567
96572
96577
96581
96586
96591
96638
96595 96600
96642 96647
96605
96609
96614
96619
96624
96628
96633
96652 ! 96656
926
96661
9«>666
96670
96675
96(>80
96685
96689 96694 96699 - 96703
927
96708
96713
96717
96722
96727
96731
96736 96741 j 96745 i 96750
928
929
^930
96755
96802
96759
96806
96764
96811
96769
96816
96774
96820
96867
96778
96825
96872
96783 96788 96792 1 96797
96830 96834 ' 96839 \ 96844
96876 96881 , 96886 : 96890
4
96848
96853
96858
96862
931
96895
96900
96904
96909
96914
96918
96923 ' 96928 96932 I 96937
1
932
96942
96946
96951
%956
96960
96965
96970 ': 96974
96979
96984
•>
1
933
96988
96993
96997
97002
97007
97011
97016 i 97021
97025
97030
3
1-
934
935
970:«
97081
97039
97044
97049
97053
97100
97058
97063 : 97067
97109 i 97114
97072
97118
97077
97123
4
5
2
2
97086
97090
97095
97104
936
97128
97132
97137
97142
97146
97151
97155
97160
97165
97169
6
2
937
97174
97179
97183
97188
97192
97197
97202
97206
97211
97216
7
3
938
97220
97225
97230
97234
97239
97243
97248
97253
97257
97262
8
15
939
So.
97267
97271
97276
97280
97285
97290
97294
97299
97304
97308
9
4
" i
1
^
3 i
'' 1
fl i ; 1 K 1
""" 1
24972°— 12-
-39
Page 770]
TABLE 42.
1
Logarithms
of Numbers.
No.
9400 10000.
Log. 97313 99996.
No.
1
2
3
4
5
6
7
8
9
1
940
941
97313
97359
97317
97364
97322
97368
97327
97373
97331
97377
97336
97382
97340
97387
97345
97391
973.50
97396
97.354
97400
5
942
97405
97410
97414
97419
97424
97428
97433
97437
97442
97447
1
1
943
97451
97456
97460
97465
97470
97474
97479
97483
97488
97493
2
1
944
945
97497
97543
97502
97506
97511
97516
97520
97525
97529
97534
97539
97585"
3
4
2
2
97548
97552
97557
97562
97566
97571
97575
97580
946
97589
97594
97598
97603
97607
97612
97617
97621
97626
97630
6
3
947
97635
97640
97644
97649
97653
97658
97663
97667
97672
97676
6
3
948
97681
97685
97690
97695
97699
97704
97708
97713
97717
97722
V
4
949
97727
97731
97736
97740
97745
97791
97836
97749
97754
97759
97763
97768
8
9
, 4
5
950
97772
97777
97782
97786
97795
97800
97804
97809
97813
951
97818
97823
97827
97832
97841
97845
97850
97855
97859
952
97864
97868
97873
97877
97882
97886
97891
97896
97900
97905
953
97909
97914
97918
97923
97928
97932
97937
97941
97946
97950
954
955
97955
97959
97964
97968
97973
97978
97982
97987
98032
97991
98037'
97996
98000
98005
98009
98014
98019
98023
98028
98041
956
98046
98050
98055
98059
98064
98068
98073
98078
98082
98087
957
98091
98096
98100
98105
98109
98114
98118
98123
98127
98132
958
98137
98141
98146
98150
98155
98159
98164
98168
98173
98177
959
98182
98186
98191
98195
98200
98204
98209
98214
98218
98263
98223
98268
960
98227
98232
98236
98241
98245
98250
98254
98259
961
98272
98277
98281
98286
98290
98295
98299
98304
98308
98313
962
98318
98322
98327
98331
98336
98340
98345
98349
98354
98358
963
98363
98367
98372
98376
98381
98385
98,390
98394
98399
98403
964
965
98408
98412
98417
98421
98426
98430
984.35
98439
98484
98444 1 98448
98489 1 98493
98453
98457
98462
98466
98471
98475
98480
966
98498
98502
98507
98511
98516
9^520
98525
98529
98.534 1 98538
967
98543
98547
98552
98556
98561
98565
9^570
98574
98579 98583
968
98588
98592
98597
98601
98605
98610
98614
98619
98623 ! 98628
969
970
98632
98637
98641
98646
98650
98655
986.59
98664
98709
98668 98673
98713 i 98717
98677
98682
98686
98691
98695
98700
98704
971
98722
98726
98731
98735
98740
98744
98749
98753
98758 98762
972
98767
98771
98776
98780
98784
98789
98793
98798
98802 : 98807
973
98811
98816
98820
98825
98829
98834
98838
98843
98847 98851
974
98856
98860
98865
98869
98874
98878
98883
98887
98892
98896
98941"
975
98900
98905
98909
98914
98918
98923
98927
98932
98936
976
98945
98949
98954
98958
98963
98967
98972
98976
98981 i 98985
977
98989
98994
98998
99003
99007
99012
99016
99021
99025
99029
978
99034
99038
99043
99047
9905?
99056
99061
99065
99069
99074
979
99078
99083
99087
99092
99096
99100
99105
99109
99114
99118
980
99123
99127
99131
99136
99140
99145
99149
99154
99158
99162
981
99167
99171
99176
99180
99185
99189
99193
99198
99202
99207
982
99211
99216
99220
99224
99229
99233
99238
99242
99247
99251
983
99255
99260
99264
99269
99273
99277
99282
99286
99291
99295
984
985
99300
99.304
99308
99313
99317
99322
99326
99330
99335
99339
99344
99348
99352
99357
99361
99366
99370
99374
99379
99383
986
99388
99392
99396
99401
99405
99410
99414
99419
99423
99427
987
99432
99436
99441
99445
99449
99454
99458
99463
99467
99471
988
989
99476
99520
99480
99524
99484
99528
99489
99533
99493
99537
99581
99498
99542
99585
99502
99546
99506
99550
99511
995.55
99515
99559
"99603
4
990
99564
99568
99572
99577
99590
99594
99599
991
99607
99612
99616
99621
99625
99629
99634
99638
99642
99647
1
992
99651
99656
99660
99664
99669
99673
99677
99682
99686
99691
2
1
993
99695
99699
99704
99708
99712
99717
99721
99726
99730
99734
3
1
994
99739
99743
99747
99752
99756
99760
99804
99765
99808
99769
99774
99778
4
5
2
2
995
99782
99787
99791
99795
99800
99813
99817
99822
996
99826
99830
99835
99839
99843
99848
99852
99856
99861
99865
6
2
997
99870
99874
99878
99883
99887
99891
99896
99900
99904
99909
V
3
998
99913
99917
99922
99926
99930
99935
99939
99944
99948 99952 j
8
3
999
99957
99961
99965
99970
99974
99978
99983
99987
99991
99996
9
4
No.
1
s
8
i
o
6
I
8
e
1
TABLE 43. [Page 771
Logarithmic Sines, Tangents, and Secants to every Point and Quarter Point of the Compass.
Points.
Sine. i Cosine. Tangent, j Cotangent.
Secant.
Cosecant.
i
i
i
1 i I
Inf. neg. : 10. 00000 Inf. neg. : Infinite.
8. 69080 9. 99948 ' 8. 69132 1 11. 30868
8.99130! 9.99790 1 8.99340 j 11.00660
9. 16652 i 9. 99527 [ 9. 17125 10. 82875
10. 00000
10. 00052
10. 00210
10. 00473
Infinite.
11. 30920
11.00870
10. 83348
8
n
7i
1
u
If
9.29024
9. 38557
9. 46282
9. 52749
9.99157
9.98679
9. 98088
9. 97384
9. 29866
9. 39879
9. 48194
9. 55365
10. 70134
10. 60121
10. 51806
10. 44635
10. 00843
10. 01321
10. 01912
10. 02616
10. 70976
10.61443
10. 53718
10. 47251
7
6|
6J
6i
2
1
9. 58284
9.63099
9. 67339
9. 71105
9.96562
9. 95616
9. 94543
9. 93335
9.61722
9. 67483
9. 72796
9. 77770
10. 38278
10. 32517
10. 27204
10. 22230
10. 03438
10. 04384
10.05457
10. 06665
10. 41716
10. 36901
10. 32661
10. 28895
6
5i
3
3i
3i
3f
9. 74474 9. 91985
9. 77.503 9. 90483
9. 80236 9. 88819
9. 82708 9. 86979
9. 82489
9. 87020
9.91417
9. 95729
10. 17511
10. 12980
10. 08583
10. 04271
10. 08015
10. 09517
10. 11181
10. 13021
10. 25526
10. 22497
10. 19764
10. 17292
5
4i
4J
4i
4
9.84949 j 9.84949
10.00000
10.00000
10. 15051
10. 15051
4
i Ck)8ine. | Sine.
Cotangent.
Tangent.
Cosecant.
Secant.
Points.
<^'i^^cy
^^
^/,'
f/
Page 772j
TABLE 44.
^
Log. Sines, Tangents, and Secants
0°
179°
M.
Hour A. M.
Hour p. M.
Sine.
DM. 1'.
Cosecant.
Tangent.
DiCf. V.
Cotangent.
Secant.
Cosino.
M.
12
Inf. neg.
Infinite.
Inf. neg.
Infinite.
10. 00000
10. 00000
60
1
11 59 52
8
6. 46373
30103
13. 53627
6. 46373
30103
1.3.53627
00000
00000
59
2
59 44
16
76476
17609
23524
76476
17609
23524
00000
00000
58
.3
59 36
24
94085
12494
05915
94085
12494
05915
00000
00000
57
4
59 28
32
7. 06579
7. 16270"
9691
12. 93421
7. 06579
9691
7918
12. 93421
12. 83730
00000
10.00000
00000
lO: 00000
.56
.5.5
5
11 59 20
40
7918
12. 83730
7. 16270
6
59 12
48
24188
6694
75812
24188
6694
75812
00000
00000
54
7
59 4
56
30882
5800
69118
30882
5800
69118
00000
00000
53
8
58 56
1 4
36682
5115
63318
36682
5115
63318
00000
00000
52
9
58 48
1 12
41797
7. 46373
4576
58203
41797
4576
58203
00000
00000
51
.-lO
10
U 58 40
1 20
4139
12. 53627
7. 46373
4139
12. 53627
10. 00000
10. om)(K)
n
58 32
1 28
50512
3779
49488
50512 3779
49488
00000
00000
49
12
58 24
1 36
54291
3476
45709
.54291 I 3476
45709
00000
00000
4,S
13
58 16
1 44
57767
3218
42233
57767
.3219
42233
00000
00000
47
14
15
58 8
1 52
60985
2997
2802
39015
12. 36018
60986
7. 63982"
2996
2803
39014
12. 36018
00000
10. 00000
00000
10. 00000
46
45"
11 58
2
7.63982
16
57 52
2 8
66784
2633
33216
66785
2633
.33215
00000
00000
44
17
57 44
2 16
69417
2483
30583
69418 \ 2482
30582
00001
9. 99999
43
18
57 36
2 24
71900
2348
28100
71900 2348
28100
00001
99999
42
19
20
57 28
2 32
74248
2227
25752
74248 2228
25752
00001
10. 00001
99999
9. 9999<T
41
40
11 57 20
2 40
7. 76475
2119
12. 23525
7.76476 1 2119
12. 23524
21
57 12
2 48
78594
2021
21406
78595 ' 2020
21405
00001.
99999
39
22
57 4
2 56
80615
1930
19385
80615 ! 1931
19385
00001
99999
:w
23
56 56
3 4
82545
1848
17455
82546 ; 1848
174.54
00001
99999
37
24
56 48
3 12
84393
7. 86166
1773
15607
84394
1773
1704
15606
00001
10. 00001
99999
9. 99999
36
35
25
11 56 40
3 20
1704
12. 13834
7. 86167
12. 13833
26
56 32
3 28
87870
1639
12130
87871 1639
12129
00001
99999
34
27
56 24
3 36
89509
1579
10491
89510 ' 1579
10490
00001
99999
33
28
56 16
3 44
91088
1524
08912
91089 1524
08911
00001
99999
32
29
56 8
3 52
92612
1472
1424
07388
92613 1 1473
7.94086 i 1424
07387
00002
10. 00002
99998
9.'99998
31
30"
30
11 56
4
7. 94084
12.0.5916
12.0.5914
31
55 52
4 8
95508
1379
04492
9.5510 ' 1379
04490
00002
99998
29
32
55 44
4 16
96887
1336
03113
96889 1336
03111
00002
99998
28
33
55 36
4 24
98223
1297
01777
98225 1297
01775
00002
99998
27
34
35
55 28
4 32
99520
1259
00480
99522 i 1259
00478
00002
10. 00002
99998
9. 99998
26
25
11 55 20
4 40
8. 00779
1223
11.99221
8.00781 1 1223
11.99219
36
55 12
4 48
02002
1190
97998
02004 : 1190
97996
00002
99998
24
37
55 4
4 56
03192
1158
96808
03194 i 1159
96806
00003
99997
23
38
54 56
5 4
04350
1128
95650
04.353 j 1128
95647
00003
99997
09
39
54 48
5 12
5~20^
05478
8.06578
1100
94522
11. 93422
05481
1100
1072
94519
11.93419
00003
10. 00003
99997
21
20
40
11 54 40
1072
8. 06.581
9. 99997
41
54 32
5 28
07650
1046
92350
07653 1047
92347
00003
99997
19
42
54 24
5 36
08696
1022
91304
08700 1022
91300
00003
99997
IS
43
54 16
5 44
09718
999
90282
09722 998
90278
00003
99997
17
44
45
54 8
5 52
10717
976
89283
10720 1 976
89280
00004
99996
16
15
11 54
6
8. 11693
954
11.88307
8.11696 9.55
11. 88304
10. 00004
9. 99996
46
53 52
6 8
12647
934
87353
12651
934
87,349
00004
9999()
14
47
53 44
6 16
13581
914
86419
13585
915
86415
00004
99996
13
48
53 36
6 24
14495
896
85505
14.500
895
85500
00004
99996
12
49
50
53 28
6 3^
15391
877
860
84609
11. 83732
1.5395
8.16273'
878
860
84605
11. 83727
00004
99996
11
10
11 53 20
6 40
8. 16268
10.00005
9. 99995
51
53 12
6 48
17128
843
82872
17133
843
82867
00005
99995
9
52
53 4
6 56
17971
827
82029
17976
828
82024
00005
99995
8
53
52 56
7 4
18798
812
81202
18804
812
81196
00005
99995
i
54
52 48
7 12
19610
797
80390
19616
8.20413
797
80384
00005
10.00006
99995
9. 99994
6
55
11 52 40
7 20
8. 20407
782
11. 79593
782
11.79587
56
52 32
7 28
21189
769
78811
21195
769
78805
00006
99994
4
57
52 24
7 36
21958
755
78042
21964
756
78036
00006
99994
3
58
52 16
7 44
22713
743
77287
22720
742
77280
00006
99994
2
59
52 8
7 52
23456
730
76544
23462
730
76538
00006
99994
1
60
M.
52
8
24186
717
75814
24192
718
75808
00007
99993
Hour p. M.
Hour A. M.
Cosine.
Diff.l'.
Secant.
Cotangent.
Did. 1'.
Tangent.
Cosecant.
Sine.
M.
90°
89°
" ^^.
-
TABLE 44.
[Page 773
1°
Log. Sines, Tangents, and Secants
178°
M.
Hour A. M.
Hour p. M.
Sine.
Difl. 1'.
Cosecant.
Tangent.
Difl. 1'.
Cotangent.
Secant.
Cosine.
M.
11 52
8
8. 24186
717
11. 75814
8. 24192
718
11. 75808
10.00007
9.99993
60
1
51 52
8 8
24903
706
75097
24910
706
75090
00007
99993
59
2
51 44
8 16
25609
695
74391
2.5616
696
74384
00007
99993
58
3
51 36
8 24
26304
684
73696
26312
684
73688
00007
99993
57
4
51 28
8 32
26988
673
73012
26996
673
73004
00008
10. 00008
99992
9.99992"
56
55
5
11 51 20
8 40
8. 27661
663
11. 72339
8. 27669
663
11. 72331
6
51 12
8 48
28324
653
71676
28332
664
71668
00008
99992
,54
7
51 4
8 56
28977
644
71023
28986
643
71014
00008
99992
53
8
50 56
9 4
29621
634
70379
29629
634
70371
00008
99992
52
9
10
50 48
9 12
30255
624
69745
.30263
625
69737
00009
99991
51
,50
11 50 40
9 20
8. 30879
616
11.69121
8. 30888
617
11. 69112
10.00009
9. 99991
n
50 32
9 28
31495
608
6^505
31505
607
68495
00009
99991
49
12
50 24
9 36
32103
599
67897
32112
599
67888
00010
99990
48
13
50 16
9 44
32702
590
67298
32711-
591
67289
00010
99990
47
14
l.V
50 8
9 52
33292
583
66708
33302
584
66698
00010
99990
9. 99990
46
4.5'
11 50
10
8. 33875
575
11.66125
8. 33886
575
11.66114
10.00010
16
49 52
10 8
34450
568
65,550
34461
568
655.39
00011
99989
44
17
49 44
10 16
awi8
560
64982
a5029
561
64971
00011
99989
43
18
49 36
10 24
35578
553
64422
3,5590
553
64410
00011
99989
42
19
20
49 28
11 49 20
10 32
36131
8. 36678
.547
63869
.36143
8:36689
546
63857
00011
10. 00012
99989
41
40
10 40
539
11. 63322
540
11.63311
9. 99988
21
49 12
10 48
37217
533
62783
37229
533
62771
00012
99988
39
22
49 4
10 56
37750
526
622,50
.37762
527
62238
00012
99988
38
23
48 56
U 4
38276
520
61724
38289
520
61711
00013
99987
37
24
25
48 48
11 12
38796
8.39310
514
61204
38809
514
61191
00013
99987
36
11 48 40
11 20
.508
11. 60690
8. 39323
509
11.60677
10.00013
9. 99987
35
26
48 32
11 28
39818
.502
60182
39832
,502
60168
00014
99986
34
27
48 24
11 36
40320
496
59680
40334
496
.5966()
00014
99986
33
28
48 16
11 44
40816
491
59184
40830
491
.59170
00014
99986
32
29
To"
48 8
11 52
41307
8.41792'
485
58693
41321
486
58679
11.58193
00015
10.00015
99985
9. 99985
31
30
11 48
12
480
11.58208
8.41807
480
31
47 52
12 8
42272
474
57728
42287
475
57713
00015
99985
29
32
47 44
12 16
42746
470
57254
42762
470
57238
00016
99984
28
33
47 36
12 24
43216
464
,56784
43232
464
.56768
00016
99984
27
34
47 28
12 32
4.3680
4,59
56320
43696
460
455
56304
11.. 5.5844
00016
99984
26
25"
11 47 20
12 40
8. 441.39
455
11.5.5861
8. 441.56
10.00017
9. 99983
36
47 12
12 48
44594
450
5.5406
44611
450
55389
00017
99983
24
37
47 4
12 56
4.5044
445
,54956
4.5061
446
54939
00017
99983
23
38
46 56
13 4
45489
441
,54511
45507
441
.54493
00018
99982
00
39
40
46 48
13 12
4.5930
436
54070
45948
437
,54052
00018
io: 00018
99982
21
20
11 46 40
13 20
8. 46,366
433
11. 53634
8. 46385
432
11.53615
9. 99982
41
46 32
13 28
46799
427
53201
46817
428
53183
00019
99981
19
42
46 24
13 36
47226
424
52774
47245
424
52755
00019
99981
18
43
46 16
13 44
47650
419
52a50
47669
420
52331
00019
99981
17
44
46 8
13 52
48069
416
51931
48089
416
51911
00020
99980
16
'15
45
11 46
f4
8. 48485
411
11. 51,515
8. 48505
412
11.51495
10. 00020
9. 99980
46
45 52
14 8
48896
408
51104
48917
408
51083
00021
99979
14
47
45 44
14 16
49304
404
50696
49325
404
50675
00021
99979
13
48
45 36
14 24
49708
400
.50292
49729
401
50271
00021
99979
12
49
50
45 28
14 32
.50108
396
49892
.501.30
397
49870
00022
99978
9. 99978
11
10
11 45 20
14 40
8. 50504
393
11.49496
8. .50527
393-
11.49473
10. 00O22
51
45 12
14 48
50897
390
49103
.50920
390
49080
(X)023
99977
9
52
45 4
14 56
51287
386
48713
51310
386
48690
00023
99977
8
53
44 56
15 4
51673
382
48327
51696
,383
48304
00023
99977
7
54
55
44 48
15 12
52055
8. 52434
379
47945
52079
380
47921
00024
99976
9. 99976
6
5
11 44 40
15 20
376
11. 47,566
8. 52459
376
11.47,541
10. 00024
56
44 32
15 28
52810
373
47190
52835
373
47165
00025
99975
4
57
44 24
15 36
.53183
369
46817
53208
370
46792
00025
99975
3
58
44 16
15 44
.5,3.552
367
46448
.53578
367
46422
00026
99974
2
59
44 8
15 52
.53919
.363
46081
53945
363
46055
00026
99974
1
60
44
16
54282
360
45718
.54308
361
45692
00026
99974
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.l'.
Secant.
Cotangent.
Diflt. 1'.
Tangent.
Cosecant.
Sine.
M.
91°
88° 1
Page 774]
TABLE U.
2°
Log. Sines, Tangents, and Secants
177°
JI.
Hour A. M.
Hour r. n..
Sine.
J)iff.l'.
Cosecant.
Tanfrent.
Difl.l'.
Cotangent.
Secant.
Cosine.
M.
60
11 44
16
8. 54282
360
11.45718
8. 54308
361
11.4,5692
10. 00026
9. 99974
1
43 52
16 8
.54642
357
45358
54669
358
45331
00027
99973
.59
9.
43 44
16 16
54999
355
4.5001
55027
355
44973
00027
99973
58
3
43 36
16 24
55354
351
44646
55382
352
44618
00028
99972
57
4
43 28
16 32
.55705
349
44295
55734
349
44266
00028
10.00029
99972
56
55
ft
11 43 20
16 40
8. 560.54
346
11.43946
8. 56083
346
11.43917
9. 99971
fi
43 12
16 48
56400
343
43600
56429
344
43571
00029
99971
54
7
43 4
16 56
56743
341
43257
56773
341
43227
00030
99970
53
S
42 56
17 4
57084
.337
42916
,57114
,338
42886
00030
99970
52
9
10
42 48
17 12
57421
336
42579
57452
336
333
42548
11.42212
00031
99969
51
11 42 40
17 20
8. 57757
332
11.42243
8. 57788
10. 00031
9. 99969
,50
11
42 32
17 28
58089
330
41911
58121
330
41879
00032
99968
49
12
42 24
17 36
58419
328
41581
58451
328
41.549
00032
99968
48
13
42 16
17 44
58747
325
412.53
58779
326
41221
00033
99967
47
14
15
42 8
17 52
59072
323
40928
59105
323
40895
00033
99967
46
45
11 42
18
8. 59.395
320
11. 40605
8. 59428
321
11.40572
10. 00033
9. 99967
16
41 52
18 8
59715
318
40285
59749
.319
40251
00034
99966
44
1"
41 44
18 16
60033
316
39967
60068
316
39932
00034
99966
43
IS
41 36
18 24
60;i49
313
39651
60384
314
39616
00035
99965
42
19
20
41 28
18 32
60662
311
309
.39338
60698
311
39302
000.36
99964
41
40
11 41 20
18 40
8. 60973
11. 39027
8. 61009
310
11. .38991
10. 00036
9. 99964
21
41 12
18 48
61282
307
38718
61319
307
38681
00037
99963
39
22
41 4
18 56
61.589
.305
38411
61626
305
38374
00037
99963
38
23
40 56
19 4
61894
302
38106
61931
303
38069
00038
99962
37
24
2o
40 48
19 12
62196
301
37804
62234
301
37766
00038
10.00039
99962
9. 99961
36
3,5
11 40 40
19 20
8. 62497
298
11.. 37503
8. 625a5
299
11. 37465
2li
40 32
19 28
62795
296
37205
62834
297
37166
00039
99961
.34
27
40 24
19 36
63091
294
36909
63131
295
.36869
00040
99960
33
2S
40 16
19 44
63385
293
36615
63426
292
36574
OOtMO
999(50
32
29
30
40 8
19 52
63678
290
36322
63718
291
289"
36282
00041
99959
31
30
11 40
20
8. 63968
288
11.36032
8.64009
11.35991
10.00041
9. 99959
31
39 52
20 8
642.56
287
35744
64298
287
35702
00042
99958
29
32
39 44
20 16
64543
284
a5457
64585
285
a5415
00042
99958
28
33
39 36
20 24
64827
283
35173
64870
284
35130
00043
99957
27
34
39 28
20 32
&5U0
8. 65391"
281
,34890
651,54
281
34846
00044
10.00044
99956
9.999.56
26
25
35
11 39 20
20 40
279
ll.;W609
8. 65435
280
11. 34565
3e>
3H 12
20 48
6.5670
277
34330
6.5715
278
34285
00045
999.55
24
37
39 4
20 56
6.5947
276
34053
6.5993
276
.34007
00045
99955
23
38
38 56
21 4
66223
274
33777
66269
274
33731
00046
999.54
22
39
40
38 48
1138 40^
21 12
66497
272
33503
66543
8. 66816
273
271
3:5457
00046
999,54
21
20
21 20
8. 66769
270
11. 33231
11. .33184
10.00047
9. 99953
41
38 32
21 28
67039
269
32961
67087
269
32913
00048
99952
19
42
38 24
21 36
67308
267
32692
67;»6
268
i 32644
00048
99952
18
43
38 16
21 44
67575
266
32425
67624
266
! 32376
00049
99951
17
44
45
38 8
21 52
67841
263
32159
67890
264
t 32110
11. 31846
00049
99951
16
11 38
22
8. 68104
263
11. 31896
8. 68154
263
10. 000,50
9. 999,50
15
4fi
37 52
22 8
68367
260
31633
68417
261
' 31583
00051
. 99949
14
47
37 44
22 16
68627
259
31373
68678
260
31322
00051
9V)949
13
48
37 36
22 24
68886
258
.31114
689,38
258
31062
00052
99948
12
49
50
37 28
11 37 20
22 32
69144
256
30856
69196
257
30804
00052
99948
9. 99947
11
10
22 40
8. 69400
254
11.30600
8. 69453
255
11.30.547
10. 00053
51
37 12
22 48
69654
253
30;?46
69708
254
30292
000,54
' 99946
9
52
37 4
22 56
69907
252
30093
69962
252
30038
00054
! 99946
8
53
36 56
23 4
701,59
2.50
29841
70214
251
29786
00055
99945
t
54
55
36 48
23 12
70409
249
29.591
70465
249
1 248
295:i5
11.29286
00056
99944
6
11 36 40
23 20
8. 70658
247-
11.29342
8. 70714
10. 00056
9.99944
n
m
36 32
23 28
70905
246
29095
70962
246
29038
00a57
99943
4
57
36 24
23 36
71151
244
28849
71208
245
28792
00058
99942
3
58
36 16
23 44
71395
243
28605
71453
244
2a547
00058
i 99942
2
59
36 8
23 52
71638
242
28362
71697
243
! 28303
00059
99941
1
60
36
24
71880
240
' 28120
71940
241
: 28060
00060
; 99940
M.
Hour p. M.
Hour A. M.
Cosine.
Dift.l'.
Secant.
Cotangent
Diff. 1'.
Tangent.
Cosecant.
Sine.
M.
02°
87°
TABLE U.
[Page 775
3°
Log. Sines, Tangents, and Secants
176°
M.
Hoar A. M.
1 Hour p. M.
Sine.
Difl. 1'.
Cosecant.
Tangent.
Diff. 1'.
Cotangent.
Secant.
Cosine.
M.
11 36
24
8. 71S80
240
11. 28120
8. 71940
241
11.28060
10.00060
9. 99940
60
1
35 52
24 8
72120
239
27880
72181
239
27819
00060
• 99940
59
2
36 44
24 16
72359
238
27641
72420
239
27580
00061
99939
58
8
35 36
, 24 24
72597
237
27403
72659
237
27341
00062
99938
57
4
5
35 28
24 32
72834
235
27166
11. 26931
72896
236
27104
00062
To. 00063
99938
56
55
11 35 20
24 40
8. 73069
234
8. 73132
234
11.26868
9. 99937
6
35 12
24 48
73303
232
26697
73366
234
26634
00064
99936
54
7
35 4
24 56
73535
232
264(i5
73600
232
26400
00064
99936
53
H
34 56
25 4
73767
2.30
26233
73832
231
26168
00065
99935
52
9
34 48
25 12
73997
229
26003
11.25774
74063
229
25937
00066
10700066^
99934
51
50
10
11 34 40
25 20
8. 74226
228
8. 74292
229
11. 25708
9. 99934
11
34 32
25 28
74454
226
25546
74521
227
25479
00067
99933
49
12
34 24
25 36
74680
226
2.5320
74748
226
25252
000(>8
99932
48
13
34 16
25 44
74906
224
25094
74974
225
25026
00068
99932
47
14
34 8
25 52
75130
223
24870
11. 24647
75199
224
24801
00069
10. 00070
99931
9. 99930
46
45
15
11 34
0-26
8. 753.53
222
8. 75423
222
11. 24577
16
33 52
26 8
75575
220
24425
75645
222
24,355
00071
99929
44
17
33 44
2() 16
75795
220
24205
. 75867
220
24133
00071
99929
43
18
33 36
26 24
76015
219
23985
76087
219
23913
00072
99928
42
19
33 28
26 32
762:i4
217
23766
76306
219
217
23694
n; 23475
00073
To. 60074
99927
9. 99926
41
40
11 33 20
26 40
8. 76451
216
II.23.549I
8. 76525
I'l
33 12
26 48
76667
216 1 233.33
76742
216
23258
00074
99926
39
22
33 4
26 56
76883
211
23117
76958
215
23042
00075
99925
38
23
32 56
27 4
77097
213
22903
77173
214
22827
00076
99924
37
24
32 48
27 12
77310
212
22690
11.22478
77387
213
22613
11.22400
00077
99923
9. 99923"
36
"3,5
25
11 32 40
27 20
8. 77522
211
8.77600
211
10. 00077
26
32 32
27 28
77733
210
22267
77811
211
22189
00078
99922
.34
27
32 24
27 36
77943
209
22057
78022
210
21978
00079
99921
33
28
32 16
27 44
78152
208
21848
78232
209
21768
00080
99920
32
29
30
32 8
11 32
27 52
78360
208
21640
78441
208
21,559
00080
99920
31
30
28
8. 78568
206
11.21432
8. 78649
206
11. 213.51
10. 00081
9. 99919
31
31 52
28 8
78774
205
21226
788-55
206
21145
00082
99918
29
32
31 44
28 16
78979
204
21021
79061
205
2W»39
00083
99917
28
33
31 36
28 24
79183
203
20817
79266
204
20734
00083
99917
27
35
31 28
28 32
79386
202
20614
79470
203
2a530
11.20327
00084
99916
26
2.5
11 31 20
28 40
8. 79588
201
11.20412
8. 79673
202
10.0(X)85
9. 99915
36
31 12
28 48
79789
201
20211
79875
201
20125
00086
99914
24
37
31 4
28 56
79990
199
20010
80076
201
19924
0(.X)87
99913
23
38
30 56
29 4
80189
199
19811
80277
199
19723
00087
99913
22
3fi
40"
30 48
29 12
80388
197
197
19612
80476
8. 80674
198
198
19524
11. 19326
00088
10. 00089
99912
9. 99911
21
20
11 30 40
29 20
8. 80585
11. 19415
41
30 32
29 28
80782
196
19218
80872
196
19128
00090
99910
19
42
30 24
29 36
80978
195
19022
81068
196
18932
00091
99909
18
43
30 16
29 44
81173
194
18827
81264
195
18736
00091
99909
17
44
30 8
29 52
30
81367
193
18633
814.59
8. 816.53
194
193
18.541
11.18347
00092
99908
16
45
11 30
8. 81560
192
11.18440
10. 00093
9. 99907
15
46
29 52
30 8
81752
192
18248
81846
192
181.54
00094
99906
14
47
29 44
30 16
81944
190
180.56
82038
192
17962
00095
99905
13
48
29 36
30 24
821:54
190
17866
82230
190
17770
00096
99904
12
49
50
29 28
30 32
82324
8.82513^
189
17676
11.17487
82420
8.82610
190
189
17580
00096
99904
11
10
11 29 20
30 40
188
11. 17390
10.00097
9. 99903
51
29 12
3Q 48
82701
187
17299
82799
188
17201
00098
99902
9
52
29 4
30 56
82888
187
17112
82987
188
17013
00099
99901
8
53
28 56
31 4
83075
186
16925
83175
186
16825
00100
999(X)
7
54
55
28 48
31 12
83261
185
16739
83361
8. 83547
186
185
16639
11. 164.53^
00101
99899
9. 99898
6
5
11 28 40
31 20
8, 83446
184
11. 16.5.54
10. 00102
56
28 32
31 28
83630
183 ! 16370
83732
184
16268
00102
99898
4
57
28 24
31 36
83813
183 16187
8.3916
184
16084
00103
99897
3
58
28 16
31 44
83996
181
16004
84100
182
15900
00104
99896
2
59
28 8
31 52
84177
181
1.5823
84282
182
15718
00105
99895
1
60
28
32
84358
181
15642
84464
182
15536
00106
99894
M.
Hour p. M.
Hour A. M.
Cosine.
Difl.l'.
Secant.
Cotangent.
Diff. 1'.
Tangent.
Cosecant.
Sina
M.
93="
86° 1
' / ^,.
Page 776
TABLE 44.
4°
Log. Sines, Tangents, and Semnte
IT.'i"
M.
Hour A. M.
Hour p. M.
Sine.
DilT.l'.
Cosecant.
Tangent.
Diff.l'.
Cotangent.
Secant.
Cosine.
M.
11 28
32
8.84358
181
11. 15642
8. 84464
182
11. 155.36
10.00106
9. 99894
60
1
27 52
32 8
84539
179
15461
84646
180
15;«4
00107
99893
59
2
27 44
32 16
84718
179
15282
84826
180
1.5174
00108
99892
58
3
27 36
32 24
S4897
178
15103
8.5006
179
14994
00109
99891
57
4
27 28
32 32
85075
177
14925
85185
178
14815
00109
99891
9. 99890
56
5.5^
5
11 27 20
32 40
8. a5252
177
11.14748
8. 85363
177
11. 14637
10.00110
6
27 12
32 48
a5429
176
14571
85.540
177
14460
00111
99889
54
7
27 4
32 56
85605
175
14395
85717
176
14283
00112
99888
53
8
26 56
33 4
85780
175
14220
85893
176
14107
00113
99887
52
9
10
26 48
11 26 40
33 12
33 20
85955
173
14045
86069
8. 8624.3
174
i;je3i
00114
99886
51
,50
8.86128
173
11. 13872
174
11. 1S757
10. 00115
9. 99885
11
26 32
33 28
86301
173
1.3699
86417
174
13583
00116
99884
49
12
26 24
33 36
86474
171
1,3526
86.591
172
13409
00117
99883
48
13
26 16
33 44
86645
171
13355
86763
172
13237
00118
99882
47
14
26 8
33 52
86816
8. 86987
171
13184
11.13013
86935
171
13065
00119
99881
46
45
15
11 26
34
169
8. 87106
171
11. 12894
10. 00120
9. 99880
16
25 52
34 8
87156
169
12844
87277
170
12723
00121
99879
44
17
35 44
34 16
87325
169
1267.5
87447
169
12553
00121
99879
43
18
25 36
34 24
87494
167
12.506
87616
169
12384
(X)122
99878
42
19
20
25 28
11 25 20
34 32
87661
168
12339
87785
168
12215
00123
99877
41
34 40
8. 87829
166
ri. 12171
8. 87953
167
11. 12047
10. 00124
9. 99876
40
21
25 12
34 48
87995
166
12005
88120
167
11880
00125
99875
39
22
25 4
34 56
88161
165
11839
88287
166
11713
00126
99874
38
23
24 56
35 4
88326
164
11674
88453
165
11,547
00127
99873
37
24
25
24 48
11 24 40
35 12
35 20
88490
8. 88654
. 164
163
11510
11.11346
88618
165
11382
00128
10.00129
99872
36
35
8. 887h3
165
11.11217
9. 99871
26
24 32
35 28
88817
163
11183
88948
163
110.52
00130
99870
34
27
24 24
35 36
88980
162
11020
89111
163
10889
00131
99869
33
28
24 16
35 44
89142
162
10858
89274
163
10726
00132
99868
32
29
30
24 8
35 52
89304
160
10696
89437
161
10563
00133
99867
31
30"
11 24
36
8. 89464
161
11. 10536
8. 89598
162
11. 10402
10. 00134
9. 99866
31
23 52
36 8
89625
159
10375
89760
160
10240
00135
99865
29
32
23 44
36 16
89784
159
10216
89920
160
10080
001,36
99864
28
33
23 36
36 24
89943
1.59
10057
9(X)80
160
09920
00137
99863
27
34
35
23 28
11 23 20
36 32
36 40
90102
158
157
09898
il. 09740
90240
1.59
158
09760
00138
99862
9. 99861
2()
25
8. 90260
8. 90399
11.09601
10.00139
36
23 12
36 48
90417
157
09583
90557
1.58
09443
00140
99860
24
37
23 4
36 56
90574
156
09426
90715
157
09285
00141
99859
23
38
22 56
37 4
90730
155
09270
90872
1.57
09128
00142
99858
22
39
22 48
37 12
0"37 2b
90885
155
09115
1 1708960
91029
156
08971
11.0881,5
00143
"10. 00144
99857
21
"20
40
11 22 40
8. 91040
155
8.91185
155
9. 99856
41
22 32
37 28
91195
154
08805
91,340
1.55
08660
00145
99855
19
42
22 24
37 36
91349
153
08651
91495
1.55
Oa505
00146
99854
18
43
22 16
37 44
91502
153
08498
91650
153
083,50
00147
99853
17
44
45
22 8
37 52
91655
152
08.345
91803
154
08197
00148
99852
16
15
11 22
38
8.91807
152
11.08193
8. 91957
153
11.08043
10.00149
9. 99851
46
21 52
38 8
91959
151
08041
92110
1,52
07890
001,50
99850
14
47
21 44
38 16
92110
151
07890
92262
152
07738
00152
99848
13
48
21 36
38 24
92261
150
07739
92414
151
07586
001,53
99847
12
49
21 28
38 32
38 4b"
92411
150
07589
n76f439
92565
151
07435
001.54
99846
11
10
50
11 21 20
8. 92561
149
8. 92716
1.50
11.07284
10. 001,55
9. 99845
51
21 12
38 48
92710
149
07290
92866
1,50
07134
001,56
99844
9
52
21 4
38 56
92859
148
07141
93016
149
06984
00157
99843
S
53
20 56
39 4
93007
147
06993
93165
148
06835
001,58
99842
/
54
20 48
39 12
93154
8.93301
147
06846
9.3313
8.9,3462"
149
06687
00159
10.00160
99841
6
55
11 20 40
39 20
147
11.06699
147
11.06,538
9. 99840
5
56
20 32
39 28
93448
146
06552
93609
147
06.391
00161
99839
4
57
20 24
39 36
93594
146
06406
93756
147
06244
00162
99838
3
58
20 16
39 44
93740
145
06260
93903
146
06097
00163
99837
2
59
20 8
39 52
9.3885
145
06115
94049
146
0,5951
00164
998.36
1
60
20
40
940.30
144
05970
94195
145
05805
00166
99834
M.
M.
Hour p. H.
Hour A. M.
Cosine.
Dift.l'.
Secant.
Cotangent.
Diff.l'.
Tangent.
Cosecant.
Sine.
94°
86°
f
<.-.
r^
:/
rT
TABLE 44.
[Page 777
V
Log.
Sines, Tangents, and Secants.
6°
A
A B
B
C
C 174°
M.
Hour A. M.
Hour r. M.
Sine.
Dift.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Diff.
Cosine.
M.
11 20 00
40 00
8. 94030
11.0.5970
8. 94195
11. 05805
10. 00166
9. 99834
60
1
19 52
40 08
94174
2
05826
94340
2
05660
00167
99833
59
2
19 44
40 16
94317
4
0.5683
94485
4
05515
00168
99832
58
3
19 36
40 24
94461
/
05539
94630
7
05370
00169
99831
57
4
19 28
40 32
94603
9
05397
94773
9
05227
00170
99830
.56
5
11 19 20
40 40
8. 94746
11
11. 052.54
8.94917-
11
11. 05083
10.00171
9. 99829
55
6
19 12
40 48
94887
13
05113
9.5060
13
04940
00172
99828
,54
7
19 04
40 56
95029
15
04971
95202
15
04798
00173
99827
53
8
18 56
41 04
95170
18
04830
95344
18
04656
00175
99825
52
9
18 48
41 12
95310
20
04690
11.04.5.50
9.5486
8.'9.562'7
20
22
04514
11.04373
00176
10.00177
99824
9. 9982,3
51
".50
10
11 18 40
41 20
8. 95450
22
11
18 32
41 28
95589
24
04411
95767
24
04233
00178
99822
49
12
18 24
41 36
95728
26
04272
95908
27
04092
00179
99821
48
13
18 16
41 44
95867
29
04133
96047
29
03953
00180
99820
47
14
15
18 08
41 52
96005
31
03995
96187
31
33
0.3813
"11.03675
00181
10.00183'
99819
'9. 99817'
46
45
11 18 00
42 00
8. 96143
33
11.03a57
8. 96325
1t>
17 52
42 08
96280
35
03720
96464
.35
0:5536
00184
99816
44
17
17 44
42 16
9(i417
37
0.3583
96602
38
03398
00185
99X15
43
18
17 36
42 24
9655a
39
03447
96739
40
. 03261
00186
99814
42
19
20'
17 28
11 17 20"
42 32
42 40
96689
8. 96825
42
'44
0.3311
11.03175
96877
42
44
03123
00187
10.00188
99813
41
8. 97013
11.02987
9.99812
40
21
17 12
42 48
96960
46
03040
97150
46
02850
00190
99810
39
22
17 04
42 56
97095
48
02905
97285
49
tl2715
00191
99809
38
23
16 56
43 04
97229
50
02771
97421
51
02579
00192
99808
37
24
25
16 48
11 16 40
43 12
97363
'8. 97496
53
55
02637
11.02504
97556
53
55
02444
11. 02309
00193
99807
36
.35
43 20
8. 97691
10. 00194
9. 99806
2()
16 32
43 28
97629
57
02371
97825
58
02175
00196
99804
34
27
16 24
43 36
97762 59
02238
97959
60
02041
tX)197
99803
.33
2W
16 16
43 44
97894 61
02106
98092
62
01908
00198
99802
32
29
16 08
43 52
98026 64
01974
98225
64
66
01775
11.01642
00199
10.00200
99801
9'.'99800
31
30'
30
11 16 00
44 00
8.98157 I 66
11.01843
8. 98358
31
15 52
44 08
98288
68
01712
98490
69
01510
00202
99798
29
32
15 44
44 16
98419
70
01581
98622
71
01378
00203
99797
28
33
15 36
44 24
98549
72
014.51
98753
73
01247
00204
99796
27
34
35
15 28
11 15 20
44 32
44 40
98679
75
77
01.321
98884
75
01116
00205
99795
26
8. 98808
11.01192
8. 99015
77
11. 00985
10. 00207
9. 99793
25
36
15 12
44 48
98937
79
01063
99145
80
008.55
00208
99792
24
37
15 04
44 56
99066
81
009.34
99275
82
00725
00209
99791
23
38
14 56
45 04
99194
83
00806
99405
84
00595
00210
99790
22
39
40'
14 48
11 14 40
45 12
45 20
99322
'8. 99450
86
00678
995.34
8. 99662'
86
89
004t)6
00212
iO. 00213
99788
21
88
11. 005.50
11. 00338
9. 99787
20
41
14 32
45 28
99577
90
00423
99791
91
00209
00214
99786
19
42
14 24
45 36
99704
92
00296
99919
93
(X)081
00215
99785
18
43
14 16
45 44
99830
94
00170
9. 00046
95
10. 99954
00217
99783
17
44
45
14 08
1 1 14 00
45 52
99956
96
'99
00044
00174
97
99826
00218
10.00219
T
99782
9.99781
16
1.5"
46 00
9.00082
10. 99918
9. 00.301
100
10. 99699
4(i
13 52
46 08
00207
101
99793
00427
102
99573
00220
99780
14
47
13 44
46 16
00332
103
99668
00553
104
99447
00222
99778
13
48
13 36
46 24
00456
105
99544
00679
106
99321
00223
99777
12
49
50
13 28
11 13 20
46 32
46 40
00581
107
99419
10. 99296
00805
9.009:»
108
111
99195
00224
99776
11
10'
9. 00704 i 1 10
10. 99070
10. 00225
9. 99775
51
13 12
46 48
00828 :112
99172
01055
113
98945
00227
99773
9
52
13 04
46 5(i
00951
114
99049
01179
115
98821
00228
99772
S
53
12 56
47 04
01074
116
98926
01303
117
98697
00229
99771
1
54
55
12 48
11 12 40
47 12
47 20
01196
9.01318"
118
121
98804
10.98682
01427
120
122
9*573
00231
99769
99768
6
.5
9. 01.550
10. 98450
10. 00232
50
12 32
47 28
01440
123
98560
01673
124
98327
00233
99767
4
o/
12 24
47 36
01.561
125
984.39
01796
126
98204
00235
99765
3
58
12 16
47 44
01682
127
98318
01918
128
98082
00236
99764
59
12 08
47 52
01803
129
98197
02040
131
97960
00237
99763
1
60
12 00
48 00
01923
132
98077
02162
1,33
97838
002.39
-1 99761
M.
Hour p. M.
Hour A. M,
Cosine.
DiiT.
Secant.
Cotangent.! niff.
Tangent.
Cosecant.
Dlff. Sine.
M.
95°
.\
A B
B
('
C 84° 1
Seconds of time .
Prop, parts of cols. < B
Ic
1"
8>
i'
e>
82 99
83 I ;oo
1 ! 1
!■
116
1
Page 778]
TABLE U.
Log. Sines, Tangents, and Secants.
6°
A A
B B
C
C 173°
M.
Hour A. M.
Hour p. M.
sine.
Dlff.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Dlff.
Cosine.
M.
n
11 12 00
48 00
9. 01923
10. 98077
9. 02162
10. 97838
10. 002,39
9. 99761
60
1
11 52
48 08
02043
2
97957
02283
2
97717
00240
99760
59
2
11 44
48 16
02163
4
97837
02404 4
97596
(K1241
997,59
58
H
11 36
48 24
02283
6
97717
02525
6
97475
00243
99757
57
4
11 28
48 32
02402
7
9
97598
10. 97480
02645
8
9
97.355
10. 97234
00244
10.00245
99756
9. 99755
56
55
ft
11 11 20
48 40
9. 02520
9. 02766
fi
11 12
48 48
02639
11
97361
02885
11
97115
00247
99753
54
11 04
48 56
02757
13
97243
03005
13
96995
00248
99752
53
8
10 56
49 04
02874
15
97126
03124
15
96876
00249
99751
52
9
10
10 48
49 12
49 20
02992
9. 03109
17
19
97008
10.96891
03242
9. 03361'
17
19
96758
10796639
00251
10. 00252"
99749
51
11 10 40
9. 99748
.50
11
10 32
49 28
03226
20
96774
03479
21
96521
00253
99747
49
12
10 24
49 36
03342
22
96658
0:5597
23
96403
(X)255
99745
48
13
10 16
49 44
03458
24
96542
03714
24
96286
002,56
99744
47
14
15
10 08
49 52
03574
26
28
96426
10. 96310
03832 1 26
96168
10. 96052
00258
10. 002,59
99742
46
'45
11 10 00
50 00
9. 03690
9.03948 : 28
9. 99741
16
9 52
50 08
03805
30
96195
04065
30
9.5935
00260
99740
44
17
• 9 44
50 16
03920
31
96080
04181
32
9.5819
(.K1262
99738
43
18
9 36
50 24
04034
33
9596<)
04297
34
95703
00263
99737
42
19
20
9 28
50 32
04149
35
95851
10. 95738
04413
36
95587
iO. 95472
00264
1(1.00266
99736
41
To
11 9 20
50 40
9. 04262
37
9.04,528 i 38
9. 99734
?.^
9 12
50 48
04376 i 39
95624
04643 ! 39
95357
ai267
99733
39
90
9 04
50 56
04490
41
95510
04758
41
95242
00269
99731
38
9.n
8 56
51 04
04603
43
95397
04873
43
95127
00270
99730
37
24
8 48
51 12
04715
44
46
95285
10.95172
04987
45
47
9501 3
10. 94899
(X)272
10.00273
99728
36
35
2o
11 8 40
51 20
9. 04828
9. 05101
9. 99727
?fi
8 32
51 28
04940 i 48 1 95060
05214
49
94786
00274
99726
34
?7
8 24
51 36
05^52 i 50 i 94948
05328 1 51
'94672
00276
99724
33
?.H
8 16
51 44
05164 i 52 1 94836
05441 53
945.59
00277
99723
32
29
30
8 08
51 52
05275
54
94725
05553 54
94447
00279
10. 00280
1
99721
9. 99720
31
30
n 8 00
52 00
9. 05386
56
10.94614
9.05666 1 56
10. 94334
31
7 52
52 08
05497
57 1 94.503
05778 58
94222
00282
99718
29
32
7 44
52 16
0.5607
59 i 94393
0.5890 i 60 ! 94110
00283
99717
28
33
7 36
52 24
05717
61 94283
06002 i 62
93998
00284
99716
27
34
35~
7 28
52 32
05827
63 94173
06113
64
66
9,3887
10.93776
00286
10. 00287
99714
26
25
11 7 20
52 40
9.05937 1 65 110.94063
9. 06224
9. 99713
3R
7 12
52 48
06046 i 67 i 93954
06335 i 68
93665
00289
99711
24
37
7 04
52 56
06155 i 69 93845
06445 i 69
93555
00290
99710
23
38
6 56
53 04
06264 1 70 93736
06556 1 71
93444
00292
99708
22
39
40
6 48
53 12
06372
9.06481'
72 j 93628
06666 1 73
9. 06775 75
93,334
10. 9,3225
00293
10.00295'
^
99707
9. 99705
21
20
U 6 40
53 20
74
10. 93519
41
6 32
53 28
06589 j 76
93411
06885 77
93115
00296
99704
19
42
6 24
53 86
06696 1 78
93,304
06994 79
93006
00298
99702
18
43
6 16
53 44
06804 1 80
93196
07103 81
92897
00299
99701
17
44
45
6 08
53 52
54 00
06911
81
9,3089
IQ. 92982
07211
83
84
92789
10. 92680
00301
99699
16
1,5
11 6 00
9. 07018
83
9. 07320
10. 00302
9. 99698
4(!
5 52
54 08
07124
85
92876
07428 ! 86
92572
00304
99696
14
47
5 44
54 16
07231
87
92769
07,536 i 88
92464
00305
99695
13
48
5 36
54 24
07337
89
92663
07643 90
92357
00307
99693
12
49
50
5 28
54 32
07442
91
93"
92558
10. 92452
07751 92
9.078.58 ! 94
92249
To. 92142
00308
10.00310
99692
9. 99690
11
10'
U 5 20
54 40
9. 07548
51
5 12
54 48
07653
94
92347
07964 i 96
9203()
00311
99689
9
52
5 04
54 56
07758
96
92242
08071 1 98
91929
00313
1
99687
8
53
4 56
55 04
07863
98
92137
08177 1 99
91823
00314
99686
/
54
4 48
55 12
07968
100
92032
08283
101
103
91717
10.91611
00316
10.00317
99684
9. 99683
6
'5
^55
11 4 40
55 20
9. 08072
102
10. 91928
9. 08389
5fi
4 32
55 28
08176 :104
91824
08495 105
915ft5
00319
99681
4
57
4 24
55 36
08280 106
91720
08600 107
91400
00320
99680
3
58
4 16
55 44
08383 il07
91617
08705 109
91295
00322
99678
2
59
4 08
55 52
08486 109
91.514
08810
111
911',K)
00323
99677
1
60
4 00
56 00
08589 llll
91411
08914
113
91086
00325
\
99675
M.
M.
Hour p. M.
Hour A. M.
Cosine. Dlff.
Secant.
Cotangent.
Dlfl.
Tangent.
Cosecant.
iDiff.
Sine.
»«°
A A
B B
C
C 83° 1
Seconds of time
!•
2"
3-
4-
5"
6-
!•
(A
Prop, parts of cols. < B
14 28
14 28
!
42
42
1
56
36
1
69
70
1
83
84
1
97
98
1
TABLE U.
[Page 779
Log. Sines, Tangents, and Secants.
JO
A A
B B
C
C Ui°
>I.
Hour A.M.
Hour p. «.
Sine.
loifl.
Cosecant.
Tangent.
Did. 1 Cotangent.
Secant.
Diff.
Cosine.
M.
60
n
U 4
56
9. 08589 j
10.91411
9.08914 10.91086
10.00325
19.99675
1
3 52
56 8
08692 i 2
91308
09019
2 : 90981
00326
99674
59
o
3 44
56 16
08795 i 3
91205
09123
3 ! 90877
00328
! 99672
58
•A
3 36
56 24
08897 ! 5
91103
09227
5 i 90773
00330
1 99670
57
4
5
3 28
•56 32
08999 i 6
9.09101 1 8
91001
10. 90899
09330
7 ! 90670
00331
; 99669
56
11 3 20
56 40
9.09434 1 8 10.90566
10. 00333
1 9. 99667
55
li
3 12
56 48
09202 1 10
90798
09537 1 10 90463
00334
\ 99(i()6
54
/
3 4
56 56
09;iO4 ; 11
90696
09640 I 11 1 903(J0
00336
1 99664
53
2 56
57 4
094a5 t 13
90595
09742 1 13 ! 90258
00337
! 996(i3
52
2 48
11 2 40
57 12
09506
14
16
90494
09845 i 15 1 90155
9.09947 1 16 ilO. 90053
00339
i 99661
51
57 20
9. 09606
10. 90394
10. 00341
9. 99659
50
11
2 32
57 28
09707 18 ! 90293
10049 18 ! 89951
00342
99658
49
IL-
2 24
57 36
09807 : 19 1 90193
10150 1 20 ' 89850
00344
99656
48
i:i
2 16
57 44
09907 21
90093
10252 21 89748
00345
99655
47
U
2 8
57 52
10006 22
89994
10353 23 89647
00347
99653
46
45
l.T
11 2
58
9. 10106 ' 24
10. 89894
9. 10454 1 24 10. 89546
10. 00349
9. 99651
1t>
1 52
58 8
10205 1 26 1 89795
10555 ! 26 ! 89445
00350
99650
44
17
1 44
58 16
10304 27 : 89696
10656
28 89344
00;i52
99648
43
IH
1 36
58 24
10402 29 i 89598
10756
29 89244
00353
99647
42
19
20
1 28
11 1 20
58 32
58 40
10501
30 i 89499
32 110. 89401
10856
31 ( 89144
33 10.89044
00;J55
10. 00357
99645
9. 99643
41
40
9. 10599
9. 10956
21
1 12
58 48
10697 j 34 : 89303
11056
34 ; 88944
00;i58
99642
39
*>•)
1 4
58 56
10795 1 35 ! 89205
11155
36 88845
00360
99640
38
2:^
56
59 4
10893 i 37 i 89107
11254
37 1 88746
00362
996;«
37
24
48
59 12
10990 i 38 i 89010
11353
39 . 88647
00363
10. 00365
1
99637
36
35
25
11 40
59 20
9. 11087 '. 40 10. 88913
9. 11452 j 41 10. 8a548
9. 99635
2<>
32
59 28
11184 i 42 \ 88816
11551 1 42 ' 88449
00367
1 j 99633
:«
27
24
59 36
11281 1 43 '■ 88719
11(>49 \ 44 88351
00368
1 1 99632
33
28
16
59 44
11377 45 88623
11747 i 46 1 88253
00370
1 ; 99630
32
29
"SO
8
11
59 52
10
11474 ! 46 88526
11845
47 1 88155
49 10.88057
00371
10. 00373
1 1 99629
1 9.99(>27
31
30
9. 11570 ! 48 10. 88430
9. 11943
HI
10 59 52
8
11(566 50 88334
12040
51 87960
00375
1 1 99625
29
Wl
59 44
16
11761 : 51
88239
12138
52 87862
tX)376
1 1 99624
28
:;:i
59 36
24
lia57 i 53
88143
12235
54 8776.-,
00378
1 i 99622
27
a4
35
59 28
10 59 20
32
11952 54
88048
12332
55
S7668
10. 87572
00380
10. 00382
1 1 99620
26
25
1 40
9. 12047 56
10. 87953
9. 12428
57
9.99618
3«
59 12
48
12142 ! 58 87858
12525
59 87475
00383
99617
24
37
59 4
56
12236 j 59 ! 87764
12621
60 87379
00385
99615
23
3S
58 56
1 4
12331 j 61 87669
12717
62 87283
00387
, 99613
22
39
40
58 48
1 12
12425 1 62 1 87575
9.12519 •■ 64 10.87481
12813
64 1 87187
00388
10. 00390
99612
21
20
10 58 40
1 1 20
9.12909
65 10. 87091
1 19.99610
41
58 32
1 28
12612 ! 66 ! 87388
13004
67 i 86996
(X)392
1 1 99608
19
42
58 24
1 36
12706 67 87294
13099
68
86901
00393
1 : 99607
18
43
58 16
1 44
12799
69 ' 87201
13194
70
86806
00395
1 99605
17
44
45'
58 8
1 52
12892
70 1 87108
13289
72
86711
00397
10.00399
1 I 99603
16
l5
10 58
1 2
9. 12985
72
10. 87015
9. 13384
73
10. 86616
1 19.99601
4(1
57 52
2 8
13078
74
86922
13478
75 86522
00400
99600
14
47
57 44
2 16
13171
75
86829
13573
77 86427
00402
99598
13
48
57 36
2 24
13263
77 86737
13667
78 1 86333
00404
9959f>
12
49
^50
57 28
10 57 20
2 32
1 2 40
13355
78 i 86645
13761
80 ! 86239
00405
99595
11
10
9. 13447 ! 80 10. 86553
9. 13854
81 !10. 86146
10. 00407
9. 99593
51
57 12
2 48
13539 1 82 ' 86461
13948 i 83 1 86052
0O4O9
99591
9
52
57 4
2 56
13630
83 86370
14041
85 , 85959
0(H11
99589
8
53
56 56
3 4
13722
85 86278
14134
86 1 8586(i
00412
99588
i
54
56 48
3 12
13813
87 86187
14227
88
8.5773
10. 85680
00414
10.0O416
2
2
99586
9. 99584
6
5
oo
10 56 40
1 3 20
9. 13904
88 10. 8(i096
9. 14320
90
5t>
56 32
3 28
13994 90 8()006
14412
91 85588
00418
2
99582
4
Ol
56 24
3 36
14085
91 85915
14504
93 85496
00419
2
99581
3
58
56 16
3 44
14175
93
85825
14597
95 85403
00421
2
9^579
2
59
56 8
3 52
14266
95
85734
14688
96 : a5312
00423
2
99577
1
60
56
4
14356
96
85644
14780
98
a5220
00425
2
99575
M.
Hour p. 5C.
Hour A.M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
9J^
A A
B B
C
C 82° 1
Seconds of time
1. 1 2. 1 8. i 4.
o*
6> ! 7» j
f A 1 12 1 24 36 1 48
I'rop. parts of cols. -^ B ' 12 24 37 i 49
(c ^ i 1 ' 1
60 1 72 ' 84
61 ' 73 88
11 1
Page 780]
TABLE 44.
Log. Sines, Tangents, and Secants.
8°
A A
B
B C
C 171'
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Dlfl.
Cotangent.
Secant.
Dia.
Cosine.
M,
10 56
1 4
9. 14356
10. 85644
9. 14780
10. 86220
10. (X)425
9. 99675
60
1
55 52
4 8
14445
1
85555
14872
1
86128
00426
99574
59
?.
55 44
4 16
14536
3
85465
14963
8
85037
00428
99672
58
•A
55 36
4 24
14624
4
85376
15054
4
84946
00430
99570
57
4
55 28
4 32
14714
6
7
85286
10. 85197
15145
9. 15236
6
7
84855
10. 84764
00432
10.00434
99568
5(i
55
5
10 55 20
1 4 40
9. 14803
9. 99566
6
55 12
4 48
14891 8
85109
1.5327
9
84(i78
00435
99565
54
7
55 4
4 56
14980 10
8.5020
1.5417
10
84588
00487
99563
58
8
54 56
5 4
1.5069 11
84981
15.508
12
84492
00439
99561
52
9
54 48
5 12
15157 13
84843
15.598
13
84402
00441
99569
9. 99557
51
.50
10
10 54 40
1 5 20
9.1.5245 14
10. 84755
9. 15688
14 10.84812
10. 00443
11
54 32
5 28
15833 16 1 84667
15777
16
84223
00444
99.556
49
12
54 24
5 36
15421 17 ! 84579
15867
17
84138
00446
995.54
48
1.S
54 16
5 44
15508 , 18 84492
1.5956
19
84044
00448
99552
47
14
54 8
5 52
1.5596 ' 20 84404
16046
9. 16136
20
83954
004.50
10. (X)452
99.550
' 9. 99,548
46
45
15
10 54
16
9.15683 21 10.84317
22 ilO. 88865
16
53 52
6 8
15770 : 23
842.30
16224
23 i 8377(1
00454
1 \ 99,546
44
17
53 44
6 16
1.5857 1 24
84143
16812
25 ' 83688
00455
1 ' 99545
48
18
53 36
6 24
15944
25
84056
16401
26 \ 88599
00457
1 I 99543
42
19
20
53 28
6 32
16030
27
"28
88970
10.'88884
16489
9.16.577
27 1 83511
29 i 10. 83428
00459
10700461
1 i 99541
1 9.99539
41
40
10 53 20
1 6 40
9.16116
21
53 12
6 48
16203
30
88797
16665
30 88885
00463
1 99537
89
22
53 4
6 56
16289 31
8.8711
16763
82 88247
00465
1 99535
88
28
52 56
7 4
16374 ] 32 i 8362()
16841
83 831.59
00467
1 99533
87
24
25
52 48
7 12
16460 ! 34
83540
la 884.55
16928
9. 17016
35 1 83072
36 |10. 82984
00468
10. 00470
1 99532
.86
"85
10 52 40
1 7 20
9. 16.545 35
1 9. 99530
2(1
52 32
7 28
16631 1 37 1 88369
17103
37 1 82897
00472
1 99528
84
27
52 24
7 36
16716 1 38 i 83284
17190
39 1 82810
00474
1 99526
83
28
52 16
7 44
16801 39 i 88199
17277
40 1 82728
- 00476
1 99624
82
29
52 8
7 52
16886
41 : 83114
42 U). 83030
17363
9. 17450
42 i 82637
43 110.82.5.50
00478
10.00480
1 i 99522
1 : 9. 99520
81
80
m
10 52
1 8
9. 16970
HI
51 52
8 8
17055 44 82945
17.536
45 : 824()4
00482
1 : 99518
29
82
51 44
8 16
17139 45 ! 82861
17622
46 82.878
00488
1 : 99517
28
88
51 36
8 24
17223 : 47 i 82777
17708
48 ; 82292
00485
1 99515
27
84
51 28
8 32
17307 i 48
82698
17794
49 ! 82206
50 10.82120
00487
lO: 00489
1 99513
1 : 9. 99511
26
25
35
10 51 20
1 8 40
9. 17,391 49
10. 820'J9
9.17880
8fi
51 12
8 48
17474 : 51
82526
17965
52 ! 820,35
00491
1 i 99509
24
87
51 4
8 56
17558 i 52
82442
18051
63 i 81949
00493
1 \ 99607
23
88
50 56
9 4
17641 i 54
823.59
18136
65 1 81864
00495
1 \ 99505
22
39
50 48
9 12
17724
55
82276
18221
9. 18306
56 81779
58 llO. 81694
00497
10. 00499
1
1
99503
21
40
10 50 40
X 9 20
9. 17807
56 110.82198
9. 99501
20
41
50 32
9 28
17890 ! 58 i 82110
18.391
59 ! 81609
00.501
1 ' 99499
19
42
50 24
9 36
17973 : 59 i 82027
18475
61 ! 81525
00503
1 99497
18
48
50 16
9 44
18055 1 61 1 81945
ia560
62 ' 81440
00.505
1 99495
17
44
45
50 8
9 52
18137 ! 62 81863
9. 18220 1 63 10.81780
18644
9. 18728
63 8185(!
66 10.81272
(K)506
10.00.508
1 i 99494
1 9.99492
16
15
10 50
1 10
4t)
49 52
10 8
18302 i 65
81698
18812
66 1 81188
(H1510
1
99490
14
47
49 44
10 16
18383 ! 66
81617
18896
68
,81104
00512
1
99488
18
48
49 36
10 24
18465
68
81585
18979
69
81021
00514
2
99486
12
49
49 28
10 32
18547
9. 18628
69
'71
814.53
10. 81372
19063
9.19146
71
72"
80937
10.808.54
00516
10.00,518
2
99484
11
10
50
10 49 20
1 10 40
2 ] 9. 99482
51
49 12
10 48
18709
72
81291
19229
74
80771
00520
2 1 99480
9
52
49 4
10 56
18790
73
81210
19312
76
80688
00522
2 ! 99478
8
58
48 56
11 4
18871 i 75
81129
19395
76
80(i05
00524
2
99476
/
54
55^
48 48
11 12
18952 i 76
81048
10. 80967
19478
9. 19661
78
79
80522
10. 80439
00526
10.00.528
2
99474
6
5
10 48 40
1 11 20
9. 19033
78
2 ! 9. 99472
56
48 32
11 28
19113
79
80887
19643
81
80857
(X),530
2
99470
4
57
48 24
11 36
19193
80
80807
19725
82
80275
00582
2
99468
8
58
48 16
11 44
19273
82
80727
19807
84
80198
00534
2
99466
2
59
48 8
11 52
19353
83 80647
19889
85
80111
tX)536
2
99464
I
60
48
12
19433
85 80567
19971
87
80029
00588
2
99462
M.
M.
Hour p. M.
Hour A. H.
Cosine.
Difl. Secant.
Cotangent.
Difl.
Tangent.
Caseeant.
Difl.
Sine.
98°
A A
B
B (•
C Sl° 1
Seconds of time 1" j 2"
3« 1 4" i 5"
1 1
6- ;■
(A 11 1 21 32 42 53
ITori. imrts of <•"!'■ -^B 11 ; 22 32 43 54
((■ coil 1 1
C3 74
65 71!
1 2
a""^^
TAE
^^^"
.LE U.
[Page 781
Log.
Sines, Tangents, and Secants.
9°
A
A
li B
C
C 170°
M.
Hour A. M.
Hour P.M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.l Cotangent.
Secant.
Diff.
Cosine.
M.
10 48
1 12
9. 19433
10. 80567
9. 19971
10.80029
10. 00538
9.99462
60
1
47 52
12 8
19513
1
80487
20053
1 1 79947
00540
99460
59
.)
•47 44
12 16
19592 i 3
80408
20134
3 1 79865
00542
99458
58
:i
47 36
12 24
19672 4
80328
20216
4
79784
00544
99456
57
4
47 28
12 32
19751 i 5
80249
10.80170
20297
9. 20378
5
6
79703
10.79622
00546
99454
9. 99452
56
55
5
10 47 20
1 12 40
9. 19830 i 6
10. 00548
(i
47 12
12 48
19909 8
80091
20459
8
79541
00550
99450
54
/
47 4
12 56
1998S i 9
80012
20540 ' 9
79460
00552
99448
53
K
46 56
13 4
20067
10
79933
20621
10
79379
00554
99446
52
To"
46 48
10 4(r40"
13 12
1 13 20
20145
11
79855
20701
9. 20782
12
13
79299
00556
10.00558
.0
99444
9. 99442
51
50
9. 20223
13
10. 79777
10. 79218
11
46 32
13 28
20302
14
79698
20862
14
79138
00560
99440
49
12
46 24
13 36
20380
15
79620
20942
16
79058
00562
99438
48
13
46 16
13 44
20458 ! 16
79542
21022
17
78978
00564
99436
47
14
15
46 8
13 52
1 14
20535 1 18
9.20613 '19
79465
21102
9. 21182"
18
19
78898
10.78818
00566
99434
46
45
10 46
10. 79387
10. 00568
9. 99432
Ki
45 52
14 8
20691 ; 20
79309
21261
21
78739
00571
99429
44
17
45 44
14 16
20768
21
79232
21341
22
78659
00573
99427
43
IS
45 36
14 24
20845
23
79155
21420 1 23
78580
00575
99425
42
lil
20
45 28
10 45 20
14 32
1 14 40
20922
24
79078
21499
25
78501
00577
9942.3
41
40
9. 20999
25
10. 79001
9. 21578
26
10. 78422
10. 00579
9.99421
21
45 12
14 48
21076
26
78924
21657
27
78343
00581
99419
39
■>■>
45 4
14 56
21153
28
78847
21736
28
78264
00583
99417
38
2:'
44 56
15 4
21229
29
78771
21814
30
78186
(.)0585
99415
37
24
2.')
44 48
15 12
2130<)
30
78694
10. 78618
21893
31
78107
10. 78029
00587
10. 00589
99413
36
"35
10 44 40
1 15 20
9.21382 ; 31
9. 21971
32
9.99411
2t>
44 32
15 28
21458 33
78542
22049
34
77951
00591
99409
34
27
44 24
15 36
21534
34
78466
22127
35
77873
00593
\
99407
33
2S
44 16
15 44
. 21610
35
78390
22205
36
77795
00596
99404
32
29
30
44 8
10 44
15 52
21685
9. 21761
37
38
78315
10. 78239
22283
38
39
77717
10. 77639
00598
99402
31
30"
1 16
9. 22361
10. (X)600
9.99400
31
43 52
16 8
21836
39
78164
22438
40
77562
00602
1
99398
29
32
43 44
16 16
21912
40
78088
22516
41
77484
006(M
99396
28
33
43 36
16 24
21987
42
78013
22593
43
77407
00606
99394
27
35
43 28
10 43 20
16 32
1 16 40
22062 43
9. 22137 1 44
77938
10. 77863
22670
"9.22747
44
45
77330
00608
99392
26
25
10. 772.53
10. 00610
9. 99390
3(i
43 12
16 48
22211 45
77789
22824
47
77176
(X)612
99388
24
37
43 4
16 56
22286 47
77714
22901
48
77099
00615
99,385
23
3K
42 56
17 4
22361 : 48
77639
22977
49
77023
00617
99383
<>•>
39
40
42 48
10 42 40
17 12
1 17 20
22435
49
77565
2.3054
9. 23130
50
52
76946
10. 76870
00619
10. 00621
99381
21
9. 225a)
50
10. 77491
9. 99379
20
41
42 32
17 28
22583
52
77417
23206
53
76794
00623
99377
19
42
42 24
17 36
22ft57
53
77;«3
23283
54
76717
00625
99375
18
43
42 16
17 44
22731 j 54
77269
23359
56
76641
00628
2
99372
17
44
45
42 8
10 42
17 52
22805 I 55
77195
23435
9:23510
57
58
76565
00630
2
2
99370
16
15
1 18
9.22878 1 57
10.77122
10. 76490
10. 00632
9. 99368
46
41 52
18 8
22952 1 58
77048
23586
60
76414
006.34
2
99366
14
47
41 44
18 16
23025 i 59
76975
23661
61
76339
00636
2
99364
13
48
41 36
18 24
23098
60
76902
23737
62
76263
00638
2
99362
12
49
50
41 28
18 32
23171
62
63
76829
23812
9.2.3887
63
76188
00641
2
99359
11
10'
10 41 20
1 18 40
9. 23244
10. 76756
10. 76113
10. 00643
2
9. 99.357
51
41 12
18 48
23317
r>4
76683
23962
66
76038
00645
2
99:355
9
52
41 4
18 56
23390
65
76610
24037
67
75963
00647
2
99353
8
53
40 56
19 4
23462
67
76538
24112
69
75888
00649
2
99351
7
54
40 48
19 12
2.35.35
9.23607
68
76465
24186
9. 24261
70
71
75814
00652
10. 00654
2
99348
6
55
10 40 40
1 19 20
69
10. 76393
10. 75739
2
9. 99346
5
56
40 32
19 28
23679
71
76321
24335
73
75665
00656
2
99344
4
57
40 24
19 36
23752
72
76248
24410
74
75590
00658
2
99342
3
58
40 16
19 44
23823
73
76177
24484
75
75516
00660
2
99340
2
59
40 8
19 52
23895
74
76105
24558
76
75442
00663
2
99337
1
60
40
20
23967
76
760.33
Secant.
24632
78
75368
00665
2
99335
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
99°
A
A
B n
C
C 80° j
Seconds of time
l-
2-
8-
4-
5>
6-
7.
(A
Prop, parts of cols.^B
9
10
19
19
1
28
29
1
38
39
1
47.
49
1
f)7
58
2
66
68
2
Page 782
TABLE U.
Log. Sines, Tangents, and Secants.
10°
A A
B B
C
C Ifi»°
M.
Hour A. M.
Hour p. M.
Sine. Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Difl.
Cosine.
M.
10 40
1 20
9.23967 '
10. 76033
9. 24632
10. 75368
10. 00665
9. 99335
60
1
39 52
20 8
24039 1
75961
24706
1
75294
00667
99333
59
*>
39 44
20 16
24110 2
75890
24779
2
75221
00669
99331
58
3
39 36
20 24
24181 ! 3
75819
24853
4
75147
00672
99328
57
4
39 28
20 32
24253 5
75747
24926
5
6
75074
10. 75000
00674
99326
.56
55
10 39 20
1 20 40
9.24324 ; 6
10. 75676
9.25000
10. (X)676
9. 99324
<)
39 12
20 48
24395 7
75605
25073
7
74927
00678
99322
54
/
39 4
20 56
24466 i 8
76bM
25146
8
74854
00681
99319
53
s
38 56
21 4
24536 9
75464
25219
9
74781
00683
99317
52
9
38 48
21 12
24607 10
9.24677 11
75.393
25292
11
74708
00685
99315
9. 99313
51
.50
10
10 38 40
1 21 20
10. 75323
9.25365 i 12
10. 746.35
10. 00687
11
38 32
21 28
24748 13
75252
2.5437 I 13
74563
00690
99310
49
12
38 24
21 36
24818 1 14
75182
2.5510 14
74490
00692
99308
48
13
38 16
21 44
24888 ' 15
75112
25582 15
74418
00694
99306
47
14
IS
38 8
21 52
24958 1 16
7.5042
25655
16
74345
00696
10. 00699
99304
46
45
10 38
1 22
9.25028 17
10. 74972
9. 25727
18
10. 74273
9. 99301
If)
37 52
22 8
25098 i 18
74902
25799
19
74201
00701
99299
44
17
37 44
22 16
25168 19
74832
25871
20
74129
00703
99297
43
18
37 36
22 24
25237
20
74763
25943
21
74057
00706
00708
99294
42
19
20
37 28
22 32
25307
22
74693
26015
9. 26086
22
. 73985
99292
9. 99290
41
40
10 37 20
1 22 40
9. 25376
23
10. 74624
24
10. 73914
10.00710
21
37 12
22 48
25445
24
74555
26158
25
73842
00712
99288
39
22
37 4
22 66
25514
25
74486
26229
26
7.3771
00715
99285
38
23
36 56
23 4
25583
26
74417
26301
27
73699
00717
99283
37
24
25"
36 48
23 12
25652
27
74348
26372
28
73628
00719
1
99281
36
.3.5
10 36 40
1 23 20
9. 25721
28
10. 74279
9. 26443
29
10. 73.557
10. 00722
9. 99278
2t>
36 32
23 28
25790
30
74210
26514 i 31
73486
00724
99276
34
27
36 24
23 36
25858
31
74142
26585
32
73415
00726
99274
33
28
36 16
23 44
25927
32
74073
26655
33
73345
00729
99271
32
29
30
36 8
23 52
25995
33
34
74005
26726
34
35
73274
00731
99269
31
30
10 36
1 24
9. 26063
10. 7.3937
9. 26797
10. 73203
10. 00733
9. 99267
31
35 52
24 8
26131
35
73869
26867
.36
73133
00736
99264
29
32
35 44
24 16
26199
36
73801
26937
38
7.3063
00738
99262
28
33
35 36
24 24
26267
38
73733
27008
.39
72992
00740
99260
27
34
35
35 28
24 32
26335
39
40
73665
10. 7,3597
27078
40
72922
00743
99257
9. 99255
2()
'25
10 35 20
1 24 40
9. 26403
9. 27148
41
10. 72852
10. 00745
36
35 12
24 48
26470
41
73530
27218
42
72782
00748
99252
24
37
35 4
24 56
265,38
42
7,3462
27288
44
72712
00750
99250
23
38
34 56
25 4
26605
43
73395
27.357
45
72643
00752
99248
22
39
40
34 48
25 12
26672
44
73328
27427
46
47
72573
00755
10. 00757"
2
2
99245
9. 99243
21
20
10 34 40
1 25 20
9. 26739
45
10. 73261
9. 27496
10. 72504
41
34 32
25 28
26806
47
73194
27566
48
72434
007.59
2
99241
19
42
34 24
25 36
26873
48
73127
27635
49
72365
00762
2
99238
18
43
34 16
25 44
26940
49
7.3060
27704
51
72296
00764
2
99236
17
44
34 8
25 52
27007
50
72993
27773
52
72227
00767
2
99233
9. 99231
16
1.5"
45
10 34
1 26
9. 27073
51
10. 72927
9. 27842
53
10.72158
10. 00769
2
4»)
33 52
26 8
27140
52
72860
27911
54
72089
00771
2
99229
14
47
33 44
26 16
27206
53
72794
27980
0.3
72020
t10774
2
99226
13
48
33 36
26 24
27273
55
72727
28049
56
71951
00776
2
99224
12
49
33 28
26 32
27339
56
72661
28117
58
71883
00779
2
99221
11
50
10 33 20
1 26 40
9. 27405
57
10. 72595
9.28186
59
10.71814
10. 00781
2
9. 99219
10
51
33 12
26 48
27471
58
72529
28254
60
7174R
00783
2
99217
9
52
33 4
26 56
27537
59
72463
28323
61
71677
00786
2
99214
8
53
32 56
27 4
27602
60
72398
28391
62
71609
00788
2
99212
i
54
32 48
27 12
27668
61
63
72332
10. 72266"
28459
9. 28527
63
65
71.541
00791
10.00793
2
2
99209
9. 99207
6
5"
55
10 32 40
1 27 20
9. 27734
10. 71473
56
32 32
27 28
27799
64
72201
2a595
66
71405
00796
2
99204
4
57
32 24
27 36
27864
65
72136
28662
67
71338
00798
2
99202
3
1 58
32 16
27 44
27930
66
72070
28730
68
71270
00800
2
99200
2
59
32 8
27 52
27995
67
72005
28798
69
71202
00803
2
99197
1
60
32
28
28060
68
71940
28865
71
71135
00805
2
99195
M.
Hour P.M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent. ! Diff.
Tangent.
Cosecant.
Difl.
Sine, j >r. 1
lOO'
A A
B B
C
c ;»°|
Seconds of time .
Prop, parts of cols..|B
Ic
26
26
1
TABLE U.
[Page 783
Log. Sines, Tangents, and Secante.
11°
A
A
B B
C
168°
M.
Hour 4. M.
1 Hour p. M.
Sine.
Difl.
Cosecant.
Tanjtent. j Diff.
Cotangent.
Secant.
Difl.
Cosine.
M.
60
10 32
' 1 28
9. 28060
ko. 71940
9. 28865 !
10.71135
10. 00805
9.99195
1
31 52
28 8
28125
1 71875
28933
1
71067
00808
99192
59
2
31 44
28 16
28190
2 ': 71810
29000
2
71000
(XI810
99190
58
3
31 36
28 24
28254
3 i 71746
29067
3
70933
(X)813
99187
57
4
31 28
! 28 32
28319
4 I 71681
29134
4
70866
00815
99185
56
55
5
10 31 20
1 1 28 40
9. 28384
5
10. 71616
9. 29201
5
10. 70799
10. 00818
9. 99182
fi
31 12
I 28 48
28448
6
71552
29268
6
70732
00820
99180
54
7
31 4
28 56
28512
/
71488
29335
8
70665
00823
99177
53
S
30 56
29 4
28577
8 : 71423
29402
9
70598
00825
99175
52
9
10
30 48
i 29 12
28641
9 i 71.359
29468 i 10
70532
00828
99172
51
50
10 30 40
1 1 29 20
9. 28705
10 10. 71295
9. 29535
11
10. 70465
10. 00830
9. 99170
11
30 32
29 28
28769
11 1 71231
29601
12
70399
00833
99167
49
12
30 24
1 29 36
28833
12 ! 71167
29668
13
70332
00835
99165
48
13
30 16
29 44
28896
13 71104
29734
14
70266
00838
99162
47
14
30 8
29 52
28960
14 ; 71040
29800
'9. 29866
15
70200
00840
1
99160
46
45
IS
10 30
1 30
9. 29024
16 10.70976
16 10.70134
10. 00843
9. 99157
If.
29 52
30 8
29087
17 ' 70913
29932
17 1 70068
(X)845
99155
44
17
29 44
30 16
29150
18 70850
29998
18 ; 70002
00848
99152
43
18
29 36
30 24
29214
19 i 70786
30064
19 i 69936
008.50
99150
42
19
29 28
30 32
29277
20 70723
30130
20 69870
00853
99147
41
20
10 29 20
1 30 40
9.29340
21 10.70660
9.30195 i 22 ilO. 69805
10. 008.55
9. 99145
40
21
29 12
30 48
29403
22 1 70597
30261 23
69739
00858
99142
.39
22
29 4
30 56
29466
23 70534
30326
24
69674
(X)860
99140
38
23
28 56
31 4
29529
24 i 70471
30.391
25
69609
1)0863
99137
37
24
28 48
31 12
29591
25 70409
30457
9. 30522
26
69543
00865
99135
36
35
25
10 28 40
1 31 20
9.29654
26 10. 70346
27
10. 69478
10. 00868
9.99132
26
28 32
31 28
29716
27 : 70284
.30587
28 1 69413
00870
99130
34
27
28 24
31 36
29779
28 i 70221
30652
29 I 69.348
00873
99127
33
28
28 16
31 44
29841
29 1 70159
30717
30 1 69283
00876
99124
32
29
28 8
31 52
29903
30 1 70097
30782
31 1 69218
00878
10. 00881
X
99122
9.99119
31
30
30
10 28
1 32
9. 29966
31 10.70034
9.30846 1 32 ;10. 69154
31
27 52
32 8
30028
32 69972
30911 ' 33 j 69089
00883
99117
29
32
27 44
32 16
30090
33 1 69910
30975 ! 35 i 69025
00886
99114
28
33
27 36
32 24
30151
34 69849
31040 36 68960
00888
99112
27
34
3o
27 28
32 32
30213
35
69787
10. 69725
31104
37
38
68896
00891
99109
26
10 27 20
1 32 40
.9.30275
36
9. 31168
10. 68832
10. (X1894
2
9. 99106
25
36
27 12
32 48
30336
37 69664
31233 39 ' H8767
00896
2
99104
24
37
27 4
32 56
30398
38 1 69602
31297 40 ! 68703
t)0899
2
99101
23
38
26 56
33 4
30459
39 69541
31361 41 68639
(X)901
2
99099
22
39
26 48
33 12
30521
40
41
69479
31425 42 1 68575
00904
2
99096
21
20
40
10 26 40
1 33 20
9. 30582
10. 69418
9. 31489 ; 43 10. 68511
10.00907
2
9. 99093
41
26 32
33 28
30643
42 69357
31552 44 i 68448
00909
2
99091
19
42
26 24
33 36
30704
43 69296
31616 ' 45 68384
00912
2
99088
18
43
26 16
33 44
30765
45 692:»
31679 46 1 68321
00914
2
99086
17
44
45
26 8
33 52
30826
46 1 69174
47 10.69113
31743 47 1 68257
00917
2
99083
16
15
10 26
1 34
9. 30887
9.31806 49 110.68194
10. 00920
2
9. 99080
46
25 52
34 8
30947
48 : 69*53
31870 50 1 68130
00922
2
99078
14
47
25 44
34 16
31008
49 68992
31933 51 , 68067
00925
2
99075
13
48
25 36
34 24
31068
50 ' 68932
31996 : 52 1 68004
00928
2
99072
12
49
25 28
34 32
31129
51 1 68871
32a59
53
54
67941
00930
2
2
99070
11
10
50
10 25 20
1 34 40
9.31189
.52 10.68811
9. 32122
10. 67878
10. 00933
9.99067
51
25 12
34 48
31250
53 68750
.32185 1 55 i 67815
00936
2
99064
9
52
25 4
34 56
31310
.54 : 68690
32248 ' 56 67752
00938
2
99062
8
53
24 56
35 4
31370
55 ; 68630
32311 1 57
67689
00941
2
99059
7
54
55'
24 48
35 12
31430
56 ! 6*570
32373 ! 58
67627
00944
10. 00946
2
99056
6
5
10 24 40
1 35 20
9. 31490
57 ilO. 68510
9. 32436 59
10. 67564
2
9.99054
56
24 32
35 28
31549
58 j 68451
32498 60
67502
00949
2
99051
4
57
24 24
35 36
31609
59 ! 68.391
32561 61
67439
00952
2
99048
3
58
24 16
35 44
31669
60
68331
32623
63
67377
00954
2
99046
2
59
24 8
35 52
31728
61
68272
326a5
64
67315
009.57-
3
99043
1
60
24
36
31788
62
68212
,32747
65
67253
00960
3
99040
M.
Hour p. M.
Hour A. M.
Cosine.
Did.
Secant.
Cotangent. Difl.
Tangent.
Cosecant.
Difl.
Sine.
M.
101°
A
A
B B
C
C 7S°|
Seconds of time .
Prop, parts of col.s. -^B
Ic
•10
2
47
49
2
Page 784]
TABLE U.
Log. Sines, Tangents, and Secants.
12°
A A
B B
C
C 167°
M.
Hour A. M. Hour p. M.
Sine.
Difl.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine. 1
M.
10 24 1 36
9. 31788
10. 68212
9. 32747
10. 67253
10. 00960
! 9. 99040
60
1
23 52 : 36 8
31847
1
68158
32810
1
67190
00962
I 99038
59
9
23 44
36 16
31907
2
68093
32872
2
67128
00965
99035
58
o
23 36
36 24
31966
8
68034
.32938
8
67067
00968
99032
57
4
23 28
36 32
32025
9. 32084
4
5
67975
10. 67916
32995
9. 33057
4
67005
00970
10. 00973
99030
56
5.5"
5
10 23 20
1 36 40
5
10. 66943
1 9. 99027 1
(i
23 12 ! 36 48
32143
6
67857
33119
6
66881
00976
99024
54
23 4 ; 36 56
32202
/
67798
33180
7
66820
00978
99022
58
K
22 56
37 4
32261
8
67739
33242
8
66758
00981
99019
52
22 48
10 22 40
37 12
32319
9
67681
83303
9. 33365
9
10
66()97
10. 66685
00984
10.00987
99016
9. 99018
51
50
1 37 20
9. 32378
10 110.67622
11
22 32
37 28
32437
10 , 67563
33426
11
66574
00989
99011
49
12
22 24
37 36
82495 11 67505
33487
12 i 66613
00992
99008
48
IS
22 16
37 44
32553 12 67447
33548
13 ; 66452
00995
99005
47
14
1,T
22 8
37 52
32612 13 67388
33609
9. 83670
14 1 66391
15 il0.66:!30
00998
10. 01000
99002
46
45
10 22 j I 38
9. 32670 i 14 10. 67380
9. 99000
1H
21 52 , 38 8
32728 15 ' 67272
83731
16 ! 6()2(i9
01003
98997
44
17
21 44 38 16
82786 16 : (17214
33792
17 . 66208
01006
1 I 98994
43
18
21 36 • 38 24
82844 1 17 67156
33853 18 66147 '
01009
1 1 98991
42
19
20
21 28 1 38 32
82902 ; 18 67098
9.32960 1 19 1 10. 67040
33913
19
66087
01011
10. 01014
1 98989
41
40
10 21 20 1 1 38 40
9. 33974
20
10. 66026
1 1 9. 98986
21
21 12 1 38 48
33018 1 20 ! 66982
34034
21
65966
01017
1 1 98988
89
22
21 4 i 38 56
38075 ! 21 i 66925
84095
22
(i5!)05
01020
1 ! 98980
38
28
20 56 i 39 4
38133 1 22 , 66867
84155
23
65845
01022
1 ; 98978
37
24
20 48 i 39 12
33190 1 23 i 66810
34215
24
65785
10. 65724
01025
io:bio28
1 98975
36
35
25
10 20 40 ' 1 39 20
9.33248 i 24 110.66752
9. 34276
25
1 9.98972
2(i
20 32 ' 39 28
33305 : 25 66695
34336
26
65664
01031
1 1 98969
84
27
20 24
39 36
33362 ! 26 ! 66638
34396
27 '. 65604
01033
98967
38
28
20 16
39 44
83420 I 27
66580
34456
28 i 65544
01036
98964
32
29
20 8
39 52
33477
28
66523
.34516
29 1 65484
01039
98961
81
10 20 ! 1 40
9. 33534
29 110.66466
9. 34576
30 10.6.5424
10. 01042
1 9.98958
80
81
19 52 40 8
33.591 29 ; (i(>409
34635
31 65.365
01045
1 98955
29
82
19 44 40 16
33647 30
663.53
84695
32 ! 65805
01(U7
1 ' 98953
28
38
19 36 1 40 24
33704 31
66296
84755
33
65245
01050
2 i. 98950
27
84
85
19 28 i 40 32
33761
32
33
66239
34814
34
65186
010.53
2 ! 98947
26
10 19 20 1 1 40 40
9.33818
10.66182
9. 34874
35
10.65126
10. 01056
2 9.98944
25
8(!
19 12 ! 40 48
33874 1 34
66126
34933
36
6.5067
01059
2 98941
24
87
19 4 1 • 40 56
33931 35
66069
34992
37 : 65008
01062
2 98938
28
38
1& 56 ! 41 4
83987 36
66018
85051
38 ! 64949
01064
2 98936
22
39
40"
18 48
41 12
34043
37
65957
10. 65900
• 35111
39
40
64889
10. 64830
01067
2 98988
2 9.98930
21
"20
10 18 40
1 41 20
9.34100
38
9. 35170
10. 01070
41
18 32
41 28
341.56
39
65844
35229
41
64771
01073
2 98927
19
42
18 24 41 36
34212
40
65788
.35288
42
64712
01076
2 98924
18
48
18 16 41 44
34268 ' 41
65732
35347
43
64653
01079
2 98921
17
44
18 8 1 41 52
34324 1 42
65676
35405
9.35464
44
45
64595
10. 64536
01081
2 98919
16
45
10 18
1 42
9. 34380
43
10. 65620
10. 01084
2 9.98916
15
4fi
17 52
42 8
34436
44
65564
35523
46
64477
01087
2 ' 98918
14
47
17 44
42 16
34491
45
65509
35581
47
64419
01090
2 ; 98910
13
48
17 36
42 24
34547
46
65453
85640
48
64360
01093
2 ! 98907
12
49
17 28
42 '32
34602
47
65398
35698
49
64302
01096
2 1 98904
11
50
10 17 20 1 1 42 40
9.34658 ; 48
10. 65342
9. 35757
50
10. 64243
10. 01099
2 9.98901
10
51
17 12
42 48
34713 48
65287
35815
51
64185
01102
2 1 98898
9
52
17 4
42 56
;«769 i 49
65281
35873
52
64127
01104
2
98896
8
58
16 56
43 4
34824 \ 50
65176
85931
53
64069
01107
2
98893
7
54
55
16 48
43 12
34879
51
52
65121
35989
54
64011
OHIO
3
98890
6
5
10 16 40
1 43 20
9.34934
10. 65066
9. 36047
55
10. 63953
10.01113
3 19.98887
56
16 32
43 28
.34989
53
65011
36105
56
63895
01116
3
98884
4
57
16 24
43 36
35044
54
64956
36163
57
63837
01119
3
98881
3
58
16 16
43 44
;%099
55
64901
36221
58
63779
01122
3
98878
2
59
16 8
43-52
35154
56
64846
36279
59
63721
01125
3
98875
1
60
16
44
35209
57
64791
36336
60
63664
01128
3
98872
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
M.
102
o
A A
B B
c
C 77° 1
Seconds of time
1«
2-
3'
4'
d> 6'
7'
i*To\y. parla of coU. { B
Ic
7
7
14 21
15 22
1 1
29
30
1
36 43
37 45
2 2 '
50
52
2
TABLE 44.
[Page 785
Log. Sines, Tangents, and Secants.
18°
A A
B B
C
C 1660
M.
Hour A.M.
Hour p. M.
Sine. J Difl. 1 Cosecant.
1 1
Tangent.
Diff.
Cottmgent.
Secant.
Difl.
Cosine.
M.
10 16
1 44
9.35209 ' 40.64791
9. 36336
10. 63664
10.01128
9. 98872
60
1
15 52
44 8
;i5268 ! 1 ! 64737
36394
1 ; 63606
01181
98869
59
•?
15 44
44 16
35318 1 2
64682
36452
2
63548
01133
98867
58
S
15 36
44 24
.35873 1 3
64627
36509
3
63491
01136
988t)4
57
4
15 28
44 82
;»427 I 4
64573
.36566
4
5
6,3434
10. 63376
01139
98861
9. 98858
56
55
o
10 15 20
1 44 40
9. :»481
4
10. 64519
9. 36624
10.01142
fi
15 12
44 48
35536
5
64464
36681
6
68319
01145
98855
54
15 4
44 56
35590
6
64410
36738
6
68262
01148
98852
53
8
14 56
45 4
:e644
7
64356
36795
7
63205
01151
98849
52
9
10
14 48
45 12
:K698
8
64302
36852
8
63148
01154
10. 01157
98846
9. 98843
51
50'
10 14 40
1 45 20
9. :i5752
9
10. 64248
9. 36909
9
10. 63091
11
14 32
45 28
a5806
10
64194
36966
10
63034
01160
98840
49
l;?
14 24
45 36
85860
11
64140
37023
11
62977
01163
98837
48
18
14 16
45 44
;55914
11
64086
37080
12
62920
01166
98834
47
14
15
14 8
45 52
35968
12
64032
37137
13
14
62868
10. 62807
01169
10.01172
— j-
9.8831
46
45
10 14
1 46
9. 86022
13
10. 63978
9. 37193
9. 98828
1(>
13 52
46 8
36075
14
63925
37250
15
62750
01175
98825
44
17
13 44
46 16
36129
15
68871
37306
16
62694
01178
98822
48
IS
13 36
46 24
36182
16
68818
37363
17
62637
01181
98819
42
19
13 28
46 32
362.86
17
63764
37419
18
19
62581
01184
98816
9.98818
41
40
10 13 20
1 4ti 40
9. 86289
18
10.63711
9. 37476
10. 62524
10.01187
I'l
13 12
46 48
86;i42
18
63658
37532
19 62468
01190
98810
89
*>o
13 4
46 56
86395
19
63605
37588
20 62412
01193
98807
38
j:!
12 56
47 4
36449
20
6.3551
37644
21 62356
01196
98804
37
24
25
12 48
10 12 40
47 12
1 47 20
3^502
9. 36555
21
63498
37700
22 62.300
01199
98801
9. 98798
36
35
22
10. 6:i445
9. 37756
23 10.62244
10. 01202
2t)
12 32
47 28
36608
28 i 63.392
37812
24
62188
01205
98795
34
27
12 24
47 36
36660
24 ! 6:i340
37868
25
62182
01208
98792
83
2!S
12 16
47 44
36713
25 1 63287
37924
26
62076
01211
98789
82
29
80
12 8
47 52
3(5766
25
26
6,3234
37980
27
62020
01214
98786
31
30
10 12
1 48
9.86819
10. 63181
9. 38035
28 10.61965
10. 01217
2
9,98783
81
11 52
48 8
36871
27 ! 63129
38091
29
61909
01220
2
98780
29
82
11 44
48 16
86924
28 i 63076
38147
30
61853
01223
2
98777
28
88
11 .36
48 24
36976
29 i 63024
:i8202
31
61798
01226
2
98774
27
84
85
11 28
48 32
87028
30
62972
10. 62919
:«257
32
61743
01229
10, 01232
2
98771
26
25
10 11 20
1 48 40
9. 37081
31
9. 38313
32
10. 61687
2
9. 98768
3«
11 12
48 48
37138
32
62867
38368
33
61632
01235
2
98765
24
87
11 4
48 56
37185
32
62815
;?8423
34
61577
01238
2
98762
23
88
10 56
49 4
37237
33
62763
38479
35
61521
01241
2
98759
22
89
10 48
49 12
37289
84
62711
«a534
36
61466
01244
2
98756
21
40
10 10 40
1 49 20
9. 37341
35
10. 62659
9. 38589
37
10. 61411
10. 01247
2
9. 98753
20
41
10 32
49 28
37393
36
62607
38644
38
61356
01250
2
98750
19
42
10 24
49 36
37445
37
62555
38699
39
61301
01254
2
98746
18
48
10 16
49 44
37497
38
62503
38754
40
61246
01257
2
98743
17
44
45
10 8
49 52
37549
9. 3760J
.39
89
62451
38808
9. 38863
41
42
61192
01260
2
98740
16
15
10 10
1 50
10. 62400
10.61137
10, 01263
2
9, 98737
4(i
9 52
50 8
37652
40
62348
38918
43
61082
01266
2
98734
14
47
9 44
50 16
37703
41
62297
38972
44
61028
01269
2
98731
13
48
9 36
50 24
37755
42
62245
39027
45
60973
01272
2
98728
12
49
50
9 28
50 32
37806
43
62194
.39082
45
46
60918
01275
2
98725
11
10
10 9 20
1 50 40
9. 37858
44
10. 62142
9.39i;?6
10. (;0864
10. 01278
3
9. 98722
51
9 12
50 48
37909
45
62091
39190
47
60810
01281
3
98719
9
52
9 4
50 56
37960
46
62040
39245
48
60755
01285
3
98715
8
58
8 56
51 4
.38011
47
61989
39299
49
60701
01288
3
98712
7
54
55
•8 48
51 12
.38062
47
'48
61938
,39.353
50
60647
01291
3
98709 .
6
10 8 40
1 51 20
9.38113
10. 61887
9. 39407
51
10. 60593
10. 01294
1 3
9. 98706
5
5<)
8 32
51 28
38164
49
61836
39461
52
60539
01297
3
98703
4
57
8 24
51 36
38215
50
61785
39515
53
60485
01800
3
98700
3
58
8 16
51 44
38266
51
617.34
39.569
54
60431
01303
3
98697
2
59
8 8
51 52
38317
52
61683
.39623
55
60377
01306
3
98694
1
tiO
8
52
38368
53
61632
39677
.56
60323
01310
3
98690
M.
Hour p. M.
Hour A. M.
Casine.
Diff.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
M.
103°
A A
B B
C
C 76° 1
Seconds of lime
I>
2-
3- 4'
5.
6-
T
(A
Prop, parts of cols. ,(B
C
7
7
13
14
1
20 28
21 28
1 1 2
33
3,5
39
46
49
3
24972°— 12-
-40.
Page 786]
TABLE 44
Log.
Sines, Tangents, and Secants.
14°
A
A
B
B
C
C 1«5°
M.
Hour A.M.
Hour p. M.
Sine.
DifF.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Difl.
Cosine.
M.
10 8
1 52
9. 38368
10. 61632
9. 39677
10. 60323
10.01310
9. 98690
60
1
7 52
52 8
38418
1
61582
39731
1
60269
01313
98687
59
2
7 44
52 16
38469
2
61531
39785
2
60215
01316
98684
58
8
7 36
52 24
38519
2
61481
39838
3
60162
01319
98681
57
4
7 28
52 32
:«570
3
61430
.39892
3
60108
01322
98678
56
55
5
10 7 20
1 52 40
38620
4
10. 61380
9. 39945
4
10. 60055
10. 01325
9. 98675
t!
7 12
52 48
38670
61.330
39999
o
60001
01329
98671
54
7
7 4
52 56
38721
6
61279
40052
6
599t8
013,32
98668
53
8
6 56
53 4
38771
/
61229
40106
7
59894
01335
98665
52
9
6 48
53 12
38821
9. 38871'
7
8
61179
40159
8
59841
01338
1
98662
9. 986.59
51
.50
10
10 6 40
1 53 20
10.61129
9.40212
9
10. .59788
10.01.341
11
6 32
53 28
38921
9
61079
40266 1 10
59734
01344
98656
4it
12
6 24
.53 36
38971
10
61029
40319
10
59681
01348
98652
4S
18
6 16
53 44
39021
11
60979
40372
11
59628
01351
98649
47
14
15
6 8
53 52
39071
11
60929
40425
12
59575
013.54
98646
46
45
10 6
1 54
9. 39121
12
10. 60879
9. 40478
13
10. 59522
10. 01357
9. 98ti43
16
5 52
54 8
39170
13
60830
40531
14
59469
01360
98(>40
44
17
5 44
54 16
39220 : 14
60780
40584
15
59416
01364
98636
43
18
5 36
54 24
39270 15
60730
40636
16
59364
01367
98633
42
19
20
5 28
54 32
39319 ! 15
60681
10:60631
40689
9. 40742
17
59311
01370
98630
9. 98627
41
'40
10 5 20
1 54 40
9. 39369 16
17
10. 59258
10. 01373
21
' 5 12
54 48
39418 , 17
60582
40795
18
59205
01.377
1
98623
311
22
5 4
54 56
39467 ' 18
60533
40847
19
591.53
01380
98620
38
23
4 56
55 4
39517 , 19
60483
40900
20
.59100
01383
98617
'H
24
4 48
55 12
39566
£. 39615 "
20
60434
40952
9. 41005
21
22
59048
10. 58995
01386
98614
9. 98610
36
35
25
10 4 40
1 55 20
20
10. 60385
10.01390 i 1
26
4 32
55 28
39664 21
603.36
41057
23
58943
01,393 ! 1
98607
34
27
4 24
55 36
.39713 22
60287
41109
23
58891
01396 ! 1
98604
33
28
4 16
55 44
.39762 23
60238
41161
24
58839
01399
2
98601
32
29
4 8
55 52
39811 24
9. 39860 24
60189
41214
25
58786
01403
2
98597
31
30
30
10 4
1 56
10. 60140
9. 41266
26 10.58734
10. 01406
2
9. 98594
31
3 52
56 8
39909 25
60091
41318
27
58682
01409
2
98591
29
32
3 44
.56 16
39958 26
60042
41370
28
58630
01412
2
98588
28
33
3 36
56 24
40006 27
59994
41422
29
58578
01416
2
98584
27
34
3 28
56 32
4(X»55
28
29'
59945
lO: 59897'
41474
30
58526
01419
2
98581
26
,35
10 3 20
1 56 40
9. 40103
9. 41526
30 10.58474
01422
2
9. 98578
25
36
3 12
56 48
40152 29
59848
41.578
31
58422
01426
2
98574
24
37
3 4
56 56
40200 30
59800
41629
32
.58371
01429
2
98571
23
38
2 56
57 4
40249 31
.59751
41681
33
58319
01432
2
98568
22
39
40
2 48
57 12
40297 32
59703
10. 59654
41733
9. 41784
34
35
58267
10. 58216
01435
2
98565
21
20
10 2 40
1 57 20
9.40346 33
10. 01439
2
9. 98561
41
2 32
57 28
40394 i 33
59606
41836
36
58164
01442
2
98558
19
42
2 24
57 36
40442 34
59558
41887
36
.58113
01445
2
98555
18
43
2 16
57 44
40490 ! :i5
59510
41939
37
58061
01449
2
98551
17
44
2 8
57 52
40538
36
59462
41990
38
58010
01452
2
2
985'±8
9. 98.545
16
15
45
10 2
1 58
9. 40586
37
10. 59414
9, 42041
39
10. 57959
10. 014.55
46
1 52
58 8
40634
37
.59366
42093
40
57907
014.59
3
98.541
14
47
1 44
.58 16
40682
38
.59318
42144
41
57856
01462
3
98538
13
48
1 36
. 58 24
40730
39
.59270
42195
42
57805
01465
3
98535
12
49
1 28
58 32
40778
9. 40825
40
■59222
42246
43
57754
10. 57703
01469
10.01472
3
3
98531
9. 98.528
11
10
50
10 1 20
1 58 40
41
10. 59175
9. 42297
43
51
1 12
58 48
40873
42
59127
42348
44
57652
01475
3
98525
52
1 4
58 56
40921
42
.59079
42399
45
57601
01479
3
98521
8
53
56
59 4
40968
43
.59032
42450
46
57550
01482
3
98518
1
54
55
48
59 12
41016
44
45
58984
42501
47
57499
01485
3
9ail5
6
10 40
1 59 20
9. 41063
10. 58937
9. 42552
48
10. 57448
10. 01489
3
9.98511
.:)
56
32
59 28
41111
46
58889
42603
49
57397
01492
3
98508
4
57
24
.59 36
41158
46
58842
42653
50
57347
01495
3
98505
3
58
16
59 44
41205
47
58795
42704
50
57296
01499
3
98501
2
59
8
59 52
41252
48
58748
42755
51
57245
01.502
3
98498
1
60
2
41300
49
58700
42805
52
57195
01.506
3
98494
M.
Hour p. M.
Hour A.M.
Cosine.
Dlff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Difl.
Sine.
M.
104°
A
A
B
B
C
C 75° 1
Seconds of time
1'
2>
»•
4" ! o-
6» f 1
(A
Prop, parts of cols. <B
6
7
12
13
1
18
20
1
24 31
26 38
2 2
37
39
2
43
46
3
TABLE U.
[Page 787 ]
-
Log. Sines, Tangents, and Secants.
15°
A
A
B
B
C C 164=' 1
M.
Hour A.M.
Hour p. M.
Sine.
Diff. j Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
10
2
9.41300
10.58700
9. 42805
10. 57196
10. 01.506
9. 98494
60
1
9 59 52
8
41347
1
58653
42856
1
57144
01.509
98491
59
2
59 44
16
41394'
2
58606
42906
2
57094
01612
98488
58
3
59 36
24
41441
2
58559
42957
2
57043
01516
98484
57
4
59 28
9 59 20
32
41488
3
58512
43007
3
56993
01619
98481
56
2 40
9. 41535
4 10.58465
9. 43067
4
10.56943
10. 01.523
•
9. 98477
.55
6
59 12
48
41582
5 i 58418
43108
5
56892
01,526
98474
.54
4
59 4
56
41628
5 ; 58372
43158
6
56842
01529
98471
53
8
58 56
1 4
41675
6 ! 58325
43208
(
56792
01,533
98467
52
9
10
58 48
9 58 40
1 12
41722
9. 41768
7
8
.58278
43258
7
56742
01536
98464
9.98460
51
"60-
2 1 20
10. 58232
9. 4;B08
8
10. .56692
10. 01540
11
58 32
1 28
41815
8 1 58185
43358
9
56642
01.543
98467
49
12
58 24
1 36
41861
9 i 58139
43408
10
66.592
01,547
98463
48
13
58 16
144
41908
10 .58092
43458
11
66642
01550
98450
47
14
58 8
1 52
41954
11
11
58046
43508
11
66492
01.553
10.bi657
98447
46
15
9 58
2 2
9. 42001
10. 57999
9. 436.58
12
10. 66442
9. 9844.'5
45
16
57 52
2 8
42047
12 j 57953
43607
13
66.393
01.560
98440
44
17
57 44
2 16
42093
13 1 57907
43&57
14
56343
01664
98436
43
18
57 3()
2 24
42140
14 i 57860
43707
15
56293
• 01567
98433
42
19
20
57 28
2 32
42186
14
15"
.57814
43766
16
66244
01571
10. 01674
98429
9. 98426
41
40
9 57 20
2 2 40
9. 42232
10. 57768
9. 43806
16
10. 56194
21
57 12
2 48
42278
16 1 57722
43865
17
66146
01678
98422
.39
22
57 4
2 56
42324
17 1 57676
43906
18
66095
01681
98419
38
23
56 56
3 4
42370
17 ! 57630
43954
19
56046
01685
98416
37
24
25
56 48
9 56 40
3 12
42416
9. 42461
18
19
57584
44004
20
55996
01588
10. 01.591
98412
.36
2 3 20
10. 57539
9. 44063
20
10. 55947
9.98409
.35
2t)
56 32
3 28
42507
20 ; 57493
44102
21
55898
01.595
2
98405
:m
27
56 24
3 36
42553
21 i 57447
44151
22
.55849
01.598
2
98402
33
28
56 16
3 44
42599
21 57401
44201
23
55799
01602
2
98398
32
29
30
56 8
3 52
2 4
42644
9. 42690
22
23
57366
44250
24
.55750
01606
10.01609
2
98395
31
.30
9 56
10. 57310
9. 44299
25
10. .55701
2
9.98391
31
55 52
4 8
42735
24 ! 57265
44348
25
55652
01612
2
98388
29
32
55 44
4 16
42781
24 i 57219
44397
26
55603
01616
2
98384
2a
33
55 36
4 24
42826
25 ' 57174
44446
27
.565,54
01619
2
98381
27
34
55 28
4 32
42872
26
57128
10757083'
44496
28
29
56505
10.55456
01623
10. 01627
2
98377
26
25
35
9 55 20
2 4 40
9.42917
27
9. 44544
2
9. 98373
36
55 12
4 48
42962
27 1 57038
44592
29
66408
016,30
2
98370
24
37
55 4
4 56
4:W08
28 ! 56992
44641
30
.553.59
01634
2
98366
23
38
54 5t)
5 4
43053
29
56947
44690
,31
55310
01637
2
98363
22
39
54 48
9 54 40
5 12
4;}098
30
30
56902
44738
32
55262
01641
2
98369
9.98356
21
20
40
2 5 20
9. 43143
10.56867
9. 44787
33
10.5.5213
10. 01644
2
41
54 32
5 28
43188
31
56812
44836
34
.55164
01648
2
98362
19
42
54 24
5 36
43233
32
56767
44884
34
55116
01661
2
98.349
18
43
54 16
5 44
43278
33
56722
44933
35
55067
016.55
3
98345
17
44
54 8
5 52
4.3:J23
33
.56677
44981
36
66019
lO: 54971
01658
3
98342
9. 98338
16
15
45
9 .54
2 6
9. 43;%7
M
10. '56633
9. 45029
37
10. 01662
3
46
53 52
6 8
4:^412
So
56588
45078
38
64922
01666
3
983.34
14
47
53 44
6 16
43457
36
56543
45126
38
64874
01669
3
98331
13
48
53 36
6 24
43502
36
56498
45174
39
54826
.01673
3
98327
12
49
50
53 28
6 32
26 40
4.3546
37
564.54
46222
40
54778
01676
10.01680
3
3
98324
9. 98320
11
10"
9 53 20
9. 43591
38
10. 56409
9. 45271
41
10. 64729
51
53 12
6 48
436a5
39
56365
45319
42
64681
01683
3
98317
9
62
53 4
6 56
43680
39
56320
46367
43
54633
01687
3
98313
8
53
52 56
7 4
43724
40
56276
4.5415
43
54585
01691
3
98309
7
54
55"
52 48
9 5240
7 12
2 7 20
43769
«. 43813
41
42
56231
46463
9.4.5511
44
45
54637
01694
10.01698
3
3
98306
9. 98302
6
5
10. 56187
10. .54489
56
52 32
7 28
43857
43
56143
45559
46
64441
01701
3
98299
4
57
52 24
7 36
43901
43
56099
46606
47
54394
01705
3
98296
3
58
52 16
7 44
4.3946
44
56054
4.5654
47
64346
01709
3
98291
9
59
52 8
7 52
43990
45
56010
45702
48
64298
01712
3
98288
1
60
52
8
440,34
46
55966
45750
49
642,50
01716
4
98284
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
105°
A
.\
B
B
C C
74°
Seconds of time
1.
2-
S*
4>
6<
6-
7' 1
A
Prop, part.s of cols. B
Ic
6
6
11
12
1
17
18
1
23
25
2
28
31
2
34 40
37 43
3 3
Page 788]
TABLE U.
Log. Sines, Tangcntf-, and Secants.
16"
A
A
B
B
C
C
168°
M.
Hour A. M Hour r. m.
Sine.
Did.
Cosecant.
Tangent. | DiCE.
Cotangent.
Secant.
Dlfl.
Cosine.
M.
9 52 12 8
9. 44034
10. 55966
9.45750
10. 54250
10.01716
9. 98284
60
1
51 52
8 8
44078
1
55922
45797 1
54203
01719
98281
.59
9
51 44
8 16
44122
1
55878
45845 1 2
55155
01723
98277
58
3
51 36
8 24
44166
2
.558:54
4.5892 : 2
54108
01727
98273
57
4
51 28
8 32
44210
3
55790
4.5940
9. 45987
3
54060
01730
10.01734
98270
9. 98266
56
"5.5
5
9 51 20 1 2 8 40
9. 44253
4
10. 55747
4
10. 54013
6
51 12 i 8 48
44297
4
55703
46035 1 5
53965
01738
98262
54
/
51 4 1 8 56
44341
55(i59
46082 5
53918
01741
98259
53
8
50 56 : 9 4
44385
6
55615
46130 i 6
53870
01745
98255
52
9
50 48 ! 9 12
44428
6
1
55572
10. 55528
46177 : 7
9:46224 : 8
53823
10:53776"
01749
10. 01 752
98251
51
50
10
9 50 40 2 9 20
9. 44472
1 19.98248
11
50 32 9 28
44516
8
55484
46271 1 9
53729
017.56
1 i 98244
49
12
50 24 : 9 36
44559
9
55441
46319 , 9
53681
01760
1 i 98240
48
13
50 16 i 9 44
44602
9
55398
46366 , 10
53634
01763
1 j 98237
47
14
15
50 8 ^ 9 52
44646
9. 44689
10
11
553.54
10. 55311
46413 '■ 11
9.46460 \ 12
53587
10. .53540
01767
10.01771
1 1 98233
46
9 50 i 2 10 0"
9. 98229
45
16
49 52 10 8
44733
11
55267
46.507 : 12
53493
01774
98226
44
17
49 44 10 16
44776
12
55224
46554 i 13
53446
01778
98222
43
18
49 36 10 24
44819
13
55181
46601 : 14
53399
01782
98218
42
19
49 28 10 32
44862
14
55138
46648
15
15
53352
10. 53.306
01785
10.01789
1
98215
41
40
20
9 49 20 2 10 40
9.44905
14
10. 55095
9.46694
1
9.98211
21
49 12 10 48
44948
15
5.5a52
46741 ' 16
53259
01793
•t
. 98207
39
22
49 4 10 56
44992
16
55008
46788 17
53212
01796
98204
38
23
48 56 114
45035
16
.54965
46835 '■ 18
531&5
01800
98200
37
24
2o
48 48
9 48 40
11 12
45077 •
17
18
54923
10.54880
46881 19
9.46928 19
.53119
10.53072
01804
10.01808
2
98196
9.98192
36
35
2 11 20
9.45120
2t>
48 32 11 28
45163
18
54837
46975 20
53025
01811
2
98189
34
27
48 24 11 36
45206
19
54794
47021 21
52979
01815
2
98185
33
28
48 16 ; 11 44
45249
20
54751
47068 i 22
52932
01819
2
■98181
32
29
48 8 ! 11 52
45292
21
54708
47114
22
23
52886
01823
2
■98177
31
30
9 48 i 2 12
9. 45334
21
10. 54666
9.47160
10. 52840
10.01826
2
9.98174
30
31
47 52 ; 12 8
45377
22 1 54ti23
47207 24
52793
01830
2
98170
29
32
47 44 ' 12 16
45419
23
54.581
47253 25
52747
01834
2
98166
28
33
47 36 12 24
45462
23
54538
47299 26
52701
01838
2
98162
27
34
3o
47 28
9 47 20
12 32
45504
9. 45547
24
25
54496
10. 54453
47346 i 26
9. 47392 1 27
52654
10. 52608
01841
10.01845
2
2
98159
9. 981.55
26
"25^
2 12 40
36
47 12 ; 12 48
45589
'26
• 54411
47438 ! 28
52562
01849
2
98151
24
37
47 4 , 12 56
45632
26
54368
47484 29
52516
01853
2
98147
23
38
46 56 ' 13 4
45674
27
54.326
47530 i 29
52470
01856
2
98144
22
39
40
46 48 1 13 12
45716
28
"28
54284
47576 1 30
52424
01860
2
98140
9. 98136
21
20
9 46 40 2 13 20
9. 45758
10. 54242
9.47622 1 31
10. 52378
10. 01864
2
41
46 32
13 28
45801
29
54199
47668 32
52332
01868
3
98132
19
42
46 24
13 36
4.5843
30
54157
47714 32
52286
01871
3
98129
18
43
46 16
13 44
45885
31
54115
47760 1 33
52240
01875
3
98125
17
44
45
46 8
13 52
45927
31
32
54073
47806
34
35
52194
10.52148
01879
10. 01883
3
3
98121
9.98117
16
15
9 46
2 14
9. 45969
10. 54031
9. 47852
46
45 52
14 8
46011
.33
53989
47897 i 36
52103
01887
3
98113
14
47
45 44
14 16
46053
33
53947
47943 1 36
52057
01890
3
98110
13
48
45 36
14 24
. 46095
34
53905
47989 i 37
52011
01894
3
98106
12
49
50
45 28
14 32
2 14 40
46136
35
36
53864
10.53822
48035 1 38
51965
01898
3
98102
11
10
9 45 20
9. 46178
9. 48080
.39
10. 51920
10. 01902
3
9. 98098
51
45 12
14 48
46220
.36
53780
48126
.39
51874
01906
3
98094
9
52
45 4
14 56
46262
37
53738
48171
40
51829
01910
3
98090.
8
53
44 56
15 4
46303
38
53697
48217
41
51783
01913
3
98087
7
54
55
44 48
15 12
46345
38
39
53655
10. 53614
48262
42
51738
01917
3
98083
9. 98079
6
'5
9 44 40
2 15 20
9. 46386
9. 48307
43
10. 51693
10. 01921
3
56
44 32
15 28
46428
40
53572
48353
43
51647
01925
3
98075
4
57
44 24
15 36
46469
41
5;5531
48398
44
51602
01929
4
98071
3
58
44 16
15 44
46511
41
53489
48443
45
51557
01933
4
98067
2
59
44 8
15 52
46552
42
53448
48489
46
.51511
01937
4
98063
1
60
44
16
46594
43
53406
48534
46
51466
01940
4
98060
M.
Hour p. M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent
Did.
Tangent.
Cosecant.
Diff,
Sine.
M.
106°
A
A
B
B
C
C
73°
Seconds of time .
Prop, parts of cola < B
Log.
TABLE 44.
Sines, Tangents, and Secants.
[Page 789
i;°
A
A
. B B
C 16'2°
M.
Hour A.M.
Hour p. M.
Sine.
Diff
Cosecant.
Tangent.
Diff
Cotangent
Secant.
Difl.
Cosine.
M.
60
9 44
2 16
9. 46594
0-
10. 53406
9. 48534
10. 51466
10. 01940
9.98060
1
43 52
16 8
46635
1
53365
48579
1
51421
01944
98056
69
•2.
43 44
16 16
i6676
1
53324
48624
1
51376
01948
98052
58
•A
43 36
16 24
46717
2
53283
48669
2
51331
01952
98048
67
4
5
43 28
16 32
46758
3
53242
48714
9. 48759
3
51286
01956
98044
56
55
9 43 20
2 16 40
9. 46800
3
10. 53200
4
10. 51241
10. 01960
9. 98040
6
43 12
16 48
46841
4
53159
48804
4
51196
01964
98036
64
(
43 4
16 56
46882
5
53118
48849
5
51151
01968
98032
.53
8
42 56
17 4
46923
5
53077
48894
6
51106
01971
98029
52
9
10"
42 48
17 12
46964
6
53036
489.39
7
51061
01975
98025
61
9 42 40
2 17 20
9. 47005
7
10.52995
9. 48984
7 10.51016
10. 01979
9. 98021
■50
11
42 32
17 28
47045 1 7
52955
49029
8 1 50971
01983
98017
49
12
42 24
17 36
47086 8
52914
49073 \ 9 1 50927
01987
98013
48
IM
42 16
17 44
47127 9
.52873
49118
10
50882
01991
98009
47
14
15
42 8
17 52
47168 1 9
52832
10. .52791
49163
10
50837
01995
98005
9. 98001
46
45
9 42
2 18
9. 47209
10
9. 49207
11 110.50793
10. 01999
16
41 52
18 8
47249
11
52751
49252
12
50748
02003
97997
44
17
41 44
18 16
47290
11
.■52710
49296
12
50704
02007
97993
43
18
41 36
18 24
47330
12
52670
49341
13
50659
02011
97989
42
19
20
41 28
18 32
47371
13
52^29
49385
14
.50615
02014
97986
41
40
9 41 20
2 18 40
9.47411
13
10. .52589
9. 49430
15
10. ,50570
10.02018
1 19.97982
21
41 12
18 48
47452
14
52548
49474
15
50526
02022
97978
39
22
41 4
18 56
47492
15
52508
49519
16
50481
02026
97974
38
23
40 56
19 4
47533
15
52467
49563
17
50437
t)2030
2
97970
37
24
40 48
19 12
47573
16
52427
49607
18
18
50393
10. 50348
o2o;m
10. 020;}8
2
2
97966
9. 97962
36
:i5
25
9 40 40
2 19 20
9.47613
17
10. 52387
9. 49652
2()
40 32
19 28
47654
17
52346
49696
19
.50.304
02042
2
97958
.34
27
40 24
19 36
47694
18
52.306
49740
20
.502t>0
02046
2
97954
33
28
40 16
19 44
47734
19
52266
49784
21
50216
02050
2
97950
32
29
30
40 8
19 52
47774
19
20
52226
49828
9. 49872
21
22
50172
10. 50128
02054
10. 02058
2
2
97946
9. 97942
31
30
9 40
2 20
9. 47814
10. 52186
31
39 52
20 8
47854
21
.52146
49916
23
50084
02062
2
97938
29
32
39 44
20 16
47894
21
52106
49960
24
50040
020(56
2
97934
28
33
39 36
20 24
47934
22
52066
50(X)4 I 24
49996
02070
2
97930
27
35
39 28
20 32
47974
23
23
52026
10. 51986
.50048
25
26
49952
10. 49908
02074
10.02078
2
2
97926
9. 97922
26
25
9 39 20
2 20 40
9. 48014
9. .50092
36
39 12
20 48
48054
24
51946
.501.36 ' 26
49864
02082
2
97918
24
37
39 4
20 56
48094
25
51906
.50180 ! 27
49820
• 02086
2
97914
23
38
38 56
21 4
48133 25
51867
.50223
28
49777
02090
3
97910
•>'>
39
40
38 48
21 12
48173
26
27
51827
10. .51 787
.50267
29
49733
02094
3
3
97906
9. 97902
21
20
9 38 40
2 21 20
9. 48213
9. .50311
29 10.49689
10. 02098
41
38 32
21 28
48252
27
51748
.50355
.30
49645
02102
3
97898
19
42
38 24
21 36
48292
28
51708
50398
31
49602
02106
3
97894
18
43
38 16
21 44
48332
29
51668
50442
.32
49558
02110
3
97890
17
44
38 8
21 52
2 22
48371
9.48411
29
30
51629
10. 51589
50485
9. .50529
32
49,515
02114
3
3
97886
9. 97882
16
f5
45
9 38
.33 ilO. 49471
10.02118
46
37 52
22 8
48450
31
51550
50572
.34
49428
02122
3
97878
14
47
37 44
22 16
48490
31
.51510
.50616
.35
49384
02126
3
97874
13
48
37 36
22 24
48529
32
.51471
50659
35
49341
02130
3
97870
12
49
50
37 28
22 32
48568
33
33
51432
10.51.393'
50703
9. .50746"
36
49297
02134
10.02139
3
3
97866
9.97'86r
11
10
9 37 20
2 22 40
9. 48607
37
10. 49254
51
37 12
22 48
48647
:m
51353
.50789
37
49211
02143
3
97867
9
52
37 4
22 56
48686
35
.51314
.508,33
38
49167
02147
3
97853
8
53
36 66
23 4
48725
35
51275
.50876
39
49124
02151
4
97849
7
54
55
36 48
9 36 40
23 12
2 23 20
48764
36
512.36
.50919
40
"40
49081
10. 49038
02155
10.02159
4
4
97845
6
5
9. 48803
37
10. .51197
9. .50962
9. 97841
56
36 32
23 28
48842
37
.51158
51005
41
489i)5
02163
4
97837
4
57
36 24
23 36
48881
38
.51119
.51048
42
48952
02167
4
97833
3
58
36 16
23 44
48920
39
51080
51092
43
48908
02171
4
97829
2
59
36 8
23 52
48959
39
51041
51135
43
48865
02175
4
97825
1
60
36
24
48998
40
51002
51178
44
48822
02179
4
97821
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent. 1 Diff.
Tangent.
Cosecant.
Diff!
Sine.
107°
K
A
B B
C
C 72"
Seconds of time . . .
!•
2-
s-
4.
5<
6-
?■
Prop, purtsof cols.
1
!c
6
10
11
1
1.5
17
1
20
22
2
25
28
2
30
33
3
35
39
3
Page 790]
TABLE 44.
Log.
Sines, Tangents, and Secants.
18°
A
A
B
B
C
C
161°
M.
Hour A.M.
Hour p. M.
Sine.
Dili.
Cosecant.
Tangent.
Did.
Cotangent.
Secant.
Diff. Cosine.
M.
9 36
2 24
9. 48998
10. 61002
9.51178
10. 48822
10. 02179
9.97821
60
1
35 52
24 8
49037
1
50963
51221
1
48779
02183
97817
59
•>
35 44
24 16
49076
1
50924.
51264
1
48736
02188
: 97812
58
■A
35 36
24 24
49115
2
50885
51306
2
48694
02192
' 97808
57
4
o
35 28
9 35 20
24 32
2 24 40
49153
3
50847
51349
3
48651
02196
97804
9. 97800
5(i
.55"
9. 49192
3
10. 50808
9. 51.392
3
10. 48608
10. 02200
(.1
35 12
24 48
49231
4
50769
51435
4
48565
02204
97796
54
1
36 4
24 56
49269
4
50731
51478
5
48522
02208
97792
53
8
:m 56
25 4
49308
50<)92
51620
6
48480
02212
97788
52
9
10
34 48
9 34 40
25 12
49347
6
50653
51563
9.51606
6
48437
02216
10. 02221
97784
9. 97779
51
.50
2 25 20
9. 49385
6
10. 50615
7
10. 48394
11
34 32
25 28
49424
7
50576
61648
8
48.352
02226
97775
49
12
34 24
25 36
49462
8
60538
61691
8
48.309
02229
97771
48
13
34 16
25 44
49500
8
50500
517.34
9
4826(i
022.33
97767
47
14
U 8
25 52
2 26
49539
9
60461
51776
10
48224
10. 48181
022.37
10.02241
97763
46
'45
15
9 34
9. 49577
9
10. 50423
9. 51819
10
9. 97769
16
33 52
26 8
49615
10
50385
51861
11
48139
02246
1 97754
44
17
33 44
26 16
49654
11
60346
61903
12
48097
02250
1 97750
43
18
33 36
26 24
49692
11
50308
51946
13
48054
02254
1 1 97746
42
19
20
33 28
9 33 20
26 32
2 26 40
49730
9. 49768
12
13
50270
10. 502.32
51988-
9. 52031
13
48012
02258
10.02262
1 1 97742
1 ; 9. 97738
41
40
14
10. 47969
21
33 12
26 48
49806
13
50194
62073
15
47927
02266
97734
.39
22
33 4
26 56
49844
14
50156
62116
15
47885
02271
2
97729
.38
23
32 56
27 4
49882
14
50118
62157
16
47843
02276
2
97726
37
24
25
32 48
27 12
49920
15
50080
62200
17
47800
02279
2
97721
36
35
9 32 40
2 27 20
9. 49958
16
10. 50042
9. 52242
17
10. 47758
10.02283
2
9. 97717
26
32 32
27 28
49996
16
50004
52284
18
47716
02287
2
97713
.34
27
32 24
27 36
50034
17
49966
52326
19
47674
02292
2
97708
33
28
32 16
27 44
50072
18
49928
52368
20
47632
02296
2
97704
32
29
30
32 8
27 52
50110
18
49890
52410
9.52462
20
47590
02300
2
97700
31
30
9 32
2 28
9. .50148
19
10. 49852
21 10.47548
10. 02304
2
9. 97696
31
31 52
28 8
50185
20
49815
62494
22
47506
02309
2
97691
29
32
31 44
28 16
50223
20
49777
52536
22
47464
02313
2
97687
28
33
31 36
28 24
50261
21
49739
52578
23
47422
02317
2
97683
27
34
31 28
28 32
50298
21
49702
52620
24
47380
02321
2
2
97679
26
25
35
9 31 20
2 28 40
9. 60336
22
10. 49664
9. 62661
24
10. 47339
10. 02326
9. 97674
36
31 12
28 48
50374
23
49626
52703
26
47297
02330
3
97670
24
37
31 4
28 56
50411
23
49589
52745
26
47255
02334
3
97666
23
38
30 56
29 4
60449
24
49561
52787
27-
47213
023.38
3
97662
22
39
40
30 48
9 30 40
29 12
60486
25
49514
52829
27
47171
10. 47130
02343
3
97667
21
20
2 29 20
9. 50523
26
10. 49477
9. 52870
28
10. 02347
3
9. 97653
41
30 32
29 28
50561
26
49439
52912
29
47088
02351
3
97649
19
42
30 24
29 36
50598
26
49402
52953
29
47047
02356
3
97645
18
43
30 16
29 44
50635
27
49365
52995
30
47005
02360
3
97640
17
44
45
30 8
9 30
29 62
50673
9. 50710
28
49327
63037
31
46963
02364
3
97636
9. 97632
16
15
2 30
28
10. 49290
9. 53078
31
10. 46922
10. 02368
3
46
29 52
30 8
50747
29
49253
53120
32
46880
02372
3
97628
14
47
29 44
30 16
50784
30
49216
63161
33
46839
02377
3
97623
13
48
29 36
30 24
50821
30
49179
53202
34
46798
02381
3
97619
12
49
29 28
30 32
50858
31
31
49142
53244
34
36
46766
02385
3
4
97615
9. 97610
11
10
50
9 29 20
2 30 40
9. 60896
10. 49104
9.53285
10. 46715
10. 02390
51
29 12
30 48
60933
32
49067
53327
36
46673
02394
4
97606
9
52
29 4
30 66
60970
33
49030
53368
36
46632
02.398
4
97602
8
53
28 56
31 4
r^007
33
48993
53409
37
46591
02403
4
97597
7
54
28 48
31 12
61043
.34
48967
63450
9. 53492
38
38
4&560
02407
4
4
97593
9. 97589
6
5
55
9 28 40
2 31 20
9. 51080
36
10. 48920
10. 46508
10.02411
56
28 32
31 28
51117
35
48883
53533
39
46467
02416
4
97584
4
57
28 24
31 36
51164
36
48846
5a574
40
46426
02420
4
97580
3
58
28 16
31 44
51191
37
48809
63616
41
46385
02424
4
97576
2
59
28 8
31 52
51227
37
48773
63666
41
46344
02429
4
97671
1
60
28
32
51264
38
48736
63697
42
46303
02433
4
97567
M.
M.
Hour p. M.
Hour A.M.
Cosine.
DM.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
108<:
A
A
B
B
C
C
71°
Seconds of time
1-
2-
S- 1 4-
&•
6. 7.
(A
Prop. parts of cols. iB
Ic
5
5
1
9
10
1
14
16
2
19
21
2
24
26
3
28 33
31 37
3 4
TABLE U.
[Page 791
Log. Sines, Tangents, and Secants.
19°
A A
B
B
C
C 160°
M.
Hour A. M.
Hour p. M.
Sine.
Did.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
n
9 28
2 32
9. 51264
10. 48736
9. 53697
10. 46303
10.02433
9. 97567
60
1
27 52
32 8
51301
1
48699
53738
1
46262
02437
97563
59
•?.
27 44
32 16
51338
1
48662
.53779
1
46221
02442
97558
58
8
27 36
32 24
51374
2
48626
53820
2
46180
02446
975.54
57
4
5
27 28
32 32
51411
9. 51447
2 i 48589
3 10.48553
53861
3
46139
024.50
10. 02455
975.50
56
55
9 27 20
2 32 40
9. 53902
3 jlO. 46098
9.97545
6
27 12
32 48
51484
4 i 48516
53943
4 46a57
02459
97541
54
7
27 4
32 56 .
51520
4 1 48480
53984
5 46016
02464
97536
53
8
26 56
33 4
51557
5 i 48443
54025
5 ' 45975
02468
97532
52
9
10
26 48
33 12
51593
5 ' 48407
54065
6 4.5935
02472
97528
51
.50
9 26 40
2 33 20
9. 51629
6 ;i0. 48371
9. 54106
7 10.4.5894
10.02477
9.97523
11
26 32
33 28
51666
7 i 48334
54147
7 1 45853
02481
97519
49
12
26 24
33 36
51702
7 1 48298
54187
8 1 45813
02485
97515
48
13
26 16
33 44
51738
8
48262
54228
9 45772
02490
97510
47
14
15
26 8
9 26
33 52
51774
8
48226
54269
9 ! 45731
02494
10.02499
97506
46
45
2 34
9.51811
9
10.48189
9. 54309
10 10. 4.5691
9. 97501
Iti
25 52
34 8
51847
10
481.53
54350
11 45650
02.503
97497
44
17
25 44
34 16
51883
10
48117
54390
11 45610
02508
97492
43
18
25 36
34 24
51919
11
48081
54431
12 4.5569
02512
97488.
42
19
25 28
34 32
51955 i 11
48045
.54471
13 ' 45529
02516
97484
41
40
20
9 25 20
2 34 40
9. 51991
12
10. 48009
9. 54512
13 10.45488
10. 02521
9. 97479
21
25 12
34 48
52027
12
47973
54552
14 45448
02525
2
97475
39
22
25 4
34 56
52063
13
47937
54593
15 45407
02530
2
97470
.38
23
24 56
35 4
52099
14
47901
54633
15 45367
02534
2
97466
37
24
25
24 48
9 24 40
35 12
521 ;«
14
47865
.54673
16 45327
17 10.4.5286
02539
10.02543
2
97461
,36
3,5
2 35 20
9.52171 1 15
10. 47829
9.54714
2
9. 97457
26
24 32
35 28
52207 15
47793
54754
17 , 45246
02.547
2
97453
34
27
24 24
. 35 36
52242 1 16
47758
54794
18 45206
02552
2
97448
33
28
24 16
35 44
52278
17
47722
54835
19 1 45165
02.556
2
97444
32
29
30
24 8
9 24
35 52
52314
17
47686
54875
19 i 45125
02561
2
2
97439
9.974,35
31
30
2 36
9.523.50 1 18 10.47650
9. .54915
20 [10.45085
10. 02565
31
23 52
36 8
52385
18 1 47615
54955
21
45045
02570
2
97430
29
32
23 44
36 16
52421
19
47579
54995
21
45005
02574
2
97426
28
33
23 36
36 24
52456
20
47544
55035
22
44965
02579
2
• 97421
27
34
23 28
36 32
52492
20
47508
55075
23
44925
02583
3
97417
26
9 23 20
2 36 40
9. 52527
21
10. 47473
9.55115
23
10. 44885
10. 02588
3
9. 97412
25
36
23 12
36 48
.52563
21
47437
.551.55
24
44845
02592
3
97408
24
37
23 4
36 56
52598
22
47402
.55195
25
44805
02597
3
97403
23
38
22 56
37 4
52634
23
47366
55235
25
44765
02601
3
97399
22
39
40
22 48
37 12
52669
9. 52705
23
24
47331
.55275
26
•Si
44725
10. 44685
02606
3
3
97394
21
9 22 40
2 37 20
10. 47295
9. 55315
10.02610
9. 97390
20
41
22 32
37 28
52740
24
47260
553.55
27
44645
02615
3
97385
19
42
22 24
37 36
• 52775
25
47225
55395
28
44605
02619
3
97381
18
43
22 16
37 44
.52811
26
47189
55434
29
44566
02624
3
97376
17
44
45
22 8
37 52
52846
9. 52881
26
27
47154
.55474
9. 55514
29
"30
44526
02628
3
97372
16
"15
9 22
2 38
lO'7119
10. 44486
10. 02&)3
3
9. 97367
46
21 52
38 8
52916
27
47084
■55554
31
44446
02637
3
97363
14
47
21 44
38 16
52951
28
47049
55593
31
44407
02642
3
97358
13
48
21 36
38 24
52986
29
47014
55633
.32
44367
02647
4
97353
12
49
50"
21 28
9 21 20
38 32
2 38 40"
.53021
9. .5.3056
29
46979
.55673
33
.33
44327
10. 44288
02&51
10."0"2().56"
4
4
97349
11
10
30
10. 46944
9. .557 12
9. 97344
51
21 12
38 48
53092
.30
46908
55752
34
44248
02660
4
97340
9
52
21 4
38 56
53126
31
46874
.55791
.35
44209
02665
4
973,35
8
53
20 56
39 4
5.3161
32
46839
55831
35
44169
02669
4
97331
7
54
55
20 48
39 12
i2 39 20"
53196
9. 53231
32
33
46804
55870
36
37
44130
10. 44090
02674
10. 02678
4
4
97326
6
5'
9 20 40
10. 4()769
9. 55910
9.97322
56
20 32
39 28
53266
33
467;«
55949
37
44051
02683
4
97317
4
01
20 24
39 36
53301
34
46699
.55989
38
44011
*02688
4
97312
3
58
20 16
39 44
53336
.34
46664
56028
39
43972
02692
4
97308
2
59
20 8
39 52
53370
.35
46630
56067
39
4.3933
02697
4
97.303
1
60
M.
20
40
53405
36
46595
56107
40
43893
02701
4
97299
M.
Hour p. M.
Hour A.M.
Cosine.
Did.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
1011°
A A
B
B
(■
(■ 70° j
Seconds of time
!•
2-
8"
4'
5-
6<
7'
fA
Prop, parts of cols. B
Ic
4
6
1
9
10
1
13
15
2
18
20
2
22
25
3
27
30
3
31
35
4
Page 792J
TABLE 44.
Log. Sines, Tangents, anil Secants.
•
20°
A A
B
B
C
C 159°
M.
Hour A.M.
Henr p. M.
sine.
Difl.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Difl.
Cosine.
M.
60
n
9 20
2 40
9. 53405
10. 46595
9. 56107
10. 43893
10. 02701
9. 97299
1
19 52
40 8
5.3440
1
46560
56146
1
43854
02706
97294
,59
9.
19 44
40 16
53475
1
46525
56185
1
43815
02711
97289
58
■A
19 36
40 24
53509
2
46491
56224
2
43776
02715
97285
57
4
5
19 28
40 32
53544
2
46456
56264
3
43736
02720
97280
56
9 19 20
2 40 40
9. 53578
3
10. 46422
9. 56303
3
10.43697
10. 02724
9. 97276
,55
6
19 12
40 48
53613
3
46387
56342
4
43658
02729
97271
54
7
19 4
40 56
.53647
4
46,353
56381
4
43619
02734
97266
53
8
18 56
41 4
53682
5
46318
56420
5
43580
02738
97262
52
9
10
18 48
41 12
,53716
5
46284
56459
6
43541
02743
97257
51
50
9 18 40
2 41 20
9. 53751
6
10. 46249
9. ,56498
6
10. 43502
10. 02748
9. 97252
11
18 32
41 28
53785
6
46215
56537
1
4.3463
02752
97248
49
12
18 24
41 36
53819
7
46181
56576
8
43424
02757
97243
48
13
18 16
41 44
53854
t
46146
56615
8
43385
02762
97238
47
14
"15
18 8
41 52
5,3888
8
'8
46112
10746078
56654
9. 56693
9
43346
02766
97234
4()
4.5"
9 18
2 42
9. ,53922
10
10. 43307
10.02771
9. 97229
16
17 52
42 8
53957
9
46043
.56732
10
43268
02776
97224
44
17
17 44
42 16
53991 10
46009
56771
11
43229
02780
97220
43
18
17 36
42 24
54025
10
4.5975
56810
12
43190
02785
97215
42
19
17 28
42 32
54059
11
11
4,5941
10. 45907
56849
12
43151
02790
1
97210
41
40
20
9 17 20
2 42 40
9. 54093
9. 56887
13
10.43113
10. 02794
9. 97206
21
17 12
42 48
.54127
12
4.')873
56926
13
43074
02799
97201
39
22
17 4
42 56
54161
12
458,39
56965
14 ; 43035
02804
97196
38
2.3
16 56
43 4
.54195
13
45805
57004
15 j 42996
02808
97192
37
24
16 48
43 12
54229
14
45771
57042
15 1 42958
02813
2 1 97187
36
.">5
25
9 16 40
2 43 20
9. .54263 ' 14
10. 45737
9. 57081
16
10. 42919
10. 028 1«
2 9.97182
26
16 32
43 28
.54297 i 15
45703
57120
17
42880
02822
2 : 97178
34
27
16 24
43 36
.54331 15
45669
571,58
17
42842
02827
2 97173
33
28
16 16
43 44
a4365 1 16
45635
57197
18 i 42803
02832
2 ] 97168
32
29
16 8
43 52
54399
16
17
4,5601
10. 45567
57235
9. .57274"
19 i 42765
19 10.42726
02837
2 i 97163
31
30
30
9 16
2 44
9. .54433
10. 02841
2 9.97159
31
15 52
44 8
.54466 : 17
45534
57312
20 1 42688
02846
2 971,54
29
32
15 44
44 16
54500 i 18
45500
57351
21
42649
02851
3 97149
28
33
15 36
44 24
54534 1 19
45466
57389
21
42611
02855
3
97145
27
34
15 28
44 32
2 44 40
54567 i 19
45433
57428
22
42572
02860
3
97140
26
25
35
9 15 20
9.54601 ; 20
10. 45399 .
9. .57466
22 10.42534
10. 02865
3 19.97135
36
15 12
44 48
.54635 ! 20 j 45365
57504
23 \ 42496
02870
3 97130
24
37
16 4
44 56
54668 ' 21 45332
57543
24 1 42457
02874
,3 97126
23
38
14 56
45 4
54702 i 21 j 45298
1 57581
24 i 42419
02879v
/3
97121
22
39
40
14 48
45 12
.54735 I 22
45265
57619
25
26
42381
02884
3
97116
21
20
9 14 40
2 45 20
9. 54769 23
10. 45281
9. 57658
10. 42342
10. 02889
3
9.97111
41
14 32
45 28
54802 23
45198
57696
26 42304
02893
3
97107
19
42
14 24
45 36
54836 ' 24
45164
57734
27 ; 42266
02898
3
97102
IS
43
14 16
45 44
54869 j 24
45131
57772
28 42228
02903
3
97097
17
44
45
14 8
45 52
54903 ' 25
4,5097
.57810
28 j 42190
02908
3
97092
16
"15
9 14
2 46
9. ,54936
25
10. 45064
9. 57849
29 10.421.51
10.02913
4
9. 97087
46
13 52
46 8
54969
26
4,5031
57887
30 1 42113
02917
4
97083
14
47
13 44
46 16
55003
26
44997
57925
.30 42075
02922
4
97078
13
48
13 36
46 24
.55036 j 27
44964*
57963
31 42037
02927
4
97073
12
49
13 28
46 32
5.5069 1 28
44931
58001
31 , 41999
02932
4
97068
11
10
50
9 13 20
2 46 40
9. 55102
28
10. 44898
9. 58039
32
110.41961
10. 02937
4
9. 97063
51
13 12
46 48
55136
29
44864
58077
33
41923
02941
4
97059
9
52
13 4
46 56
55169
29
44831
58115
33
41885
02946
4
97054
s
53
12 56
47 4
55202
30
44798
58153
34
41847
02951
4
97049
1
54
12 48
47 12
55235
30
44765
58191
1 35
41809
02956
4
97044
9. 97039
6
5
55
9 12 40
2 47 20
9. 55268
31
10. 44732
9. 58229
j 35
!10. 41771
10. 02961
4
56
12 32
47 28
. 55301
32
44699
58267
' .36 i 41733
02965
4
970.35
4
57
12 24
47 36
55334
.32
44666
58304
37 1 41696
02970
4
97030
3
58
12 16
47 44
55367
33
44633
,58342
37 i 41658
02975
5
97025
O
59
12 8
47 52
55400
33
44600
58380
38 1 41620
02980
5
97020
f
60
12
48
55433
34
44567
58418
39 i 41582
1
02985
5
97015
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent
Diff.' Tangent.
Cosecant.
Diff.
Sine.
M
110<
)
A A
B
B
C
C 69° 1
Seconds of time ] 1'
2<
3"
4-
6>
6<
■■■\
(A 1 4
Prop, parts of cols.-jB S
1 C 1
8
10
1
13
14
17
19
2
21
24
3
25 30
29 34
4 i 4
TABLE 44.
[Page 793
Log. Sines, Tangents, and Secants.
21°
A A
B
B
C
C 158°
M.
Hour A.M.
Hour P.M.
Sine.
Dlff.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Diff.
Cosine.
M.
9 12
2 48
9. 55433
10. 44567
9. .58418
10.41582
10. 02985
9. 97015
60
1
11 52
48 8
55466
1
44534
58466
1
41.545
02990
97010
59
2
11 44
48 16
55499
1
44601
68493
1
41507
02995
97005
58
8
11 36
48 24
65532
2
44468
58531
2
41469
02999
97001
57
4
11 28
48 32
2 48 40
555(>4
9; 55.597
2
3
44436
10. 44403
58.569
9758606
2
3
41431
03004
96996
56
55
5
9 11 20
10. 41394
10. 03009
9. 96991
6
11 12
48 48
66630
3
44370
58644
4
413.56
03014
96986
54
7
11 4
48 56
55663
4
44337
.58681
4
41319
03019
96981
53
8
10 56
49 4
55695
4
44305
58719
6
41281
03024
96976
52
9
10 48
49 12
2 49 20"
55728
9. 55761
6
5
44272
58757
6
6
41243
10. 41206
03029
1
96971
51
60
10
9 10 40
10. 44239
9. 58794
10. 03034
9. 96966
n
10 32
49 28
.16793
6
44207
58832
t
41168
03038
96962
49
12
10 24
49 36
55826
6
44174
68869
7
41131
03043
96957
48
13
10 16
49 44
.55858
7
44142
58907
8
41093
03048
96952
47
14
15
10 8
9 10
49 52
55891
9. 55923
7
8
44109
10. 44077
58944
9
41056
03053
96947
46
2 60
9. 58981
9
10. 41019
10. 03058
9. 96942
45
16
9 52
50 8
55956
9
44044
59019
10
40981
03063
96937
44
17
9 44
50 16
65988
9
44012
59056
10
40944
03068
96932
43
18
9 36
50 24
66021
10
43979
.59094
11
40906
03073
96927
42
19
9 28
50 32
56053
9.56685
10
"11
43947
10. 43915
69131
12
40869
10. 40832
03078
2
96922
9.96917
41
40
20
9 9 20
2 50 40
9.69168
12
10. 03083
2
21
9 12
50 48
56118
11
43882
69205
13
40796
03088
2
96912
39
22
9 4
50 56
56150
12
43860
59243
14
40767
03093
2
96907
38
23
8 56
51 4
66182
12
43818
59280
14
40720
03097
2
96903
37
24
25
8 48
9 8 40
51 12
2 51 20
56215
13
43785
59317
16
15
40683
03102
2
96898
36
9. 56247
13
10. 43753
9.59354
10. 40646
10. 03107
2
9. 96893
26
8 32
b{ 28
.56279
14
43721
69391
16
40609
03112
2
96888
34
27
8 24
51 36
.56311
14
43689
59429
17
40571
03117
2
96883
33
28
8 16
51 44
56.343
15
43667
59466
17
40534
03122
2
96878
32
29
8 8
51 62
.56375
16
43625
59503
18
19
40497
10: 40460
03127
2
96873
31
30
30
9 8
2 52
9. 56408
16
10. 43592
9. 59540
10. 03132
2
9. 96868
31
7 52
62 8
56440
17 43560
69677
19
40423
03137
3
968()3
29
32
7 44
52 16
56472
17 43528
69614
20
40386
03142
3
96858
28
33
7 36
52 24
66504
18 43496
59651
20
40349
03147
3
96853
27
34
36
7 28
52 32
56536
18 i 43464
19 110.43432"
59688
21
40312
10.46275'
03152
3
96848
26
25
9 7 20
2 52 40
9. 56568
9. 59725
22
10.03157
3
9. 96843
36
7 12
52 48
56599
19 1 43401
59762
22
40238
03162
3
96838
24
37
7 4
52 56
56631
20 1 43369
59799
23
40201
03167
3
96833
23
38
6 56
53 4
66663 ! 20 43337
59835
23
40165
03172
3
96828
22
39
40
6 48
9 6 40
53 12
66696 i 21 43.305
59872
24
40128
10.40091
03177
3
96823
21
"20
2 53 20
9.66727 : 21 |10. 43273
9. 69909
25
10. 03182
3
9.96818
4J
6 32
53 28
66769
22
43241
59946
25
40054
03187
3
96813
19
42
6 24
53 36
.56790
22
43210
59983
26
40017
03192
3
96808
18
43
6 16
53 44
.56822
23
43178
60019
27
39981
03197
4
96803
17
44
6 8
53 52
2 54
568-54 1 24
43146
60056
27
28
39944
03202
4
96798
16
45
9.6
9. .56886 24 110.43114
9.60093
10. 39907
10. 03207
4
9. 96793
15
46
5 52
54 8
56917 25 1 43083
60130
28
39870
03212
4
96788
14
47
5 44
54 16
56949 25 - 4.3051
60166
29
39834
03217
4
96783
13
48
5 36
54 24
66980 ! 26
43020
60203
30
39797
03222
4
96778
12
49
50
5 28
9 5 20
54 32
2 54 40
.57012
9. 57044
26
42988
60240
9.60276
30
39760
03228
10. 03233
4
4
96772
11
10
27
10. 42056
31
10. 39724
9. 96767
51
5 12
54 48
57075 , 27
42925
60313
31
39687
03238
4
96762
9
52
5 4
54 56
.57107 ! 28
42893
60349
32
39651
tl3243
4
96757
8
53
4 56
55 4
.57138 1 28
42862
60386
33
39614
03248
4
96752
7
54
55"
4 48
55 12
2 56 20
57169
9. 57201
29
42831
60422
33
39578
10. 39541
03253
4
96747
6
9 4 40
29
10. 42799
9. 60459
34
10. 03258
5
9. 96742
5
56
4 32
55 28
57232 30
42768
60495
36
39505
03263
6
96737
4
57
4 24
55 36
57264 30
42736
60532
.35
.39468
03268
5
96732
3
58
4 16
55 44
57295 31
42705
60568
36
39432
03273
5
96727
2
59
4 8
55 52
57326 1 32
42674
60605
36
39.395
03278
5
96722
1
60
4
56
57368 32
42642
60641
37
39359
03283
5
96717
M.
Hour P.M.
Hour A. M.
Cosine. 1 Diff.
Secant.
Cotangent.
ma.
Tangent.
Cosecant.
Diff.
Sine.
M.
111°
A A
B
B
C
C 68°j
Second of time
!•
2"
3.
4>
S*
6-
J-
fA
Prop, parts of cols.-fB
4
5
1
8 12
9 14
1 2
16
19
2
20
23
3
24
28
4
28
32
4
Page 794]
TABLE U.
Log. Sines, Tangents, and Secants.
42°
A A
B B
C 157°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent. ,Difl.
Cotangent.
Secant.
Diff.
Cosine.
M.
n
9 4
2 56
9. 57358
10. 42642
9.60641
10. 39359
10. 03283
9.96717
60
1
3 52
56 8
57389
1
42611
60677 i 1
39323
03289
96711
59
2
3 44
56 16
57420
1
42580
60714 j 1
39286
03294
96706
58-
:h
3 36
56 24
57451
2
42549
60750 2
39250
03299
96701
57
4
ft
3 28
56 32
57482
2
42518
60786 1 2
9.60823 3
39214
10. 39177
03304
96696
9. 96691
56
55
9 3 20
2 56 40
9.57514
3
10. 42486
10. 03309
»i
3 12
56 48
57.545
3
424.55
60859 4
39141
03314
96686
54
3 4
56 56
57576
4
42424
60895
4
39105
03319
96681
53
S
2 56
57 4
57607
4
42393
60931
5
39069
03324
96676
52
9
1(V
2 48
57 12
57638
5
42362
60967
5
39033
03330
10. 03335
~r
96670
51
50
9 2 40
2 57 20
9. 57669
5
10. 42331
9.61004
6
10. 38996
9. 96665
11
2 32
57 28
57700
6
42300
61040 ; 7
38960
03340
96660
49
12
• 2 24
57 36
57731
6
42269
61076
7
38924
03345
96655
48
18
2 16
57 44
57762
7
42238
61112
8
38888
03350
96650
47
14
15
2 8
57 52
57793
7
42207
61148
8
38852
03355
10.03360
96645
9.96640
46
45
9 2
2 58
9. 57824
8
10.42176
9. 61184 9
10. 38816
1«
1 52
58 8
57855
8
42145
61220
10
38780
03366
96634
44
17
1 44
58 16
57885
9
42115
612.56
10
38744
03371
96629
43
IS
1 36
58 24
57916
9
42084
61292
11
38708
03376
2
96624
42
19
20"
1 28
58 32
57947
10
42053
61328
11
38672
03381
2
^2
96619
9. 96614
41
40
9 1 20
2 58 40
9. 57978
10
10. 42022
9. 61364
12
10. 38636
10. 03386
21
1 12
58 48
58008
11
41992
61400
13
38600
03392
2
96608
39
22
1 4
58 56
58039
11
41961
61436
13
38564
03397
2
96603
38
2:-!
56
59 4
58070
12 ; 41930
61472
14
38528
03402
2
96598
37
24
2o"
48
9 40
59 12
2 59 20"
58101
•12
13
41899
61508
14
38492
03407
2
9^593
9. 96588
36
35"
9. 58131
10. 41869
9. 61544
15
10. 38456
10. 03412
2
211
32
59 28
58162
13 i 41838
61579
15
38421
03418
2
96582
34
27
24
59 36
58192
14
41808
61615
16
38385
03423
2
96577
33
28
16
59 44
58223
14
41777
61651
17
38349
03428
2
96572
32
29
30
8
59 52
58253
15
41747
61687
17
18
38313
10. 38278
03433
3
96567
31
30
9
3
9. 58284
15
10.41716
9. 61722
10. 03438
3
9. 96562
■M
8 59 52
8
58314
16 41686
61758
18
38242
03444
3
96556
29
32
59 44
16
58345
16 41655
61794
19
38206
03449
3
96551
28
33
59 36
24
58375
17 1 41625
61830
20
38170
03454
3
96546
27
34
35
59 28
32
58406
17
18
41594
10.41564
61865
20
38135
034.59
3
3"
96541
9.96.535
26
25
8 59 20
3 40
9. 58436
9.61901 j 21
10. 38099
10. 03465
38
59 12
48
58467
18
41533
61936
21
38064
03470
3
96530
24
37
59 4
56
58497
19
41,503
61972
22
38028
03475
3
9&525
23
3H
58 56
1 4
58527
19
41473
62008
23
37992
03480
3
96520
22
39
40
58 48
1 12
58.557
20
41443
62043
23
24
37957
10. 37921
03486
3
3
96514
9. 96509
21
20'
8 58 40
3 1 20
9. 58588
20
10.41412
9. 62079
10. 03491
41
58 32
1 28
58618
21
41382
62114
24
37886
03496
4
96504
19
42
58 24
1 36
58648
21
41352
621.50
25
37850
03502
4
96498
IS
43
58 16
1 44
58678
22 1 41322
62185
26
37815
03507
4
96493
17
44
58 8
1 52
58709
22
23
41291
62221
26
37779
03512
10. 03517
4
96488
16
15
45
8 58
3 2
9. 58739
10.41261
9.62256 ! 27
10. 37744
4 : 9. 96483
4(1
57 52
2 8
58769
23
41231
62292
27
37708
03523
4 : 96477
14
47
57 44
2 16
58799
24
41201
62327
28
37673
03528
4
96472
13
48
57 86
2 24
58829
24
41171
62362
29
376;i8
03533
4
96467
12
49
57 28
2 32
58859
25
25
41141
10.41111
62398
29
37602
035.39
10. 03544
4
4
96461
9796456
11
10'
50
8 57 20
3 2 40
9. 58889
9. 62433
30
10. 37567
51
57 12
2 48
58919
26
41081
62468
30
37532
03549
4
96451
9
52
57 4
2 56
58949
26
41051
62504
31
37496
03555
5
96445
8
53
56 56
3 4
58979
27
41021
62539
32
37461
03560
5
96440
1
54
55
56 48
3 12
59009
27
28
40991
10.4(J961
62574
9. 62609
32
37426
03565
1(3. 03571
' 5
96435
9. 96429
6
5
8 56 40
3 3 20
9. 59039
33
10. 37391
5(1
56 32
3 28
59069
28
40931
62645
33
37355
03576
5
96424
4
f>7
56 24
3 36
59098
29
40902
62680
34
37320
03581
5
96419
3
5r
56 16
3 44
59128
29
40872
62715
35 37285
Oa587
5
96413
2
09
56 8
3 52
59158
30
40842
62750
35 37250
03592
5
96408
1
60
56
4
59188
31
40812
62785
36
37215
03597
5
96403
M.
Hour p. M.
Hour A.M.
Cosine.
Diff.
Seennt.
Cotangent, j Diff.
Taneent.
Cosecant.
Diff.
Sine.
M.
112'
A A
B I!
(■
C 67° j
Seconds of time
'l-
2"
S-
4'
o-
8' r 7'
A
Prop, parts of cols. B
C
•1
4
1
8
9
1
11
IS
2
15
18
3
19
22
3
23 27
27 31
4 5
TABLE 44.
[Page 795
Log. Sines, Tangyits, and Secants.
48°
A A
B B
C
C 156°
M.
Hour A. M. i Hour p. M.
Sine.
Did.
Cosecant.
Tangent.
Diff. Cotangent.
Secant.
Diff.
Cosine.
M.
8 56 1 3 4
9. 59188
10.40812
9. 62785
10. 37215
10. 0:i597
9. 96403
60
1
55 52 ; 4 8
59218
40782
62820
1
37180
03603
96397
59
O
55 44
4 16
.59247
1
40753
62855
1
.37145
03608
96392
58
:^
55 36
4 24
59277
1
40723
62890 : 2
37110
03613
96387
57
4
5
55 28
8 55 20
4 32
59307
2
2
40693
10.40664
62926 1 2
37074
03619
96381
56
3 4 40
9. 59336
9. 62961 3
10. 37039
10. 03624
9. 96376
55
6
55 12
4 48
59366
3
406.34
62996 3
37004
03630
96370
54
/
55 4
4 56
59396
3
40604
63031 1 4 : 36969
03635
96365
53
s
54 56 ' 5 4
59425
4
40575
63066 ! 5 ' 369;?4
03640
96360
52
9
10
54 48
8 5440
5 12
59455
4
5
40545
63101 i 5 ! 36899
03646
10. 03651
96354
51
3 5 20
9. .59484
10.40516
9. 63135 1 6 ilO. 36865
9. 96349
50
11
.54 32 5 28
59514
5
40486
63170 ' 6 36830
03657
96.343
49
12
54 24 5 36
59,543
6
40457
63205 ' 7 36795
03662
96338
48
13
54 16 5 44
" 59573
6
40427
63240 7 36760
03667
96333
47
14
15'
54 8
8 54
5 52
59602
7
40398
6.3275 8 36725
03673
96327
46
45
3 6
9.59632 1 7
10. 40368
9.63310 1 9 10.36690
10. 03678
9.96322
1()
53 52 6 8
59661
8
40339
63345 9 36655
03684
96316
44
17
53 44 6 16
.59690
8
40310
63379 10 36621
03689
2
96311
4:!
18
53 36 6 24
.59720
9
402,80
63414 10 36.586
03695
2 1 96305
42
19
20
53 28
6 32
3 6 40
59749
9. 59778
9
10
40251
63449 ; 11 36551
03700
10. 03706
2
2
96300
41
40~
8 53 20
10. 40222
9. 63484 12 10. 36516
9. 96294
21
53 12 6 48
,59808
10
40192
63519 12 36481
03711
2 : 96289
39
')■>
53 4 6 56
59837
11
40163
63553 13 36447
03716
2 j 96284
38
2^
52 56 : 7 4
59866
11'
40134
63588 13 36412
03722
2 1 96278
37
24
2.V
52 48
8 52 40
7 12
59895
9. 59924
12
40105
63623 14 36377
03727
2 1 96273
36
3 7 20
12
10. 40076
9.63657 14 10.36343
10. 03733
2 1 9. 96267
35
2G
52 32 7 28
59954
13
40046
63692 15 36308
03738
2 1 96262
.34
27
52 24 7 36
59983
13
40017
63726 16 36274
03744
2 ! 96256
33
28
52 16 ; 7 44
60012
14
39988
63761 16 36239
03749
3 ! 96251
32
2V»
"80"
52 8
7 52
60041
14
15
39959
63796 17 36204
037.55
3 96245
31
'30
8 52
3 8
9. (30070
10. 39930
9.6.3830 17 10.36170
10. 03760
3 9.96240
■.n
51 52 : 8 8
60099
15
39901
63865 , 18 36i;«
03766
3 ! 96234
29
32
51 44 8 16
60128
15
39872
63899 18 36101
03771
3 : 96229
28
83
51 36 1 8 24
60157
16
39843
6.3934 19 36066
03777
3
96223
27
34
35
51 28
8 51 20
8 32
60186
9.60215
16
17
39814
10. 39785
63968
9. 64003
20 36032
03782
10. 03788
3
3
96218
26
25
3 8 40
20 10.35997
9. 96212
36
51 12 1 8 48
60244
17
39756
64037 i 21 35963
03793
3
%207
24
37
51 4 1 8 56
60273
18
39727
64072 ' 21 .35928
03799
3
96201
23
3S
50 56 ! 9 4
60.302
18
39698
64106 , 22 35894
03804
3
96196
22
39
40
50 48 i 9 12
60331
19
39669
64140 1 22 35860
03810
4
96190
21
20
8 50 40
3 9 20
9. 603,59
19
10. 39641
9.64175 i 23 i 10. 35825
10. 03815
4
9. 96185
41
50 32
9 28
60388
20
39612
64209 i 24 35791
03821
• 4
96179
19
42
50 24
9 36
60417
20
39583
64243 1 24 35757
03826
4
96174
18
43
50 16
9 44
60446
21
.39554
64278
25 1 35722
03832
4
96168
17
44
45
50 8
9 52
60474
21
39528
10. 39497
64312
25 i 35688
03838
4
96162
16
8 50
3 10
9. 60.503
22
9.64346
26 10.35a54
10. 03843
4
9. 96157
15
4(i
49 52
10 8
60532
22
39468
64381
26 1 a5619
03849
4
96151
14
47
49 44
10 16
60561
23
39439
64415
27 1 35585
0.3854
4
96146
13
4.H
49 36
10 24
60589
23
39411
64449
28 ; 35551
03860
4
96140
12
49
50
49 28
10 32
3 10 40
60618
24
39382
64483
9. 64517
28 1 35517
03865
4
96135
9.96129
11
10
8 49 20
9. 60646
24
10. 393.54
29
10. ;?5483
10. 03871
5
51
49 12
10 48
60675
25
39325
64552
29
3,5448
03877
5
96123
9
52
49 4
10 56
60704
25
39296
64586
30
35414
03882
5
96118
8
53
48 56
11 4
60732
26
39268
64620
31
35380
03888
5
96112
7
54
48 48
11 12
60761
26
39239
10. 39211
64654
9. 64688
31
32
36346
10. 35312
03893
5
96107
6
55
8 48 40
3 11 20
9. 60789
27
10. 03899
5
9. 96101
5
56
48 32
11 28
60818
27
39182
64722
32
35278
03905
5
96095
4
57
48 24
11 36
60846
28
391.54
647.56
33
35244
.03910
5
96090
3
58
48 16
11 44
60875
28
39125
64790
33
35210
03916
5
96084
2
59
48 8
11 52
60903
29
39097
64824
34
35176
03921
5
96079
1
60
M.
48
12
60931
29
39069
64858
35
35142
03927
6
96073
Hour p. M.
Hour A. M.
Cosine.
Dift.
Secant.
Cotangent.
Diff,
Tangent.
fCosecant.
Difif.
Sine.
M.
11S°
A A
B B
C
C 66° 1
Seconds of time
1'
2'
8>
4-
5"
6'
J-
(A
Prop, parts of cols. ■{ B
{c
4
4
1
7
9
1
11
13
2
16
17
3
18
22
3
22
26
4
25
31
5
Page 796]
tablp: u.
Log. Sinef, Tai
gontp, and Secants.
24°
A
A
B
B
C
C 1
t>5°
M.
Hour A.M.
Hour p. M.
Sine.
Did.
Cosecant.
Tangent.
Diff.
(Jotangent.
Secant.
Diff.
Cosine.
M.
(>0
8 48
3 12
9.60931
10. 39069
9.64858
10. 35142
10. 03927
9. 96073
1
47 52
12 8
60960
39040
t>4892
1
35108
03933
96067
59
2
47 44
12 16
60988
1
39012
64926
1
35074
03938
96062
5K
■A
47 36
12 24
61016
1
38984
(54960
2
35040
03944
96056
57
4
5
47 28
12 32
61045
2 • 38955
64994
2
3
35006
03950
96050
9. 96(j45
56
55
8 47 20
3 12 40
9. 61073
2 110.38927
9. 65028
10. 34972
10. 03955
6
47 12
12 48
61101
3
38899
650B2
3
34938
03961
96039
54
7
47 4
12 56
61129
3
38871
(J5090
4
34904
03966
96034
53
8
46 56
13 4
61158
4
38842
65130
4
34870
03972
96028
52
9
10
46 48
13 12
61186
4
38814
65164
5
34836
03978
96022
51
.50
8 46 40
3 13 20
9.61214
5 110.38786
9. 65197
6
10. 34803
10.03983
9.96017
11
46 32
13 28
61242
5
38758
65231
6
34769
0.3989
• 96011
49
12
46 24
13 36
61270
6
38730
(i5265
{
34735
03995
1 96005
48
13
46 16
13 44
61298
6
38702
65299
7
34701
04000
1 1 96000
47
14
46 8
13 52
61326
9. 61354
6
7
38674
10. 386«
65333
9. 65366
8
8
346<j7
04006
10. 04012
1 : 95994
1 19.95988
46
45
15
8 46
3 14
10. 34634
16
45 52
14 8
61382
7
38618
65400
9
34600
04018
2 1 95982
44
17
45 44
14 16
61411
8
38589
65434
9
34566
04023
2 ! 95977
43
18
45 36
14 24
61438
8
38562
65467
10
34533
04029
2 1 95971
42
19
20
45 28
14 32
61466
9
9
38584
10. 38506
65501
9.65535
11
34499
04035
2
2
95965
9. 95960
41
40
8 45 20
3 14 40
9. 61494
11
10. 34465
10. 04040
21
45 12
14 48
61522
10
38478
65568
12
34432
04046
2
95954
.39
22
45 4
14 56
61550
10
38450
65602
12
, 34398
04052
2
95948
38
23
44 56
15 4
61578
11
38422
65636
13
. 34364
04058
2
95942
37
24
25
44 48
15 12
61606
11
12
38394
10. 38366
65669
9. 65703
■13
14
34331
10. 34297
04063
2
95937
3()
3.5"
8 44 40
3 15 20
9. 61634
10. 04069
2 i 9. 95931
26
44 32
15 28
61662
12
38338
65736
15
34264
04075
2
95925
34
27
44 24
15 36
61689
12
38311
65770
15
34230
04080
3
95920
.33
28
44 16
15 44
61717
13
38283
65803
16
34197
04086
3 i 95914
32
29
30
44 8
15 52
61745
13
14
38255
65837
16
34163
04092
3
3
95908
9. 95902
31
30
8 44
3 16
9.61773
10. 38227
9.65870 1 17
10. 34130
10.04098
31
43 52
16 8
61800
14
38200
65904 1 17
34096
04103
3
95897
29
32
43 44
16 16
61828
15
38172
65937 I 18
34063
04109
3
95891
28
33
43 36
16 24
()1856
15
38144
65971
18
34029
04115
3
95885
27
34
35
43 28
16 32
61883
16
38117
66004
19
33996
04121
3
3
95879
9.95873
26
25
8 43 20
3 16 40
9. 61911
16
10. 38089
9.66038 20
10. 33962
10.04127
36
43 12
16 48
61939
17
38061
66071
20
33929
04132
3
95868
24
37
43 4
16 56
61966
17
38034
66104
21
33896
04138
4
95862
23
38
42 56
17 4
61994
18
38006
(56138 1 21
33862
04144
4
95856
'>•>
39
42 48
17 12
62021
18
37979
66171 ! 22
33829
04150
4
95850
9. 95844
21
20
40
8 42 40
3 17 20
9. 62049
18
10. 37951
9. 66204
22
10. 33796
10. 04156
4
41
42 32
17 28
62076
19
37924
66238
23
33762
04161
4
95839
19
42
42 24
17 36
62104
19
37896
66271
23
33729
04167
4
95833
IS
43
42 16
,17 44
62131
20
37869
66304
24
33696
04173
4
95827
17
44
45"
42 8
17 52
62159
20
37841
66337
25
25
33663
10. 33629
04179
4
95821
9. 95815
16
15
8 42
3 18
9. 62186
21
10. 37814
9. 66371
10.04185
4
46
41 52
18 8
62214
21
37786
66404
26
33596
04190
4
95810
14
47
41 44
18 16
62241
22
37759
66437
26
33563
04196
5
95804
13
48
41 36
18 24
62268
22
37732
66470
27
33530
04202
5
95798
12
49
41 28
18 32
62296
23
37704
66503
9.66537
27
33497
04208
10.04214"
5
5
95792
9. 95786
11
10
50
8 41 20
3 18 40
9. 62323
23 10.37677
28
10.33463
51
41 12
18 48
62350
24
37650
66570
28
33430
04220
5
95780
9
52
41 4
18 56
62377
24
37623
66603
29
33397
04225
5
95775
8
53
40 56
19 4
62405
24
37595
66636
30
33364
04231
5
95769
(
54
55
40 48
19 12
62432
25
37568
66669
30
33331
04237
5
5
95763
9. 95757
6
5
8 40 40
3 19 20
9. 62459
25 110.37541
9. 66702
31
10. 33298
10. 04243
56
40 32
19 28
62486
26
37514
66735
31
33265
04249
5
95751
4
57
40 24
19 36
(52513
26
37487
66768
32
33232
04255
5
95745
;5
58
40 16
19 44
62541
27
37459
66801
32
33199
04261
6
95739
2
59
40 8
19 52
62568
27
37432
66834
33
33166
04267
6
95733
1
60
40
20
62595
28
37405
66867
33
33133
04272
6
95728
M.
M.
Hour P.M.
Hour A.M.
Cosine.
Difl.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
114°
A
A
B
B
C
C
(i.5°
Seconds of time
1>
•2- 3" 4-
5-
«■
7-
(A
Prop, parts of cols.^B
\c
3
4
1
7
8
1
10 14
IS 17
2 3
17
21
4
21
25
4
24
29
5
TABLE U.
[Page 797 •
log. Sines, Tangent'-, and Secants.
25°
A
A
B
B
C
C 154°
M.
Hour A. M.
Hour p. M.
Sine.
Dlff.
Cosecant.
Tangent.
DiCf.
Cotangent.
Secant.
Diff.
Cosine.
M.
8 40
3 20
9. 62595
10. 37405
9. 66867
10. 33133
10. 04372
9.95728
60
1
39 52
20 8
62622
37378
66900
1
33100
04278
95722
59
2
39 44
20 16
62t>49
1
37351
66933
1
33067
04284
95716
58
S
39 36
20 24
62676
1
37324
66966
2
33034
04290
95710
57
4
5
39 28
20 32
62703
9. 62730
2
2
37297
10. 37270
66999
2
33001
04296
95704
56
55
8 39 20
3 20 40
9. 67032
3
10. 32968
10. 04302
9. 95698
fi
39 12
20 48
62757
3
37243
67065
3
32935
04308
9.5692
54
/
39 4
20 56
62784
3
37216
67098
4
32902
04314
95686
53
K
38 56
21 4
62811
4
37189
67131
4
32869
04320
95680
52
9
10
38 48
8 38 40
21 12
62838
4
37162
67163
5
5
32837
04326
95674
51
50
3 21 20
9. 62865
4
10. 37135
9. 67196
10. 32804
10.04332
9.95668
11
38 32
21 28
62892
5
37108
67229
6
32771
04337
95663
49
12
38 24
21 36
62918
5
37082
67262
/
32738
04343
95657
48
18
38 16
21 44
62945
6
37055
67295
7
32705
04349
95651
47
14
l.V
38 8
21 52
62972
6
37028
67327
8
32673
04355
10. 04361
95645
46
45
8 38
3 22
9. 62999
7
10. 37001
9. 67360
8
10. 32640
2
9. 95639
l(i
37 52
22 8
63026
7
36974
67393
9
32607
04367
2
95633
44
17
37 44
22 16
63052
8
36948
67426
9
32574
04373
2
95627
43
IH
37 36
22 24
63079
8
36921
67458
10
32542
04379
2
95621
42
1!»
2(r
37 28
22 32
63106
8
36894
67491
10
11
32509
04385
10. 04391
2
2
9.5615
9. 95609
41
40
8 37 20
3 22 40
9. 63133
9
10. 36867
9. 67524
10. 32476
2!
37 12
22 48
63159
9
36841
67556
11
32444
04397
2
95603
39
'>•>
37 4
22 56
63186
10 ! 36814
67589
12
32411
04403
'>
95597
38
•s.i
36 56
23 4
63213
10 ; 36787
67622
12
32378
04409
2
95591
37
24
2.'".
36 48
8 36 40
23 12
63239
11 36761
67654
13
14
32346
10. 32313
04415
10. 04421
2
3^
9558.5
9. 95579
36
35
3 23 20
9. 63266
11 10.36734
9. 67687
2(1
36 32
23 28
63292
11
36708
67719
14
32281
04427
3
95573
.34
27
36 24
23 36
63319
12
36681
67752
15
32248
04433
3
95567
33
2N
36 16
23 44
63345
12
36655
67785
15
,32215
04439
3
95561
32
2il
36 8
23 52
63372
13
36628
67817
16
32183
04445
3
9.5555
31
:«i
8 36
3 24
9. 63398
13 10.36602
9. 67850
16 (10. 32150
10. 04451
3
9. 85549
30
31
35 52
24 8
63425
14 36575
67882
17 : 32118
04457
3
95543
29
32
35 44
24 16
63451
14 36549
67915
17 i 32085
04463
3
95537
28
33
35 36
24 24
63478
15 36522
67947
18 i 32053
04469
3
95531
27
34
35^
35 28
8 :?5 20"
24 32
6^504
15
36496
67980
18
32020
04475
3
95525
26
25
3 24 40
9. 63531
15
10. 36469
9. 680X2
19
10. 31988
10.04481
4 9.9.5519
3ti
35 12
24 48
63557
16
, 36443
68044
20
31956
04487
4 1 9.5513
24
37
35 4
24 56
63583
16
36417
68077
20
31923
04493
4 1 95507
23
3.S
34 56
25 4
63610
17
36390
68109
21
31891
04500
4 j 95.500
22
39
40
34 48
25 12
63636
17
36364
10. 36338
68142
21
31858
04.506
10.04512
4 ; 95494
4 9.95488
21
20
8 34 40
3 25 20
9. 63662
18
9.68174
22 110.31826
41
34 32
25 28
63689
18
36311
68206
22
31794
04518
4 9.5482
19
42
34 24
25 36
63715
19
36285
68239
23
31761
04524
4 1 9.5476
18
43
34 16
25 44
63741
19
36259
68271
23
31729
04530
4 ! 95470
17
44
45
34 8
8 34
25 52
63767
19
36233
68303
24
24
31697
04536
4 i 95464
16
15
3 26
9. 63794
20
10. 36206
9. 68336
10. 31664
10. 04542
5 1 9. 9.5458
4(i
33 52
26 8
63820
20
36180
68,368
25
31632
04.548
5 1 95452
14
47
33 44
26 16
63846
21
36154
68400
25
31600
04554
5 1 95446
13
4K
33 36
26 24
63872
21
36128
68432
26
31568
04.560
5 1 95440
12
49
off
33 28
"8 33^20'
26 32
3 26 40
63898
9. 63924
22
22
36102
68465
27
31535
04566
5
95434
9. 95427
11
10
10. 36076
9. 68497
27 110.31503
10. 04573
5
51
33 12
26 48
63950
23
36050
68529
28
31471
04579
5 9.5421
9
52
33 4
26 56
63976
23
36024
68561
28
31439
04585
5
95415
8
53
32 56
27 4
64002
23
35998
68593
29
31407
04591
5
95409
/
54
55
32 48
27 12
64028
9. 64054
24
24
35972
68626
29
31374
10. 31342
04597
5
6
95403
9. 95397
6
5
8 32 40
3 27 20
10, .35946
9. 68658
30
10. 04603
56
32 32
27 28
64080
25
35920
68690
30
31310
04609
fi
95391
4
57
32 24
27 36
64106
25
35894
68722
31
31278
04616
6
95384
3
58
32 16
27 44
()4132
26
.35868
68754
31
31246
04622
6
95378
2
59
32 8
27 52
64158
26
35842
68786
32
31214
04628
6
95372
1
60
3S
28
64184
26
35816
68818
33
31182
04634
6
95366
M.
Hour p. M.
Hour A. H.
Cosine.
Diff.
Secant.
Cotangent.
Did.
Tangent.
Cosecant.
Diff.
Sine.
M.
115°
A
A
B
B
C 64° j
Seconds of time .
Prop, parts
of cols. <
5>
7-
• Page 798]
TABIvE U.
Log. Sineg, Tangents, and Secants.
26°
A
A
B B
C
C
l.J3°
Jl.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
8 32
3 28
9.64184
10. a5816
9. 68818
10. 31182
10. 04634
9. 95366
1)0
1
31 52
28 8
64210
35790
68850
1
.311.50
(M640
i 95360
59
2
31 44
28 16
64236
1
35764
68882
1
31118
04646
95354
58
:i
31 36
28 24
64262
1
35738
68914
2
31086
04652
95348
57
4
31 28
28 32
3 28 40
64288
9. 64313
2
2
35712
10. 35687
68946
9. 68978
2
3
310,54
10. 31022
04659
10.04665
95341
1 19.95335
56
55
8 31 20
6
31 12
28 48
64339
3
35661
69010
3
,30990
04671
1 95329
54
i
31 4
28 56
64365
3
356,35
69042
4
30958
04677
1 95323
53
8
30 56
29 4
64391
3
,3.5609
69074
4
3(»2(i
04683
1 9.5317
52
9
10
30 48
8 30 40
29 12
3 29 20"
64417
4
3,5583
69106
5
30894
10. 30862
04690
10. 04696
1 95310
1 19. 9.5.304
51
50
9.64442
4
10. 35,558
9. 69138
5
11
30 32
29 28
64468
5
35532
69170
6
308,30
04702
1 9529S
49
12
30 24
29 36
64494
5
3,5506
69202
6
30798
04708
1 95292
4S
18
30 16
29 44
64519
5
3,5481
69234
7
30766
04714
1 1 95286
47
14
15^
30 8
29 52
64545
6
354,55
69266
7
30734
10. 30702
04721
10.04727
1 : 95279
2 i 9. 95273
46
45
8 30
3 30
9. 64571
6
10. 3.5429
9. 69298
8
It)
29 52
30 8
64596
7 1 35404
69329
8 .30671
04733
2 : 95267
44
17
29 44
30 16
64622
7
35378
(i9361
9
;%639
04739
2 1 95261
43
18
29 36
30 24
64647
8
35;»3
69393
9
30607
04746
2 95254
42
19
20"
29 28
30 32
3 30 40
64673
9.64698
8
;«)327
69425
10
30575
04752
2 ; 9524S
2: 9. 95242'
41
40
8 29 20
8
10. 35302
9. 69457
11 10.30.543
10. 04758
21
29 12
30 48
64724
9
35276
69488
11 30,512
04764
2 ; 95236
:!9
22
29 4
30 56
64749
9 1 35251
69520
12 30480
04771
2 95229
38
2S
28 56
31 4
64775
10
35225
69-552
12 ! 30448
04777
• 2 , 95223
w
24
28 48
31 12
64800
10
11
35200
10.3.5174
69584
13 1 30416
13 10. ,30385
0478.3
10. 04789
,3 : 95217
3 j 9. 95211
3<)
.■J5
25
8 28 40
3 31 20
9. 64826
9. 69615
2«
28 32
31 28
64851
11
35149
69647
14 30353
04796
3 ! 95204
34
27
28 24
31 36
64877
11
35123
69679
14 30321
04802 »^ 3 951 9S
:'.3
28
28 16
31 44
64902
12
3.5098
69710 15 30290
04808
3 95192
32
29
"30"
28 8
31 52
64927
9. 64953
12
13
;»073
10.3.5047
69742 15 30258
1X69774 , 16 10730226"
04815
10. 04821
3 95185
3 19.95179
31
30
8 28
3 32
31
27 52
32 8
64978
13 ; 35022
69805 16 i ,30195
04827
3 95173
29
32
27 44
32 16
65003
14 1 34997
69837
17 i 30163
048,33
3 95167
28
33
27 36
32 24
65029
14 ! .34971
(iltStiS
17 1 30132
04840
3 95160
27
34
3o
27 28
8 27 20
32 32
65054
9. 65079
14 1 3494<i
15 10.34921
69900
18 1 30100
04846
io:04852
4 1 95154
26
25
3 32 40
9. 69932
18 10.30068
4 9.95148
36
27 12
32 48
65104
15 ! 34896
69963
19 1 30037
04859
4 i 95141
24
37
27 4
32 56
65130
16 1 34870
69995 1 ?0 1 300a5
04865
4 95135
23
38
26 56
33 4
65155
16 j 34845
70026 20 j 29974
04871
4 ! 95129
22
39
40
26 48
8 26 40
33 12
65180
16 : 34820
17 10.34795
70058 21 : 29942
9.70089 21 110.29911
04878
10. 04884
4 95122
'4 '9.95116
21
"20
3 33 20
9. 65205
41
26 32
33 28
65230
17 i 34770
70121 22 : 29879
04890
4 95110
19
42
26 24
33 36
65255
18 1 34745
70152 1 22 i 29848
04897
4 95103
IS
43
26 16
33 44
65281
18 .34719
70184 23 29816
04903
5 95097
17
44
45
26 8
33 52
3 34
65306
19 ! 34694
19 10.34669
70215 2.-!
9. 70247 24"
29785
04910
10. 04916
5 • 95090
5 9.9.5084
16
15
8 26
9. 65331
10. 29753
46
25 52
34 8
65.356
19 1 34644
70278 24 1 29722
04922
5 95078
14
47
25 44
;« 16
65381
20 ' 34619
70309 25 29691
04929
5 95071
13
48
25 36
34 24
65406
20 34594
70.341 25 1 29659
04935
5 9,5065
12
49
50'
25 28
M 32
ft5431
21 1 :«569
70372
26
26
29628
04941
5 95059
5 I 9. 95052
11
"10
8 25 20
3 34 40
9. 65456
21
10. 34544
9,70404
10. 29596
10. 04948
51
25 12
34 48
65481
22
.34519
70435
27 29,565
049,54
5 ! 95046
9
52
25 4
34 56
65.506
22
• 34494
70466
27
29534
04961
5 950,39
8
53
24 56
35 4
65531
22
;M469
70498
28
29502
04967
6 ' 9.5033
/
54
24 48
35 12
6.5556
23
23
34444
10.34420"
70529
9. 705(iO
28
29471
04973
6
6
95027
6
5
55
8 24 40
3 35 20
9. 65580
29 10.29440
10. 04980
9. 95020
56
24 32
35 2t
65605
24
34.395
70592
30
29408
04986
6 ' 95014
4
57
24 24
35 36
656.30
24
34370
70623
30
29377
04993
6 ! 9,5007
.)
58
24 16
35 44
65655
25
34;M5
70654
31
29346
04999
6 95001
■)
59
24 8
35 52
65680
25
34320
70685
31
29315
05005
6
94995
i
60
24
36
65705
25
34295
70717
32
29283
05012
6
94988
M.
Hour p. M.
Hour A. M.
Cosine.
Dlff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
116°
A
A
B B
C
C
63°
Seconds of time
Prop, parts of ools. -^ B
!• i 2> S-
4'
5« fi-
?•
3 i 6 10
4 18 12
1 ' 2 '2
13
16
3
le 1 19
20 24
4
22
28
6
r"
TABLE U.
[Page 799
Log. Sines, Tangents, and Secants.
27°
A A
B
B
C
C 152°
M.
Hour A.M.
Hour p. M.
Sine. ; Dlff.
CosecHiit.
Tangent.
Difl.
Cotangent.
Secant.
Difl.
Cosine.
M.
60
8 24
3 36
9. 65705
10. 34295
9. 70717
10. 29283
10. 05012
9. 94988
1
23 52
36 8
65729
34271
70748
1
29252
05018
94982
59
f
23 44
36 16
65754 1
34246
70779
1
29221
05025
94975
58
H
23 36
36 24
65779 1 1
;«221
70810
2
29190
05031
94969
57
4
5
23 28
'8 23 20
36 32
a5804
2
3419(5
70841
2
29159
05038
10. 05044
1
94962
56
"55
3 36 40
9. 65828
2
10. 34172
9. 70873
3
10. 29127
9. 94956
(i
23 12
36 48
65853
9
34147
70904
3
2909(5
05a51
1
94949
54
23 4
36 56
65878
3
:«122
70935
4
29065
05057
1
94943
53
8
22 56
37 4
(55902
3
34098
70966
4
29034
050(54
1
94936
52
9
22 48
37 12
65927
9.65952
4
4
34073
70997
29003
05070
1
94930
9. 94923
51
50
10
8 22 40
3 37 20
10. 34048
9. 71028
o
10. 28972
10. 05077
1
11
22 32
37 28
65976
4
34024
71059
6
28941
05083
1
94917
49
1'^
22 24
37 36
66001
33999
71090
6
28910
05089
1
94911
48
13
22 16
37 44
66025
5
33975
71121
I
28879
05096
1
94904
47
U
15
22 8
8 22
37 52
66050
6
6
33950
10. 33925
71153
'9:71184
4
"8
28847
lO: 28816
05102
10.05109
2
2
94898
9. 94891
46
45
3 38
9. 66075
l»i
21 52
38 8
66099
6
33901
71215
8
28785
05115
9
94885
44
17
21 44
38 16
66124
t
33876
71246
9
28754
05122
2
94878
43
18
21 36
38 24
66148
1
33852
71277
9
28723
05129
9
94871
42
19
21 28
38 32
66173
8
33827
10. 33803
71308
10
28692
05135
10.05142
2
2
94865
41
40
20
8 21 20
3 38 40
9.66197 1 8
9. 71339
10
10.28661
9. 94858
?\
21 12
38 48
66221 ' 8
33779
71370
11
28630
05148
2
94852
.39
?:?,
21 4
38 56
66246 9
33754
71401
11
28599
05155
9
94845
38
2A
20 56
39 4
66270 9
33730
71431
12
28569
05161
3
94839
37
24
25
20 48
8 20 40
«?9 12
3 39 20
66295 10
9.66319 ; 10
33705
71462
12
13
28538
10. 28507
05168
3
3
94832
36
35
10. 33681
9. 71493
10.05174
9. 94826
26
20 32
39 28
66343 ; 11
33657
71524
13
28476
05181
3
94819
34
27
20 24
39 36
6(i.368 11 1 3.3632
71555
14
2844/i
05187
3
94813
33
28
20 16
39 44
6()392 11 : 33608
71586
14
28414
05194
3
94806
32
29
20 8
39 52
(56416 12 1 33584
71617
15
28383
05201
3
94799
31
30
8 20
3 40
9.66441 i 12 10.33559
9. 71648
15
10. 28352
10. 05207
3
9. 94793
31
19 52
40 8
66465 ; 13 33535
71679
16
28321
05214
3
9478(5
29
32
19 44
40 16
(56489 13
33511
71709
16
28291
05220
4
94780
28
33
19 36
40 24
66513 1 13
33487
71740
17
28260
05227
4
94773
27
34
19 28
40 32
66537 14
33463
71771
17
28229
05233
ib. 05240
4
94767
26
25
8 19 20
3 40 40
9.66562 j 14
10. 33438
9. 71802
18
10. 28198
4
9. 94760
36
19 12
40 48
66586 15
33414
71833
19
28167
05247
4
94753
24
37
19 4
40 56
66610 15
33390
71863
19
28137
05253
4
94747
23
38
18 56
41 4
66634 15
33366
71894
20
28106
05260
4
94740
99
39
18 48
41 12
66658 16
33342
71925
20
21
28075
05266
4
4
94734
21
20
40
8 18 40
3 41 20
9. 66682 1 16
10. 33318
9. 71955
10. 28045
10. 05273
9. 94727
41
18 32
41 28
66706 j 17
33294
71986
21
28014
05280
4
94720
19
42
18 24
41 36
66731 17
33269
72017
22
27983
05286
5
94714
18
43
18 16
41 44
66755 t 17
33245
72048
22
27952
05293
5
94707
17
44
45
18 8
41 52
6(5779
18
18
33221
72078
23
27922
05300
5
94700
9. 94694
16
15'
8 18
3 42
9.66803
10. 33197
9. 72109
23
10. 27891
10. 05306
5
4()
17 52
42 8
66827 19
33173
72140
24
27860
05313
5
94687
14
47
17 44
42 16
66851 1 19
33149
72170
24
27830
05320
5
94680
13
48
17 36
42 24
66875 1 19
33125
72201
25
27799
05326
5
94674
12
49
50
17 28
8 17.20
42 32
66899 : 20
33101
72231
9. 72262
25
26
27769
05333
10. b5;M)
5
5
94667
9. 94660
11
10
3 42 40
9.66922 i 20
10. 33078
10. 27738
51
17 12
42 48
6(5946 ! 21
33054
72293
26
27707
05346
6
946.54
9
52
17 4
42 56
66970 21
33030
72323
27
27677
05353
6
94647
8
53
16 56
43 4
66994
21
33006
72354
27
27646
05360
6
94640
7
54
55
16 48
43 12
67018
22
32982
72384
28
27616
05366
6
94634
6
8 16 40
3 43 20
9. 67042
22
10. 32958
9. 72415
28
10. 27585
10.05373'
6
9. 94627
5
56
16 32
43 28
67066
23
32934
72445
29
27555
05380
6
94620
4
57
16 24
43 36
67090
23
32910
72476
29
27524
05386
6
94614
3
58
16 16
43 44
67113 i 23
32887
72506
30
27494
05393
6
94607
2
59
16 8
43 52
67137
24
32863
72537
30
27463
05400
6
94600
1
60
16
44
67161
24
32839
72567
31
274.33
05407
7
94593
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Dlff.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
117°
A A
H
B
C
C 62° 1
Seconds o£ time .
Prop, parts of cols. .^B
9
12
12
15
Page 800
TABLE 44.
Log. Sines, Tangents, and Secants.
28°
A A
B
B
C
C 161°
M.
Hour A. M.
Hour p. M.
Sine.
Di£E.
Cosecant.
Tangent.
ma.
Cotangent.
Secant.
Dlfl.
Cosine.
M.
8 16
3 44
9.67161
10. 32839
9. 72567
10. 27433
10. 05407
9. 94593
60
1
15 52
44 8
67185
32815
72598
1
27402
05413
94587
59
2
15 44
44 16
67208
1
32792
72628
1
27372
0.5420
94580
58
H
15 36
44 24
67232
1
32768
72659
2
27.341
05427
94573
57
4
5
15 28
8 15 20
44 32
67256
2
2"
32744
72689
2
3
27311
10. 27280
05433
10. 0o440 '
94567
56
,5.5
3 44 40
9. 67280
10. 32720
9. 72720
1
9. 94560
(>
15 12
44 48
67303
2
32697
72750
3
27250
0.5447
1
94553
54
/
15 4
44 56
67327
3
32673
72780
4
27220
05454
1
94546
53
8
14 56
45 4
67350
3
32650
72811
4
27189
05460
1
94540
52
9
10
14 48
8 U 40
45 12
67374
9. 67398
3
32626
72841
5
5
27159
10.27128
0.5467
10. 05474
1
1
94533
51
.50"
3 45 20
4
10. 32602
9. 72872
9. 94526
11
14 32
45 28
67421
4
32579
72902
6
27098
05481
1
94519
49
12
14 24
45 36
67445
5
32555
72932
6
27068
05487
1
94513
48
13
14 16
45 44
67468
5
32532
72963
7
27037
05494
1
94506
47
14
14 8
45 52
67492
6
32508
72993
7
27007
10. 26977
05501
2
94499
46
45
MS
8 14
3 46
9. 67515
6
10. 32485
9. 73023
8
10. 05508
2
9. 94492
^(■>
13 52
46 8
67539
6
32461
73054
8
26946
05515
2
94485
44
17
13 44
46 16
67562
7
32438
73084
9
26916
05521
*>
94479
43
18
13 36
46 24
67586
7
32414
73114
9
26886
05528
o
94472
42
•19
13 28
46 32
67609
7
32391
73144
9. 73175
10
10
26856
10. 26825
05535
10. 05542
2
94465
41
40
20
8 13 20
3 46 40
9. 67633
8
10. 32367
2
9. 94458
21
13 12
46 48
67656
8
32344
73205
11
26795
05.549
2
94451
39
22
13 4
46 56
67680
9
32320
73235
11
26765
05555
3
94445
38
2:i
12 56
47 4
67703
9
32297
73265
12
26735
05562
3
94438
37
24
25
12 48
47 12
3 47 20
67726
9. 677.50
9
10'
32274
73295
12
26705
05569
3
94431
9. 94424
36
35
8 12 40
10. 32250
9. 73326
13
10. 26674
10. 0.5576
26
12 32
47 28
67773
10
32227
73356
13
26644
05583
3
94417
34
27
12 24
47 36
67796
10
32204
73386
14
26614
05590
3
94410
33
28
12 16
47 44
67820
11
32180
73416
14
26584
05596
3
94404
32
29
12 8
47 52
67843
11
32157
73446
9. 73476
15
15
26554
05603
3
3
94397
31
30
30
8 12
3 48
9. 67866
12
10. 321.34
10. 26524
10.0.5610
9. 94390
31
11 52
48 8
67890
12
32110
73507
16
26493
05617
4
94383
29
32
11 44
48 16
67913
12
32087
73537
16
26463
05624
4
94376
28
33
11 36
48 24
67936
13
32064
73567
17
26433
05631
4
94369
27
34
35
11 28
48 32
67959
13
32041
73597
17
26403
10. 26373
05638
10.05645
4
4
94.362
9. 94355
26
25"
8 11 20
3 48 40
9. 67982
14
10. 32018
9. 73627
18
36
11 12
48 48
68006
14
31994
73657
18
26343
05651
4
94349
24
37
11 4
48 56
68029
14
31971
73687
19
26313
05658
4
94342
23
38
10 56
49 4
68052
15
31948
73717
19
26283
05665
4
94335
•>■>
39
10 48
49 12
68075
15
31925
73747
9. 73777
20
20
26253
10. 26223
05672
10. 05679
4
5
94328
9. 94321
21
20
40
8 10 40
3 49 20
9. 68098
16
10. 31902
41
10 32
49 28
68121
16
31879
73807
21
26193
05686
5
94314
19
42
10 24
49 36
68144
16
31856
7.3837
21
26163
05693
5
94307
18
43
10 16
49 44
68167
17
31833
73867
22
26133
05700
5
94300
17
44
45
10 8
49 52
68190
17
31810
73897
9. 73927
22
23
26103
10.26073
05707
10. 05714
5
94293
16
1.5'
8 10
3 50
9. 68213
17
10. 31787
5
9. 94286
46
9 52
50 8
68237
18
31763
73957
23
26043
05721
5
94279
14
47
9 44
50 16
682.60
18
31740
73987
24
26013
05727
5
94273
13
48
9 36
50 24
68283
19
31717
74017
24
25983
05734
5
94266
12
49
50
9 28
50 32
68305
19
31695
74047
25
25953
10. 2.5923
05741
lO: 0.5748
6
94259
11
10
8 9 20
3 50 40
9. 68328
19
10.31672
9. 74077
25
6
9. 94252
51
9 12
50 48
68351
20
31649
74107
26
25893
05755
6
94245
9
52
9 4
50 56
68374
20 i 31626
74137
26
25863
05762
6
94238
8
53
8 56
51 4
68397
21 ; 31603
74166
27
258.34
05769
6
942.31
7
54
8 48
51 12
68420
21
31580
74196
9. 74226
27
28
25804
10.2.5774
05776
10.0.5783
6
6
94224
9. 94217
6
" 5
55
8 8 40
3 51 20
9. 68443
21
10. 31557
56
8 32
51 28
68466
22
31534
74256
28
25744
05790
6
94210
4
57
8 24
51 36
68489
22
31511
74286
29
25714
05797
7
94203
3
58
8 16
51 44
68512
22
31488
74316
29
25684
05804
7
94196
2
59
8 8
51 52
68534
23
31466
74345
30
2.5655
0.5811
(
94189
1
60
8
52
68557
23
31443
74375
30
25625
05818
7
94182
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M
1180
A A
B
B
C
61° 1
Seconds of time
Prop, parts of cols, iB
Ic
TABLE U.
[Page 801
Log.
Sines, Tangents, and Secants.
29°
A
A
B B
C
C 160°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
DiiT.
Cotangent
Secant.
Diff.
Cosine.
M.
8 8
3 52
9. 68557
10. 31443
9. 74375
10. 25625
10. 05818
9. 94182
60
1
7 52
52 8
68580
31420
74405
25595
05825
94175
59
2
7 44
52 16
68603
1
31397
74435
1
25565
05832
94168
58
3
7 36
52 24
68625
1
31375
74465
1
25535
05839
94161
57
4
7 28
52 32
68648
1
31352
74494
9. 74524
2
25506
0.5846
94154
56
55
5
8 7 20
3 52 40
9. 68671
2
10. 31329
2
10. 25476
10. 05853
9. 94147
6
7 12
52 48
68694
2
31306
74554
3
25446
05860
94140
54
7
7 4
52 56
68716
3
31284
74583
3
25417
05867
94133
53
8
6 56
53 4
68739
3
31261
74613
4
25387
05874
94126
52
9
6 48
53 12
68762
3
31238
74643
4
25357
05881
94119
51
50
10
8 6 40
3 53 20
9. 68784
4
10. 31216
9. 74673
5
10. 25327
10. 05888
9.94112
n
6 32
53 28
68807
4
31193
74702
5
25298
05895
94105
49
12
6 24
53 36
68829
4
31171
74732
6
25268
05902
94098
48
13
6 16
53 44
68852
5
31148
74762
6
25238
05910
2
94090
47
14
15
6 8
53 52
68875
5
31125
74791
7
25209
05917
2
94083
46
45
8 6
3 54
9. 68897
6
10. 31103
9. 74821
7
10. 25179
10. 0.5924
2
9. 94076
16
5 52
54 8
68920
6
31080
74851
8
25149
05931
2
94069
44
17
5 44
54 16
68942
6
31058
74880
8
25120
05938
2
94062
43
18
5 36
54 24
68965
7
31035
74910
9
25090
05945
2
94055
42
19
20
5 28
54 32
68987
7
7
31013
10. 30990
74939
9
25061
05952
10. 05959
2
2
94048
9. 94041
41
40
8 5 20
3 54 40
9. 69010
9. 74969
10
10. 25031
21
5 12
54 48
69032
8
30968
74998
10
25002
05966
3
94034
39
22
5 4
54 56
69055
8
30945
75028
11
24972
05973
3
94027
38
28
4 56
55 4
69077
9
30923
75058
11
24942
05980
3
94020
37
24
25
4 48
55 12
69100
9
30900
75087
12
12
24913
10.24883
05988
3
94012
9. 94005
36
,35
8 4 40
3 55 20
9. 69122
9
10. 30878
9. 75117
10. 05995
3
26
4 32
55 28
69144
10
30856
75146
13
24854
06002
3
93998
.34
27
4 24
55 36
69167
10
30833
75176
13
24824
06009
3
93991
33
28
4 16
55 44
69189
10
30811
75205
14
24795
06016
3
93984
32
29
30
4 8
55 52
69212
11
11
30788
10. 30766
75235
14
24765
06023
3
93977
9. 93970
31
■.V)
8 4
3 56
9. 69234
9. 75264
15
10. 24736
10. 06030
4
31
3 52
56 8
69256
12
30744
75294
15
24706
06037
4
93963
29-
32
3 44
56 16
69279
12
30721
75323
16
24677
06045
4
93955
28
33
3 36
56 24
69301
12
30699
75353
16
24647
06052
4
93948
27
34
35
3 28
56 32
69323
13
30677
75382
17
17
24618
10. 24589
06059
10. 06066
4
4
93941
26
8 3 20
3 56 40
9. 69:M5
13
10. 30655
9.75411
9. 939;W
25
36
3 12
56 48
69368
13
30632
75441
18
245.59
06073
4
93927
24
37
3 4
56 56
69390
14
30610
75470
18
24530
06080
4
93920
23
38
2 56
57 4
69412
14
30588
75500
19
^4500
0<i088
5
93912
22
39
2 48
57 12
69434
15
.30566
75529
19
20
24471
10. 24442
06095
5
93905
21
20
40
8 2 40
3 57 20
9. 69456
15
10. 30544
9. 75358
10. 06102
5
9. 93898
41
2 32
57 28
69479
15
30521
75588
20
24412
06109
5
93891
19
42
2 24
57 36
69501
16
30499
75617
21
24383
06116
5
93884
18
43
2 16
57 44
69523
16
30477
75647
21
24353
06124
5
93876
17
44
45
2 8
57 52
69545
16
17
30455
10.30433
75676
9. 75705"
22
24324
06131
5.
93869
16
1,5
8 2
3 58
9. 69567
22
10. 24295
10. 06138
5
9. 93862
46
1 52
58 8
69589
17
30411
75735
23
24265
06145
5
938.55
14
47
1 44
58 16
69611
17
30389
75764
23
24236
06153
6
93847
13
48
1 36
58 24
69633
18
30367
75793
24
24207
06160
6
93840
12
49
50
1 28
58 32
69655
18
30345
7.5822
24
25
24178
10. 24148
06167
6
93833
9. 93826
11
10
8 1 20
3 58 40
9. 69677
19
10. 30323
9. 75852
10.06174
6
51
1 12
58 48
69699
19
30301
75881
25
24119
06181
6
93819
9
52
1 4
58 56
69721
19
30279
75910
26
24090
06189
6
93811
8
53
56
59 4
69743
20
30257
75939
26
24061
06196
6
93804
7
54
55
48
59 12
69765
20
20
302^5
75969
27
27
24031
10724002
06203
6
93797
6
5
8 40
3 59 20
9. 69787
10. 30213
9. 75998
10. 06211
7
9. 93789
56
32
59 28
69809
21
30191
76027
28
23973
06218
7
93782
4
57
24
59 36
69831
21
30169
76056
28
2.3944
06225
7
93775
3
58
16
59 44
69853
22
30147
76086
29
23914
06232
7
93768
2
59
8
59 52
69875
22
30125
76115
29
23885
06240
7
93760
1
60
M.
4
69897
22
30103
76144
29
23856
06247
7
93753
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
11»°
A
A
B B
C
C
60°
24972°— 12-
1'
2-
8-
4-
5>
6i
7'
Prop, parts of cols.
A
B
c
3
i
6
7
2
8
11
3
11
15
4
14
18
4
17
22
5
20
26
6
-41
Page 802]
TABLE U.
Log. Sines, Tangents, and Secants.
80°
..
A
A
B
B
C
C 1490
M.
Hour A. M.
Hour p. M.
Sine.
Diff. 1 Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
8
4
9. 69897
10. 30103
9. 76144
10. 23856
10. 06247
9. 93753
60
1
7 59 52
8
69919
30081
76173
23827
06254
93746
59
2
59 44
16
69941
1
30059
76202
1
23798
06262
93738
58
a
59 36
24
69963
1
30037
76231
1
23769
06269
93731
57
4
59 28
32
69984
1
30016
76261
2
23739
06276
10. 06283
93724
9. 93717
56
55
s
7 59 20
4 40
9.70006
2
10. 29994
9. 76290
2
10. 23710
6
59 12
48
70028
2
29972
76319
3
23681
06291
93709
54
7
59 4
56
70050
3
29950
76348
3
23652
06298
93702
.53
8
58 56
1 4
70072
3
29928
76377
4
23623
06305
93695
52
9
58 48
1 12
70093
3
29907
76406
4
23594
06313
93687
51
10
7 58 40
4 1 20
9. 70115
4
10. 29885
9. 76435
5
10. 23565
10.06320
9. 93680
50
n
58 32
1 28
70137
4
29863
76464
5
23536
06327
93673
49
12
58 24
1 36
70159
4
29841
76493
6
2;i507
063.35
93665
48
13
58 16
1 44
70180
5
29820
7a522
6
23478
06342
2
93658
47
14
58 8
1 52
70202
5
29798
76551
7
23449
06.350
2
93650
46
45
15
7 58
4 2
9. 70224
5
10. 29776
9. 76580
7
10. 23420
10. 06357
2
9. 93643
16
57 52
2 8
70245
6
29755
76609
8
23391
06364
2
93636
44
17
57 44
2 16
70267
6
29733
76639
8
23.361
06372
2
98628
43
18
57 36
2 24
70288
6
29712
76668
9
23332
06379
2
93621
42
19
57 28
2 32
70310
7
29690
76697
9
23303
06386
2
93614
41
20
7 57 20
4 2 40
9. 70332
7
10. 29668
9. 76725
10
10. 23275
10. 06394
2
9. 93606
40
21
57 12
2 48
70353
8
29647
767.54
10
23246
06401
3
93599
39
22
57 4
2 56
70375
8
29625
76783
11
23217
06409
3
93591
38
23
56 56
3 4
70396
8
29604
76812
11
23188
06416
3
915584
37
24
56 48
3 12
70418
9
9
29582
10. 29561
76841
12
23159
06423
3
93577
36
35
25
7 56 40
4 3 20
9. 70439
9. 76870
12
10. 23130
10. 06431
3
9. 93569
26
56 32
3 28
70461
9
295.39
76899
13
23101
06438
3
93562
34
27
56 24
3 36
70482
10
29518
76928
13
23072
06446
3
9a5.54
33
28
56 16
3 44
70504
10
29496
76957
13
23043
06453
3
9.3,547
32
29
30
56 8
3 52
70525
10
29475
76986
14
2.3014
•06461
10. 06468
4
4
93539
31
7 56
4 4
9. 70547
11
10. 29453
9. 77015
14
10. 22985
9. 93532
30
*31
55 52
4 8
70568
11
29432
77044
15
22956
06475
4
93525
29
32
55 44
4 16
70.590
11
29410
77073
15
22927
06483
4
9.3517
28
33
55 36
4 24
70611
12
29389
77101
16
22899
0r>490
4
9.3510
27
34
55 28
4 32
70633
12
13
29367
77130
16
17
22870
10. 22841
06498
4
93502
26
35
7 55 20
4 4 40
9. 70654
10. 29346
9.77159
10. 0ft505
4
9. 93495
25
36
55 12
4 48
70675
13
29325
77188
17
22812
06513
4
93487
24
37
55 4
4 56
70697
13
29303
77217
18
22783
06520
5
9.3480
23
38
54 56
5 4
70718
xl4
29282
77246
18
22754
06528
5
93472
22
39
54 48
5 12
70739
14
29261
10. 29239
77274
19
22726
06535
5
9.3465
21
40
7 54 40
4 5 20
9. 70761
14
9. 77303
19
10. 22697
10. 06543
5
9. 93457
20
41
54 32
5 28
70782
15
29218
773.32
20
22668
06550
5
93450
19
42
54 24
5 36
70803
15
29197
77.361
20
22639
06.558
5
93442
18
43
54 16
5 44
70824
15
29176
77.390
21
22610
06565
5
93435
17
44
45
54 8
7 54
5 52
70846
16
29154
77418
21
22
22582
10. 22.553
06573
5
6
93427
16
15
4 6
9. 70867
16
10. 29133
9. 77447
10. 06.580
9. 93420
46
53 52
6 8
70888
16
29112
77476
22
22524
06588
6
93412
14
47
53 44
6 16
70909
17
29091
77505
23
22495
06595
6
93405
13
48
53 36
6 24
70931
17
29069
77533
23
22467
06603
6
93397
12
49
50
53 28
6 32
70952
9. 70973
18
18
29048
10. 29027
77562
9. 77591
24
22438
06610
6
6
93390
11
10
7 53 20
4 6 40
24
10. 22409
10. 06618
9. 93382
51
53 12
6 48
70994
18
29006
77619
25
22.381
06625
6
93375
9
52
53 4
6 56
71015
19
28985
77648
25
22352
06633
6
93367
8
53
52 56
7 4
71036
19
28964
77677
26
22323
06640
7
9,3360
7
54
52 48
7 12
71058
19
28942
77706
26
22294
06648
7
93352
6
5
55
7 52 40
4 7 20
9. 71079
20
10. 28921
9. 777.34
26
10. 22266
10. 06656
7
9. 93344
56
52 32
7 28
71100
20
28900
77,763
27
22237
06663
7
93337
4
57
52 24
7 36
71121
20
28879
77791
27
22209
06671
7
93329
3
58
52 16
7 44
71142
21
28858
77820
28
22180
06678
7
93322
2,
59
52 8
7 52
71163
21
28837
77849
28
221,51
06686
7
93314
1
60
52
8
71184
21
28816
77877
29
22123
06693
7
93307
Sine.
M.
M.
Hour p. M,
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
12(f
A
A
B
B
C
C 59° 1
Seconds of time
1'
2-
8"
4-
5'
6>
J-
A
Prop, parts of cols. B
Ic
3
4
1
5
7
2
8
11
3
11
14
4
13
18
6
16
22
6
19
25
7
TABLE 44.
Log. Sines, Tangents, and Secants.
[Page 803
31=
A A
B B
C
, C 148°
M.
Hour A. M.
Hour p. M.
sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent
Secant.
Diff.
Cosine.
M.
7 52
4 8
9. 71184
10. 28816
9. 77877
10. 22123
10. 06693
9. 93307
60
1
51 52
8 8
71205
28795
77906
22094
06701
93299
59
2
51 44
8 16
71226
1
28774
77935
1
22065
06709
93291
58
3
51 36
8 24
71247
1
28753
77963
1
22037
06716
93284
57
4
51 28
8 32
71268
1
2
28732
10. 28711
77992
2
22008
06724
93276
56
55
5
7 51 20
4 8 40
9. 71289
9. 78020
2
10. 21980
10. 06731
9. 93269
6
51 12
8 48
71310
2
28690
78049
3
21951
06739
93261
54
7
51 4
8 56
71331
2
28669
78077
3
21923
06747
93253
53
K
50 56
9 4
71352
3
28648
78106
4
21894
06754
93246
52
9
50 48
9 12
71373
3
28627
10. 28607
78135
4
21865
06762
93238
51
10
7 50 40
4 9 20
9. 71393
3
9. 78163
5
10. 21837
10. 06770
9. 93230
50
11
50 32
9 28
71414
4
28586
78192
5
21808
06777
93223
49
12
50 24
9 36
71435
4
28565
78220
6
21780
06785
2
9.3215
48
18
50 16
9 44
71456
4
28544
78249
6
21751
06793
2
93207
47
14
50 8
9 52
71477
5
28523
78277
7
21723
06800
2
2
93200
9.93192
46
45
1ft
7 50
4 10
9. 71498
5
10. 28502
9. 78306
7
10. 21694
10. 06808
16
49 52
10 8
71519
5
28481
78334
8
21666
06816
9
93184
44
17
49 44
10 16
71539
6
28461
78363
8
21637
06823
2
93177
43
18
49 36
10 24
71560
6
28440
78391
9
21609
06831
2
93169
42
19
20
49 28
10 32
71581
7
28419
78419
9
21581
06839
2
93161
41
40
7 49 20
4 10 40
9. 71602
7
10. 28398
9.78448
9
10. 21552
10.06846
3
9. 93154
21
49 12
10 48
71622
7
28378
78476
10
21524
06854
3
93146
39
22
49 4
10 56
71643
8
28357
78505
10
21495
06862
3
93138
38
23
48 56
11 4
71664
8
28.336
78533
11
21467
06869
3
93131
37
24
48 48
11 12
71685
8
28315
78562
11
21438
06877
3
93123
36
.35
25
7 48 40
4 11 20
9. 71705
9
10. 28295
9. 78590
12
10. 21410
10. 06885
3
9. 93115
26
48 32
11 28
71726
9
28274
78618
12
21382
06892
3
93108
34
27
48 24
11 36
71747
9
28253
78647
13
21353
06900
3
93100
33
28
48 16
11 44
71767
10
28233
78675
13
21325
06908
4
93092
32
29
30
48 8
11 52
71788
10
28212
78704
14
21296
06916
4
93084
31
30
7 48
4 12
9. 71809
10
10. 28191
9. 78732
14 10. 21268
10. 06923
4
9. 93077
31
47 52
12 8
71829
11
28171
78760
15 j 21240
06931
4
930()9
29
32
47 44
12 16
71850
11
28150
78789
15 1 21211
06939
4
93061
28
33
47 36
12 24
71870
11
28130
78817
16 1 21183
06947
4
930.53
27
34
35
47 28
12 32
71891
12
12
28109
78845
16 i 21155
06954
4
93046
26
25
7 47 20
4 12 40
9. 71911
10. 28089
9. 78874
17 10.21126
10. 06962
5
9. 93038
36
47 12
12 48
71932
12
28068
78902
17
21098
06970
5
93030
24
37
47 4
12 56
71952
13
28048
78930
17
21070
06978
5
93022
23
38
46 56
13 4
71973
13
28027
78959
18
21041
06986
5
93014
22
39
46 48
13 12
71994
13
28006
78987
18
21013
06993
10. 07001
5
5
93007
21
40
7 46 40
4 13 20
9. 72014
14
10. 27986
9. 79015 19 10. 20985
9. 92999
20
41
46 32
13 28
720.34
14
27966
79043
19
20957
07009
5
92991
19
42
46 24
13 36
72055
14
27945
79072
20
20928
07017
5
92983
18
43
46 16
13 44
72075
15
27925
79100
20
20900
07024
6
92976
17
44
45
46 8
7 46
13 52
72096
15
27904
79128
21
20872
07032
6
92968
16
4 14
9. 72116
15
10. 27884
9. 79156
21
10. 20844
10. 07040
6
9.92960
15
46
45 52
14 8
72137
16
27863
79185
22
20815
07048
6
92952
14
47
45 44
14 16
72157
16
27843
79213
22
20787
07056
6
92944
13
48
45 36
14 24
72177
16
27823
79241
23
20759
07064
6
92936
12
49
45 28
14 32
72198
17
27802
79269
23
20731
07071
6
92929
11
"10
50
7 45 20
4 14 40
9. 72218
17
10. 27782
9. 79297
24
10. 20703
10. 07079
6
9. 92921
51
45 12
14 48
72238
18
27762
79326
24
20674
07087
7
92913
9
52
45 4
14 56
72259
18
27741
79354
25'
20646
07095
7
92905
8
53
44 56
15 4
72279
18
27721
79382
25
20618
07103
7
92897
7
54
44 48
15 12
72299
19
27701
79410
26
26
20590
07111
7
92889
6
5
55
7 44 40
4 15 20
9. 72320
19
10. 27680
9. 79438
10. 20562
10. 07119
7
9. 92881
56
44 32
15 28
72340
19
27660
79466
26
20.534
07126
7
92874
4
57
44 24
15 36
72360
20
27640
79495
27
20505
07134
7
92866
3
58
44 16
15 44
72381
20
27619
79523
27
20477
07142
7
92858
2
59
44 8
15 52
72401
20
27599
79551
28
20449
07150
8
92850
1
60
44
16
72421
21
27579
79579
28
20421
07158
8
92842
M.
Hour p. M.
Hour A.M.
Cosine.
Di£F.
Secant.
Cotangent.
Diff. j Tangent.
Cosecant.
Diff.
Sine.
M.
121°
A A
B B
C
C 68° 1
Seconds of time
1-
2-
8-
4-
5>
6'
7-
(A
Prop, parts of cols.! B
Ic
3
4
1
5
7
2
8
11
3
10
14
4
13
18
5
16
21
6
18
26
7
Page 804]
TABLE U.
Log. Sines, Tangents, and Secants.
82°
A
A
B
B
C
C
14J°
M.
Hour A.M.
Hour p. M.
Sine.
DM.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Difl.
Cosine.
M.
60
7 44
4 16
9. 72421
10. 27579
9. 79579
10. 20421
10. 07158
9. 92842
1
43 52
16 8
72441
27559
79607
20393
07166
92834
59
3
43 44
16 16
72461
1
27539
79635
1
20365
07174
92826
58
3
43 36
16 24
72482
1
27518
79663
1
20337
07182
92818
57
4
43 28
16 32
72502
1
2
27498
79691
2
20309
10. 20281
07190
1
92810
56
55
5
7 43 20
4 16 40
9. 72522
10. 27478
9. 79719
2
10. 07197
1
9. 92803
6
43 12
16 48
72542
2
27458
79747
3
20253
07205
1
92795
54
7
43 4
16 56
72562
2
27438
79776
3
20224
07213
1
92787
53
8
42 56
17 4
72582
3
27418
79804
4
20196
07221
1
92779
52
9
10
42 48
17 12
72602
3
27398
79832
4
20168
07229
1
1
92771
51
50
7 42 40
4 17 20
9. 72622
3
10. 27378
9. 79860
5
10.20140
10. 07237
9. 92763
11
42 32
17 28
72643
4
27357
79888
5
20112
07245
1
92755
49
12
42 24
17 36
72663
4
27337
79916
6
20084
07253
2
92747
48
13
42 16
17 44
72683
4
27317
79944
6
20056
07261
2
92739
47
14
15
42 8
17 52
72703
5
27297
79972
7
20028
07269
2
~^2"
92731
46
45
7 42
4 18
9. 72723
5
10. 27277
9.80000
7
10. 20000
10. 07277
9. 92723
16
41 52
18 8
72743
5
27257
80028
7
19972
07285
2
92715
44
17
41 44
18 16
72763
6
27237
80056
8
19944
07293
2
92707
43
18
41 36
18 24
72783
6
27217
80084
8
19916
07301
2
92699
42
19
20
41 28
18 32
72803
6
27197
80112
9
19888
07309
3
92691
9. 92683
41
40
7 41 20
4 18 40
9. 72823
7
10.27177
9. 80140
9
10. 19860
10. 07317
3
21
41 12
18 48
72843
7
27157
80168
10
19832
07325
3
92675
39
22
41 4
18 56
72863
7
27137
80195
10
19805
07333
3
92667
38
23
40 56
19 4
72883
8
27117
80223
11
19777
07341
3
92659
37
24
40 48
19 12
72902
8
27098
80251
11
19749
07349
3
3
92651
36
35
25
7 40 40
4 19 20
9. 72922
8
10. 27078
9. 80279
12
10. 19721
10. 07357
9. 92643
26
40 32
19 28
72942
9
27058
80307
12
19693
07365
3
92635
34
27
40 24
19 36
72962
9
27038
80335
13
19665
07373
4
92627
33
28
40 16
19 44
72982
9
27018
80363
13
19637
07381
4
92619
32
29
30
40 8
19 52
73002
10
10
26998
10. 26978"
80391
9. 80419
13
14
19609
07389
4
92611
31
7 40
4 20
9. 73022
10. 19581
10. 07397
4
9. 92603
30
31
39 52
20 8
73041
10
269.59
80447
14
19553
07405
4
92595
29
32
39 44
20 16
73061
11
26939
80474
15
19526
07413
4
92587
28
33
39 36
20 24
73081
11
26919
80502
15
19498
07421
4
92579
27
34
39 28
20 32
73101
11
26899
80530
16
19470
07429
5
92571
26
25
35
7 39 20
4 20 40
9. 73121
12
10. 26879
9. 80558
16
10. 19442
10. 07437
5
9. 92563
36
39 12
20 48
73140
12
26860
80586
17
19414
07445
5
92555
24
37
39 4
20 56
73160
12
26840
80614
17
19386
07454
5
92546
23
38
38 56
21 4
73180
13
26820
80642
18
19358
07462
92538
22
39
38 48
21 12
73200
13
26800
80669
18
19331
07470
5
5
92530
21
'2b
40
7 38 40
4 21 20
9. 73219
13 110.26781
9. 80697
19
10. 19303
10. 07478
9. 92522
41
38 32
21 28
73239
14
26761
80725
19
19275
07486
6
92514
19
42
38 24
21 36
73259
14
26741
80753
20
19247
07494
6
92506
18
43
38 16
21 44
73278
14
26722
80781
20
19219
07502
6
92498
17
44
45
38 8
21 52
73298
15
26702
80808
20
19192
07510
6
92490
16
7 38
4 22
9. 73318
15
10. 26682
9. 80836
21
10. 19164
10. 07518
6
9. 92482
15
46
37 52
22 8
73337
15
26663
80864
21
19136
07527
6
92473
14
47
37 44
22 16
73357
16
26643
80892
22
19108
07535
6
92465
13
48
37 36
22 24
73377
16
26623
80919
22
19081
07543
6
92457
12
49
37 28
22 32
73396
16
26604
10. 26584
80947
23
23
19053
07551
7
92449
11
10
50
7 37 20
4 22 40
9. 73416
17
9. 80975
10. 19025
10. 07559
7
9. 92441
51
37 12
22 48
73435
17
26565
81003
24
1S997
07567
7
92433
9
52
37 4
22 56
73455
17
- 26545
81030
24
18970
07575
7
92425
8
53
36 56
23 4
73474
18 1 26526
81058
25
18942
07584
/
92416
7
54
36 48
23 12
73494
18
18
26506
81086
25
26
18914
07592
7
7
92408
6
5
55
7 36 40
4 23 20
9. 73513
10. 26487
9.81113
10. 18887
10. 07600
9. 92400
56
36 32
23 28
73533
19
26467
81141
26
18859
07608
8
92392
4
57
36 24
23 36
7.3552
19
26448
81169
26
18831
07616
8
92384
3
58
36 16
23 44
73572
19
26428
81196
27
18804
07624
8
92376
2
59
36 8
23 52
73591
20
26409
81224
27
18776
07633
8
92367
1
60
36
24
73611
20
26389
81252
28
18748
07641
8
92359
M.
Hour p. M.
Hour A. H.
Osine.
Dlff.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
M.
128°
A
A
B
B
C
C
57°
Seconds of time
1-
2-
8"
4'
5>
6>
7-
Prop, parts of cols. ^B
Ic
2
3
1
5
7
2
7
10
3
10
U
4
12
17
6
15
21
6
17
24
7
TABLE 44.
[Page 805
Liog. Sines, Tangents, and Secants.
33°
A
A
B
B
C
. C 146°
M.
Hour A.M.
7 36
Hour p. M.
Sine.
Difl.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
4 24
9. 73611
10. 26389
9. 81252
10. 18748
10. 07641
9. 92359
60
1
35 52
24 8
73630
26370
81279
18721
07649
92361
59
2
35 44
24 16
73650
1
26350
81307
1
18693
07657
92343
58
3
35 36
24 24
73669
1
26331
81335
1
18665
07665
92335
57
4
35 28
24 32
73689
1
26311
81362
9. 81390
2
18638
07674
92326
66
56
5
7 35 20
4 24 40
9. 73708
2
10. 26292
2
10. 18610
10. 07682
9. 92318
6
-35 12
24 48
73727
2
26273
81418
3
18582
07690
92310
.54
7
35 4
24 56
73747
2
26253
81445
3
18555
07698
92302
53
8
34 56
25 4
73766
3
26234
81473
4
18527
07707
92293
62
9
10
•34 48
25 12
73785
3
26215
81500
4
18500
07715
92285
51
50
7 34 40
4 25 20
9. 73805
3
10. 26195
9. 81528
5
10. 18472
10. 07723
9. 92277
11
■M 32
25 28
73824
3
26176
81556
5
18444
07731
2
92269
49
12
34 24
25 36
73843
4
26157
81583
5
18417
07740
2
92260
48
13
34 16
25 44
73863
4
26137
81611
6
18389
07748
2
92252
47
14
34 8
25 62
73882
4
26118
81638
6
18362
07756
2
92244
9. 92235
46
45
15
7 34
4 26
9. 73901
5
10. 26099
9. 81666
/
10. 18334
10. 07765
2
16
33 52
26 8
73921
5
26079
81693
7
18307
07773
2
92227
44
17
33 44
26 16
73940
5
26060
81721
8
18279
07781
2
92219
43
18
33 36
26 24
73959
6
26041
81748
8
18252
07789
3
92211
42
19
33 28
26 32
73978
6
26022
81776
9
18224
07798
3
92202
41
20
7 33 20
4 26 40
9. 73997
6
10. 26003
9. 81803
9
10. 18197
10. 07806
3
9. 92194
40
21
33 12
26 48
74017
7
25983
81831
10
18169
07814
3
92186
i^9
22
33 4
26 56
74036
7
25964
81858
10
18142
07823
3
92177
.38
23
32 56
27 4
74055
7
25945
81886
11
18114
07831
3
92169
37
24
32 48
27 12
74074
8
25926
81913
11
18087
07839
3
92161
36
25
7 32 40
4 27 20
9. 74093
8
10. 25907
9. 81941
11
10. 18059
10. 07848
3
9. 92152
26
32 32
27 28
74113
8
25887
81968
12
18032
07856
4
92144
34
27
32 24
27 36
74132
9
25868
81996
12
18004
07864
4
92136
33
28
32 16
27 44
74151
9
25849
82023
13
17977
07873
4
92127
32
29
30'
32 8
27 52
74170
9
25830
10. 25811
82051
13
17949
07881
4
4
92119
31
7 32
4 28
9. 74189
10
9. 82078
14
10. 17922
10. 07889
9.92111
30
31
31 52
28 8
74208
10
25792
82106
14
17894
07898
4
92102
29
32
31 44
28 16
74227
10
25773
82133
15
17867
07906
4
92094
28
33
31 36
28 24
74246
10
25754
82161
15
17839
07914
5
92086
27
34
31 28
28 32
74265
11
11
25735
82188
16
17812
07923
5
92077
26
35
7 31 20
4 28 40
9. 74284
10. 25716
9. 82215
16
10. 17785
10. 07931
5
9. 92069
25
36
31 12
28 48
74303
11
25697
82243
16
17757
07940
5
92060
24
37
31 4
28 56
74322
12
25678
82270
17
17730
07948
5
92052
23
38
30 56
29 4
74341
12
25659
82298
17
17702
07956
5
92044
22
39
40
30 48
7 30 40
29 12
4 29 20
74360
9. 74379
12
25640
82325
18
17675
07965
5
92035
9. 92027
21
20
13
10. 25621
9. 82352
18
10. 17648
10. 07973
6
41
30 32
29 28
74398
13
25602)
. 82380
19
17620
07982
6
92018
19
42
30 24
29 36
74417
13
25583
82407
19
17593
07990
6
92010
18
43
30 16
29 44
74436
14
25564
82435
20
17565
07998
6
92002
17
44
30 8
29 52
74455
14
25545
82462
20
17538
08007
6
91993
16
16
45
7 30
4 30
9. 74474
14
10. 25526
9. 82489
21
10. 17511
10. 08015
6
9.91985
46
29 52
30 8
74493
15
25507
82517
21
17483
08024
6
91976
14
4V
29 44
30 16
74512
15
25488
82544
22
17456
08032
7
91968
13
48
29 36
30 24
74531
15
25469
82571
22
17429
08041
7
91959
12
49
29 28
30 32
74549
16
25451
82599
22
17401
08049
7
91961
11
50
7 29 20
4 30 40
9. 74568
16
10. 25432
9. 82626
23
10. 17374
10. 08058
7
9. 91942
10
51
29 12
30 48
74587
16
25413
82653
23
17347
08066
7
91934
9
52
29 4
30 56
74606
17
25394
82681
24
17319
08075
7
91925
8
53
28 56
31 4
74625
17
25375
82708
24
17292
08083
7
91917
7
54
28 48
31 12
74644
17
25356
10. 25338
82735
25
25
17265
08092
8
8
91908
9.91900
6
5
55
7 28 40
4 31 20
9. 74662
17
9. 82762
10.17238
10. 08100
56
28 32
31 28
74681
18
25319
82790
26
17210
08109
8
91891
4
57
28 24
31 36
74700
18
25300
82817
26
17183
08117
8
91883
3
58
28 16
31 44
74719
18
25281
82844
27
17156
08126
8
91874
2
59
28 8
31 52
74737
19
25263
82871
27
17129
08134
8
91866
1
60
28
32
74756
19
25244
82899
27
17101
08143
8
91857
M.
Hour p. M.
Hour A.M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
128°
A
A
B
B
C
C 56° 1
Seconds of time
1»
2-
8>
4"
5"
6>
7'
fA
Prop, parts of cols. B
C
2
3
1
B
7
2
7
10
3
10
14
4
12
17
B
14
21
6
17
24
7
Page 806]
TABLE U.
Log. Sines, Tangents, and Secants.
84°
A
A
B
B
C
C 145°
M.
Hour A.M.
Hour p. M.
Sine.
Di£E.
Cosecant
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
M.
7 28
4 32
9. 74756
10. 25244
9. 82899
10. 17101
10.08143
9. 91857
60
1
27 52
32 8
74775
25225
82926
17074
08151
91849
.59
2
27 44
32 16
74794
1
25206
82953
1
17047
08160
91840
58
3
27 36
32 24
74812
1
25188
82980
1
17020
08168
91832
57
4
27 28
32 32
74831
1
25169
83008
2
16992
08177
91823
56
5
6
7 27 20
27 12
4 32 40
32' 48
9. 74850
74868
2
2
10. 25150
25132
9. 83035
8.3062
2
3
10. 16965
16938
10. 08185
08194
9. 91815
91806
55
.54
7
27 4
32 56
74887
2
25113
83089
3
16911
08202
91798
53
8
26 56
33 4
74906
2
25094
83117
4
16883
08211
91789
.52
9
26 48
33 12
74924
3
25076
83144
4
16856
08219
91781
51
50
10
7 26 40
4 33 20
9. 74943
3
10. 25057
9. 83171
5
10. 16829
10. 08228
9.91772
11
26 32
33 28
74961
3
25039
83198
16802
08237
2
91763
49
12
26 24
33 36
74980
4
25020
83225
o
16775
08245
2
91755
48
13
26 16
33 44
74999
4
25001
8.3252
6
16748
08254
2
91746
47
14
15
26 8
33 52
75017
4
24983
83280
6
16720
08262
10. 08271
2
2
91738
9. 91729
46
45
7 26
4 34
9. 75036
5
10. 24964
9. 83307
7
10. 16693
16
25 52
34 8
75054
5
2494(')
83334
i
16666
08280
2
91720
44
17
25 44
34 16
75073
5
24927
83361
8
16639
08288
2
91712
43
18
25 36
34 24
75091
6
24909
83388
8
16612
08297
3
91703
42
19
20
25 28
34 32
75110
6
24890
83415
9
16585
08305
10. 68314
3
3
91695
41
40
7 25 20
4 34 40
9. 75128
6
10. 24872
9. 8;W42
9
10. 16558
9. 91686
21
25 12
34 48
75147
6
24853
83470
9
16530
08323
3
91677
39
22
25 4
34 56
75165
7
24835
8.3497
10
16503
08331
3
91669
38
28
24 56
35 4
75184
7
24816
83524
10
16476
08340
3
91660
37
24
24 48
35 12
75202
7
24798
83551
11
16449
08349
3
91651
36
.35
25
7 24 40
4 35 20
9. 75221
8
10. 24779
9. 83578
11
10. 16422
10. 08357
4
9. 91643
26
24 32
35 28
75239
. 8
24761
83605
12
16395
08366
4
91634
34
27
24 24
35 36
75258
8
24742
83632
12
16368
08375
4
91625
33
28
24 16
35 44
75276
9
24724
83659
13
16341
08383
4
91617
32
29
24 8
35 52
75294
9
24706
83686
13
16314
08392
4
91608
31
30
30
7 24
4 36
9. 75313
9
10. 24687
9. 83713
14
10. 16287
10. 08401
4
9. 91599
31
23 52
36 8
75331
9
24669
83740
14
16260
08409
4
91-591
29
32
23 44
36 16
75350
10
24650
83768
14
16232
08418
5
91582
28
33
23 36
36 24
75368
10
24632
83795
15
16205
08427
5
91573
27
34
35
23 28
36 32
75386
10
11
24614
83822
15
16
16178
08435
5
91565
26
25
7 23 20
4 36 40
9. 75405
10. 24595
9. 83849
10. 16151
10. 08444
5
9. 91556
36
23 12
36 48
75423
11
24577
83876
16
16124
08453
5
91.547
24
37
23 4
36 56
75441
11
24559
8.3903
17
16097
08462
5
91538
23
38
22 56
37 4
75459
12
24541
8.3930
17
16070
08470
5
91530
22
39
22 48
37 12
75478
12
24522
10. 24504
8,3957
18
16043
08479
6
91521
21
20
40
7 22 40
4 37 20
9. 75496
12
9. 83984
18
10.16016
10. 08488
6
9. 91512
41
22 32
37 28
75514
13
24486
84011
18
15989
08496
6
91504
19
42
22 24
37 36
75533
13
24467
84038
19
15962
08505
6
91495
18
43
22 16
37 44
75551
13
24449
84065
19
15935
08514
6
91486
17
44
22 8
37 52
75569
13
14
24431
84092
20
15908
08523
6
91477
16
45
7 22
4 38
9. 75587
10. 24413
9. 84119
20
10. 15881
10. 08631
7
9. 91469
15
46
21 52
38 8
75605
14
24395
84146
21
15854
08.540
/
91460
14
47
21 44
38 16
75624
14
24376
84173
21
15827
08549
/
91451
13
48
21 36
38 24
75642
15
24358
84200
22
15800
08558
7
91442
12
49
21 28
38 32
4 38 40
75660
15
15
24340
10. 24322
84227
22
15773
08567
7
91433
11
50
7 21 20
9. 75678
9. 84254
23
10. 15746
10. 08575
7
9. 91425
10
51
21 12
38 48
75696
16
24304
84280
23
15720
08584
7
91416
9
52
21 4
38 56
75714
16
24286
84307
23
15693
08593
8
91407
8
53
20 56
39 4
75733
16
24267
84334
24
15666
08602
8
91398
7
54
55
20 48
39 12
75751
17
17
24249
10. 24231
84,361
24
25
15639
10. 15612
08611
8
91389
6
7 20 40
4 39 20
9. 75769
9.84388
10. 08619
8
9. 91381
5
56
20 32
39 28
75787
17
24213
84415
25
15585
08628
8
91372
4
57
20 24
39 36
75805
17
24195
84442
26
15558
08637
8
91363
3
58
20 16
39 44
75823
18
24177
84469
26
15531
08646
8
91354
2
59
20 8
39 52
75841
18
24159
84496
27
15504
08655
9
91345
1
60
20
40
75859
18
24141
84523
27
15477
08664
9
91336
M.
M.
Hour p. M.
Hour A.M.
Cosine.
Did.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
124'
>
A
A
B
B
C
C 65 1
Seconds oj time 1 X'
2'
3<
f
5"
6<
J-
A 2
Prop, parts of cols. ^B 3
CI
5
7
2
7
10
3
9
14
4
11
17
5
14
20
7
16
24
8
TABLE 44.
[Page 807
T-og.
Sines, Tangents, and Secants.
Si"
A
A
B
B
C
C 144°
M.
Hour A.M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent. DifE.
Cotangent.
Secant.
Diff. 1 Cosine.
M.
7 20
4 40
9. 75859
10. 24141
9.84523
10. 1.5477
10. 08664
9. 91336
60
1
19 52
40 8
75877
24123
84550
15450
08672
91328
59
?,
19 44
40 16
75895
1
24105
84576
1
15424
08681
91319
58
3
19 36
40 24
75913
1
24087
84603
1
15397
08690
91310
57
4
19 28
40 32
75931
9. 75949
1
24069
84630
2
2
15370
08699
91301
56
5
7 19 20
4 40 40
1
10. 24051
9. 84657
10. 15343
10. 08708
9. 91292
55
fi
19 12
40 48
75967
2
24033
84684
3
15316
08717
91283
54
7
19 4
40 56
75985
2
24015
84711
3
15289
08726
91274
53
8
18 56
41 4
76003
2
23997
84738
4
15262
08734
91266
52
9
10
18 48
41 12
76021
3
23979
84764
4
15236
08743
91257
51
7 18 40
4 41 20
9. 76039
3
10. 23961
9. 84791
4
10. 15209
10. 08752
2
9. 91248
50
11
18 32
41 28
76057
3
23943
84818
5
15182
08761
2
91239
49
1ft
18 24
41 36
76075
4
23925
84845
5
15155
08770
2
91230
48
13
18 16
41 44
76093
4
23907
84872
6
15128
08779
2
91221
47
14
15
18 8
41 52
76111
4
23889
84899
6
15101
08788
2
91212
4«
45
7 18
4 42
9. 76129
4
10. 23871
9. 84925
7
10. 15075
10. 08797
2
9. 91203
Ifi
17 52
42 8
76146
5
23854
84952
/
1.5048
08806
2
91194
44
17
17 44
42 16
76164
5
23836
84979
8
15021
08815
3
91185
43
18
17 36
42 24
76182
5
23818
85006
8
14994
08824
3
91176
42
19
20
17 28
7 17 20
42 32
4 42 40
76200
6
23800
10. 23782
85033
9. 85059
8
9
14967
08833
3
91167
41
9. 76218
6
10. 14941
10. 08842
3
9. 91158
40
21
17 12
42 48
76236
6
23764
85086
9
14914
08851
3
91149
39
22
17 4
42 56
76253
6
23747
85113
10
14887
08^59
3
91141
38
23
16 56
43 4
76271
i
23729
85140
10
14860
08868
3
91132
37
24
25
16 48
43 12
76289
7
23711
85166
9. a5193
11
11
14834
08877
4
4
91123
36
35
7 16 40
4 43 20
9. 76307
7
10. 23693
10. 14807
10. 08886
9.91114
26
16.32
43 28
76324
8
23676
85220
12
14780
08895
4
91105
34
27
16 24
43 36
76342
8
23t358
85247
12
14753
08904
4
91096
33
28
16 16
43 44
76360
8
23640
85273
12
14727
08913
4
91087
32
29
30
16 8
43 52
76378
9
9
23622
10. 23605
85.300
9. 85327
13
14700
08922
4
91078
31
7 16
4 44
9. 76395
13
10. 14673
10. 08931
5
9. 91069
30
31
15 52
44 8
76413
9
23587
85354
14
14646
08940
5
91060
29
32
15 44
44 16
76431
9
23569
85380
14
14620
08949
5
91051
28
33
15 36
44 24
76448
10
23552
85407
15
14593
08958
5
91042
27
34
35
15 28
44 32
76466
10
2.3534
85434
15
14566
08967
5
91033
26
7 15 20
4 44 40
9.76484
10
10. 23516
9. 8.5460
16
10. 14540
10. 08977
5
9. 91023
25
36
15 12
44 48
76501
11
2;«99
85487
16
14513
08986
5
91014
24
37
15 4
44 56
76519
11
23481
8.5514
16
14486
08995
6
91005
23
38
14 56
45 4
76537
11
2.'«63
8,5540
17
14460
09004
6
90996
22
39
14 48
45 12
76554
12
12
23446
85567
9. 85594
17
14433
09013
6
6
90987
21
20
40
7 14 40
4 45 20
9. 76572
10. 23428
18
10. 14406
10. 09022
9.90978
41
14 32
45 28
76590
12
23410
85620
18
14380
09031
6
90969
19
42
14 24
45 36
76607
12
2.3393
85647
19
14353
09040
6
90960
18
43
14 16
45 44
76625
13
23375
85674
19
14.326
09049
6
90951
17
44
14 8.
45 52
76642
9.76660
13
2.3358
85700
20
14300
09058
7
90942
16
15
45
7 14
4 46
13
10. 23340
9. a5727
20
10. 14273
10.09067
7
9.90933
46
13 52
46 8
76677
14
2,3323
857.54
20
14246
09076
7
90924
14
47
13 44
46 16
76695
14
23305
85780
21
14220
09085
7
90915
13
48
13 36
46 24
76712
14
23288
85807
21
14193
09094
7
90906
12
49
50
13 28
46 32
76730
14
23270
a5834
^9. 85860
22
14166
09104
10.09113
7
8
90896
11
10
7 13 20
4 46 40
9. 76747
15
10. 23253
22
10. 14140
9. 90887
51
13 12
46 48
76765
15
232^5
85887
23
14113
09122
8
90878
9
52
13 4
46 56
76782
15
23218
a5913
23
14087
09131
8
90869
8
53
12 56
47 4
76800
16
23200
85940
24
14060
09140
8
90860
7
54
55
12 48
7 12 40
47 12
4 47 20
76817
9. 76835
16
16
23183
10. 23165
85967
9.85993
24
24
14033
10. 14007
09149
8
8
90851
9. 90842
6
5
10. 09158
56
12 32
47 28
76852
17
23148
86020
25
13980
09168
8
90832
4
57
12 24
47 36
76870
17
23130
86046
25
13954
09177
9
90823
3
58
12 16
47 44
76887
17
23113
86073
26
13927
09186
9
90814
2
59
12 8
47 52
76904
17
2.3096
86100
26
13900
09195
9
90805
1
60
M.
12
48
76922
18
23078
86126
27
13874
09204
9
90796
M.
Hour p. M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
lib''
A
A
B
B
C
C 54° 1
Seconds of time 1'
2-
8«
i-
5<
6-
7-
A 2
Prop, parts of cols.' B 3
[c 1
4
7
2
3
9
13
5
11
17
6
13
20
16
23
8
Page 808]
TABLE U.
Log. Sines, Tangents, and Secants.
86°
A
A
B
B
C
C 143°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Ck)secant.
Tangent.
Diff.
Cotangent.
Secant.
Diff. Cosine. 1
M.
7 12
4 48
9. 76922
10. 23078
9. 86126
10. 13874
10. 09204
9. 90796
60
1
11 52
48 8
76939
23061
86153
13847
09213
90787
59
2
11 44
48 16
76957
1
23043
86179
1
13821
09223
90777
58
8
11 36
48 24
76974
1
23026
86206
1
13794
09232
90768
57
4
11 28
48 32
76991
1
23009
86232
2
13768
09241
90759
56
55
5
7 11 20
4 48 40
9.77009
1
10. 22991
9. 86259
2
10. 13741
10. 09250
9. 90750
6
11 12
48 48
77026
2
22974
86285
3
13715
09259
90741
54
7
11 4
48 56
77043
2
22957
86312
3
13688
09269
90731
53
8
10 56
49 4
77061
2
22939
86338
4
13662
09278
90722
52
9
10
10 48
49 12
77078
3
3
22922
10. 22905
86365
9. 86392
4
4
13635
09287
90713
51
50
7 10 40
4 49 20
9. 77095
10. 13608
10. 09296
2
9. 90704
11
10 32
49 28
77112
3
22888
86418
5
13582
09306
2
90694
49
12
10 24
49 36
77130
3
22870
86445
5
13555
09315
2
90685
48
13
10 16
49 44
77147
4
22853
86471
6
13529
09324
2
90676
47
14
10 8
49 52
77164
4
22836
86498
6
13502
09.333
2
2
90667
46
45
15
7 10
4 50
9. 77181
4
10. 22819
9. 86524
7
10. 13476
10. 09343
9. 90657
16
9 52
50 8
77199
5
22801
86551
7
13449
09352
2
90648
44
17
9 44
50 16
77216
5
22784
86577
7
13423
09361
3
906.39
43
18
9 36
50 24
77233
5
22767
86603
8
13397
09370
3
90630
42
19
9 28
50 32
77250
5
22750
86630
8
13370
09380
3
90620
41
20
7 9 20
4 50 40
9. 77268
6
10. 22732
9. 86656
9
10. 13344
10. 09389
3
9.906U
40
21
9 12
50 48
77285
6
22715
86683
9
13317
09398
3
90602
39
22
9 4
50 56
77302
6
22698
86709
10
13291
09408
3
90592
38
23
8 56
51 4
77319
7
22681
86736
10
13264
09417
4
90583
37
24
25
8 48
51 12
77336
7
22664
86762
11
13238
09426
4
90574
36
35
7 8 40
4 51 20
9. 77353
7
10. 22647
9. 86789
11
10. 13211
10. 09435
4
9. 90565
20
8-32
51 28
77370
7
22630
86815
11
13185
09445
4
90555
34
27
8 24
51 36
77387
8
22613
86842
12
13158
09454
4
90546
33
28
8 16
51 44
77405
8
22595
86868
12
13132
09463
4
90537
32
29
8 8
51 52
77422
8
22578
86894
13
13
13106
09473
5
90527
31
30
30
7 8
4 52
9. 77439
9
10. 22561
9. 86921
10. 13079
10. 09482
5
9.90518
31
7 52
52 8
77456
9
22544
86947
14
13053
09491
5
90509
29
32
7 44
52 16
77473
9
22527
86974
14
13026
09501
5
90499
28
33
7 36
52 24
77490
9
22510
87000
15
13000
09510
5
90490
27
34
7 28
52 32
77507
10
10
22493
87027
15
. 12973
09520
5
90480
26
25
35
7 7 20
4 52 40
9. 77524
10. 22476
9. 87053
15
10. 12947
10. 09529
5
9. 90471
36
7 12
52 48
77541
10
22459
87079
16
12921
09538
6
90462
24
37
7 4
52 56
77558
11
22442
87106
16
12894
09548
6
90452
23
38
6 56
53 4
77575
11
22425
87132
17
12868
09557
6
90443
22
39
6 48
53 12
77592
11
11
22408
10. 22391
87158
17
12842
09566
6
90434
21
20
40
7 6 40
4 53 20
9.77609
9.87185
18
10. 12815
10. 09576
6
9. 90424
41
6 32
53 28
77626
12
22374
87211
18
12789
09585
6
90415
19
42
6 24
53 36
77643
12
22357
87238
18
12762
09595
7
90405
18
43
6 16
53 44
77660
12
22340
87264
19
12736
09604
7
90396
17
44
6 8
53 52
77677
13
13
22323
10. 22306
87290
19
12710
09614
7
90386
9. 90377
16
15
45
7 6
4 54
9. 77694
9. 87317
20
10. 12683
10. 09623
7
46
5 52
54 8
77711
13
22289
87343
20
12657
09632
7
90368
14
47
5 44
54 16
77728
13
22272
87369
21
12631
09642
7
90358
13
48
5 36
54 24
77744
14
22256
87396
21
12604
09651
7
90349
12
49
5 28
54 32
77761
14
22239
87422
22
12578
09661
8
90339
11
10
50
7 5 20
4 54 40
9. 77778
14
10. 22222
9. 87448
22
10. 12552
10. 09670
8
9. 90330
51
5 12
54 48
77795
15
22205
87475
22
12525
09680
8
90320
9
52
5 4
54 56
77812
15
22188
87501
23
12499
09689
8
90311
8
53
4 56
55 4
77829
15
22171
87527
23
12473
09699
8
90301
7
54
4 48
55 12
77846
15
22154
87554
24
12446
10. 12420
09708
8
9
90292
9. 90282
6
55
7 4 40
4 55 20
9. 77862
16
10.22138
9. 87580
24
10. 09718
5
56
4 32
55 28
77879
16
22121
87606
25
12394
09727
9
90273
4
57
4 24
55 36
77896
16
22104
87633
25
12367
09737
■9
90263
3
58
4 16
55 44
77913
16
22087
87659
26
12,341
09746
9
90254
2
59
4 8
55 52
77930
17
22070
87685
26
12315
09756
9
90244
1
60
4
56
77946
17
22054
87711
26
12289
09765
9
90235
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent.
DiiT.
Tangent.
Cosecant.
Diff.
Sine.
126<
)
A
A
B
B
C
(■ 58° 1
Seconds of time ...
1<
3*
8>
4-
6<
6"
7-
Prop, parts of cols.
Is
2
3
1
4
7
2
6
10
4
9
13
6
11
17
6
13
20
7
16
23
8
TABLE U.
[Page 809
Log.
Sines, Tangents, and Secants.
8!°
A
A B
B
C
C 142°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Difl.
Cosine.
M.
7 4
4 56
9. 77946
10. 22054
9. 87711
10. 12289
10. 09765
9. 90235
60
1
3 52
56 8
77963
22037
87738
- 12262
09775
90225
59
2
3 44
56 16
77980
1
22020
87764
1
12236
09784
90216
58
3
3 36
56 24
77997
1
22003
87790
1
12210
09794
90206
57
4
5
3 28
7 3 20
56 32
78013
1
21987
87817
2
2
12183
09803
90197
56
4 56 40
9. 78030
1
10. 21970
9. 87843
10. 12157
10. 09813
9. 90187
55
6
3 12
56 48
78047
2
21953
87869
3
12131
09822
90178
,54
7
3 4
56 56
78063
2
21937
87895
3
12105
09832
90168
53
8
2 56
57 4
78080
2
21920
87922
3
12078
09841
90159
52
9
2 48
57 12
78097
2
21903
87948
4
12052
09851
90149
51
50
10
7 2 40
4 57 20
9. 78113
3
10. 21887
9. 87974
4
10. 12026
10. 09861
2
9. 90139
11
2 32
57 28
78130
3
21870
88000
5
12000
09870
2
90130-
49
12
2 24
57 36
78147
3
21853
88027
11973
09880
2
90120
48
13
2 16
57 44
78163
4
21837
88053
6
11947
09889
2
90111
47
14
2 8
57 52
78180
4
21820
88079
6
7
11921
09899
2
90101
46
45
15
7 2
4 58
9. 78197
4
10. 21803
9. 88105
10. 11895
10. 09909
2
9. 90091
16
1 52
58 8
78213
4
21787
88131
7
11869
09918
3
90082
44
17
1 44
58 16
78230
5
21770
88158
7
11842
09928
3
90072
43
18
1 36
58 24
78246
5
21754
88184
8
11816
09937
3
90063
42
19
1 28
58 32
78263
5
21737
88210
8
11790
09947
3
90053
9.90043
41
40
20
7 1 20
4 58 40
9. 78280
5
10. 21720
9. 88236
9
10. 11764
10. 09957
3
21
1 12
58 48
78296
6
21704
88262
9
11738
09966
3
90034
.39
22
1 4
58 56
78313
6
21687
88289
10
11711
09976
4
90024
38
23
56
59 4
78329
6
21671
88315
10
1168,5
09986
4
90014
37
24
48
59 12
78346
7
21654
88341
10
11659
09995
4
90005
36
35
25
7 40
4 59 20
9. 78362
7
10. 21638
9. 88367
11
10. 11633
10. 10005
4
9. 89995
26
32
59 28
78379
7
21621
88393
11
11607
10015
4
89985
.34
27
24
59 36
78395
7
21605
88420
12
11580
10024
4
89976
33
28
16
59 44
78412
8
21588
88446
12
11554
10034
5
89966
32
29
30
8
59 52
78428
8
21572
88472
13
11528
10044
5
89956
9. 89947
31
30
7
5
9. 78445
8
10. 21555
9. 88498
13
10. 11502
10.10053
5
31
6 59 52
8
78461
9
21539
88524
14
11476
10063
5
89937
29
32
59 44
16
78478
9
21522
88550
14
11450
10073
5
89927
28
33
59 36
24
78494
9
21506
88577
14
11423
10082
5
89918
27
34
35
59 28
32
78510
9
21490
88603
15
11397
10092
5
89908
26
25
6 59 20
5 40
9. 78527
10
10. 21473
9. 88629
10. 11371
10. 10102
6
9. 89898
36
59 12
48
78543
10
21457
88656
16
11345
10112
6
89888
24
37
59 4
56
. 78560
10
21440
88681
16
11319
10121
6
89879
23
38
58 56
1 4
78576
10
21424
88707
17
11293
10131
6
89869
22
39
58 48
1 12
78592
11
11
21408
88733
17
11267
10141
6
89859
9. 89849
21
20
40
6 58 40
5 1 20
9. 78609
10. 21391
9. 88759
17
10. 11241
10. 10151
6
41
58 32
1 28
78625
11
21375
88786
18
11214
10160
7
89840
19
42
58 24
1 36
78642
12
21358
88812
18
11188
10170
7
89830
18
43
58 16
1 44
78658
12
21342
88838
19
11162
10180
7
89820
17
44
58 8
1 52
78674
12
21326
88864
19
11136
10.11110
10190
10. 10199
7
7
89810
9. 89801
16
15
45
6 58
5 2
9. 78691
12
10. 21309
9. 88890
20
46
57 52
2 8
78707
13
21293
88916
20
11084
10209
7
89791
14
47
57 44
2 16
78723
13
21277
88942
20
11058
10219
8
89781
13
48
57 36
2 24
78739
13
21261.
88968
21
11032
10229
8
89771
12
49
50
57 28
2 32
78756
9. 78772
13
21244
88994
9. 89020
21
22
110O6
10. 10980
10239
8
89761
11
10
6 57 20
5 2 40
14
10. 21228
10. 10248
8
9. 89752
51
57 12
2 48
78788
14
21212
89046
22
10954
10258
8
89742
9
52
57 4
2 56
78805
14
21195
89073
23
10927
10268
8
89732
8
53
56 56
3 4
78821
15
21179
89099
23
10901
10278
9
89722
7
54
55
56 48
3 12
78837
15
21163
10.21147
89125
9. 89151
24
24
10875
10. 10849
10288
10. 10298
9
9
89712
6
5
6 56 40
5 3 20
9. 78853
15
9. 89702
56
56 32
3 28
78869
15
21131
89177
24
10823
10307
9
89693
4
57
56 24
3 36
78886
16
21114
89203
25
10797
10317
9
89683
3
58
56 16
3 44
78902
16
21098
89229
25
10771
10327
9
89673
*>
59
56 8
3 52
78918
16,
21082
89255
26
10745
10337
10
89663
1
60
56
4
78934
16
21066
89281
26
10.719
10347
10
89653
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Difl.
Sine.
127°
A
A B
B
C
C 52° 1
Seconds of time
l-
2'
8<
4'
5>
6>
7-
(A
Prop, parts of eols.<B
Ic
2
3
1
1
7
2
6
10
8
13
5
10
16
G
12
20
7
14
23
8
Page 810]
TABLE U.
Log. Sines, Tangents, and Secants.
88°
A
A
B
B
• C
141°
M.
Hour A. M.
Hour p. M.
Sine.
Did.
Coseeaut.
Tangent.
Difl.
Cotaugent,
Secant.
Difl.
Cosine.
M.
6 56
5 4
9. 78934
10. 21066
9. 89281
10. 10719
10. 10347
9.89653
60
1
00 52
4 8
78950
.0
21050
89307
10693
10357
89643
59
2
55 44
4 16
78967
1
21033
89333
1
10667
10367
89633
58
8
55 36
4 24
78983
1
21017
89359
1
10641
10376
89624
57
4
5
55 28
4 32
78999
1
21001
89385
2
2
10615
10. 10589
10386
10. 10396
89614
56
55
6 55 20
5 4 40
9. 79015
1
10. 20985
9. 89411
9. 89604
6
55 12
~ 4 48
79031
2
20969
89437
3
10563
10406
89594
54
7
55 4
4 56
79047
2
20953
89463
3
10537
10416
89584
53
8
54 56
5 4
79063
2
20937
89489
3
10511
10426
89574
52
9
54 48
5 12
79079
2
20921
10. 20905^
89515
9. 89541
4
10485
10436
89564
9. 89554
51
50
10
6 54 40
5 5 20
9. 79095
3
4
10. 10459
10. 10446
n
54 32
5 28
79111
3
20889
89567
5
10433
10456
89544
49
12
54 24
5 36
79128
3
20872
89593
5
10407
10466
89534
48
IS
54 16
5 44
79144
3
20856
89619
6
10381
10476
2
89524
47
14
54 8
5 52
79160
4
20840
89645
6
6
10355
10486
2
89514
46
15
6 54
5 6
9. 79176
4
10. 20824
9. 89671
10. 10329
10. 10496
3
9. 89504
45
16
53 52
6 8
79192
4
20808
89697
7
10303
10505
3
89495
44
17
53 44
6 16
79208
5
20792
89723
(
10277
10515
3
89485
43
18
53 36
6 24
79224
20776
89749
8
10251
10525
3
89475
42
19
53 28
6 32
79240
5
20760
89775
8
9
10225
10535
3
89465
41
20
6 53 20
5 6 40
9. 79256
5
10. 20744
9. 89801
10. 10199
10. 10545
3
9. 89455
40
21
53 12
6 48
79272
6
20728
89827
9
10173
10555
4
89445
39
22
53 4
6 56
79288
6
20712
89853
10
10147
10565
4
89435
38
23
52 56
7 4
79304
6
20696
89879
10
10121
10575
4
89425
37
24
52 48
7 12
79319
6
20681
10.'20665
89905
10
10095
10585
4
89415
36
25
6 52 40
5 7 20
9. 79335
7
9. 89931
11
10. 10069
10. 10595
4
9. 89405
35
26
52 32
7 28
79351
7
20649
89957
11
10043
10605
4
89395
34
27
52 24
7 36
79367
7
20633
89983
12
10017
10615
89385
33
28
52 16
7 44
79383
7
20617
90009
12
09991
10625
o
89375
32
29
52 8
7 52
79399
8
20601
10. 20585
90035
13
09965
10636
5
5
89364
31
80
6 52
5 8
0. 79415
8
9. 90061
13
10. 09939
10. 10646
9. 89354
30
31
51 52
8 8
79431
8
20569
90086
13
09914
10656
5
89344
29
32
51 44
8 16
79447
8
20553
90112
14
09888
10666
5
89334
28
33
51 36
8 24
79463
9
20537
90138
14
09862
10676
6
89324
27
34
51 28
8 32
79478
9
20522
90164
15
09836
10686
6
89314
26
25
35
6 51 20
5 8 40
9. 79494
9
10. 20506
9. 90190
15
10. 09810
10. 10696
6
9. 89304
36
51 12
8 48
79510
10
20490
90216
16
09784
10706
6
89294
24
37
51 4
8 56
79526
10
20474
90242
16
09758
10716
6
89284
23
38
50 56
9 4
79542
10
20458
90268
16
09732
10726
6
89274
22
39
40
50 48
9 12
79558
10
20442
90294
9. 90320
17
17
09706
10. 09680
10736
7
89264
9. 89254
21
20
6 50 40
5 9 20
9. 79573
11
10. 20427
10. 10746
7
41
50 32
9 28
79589
11
20411
90346
18
09654
10756
7
89244
19
42
50 24
9 36
79605
11
20395
90371
18
09629
10767
7
89233
18
43
50 16
9 44
79621
11
20379
90397
19
09603
10777
7
89223
17
44
45
50 8
9 52
79636
12
20364
90423
9.90449
19
09577
10787
/
89213
16
15
6 50
5 10
9. 79652
12
10. 20348
19
10.09551
10. 10797
8
9. 89203
46
49 52
10 8
79668
12
20332
90475
20
09525
10807
8
89193
14
47
49 44
10 16
79684
12
20316
90501
20
09499
10817
8
89183
13
48
49 36
10 24
79699
13
20301
90&27
21
09473
10827
8
89173
12
49
50
49 28
10 32
79715
13
20285
90553
21
09447
10838
8
89162
11
10
6 49 20
5 10 40
9. 79731
13
10. 20269
9. 90578
22
10. 09422
10. 10848
8
9. 89152
51
49 12
10 48
79746
14
20254
90604
22
09396
10858
9
89142
9
52
49 4
10 56
79762
14
20238
90630
22
09370
10868
9
89132
8
53
48 56
11 4
79778
14
20222
90656
23
09344
10878
9
89122
I
54
48 48
11 12
79793
14
20207
90682
23
24
09318
10888
9
89112
6
5
55
6 48 40
5 11 20
9. 79809
15
10. 20191
9. 90708
10. 09292
10. 10899
9
9. 89101
56
48 32
11 28
79825
15
20175
90734
24
09266
10909
9
89091
4
57
48 24
11 36
79840
15
20160
90759
25
09241
10919
10
89081
3
58
48 16
11 44
79856
15
20144
90785
25
09215
10929
10
89071
2
59
48 8
11 52
79872
16
20128
90811
26
09189
10940
10
89060
1
60
48
12
79887^
16
20113
90837
26
09163
10950
10
89050
M.
M.
Hour P.M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
128
5
A
A
B
B
C
c
ol°
Seconds of time
l-
*■
8>
4-
6<
6«
J«
(A
Prop, parts of cols.-iB
Ic
2
3
1
4
6
3
6
10
4
8
13
6
10
16
6
12
19
8
14
23
9
TABLE 44.
[Page 811
'Mg. Sines, Tangent.^, and Secants.
89°
A
A
B
B
C
C 140°
M.
Hour A. M.
Hour p. M.
Sine.
Difl.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Difl.
Cosine.
M.
6 48
5 12
9. 79887
10. 20113
9. 90837
10. 09163
10. 10950
9. 89050
60
1
47 52
12 8
79903
20097
90863
09137
10960
89040
59
2
47 44
12 16
79918
1
20082
90889
1
09111
10970
89030
58
3
47 36
12 24
79934
1
20066
90914
1
09086
10980
89020
0/
4
5
47 28
12 32
79950
1
20050
10. 20035
90940
2
09060
10991
89009
56
55
6 47 20
5 12 40
9.79965
1
9. 90966
2
10. 09034
10. 11001
9. 88999
6
47 12
12 48
79981
2
20019
90992
3
09008
11011
88989
54
7
47 4
12 56
79996
2
20004
91018
3
08982
11022
88978
53
8
46 56
13 4
80012
2
19988
91043
3
08957
11032
88968
52
9
46 48
13 12
80027
2
19973
91069
4
4
08931
10. 08905
11042
2
88958
51
50
10
6 46 40
5 13 20
9. 80043
3
10. 19957
9. 91095
10. 11052
2
9. 88948
n
46 32
13 28
80058
3
19942
91121
5
08879
11063
2
88937
49
12
46 24
13 36
80074
3
19926
91147
5
08853
11073
2
88927
48
13
46 16
13 44
80089
3
19911
91172
6
08828
11083
2
88917
47
14
46 8
13 52
80105
4
19895
91198
6
08802
11094
2
88906
46
45
15
6 46
5 14
9. 80120
4
10. 19880
9. 91224
6
10. 08776
10. 11104
3
9. 88896
It)
45 52
14 8
80136
4
19864
91250
7
08750
11114
3
88886
44
17
45 44
14 16
80151
4
19849
91276
7
08724
11125
3
88875
43
18
45 36
14 24
80166
5
19834
91301
8
08699
11135
3
88865
42
19
20
45 28
14 32
80182
9. 80197
.5
5
19818
10. 19803
91327
8
08673
11145
3
3
88855
41
40
6 45 20
5 14 40
9.91353
9
10. 08647
10.11156
9.88844
21
45 12
14 48
80213
5
19787
91379
9
08621
11166
4
88834
39
22
45 4
14 56
80228
6
19772
91404
9
08596
11176
4
88824
38
23
44 56
15 4
80244
6
19756
91430
10
08570
11187
4
88813
37
24
25
44 48
6 44 40
15 12
5 15 20
80259
6
19741
91456
10
08544
11197
4
4
88803
9. 88793
36
35
9. 80274
6
10. 19726
9. 91482
11
10. 08518
10. 11207
26
44 32
15 28
80290
7
19710
91507
11
08493
11218
5
88782
.34
27
44 24
15 36
80305
7
19695
91533
12
08467
11228
5
88772
33
28
44 16
15 44
80320
7
19680
91559
12
08441
11239
5
88761
32
29
30
44 8
6 44
15 52
80336
7
19664
91585
12
13
08415
11249
5
88751
31
30
5 16
9. 80351
8
10. 19649
9. 91610
10. 08390
10.11259
5
9. 88741
31
43 52
16 8
80366
8
19634
91636
13
08364
11270
5
88730
29
32
43 44
16 16
80382
8
19618
91662
14
08338
11280
6
88720
28
33
43 36
16 24
80397
8
19603
91688
14
08312
11291
6
88709
27
34
43 28
16 32
80412
9
19588
91713
15
08287
11301
6
88699
9. 88688
26
25
35
6 43 20
5 16 40
9. 80428
9
10. 19572
9. 91739
15
10. 08261
10. 11312
6
36
43 12
16 48
80443
9
19557
91765
15
08235
11322
6
88678
24
37
43 4
16 56
80458
9
19542
91791
16
08209
11332
6
88668
23
38
42 56
17 4
80473
10
19527
91816
16
08184
11343
7
88657
22
39
40
42 48
17 12
80489
10
19511
91842
9. 91868
17
17
08158
11353
7
88647
21
20
6 42 40
5 17 20
9. 80504
10
10. 19496
10. 08132
10. 11364
7
9. 88636
41
42 32
17 28
80519
10
19481
91893
18
08107
11374
7
88626
19
42
42 24
17 36
80534
11
19466
91919
18
08081
11385
7
88615
18
43
42 16
17 44
80550
11
19450
91945
18
08055
11395
7
88605
17
44
45
42 8
17 52
80565
11
19435
91971
19
08029
11406
8
88594
16
6 42
5 18
9.80580
12
10. 19420
9. 91996
19
10. 08004
10. 11416
8
9. 88584
15
46
41 52
18 8
80595
12
19405
92022
20
07978
11427
8
88573
14
47
41 44
18 16
80(510
12
19390
92048
20
07952
11437
8
88563
13
48
41 36
18 24
80625
12
19375
92073
21
07927
11448
8
88552
12
49
50
41 28
6 41 20
18 32
80641
13
19359
92099
21
07901
11458
9
9
88542
9. 88531
11
10
5 18 40
9.80656
13
10. 19344
9. 92125
21
10. 07875
10. 11469
51
41 12
18 48
80671
13
19329
92150
22
07850
11479
9
88521
9
52
41 4
18 56
80686
13
19314
92176
22
07824
11490
9
88510
8
53
40 56
19 4
80701
14
19299
92202
23
07798
11501
9
88499
7
54
55
40 48
6 40 40
19 12
80716
14
14
19284
92227
23
07773
11511
9
88489
6
5
5 19 20
9. 80731
10. 19269
9. 92253
24
10. 07747
10. 11522
10
9. 88478
56
40 32
19 28
80746
14
19254
92279
24
07721
11532
10
88468
4
57
40 24
19 36
80762
15
19238
92304
24
07696
11543
10
88457
3
58
40 16
19 44
80777
15
19223
92330
25
07670
11553
10
88447
2
59
40 8
19 52
80792
15
19208
92356
25
07644
11564
10
88436
1
60
40
20
80807
15
19193
92381
26
07619
11575
10
88425
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
M.
129'^
A
A
B
B
n
C 60° 1
Seconds of time 1 •
2'
S-
*'
o- 6-
T
fA 2
Prop, parts of cols.-(B 3
Ic 1
4
6
3
6
10
4
8
13
6
10 12
16 19
7 8
13
23
9
Page 812]
Log.
TABLE 44.
Sines, Tangents, and Secants.
40°
A
A
B B
C
C
139°
M.
M.
Hour A. M.
Hour p. M.
Sine. Diff.
Cosecant.
Tangent.
Diff.
Cotangent.
Secant.
Diff.
Cosine.
6 40
5 20
9. 80807
10. 19193
9. 92381
10. 07619
10. 11575
9. 88425
60
1
39 52
20 8
80822
19178
92407
07593
11585
88415
59
2
39 44
20 16
80837
19163
92433
1
07567
11596
88404
58
3
39 36
20 24
80852
19148
9245S
1
07542
11606
88394
57
4
39 28
20 32
80867
19133
92484
2
07516
10. 07490
11617
10. 11628
88383
56
5
6 39 20
5 20 40
9. 80882
10. 19118
9. 92510
2
9. 88372
.55
6
39 12
20 48
80897
19103
92535
3
07465
11638
88362
54
7
39 4
20 56
80912
2
19088
92561
3
07439
11649
-1
88351
53
8
38 56
21 4
80927
2
19073
92587
3
07413
11660
88340
52
9
38 48
21 12
80942
9. 80957
2
2
19058
92612
4
07388
10.07362
11670
2
88330
51
10
6 38 40
5 21 20
10. 19043
9. 92638
4
10. 11681
9. 88319
50
11
38 32
21 28
80972
3
19028
92663
5
07337
11692
2
88308
49
12
38 24
21 36
80987
3
19013
92689
07311
11702
2
88298
48
13
38 16
21 44
81002
3
18998
92715
6
07285
11713
2
88287
47
14
38 8
21 52
81017
9. 81032
3
18983
92740
6
07260
11724
3
3
88276
46
45
15
6 38
5 22
4
10. 18968
9. 92766
6
10. 07234
10.11734
9. 88266
16
37 52
22 8
81047
4
18953
92792
t
07208
11745
3
88255
44
17
37 44
22 16
81061
4
18939
92817
7
07183
11756
3
88244
43
18
37 36
22 24
81076
4
18924
92843
8
07157
11766
3
882.34
42
19
20
37 28
22 32
81091
5
18909
92868
8
07132
11777
3
4
88223
41
40
6 37 20
5 22 40
9. 81106
5
10. 18894
9. 92894
9
10. 07106
10. 11788
9.88212
21
37 12
22 48
81121
5
18879
92920
9
07080
11799
4
88201
39
22
37 4
22 56
81136
5
18864
92945
9
07055
11809
4
88191
38
23
36 56
23 4
81151
6
18849
92971
10
07029
11820
4
88180
37
24
36 48
23 12
81166
9. 81180
6
18834
92996
10
11
07004
11831
4
88169
36
35
25
6 36 40
5 23 20
6
10. 18820
9. 93022
10. 06978
10. 11842
4
9. 88158
26
36 32
23 28
81195
6
18805
93048
11
06952
11852
5
88148
34
27
36 24
23 36
81210
i
18790
93073
12
06927
11863
5
88137
33
28
36 16
23 44
81225
7
18775
93099
12
06901
11874
5
88126
32
29
36 8
23 52
81240
7
18760
93124
12
06876
11885
10711895
5
5
88115
9. 88105
31
30
30
6 36
5 24
9. 81254
7
10. 18746
9. 93150
13
10. 06850
31
35 52
24 8
81269
8
18731
93175
13
06825
11906
6
88094
29
32
35 44
24 16
81284
8
18716
93201
14
06799
11917
6
88083
28
33
35 36
24 24
81299
8
18701
93227
14
06773
11928
6
88072
27
34
35 28
24 32
81314
8
9
18686
10. 18672
93252
14
06748
11939
6
88061
26
25
35
6 35 20
5 24 40
9. 81328
9. 93278
15
10. 06722
10. 11949
6
9,88051
36
35 12
24 48
81343
9
18657
93303
15
06697
11960
6
88040
24
37
35 4
24 56
81358
9
18642
93329
16
06671
11971
7
88029
23
38
34 56
25 4
81372
9
18628
93354
16
06646
11982
7
88018
22
39
40
34 48
25 12
81387
10
18613
93380
17
06620
11993
7
7
88007
9. 87996
21
20
6 34 40
5 25 20
9. 81402
10
10. 18598
9. 93406
17
10. 06594
10. 12004
41
34 32
25 28
81417
10
18583
93431
17
06569
12015
7
87985
19
42
34 24
25 36
81431
10
18569
93457
18
06543
12025
8
87975
18
43
34 16
25 44
81446
11
18554
93482
18
06518
12036
8
87964
17
44
34 8
25 52
81461
11
18539
93508
19
06492
12047
8
87953
16
15
45
6 34
5 26
9. 81475
11
10. 18525
9. 93533
19
10. 06467
10. 12058
8
9. 87942
46
33 52
26 8
81490
11
18510
9,3559
20
06441
12069
8
87931
14
47
33 44
26 16
81505
12
18495
93584
20
06416
12080
8
87920
13
48
33 36
26 24
81519
12
18481
93610
20
06390
12091
9
87909
12
49
50
33 28
26 32
81534
12
18466
93636
"9. 93661
21
06364
12102
9
87898
11
10
6 33 20
5 26 40
9. 81549
12
10. 18451
21
10. 06339
10. 12113
9
9. 87887
51
33 12
26 48
81563
13
18437
93687
22
06313
12123
9
87877
9
52
33 4
26 56
81578
13
18422
93712
22
06288
12134
9
878()6
8
53
32 56
27 4
81592
13
18408
93738
23
0<i262
12145
10
87855
1
54
55
32 48
27 12
81607
13
14
18393
10. 18378
93763
9. 93789
23
23
06237
10.06211
12156
10
87844
9. 87833
6
5
6 32 40
5 27 20
9. 81622
10. 12167
10
56
32 32
27 28
81636
14
18364
93814
24
06186
12178
10
87822
4
57
32 24
27 36
81651
14
18349
93840
24
06160
12189
10
87811
3
58
32 16
27 44
81665
14
18335
93865
25
061 ;»
12200
10
87800
2
59
32 8
27 52
81680
15
18320
93891
25
06109
12211
11
87789
1
60
32
28
81694
15
18306
93916
26
06084
12222
11
87778
M.
M.
Hour p. M.
Hour A. M.
Cosine.
Diff.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
130°
A
A
B B
C
C
49°
Seconds of time 1 • j 2
3> 4" 5- 6' ;■ 1
|A 2
Prop, parts of cols.<B 3
Ic 1
4
6
3
6 7
10 13
4 5
9
16
7
11
19
8
13
22
9
TABLE 44.
[Page 813
Log.
Sines, Tangents, and Secants.
41°
A
A
B
B
C
C 138°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Diff.
Cosine.
11.
6 32
5 28
9. 81694
10. 18306
9. 93916
10.06084
10. 12222
9. 87778
60
1
31 52
28 8
81709
18291
93942
06058
12233
87767
59
2
31 44
28 16
81723
18277
93967
1
06033
12244
87756
58
3
31 36
28 24
81738
1
18262
93993
1
06007
12255
87745
57
4
5
31 28
28 32
81752
1
18248
94018
2
05982
12266
,87734
56
55
6 31 20
5 28 40
9. 81767
1
10. 18233
9.94044
2
10. 05956
10. 12277
9. 87723
6
31 12
28 48
81781
1
18219
94069
3
05931
12288
87712
54
7
31 4
28 56
81796
2
18204
94095
3
05905
12299
87701
53
8
30 56
29 4
81810
2
18190
94120
3
05880
12310
87690
52
9
10
30 48
29 12
81825
2
18175
94146
4
05854
12321
2
2
87679
51
6 30 40
5 29 20
9. 81839
2
10. 18161
9.94171
4
10. 05829
10. 12332
9. 87668
50
11
30 32
29 28
81854
3
18146
94197
6
05803
12343
2
87657
49
1«
30 24
29 36
81868
3
18132
94222
5
05778
12354
2
87646
48
13
30 16
29 44
81882
3
18118
,94248
6
05752
12365
2
87635
47
14
15
30 8*
29 52
81897
3
18103
94273
6
05727
12376
3
87624
46
45
6 30
5 30
9.81911
4
10. 18089
9. 94299
6
10. 05701
10. 12387
3
9. 87613
16
29 52
30 8
81926
4
18074
94324
1
05676
12399
3
87601
44
17
29 44
30 16
81940
4
18060
94350
t
05650
12410
3
87590
43
18
29 36
30 24
81955
4
18045
94375
8
05625
12421
3
87579
42
19
20
29 28
30 32
81969
5
18031
94401
8
05599
10. 05574
12432
4
87568
41
40
6 29 20
5 30 40
9. 81983
5
10. 18017
9. 94426
8
10. 12443
4
9. 87557
21
29 12
30 48
81998
5
18002
94452
9
05548
12454
4
87546
39
22
29 4
30 56
82012
5
17988
94477
9
05523
12465
4
87535
38
23
28 56
31 4
82026
5
17974
94503
10
05497
12476
4
87524
37
24
25
28 48
31 12
82041
6
6
17959
94528
10
05472
12487
4
87513
36
35
6 28 40
5 31 20
9. 82055
10. 17945
9.94554
11
10. 05446
10. 12499
5
9. 87501
26
28 32
31 28
82069
6
17931
94579
11
05421
12510
5
87490
34
27
28 24
31 36
82084
6
17916
94604
11
03396
12521
5
87479
33
28
28 16
31 44
82098
7
17902
94630
12
05370
12532
5
87468
32
29
28 8
31 52
82112
7
17888
94655
"9. 94681"
12
05345
12543
5
87457
31
30
6 28
5 32
9. 82126
7
10. 17874
13
10. 05319
10. 12554
6
9. 87446
30
31
27 52
32 8
82141
7
178.59
94706
13
05294
12566
6
87434
29
32
27 44
32 16
82155
8
17845
94732
14
05268
12577
6
87423
28
33
27 36
32 24
82169
8
17831
94757
14
05243
12588
6
87412
27
34
35
27 28
32 32
82184
8
17816
94783
14
05217
12599
6
87401
26
25
6 27 20
5 32 40
9. 82198
8
10. 17802
9. 94808
15
10. 05192
10. 12610
7
9. 87390
36
27 12
32 48
82212
9
17788
94834
15
05166
12622
/
87378
24
37
27 4
32 56
82226
9
17774
94859
16
05141
12633
7
87367
23
38
26 56
33 4
82240
9
17760
94884
16
05116
12644
7
87356
22
39
40
26 48
33 12
82255
9
17745
94910
17
05090
12655
/
87345
21
20
6 26 40
5 33 20
9. 82269
10
10. 17731
9. 94935
17
10. 05065
10. 12666
7
9. 87334
41
26 32
33 28
82283
10
17717
94961
17
05039
12678
8
87322
19
42
26 24
33 36
82297
10
17703
94986
18
05014
12689
8
87311
18
43
26 16
33 44
82311
10
17689
95012
18
04988
12700
8
87300
17
44
45
26 8
33 52
82326
10
17674
95037
19
04963
12712
8
87288
16
15
6 26
5 34
9. 82340
11
10. 17660
9.95062
19
10. 04938
10. 12723
8
9. 87277
46
25 52
34 8
82354
11
17646
95088
20
04912
12734
9
87266
14
47
25 44
34 16
82368
11
17632
95113
20
04887
12745
9
87255
13
48
25 36
34 24
82382
11
17618
95139
20
04861
12757
9
87243
12
49
25 28
34 32
82396
12
12
17604
10. 17590
95164
21
04836
12768
9
87232
11
10
50
6 25 20
5 34 40
9. 82410
9. 95190
21
10. 04810
10. 12779
9
9. 87221
51
25 12
34 48
82424
12
17576
95215
22
04785
12791
10
87209
9
52
25 4
34 56
82439
12
17561
95240
22
04760
12802
10
87198
8
53
24 56
35 4
82453
13
17547
95266
22
04734
12813
10
87187
7
54
24 48
35 12
82467
13
17533
95291
23
04709
10. 04683
12825
10. 12836
10
10
87175
6
55
6 24 40
5 35 20
9. 82481
13
10. 17519
9. 95317
23
9. 87164
5
56
24 32
35 28
82495
13-
17505
95342
24
04658
12847
10
87153
4
57
24 24
35 36
82509
14
17491
95368
24
04632
12859
11
87141
3
58
24 16
35 44
82523
14
17477
95393
25
04607
12870
11
87130
2
59
24 8
35 52
82537
14
17463
95418
25
04582
12881
11
87119
1
60
M.
24
36
82551
14
17449
95444
25
04556
12893
u
87107
Hour p. M.
Hour A. M.
Cosine.
Difl.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
M.
131°
A
A
B
B
C
C 48° 1
Seconds of time
1-
2>
3'
4'
if
6>
?■
A
Prop, parts of cols. B
Ic
2
S
2
4
6
3
5
10
4
7
13
6
9
16
7
11
19
8
12
22
10
Page 814]
TABLE M.
Ix3g.
Sines, Tangents, and Secants.
42°
A
A
B
B C
C
187°
M.
Hour A. M.
Hour P.M.
Sine.
Difl.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Difl.
Cosine.
M.
6 24
5 36
9. 82551
10. 17449
9.95444
10. 04556
10. 12893
9.87107
60
1
23 52
36 8
82565
17435
95469
04531
12904
87096
59
2
23 44
36 16
82579
17421
9.5495
1
04505
12915
87085
58
3
23 36
36 24
82593
1
17407
95520
1
04480
12927
87073
57
4
23 28
36 32
82607
1
17393
95545
2
04455
12938
87062
9. 87050"
56
,55
5
6 23 20
5 36 40
9. 82621
1
10. 17379
9. 95571
2
10. 04429
10. 12950
6
23 12
36 48
82635
1
17365
95596
3
04404
12961
87039
,54
7
23 4
36 56
82649
2
17351
95622
3
04378
12972
87028
53
8
22 56
37 4
82663
2
17337
95647
3
04353
12984
2
87016
52
9
22 48
37 12
5 37 20
82677
9. 82691
2
2
17323
10. 17309
95672
4
04328
12995
10. 13007
2
2
87005
9. 86993
51
.50
10
6 22 40
9. 95698
4
10. 04302
11
22 32
37 28
82705
3
17295
95723
5
04277
13018
2
86982
49
12
22 24
37 36
82719
3
17281
95748
5
01^252
1.3030
2
86970
48
13
22 16
37 44
82733
3
17267
95774
5
04226
13041
3
869.59
47
14
15'
22 8
37 52
5 38
82747
3
17253
95799
6
6
04201
13053
3
86947
46
45
6 22
9. 82761
3
10. 17239
9. 95825
10. 04175
10. 13064
3
9. 86936
16
.21 52
38 8
82775
4
17225
95850
(
04150
13076
3
86924
44
17
21 44
38 16
82788
4
17212
95875
7
04125
13087
3
86913
43
18
21 36
38 24
82802
4
17198
95901
8
04099
1.3098
3
86902
42
19
21 28
38 32
82816
4
17184
95926
8
04074
13110
4
86890
9. 86879
41
40
20
6 21 20
5 38 40
9. 82830
5
10. 17170
9. 9.5952
8
10. 04048
10. 13121
4
21
21 12
38 48
82844
5
17156
95977
9
04023
13133
4
86867
,39
22
21 4
38 56
82858
5
17142
96002
9
03998
13145
4
86855
38
23
20 56
39 4
82872
5
17128
96028
10
03972
13156
4
86844
37
24
20 48
39 12
82885
6
17115
96053
10
11
03947
10. 03922
13168
86832
36
35
25
6 20 40
5 39 20
9. 82899
6
10. 17101
9. 96078
10. 13179
5
9. 86821
26
20 32
39 28
82913
6
17087
96104
11
03896
13191
5
86809
34
27
20 24
39 36
82927
6
17073
96129
11
03871
13202
5
86798
33
28
20 16
39 44
82941
6
17059
96155
12
03845
13214
5
86786
32
29
30
20 8
39 52
82955
7
7
17045
96180
12
03820
13225
6
86775
31
30
6 20
5 40
9. 82968
10. 17032
9. 96205
13
10. 03795
10. 13237
6
9. 86763
31
19 52
40 8
82982
7
17018
96231
13
03769
13248
6
86752
29
32
19 44
40 16
82996
/
17004
96256
14
03744
13260
6
86740
28
33
19 36
40 24
83010
8
16990
96281
14
03719
13272
6
86728
27
34
19 28
40 32
83023
8
16977
96307
14
03693
13283
7
86717
26
35
6 19 20
5 40 40
9. 83037
8
10. 16963
9. 96332
15
10. 03668
10. 13295
7
9. 86705
25
36
19 12
40 48
83051
8
16949
. 96357
15
03643
13.306
7
86694
24
37
19 4
40 56
83065
8
16935
96383
16
03617
13318
7
86682
23
38
18 56
41 4
83078
9
16922
96408
16
03592
13330
7
86670
22
39
18 48
41 12
83092
9
9
16908
96433
16
03567
13341
8
86659
21
40
6 18 40
5 41 20
9. 83106
10. 16894
9. 96459
17
10. 03541
10. 13353
8
9. 86647
20
41
18 32
41 28
83120
9
16880
96484
17
03516
13365
8
866.35
19
42
18 24
41 36
83133
10
16867
96510
18
03490
13376
8
86624
18
43
18 16
41 44
83147
10
168.53
96535
18
03465
13388
8
86612
17
44
18 8
41 52
83161
10
16839
96560
19
03440
13400
10. 13411
8
9
86600
9. 86589
16
15
45
6 18
5 42
9. 83174
10
10. 16826
9. 96586
19
10. 03414
46
17 52
42 8
83188
11
16812
96611
19
03389
13423
9
86577
14
47
17 44
42 16
83202
11
16798
96636
20
03364
13435
9
86565
13
48
17 36
42 24
83215
11
16785
96662
20
03338
13446
9
86554
12
49
17 28
42 32
83229
11
16771
96687
21
21
0,3313
13458
9
86542
11
10
50
6 17 20
5 42 40
9. 83242
11
10. 16758
9. 96712
10. 03288
10. 13470
10
9. 86530
51
17 12
42 48
83256
12
16744
96738
22
03262
13482
10
86518
9
52
17 4
42 56
83270
12
16730
96763
22
03237
13493
10
86507
8
53
16 56
43 4
83283
12
16717
96788
22
03212
13505
10
86495
7
54
55
16 48
43 12
83297
12
13
16703
10. 16690
96814
23
23
03186
13517
10
11
86483
6
6 16 40
5 43 20
9. 83310
9. 96839
10. 03161
10. 13528
9. 86472
5
56
16 32
43 28
83324
13
16676
96864
24
03136
13540
11
86460
4
57
16 24
43 36
83338
13
16662
96890
24
03110
13552
11
86448
3
58
16 16
43 44
83351
13
16649
96915
25
03085
13564
11
86436
2
59
16 8
43 52
83365
14
166.35
96940
25
03060
13575
11
86425
1
60
16
44
83378
14
16622
96966
25
03034
13587
12
86413
M.
Hour P.M.
Hour A. M.
Cosine.
Did.
Secant.
Cotangent.
Difl.
Tangent.
Cosecant.
Difl.
Sine.
M.
Wif
3
A
A
B
B C
C
47'^
Seconds of time
1'
2'
8-
4-
5-
6-
«■
(A
Prop, parts of cols. < B
C
•2
3
1
3
6
3
5
10
4
7
13
(
9
16
7
10
19
9
12
22
10
TABLE U.
[Page 816
Log.
Sines, Tangents, and Secants.
48°
A
A
B
B
C
C 136°
M.
Hour A. M.
Hour p. M.
Sine.
Diff.
Cosecant.
Tangent.
Difl.
Cotangent.
Secant.
Di£E.
Cosine.
M.
6 16
5 44
9. 83378
10. 16622
9. 96966
10. 03034
10. 13587
9. 86413
60
.1
15 52
44 8
83392
16608
96991
03009
13599
86401
59
2
15 44
44 16
83405
16595
97016
1
02984
13611
86389
58
3
15 36
44 24
83419
1
1658]
97042
1
02958
13623
86377
57
4
15 28
44 32
83432
1
16568
97067
2
02933
13634
86366
56
5
6 15 20
5 44 40
9. 83446
1
10. 16554
9. 97092
2
10. 02908
10. 13646
9. 86354
55
6
15 12
44 48
83459
1
16541
97118
3
02882
13658
86342
54
7
15- 4
44 56
83473
2
16527
97143
3
02857
13670
86330
53
8
14 56
45 4
83486
2
16514
97168
3
02832
13682
2
86318
52
9
10
14 48
45 12
83500
2
16500
97193
4
02807
13694
2'
86306
51
"50
6 14 40
5 45 20
9. 83513
2
10. 16487
9. 97219
4
10. 02781
10. 13705
2
9. 86295
11
14 32
45 28
83527
2
16473
97244
5-
02756
13717
2
86283
49
12
14 24
45 36
83540
3
16460
97269
5
02731
13729
2
86271
48
13
14 16
45 44
83554
3
16446
97295
02705
13741
3
86259
47
14
14 8
45 52
83567
3
16433
97320
6
02680
13753
3
86247
46
45
15
6 14
5 46
9. 8;«81
3
10. 16419
9. 97345
6
10. 02655
10. 13765
3
9. 86235
16
13 52
46 8
83594
4
16406
97371
7
02629
13777
3
86223
44
17
13 44
46 16
83608
4
16392
97396
7
02604
13789
3
86211
43
18
13 36
46 24
83621
4
16379
97421
8
02579
13800
4
86200
42
19
13 28
46 32
83634
4
16366
10. 16352
97447
8
02553
13812
4
86188
41
20
6 13 20
5 46 40
9. 83648
4
9. 97472
8
10. 02528
10. 13824
4
9. 86176
40
21
13 12
46 48
83661
5
16339
97497
9
02503
13836
4
86164
,39
22
13 4
46 56
83674
5
16326
97523
9
02477
13848
4
86152
38
23
12 56
47 4
83688
16312
97548
10
02452
13860
5
86140
37
24
12 48
47 12
83701
5
16299
97573
10
02427
13872
5
86128
36
25
6 12 40
5 47 20
9. 83715
6
10. 16285
9. 97598
11
10. 02402
10. 13884
5
9.86116
35
26
12 32
47 28
83728
6
16272
97624
11
02376
13896
5
86104
34
27
12 24
47 36
83741
6
16259
97649
11
02351
13908
5
86092
33
28
12 16
47 44
83755
6
16245
97674
12
02326
13920
6
86080
32
29
12 8
47 52
83768
6
16232
97700
12
02300
13932
6
86068
31
.30
30
6 12
5 48
9. 83781
7
10. 16219
9. 97725
13
10. 02275
10. 13944
6
9. 86056
31
11 52
48 8
83795
7
16205
97750
13
02250
13956
6
86044
29
32
11 44
48 16
83808
7
16192
97776
13
02224
13968
6
86032
28
33
11 36
48 24
83821
7
16179
97801
14
02199
13980
7
86020
27
34
11 28
48 32
83834
8
16166
97826
14
02174
13992
7
86008
26
35
6 11 20
5 48 40
9. 83848
8
10. 16152
9. 97851
15
10. 02149
10. 14004
7
9. 85996
25
36
11 12
48 48
83861
8
16139
97877
15
02123
14016
7
85984
24
37
11 4
48 56
83874
8
16126
97902
16
02098
14028
7
85972
23
38
10 56
49 4
83887
8
16113
97927
16
02073
14040
8
85960
?;?
39
40
10 48
49 12
83901
9
16099
97953
16
02047
14052
8
85948
21
20
6 10 40
5 49 20
9. 83914
9
10. 16086
9. 97978
17
10. 02022
10. 14064
8
9. 85936
41
10 32
49 28
83927
9
16073
98003
17
01997
14076
8
85924
19
42
10 24
49 36
83940
9
16060
98029
18
01971
14088
8
85912
18
43
10 16
49 44
83954
10
16046
98054
18
01946
14100
9
85900
17
44
10 8
49 52
83967
10
16033
98079
19
01921
14112
9
85888
16
45
6 10
5 50
9. 83980
10
10, 16020
9. 98104
19
10. 01896
10. 14124
9
9. 85876
15
46
9 52
50 8
83993
10
16007
98130
19
01870
14136
9
85864
14
47
9 44
50 16
84006
10
15994
98155
20
01845
14149
9
85851
13
48
9 36
50 24
84020
11
15980
98180
20
01820
14161
10
85839
12
49
50
9 28
50 32
84033
11
11
15967
98206
21
01794
14173
10
85827
11
6 9 20
5 50 40
9. 84046
10. 15954
9. 98231
21
10.01769
10. 14185
10
9. 85815
10
51
9 12
50 48
84059
11
15941
98256
22
01744
14197
10
85803
9
52
9 4
50 56
84072
12
15928
98281
22
01719
14209
10
85791
8
53
8 56
51 4
84085
12
15915
98307
22
01693
14221
n
85779
7
54
55"
8 48
51 12
84098
12
15902
98332
23
01668
14234
11
85766
6
6 8 40
5 51 20
9.84112
12
10. 15888
9. 98357
23
10. 01643
10. 14246
n
9. 85754
5
56
8 32
51 28
84125
12
15875
98383
24
01617
14258
11
a5742
4
57
8 24
51 36
84138
13
15862
98408
24
01592
14270
n
85730
3
58
8 16
51 44
84151
13
15849
98433
24
01567
14282
12
85718
2
59
8 8
51 52
84164
13
15836
98458
25
01542
14294
12
85706
1
60
M.
8
52
84177
13
15823
98484
25
01516
14307
12
85693
Hour p. M.
Hour A.M.
Ckwine.
Di£f.
Secant.
Cotangent.
Diff.
Tangent.
Cosecant.
Diff.
Sine.
M.
183°
A
A
B
B
C
C 46° j
Secondsof time
1- 2> »•
4-
4y
e-
7*
(A
Prop, parts of cols.-IB
Ic
2
3
2
3 5
6 9
8 ; 5
7
13
6
8 10
16 19
8 9
12
22
11
Page 816]
TABLE U.
Log.
Sines, Tangents, and Secanta.
44°
A
A
B
B
C
C 186°
M.
Hour A. M.
Hour p. M.
Sine.
DitE.
Cosecant.
Tangent.
Dlff.
Cotangent.
Secant.
Difl.
Cosine.
M.
60
6 8
5 52
9.84177
10. 15823
9.98484
10. 01516
10. 14307
9. 85693
1
7 52
52 8
84190
15810
98509
01491
14319
85681
,59
2
7 44
52 16
84203
15797
985.34
1
01466
14331
85669
58
3
7 36
52 24
84216
1
15784
98560
1
01440
14343
85657
57
4
7 28
52 32
84229
1
1
15771
10. 157.58
98585
9. 98610
2
2
01415
10. 01390
14355
85645
56
5
6 7 20
5 52 40
9. 84242
10. 14368
9. 85632
55
6
7 12
52 48
84255
1
15745
98635
3
01365
14380
85620
,54
7
7 4
52 56
84269
2
15731
98661
3
01339
14.392
85608
53
8
6 56
53 4
84282
2
15718
98686
3
01314
14404
2
85596
52
9
10
6 48
53 12
84295
2
15705
98711
4
01289
14417
2
2
85583
51
6 6 40
5 53 20
9. 84308
2
10. 15692
9. 98737
4
10. 01263
10. 14429
9. 85571
.50
11
6 32
53 28
84321
2
15679
98762
5
01238
14441
2
85559
49
12
6 24
53 36
84334
3
15666
98787
5
01213
14453
2
85547
48
13
6 16
53 44
84347
3
15653
98812
5
01188
14466
3
85534
47
14
6 8
53 52
84360
3
15640
988.38
6
01162
14478
3
3
85522
46
45
15
6 6
5 54
9. 84373
3
10. 15627
9. 98863
6
10. 011.37
10. 14490
9. 85510
16
5 52
54 8
84385
3
1,5615
98888
7
01112
14503
3
85497
44
17
5 44
54 16
84398
4
15602
98913
7
01087
14515
4
85485
43
18
5 36
54 24
84411
4
15589
98939
8
01061
14527
4
85473
42
19
5 28
54 32
84424
4
15576
98964
8
01036
14.540
4
85460
41
40
20
6 5 20
5 54 40
9.84437
4
10. 15563
9. 98989
8
10. 01011
10. 14552
4
9. 85448
21
5 12
54 48
84450
5
15550
99015
9
00985
14564
4
85436
.39
22
5 4
54 56
84463
5
15537
99040
9
00960
14577
5
85423
38
23
4 56
55 4
84476
5
15524
99065
10
00935
14589
5
85411
37
24
4 48
55 12
84489
5
15511
99090
10
00910
14601
5
85399
36
"35
25
6 4 40
5 55 20
9. 84502
5
10. 15498
9.99116
11
10. 00884
10. 14614
5
9. 85386
26
4 32
55 28
84515
6
1.5485
99141
11
00859
14626
5
85374
.34
27
4 24
55 36
84528
6
15472
99166
11
00834
14639
6
85361
33
28
4 16
55 44
84540
6
15460
99191
12
00809
14651
6
85349
32
29
4 8
55 52
84553
6
15447
99217
12
13
00783
10. 00758
14663
6
6
85337
9. 85324
31
3b
29
30
6 4
5 56
9. 84566
6
10. 15434
9. 99242
10. 14676
31
3 52
56 8
84579
7
15421
99267
13
00733
14688
6
85312
32
3 44
56 16
84592
7
15408
99293
13
00707
14701
7
85299
28
33
3 36
56 24
84605
7
15395
99318
14
00<382
14713
7
85287
27
34
3 28
56 32
84618
7
15382
99.343
14
15
00657
10. 00632
14726
10. 14738
7
85274
26
25
36
6 3 20
5 56 40
9. 84630
8
10. 15370
9. 99368
7
9. 85262
36
3 12
56 48
84643
8
15357
99394
15
00606
14750
7
85250
24
37
3 4
56 56
84656
8
15344
99419
16
00581
14763
8
85237
23
38
2 56
57 4
84669
8
15331
99444
16
00556
14775
8
85225
22
39
40
2 48
57 12
84682
8
15318
99469
16
00531
14788
8
85212
21
20
6 2 40
5 57 20
9. 84694
9
10. 15306
9. 99495
17
10. 00505
10. 14800
8
9. 85200
41
2 32
57 28
84707
9
15293
99520
17
00480
14813
8
85187
19
42
2 24
57 36
84720
9
15280
99545
18
00455
14825
9
85175
18
43
2 16
57 44
84733
9
15267
99570
18
00430
14838
9
85162
17
44
2 8
57 52
84745
9
15255
99596
9. 99621
19
00404
14850
9
85150
16
15
45
6 2
5 58
9. 84758
10
10. 15242
19
10. 00379
10. 14863
9
9. 85137
46
1 52
58 8
84771
10
15229
99646
19
003.54
14875
10
85125
14
47
1 44
58 16
84784
10
15216
99672
20
00328
14888
10
85112
13
48
1 36
58 24
84796
10
15204
99697
20
00303
14900
10
85100
12
49
1 28
58 32
84809
11
11
15191
10.15178
99722
9. 99747
21
21
00278
10. 00253
14913
10
10
85087
9. 85074
11
10
50
6 1 20
5 58 40
9. 84822
10. 14926
51
1 12
58 48
84835
11
15165
99773
21
00227
14938
11
85062
9
52
1 4
58 56
84847
11
15153
99798
22
00202
14951
11
85049
8
53
56
59 4
84860
11
15140
99823
22
00177
14963
11
85037
7
54
48
59 12
84873
12
15127
99848
23
00152
14976
11
11
8.5024
9. 85012
6
5
55
6 40
5 59 20
9. 84885
12
10. 15115
9. 99874
23
10. 00126
10. 14988
56
32
59 28
84898
12
15102
99899
24
00101
15001
12
84999
4
57
24
59 36
84911
12
15089
99924
24
00076
15014
12
84986
3
58
16
59 44
84923
12
1.5077
99949
24
IX)051
15026
12
84974
2
59
8
59 52
84936
13
15064
99975
25
00025
15039
12
84961
1
60
6
84949
13
15051
10.00000
25
00000
15051
12
84949
M.
Hour p. M.
Hour A. M.
Cosine.
Dlfl.
Secant.
Cotangent.
Did.
Tangent.
Cosecant.
Difl.
Sine.
M.
1S4°
A
A
B
B
C
C 45° 1
Seconds of time
!•
»
»
4*
&•
6>
7"
Prop, parts of col8.{B
Ic
2
I
3
6
3
5
9
5
6
13
6
8
16
8
10
19
9
11
22
11
TABLE 45. [Page 817
Haversiues.
B '
Oh Om 0° 6'
Oh 2m 0° 30'
Oh 4m 1° (K
Oh 6m 1° 30'
Oh 8m 3° 0'
s
60
Log. nav.
Nat. Hav.
Log. Ilav.
Nat Ilav;
Log. Hav. iXat. ITav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
-00
0.00000
0.27963
0.00003
5.88168 0.00008
6.23385
0.00017
6.48371 0.00030
2
1.72333
.00000
.29399
.00003
.88889
.00008
.23866
.00017
.48732 ,00031
58
4+ 1
2.32539
.00000
.30811
.00003
.89604
.00008
.24345
.00018
.49092
.00031
56
6
2.67757
.00000
.32201
5.33509
.00003
0.00003
.90313
.00008
0.00008
.24821
.00018
O.O6OI8
.49450
.00031
54
52
8+ 2
2.92745
0.00000
5.91016
6.25294
6.49807
0.00031
10
3.12127
.00000
.31916
.00003
.91714
.00008
.25765
.00018
..50162
.00033
50
12+ 3
3.27963
.00000
.36242
.00003
.92406
.00008
.26233
.00018
.50516
.00033
48
14
3.41353
.00000
.37548
.00003
.93093
.00009
.26099
.00018
.50868
.00032
46
16+ 4
3.52951
0.00000
5.38835
0.00003
5.93774
0.00009
6.27162
0.00019
6.51219
0.00033
44
18
3.63182 1 .00000
.40103
.00003
.94450
.00009
.27023
.00019
.51508
.00033
42
20+ S
3.72333 i .00000
.41352
.00003
.95121
.00009
.28081
.00019
.51916
.00033
40
22
3.80612
.00000
0.00000
.42,585
5.43799
.00003
0.00003
.95786
5.96447
.00009
0.00009
.28537
0.28991
.00019
0.00019
.52263
6.52608
.00033
38
24+ 6
3.88169
0.00034
36
26
3.95122 1 .00000
.44997
.00003
.97102
.00009
29442
.00030
.52952
.00034
34
28+ 7
4.01559 i .00000
.46179
.00003
.97753
.00010
.29891
.00030
.53295
.00034
32
SO
4.07551 .00000
.47345
.00003
.98399
.00010
.30337
.00030
.53636
.00034
30
32+ 8
4.131.57 0.00000
5.48496
0.00003
5.99040
0.00010
6.30781
0.00030
6.53976
0.00035
28
34
.18423 , .00000
.49631
.00003
5.99676
.00010
.31223
.00031
.54315
.00035
26
36+ 9
.23388 .00000
..50752
.00003
6.00308
.00010
.31003
.00031
.54652
.00035
24
38
40+19
.28084 .00000
4.32539 0.00000
.51858 ! .00003
5.52951 0.00003
.00935
.00010
,32101
6.32530
.00021
0.00031
.54988
.00035
0.00036
22
20
6.01557
0.00010
6.55323
42
.36777 .00000
.54030 .00003
.02176
.00011
.32969
.00031
.55656
.00036
18
u+n
.40818 .00000
.55095 .00004
.02789
.00011
.33400
.00022
.55988
.00036
16
46
.44679 .00000
.56148 .00004
.03399
.00011
.33829
.00022
.56319
.00037
14
48+1%
4.48375 0.00000
5.57189 I 0.00004
6.04004
0.00011
6.34250
0.00022
6.56649
0.00037
12
50
.51921 .00000
.58216 ' .00004
.04605 i .00011
.34081
.00033
.50977
.00037
10
52+13
.55328 .00000
.59232 .00004
.05202 .00011
.35103
.00033
.57304
.00037
8
54
.58606
.00000
0.00000
.60236 .00004
5.61229 1 0.00004
.05795 1 .00011
6.06384 0.00013
.35524
6.35943
.00033
.57630
6.57955^
.00038
6
56+14
4.61765
0.00033
0.00038
4
58
4.64813 0.00000
5.62211 \ 0.00004
6.06969 0.00013
6.36359
0.00033
6.58278 j 0.00038
2
23h 59m
23h 57m
23h r,-,"'
23h 53m
23h Sim
s '
0+15
Oh ;m 0° 0'
Oh Sm 0° SO'
Oh r,m 1° W
Oh im 1° W
Oh 9m 3° 0'
60
4.67757
0.00000
5.63181
0.00004
6.075.50
0.00013
6.36774
0.00033
6.58600 \ 0.00039
2
.70605
.00000
.64141
.00004
.08127
.00013
.37180
.00024
.58921
.00039
58
■4+16
.73363
.00001
.6.5090
.00004
.08700
.00013
.37597
.00034
.59241
.00039
56
6
.76036
.00001
.66029
5.669.58*
.00005
.09270
.00013
0.00013
.38000
.00034
0.00034
.59500 ' .09039
6.59878 ; 0.00040
54
52
8+n
4.78629
0.00001
0.00005
6.09830
6.38412
10
.81147
.00001
.07877
.00005
.10398
.00013
.38817
.00034
.60194 .00040
50
12+i8
.83594
.00001
.68787
.00005
.10950
.00013
.39220
.00025
.60.509 .00040
48
14
.85973
.00001
.09087
.00005
.11511
.00013
.39022
.00025
.60823 i .00041
46
16+19
4.88290
0.00001
5.70578
0.00005
6.12063
0.00013
0.40021
0.00025
.0.61136 0.00041
44
18
.90546
.00001
.71460
.00005
.12611
.00013
.40418
.00025
.61448 1 .00041
42
20+Z0
.92745
.00001
.72332
.00005
.13155
.00014
.40814
.00036
.61759 .00041
40
22
.94890
.00001
.73197
5.74052
.00005
0.00006
.13696
.00014
.41208
.00036
.62068
.00043
0.00043
38
36
24+21
4.96983
0.00001
6.14234
0.00014
6.41600
0.00036
6.62377
26
4.99027
.00001
.74900
.00006
.14769
.00014
.41990
.00026
.62684 .00043
34
28+Zi
5.01024
.00001
.75739
.00006
.15300
.00014
.42379
.00027
.62991 .00043
32
SO
.02976
.00001
.76670
.00006
.15828
.00014
.42766
.00037
.63296 ; .00043
30
32+'iZ
5.04885
0.00001
5.77394
0.00006
6.16353
0.00015
6.43151
0.00037
6.03600 0.00043
28
34
.06753
.00001
.78209
.00006
.10874
.00015
.43534
.00037
.03903
.00044
9.6
36 +U
.08581
.00001
.79017
.00006
.17393
.00015
.43916
.00037
.04205
.00044
24
38
40+Z5
.10372
.00001
0.00061
.79818
5.80011
.00006
0.00006
.17908
.00015
.44296
.00028
0.00028
.64504
.00044
22
20
5.12127
6.18421
0.00015
6.44075
6.64806
0.00044
42
.13847
.00001
.81397
.00007
.18930
.00015
.450.52
.00028
.65105
.00045
18
44+26
.15.534
.00001
.82176
.00007
.19437
.00016
.4,5427
.00028
.6,5403
.00045
16
46
.17188
.00001
.82948
.00007
.19940
.00016
.45800
.00029
.65700
.00045
14
48+21
5.18812
0.00003
5.83713
0.00007
6.20441
0.00016
6.46172
0.00029
6.6,5996
0.00046
12
60
.20406
.00003
.84472
.00007
.20938
.00016
.40543
.00039
.66291
.00046
10
52+28
.21971
.00003
.85224
.00007
.21433
.00016
.46911
.00039
.66,585
.00046
8
54
.23.508
.00003
.85909
5.86709
.00007
0.00007
.21925
6.22415
.00017
0.00017
.47279
6.47644
.00030
0.00030
.66878
0.67170
.00047
0.00047
6
4
56+29
5.25019
0.00003
58
.26503
.00003
.87442
.00008
.22901
.00017
.48008
.00030
.67461
.00047
2
60+30
5.27963
0.00003
5.88168
0.00008
6.23385
0.00017
6.48371
o.ooo.to
6.67751
0.00048
23h oSm
2.Sh 56m
23h 54"'
23h 52m
23h 50m
24972°— 12-
-42
Page 818] TABLE 45.
Haversines.
s '
0* lOm 2° 30'
O* 12m 3° O'
■0*i4™3°3r
Oh 16m 4° (K
Oft w™ 4° 30'
s
Log. Itav. Nat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.' Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
6.67751 0.00048
6.83584
0.00069
6.96970
0.00093
7.08564
0.00122
7.18790
0.00154
6Y)
2
.68040 .00048
.83825
.00069
.97176
.00094
.08745
.00133
.189,50
.00135
58
4+ 1
.68328 .00048
.84065
.00009
.97382
.00094
.08925
.00133
.19111
.00155
56
6
.68615
.00049
0.00049
.84304
6.84543
.00070
0.00070
.97588
6.97793
.00095
O.OOO95
.09105
7.09284
.00123
0.00124
.19271
7.19430
.00156
0.00156
54
52
8+ 3
6.68901
10
.69186
.00049
.84782
.00070
.97997
.00095
.09464
.00124
.19.590
.00157
50
12+ 3
.69470
.00050
.8,50 J 9
.00071
.98201
.00096
.09642
.00125
.19749
.00158
48
14
.69754
.00050
.85256
.00071
.98405
.00096
.09821
.00135
.19908
.00158
46
16+ i
6.70036
0.00050
6.8.5492
0.00072
6.98608
0.00097
7.09999
0.00136
7.20066
0.00159
44
18 '
.70318
.00050
.85728
.00072
.98811
.00097
.10177
.00136
.20225
.00159
42
20+ 5
.70598
.00051
.85963
.00072
.99013
.00098
.10354
.00137
.20383
.00160
40
22
.70878
.00051
.86197
.00073
0.00073
.99214
.00098
.10.531
.00137
0.00128
.20540
7.20698
.00160
0.00161
38
36
24+ 6
6.71157
0.00051
6.86431
6.99416
0.00099
7.10708
26
.71435
.00053
.86664
.00074
6.99616
.00099
.10884
.00128
.20855
.00163
34
28+ 7
.71712
.00052
.86897
.00074
6.99817
.00100
.11060
.00139
.21012
.00162
32
30
.71988
.00052
.87129
.00074
7.00017
.00100
.11236
.00130
.21168
.00163
30
32+ 8
6.72263
0.00053
6.87360
0.00075
7.00216
0.00101
7.11411
0.00130
7.21325
0.00163
28
34
.72537
.00053
.87591
.00075
.00415
.00101
.11586
.00131
.21481
.00164
26
36+ 9
.72811
.00053
.87821
.00076
.00613
.00101
.11760
.00131
.21636
.00165
24
38
.73084
.00054
0.OOO54
.88050
6.88279"
.00076
.00811
.00102
0.00103"
.11934
.00133
0.00133
.21792
.00165
22
"27r
40+10
6.73355
0.00076
7.01009
7.12108
7.21947
0.00166
•42
.73626
.00054
.88.507
.00077
.01206
.00103
.12282
.00133
.22102
.00166
18
44+11
.73896
.00055
.88735
.00077
.01403
.00103
.124.55
.00133
.22256
.00167
16
46
.74166
.00055
.88962
.00078
.01,599
.00104
.12627
.00134
.22411
.00168
14
48+n
6.74434
0.00056
6.89188
0.00078
7.01795
0.00104
7.12800
0.00134
7.22565
0.00168
12
50
.74702
.00056
.89414
.00078
.01990
.00105
.12972
.00135
.22718
.00169
10
52+13
.74969
.00056
.89639
.00079
.02185
.00105
.13144
.00135
.22872
.00169
8
54
.75235
.00057
.89864
.00079
0.00080
.02379
7.02,573
.00106
.13315
.00136
0.00136
.23025 .00170
7.23178, 0.00171
6
4
56+U
6.75500
0.00057
6.90088
0.00106
7.13486
58
6.75764
0.00057
6.90312
0.00080
7.02767
0.00107
7.13657
0.00137
7.23331 ! 0.00171
2
23h 59m
23h 47m
231' 45m
«»4^m
23h 41™
s '
0+15
0" lim 2° 30^
0* 13'n 3° 0'
Oh 15m 3° 30'
Oh nm 4° 0'
Oh 19m i" 30'
s
60
6.76028
0.00058
6.90535
0.00080
7.02960
0.00107
7.13827
0.00137
7.23483
0.00173
2
.76290
.00058
.90757
.00081
.03153
.00108
.13997
.00138
.23635
.00173
58
4+16
.76552
.00058
.90979
.00081
.03345
.00108
.14167
.00139
.23787
.00173
56
6
.76814
.00059
.91200
6.91421"
,00082
O.OOO82
.03537
00108
.14337
7.14506
.00139
0.00140
.23939
7.24090
.00174
0.00174
54
52
S+17
6.77074
0.00059
7.03729
0.00109
70
.77334
.00059
.91641
.00083
.03920
.00109
.14674
.00140
.24241
.00175
50
72 + 18
.77592
.00060
.91860
.00083
.04110
.00110
.14843
.00141
.24392
.00175
48
U
.77851
.00060
.92079
.00083
.04300
.00110
.15011
.00141
.24,543
.00176
46
16+19
6.78108
0.00060
6.92298
0.00084
7.04^90
0.00111
7.15179
0.00143
7.24693
0.00177
44
18
.78364
.00061
.92516
.00084
.04680
.00111
.15346
.00143
.24843
.00177
42
20+20
.78620
.00061
.92733
.00085
.04869
.00112
.15513
.00143
.24993
.00178
40
22
.78875
.tMH)61
.929.50
6.93166
.00085
.0.5057
.00112
0.00113
.15680
7.15846
.00143
O.OO144
.25143
7:25292
.00178
0.00179
38
36
24+2\
6.79129
0.00062
0.00085
7.05245
26
.79383
.00062
.93382
.00086
.05433
.00113
.16013
.00145
.25441
.00180
34
28+21i
.79630
.00063
.93597
.00080
.05620
.00114
.16178
.00145
.25590
.00180
32
30
.79888
.00063
.93812
.00087
.05807
.00114
.16344
.00146
.25738
.00181
30
32+Z3
6.80139
0.00063
6.94026
0.00087
7.05994
0.00115
7.16.509
0.00146
7.25886
0.00181
28
34
.80390
.00064
.94239
.00088
.06180 ! .00115
.16674
.00147
.26034
.00183
26
36+Zi
.80640
.00064
.94453
.00088
.06366
.00116
.16839
.00147
.26182
.00183
24
. 38
.80889
6.81137
.00064
0.00065~
.94665
.00088
O.O0O89
.06,551
7.06736
.00116
0.00117
.17003
7.17167
.00148
0.00148
.26330
7.26477
.00183
0.00184
22
20
40+25
6.94877
42
.81385
.00065
.95089
.00089
.06920
.00117
.17331
.00149
.26624
.00185
18
44+26
.81632
.00066
.95300
.00090
.07105* .00118
.17494
.00150
,26771
.00185
16
46
.81879
.00066
.95510
.00090
.07288 1 .00118
.170.57
.00150
.26917
.00186
14
45+27
6.82124
0.00066
6.95720
0.00091
7.07472
0.00119
7.17820
0.00151
7.27064
0.00186
12
50
.82369
.00067
.95930
.00091
.076,55
.00119
.17982
.00151
.27210
.00187
10
52+28
.82614
.00067
.96139
.00091
.07837
.00120
.18144
.00152
.273,55
.00188
8
54
56+29
.82857
.00067
.90347
.00092
.08019
7.08201
.00120
0.00121
.18306
7.18468
.00132
0.00153
.27501
7.27646
.00188
0.00189
6
4
6.83100
0.00068
6.96.5.55
0.00092
5,?
.83342
.00068
.66763
.00093
.08383
.00121
.18629
.00154
.27791
.00190
2
60+30
6.83584 i 0.00069
6.96970
0.00093
7.08564
0.00122
7.18790
0.00154
7.27936
0.00190
2Sh 48<n
2.Sh 46m
2Sh44m
2Sh 42«
23h 40'"
TABLE 45.
[Page 819
Ilaversiiies.
s '
Oh 20"> 5° 0'
0»fi">5°30'
Oh 24"' 6° ff
0» 26m 6° 30'
Oh ogm 7° (f
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. llav.
Nat. Hav,
Log. Hav.
Nat. Hav.
7.27936
0.00190
7.36209
0.00230
7.43760
0.00274
7..50706 1 0.00331
7. .57135
0.00373
60
2
.28080
.00191
.36340
.00231
.43880
.00275
.50817 1 .00333
.57238
.00374
58
4+ 1
.2822-5
.00192
.36471
.00332
.44001
.00275
.50928 1 .00333
.57341
.00374
56
6
.28369
.00192
0.00193
.36602
7.36733
.00233
0.00333
.44121
7.4424r
.00276
0.00277
.51039 ! .00334
.57444
.00375
54
8+ 2
7.28513"
7.51149
0.00335
7.57547
0.00376
52
10
.28656
'.00193
.36864
.00334
.44361
.00278
.51260
.00336
.75650
.00377
50
12+ 3
.28800
.00194
.36994
.00234
.44480
.00278
.51370
.00336
.57752
.00378
48
14
.28943
.00195
.37124
.00335
.44600
.00279
.51481
.00337
.57855
.00379
46
16+ i
7.29086
0.00195
7.37254
0.00336
7.44719
0.00280
7.51591
0.00338
7.57957
0.00380
44
18
.29228
.00196
.37384
.00237
.44838
.00281
.51701
.00329
.58060
.00381
42
20+ 5
.29371
.00197
.37514
.00237
.44957
.00283
.51811
.00330
.58162
.00383
40
22
.29513
7.29655
.00197
0.00198
.37643
7:37773"
.00238
0.00339
.45076
7.45194
.00383
.51921
.00331
0.00331
.58264
7.58366"
.00383
0.00383
38
36
24+ 6
0.00383
7.52030
26
.29797
.00199
.37902
.00339
.45313
.00384
..52140
.00333
.58467
.00384
34
28+ 7
.29938
.00199
.38030
.0034fr
.45431
.00385
.52249
.00333
.58569
.00385
32
30
.30079
.00200
.38159
.00341
.45549
.00385
.52358
.00334
.58670
.00386
30
32+ 8
7.30220
0.00201
7.38288
0.00341
7.45667
0.00386
7.52467
0.00335
7.58772
0.00387
28
34
.30361
.00201
.38416
.00343
.45785
.00387
..52576
.00336
.58873
.00388
26
36+ 9
.30502
.00302
.38.544
.00343
.45903
.00388
.52685
.00336
.58974
.00389
24
38
.30642
.00203
.38672 .00244
.46020
.00389
.52794
.00337
.59075
.00390
22
40+W
7.30782
0.00203
7.38800 0.00244
7.46138
0.00389
7.52902"
0.00338
7.59176
0.00391
~20
42
.30922
.00204
.38927 1 .00245
.46255
.00390
..53011
.00339
.59277
.00393
18
u+n
.31062
.00204
.39054 .00246
.46372
.00391
.35119
.00340
.59378
.00393
16
46
.31201
.0020r.
.39182
.00347
.46489
.00293
..53227
.00341
.59478
.00393
14
48+U
7.31340
0.00206
7.39309
0.00347
7.46605
0.00392
7. .53335
0.00341
7.59579
0.00394
12
SO
.31479
.00206
.39435
.00348
.46722
.00393
.53443
.00343
.59679
.00395
10
52+U
.31618
.00207
.39.562
.00349
.46838
.00394
.535.50
.00343
.59779
.00396
8
64
.31757
7.31895
.00208
0.0020S
.39688
7.39815
.00349
0.00350
.46955
7.47071
.00395
0.00396
.53658
7. .53766
.00344
0.00345
.59879
.00397
6
56+14
7. .59979
0.00398
4
58
7.32033
0.00209
7,39941
0.00351
7.47187
0.00396
7.53873
0.00346
7.60079
0.00399
2
23 1 39'"
23 h .)7'»
23h 35">
23h 33 m
23'' 31m '
s '
0+15
Oh 21'" 5° 0'
Oh 23m 5° W
0" 25- 6° O'
O" 21m 6° SO'
Oh 29m 7° if
s
60
7.32171
0.00210
7.40067
0.00353
7.47302
0.00397
7. .53980
0.00347
7.60179
0.00400
2
.32309
.00210
.10192
.00353
.47418
.00338
..54087
.00347
.60279
.00401
58
4+16
.32446
.00211
.40318
.00253
.47533
.00399
..54194
.00348
.60378
.00403
56
6
,32583
.00213
0.00212
.40443
7.40568"
.00254
0.00255
.47649
7.47764
.00300
0.00300
..54301
7. .54407
.00349
0.00350
.60478
7.60577
.00403
0.00403
54
52
8+Vl
7.32720'
10
.32857
.00213
.40693
.00255
.47879
.00301
..54514
.00351
.60676
.00404
50
7^+18
.32994
.00214
.40818
.00256
.47994
.00303
.54620
.00352
.60775
.00405
48
14
.33130
.00214
.40943
.00257
.48109
7.48223
.00303
..54727
.00353
.60874
.00406
46
16+19
7.33266
0.00215
7.41067
0.00257
0.00304
7. .54833
0.00353
7.60973
0.00407
44
18
.33402
.00216
.41191
.00258
.48337
.00304
..54939
.00354
.61072
.00408
42
20+30
.33538
.00216
.41315
.00359
.484.52
.00305
.5.5045
.00355
. .61170
.00409
40
22,
.33673
.00217
0.00218
.41439
7.41.563
.00260
0.00360
.48566
7.48680
.00306
0.00307"
..551.50
'7. .5.5256"
.00356
0.00357
.61269
.00410
0.00411
38
36
24+il
7.33809
7.61367
26
.33944
.00218
.41686
.00361
.48794
.00308
..55361
.00358
.61466
.00413
34
28+Zt
.34079
.00219
.41810
.00262
.48907
.00308
.5.5467
.00359
.61564
.00413
32
30
.34213
.00220
.41933
.00263
.49021
.00309
..55572
.00360
.61662
.00414
30
32+Z3
7.34348
0.00221
7.42056
0.00263
7.49134.
0.00310
7. .55677
0.00360
7.61760
0.00415
28
34
.34482
.00221
.42179
.00264
.49247
.00311
..55782
.00361
.61858 .00416
26
36+U
.34616
.00222
.42301
.00265
.49360
.00312
..55887
.00363
.61955 j .00416
24
38
..34750
7.34884
.00223
0.00223
.42424
7.42.546
.00266
0.00266
.49473
Y.49586'
.00312
0.00313
..5.5992
7.56096
.00363
0.00364
.62053 1 .00417
22
~20
40+^
7.62151 ; 0.00418
42
.3.5017
.00224
.12668
.00267
.49699
.00314
.56201
.00365
.62248 1 .00419
18
44+36
.351.50
.00225
.42790
.00268
.49811
.00315
.56305
.00366
.62345 ; .00420
16
46
.35283
.00225
.42912
.00269
.49923
.00316
.56409
.00367
.62442 ! .00431
14
48+%l
7.35416
0.00226
7.43034
0.00269
7.. 50036
0.00316
7..56513
0.00367
7.62540 1 0.00433
12
50
.3.5549
.00227
.431.55
.00270
.50148
.00317
.56617
.00368
.62636 .00433
10
52+3»
.35681
.00227
.43277
.00271
.50259
.00318
.56721
.00369
.62733 .00424
8
54
.35813
.00228
0.00239
.4,3398
7.43519
.00273
0.00373
.50371
7. '50483
.00319
0.00320
.56825
7"."56928"
.00370
0.0037i
.62830 1 .00425
7.62927 , 0.00426
6
4
56+39
7.3.5945
58
.36077
.00229
.43639
.00373
.50594
.00321
.57032
.00372
.63023 •• .00427
2
60+30
7.36209
0.00230
7.43760
0.00374
7.50706
0.00321
7.57135
0.00373
7.63120 0.00438
231' 38'"
23" 36"
23h 34"
23h 32m
23 h 30'"
Page 820]
TABLP: 45.
Haversines.
S '
0* SO-n 7° 30^
Oh 32"' 8° 0' 1
0* 54"' 8° 30'
0* 36in 9° ty 1
Oh 38'" 9° W 1
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
7.63120
0.00428
7.68717
0.00487
7.73974
0.00549
7.78929
0.00616
7.83615
0.00686
60
2
.63216
.00429
.68807
.00488
.74059
.00550
.79009
.00617
.83691
.00687
58
4+ 1
.63312
.00430
.68897
.00489
.74143
.00551
.79089
.00618
.83767
.00688
56
6
.63408
.00431
.68987
.00490
.74228
.00552
.79169
.00619
.83842
.00689
54
S+ 2
7.63504
0.0(>432
7.69077
0.00491
7;7"4313"
0.00554
7.79249
0.00630
7.83918
0.00691
52
10
.63600
.00433
.69167
.00492
.74398
.00555
.79329
.00621
-.83994
.00692
50
1S!+ 3
.63696
.00433
.69257
.00493
.74482
.00556
.79409
.00622
.84070
.00693
48
U
.63792
.00434
.69347
.00494
.74567
.00557
.79489
.00624
.84145
.00694
46
16+ 4
7.63887
0.00435
7.69437
0.00495
7.74651
0.00558
7.79568
0.00625
7.S4221
0.00695
44
IS
.63983
.00436
.69526
.00496
74735
.00559
.79648
.00626
.S4296
.00697
42
20+ 5
.64078
.00437
.69616
.00497
.74819
.00560
.79728
.00627
.84372
.00698
40
22
24+ 6
.64173
.00438
0.00439
.69705
7.69794"
.00498
0.00499
.74904
7.74988'
.00561
.79807
.00628
0.00629
.84447
7.84522
.00699
0.00700
38
36
7.64269
0.00562
7.79886
26
.64364
.00440
.69883
.00500
.75072
.00563
.79966
.00630
.84.597
.00701
34
2S+ 7
.64458
.00441
.69972
.00501
.75155
.00564
.80045
.00632
.84672
.00703
32
^0
.64553
.00442
.70061
.00502
.75239
.00565
.80124
.00633
.84747
.00704
30
52+ 8
7.64648
0.00443
7.70150
0.00503
7.75323
0.00567
7.80203
0.00634
7.84822
0.00705
28
S4
.64743 .00444
.70239
.00504
.75407
.00568
.80282
.00635
.84897
.00706
26
S6+ 9
.64837 : .00445
.70328
.00505
.75490
.00569
.80361
.00636
.84972
.00707
24
^«
.64932
.00446
.70416
.00506
.75574
.00570
.80440
.00637
.85047
.00709
22
40+10
7.65026
0.00447
7.70505
0.00507
7.75657
0.00571
7.80519
0.00639
7.85122'
0.00710
20
42
.65120
.00448
.70593
.00508
.75740
.00572
.80598
.00640
.85196
.00711
18
44+11
.65214
.00449
.70682
.00509
.75824
.00573
.80677
.00641
.85271
.00712
16
46
.65308
.00450
.70770
.00510
.75907
.00574
.80755
.00642
.85346
.00714
14
4ii+n
7.65402
0.00451
7.70858
0.00511
7.75990
0.00575
7.80834
0.00643
7.85420
0.00715
12
50
.65496
.00452
.70946
.00512
.76073
.00576
.80912
.00644
.85494
.00716
10
52+13
.65590
.00453
.71034
.00513
.76156
.00578
.80991
.00646
.85569
.00717
8
54
.65683
.00454
0.00455
.71122
7.71210
.00514
0.00515
.76239
.00579
0.00580
.81069
'7.81147
.00647
0.00648
.85643
7.85717
.00719
0.00720
6
4
56+1*.
7.65777
7.76321
58
7.65870
0.00456
7.71298
0.00516
7.76404
0.00581
7.81225
0.00649
7.85791
0.00721
2
2J'' 29"'
2J!' 27"!
25* 2.5™
25* 23'"
23 !• 21'"
s '
0+15
0i'31->^°W
0" 33m 8° O'
0* 35"' 8° 30'
01- 37"' 9° 0'
Oh 39'" 9° 30'
s
60
7.65964 ] 0.00457
7.71385 ' 0.00517
7.76487
0.00582
7.81303
0.00650
7.85866
0.00722
2
.66057 .00458
.71473 .00518
.76569
.00583
.81382
.00651
.85940
.00723
58
4+16
.66150 .00459
.71560 .00520
.76652
.00584
.81459
.00653
.86014
.00725
56
6
.66243 .00460
.71648 .00521
.76734
.00585
0.00586
.81537
7.81615
.00654
0.00655
.86087
7.86161
.00726
0.00727
54
52
8+n
7.66336 0.00461
7.71735
0.00523
7.76816
10
.66429 .00462
.71822
.00523
.76898
.00587
.81693
.00650
.86235
.00728
50
72+18
.66521 .00463
.71909
.00524
.76981
.00589
.81771
.00657
.86309
.00730
48
U
.66614 .00464
.71996
.00525
.77063
.00590
.81848
.00658
.86382
.00731
46
16+19
7.66706 0.00465
7.72083 0.00526
7.77^45
0.00591
7.81926
0.00660
7.86456
0.00732
u
IS
.66799 .00466
.72170 .00527
.77227
.00592
.82003
.00661
.86530
.00733
42
20+ZO
.66891 .00467
.72257 ; .00528
.77308
.00593
.82081
.00662
.86603
.00735
40
22
.66983
j«0468
0.00469
.72343 i .00529
7.72430': 0.00530
.77390
.00594
0.00595
.82158
7.82235
.00663
0.00664
.86676
7.86750
.00736
0.00737
38
36
24+21
7.67075
7.77472
26
.67167 .00470
.72516 1 .00531
.77553
.00596
.82313
.00665
.86823
.00738
34
28+n
.67259 ; .00471
.72603 , .00532
.77635
.00598
.82390
.00667
.86896
.00740
32
SO
.67351
.00472
.72689
.00533
.77716
.00599
.82467
.00668
.86969
.00741
30
52+33
7.67443
0.00473
7.72775
0.00534
7.77798
0.00600
7.82544
0.00669
7.87042
0.00742
28
S4
.67535
.00474
.72861
.00535
.77879
.00601
.82621
.00670
.87115
.00743
26
56+24
.67626
.00475
.72948
.00536
.77960
.00602
.82698
.00671
.87188
.00745
24
38
.67718
.00476
0.00477
.73034
7.73119
.00537
0.00539
.78041
.00603
0.00664
.82774
7.82851'
.00673
0.00674
.87261
7.87334
.00746
0.00747
22
20
40+%&
7.67809
7.78122
42
.67900
.00478
.73205
.00540
.78203
.00605
.82928
.00675
.87407
.00748
18
44+Z6
.67991
.00479
.73291
.00541
.78284
.00607
.83004
.00676
.87480
.00750
16
46
.68082
.00480
.73377
.00542
.78365
.00608
.83081
.00677
.87552
.00751
14
4S+Z7
7.68173
0.00481
7.73462
0.00543
7.78446
0.00609
7.83157
0.00679
7.87625
0.00753
12
50
.68264
.00482
.73548
.00544
.78526
.00610
.83234
.00680
.87697
.00753
10
52+2S
.68355
.00483
.73633
.00545
.78607
.00611
.83310
.00681
.87770
1 .00755
8
54
.68445
.00484
0.00485
.73718
7.73803
.00546
0.00547
.78688
7.78768
.00613
0.00613
.83386
7.83463
.00682
0.00683
.87842
.00756
0.00757
6
4
56+29
7.68536
7.87915
5S
.68627
.00486
.73889
.00548
.78848
.00614
.83539
.0068.5
.87987
.00758
2
60+30
-
7.68717
0.00487
7.73974
0.00549
7.78929
0.00616
7.83615
0.00686
7.88059
0.00760
25" 28"'
25* 26"'
25* 24"'
25* 22"'
23h 20"'
TABLE 45. [Page G21
Haversines.
s '
Oh 40m 10° C
Oh 42m 10° 30'
Oh 44m 11° 0'
Oh 46m 11° 30'
Oh 48m 13° 0'
s
Log.Hav. N'at.Hav.
Log. Hav.
Nat, Hav.
Log.IIav. Nat. Hav,
Log. Ilav, Nat. Hav,
Log. Hav., Nat. Hav,
7.88059
0.00760
7.92286
0.00837
7.96315 ; 0.00919
8.00163 0.01004
8.03847
0.01093
60
t
.88131
.00761
.923.54
.00839
.96380 j .00920 - .00226 ' .01005
.03907
.01094
58
4+ 1
.88203
.00763
.92423
.00840
.96446 .00931'
.00289 ] .01007
,03967
.01096
56
6'
.88276
.00763
0.00765
.92492
7.92.560
.00841
0.00843
.96511
7.96577'
.00923
0.00924
.00351 .01008
8.00414 ! 0.01010
.04027
8.04087
.01097
0.01099
54
52
S+ %
7.88348
10
.88419
.00766
.92629
.00844
.96642
.00926
,00476 ; .01011
.04147
.01100
50
12+ 3
.88491 ! .00767
.92697
.00845
.96707
.00927
.00539 : .01013
.04207
.01103
48
14
.88503
.00768
,92766
.00847
.96773
.00928
.00601 : .01014
.04267
.01103
46
16+ 4
7.88635
0.00770
7.92834
0.00848
7.96838
0.00930
8.00664 0.01015
8.04326
0.01105
44
18
.88707
.00771
.92902
.00849
.96903
.00931
.00726 .01017
.04386
.01106
42
20+ 5
88778
.00772
.92970
.00851
.96968
.00933
.00788 .01018
.04446
.01108
40
n
.888.50
7.88921
.00774
0.00775
.93039
7.93107
.00852
0.00853
.97033
.00934
.00851 .01030
8700913 1 0.01021
.04.506
8.04565
.01109
O.Oilll
38
36
U+ 9
7.97098 1 0.00935
26
.88993
.00776
.93175
.00855
.97163
.00937
.00975 .01023
.04625 .01113
34
28+ 7
.89064
.00777
.93243
.00856
.97228
.00938
.01037 ' .01034
.04684
.01114
32
SO
.89135
.00779
.93311
.00857
.97293
.00940
.01099 .01036
.04744
,01115
30
S2+ 8
7.89207
0.00780
7.93379
0.00859
7.97358
0.00941
8.01161 0.01037
8.04803
0.01117
28
34
.89278
.00781
.93447
.00860
.97423
.00942
.01223 ; .01039
.04863
.01118
26
36+ 9
.89349
.00783
.93514
.00861
.97478
.00944
.01285 .01030
.04922
.01120
24
38
40+10
.89420
7.8949r
.00784
0.00785
.93582
7.936.50
.00863
0.00864
.97552
7.97617
.00945
0.00947
.01347 ! .01033
8.01409 t 0.01033
.04981
8.0.5041
.01133
22
20
0.01133
42
.89562
.00786
.93717
.00865
.97681 .00948
.01471 .01034
.05100
.01125
18
44+11
.89633
.00788
.93785
.00867
.97746 1 .00949
.01.532 .01036
.05159
.01126
16
46
.89704
.00789
.93852
.00868
.97810 ; .00951
.01.594 .01037
.05218
.01128
14
48+n
7.89775
0.00790
7.93920
0.00869
7.97875 ' 0.00953
8.01656 0.01039
8.05277
0.01139
12
so
.89846
.00793
.93987
.00871
.97939 1 .00954
.01717 .01040
.05336
.01131
10
52+13
.89916
.00793
.94055
.00872
.98003 ' .00955
.01779 .01043
.05395
.01133
8
S4
.89987
.00794
0.00795
.94122
7.94189
.00873
0.00875
.98068 ! .00956
7.98132 0.00958
.01840 .01043
8.01902 0.01045'
.05454
.01134
6
56+14
7.90057
8.05513 0.01135
4
58
7.90128
0.00797
7.94257
0.00876
7.98196 0.00959
8.01963 - 0.01046
8.05572 0.01137
2
23 h 19m
23 h 17'"
23 h 15 m
23h 13m
23h llm
0+18
Oh 41m 10° 0'
Oh 43m 10° W
Oh 45m 11° 0'
Oh 47" 11° 30'
Oh 49" n° 0'
s
60
7.90198
0.00798
7.94324
0.00877
7.98260
0.00961
8.02025
0.01048
8.05631
0.01138
2
.90269
.00799
.94391
.00879
.98325
.00963
.02086
.01049
.05690
.01140
58
4+16
.90339
.00801
.94458
.00880
.98389
.00964
.02148
.01051
.05749
.01142
56
6
8+n
.90409
7.90480
.00802
0.00803
.94525
7:94.592'
.00882
.98453
.00965
0.00968
.02209
8'.02270
.01053
0.0i054
.05808
8.05866
.01143
0.01145
54
52
0.00883
7.98517
10
.90550
.00804
.94659
.00884
.98581
.00968
.02331
.01055
.05925
.01146
50
72+18
.90620
.00806
.94726
.00886
.98644
.00969
.02392
.01057
.05984
.01148
48
14
.90690 ' .00807
.94792
.00887
.9870g
.00971
.024.53
.01058
.06042
.01149
46
76+19
7.90760 : 0.00808
7.948.59
0.00888
7.98772
0.00973
8.02515
0.01060
8.06101
0.01151
44
18
.90830
.00810
.91926
.00890
.98836
.00974
.02576
.01061
.06159
.01152
42
20+20
.90900
.00811
.91992
.00891
.98899
.00975
,02637
.01663
, .06218
.01154
40
22
.90970
.00813
.9.5059
7.95126
.00892
0.00894
.98963
7.99027
.00976
0.00978
.02697
■8.02758
.01064
.06276
.01155
0.01157
38
36
24+21
7.91039
0.00814
0.01066
8.06335
26
.91109
.00815
.9.5192
.00895
99090
.00979
.02819
.01087
.06393
.01159
34
28+Zi
.91179
.00816
.9.5259
.00897
.99154
.00981
.02880
.01089
.06451
.01160
32
30
.91248
.00817
.95325
.00898
.99217
.00982
.02941
.01070
.06510
.01162
30
52+23
7.91318
0.00819
7.9.5391
0.00899
7.99281
0.00SV4
8.03001
0.01073
8.06568
0.01163
28
34
.91387
.00830
.954.58
.00901
.99344
.00985
.03062
.01073
.06626
.01165
26
56+24
.91457
.00821
.95524
.00902
.99407
.00986
.03123
.01075
.06684
.01166
24
38
40+25
.91526
7.91596
.00823
0.00834
.95590
7.95656
.00903
0.00905
.99470
7.99534
.00988
0.00989
.03183
.01076
.06742
.01168
0.01170
22
'20
8.03244
0.01078
8.06800
49
.91665
.00835
.95722
.00906
.99.597
.00991
.03304
.01079
.06859
.01171
18
44+26
.91734
.00837
.95788
.00908
.99660
.00992
.03365
.01081
.06917
.01173
16
46
.91803
.00838
.958.54
.00909
.99723
.00994
.03425
.01083
.06975
.01174
14
4^+27
7.91872
0.00839
7.95920
0.00910
7.99786
0.00995
8.03486
0.01084
8.07032
0.01176
12
50
.91941
.00831
.95986
.00912
.99849
.00997
.03546
.01085
.07090
.01177
10
52+28
.92010
.00833
.96052
.00913
.99912
.00998
.03606
.01087
.07148
.01179
8
54
56+29
.92079
7.92148
.00833
.96118
.00914
0.00916
7.99975
8.00038'
.00999
0.01001
.03666
8.03727
.01088
0.01090
.07206
8.07264
.01180
6
0.00835
7.96183
0.01182
4
5«
.92217
.00836
,96249
.00917
.00100
.01003
.03787
.01091
.07322
.01184
2
60+30
7.92286
0.00837
7.96315
0.00919
8.00163
0.01004
8.03847
0.01093
8.07379
0.01185
23h 18m
23h 16m
23'' 14">
S3h 12m
23h lOm
Page 822] TABLE 45.
«
Haversines.
s '
0* 50™ 12° 30'
Oh 52m 13° 0'
Ohs^m 13° 30'
Oh 56m 14° 0'
Oh 58m 14° 30'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav,
Log. Hav. Nat. llav.
Log. Hav.' Nat. Hav.
Log. nav.| Nat. Hav.
8.07379
0.01185
8.10772
0.01282
8.14035 1 0.01382
8.17179 i 0.01485
8.20211 1 0.01593
60
2
.07437
.01187
.10827
.01283
.14089 \ .01383
17230 1 .01487
.20261 1 .01594
58
•^+ I
.07494
.01188
.10883
.01285
.14142 .01385
17282 .01489
.20310 .01596
56
6
.07552
8.07610"
.01190
0.01192
.10938
8.10993
.01286
0.01288
.14195 : .01387
8.14248 1 0.01388"
"8
17333
.01491
.20360 ! .01598
8:20410 i 0.01600
54
52
8+ Z
"17384
0.01493
10
.07667
.01193
.11049
.01390
.14302 1 .01390
17436
.01494
.20459 .01602
50
12+ 3
.07725
.01195
.11104
.01391
.14355 ! .01392
17487
.01496
.20509
.01604
48
14
.07782
.01196
.11159
.01393
.14408 .01393
17538
.01498
.20558
.01605
46
16+ 4
8.07839
0.01198
8.11214
0.01395
8.14461 0.01395
8
17590
0.01499
8.20608
0.01607
44
18
.07897
.01199
.11269
.01396
.14514 .01397
17641
.01501
.20657 \ .01609
42
20+ 5
.07954
.01201
.11324
.01298
.14567 .01399
17692
.01503
.20706 ; .01611
40
22
.08011
.01203
0.01204
.11379
8.11435"
.01300
.14620 .01400
"8
17743
17794
.01505
0.01506
.20756 I .01613
8.20805 ; 0.01615
38
36
24+ 6
8.08069
0.01301
8.14673 ! 0.01402
26
.08126
.01206
.11490
.01303
.14726 i .01404
17845
.01508
.20854
.01616
34
28+ 7
.08183
.01207
.11544
.01305
.14779 1 .01405
17896
.01510
.20904
.01618
32
30
.08240
.01309
.11599
.01306
.14832
.01407
17947
.01513
.20953
.01630
30
82+ 8
8.08297
0.01311
8.11654
0.01308
8.14885
0.01409
8
17998
0.01513
8.21002 1 0.01632
28
34
.08354
.01313
.11709
.01309
.14938
.01411
18049
.01515
.21051 1 .01624
26
36+ 9
.08411
.01314
.11764
.01311
.14991
.01412
18100
.01517
.21100
.01636
24
38
40+10
.08468 .01215
.11819
8.11873
.01313
0.01314
.15043
8.15096
.01414
6.01416
""8
18151
18202"
.01519
0.01521
.21149
8.21199
.01627
0.01629
22
8.08525 1 0.01217
42
.08582 [ .01218
.11928
.01316
.15149
.01417
18253
.01522
.21248
.01631
IS
44+U
.08639 1 .01220
.11983
.01317
.15201
.01419
18303
.01524
.21297
.01633
16
46
.08696 j .01222
.12038
.01319
.1.5254
.01421
18354
.01526
.21346
.01635
14
48+n
8.08752 ! 0.01223
8.12092 0.01321
8.15307
0.01423
8
18405
0.01528
8.21395
0.01637
1!
50
.08809
.01235
.12147
.01323
.15359
.01424
18455
.01530
.21444
.01638
in
52+13
.08866
.01236
.12201
.01324
.15412
.01426
18506
.01531
.21493
.01640
S
64
.08922
.01238
0.01230
.12256
"8.12310"
.01326
0.01328
.15464
8.15517
.01428
0.01429
"8
18557
.01533
.21541
8.21.590
.01642
0.01644
H
4
56+14
8.08979
"18607 0.01535
58
8.09036
0.01231
8.12365
0.01329
8.15569
0.01431
8
18658 0.01537
8.21639
0.01646
2
231' 9m
23h1m
23'* 5m
23'' 3m
23h Im
0+15
Oi'SlmWSO'
Oft oSm 13° O'
Oh 55m 13° 30'
Oh 57m 14° 0'
Oh 59m 14° 3r
s
60
8.09092 1 0.01233
8.12419
0.01331
8.15622
0.01433
8.18709
0.01538
8.21688
0.01648
2
.09149 .01234
.12473
.01333
.15674
.01435
.18759
.01540
.21737
.01650
58
4+16
.09205 .01236
.12528
.01334
.15726
.01436
.18810
.01543
.21785
.01651
56
6
.09262 .01238
8.09318" 6.01339
.12582
.01336
0.01338
.15779
.01438
0.01440
.18860
8.18910
.01544
0.01546
.21834
8.21883
.01653
0.01655
54
~5>
S+17
8.12636
8.15831
iO
.09374 .01241
.12691
.01339
.15883
.01442
.18961
.01547
.21932
.01657
50
12+l'i
.09431 .01243
.12745
.01341
.15935
.01443
.19011
.01549
.21980
.01659
48
14
.09487 ; .01244
.12799
.01343
.15987
.01445
.19062
.01551
.22029
.01661
46
16+19
8.09543 . 0.01246
8.12853
0.01344
8.16040
0.01447
8.19112
0.01553
8.22077
0.01663
44
18
.09600 .01247
.12907 ! .01346
.16092
.01448
.19162
.01555
.22126
.01664
42
20+%0
.09656 i .01249
.12961
.01348
.16144
.01450
.19212
.01556
.22175
.01666
40
22
.09712 1 .01251
.13015
.01349
.16196
.01452
0.01454
.19263
8.19313
.01558
0.01560
.22223
~8. 22272
.01668
0.01670
38
36
24+n
8.09768 i 0.01252
8.13069
0.01351
8.16248
26
.09824 i .01254
.13123
.01353
.16300
.01455
.19363
.01563
.22320
.01673
34
28+Z2
.09880 j .01255
.13177
.01354
.16352
.01457
.19413
.01564
.22368
.01674
32
30
.09936 .01257
.13231
.01356
.16404
.01459
.19463
.01565
.22417
.01676
30
32+%^
8.09992 ; 0.01259
8.13285
0.01358
8.16456
0.01461
8.19513
0.01567
S. 22465
0.01677
28
34
.10048
.01260
.13339
.01360
.16508
.01462
.19563
.01569
.22514
.01679
26
56+24
.10104
.01262
.13392
.01361
.16559
.01464
.19613
.01571
.22562
.01681
24
38
.10160
8a0216
.01264
0.01265
.1.3446
.01363
.16611
.01466
0.01468
.19663
"8.19713"
.01573
0.01574
.22610
"8.22658"
.01683
0.01685
22
40+^5
8:i3500
0.01365
8.16663
~20~
42
.10271
.01267
.13554
.01366
.16715
.01469
.19763
.01576
.22707
.01687
IS
44+26
.10327
.01268
.13607
.01368
.16766
.01471
.19813
.01578
.22755
.01689
16
46
.10383 1 .01270
.13661
.01370
.16818
.01473
.19863
.01580
.22803
.01691
14
48+Z7
8.10439
0.01272
8.13714 j 0.01371
8.16870
0.01475
8.19913
0.01583
8.22851
0.01692
12
50
.10494
.01273
.13768 1 .01373
.16921
.01476
.19963
.01584
.22899
.01694
10
52+28
.10550
.01375
.13822
.01375
.16973
.01478
.20012
.01585
.22947
.01696
8
54
56+29
.10605
8.10661
.01377
.13875
.01376
.17024
.01480
0.01482
.20062
8.20112
.01587
0.01589
.22996
8.23044
.01698
0.01700
6
4
0.01378
8.13928
0.01378
8.17076
58
.10716
.01380
.13982
.01380
.17127
.01483
.20162
.01591
.23092
.01702
2
60+30
8.10772
0.01383
8.14035
0.01382
8.17179
0.01485
8.20211
0.01593
8.23140
0.01704
23» 8<n
«»6">
25*4™
gShgm
23h0m
TABLE 45.
Haversines,
[Page 823
s
lhO->
15° 0'
1" l"
15° 15'
li'J'"15°30'
ll'3m
15° 45'
Ih 4m
16° 0'
s
Log. Hav.
Nat. Hav.
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.23140
.231()4
.23188
.23212
.01704
.01705
.01706
.01707
.01707
.01708
.01709
.01710
.01711
.01713
.01713
.01714
8.24567
.24591
.24614
.24638
8.24661
.24685
.24708
.24732
8.24755
.24779
.24803
.24826
.01761
.01763
.01763
.01764
8.25971
.25994
.26017
.26040
.01818
.01819
.01830
.01831
8.273.52
.27375
.27398
.27420
8.27443
.27466
.27489
.27512
.01877
.01878
.01879
. .01880
.01881"
.01883
.01883
.01884
.01885
.01886
.01887
.01888
.01889
.01890
.01891
.01893
8.28711
.28734
.28756
.28779
.01937
.01938
.01939
.01940
.01941
.01943
.01943
.01944
60
59
58
57
56
55
54
53
+ 1'
5
6
7
8.2323.5
.23259
.23283
.23307
.01764
.01765
.01766
.01767
8.26064
.26087
.26110
.26133
.01833
.01833
.01834
.01835
8.28801
.28823
.28846
.28868
+ 3'
9
10
11
8.23331
.23355
.23379
.23403
.01768
.01769
.01770
.01771
8.26156
.26179
.26203
.26226
.01836
.01837
.01838
.01839
8.27534
.27557
.27580
.27603
8.28891
.28913
.28936
.28958
8.'289"80"
.29003
.29025
.29048
8.29070
.29092
.29115
.29137
8.291.59
.29182
.29204
.29226
.01945
.01946
.01947
.01948
52
51
50
49
+ 3'
13
14
15
8.23427
.23451
.23475
.23499
.01715
.01716
.01717
.01718
.01719
.01730
.01731
.01733
.01733
.01734
.01734
.01735
8.248.50
.24873
.24897
.24920
8.24944
.24967
.24991
.25014
"8.25037
.25061
.25084
.25108
.01773
.01773
.01774
.01775
8.26249
.26272
.26295
.26318
.01830
.01831
.01833
.01833
8.27626
.27648
.27671
.2"694
.01949
.01950
.01951
.01953
.01953
.01954
.01955
.01956
.01957
.01958
.01959
.01960
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
S3
32
SI
SO
29
28
27
26
25
+ *'
17
IS
19
8.23523
.23.546
.23570
.23594
8.23618
.23642
.23666
.23690
.01776
.01777
.01778
.01779
8.26341
.26364
.26388
.26411
.01834
.01835
.01836
.01837
8.27717
.27739
.27762
.27785
.01893
.01894
.01895
.01896
.01897
.01898
.01899
.01900
+ 5'
n
22
23
."01780
.01781
.01783
.01783
8.26434
.26457
.26480
.26.503
.01838
.01839
.01840
.01841
8.27807
.27830
.27853
.2-876
+ 6'
25
26
27
8.23713
.23737
.23761
.23785
.01736
.01737
.01738
.01739
8.25131
.25155
.25178
.25202
.01784
.01785
.01786
.01787
8.26526
.26549
.26572
.26595
8.26618
.26641
.26664
.26687
.01843
.01843
.01844
.01845
.01846"
.01847
.01848
.01849
.01850
.01851
.01853
.01853
8.27898
.27921
.27944
.27966
8.27989"
.28012
.28034
.28057
8.28080
.28102
.28125
.28147
.01901
.01903
.01903
.01904
8.29249
.29271
.29293
.29316
.01961
.01963
.01963
.01964
.01965
.01966
.01967
.01968
.01969
.01970
.01971
.01973
+ r
29
SO
31
8.23809
.23832
.23856
.23880
"8.23904
.23928
.23951
.23975
"8.23999
.24022
.24046
.24070
.01730
.01731
.01733
.01733
.01734
.01735
.01736
.01737
.01738
.01739
.01740
.01741
.01743
.01743
.01743
.01744
.01745
.01746
.01747
.01748
8.2.5225
.25248
.25272
.25295
8.25319
.2.5342
.2.5365
.25389
8.2.5412
.25435
.25459
.25482
.01788
.01789
.01789
.01790
.01905
.01906
.01907
.01908
.01909
.01910
.01911
.01913
8.29338
.29360
.29383
.29405
+ 8'
33
34
35
.01791
.01793
.01793
.01794
8.26710
.26733
.26756
.26779
8.29427
.29449
.29472
.29494
+ »'
37
38
39
.01795
.01796
.01797
.01798
8.26802
.26825
.26848
.26871
.01854
.01855
.01856
.01857
8.28170
.28193
.28215
.28238
.01913
.01914
.01915
.01916
8.29516
.29539
.29561
.29.583
.01973
.01974
.01975
.01976
.01977
.01978
.01979
.01980
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ IC
41
42
43
8.24094
.24118
.24141
.24165
8.25.505
.25529
.25.552
.25575
8.25599"
.25622
.25645
.25669
.01799
.01800
.01801
.01803
.01803
.01804
.01805
.01806
8.26894
.26917
.26940
.26963
8.26986"
.27009
.27032
.270.55
.01858
.01859
.01860
.01861
8.28260
.28283
.28300
.28328
.01917
.01918
.01919
.01930
.01931
.01933
.01933
.01934
8.29605
.29628
.29650
.29672
+ 11'
45
46
47
8.24189
.24212
.24236
.24260
.oiaei
.01863
.01863
.01864
8.28351
.28373
.28396
.28418
8.29694
.29^16
.29739
.29761
8.29783
.29805
.29827
.29850
8.29872
.29894
.29916
.29938
.01981
.01983
.01983
.01984
.01985
.01986
.01987
.01988
.01989
.01990
.01991
.01993
+ 13'
49
50
51
8.24283
.24307
.24331
.243.54
.01749
.01750
.01751
.01753
.01753
.01754
.01755
.01756
.01757
.01758
.01759
.01760
.01761
8.25692
.2.5715
.25738
.25762
.01807
.01808
.01809
.01810
.01811
.01813
.01813
.01814
8.27078
.27100
.27123
.27146
.01865
.01866
.01867
.01868
8.28441
.28464
.28486
.28509
.01935
.01936
.01937
.01938
+ 13'
53
54
55
8.24378
.24402
.24425
.24449
8.25785
.25808
.25831
.25855
8.27169
.27192
.27215
.27238
.01869
.01870
.01871
.01873
.01873
.01874
.01875
.01876
8.28.531
.28554
.28576
.28599
"8.28621
.28644
.28666
.28689
8.28711
.01939
.01930
.01931
.01933
.01933
.01934
.01935
.01936
.01937
+ U'
57
58
59
8.24473
.24496
.24520
.24543
8.2.5878
.2.5901
.25924
.25948
.01815
.01816
.01817
.01818
.01818
8.27261
.27283
.27306
.27329
8.29960
.29982
.30005
.30027
8.30049
.01993
.01994
.01995
. .01997
.01998
+ 15'
8:24567
8.25971
8.27352
.01877
22"
59m
22 K
58m
22"
57-"
22"
56"
22"
55m
Page 824]
TABLE 45.
Haversines.
s
Ih^mWlS'
i* 6". 16° 30'
lh7'nU°ii'
IhSm
17° 0'
i»9".17°15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
hog. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.30049
.30071
.30093
.30115
.01998
.01999
.02000
.02001
8.31366
.3138,
.31410
.31431
.02059
.03060
.02061
.02062
8.32663
.32684
.32706
.32727
8.32749
.32770
.32792
.32813
8.32834
.32856
.32877
.32899
.03121
.02122
.02124
.02125
8.33940
.33962
.33983
.34004
.03185
.02186
.02187
.02188
8.35199
.35220
.35241
.35261
.03349
.03350
.03351
.03352
.03253
.03354
.03355
.03357
.03258
.02259
.02360
.03261
.03262
.02263
.02264
.02365
60
59
58
57
56
55
54
53
62
61
60
49
'4S
47
46
45
'44
4J
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
'24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ 1'
5
6
7
8.30137
.30159
.30182
.30204
.03002
.03003
.02004
.02005
.02006
.02007
.03008
.03009
8.31453
.31475
.31497
.31518
'8.3i54d
.31562
.31584
.31605
.02063
.02064
.02065
.03066
.02126
.02127
.02128
.02129
.02130
.02131
.02133
.03133
8.34025
.34046
.34067
.34088
8.34109
.34130
.34152
.34173
.02189
.02190
.03191
.02192
8.35282
.35303
.35324
.35345
+ V
9
10
11
8.30226
.30248
.30270
.30292
.03067
.03068
.02069
.02070
.02193
.03194
.02195
.03196
.03198
.02199
.02200
.02201
.02202
.02303
.03304
.03305
.02206
.02307
.03308
.02209
8.35365
.35386
.35407
.35428
8.35449
.35469
.35490
.35511
+ 3'
IS
u
15
8.30314
.30336
.30358
.30380
8.30402
.30424
.30446
.30468
8.30490
.30512
.30534
.30556
.03010
.03011
.03013
.03013
8.31627
.31649
.31670
.31692
'8.31714
.31735
.31757
.31779
.02071
.02072
.02074
.02075
.03076
.03077
.03078
.03079
.03080
.02081
.02082
.03083
8.32920
.32941
.32963
.32984
8.33006
.33027
.33048
.33070
.03134
.03135
.03136
.03137
.03138
.03139
.02140
.02141
8.34194
.34215
.34236
.34257
+ i'
n
18
19
.03014
.03015
.03016
.03017
8.34278
,34299
.34320
. .34341
8.34362
.34383
.34404
.34425
8.34446
.34467
.34488
.34509
8.35532
.35552
.35573
.35594
8.35614
.35635
.35656
.35677
.03366
.02267
.02268
.02270
.02271
.02272
.02273
.02274
.02275
.02276
.02377
.02278
.02279
.02280
.02281
.02283
.03384
.03385
.03286
.02287
.02288
.02289
.02290
.02291
.02293
.03393
.03395
.03396
.03397
.03298
.02299
.02300
.02301
.03302
.02303
.03304
.03305
.03307
.03308
.03309
.03310
.03311
.03313
.03313
.03314
+ 5'
21
- 22
23
.03018
.03019
.03030
.03021
8.31800
.31822
.31844
.31865
8.31887
.31909
.31930
.31952
8.31974
.31995
.32017
.32039
8.33091
.33112
.33134
.33155
.02142
.02143
.02145
.02146
.02147
.02148
.02149
.02150
+ 6'
25
26
27
8.30578
.30600
.30622
.30644
8.30666
.30688
.30710
.30732
.02023
.03033
.03034
.03035
.02026
.02027
.02028
.02029
.03084
.02085
.03086
.03087
8.33176
.33198
.33219
.33240
.02310
.03311
.03312
.03314
8.35697
.35718
.35739
.35759
8.35780
.35801
.35821
.35842
+ r
29
SO
31
.03088
.02089
.02090
.02091
.02092
.02093
.02094
.02095
8.33262
.33283
.33304
.33325
.02151
.02152
.02153
.02154
8.34530
.34551
.34572
.34593
8.34614
.34635
.34656
.34677
.02315
.02216
.02317
.03318
.02219'
.02220
.03231
.03232
.02333
.02224
.02225
.02226
.023^7
.03339
.03330
.02331
+ 8'
33
34
35
8.30754
.30776
.30798
.30820
.02030
.02031
.02032
.03033
.03034
.03035
.03036
.02037
8.32060
.32082
.32103
.32125
8.32147
.32168
.32190
.32211
8.32233
.32254
.32276
.32297
8.33347
.33368
.33389
.33411
.02155
.02156
.02157
.02158
8.35863
.35883
.35904
.35925
8.35945
.35966
.35987
.36007
8.36028
.36048
.36069
.36090
+ 9'
37
38
39
8.30842
.30863
.30885
.30907
.03096
.03097
.03098
.03099
8.33432
.33453
.33474
.33496
.03159
.03160
.03161
.03162
8.34698
.34719
.34740
.34761
+ lO'
41
42
43
8.30929
.30951
.30973
.30995
.02038
.03039
.03040
.03042
.02101
.03102
.03103
.03104
8.33517
.33538
.33559
.33580
.03164
.03165
.03166
.03167
8.34782
.34803
.34823
.34844
+ 11'
45
46
47
8.31017
.31039
.31060
.31082
.02043
.02044
.02045
.02046
.02047
.02048
.03049
.03050
8.32319
.32341
.32362
.32384
8.32405'
.32427
.32448
.32470
.02105
.02106
.02107
.02108
.02109
.02110
.02111
.02113
.03113
.02114
.02115
.03116
8.33602
.33623
.33644
.33665
8.33686
.33708
.33729
.33750
.03168
.02169
.02170
.02171
8.34865
.34886
.34907
.34928
.02333
.03333
.03234
.03335
.02236
.02237
.03338
.03339
.'03340
.03341
.03343
.03344
.03245
.03246
.03347
.02248
.03249
8.36110
.36131
.36151
.36172
8.36193
.36213
.36234
.362.54
+ 13'
49
50
51
8.31104
.31126
.31148
.31170
.02172
.03173
.03174
.03175
8.34949
.34970
.34991
.35011
+ 13'
53
54
55
8.31192
.31213
.31235
.31257
.02051
.02053
.02053
.02054
8.32491
.32513
.32534
.32556
8.33771
.33792
.33814
.33835
.63176
.03177
.03178
.03179
8.35032
.35053
.35074
.35095
8.35116
.35137
.35157
.35178
8.36275
.36295
.36316
.36337
+ w
57
58
59
8.31279
.31301
.31322
.81344
.02055
.02056
.03057
.03058
8.32577
.32599
.32620
.32642
.03117
.03118
.03119
.03130
.02121
8.33856
.33877
.33898
.33919
.03181
.03183
.03183
.03184
8.36357
.36378
.36398
.36419
8.3'6'439
+ 15'
8.31366
.02059
8.32663
8.33940
.02185
8.35199
22 h
54m
221'
SSm
22 1'
52 m
22''
57 ">
22 h
50 m
TABLE 45.
Haversines.
[Page 825
s
Ih IQm
17 30'
IhUm
17° 45'
Ih 12m
18° 0'
Ih 13m
18° 15'
11, 14m
18° 30'
s
Log. Hav.
Nat. Hav.
log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.36439
.36460
.36480
.36501
.02311
.02315
.02316
.03317
8.37662
.37682
.37702
.37722
8.37742'
.37763
.37783
.37803
.03380
.03381
.02383
.02384
.02385
.02386
.02387
.02388
8.38867
.38886
.38906
.38926
8.38946~
.38966
.38986
.39006
.02447
.02448
.02449
.02451
.02452
.02453
.02454
.02455
.02456
.02457
.02458
.02460
8.40055
.40074
.40094
.40114
8.40133
.40153
.40172
.40192
8.40212
.40231
.40251
.40271
.02515
.03516
.02517
.03518
.03530
.02521
.02522
.03533
.03534
.03535
.02526
.02528
8.41226
.41246
.41265
.41284
'8.41304
.41323
.41343
.41362
'8.41381
.41401
.41420
.41439
8.414.59
,41478
.41497
.41517
.03584
.03585
.02586
.02587
.02588
.02590
.02591
.02592
60
59
58
57
56
55
54
53
52
51
50
49
48'
47
46
45
+ 1'
5
6
7
8.36521
.36542
.36562
.36583
.02319
.02320
.02321
.02322
+ r
9
10
11
+ 3'
13
14
15
8.36603
.36624
.36644
.36665
8.36685
.36706
.36726
.36746
.02323
.02324
.02335
.02326
.02327
.02328
.03329
.02331
.02332
.02333
.02331
.02335
.02336
.02337
.02338
.02339
.02340
.02342
.03343
.02344
.02345
.02346
.02347
.02348
.02349
.03350
.03351
.02353
.02354
.02355
.02356
.02357
.02358
.03359
.03360
.03361
8.37823
.37843
.37864
.37884
8.37904
.37924
.37944
.37964
8.37985"
.38005
.38025
.38045
8.38065
.38085
.38105
.38126
8.38146
.38166
.38186
.38206
8.38226
.38246
.38266
.38286
8.38306
.38326
.38346
.38367
8.38387
.38407
.38427
.38447
.03389
.03390
.02391
.02392
.03394
.03395
.03396
.02397
8.39026
.39046
.39066
.39086
.03593
.03594
.02595
.02597
.03598
.03599
.02600
.02601
8.39105
.39125
.39145
.39165
.02461
.02462
.02463
.02464
8.40290
.40310
.40329
.40349
8.40369
.40388
.40408
.40427
.02529
.02530
.02531
.02532
+ *'
17
18
19
8.36767
.36787
.36808
.36828
.03398
.03399
.02400
.03401
.03403
.03404
.03405
.03406
.02407
.02408
.02409
.02410
.02411
.03413
.03414
.03415
.02416
.02417
.02418
.03419
.02430
.02421
.02423
.02424
8.39185
.39205
.39225
.39245
8.39264
.39284
.39304
.39324
8.39344"
.39364
.39384
.39403
8.39423"
.39443
.39463
.39482
.02465
.02466
.03467
.03469
.02533
.02534
.03536
.02537
.02538
.02539
.03540
.02541
.02542
.02544
.03545
.03546
.02547
.03548
.03549
.03550
.03553
.03553
.02554
.03555
8.41536
.41555
.41575
.41594
"8:41613
.41632
.41652
.41671
8.41690
.41710
.41729
.41748
8.41767
.41787
.41806
.41825
.02602
.02603
.02605
.02606
.02607
.02608
.03609
.03610
.03612
.02613
.02614
.02615
44
43
42
41
40
39
38
37
36
35
34
33
+ S'
21
22
23
8.36849
.36869
.36889
.36910
8.36930
.36951
.36971
.36991
.03470
.02471
.02472
.02473
.02474
.02475
.03476
.03478
.03479
.02480
.02481
.03483
.03483
.02484
.03486
.03487
.02488
.02489
.02490
.02491
8.40447
.40467
.40486
.40506
"8.4052b
.40545
.40564
.40584
"8.40603
.40623
.40642
.40662
8.40681
.40701
.40721
.40740
+ 6'
25
/6
27
+ r
29
30
31
+ 8'
33
34
35
8.37012
.37032
.37053
.37073
8.37093
.37114
.37134
.37154-
.02616
.02617
.02619
.03630
.03631
.03632
.02623
.02624
32
31
30
29
28
it i
26
25
24
23
22
21
8.39502
.39522
.39542
.39562
8.3958 L
.39601
.39621
.39641
8.39660
.39680
.39700
.39720
8.41845
.41864
.41883
.41902
+ 9^
37
38
39
8.37175
.37195
.37215
.37236
8,37256
.37276
.37297
.37317
8,40760
.40779
.40799
.40818
.02556
.03557
.02559
.03560
8.41921
.41941
.41960
.41979
.02626
.02627
.02638
.03629
+ W
41
42
43
8,38467
.38487
.38.507
.38527
8.38547
.38.567
.38587
.38607
8.38627
.38647
.38667
.38687
8.38707
.38727
.38747
.38767
8.38787
.38807
.38827
.38847
8.38867'
.02425
.02426
.02427
.02428
.02492
.02493
.02495
.03496
8.40837
.40857
.40876
.40896
.02561
.03563
.03563
.03564
8.41998
.42018
.42037
.42056
.03630
.03631
.03633
.03634
.03635
.02636
.02637
.02638
20
19
18
n
16
15
14
13
12
11
10
9
+ 11'
45
46
47
8.37337
.37358
.37378
.37398
.03363
.02364
.03365
.03366
.02367
.02368
.02369
.02370
.02371
.03373
.03374
.02375
.02376
.02377
.02378
.02379
.02380
.02429
.02430
.03431
.02433
.02434
.03435
.03436
.03437
.02438
.02439
.02440
.02442
.03443
.02444
.02445
.02446
.02447
8.39739
.39759
.39779
.39799
8.39818
.39838
.39858
.39877
8.39897
.39917
.39937
.39956
8.39976
.39996
.40015
.40035
8.40055"
.02497
.03498
.02499
.02500
8.40915
.40935
.40954
.40974
.03565
.02567
.03568
.03569
8.42075
.42095
.42114
.42133
+ 12'
49
50
51
8.37419
.37439
.37459
.37479
.02501
.02503
.02501
.02505
.02506
.02507
.02508
.02509
.02510
.02512
.02513
.02514
.02515
8.40993
.41013
.41032
.41052
8.41071
.41090
.41110
.41129
8.41149
,41168
.41187
.41207
8.41226
.03570
.02571
.03573
.03573
.03575
.03576
.02577
.02578
.02579
.03580
.03583
.03583
.03584
8.42152
.42171
.42190
.42210
8.42229
.42248
.42267
.42286
8.42305
.42324
.42344
.42363
.02639
.02641
.02643
.02643
+ 13'
53
64
65
8.37500
.37520
.37540
.37.560
.03644
.03645
.02646
.02648
.02649
.02650
.02651
.02652
8
1
6
5
4
3
2
1
+ U'
57
58
59
8.37581
.37601
.37621
.37641
+ 15'
8.37662
8.42382
.02653
22>'
49 m
22''
4Sm
221'
47 m
22"
46m
22''
45m
Page 826]
TABLE 45.
Ilaversines.
s
Ihism
18° 45'
Ih 16m 19° 0'
Ih irm
19° 15'
Ih 18m 19= 30'
ihigm
19° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.42382
.42401
.42420
.42439
.03653
.03655
.03656
.03657
8.43522
.43541
.43560
.43578
.03734
.03735
.03736
.03738
8.44647
.44665
.44684
.44703
.03796
.03797
.03798
.03799
8.45757
.45775
.45794
.45812
.03868
.03869
.03870
.03871
8.46852
.46871
.46889
.46907
.03941
.03943
.02944
.02945
60
69
58
57
+ 1'
5
6
7
8.42458
.42477
.42497
.42516
.03658
.03659
.03661
.03663
8.43597
.43616
.43635
.43654
.03739
.03730
.03731
.03733
8.44721
.44740
.44758
.44777
8.44796
.44814
.44833
.44851
8.44870
.44889
.44907
.44926
.03800
.03803
.03803
.03804
.02805
.02806
.02808
.03809
8.45830
.45849
.45867
.45885
.03873
.03874
.03875
.03376
8.46925
.46943
.46961
.46979
.03946
.03947
.03949
.03950
56
55
54
53
+ 3'
9
10
11
8.42535
.42554
.42573
.42592
.03663
.03664
.03665
.03666
8.43673
.43692
.43710
.43729
8.43748
.43767
.43786
.43805
.02734
.03735
.03736
.03737
8.45904
.45922
.45940
.45959
.03878
.03879
.03880
.03881
8.46998
.47016
.47034
.47052
.03951
.03953
.03954
.03955
52
51
50
49
+ 3'
14
15
8.42611
.42630
.42649
.42668
.03668
.03669
.03670
.03671
.03738
.03739
.03741
.03743
.03810
.03811
.03813
.03814
.03815
.03816
.03817
.02818
8.45977
.45995
.46014
.46032
.02883
.03884
.02885
.03886
8.47070
.47088
.47106
.47124
.03956
.03957
.03958
.03960
48
47
46
45
+ i'
n
18
19
8.42687
.42706
.42725
.42745
.03673
.03673
.03675
.03676
8.43823
.43842
.43861
.43880
.03743
.03744
.03745
.02747
8.44944
.44963
.44981
.45000
8.45018
.45037
.45055
.45074
8.45093
.45111
.45130
.45148
8.46050
.46069
.46087
.46105
.03887
.03889
.03890
.03891
8.47142
.47160
.47178
.47197
.03961
.03963
.03963
.03965
44
43
42
41
+ 5'
21
22
23
8.42764
.42783
.42802
.42821
.03677
.03678
.03679
.03680
8.43899
.43917
.43936
.43955
8.43974
.43992
.44011
.44030
8.44049
.44067
.44086
.44105
.03748
.03749
.03750
.03751
.03830
.02821
.03823
.03833
.03834
.03836
.03837
.03838
8.46124
.46142
.46160
.46179
.03893
.02893
.02895
.02896
8.47215
.47233
.47251
.47269
.03966
.03967
.03968
.02970
40
39
38
37
36
35
34
33
+ 6'
25
26
27
8.42840
.42859
.42878
.42897
.03683
.03683
.03684
.03685
.03753
.03754
.03755
.03756
8.46197
.46215
.46233
.46252
.03897
.02898
.03900
.03901
8.47287
.47305
.47323
.47341
.02971
.03972
.02973
.02974
+ r
29
30
31
8.42916
.42935
.42954
.42973
.03686
.03688
.03689
.03690
.03757
.03759
.03760
.03761
8.45167
.45185
.45204
.45222
.03839
.03830
.03833
.03833
.03834
.03835
.03836
.03838
.02839
.02840
.03841
.03843
8.46270
.46288
.46306
.46325
8.46343
.46361
.46379
.46398
.03903
.02903
.03904
.03906
.02907
.03908
.03909
.03911
8.47359
.47377
.47395
.47413
.02976
.03977
.02978
.03979
32
31
30
29
+ S'
S3
34
35
8.42992
.43011
.43030
.43049
.03691
.03693
.03693
.03695
8.44124
.44142
.44161
.44180
.03763
.03763
.02764
.03766
8.45241
.45259
.45278
.45296
8.47431
.47449
.47467
.^7485
.02981
.02983
.03983
.03984
28
27
26
25
+ 9'
37
38
39
8.43068
.43087
.43106
.43125
.03696
.03697
.03698
.03699
8.44199
.44217
.44236
.44255
.03767
.03768
.03769
.03771
8.45315
.45333
.45352
.45370
8.46416
.46434
.46452
.46471
.03912
.03913
.03914
.03915
8.47503
.47521
.47539
.47557
.03986
.03987
.03988
.03989
24
23
22
21
20
19
18
17
+ W
41
42
43
8.43144
.43163
.43181
.43200
.03700
.03703
.03703
.03704
8.44273
.44292
.44311
.44330
.03773
.03773
.03774
.03775
8.45388
.45407
.45425
.45444
.02844
.02845
.02846
.02847
8.46489
.46507
.46525
.46544
.03917
.03918
.03919
.03930
8.47575
.47593
.47611
.47629
.03991
.03993
.02993
.02994
+ 11'
45
46
47
8.43219
.43238
.43257
.43276
.03705
.03706
.03708
.03709
8.44348
.44367
.44386
.44404
.03776
.03778
.03779
.03780
8.45462
.45481
.45499
.45518
.03849
.03850
.03851
.03853
.03853
.03855
.02856
.02857
8.46562
.46.580
.46598
.46616
"^S. 46634
.46653
.46671
.46689
.03933
.03933
.03934
.03935
8.47647
.47665
.47683
.47701
.02996
.03997
.03998
.03999
16
15
14
13
+ 13'
49
50
51
8.43295
.43314
.43333
.43352
.03710
.03711
.03713
.03713
8.44423
.44442
.44460
.44479
.03781
.03783
.03784
.03785
8.45536
.45554
.45573
.45591
.03936
.03938
.03939
.02930
8.47719
.47737
.47755
.47773
.03000
.03003
.03003
.03004
12
11
10
9
+ 13'
5S
54
55
8.43371
.43390
.43409
.43427
.03715
.03716
.03717
.03718
8.44498
.44516
.44535
.44554
.03786
.03787
.03788
.03790
8.45610
.45628
.45646
.45665
.02858
.02859
.02861
.03862
8.46707
.46725
.46744
.46762
8.46780
.46798
.46816
.46834
.03931
.03933
.03934
.03935
8.47791
.47809
.47827
.47844
.03005
.03007
.03008
.03009
8
7
6
5
4
3
2
1
+ 14'
57
58
59
8.43446
.43465
.43484
.43503
.03719
.03731
.03733
.03733
8.44572
.44591
.44610
.44628
.03791
.03793
.03793
.03794
8.45683
.45702
.45720
.45738
.03863
.03864
.03866
.03867
.03936
.03938
.03939
.03940
8.47862
.47880
.47898
.47916
.03010
.03013
.03013
.03014
+ 15'
8.43522
.03734
8.44647
.03796
8.45757
.03868
8.46852
.03941
8.47934
.03015
22"
44'"
22h
43m
22"
42m
22"
41m
22"
40m
TABLE 45.
Ilaversines.
[Page 827
s
Ih20m20°0'
lit 21m
30° 15'
Ih 22^90° W
Ih 23m Z0°i5'
lh24m
21° 0'
a
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Uav,
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.47934
.47952
.47970
.47988
.03015
.03017
.03018
.03019
8.49002
.49020
,49037
.49055
.03090
.03093
.03093
.03094
8. -50056
.50074
.50091
.50109
.03166
.03168
.03169
.03170
.03171
.03173
.03174
.03175
8.51098
..51115
.51132
.51150
.03243
.03245
.03246
.03247
8.52127
.52144
.52161
.52178
.03321
.03322
.03324
.03335
60
59
68
57
+ 1'
5
6
7
8.48006
.48024
.48041
.48059
.03030
.03033
.03033
.03034
8.49073
.49090
.49108
.49126
.03095
.03097
.03098
.03099
8.50126
.50144
.50161
.50179
8.511G7
.51184
.51201
.51219
.03248
.03350
.03351
.03353
.03354
.03355
.03356
.03357
8.52195
..52212
.52229
.52246
.03336
.03338
.03329
.03330
56
55
54
53
+ r
9
10
11
8.48077
.48095
.48113
.48131
.03035
.03037
.03038
.03039
8.49143
.49161
.49179
.49196
S. 492 14
.49232
.49249
.49267
.03101
.03103
.03103
.03104
.03106
.03107
.03108
.03109
8.50196
.50214
.50231
.50248
.03177
.03178
.03179
.03180
8.51236
.51253
.51270
.51287
8.52263
.52280
.,52297
.52314
.03331
.03333
.03334
.03335
52
51
50
49
48
47
46
45
+ 3'
13
14
15
8.48149
.48167
.48184
.48202
.03030
.03033
.03033
.03031
.03035
.03037
.03038
.03039
8.50266
.50283
.50301
.50318
.03183
.03183
.03184
.03186
8.51305
.51322
.51339
.513.56
.03359
.03360
.03261
.03263
8.52331
.52348
.52365
.52382
.03337
.03338
.03339
.03341
+ 4'
17
18-
19
8.48220
.48238
.48256
.48274
8.49284
.49302
.49320
.49337
.03111
.03113
.03113
.03114
.03116
.03117
.03118
.03119
8.50335
.50353
.50370
.50388
8..50405
.50422
.50440
.504.57
.03187
.03188
.03189
.03191
8.51374
.51391
.51408
.51425
.03264
.03265
.03266
.03268
8.52399
.52416
..52433
.52450
.03342
.03343
.03344
.03346
44
43
42
41
+ 5'
21
22
23
8.48292
.48309
.48327
.48345
.03040
.03043
.03013
.03044
8.49355
.49373
.49390
.49408
.03193
.03193
.03194
.03196
8.51442
.51459
.51477
.51494
.03269
.03270
.03272
.03273
8.52467
.52484
.52501
.52518
.03347
.03348
.03350
.03351
40
39
38
37
+ 6'
25
26
27
8.48363
.48381
.48399
.48416
.03045
.03047
.03048
.03019
8.49425
.49443
.49461
.49478
.03131
.03133
.03133
.03135
8.50475
.50492
.50509
.50527
.03197
.03198
.03300
.03301
8.51511
.51.528
.51545
.51562
.03274
.03275
.03277
.03278
8.52535
.52552
.52569
.52585
.03352
.03354
.03355
.03356
36
35
34
33
+ r
29
30
31
8.48434
.48452
.48470
.48488
.03050
.03053
.03053
.03054
8.49496
.49513
.49.531
.49548
.03136
.03137
.03138
.03130
8.50544
.50561
.50579
.50596
.03303
.03304
.03305
.03306
8.51580
.51597
,51614
.51631
8,51648
.51665
.51682
.51700
.03279
.03281
.03282
.03283
.03285
.03286
.03387
.03288
8.,52602
.52619
..52636
.52653
.03358
.03359
.03360
.03361
32
31
30
29
+ 8'
33
34
35
8.48505
.48523
.48541
.48559
.03055
.03057
.03058
.03059
8.49566
.49.584
.49601
.49619
.03131
.03133
.03133
.03135
8.50614
..50631
.50648
.50666
.03307
.03309
.03310
.03311
8.52670
.52687
.52704
.52721
.03363
.03364
.03365
.03367
28
27
26
25
+ 9'
37
38
39
8.48576
.48594
.48612
.48630
.03000
.03063
.03063
.03064
8.49636
.49654
.49671
.49689
.03136
.03137
.03138
.03140
8.50683
.50700
..50718
.50735
.03313
.03314
.03315
.03316
8.51717
.51734
.51751
.51768
.03290
.03291
.03292
.03294
8.52738
.52755
.52772
..52789
.03368
.03369
.03371
.03372
24
23
22
21
+ W
41
42
43
8.48648
.48665
.48683
.48701
.03065
.03067
.03068
.03069
8.49706
.49724
.49742
.49759
.03141
.03143
.03144
.03145
8.50752
.50770
.,50787
.50804
.03318
.03319
.03330
.03331
8.51785
.51802
.51819
.51836
.03295
.03396
.03398
.03299
8.52806
.52822
.,52839
.52856
.03373
.03375
.03376
.03377
20
19
18
'17
+ 11'
45
46
47
8.48719
.48736
.48754
.48772
.03070
.03073
.03073
.03074
8.49777
.49794
.49812
.49829
8.49847"
.49864
.49882
.49899
.03146
.03147
.03149
.03150
8.50821
.50839
..50856
..50873
.03223
.03224
.03335
.03237
8.51854
.51871
.51888
.51905
.03300
.03301
.03303
.03304
8.52873
.52890
.52907
.52924
.03379
.03380
.03381
.03382
16
15
14
is
12'
11
10
9
+ 13'
49
50
51
8.48789
.48807
.48825
.48843
.03075
.03077
.03078
.03079
.03151
.03153
.03154
.03155
8.50891
..50908
.50925
.50943
.03238
.03239
.03330
.03333
8,51922
.51939
.519,56
.51973
.03305
.03307
.03308
.03309
8.52941
.52958
.52974
.52991
.03384
.03385
.03386
.03388
f 13'
53
. 54
55
8.48860
.48878
.48896
.48914
.03080
.03083
.03083
.03084
8.499 J 7
.49934
.49952
.49969
.03156
.03157
.03159
.03160
8.. 50960
.50977
.50994
.51012
.03333
.03334
.03336
.03337
8.51990
..52007
.,52024
..52041
.03311
.03312
.03313
.03314
8.53008
.5,3025
.53042
.53059
.03389
.03390
.03392
.03393
8
7
6
5
f 14'
57
58
59
8.48931
.48949
.48967
.48984
.03085
.03087
.03088
.03089
8.49987
.•50004
.50022
..50039
.03161
.03163
.03164
.03165
8.51029
.51046
.51063
.51081
.03338
.03239
.03241
.03242
8.. 520,58
.,52076
.52093
.,52110
.03316
.03317
.03318
.03320
8.53076
.53092
.53109
..53126
.03394
.03396
.03397
.03398
4
3
2
1
t- 15'
8.49002
.03090
8,50056
.03166
8.51098
.03243
8.52127
.03321
8.53143
.03400
22li
39m
92h
SSm
22>i 37m
22^ 36^
221^
35m
Page 828]
TABLE 45.
Haversines.
1
1
s
J ft 25m
21° 15'
Ih 26m 21° 30'
Ih 27m 21° 45'
Ik 28m 22° O'
111- 29m
22° 15'
s
Log. Ilav.
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav.
Nat. }Iav.
Log. Hav.
Nat. Hav.
1
2
3
8.53143
..53160
.53177
.53193
.03400
.03401
.03402
.03404
8.54147
..54164
.54180
.54197
.03479
.03480
.03482
.03483
.03484
.03486
.03487
.03488
.03490
.03491
.03492
.03494
.03495
.03496
.03498
.03499
.03500
.03502
.03503
.03504
.03506
.03507
.03509
.03510
.03511
.03513
.03514
.03515
.03517
.03518
.03519
.03521
.03523
.03533
.03535
.03530
8.55139
..55156
55172
..55189
8.55205
.55221
55238
.55254
8.5.5271
.55287
.5.5303
.55320
8.5.5336
.5.5353
.55369
« .5.5385
8.5.540'I
..5.5418
.•55435
..5.5451
8. .5.5467
..55484
.55.500
.5,5516
8.55.533
.•55.549
..5.5560
.55.582
8.,55.598
..5,5615
.55631
.5.5647
S..55664
.55680
.55696
..5^5713
8. •5^5729
.•55745
.55762
..55778
8.5.5794
..5.5811
.55827
.55843
.03560
.03561
.03562
.03564
.03565
.03566
.03568
.03569
.03570
.03573
.03573
.03574
.0:i576
.03577
.03578
.03580
.03581
.03583
.03584
.03585
.03587
.03588
.03589
.03591
,03593
.03593
.03595
.03596
.03597
.03599
.03600
.03601
.03603
.03604
.03605
.03607
.03608
.03610
.03611
.03612
.03614
.03615
.03616
.03618
.03619
.03620
.03633
.03623
.03624
.03626
.03627
.03629
8.56120
.56136
.56152
.56169
.03641
.03642
.03644
.03645
.03646
.03648
.03649
.03650
.03652
.03653
.03654
.03656
.03657
.03659
.03660
.03661
.03663
.03664
.03665
.03667
.03668
.03669
.03671
.03672
.03674
.03675
.03676
.03678
.03679
.03680
.03683
.03683
.03685
.03686
.03687
.03689
8.57089
.57105
.57121
.57137
.03723
.03734
.03J26
.03727
60
59
68
57
+ 1'
5
6
7
8.53210
.53227
.53244
.53261
8.53277
.53294
.53311
.53328
.03405
.03406
.03408
.03409
.03410
.03411
.03413
.03414
.03415
.03417
.03418
.03419
8.54214
.54230
.54247
.54263
8.54280
.54297
.54313
.54330
8..54346
.•54363
.54380
.•54396
8.56185
.56201
.56217
.56233
8.56250
.56266
.56282
.56298
8.56315
.56331
.56347
.56363
8.56379
.56396
.56412
.56428
8.564T4'
..56460
..56477
.56493
8.56509'
.,56.525
.56541
.,56557
8. ,56574
.56590
.56006
.56622
8.,56638
.566,54
.56670
.56687
8.57153
.57169
.57185
.57201
.03728
.03730
.03731
.03733
56
55
64
5-1
+ 2'
9
10
11
8.57217
.57233
.57230
.57266
.03734
.03735
.03737
.03738
52
61
50
43
48
47
46
45
44
43
42
41
+ 3'
13
14
15
8.53345
.53361
.53378
.53395
8.57282
.57298
.57314
.57330
.03740
.03741
.03742
.03744
+ 4'
n
18
19
8.53412
.53429
.53445
.53462
.03421
.03422
.03423
.03425
8.54413
..54429
.•54446
..54462
8.57346
.57362
.57378
.57394
.03745
.03746
.03741?
.03749
+ 5'
22
23
8.53479
.53496
.53512
.53529
.03426
.03427
.03429
.03430
8.54479
..54496
.•54512
..54529
'8.. 54545
..54.562
.54578
.54595
8.,57410
.57426
.57442
.57458
.C3751
.03753
.03753
.03755
.03756
.03757
.03759
.03760
40
39
38
37
06
35
34
33
+ 6'
25
26
27
8.53546
.53563
.53580
.53596
.03431
.03433
.03434
.03435
.03437
.03438
.03439
.03441
8.57474
.57490
.57.506
.57522
+ r
29
30
31
8.53613
.53630
.53646
.53663
8.54612
..54628
.54645
.54661
8..54678
.54694
.54711
.54727
8.57,538
.57554
.57570
.57,585
.03763
.03763
.03764
.03766
32
31
30
29
+ 8'
55
34
35
+ a'
37
38
39
8.53680
.53697
.53713
.53730
.03442
.03443
.03445
.03446
8.57601
.57617
.57633
.57649
.03767
.03769
.03770
.03771
28
27
26
25
24
23
22
21
8.53747
.53764
.S3780
.53797
.03447
.03449
.03450
.03451
8..54744
.54760
.54777
.54793
.03537
.03539
.03530
.03531
8.56703
.,56719
.56735
.56751
8.56767
.56783
.56799
.,56816
8.56832
.56848
.56864
.56880
.03690
.03691
.03693
.03694
.03695
.03697
.03698
.03700
8.57665
.57681
.57697
.57713
8..57729
.57745
.57761
.57777
.03773
.03774
.03775
.03777
+ 10'
41
42
43
8.53814
.53830
.53847
.53864
.03453
.03454
.03455
.03457
8..54810
.•54826
.•54843
.54859
8.54876
.54892
.54909
.54925
.03533
.03534
.03535
.03537
.03538
.03539
.03541
.03542
.03778
.03780
.03781
.03782
20
19
18
17
16
15
14
13
+ 11'
45
46
47
8.53880
.53897
.53914
.53930
.03448
.03459
.03460
.03462
.03463
.03464
.03466
.03467
8.5.58,59
..5.5876
.5.5892
.55908
"8.,5,5925
,5.5941
.5.5957
.5,5973
8.5.5990
56006
.56022
.56039
8.5605,5'
.56071
.56087
.,56104
.03701
.03702
.03704
.03705
.03706
.03708
.03709
.03711
8.57793
.57809
.57825
.57841
.03784
.03785
.03787
.03788
+ 12'
49
50
51
8.53947
.53964
.53980
.53997
8..54942
.•549^58
.54975
.54991
.03543
.03545
.03546
.03547
.03549
.03550
.03551
.03553
.03554
.03555
.03557
.03558
.03560
8.-56896
.,56912
56928
.56944
8.57856
.57872
.57888
.57904
.03789
.03791
.03792
.03794
12
11
10
9
8
7
&
5
4
3
2
1
+ 13'
55
54
55
8.54014
.54030
.54047
.4.5064
.03468
.03470
.03471
.03472
8.55008
.55024
.,5.5041
.5.5057
.03630
.03631
.03633
.03634
.03635
.03637
.03638
.03639
8.56960
56977
.56993
.57009
8.57025
.57041
.57057
.57073
8.57089
.03712
.03713
.03715
.03716
8.57920
.57936
57952
.57968
.03795
.03796
.03798
.03799
.03800
.03802
.03803
.03805
+ U'
57
58
59
8.54080
.54097
.54114
.54130
.03474
.03475
.03476
.03478
8.5.5073
.5.5090
.55106
.55123
.03717
.03719
.03720
.03723
.03723
8.57984
.58000
.58015
.58031
+ 15'
8.54147
.03479
8.55139
8.56120
.03641
8.58047
.03806
22^
34m
22^
SSm
22f^
S2m
22^^
Sim
.'?'»
30m
TABLE 45.
Haversines.
[Page 829
s
1ft 50™ 22° 30' 1
IhSlm
?2°«'
Ih spn 330 (K 1
Ih 33m 33° 15' 1
ihS4m
33° 30'
s
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.58047
.58063
.58079
.58095
.03806
.03807
.03809
.03810
,03812
.03813
.03814
.03816
8.58994
.59010
.59026
.59042
8.59057'
.59073
.59089
.59104
.03890
.03891
.03893
.03894
8.59931
.59947
.59962
.59978
.03975
.03976
.03978
.03979
8.60857
.60873
.60888
.60903
.04060
.04062
.04063
.04065
8.61773
61789
.61804
.61819
.04147
.04148
.04150
.04151
60
59
58
57
56
55
54
53
52
51
50
49
+ r
5
6
7
8.58111
.58127
.58142
.58158
.03896
.03897
.03898
.03900
8.59993
.60009
.60024
.60040
.03980
.03982
.03983
.03985
8.00919
.60934
.60949
.60965
8.60980
.60995
.61011
.61026
.04066
.04068
.04069
.04070
.04072
.04073
.04075
.04076
8.61834
.01849
.61864
.61880
.04153
.04154
.04156
.04157
+ y
9
10
11
8.58174
.58190
.58206
.58222
.03817
.03819
.03830
.03821
8.59120
..59136
..59151
.59167
.03901
.03903
.03904
.03905
8.60055
.60071
.60086
.60102
.03986
.03988
.03989
.03990
8.61895
.61910
.61925
.61940
.04159
.04160
.04162
.04163
+ 3'
IS
14
15
8.58238
.58253
.58269
.58285
.03823
.03824
.03826
.03827
.03828
.03830
.03831
.03833
.03834
.03835
.03837
.03838
8.59183
.59198
.59214
.59230
.03907
.03908
.03910
.03911
8.60117
.60133
.60148
.60164
.03992
.03993
.03995
.03996
8.61041
.61057
.61072
.61087
.04078
.04079
.04081
.04082
8.61955
.61971
.61986
.62001
.04164
.04166
.04167
.04169
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
+ 4'
n
IS
19
8.58301
.58317
.58333
.58348
8.59245
.59261
.59277
.59292
.03912
.03914
.03915
.03917
8.60179
.60195
.60210
.60226
.03998
.03999
.04000
.04003
8.61103
.61118
.61133
.61149
8.61164
.61179
.61194
.61210
.04083
.04085
.04086
.04088
8.62016
.62031
.62046
.62061
.04170
.04172
04173
.04175
+ 5'
21
22
23
8.58364
.58380
.58396
.58412
8.59308
.59323
.59339
.59355
8.59370
.59386
.59402
..59417
.03918
.03930
.03921
.03923
8.60241
.60256
.60272
.60287
.04003
.04005
.04006
.04007
.04089
.04091
.04092
.04094
8.62077
.62092
.62107
.62122
.04176
.04177
.04179
.04180
+ 6'
25
26
27
8.58427
.58443
.58459
.58475
.03839
.03841
.03842
.03844
.03845
.03846
.03848
.03849
.03934
.03935
.03927
.03938
8.60303
.60318
.60334
.60349
.04009
.04010
.04013
.04013
.04015
.04016
.04017
.04019
8.61225
.61240
.61256
.61271
.04095
.04096
.04098
.04099
8.62137
.62152
.62167
.62182
.04182
.04183
.04185
.04186
+ r
29
30
31
8.58491
.58.506
.58522
.58538
8..59433
.59448
.59464
.59480
.03929
.03931
.03932
.03934
8.60365
.60380
.60396
.60411
8.61286
.01301
.01317
.61332
.04101
.04102
.04104
.04105
8.62197
.62213
.62228
.62243
.04188
.04189
.04191
.04192
+ 8'
33
34
35
8.58554
.58570
.58585
.58601
.03851
.03852
.03853
.03855
8.59495
.59511
..59.527
.59542
8..59558
..59573
..59.589
.59604
.03935
.03936
.03938
.03939
.03941
.03942
.03944
.03945
8.60426
.60442
.60457
.60473
8.60488
.60504
.60519
.60.534
.04020
.04022
.04023
.04025
8.61347
.61362
.61378
.61393
.04106
.04108
.04109
.04111
.04112
.04114
.04115
.04117
8.62258
.62273
.62288
.62303
.04194
.04195
.04196
.04198
28
27
26
25
+ 9'
37
38
39
8.58617
.58633
.58648
..58664
8.58680
.58696
.58711
.58727
.03856
.03858
.03859
.03860
.04026
.04027
.04029
.04030
8.01408
.01423
.01439
.014.54
8.62318
.62333
.62348
.62363
.04199
.04201
.04202
.04204
24
23
22
2~1
20
19
18
17
16
15
14
13
+ 10'
41
42
43
.03862
.03863
.03865
.03866
8.59fi20
.59636
.59651
..59667
"8.59682
.59698
..59714
.59729
.03946
.03948
.03949
.03951
8.605.50
.60565
.60581
.60596
.04032
.04033
.04035
- .04036
8.61469
.61484
.01.500
.61515
.04118
.04119
.04121
.04122
8.62379
.62394
.62409
.62424
8.62439
.62454
.62469
.62484
.04205
.04207
.04208
.04210
.04211
.04212
.04214
.04215
+ 11'
45
46
47
8.58743
.58759
.58774
.58790
.03867
.03869
.03870
.03872
.03873^
.03875
.03876
.03877
.03879
.03880
.03882
.03883
.03952
.03953
.03955
.03956
8.60611
.60627
.60642
.60658
.04038
.04039
.04040
.04043
8.61.530
.61545
.61561
.01.576
.04124
.04125
.04127
.04128
+ 12'
49
50
51
8.58806
.58822
.58837
.58853
8.59745
..59760
.59776
..59791
.03958
.03959
.03961
.03962
.03963
.03965
.03966
.03968
.03969
.03971
.03972
.03973
.03975
8.60673
.60688
.60704
.60719
8.60734
.607,50
.60765
.60781
.04043
.04045
.04046
.04048
.04049
.04050
.04052
.04053
8.61,591
.61006
.61621
.61637
.04130
.04131
.04133
.04134
.04135
.04137
.04138
.04140
8.62499
.62514
.62529
.62544
.04217
.04318
.04230
.04231
12
11
10
9
8
7
6
5
+ 13'
5S
. 54
■55
8.58869
.58885
.58900
.58916
8.58932
.58947
.58963
.58979
8.59807
..59822
.59838
..59853
8.610,52
.61067
.61682
.61697
8.62559
.62574
.62589
.62604
.04333
.04234
.04226
.04237
+ 14'
57
58
59
.03884
.03886
.03887
.03889
.03890
5..59869
..59885
.59900
..59916
8..59931
8.60796
.60811
.60827
.60842
.04055
.04056
.04058
.04059
8.61713
.61728
.01743
.01758
8.01773
.04141
.04143
.04144
.04146
.04147
8.62619
.62034
.62049
.62664
8.62680
.04229
.04230
.04333
.04333
.04334
4
3
2
1
+ 15'
8.58994
8.60857
.04060
?;?ft
?9™
22 ft
2«m
22h. 27m
22*
26™
22 ft 25m
Page 830]
TABLE 45.
Haversines.
s
IhS.ym
23° 45'
iAj6'm24°0'
lh37m
34° 15'
Ih 38^ 24° 30'
lh.39m 24° 45'
s
60
59
58
57
66
55
54
53
Log. llav.
Nat. Ilav.
Log. TIav.
Nat. llav.
Log. Hav.
Nat. JIav.
Log. Ilav.
Nat. Ilav.
Log. llav.
Nat. Hav.
1
2
3
8.62680
.62695
.62710
.62725
.04234
.04236
.04237
.04239
8.63576
.63591
.63606
.63620
8.63635
.63650
.63665
.63680
8.63695
.63709
.63724
.63739
.04323
.04324
.04336
.04337
.04329
.04330
.04332
.04333
.04335
.04336
.04338
.04339
.04340
.04342
.04343
.04345
.04346
.04348
.04349
.04351
.04352
.04354
.04355
.04357
.04358
.04360
.04361
.04363
8.64463
.64477
.64492
.64507
.04412
.04413
.04415
.04416
8.65340
.65355
.65369
.6-5384
.04502
.04503
.04505
.04506
.04508
.04509
.04511
.04512
8.66208
.66223
.66237
.66251
.04593
.04594
.04596
.04597
+ 1'
5
6
7
8.62740
.62755
.62770
.62785
.04240
.04243
.04243
.04245
8.64521
.64536
.64551
.64565
.04418
.04419
.04421
.04422
8.65398
.65413
.65427
.65442
8.66266
.66280
.66295
.66309
8.66323
.66338
.66352
.66366
.04599
.04600
.04603
.04604
.04605
.04607
.04608
.04610
+ 3'
9
10
11
8.62800
.62815
.62830
.62845
.04246
.04248
.04249
.04251
8.64580
.64595
.64609
.64624
8.64639
.64653
.64668
.64683
.04434
.04425
.04427
.04428
8.65456
.65471
.65485
.65500
.04514
.04516
.04517
.04519
52
51
50
49
+ 3'
13
14
15
8.62860
.62875
.62890
.62904
8.62919^
.62934
.62949
.62964
.04252
.04253
.04255
.04256
.04258
.04259
.04261
.04262
.04264
.04265
.04267
.04668
.04270
.04271
.04273
.04274
.04276
.04277
.04278
.04280
.04281
.04283
.04284
.04286
.04287
.04289
.04290
.04292
.04293
.04295
.04296
.04298
.04299
.04301
.04302
.04304
.04305
.04306
.04308
.04309
8.63754
.63769
.63784
.63798
.04430
.04431
.04433
.04434
.04436
.04437
.04439
.04440
.04443
.04443
.04445
.04446
8.65514
.65529
.6.5543
.65558
8.65572'
.65.587
.6.5601
.65616
.04520
.04522
.04523
.04525
8.66381
.66395
.66409
.66424
.04611
.04613
.04614
.04616
.04617"
.04619
.04620
.04622
.04623
.04635
.04626
.04628
.04629
.04631
.04633
.04634
48
47
46
45
+ i'
17
18
19
+ 5'
21
22
23
8.63813
.63828
.63843
.63858
8.63872
.63887
.63902
.63917
8.64697
.64712
.64727
.64741
8.64756
.64771
.64785
.64800
.04526
.04528
.04529
.04531
8.66438
.66453
.66467
.66481
8.66496
.66510
.66524
.66539
8.66553
.66567
.66582
.66596
8.66610
.66625
.66639
.666.53
8.66668
.66682
.66696
.66710
8.66725
.66739
.66753
.66768
44
43
42
41
40
39
38
37
36
35
34
33
8.62979
.62994
.63009
.63024.
8.63039
.63054
.63069
.63084
8.63099
.63114
.63129
.63144
8.63159
.63174
.63189
.63204
8.63218
.63233
.63248
.63263
8.65630
.65645
.65659
.65674
8.65688
.65703
.65717
.65732
.04532
.04534
.04535
.04537
.04538
.04540
.04541
.04543
+ 6'
25
26
27
8.63932
.63946
,63961
.63976
8.63991
.64006
.64020
.64035
8.64815
.64829
.64844
.64859
.04448
.04449
.04451
.04453
+ V
29
30
31
.04364
.04366
.04367
.04369
.04370
.04372
.04373
.04375
8.64873
.64888
.64902
.64917
8.64932
.64946
.64961
.64976
.04454
.04455
.04457
.04458
8.65746
.65761
.65775
.65790
8.65804
.65819
.65833
.6.5848
8.65862'
.65876
.65891
.65905
8.65920
.65934
.65949
.65963
8.65978
.65992
.66006
.66021
.04544
.04546
.04547
.04549
.04550
.04552
.04553
.04555
.04556
.04558
.04559
.04561
.04562
.04564
.04565
.04567
.04569'
.04570
.04572
.04573
.04636
.04637
.04639
.04640
32
31
30
29
+ 8'
S3
34
35
8.64050
.64065
.64079
.64094
8.64109
.64124
.64139
.641.53
8.64168
.64183
.64198
.64212
8.64227
.64242
.64257
.64271
8:64286
.64301
.64315
.64330
.04460
.04461
.04463
.04464
.04466
.04467
.04469
.04470
.04472
.04473
.04475
.04476
.04642
.04643
.04645
.04646
28
27
26
25
+ 9'
37
38
39
.04376
.04378
.04379
.04381
8.64990
.65005
.65019
.65034
.04648
.04649
.04651
.04653
24
23
22
21
+ 10'
41
42
43
8.63278
.63293
.63308
.63323
8.63338
.63353
.63368
.63382
.04382
.04384
.04385
.04387
.04388
.04390
.04391
.04393
.04394
.04395
.04397
.04398
8.65049
.65063
.65078
. .65092
8.65107
.65122
.65136
.65151
8.66782
.66796
.66811
.66825
8,66839
.66853
.66868
.66882
.04654
.04655
.04657
.04659
.04660
.04662
.04663
.04665
20
19
18
n
16
15
14
13
+ 11'
45
46
47
.04478
.04479
.04481
.04482
+ 12'
49
50
51
8.63397
.63412
.63427
.63442
8.65165
.65180
.65194
.65209
.04484
.04485
.04487
.04488
8.66035
.66050
.66064
.66079
8.66093
.66107
.66122
.66136
8.66151
.66165
.66179
.66194
.04575
.04576
.04578
.04579
.04581
.04582
.04584
.04585
.04587
.04588
.04590
.04591
8.66896
.66911
,66925
,66939
8,66953
,66968
,66982
,66996
.04666
.04668
.04669
.04671
.04672
.04674
.04675
.04677
12
11
10
9
8
7
6
5
4
3
2
1
+ 13'
53
54
55
8.63457
.63472
.63487
.63502
.04311
.04312
.04314
.04315
8.64345
.64360
.64374
.64389
8.64404^
.64418
.64433
.64448
8.64463
.04400
.04401
.04403
.04404
.04405
.04407
.04409
.04410
8.65224
.65238
.65253
.65267
8.65282
.65296
.65311
.65325
.04490
.04491
.04493
.04494
.04496
.04497
.04499
.04500
+ M'
57
58
59
8.63516
.63531
.63546
.63561
8:63576
.04317
.04318
.04320
.04321
.04323
8,67010
,67025
,67039
,67053
8,67067
.04678
.04680
.04682
.04683
.04685
+ 15'
.04413
8.65340
.04502
8.66208
.04593
22h
24m
22^ 23m
22ft
22m
22 A
21m
22h
20">
TABLE 45.
Haversines.
[Page 831
s
Ih^om
25° 0'
Ih 4im
35° 15'
lh42mzs°afy
lh4sm
25° 45'
lh-44m26°0' |
s
Log. nav.
Nat. llav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.67067
.67082
.67096
.67110
.04685
.04686
.04688
.04689
8.67918
.67932
.67946
.67960
.04777
.04779
.04780
.04783
8.68760
.68773
.68787
.68801
.04871
.04873
.04874
.04875
8.69593
.69607
.69620
.69634
.04965
.04967
.04968
.04970
8.70418
.70431
.70445
.70459
.05060
.05063
.05063
.05085
60
59
58
57
+ 1'
5
6
7
8.67124
.67139
.67153
.67167
.04691
.04693
.04694
.04695
8.67974
.67988
.68002
.68016
.04783
.04785
.04787
.04788
8.68815
.68829
.68843
.68857
.04877
.04879
.04880
.04883
8.69648
.69662
.69676
.69690
.04971
.04973
.04975
.04976
8.70472
.70486
.70500
.70513
.05067
.05068
.05070
.05071
56
55
64
53
+ 2'
9
10
11
8.67181
.67196
.67210
.67224
.04697
.04698
.04700
.04703
8.68030
.68045
.68059
.68073
.04790
.04791
.04793
.04794
8.68871
.68885
.68899
.68913
.04883
.04885
.04886
.04888
8.69703
.69717
.69731
.69745
.04978
.04979
.04981
.04982
8.70527
.70541
.70554
.70568
.05073
.05075
.05076
.05078
52
51
50
49
+ 3'
IS
14
15
8.67238
.67252
.67267
.67281
.04703
.04705
.04706
.04708
8.68087
.68101
.68115
.68129
.04796
.04797
.04799
.04801
8.68927
.68941
.68955
.68969
.04890
.04891
.04893
.04894
8.69758
.69772
.69786
.69800
.04984
.04986
.04987
.04989
8.70582
.70595
.70609
.70623
.05079
.05081
.05083
.05084
48
47
46
45
+ 4'
17
18
19
8.67295
.67309
.67323
.67338
.04709
.04711
.04713
.04714
8.68143
.68157
.68171
.68185
.04802
.04804
.04805
.04807
8.68983
.68996
.69010
.69024
.04896
.04897
.04899
.04901
8.69814
.69827
.69841
.698.55
.04990
.04993
.04994
.04995
8.70636
.70650
.70664
.70677
.05086
.05087
.05089
.05091
44
43
42
41
+ 5'
21
22
23
8.67352
.67366
.67380
.67394
.04715
.04717
.04718
.04730
8.68199
.68213
.68227
.68241
.04808
.04810
.04811
.04813
8.69038
.69052
.69066
.69080
.04902
.04904
.04905
.04907
8.69869
.69882
.69896
.69910
.04997
.04998
.05000
.05001
8.70691
.70704
.70718
.70732
.05092
.05094
.05095
.05097
40
39
SS
37
+ 6'
25
26
27
8.67409
.67423
.67437
.67451
.04733
.04733
.04735
.04726
8.68256
.68270
.68284
.68298
.04815
.04816
.04818
.04819
8.69094
.69108
.69122
.69136
.04908
.04910
.04912
.04913
8.69924
.69937
.69951
.69965
.05003
.05005
.05006
.05008
8.70745
.70759
.70773
.70786
.05099
.05100
.05102
.05104
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
+ T
29
30
31
8.67465
.67480
.67494
.67508
.04728
.04739
.04731
.04733
8.68312
.68326
.68340
.68354
.04831
.04832
.04824
.04835
8.69149
.69163
.69177
.69191
.04915
.04916
.04918
.04919
8.69979
.69992
.70006
.70020
.05009
.05011
.05013
.05014
8.70800
.70813
.70827
.70841
.05105
.05107
.05108
.05110
+ 8'
S3
34
35
8.67522
.67536
.67550
.67565
.04734
.04735
.04737
.04739
8.68368
.68382
.68396
.68410
.04837
.04839
.04830
.04833
8.69205
.69219
.69233
.69247
.04921
.04923
.04924
.04926
8.70034
.70047
.70061
.70075
.05016
.05017
.05019
.05031
8.70854
.70868
.70881
.70895
.05111
.05113
.05115
.05116
+ S'
37
38
39
8.67579
.67593
.67607
.67621
.04740
.04743
.04743
.04745
8.68424
.68438
.68452
.68466
.04833
.04835
.04836
.04838
8.69260
.69274
.69288
.69302
.04927
.04939
.04930
.04933
8.70089
.70102
.70116
.70130
.05022
.05024
.05025
.05037
8.70909
.70922
.70936
.70949
.05118
.05119
.05121
.05133
+ W
41
42
43
8.67635
.67649
.67664
.67678
.04746
.04748
.04749
.04751
8.68480
.68494
.68508
.68522
.04839
.04841
.04843
.04844
8.69316
.69.330
.69344
.69358
.04934
.04935
.04937
.04938
8.70144
.70157
.70171
.70185
.05038
.05030
.05032
.05033
8.70963
.70977
.70990
.71004
.05134
.05136
1 .05137
.05139
+ 11'
45
46
47
8.67692
.67706
.67720
.67734
.04753
.04754
.04756
.04757
8.68536
.68550
.68564
.68.578
.04846
.04847
.04849
.04850
.04853
.04854
.04855
.04857
8.69371
.69385
.69399
.69413
.04940
.04941
.04943
.04945
8.70198
.70212
.70226
.70240
.05035
.05036
.05038
.05040
8.71017
.71031
.71045
.71058
.05131
.05132
.05134
.05135
16
15
14
IS
+ 13'
49
50
51
8.67748
.67763
.67777
.67791
.04759
.04760
.04763
.04763
8.68592
.68606
.68620
.68634
8.69427
.69441
.69454
.69468
.04946
.04948
.04949
.04951
8.70253
.70267
.70281
.70294
.05041
.05043
.05044
.05046
8.71072
.71085
.71099
.71112
.051.37
.05139
.05140
.05142
12
11
10
9
+ 13'
53
54
55
8.67805
.67819
.67833
.67847
.04765
.04766
.04768
.04769
8.68648
.68662
.68676
.68690
.04858
.04860
.04861
.04863
8.69482
.69496
.69510
.69524
.04952
.04954
.04956
.04957
8.70308
.70322
.70336
.70349
8.70363
.70377
.70390
.70404
.05048
.05049
.05051
.05052
.6.?054
.05055
.05057
.05059
.05060
8.71126
.71140
.71153
.71167
.05144
.05145
.05147
.05148
.05150
.05152
.05153
.05155
.05156
8
7
6
5
4
3
2
1
+ 14'
57
58
59
8.67861
.67875
.67890
.67904
.04771
.04773
.04774
.04776
8.68704
.68718
.68732
.68746
.04864
.04866
.04868
.04869
8.69537
.69551
.69565
.69579
.04959
.04960
.04963
.04964
8.71180
.71194
.71207
.71221
+ 15'
8.67918
.04777
8.68760
.04871
8.69593
.04965
8.70418
8.71234
22h
igm
22^
ISm
2^*
17m
22>t
16m
^2"
15m
Page 832J
TABLE 45.
Haversines.
S
7ft ^m
26° 15'
Ih 46m
36° 30'
Ih jftm 36° 45'
Ih/f^m
37° 0'
lh49m
37° 15'
s
Log. Hav.
Nat. Hav.
lK)g. Hav
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
d
8.71234
.71248
.71261
.71275
.05156
.05158
.05160
.05161
8.72043
.72057
.72070
.72083
8.72097
.72110
.72124
.72137
.05253
.05355
.05357
.05358
8.72844
.72857
.72871
.72884
.05351
.05353
.05354
.05356
8.73637
.73650
.73663
.73677
.05450
.05451
.05453
.05455
8.74423
.74436
.74449
.74462
.05549
.05551
.05552
.05554
60
59
58
57
56
55
54
53
+ .1'
5
6
7
8.71289
.71302
.71316
.71329
.05163
.05164
.a5166
.05168
.05260
.05261
.05283
.05265
8.72897
.72910
.72924
.72937
.05358
.05359
.05361
.05363
8.73690
.73703
.73716
.73729
.05456
.05458
.05460
.05461
.05463
.05464
.05468
.05468
.05470
.05471
.05473
.05474
8.74475
.74488
.74501
.74514
8.74527
.74540
.74553
.74566
8.74579
.74592
.74605
.74618
.05556
.05557
.05559
.05561
+ V
9
10
11
8.71343
.71356
.71370
.71383
.05169
.05171
.05172
.05174
8.72150
.72164
.72177
.72191
8.72204
.72217
.72231
.72244
.05266
.05208
.05270
.05271
.05373
.05374
.05376
.05378
.05279
.05281
.05283
.05284
8.72950
.72963
.72977
.72990
.05364
.05366
.05367
.05369
8.73742
.73755
.73769
.73782
.05563
.05564
.05566
.05567
52
51
50
49
48
47
46
45
44
43
42
41
+ 3'
IS
14
15
8.71397
.71410
.71424
.71437
.05176
.05177
.05179
.05181
8.73003
.73016
.73030
.73043
.05371
.05373
.05374
.05376
8.73795
.73808
.73821
.73834
.05569
.05571
.05573
.05574
+ 4'
17
18
19
+" '5'
21
22
23
8.71451
.71464
.71478
.71491
.05182
.05184
.05185
.05187
8.72257
.72271
.72284
.72298
8.73056
.73069
.73083
.73096
.05377
.05379
.05381
.05383
8.73847
.73860
.73874
.73887
.05476
.05478
.05479
.05481
.05483
.05484
.05486
.05488
.05489
.05491
.05493
.05994
8.74631
.74644
.74657
.74670
8.74683
.74696
.74709
.74722
8.74735
.74748
.74761
.74774
.05576
.05577
.05579
.05581
8.71505
.71518
.71532
.71545
.05189
.05190
.05192
.05193
8.72311
.72324
.72338
.72351
8.72364
.72378
.72391
.72404
.05386
.05387
.05389
.05391
8.73109
.73122
.73136
.73149
.05384
.05385
.05387
.05389
8.73900
.73913
.73926
.73939
.05583
.05584
.05586
.05587
.05589
.05591
.05593
.05594
40
39
38
37
36
35
34
S3
+ 6'
25
26
27
8.71559
.71572
.71586
.71599
.05195
.05197
.05198
.05200
.05392
.05294
.05396
.05397
8.73162
.73175
.73189
.73202
.05390
.05393
.05394
.05395
8.73952
.73965
.73978
.73992
8.74005
.74018
.74031
.74044
8.74057"
.74070
.74083
.74096
+ r
29
SO
31
8.71613
.71626
.71640
.71653
.05201
.05203
.05205
.05206
8.72418
.72431
.72445
.72458
.05299
.05300
.05302
.05304
8.73215
.73228
.73241
.73255
8.73268
.73281
.73294
.73308
.05397
.05399
.05400
.05403
.05404
.05405
.05407
.05408
.05410;
.05413
.05513
.05415
.05496
.05498
.05499
.05501
.05503
.05504
.05506
.05508
.05509
.05511
.05513
.05514
8.74787
.74800
.74813
.74826
.05596
.05597
.05599
.05601
32
31
SO
29
+ 8'
33
34
S5
8.71667
.71680
.71694
.71707
.05208
.05210
.05211
.05213
8.72471
.72485
.72498
.72511
.05305
.05307
.05309
.05310
8.74839
.74852
.74864
.74877
.05603
.05604
.05606
.05807
28
27
26
25
+ 9'
57
3S
39
8.71721
.71734
.71748
.71761
.05214
.05216
.05218
.05219
8.72525
.72538
.72551
.72565
.05312
.05314
.05315
.05317
8.73321
.73334
.74147
.73360
8.74109
.74122
.74135
.74149
8.74162
.74175
.74188
.74201
8.74890
.74903
.74916
.74929
.05609
.05611
.05613
.05614
24
23
22
21
+ W
41
42
43
8.71774
.71788
.71801
.71815
.05221
.05222
.05224
*.05226
8.72578
.72591
.72605
.72618
.05318
.05320
.05322
.05323
8.73374
.73387
.73400
.73413
8.73426
.73440
.7.3453
.73466
.05417
.05418
.05430
.05433
.05433
.05435
.05437
.05438
.05516
.05518
.05519
.05531
8.74942
.74955
.74968
.74981
.05616
.05818
.05619
.05631
20
19
18
17
+ 11'
45
46
47
8.71828
.71842
.71855
.71869
.05327
.05329
.05231
.05332
.05234
.05335
.05337
.05339
8.7263J
.72614
.72658
,72671
.05335
.05336
.05338
.05330
8.74214
.74227
.74240
.74253
.05533
.05524
.05526
.05528
.05529
.05531
.05533
.05534
8.74994
.75007
.75020
.75033
.05623
.05634
.05626
.05638
16
15
14
13
+ 13'
49
50
51
8.71882
.71895
.71909
.71922
8.72084
.72098
.72711
.72724
.05331
.05333
.05335
.05336
8.73479
.73492
.73505
.73519
.05430
.05431
.05433
.05435
8.74266
.74279
.74292
.74305
8.75046
.75059
.75072
.75084
.05839
.05831
.05833
.05634
1!
11
10
9
8
6
5
4
S
2
1
+ 13'
53
54
55
8.71936
.71949
.71963
.71976
.05340
.05343
.05344
.05345
8.72738
.72751
.72764
.72778
.05338
.05340
.05341
.05343
:05345
.05346
.05348
.05349
.05351
8.73532
.73545
.73558
.73571
8.73584
.73598
.73611
.73624
.05436
.05438
.05440
.05441
.05443
.05145
.05446
.05448
8.74318
.74331
.74344
.74357
.05536
.05537
.05539
.05541
.05542
.05544
.05546
.05547
8.75097
.75110
.75123
.75136
8.75149
.75162
.75175
.75188
.05636
.05638
.05639
.05641
.05643
.05644
.05646
.05648
+ U'
54
58
59
8.71989
.72003
.72016
.72030
.05347
.05348
.05350
.05353
8.72791
.72804
.72817
.72831
8.72844
8.74371
.74384
.74397
.74410
+ 15'
8.72043
.05353
8.73637
.05450
8.74423
.05549
8.75201
.05849
22h.
IJ^m
2,>h
13m
22^
l->m
22h
11"'
ajft
10">
TABLE 45.
Haversines.
[Page 833
s
iAscrniaTosr
ift5/™37°45'
J* 52^ 28° C
.Z* 53m 28° 15'
lh.54^
28° 30'
s
Log. nav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.75201
.75214
.75227
.75239
.05649
.05651
.05653
.05655
8.75972
.75984
.75997
.76010
.05751
.05753
.05754
.05756
.05757
.05759
.05761
.05763
.05764
.05766
.05768
.05769
.05771
.05773
.05774
.05776
.05778
.05779
.05781
.05783
.05785
.05786
.05788
.05790
.05791
.05793
.05795
.05796
.05798
.05800
.05803
.05803
.05805
.05807
.05808
.05810
.05813
.05813
.05815
.05817
8.76735
.76748
.76760
.76773
.05853
.05854
.05856
.05858
8.77492
.77504
.77517
.77529
.05955
.05957
.05959
.05961
.05963
.05964
.05966
.05968
8.78241
.78254
.78266
.78278
.06059
.06061
.06063
.06064
60
59
58
57
56
55
54
53
+ 1'
5
6
7
8.75252
.75265
.75278
.75291
.05656
.05658
.05660
.05661
.05663
.05665
.05666
.05668
.05(B70
.05671
.05673
.05675
8.76023
.76035
.76048
.76061
8.76074
.76086
.76099
.76112
8.76125
.76138
.761.50
.76163
8.76786
.76798
76811
.76824
.05859
.05861
.05863
.05865
.05866
.05868
.05870
.05871
.05873
.05875
.05877
.05878
8.77542
.77554
.77567
.77579
8.78291
.78303
.78316
.78328
.06066
.06068
.06070
.06071
+ r
9
10
11
8.75304
.75317
.75330
.75343
8.76836
.76849
.76862
.76874
8.77592
.77604
.77617
.77630
8.77642
.77655
.77667
.77680
8.77692
.77705
.77717
.77730
8.77742
.77755
.77767
.77780
.05969
.05971
.05973
.05974
.05976
.05978
.05980
.05981
.05983
.05985
.0.5986
.05988
8.78341
.78353
.78365
.78378
.06073
.06075
.06077
.06078
52
51
50
49
+ 3'
13
14
15
8.75355
.75368
.75381
.75394
8.76887
.76900
.76912
.76925
8.78390
.78403
.78415
.78428
8.78440
.78452
.78465
.78477
.06080
.06082
.06083
.06085
48
47
46
45
44
43
42
41
+ 4'
17
18
19
8.75407
.75420
.75433
.75446
.05676
.05678
.05680
.05681
.05683
.05685
.05686
.05688
8.76176
.76189
,76201
.76214
8.76227
.76240
.76252
.76265
8.76278
.76291
.76303
.76316
8.76329"
.76341
.763.54
.76367
8.76380
.76392
.76405
.76418
8.76431
.76443
.76456
.76469
8.76938
.76950
.76963
.76975
8J6988
.77001
.77013
.77026
8.77039
.77051
.77064
.77076
8.77089"
.77102
.77114
.77127
8.77139
.77152
.77165
.77177
.05880
.05883
.05883
.05885
.05887
.05888
.05890
.05893
.06087
.06089
.06090
.96092
+ 5'
HI
22
23
8.75458
.75471
.75484
.75497
.05990
.05993
.05993
.05995
.05997
.05999
.06000
.06003
8.78490
.78502
.78514
.78527
.06094
.06096
.06097
.06099
40
39
38
37
+ 6'
25
26
27
8.75510
.75523
.75536
.75548
.05690
.05691
.05693
.05695
.05697
.05698
.05700
.05703
.05894
.05895
.05897
.05899
8.77792
.77805
.77817
.77830
8.78539
.78551
.78564
.78576
.06101
.06103
.06104
.06106
36
35
34
33
+ r
29
30
31
8.75561
.75574
.75587
.75600
.05901
.05903
.05904
.05906
.05907
.05909
.05911
.05913
8.77842
.778.55
.77867
.77880
8.77892
.77905
.77917
.77930
.06004
.06005
.06007
.06009
8.78.589
.78601
.78613
.78626
.06108
.06110
.06111
.06113
.06115
.06117
.06118
.06120
.06122
.06124
.06125
.06127
32
31
30
29
28
27
26
25
'24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ 8'
33
34
35
+ 9'
57
38
39
8.75613
.75626
.75638
.75651
8.75664
.75677
.75690
.75703
.05703
.05705
.05707
.05708
.05710
.05713
.05713
.05715
.06011
.06013
.06014
.06016
8.78638
.78651
.78663
.78675
8.77190
.77202
.77215
.77228
.05914
.05916
.05918
.05919
8.77942
.77955
.77967
.77980
.06018
.06019
.06021
.06023
8.78688
.78700
.78712
.78725
+ w
41
42
43
+ 11'
45
46
47
8.75715
.75728
.75741
.75754
8.75767
.75779
.75792
.75805
.05717
.05718
.05730
.05733
.05734
.05735
.05737
.05739
.05730
.05733
.05734
.05735
.05737
.05739
.05740
.05743
8.76481
.76494
.76507
.76519
8.76532
.76.545
.76.558
.76570
8.76.583
.76.596
.76608
.76621
.05819
.05830
.05833
.05834
.05835
.05837
.05839
.05830
".05833
.05834
.05836
.05837
.05839
.05841
.05843
.05844
.05846
.05847
.05849
.05851
8.77240
.77253
.77265
.77278
.05931
.05933
.05935
.05936
8.77992
.78005
.78017
.78029
8.78042
.78054
.78067
.78079
8.78092
.78104
.78117
.78129
8.78142
.78154
.78167
.78179
.06034
.06026
.06028
.06030
.06031
.06033
.06035
.06037
.060.38
.06040
.06042
.06044
.06045
.06047
.06049
.06050
.06052
.06054
.06056
.06057
.06059
8.78737
.78749
.78762
.78774
.06129
.06130
.06132
.06134
.06136
.06137
.06139
.06141
.06143
.06144
.06146
.06148
.06150
.06151
.06153
.06155
.06157
.06158
.06160
.06162
8.77291
.77303
.77316
.77328
.05928^
.05930
.05931
.05933
8.78787
.78799
.78811
.78824
+ 13'
49
50
51
8.75818
.75831
.75844
.75856
8.77341
.77353
.77366
.77379
.05935
.05936
.05938
.05940
.05943
.05943
.05945
.05947
8.78836
.78848
.78861
.78873
8.78885
.78898
.78910
.78922
8.78935
.78947
.78959
.78972
+ 13'
53
54
55
8.75869
.75882
.75895
.75908
8.75920
.75933
.75946
.75959
8.766.34
.76646
.76659
.76672
8.77391
.77404
.77416
.77429
+ 14'
57
58
59
.05744
.05745
.05747
.05749
.05751
8.76684
.76697
.76710
.76722
8.76735
8.77441
.77454
.77466
.77479
.05949
.05950
.05953
.05954
8.78191
.78204
.78216
.78229
+ 15'
8.75972
.05853
8.77492
.05955
8.78241
8.78984
.06164
^fft
9m
22h8m
22h
7m
«A
6m
22^ 5m
24972°— 12-
-43
Page 834]
TABLE 45.
Haversines.
s
JftS5m38°46'
;'>56™29°0'
7ft 57m 29° 15'
Ih 58^19° W 1 ;ft59'n39°45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav,
1
2
3
8.78984
.78996
.79009
.79021
.06164
.06165
.06167
.06169
8.79720
.79732
.79744
.79757
.06269
.06271
.06273
.06274
8.80449
- .80462
' .80474
.80486
8.80498
.80510
.80522
.80534
8.80546
.80558
.80570
.80582
.06375
.06377
.06379
.06381
8.81172
.81184
j|.81196
».81208
.06483
.06484
.06486
.06488
8.81889
.81901
.81913
.81925
.06590
.06593
.06594
.06595
60
59
58
57
+ 1'
5
6
7
8.79033
.79046
.79058
.79070
.06171
.06172
.06174
.06176
8.79769
.79781
.79793
.79805
.06376
.06378
.06380
.06381
.06382
.06384
.06386
.06388
8.81220
1.81232
1.81244
*.81256
.06489
.06491
.06493
.06495
8.81937
.81948
.81960
.81972
8.81984
.81996
.82008
,82020
.06597
.06599
.06601
.06603
56
55
54
5.1
+ V
9
10
11
8.79082
.79095
.79107
.79119
.06178
.06179
.06181
.06183
8.79818
.79830
.79842
.79854
.06383
.06385
.06287
.06388
/. 06389
.06391
.06393
.06395
8.81268
.81280
' .81292
'.81304
.06497
.06498
.06500
.06503
.06605
.06606
.06608
.06610
52
51
50
49
+ 3'
IS
14
15
8.79132
.79144
.79156
.79169
.06185
.06186
.06188
.06190
8.79866
.79879
.79891
.79903
.06390
.06393
.06394
.06395
8.80595
.80607
.80619
.80631
.06397
.06398
.06400
.06402
8.81316
.81328
.81340
.81352
.06504
.06505
.06507
.06509
.06511
.06513
.06514
.06516
.06518
.06530
.06533
.06533
8,82032
,82043
,82055
.82067
.06613
.06614
.06615
.06617
4S
47
46
45
+ i'
17
18
19
8.79181
.79193
.79205
.79218
.06193
.06193
.06195
.06197
8.79915
.79927
.79940
.79952
.06397
.06399
.06301
.06303
8.80643
.80655
.80667
.80679
.06404
.06405
.06407
.06409
8.81364
.81376
.81388
,81400
8.82079
.82091
.82103
.82115
.06619
.06631
.06633
.06634
44
43
42
41
+ 5'
21
22
23
8.79230
.79242
.79255
.79267
.06199
.06300
.06303
.06304
8.79964
.79976
.79988
.80000
.06304
.06306
.06308
.06310
8.80691
.80703
.80715
.80727
.06411
.06413
.06414
.06416
8.81412
.81424
.81436
.81448
8.82126
.82138
.821.50
.82162
.06626
.06628
.06630
.06632
40
39
38
37
+ 6'
25
26
27
8.79279
.79291
.79304
.79316
.06306
.06307
.06309
.06311
8.80013
.80025
.80037
.80049
.06311
.06313
.06315
.06317
8.80739
.80751
.80764
.80776
.06418
.06420
.06421
.06423
8.81460
.81472
.81484
.81496
.06535
.06537
.06539
.06531
8,82174
.82186
.82198
.82209
.06633
.06635
.06637
.06639
36
35
34
33
+ r
29
SO
31
8.79328
.79341
.79353
.79365
.06313
.06214
.06216
.06218
8.80061
.80073
.80086
.80098
8.80110
.80122
.80134
.80146
.06318
.06330
.06333
.06324
8.80788
.80800
.80812
.80824
.06425
.06427
.06429
.06430
8.81508
.81520
.81531
.81543
.06533
.06534
.06536
.06538
.06540
.06541
.06543
.06545
8.82221
.82233
.82245
.82257
.06641
.06643
.06644
.06646
32
31
30
29
+ 8'
33
34
35
8.79377
.79390
.79402
.79414
.06220
.06221
.06333
.06335
.06336
.06337
.06329
.06331.
8.80836
.80848
.80860
.80872
.06432
.06434
.06436
.06438
8.81555
.81567
.81579
.81591
8.82269
.82280
' .82292
.82304
.06648
.06650
.06653
.06653
28
27
26
25
+ 9'
37
38
39
8.79426
.79439
.79451
.79463
.06237
.06339
.06330
.06332
8.80158
.80171
.80183
.80195
.06333
.06334
.06336
.06338
8.80884
.80896
.80908
.80920
8780932^
.80944
.80956
.80968
X. 80980
.80992
.81004
.81016
.06439
.06441
.06443
.06445
8.81603
.81615
.81627
.81639
.06547
.06549
.06550
.06553
8.82316
.82328
.82340
.82351
.06655
.06657
.06659
.06661
24
23
22
21
+ W
41
42
43
8.79475
.79488
.79500
.79512
.06234
.06336
.06337
.06339
8.80207
.80219
.80231
.80243
.06340
.06341
.06343
.06345
.06446
.06448
.06450
.06453
.06454
.06455
.06457
.06459
8.81651
.81663
.81675
.81687
.06554
.06556
.06558
.06559
8.82363
.82375
.82387
.82399
.06663
.06664
.06666
.06668
20
19
IS
n
+ 11'
45
46
47
8.79524
.79537
.79549
.79561
.06341
.06343
.06344
.06346
8.80256
.80268
.80480
.80292
.06347
.06349
.06350
.06353
8.81699
.81710
.81722
.81734
.06561
.06563
.06565
.06567
8.82410
.82422
.82434
.82446
.06670
.06671
.06673
.06675
16
15
14
13
12
11
10
9
+ 13'
49
50
51
8.79573
.79586
.79598
.79610
.06348
.06350
.06351
.06353
8.80304
.80316
.80328
.80340
.06354
.06356
.06357
.06359
8.81028
.81040
.81052
.81064
.06461
.06463
.06464
.06466
8.81746
.81758
.81770
.81782
.06568
.06570
.06573
.06574
8.82458
.82470
.82481
.82493
.06677
.06679
.06681
.06683
+ 13'
53
54
55
8.79622
.79634
.79647
.79659
.06355
.06257
.06258
.06260
8.80353
.80365
.80377
.80389
.06361
.06363
.06365
.06366
8.81076
.81088
.81100
.81112
.06468
.06470
.06471
.06473
8.81794
.81806
.81818
.81830
.06576
.06577
.06579
.06581
8.82505
.82517
.82529
.82540
.06684
.06686
.06688
.06690
S
7
6
5
4
3
~1
+ 14'
57
58
59
8.79671
.79683
.79696
.79708
.06263
.06364
.06265
.06367
8.80401
.80413
.80425
.80437
.06368
.06370
.06372
.06373
8.81124
.81136
.81148
.81160
.06475
.06477
.06479
.06480
8.81841
.81853
.81865
.81877
.06583
.06585
.06586
.06588
8.82552
.82564
.82576
.82588
.06691
.06693
.06695
.08697
+ 16'
8.79720
.06269
8.80449
.06375
8.81172
.06482
8.81889
.06590
8.82599
.06699
22>'
4m
22h3m
22'' 2™
221^
im
}^h
0'"
TABLE
45.
[Page 836
Ilaversines.
s
2A Oro 30° 0'
2h im 30° 15'
>h im 30° 30'
i% jm 30° 45' 1 ^ft 4"
31° 0'
s
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
8.82599
.06699
8.83303
.06808
8.84002
.06919
8.84694
.07030
8.85380
.07142
60
1
.82611
.06;01
.83315
.06810
.84013
.06920
.84705
.07033
.85391
.07144
59
2
.82623
.06J03
.83327
.06813
.84025
.06932
.84717
.07033
.85403
.07145
58
3
,82635
.06704
.06706
.83338
8.83350
.06814
.06816
.84036
.06924
.84728
.07035
.85414
.07147
57
56
+ 1'
8.82646
8.84048
.06926
8.84740
.07037
8.85425
.07149
5
.82658
.06708
.83362
.06817
.84059
.06928
.84751
.07039
.85437
.07151
55
6
.82670
.06710
.83374
.06819
.84071
.06930
.84762
.07041
.85448
.07153
54
7
.82682
.06711
.06713
.83385
8.83397
.06821
.06823
.84083
8.84094
.06931
.06933
.84774
.07043
.07045
.85459
8.85471
.07155
53
+ 3'
8.82694
8.84785
.07157
52
9
.82705
.06715
.83409
.06835
.84106
.06935
.84797
.07046
.85482
.07158
51
10
.82717
.06717
.83420
.06836
.84117
.06937
.84808
,07048
.85494
.07160
50
U
.82729
.06719
.06721
.83432
8.83444
.06838
.06830
.84129
8.84140
.06939
.06941
.84820
8.84831
.07050
.07953
.85505
.07162
.07164
49
48
+ 3'
8.82741
8.85516
13
.82752
.07723
.83455
.06832
.84152
.06943
.84843
.07054
.85528
.07166
47
14
.82764
.06724
.83467
.06834
.84164
.06944
.84854
.07056
.85539
.07168
46
15
.82776
.06726
.06728
.83479
8.83490
.06836
.06838
.84175
.06946
.06948
.84866
8.8"4877
.07058
.07059
.85550
.07170
45
44
+ i'
8.82788
8.84187
8.85562
.07172
17
.82799
.06730
.83502
.06839
.84198
.06950
.84889
.07061
.85573
.07173
43
18
.8281 1
.06731
.83513
.06841
.84210
.06952
.84900
.07063
.85585
.07175
42
19
.82823
.8.82835"
.06733
.06735
.83525
.06843
.84221
.06954
.06956
.84912
.07065
.07067
.85596
8.85607
.07177
.07179
41
40
+ 6'
8.83.537
.06845
8.84233
8.84923
21
.82846
.06737
.83548
.06847
.84244
.06957
.84934
.07069
.85619
.07181
39
n
.82858
.06739
.83560
.06849
.84350
.06959
.84946
.07071
.85630
.07183
38
23
.82870
8.82882
.06741
.06743
.83572
8.83583
.06850
.06853
.84268
"8.84279
.06961
.06963
.84957
8.84969
.07073
.07074
.85641
8.85653
.07185
.07187
37
36
+ «'
25
.82893
.06744
.83595
.06854
.84291
.06965
.84980
.07076
.85664
.07189
35
26
.82905
.06746
.83607
.06856
.84302
.06967
.84992
.07078
.85675
.07190
34
27
.82917
.06748
.06750
.83618
8.83630
.06858
.06860
.84314
8.84325
.06968
.06970
.8.5003
8.85015
.07080
.07083
.85687
.07192
.07194
33
39.
+ r
8.82929
8.85698
29
.82940
.06753
.83642
.06861
.84337
.06972
.85026
.07084
.85709
.07196
3t
30
.82952
.06753
.83653
.06863
.84348
.06974
.8.5037
.07086
.85721
.07198
30
31
.82964
.06755
.06757
.83665
8.83676
.06865
.06867
.84360
8.84371
.06976
.06978
.85049
8.8.5000
.07087
.07089
.85732
.07200
29
'28
+ 8'
8.82976
8.85743
.07303
S3
.82987
.06759
.83688
.06809
.84383
.06980
.8.5072
.07091
.85755
.07204
27
24
.82999
.08761
.83700
.06871
.84394
.06981
.8-5083
.07093
.85706
.07205
9.6
35
.83011
.06763
.06764
.83711
.06872
.84406
8.84417
.06983
.06985
.85095
878.5106
.07095
.07097
.85777
8.85789
.07207
.07209
25
94
+ 9"
8.83023
8.83723
.06874
37
.83034
.06766
.83735
.06876
.84429
.06987
.85117
.07099
.85800
.07211
9.3
38
.83046
.06788
.83746
.06878
.84441
.06989
.85129
.07100
.85811
.07213
■■)^
39
.83058
.06770
.83758
.06880
.84452
.06991
.85140
.07103
.85823
.07215
21
+ 10'
8.83069
.06772
8.83769
.06883
8.84464
.06993
8.851.52
.07104
8.85834
.07217
9.0
41
.83081
.06773
.83781
.06884
.84475
.06994
.85163
.07106
.85845
.07219
19
42
.83093
.06775
.83793
.06885
.84487-
.06996
,85175
.07108
.85857
.07230
18
4S
.83105
8.83116
.06777
.06779
.83804
.06887
.06889
.84498
8.8451"0
.06998
.07000
.85186
8.85197
.07110
.07113
.85868
8.85879
.07233
.07324
17
16
+ 11'
8.83816
45
.83128
.06781
.83828
.06891
.84521
.07003
.85209
.07114
.85891
.07336
15
46
.83140
.06783
.83839
.06893
.84533
.07004
.85220
.07115
.85902
.07338
14
47
.83151
.06784
.83851
"8.83862
.06895
.06896
.84544
8.84556
.07006
.07007
.85232
8.85243
.07117
.85913
.07230
.07232
13
19
+ n'
8.83163
.06786
.07119
8.8-5925
49
.83175
.06788
.83874
.06898
.84.567
.07009
.85254
.07131
.85936
.07234
11
50
.83187
.06790
.83886
.06900
.84579
.07011
.85266
.07133
.85947
.07236
10
51
.83198
.06793
06794
.83897
8.83909
.06902
.06904
.84590
8.84602
.07013
.07015
.85277
8;"85289"
.07135
.07127
.85959
8.85970
.07337
.07339
9
8
+ 13'
8.83210
53
.83222
.06795
.83920
.06906
.84613
.07017
.85300
.07129
.8-5981
.07341
7
54
.83233
.06797
.83932
.06907
.84625
.07019
,8.5311
.07130
.85992
.07343
6
55
+ 14'
.83245
.06799
.06801
.83944
"8.83955
.06909
.06911
.84636
.07030
.07033
,8.5323
8,85334
.07132
.07134'
.86004
8.86015
.07345
.07247
5
4
8.83257
8.84648
57
.83268
.06803
.83967
.06913
.84659
.07034
,85346
.07136
.86026
.07349
3
58
.83280
.06805
.83978
.06915
.84671
.07036
,85357
.07138
.86038
.07251
2
59
.83292
.06806
.06808
.83990
8.84002
.06917
.84682
8.84694
.07028
.07030
,85368
8.85380
.07140
.07142
.86049
8.86060
.07253
.07254
1
+ 15'
8.83303
.06919
21h
59m
21>i
58™
21^
57m
21h
56m
21>t 55m
Page 836]
TABLE 45.
Haversines.
}
s
2A Sm 31° 15'
2h gm 31° 30'
2h 7m 31° 45'
^ft 5™ 32° 0'
2h 9m 33° 15'
s
Ix)g. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.86060
.86072
.86085
.86094
.07354
.01356
.07358
.07360
8.86735
.86746
.86757
.86769
.07368
.07370
.07373
.07374
8.87404
.87415
.87426
.87437
.07482
.07484
.07486
.07488
8.88068
.88079
.88090
.88101
.07598
.07600
.07601
.07603
8.88726
.88737
.88748
.88759
.07714
.07716
.07717
.07719
60
59
58
57
56
55
54
53
+ 1'
5
6
7
8.86105
.86117
.86128
.86139
.07363
.07364
.07366
.07368
8.86780
.86791
.86802
.86813
.07376
.07377
.07379
.07381
.07383
.07385
.07387
.07389
8.87448
.87460
.87471
.87482
.07490
.07493
.07494
.07496
8.88112
.88123
.88134
.88145
.07605
.07607
.07609
.07611
8.88769
.88780
.88791
.88802
.07731
.07733
.07735
.07737
+ 2'
9
10
11
8.86151
.86162
.86173
.86184
.07370
.07371
.07373
.07375
8.86825
.86836
.86847
.86858
8.87493
.87504
.87515
.87526
8.87537
.87548
.87559
.87570
.07498
.07500
.07503
.07503
8.88156
.88167
.88178
.88189
.07613
.07615
.07617
.07619
.07631
.07633
.07635
.07637
.07638
.07630
.07633
.07634
.07636
.07638
.07640
.07643
.07644
.07646
.07648
.07650
8.88813
.88824
.88835
.88846
.07739
.07731
.07733
.07735.
52
51
50
49
+ 3'
13
14
15
8.86196
.86207
.86218
.86229
.07377
.07379
.07381
.07383
8.86869
.86880
.86892
.86903
.07391
.07393
.07395
.07397
.07505
.07507
.07509
.07511
8.88200
.88211
.88222
.88233
8.88857
.88868
.88879
.88890
.07737
.07739
.07741
.07743
48
47
46
45
+ *'
17
18
19
8.86241
.86252
.86263
.86275
.07385
.07387
.07388
.07390
.07393
.07394
.07396
.07398
8.86914
.86925
.86936
.86947
.07398
.07400
.07403
.07404
8.87582
.87593
.87604
.87615
.07513
.07515
.07517
.07519
8.88244
.88255
.88266
.88277
8.88900
.88911
.88922
.88933
.07745
.07747
.07749
.07751
.07753
.07754
.07756
.07758
.07760
.07762
.07764
.07766
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
21
22
23
8.86286
.86297
.86308
.86320
8.86959
.86970
.86981
.86992
.07406
.07408
.07410
.07413
.07414
.07416
.07417
.07419
8.87626
.87637
.87648
.87659
.07531
.07533
.07535
.07537
.07538
.07530
.07533
.07534
.07536
.07538
.07540
.07543
.07544
.07546
.07548
.07549
8.88288
.88299
.88310
.88321
8.88332
.88343
.88354
.88364
8,88944
.88955
.88966
.88977
+ 6'
25
26
27
8.86331
.86342
.86353
.86365
.07300
.07303
.07304
.07305
8.87003
.87014
.87026
.87037
8.87670
.87681
.87692
.87703
8.88988
.88998
.89009
.89020
+ r
29
30
31
8.86376
.86387
.86398
.86410
.07307
.07309
.07311
.07333
8.87048
.87059
.87070
.87081
.07431
.07433
.07435
.07437
8.87714
.87725
.87737
.87748
8.88375
.88386
.88397
.88408
8.88419
.88430
.88441
.88452
.07653
.07654
.07656
.07657
.07659
.07661
.07663
.07665
8.89031
.89042
.89053
.89064
.07768
.07770
.07773
.07774
+ 8'
33
34
35
8.86421
.86432
.86443
.86455
.07315
.07317
.07319
.07321
8.87093
.87104
.87115
.87126
.07439
.07431
.07433
.07435
8.87759
.87770
.87781
.87792
8.87803
.87814
.87825
.87836
8.89075
.89086
.89096
.89107
.07776
.07778
.07780
.07783
28
27
26
25
+ 9'
57
38
39
8.86466
.86477
.86488
.86499
8.86511
.86522
.86533
.86544
.07333
.07334
.07336
.07338
8.87137
.87148
.87159
.87171
.07437
.07438
.07440
.07443
.07444
.07446
.07448
.07450
.07551
.07553
.07555
.07557
8.88463
.88474
.88485
.88496
.07667
.07669
.07671
.07673
8.89118
.89129
.89140
.89151
.07784
.07786
.07788
.07789
24
23
22
21
+ IC
42
43
.07330
.07333
.07334
.07336
8.87182
.87193
.87204
.87215
8.87847
.87858
.87869
.87880
.07559
.07561
.07563
.07565
.07567
.07569
.07571
.07573
.07574
.07576
.07578
.07580
8.88507
.88518
.88529
.88540
8.88551
.88562
.88573
.88584
.07675
.07677
.07679
.07681
8.89162
.89172
.89183
.89194
.07791
.07793
.07795
.07797
20
19
18
17
16
15
14
13
12
11
10
9
' f
7
6
5
4
3
2
1
+ 11'
46
47
8.86556
.86567
.86578
.86589
.07338
.07340
.07341
.07343
8.87226
.87237
.87248
.87260
.07453
.07454
.07456
.07458
8.87891
.87902
.87913
.87924
8.87935
.87946
.87957
.87968
.07683
.07685
.07686
.07688
8.89205
.89216
.89227
.89238
.07799
.07801
.07803
.07805
+ 13'
60
51
8.86600
.86611
.86623
.86634
.07345
.07347
.07349
.07351
8.87271
.87282
.87293
.87304
.07459
.07461
.07463
.07465
8.88595
.88606
.88616
.88627
.07690
.07693
.07694
.07696
8.89248
.89259
.89270
.89281
.07807
.07809
.07811
.07813
.07815
.07817
.07819
.07821
.07833
.07835
.07837
.07839
+ 13'
55
54
55
8.86645
.86657
.86668
.86679
.07353
.07355
.07357
.07359
8.87315
.87326
.87337
.87349
.07467
.07469
.07471
.07473
8.87980
.87991
.88002
.88013
8.88024
.88035
.88046
.88057
8:880(38
.07583
.07584
.07586
.07588
8.88638
.88649
.88660
.88671
.07698
.07700
.07703
.07704
8.89292
.89303
.89314
.89324
+ U'
57
58
59
8.86690
.86701
.86713
.86724
.07360
.07363
.07364
.07366
8.87360
.87371
.87382
.87393
.07475
.07477
.07479
.07480
.07590
.07593
.07594
.07590
.07598
8.88682
.88693
.88704
.88715
.07706
.07708
.07710
.07713
8.89335
.89346
.89357
.89368
+ 16'
8.86735
.07368
8.87404
.07483
8.88726
.07714
8.89379
.07830
.22 A
54m
^Ihc
jm
■21h
5^m
21h
5lm
21h
50"'
TABLE 45.
Haversines.
[Page 837
s
2ft^0»i33°30'
2ftiin'33°45'
2h 12m 33° V
2h 13m 33' 15'
thl4m
33° 30'
s
Log. 11 av.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat, Hav.
Log. Hav.
Nat. Hav.
1
2
3
8.89379
.89389
.89400
.89411
.07830
.07833
.07834
.07836
.07838
.07840
.07843
.07844
.07846
.07848
.07850
.07853
8.90026
.90037
.90048
,90058
8.90069
.90080
.90091
.90101
8.90112
.90123
.90134
.90144
8.90155"
.90166
.90176
.90187
8.90198
.90209
.90219
.90230
8.90241
.90252
.90262
.90273
8790284
.90294
.90305
.90316
8^90326
.90337
.90348
.903.59
8.90369
.90380
.90391
.90401
8.90412
.90423
.90433
.90444
8.90455
.90466
.90476
.90487
8.90498
.90.508
.90519
.90530
"8.90540
.90551
.90562
.90572
8J0.583
.90594
.90604
.90615
8.90626
.90636
.90647
.90658
8.90668
.07948
.07950
.07953
.07954
.07956
.07958
.07960
.07963
.07964
.07966
.07968
.07970
.07972
.07974
.07976
.07978
.07980
.07982
.07983
.07985
.07987
.07989
.07991
.07993
.07995
.07997
.07999
.08001
8.90668
.90679
.90690
.90700
8.90711
.90722
.90732
.90743
8.90754
.90764
.90775
.90786
8.90796
.90807
.90818
.90828
8790839
.90849
.90860
.90871
8" 90881
.90892
.90903
.90913
8.90924"
.90935
.90945
.90956
.08066
.08068
.08070
.08072
.08074
.08076
.08078
.08080
.08083
.08084
.08086
.08088
.08090
.08093
.08094
.08096
.08098
.08100
.08103
.08104
.08106
.08108
.08110
.08112
.08114
.08116
.08118
.08130
8.91306
,91316
,91327
,91337
8,91348
.91358
,91369
,91380
.08186
.08188
.08190
,08193
8.91938
.91948
.91959
.91969
.08306
.08308
.08310
.08312
60
59
38
57
56
55
64
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
+ 1'
5
6
7
8.89422
.89433
.89444
.89454
.08194
.08196
.08198
.08300
.08202
.08204
.08206
.08208
.08210
.08212
.08214
.08216
8.91980
.91990
.92001
.92011
8.92022
.92032
.92043
.92053
.08314
.08316
.08318
.08320
.08322
.08334
.08336
.08328
+ r
9
10
11
8.89465
.89476
.89487
.89498
8.91390
.91401
.91411
.91422
+ 3'
13
14
15
8.89509
.89519
.89530
.89541
.07854
.07856
.07858
.07860
.07862
.07864
.07866
.07868
.07870
.07873
.07873
.07875
.07877
.07879
.07881
.07883
8.91432
.91443
.91454
.91464
8.91475
.91485
.91496
.91506
8.92064
.92074
.92084
.92095
.08330
.08333
.08334
.08336
+ 4'
n
18
19
8.89552
.89563
.89573
.89584
.08218
.08220
.08222
.08224
8.92105
.92116
.92126
.92137
8.92147
.92158
.92168
.92179
.08338
.08340
.08343
.08344
.08346
.08348
.08350
.08352
+ 5'
21
22
23
8.89.595
.89606
.89617
.89627
8.89638
.89649
.89660
.89671
8.91.517
.91.527
.91.538
.91549
.08226
.08228
.08230
.08232
+ 6'
25
26
27
8.91559
.91570
.91.580
.91591
.08334
.08336
.08338
.08340
.08343
.08344
.08246
.08248
.08250
.08352
.08254
.08256
.08258
.08260
.08262
.08264
8.92189
.92200
.92210
.92221
.08354
.08356
.08358
.08360
+ r
29
30
31
8.89681
.89692
.89703
.89714
.07885
.07887
.07889
.07891
.07893
.07895
.07897
.07899
.07901
.07903
.07905
.07907
.07909
.07911
.07913
.07915
.08003
.08005
.08007
.08009
8.90966
.90977
.90988
.90998
.08123
.08134
.08126
.08128
8.91601
.91612
.91622
.91633
8.92231
.92241
.92252
.92262
.08363
.08364
.08366
.08368
32
31
30
29
28
27
26
25
24
23
22
21
+ 8'
33
34
35
8.89725
.89735
.89746
.89757
8.89768
.89779
.89789
.89800
.08011
.08013
.08015
.08017
8.91009
.91019
.91030
.91041
.08130
.08132
.08134
.08136
.08138
.08140
.08143
.08144
8.91643
.916.54
.91664
.91675
8.91685
.91696
.91707
.91717
8.92273
.92283
.92294
.92304
8.92315
,92325
,92335
,92346
.08370
.08373
.08374
.08376
+ y
57
5,?
.59
.08019
.08031
.08033
.08035
.08037
.08039
.08031
.08033
.08035
.08037
.08039
.08041
.08043
.08045
.08047
.08049
.08051
.08053
.08055
.08057
.08059
.08061
.08063
.08065
8.91051
.91062
.91073
.91083
.08378
.08380
.08383
.08384
+ W
41
42
43
8.89811
.89822
.89832
.89343
8.91094
.91104
.91115
.91126
.08146
.08148
.08150
.08153
.08154
.08156
.08158
.08160
.08163
.08164
.08166
.08168
.08170
.08172
.08174
.08176
8.91728
.91738
,91749
,91759
8,91770
,91780
,91791
,91801
.08266
.08268
.08270
.08272
.08274
.08276
.08278
.08280
8,92356
,92367
,92377
,92388
.08386
.08388
.08390
.08393
.08394
.08396
.08398
.08403
.08404
.08406
.08408
20
19
18
17
16
15
14
13
12
11
10
9
+ 11'
45
46
47
8.89854
.89865
.89875
.89886
.07917
.07919
.07931
.07933
.07934
.07926
.07938
.07930
.07933
.07934
.07936
.07938
.07940
.07942
.07944
.07946
.07948"
8.91136
.91147
.911.57
.91168
"8.91179"
.91189
.91200
.91210
8.91221
.91232
.91242
.91253
8,92398
.92409
.92419
.92429
8.92440
.92450
.92461
.92471
49
30
51
8.89897
.89908
.89919
.89929
8,91812
,91822
,91833
,91843
.08282
.08284
.08286
.08288
.08290
.08393
.08394
.08396
.08298
.08300
.08302
.08304
.08306
+ 13'
53
54
55
8.89940
.89951
.89962
.89972
8,918.54
.91864
,91875
.91885
8,91896
,91906
,91917
,91927
8,919,38
8.92482
.92492
.92502
.92513
.08410
.08413
.08414
.08416
8
7
6
5
4
3
1
+ 14'
57
5S
59
8.89983
.89994
.90005
.90015
8.90026
8.91263
.91274
.91284
.91295
.08178
.08180
.08182
.08184
8,92523
,92534
,92544
.92554
8.92565
.08418
.08430
.08433
.08435
.08437
+ 15'
.08066
8.91,306
.08186
21'>'
49m
, Slli
48m
.gift
■47m
21 h
46m
21^ 46m
Page 838]
TABLE 45.
Haversines.
s
2A ISm 33° 45'
2>i 16^ 34° 0'
2h nm 34° 15'
2h 18m 34° 30'
2h 19m 34° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Ilav.
1
2
3
8.92565
.92575
.92586
.92596
.08427
.08429
.08431
.08433
8.93187
.93197
.93208
.93218
.08548
.08550
.08552
.08554
8.93805
.93815
.93825
.93835
.08671
.08673
.08675
.08677
8.94417
.94427
.94438
.94448
.08794
.08796
.08798
.08800
8.95025
,95035
,95045
,9.5055
.08918
.08920
.08922
.08924
60
59
58
57
+ 1'
5
6
7
8.92607
.92617
.92627
.92638
.08435
.08437
.08439
.08441
8.93228
.93239
.93249
.93259
.08556
.08558
.08560
.08562
8.93846
.93856
.93866
.93876
.08679
.08681
.08683
.08685
8.94458
.94468
.94478
.94488
,08802
.08804
.08806
.08808
8,95065
,95076
,9.5086
,9.5096
.08926
.08928
.08930
.08932
56
55
54
53
+ r
9
10
11
8.92648
.92659
.92669
.92679
.08443
.08445
.08447
.08449
8.93270
.93280
.93290
.93301
.08564
.08566
.08568
.08571
8.93886
.93897
.93907
.93917
.08687
.08689
.08691
.08693
8.94498
.94509
.94519
.94529
.08810
.08812
.08814
.08816
8,95106
,95116
.95126
.95136
.08934
.08936
.08938
.08940
.08943
.08945
.08947
.08949
52
51
50
49
48
47
46
45
+ 3'
13
14
15
8.92690
.92700
.92710
.92721
.08451
.08453
.08455
.08457
8.93311
.93321
.93332
.93342
8.93352
.93363
.93373
.93383
.08573
.08575
.08577
.08579
.08581
.08583
.08585
.08587
8.93927
.93938
,93948
,93958
.08695
.08697
.08699
.08701
8.94539
.94549
.94559
.94570
.08818
.08820
.08823
.08825
8.95146
.95156
.95166
.95176
+ *'
n
18
19
8.92731
.92742
.92752
.92762
.08459
.08461
.08463
.08465
8,93968
.93979
,93989
,93999
.08703
.08705
.08707
.08709
8.94580
.94590
.94600
.94610
8,94620
,94630
,94641
,94651
8.94661
.94671
.94681
.94691
.08827
.08829
.08831
.08833
.08835
.08837
.08839
.08841
8.95186
.95197
.95207
.95217
.08951
.08953
.08955
.08957
44
43
42
41
40
39
38
37
+ 5'
21
22
23
8.92773
.92783
.92794
.92804
.08467
.08469
.08471
.08473
8.93393
.93404
.93414
.93424
.08589
.08591
.08593
.08595
8,94009
,94019
,94030
.94040
.08711
.08714
.08716
.08718
8.95227
.95237
.95247
.95257
.08959
.08961
.08963
.08965
+ 6'
25
26
27
8.92814
.92825
.92835
.92845
.08475
.08477
.08479
.08481
8.93435
.93445
.93455
.93466
.08597
.08599
.08601
.08603
8.94050
.94060
.94071
.94081
.08720
.08722
.08724
.08726
.08843
.08845
.08847
.08849
8.95267
.95277
.95287
.95297
.08967
.08970
.08972
.08974
36
35
34
33
+ r
29
30
31
8.92856
.92866
.92877
.92887
.08483
.08485
.08487
.08489
8,93476
.93486
.93496
.93507
.08605
.08607
.08609
.08611
8.94091
.94101
,94111
,94122
.08728
.08730
.08732
.08734
8.94701
.94712
.94722
.94732
.08851
.08853
.08856
.08858
8.95307
.9.5317
.9.5327
.95337
.08976
.08978
.08980
.08982
32
31
30
29
28
27
26
25
+ 8'
33
34
35
8,92897
.92908
.92918
.92928
.08491
.08493
.08495
.08497
.08499
.08501
.08503
.08505
8.93517
.93527
.93538
.93548
.08613
.08615
.08617
.08619
.08621
.08624
.08626
.08628
.08630
.08633
.08634
.08636
8,94132
,94142
,94152
,94162
.08736
.08738
.08740
.08742
8.94742
.94752
.94762
.94772
8.94782
.94793
.94803
.94813
.08860
.08862
.08864
.08866
8.95347
.95357
.9.5368
.9.5378
.08984
,08986
.08988
.08990
+ 9'
57
38
39
8.92939
.92949
.92960
.92970
8.93558
.93568
.93579
.93589
8,94173
,94183
,94193
,94203
.08744
.08746
.08748
.08750
.08868
.08870
.08872
.08874
8.9.5388
.95398
.95408
.95418
.08992
.08994
.08997
.08999
24
23
22
21
20
19
18
n
16
15
U
13
+ W
41
42
43
8.92980
.92991
.93001
.93011
.08508
.08510
.08512
.08514
8,93599
,93610
.93620
.93630
8,94213
,94224
.94234
.94244
8,942.54
,94264
,94275
,94285
.08753
.08755
.08757
.08759
.08761
.08763
.08765
.08767
8.94823
.94833
.94843
.94853
.08876
.08878
.08880
.08882
.08885
.08887
.08889
.08891
8.9.5428
.95438
.95448
.95458
.09001
.09003
.09005
.09007
+ 11'
45
46
47
8.93022
.93032
.93042
.93053
.08516
.08518
.08520
.08522
8.93640
,93651
,93661
,93671
.08638
.08640
.08642
.08644
8.94863
.94874
.94884
.94894
8.95468
.9.5478
.95488
.95498
.09009
.09011
.09013
.09015
+ 12'
49
50
51
8.93063
.93073
.93084
.93094
8.93104
.93115
.93125
.93135
8.93i46
.93156
.93166
.93177
.08524
.08526
.08528
.08530
8,93681
,93692
,93702
,93712
.08646
.08648
.08650
.08652
8,94295
.94305
,94315
,94326
8.94336
,94346
,943.56
,94366
8.94376
.94387
.94397
.94407
.08769
.08771
.08773
.08775
.08777
.08779
.08781
.08783
.08785
.08788
.08790
.08792
8.94904
.94914
.94924
.94934
.08893
.08895
.08897
.08899
.68901
.08903
.08905
.08907
8.95.508
.95518
.9.5528
.95.538
.09017
.09019
.09022
.09024
12
11
10
9
+ 13'
53
54
55
.08532
.08534
.08536
.08538
8,93722
,93733
,93743
.93753
.08654
.08656
.08658
.08660
.08662
.08664
.08666
.08668
8.94944
.94954
.94965
.94975
8.95548
.95.558
.95568
.95578
8'.95588
.9.5598
.95608
.95618
.09026
.09028
.09030
.09032
8
i
6
5
+ w
57
58
59
.08540
.08542
.08544
.08546
8,93764
,93774
.93784
.93794
8.94985
.94995
.95005
.95015
.08909
.08911
.08914
.08916
.09034
.09036
.09038
.09040
.09042
4
3
2
1
+ 15'
8.93187
.08548
8.93805
.08671
8.94417
.08794
8.95025
.08918
8.95628
21^
44m
2;ft
4.3m
27 A
42m
21h
4tm
fl*
4(pn.
TABLE 45.
Haversines.
[Page 839
s
2A 20m 35° C
2h £im
35° 15'
2h 22"^
35° sr
2h 23"'
35° 45'
2h 24m
36° 0'
s
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Hav-.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. ]Iav.
Nat. Hav.
1
2
3
8.95628
.95638
.9.5648
.956.58
.09042
.09044
.09047
.09049
.09051
.09053
.09055
.09057
8.96227
.96237
.96247
.96257
.09168
.09170
.09172
.09174
8.96821
.96831
.96841
.96851
.09294
.09296
.09298
.09301
8.97411
.97421
.97431
.97441
.09421
.09423
.09426
.09428
8.97997
.98006
.98016
.98026
.09549
.09551
.09553
.09556
60
59
58
57
+ 1'
5
6
7
8.95668
.95678
.95688
.9.5698
8.96267
.96277
.96287
.96297
8.96307
.96317
.96326
.96336
.09176
.09178
.09181
.09183
8.96861
.96871
.96881
.96890
.09303
.09305
.09307
.09309
8.97450
.97460
.97470
.97480
.09430
.09432
.09434
.09436
8.98035
.98045
.98055
.98065
.09558
.09560
.09562
.09564
56
55
54
58
+ 2'
9
10
11
8.95709
.95719
.95729
.95739
.09059
.09061
.09063
.09065
.09185
.09187
.09189
.09191
8.96900
.9691D
.96920
.96930
.09311
.09313
.09315
.09317
8.97489
.97499
.97509
.97519
.09438
.09440
.09443
.09445
8.98074
.98084
.98094
.98103
.09566
.09568
.09571
.09573
52
51
50
49
48
47
46
45
44
43
42
41
+ 3'
13
14
15
8.95749
.95759
.95769
.9.5779
.09067
.09070
.09072
.09074
8.96346
.96356
.96366
.96376
.09193
.09195
.09197
.09199
8.96940
.96950
.96959
.96969
.09320
.09322
.09324
.09326
8.97529
.97538
.97548
.97.558
.09447
.09449
.09451
.09453
8.98113
.98123
.98132
.98142
.09575
.09577
.09579
.09581
.09583
.09586
.09588
.09590
+ 4'
17
18
19
8.95789
.95799
.95809
.95819
.09076
.09078
.09080
.09082
8.96386
.96396
.96406
.96416
.09202
.03204
.09206
.09208
8.96979
.96989
.96999
.97009
.09328
.09330
.09333
.09334
8.97568
.97577
.97587
.97597
.09455
.09457
.09460
.09462
8.98152
.98162
.98171
.98181
+ 5'
21
22
23
8.95828
.95838
.95848
.95858
8.95868
.95878
.95888
.95898
.09084
.09086
.09088
.09090
8.96426
.96436
.96446
.96455
.09210
.09212
.09214
.09216
8.97018
.97028
.97038
.97048
.09337
.09339
.09341
.09343
8.97607
.97617
.97626
.97636
.09464
.09466
.09468
.09470
.09472
.09474
.09477
.09479
8.98191
.98200
.98210
.98220
.09592
.09594
.09596
.09598
40
39
38
37
+ 6'
25
26
27
.09093
.09095
.09097
.09099
.09101
.09103
.09105
.09107
8.96465
.96475
.96485
.96495
8.96505
.96515
.96525
.96535
.09218
.09220
.09223
.09225
8.970.58
.97068
.97077
.97087
.09345
.09347
.09349
.09351
.09353
.09356
.09358
.09360
8.97646
.976.56
.97665
.97675
8.98229
.98239
.98249
.98259
.09601
■09603
.09605
.09607
36
35
34
33
+ r
29
30
31
8.95908
.95918
.95928
.95938
.09227
.09229
.09231
.09233
8.97097
.97107
.97117
.97127
8.97685
.97695
.97704
.97714
.09481
.09483
.09485
.09487
8.98268
.98278
.98288
.98297
.09609
.09611
.09613
.09616
32
31
30
29
28
27
26
25
+ 8'
33
34
35
8.95948
.95958
.95968
.95978
.09109
.09111
.09113
.09116
8.96.545
.96555
.96564
.96574
8.96584
.96594
.96604
.96614
.09235
.09237
.09239
.09242
.09244
.09246
.09248
.09250
8.97136
.97146
.97156
.97166
.09362
.09364
.09366
.09368
8.97724
.97734
.97743
.977.53
.09489
.09492
.09494
.09496
.09498
.09500
.09502
.09504
8.98307
.98317
.98326
.98336
.09618
.09620
.09622
.09624
+ V
37
38
39
8.95988
.95998
.96008
.96018
.09118
.09120
.09122
.09124
8.97176
.97186
.97195
.97205
.09370
.09372
.09375
.09377
8.97763
.97773
.97782
.97792
8.98346
.98355
.98365
.98375
.09626
.09628
.09631
.09633
24
23
22
21
+ w
41
42
43
8.96028
.96038
.96048
.96058
.09126
.09128
.09130
.09132
8.96624
.96634
.96644
.96653
.09252
.09254
.09256
.09258
8.97215
.97225
.97235
.97244
.09379
.09381
.09383
.09385
8.97802
.97812
.97821
.97831
.09506
.09509
.09511
.09513
8.98384
.98394
.98404
.984)3
8.98423
.98433
.98442
.98452
.09635
.09637
.09639
.09641
.09643
.09646
.09648
.09650
20
19
18
17
16
15
14
13
+ 11'
45
46
47
8.96068
.96078
.96088
.96098
.09134
.09136
.09139
.09141
8.96663
.96673
.96683
.96693
.09260
.09263
.09265
.09267
8.972.54
.97264
.97274
.97284
.09387
.09389
.09392
.09394
8.97841
.97851
.97860
.97870
.09515
.09517
.09519
.09521
+ 12'
49
50
51
8.96108
.96118
.96128
.96138
.09143
.09145
.09147
.09149
8.96703
.96713
.96723
.96733
.09269
.09271
.09273
.09275
8.97294
.97303
.97313
.97323
.09396
.09398
.09400
.09402
8.97880
.97890
.97899
.93909
.09524
.09526
.09528
.09530
8.98462
.98471
.98481
.98491
.09652
.09654
.09656
.09658
12
11
10
9
8
7
6
5
+ 13'
53
54
55
8.96148
.96158
.96167
.96177
.09151
.09153
.09155
.09157
8.96742
.96752
.96762
.96772
.09277
.09280
.09282
.09284
8.97333
.97343
.97352
.97362
.09404
.09406
.09409
.09411
8.97919
.97928
.97938
.9V948
8.979.58
.97967
.97977
.97987
.09532
.09534
.09536
.09538
.09541
.09543
.09545
.09547
8.98500
.98510
.98520
.98529
.09661
.096a
.09665
.09667
+ 14'
57
58
59
8.96187
.96197
.96207
.96217
.09160
.09162
.09164
.09166
8.96782
.96792
.96802
.96812
.09286
.09288
.09290
.09292
8.97372
.97382
.97392
.97401
.09413
.09415
.09417
.09419
8.98539
.98549
.98558
.98568
.09669
.09671
.09673
•09676
4
3
2
"1
+ 15'
8.96227
.09168
8.96821
.09294
8.97411
.09421
8.97997
.09549
8.98578
.09678
21^
Sgm
2/ft
38m
21^
STm
21h sem
21^
35in
Page 840]
TABLE 45.
Havereines.
s
^ft 25m 36° 15'
2h 26m -36° 30'
2h iTm 36° 45'
2li 28m 37° (K
2'i 29m
37° 15'
s
60
59
58
57
56
35
54
53
52
51
50
49
Log. Ilav.
Nat. Ilav.
Log. Ilav.
Nat. Ilav.
Log. Hav.
Nat.llav.
Log. Ilav.
Nat. Ilav.
Log. Hav.
Nat. Ilav.
1
2
3
8.98578
.98587
.98597
.98606
.09678
.09680
.09683
.09684
.09686
.09689
.09691
.09693
.09695
.09697
.09699
.09701
8.99154
.99164
.99173
.99183
8.99193"
.99202
.99212
.99221
8.99231
.99240
.99250
.99260
.09807
.09809
.09811
.09814
.09816
.09818
.09820
.09823
.09834
.09827
.09839
.09831
.0983;$
.09835
.09837
.09840
.09843
.09844
.09846
.09848
.09850
.09853
.09855
.09857
.09859
.09861
.09863
.09866
.09868
.09870
.09873
.09874
.69876
.09879
.09881
.09883
.09885
.09887
.09890
.09892
.09894
.09896
.09898
.09900
.09903
.09905
.09907
.09909
.09911
.09913
.09916
.09918
.09930
.09932
.09934
.09936
.09929
.09931
.09933
.09935
.09937
8.99727
.99736
.99746
.99755
8.99765"
.99774
.99784
.99793
8.99803"
.99812
.99822
.99831
8.99841
.99850
.99860
.99869
8.99879
.99888
.99898
.99907
"8.99917
.99926
.99936
.99945
.09937
.09939
.09952
.09944
.09946
.09948
.09950
.09953
.09955
.09957
.09959
.09961
.09963
.09966
.09968
.09970
,09972
.09974
.09977
.09979
.09981
.09983
.09985
.09987
.09990"
.09992
.09994
.09996
.09998
.10000
.10003
.10005
9.00295
.00305
.00314
.00324
.10068
.10070
.10073
.10075
" .10077
.10079
.10081
.10134
.10086
.10088
.10090
.10093
.10095
.10097
.10099
.10101
9.00860
.00869
.00878
.00888
9.00897
.00906
.00916
.00925
9.00935
.00944
.00953
.00903
9.00972
.00981
.1)0991
.01000
.10300
.10303
.10304
.10306
.10309
.10311
.10313
.10315
.10218
.10230
.10222
.10224
.10226
.10238
.10331
.10333
+ 1'
5
6
7
8.98616
.98626
.98635
.98645
9.00333
.00342
.00352
.00361
9.00371
.00380
.00390
.00399
+ V.
9
10
11
+ 3'
13
14
15
8.98655
.98664
.98674
.98684
8.98693
.98703
.98712
.98722
.09704
.09706
.09708
.09710
.09713
.09714
.09717
.09719
.09721
.09733
.09735
.09737
.09739
.09733
.09734
.09736
.09738
.09740
.09742
.09745
8.99269
.99279
.99288
.99298
8.99307
.99317
.99327
.99336
8.99346
.99355
.99365
.99374
8.99384
.99393
.99403
.99412
8.99422
.99432
.99441
.99451
9.00408
.00418
.00427
.00437
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
+ 4'
n
18
19
8.98732
.98741
.98751
.98761
9.00446
.00456
.00465
.00474
9.0b"484
.00493
.00503
.00512
9.0052Y
.00531
.00540
.00550
.10103
.10105
.10108
.10110
.10112
.10114
.10116
.10119
.10131
.10133
.10135
.10127
9.01009
.01019
.01028
.01037
9.01047
.01056
.01065
.01075
"9.01084
.01094
.01103
01112
.10335
.10337
.10340
.10343
.10344
.10246
.10348
.10251
.10253
.10255
.10257
.10359
+ 5'
21
22
23
+ 6'
25
26
27
8.98770
.98780
.98790
.98799
8.98809
.98818
.98828
.98838
8.99955
.99964
.99974
.99983
8.99993"
9.00002
.00012
.00021
+ r
29
30
31
8.98847
.98857
.98866
.98876
8.98886
.98895
.98905
.98915
9.00559
.00569
.00578
.00587
.10130
.10132
.10134
.10136
.10138
.10141
.10143
.10145
.10147
.10149
.10152
.10154
.10156
.10158
.10160
.10163
.10165
.10167
.10169
.10171
.10174
.10176
.10178
.10180
.10182
.10184
.10187
.10189
.10191
.10193
.10196
.10198
.10200
9.01122
.01131
.01140
.01150
9.01159
.01168
.01178
.01187
.10363
.10364
.10366
.10368
.10270
.10273
.10275
.10277
+ 8'
33
34
35
.09747
.09749
.09751
.09753
8.99460
.99470
.99479
.99489
9.00031
.00040
.00049
.00059
.10007
.10009
.10011
.10014
.10016
.10018
.10020
.10022
.10025
.10027
.10029
.10031
9.00597
.00606
.00616
.00625
9.00634
.00644
.00653
.00663
9.00672
.00681
.00691
.00700
+ »'
37
38
39
8.98924
.98934
.98943
.98953
.09755
.09757
.09760
.09763
.09764
.09766
.09768
.09770
.09773
.09775
.09777
.09779
.09781
.09783
.09786
.09788
.09790
.09792
.09794
.09796
.09799
.09801
.09803
.09805
.09807
8.99498
.99508
.99517
.99527
9.00068
.00078
.00087
.00097
9.00106
.00116
.00125
.00135
9.00144
.00154
.00163
.00172
9.00182
.00191
.00201
.00210
9.00220
.00229
.00239
.00248
9.00258
.00267
.00276
.00286
9.01196
.01206
.01215
.01224
9.01234
.01243
.01252
.01262
9.01271"
.01280
.01289
.01299
.10379
.10381
.10284
.10286
.10288
.10290
.10393
.10395
.10397
.10399
.10301
.10304
.10306
.10308
.10310
.10313
.10315
.10317
.10319
.10331
.10323
.10326
.10328
.10330
.103.32
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ 10'
41
42
43
+ 11'
45
46
47
8.98963
.98972
.98982
.98991
8.99001
.99011
.99020
.99030
8.99536
.99546
.99556
.99565
8.9^575
.99584
.99594
.99603
8.99613
.99622
.99632
.99641
8.9965r
.99660
.99670
.99679
8.99689
.99698
.99708
.99717
8.99727
.10033
.10035
.10038
.10040
.10042
.10044
.10046
.10049
.10051
.10053
.10055
.10057
9.00710
.00719
.00728
.00738
+ 12'
50
51
8.99039
.99049
.99058
.99068
9.00747
.00756
.00766
.00775
9.00785
.00794
.00803
.00813
9.01308
.01317
.01327
.01330
+ 13'
55
54
55
8.99078
.99087
.99097
.99106
9.01345
.01355
.01364
.01373
+ w
57
58
59
8.99116
.99126
.99135
.99145
.10059
.10C62
.10064
.10066
.10068
9.00822
.00831
.00841
.00850
9.01383
.01392
.01401
.01411
9.01420
+ 15'
8.99154
9.00295
9.00860
<2ih
54™
Slh
33m
2/*
Sim
21t^
Sim
21h
SQm
TABLE 45. [Page 841
Haversines.
s
gft 50ra 37° SO'
2h 3lm 37° 45'
2h 32m 38° 0'
2h asm 38° 15'
2h S4m 38° 30'
s
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
1
2
3
9.01420
.01429
.01438
.01448
.10332
.10335
.10337
.10339
9.01976
.01985
.01995
.02004
.10466
.10468
.10470
.10472
9.02528
.02538
.02547
.02556
.10599
.10602
.10604
.10606
9.03077
.03086
.03095
.03104
.10734
.10736
.10739
.10741
9.03621
.03630
.03639
.03648
.10870
.10872
.10874
.10876
60
.5,9
,5,?
.57
.56
55
54
53
52
51
50
49
■is
47
46
45
+ 1'
5
6
7
9.01457
.01466
.01476
.01485
.10341
.10343
.10346
.10348
9.02013
.02022
.02031
.02041
.10474
.10477
.10479
.10481
9.02565
.02574
.02.583
.02.593
.10608
.10611
.10613
.10615
.10617
.10620
.10622
.10624
9.03113
.03122
.03131
.03141
.10743
.10745
.10748
.10750
9.03657
.03667
,03676
.03685
.10879
.10881
.10883
.10885
+ 3'
9
10
11
9.01494
.01504
.01513
.01.522
.10350
.10353
; .10354
.10357
«.020.50
.02059
.02068
.02078
.10483
.10486
.10488
.10490
9.02602
.02611
.02620
.02629
9.03150
.03159
.03168
.03177
.10752
.10754
.10757
.10759
9.03694
.03703
,03712
,03721
.10888
.10890
.10892
.10895
+ 3'
13
14
15
9.01531
.01541
.01550
.01.559
.10359
.10361
.10363
.10366
9.02087
.02096
.02105
.02115
.10492
.10494
.10497
.10499
9.02638
.02648
.02657
.02666
.10626
.10629
.10631
.10633
9.03186
.03195
.03204
.03213
.10761
.10763
.10766
.10768
9.03730
.03739
,03748
.03757
.10897
.10899
.10901
.10904
+ *'
17
18
19
9.01569
.01578
.01587
.01596
.10368
.10370
.10373
.10374
9.02124
.02133
.02142
.02151
.10501
.10503
.10506
.10508
9.02675
.02684
.02693
.02702
.10635
.10638
.10640
.10642
9.03222
.03231
.03241
.032.50
.10770
.10772
.10775
.10777
9.03766
.03775
,03784
,03793
.10906
.10908
.10910
.10913
44
43
42
41
+ 5'
21
22
23
9.01606
.01615
.01624
.01634
,10377
.10379
.10381
.10383
9.02161
.02170
.02179
.02188
.10510
.10512
.10515
.10517
9.02712
.02721
.02730
.02739
.10644
.10647
.10649
.10651
9.03259
.03268
.03277
.03286
.10779
.10781
.10784
.10786
9.03802
,03811
,03820
.03829
.10915
.10917
.10919
.10922
40
39
38
37
36
35
34
33
32
31
SO
29
28
27
26
25
+ 6'
25
26
27
9.01643
.01652
.01661
.01671
.10386
.10388
.10390
.10392
9.02197
.02207
.02216
. .02225
.10519
.10531
.10523
.10526
9,02748
.02757
.02767
.02776
.10653
.10655
.10658
.10660
9.03295
.03304
.03313
.03322
.10788
.10790
.10793
.10795
9.03838
,03847
.03856
.03865
.10924
.10926
.10929
.10931
+ r
29
30
31
9.01680
.01689
.01698
.01708
.10394
.10397
.10399
.10401
9.02234
.02244
.02253
.02262
.10528
.10530
.10532
.10535
9.02785
.02794
.02803
.02812
9.02821
.02830
.02840
.02849
.10662
.10664
.10667
.10669
.10671
.10673
.10676
.10678
9.03331
.03340
.03350
.03359
.10797
.10799
.10802
.10804
9.03874
.03883
.03892
.03901
.10933
.10935
.10938
.10940
+ 8'
33
34
35
9.01717
.01726
.01736
.Cil745
.10403
.10405
.10408
.10410
9.02271
.02280
.02290
.02299
.10537
.10539
.10541
.10544
9.03368
.03377
.03386
.03395
.10806
.10809
.10811
.10813
9.03910
.03919
.03928
.03937
.10942
.10944
.10947
.10949
+ 9'
37
38
39
9.01754
.01763
.01773
.01782
.10412
.10414
.10417
.10419
9.02308
.02317
.02326
.02336
.10546
.10548
.10550
.10552
9.02858
.02867
.02876
.02885
.10680
.10682
.10685
.10687
9.03404
.03413
.03422
.03431
.10815
.10818
.10820
.10822
9.03946
,03955
.03964
.03973
.10951
.10953
.10956
.10958
24
23
22
21
+ 1(K
41
42
43
9.01791
.01800
.01810
.01819
.10431
.10423
.10425
.10428
9.02345
.02354'
.02363
.02372
.10555
.10557
.10559
.10561
9.02894
.02904
.02913
.02922
.10689
.10691
.10694
.10696
9.03440
.03449
.03458
.03467
.10824
.10827
.10829
.10831
9.03982
.03991
.04000
,04009
.10960
.10963
.10965
.10967
20
19
18
17
+ 11'
45
46
47
9.01828
.01837
.01847
.018.56
.10430
.10432
.10434
.10436
9.02381
.02391
.02400
.02409
.10564
.10566
.10568
.10570
9.02931
.02940
.02949
.02958
.10698
.10700
.10703
.10705
9.03476
03486
.03495
.03504
.10833
.10836
.10838
.10840
9,04018
,04027
.04036
.04045
.10969
.10972
.10974
.10976
16
15
14
13
12
11
10
9
+ 13'
49
50
51
9.01865
.01874
.01884
.01893
.10439
.10441
.10443
.10445
9.02418
.02427
.02437
.02446
.10573
.10575
.10577
.10579
9.02967
.02977
.02986
.02995
.10707
.10709
.10712
.10714
9.03513
.03522
.03531
.03540
.10842
.10845
.10847
.10849
9.04054
.04063
.04072
.04081
.10978
.10981
.10983
.10985
+ 13'
53
54
55
9.01902
.01911
.01921
.01930
.10448
.10450
.10452
.10454
9.02455
.02464
.02473
.02483
.10582
.10584
.10586
.10588
9.03004
.03013
.03022
.03031
.10716
.10718
.10721
.10723
9.03549
.03558
,03567
.03576
.10851
.10854
.10856
.10858
9.04090
.04099
.04108
,04117
.10988
.10990
.10992
.10994
8
7
6
5
+ 14'
57
58
59.
9.01939
01948
.019.58
.01967
.10457
.10459
.10461
.10463
9.02492 1 .10591
.02.501 \ .10593
.02510 i .10595
.02519 i .10597
9.03040
.03050
.03059
.03068
.10725
.10727
.10730
.10732
9,03.585
.03594
.03603
.03612
.10861
.10863
.10865
.10867
9.04126
.04135
.04144
.04153
.10997
.10999
.11001
.11004
4
3
2
1
+ 15'
9.01976] .10466
9.02528 ! .10599
9.03077
.10734
9.03621
.10870
9.04162
.11006
21h 29m
9ih ■28m
21h27m
21^ 26m 1
21^ 25m
Page 842]
TABLE 45.
Haversines.
s
2h 35m 38° 45'
2h sem 390 (K
th Sim
39° 16'
2h S8m 39° 30^
2h 39m 39° 45'
s
Log. HaT.
Nat. llav.
Log. Hav.
Nat. Ilav
Log. Uav.
Nat. Hav
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav.
1
2
3
9.04162
.04171
.04180
.04189
.11006
.11008
.11010
.11013
9.04699
.04708
.04717
.04726
.11143
.11145
.11147
.11150
9.05232
.05241
.05250
.05259
.11380
.11383
.11385
.11387
.11390
.11393
.11394
.11396
9.05762
.05771
.05780
.05788
.11419
.11431
.11433
.11436
9.06288
.06297
.06305
.06314
9.06323
.06332
.06340
.06349
9.06358
.06367
.06375
.06384
.11558
.11560
.11563
.11565
.11567
.11569
.11573
.11574
.11577
.11579
.11581
.11584
60
59
58
57
56
55
54
53
52
51
SO
49
'48
47
46
45
44
43
42
41
40
39
38
37
'36
35
34
33
+ 1'
5
6
7
9.04198
.04207
.04216
.04225
.11015
.11017
.11019
.11033
9.04735
.04744
.04753
.04761
.11153
.11154
.11156
.11159
9.05268
.05277
.05285
.05294
9.05797
.05806
.05815
.05823
9.05832
.05841
.05850
.05859
9.05867
.05876
.05885
.05894
.11438
.11430
.11433
.11435
.11437
.11440
.11443
.11444
+ 3'
9
10
11
9.04234
.04243
.04252
.04261
.11034
.11036
.11039
.11031
9.04770
.04779
.04788
.04797
.11161
.11163
.11166
.11168
.11170
.11173
.11175
.11177
9.05303
.05312
.05321
.05330
9.05339
.05347
.05356
.05365
.11399
.11301
.11303
.11306
.11308
.11310
.11313
.11315
+ 3'
13
14
15
9.04270
.04279
.04288
.04297
.11033
.11035
.11038
.11040
9.04806
.04815
.04824
.04833
.11447
.11449
.11451
.11453
9.06393
.06401
.06410
.06419
.11586
.11588
.11590
.11593
+ i'
n
18
19
9.04306
.04315
.04324
.04333
.11043
.11044
.11047
.11049
9.04842
.04851
.04859
.04868
.11179
.11183
.11184
11186
9.05374
.05383
.05392
.05400
.11317
.11330
.11333
.11334
9.05903
.05911
.05920
.05929
9.05938
.05946
.05955
.05964
.11456
.11458
.11460
.11463
.11465
.11467
.11470
.11473
.11474
.11477
.11479
.11481
9.06428
.06436
.06445
.06454
9.06462
.06471
.06480
.06489
.11595
.11597
.11600
.11603
.11604
.11607
.11609
.11611
+ 5'
21
22
23
9.04341
.04350
.04359
.04368
.11051
.11054
.11056
.11058
9.04877
.04886
.04895
.04904
.11189
.11191
.11193
.11195
9.05409
.05418
.05427
.05436
.11336
.11339
.11331
.11333
+ 6'
25
26
27
9.04377
.04386
.04395
.04404
.11060
.11063
.11065
.11067
9.04913
.04922
.04931
.04939
.11198
.11300
.11303
.11305
.11307
.11309
.11311
.11314
9.05445
,05453
.05462
.05471
.11336
.11338
.11340
.11343
9.05973
.05982
.05990
.05999
9.06497
.06506
.06515
.06523
.11614
.11616
.11618
.11631
+ r
29
SO
31
9.04413
.04422
.04431
.04440
.11070
.11073
.11074
.11076
9.04948
.04957
.04966
.04975
9.05480
.05489
.05498
.05506
.11345
.11347
.11349
.11353
9.06008
.06017
.06025
.06034
.11484
.11486
.11488
.11491
.11493
.11495
.11498
.11500
9.06532
.06541
.06550
.06558
9.06567
.06576
.00584
.06593
.11633
.11635
.11638
.11630
32
31
30
29
+ 8'
33
34
35
9.04449
.04458
.04467
.04476
.11079
.11081
.11083
.11086
9.04984
.04993
.05002
.05011
.11316
.11318
.11331
.11333
9.05515
.05524
.05533
.05542
.11354
.11356
.11359
.11361
9.06043
.06052
.06060
.06069
.11633
.11635
.11637
.11639
.11643
.11644
.11646
.11649
28
27
26
25
24
23
22
21
20
19
18
n
16
15
14
13
12
11
10
9
+ 9'
37
38
39
9.04485
.04494
.04503
.04512
.11088
.11090
.11093
.11095
9.05019
.05028
.05037
.05046
.11335
.U338
.11330
.11333
9.05551
.05559
.05568
.05577
.11363
.11366
.11368
.11370
9.06078
.06087
.06095
.06104
.11503
.11504
.11507
.11509
9.06602
.06611
.06619
.06628
+ 10'
41
42
43
9.04520
.04529
.04538
.04547
.11097
.11099
.11103
.11104
9.05055
.05064
.05073
.05082
.11334
.11337
.11339
.11341
.11344
.11346
.11248
.11351
9.05586
.0.5595
.05603
.05612
9.05621
.05630
.05639
.05648
.11373
.11375
.11377
.11379
.11383
.11384
.11386
.11389
9.06113
.06122
.06131
.06139
.11511
.11514
.11516
.11518
9.06637
.06645
.06654
.06663
.11651
.11653
.11656
.11658
+ 11'
45
46
47
9.04556
.04565
.04574
.04583
.11106
.11108
.11111
.11113
9.05090
.05099
.05108
.05117
9.06148
.06157
.06166
.06174
.11531
.11533
.11535
.11538
.11530
.11533
.11535
.11537
9.06671
.06680
.06689
.06697
9.06706
.06715
.06724
.06732
.U660
.11663
.11665
.11667
.11670
.11673
.11674
.11677
+ 13'
49
50
51
9.04592
.04601
.04610
.04619
.11115
.11117
.11130
.11133
9.05126
.05135
.05144
.05153
.11353
.11355
.11357
.11360
9.05656
.05665
.05674
.05683
.11391
.11393
.11396
.11398
9.06183
.06192
.06201
.06209
+ 13'
53
54
55
9.04628
.04637
.04646
.04654
.11134
.11137
.11139
.11131
9.05161
.05170
.05179
.05188
.11363
.11364
.11367
.11369
9.05692
.05700
.05709
.05718
.11400
.11403
.11405
.11407
9.06218
.06227
.06235
.06244
.11539
.11543
.11544
.11546
9.06741
.06750
.06758
.06767
.11679
.11681
.11684
.11686
8
7
6
5
+ w
57
58
59
9.04663
.04672
.04681
.04690
.11134
.11136
.11138
.11140
9.05197
.05206
.05215
.05223
9.05232
.11371
.11374
.11376
.11378
.11380
9.05727
.05736
.05744
.05753
9.05762
.11410
.11413
.11414
.11416
.11419
9.062.53
.06262
.06270
.06279
.11549
.11551
.11553
.11556
.11558
9.06776
.06784
.06793
.06802
.11688
.11691
.11693
.11695
.11698
4
3
2
1
+ IS'
9.04699
.11143
9.06288
9.06810
21^
24m
2; ft
23m
21h
22'^
21^
21m
^Ih 20m
TABLE 45.
Haversines.
[Page 843
s
2* 40m 40° 0'
2h4im
40° 15'
21^4^™
40° 30'
2ft 43m 40° 45'
2h 4^m
41° 0'
s
Log. Hav.
N'at. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
3
9.06810
.06819
.06828
.06836
.11698
,11700
.11703
.11705
9.07329
.07338
.07346
.07355
.11838
.11841
.11843
.11845
9.07845
.07853
.07862
.07870
.11980
.11983
.11984
.11987
.11989
.11993
.11994
.11996
9.08357
.08365
.08374
.08382
.12122
.13134
.13137
.13139
9.08865
.08874
.08882
.08890
.13365
.13367
.13369
.13372
.12374
.13376
.13379
.12281
60
59
58
57
56
55
54
53
+ 1'
5
6
7
9.06845
.06854
.06862
.06871
.11707
.11709
.11713
.11714
.11716
.11719
.11731
.11734
9.07364
.07372
.07381
.07390
.11848
.11850
.11853
.11855
9.07879
.07887
.07896
.07905
9.08391
.08399
.08408
.08416
.13131
.13134
.13136
.13138
9.08899
.08907
.08916
.08924
+ 2'
9
10
11
+ 3'
13
14
15
9.06880
.06888
.06897
.06906
9.07398
.07407
.07415
.07424
.11857
.11860
.11863
.11864
9.07913
.07922
.07930
.07939
.11999
.13001
.13003
.13006
9.08425
.08433
.08442
.08450
9.08459
.08467
.08475
.08484
.13141
.13143
.13146
.13148
.13150
.13153
.13155
.13157
9.08933
.08941
.08949
.08958
9.08966
.08975
.08983
.08992
.12384
.13286
.13388
.13391
.13393
.13296
.13298
.13300
52
51
50
49
48
47
46
45
U
43
4i
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
9.06914
.06923
.06932
.06940
9.06949
.06958
.06966
.06975
.11736
.11738
.11731
.11733
.11735"
.11738
.11740
.11743
9.07433
.07441
.07450
.07458
.11867
.11869
.11871
.11874
.11876
.11878
.11881
.11883
9.07947
.07956
.07964
.07973
.13008
.12010
.12013
.12015
+ *'
n
IS
19
9.07467
.07476
.07484
.07493
9.07o0f
.07510
.07519
.07527
9.07536
.07544
.07553
.07562
9.07570
.07579
.07587
.07596
9.07605"
.07613
.07622
.07630
9.07981
.07990
.07999
.08007
.12018
.12020
.13033
.13035
9.08492
.08501
.08509
.08518
.13160
.13163
.13165
.13167
9.09000
.09009
.09017
.09025
9.09034
.09042
.09051
.09059
.13303
.13305
.13307
.13310
.13313
.13315
.13317
.13319
.13333
.13334
.13337
.13339
.13331
.13334
.13336
.13339
.13341
.13343
.13346
.13348
.13351
.13353
.13355
.13358
.13360
.13363
.13365
.13367
+ S'
9.06984
.06992
.07001
.07010
.11745
.11747
.11749
.11753
.11754
.11756
.11759
.11761
.11763
.11766
.11768
.11770
" .11773
.11775
.11777
.11780
.11783
.11784
.11787
.11789
.11885
.11888
.11890
.11893
.11895
.11897
.11900
.11903
.11904
.11907
.11909
.11911
.11914
.11916
.11918
.11931
9.08016
.08024
.08033
.08041
.13037
.13039
.13033
.13034
9.08526
.08535
.08543
.08552
9.08560
.08569
.08577
.08586
.13169
.13173
.13174
.13176
.13179
.13181
.13184
.13186
+ 6'
2.5
9.07018
.07027
.07036
.07044
9.07053
.07062
.07070
.07079
9.08050
.08058
.08067
.08075
.13036
.13039
.13041
.13044
9.09068
.09076
.09084
.09093
9.09101
.09110
.09118
.09126
9.09135
.09143
.09152
.09160
9.09169
.09177
.09185
.09194
9.09202
.09211
.09219
.09227
9.09236
.09244
.09253
.09201
9.09269
.09278
.09286
.09295
9:09303
.09311
.09320
.09328
+- r
29
SO
31
9.08084
.08092
.08101
.08110
.13046
.12048
.13051
.13053
.13055
.13058
.13060
.13062
.13065
.13067
.13070
.13073
9.08594
.08603
.08611
.08620
9.08628
.08637
.08645
.08654
.13188
.13191
.13193
.13195
.13198
.13300
.13303
.13305
.13307
.13310
.13313
.13314
+ 8'
33
34
35
9.0V088
.07096
.07105
.07113
9.07122
.07131
.07139
.07148
9.08118
.08127
.08135
.08144
+ V
37
38
39
9.07639
.07647
.07656
.07665
.11933
.11935
.11938
.11930
.11933
.11935
.11937
.11940
9.08152
.08161
.08169
.08178
9.08662
.08671
.08679
.08687
+ IC
41
42
43
9.07157
.07165
.07174
.07183
.11791
.11794
.11796
.11798
9.07673
.07682
.07690
.07699
9.07708
.07716
.07725
.07733
9.07742
.07750
.07759
.07768
9.07776
.07785
.07793
.07802
9.08186
.08195
.08203
.08212
.13074
.13077
.13079
.12081
9.08696
.08704
.08713
.08721
.13317
.13319
.13333
.13334
+ t1/
45
46
47
9.07191
.07200
.07208
.07217
.11801
.11803
.11806
.11808
.11943
.11944
.11947
.11949
9.08220
.08229
.08237
.08246
.13084
.13086
.12089
.13091
9.08730
.08738
.08747
.08755
.13336
.13339
.13331
.13233
.13370
.13373
.13374
.13377
.13379
.13383
.13384
.13386
.13389
.13391
.13394
.13396
16
15
14
13
12
11
10
9
8
7
6
5
+ IV
49
50
51
9.07226
.07234
.07243
.07252
.11810
.11813
.11815
.11817
.11830
.11833
.11834
.11837
.11839
.11831
.11834
.11836
.11838
.11951
.11954
.11956
.11958
.11961
.11963
.11966
.11968
9.08254
.08263
.08271
.08280
.12093
.13096
.13098
.13100
9.08764
.08772
.08781
.08789
.13336
.13338
.13341
.13343
+ 13'
53
54
55
9.07260
.07269
.07277
.07286
9.08288
.08297
.08306
.08314
.13103
.13105
.13108
.13110
9.08797
.08806
.08814
.08823
.13345
.13348
.13350
.13253
+ 14'
57
58
59
9.07295
.07303
.07312
.07321
9.07810
.07819
.07827
.07836
9.07845
.11970
.11973
.11975
.11977
.11980
9.08323
.08331
.08340
.08348
.13113
.13115
.13117
.13119
.13133
9.08831
.08840
.08848
.08857
.12355
.13357
.13360
.13363
9.09,337
.09345
.09353
.09362
9.09370
.12398
.12401
.12403
.12406
.13408
4
3
2
1
+ 15'
9.07329
9.08357
9.08865
.13365
eih igm
21h 18m
21h IJm
2/ft le^n
21h
75™
Page 844]
TABLE 45.
Haversines.
s
2h4sm il°W 1
ok 46m 41° 30'
9h 47m
U°45'
2k 48m
42° 0'
ok 49m
12° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Ilav,
1
2
3
9.09370
.09379
.09387
.09395
.12408
.12410
.12413
.12415
9.09872
.09880
.09889
.09897
.12552
.12555
.12557
.12559
9.10371
.10379
.10387
.10395
.12697
.12700
.12702
.12704
9.10866
.10874
.10882
.10891
.13843
.13845
.12848
.12850
9.11358
.11360
.11374
.11382
.12989
.12992
.12994
.12996
60
59
58
57
56
55
54
53
52
51
50
49
+ 1'
5
6
7
9.09404
.09412
.09421
.09429
.12418
.12420
.12422
.12425
9.09905
.09914
.09922
.09930
.12562
.12564
.12567
.12569
9.10404
.10412
.10420
.10429
.13707
.12709
.13713
.12714
9.10899
.10907
.10915
.10923
.13852
.12855
.12857
.13860
9.11391
.11399
.11407
.11415
.12999
.13001
.13004
.13006
.13009
.13011
.13014
.13016
+ 2'
9
10
11
9.09437
.09446
.09454
.09462
.12427
.12430
.12432
.12434
9.09939
.09947
.09955
.09964
.12572
.12574
.12576
.12579
9.10437
.10445
.10453
.10462
.12717
.12719
.12721
.12724
.13736
.12729
.12731
.12733
9.10932
.10940
.10948
.10956
.12862
.12865
.12867
.12870
9.11423
.11431
.11440
.11448
+ 3'
13
14
15
9.09471
.09479
.09488
.09496
.12437
.12439
.12442
.12444
9.09972
.09980
.09989
.09997
.12581
.12584
.12586
.12588
9.10470
.10478
.10486
.10495
9.10965
.10973
.10981
.10989
.12872
.12874
.12877
.12879
9.114.56
.11464
.11472
.11480
.13018
.13021
.13023
.13026
48
47
46
45
44
43
42
41
+ i'
n
18
19
9.09504
.09513
.09521
.09529
.12446
.12449
.12451
.12454
9.10005
.10014
.10022
.10030
.12591
.12593
.12596
.12598
.12600
.12603
.12605
.12608
.13610
.12613
.12615
.12617
9.10503
.10511
.10519
.10528
.12736
.12738
.12741
.12743
9.10997
.11006
.11014
.11022
.12882
.12884
.12887
.12889
9.11489
.11497
.11505
.11513
.13028
.13031
.13033
.13036
+ 5'
21
22
23
9.09538
.09546
.09555
.09563
.12456
.12458
.12461
.12463
9.10039
.10047
.10055
.10064
9.10536
.10544
.10553
.10561
.12746
.12748
.12750
.12753
9.11030
.11038
.11047
.11055
.12891
.12894
.12896
.13899
9.11521
.11529
.11538
.11546
.13038
.13041
.13043
.13045
40
39
38
37
+ 6'
25
26
27
9.09571
.09580
.09588
.09596
.12466
.12468
.12470
.12473
9.10072
.10080
.10088
.10097
9.10569
.10577
.10586
.10594
.12755
.12758
.13760
.13763
9.11063
.11071
.11079
.11088
.13901
.13904
.12906
.12909
9.11554
.11562
.11570
.11578
.13048
.13050
.13053
.13055
36
35
34
33
32
31
SO
29
28
27
26
25
24
23
22
21
+ r
29
SO
SI "
9.09605
.09613
.09622
.09630
.12475
.12478
.12480
.12482
9.10105
.10113
.10122
.10130
.12620
.12623
.12625
.12627
9.10602
.10610
.10619
.10027
.13765
.13767
.13770
.13772
9.11096
.11104
.11112
.11120
.12911
.12913
.12916
.13918
9.11586
.11595
,11603
,11611
.13058
.13060
.13063
.13065
+ 8'
33
34
35
9.09638
.09647
.09655
.09663
.12485
.12487
.12490
.12492
9.10138
.10147
.10155
.10163
.12639
.12632
.12634
.12637
9.10635
.10643
.10652
.10660
.12775
.12777
.12780
.12782
9.11129
.11137
.11145
.11153
.13931
.13933
.13936
.13938
9.11619*
.11627
.11635
.11643
.13067
.13070
.13073
.13075
+ 9'
37
38
39
9.09672
.09680
.09688
.09697
.12494
.12497
.12499
.12502
9.10172
.10180
.10188
.10196
.12639
.12641
.12644
.12646
9.10668
.10676
.10685
.10693
.12784
.12787
.12789
.12793
9.111G1
.11170
.11178
.11186
.13930
.12933
.12935
.12938
9.11652
.11660
.11668
.11676
.13077
.13080
.13083
.13085
+ 10'
41
42
43
9.09705
.09713
.09722
.09730
.12504
.12506
.12509
.12511
9.10205
.10213
.10221
.10230
.12649
.13651
.13654
.13656
.12658
.12661
.12663
.12666
.12668
.12671
.12673
.12675
9.10701
.10709
.10718
.10726
.13794
.12797
.12799
.12801
9.11194
.11202
.11211
.11219
.13940
.13943
.13945
.13948
9.11684
.11692
.11700
.11709
.13087
.13090
.13093
.13095
20
19
IS
17
+ 11'
45
46
47
9.09739
.09747
.09755
.09764
.12514
.12516
.12519
.12521
9.10238
.10246
.10255
.10263
9.10734
.10742
.10751
.10759
.12804
.12806
.12809
.12811
9.11227
.11235
.11243
.11252
.13950
.13952
.12955
.12957
9.11717
.11725
.11733
.11741
.13097
.13099
.13103
.13104
16
15
14
13
12
11
10
9
+ 12'
49
50
51
9.09772
.09780
.09789
.09797
.12523
.12526
.12528
.12531
9.10271
.10279
.10288
.10296
9.10767
.10775
.10784
.10792
.13814
.13816
.13818
.12SM
9.11260
.11268
.11276
.11284
9.11291
.11301
.11309
.11317
.12960
.12962
.12965
.12967
.12970
.12972
.12974
.12977
9.11749
.11757
.11766
.11774
.13107
.13109
.13112
.13114
+ 13'
53
54
55
9.09805
.09814
.09822
.09830
.12533
.12536
.12538
.12540
9.10304
,10313
.10321
.10329
.12678
.12680
.12683
.12685
9.10800
.10808
.10816
.10825
.1282:{
.13836
.13838
.12831
9.11782
.11790
.11798
.11806
.13116
.13119
.13121
.13124
8
7
6
5
+ 1*'
57
58
59
9.09839
.09847
.09856
.09864
.12543
.12545
.12547
.12550
9.10337
.10346
.10354
.10362
.12687
.12690
.12692
.12695
9.10833
.10841
.10849
.10858
.12833
.12836
.12838
.12840
9.11325
.11333
.11342
.11350
.12979
.13983
.12984
.13987
9.11814
.11822
.11831
.11839
.13126
.13129
.13131
.13134
4
3
2
1
+ IS'
9.09872
.12552
9.10371
.12697
9.10866
.12843
9.11358
.13989
9.11847
.13136
Slh
14m
21h
13™
21h
12m
21k
lim
21k
lO"'
TABLE 45. [Page 845
Haversine.-.
s
2A 50™ 42° SO'
%h 5im 43° 45'
2A 52m 43° 0'
2* 5J"' 43° 15'
2h 54m 43° 30'
s
Log. Hav.i Nat. Ilav
Log. Ilav. Nat. Hav
Log. Hav. Nat. Hav
Log, Hav, Nat, Hav
Log, Hav,| Nat. Hav
1
2
3
9.11847
.11855
.11863
.11871
.13136
.13139
.13141
.13143
9.12332
.12341
.12349
.12357
.13284
.13386
.13289
.13291
.13294
.13296
.13299
.13301
9.12815
.12823
.12831
.12839
.13432
.13435
.13437
.13440
9,13295 .13581
.13303 .13584
.13311 , .13586
.13319 .13589
9.13771
.13779
.13787
.13795
.13731
.13734
.13736
.13739
60
59
58
57
56
55
64
53
52
51
50
49
+ 1'
5
6
t
9.11879
.11887
.11895
.11904
.13146
.13148
.13151
.13153
9.12365
.12373
.12381
.12389
9.12847
.12855
.12863
.12871
.13443
.13445
.13447
.13450
9.13326 .13591
.13334 .13594
.13342 .13596
.13350 .13599
9.13358, .13601
.13366 .13604
.13374 ! .13607
.13382 \ .13609
9.13803
.13811
.13819
.13827
.13741
.13744
.13746
.13749
+ - 2'
9
10
11
9.11912
.11920
.11928
.11936
.13156
.13158
.13161
.13163
9.12397
.12405
.12413
.12421
.13304
.13306
.13309
.13311
.13314
.13316
.13318
.13321
.13323
.13326
.13328
.13331
9.12879
.12887
.12895
.12903
.13452
.13455
.13457
.13460
9.13834
.13842
.13850
.13858
.13751
.13754
.13756
.13759
+ 3'
13
14
15
9.11944
.11962
.11960
.11968
.13166
.13168
.13171
.13173
9.12429
.12437
.12445
.12453
9.12911
.12919
.12927
.12935
.13462
.13465
.13467
.13470
.13472
.13474
.13477
.13479
9.13390; .13611
.13398 .13614
.13406 .13616
.13414 .13619
9.13422 .13621
.13430 .13634
.13438 .13626
,13446 .13629
9.13866
.13874
.13882
.13890
9.13898
.13906
.13913
.13921
9.13929
.13937
.13945
,139.53
.13761
.13764
.13766
.13769
.13771
.13774
.13776
.13779
.13781
.13784
.13786
.13789
48
47
46
45
44
43
42
41
40
39
38
37
+ 4'
17
18
19
9.11977
.11985
.11993
.12001
.13175
.13178
.13180
.13183
9.12401
.12470
.12478
.12486
9.12943
.12951
.12959
.12967
+ 5'
f5
9.12009
.12017
.12025
.12033
.13185
.13188
.13190
.13193
.13195
.13198
.13200
.13203
9.12494
.12502
.12510
.12518
^9.12526
.12534
.12542
.12.5.50
9.12.55~8
.12566
.12574
.12582
.13333
.13336
.13338
.13341
9.12975
.12983
.12991
.12999
.13482
.13484
.13487
.13489
9.134.54 .13631
,13462 .13634
,13470 .13636
,13478 .13639
+ 6'
26
«7
9.12041
.12050
.12058
.12066
.13343
.13346
.13348
.13351
.13353
.13356
.13358
.13360
9.13007
.13015
.13023
.13031
.134tS
.13494
.134»7
.13499
.13592
.13594
.13597
.13599
.13512
.13514
.13517
.13519
.13522
.13524
.13527
.13529
9.13486 .13641
,13494 .13644
,13.501 ; .13646
,13.509 ' .13649
9,13517 ; .13651
.13.525 .13654
.13.533 \ .13656
.13541 i .13659
9.13.549 .13661
.13.557 .i;}664
.13565! .13666
.13573 .13669
9.13961
.13969
.13977
,13985
.13791
.13794
.13796
.13799
36
35
34
33
+ r
29
30
31
9.12074
.12082
.12090
.12098
.13205
.13207
.13210
.13212
9.13039
.13047
.13055
.13063
9,13992
,14000
,14008
,14016
.13801
.13804
.13806
.13809
34
31
30
29
28
21
26
25
+ 8'
S3
34
35
9.12106
.12114
,12122
.12130
9.12139
.12147
.12155
.12163
9.12171
.12179
.12187
.12195
.13215
.13217
.13220
.13222
.13225
.13227
.1.3?30
.13232
.13235
.13237
.13239
.13242
9.12590
.12598
.12606
.12614
9: 12622
.12630
.12638
.12647
.13363
.13365
.13368
.13370
.13373
.13375
.13378
.13380
.13383
.13385
.13388
.13390
.13393
.13395
.13398
.13400
.13403'
.13405
.13408
.13410
.13412
.13415
.13417
.13420
9.13071
.13079
.13087
.13095
9.13103
.13111
.13119
.13127
9,14024
,14032
,14040
,14048
.13811
.13814
.13816
.13819
+ 9'
37
38
39
9.13.581 .13671
.13.589 \ .13674
.13.597 ! .13676
.13605 i .13679
9,140.56
.14063
.14071
.14079
.13822
.13824
.13827
.13829
24
23
22
21
20
19
18
n
+ 10'
41
42
4-i
9.12655
,12663
.12671
.12679
9.12687
.12695
.12703
,12711
9,12719
,12727
.12735
,12743
9.12751
.12759
.12767
.12775
9.13135
.13143
.13151
.13159
.13532
.13534
.13537
.13539
9.13613
.13621
.13628
.13636
.13681
.13684
.13686
.13689
.13691
.13694
.13696
.13699
.13701
.13704
.13706
.13709
9.14087
,14095
.14103
,14111
9,14119
,14127
,14134
,14142
.13832
.13834
.13837
.13839
+ 11'
45
46
47
+ 12'
' 49
50
51
+ " 13'
53
54
55
+"_J14'^
57
58
59
+ 15'
9.12203
.12211
.12219
.12228
.13244
.13247
.13249
.13252
9.13167
.13175
.13183
.13191
.13542
.13544
.13547
.13549
.13552
.13554
.13557
.13559
9.13644
.13652
.13660
.13668
.13842
.13844
.13847
.13849
.13852
.13854
.13857
.13859
Id
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
9.12236
.12244
.12252
.12260
.13254
.13257
.13259
.13262
9.13199
.13207
.13215
.13223
9.13231
.13239
.13247
.13255
9.13676
.13684
.13692
.13700
9,14150
,141.58
,14166
.14174
9.12268
.12276
.12284
.12292
.13264
.13267
.13269
.13272
.13562
.13564
.13567
.13569
9.13708
.13716
.13724
.13732
.13711
.13714
.13716
.13719
9,14182
,14190
.14197
,14205
.13862
.13864
.13867
.13869
9.12300
.12308
.12316
.12324
.13274
.13276
.13279
.13281
9.12783
.12791
,12799
,12807
.13422
.13425
.13427
.13430
9.13263
.13271
.13279
.13287
9.13295
.13571
.13574
.13576
.13579
.13581
9.13739
.13747
.13755
.13763
.13721
.13724
.13726
.13729
9,14213
,14221
.14229
.14237
.13872
.13874
.13877
.13879
9.12332 ! .13284
9,12815 1 .13432
9.13771 .13731
9,14245 .13882
tlhgm
^IhSm
^Ih im 1
2th sm
2; asm
Page 846]
•
TABLE 45.
Haversines.
s
2h 55m
43° 45' 2* 56m 44° (K
2h sym ^^° 15'
2h. S8m 44° 30'
2h S9m 44° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.14245
.14252
.14260
.14268
.13882
.13884
.13887
.13889
9.14715
.14723
.14731
.14739
.14033
.14035
.14038
.14041
9.15183
.15190
.15198
.15206
.14185
.14187
.14190
.14193
9.15647
. 15655
.15663
.15670
9.15678
.1.5686
.15694
.15701
9.15709
.15717
.15724
.15732
9.15740
.15748
.15755
.15763
.14337
.14340
.14343
.14345
.14348
.14350
.14353
.14355
.14358
.14360
.14363
.14366
.14368
.14371
.14373
.14376
9.16109
.16117
.16124
.16132
.14491
.14493
.14496
.14498
.14501
.14504
.14506
.14509
.14511
.14514
.14516
.14519
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
'44
43
42
41
40
39
38
37
"S6
35
34
33
32
31
30
29
28
27
26
25
24
23
22
Vl
20
19
18
n
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ 1'
5
6
7
9.14276
.14284
.14292
.14300
.13892
.13894
.13897
.13899
9.14746
.14754
.14762
.14770
9.14778
.14785
.14793
.14801
9.14809"
.14817
.14824
,14832
.14043
.14046
.14048
.14051
.14053
.14056
.14058
.14061
.14063
.14066
.14068
.14071
9.15214
.15321
.15329
.15237
.14195
.14198
.14300
.14303
9.16140
.16147
.16155
.16163
+ V
9
10
11
9.14307
.14315
.14323
.14331
.13903
.13904
.13907
.13909
9.15245
.15253
.15260
.15268
.14305
.14308
.14210
.14213
.14315
.14318
.14330
.14323
.14236
.14228
,14231
.14233
9.16170
.16178
.16186
.16193
+ 3'
13
14
15
9.14339
.14347
.14355
.14362
.13912
.13914
.13917
.13930
9.15276
.15284
.15291
.15299
9.16201
.16209
.16216
.16224
.14531
.14534
.14537
.14539
+ 4'
n
18
19
9.14370
.14378
.14386
.14394
.13933
.13935
.13927
.13930
9.14840
.14848
.14856
-.14863
9.14871
.14879
.14887
.14895
.14073
.14076
.14079
.14081
.14084
.14086
.14089
.14091
9.15307
.15315
.15322
.15330
9.15771
.1.5778
.15786
.15794
.14378
.14381
.14383
.14386
9.16232
.16239
.16247
.16255
.14533
.14534
.14537
.14539
.14542
,14545
,14547
,14550
.14553
.14555
.14557
.14560
+ 5'
21
22
23
9.14402
.14410
.14417
.14425
.13933
.13935
.13937
.13940
9.15338
.15346
.15353
.15361
.14236
.14238
.14341
.14243
9.15802
.15809
.15817
.15825
.14388
.14391
.14394
.14396
9.16262
.16270
.16278
.16285
9.1629'3'
.16301
.16308
.16316
+ 6'
25
26
27
9.14433
.14441
.14449
.14457
.13942
.13945
.13947
.13950
9.11902
.14910
.14918
.14926
.14094
.14096
.14099
.14101
9.15369
."15377
.15384
.15392
.14346
.14248
.14351
.14353
.14256
.14259
.14361
.14364
.14366
.14269
.14271
.14274
9.15832
.1.5840
.15848
.1,58.55
.14399
.14401
.14404
.14406
.14409
.14411
.14414
.14417
.14419
,14423
,14434
,14437
+ T
29
30
31
9.14465
.14472
.14480
.14488
9.14496
.14504
.14512
.14519
.13952
.13955
.13957
.13960
.13962
.13965
.13967
.13970
9.14934
.14941
.14949
.14957
9.14965
.14973
.14980
.14988
.14104
.14106
.14109
.14111
.14114
.14116
.14119
.14132
9.15400
.15408
.15415
.15423
9.15863
.15871
.1.5879
.15886
9.15894
.1.5902
.15909
.15917
9.16324
.16331
.16339
.16346
9.16364
.16362
.16369
.16377
.14562
.14565
.14568
.14570
.14573
.14575
.14578
.14580
+ 8'
33
34
35
9.15431
.15439
.15446
.15454
+ 9'
37
38
39
9.14527
.14535
.14543
.14551
.13973
.13975
•13977
.13980
9.14996
.15004
.1.5012
.15019
.14134
.14137
.14139
.14133
9.15462
.15470
.15477
.15485
9.15493
.15500
.15508
.15516
9.15524
.1.5531
.15539
.15547
.14276
.14279
.14381
.14384
.14287
,14289
,14292
,14294
,14297
,14299
,14302
,14304
9.15925
.15932
.15940
.15948
9.15955
.15963
.15971
.15978
,14429
,14432
,14434
.14437
9.16385
.16392
.16400
.16408
.14583
.14586
.14588
.14591
.14593
.14596
.14598
.14601
+ KK
41
42
43
9.14559
.14566
.14574
.14582
.13983
.13985
.13988
.13990
9.15027
. L5035
.15043
.15050
9.1.5058
.1.5066
.1.5074
.1.5082
9.15089
.1.5097
.15105
.15113
.14134
.14137
.14139
.14143
.14440
.14443
.14445
.14447
9.16415
.16423
.16431
.16438
+ 11'
45
46
47
9.14590
.14598
.14606
.14613
.13993
.13995
.13998
.14000
.14144
.14147
.14149
.14153
.14154
.14157
.14160
.14163
9.15986
.15994
.16002
.16009
9:10017
.16025
.16032
. 16040
.14450
.14453
.14455
.14457
.14460
,14463
,14465
,14468
9.16446
.16453
.16461
.16469
9.16476
.16484
.16492
.16499
.14604
.14606
,14609
.14611
.14614
.14616
.14619
.14633
+ 13'
49
50
51
9.14621
.14629
.14637
.14645
.14003
.14005
.14008
.14010
9.15555
.15562
.15570
.15578
.14307
.14309
.14312
.14315
+ 13'
53
54
55
9.14653
.14660
.14668
.14676
.14013
.14015
.14018
.14030
9.15120
.15128
.15136
.15144
.14165
.14167
.14170
.14173
9.15585
.15593
.15601
.15609
.14317
.14330
.14332
.14335
9.16048
.160.55
,16063
.16071
,14470
,14473
,14475
,14478
9.16507
.16515
.16522
.16530
.14634
.14637
.14629
.14632
.146.34
.14637
.14639
.14642
.14645
+ 14'
57
58
59
9.14684
.14692
.14699
.14707
.14023
.14025
.14028
.14030
.14033
9.15152
.15159
.15167
.15175
9.15183
.14175
.14177
.14180
.14183
.14185
9.15616
.15624
.15632
.15640
.14327
.14330
.14332
.14.335
9,16078
.16086
.16094
.16101
9.16169
,14480
,14483
.14486
.14488
.14491
9,16537
.16545
.16553
.16560
9.16568
+ 15'
9.14715
9.15647
.14337
21h
4m
211>
Sm
2in2m
21h im
21^
Om
TABLE 45.
Haversines.
•
[Page 847
s
3h om 45° 0'
Sh in 45° 15'
5* 2m 45° 30'
3'>3^iS°iS'
3h4m
46° 0'
s
Log. Hav.
Nat. nav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav,
1
2
3
9.16568
.16576
.16583
.16591
.14645
.14647
.14650
.14653
9.17024
.17032
.17039
.17047
.14799
.14802
.14804
.14807
9.17477
.17485
.17492
.17500
.14955
.14957
.14960
.14963
9.17928
.17935
.17943
.17950
.15110
.15113
.15116
.15118
9.18376
.18383
.18390
.18398
.15267
.15370
.15272
.15275
60
59
58
57
+ 1'
5
6
7
9.16598
.16606
.16614
.16621
.14655
.14658
.14660
.14663
9.17054
.17062
.17069
.17077
.14810
.14812
.14815
.14817
9.17507
.17515
.17522
.17530
.14965
.14968
.14970
.14973
9.17958
.17965
.17973
.17980
.15121
.15123
.15126
.15129
9,18405
.18413
.18420
.18428
9.18435
.18443
.18450
.18457
.15378
.15380
,15283
.15285
56
55
54
53
+ V
9
10
11
9.16629
.16637
.16644
.16652
.14665
.14668
.14670
.14673
9.17085
.17092
.17100
.17107
.14820
.14822
.14825
.14828
9.17538
.17545
.17553
.17560
.14975
.14978
.14981
.14983
9.17988
.17995
.18003
.18010
.15131
.15134
.15137
.15139
.15388
,15391
,15393
.15296
52
51
50
49
48
47
46
45
+ 3'
13
14
15
9.16659
.16667
.16675
.16682-
.14676
.14678
.14681
.14683
9.17115
.17122
.17130
.17138
.14830
.14833
.14835
.14838
9.17568
.17575
.17583
.17590
.14986
.14988
.14991
.14993
9.18018
.18025
.18033
.18040
.15142
.15144
.15147
.15150
9.18465
.18472
.18480
.18487
.15298
.15301
.15304
,15306
+ 4'
17
18
19
9.16690
.16697
.16705
.16713
.14686
.14688
.14691
.14693
9.17145
.17153
.17160
.17168
.14841
.14843
.14846
.14848
9.17598
.17605
.17615
.17620
,14996
.14999
.15001
.15004
9.18048
.18055
.18062
.18070
.15152
.15155
.15157
.15160
9.18495
.18502
.18509
,18517
,15309
,15312
,15314
.15316
44
43
42
41
+ 5'
21
22
23
9.16720
.16728
.16735
.16743
.14696
.14699
.14701
.14704
9.17175
.17183
.17191
.17198
.14851
.14853
.14856
.14859
9.17628
.17635
.17643
.17650
.15006
.15009
.15012
.15014
9.18077
.18085
.18092
.18100
.15163
.15165
.15168
.15170
9.18524
.18.532
.18539
.18547
.15319
.15323
.15325
.15327
40
39
38
37
+ 6'
25
26
27
9.16751
.16758
.16766
.16774
.14706
.14709
.14712
.14714
9.17206
.17213
.17221
.17228
.14861
.14864
.14866
.14869
9.17658
.17665
.17673
.17680
.15017
.15019
.15033
.15035
9.18107
.18115
.18122
.18130
.15173
.15176
.15178
.15181
9.18554
.18561
.18569
.18576
.15330
.15333
.15335
.15337
36
35
34
33
+ r
29
30
31
9.16781
.16789
.16796
.16804
.14717
.14719
.14723
.14724
9.17236
.17243
.17251
.17259
.14872
.14874
.14877
.14879
9.17688
.17695
.17703
.17710
.15037
.15030
.15032
.15035
9.18137
.18145
.18152
.18160
.15183
.15186
.15189
.15191
9,18584
.18591
.18598
.18606
.15340
.15343
.15346
.15348
32
31
30
29
+ 8'
33
34
35
9.16812
.16819
.16827
.16834
.14727
.14730
.14732
.14735
9.17266
.17274
.17281
.17289
9.17296"
.17304
.17311
,17319
9.17327
.17334
• .17342
.17349
.14882
.14885
.14887
.14890
9.17718
.17725
.17733
.17740
.15038
.15040
.15043
.15045
9.18167
.18174
.18182
.18189
.15194
.15197
.15199
.15202
9.18613
.18621
.18628
.18636
,15351
,15353
,15356
,15359
28
27
26
25
+ 9'
37
38
39
9.16842
.16850
.16857
.16865
.14737
.14740
.14743
.14745
.14892
.14895
.14898
.14900
.14903
.14905
.14908
.14910
9.17748
.17755
.17763
.17770
.15048
.15051
.15053
.15056
9.18197
.18204
.18212
.18219
.15204
.15307
.15310
.15212
9.18643
.186.50
.18658
.18665
,15361
,15364
,15367
.15369
24
23
22
Tl
+ W
41
42
43
9.16872
.16880
.16887
.16895
.14748
.14750
.14753
.14755
9.17778
.17785
.17793
.17800
.15058
.15061
.15064
.15066
9.18227
.182,34
.18242
.18249
.15215
.15217
.15220
.16233
9.18673
.18680
.18687
.18695
.15372
.16374
.15377
.15379
20
19
18
17
+ 11'
45
46
47
9.16903
.16910
.16918
.16925
.14758
.14760
.14763
.14766
9.17357
.17364
.17372
.17379
.14913
.14916
.14918
.14921
9.17808
.17815
.17823
.17830
.15069
.15071
.15074
.15077
9.18256
.18264
.18271
.18279
.15225
.15228
.15230
.15233
9.18702
.18710
.18717
.18724
.15383
,15385
,15388
.15390
16
15
14
13
12
11
10
9
+ ir
49
60
51
9.16933
.16941
.16948
.16956
.14768
.14771
.14773
.14776
9.17387
.17394
.17402
.17409
'9.17417
.17425
.17432
.17440
.14923
.14926
.14929
.14931
9.17838
.17845
.17853
.17860
.15079
.15082
.15084
.15087
9.18286
.18294
.18.301
.18309
.15236
.15238
.15241
.15244
9.18732
.18739
.18747
.18754
.15393
.15395
.15398
.16401
+ 13'
53
54
55
9.16963
.16971
.16979
.16986
.14779
.14781
.14784
.14786
.14934
.14936
.14939
.14942
9.17868
.17875
.17883
.17890
.15090
.15092
.15095
.15097
9.18316
.18324
.18331
.18338
.15246
,15249
.15351
.15354
9.18762
.18769
.18776
.18784
.16403
.15406
.15409
.15411
8
7
6
5
+ 14'
57
58
59
9.16994
.17001
.17009
.17016
.14789
.14791
.14794
.14797
9.17447
.17455
.17462
.17470
.14944
.14947
.14949
.14952
9.17898
.17905
.17913
.17920
.15100
.15103
.15105
.15108
9.18346
.183.53
.18361.
.18368
.15257
.15259
.15262
.15264
9.18791
.18798
.18806
.18813
.15414
.15416
.15419
.15433
4
3
2
1
+ IS'
9.17024
.14799
9.17477
.14955
9.17928
.15110
9.18376
.15267
9,18821
.15434
20^
sgm
20h oSm
20>i
57m
20*
56m
20h
55m
Page 848]
«
TABLE 45.
Haversines.
•
s
3h5m
16° 15'
Sh em 46° 30'
3h 7m 46° 45'
jA5m47°0'
3h 9m 47° 15'
a
Log. Ilav.
Nat. Hav.
Log. Ilav.
Nat. Ilav.
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Hav.
1
i
3
9.18821
.18828
.18835
.18843
.15424
.15427
.15430
.15432
9.19263
.19270
.19278
.19285
.15582
.15585
.15588
.15590
9.19703
.19710
.19717
.19725
.15741
.15743
.15746
.15748
9.20140
.20147
.20154
.20162
.15900
.15903
.15905
.15908
.15911
.15913
.15916
.15919
.15921
.15924
.15927
.15929
.15932
.15935
.15937
.15940
9.20574
.20582
.20589
.20596
9.20603
.20611
.20618
.20625
9.20632
.20639
.20047
.206.54
9.20661
.20668
.20675
.20683
9.20690
.20697
.20704
.20712
9.20719
.20726
.20733
.20740
9.20748
.20755
.20762
.20769
.16060
.16063
.16065
.16068
60
59
58
57
+ 1'
5
6
7
9.18850
.18858
.18865
.18872
.15435
.15437
.15440
.15443
9.19292
.19300
.19307
.19315
9.19322
.19329
.19337
.19344
9.19351
.19359
.19366
.19373
9.19381"
.19388
.19395
.19403
9.194i0
.19417
.19425
.19432
9.19439
.19447
.19454
.19461
9.19469
.19476
.19483
.19491
9 J 9498
.19505
.19513
.19520
9.19527
.19535
.19542
.19549
9.19557
.19564
.19571
.19579
.15593
.15595
.15598
.15601
9.19732
.19739
.19747
.19754
.15751
.15754
.15757
.15759
.15762
.15765
.15767
.15770
.15773
.15775
.15778
.15781
9.20169
.20176
.20184
.20191
9.20198
.20205
.20213
.20220
"9.20227
.20234
.20242
.20249
"9^20256
.20263
.20271
.20278
9.20285'
.20292
.20300
.20307
.16071
.16073
.16076
.16079
56
55
54
S3
52
51
50
49
+ V
9
10
11
9.18880
.18887
.18895
.18902
.15445
.15448
.15451
.15453
.15456
.15458
.15461
.15464
.15603
.15606
.15609
.15611
.15614
.15617
.15619
.15623
9.19761
.19769
.19776
.19783
9.19790
.19798
.19805
.19812
.16081
.16084
.16087
.16089
+ 3'
13
14
15
9.18909
.18917
.18924
.18932
.16092
.16095
.16097
.16100
.16103
.16105
.16108
.16111
.16113
.16116
.16119
.16121
48
47
46
45
44
43
42
41
40
39
38
37
+ 4'
17
18
19
9.18939
.18946
.18954
.18961
.15466
.15469
.15472
.15474
.15625
.15627
.15630
.15632
.15635
.15638
.15640
.15643
.15646
.15648
.15651
.15654
.15656
.15659
.15662
.15664
.15667
.15670
.15672
.15675
.15677
.15680
.15683
.15685
.15688
.15691
.15693
.15696
9.19820
.19827
.19834
.19S42
9.19849
.19856
.19863
.19871
9.19878
.19885
.19893
.19900
9. 19907"
.19914
.19922
.19929
.15783
.15786
.15789
.15791
.15794
.15796
.15799
.15802
.15943
.15945
.15948
.15951
.15953
.15956
.15959
.15961
.15964
.15967
.15969
.15972
.15975
.15977
.15980
^.15983
"^.15985
.15988
.15991
.15993
.15996
.15999
.16001
.16004
.16007
.16009
.16012
.16015
.I6OI7
.16030
.16023
.16035
.16038
.16031
.16033
.16036
+ 5'
21
22
23
9.18968
.18976
.18983
.18991
.15477
.15479
.15482
.15485
+ 6'
25
26
27
9.18998
.19005
.19013
.19020
.15487
.15490
.15493
.15495
.15804
.15807
.15810
.15812
.15815
.15818
.15820
.15823
9.20314
.20321
.20329
.20336
9.20343
.20350
.20358
.20365
"9:20372
.20379
.20386
.20394
9720401
.20408
.20415
.20423
9.20430
.20437
.20444
.20452
"9.20459
.20466
.20473
.20481
9.20488
.20495
.20502
.20509
.16124
.16127
.16129
.16132
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
2.
20
19
18
17
16
IS
14
13
+ r
29
SO
31
9.19027
.19035
.19042
.19050
.15498
.15501
.15503
.15506
9.20776
.20784
.20791
.20798
.16135
.16137
.16140
.16143
+ 8'
33
34
35-
9.19057
.19064
.19072
.19079
.15509
.15511
.15514
.15516
9.19936
.19944
.19951
.19958
.15826
.15828
.15831
.15834
9.20805
.20812
.20820
.20827
.16146
.16148
.16151
.16154
+ 9'
37
38
39
9.19086
.19094
.19101
.19109
.15519
.15523
.15524
.15527
9,19965
.19973
.19980
.19987
.15836
.15839
.15842
.15844
9.20834
.20841
.20848
.20856
9.20863
.20870
.20877
.20884
.16156
.16159
.16162
.16164
.16167
.16170
.16172
.16175
+ 10'
41
42
43
9.19116
.19123
.19131
.19138
9.19145
.19153
.19160
.19167
9.19175
.19182
.19190
.19197
.15530
.15532
.15535
.15537
9.19995
.20002
.20009
.20016
.15847
.15850
.15852
.15855
.15858
.15860
.15863
.15866
.15868
.15871
.15874
.15876
.15879
.15881
.15884
.15887
.15889
.15892
.15895
.15898
+ U'
45
46
47
.15540
.15543
.15545
.15548
.15551
.15553
.15556
.15559
9.19586
.19593
.19600
.19608
9.19615
.19622
.19630
.19637
9.19644
.19652
.19659
.19666
9.19674
.19681
.19688
.19696
"9.19703
.15699
.15701
.15704
.15706
9.20024
.20031
.20038
.20045
9.20053
.20060
.20067
.20075
9.20082"
.20089
.20096
.20104
9.20891
.20899
.20906
.20913
.16178
.16180
.16183
.16186
+ 13'
49
SO
51
.15709
.15712
.15714
.15717
.15720
.15722
.15725
.15728
.15730
.15733
.15736
.15738
.15741
9.20920
.20927
.20935
.20942
.16188
.16191
.16194
.16196
12
11
10
9
+ 13'
53
54
55
+ 14'
57
58
59
9.19204
.19212
.19219
.19226
.15561
.15564
.15566
.15569
9.20517
.20524
.20531
.20538
9.20546
.20553
.20560
.20567
.16039
.16041
.16044
.16047
9.20949
.20956
.20963
.20971
9.20978
.20985
.20992
.20999
9.21006
.16199
.16202
.16204
.16207
8
7
6
5
9.19234
.19241
.19248
.19256
9.19263
.15572
.15574
.15577
.15580
.15583
9.20111
.20118
.20125
.20133
9.20140
.16049
.16052
.16055
.16057
.16060
.16310
.16312
.16315
.16218
.16330
4
3
2
~1
+ 15'
.15900
9.20574
go*
54m
20h 53m
20''
52m
20h
51™
20h
50m
TABLE 45.
Haversines.
•
[Page 849
s
ShlOm
47° 30'
Shllm
47° 45'
3% 12m 48° 0^
■Sh ISm 48° 15'
Shl4m
48° 30'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
a
3
9.21006
.21014
.21021
.21028
.16230
.16323
.16336
.16339
.16331
.16334
.16337
.16339
9.21436
.21443
.21450
.21457
.16383
.16384
.16387
.16390
9.21863
.21870
.21877
.21884
.16543
.16546
.16549
.16553
9.22287
.22294
.22301
.22308
.16706
.16709
.16711
.16714
9.22709
.22716
.22723
.22730
.16869
,16873
.16874
.16877
60
59
58
57
+ r
5
6
7
9.21035
.21042
.21049
.21057
9.21464
.21471
.21479
.21486
9.21493
.21500
.21507
.21514
.16393
.16395
.16398
.16401
9.21891
.21898
.21905
.21912
.16554
.16557
.16560
.16563
9.22315
.22322
.22329
.22336
9.22343
.22350
.22358
.22365
.16717
.16730
.16733
.16735
9.22737
.22744
.22751
.22758
.16880
.16883
.16885
.16888
56
55
54
53
+ 2'
9
10
11
9.21064
.21071
.21078
.21085
.16343
.16345
.16347
.16350
.16403
.16406
.16409
.16411
9.21919
.21926
.21934
.21941
.16565
.16568
.16571
.16573
.16576
.16579
.16581
.16584
.16738
.16730
.16733
.16736
9.22765
.22772
.22779
.22786
.16891
.16893
.16896
.16899
.16903
.16904
.16907
.16910
52
51
50
49
48
47
46
45
44
43
42
41
+ 3'
13
14
15
9.21092
.21100
.21107
.21114
.16353
.16355
.16358
.16361
9.21521
.21529
.21536
.21543
.16414
.16417
.16419
.16433
9.21948
.21955
.21962
.21969
9.22372
.22379
.22386
.22393
9.22400
.22407
.22414
.22421
.16738
.16741
.16744
.16747
.16749
.16752
.16755
.16757
9.22793
.22800
.22807
.22814
+ 4'
n
18
19
9.21121
.21128
.21135
.21143
9.21150
.21157
.21164
.21171
.16363
.16366
.16369
.16371
9.21550
.21557
.21564
.21571
.16435
.16437
.16430
.16433
9.21976
.21983
.21990
.21997
.16587
.16589
.16593
.16595
.16598
.16600
.16603
.16606
9.22821
.22828
.22835
.22842
.16913
.16915
.16918
.16921
+ 5'
21
22
23
.16374
.16377
.16380
.16383
9.21578
.21585
.21593
.21600
.16436
.16438
.16441
.16444
9.22004
.22011
.22019
.22026
9.22428
.22435
.22442
.22449
9.22456
.22463
.22470
.22477
.16760
.16763
.16766
.16768
.16771
.16774
.16777
.16779
9.22849
.22856
.22863
.22870
.16934
.16926
.16939
.16933
40
39
38
37
36
35
34
33
+ «'
25
26
27
9.21178
.21186
.21193
.21200
.16385
.16388
.16390
.16393
9.21607
.21614
.21621
.21628
.16446
.16449
.16453
.16454
.16457
.16460
.16463
.16465
9.22033
.22040
.22047
.22054
.16608
.16611
.16614
.16616
9.22877
.22884
.22891
.22898
.16934
.16937
.16940
.16943
+ r
29
SO
31
9 21207
.21214
.21221
.21229
.16396
.16398
.16301
.16304
9.21635
.21642
.21650
.21657
9.22061
•.22068
.22075
.22082
.16619
.16633
.16625
.16637
.16630"
.16633
.16635
.16638
9.22484
.22491
.22498
.22505
9.22512
.22519
.22526
.22533
9.22540
.22547
.22555
.22362
9.2256<r
,22576
.22583
.22590
9.22.197
.22604
.22611
.22018
9.22625
.22632
.226,39
.22646
9.226.53
.22660
.22007
.22074
9.22681
.22688
.22695
.22702
.16783
.16785
.16787
.16790
9.22905
.22912
.22919
.22926
.16945
.16948
.16951
.16953
32
31
30
29
+ 8'
S3
34
35
9.212,36
.21243
.21250
.21257
.16306
.16309
.16313
.16314
9.21664
.21671
.21678
.21685
.16468
.16471
.16473
.16476
9.22089
.22096
.22103
.22111
.16793
.16795
.16798
.16801
.16804
.16806
.16809
.16813
.16815
.16817
.16830
.16833
.16835
.16838
.16831
.16834
.16836
.16839
.16842
.16844
.16847
.16850
.16853
.16855
.16858
.16861
.16864
.16866
9.22933
.22940
.22947
.22954
.16956
.16959
.16963
.16964
28
27
26
25
+ »'
57
38
39
9.21264
.21272
.21279
.21286
9.21293"
.21300
.21307
.21314
.16317
.16330
.16333
.16335
.16338
.16331
.16333
.16336
9.21692
.21699
.21706
.21714
.16479
.16481
.16484
.16487
9.22118
.22125
.22132
.22139
.16641
.16644
.16646
.16649
.16653
.16654
.16657
.16660
.16663
.16666
.16668
.16671
.16673
.16676
.16679
.16681
.16684
.16687
.16690
.16693
.16695
.16698
.16701
.16703
9.22961
.22968
.22975
.22982
.16967
.16970
.16973
.16975
24
23
22
21
+ W
41
42
43
9.21721
.21728
.21735
21742
.16489
.16493
.16495
.16498
9.22146
.22153
.22160
.22167
9.22989
.22996
.23003
.23010
.16978
.16981
.16984
.16986
20
19
IS
17
16
15
14
13
+ 11'
45
46
47
9.21322
.21329
.21336
.21343
.16339
.16341
.16344
.16347
9.21749
.21756
.21763
.21770
.16500
.16503
.16506
.16508
9.22174
.22181
.22188
.22195
9.22202
.22209
.22216
.22224
9.22231
.22238
.22245
.22252
9.22259
.22266
.22273
.22280
9.23017
.23024
.23031
.23038
.16989
.16993
.16994
.16997
+ 18'
49
50
51
9.21350
.21357
.21364
.21372
.16349
.16353
.16355
.16357
.16360
.16363
.16366
.16368
.16371
.16374
.16376
.16379
.16383
9.21778
.21785
.21792
.21799
.16511
.16514
.16516
.16519
9.23045
.23052
.23059
.23066
.17000
.17003
.17005
.17008
12
11
10
9
+ 13'
53
54
55
9.21379
.21386
.21393
.21400
9;2140f
.21414
.21422
.21429
9.21436
9.21806
.21813
.21820
.21827
.16533
.16534
.16537
.16530
.16533
.16535
.16538
.16541
9.23073
.23080
.23087
.23094
.17011
.17014
.17016
.17019
8
7
6
5
4
3
2
1
+ U'
57
58
59
9.21834
.21841
.21848
.21856
9.21863
9.23100
.23107
.23114
.23121
.17033
.17034
.17037
.17030
.17033
+ 16'
.16543
9.22287
.16706
9.22709
.16869
9.23128
20h
49m
20^ 48m
20fi 47™
20^ 46^
«0A
45m
24972°— 12-
-44
Page 850] TABLE 45.
Haversines.
s
5ftj,5m48°_45' |
Sh lem 4fl° 0' 1
Sh 17m 49" 15'
Sh igm 49° W
Sh igm 49° 45'
s
Log. nav.
Nat. Ilav.
Log, Hav,
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.! Nat. Hav,
1
2
3
9.23128
.23135
.23142
.23149
.17033
.17035
.17038
.17041
9,23545
.23552
.23559
.23566
.17197
.17200
.17203
.17205
9.23960
.23967
.23974
.23981
.17362
.17365
.17368
.17370
9.24372
.24379
.24386
.24393
.17528
.17530
.17533
.17536
9.24782
.24789
.24796
.24803
.17694
.17697
.17699
.17702
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
+ 1'
5
6
7
9.23156
.23163
.23170
.23177
.17044
.17046
.17049
.17052
9.23573
.23580
.23587
.23594
.17208
.17211
.17214
.17216
9.23988
.23994
.24001
.24008
.17373
.17376
.17379
.17381
9.24400
,24406
.24413
.24420
.17539
.17541
.17544
.17547
9.24809
.24816
.24823.
.24830
.17705
.17708
.17710
.17713
+ 3'
9
10
11
9.23184
.23191
.23198
.23205
.17055
.17057
.17060
.17063
9.23601
.23608
.23615
.23622
.17219
.17222
.17225
.17227
9.24015
.24022
.24029
.24036
.17384
.17387
.17390
.17392
9.24427
.24434
.24441
.24448
.17550
.17552
.17555
.17558
9.24837
.24843
.24850
.24857
.17716
.17719
.17722
.17724
+ 3'
13
14
15
9.23212
.23219
.23226
.23233
.17066
.17068
.17071
.17074
9.23629
.23635
.23642
.23649
.17230
.17233
.17235
.17238
9.24043
.24050
.24056
.24063
9.24070
.24077
.24084
.24091
.17395
.17398
.17401
.17403
.17406
.17409
.17412
.17414
9.24454
.24461
,24468
,24475
.17561
.17563
.17566
.17569
9.24864
.24871
.24877
.24884
.17727
.17730
.17733
.17735
+ 4'
17
18
19
9.23240
,23247
.23254
.23261
.17076
.17079
.17082
.17085
9.23656
.23663
.23670
.23677
.17241
.17244
.17246
.17249
9.24482
.24489
.24495
.24502
.17572
.17575
.17577
.17580
.17583
.17586
.17588
.17591
9.24891
.24898
.24905
.24911
.17738
.17741
.17744
.17746
+ 6'
21
22
23
9.23268
.23275
.23282
.23289
.17087
.17090
.17093
.17096
9.23684
.23691
.23698
.23705
.17252
.17255
.17257
.17260
9.24098
.24105
.24111
.24118
.17417
.17420
.17423
.17425
9.24509
.24516
.24523
.24530
9.24918
.24925
.24932
.24939
.17749
.17752
.17755
.17758
40
39
38
37
+ 6'
25
26
27
9.23295
.23302
.23309
.23316
.17098
.17101
.17104
.17107
9.23712
.23718
.23725
.23732
.17263
.17266
.17268
.17271
9.24125
.24132
.24139
.24146
.17428
.17431
.17434
.17436
9.24536
.24543
.24550
.24557
.17594
.17597
.17600
.17602
9.24945
.24952
.24959
.24966
.17760
.17763
.17766
.17769
36
35
34
33
+ r
29
30
31
9.23323
.23330
,23337
.23344
.17109
.17112
.17115
.17117
9.23739
.23746
.23753
.23760
.17274
.17277
.17279
.17282
9.24153
.24160
.24166
.24173
.17439
.17442
.17445
.17447
9.24564
.24571
.24577
.24584
.17605
.17608
.17611
.17613
9.24973
.24979
.24986
.24993
9.25000
.25007
.25013
.25020
.17772
.17774
.17777
.17780
32
31
SO
29
+ 8'
33
34
35
9.23351
.23358
.23365
.23372
.17120
.17123
.17126
.17128
9.23767
.23774
.23781
.23788
.17285
.17288
.17290
.17293
9.24180
.24187
.24194
.24201
.17450
.17453
.17456
.17458
9.24591
,24598
.24605
.24612
.17616
.17619
.17622
.17624
.17783
.17785
.17788
.17791
28
27
26
25
24
23
22
21
+ 9'
37
38
39
9.23379
.23386
.23393
.23400
.17131
.17134
.17137
.17139
9.23794
.23801
.23808
.23815
*17296
.17299
.17301
.17304
9.24208
.24215
.24221
.24228
.17461
.17464
.17467
.17470
9.24618
.24625
.24632
.24639
.17627
.17630
.17633
.17636
9.25027
.25034
.25040
.25047
.17794
.17797
.17799
.17802
+ 10'
41
42
43
9.23407
.23414
.23421
.23427
.17142
.17145
.17148
.17150
9.23822
.23829
.23836
.23843
.17307
.17310
.17313
.17315
9.24235
.24242
,24249
,24256
.17472
.17475
.17478
.17481
9.24646
.24653
.24659
.24666
.17638
.17641
.17644
.17647
9.25054
.25061
.25068
.25074
.17805
.17808
.17811
.17813
20
19
18
17
+ 11'
45
46
47
9.23434
.23441
.23448
.23455
.17153
.17156
.17159
.17161
9.23850
.23857
.23863
.23870
.17318
.17321
.17323
.17326
9,24263
,24269
.24276
.24283
.17483
.17486
.17489
.17492
9.24673
.24680
.24687
.24694
.17649
.17652
.17655
.17658
9.25081
.25088
.25095
.25102
.17816
.17819
.17822
.17824
16
15
14
13
+ 12'
49
50
51
9.23462
.23469
.23476
.23483
.17164
.17167
.17170
.17172
9.23877
.23884
.23891
.23898
.17329
.17332
.17335
.17337
9.24290
.24297
.24304
.24311
.17494
.17497
.17500
.17503
9.24700
.24707
.24714
.24721
.17661
.17663
.17666
.17669
9.25108
,25115
,25122
,25129
.17827
.17830
.17833
.17836
12
11
10
,9
+ 13'
53
54
55
9.23490
.23497
.23504
.23511
.17175
.17178
.17181
.17183
9.23905
.23912
.23919
.23926
.17340
.17343
.17346
.17348
9.24317
.24324
.24331
.24338
.17505
.17508
.17511
.17514
9.24728
.24734
.24741
.24748
.17672
.17674
.17677
.17680
9,25135
,25142
.25149
.25156
.17838
.17841
.17844
.17847
8
7
6
5
4
3
1
+ 14'
57
58
59
9,23518
.23525
.23532
.23538
.17186
.17189
.17192
.17194
9.23932
.23939
.23946
.23953
.17351
.17354
.17357
.17359
9,24345
,24352
.24359
.24365
.17517
.17519
.17522
.17525
9,24755
,24762
,24768
,24775
.17683
.17686
.17688
.17691
9.25163
,25169
,25176
,25183
.17849
.17852
.17855
.17858
+ 15'
9.23545
.17197
9.23960
.17362
9.24372
.17528
9,24782
.17694
9.25190
.17861
20^ 44™-
20'i- 43™
oQh ^2m
fOA 41™
20h 40™
TABLE 45.
Haversines.
[Page 861
s
5'' 20™ 50° 0'
5A 2m 50
°15'
gh 22™
50° 30'
S^ 23m 50° 45'
3I1 24^ 61° 0'
s
Log. Hav.
Nat. Hav.
Log. Hav. Ns
t. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9,25190
.25196
.25203
.25210
.17861
.17863
.17866
.17869
.17873
.17875
.17877
.17880
.17883
.17886
.17888
.17891
9.25595
.25602
.25608
.25615
18038
18031
18034
18036
9.25998
.26005
.26011
.26018
.18196
.18199
.18303
.18305
9.26398
.26405
.26412
.26418
.18365
.18368
.18370
.18373
.18376
.18379
.18383
.18384
9.26797
.26804
.26810
.26817
.18534
.18537
.18540
.18543
60
59
58
57
+ 1'
5
6
7
9.25217
.25224
.25230
.25237
9.25622
.25629
.2.5635
.25642
.18039
.18043
.18045
.18048
9.26025
.26031
.26038
.26045
.18307
.18310
.18313
.18316
.18319
.18331
.18234
.18337
.18330
.18333
.18335
.18338
9.26425
.26432
.26438
.26445
9.26452
.264.58
.26465
.26472
9.26478
.26485
.26492
.26498
9.26823
.26830
.26837
.26843
.18545
.18548
.18551
.18554
.18557
.18559
.18563
.18565
.18568
.18571
.18574
.18576
56
55
54
53
62
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
+ 2'
9
10
11
9.25244
.25251
.25257
.25264
9.25049
.2.5655
.25662
.25669
.18050
.18053
.18056
.18059
.18063
.18064
.18067
.18070
.18073
.18076
.18078
.18081
9.26051
.26058
.26065
.26071
9.26078
.26085
.26091
.26098
.18387
.18390
.18393
.18396
.18399
.18401
.18404
.18407
9.26850
.26856
.26863
.26870
9.26876
.26883
.26890
.26896
+ 3'
75
9.25271
.25278
.25284
.25291
.17894
.17897
.17900
.17903
.17905
.17908
.17911
.17914
9.25676
.25682
.25689
.25696
+ 4'
77
19
9.25298
.25305
.25311
.25318
9.2"5703
.25709
.25716
.25723
9.26105
.26112
.26118
.26125
.18341
.18244
.18347
.18349
9.26505
.26512
.26518
.26525
9.26532
.26538
.26545
.26551
9.26558
.26565
.26571
.26578
.18410
.18413
.18415
.18418
.18431
.18434
.18437
.18430
.18433
.18435
.18438
.18441
.18444
.18446
.18449
.18453
9.26903
.26909
.26916
.26923
9.26929
.26936
.26942
.26949
.18579
.18582
.18585
.18588
.18591
.18593
.18596
.18599
+ 5'
9.25325
.25332
.25339
.25345
.17916
.17919
.17923
.17935
9.25729
.25736
.25743
.25750
9^25756"
.25763
.25770
.25776
.18084
.18087
.18090
.18093
.18095
.18098
.18101
.18104
.18106
18109
18113
18115
9.26132
.26138
.26145
.26152
9.26158
.26165
.26172
.26178
.18253
.18355
.18358
.18361
.18363
.18366
.18269
.18273
.18375
.18377
.18380
.18383
+ 6'
25
26
27
9.25352
.25359
.25366
.25372
.17938
.17930
.17933
.17936
9.26956
.26962
.26969
.26975
9.26982
.26989
.26995
.27002
9.27008
.27015
.27022
.27028
9.27035
.27041
.27048
.27055
.18603
.18605
.18608
.18610
.18613
.18616
.18619
.18633
36
35
34
33
32
31
30
29
+ r
29
30
31
+ 8'
33
34
35
9.25379
.25386
.25393
.25399
.17939
.17941
.17944
.17947
.17950
.17953
.17955
.17958
.i7961
.17964
.17967
.17969
.17973
.17975
.17978
.17981
.17983
.17986
.17989
.17993
.17995
.17997
.18000
.18003
9.25783
.25790
.25797
.25803
9.25810
.2.5817
.25823
.25830
9.26185
.26192
.26198
.26205
9.26585
.26591
.26598
.26605
9.26611
.26618
.26625
.26631
9.26638
.26644
.26651
.26658
9.25406
.25413
.25420
.25426
18118
18130
.18133
.18136
9.26212
.26218
.26225
.26232
.18386
.18389
.1839*
.18394
.18455
.18458
.18461
.18463
.18466
.18469
.18473
.18475
.18634
.18637
.18630
.18633
28
27
26
25
+ 9'
37
38
39
9.25433
.25440
.25447
.25453
9.25837
.25844
.25850
.25857
9.25864
.25870
.25877
.25884
9.2589r
.25897
.25904 ;
.2.5911 1
9.25917
.25924
.25931
.25938 1
9.25944
.25951
.25958
.25964
.18139
.18133
.18134
.18137
.18140
.18143
.18146
.18148
9.26238
.26245
.26252
.26259
9.26265
.26272
.26279
.26285
.18397
.18300
.18303
.18306
.18308
.18311
.18314
.18317
.18636
.18639
.18641
.18644
.18647
.18650
.18653
.18656
24
23
22
21
20
19
18
17
+ W
41
42
43
9.25460
.25467
.25474
.25480
9.26664
.26671
.26678
.26684
.18478
.18480
.18483
.18486
9.27061
.27068
.27074
.27081
+ 11'
45
46
47
9.25487
.25494
.25500
.25507
.18151
18154
18157
18160
.18163
18165
.18168
18171
18174
18176
18179
18183
18185
18188
18190
18193
18196
9.26292
.26299
.26305
.26312
.18320
.18333
.18335
.18338
9.26691
,26697
.26704
.26711
.18489
.18493
.18494
.18497
9.27088
.27094
.27101
.27107
.18658
.18661
.18664
.18667
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ ir
49
50
51
+ W
53
54
55
9.25514
.25521
.25528
.25534
9.26319
.26325
.26332
.26339
9.26345
.26352
.26359
.26365
.18331
.18334
.18337
.18339
.18343
.18345
.18348
.18351
.18353
.18356
.18359
.18362
.18365
9.26717
.26724
.26731
.26737
.18500
.18503
.18.506
.18509
9.27114
.27121
.27127
.27134
.18670
.18673
.18675
.18678
9.25541
.25548
.25544
.25561
9^25568
.25575
.25581
.25588
.18006
.18008
.18011
.18014
.18017
.18030
.18033
.18035
.18038
9.26744
.26751
.26757
.26764
9:26770
.26777
.26784
.26790
.18511
.18514
.18517
.18530
.18533
.18536
.18538
.18531
9.27140
.27147
.27154
.27160
9.27167
.27173
.27180
.27186
.18681
.18684
.18687
.18690
.18693
.18695
.18698
.18701
+ W
57
58
59
9.25971
.25978
.25984
.25991
9.25998
9.26372
.26378
.26385
.26.392
9.26398
+ 15'
9.22.595
9.26979
.18534
9.27193
.18704
20h
59m
20h S8m
f Oft 57m
20h 36m
20h S5m
Page 852]
TABLE 45.
Haversinea.
s
5ft 25m 51° 15'
snt6m&l°W 1
jA 97m 51° 45' 1
Sh 28m 62° 0'
5* 29m 52° 15' 1
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Ilav,
Nat. Hav.
1
2
3
+ 1'
5
6
7
9.27193
.27200
.27206
.27213
.18704
.18707
.18710
.18713
9.27587
..27594
.27600
.27607
.18874
.18877
.18880
.18883
9.27979
.27985
.27992
.27998
.19045
.19048
.19051
.19054
9.28368
.28375
.28381
.28388
.19217
.19220
.19223
.19326
9,28756
,28762
.28769
.28775
.19389
.19392
.19395
.19398
60
59
58
57
56
56
54
53
52
51
50
49
48
47
46
45
44
43
42
41
9.27219
.27226
.27233
.27239
.18715
.18718
.18721
.18724
9.27613'
.27620
.27626
.27633
.18886
.18888
.18891
.18894
9.28005
.28011
.28018
.28024
.19057
.19060
.19082
.19065
9.28394
.28401
.28407
.28414
.19238
.19231
.19334
.19337
9,28782
.28788
.28794
.28801
.19401
.19404
.19406
.19409
+ 2'
9
10
11
9.27246
.27252
.27259
.27265
.18727
.18729
.18732
.18735
9.27639
.27646
.27652
.27659
.18897
.18900
.18903
.18906
9,28031
,28037
.28044
.28050
.19068
.19071
.19074
.19077
9.28420
.28427
.28433
.28440
.19240
.19243
.19246
.19248
9,28807
,28814
,28820
.28827
.19412
.19415
.19418
.19421
+ 3'
13
14
15
9.27272
.27279
.27285
.27292
.18738
.18741
.18744
.18746
9.27666
.27672
.27679
.27685
.18908
.18912
.18914
.18917
9.28057
.28063
.28070
.28076
.19080
.19082
.19085
9.28446
.28453
.28459
,28465
.19251
.19254
.19257
.19260
9,28833
,28840
,28846
.28852
.19424
.19427
.19429
.19433
+ *'
17
18
19
9.27298
.27305
.27311
.27318
.18749
.18752
.18755
.18758
9.27692
.27698
.27705
.27711
.18920
.18923
.18926
.18928
9.28083
.28089
.28096
.28102
.19091
.19094
.19097
.19100
9,28472
,28478
,28485
,28491
.19263
.19366
.19369
.19371
9.28859
.28865
.28872
.28878
.19435
.19438
.19441
.19444
+ y
21
22
23
9.27325
.27331
.27338
.27344
.18761
.18763
.18766
.18769
9.27718
.27724
,27731
,27737
.18931
.18934
.18937
.18940
9,28109
,28115
,28112
,28128
.19102
.19105
.19108
.19111
9.28498
,28504
,28511
,28517
.19274
.19377
.19380
.19383
.19386
.19389
.19291
.19394
9.28885
,28891
,28897
,28904
.19447
.19450
.19452
.19455
40
39
38
37
+ 6'
25
26
. 27
9.27351
.27357
.27364
.27371
.18772
.18775
.18778
.18780
9.27744
.27751
.27757
.27764
.18943
.18945
.18948
.18951
9.28135
.28141
.28148
.28154
.19114
.19117
.19120
.19122
9,28524
,28530
,28537
,28543
9,28910
,28917
,28923
,289.30
.19458
.19461
.19464
.19467
.19470
.19473
.19475
.19478
36
35
34
33
32
31
30
29
+ r
29
30
31
9.27377
.27384
.27390
.27397
.18783
.18786
.18789
.18792
9.27770
.27777
.27783
.27790
.18954
.18957
.18960
.18963
.18965
.18968
.18971
.18974
9.28161
.28167
.28174
.28180
.19125
.19128
.19131
.19134
9,28549
.28556
.28562
.28569
.19397
.19300
.19303
.19306
9,28936
,28942
,28949
,28955
+ 8'
33
34
35
9.27403
.27410
.27417
.27423
.18795
.18797
.18800
.18803
9.27796
.27803
.27809
.27816
9.27822
,27829
,27835
,27842
9.28187
.28193
.28200
.28206
.19137
.19140
.19142
.19145
9.28575
.28582
.28588
.28595
9.28601
.28608
.28614
.28620
9.28627
.28633
.28640
.28646
.19309
.19311
.19314
.19317
9,28962
,28968
,28974
.28981
.19481
.19484
.19487
.19490
28
27
26
25
+ »'
37
38
39
9.27430
.27436
.27443
.27449
.18806
.18809
.18812
.18815
.18977
.18980
.18983
.18985
9.28213
.28219
.28226
.28232
.19148
.19151
.19154
.19157
.19160
.19163
.19165
.19168
.19330
.19333
.r336
.19339
.19333
.19335
.19337
.19340
9.28987
,28994
,29000
,29007
.19493
.19496
.19499
.19501
.19504
.19507
.19510
.19513
.19516
.19519
.19522
.19534
.19537
.19530
.19533
.19536
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
+ W
41
42
43
9,27456
.27463
.27469
.27476
.18817
.18820
.18823
.18826
9.27848
.27855
.27861
.27868
.18988
.18991
.18994
.18997
9.28239
.28245
.28252
.28258
9,29013
,29019
.29026
.29032
+ 11'
45
46
47
9.27482
.27489
.27495
.27502
.18829
.18832
.18834
.18837
9.27875
.27881
.27888
.27894
.19000
.19002
.19005
.19008
.19011
.19014
.19017
.19020
9.28265
.28271
.28278
.28284
.19171
.19174
.19177
.19180
9,28653
,28659
,28666
,28672
9,28679
,28685
,28691
.28698
.19343
.19346
.19349
.19353
9.29039
.29045
.29051
.29058
+ ir
49
50
51
9.27508
.27515
.27522
.27528
.18840
.18843
.18846
.18849
9.27901
,27907
,27914
,27920
9.28291
.28297
.28304
.28310
.19183
.19185
.19188
.19191
.19355
.19358
.19360
.19363
9.29064
.29071
.29078
.29084
9.29090
.29096
.29103
.29109
+ 13'
5,?
54
55
9.27535
.27541
.27548
.27554
.18852
.18854
.18857
.18860
9,27927
.27933
.27940
.27946
.19022
.19025
.19028
.19031
9.28317
.28323
.28330
.28336
.19194
.19197
.19200
.19203
9.28704
.28711
.28717
.28724
.19366
.19369
.19373
.19375
.19539
.19542
.19545
.19548
8
7
6
5
+ li'
57
58
59
9.27561
.27567
.27574
.27580
.18863
.18866
.18869
.18871
9,27953
,27959
,27966
,27972
9,27979
.19034
.19037
.19040
.19042
.19045
9.28342
.28349
.28355
.28362
.19205
.19208
.19211
.19214
9.28730
.28737
.28743
.28749
9.28756
.19378
.19381
.19383
.19386
.19389
9,29116
.29122
.29128
.29135
.19550
.19553
.19556
.19559
4
3
2
1
+ 18'
9.27587
.18874
9.28368
.19217
9.29141
.19562
20h
34™
20h
SSm
20% S2m
20li-
Sim
20h SOm
TABLE 45.
Haversines.
[Page 853
s
JA SOm 53° 30'
ShSim
53° 45'
Sh 32m 53° 0'
3h 33^ 53° 15'
Sh .34m
53° 30'
s
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
1
2
3
9.29141
.29148
.29154
.29160
.19563
.19565
.19568
.19571
9.29524
.29531
.29537
.29543
.19735
.19738
.19741
.19744
.19747
.19750
.19753
.19756
9.29906
.29912
.29918
.29925
.19909
.19913
.19915
.19918
.19931
.19934
.19937
.19930
.19933
.19935
.19938
.19941
9.30285
.30291
.30207
.30303
9.30310
.30316
.30322
.30329
.30084
.30087
.30090
.30093
9.30662
.30668
.30674
.30680
.30359
.30363
.30365
.30368
60
59
68
57
+ r
5
6
7
9.29167
.29173
.29180
.29186
.19573
.19576
.19579
.19583
.19585
.19588
.19591
.19594
9.29550
.29556
.29563
.29569
9.29931
.29937
.29943
.29950
9.29956
.29962
.29969
.29975
9.29981
.29988
.29994
.30000
9.30007
.30013
.30019
.30026
.30095
.30098
.30101
.30104
.30107
.30110
.30113
.30116
9.30687
.30693
.30699
.30705
9.30712
.30718
.30724
.30730
.30371
.30373
.30376
.30379
56
55
54
53
+ r
9
10
11
9.29192
.29199
.29205
.29212
9.29575
.29582-
.29588
.29594
9.29601
.29607
.29614
.29620
9.29626
.29633
.29639
.29645
9.29652
.29658
.29664
.29671
9.29677
.29683
.29690
.29696
9.29703
.29709
.29715
.29722
9.29728
.29734
.29741
.29747
.19758
.19761
.19764
.19767
9.30335
.30341
.30348
.30354
.30383
.30385
.30388
.30391
52
51
50
49
+ 3'
13
14
15
9.29218
.29224
.29231
.29237
.19597
.19599
.19603
.19605
.19608
.19611
.19614
.19617
.19770
.19773
.19776
.19779
.19783
.19785
.19787
.19790
.19793
.19796
.19799
.19803
.19805
.19808
.19811
.19814
.19816
.19819
.19833
.19835
.19838
.19831
.19834
.19837
.19840
.19843
.19845
.19848
.19851
.19854
.19857
.19860
.19944
.19947
.19950
.19953
.19956
.19959
.19963
.19964
.19967
.19970
.19973
.19976
.19979
.19983
.19985
.19988
9.30360
.30366
.30373
.30379
.30119
.30133
.30135
.30137
.30130
.30133
.30136
.30139
.30143
.30145
.30148
.30151
.30154
.30157
.30160
.30163
9.30737
.30743
.30749
.30755
.30394
.30397
.30300
.30303
48
47
46
45
44
43
42
41
40
39
38
37
36
35
S4
S3
+ 4'
17
18
19
9.29244
.29250
.29256
.29263
9.30385
.30392
.30398
.30404
9.30762
.30768
.30774
.30780
.30306
.30309
.30313
.30314
+ 5'
21
22
23
+ .6'
25
26
27
9.29269
.29276
.29282
.29288
.19630
.19633
.19635
.19638
9.30032
.30038
.30045
.30051
9.30410
.30417
.30423
.30429
9.30436
.30442
.30448
.30454
9.30787
.30793
.30799
.30805
9.30812
.30818
.30824
.30830
.30317
.30330
.30333
.30336
.30339
.30333
.30335
.30338
9.29295
.29301
.29307
.29314
.19631
.19634
.19637
.19640
.19643
.19646
.19649
.19651
9.30057
.30064
.30070
.30076
9.30083
.30089
.30095
.30102
9.30108
.30114
.30121
.30127
9.30133
.30139
.30146
.30152
+ r
29
30
31
9.29320
.29327
.29333
.29339
.19991
.19994
.19996
.19999
.30003
.30005
.30008
.30011
9.30461
.30467
.30473
.30480
.30165
.30168
.30171
.30174
9.30837
.30843
.30849
.30855
.30341
.30344
.30347
.30350
32
31
30
29
+ 8'
33
S4
35
9.29346
.29352
.29359
.29365
.19654
.19657
.19660
.19663
9.30486
.30492
.30498
.30505
.30177
.30180
.30183
.30186
.30189
.30193
.30195
.30198
9.30862
.30868
.30874
.30880
9.30887
.30893
.30899
.30905
.30353
.30355
.30358
.30361
.30364
.30367
.30370
.30373
28
27
26
25
24
23
22
21
20
19
18
17
+ 9'
37
38
39
+ w
41
42
43
9.29371
.29378
.29384
.29391
.19666
.19669
.19673
.19675
.19677
.19680
.19683
.19686
9.297.53
.29760
.29766
.29772
9.29779"
.29785
.29791
,29798
.30014
.30017
.30030
.30033
9.30511
.30517
.30524
.30530
9.29397
.29403
.29410
.29416
9.301.58
.30165
.30171
.30177
.30026
.30038
.30031
.30034
9.30536
.30542
.30549
.30555
.30300
.30303
.30306
.30309
9.30912
.30918
.30924
.30930
.30376
.30379
.30383
.30385
.30388
.30391
.30393
.30396
+ 11'
45
46
47
9.29422
.29429
.29435
.29442
.19689
.19693
.19695
.19698
.19701
.19703
.19706
.19709
.19713
.19715
.19718
.19731
9.29804
.29810
.29817
29823
9.29829
.29836
.29842
.29848
9.298.55
.29861
.29867
.29874
9.29880
.29886
.29893
.29899
9.29906
.19863
.19866
.19869
.19873
.19874
.19877
.19880
.19883
9.30184
.30190
.30196
.30203
9.30209
.30215
.30222
.30228
.30037
.30040
.30043
.30046
.30049
.30053
.30055
.30058
.30060
•«0063
.30066
.30069
.30073
.30075
.30078
.30081
9.30561
.30567
.30574
.30580
9.30.586
.30593
.30599
.30605
.30313
.30315
.30318
.30331
.30334
.30337
.30330
.30333
.30335
.30338
.30341
.30344
9.30937
.30943
.30949
.30955
9T30962
.30968
.30974
.30980
"9.30987
.30993
.30999
.31005
16
15
14
13
+ ir
49
50
51
+ W
53
54
55
9.29448
.29454
.29461
.29467
9.29473
.29480
.29486
.29493
.30399
.30403
.30405
.30408
12
11
10
9
8
7
6
5
.19886
.19889
.19893
.19895
.19898
.19901
.19903
.19906
.19909
9.30234
.30240
.30247
.30253
9.302.59
.30266
.30272
.30278
9.30611
.,30618
.30624
.30630
9.30636
.30643
.30649
.30655
.30411
.30414
.30417
.30430
+ w
57
58
59
9.29499
.29505
.29512
.29518
9.29524
.19734
.19737
.19730
.19733
.19735"
.30347
.30350
.30353
.30356
.30359
9.31012
.31018
.31024
.31030
.30433
.30436
.30439
.30433
.30435
4
3
2
1
+ 15'
9.30285
.30084
9.30662
9.31036
20*
99m
20^^28^
20h
27m
20h26m
2nh
?.5m
Page 854]
TABLE 45.
Haversines.
s
^ft 55"! 53° 45'
3li S&n 54° 0'
Sh sira 54° 15'
5* 38m 54° 30'
3h39m
54° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav,
Ix)g. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.31036
.31043
.31049
.31055
.20435
.20437
.30440
.30443
.20446
.20449
.20452
.20455
.30458
.30461
.30464
.30467
9.31409
.31416
.31422
.31428
9.31434
.31440
.31447
.31453
9.31459
.31465
.31471
.31478
9.31484
.31490
.31496
.31502
9.31508
.31515
.31521
.31527
.30611
.30614
.30617
.30630
.20633
.20636
.20629
.20631
.20634
.20637
.20640
.20643
.20646
.20649
.20652
.20655
.20658
.30661
.20664
.20667
.20670
.20673
.20675
.20678
.20681
.20684
.20687
.20690
9.31780
.31786
.31793
.31799
9.31805"
.31811
.31817
.31823
.20788
.30790
.30793
.30796
.30799
.20802
.20805
.30808
.30811
.30814
.30817
.30830
9.32149
.32155
.32161
.32168
.30965
.30968
.30971
.30974
.30977
.30980
.20983
.20986
~ .20989
.30991
.30994
.30997
.31000
.21003
.3100G
.21009
.21012
.21015
.21018
.21031
9.32516
.32522
.32528
.32534
.21143
.21146
.31149
.31153
60
59
58
57
+ 1'
5
6
7
9.31061
.31068
.31074
.31080
9.31086
.31093
.31099
.31105
9.32174
.32180
.32186
.32192
9.32198
.32204
.32210
.32217
9.32223
.32229
.32235
.32241
9.32247
.32253
.32259
.32266
9.32.541
.32547
.32553
.32559
.31155
.31158
.31161
.31164
56
55
54
53
52
51
50
49
+ 2'
9
10
11
9.31830
.31836
.31842
.31848
9.31854
.31860
.31867
.31873
9.31879
.31885
.31891
.31897
9.31903
.31910
.31916
.31922
9.31928
.31934
.31940
.31947
9.31953
.31959
.31965
.31971
9.32565
.32571
.32577
.32583
.31167
.31169
.31173
.31175
+ 3'
13
14
15
9.31111
.31117
.31124
.31130
.30470
.30473
.30476
.30479
.20823
.20826
.20839
.20832
.20835
.20838
.20841
.30844
.30847
.30850
.30853
.30855
.30858"
.30861
.30864
.30867
.30870
.30873
.30876
.30879
.30883
.30885
.20888
.30891
9.32589
.32595
.32601
.32608
9.32614
.32620
.32626
.32632
9.32638
.32644
.32650
.32656
.31178
.21181
.21184
.21187
.31190
.21193
.21196
.21199
48
47
46
45
44
43
42
41
+ 4'
n
18
19
9.31136
.31142
.31149
.31155
.30481
.30484
.30487
.30490
.30493
.30496
.30499
.30503
+ 5'
21
22
23
9.31161
.31167
.31173
.31180
9.31533
.31.539
.31546
.31552
9.32272
.32278
.32284
.32290
9.32296
.32302
.32308
.32315
9.32321
.32327
.32333
.32339
9.32345
.32351
.32357
.32363
.31024
.31027
.21030
.21033
.21036
.21039
.21042
.31045
.31048
.21051
.31054
.21057
.21060
.31063
.21066
.31069
.21072
.21074
.21077
.21080
.21083
.21086
.21089
.21092
.21095
.21098
.21101
.31104
.31303
.31305
.31308
.21311
.31314
.31317
.31230
.31323
40
39
38
37
36
35
34
33
+ 6'
25
■2€
27
9.31186
.31192
.31198
.31205
.30505
.30508
.30511
.30514
9.31.558
.31564
.31570
.31577
9.32662
.32668
.32675
.32681
9.32687
.32693
.32699
.32705
9.32711
.32717
.32723
.32729
9.32735
.32741
.32748
.32754
9T32760
.32766
.32772
.32778
9.32784'
.32790
.32796
.32802
9.32808
.32814
.32820
.32827
9".32S33
.32839
.32845
.32851
9.32857
.32863
.32869
.32875
+ r
29
30
SI
9.31211
.31217
.31223
.31229
.30517
.30530
.30533
.30535
9.31583
.31589
.31595
.31601
.20693
.20696
.20699
.20702
.20705
.20708
.20711
.30714
.20717
.20720
.20733
.20736
.30729
.20731
.20734
.30737
.31236
.21339
.21332
.31335
.3i338
.31341
.31344
.31247
.31350
.31253
.21256
.21259
.31362
.31365
.31368
.31371
.31374
.31377
.21380
.31383
.31385
.21288
.31391
.31394
.31397
.31300
.31303
.31306
.31309
.31313
.31315
.21318
32
31
30
29
+ 8'
SS
34
35
9.31236
.31242
.31248
.31254
.30528
.30531
.30534
.30537
.30540
.20543
.20546
.20549
9.31607
.31614
.31620
.31626
9.31977
.31983
.31990
.31996
9..'52002
.32008
.32014
.32020
9.32026
.32033
.32039
.32045
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
+ 9'
57
38
39
9.31260
.31267
.31273
.31279
9.31632
.31638
.31644
.31651
.20894
.30897
.30900
.30903
.20906
.20909
.30912
.30915
.30918
.30920
.30933
.30936
.20939
.20932
.30935
.30938
.30941
.20944
.30947
.30950
.30953
.30956
.30959
.30963
.30965
9.32370
.32376
.32382
.32388
9.32394
.32400
.32406
.32412
9.32418
.32425
.32431
.32437
+ 10'
41
42
43
9.31285
.31291
.31298
.31.304
.30553
.30555
.30558
.30561
.20564
.20567
.20570
.30573
9.31657
.31663
.31669
.31675
9.31682
.31688
.31694
.31700
+ 11'
45
46
47
9.31310
.31316
.31323
.31329
.30740
.20743
.20746
.20749
.20753
.30755
.20758
.20761
9.32051
.32057
.32063
.32069
9.32076
.32082
.32088
.32094
9.32100
.32106
.32112
.32119
9.3212.5
.32131
.321.37
.32143
9.32149"
+ 12'
49
50
51
9.31335
.31341
.31347
.31354
.30575
.30578
.30581
.20584
.30587
.30S90
.30593
.30596
.30599
.30603
.30605
.20608
9.31706
.31712
.31719
.31725
9.32443
.32449
.32455
.32461
9.32467
.32473
.32480
.32486
9.32492
.32498
.32504
.32510
9..32516
.31107
.31110
.31113
.21116
.31119
.31132
.21125
.21138
.21131
.21134
.21137
.31140
+ 13'
5S
54
55
9.31360
.31366
.31372
.31378
9.31731
.31737
.31743
.31749
9.31756
.31762
.31768
.31774
.20764
.20767
.20770
.20773
.20776
.20779
.20782
.20785
.30788
+ 14'
57
58
59
9.31385
.31391
.31397
.31403
4
3
2
1
+ 15'
9.31409
.20611
9.31780
.31143
9.32881
.21331
20h
24^
20h
23VI
20 ft
22VI
20*
21"'
20^ 20m
TABLE 45.
Haversines.
[Page 855
s
^''^Om
55° 0'
Sh4lm
55015'
5*4»">
55° 30'
3h.43m
55° 46'
gh ^m
56° 0'
s
I-og. nav.
Xat. Ilav
Log. Ilav.
Nat. Ilav.
Log. Ilav
Nat. Ilav.
Log. nav.
Nat. Ilav.
Log. Ilav.
Nat. Hav.
1
2
3
9.32881
.32887
.32893
.32899
.31321
.21324
.21327
.21330
.21333
.21336
.21339
.21342
9.33244
.33250
.33256
.33262
.21500
.21503
.21506
.21609
9.33605
.33611
.33617
.33623
.21680
.21683
.21686
.21689
9.33965
.33971
.33976
.33982
.21860
.21863
.21866
.21869
9.34322
.34328
.34334
.34340
.22040
.22043
.33046
.22049
60
59
58
57
+ 1'
5
6
7
9.32905
.32911
.32918
.32924
9.33268
.33274
.33280
.33286
.21512
.21515
.21518
.21521
9.33629
.33635
.33641
.33647
.21692
.21695
.21698
.21701
9.33988
.33994
.34000
.34006
.31873
.21876
.21878
.21881
.21884
.21887
.21890
.21893
9.34346
.34352
.34358
.34363
.22052
.33055
.32058
.33061
56
55
54
53
+ 3'
9
10
11
9.32930
.32936
.32942
.32948
.21345
.21348
.21351
.21354
9.33292
.33298
.33305
..3.3311
.21524
.21527
.21530
.21533
9.33653
.33659
.33665
.33671
.21704
.21707
.21710
.21713
9.34012
.34018
.34024
.34030
9.34369
.34375
.34381
.34387
.32064
.32067
.22071
.22074
52
51
50
49
48
47
46
45
+ 3'
13
14
. 15
9.32954
.32960
.32966
.32972
9.32978
.32984
.32990
.32996
.21357
.21360
.21363
.21366
.21369
.21372
.21375
.21378
.21381
.21384
.21387
.21390
.21393
.21396
.21399
.21402
9.33317
.33323
.33329
.33335
9.33M1
.33347
.33353
.33359
.21536
.21539
.21542
.21545
.21548
.21551
.21554
.21557
9.33677
.33683
.33689
.33695
.21716
.21719
.21722
.21726
9.34036
.34042
.34048
.34054
.21896
.21899
.21902
.21905
9.34393
.34399
.34405
.34411
.22077
.22080
.32083
.22086
+ *'
77
IS
19
9.33701
.33707
.33713
.33719
.21728
.21731
.21734
.21737
9.34060
.34066
.34072
.34078
.21908
.31911
.31914
.21917
.21920
.21923
.21936
.21929
9.34417
.34423
.34429
.34435
.22089
.22092
.22095
.33098
44
43
42
41
+ 5'
21
22
23
9.33002
.33008
.33014
.33021
9.33365
.33371
.33377
.33383
9.33389"
.33395
.33401
.33407
9,33413
.33419
.33425
.33431
.21560
.21563
.21566
.21569
.21572
. .21575
.21578
.21581
.21584
.21587
.21590
.21593
9.33725
.33731
.33737
.33743
.21740
.21743
.21746
.21749
9.34084
.34090
.34096
.34102
9.34108
.34114
.34120
.34126
9.34441
.34446
.34452
.34458
.33101
.23104
.22107
.22110
40
39
38
37
+ e'
25
26
27
9.33027
.33033
.33039
.33045
9.33749
.33755
.33761
.33767
.21762
.21765
.21758
.21761
.21932
.21936
.21938
.21941
9.34464
.34470
.34476
.34482
.23113
.32116
.22119
.22122
36
35
34
3S
+ T
29
30
31
9.33051
.33057
.33063
.33069
.21405
.21408
.21411
.21414
9.33773
.33779
.33785
.33791
.21764
.21767
.21770
.21773
9.34132
.34137
.34143
.34149
.21944
.21947
.31950
.21953
.21966
.21959
.21963
.21966
9.34488
.34494
.34500
.34506
9.34512
.34518
.34524
.34529
.33135
.33138
.22131
.33134
32
31
SO
29
+ 8'
S3
34
85
9.33075
.33081
.33087
.33093
.21417
.21420
.21423
.21426
9.33437
.33443
.33449
.33455
.21596
.21599
.21602
.21605
9.33797
.33803
.33809
.33815
9.33821
.33827
.33833
.33839
.21776
.21779
.21782
.21785
9.,34155
..34161
.34167
.34173
.22137
.22140
.22143
.22146
28
27
26
25
+ 9'
37
38
39
9.33099
.33105
.33111
.33117
.21429
.21431
.21434
.21437
9.33461
.33467
.33473
.33479
.21608
.21611
.21614
.21617
.21788
.21791
.21794
.21797
9.34179
.34185'
.34191
.34197
.21968
.21971
.21974
.21977
9.34535
.34541
.34547
.34553
.22149
.22152
.22165
.22168
24
23
22
21
20
19
18
77
16
15
14
13
12
11
10
9
+ lO'
41
42
43
9.33123
.33129
.33135
.33142
.21440
.21443
.21446
.21449
9.33485
.33491
.33497
.33503
.21620
.21623
.21626
.21629
9.33845
.33851
.33857
.33863
.21800
.31803
.21806
.21809
9.34203
.34209
.34215
.34221
.31980
.31983
.31986
.21989
9.34559
.34565
.34571
.34577
.22161
.22164
.22167
.22170
+ 11'
45
46
47
9.33148
.33154
.33160
.33166
.21452
.21455
.21458
.21461
9.33509
.33515
.33521
.33527
.21632
.21635
.21638
.21641
9.33869
.33875
.33881
.33887
9.33893
.33899
.33905
.33911
.21812
.21815
.21818
.21821
.21824
.21827
.21830
.21833
9.34227
.34233
.34239
.34245
.21992
.21995
.21998
.22001
9.34583
.34589
.34595
.34600
.22173
.32176
.22179
.22182
+ ir
49
50
51
9.33172
.33178
.33184
.33190
.21464
.21467
.21470
.21473
.21476
.21479
.21482
.21485
9.33533
.33539
.33545
.33551
.21644
.21647
.21650
.21653
9.34251
.34256
.34262
.34268
9.34274
.34280
.34286
.34292
9.34298
.34304
34310
.34316
.22004
.23007
.22010
.22013
.22016
.22019
.22033
.32035
.22028
.22031
.22034
.22037
9.34606
.34612
.34618
.34624
.22185
.23188
.22191
.22194
+ 13'
53
54
55
9.33196
.33202
.33208
.33214
9.33557
.33563
.33569
.33575
9.33581
.33587
.33593
.33599
.21656
.21659
.21662
.21665
.21668
.21671
.21674
.21677
9.33917
.33923
.33929
.33935
.21836
.21839
.21842
.21845
9.34630
.34636
.34642
.34648
.22197
.23300
.22303
.22306
.33309
.22212
.22215
.22318
8
7
6
5
4
S
2
1
+ U'
57
5S
59
9.33220
.33226
.33232
.33238
.21488
.21491
.21494
.21497
9.33941
.33947
.33953
.33959
.21848
.21851
.21864
.21867
9.34654
.34660
.34666
.34671
+ 15'
•
9.33244
.21500
9.33605
.21680
9.33965
.21860
9.34322
.22040
9.34677
.22231
f OA 79m
'jOh 18^
20h
77"»
20* 76™
20* 75m
Page 856]
TABLE
45.
Haversines.
s
3>^45">
66° 15'
3h 46m 56° 30'
3h47m
56° 45'
3h 48^51° if
3h 49m 5^° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat .Hav.
9.34677
.23231
9.35031
.22403
9.35383
.32585
9.35733
.22768
9.36081
.32951
60
1
.34683
.23235
.35037
.22406
.35389
.22588
.35738
.22771
.36086
.22954
59
. 2
.34689
.33228
.35043
.22409
.35394
.22591
.35744
.22774
.36092
.22957
58
3
.34695
.23231
.23234
.35049
.22412
.35400
.32594
.35750
9.35756
.22777
.22780
.36098
9,36104
.23960
.22964
57
56
+ 1'
9.34701
9.35054
.22415
9.35406
.33598
S
.34707
.22237
.35060
.22418
.35412
.32601
.35762
.22783
.36110
.22967
55
6
.34713
.22240
.35066
.22421
.35418
.22604
.35767
.22786
.36115
.22970
54
7
.34719
.22243
.35072
9.35078
.22424
.22427
.35424
'9.35429
.22607
.33610
.35773
9.35779
.22789
.22792
.36121
¥.36127
.22973
.33976
53
52
+ V
9.34725
.22246
9
.34730
.22249
.35084
.22430
.35435
.33613
.35785
.22795
.36133
.33979
51
10
.34736
.22252
.35090
.22433
.35441
.33616
.35791
.22799
.36139
.33983
50
11
.34742
.22355
.32258
.35096
9.35101
.22437
.22440
.35447
9.35453
.33619
.35797
.22802
.32805
.36144
9.36150
.33985
.33988
49
48
+ 3'
9.34748
.33633
9.35802
13
.34754
.22261
.35107
.22443
.35459
.33625 .35808
.32808
.36156
.33991
47
14
.34760
.22264
.35113
.22446
.35464
.33638 .35814
.22811
.36162
.33994
46
15
.34766
.23267
.35119
.22449
.35470
9.35476
.33631 .35820
.33634 9.35826
.22814
.22817
.36167
9.36173
.33997
.33000
45
U
+ i'
9.34772
.33270
9.35125
.22453
n
.34778
.23273
.35131
.32455
.35482
.33637
.35831
.22820
.36179
.33003
4-?
IS
.34784
.22376
.35137
.32458
.35488
.22640
.35837
.22823
.36185
.33006
42
19
.34789
.22379
.35143
.32461
.35494
.22643
.23646
.35843
9.35849
.22826
.32829
.36191
9.36196"
.33009
.23012
41
40
+ 5'
9.34795
.32282
9.35148
.33464 9.35500
21
.34801
.22285
.35154
.32467 .35505
.23649
.35855
.32833
.36202
.23016
39
22
.34807
.22288
.35160
.32470 .35511
.32653
.35860
.33835
.36208
.23019
38
23
+ 6'
.34813
9.34819
.22291
.22394
.35166
9.35172
.22473
.33476
.35517
9.35523
.33655
.35866
9735872
.23838
.22841
.36214
9.36219"
.23022
.23025
37
36
.33658
25
.34825
.22297
.35178
.32479
.35529
.33661
.35878
.22844
.36225
.23028
35
26
.34831
.23300
.35184
.33483
.35535
.33664
.35884
.22847
.36231
.23031
34
27
.34837
.32303
.35189
9:35195
.32485
.33488
.35540
.33667
.35889
.22850
.22853
.36237
9.36243"
.23034
33
+ r
9.34843
.23306
9.35546
.33671
9.35896
.23037
32
29
.34848
.22309
.35201
.32491
.35552
.33674
.35901
.22857
.30248
.23040
31
SO
.34854
.22312
.35207
.32494
.35558
.32677
.35907
.22860
.36254
.23043
30
31
.34860
.22315
.35213
9.35219
.22497
.22500
.35564
9.35570
.22680
.23683
.35913
9.35918
.23863
.33866
.36260
9:36266
.23046
.23049
29
28
+ 8'
9.34866
.22318
33
.34872
.22321
.35225
.22503
.35575
.33686
.35924
.32869
.36271
.23053
27
34
.34878
.22324
.35230
.22506
.35581
.33689
.35930
.22873
.36277
.23055
26
35
.34884
.22327
.22330
.35236
9.35242
.32509
.32513
.35587
9.35593
.33693
.33695
.35936
9.35942
.33875
.22878
.36283
9.36289
.23058
.23061
25
24
+ 9'
9.34890
57
.34896
.23333
.35248
.33515
.35599
.32698
.35947
.23881
.36294
.23065
23
38
.34901
.22336
.35254
.33518
.35604
.22701
.35953
.23884
.36300
.23068
22
39
.34907
.22340
.23343
.35260
9.35266
.32522
.32525
.35610
9.35616
.22704
.33707
.35959
9.35965
.33887
.36306
.23071
21
+ W
9.34913
.22890
9.36312
.23074
20
41
.34919
.23346
.35271
.22528
.35622
.33710
.35971
.22893
.36318
.33077
19
42
.34925
.33349
.35277
.22531
.35628
.33713
.35976
.22896
.36323
.33080
18
43
.34931
.33353
.35283
.22534
.22537
.35634
9.35639
.23716
.33719
.35982
9.35988
.22899
.23903
.36329
9.36335
.33083
.33086
n
16
+ 11'
9.34937
.23355
9.35289
4-5
.34943
.23358
.35295
.22540
.35645
.33733
.35994
.33905
.36341
.33089
15
46
.34949
.33361
.35301
.32543
.35651
.33735
.36000
.23908
.30346
.33093
14
47
.34954
.33364
.35307
9.35312
.33546
.22549
.35657
9.35663
.22728
.22731
.36005
9.36011
.33913
.33915
.36352
9.36358
.33095
.23098
13
12
+ 13'
9.34960
.32367
49
.34966
.32370
.35318
.22552
.35669
.22735
.36017
.22918
.36304
.23101
11
50
.34972
.32373
.35324
.22555
.35674
.22738
.36023
.22921
.36369
.23104
10
51
.34978
.32376
.35330
.22558
.35680
.23741
.36029
.22924
.36375
.23107
9
+ 13'
9.34984
.32379
9.35336
.33561
9.35686
.22744
9.36034
.33937
9.36381
.23110
8
53
.34990
.32383
.35342
.33564
.35692
. .22747
,36040
.23930
.36387
.23114
7
54
.34996
.32385
.35348
.23567
.35698
.23750
.36046
.33933
.36392
.23117
6
55
.35002
.22388
.22391
.35353
9.35359
.22570
.23573
.35703
9.35709
.22753
.22756
.36052
9.36058
.33936
.32939
.36398
9.36404
.23130
.23133
5
4
+ 14'
9.35007
57
.35013
.22394
.35365
.23576
.35715
.22759
.36063
.22942
.36410
.33136
3
58
.35019
.22397
.35371
.23579
.35721
.22762
.36069
.22945
.36415
.33139
2
59
.35025
.22400
.35377
.22583
.23585
.35727
9.3573y
.22765
.22768
.36075
9.36081
.33948
.33951
.36421
9.36427
.33133
.33135
1
+ 15'
9.35031
.32403
9.35383
20^
14m
201'
l.pn
20*
7gm
20h
nm
20* lOT"
TABLE
Haversir
45.
es.
[Page 857
s
■?ft SOm 57° SO'
3h Sim 57° 45'
3f^ 52m
58° 0'
3h 53m 68° 15'
5ft 54m 58° 30'
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav.
fcog. Ilav.
Nat Hav.
s
1
3
9.36427
.36433
.36439
.36444
.33135
.33138
.33141
.33144
9.36772
.36777
.36783
.36789
.33319
,33333
.33335
.33339
.33333
.33335
.33338
.33341
.33344
.33347
.33350
.33353
.33356
.33359
.33363
.33365
9.37114
.37120
.37126
.37131
9.37137
.37143
.37148
.37154
.33504
.33507
.33510
.33513
9.37455
.37461
.37467
.37472
.33689
.33693
.33695
.33699
.33703
.33705
.33708
.33711
.33714
,33717
,33730
.33733
9.37794
.37800
.37806
.37811
9.37817
.37823
.37828
.37834
9.37840
.37845
.37851
.378.56
9., 37862
.37868
.37873
.37879
9.37885
.37890
.37896
.37902
9.37907
.37913
.37918
.37924
,33875
,33878
,33881
.33884
.33887
.33891
.33894
,23897
.33900
.33903
.33906
.33909
60
59
58
57
56
53
54
53
52
51
50
49
+ 1'
5
6
7
9.36450
.36456
.36462
.36467
.33147
.33150
.33153
.33156
.33160
.33163
.33166
.33169
9.36794
.36800
.36806
.36812
9.36817"
' .36823
.36829
.36834
9.36840
.36846
.368.52
.36857
,33516
.33519
.33533
.33536
9.37478
.37484
.37489
.37495
+ 2'
9
10
11
9.36473
.36479
.36485
.36490
9.37160
.37166
.37171
.37177
9.37183
.37188
.37194
.37200
9.37205
.37211
.37217
.37222
.33539
.33533
,33535
,33538
,33541
,33544
,33547
,33550
9.37501
.37506
.37512
.37518
+ 3'
13
14
15
9.36496
.36502
.36508
.36513
.33173
.33175
.33178
.33181
.33184
.33187
.33190
.33193
.33196
,33199
.33303
.33306
.33309
.33313
.33315
.33318
9.37523
.37529
.37535
.37540
,33736
,33739
,33733
,33736
,33739
.33742
.33745
.33748
,33751
,33754
,23757
.23760
.23764
.23767
.23770
.23773
.23913
.23915
.23918
,23933
,33935
.33938
.33931
.33934
.33937
.33940
.33943
.23946
,23950
,33953
,33956
,33959
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
+ 4'
77
18
19
9.36519
.36525
.36531
.36536
9.36863
.36869
.36875
.36880
9.36886
.36892
.36897
.36903
9.36909
.36915
.36920
.36926
.33368
.33373
.33375
,33378
.33553
.33556
.33560
.33563
.33566
.33569
.33573
.33575
9.37546
.37552
.37557
.37563
9.37569
.37574
.37580
.37585
+ 5'
21
22
23
9.36542
.36548
.36554
.36559
,33381
,33384
,33387
,33390
.33393
.33396
.33399
,33403
9.37228
.37234
.37239
.37245
9.37251
.37257
.37262
.37268
+ 6'
25
26
27
9.36565
.36571
.36577
.36582
.33578
.33581
.33584
,33587
9.37591
.37597
.37602
.37608
9.37930
.37935
.37941
.37947
+ r
29
30
31
+ 8''
33
34
35
9.36588
.36594
.36599
.36605
,33331
.33334
.33337
.33330
9.36932
.36937
.36943
.36949
9.36955
.36960
.36966
.36972
9.36977
.36983
.36989
.36995
9.37000
.37006
.37012
.37017
9.37023
.37029
.37034
.37040
9.37046
.37052
.37057
.37063
.33405
.33409
.33413
.33415
9.37274
.37279
.37285
.37291
,33590
.33594
.33597
.33600
.33603
.33606
.33609
.33613
9.37614
.37619
.37625
.37631
9.37636
.37642
.37648
.37653
9.376.59
.37665
.37670
.37676
,33776
,33779
.33783
.33785
.33788
.33791
.33795
.33798
.33801
.33804
.33807
.33810
.33813
,33818
,33819
,33833
,33835
,33839
,33833
.33835
.33838
.33841
.33844
.33847
9.37952
.379.58
.37963
.37969
9.37975
.37980
.37986
.37992
,33983
,33985
,33968
,33971
.33974
.33977
.33981
.33984
.33987
.33990
.33993
,33996
.33999
.34003
.34005
.34009
.34012
.34015
.34018
.24031
.34034
.34037
.34030
.24033
.24036
.24040
.24043
,24048
,24049
.24053
.34055
.34058
.34061
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
77
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
9.36611
.36617
.36622
.36628
.33333
.23338
.33239
.33343
.33418
.33431
,33434
,33437
.33430
.33433
.33436
.33439
9.37296
.37302
,37308
.37313
+ 9'
.57
38
39
9.36634
.36640
.36645
.36651
9.36657
.36663
.36668
.36674
.33346
.33349
.33353
,33355
.33358
.33361
.33364
.33367
.33370
.33373
.33376
,33379
9.37319
.37325
.37330
.37336
.33615
.33618
.33631
.33634
.33637
.33631
.33634
.33637
.33640
.33643
.33646
.23649
.33653
.33655
,33658
,33661
.33665
.33668
.33671
.33674
9.37997
.38003
.38008
..38014
¥.38020
.38025
.38031
.38037
9.38042
.38048
.38053
.38059
9.38065
.38070
.38076
.38081
9.38087
.38093
.38098
.38104
9^38110"
.38115
.38121
.38126
9.38132
+ IC
41
42
43
.33443
.33445
.33449
.33453
.33455
.33458
.33461
.33464
9.37342
.37347
.37353
.37359
9.37364
.37370
.37376
.37382
9.37682
.37687
.37693
.37699
9.37704
.37710
.37715
.37721
+ 11'
45
46
47
9.36680
.36686
.36691
.36697
4- 13'
49
50
51
9.36703
.36708
.36714
.36720
,33383
.33385
.33389
.33393
.3;M67
,33470
.33473
.33476
9.37387
.37393
.37399
.37404
9.37410
.37416
.37421
.37427
9.37727
.37732
.37738
.37744
+ 13'
53
54
55
9.36726
.36731
.36737
.36743
9.36749"
.36754
.36760
.36766
9.36772
.33395
.33393
.33301
,33304
9.37069
.37074
.37080
.37086
.33479
.33483
.33486
.33489
9.37749
.37755
.37761
.37766
9.37772
.37778
.37783
.37789
.33850
.33853
.33856
.33860
,23863
.23888
.33869
.23873
+ 14'
57
58
59
,33307
,33310
,33313
,23316
' ,33319
9.37091
.37097
.37103
.37109
9.37114
.33493
.33495
.33498
.33501
9.37433
.37438
.37444
.37450
.33677
.33680
.33683
.33686
.33689
+ 15'
.33504
9.37455
9.37794
,33875
20k 9m
20^ 8m
foil
7m
20^6^
20^
Sm
Page 858]
TABLE 45.
Haversines.
s
3^ 55^n 58° 45'
3^ Ser" 59° 0'
3h 57™ 59° 15'
5ft 55^59° 30'
,?A 59™ 59° 45' 1
s
Log. Hav.
Na*. Ilav.
Log. Hav.
Nat. JIav.
Log. Hav.
Nat. Hav.
Log. Hav.
Xat. Hav.
Log. Hav.
Nat. Uav.
1
2
3
9.38132
.38138
.38143
.38149
.24061
.24064
.24068
.24071
9.38468
.38473
.38479
.38485
9.38490
.38496
.38501
.38507
.24348
.24351
.24254
.24257
9.38802
.38807
.38813
.38819
9.38824
.38830
.38835
.38841
.24435
.24438
.24442
.34445
.34448
.34451
.24454
.24457
9.39134
.39140
.39145
.39151
.24623
.34636
.34639
.34633
9.39465
.39470
.39476
.39481
.34811
.34814
.34818
.34831
60
59
58
57
+ r
5
6
7
9.38154
.38160
.38166
.38171
.24074
.24077
.24080
.24083
.24086
.24089
.24093
.24096
.24099
.24102
.34105
.34108
.34261
.34264
.24367
.24270
9.39156
.39162
.39167
.39173
.24636
.24639
.24642
.24645
9.39487
.39492
.39498
.39503
.34834
.34837
.34830
.34833
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
+ 2'
9
10
11
9.38177
.38182
.38188
.38194
9.38512
.38518
.38524
.38529
.24273
.24276
.24279
.24282
9.38846
.38852
.38857
.38863
.24460
.34463
.34467
.34470
9.39178
.39184
.39189
.39195
.24648
.24651
.24654
.24658
.24661
.24664
.24667
.24670
9.39509
.39514
.39520
.39525
9.,3953i
.39536
.39542
.39547
.24836
.24840
.24843
.34846
.34849
.34852
.24855
.34858
+ 3'
13
14
15
9.38199
.38205
.38210
.38216
9.38535
.38540
.38546
.38551
.34386
.34389
.34393
.34395
9.38868
.38874
.38880
.38885
.34473
.34476
.24479
.24483
9.39201
.39206
.39212
.39217
+ 4'
17
18
19
9.38222
.38227
.38233
.38239
.24111
.24114
.24117
.24120
.24134
.34137
.34130
.34133
.24136
.24139
.24142
.34145
9.38557
.38563
.38568
.38574
.34298
.24301
.24304
.34307
9.38891
.38896
.38902
.38907
9.38913
.38918
.38924
.38929
9.38935
.38941
.38946
.38952
.34485
.24488
.24492
.24495
.24498
.34501
.34504
.34507
.24510
.24514
.24517
.34530
9.39223
.39228
.39234
.39239
.24673
.24676
.24680
.24683
9.39553
.39558
.39564
.39569
.24862
.24865
.24868
.34871
+ 5'
21
22
23
9.38244
.38250
.38255
.38261
9.38267
.38272
.38278
.38283
9.38579
.38585
.38590
.38596
9.38602"
.38607
.38613
.38618
.34310
.34314
.24317
.24320
.34323
.34336
.34339
.34332
.24335
.24339
.24342
.24345
.34348
.34351
.34354
.34357
9.39245
.39250
.39256
.39261
9.39267
.39272
.39278
.39283
.24686
.24689
.24692
.24695
.24698
.24701
.34705
.34708
.34711
.24714
.24717
.24720
9.39575
.39580
.39586
.39591
9.39.597
.39602
.39(i08
.39013
9.39619
.39624
.39630
.39635
T.39641
.39646
.39652
.39657
.34874 40
.24877 39
.24880 38
.24884 37
+ 6'
25
26
27
.24887
.24890
.24893
.24896
.24899
.24902
.24906
.24909
.24912
.34915
.34918
.34931
36
35
34
33
32
31
30
29
28
27
28
25
24
23
22
21
+ r
29
30
31
9.38289
.38295
.38300
.38306
.34148
.34153
.34155
.34158
9.38624
.38629
.38635
.38641
9738646
.38652
.38657
.38663
9.38957
.38963
.38968
.38974
9.38979
.38985
.38990
.38996
.34533
.34536
.34539
.34533
.34535
.34539
.34543
.24545
9.39289
.39294
.39300
.39305
9.39311
.39316
.39322
.39327
9.39333
.39338
.39344
.39349
9.39355
.39360
.39366
.39371
9.39377
.39382
.39388
.39393
9.39399
.39404
.39410
.39415
9.39421
.39426
.39432
.39437
+ 8'
33
34
35
9.38311
.38317
.38322
.38328
.24161
.24164
.24167
.24170
.24723
.24737
.24730
.24733
.24736
.24739
.24743
.24745
+ 9'
37
38
39
9.38334
.38339
.38345
.38350
.24173
.34176
.34180
.34183
9.38668
.38674
.38680
.38685
9.38691
.38696
.38702
.38707
.34360
.34364
.34367
.34370
9.39002
.39007
.39013
.39018
.24548
.24551
.24554
.24557
9.396(i3
.39668
.39674
.39679
'9.39685
.39690
.39695
.39701
.34934
.24928
.24931
.24934
+ 10'
41
42
43
9.38356
.38362
.38367
.38373
.24186
.24189
.24192
.24195
.24373
.24376
.24379
.24382
9.39024
.39029
.39035
.39040
.34560
.34564
.34567
.34570
.24749
.24752
.24755
.24758
.24937
.34940
.34943
.34946
.34950
.24953
.24956
.24959
.34962
.24965
.24969
.24972
.24975
.34978
.34981
.34984
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
+ 11'
45
46
47
9.38378
.38384
.38390
.38395
.24198
.24201
.24204
.24208
9.38713
.38719
.38724
.38730
9.38735
.38741
.38746
.38752
9.38757
.38763
.38769
.38774
.24385
.24388
.24392
.34395
9.39046
.39051
.39057
.39062
.34573
.34576
.34579
.34582
.34586
.24589
.24592
.24595
.24761
.34764
.24767
.24770
9.39706
.39712
.39717
.39723
+ 12'
49
50
51
9.38401
.38406
.38412
.38418
9.38423'
.38429
.38434
.38440
.34311
.34314
.34317
.34330
.24223
.24226
.24229
.24233
.24236
.24339
.24243
.24245
.24248
.34398
.34401
.34404
.24407
.24410
.24413
.24417
.24420
.24423
.24436
.24429
.24433
.24436
9.39068
.39073
.39079
.39085
.24774
.24777
.24780
.247*3
.24786
.24789
.24792
.24796
9.39728
.39734
.39739
.39745
9.39750
.39756
.39761
.39767
+ 13'
53
54
55
9.39090
.39096
.39101
.39107
.24598
.24601
.24604
.24607
+ 1*'
57
58
59
9.38445
.38451
.38457
.38462
9.38780
.38785
.38791
.38796
9.38802
9.39112
.39118
.39123
.39129
9.39134
.24611
.24614
.24617
.24620
.24623
9.39443
.39448
.39454
.39459
9.39465
.24799
.24802
.24805
.24808
.24811
9.39772
.39778
.39783
.39789
9.39794
.34987
.34991
.34994
.34997
.35000
4
3
2
1
+ 15'
9.38468
20^ 4'^
20li
Sm
20>i
om
20l>
im
20>i0m
TABLE 45.
Ilaveraines.
[Page 859
s
4* am 60° (K
4h im 60° 15'
4h. ^ 60° W
4h sm 60° 45'
4h 4m
61° 0'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log.Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.39794
.39799
.39805
.39810
.35000
.35003
.35006
.35009
9.40121
.40127
.40132
.40138
.35189
.35193
.35195
.35199
9.40447
.40453
.40458
.40463
.35379
.35383
.35385
.35388
9.40771
.40777
.40782
.40787
.35569
.35573
.35575
.35578
9.41094
.41099
.41105
.41110
.35760
.35763
.35766
.35769
60
59
58
57
+ 1'
5
6
7
9.39816
.39821
.39827
.39832
.35013
.35016
.35019
.35033
9.40143
.40149
.40154
.40159
.35303
.35305
.35308
.35311
9.40469
.40474
.40480
.40485
.35391
.35395
.35398
.35401
9.40793
.40798
.40804
.40809
.35583
.35585
.35588
.35591
.35594
.35597
.35601
.35604
.35607
.35610
.35613
.35617
.35630
.35633
.35636
.35639
9.41115
.41121
.41126
.41131
.35773
.35775
.35779
.35783
56
55
54
53
+ V
9
10
11
9.39838
.39843
.39849
.39854
.35035
.35038
.35033
.35035
9.40165
.40170
.40176
.40181
9.40187
.40192
.40198
.40203
9.40208
.40214
.40219
.40225
.35314
.35318
.35331
.35334
.35337
.35330
.35333
.35337
9.40490
.40496
.40501
.40507
.35404
.35407
.35410
.35414
9.40814
.40820
.40825
.40831
9.40836
.40841
.40847
.40852
9.41137
.41142
.41147
.41153
.35785
.35788
.25791
.35795
5-2
51
50
49
+ 3'
13
14
15
9.39860
.39865
.39871
.39876
.35038
.35041
.35044
.35047
.35050
.35054
.35057
.35060
.35063
.35066
.35069
.35073
9.40512
.40518
.40523
.40528
.35417
.35430
.35433
.35436
9.41158
.41163
.41169
.41174
.35798
.35801
.35804
.35807
48
47
46
45
+ 4'
17
18
19
9.39881
.39887
.39892
.39898
.35340
.35343
.35346
.35349
9.40534
.40539
.40545
.40550
.35439
.35433
.35436
.35439
9.40858
.40863
.40868
.40874
9.41180
.41185
.41190
.41196
.35810
.35814
.35817
.35830
44
43
42
41
+ 5'
21
22
23
9.39903
.39909
.39914
.39920
9.40230
.40236
.40241
.40246
9.40252
.40257
.40263
.40268
9.40274
.40279
.40284
.40290
.35353
.35355
.35359
.35363
.35365
.35368
.35371
.35374
.35378
.35381
.35384
.35387
9.40555
.40561
.40566
.40572
9.40577
.40582
.40588
.40593
.36443
.35445
.35448
.35453
9.40879
.40884
.40890
.40895
.35633
.35636
.35639
.35643
.35645
.35648
.35651
.35655
9.41201
.41206
.41212
.41217
.35833
.35836
.35830
.35833
40
39
38
37
+ «'
25
26
27
9.39925
.39931
,39936
.39942
9.39947
.39952
.39958
.39963
.35076
.35079
.35083
.35085
.35455
.35458
.35461
.35464
.35467
.35471
.35474
.35477
9.40900
.40906
.40911
40917
9.41222
.41228
.41233
.41238
.35836
.35839
.35843
.35845
36
35
34
33
+ r
29
30
31
.35088
.35091
.35095
.35098
9.40599
.40604
.40609
.40615
9.40922
.40927
.40933
.40938
.35658
.35661
.35664
.35667
9.41244
.41249
.41254
.41260
.35849
.35853
.35855
.35858
32
31
30
29
+ 8'
S3
34
35
9.39969
.39974
.39980
.39985
.35101
.35104
.35107
.35110
.35113
.35117
.35130
.35133
9.40295
.40301
.40306
.40312
.35390
.35393
.35397
.35300
9.40620
.40626
.40631
.40636
9.40642
.40647
.40653
.40658
.35480
.35483
.35487
.35490
9.40943
.40949
.40954
.40960
.35671
.35674
.35677
.35680
.35683
.35686
.35690
.35693
9.41265
.41270
.41276
.41281
.35861
.35865
.35868
.35871
28
27
26
25
24
23
22
21
+ 9'
37
38
39
9.3999]
.39996
.40002
.40007
9.40317
.40322
.40328
.40333
.35303
.35306
.35309
.35313
.35316
.35319
.35.333
.35335
.35338
.35331
.35335
.35338
.35341
.35344
.35347
.353.50
.35354
.35357
.35360
.35363
.35493
.35496
.35499
.35503
.35506
.35509
.35513
.35515
9.40965
.40970
.40976
.40981
9.41287
.41292
.41297
.41303
.35874
.35877
.35880
.35884
+ W
41
42
43
9.40012
.40018
.40023
.40029
.35136
.35139
.35133
.35136
9.40339
.40344
.403-00
.40355
9.40360
.40366
.40371
.40377
9.40382
.40388
.40393
.40398
9.40663
.40669
.40674
.40680
9.40986
.40992
.40997
.41003
.35696
.35699
.35703
.35705
9.41308
.41313
.41319
.41324
.35887
.35890
.35893
.35896
20
19
18
n
+ 11'
45
46
47
9.40034
.40040
.40045
.40051
9.40056
.40062
.40067
.40072
.35139
.35143
.35145
.35148
.35151
.35154
.35158
.35161
9.40685
.40690
.40696
.40701
.35518
.35531
.35535
.35538
9.41008
.41013
.41019
.41024
.35709
.35713
.35715
.35718
9.41329
.41335
.41340
.41345
.35900
.35903
.35906
.35909
16
15
14
13
+ ir
49
50
51
9.40707
.40712
.40717
.40723
.35531
.35534
.35537
.35540
9.41029
.41035
.41040
.41046
.35731
.35734
.35738
.35731
9.41351
.41356
.41361
.41367
.35913
.35915
.35919
.35933
12
11
10
9
+ 13'
53
54
55
9.40078
.40083
.40089
.40094
9.40100
.40105
.40111
.40116
.35164
.35167
.35170
.35173
.35177
.35180
.35183
.35186
9.40404
.40409
.40415
.40420
9.40728
.40734
.40739
.40744
.35544
.35547
.35550
.35553
9.41051
.41056
.41062
.41067
.35734
.35737
.35740
.35744
9.41372
.41377
.41383
.41388
.35935
.35938
.35931
.35935
8
7
6
5
4
3
2
1
+ W
57
58
59
9.40425
.40431
.40436
.40442
.35366
.35.369
.35373
.35376
9.40750
.40755
.40761
.40766
9.40771
.35556
.35559
.35563
.35566
9.41072
.41078
.41083
.41088
.35747
.35750
.35753
.35756
9.41393
.41399
.41404
.41409
.35938
.35941
.35944
.35947
+ 15'
9.40121
.35189
9.40447
.35379
.35569
9.41094
.35760
9.41415
.35951
79A
59m
19^ 58m
/9A
57m
/9A 5Gm
19l> 55m
Page 860] TABLE 45.
Haversines.
s
4h 5m 61° 15' 1
4h em 61° 30'
4h 7m 61° 45'
4h 8m 63° 0'
4h gm 63° 15' 1
s
Log. Hav.
Nat. Hav.
Log. llav. Xat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Xat. Hav.
1
3
9.41415
.41420
.41425
.41431
.35951
.25954
.25957
.25960
9.41734 .26143
.41739 .36145
.41745 : .36148
.41750 .36153
9.42052
.42057
.42062
.42068
.26334
.26337
.36340
.36344
9.42368
.42373
.42378
.42384
.36536
.36530
.36533
.36536
9.42682
.42688
.42693
.42698
.36719
.36723
.36726
.26729
60
59
58
57
+ 1'
5
6
7
9.41436
.41441
.41447
.41452
.25963
.25966
.25970
.25973
9.41755
.41761
.41766
.41771
.26155
.36158
.36161
.36164
.26168
.26171
.26174
.26177
.36180
.36184
.36187
.26190
.26193
.26196
.36300
.36303
9.42073
.42078
.42083
.42089
.36347
.36350
.36353
.36356
9.42389
.42394
.42399
.42405
.26539
.26543
.26546
.26549
9.42703
.42709
.42714
.42719
.26732
.36735
.36739
.36743
56
55
54
S3
+ r
9
10
•11
9.41457
.41463
.41468
.41473
9.41479
.41484
.41489
.41495
.25976
.25979
.25982
.25986
.25989
.25992
.25995
.25998
9.41776
.41782
.41787
.41792
!) .41798
.41803
.41808
.41814
9.41819
.41824
.41829
.41835
9.42094
.42099
.42105
.42110
.36360
.36363
.36366
.36369
9.42410
.42415
.42420
.42426
9.42431
.42436
.42441
.42447
.26552
.26555
.26559
.36562
.26565
.36568
.26571
.26575
9.42724
.42730
.42735
.42740
9.42745"
.42750
.42756
.42761
.36745
.36748
.36751
.36755
52
51
SO
49
+ 3'
13
14
15
9.42115
.42120
.42126
.42131
.36373
.36376
.36379
.36383
.36758
.26761
.26764
.26768
.26771
.36774
.36777
.36780
48
47
46
45
U
43
42
41
+ 4'
17
18
19
9.41500
.41505
.41511
.41516
.26002
.26005
.26008
.26011
9.42136
.42141
.42147
.42152
.26385
.26389
.26392
.26395
9.42452
.42457
.42462
.42468
.26578
.26581
.26584
.26587
9.42766
.42771
.42777
.42782
+ 5'
21
22
23
9.41521
.41527
.41532
.41537
.26014
.26017
.26021
.26024
9.41840
.41845
.41851
.41856
.26206
.26209
.26212
.26316
.36319
.36332
.26235
.36228
9.42157
.42163
.42168
.42173
.26398
.26402
.26405
.26408
9.42473
.42478
.42483
.42489
.26591
.26594
.26597
.36600
9.42787
.42792
.42797
.42803
.36784
.36787
.36790
.26793
40
39
38
37
+ 6'
25
26
27
9.41543
.41548
.41553
.41559
.26037
.26030
.26033
.26037
9.41861
.41S67
.41S72
.41877
9.42178
.42184
.42189
.42194
.26411
.26414
.26417
.26431
9.42494
.42499
.42504
.42510
.36604
.36607
.36610
.26613
.26616
.26620
.26623
.26626
9.42808
.42813
.42818
.42824
.26797
.26800
.26803
.26806
36
35
34
33
+ r
29
30
31
9.41564
.41569
.41575
.41580
.26040
.26043
.26046
.26049
.26053
.26056
.26059
.26062
.26065
.26069
.26073
.36075
9.41882
.41888
.41893
.41898
9.41904
.41909
.41914
.41920
9.41925
.41930
.41935
.41941
.26233
.36335
.36338
.36241
.36344
.36248
.26251
.36354
.36357
.36360
.36364
.36367
.36370
.36373
.26376
.36380
9.42199
.42205
.42210
.42215
.36424
.26427
.26430
.26433
.26437
.26440
.26443
.26446
.26449
26453
.26456
.26459
.36462
.26465
.26469
.26472
9.42515
.42520
.42525
.42531
9.42829
.42834
.42839
.42844
.26809
.36813
.36816
.26819
.26822
.36836
.36839
.36832
32
31
30
29
28
27
26
25
+ 8'
33
34
35
9.41585
.41590
.41596
.41601
9.42221
.42226
.42231
.42236
9.42242
.42247
.42252
.42257
9.42263
.42268
.42273
.42278
9.42536
.42541
.42546
.42552
9.42557
.42562
.42567
.42573
9:42578
.42583
.42588
.42593
.26629
.26632
.26636
.26639
.26642
.26645
.26649
.26653
.26655
.36658
.36661
.36665
9.42850
.42855
.42860
.42865
9.42870
.42876
.42881
.42886
+ 9^
37
38
39
9.41606
.41612
.41617
.41622
.26835
.36838
.36842
.26845
.26848
.26851
.26855
.26858
24
23
22
~2~1
20
19
18
n
+ W
41
42
43
9.41628
.41633
41638
.41644
.36078
.26081
.26085
.26088
9.41946
.41951
.41957
.41962
9.41967
.41972
.41978
.41983
9.41988
.41994
.41999
.42004
9.42009
.42015
.42020
.42025
9.42891
.42897
.42902
.42907
+ 11'
45
46
47
9.41649
.41654
.41660
.41665
.26091
.26094
.26097
.26101
.36383
.36386
.36389
.36393
9.42284
.42289
.42294
.42300
.36475
.36478
.36481
.36485
9.42599
.42604
.42609
.42614
9.42620
.42625
.42630
.42635
9.42641
.42646
.42651
.42656
.26668
.26671
.26674
.26677
9.42912
.42917
.42923
.42928
.26861
.36864
.36867
.36871
16
15
14
13
+ 13'
49
50
51
9.41670
.41676
.41681
.41686
.26104
.36107
.36110
.36113
.26il7
.26120
.26123
.26126
.36296
.26299
.26302
.26305
.26308
.26312
.36315
.36318
9.42305
.42310
.42315
.42321
9.42326
.42331
.42336
.42342
.36488
.36491
.36494
.36498
.26501
.26504
.26507
.26510
.36681
.36684
.36687
.36690
.36694
.26697
.26700
.26703
9.42933
.42938
.42943
.42949
9:42954
.42959
.42964
.42969
9.42975
.42980
.42985
.42990
.36874
.36877
.26880
.26883
.26887
.26890
.26893
.26896
.36900
.36903
.36906
.36909
12
U
10
9
8
7
6
5
4
3
2
1
+ 13'
53
54
55
9.41692
.41697
.41702
.41707
+ 14'
57
58
59
9.41713
.41718
.41723
.41729
.26129
.26133
.36136
.36139
.36143
9.42031
.42036
.42041
.42046
.26331
.26334
.26328
.26331
9.42347
.42352
.42357
,42363
.26514
.26517
.26520
.26523
9.42662
.42667
.42672
.42677
.36706
.36710
.36713
.36716
+ 15'
9.41734
9.42052 1 .36334
9.42368
.26536
9.42682 1 .36719
9.42996 j .36913
igh 54m
i9ft 53m
i9ft 52m
iglt 5lm
19Ji SOm
TABLE 45. [Page 861
Haversinee.
s
4h lom 63° W
4h nm 62° 45'
4h 12m 63° 0'
4h 13m 63° 15'
4h 14m 63° 30'
s
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Hav,
Log, Ilav,
Nat. Hav.
Log. Hav,
Nat, Hav.
Log, Hav,
Nat, Hav.
1
-2
3
9.42996
.43001
.43006
.43011
.26913
.26916
.26919
.26922
9.43307
.43312
.43317
.43323
.27106
.27110
.27113
.27116
9,43617
,43622
,43627
,43632
,27300
,27304
.37307
.27310
9,43926
,43931
.43936
.43941
.27495
.27498
.27502
.27505
9,44232
,44238
,44243
,44248
.37690
.37693
.37697
.37700
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
+ 1'
5
6
7
9.43016
.43022
.43027
.43032
.26925
.26929
.26932
.26935
9.43328
.43333
.43338
.43343
.27119
.27122
.27126
.37129
9,43638
,43643
,43648
,43653
.37313
.27317
.27320
.27323
9,43946
.43951
.43956
,43961
.37508
.27511
.27515
.27518
9,44253
,44258
,44263
.44268
.37703
,27706
,27710
.27713
+ r
9
10
11
9.43037
.43042
.43048
.43053
.26938
.26942
.26945
.26948
9.43348
.43354
.43359
.43364
.37132
.27135
.27139
.27142
9,43658
,43663
,43669
,43674
.27326
.27330
.27333
.27336
9,43967
,43972
,43977
,43982
.27521
.27534
.37538
,37531
9.44273
,44278
,44283
.44289
.37716
,37719
,37733
,37736
+ 3'
13
14
15
9.430.58
.43063
.43068
.43074
.26951
.26955
.26958
.26961
9.43369
.43374
.43380
.43385
.27145
.27148
.27152
.27155
9,43679
,43684
,43689
,43694
.37339
.27343
.27346
.27349
9,43987
,43992
.43997
,44002
.37534
.37537
.37541
.37544
9,44294
,44299
.44304
.44309
,37729
.37733
.27736
.27739
+ i'
n
18
19
9.43079
.43084
.43089
.43094
.26964
.26967
.26971
.26974
9,43390
.43395
.43400
.43405
,27158
.27161
.27165
.27168
9,43699
.43705
,43710
,43715
.27352
.27356
.27359
.27362
9,44008
,44013
.44018
.44023
,27547
,37550
,37554
,37557
9.44314
,44319
,44324
,44329
.37743
.27745
.27749
.27753
44
43
42
41
+ S'
21
23
9.43100
.43105
.43110
.43115
.36977
.36980
.36984
.26987
9.43411
.43416
.43421
.43426
.37171
.37174
.37177
.37181
9.43720
.43725
,43730
,43735
.27365
.27369
.27373
.27375
9.44028
.44033
.44038
.44043
.37560
.27563
.27567
,27570
9,44334
.44340
.44345
.44350
.37755
.37758
.37762
.27765
40
39
38
37
36
35
34
33
+ 6'
25
26
27
9.43120
.43126
.43131
.43136
.26990
.26993
.26996
.27000
9.43431
.43436
.43442
.43447
.37184
.37187
,37190
,27194
9,43741
,43746
.43751
.43756
.27378
.27382
.27385
.27388
9.44048
.44054
.440.59
,44064
,27573
,37576
.37580
.37583
9,44355
,44360
,44365
,44370
.37768
.37773
.37775
.37778
+ r
29
30
31
9.43141
.43146
.43151
43157
.27003
.27006
.37009
.27013
9.43452
.43457
.43462
.43467
,27197
,27200
,27303
,37307
9.43761
.43766
.43771
.43777
.27391
.37394
.37398
.37401
9,44069
,44074
,44079
,44084
.37586
.37589
.37593
.27596
9,44375
,44380
,44385
,44390
.37781
.37785
.27788
.27791
32
31
30
29
+ 8'
33
34
35
9.43162
.43167
.43172
.43177
.27016
.27019
.27022
.27025
9.43473
.43478
.43483
.43488
,27310
,37213
,37316
,37330
9.43782
.43787
.43792
.43797
.37404
.37407
.37411
.37414
9.44089
,44095
.44100
,44105
.27599
.27603
.37606
.37609
9,44396
,44401
.44406
.44411
.27794
.27798
.27801
.27804
,37807
.37811
.27814
,27817
28
27
26
25
24
23
22
21
+ 9'
37
38
39
9.43183
.43188
.43193
.43198
.27029
,27032
.27035
.27038
9.43493
.43498
.43504
.43509
9.43514
,43519
.43524
.43.529
,37333
,37336
,37339
,37233
9.43802
.43807
.43813
.43818
.37417
.37430
.37434
,27427
9,44110
.44115
.44120
.44125
.37613
.27615
.27619
.27622
9.44416
.44421
.44426
.44431
+ W
41
42
43
9.43203
.43209
.43214
.43219
.27043
.37045
.27048
.27051
,37236
,27239
,27242
,27245
9.43823
.43828
.43833
.43838
.27430
.27433
.27437
.27440
.27443
.27446
,27450
,27453
9.44130
.44135
.44141
.44146
.27625
.27638
.37632
,27635
9.44436
.44441
.44446
.44452
,27820
,27824
,27827
.27830
20
19
18
17
+ 11'
45
46
47
9.43224
.43229
.43234
.43240
.37055
.37058
.37061
.37064
9.43535
.43540
,43545
,435.50
,27249
,27253
,37255
,27258
9.43843
.43849
.43854
.438.59
9.44151
.44156
.44161
.44166
,27638
,27641
,27645
,27648
9.44457
.44462
,44467
,44472
.27833
.27837
,27840
,37843
16
15
14
13
+ w
49
50
51
9.43245
.43250
.43255
.43260
.37068
.37071
.37074
.37077
9,43555
,43560
,43565
,43571
,27262
,37265
,27268
,27271
9.43864
.43869
.43874
.43879
.27456
,37459
,27463
,37466
9,44171
44176
,44181
.44187
,27651
.27654
.27658
.27661
.37664
.37667
.37671
.27674
9,44477
,44482
,44487
,44492
9,44497
.44502
.44507
.44513
,37846
.37850
.27853
.27856
.27859
.37863
.37866
.27869
12
11
10
9
8
7
6
5
4
3
1
+ 13'
53
•54
55
9.43266
.43271
.43276
.43281
.37080
.37084
.27087
.27090
9,43576
.43581
,43586
,43591
,27275
,27278
.37381
.37384
9.43884
.43890
.43895
.43900
,37469
,37472
,27476
,27479
9.44192
.44197
.44202
,44207
+ _U'
58
59
9.43286
.43291
.43297
.43302
.27093
.27097
,37100
.37103
9.43596
.43602
.43607
.43612
.37388
,37291
,27294
,27297
9.43905
.43910
.43915
.43920
.37482
,27485
,27489
.27492
9,44212
,44217
.44222
,44227
.27677
.27680
.27684
.27687
9,44518 .27873
,44523 .37876
,44528 .37879
,44533 1 .37883
+ 15'
9.43307
.37106
9.43617 1 .27300
9.43926
.27495
9.44232
.27690
9,44538 .37886
19^ 49^
19h 4sm
19h 47m
19h 46m
19>i45">
Page 862]
-
TABLE 45.
Ilaversines.
s
4h lorn
63° 45'
4h 16m 64° 0'
4hi7mu°15' 1
4h ism 64° 30'
4ft i9m 64° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Xat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
3
9.44538
.44543
.44548
.44553
.37886
.37889
.37893
.37895
9.44842
.44847
.44852
.44857
.38081
.38085
.38088
.38091
9.45144
.45149
.45155
.45160
.38378
.38381
.38384
.38388
9.45446
,45451
.45456
.45461
.28474
.28478
.28481
.38484
9.45745
.45750
.45755
.45760
.38673
.38675
.38678
.38681
60
59
58
o7
+ 1'
5
6
7
9.44558
.44563
.44568
.44573
.37899
.37903
.37905
.37908
9.44862
.44867
.44872
.44877
.38095
.38098
.38101
.38104
9.45165
.45170
.45175
.45180
.38291
.38394
.28297
.28301
9,45466
.45471
.45476
.45481
.38488
.38491
.38494
.38497
9.45765
.45770
.45775
.45780
.38685
.38688
.38691
.38695
56
55
54
5S
52
51
50
49
+ 2'
9
10
11
9.44579
.44584
.44589
.44594
.37913
.37915
.37918
.37931
9.44882
.44887
.44892
.44898
.38108
.38111
.38114
.38117
9.45185
.45190
.45195
.45200
.38304
.38307
.38310
.38314
9.45486
.45491
.45496
.45501
.38501
.38504
.38507
.38511
9.45785
.45790
.45795
.45800
.38698
.38701
.38704
.38708
+ 3'
13
14
15
9.44599
.44604
.44609
.44614
.37935
.37938
.37931
.37935
9.44903
.44908
.44913
.44918
.38131
.38134
.38137
.38130
9.45205
.45210
.45215
,45220
.38317
.38330
.38334
.38337
9.45506
.45511
.45516
.45521
.38514
.38517
.38530
.38534
9.45805
.45810
.45815
.45820
.38711
.38714
.38718
.38731
48
47
46
45
+ 4'
17
18
19
9.44619
.44624
.44629
.44634
.37938
.37941
.37944
.37948
9.44923
.44928
.44933
.44938
.38134
.38137
.38140
.38144
9.45225
.45230
.45235
.45240
.38330
.38333
.38337
.38340
9.4.5526
.4-5.531
.45536
,45541
.38537
.38530
.38534
.38537
9.45825
.45830
.45835
.45840
.38734
.38737
.38731
.38734
44
43
42
41
+ 5'
21
22
23
9.44639
.44645
.44650
.44655
.37951
.37954
.37957
.37961
9.44943
.44948
.44953
.44958
.38147
.38150
.38153
.38157
9.45245
.45250
.45255
.45260
.28343
.28347
.28350
.28353
9,45546
,45551
.4.5556
.45561
.38540
.38543
.38547
.38550
9.45845
.45850
.45855
.45860
.38737
.38741
.38744
.38747
40
39
38
37
+ ^
25
26
27
9.44660
.44665
.44670
.44675
.37964
.37967
.37970
.37974
9.44963
.44968
.44973
.44978
.38160
.38163
.38166
.38170
9.45265
.45270
.45275
.45280
.38356
.38360
.38363
.38366
9.45566
.45571
.45576
.45581
.28553
.38557
.38560
.38563
9.45865
.45870
.45875
.45879
.38751
.38754
.38757
.38760
36
35
34
33
+ r
29
30
31
9.44680
.44685
.44690
.44695
.37977
.37980
.37983
.37987
9.44983
.44988
.44993
.44998
.38173
.38176
.38180
.38183
9.4.5285
.45290
.4.5295
.45300
.38369
.38373
.38376
.38379
9.45586
,4.5591
.45596
.45601
.28566
.28570
.38573
.38576
9.45884
.45889
.45894
.45899
.38764
.28767
.28770
.28774
32
31
30
29
28
27
26
25
+ 8'
33
34
35
9.44700
.44705
.44710
.44715
.37990
.37993
.37997
.38000
.38003
.38006
.38010
.38013
9.45003
.45009
.45014
.45019
.38186
.38189
.28193
.38196
9.45305
.45310
.45315
.45320
.38383
.38386
.38389
.38393
9.45606
.45610
.45615
.45620
.38580
.38583
.38586
.38589
9.45904
.45909
.45914
.45919
.38777
.38780
.38783
.28787
+ 9'
57
38
39
9.44721
.44726
.44731
.44736
9.45024
.45029
.45034
.45039
.38199
.38303
.38306
.38309
9.45325
.45330
.45335
.45340
.38396
.38399
.38403
.38406
9.45625
,4.5630
,45635
,45640
.38593
.38596
.38599
.38603
9.45924
.45929
.45934
.45939
.28790
.38793
.38797
.38800
24
23
22
21
+ W
41
42
43
9.44741
.44746
.44751
.44756
.38016
.38019
.38033
.38036
9.45044
.45049
.4.5054
.45059
.38313
.38316
.38319
.38333
9.45345
.45350
.45355
.45360
.38409
.28412
.28415
.28419
9.45645
.45650
.45655
.45660
.38606
.38609
.38613
.38616
.38619
.38633
.38636
.38639
9.45944
.45949
.45954
.45959
.38803
.38807
.38810
.28813
20
19
18
17
16
15
14
13
12
11
10
9
7
6
5
+ 11'
45
46
47
9.44761
.44766
.44771
.44776
.38039
.38033
.38036
.38039
9.45064
.45069
.45074
.4.5079
.38325
.28229
.38333
.38335
9.45365
.45370
.4.5375
.45380
.28432
.38435
.38439
.38433
9.45665
.45670
.45675
.45680
9.45964
.45969
.45974
.45979
.28816
.28820
.28833
.28836
+ 13'
49
50
51
9.44781
.44786
.44791
.44796
.38043
.38046
.38049
.38053
9.45084
.45089
.45094
.45099
.38338
.28343
.38345
.38348
9.4.5385
.45390
.45395
.45400
.38435
.38438
.38443
.38445
9.45685
,45690
,45695
,45700
.38632
.28635
.38639
.38643
9.45984
.45989
.45994
.45999
.38830
.38833
.38836
.38839
+ 13'
53
54 ,
55
9.44801
.44807
.44812
.44817
.38055
.38059
.38063
.38065
9.45104
.45109
.45114
.45119
.38353
.38355
.38358
.38361
9.45405
.45410
.45415
.45420
.28448
.28451
.28455
.28458
9,45705
.45710
.45715
.45720
.38645
.38649
.38653
.38655
9.46004
.46009
.46014
.46019
.38843
.38846
.38849
.38853
+ W
57
58
59
9.44822
.44827
.44832
.44837
.38068
.38073
.38075
.38078
9.45124
.45129
.45134
.45139
,38365
.38368
.28271
.28274
9.45426
.45431
.45436
.45441
.28461
.38465
.38468
.38471
9.45725
.45730
.45735
,45740
.38658
.38663
.38665
.38668
9.46023
.46028
.46033
.46038
.38856
.38859
.38863
.38866
.38869
4
3
2
1
+ 15'
9.44842
.38081
9.45144
.28378
9.45446
.38474
9,45745
.38673
9.46043
ipn
44m
19h
4.5m
19h
42m
igJi
41m
19h40m
TABLE 45.
Haversines.
[Page 863
s
4'>- 20m 65° C
4h21™
65° 15'
4* 22^
65° 30'
4h23m
65° 45'
4h24m
66° 0'
a
Log. Hav.
Nat. Hav
Log. llav.
Nat. Hav
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
1
2
3
9.46043
.46048
.46053
.46058
.38869
.28873
.38876
.38879
.38883
.38886
.28889
.28893
9.46340
.46345
.46350
.463.55
9.46360
.46365
.46370
.46375
9.46380
.46384
.46389
.46394
"9746399
.46404
.46409
.46414
.29067
.29070
.39074
.39077
.39080
.29084
.29087
.29090
.39093
.39097
.39100
.39103
.39107
.39110
.39113
.39117
9.46635
.46640
.46645
.46650
.29265
.29269
.29273
.39375
9.46929
.46934
.46939
.46944
9.46949
.46954
.46959
.46963
9.46968
.46973
.46978
.46983
9.46988"
.46993
.46998
.47003
.39464
.39467
.39471
.39474
9.47222
.47227
.47231
.47236
.39663
.39666
.39670
.39673
60
69
58
57
+ 1'
5
6
7
9.46063
.46068
.46073
.46078
9.46655
.46660
.46665
.46670
.39279
.39383
.39385
.29289
.29393
.39395
.39398
.39303
.39305
.39308
.39313
.39315
.39318
.39323
.39325
.29328
.39477
.29481
.29484
.39487
.39491
.29494
.29497
.29501
.29504
.29507
.29510
.29514
9.47241
.47246
.47251
.47256
.39676
.39680
.39683
.39686
56
55
54
53
52
51
50
49
+ r
9
10
11
+ 3'
13
14
15
9.46083
.46088
.46093
.46098
.28895
.28899
.38902
.28905
9.46675
.46680
.46684
.46689
9.47261
.47266
.47270
.47275
9.47280
.47285
.47290
.47295
.29690
.29693
.29696
.29700
9.46103
.46108
.46113
.46118
.28909
.38912
.38915
.38918
.38922
.28925
.28938
.38933
9.46694
.46699
.46704
.46709
.39703
.39706
.39710
.39713
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34.
33
32
31
30
29
28
27
26
25
24
23
22
21
+ 4'
17
IS
19
9.46123
.46128
.46132
.46137
9.46419
.46424
.46429
.46434
.39130
.29133
.39136
.39130
.39133
.29136
.29140
.29143
.39146
.39150
.39153
.39156
.39160
.39163
.39166
.39169
.29173
.29176
.39179
.39183
9.46714
.46719
.46724
.46729
9.47007
.47012
.47017
.47022
.29517
.29520
.29524
.39527
.29530
.29534
.29537
.29540
9.47300
.47304
.47309
.47314
.39716
.29730
.39733
.39736
+ 5'
21
22
23
9.46142
.46147
.46152
.46157
.38935
.28938
.28943
.28945
.38948
.38953
.38955
.28958
.38961
.38965
.38968
.28971
9.46439
.46444
.46448
.46453
9.46458
.46463
.46468
.46473
9.46478
.46483
.46488
.46493
9.46733
.46738
.46743
.46748
.29332
.29335
.29338
.29341
9.47027
.47032
.47037
.47042
9.47319
.47324
.47329
.47334
.39730
.39733
.39736
.39740
.39743
.39746
.39750
.39753
.39756
.39760
.39763
.39766
+ 6'
25
26
9.46162
.46167
.46172
.46177
9.46763
.46758
.46763
.46768
.29345
.29348
.39351
.39355
9.47046
.47051
.47056
.47061
.29544
.29547
.29550
.39554
9.47338
.47343
.47348
.47353
+ r
29
SO
31
9.46182
.46187
.46192
.46197
9.46773
.46778
.46782
.46787
.39358
.39361
.39365
.39368
.39371
.39375
.29378
.39381
.39385
.39388
.39391
.39394
9.47066
.47071
.47076
.47081
.39557
.29560
.29564
.29567
.39570
.29573
.39577
.29580
.29583
.29587
.29590
.29593
.29597
.29600
.29603
.29607
9.47358
.47363
.47367
.47372
+ 8'
33
34
35
9.46202
.46207
.46212
.46217
.38975
.38978
.38981
.38985
9.46498
.46503
.46508
.46512
9.46792
.46797
.46802
.46807
9.46812
.46817
.46822
.46827
9.47085
.47090
.47095
.47100
9.47377
.47382
.47387
.47392
9.47397
.47401
.47406
.47411
9.47416
.47421
.47426
.47431
.39770
.39773
.39776
.39779
.39783
.39786
.29789
.39793
+ 9'
57
38
39
9.46222
.46226
.46231
.46236
.38988
.28991
.28994
.28998
9.46517
.46522
.46527
.46532
.39186
.39189
.29193
.29196
9.47105
.47110
.47115
.47120
+ W
41
42
43
9.46241
.46246
.46251
.46256
.29001
.39004
.39008
.29011
9.46537
.46542
.46547
.46552
9.46557
.46562
.46567
.46571
.29199
.29202
.29206
.39309
.39313
.29316
.29319
.29232
.29226
.29339
.39332
.39236
9.46831
.46836
.46841
.46846
.29398
.29401
.29404
.39408
9.47124
.47129
.47134
.47139
.39796
.39799
.39803
.39806
20
19
18
17
16
15
14
13
+ 11'
45
46
47
9.46261
.46266
.46271
.46276
.29014
.39017
.39031
.39034
9.46851
.46856
.46861
.46866
9.4687T
.46875
.46880
.46885
9.46890
.46895
.46900
.46905
9.46910
.46915
.46919
.46924
9.46929
.39411
.39414
.39418
.29421
.29424
.29428
.29431
.29434
.29438
.39441
.29444
.39447
9.47144
.47149
.47154
.47159
.29610
.29613
.39617
.29620
.29623
.29627
.39630
.39633
9,47435
.47440
.47445
.47450
9.47455
.47460
.47464
.47469
.39809
.39813
.39816
.39819
+ 13'
49
SO
51
9.46281
.46286
.46291
.46296
.39037
.29031
.29034
.39037
9.46576
.46581
.46.586
.46591
9.47163
.47168
.47173
.47178
.39833
.39836
.39839
.29833
.39836
.39839
.29843
.39846
12
11
10
9
8
7
6
5
4
3
2
1
+ 13'
S3
54
55
9.46301
.46305
.46310
.46315
.39041
.39044
.39047
.29051
9.46596
.46601
.46606
.46611
.29239
.29242
.39345
.29249
9.47183
.47188
.47193
.47197
.39637
.39640
.39643
.29647
.29650
.29653
.29657
.29660
9.47474
.47479
.47484
.47489
+ 14'
57
58
59
9.46320
.46325
.46330
.46335
.29054
.39057
.39060
.39064
9.46616
.46621
.46626
.46630
.29252
.39255
.39259
.39362
.39451
.39454
,39457
.39461
.29464
9.47202
.47207
.47212
.47217
9.47493
.47498
.47503
.47508
.39849
.39853
.39856
.39859
.39863
+ 15'
9.46340
.29067
9.46635
.29265
9.47222
.39663
9.47513
19h
S9m
19li 38^
19h
S~m
19h36vi
19^
35m
Page 864] TABLE 45.
Haversines,
s
4^ 25rn 66° 15'
4^ 26m 66° W
.^ft 07m 66° 45'
4h 28^ 67° 0'
4h 29m 67° 15'
s
Log. Ilav.
Nat. Hav.
Log. Hav,
Nat. Hav.
Ix)g. Hav.
Nat. Hav,
Log, Hav.
Nat, Hav,
Log, Hav,
Nat. Hav.
1
3
9.47513
.47518
.47523
.47527
.39863
.29866
.29869
.29873
9.47803
.47807
.47812
.47817
.30063
.30066
.30969
.30073
9.48091
.48096
.48101
.48105
.30263
.30266
.30269
.30373
9.48378
.48383
.48387
.48392
.30463
.30467
.30470
.30473
9,48664
,48668
,48673
,48678
.30664
.30668
.30671
.30675
60
59
58
57
+ y
5
6
7
9.47532
.47537
.47542
.47547
.29876
.29879
.39883
.39886
9.47822
.47827
.47831
.47836
9.47841
.47846
.47851
.47856
.30076
.30079
.30083
.30086
9.48110
.48115
.48120
.48124
.30376
.30280
.30283
.30286
9,48397
,48402
,48407
,48411
.30477
.30480
.30484
.30487
9,48683
,48687
,48692
.48697
.30678
.30681
.30685
.30688
56
55
54
53
+ 3'
9
10
11
9.47552
.47556
.47561
.47566
.29889
.39893
.39896
.39899
.30089
.30093
.30096
.30099
9.48129
.48134
.48139
.48144
.30290
.30293
.30296
.30300
9,48416
.48421
.48426
.48430
.30490
.30494
.30497
.30500
9.48702
.48706
.48711
.48716
.30691
.30695
.30698
.30701
52
51
50
49
+ 3'
13
14
15
9.47571
.47576
.47581
.47585
.39903
.39906
.39909
.39913
9.47860
.47865
.47870
.47875
.30103
.30106
.30109
.30113
9.48148
.48153
.48158
.48163
.30303
.30306
.30310
.30313
9.48435
.48440
.48445
.48449
.30504
.30507
.30510
.30514
9.48720
.48725
.48730
.48735
.30705
.30708
.30711
.30715
48
47
46
45
+ *'
17
18
19
9.47590
.47595
.47600
.47605
.39916
.29919
.29923
.29926
9.47880
.47884
.47889
.47894
.30116
.30119
.30123
.30126
9.48168
.48172
.48177
.48182
.30316
.30320
.30323
.30326
9.48454
.48459
.48464
.48468
.30517
.30530
.30534
.30537
9.48739
.48744
.48749
.48754
.30718
.30721
.30725
.30728
44
43
42
41
40
39
38
37
+ 5'
21
22
23
9.47610
.47614
.47619
.47624
.29939
.29933
.29936
.29939
.39943
.39946
.39949
.39953
9.47899
.47904
.47908
.47913
.30139
.30133
.30136
.30139
9.48187
.48192
.48196
.48201
.30330
.30.333
.30336
.30340
9,48473
,48478
,48483
,48488
9,48492"
,48497
,48502
,48507
.30530
.30534
.30537
.30540
9.48758
.48763
.48768
.48773
.30732
.30735
.30738
.30742
+ 6'
25
26
27
9.47629
.47634
.47639
.47643
9.47918
.47923
.47928
.47933
.30143
.30146
.30149
.30153
9.48206
.48211
.48215
.48220
.30343
.30346
.30:t50
.30353
.30544
.30547
.30551
.30554
9.48777
,48782
.48787
.48792
.30745
.30748
.30752
.30755
36
35
34
33
+ r
29
SO
31
9.47648
.47653
.47658
.47663
.29956
.29959
.29963
.29966
9.47937
.47942
.47947
.47952
.30156
.30159
.30163
.30166
9.48225
.48230
.48235
.48239
.30356
.30360
.30363
.30366
9,48511
,48516
,48521
,48526
.30557
.30561
.30564
.30567
9.48796
.48801
.48806
.48811
.30758
.30762
.30765
.30768
32
31
30
29
+ 8'
33
34
35
9.47668
.47672
.47677
.47682
.39969
.39973
.39976
.39979
9.47957
.47961
.47966
.47971
.30169
.30173
.30176
.30179
9.48244
.48249
.48254
.48258
.30370
.30373
.30376
.30380
.30383
.30386
.30390
.30393
.30397
.30400
.30403
.30407
9,48530
.48535
.48540
.48545
.30571
.30574
.30577
.30581
9.48815
.48820
.48825
.48830
.30772
.30775
.30779
.30782
28
27
26
25
+ 9'
37
38
39
9.47687
.47692
.47697
.47701
.29983
.29986
.29989
.29993
.39996
.39999
,30003
.30006
9.47976
.47981
.47985
.47990
.30183
.30186
.30189
.30193
9.48263
.48268
.48273
.48278
9,48549
,48554
,48559
,48564
.30584
.30587
.30591
.30594
9,48834
,48839
,48844
,48848
.30785
.30789
.30792
.30795
24
23
22
21
+ 1(K
41
42
43
9.47706
.47711
.47716
.47721
9.47995
.48000
.48005
.48009
.30196
.30199
.30303
.30306
9.48282
.48287
.48292
.48297
9,48568
,48573
.48578
,48583
.30597
.30601
.30604
.30607
9,48853
,48858
,48863
,48867
.30799
.30802
.30805
.30809
20
19
IS
n
+ 11'
45
46
47
9.47725
.47730
.47735
.47740
.30009
.30013
.30016
.30019
9.48014
.48019
.48024
.48029
.30309
.30313
.30316
.30319
9.48302
.48306
.48311
.48316
.30410
.30413
.30417
.30430
9,48587
.48592
.48597
.48602
.30611
.30614
.30618
.30631
.30624'
.30638
.30631
.30634
9,48872
,48877
.48882
,48886
9,48891
,48896
,48901
,48905
.30812
.30815
.30819
.30823
16
15
14
13
+ 12'
49
50
51
9.47745
.47750
.47754
.47759
.30033
.30036
.30039
.30033
9.48033
.48038
.48043
.48048
.30323
.30336
.30339
.30333
9.48321
.48325
.48330
.48335
.30433
.30437
.30430
.30433
.30437
.30440
.30443
.30447
.30450
.30453
.30457
.30460
9,48607
,48611
,48616
,48621
.30836
.30839
.30833
.30836
12
11
10
9
8
7
6
5
4
3
2
~1
+ 13'
53
54
55
9.47764
.47769
.47774
.47778
.30036
.30039
.30043
..30046
9.48053
.48057
.48062
.48067
9.48072
.48077
.48081
.48086
.30236
.30239
.30343
.30346
9.48340
.48344
.48349
.48354
9,48626
,48630
.48635
.48640
.30638
.30641
.30644
.30648
9,48910
.48915
.48919
.48924
.30839
.30842
.30846
.30849
+ U'
57
58
59
9.47783
.47788
.47793
.47798
.30049
.30053
.30056
.30059
.30249
.30253
.30256
.30259
9.48359
.48364
.48368
,48373
9.48645
.48649
.48654
.486.59
.30651
.30655
.30658
.30661
9.48929
.48934
.48938
.48943
.30852
.30856
.30859
.30862
+ 15'
9.47803
.30063
9.48091
.30263
9.48378
.30463
9.48664
.30664
9.48948
.30866
79* 34^
191>- 33m
29h 32m
19h dpn 1 19>t 30m
TABLE 45.
Haversines.
[Page 865
s
4h som 67° 30'
4h Sim 67° 45'
Jfh sjm
68° 0'
4hS3m
68° 15'
4h64m6S°3ty
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hcv,
Log. Hav.
Xat.llav.
1
■i
9.48948
.48953
.48957
.48962
.30866
.30869
.30873
.30876
9.49231
.49235
.49240
.49245
9,49250
.49254
.49259
.49264
.31068
.31071
.31074
.31078
9.49512
.49517
.49522
.49226
.31370
.31373
.31276
.31380
9.49793
.49797
.49802
.49807
.31472
.31475
.31479
.31482
.31486
.31489
.31493
.31496
9.-50072
.50076
.50081
.50085
.31675
.31678
.31682
.31685
60
59
58
57
5
6
9.48967
.48971
.48976
.48981
.30879
.30883
.30886
.30889
.31081
.31084
.31088
.31091
9.49531
.49536
.49.540
.49545
.31383
.31387
.31290
.31393
.31297
.31300
.31303
.31307
9.49811
.49816
.49821
.49825
9.50090
.-50095
.50099
.50104
.31688
.31693
.31695
.31699
56
55
54
5S
+ V
.9
1(1
11
9.48986
.48990
.48995
.49000
.30893
.30896
.30899
.30903
9.49268
.49273
.49278
.49282
9.49287
.49292
.49297
.49301
.31095
.31098
.31101
.31105
.31108
.31111
.31115
.31118
9.49550
.49554
.495-59
.49-564
9.49568
.49573
.49578
.49583
9.49830
.49835
.49839
.49844
.31499
.31503
.31506
.31509
9.50109
.50113
,.50118
.-50123
.31703
.31705
.31709
.31712
5J
51
50
49
48
47
46
45
44
4S
42
41
40
39
SS
S7
+ 3'
IS
14
15
9.49004
.49009
.49014
.49019
9.49023
.49028
.49033
.49038
.30906
.30910
.30913
.30916
.31310
.31314
.31317
.31320
9.49849
.49853
.49858
.49862
.31513
.31516
.31519
.31523
9.50127
.50132
.50136
..50141
9,50146
,.501-50
,-50155
,50160
.31716
.31719
.31723
.31736
.31739
.31732
.31736
.31739
+ i'
17
18
19
.30930
.30923
.30936
.30930
.30933
.30936
.30940
.30943
.30946
.30950
.30953
.30957
.30960
.30963
.30967
.30970
.30973
.30977
.30980
.30983
9.49306
.49311
.49315
.49320
.31121
.31125
.31128
.31132
9.49-587
.49592
.49-597
.49601
.31324
.31327
.31330
.31334
.31337"
.31341
.31344
.31347
9.49867
.49872
.49876
.49881
9.49886
.49890
.49895
.49900
.31526
.31530
.31533
.31536
.31540
.31543
.31546
.31550
.31553
.31557
.31560
.31563
.31567
.31570
.31573
.31577
+ 5'
9.49042
.49047
.490.52
.49056
9.49325
.49329
.49334
.49339
9.49344
.49348
.49353
.49358
.31135
.31138
.31142
.31145
.31148
.31152
.31155
.31158
9.49606
.4W11
.49615
.49620
9.49625
.49629
,49634
.49639
9,-50164
,50169
.50174
..50178
.31743
.31746
.31749
.31753
+ 6'
Jo
,'.6
J7
9.49001
.49066
.49071
.49075
.31351
.31354
.31357
.31361
9.49904
.49909
.49914
.49918
9.-50183
.,50187
,,50192
,50197
.31756
.31760
.31763
.31766
J6
S5
34
33
32
31
30
29
28
27
26
25
24
23
22
21
+ r
.'.9
',11
■i!
9.49080
.49085
.49089
.49094
9.49099
.49104
.49108
.49113
9.49362
.49367
.49372
.49370
.31162
.31165
.31169
.31172
9.49643
.49648
.490-53
.49657
9.49662
.49467
.49671
.49676
9.49681
.49685
,49690
,49695
9,49699
,49704
.49709
,49713
.31364
.31367
.31371
.31374
.31378
.31381
.31384
.31388
9.49923
.49928
.49932
.49937
9,50201
,50206
,-50211
,-50215
9,50220"
.-50224
-50229
,50234
9,50238
.-50243
.50248
.50252
.31770
.31773
.31776
.31780
.31783
.31787
.31790
.31793
.31797
.31800
.31804
.31807
+ 8'
■iS
S4
S5
9.49381
.49386
.49390
.49395
.31175
.31179
.31182
.31185
.31189
.31192
.31196
.31199
9.49942
.49946
.49951
.499-56
.31580
.31584
.31587
.31590
.31594
.31597
.31601
.31604
.31607
.31611
.31614
.31617
.31621
.31624
.31628
.31631
+ 9'
■i7
68
■39
+ 10'
41
-t i
4-i
+ yil'
4-1
■i'i
47
9.49118
.49122
.49127
.49132
9.49137
.49141
.49146
.49151
.30987
.30990
.30994
.30997
9.49400
.49405
.49409
.49414
.31391
.31394
.31398
.31401
9.49960
.49965
.49969
.49974
.31000
.31004
.31007
.31010
9.49419
.49423
.49428
.49433
.31202
.31206
.31209
.31212
.31405
.31408
.31411
.31415
.31418
.31421
.31425
.31428
.31433
.31435
.31438
.31442
9.49979
.49983
.49988
,49993
9,49997
,50002
,50007
,-50011
9.50257
.-50261
.50260
.50271
.31810
.31814
.31817
.31830
.31834
.31837
.31831
.31834
20
19
18
17
16
15
14
13
9.49155
.49160
.49165
.49170
9.49174
.49179
.49184
.49188
.31014
.31017
.31020
.31024
9.49437
.49442
.49447
.49451
.31216
.31219
.31223
.31226
9,49718
,49723
.49727
,49732
9,49737
,49741
,49746
,49751
9,497-55
,49760
,49765
,49769
9,49774
,49779
,49783
,49788
9..50275
.-50280
.-50284
.50289
+ ir
49
■'>')
51
.31027
.31031
.31034
.31037
.31041
.31044
.31047
.31051
9.49456
.49461
.49465
.49470
9749475
.49480
.49484
.49489
.31229
.31233
.31236
.31239
.31243
.31246
.31249
.31253
9,50016
,.50021
,-50025
,50030
.31634
.31638
.31641
.31644
9.-50294
.-50298
.50303
.-50308
.31837
.31841
.31844
.31848
12
11
10
9
8
7
6
5
4
3
2
1
+ 13'
.>;
54
■j-'t
9.49193
.49198
.49202
.49207
.31445
.31448
.31452
.31455
9.50034
.-50039
.-50044
.50048
.31648
.31651
.31655
.31658
.3i66i
.31665
.31668
.31672
9.-50312
..50317
..50322
.50326
9.-50331
.-50335
.-50340
.-50345
9..50349
.31851
.31854
.31858
.31861
.31865
.31868
.31871
.31875
+ 14'
57
58
■59
9.49212
.49217
.49221
.49226
.31054
.31057
.31061
.31064
.31068
9.49494
.49498
.49503
.49508
.31256
.31260
.31363
.31266
.31459
.31462
.31465
.31469
9.50053
.-50058
.50062
.50067
-L 15'
9.49231
9.49512
.31270
9,49793
.31472
9.50072
.31675
.31878
19h
J9m
19h
28rf
19h
27m
19^ 26m
19>i
~'.5™
24972°--12 45
Page 866]
TABLE 45.
Haversines.
s
4h So™
68° 45'
4'i 36m 69° 0'
4h Jpn
69° 15'
4h 38m
69° 30'
4h S9m 69° 45'
s
60
59
.5iV
.57
5¥
55
54
53
.5J
51
51)
49
4>i
47
46
45
44
■4-i
4.1
41
4o'
39
3S
3i'
35
■U
33
'32"
31
30
29
2S
27
26
25
24
23
22
21
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
^4
3
2
1
"77
Log. Hav.
Xat. Hav.
Log. Hav.
N'at. Uav.
Log. Hav.
N'at. Hav.
Log. Hav.
N'at. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.50349
.50354
.50358
.50363
9.50368
.50372
..50377
.50382
9.50386
.50391
.50395
.50400
9;50405
.50409
.50414-
.50418
9;50423
..50428
.50432
.50437
.31878
.31881
.31885
.31888
.31893
.31895
.31898
.31903
.31905
.31909
.31912
.31915
.3i919
.31922
.31926
.31929
.31932
.31936
.31939
.31942
.31946
.31949
.31953
.31956
.31959
.31963
.31966
.31970
9.50626
.50630
.50635
.50639
9.50644
.50649
.50653
.50658
9..50662
.50667
.50672
.50676
9.50681
..50685
.50690
.50694
9.50699
..50704
.50708
.50713
.32082
.32085
.32088
.32092
.32095
.32099
.32102
.32105
.32109
.32112
.32116
.32119
.32122
.32126
.32129
.32133
.32136
.32139
.32143
.32146
9..50901
..50905
.,50910
..50914
9..50919
..50924
.50928
.50933
9.50937
.50942
..50946
..50951
9..50956
.50960
.50965
..50969
.32285
.32289
.32292
.32296
.32299
.32302
.32306
.32.309
.32313
.32316
.32319
.32323
.32326
.32330
.32333
.32336
9.51174
.51179
.51184
.51188
.32490
.32493
.32496
.32500
.32503
.32507
.32510
.32513
9.51447
.51452
.51456
.51461
.32694
.32698
.32701
.32704
.32708
.32711
.32715
.32718
+ r
5
6
7
+ V
9
10
11
9.51193
.51197
.51202
.51206
9.51465
.51470
.51474
.51479
9..51483
.51488
.51492
.51497
9.51501
.51506
.51510
.51515
9.51211
.51215
.51220
.51225
.32517
.32520
.32524
.32527
.32721
.32725
.32728
.32732
.32735
.32738
.32742
.32745
.32749
.32752
..32756
.32759
.32762
.32766
.32769
.32773
.32776
.32779
.32783
.32786
.32790
.32793
.32797
.32800
.3280.3
.32807
.32810
.32814
+ 3'
13
14
15
9.51229
.51234
.51238
.51243
9.51247
.51252
.51256
.51261
.32531
.32534
.32537
.32541
+ i'
17
18
19-
9.50974
.50978
.50983
.50988
9.50992
..50997
.5)001
.51006
.32340
.32343
.32347
.32350
.32353
.32357
.32360
.32364
.32544
.32547
.32551
.32554
9.51519
.51524
.51.529
.51533
+ «'
21
22
23
+ 6'
25
26
27
9.50442
.50446
.50451
.50455
9.50460
.50465
.50469
.50474
9.50717
.50722
.50727
.50731
9.50736
.50740
.50745
.50750
.32150
.32153
.32156
.32160
.32163
.32166
.32170
.32173
9.51265
.51270
.51275
.51279
.32558
.32561
.32565
.32568
.32571
.32575
.32578
.32582
.32585
.32588
.32592
.32595
.32599
.32602
.32605
.32609
9.51538
.51542
.51547
.51551
9.51556
.51560
.51565
.51569
9.51574
.51578
.51583
.51587
9.51010
.51015
..51019
.51024
9.51029
.51033
.51038
.51042
9.51047
.51051
.51056
.51061
.32367
.32370
.32374
.32377
.32381
..32384
.32388
.32391
.32394
.32398
.32401
.32405
9.51284
.51288
.51293
.51297
+ r
29
so
31
9.50478
.50483
.50488
.50492
9:50497
.50501
.50506
.50511
.31973
.31976
.31980
.31983
.31987
.31990
.31993
.31997
.32000
.32004
.32007
.32010
9.50754
.50759
.50763
.50768
.32177
.32180
.32183
.32187
9.51302
.51306
.51311
.51315
+ 8'
33
34
35
9.50772
..50777
..50782
.50786
9.50791
.50795
.50800
.50805
.32190
.32194
.32197
.32200
.32204
.32207
' .32211
.32214
9.51320
.51325
.51329
.51334
9.51592
.51596
.51601
.51605
+ 9'
37
38
39
9.50515
.50520
.50524
.50529
9.51065
.51070
.51074
.51079
.32408
.32411
.32415
.32418
9.51338
.51343
.51347
.51352
.32612
.32616
.32619
.326^3
9.51610
.51614
.51619
.51623
.32817
.32820
.32824
.32827
+ 10'
41
42
43
9.50.534
.50538
.50543
.50547
.32014
.32017
.32021
.32024
.32027
.32031
.32034
.32037
9.50809
..50814
.50818
.50823
9.50827
.50832
.50837
.50841
.32217
.32221
.32224
.32228
9.51083
.51088
.51092
.51097
.32422
.32425
.32428
.32432
9.51356
.51361
.51365
.51370
.32626
.32629
.32633
.32636
9.51628
.51633
.51637
.51642
.32831
.32834
.32838
.32841
+ 11'
45
46
47
9.50552
.50557
.50.561
.50566
9.50.570"
.50575
..50580
.50584
.32231
.32235
.32238
.32241
9.51102
.51106
.51111
.51115
.32435
.32438
.32442
.32445
9.51374
.51379
.51384
.51388
.32640
.32643
.32646
.32650
9.51646
.51651
.51655
.51660
.32844
.32848
.32851
.32855
:32858
.32861
.32865
.32868
.32872
.32875
.32878
.32882
+ 12'
49
SO
51
.32041
.32044
.32048
.32051
.32054
.32058
.32061
.32065
.32068
.32071
.32075
.32078
9..50846
.50850
.50855
.50860
9.50864
.50869
.50873
..50878
9.50882
..50887
.50892
.50896
.32245
.32248
.32251
.32255
.32258
.32262
.32265
.32268
.32272
.32275
.32279
.32282
9.51120
.51124
.51129
.51133
9.51138
.5] 143
.31147
.51152
9.51156
.51161
.51165
.51170
.32449
.32452
.32456
..32459
9.51393
.51397
.51402
.51406
.32653
.32657
.32660
.32663
9.51664
.51669
.51673
.51678
+ 13'
53
54
55
9.50589
.50593
.50598
.50603
.32462
.32466
..32469
.32473
9.51411
.51415
.51420
.51424-
.32667
.32670
.32674
.32677
9.51682
..51687
.51691
.51696
+ M'
57
58
59
9.50607
.50612
.50616
.50621
.32476
.32479
.32483
.32486
9.51429
.51433
.51438
.51442
.32681
.32684
.32687
.32691
9.51700
.51705
.51709
.51714
.32885
.32889
.32892
.32896
+ 15'
9.50626
.32082
9.50901
.32285
9.51174
.32490
9.51447
.32694
9.51718
.32899
19h
34'"
19h
23m
19^
22m
19h
2im
19^
20m
TABLE 45.
Haversines.
[Page 867
s
4h4()m
70° (K
4h .j.im
70° 15'
4h 42m
70° 30^
4h 4Sm
70° 45'
4n 44m
71° 0'
s
Log. Ilav
Nat.Hav.
Log. Hav
Nat. Ilav.
Log. Hav.
Nat, Hav,
Log. Hav.
Nat, llav.
Log, Hav,
Nat. Hav.
1
2
~3
9.51718
.51723
.51727
.51732
.33899
.33909
.32906
.32909
9.51988
.51993
,51997
.52002
.33104
.33108
! .33111
.33114
9.52257
.52261
,52266
.52270
.33310
.33313
.33317
.33.320
9.52.525
.52529
.52533
.52538
.3.3515
.33519
.33522
.33526
9,. 52791
.52795
,.-)2S0O
.52801
.33723
.33725
.33728
.33732
60
59
58
57
+ 1'
5
6
7
9.51736
.51741
.51745
.51750
.32913
.32916
.32920
.32923
.32926
.32930
.32933
.32937
9.52006
.52011
..52015
.52020
9..52()24
.52029
.52033
.52038
i .33118
' .33121
i .33125
.33128
9.52275
..52279
.52284
.52288
.33323
.33327
.33330
.33334
9.52542
,52.547
,52551
,52556
9.52560
.52565
.52569
.52573
.33529
.33533
.33536
.33540
9,. 52809
,52813
.52817
.52822
.33735
.33739
.33743
.33746
56
55
54
53
+ 3'
9
10
11
9.51754
.51759
.51763
.51768
i .33132
j .33135
.33138
.33142
9.52293
.52297
..52302
.52306
.33337
.33341
.33344
.33347
.33543
.33546
.33,550
.33553
9.52826
.52831
.52835
..52839
.33749
.33753
.33756
.33759
52
51
50
49
48
47
46
45
44
43
42
41
+ 3'
IS
14
15
9.51772
.51777
.51781
.51786
.32940
.32913
.32947
.32930
9.52042
..52047
..52051
.52056
.33145
.33149
.33152
.33156
9,52311
,52315
.52320
.52324
.33351
.33354
.33358
.33361
9.52.578
,.52.582
,52.587
.52591
.33557
.33560
.33564
.33567
9.52S44
.52848
.52853
.52857
.:J3763
.33766
.33770
.33773
+ i'
n
18
19
9.51790
.51795
.51799
.51804
.32954
.32957
.32961
.32964
9.520C0
.52065
.52069
.52074
.33159
.33162
.33166
.33169
9.52328
.52333
.52337
..52342
.33365
.33368
.33371
.33375
9.52596
.52600
.52605
.52609
.33570
.33574
.33577
.33581
.33584
.33588
.33591
.33594
9.52862
..52866
.,52870
,52875
.33777
.33780
.33783
.33787
+ 5'
21
22
23
9.51808
.51813
.51817
.51822
.32967
.32971
.32974
.32978
9.52078
.52082
,.52087
,.52091
.33173
.33176
.33179
.33183
9.52346
.52351
.52355
.52360
.33378
.33382
.33385
.33389
9.52613
.52618
.52622
.52627
9,52879
.52884
.52888
.52893
.33790
.33794
.33797
.33801
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
+ 6'
25
26
27
9.51826
.51831
.51835
.51840
.32981
.32984
.32988
.32991
9..52096
..52100
..52105
.52109
.33186
.33190
.33193
.33197
9.52364
.52369
..52373
.52378
.33392
.33395
.33399
.33402
9.52631
.52636
.52640
,52645
.33598
.33601
.33605
.33608
9.52897
.52901
.52906
.52910
9.52915
.52919
.52923
..52928
.33804
.33808
.33811
.33814
.33818
.33821
.33825
.33828
+ r
29
SO
31
9.51844
.51849
.51853
.51858
.32995
.32998
.33002
.33005
9.52114
.52118
.52123
.52127
.33200
.33203
.33207
.33210
.33214
.33217
.33221
.33224
9.52382
.52386
.52391
,52395
.33406
.33409
.33413
.33416
9.52649
.52653
.52658
.62662
.33612
.33615
.33618
.33622
+ 8'
S3
34
35
9.51862
.51867
.51871
.51876
.33008
.33012
.33015
.33019
9.52132
.52136
.52141
.52145
9.52400
.52404
.52409
.52413
.33419
.33423
.33426
.33430
9.52667
.52671
.52676
.52680
9.52684
.52689
.52693
.52698
.33625
.33629
.33632
.33636
9.52932
.52937
.52941
.52946
.33832
.33835
.33839
.33842
.33845
.33849
.33852
.33856
+ -9'
^7
38
39
9.51880
.51885
.51889
.51894
.33022
.33025
.33029
.33032
9.52150
.52154
.52159
.52163
.33227
.33231
.33234
.33238
9.52418
.52422
.52427
.52431
.33433
.33436
.33440
.33444
.33447
.33450
.33454
.33457
.33639
.33642
.33646
.33649
9,. 52950
.52954
.52959
..52963
+ W
41
42
43
9.51898
.51903
.51907
.51912
.33036
.33039
.33043
.33046
9.52168
.52172
,52177
.52181
.33241
.33245
.33348
.33251
9,52436
,52440
..52444
.52449
9.52702
.52707
.52711
,52715
.33653
.336.56
.33660
.33663
9.52968
..52972
,52976
.52981
.33859
.33863
.33866
.33869
+ 11'
45
46
47
9.51916
.51921
.51925
.51930
.33049
.33053
.33056
.33060
9.52185
.52190
.52194
.52199
.;I32S5
.33258
.33262
.33265
.33269
.33272
.33275
.33279
.3.3282
.33286
.33289
.33293
.33296
.33299
.33.303
.33306
9.52453
.52458
.52462
,52467
.33461
.33464
.33467
.33471
.33474
.33478
.:{3481
.33485
.33488
.33491
.33495
.33498
9,. 52720
,.52724
,52729
.52733
.33667
.3.3670
.33673
.33677
9.. 52985
.52990
.52994
..52909
.33873
.33876
..33880
.33883
16
15
14
13
12
11
10
9
+ W
49
50
51
9.51934
.51939
.51943
.51948
.33063
.33067
.33070
.33073
9.52203
.52208
..52212
.52217
9,52471
.52476
..52480
..52484
.52493
,52498
,52.502
9:525by
,52511
,.52516
,52520
9^52525
9.52738
.52742
.52747
.52751
.33680
.33684
.33687
.33691
9,. 53003
.53007
.5,3012
..53016
.3.3887
.33890
.3.3894
.33897
+ 13'
53
54
55
9.51952
.51957
.51961
.51966
.3.3077
.33080
.33084
.33087
9.52221
.52226
.52230
.52235
9.52755
.52760
.52764
.52769
.33694
.33698
.33701
.33704
.33708
.33711
.33715
.33718
9.,53021
,53025
,,53029
,53034
.33900
.3.3904
.33907
.33911
8
7
6
5
4
3
2
1
+ 14'
57
58
59
9.51970
.51975
.51979
.51984
.33090
.33094
.33097
.33101
.33104
9.52239
.52244
.52248
.52253
.33502
.33505
.33509
.33512
9.52773
.52778
.52782
.52786
9.,53038
.53043
,,53047
,,5,3051
9,53056
..33914
.33918
.33921
.33935
+ IS'
9.51988
9.52257
.33310
.33515
9.52791
.33722
.33928
igh ]<)m
19h ism
](jh nm
igh lem
igh 15m
Page 868]
TABLE
45.
Haversines.
s '
5^45"^
n° IS'
4h 46m
71° 30'
4h 47m
71° 45'
4h4Sm
72° 0'
4h49m1Z°U' 1
s
Log. Ilav.
Nat. llav.
Log. Ilav.
Xat. Ilav.
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Ilav.
9.53056
.33928
9.53320
.34135
9.53582
.34342
9.53844
.34549
9.54104
.34757
60
1
.53000
,33931
.53324
.34138
.53587
.34345
.53848
.34553
.54108
.34760
59
2
.530(i5
.33935
.53328
.34142
.53591
.34349
.53852
.34556
.54113
.34764
58
3
.53069
9.53073
.33938
.33942
.53333
9.53337
.34145
.34149
.53595
.34352
.34356
.53857
9.53861
.34560
.54117
.34767
57
56
+ 1'
9.53600
.34563
9.54121
.34771
5
.53078
.33945
.53342
.34152
.53604
.34359
.53805
.34566
.54126
.34774
•>o
6
.53082
.33949
.53346
.34155
.53609
.34363
..53870
.34570
.54130
.34778
54
7
.53087
.33952
.33956
.53350
'9.. 53355
.34159
.34162
.53613
.34366
.34369
.53874
9.53879
.34573
.34577
.54134
9.54139
.34781
54
5i
+ 3'
9.53091
9.53617
.34784
9
.53096
.33959
.53359
.34166
.53622
.34373
.53883
.34580
.54143
.34788
51
10
.53100
.33962
.53364
.34169
.53626
.34376
.53887
.34584
.54147
.34791
50
11
.53104
.33966
.33969
.53368
9.53372
.34173
.34176
.53630
.34380
.34383
.53892
9.53896
.34587
.34591
..54152
9.54156
.34795
.34798
49
+ 3'
9.53109
9.53635
13
.53113
.33973
.53377
.34180
.53639
.34387
.53900
.34594
.54160
.34802
47
14
.53118
.33976
.53381
.34183
.53643
.34390
.53905
.34598
.54165
.34805
46
15
.53122
.33980
.33983
.53385
9.53390
.34186
.34190
.53648
.34394
.34397
.53909
9.53913
.34601
.54169
9.54173
.34809
.34812
45
44
+ *'
9.53126
9.53652
.34604
17
.53131
.33986
.53394
.34193
.53657
.34400
.53918
.34608
.54177
.34816
43
18
.53135
.33990
.53399
.34197
.53661
.34404
.53922
.34611
.54182
.34819
42
19
.53140
.33993
.33997
.53403
9:53407
.34200
.34204
.53665
9.53670
.34407
.34411
.53926
9.53931
.34615
.54186
.34823
41
40
+ 5'
9.53144
.34618
9.54190
.34826
^1
.53148
.34000
..53412
.34207
.53674
.34414
.53935
.34622
.54195
.34830
■19
2t
.53153
.34004
.53416
.34211
.53678
.:M418
.53939
.34625
.54199
.34833
.)'*■
23
..53157
.34007
..53421
9.53425
.34214
.34218
.53683
.34421
.34425
.53944
9.53948
.34629
.54203
.34836
■17
~i6~
+ 6'
9.53162
.34011
9.53687
.34632
9.54208
.34840
25
.53166
.34014
.53429
.34221
.53091
.34428
..53952
.34636
.54212
.34843
■i.',
26
.53170
.34018
.53434
.34224
.53696
.34432
.53957
.34639
.54210
.34847
■14
27
.53175
.34021
.53438
.34228
.53700
.34435
.53961
.34643
.54221
9.54225
.34850
.34854
■i.J
■i£
+ r
9.53179
.34024
9.53442
.34231
9.53704
.34439
9.53906
.34646
29
.53184
.34028
.53447
.34235
..53709
.34442
..53970
.34649
.54229
.34857
■11
30
.53188
.34031
..53451
.34238
.53713
.34445
.53974
.34653
.54234
.34861
■iO
31
.53192
.34035
.34038
..53456
9.53460
.34242
.34245
.53718
.34449
.34452
.53978
9..53983
.34656
.54238
.34864
29
28
+ 8'
9.53197
9.53722
.34660
9.54242
.34868
33
.53201
.34042
.53464
.34249
.53726
.34456
..53987
.34663
.54247
.34871
oy
34
.53206
.34045
.53469
.34252
.53731
.34459
.53991
.34667
.54251
.34875
26
35
.53210
.34049
.34052
.53473
.34256
.53735
9.53739
.34463
.34466
.53996
9.54000"
.34670
.34674
.54255
.34878
25
24
+ 9'
9.53214
9.53477
.34259
9.54260
.34882
37
.53219
.34055
.53482
.34262
.53744
.34470
.54004
.34677
.54264
.34885
2.1
38
.53223
.34059
.53486
.34266
.53748
.34473
.54009
.34681
.54268
.34888
22
39
.53228
.34062
.53491
9.53495
.34269
.34273
.53752
.34477
.34480
..54013
9.54017
.34684
.54272
9.54277
.34892
.34895
21
20
+ W
9.53232
.34066
9.53757
.34688
41
.53236
.34069
.53499
.34276
.53761
.34483
..54022
.34691
.54281
.34899
19
42
.53241
.34073
.53.504
.34280
..53765
.34487
..54026
.34694
.54285
.34902
18
43
+ 11'
.53245
9;53249"
.34076
.34080
.53.508
9.53512
.34283
.34287
.53770
9.53774
.34490
.34494"
..54030
9.54035
.34698
.54290
.34906
.34909
17
IH
.34701
9.54294
45
.532.54
.34083
.53517
.34290
..53778
.34497
.54039
.34705
.54298
.34913
1.;
46
.53258
.34087
.53521
.34293
.53783
.34501
.54043
.34708
.54303
.34916
14
47
.53263
.34090
.53526
.34297
.53787
.34504
.54048
.34712
..54307
.34920
hi
+ 12'
9.53267
.34093
9..53530
.34300
9.53792
.34508
9.54052
.34715
9.54311
.34923
12
49
.53271
.34097
.53534
.34304
.53796
.34511
.54056
.34719
.54316
.34927
11
50
.53276
.34100
..53539
.34307
.53800
.34515
..54061
.34722
.54320
.3493*
10
51
+ 13'
.53280
9.53285
.34104
.34107
..53.543
9:53547
.34311
.53805
9.53809
; .34518
.34,521
..54065
9.54069
.34726
.34729
.54324
.34933
9
8
.34314
9.54329
.34937
53
..53289
.34111
.53552
.34318
.53813
.34525
.54074
.34733
..54333
.34940
1
54
.53293
.34114
..53556
.34321
..53818
.34528
.54078
.34736
.54337
.34944
6
55
.53298
.34118
.a4121
.53560
9.53565
.34325
.34328
..53822
9.53826
.34532
i .34535
..54082
9.54087
.34739
.34743
.54341
9.54346
.34947
.34951
5
4
+ 14'
9.53302
57
.53307
.34124
.53569
.34331
.53831
.34539
..54091
.34746
.543.50
.34954
3
58
.53311
.34128
.53574
.34335
.53835
.34542
..54095
.34750
..54354
.34958
2
59
.53315
.34131
.34135
.53578
.34338
.53839
9.53844
1 .34546
j .34549"
.54100
"9.54104
.34753
.34757
.54359
9.54363
.34961
.34965
1
+ 15'
9.53320
9.53582
.34342
19h
W"
19h IJm
19^
l^m
19^
lim
19h
lO'i'
TABLE 45. [Page 869
Haversines.
s
4^ 50^ 72° 30'
4h 5lm 73° 45'
4h 52m 73° r
4* 53^ 73° 15'
4h 54m 73° 3(K
s
Log. Hav.] Nat. Hav,
Log. Hav.
Nat. Hav.
Log. Hav.l Nat. Hav.
Log. Hav.' Nat. Hav.
Log. Hav.j Nat. Hav.
1
2
~3
9.54363 1 .34965
.54367 \ .34968
.54372 i .34972
.54376 1 .34975
9.54621
..54625
.54629
..54634
9^54638"
.54642
.54647
.54651
.35173
.35176
.35180
.35183
.35187
.35190
.35194
.35197
9.-54878
.54882
.54886
.54890
.35381
.35385
.35388
.35393
9. ,55133
.55137
.55142
.55146
.35590
.35594
.35597
.35601
9.55387
.55392
.55396
.55400
.35799
.35803
.35806
.35810
60
59
58
57
56'
55
54
53
5.;
51
50
49
48
47
46
45
+ y
6
7
a.54380
.54385
.54389
.54393
.34979
.34982
.34986
.34989
9.54895
.54899
.54903
.54907
.35395
.35399
.35403
.35406
9.55150
..551,54
.551.59
.55163
.35604
.35608
.35611
.35615
9.5.5404
.5.5409
.5.5413
.55417
.35813
.35817
.35830
.35834
+ V
9
10
11
9.54397
.54402
.54406
..54410
.34993
.34996
.34999
.35003
9.54655
.54659
.54664
..54668
.35301
.35204
.35208
.35211
.35215
.35218
.35222
.35325
9.54912
.54916
.54920
.54924
.35409
.35413
.35416
.35430
9.55167
.55171
.55176
.55180
.35618
.35623
.35625
.35628
9.55421
.55425
.55430
.55434
.35837
.35831
.35834
.35838
.35841
.35845
.35848
.35852
+ 3'
13
14
15
9.54415
..54419
.54423
.54428
.35006
.35010
.35013
.35017
9.54672
..54677
..54681
. .54685
9.54929
.54933
.54937
.-54942
.35423
.35427
.35430
.35434
9.55184
.55188
.55192
.55197
9.55201
.55205
.55209
..5.5214
9.55218
..55222
.55226
..55231
.3.5633
.35635
.35639
.35643
.35646
.35649
.35653
.35656
..%5660
..^5663
.35667
.35670
9.55438
.55442
.5.5447
.5.5451
9. .554.55
.55459
.55463
.5.5468
+ i'
17
IS
19
9.54432
.54436
.54440
.54445
9.54449
.54453
.54458
..544G2
.35030
.35034
.35037
.35031
.35034"
.35038
.35041
.35044
9.54689
.54694
.54698
.54702
9.54707
.547 1 1
.54715
.54719
.35228
.35232
.35235
.;{5339
.35342
.35246
.:}5249
.35253
9.54946
.54950
.54954
.54959
9.54963
.-54967
.-54971
.-54976
.35437
.35441
.35444
.35448
.35451
.35454
.35458
.35461
.35855
.35859
.35863
.35865
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
2~1
20
19
18
17
+ 5'
21
22
23
9.55472
..55476
.55480
..55485
.35869
.35873
.35876
.35879
+ 6'
25
26
27-
9.54466
.54471
.54475
.54479
.35048
.35051
.35055
.35058
9.54724
.54728
.54732
.54736
.35256
.35260
.3.5263
.35267
.35370
.35274
.35277
.35381
.35384
.35388
.35391
.35394
.35398
.35301
.35305
.35308
9.-54980
.54984
.-54988
.54993
9.,54997
.55001
.55005
.55010
9.-5-5014
.55018
.55022
.55027
.35465
.35468
.35472
.35475
9. .5.5235
..5-5239
.55243
.-55248
9..5.52.52
..5.52.56
.55260
.55265
9..55269
.5.5273
..5.5277
..55282
9.5.5286
..55290
..5.5294
.5.5298
9.. 5.5303
.55307
..5.5311
.5.5315
.35674
.35677
.35681
.35684
9.55489 i .35883
.55493 : .35886
.5.5497 : .35890
.55501 i .35893
+ r
29
30
31
9.54483
.54488
.54492
.54496
.35062
.35065
.35069
.35073
9.54741
.54745
.54749
.54754
9.547.58
.54762
.54766
.54771
9.54775
.54779
.54784
.54788
.35479
.35482
.35486
.35489
.35493
.35496
.35500
.35503
.35688
.35691
.35695
.35698
.35702
.35705
.35709
.3.5712
9. .55.506 1 .35897
.55510 .35900
.55514 ; .35904
..5-5518 : .35907
9.5-5523 .35911
.55527 , .35914
.5,5.531 .35918
.55535 .35921
9.55539" .35925
.55.544 ; .35928
.55548 J .35933
.55552 ! .35935
+ 8'
33
34
35
9.54501
.54505
.54509
..54514
.35076
.35079
.35083
.35086
+
9'
37
39
9.54518
.54522
.54.526
.54531
.35090
.35093
.35097
.35100
9.5-5031 ; .35507
.55035! .35510
.55039 ! .35514
.55044 i .35517
9.-5-5048 .35521
.5.5052 . .35524
.5.5057 .35538
.5-5061 .35531
9.5-5065 .35534
.-5-5069 .35538
.-5-5074 .35541
.5-5078 .35545
.35716
.35719
.35733
.35736
.35730
.35733
.35737
.35740
.35743
.35747
.35750
.35754
.35757
.35761
.3.5764
.35768
.35771
,35775
.35778
.35783
.35785
.35789
.35793
.35796
+ 10'
41
42
43
9.-54535 1 .35103
.54539 ; .35107
.54544 : .35110
.54548 .35114
9.54552 1 .35in
.54556 .35121
.54561 .35124
.54565 .35128
9.54792
.54796
..54801
.54805
9.54809
..54813
.54818
..54822
9,.54826
..54831
.54835
.54839
.35313
.35315
.35319
.35.333
.35326
.35329
.3.5333
.3.5336
.35340
.35343
.35347
.35350
.35354
.35357
.35361
.35364
.35368
.35371
.35374
.35378
.35381
9..55.556
.55561
.55565
.55569
.35939
.35943
.35946
.35949
+ 11'
45
46
47
9..5.5320
.55324
.5.5328
.5.5332
9..5.5337
.55341
.5.5345
.55349
9. .5.5354
..55358
.55362
.55366
9..5.5573
..5.5.577
.5.5582
..55.586
9. .55.590
.55594
.55598
.55603
9.55607
.55611
..55615
.55620
9.55624
..5.5628
.55632
.55636
9.55641
.35953
.35956
.35960
.35963
.35967
.35970
.35974
.35977
.35981
.35984
.35988
.35991
.35995
.35998
.36003
.36005
.36009
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ 13'
49
50
51
9.54.569
.54574
.54578
.54582
9. .54.587
..54591
.54595
.54599
.35131
.35135
.35138
.35143
9.-5-5082
.-5.50S6
.5.5091
.5.5095
9..55099
..55103
.55108
.55112
.35548
.35552
.35555
.35559
.35563
.35566
.35569
.35573
+ 13'
53
54
55
.35145
.35149
.35153
.35156
9.54843
..54848
.54852
..54856
9..54860
.54865
..54869
.54873
9.-54878
+ 1*'
57
58
59
9.54604
.54608
.54612
.54617
.35159
.35162
.35166
_j35169
.35173
9.5.5116
..55120
..55125
.55129
9..55133
.35576
.35580
.35583
.35587
9.5.5370
.5.5375
.5.5379
.55383
+ 15'
9.54621
.35590
9.55387 i .35799
lf)h gm
1.9A Sm
ignym
79ft gm
19h5m
Page 870]
TABLE 45.
Haversines.
s
4h ,5,5m
73° 45'
4h afjm
74° 0'
4h 5~m 74° 15'
4^ 5S"i
74° 30'
4h 59m
74° 45'
3
I^g. Ilav.
Nat. Hav.
Ix>g. TIav.
Nat. Ilav.
Log. Ilav.' Nat. Ilav.
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Ilav.
1
2
3
9.55G41
.55645
.55649
.55653
.36009
.36012
.36016
.36019
9.55893
.55897
.55901
.55905
9.55909
.55914
.55918
.55922
,36318
.36333
.36335
.36239
9.56144
.56148
.56152
.56156
,36428
,36431
.36435
.36438
.36442
.36445
.36449
.36452
9.56393
.56397
.56402
,56406
9.56410
.56414
.56418
.56422
.36638
.36642
.36645
.36649
.36652
.36656
.36659
.36663
.36666
.36670
.36673
.36677
,36680
,36684
,36687
.36691
9.56642
.56646
.56650
.566.54
9.56658
.56663
.56667
.56671
9.56675
.56679
.56683
.56687
9.56692'
.56696
.56700
.56704
,36848
,36853
,36855
,36859
,36863
,36866
.36869
.36873
,36877
,36880
,36884
.36887
.36891
.36894
,36898
.36901
.36905
.36908
.36913
.36915
60
59
■5S
.57
'56 '
55
■54
5-i
~5j
51
50
49
4S
47
46
45
44
4-',
■u
40
■i'J
.Ifi
■iff
■15
!4
d-l
Jl
.10
J9
+ 1'
5
6
7
9.55657
.55662
.55666
.55670
.36033
.36036
.36030
.36033
.36636
.36040
.36043
.36047
.36333
.36336
.36239
.36343
9.56160
.56164
.56169
.56173
+ 3'
9
10
11
9,55674
,55678
.55683
.55687
9.55926
.55930
.55935
..55939
9.55943
.55947
.55951
.55955
9.55960
.5.5964
.55968
.55972
9.55976
.55981
.55985
.5.5989
.36246
.36250
.36253
.36257
9.56177
.56181
.56185
.56189
.36456
.36459
.36463
.36466
.36470
.36473
.36477
.36480
.36484
.36487
.36491
.36494
.36498
.36501
.36505
.3650.^
.36513
.36515
.3651;
.36523
,36536
.36539
.36i533
.36536
.36540
.36543
.36547
.36551
.36554
.36558
.36561
.36565
.36568
.36573
.36575
.36579
.36583
.36586
.36589
.36593
.36596
.36600
.36603
.36607
.36610
.36614
.36617
.36631
.36624
.36628
.36631
.36635
.36638'
9.56426
.56431
.56435
.56439
9.56443
.56447
.56451
.56456
9.56460
.56464
.56468
.56472
9'56476
.56480
.56485
.56489
9':.56493
.56497
.56501
.56505
9.56509
..56514
.56518
.56522
9. .56526
.56530
.56534
.56538
9^56543'
.56547
.56551
.56555
9.56559
.56563
.56567
.56572
9.56576"
.56580
.56584
.56588
9. .56592
.56596
.56601
.56605
9.56609
..56613
.56617
..56621
9.5662.5
.56630
.56634
.56638
9.56642
+ 3'
13
14
15
9,55691
,55695
,55699
,55704
.36050
.36054
.36057
.36061
,36260
,36864
.36367
,36371
.36274
.36278
.36281
.36285
.36388
.36393
.36395
.36399
.36302
.36306
.36309
.36313
.36316
.36330
.36333
.36337
.36330
.36334
.36337
.36341
.36344
.36348
.36351
.36355
.36358
.36363
.36365
.36368
9.56194
.56198
.56202
.56206
9.5B2IO
.56214
..56219
.56223
9.56227
.56231
.56235
.56239
'9.56244
.56248
.56252
.56256
9;56260
.56264
.56269
..56273
9;56'277
.56281
..56285
.56289
9.56294
..56298
.56302
.56306
+ 4'
17
IS
19
9.55708
.55712
,55716
,55721
.36064
.36068
.36071
.36075
.36078
-.36083
.36085
.36089
.36093
.36096
.36099
.36103
.36694
,36698
,36701
.36705
.36708
.36712
.36715
.36719
.36723
.36736
.36739
.36733
.36736
.36740
.36743
,36747
9.56708
.56712
.56716
..56720
+ 6'
21
22
23
9.55725
.55729
.55733
.55737
9.56725
.56729
.56733
.56737
9.56741
.56745
.56749
.56753
9.56758
.56762
.56766
.56770
.36919
.36923
.36936
.36929
.36933
.36936
.36940
.36943
.36947
.36950
.36954
.36957
+ 6'
25
26
27
9.55742
.55746
.55750
.55754
9.5.5993
..55997
.56001
.56006
9.56010
.56014
.56018
.56022
9.56027
.56031
.56035
.56039
9.56043
.56047
.56052
.56056
9.56060
.560<i4
.56068
..56073
9.56077
.56081
.56085
.56089
9.56093
..56098
.56102
.56106
+ r
29
30
SI
9.55758
.55763
.55767
.55771
.36106
.36110
.36113
.36117
+ 8'
ss
34
35
9.55775
.55779
.55784
.55788
.36130
.36134
.36137
.36131
.36134
.36138
.36141
.36145
.36148
.36153
.36155
.36159
,36750
,36754
.36757
.36761
9.56774
.56778
.56782
.56786
9..56791
.56795
.56799
.56803
'9.56807
.56811
.56815
.56819
.36961
,36964
,36968
,36971
ii8
27
26
25
'24
22
21
20
19
IS
n
16
15
14
13
12
11
10
9
+ V
37
38
39
9,55792
,55796
,55800
.55805
.36764
.36768
.36771
,36775
,36778
.36782
.36785
.36789
.36975
.36978
.36982
.36985
.36989
.36992
.36996
.36999
.37003
.37006
.37010
.37013
.37017
.37030
.37034
.37037
+ 10'
■41
42
43
9.55809
.55813
..55817
.55821
9.56310
.56314
.56318
.56323
+ 11'
45
46
47
9.55826
.55830
.55834
.55838
.36163
.36166
.36169
.36173
.36373
.36376
.36379
.36383
.36386
.36389
.36393
.36396
9.56327
.56331
.56335
.56339
9.56343
.56348
.56352
.56356
9. 56360
.56364
.56368
.56373
.36792
.36796
.36799
.36803
9.56824
.56828
.56832
.56836
+ 13'
49
50
51
9,55842
,55846
,55851
,55855
.36170
.36180
,36183
.36187
.36809
.36810
.36813
.36817
9.56840
.56844
.56848
.56852
+ 13'
53
54
55
9.55859
.55863
.55867
.55872
.36190
.36194
.36197
.36301
9.56110
.56114
.56118
.56123
.36400
.36403
,36407
,36410
.36820
.36824
.36827
.36831
9.56856
.56861
.56865
.56869
.37031
,37034
,37038
,37041
,37045
,37049
,37053
.37055
8
7
6
5
4
3
2
1
+ 14'
57
58
59
+ 15'
9,55876
,55880
.55884
.55888
9.55893
.36304
.36308
.36311
.36315
9.56127
.56131
.56135
.56139
'9.56144
.36414
.36417
.36421
,36424,
9.56377
.56381
.56385
.56389
.36834
,36838
,36841
,36845
9.56873
.56877
..56881
,.56885
,36318
,36428
9.56393
,36848
9.56889
.37069
19>
I 4m
19>>
,Sm
2f)h ^m
19l>
im
IQhOm
TABLE 45.
Haversines.
[Page 871
s
5* 0'"
75° 0'
5ft im 75° 15'
5ft «m
1S° 30'
5A sm 75° 45'
5h4m
76° 0'
s
Log. Uav.
Xat. Hav.
Log. Hav.
Xat. Hav.
Log. Hav,
N'at. Hav.
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Hav,
1
3
9.56889
..56893
.56898
.56902
.37039
.37063
.37066
.37070
.37073
.37077
.37080
.37084
.37087
.37091
.37094
.37098
.37101
.37105
.37108
.37112
.37115
.37119
.37123
.37126
.37129
.37133
.37136
.37140
.37143
.37147
.37150
.37154
9.57136
.57140
.57144
.57148
9.571.52
..57156
.57160
.57165
9,57169
.57173
.57177
..57181
9..57185"
.57189
..57193
.57197
9.57201
.57205
..57210
..57214
9.57218
.57222
.57226
.57230
9.57234
.57238
.57242
.57246
.37270
.37273
.37277
.37280
9.57381
.57385
.57389
.57393
.37481
.37485
.37488
.37492
9.57625
.57629
.57633
.57637
.37693
.37696
.37699
.37703
.37706
.37710
.37713
.37717
9,57868
.57872
.57876
.57881
9.57885
.57889
.57893
.57897
.37904
.37907
.37911
.37914
.37918
.37933
.37935
.37939
60
59
58
57
56
55
54
53
+ 1'
5
6
7
9.56906
.56910
.56914
.56918
.37284
.37287
.37291
.37395
.37298
.37303
.37305
.37309
9..57397
.57402
.57406
.57410
.37495
.37499
.37503
.37506
9.57642
.57646
.57650
.576-54
+ 2'
y
10
11
9.56922
.56926
..56931
.56935
9.57414
.57418
.57422
.57426
.37509
.37513
.37516
.37530
.37533'
.37537
.37530
.37534
9.576,58
.57662
.57666
.57670
9.57674
.57678
.57682
.57686
.37721
.37734
.37728
.37731
.37735
.37738
.37742
.37745
.37749
.37752
.37756
.37759
.37763
.37766
.37770
.37773
.37777
.37780
.37784
.37788
9.57901
.57905
.57909
.57913
.37932
.37936
.37939
.37943
.37946
.37950
.37953
.37957
52
51
50
49
48
47
46
45
+ 3'
13
14
15
9.56939
.56943
.56947
.56951
.37312
.37316
.37319
.37333
.37326
.37330
.37333
.37337
.37340
.37344
.37347
.37351
.37354
.37358
.37361
.37365
.37368
.37373
.37375
.37379
9.57430
.57434
.57438
.57442
9..57917
.57921
.57925
.57929
9.-57933
.57937
.57941
.57945
9.57949
, .57953
.57957
.57961
9.5796,5"
.57969
.57973
.57977
9.57981
.57086
.57990
.57994
9,57998
.58002
.58006
.-58010
'9.-580 14
.-58018
.58022
.58026
9.58030
.58034
.58038
.-58042
9.,58046
.58050
.58054
.58058
9.58062
.58066
.58070
.58074
9..58078"
.-58082
■-58086
.58090
9,58094
.58098
.-58102
..58106
9,581 jo'
+ i'
17
18
19
9.56955
.56959
.56963
.56968
9.56972
..56976
.56980
.56984
9.56988
.56992
.56996
.57000
9.57446
.574.50
.57454
.57459
9.57463
.57467
.57471
.57475
.37537
.37541
.37544
.37548
9.57690
.57694
.57698
.57702
.37960
.37964
.37967
.37971
.37974
.37978
.37982
.37985
.379891
.37993
.37996
.37999
.38003
.38006
.38010
.38013
.38017
.38030
.38034
.38037
.38031
.38034
.38038
.38042
.38045
.38049
.38052
.38056
.38059
.38063
.38066
.38070
.38073
.38077
.38080
.38084
.38087
.38091
.38095
.38098
.38102
.38105
.38109
.38112
.38116
44
43
42
41
40
39
38
37
36
35
34
S3
32
31
30
29
~28
27
26
25
24
23
22
21
20
19
18
17
16
13
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ 5'
21
22
23
.37551
.37555
.37558
.37563
.37566
.37569
.37573
.37576
9.57706
..57711
.57715
.57719
9.57723'
.57727
.57731
.57735
+ 6'
25
26
27
9.57479
.57483
.57487
.57491
9.57495
.57499
.57503
.57507
+ r
29
SO
31
9.57005
.57009
.57013
.57017
.37157
.37161
.37164
.37168
9.572.50
.57255
.572.59
.57263
.37580
.37583
.37587
.37590
9.-57739
.57743
.57747
.57751
.37791
.37794
.37798
.37802
.37805
.37809
.37812
.37816
.37819
.37833
.37836
.37830
.37833
.37837
.37840
.37844
.37847
.37851
.37855
.37858
.37863
.37865
.37869
.37872
.37876
.37879
.37883
.37886
.37890
.37893
.37897
.37900
.37904
+ 8'
33
34
35
9.57021
.57025
.57029
.57033
9.57037
.57042
.57046
.57050
.37171
.37175
.37179
.37182
.3718(8
.37189
.37193
.37196
.37200
.37203
.37207
.37210
9.57267
.57271
.57275
.57279
9.57283
.57287
.57291
..57295
9.57299
.57304
.57308
..57312
.37383
.37386
.37389
.37393
.37^7
.37400
.37404
.37407
9.57511
.57516
.57520
.57524
.37594
,37597
.37601
.37604
.37608
.37611
.37615
.37618
9.57755
.577-59
.57763
.57767
9.57771
.57775
.57779
.57783
9.57787
.57792
.57796
.57800
+ 9'
37
38
39
9.57528
.57532
.57536
.57540
+ W
41
42
43
9.57054
.57058
.57062
.57066
.37411
.37414
.37418
.37431
9.57544
.57548
.57552
.57556'
.37622
.37625
.37629
.37632
+ 11'
45
46
47
9.57070
.57074
.57078
.57083
.37214
.37217
.37221
.37224
9.57316
.57320
.57324
.57328
9.57332
.57336
.57340
.57344
9.57348
.57353
.57357
.57361
9.57365
.57369
.57373
.57377
.37435
.37428
.37432
.37435
.37439
.37443
.37446
.37449
.37453
.37456
.37460
.37463
9.57560
.57564
.57568
..57572
9.-57577
.57.581
• .57585
.57589
.37636
.37639
.37643
.37647
.37650
.37654
.37657
.37661
9.57804
.57808
.-57812
.57816
9.57820
.57824
.57828
.57832
9.57836
.57840
.57844
.57848
+ 12'
49
50
51
9.57087
.57091
.57095
.57099
.37228
.37231
.37235
.37238
+ 13'
53
54
55
9.57103
.57107
.57111
.57115
.37242
.37245
.37249
.37252
.37256"
.37259
.37263
.37266
9.57593
.57-597
.57601
.57605
.37664
.37668
.37671
.37675
+ 14'
57
58
59
9.57119
.57124
.57128
..57132
.37467
.37470
.37474
.37477
9.57609
.57613
.57617
.-57621
.37678
.37683
.37685
.37689
9.57852
.57856
.57860
.57864
+ 15'
9.57136
.37270
9..57381
.37481
9.57625
.37692
9.57868
i^ft
59m
18h 58m
18h
57m
iS*56m
181^ 55^
Page 872]
TABLE 45.
Haversines.
s
.5ft .5"> 76° 15'
3h em 76° 30'
.5ft 7m
16° 45'
oh sm ^^° (f
.5ft 9m 77° 15'
s
Ix)g. ITav.
Xat. Hav.
Log. Hav.
Nat. Iliv.
Log. llav.
Nat. Itav,
I/Og, Hav,
Xat. Hav.
Log, Hav,
Xat, Hav,
1
2
3
9..58110
..58114
..58118
..58122
.38116
.38119
.38133
.38136
9.58351
.58355
..58359
..58363
.38338
.38331
.38335
.38338
9.58591
..58595
..58.599
.58603
9., 58607
.58611
..58615
.,58619
.38540
.38544
.38547
.38551
9,, 58830
,,58834
.58838
.58842
.38753
.38756
.38760
.38763
9,,59068
,59072
,59076
,,59079
.38965
.38969
.38973
.38976
5!)
■'hS
.'>7
+ 1'
5
6
7
9.58126
..58131
..58135
..58139
.38130
.38133
.38137
.38140
9. .58367
..58371
.58375
.,58379
.38343
.38345
.38349
.38352
.38554
.38358
.38561
.38563
9.. 58846
.58850
.588.54
.588.58
.38767
.38770
.38774
.38777
9,. 59083
.59087
.,59091
.59095
.38979
.38983
.38986
.38990
55
54
53
+ 3'
9
10
11
9.. 58 143
.58147
.58151
..581.55
.38144
.38148
.38151
.38155
9.58383
..58387
.58391
.58395
.38356
.38360
.38363
.38367
9..58623
..58627
..58631
.,58635
.38568
.38572
.38575
.38579
9.58862
.,58866
.58870
,.58874
9,.58S78
..58,S82
..58885
..58889
.38781
.38784
.38788
.38791
9,59099
,59103
,59107
,59111
.38994
.38997
.39001
.39004
51
50
49
-i.s-
47
46
45
44
43
4i
41
40
39
iS
3/
+ 3'
13
14
15
9..581.59
..58163
..58167-
..58171
.38158
.38163
.38165
.38169
9.58399
.58403
..58407
..58411
.38370
.38374
.38377
.38381
9.. 58639
.,58643
.58647
.,58651
.38383
.38386
.38590
.38593
.38795
.38799
.38803
.38806
9, .59115
..59119
.59123
..59127
.39008
.39011
.39015
.39018
+ 4'
17
18
19
9..58175
..58179
.58183
..58187
.38173
.38176
.38179
.38183
9..58415
..58419
.58423
..58427
.38384
.38388
.38391
.38395
9..58655
.586,59
.58663
.58667
.38597
.38600
.38604
.38607
9.. 58893
,.58897
,.58901
..58905
.38809
.38813
.38816
.38830
9,59131
,59135
,,59139
,59143
.39033
.39035
.39039
.39033
+ S'
22
23
9.58191
..58195
.58199
..58203
.38186
.38190
.38193
.38197
9.. 58431
..58435
.58439
.58443
.38398
.38403
.38406
.38409
9.58671
.,58675
..58679
..58683
.38611
.38614
.38618
.38621
9., 58909
.,58913
,,58917
.,58921
.38823
.38827
.38830
.38834
9,,59147
..59151
.591.55
..591.58
.39036
.39040
.39043
.39047
+ 6'
26
27
9..58207
.58211
.58215
.58219
.38300
.38304
.38308
.38311
9.58447
..58451
..58455
..58459
9. .58463
..58467
.58471
.58475
.38413
.38416
.38430
.38433
.38437"
.38430
.38434
.38437
9.58687
..58691
..58695
.58699
.38635
.38638
.38633
.38636
9.58925
,,58929
..58933
.,58937
.38837
.38841
.38845
.38848
9,59162
,.59166
..59170
.59174
.39050
.39054
.39057
.39061
3fi
35
34
33
■11
10
.'9
+ r
30
31
9..58223
.58227
..58231
.58235
.38315
.38318
.38333
.38335
9., 58703
..58707
..58711
,.58715
.38639
.38643
.38646
.38650
9,58941
.58945
,.58949
,589.53
.38852
.38855
.38839
.38863
9, .59178
.,59182
.59186
.59190
.39064
.39068
.39073
.39075
+ 8'
^^
34
35
9.58239
..58243
.58247
.58251
.38339
.38333
.38336
.38339
9.58479
.58483
..58487
.58491
9.. 58495
.58499
.58503
.58.507
.38441
.38444
.38448
.38451
9..58719
.58723
.58727
..58731
.38653
.38657
.38660
.38664
9..58957
..58961
,.58965
,,58969
9,58973
,,58977
,,58981
,,58985
.38866
.38869
.38873
.38876
9.59194
.59198
.59202
.59206
.39079
.39083
.39086
.39089
'S
27
!G
.!5
'.'4
21
+ S'
38
39
9.582.55
.582.59
.58263
.58267
.38343
.38346
.38350
.38354
.38455
.38459
.38462
.38466
9. .58735
.58739
..58742
..58746
.38667
.38671
.38675
.38678
.38683
.38685
.38689
.38693
.38696
.38699
.38703
.38706
.38880
.38884
.38887
.38891
9,.59210
.59214
..59218
.59222
.39093
.39096
.39100
.39103
+ IC
42
43
9.58271
..58275
.58279
..58283
.38357
.38361
.38364
.38368
9. ,58511
.58515
.58519
..58523
.38469
.38473
.38476
.38480
9.. 58750
..58754
.58758
.58762
9.58766'
..58770
..58774
.,58778
9., 58782
.,58786
,58790
..58794
9,58989
,,58992
,58996
,59000
.38894
.38898
.38901
.38905
9,59225
,59229
,59233
,59237
.39107
.39111
.39114
.39118
21)
19
IS
17
+ 11'
•45
46
47
9..58287
..58291
.58295
..58299
.38371
.38275
.38378
.38383
9. .58527
..58531
..58535
.58.539
.38483
.38487
.38490
.38494
9,59004
.59008
„59012
,59016
.38908
.38913
.38913
.38919
9,59241
,59245
,.59249
.59253
.39131
.39125
.39128
.39132
16
15
14
13
+ 13'
50
51
9.58303
.58307
.58311
.58315
.38385
.38389
.38393
.38396
9., 58543
..58547
.58551
.58555
.38498
.38501'
.38503
.38508
.38710
.38713
.38717
.38721
9, ,59020
,.59024
..59028
.59032
.38933
.38926
.38930
.38933
9.59257
.59261
.59265
.59269
.39135
.39139
.39143
.39146
12
U
111
9
"'8
6
■')
'T
•J
1
II
+ 13'
54
55
9.58319
.58323
.58327
.58331
.38399
.38303
.S8307
.38310
9.58,559
.,58563
.58567
.58571
.38512
.38515
.38519
.38522
9..58798
.58802
.58806
.,58810
.38724
.38738
.38731
.38733
9.59036
.59040
.59044
.59048
.38937
.38940
.38944
.38947
9.59273
..59277
.59281
,59285
9:59289
,,59292
,59296
,59300
.39150
.39153
.39157
.39160
+ 14'
.57
58
59
9. .58335
.58339
.58343
.58347
.38314
.38317
.38321
.38334
9.58575
.58579
.58583
.58587
.38526
.38529
.38533
.38536
9.,58814
.,58818
.58822
.,58826
.38738
.38743
.38745
.38749
9.,59052
..59056
.59060
.59064
.38931
.38954
.38958
.38963
.39164
.39167
.39171
, .39174
+ 15'
9.58351
.38338
9.58.591
.38540
9,58830
.38752
9.59068
.38965
9,59304
.39178
ISh
54>"
181^
53">
ISh
5.""
18h
.'ipn
ISh
51 im
TABLE 45.
Haversines.
[Page 873
s
5h lom 77° 30'
oh lim
77° 45'
Sh 12m
78° 0'
oh ism 78° 15'
Shl4m
78° 30'
s
Log. Hav.
Nat. H,iv.
lx)g. TTav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav,
Nat. Hav.
Log. Hav.
Nat. Hav.
1
9.59304
..59308
.59312
..59316
.39178
.39183
.39185
.39189
9.59.540
..59544
.59.548
..59-552
.39391
.39395
.39398
.39403
9.59774
..59778
..59782
.59786
9..59790
..59794
..59798
.59802
.39604
.39608
.39613
.39615
.39619
.38622
.39626
.39639
9.60008
.60012
.60016
.60020
9.60023
.60027
.60031
.60035
.39818
.39831
.39825
..39839
.39833
.39836
.39839
..39843
9,60240
,60244
,60248
,60252
.40032
.40035
.40039
.40042
60
59
5S
•57
- 1'
■J
6
+ r
9
10
11
9..59320
..59324
.59328
.59332
.39193
.39196
.39199
.39203
.39306
.39210
.39214
.39217
9.59556
.59559
.59563
.59567
"9.59571
..59575
.,59579
.59583
9..59587
.59591
.59595
..59599
.39405
.39409
.39413
.39416
9.60256
,60260
,60263
,60267
.40046
.40049
.40053
.40057
.40060
.40064
.40067
.40071
06
55
54
oS
52
51
50
49
4S
47
46
45
44"
4S
42
■41
~40
■i9
■38
■i7
9.59336
.59340
.59344
.59348
.39430
.39433
..39427
.39430
.39434
.39437
..39441
.39444
.39448"
..39451
.39455
.39459
.39462
..39466
..39409
.39473
..39476
.39480
.39484
.39487
.,39491
.39494
.39498
..39501
9. .59806
.59809
..59813
..59817
.39633
.39636
.39640
.39644
9.60039
.60043
.60047
.60051
.39846
.39850
.39854
..39857
9.60271
,60275
.60279
,60283
9760287"
.60291
.60294
,60298
9.60302
,60306
,60310
.60314
+ 3'
l.i
14
15
9.59351
.59355
.59359
..59363
.39221
.39224
.39228
.39231
9.59821
.59825
.59829
.59833
9..59"837
..59841
..59845
.59848
9..59852"
..598,56
..59860
..59864
9.. 59868
..59872
.59876
..59880
9.59883
..59887
..59891
.59895
.39647
.39651
.39654
.39658
9.60054
.60058
.60062
.60066
9.60070"
.60074
.60078
.60082
.39861
..39884
.39868
.39871
.40074
.40078
.40081
.40085
.40089
.40092
.40096
.40099
+ i'
17
IS
19
9.59367
..59371
..59375
.59379
975938.3"
.59387
.59391
.59395
9:593S(9
.59403
.59406
..59410
.39235
.39238
.39242
.39245
.39249
.39253
.39256
..39260
.39263
.39267
.39270
.39274
.39277
.39281
.39285
.39288
9. .59602
.59606
..59610
.,59614
.39661
.39665
.39668
..39673
.39676
.39679
.39683
.39686
.39875
.39878
.39883
.39886
+ 5'
,'1
J-!
~+ 6'
25
K
•T
29
SO
SI
9..5961S
..59622
..59626
.59630
9.. 59634
.59638
..59642
..59646
9.59649
..59653
.,59657
..59661
9.60085
.60089
.60093
.60097
.39889
.39893
.39,896
.39900
9.60318
.60321
,60325
.60329
.40103
.40106
.40110
.40114
.39690
.39693
.39697
.39700
.39704
.39708
.39711
.39715
9,60101
,60105
,60109
.60113
9.60116
.60120
.60124
.60128
•39903
..39907
..39910
..39914
.39918
.39921
.39925
.39928
9,60333
,60337
,60341
,60345
"9.60348
,60352
,60356
,60360
9.60364
,60368
.60372
,60375
9,60379
,60383
.60387
,60391
.40117
.40131
.40134
.40138
.40131
.40135
.401.39
.40142
36
So
■U
■IS
'32
31
■iO
29
28
27
26
25
24
23
22
21
9..59414
..59418
.59422
.59426
4- 8'
.).J
24
So
9..59430
.59434
..59438
..59442
"9.59446
.594.50
.594.54
..594,58
.39292
.39295
.39299
.39302
.39306
.39309
.39313
.39317
9.59665
..59669
..59673
.59677
.39505
.39508
.39513
..39516
9.. 59899
..59903
.59907
.59911
9.59915
.59918
..59922
..59926
9.59930
.59934
..59938
..59942
9.. 59946
.599.50
.599.53
.59957
9.. 59961
..59965
.59969
.59973
"9., 5997 7
.,59981
.,59985
.59988
"9.. 59992
..59996
.(iOOOO
.60004
9.60008
..39718
.39732
..39725
.39729
.39732
..39736
..39739
.39743
.39746
.39750
.39754
..39757
9.60132
.60136
.60140
.60144
9,60147
.60151
.60155
.60159
.39932
.39935
.399.39
.39943
.39946
.39950
.39953
.39957
.40146
.40149
.40153
.40156
.40160
.40163
.40167
.40171
+ 9'
2S
29
9.,59681
.59685
.59688
..59692
.39519
..39533
..39536
.39530
..395.33
.39537
..39540
..39544
+ w
41
42
■'fi
+ 11'
45
if:
4:
9..59461
..59465
..59469
..59473
.39320
.39324
.39327
.39331
.39334
.39338
.39341
.39345
9..59696
..59700
.59704
..59708
9.60163
.60167
.60171
.60175
.39960
.39964
.39967
.39971
.39975
.39978
.39982
.39985
.39989
.39993
.39996
.40000
9,60395
,60399
,60402
,60406
.40174
.40178
.40181
.40185
.40188
.40193
.40196
.40199
.40303
.40206
.40310
.40313
20
!9
18
17
16
15
14
13
12
11
10
9
S
7
6
5
4
3
2
}
9..59477
..59481
..59485
.59489
9..59712
.59716
,.59720
..59724
.39548
.39551
..39.558
.39562
.39.565
..39569
..39573
.39761
..39765
.39768
..39773
.39775
..39779
.39783
..39786
.39789
.39793
..39796
.39800
9.60178
.60182
.60186
.60190
"9. 60194
.60198
.60202
.60206
9.60209
.60213
.60217
.60221
9,60410
.60414
.60418
,60422
9,60426
,60429
,60433
,60437
+ W
49
50
51
9.,59493
.59497
.59.501
.59,505
.39348
.39352
.39356
.39359
9.. 59728
,.59731
.,59735
.,59739
+ 13'
52
54-
,5,5
•)7
58
59
9..59.508
..59512
..59516
..59520
.39363
.39366
.39370
.39373
9,.59743
.,59747
.,59751
.,597,55
.39576
.39580
.39583
.39587
.39590
..39.594
.39597
..39601
.40003
.40007
.40010
.40014
9,60441
.60445
.60449
.60452
9,60456
.60460
.60464
.60468
.40317
.40330
.40334
.40338
.40331
.40335
.40338
.40343
.40245
9.-59.524
.59.528
..59532
.59536
.39377
.39380
.39384
.39388
.39391
9..597,59
..59763
.59767
.59770
..39803
.39807
..39811
..39814
.39818
9.60225
.60229
.60233
.60236
9.60240
.40017
.40031
.40034
.40038
+ 15'
9..59.540
9. .59774
.39604
.40033
9.60472
1SI>- 49">
ISk/fg™
ISh
47™
18h 46m
ISh
(.5m
Page 874]
TABLE 45.
Haversines.
s
5A ;,5m
78° 45'
r,h iGm 79° 0'
Sh nm 79° 15/
5h Ign 79° 30'
5h 19m 79° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat, Hav
Log. Hav.
Nat. Hav,
Log, Hav.
Nat. Hav,
Log, Hav,
Nat. Hav.
1
2
3
9.60472
.60476
.60479
.60483
.4034S
.40349
.40?53
.40356
9.60702
.60706
.60710
.60714
.40460
.40463
.40467
.40470
9.60931
,60935
,60939
,60943
.40674
.40677
.40681
.40685
.40688
.40693
.40695
.40699
.40703
.40706
.40710
.40713
.40717
.40730
.40734
.40737
9.61160
.61164
.61167
.61171
.40888
.40892
.40895
.40899
9.61387
.61391
.61395
.61399
.41103
.41106
.41110
.41114
60
59
58
57
56
55
54
53
+ 1'
5
6
7
9.60487
.60491
.60495
.60499
.40360
.40363
.40367
.40270
.40274
.40277
.40281
.40285
9.60717
.60721
.60725
.60729
9.60733
.60737
.60740
.60744
.40474
.40477
.40481
.40485
.40488
.40492
.40495
.40499
9,60947
.60951
.60954
.60958
9.60962
.60966
,60970
.60973
9.61175
.61179
.61183
.61186
.40903
.40906
.40910
.40913
9.61402
.61406
.61410
,61414
.41117
.41121
.41124
.41128
+ 3'
9
10
11
9.60502
.60506
.60510
.60514
9.61190
.61194
.61198
.61202
9,61205"
,61209
,61213
.61217
.40917
.40930
.40934
.40938
.40931
.40935
.40938
.40943
9.61417
.61421
.61425
.61429
.41131
.41135
.41139
.41142
.41146
.41149
.41153
.41156
5>
51
50
49
+ 3'
13
14
15
9.60518
.60522
.60526
.60529
.40388
.40393
.40395
.40399
9.60748
.60752
.60756
.60760
.40503
.40506
.40510
.40513
9,60977
.60981
.60985
.60989
9.61433
.61436
.61440
.61444
48
47
46
45
+ 4'
17
18
19
9.60533
.60537
.60541
.60545
.40303
.40306
.40310
.40313
9.60763
.60767
.60771
.60775
.40517
.40520
.40524
.40537
9.60992
.60996
.61000
.61004
.40731
.40735
.40738
.40742
.40745
.40749
10752
.40756
9.61221
.61224
.61228
,61232
.40945
.40949
.40953
.40956
9.61448
.61451
.614.55
.61459
.41160
.41164
.41167
.41171
44
43
42
41
+ S'
21
22
23
9.60549
.60552
.60556
.60560
9.60564
.60568
.60572
.60576
.40317
.40320
.40324
.40328
.40331
.40335
.40338
.40342
9.60779
.60783
.60786
.60790
.40531
.40535
.40538
.40543
9.61008
.61012
.61015
.61019
9,61236
.61240
.61243
.61247
.40960
.40963
.40967
.40970
9.61463
.61467
.61470
.61474
.41174
.41178
.41182
.41185
40
39
38
37
36
35
34
33
31
30
29
+ 6'
^5
26
27
9,60794
.60798
.60802
.60805
.40545
.40549
.40552
.40556
9.61023
.61027
.61031
.61034
9,61038
,61042
,61046
,61050
.40760
.40763
.40707
.40770
.40774
.40777
.40781
.40785
9.61251
.61255
.61258
.61262
9.61266
.61270
.61274
.61277
.40974
.40978
.40981
.40985
9,61478
.61482
.61485
.61489
.41189
.41192
.41196
.41199
.41203
.41307
.41310
.41314
+ r
29
SO
SI
9.60579
.60583
.60587
.60591
.40345
.40349
.40352
.40356
.40360
.40363
.40367
.40370
.40374
.40377
.40381
.40385
9.60809
.60813
.60817
.60821
.40560
.40563
.40567
.40570
.40988
.40992
.40996
.40999
9.61493
.61497
.61500
.61.504
+ 8'
33
34
35
9.60595
.60599
.60602
.60606
9.60825
.60828
.60832-
.60836
9.60840
.60844
.60847
.60851
.40574
.40577
.40581
.40585
9,61053
,61057
.01061
.61005
.40788
.40792
.40795
.40799
.40802
.40806
.40810
.40813
9.61281
.61285
.61289
.61293
.41003
.41006
.41010
.41013
9.61508
.01512
.61516
.61519
.41217
.41221
.41225
.41233
28
27
26
25
24
:>S
23
31
+ r
37
38
39
9.60610
.60614
.60618
.60622
.40588
.40593
;40595
.40599
9,61069
.61072
.61076
.61080
9.61296
.61300
.61304
.61308
.41017
.41031
.41034
.41038
9.61523
,61527
,61531
.61534
.41233
.41235
.41239
.41243
+ 10'
41
42
43
9.60625
.60629
.60633
.60637
.40388
.40393
.40395
.40399
.40402
.40406
.40410
.40413
9.60855
.60859
.60863
,60867
.40603
.40606
.40610
.40613
9.61084
.61088
.61091
.61095
.40817
.40820
.40824
.40837
9.61312
.61315
,61319
,61323
.41031
.41035
.41039
.41043
9,61538
.61542
.61546
.61549
.41246
.41250
.41253
.41257
20
19
18
n.
+ 11'
45
46
47
9.60641
.60645
.60648
.60652
9.60870
.60874
.60878
.60882
.40617
.40630
.40634
.40627
9.61099
.61103
.61107
.61110
.40831
.40835
.40838
.40843
9.61327
.61330
.61334
.61338
.41046
.41049
.41053
.41056
9.61553
.61557
.61561
.61565
.41260
.41364
.41367
.41371
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
+ 13'
49-
SO
51
9.60656
.60660
.60664
.60668
,40417
.40420
.40434
.40437
9.60886
.60890
.60893
.60897
.40631
.40635
.40638
.40642
9.61114
.61118
.61122
.01120
.40845
.40849
.40852
.40856
.40860
.40863
.40867
.40870
9.61342
.61346
.61349
.61353
.41060
.41063
.41067
.41071
9.61568
.61572
.61576
,61580
.41375
.41378
.41383
.41385
+ 13'
S3
54
55
9.60671
.60675
.60679
.60683
.40431
.40434
.40438
.40442
9.60901
.60905
.60909
.60912
.40645
.40649
.40653
.40656
9.61129
.61133
,61137
.61141
9.61357
.61361
.61364
,61368
.41074
.41078
.41083
.41085
9,61583
.61587
.61591
,61.595
.41289
.41293
.41296
.41300
+ U'
57
58
59
9.60687
.60691
.60694
.60698
.40445
.40449
.40453
.40456
9.60916
.60920
.60924
.60928
.40660
.40663
.40667
.40670
9,61145
,61148
.61152
.61156
.40874
.40878
.40881
.40885
9,61372
.61376
.61380
,61383
.41089
.41092
.41096
.41099
9.61598
.61602
.61606
.61610
9.61614
.41303
.41307
.41310
.41314
+ 15'
9.60702
.40460
9.60931
.40674
9.61160
.40888
9.61387
.41103
.41318
18h
U'n 18h
43"'
W>
f_>m
18^
41m
18h
40m
TABLE 45.
Haversines.
[Page 875
,.
5h 20m 80° O'
5h 21m 80° 15'
5ft ojm
80° 30'
Sh ism 80° 45'
5h24^
81° 0'
s
Log. Hav.
Nat, Hav,
Log, Hav,
Nat. Hav.
Log. Hav.
Nat, Hav
Log, Hav.
Nat. Hav,
Log, Hav.
Nat. Hav.
1
9.6IG14
.61017
.61(i21
.01625
9.61029
.61632
.61636
.61640
.11318
.41321
.41323
.41328
9,61839
.01843
.61846
.61850
.41533
.41536
.41540
.41543
9.62063
.62067
,62071
,62074
.41748
.41751
.41755
.41758
9.62287
.62290
.62294
,62298
.41963
.41966
.41970
.41974
.41977
.41981
.41984
.41988
.41992
.41995
.41999
.42002
.42006
.42010
.42013
.42017
.42020
.42024
.42027
.42031
.42035
.42038
.42042
.42045
.42049
.42053
.42056
.42060
9.62509
.62513
.62516
.62520
9.62524
.62,527
,62531
.62535
9.62.538
,62.542
,62546
.62.550
9.62.5.53
.62.557
.62.561
.62564
.42178
.42182
.42185
.42189
60
59
58
.57
!)
C
7
9
10
11
.41332
.41335
.41339
.41343
9.018.54
.618.58
.61801
.61865
.41547
.41550
.41554
.41558
.41561
.41565
.41568
.41572
9.62078
.62082
.02086
.»)2()S9
9.02093
.02097
.02100
,62104
.41762
.41766
.41769
.41773
.41776
.41780
.41783
.41787
9,62301
,62305
,62309
,623145
.42193
.42196
.42200
.42203
56
55
54
53
9.61044
.61047
.61051
,61655
.41346
.41350
.41353
.41357
9.61809
.61873
.61876
,61880
9.62316
.62320
.02324
.02327
.42207
.42211
.42214
.42218
.42221
.42225
.42229
.42232
.42236
.42239
.42243
.42247
.42250
.42254
.42257
.42261
52
51
50
49
48~
47
46
45
+ 3'
l.i
14
ir,
9.61659
.61662
.01606
.61670
.41361
.41364
.41368
.41371
9.01884
.01888
.01891
.01895
.41576
.41579
.41583
.41586
.41590
.41593
.41597
.41601
.41604
.41608
.41611
.41615
.41619
.41622
.41626
.41629
9,02108
,62112
,62115
,62119
9.62123
.62127
.62130
.62134
.41791
.41794
.41798
.41801
.41805
.41809
.41812
.41816
9.02331
.02335
.62338
.62342
9.62346
.623.50
.62353
.62357
9.62361
.62364
.62368
.62372
9.62376
.62379
,62383
,62387
+ *'
17
IK
19
9.61674
.01677
.61681
.01685
9701689"
.61692
.61696
.61700
.41375
.41378
.41382
.41386
.41389
.41393
.41396
.41400
9.61899
.61903
.01900
.61910
9.61914
,01917
,01921
.61925
9,62568
,62572
.62575
.62579
9.62583
,62586
,62590
.62594
44
43
42
41
40
39
38
■S7
36
35
.S4
33
32
31
30
29
+ 5'
21
.'-1 -■>
23
9.62138
,62141
,62145
,62149
.41819
.41823
.41827
.41830
.41834
.41837
.41841
.41844
+ 6'
2a
26
27
9.01704
.01708
.61711
.61715
.41404
.41407
.41411
.41414
9.01929
.01932
.01936
.01940
9,62153
,62156
,62160
-.62164
9.62598
.62601
.62605
.62609
9.62612
.62616
.62620
.62623
9.62627
.62631
.62634
.62638
.42264
.42268
.42272
.42275
.42279
.42282
.42286
.42290
+ r
29
■SO
31
+ 8'
■S3
34
•';.5
9.01719
.01723
.01720
.61730
.41418
.41421
.41425
.41429
9.61944
.01947
.61951
.619.55
9.619.59
.61962
.61966
.61970
.4163:1
.41636
.41640
.41644
.41647
.41651
.41654
.41658
.41662
.41665
.41669
.41672
.41676
.41679
.41683
.41687
.41690
.41694
.41697
.41701
.41705
.41708
.41712
.41715
.41719
.41722
.41726
.41730
.41733
.41737
.41740
.41744
.41748
9.62168
.62171
.62175
.62179
.41848
.41852
.41855
.41859
9,62390
.62394
.62398
.62402
.42063
.42067
.42071
.42074
9.01734
.61738
.01741
.01745
.41432
.41436
.41439
.41443
9.62182
.62186
.62190
.62194
9.62197
.02201
.62205
.62208
9.62212
.62216
.62220
.62223
9.62227
.62231
.62234
.62238
9.62242
.62246
.62249
.622.53
.41862
.41866
.41870
.41873
.41877
.41880
.41884
.41888
:41891
.41895
.41898
.41902
.41905
.41909
.41913
.41916
.41920
.41923
.41927
.41931
9.62405
.62409
.62413
.62416
9.62420
.62424
,62427
,62431
.42078
.42081
.42085
.42089
.42092
.42096
.42099
.42103
.42106
.42110
.42114
.42117
.42293
.42297
.42300
.42304
.42308
.42311
.42315
.42318
.42322
.42326
.42329
.42;J33
.42336
.42340
.42344
.42347
.423.51
.423.54
.42358
.42361
.42365
.42369
.43372
.42376
.42379
.42383
.42387
.42390
28
27
26
25
24
23
22
21
20
19
18
17
+ 9'
■S7
.SS
39
+ 10'
41
42
43
.<.5
46
47
9,01749
.017.53
.01756
.61760
9.61764
.61768
.61771
.61775
9.61779
.61783
.61786
.61790
.41447
.41450
.41454
.41457
.41461
.41464
.41468
.41472
9.01974
.01977
.01981
.01985
9.01989
.01992
.01996
.62000
9.62003
.62007
.62011
.62015
9.62018
.62022
.62026
.62030
9.02033
.02037
.02041
.02045
9.02048
,02052
.620.56
.62059
9.62642
.62646
.62649
.62653
9.62657
.62660
,62661
,62668
9.6267 1
.62675
.02679
.62682
9.62686
.62690
.62693
.62697
9.62701"
.62704
.62708
.62712
9,62435
,02439
,62442
,02446
.41475
.41479
.41482
.41486
9,624.50
.024,53
.62457
.02401
9,02464
,62468
,62472
,62476
.42121
.42124
.42128
.42132
.42135
.42139
.42142
.42146
16
15
14
13
12
11
10
9
8
7
6
5
4
3
. 2
1
+ 12'
49
,50
.',1
9.61794
.61798
.61801
.61805
.41490
.41493
.41497
.41500
+ 13',
.53
■54
.5.5
4- 14'
.57
■5S
■59
9.61809
.61813
.61816
.61820
9.61824
.61828
.61831
.61835
.41504
.41507
.41511
.41515
9.62257
.62261
.62264
.62268
9.62272'
.62275
,62279
,62283
9.62287
.41934
.41938
.41941
.41945
9,62479
,62483
,62487
,62490
.42150
.42153
.42157
.42160
.41518
.41522
.41525
.41529
.41949
.41952
.41956
.41959
9.62494
.62498
.62501
,62505
.42164
.42168
.42171
.42175
9.62716
,62719
,62723
,62727
+ 15'
9.61839
*. 41533
9.62063
.41963
9.62509
.42178
9.62730
.42394
ISli 39m
1«A SSm
18h srm
18^ 36m
18h 35^
Page 876]
TABLE 45.
Haversines.
s
Sh 2.5m 81° 15'
5h 26m
81° 30'
5^ 27">
81° 45'
5h :'8m
82° 0'
5h 29m 82° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
lx)g. Hav.
Xal.Hav.
Log. Hav.
Nat. Hav,
Log. Hav
Nat. Hav.
1
2
3
9.62730
.62734
.62738
.62741
.42394
.42397
.42401
.42405
9.62951
.62954
,62958
.62962
.42610
.42613
.42617
.42620
9.63170
.63174
.63177
.63181
.42825
.42829
.42833
.42836
9.63389
.63392
.63396
.63399
.43041
.43045
.43049
.43053
9.63606
.63610
.63013
.63617
.43257
.43261
.43365
.43368
60
69
+ _1'
5
6
7
9.62745
.62749
.62752
.62756
.42408
.42413
.42415
.42419
9.62965
.62969
.62973
.62976
.42624
.42628
.43631
.43635
9.63185
.63188
.63192
.63196
.42840
.42843
,42847
.42851
9.63403
.63407
.63410
.63414
.43056
.43059
.43063
.43067
9.63621
.63624
.63628
.63631
.43272
.43275
.43279
.43383
55
54
)-i
52
51
50
4!)
+ 3'
9
10
11
9.62760
.62763
.62767
.62771
.43423
.43426
.43430
.43433
9.62980
.62984
.62987
.62991
.42638
.43642
.43645
.43649
9.63199
.63203
.63207
.63210
9.63214
.63218
.63221
.63225
.42854
.42858
.42861
.42865
9.63418
.63421
.63425
.63429
.43070
.43074
.43077
.43081
9.63635
.63639
.63642
.63646
.43286
.43290
.43293
.43297
+ 3'
13
14
15
9.62774
.62778
.62782
.62785
.43437
.42441
.42444
.42448
9.62995
.62998
.63002
.63006
.42653
.42656
.42660
.42663
.43869
.42872
.43876
.42879
9.63432
.63436
.63439
.63443
.43085
.43088
.43093
.43095
9.63649
.63653
.63657
,63660
.43301
.43304
.43308
.43312
48
47
41^
45
+ 4'
17
18
19
9.62789
.62793
.62796
.62800
.42451
.42455"
.42459
.43402
9.63009
.63013
.63017
.63020
.42667
.42671
.43674
.42678
9.63228
.63232
.63236
.63239
.42883
.42887
.42890
.42894
9.63447
.63450
.63454
.63458
.43099
.43103
.43106
.43110
9,63604
,63068
.03671
,03675
.43315
.43319
.43323
.43326
■',4
43
-(-'
41
40
!9
■J8
01
of)
00
34
33
■Jl
■JO
29
+ «'
21
22
23
9.62804
.62808
.62811
.62815
.42466
.42469
.42473
.42477
9.63024
.63028
.63031
.63035
.43681
.42685
.42689
.42692
9.63243
.63247
.63250
.«3254
.42897
,42901
,43905
.43908
9.63461
.63465
.63468
.63472
.43113
.43117
.43121
.43124
9,63678
.63682
.63686
.63689
.43330
.43333
.43337
.43340
+ 6'
25
26
27
9.62819
.62822
.62826
.62830
.42480
.42484
.43487
.42491
9.63039
.63042
.63046
.63050
.42696
.42699
.42703
.43707
9.63258
.63261
.63265
.63269
.42912
.43915
.42919
.42923
9.63476
.63479
,63483
.63487
.43128
.43131
.43135
.43139
9.63693
.63696
.63700
.63704
.43344
.43348
.43351
.43355
+ ''
29
30
31
9.62833
.62837
.62841
.62844
.42494
.42498
,42502
.43505
9.63063
.63057
.63061
.63064
.42710
.42714
.42717
.42721
9.63272
.63276
.63279
.63283
.42926
.42930
.42933
.42937
9.63490
.03494
,63497
,63501
9.63505
.63508
.63512
.63516
.43142
.43146
.43149
.43153
9.63707
.63711
.63714
.63718
9.63722
.63725
.63729
.63733
.43358
.43363
.43366
.43369
+ 8'
33
34
35
9.62848
.62852
.62855
.62859
.42509
.43512
.42516
.42520
.43533
.42537
.43530
.42534
9.63068
.63071
.63075
.03079
.42725
.43728
.42732
.42735
9.63287
.63290
.63294
.63298
.43941
.43944
.42948
.42951
.43157
.43160
.43164
.43167
.43373
.43376
.43380
.43384
28
27
26
15
^24
23
22
21
+ r
37
38
39
9.62863
.62866
.62870
.62874
9.63082
.63086
.03090
.03093
9.63097
.63101
.63104
.63108
.42739
.42743
.42746
.42750
.43753
.43757
.42761
.43764
9.63301
.63305
.63309
.63312
.42955
.42959
.42962
.42966
9.63519
,63523
.63526
.63530
.43171
.43175
.43178
.43183
9.63736
.63740
.63743
.63747
.43387
.43391
.43394
.43398
+ W
41
42
43
9.62877
.62881
.62885
.62888
.42538
.42541
.42545
.42548
9.63316
.63320
.63323
.63327
.42969
.42973
.42977
.42980
9.63534
.63537
.63541
.63545
.43185
.43189
.43193
.43196
9.63751
.63754
.63758
.63761
,43402
.43405
.43409
.43412
20
19
IS
17
l.~,
14
13
+ 11'
45
46
47
9.62892
.62896
.62899
.62903
.43552
.42556
.42559
.42563
9.63112
.63115
.63119
.63123
.43768
.43771
.43775
.43779
9.63330
.63334
.63338
.63341
.42984
.42987
.42991
.42995
9.63548
.63552
.63555
.63559
.43300
.43303
.43207
.43311
9.63765
.63769
.63772
.63776
.43416
.43420
.43423
.43427
+ 13'
49
50
51
9.62907
.62910
.62914
.62918
.42566
.42570
.42574
.42577
9.63126
.63130
.63134
.63137
.43782
.43786
.42789
.42793
9.63345
.63349
.63352
.63356
.42998
.43002
.43005
.43009
9.63563
.63566
.63570
.63574
.43314
.43318
.43221
.43225
9.63779
.63783
.63787
.63790
.43430
.43434
.43438
.43441
12
11
10
9
+ 13'
53
54
55
9.62921
.62925
.62929
.62932
.42581
.42584
.42588
.42592
9.63141
.63145
.63148
.631.52
.42797
.42800
.42804
.42807
9.63360
.63363
.63367
.63370
.43013
.43016
.43020
.43023
9.63577
.63581
.63.584
.63588
.43229
.43232
.43236
.43239
9.03794
.63797
.03801
.63805
.43445
.43448
.43452
.43456
8
I
1!
■t
4
3
2
I
+ 1*'
57
68
59
9.62936
.62940
.62943
.02947
.43595
.43599
.42603
.42606
9.63156
.63159
.63163
.63166
.42811
.43815
.42818
.42823
9.63374
.63378
.63381
.63385
.43027
.43031
.43034
.43038
9.63592
.03595
.63599
.63602
.43343
.43347
.43350
.43354
9.63808
.63812
.63815
.63819
.43459
.43463
.43466
.43470
+ 15'
9.62951
.42610
9.63170
.43835
9.63389
.43041
9.63606
.43357
9.63823
.43474
;,s''>
34">-
18^
33m
m
S2m
18h
J /"I
ISh
JOf
TABLE
45.
[Page 877
Havers! lies.
s
5A .SOm 82° SC
5* 31'"
83° 45'
oh 32">
83° 0'
5h 33m 83° 15'
5ft 34m
83° 30'
s
Log. ilav.
Nat. Hav.
Log. 1 lav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Ilav.
Nat. Hav.
Log. Ilav.
Nat. Hav
9.63823
.43474
9.64038
.43690
9.64253
.43907
9.64467
.44133
9.64679
.44340
60
1
.63826
.43477
.64042
.43694
.64256
.43910
.64470
.44137
.64683
.44343
59
->
.63830
.43481
.64046
.43697
.64260
.43914
.64474
.44130
.64686
.44347
58
3
.63833
.43485
.43488
.64049
9.640.53
.43701
:43704
.64264
9.64267
.43917
.43931
.64477
.44134
.44138
.64690
9.64694
.44351
.44354
57
56
+ 1'
9.03837
9.64481
5
.63841
.43493
.64056
.43708
.64271
.43935
.04484
.44141
.64697
.44358
55
6
.63844
.43495
.64060
.43713
.04274
.43938
.04488
.44145
.64701
.44363
54
7
+ 2'
.63848
9.63851
.43499
.43503
.64063
9^64067
.43715
.43719
.64278
9.64281
.43933
.43935
.04492
9.64495
.44148
.44153
.64704
.44365
53
'52
9.64708
.44369
9
.638.5.5
.43506
.64071
.43733
.64285
.43939
.64499
.44156
.64711
.44373
51
10
.63859
.43510
.64074
.43736
.64289
.43943
.04502
.44159
.64715
.44376
50
11
.63862
.43513
.64078
.43730
.43733
.64292
.43946
.64506
9.64.509
.44163
.44166
.64718
9.64722
.44380
.44383
49
48
+ 3'
9.63866
.43517
9.6408 L
9.04296
.43950
IS
.63869
.43531
.64085
.43737
.64299
.43953
.64513
.44170
.64725
.44387
47
U
.63873
.43534
.64088
.43741
.64303
.43957
.64516
.44174
.64729
.44390
46
15
.63877
.43538
.43531
.64092
9.6409(f
.43744
.43748
.64306
9.64310
.43961
.43964
.04520
.44177
.44181
.64732
9.64736
.44394
.44398
45
44
+ i'
9.63880
9.64523
n
.63884
.43535
.64099
.43751
.04314
.43968
.64527
.44185
.64740
.44401
43
18
.63887
.43539
.64102
.43755
.04317
.43973
.64531
.44188
.64743
.44405
42
19
.63891
.43543
.43546
.64106
9.64110
.43759
.43763
.04321
9.04324
.43975
.43979
.04534
.44193
.44195
.64747
.44408
41
+ 5'
9.63895
9.04.538
9.64750
.44413
40
ei
.63898
.43549
.64113
.43766
.64328
.43983
.64541
.44199
.647.54
.44416
39
22
.63902
.43553
.64117
.43769
.64331
.43986
.64545
.44303
.64757
.44419
38
2-i
.63905
.43557
.43560
.64121
9.64124
.43773
.43777
.64335
9.64339
.43990
.43993
.64548
9.64552
.44308
.44310
.64761
9.04764
.44433
.44437
37
36
+ »'
9.63909
25
.63913
.43564
.64128
.43780
.64342
.43997
.64.555
.44313
.64768
.44430
35
26
.63916
.43567
.64131
.43784
.64340
.44000
.64559
.44317
.64771
.44434
34
27
.63920
.43571
.43575
.64135
9.64139
.43787
.04349
.44004
.44008
.04.503
9.64.566
.44331
.44334
.64775
9.64778
.44437
.4444:1
33
32
+ r
9.63923
.43791
9.643.53
29
.63927
.43578
.64142
.43795
.64356
.44011
.64570
.44338
.64782
.44445
31
30
.63931
.43583
.64146
.43798
.64360
.44015
.64573
.44331
.64785
.44448
30
31
.63934
.43585
.43589
.64149
"9.641.53
.43803
.43805
.64363
9.64367
.44018
.44033
.64577
"9T64580
.44335
.44339
.04789
9.64793
.44453
.44455
29
28
+ 8'
9.63938
33
.63941
.43593
.641.56
.43809
.64371
.44036
.64584
.44343
.64796
.44459
27
34
.63945
.43596
.64160
.43813
.64374
.44039
.64587
.44346
.64800
• .44463
26
35
.63949
.43600
.43603
.64164
9.64167
.43816
.43830
.64378
9.04381
.44033
.44036
.64591
9.64.594
.44350
.44353
.64803
9.64807
.44466
.44470
25
24
+ r
9.63952
37
.63956
.43607
.64171
.43834
.64385
.44040
.04.598
.44357
.64810
.44474
23
38
.63959
.43611
.64174
.43837
.64388
.44044
.04002
.44360
.64814
.44477
22
39
.63963
.43614
.64178
.43831
.64392
.44047
.04005
.44364
.64817
.44481
21
+ W
9.63966
.43618
9.64181
.43834
9.04396
.44051
9.64609
.44368
9.64821
.44484
20
41
.63970
.43633
.64185
.43838
.64399
.44055
.64012
.44371
.64824
.44488
19
42
.63974
.43635
.64189
.43843
.64403
.44058
.64616
.44375
.64828
.44493
18
43
.63977
.43639
.64192
.43845
:43849
.64406
9.64410
.44063
.64619
9.646"23"
.44378
.64831
.44495
.44499
17
16
+ 11'
9.63981
.43633
9.64196
.44065
.44383
9.64835
45
.63984
.43636
.64199
.43853
.04413
.44069
.64626
.44386
.64838
.44503
15
46
.63988
.43640
.64203
.43856
.04417
.44073
.64630
.44389
.64842
.44506
14
47
.63992
9.63995
.43643
.43647"
.64206
9.64210
.43860
.43863
.64420
9.64424
.44076
.64633
.44393
.44396'
.64845
9.64849
.44510
.44513
13
12
+ Vt'
.44080
9.64637
49
.63999
.13650
.64214
.43867
.64428
.44083
.64040
.44300
.64852
.44517
11
50
.64002
.43654
.64217
.43870
.64431
.44087
.64644
.44304
.64856
.44531
in
51
.64006
.43658
.43661
.64221
9.64224
.43874
.43878
.64435
9,64438
.44091
.44094
.64648
9.64651
.44307
.44311
.64860
9.648"63
.44534
.44538
9
8'
+ 13'
9.64010
53
.64013
.43665
.64228
.43881
.64442
.44098
.04655
.44315
.04807
.44531
7
54
.64017
.43668
.64231
.43885
.64445
.44101
.040.58
.44318
.04870
.44535
6
55
.64020
.43673
.64235
.43888
.43893
.64449
9.64452'
.44105
.44109
.04602
9^04005
.44333
.44335
.64874
.44539
.44543
5
4
+ 14'
9.64024
.43676
9.64239
9.64877
57
.64028
.43679
.64242
.43896
.64456
.44113
.04669
.44339
.64881
.44546
3
58
.64031
.43683
.64246
.43899
.64460
.44116
.64672
.44333
.64884
.44549
2
59
.64035
.43686
.43690
.64249
9.642.53
.43903
.43907
.64463
"9.64467
.44130
.44133
.64670
9.04679
.44336
.44340
.64888
9.64891
.44553
.44557
1
+ 15'
9.64038
18h
29^"
ISh 28m
18k
27m
18h
26m
18h.
2.5"!
Page 878]
TABLE
45.
Havbrsines.
-
s
5* 55™ 83° 45'
oft 36-m 84° 0' 1
oh Sim
84° 15'
oh 3S™ 84° 30' 1
5ft .39"' 84° 45' j
s
60
Log. Hav.j
Xat. Ilav.
Log. Ilav.
Sat. Ilav.
LoK. Ilav.
Nat. Ilav.
Log. Ilav.
Xat. Hav.
Log. Ilav.
Nat. Hav.
9.64891 1
.44557
9.65102
.44774
9.65312
.44991
9.65521
.45208
9.66729
.45425
1
.64895
.44560
.65106
.44777
.65316
.44994
.65525
.45311
.65733
.45429
59
o
.64898
.44564
.65109
.44781
.65319
.44998
.65528
.45315
.65736
.45432
5*'
s
.64902 :
9.64905
.44568
.44571
.65113
.44784
.44788
.65323
9.65326
.45001
.45005
.65532
.45319
.65740
9.65743
.45436
.45439
51
56
+ 1'
9.65116
9.65535
.45222
5
.64909
.44575
.65120
.44792
.65330
.45009
.65539
.45236
.65747
.45443
00
6
.64912
.44578
.65123
.44795
.65333
.45012
.65542
.45339
.65750
.45447
54
7
.64916
.44582
.65127 ,
.44799
.65337
.45016
.65546
.45333
.65754
.45450
.45454
5^
+ 3'
9.64919 1
.44586
9.65130
.44803
9.65340
.45020
9.65549
.45237
9.65757
9
.64923
.44589
.65134
.44806
.65344
.45023
.65553
.45240
.65761
.45458
51
10
.64926
.44593
.65137
.44810
.65347
.45027
.65556
.45344
.65764
.45461
50
11
.64930 i
9.64934
.44596
.65141
.44813
.65351
.45030
.65559
.45248
.65767
.45465
.45468
4S
+ 3'
.44600
9.65144
.44817
9.65364
.45034
9.65563
.45251
9.65771
13
.64937
.44604
.65148
.44821
.65358
.45038
.65566
.45335
.65774
.45472
-i '
U
.64941 !
.44607
.65151 j
.44824
.65361
.45041
.65570
.45358
.65778
.45476
46
15
.64944 1
9.64948^
.44611
.44614
.65155 1
9.65158
.44828
.65365
.45045
.65573
9.65577
.45362
.45366
.65781
.45479
45
44
+ 4'
.44831
9.65368
.45048
9.65785
.45483
11
.64951
.44618
.65162
.44835
.65372
.45052
.65580
.45369
.65788
.45486
43
IS
.64955
.44623
.65165
.44839
.65375
.45056
.65584
.45373
.65792
.45490
4-^
19
.64958
.44625
.65169
.44842
.65378
.45059
.65587
.45276
.65795
.45494
41
9.64962
.44629
9.65172
.44846
9.65382
.45063
9.65591
.45280
9.65799
.45497
40
n
.64965
.44633
.65176
.44850
.65385
.45067
.65594
.45384
.65802
.45501
39
n
.64969
.44636
.65179
.44853
.65389
.45070
.65598
.45287
.65806
.45505
oS
u
.64972
.44640
.65183
.44857
.65392
.45074
.45077
.65601
9.65605
.45391
.65809
9.65812
.45508
36
+ 6'
9.64976
.44643
9.65186
.44860
9.65396
.45295
.45513
^5
.64979
.44647
.65190
.44864
.65399
.45081
.65608
.45298
.65816
.45515
35
t6
.64983
.44651
.65193
.44868
.65403
.45085
.65612
.45302
.65819
.45519
34
21
.64986
9.64990
.44654
.44658
.65197
9.65200
.44871
.44875
.65406
.45088
.65615
.45305
.65823
.45523
.45526
33
+ 7'
9.65410
.45092
9.65619
.45309
9.65826
29
.64993
.44661
.65204
.44878
.65413
.45096
.65622
.45313
.65830
.45530
31
SO
.64997
.44665
.65207
.44882
.65417
.45099
.65625
.45316
.65833
.45534
3(1
SI
.65000
.44669
.44672
.65211
9.65214
.44886
.65421
9.65424"
.45103
.45106
.65629
.45320
.65837
.45537
29
+ 8'
9.65004
.44889
9.65632
.45324
9.65840
.45541
_'.S'
55
.65007
.44676
.65218
.44893
.6.5427
.45110
.65636
.45327
.65844
.45544
21
54
.65011
.44680
.65221
.44897
.65431
.45114
.65639
.45331
.65847
.45548
26
55
.65014
.44683
.65225
.44900
.44904
.65434
9^65438"
.45117
.45121
.65643
9.65646
.45334
.65850
.45552
.45555
25
34
+ 9'
9.65018
.44687
9.65228
.45338
9.65854
57
.65021
.44690
.65232
.44907
.65441
.45124
.65650
.45342
.65857
.45559
23
38
.65025
.44694
.65235
.44911
.65445
.45128
.65653
.45345
.65861
.45563
> >
S9
.65028
.44698
.65239
.44915
.65448
.45132
.65657
.45349
.65864
9.65868
.45566
.45570
31 .
20
+ W
9.65032
.44701
9.65242
.44918
9.65452
.45135
9.65660
.45353
41
.65035
.44705
.65246
.44922
.6.5455
.45139
.65664
.45356
.65871
.45573
19
42
.65039
.44708
.65249
.44925
.6.5459
.45143
.65667
.45360
.65875
.45577
IS
4S
.65043
.44712
.65253
.44929
.44933
.65462
.45146
.65671
.45363
.65878
.45581
.45584
11
Hi
+ 11'
9.65046
.44716
9.65256
9.65466
.45150
9.6.5674
.45367
9.65881
■45
.65050
.44719
.65260
.44936
.65469
.45153
.65677
.45371
.65885
.45588
15
46
.65053
.44723
.65263
.44940
.65473
.45157
.65681
.45374
.65888
.45592
14
41
.65057
.44727
.65267
.44944
.44947
.65476
.45161
.65684
.45378
.65892
.45595
13
+ 13'
9.65060
.44730
9.65270
9.65480
.45164
9.65688
.45381
9.65895
.45599
13
49
.65064
.44734
.65274
.44951
.65483
.45168
.65691
.45385
.65899
.45602
11
50
.65067
.44737
.65277
.44954
.65486
i .45172
.65695.
.45389
.65902
.45606
10
51
.65071
.44741
.65281
.44958
.65490
.45175
.65698
.45392
.65906
.45610
9
+ 13'
9.65074
.44745
9.65284
.44962
9.65493
.45179
9.65702
.45396
9.65909
.45613
*'
55
.65078
.44748
.65288
.44965
,6.5497
.45182
.65705
.45400
.65913
.45617
/
54
.65081
.44752
.65291
.44969
.65500
.15186
.65709
.45403
.65916
.45620
6-
55
.65085
.44755
.65295
.44973
.65504
.45190
.65712
.45407
.65919
.45624
5
4
+ 14'
9.65088
.44759
9.65298
.44976
9.65507
.45193
9.65716
.45410
9.65923
.45628
57
.65092
.44763
.65302
.44980
.65511
.45197
.65719
1 .45414
.65926
.45631
3
58
.65095
.44766
.65305
.44983
.65514
.45200
.65722
.45418
.65930
.45635
2
59
.65099
.44770
.65309
.44987
.44991
.65518
.45204
.65726
.45421
.65933
.45639
.45642
1
+ IS'
9.65102
.44774
9.65312
9.65521
I .45208
9.65729
.45425
9.65937
75ft
24m
ISli
23m
ISh
22m
ISh 21m
ISh 2Qm
TABLE 45.
Haversines.
[Page 879
s
5h4ii^»5°V
.5A 4im
85° 15'
,;A j^m
85° 30'
5h 4jm
85° 45'
5h44m
86° 0'
s
Log. Hav,
Nat. llav.
L/Og. Hav.
Nat. Ilav.
Log. Hav.
Nat. llav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
"s
9.65937
.65940
.65944
.65947
.45642
.4d646
.45649
.45653
9.66143
.66146
.661.50
.66153
.45860
.45863
.45867
.45870
9.66348
.66352
.66355
.663-59
.46077
.46081
.46084
.46088
9.66.5.53
.66.556
.66560
.66563
9.66567
.66570
,66573
.66577
9.66580
.66584
.66587
.66590
9.66594
.66-597
.66601
.66604
.46295
.46398
.46303
.46305
.46309
.46313
.46316
.46330
.46334
.46337
.46331
.46334
.46338
.46343
.46345
.46349
.46353
.46356
.46360
.46363
9.66757
.66760
.66763
.66767
.46512
.46516
.46519
.46533
60
59
S8
67
56
55
54
S3
+ 1'
5
6
7
9.659-50
.65954
.65957
.65961
.45657
.45660
.45664
.45668
.45671
.45675
.45678
.45683
9.661-57
.66160
.66164
.66167
.45874
.45878
.45881
.45885
9.66362
.66366
.66369
.66372
.46092
.46095
.46099
.46102
.46106
.46110
.46113
.46117
.46121
.46124
.46138
.46131
9.66770
.66774
.66777
.66780
.46537
.46530
.46534
.46538
+ V
9
10
11
9.65964
.65968
.65971
.65975
9.66170
.66174
.66177
.66181
9.66184
.66188
.66191
.66194
9.66198
.66201
.66205
.66208
9.66212
.66215
.66218
.66222
9.66225"
.66229
.66232
.66236
.45889
.45892
.45896
.45899
.45903
.45907
.45910
.45914
.45918
.45921
.45925
.45928
.45933
.45936
.45939
.45943
.45947
.45950
.45954
.45957
9.66376
.66379
.66383
.66386
9.66389
.66393
.66396
.66400
9.66784
.66787
.66791
.66794
9.66797
.66801
.66804
.66807
9.66811
.66814
.66818
.66821
9^66824"
.66828
.66831
.66835
9.66838
.66841
.66845
,668(8
9,6685 i
,668.55
,66858
.66862
9.66865
.66868
.66872
.66875
9.6687S
.66SS2
.66SS5
.66S,S9
9.66892
.66895
.66899
.66902
9 6690.5
.66909
.66912
.66916
»:66919
,66922
,66926
.66929
9.66932"
.66936
.66939
.66943
.46541
.46545
.46548
.46553
52
51
50
49
48
47
46
45
+ 3'
13
14
15
9.65978
.65981
.65985
.65988
.45686
.45689
.45693
.45697
.46556
.46559
.46563
.46567
+ 4'
n
18
19
+ 5'"
21
22
23
+ 6'
25
26
27
9.65992
.65995
.65999
.66002
.45700
.45704
.45707
.45711
9.66403
.66407
.66410
.66413
9.66417
.66420
.66424
.66427
9.66430
.66434
.66437
.66441
9.66444
.66447
.66451
.66454
9.664.58
.66461
.66464
.66468
9. 664717
.66475
.66478
.66482
9.66485
.66488
.66492
.66495
9^66499
,66.502
.66505
.66-509
.46135
.46139
.46142
.46146
9.66607
.66611
.66614
.66618
.46570
.46574
.46577
.46581
.46585
.46588
.46593
.46596
.46599
.46603
.46606
.46610
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
IS
17
IT
15
14
13
12
11
10
.9
8
7
6
5
T
3
2
1
9.66006
.66009
.66012
.66016
9.66019
.66023
.66026
.66030
9.66033
.66037
.66040
.66043
.45715
.45718
.45723
.45726
.45729
.45733
.45736
.45740
■.45744
.45747
.45751
.45755
.46150
.46153
.46157
.46161
.46164
.46168
.46171
.46175
9.66621
.66624
.66628
.66631
.46367
.46371
.46374
.46378
9.66635
.66638
.66641
.66645
9.66648"
.666,52
.66655
.666-58
9.66662"
.66665
.66669
.66672
9.66(575
.66679
.66682
.66685
9.66689
.66692
.6669()
.66699
9.66702
.66706
.66709
.66713
9.66716
.66719
.66723
.66726
9.66730
.66733
.66736
.66740
9;66"743"
.66747
.66750
.66753
.46383
.46385
.46389
.46392
.46396
.46400
.46403
.46407
+ r
29
so
SI
9.66239
.66242
.66246
.66249
9.662.53
.66256
.66260
.66263
9.66266
.66270
.66273
.66277
9.66280
.66284
.66287
.66290
9.66294
.66297
,6(i301
.66304
9.66307
.66311
.66314
.66318
9.66321
.66325
.66328
.66331
9;6(i335
.66338
.66342
.66.345
9.66348
.45961
.45965
.45968
.45972
.45976
.45979
.45983
.45986
.45990
.45994
.45997
.46001
.46005
.46008
.46013
.46015
.46019
.46033
.46036
.46030
Amu
.46037
.46041
.46044
.46048
.46052
.46055
.46059
.46063
.46066
.46070
.46073
.46179
.46183
.46186
.46189
.46193
.46197
.46300
.46304
.46308
.46311
.46315
.46318
.46233
.46226
.46229
.46233
.46237
.46240
.46344
.46247
.46351
.46355
.46358
.46363
.46366
.46369
.46373
.46276
.46614
.46617
.46631
.46635
+ 8'
S3
S4
35
9.66047
.66050
.660.54
.66057
.45758
.45762
.45765
.45769
.45773
.45776
.45780
.45783
.46411
.46414
.46418
.46421
.46435
.46439
.46433
.46436
.46440
.46443
.46447
.46431
.464.54
.46458
.46461
.46465
.46469
.46472
.46476
.46480
.46483
.46487
.46490
.46494
.46628
.46632
.46636
.46639
.46643
.46646
.46&50
.46654
.46657
.46661
.46665
.46668
.46672
.46675
.46679
.46683
.46686
.46690
.46694
.46697
.46701
.46704
.46708
.46712
.46715
.46719
.46733
.46736
+ 9'
37
38
39
+ 10'
41
42
43
+ n'
45
46
47
+ 13'
49
SO
SI
9.66061
.66064
.66067
.66071
9.66074
.66078
.66081
.66085
9.66088^
.66092
.66095
.66098
9.66102
.66105
.66109
.66112
.45787
.45791
.45794
.45798
:45802
.45805
.45809
.45812
.45816
.45820
.45823
.45837
9.66512
.66516
.66.519
.66522
9.66.526
.66529
.66-533
.66536
9.66539
.66.543
.66-546
.66-550
+ 13'
S3
54
55
9.66116
.66119
.66122
.66126
9.66129
.66133
.66136
.66140
.45831
.45834
.45838
.45841
.45845
.45849
.45852
.45856
+ 14'
57
58
59
.46380
.46284
.46287
.46291
.46295
.46498
.46501
.46505
.46509
9.66946
.66949
.66953
.66956
+ 15'
9.66143
.45860
.46077
9.66.5.53
9.66757
.46512
9.66959
.46730
1ST>-
19m
18h 18m
18^
/7m
Igh 16m
ISJi ISm
Page 880]
TABLE
45.
Haversines.
s
5h 43m
86° 15'
5h 4^tn
86° 30'
5h 47m
86° 15'
Sh 4Sm
87° 0'
Sh 4<)m
87° 15'
s
Ijog. Hav.
Xat. Uav.
Log. Uav.
Xat. Hav.
Log. Hav.
Xat. Hav.
Log. Uav.
Xat. Hav.
Log. Hav.
Nat. Hav.
9.66959
.46730
9.67161
.46948
9.67362
.47165
9.67562
.17383
9.67762
.47601
60
1
.66963
.46733
.67165
.46951
.67366
.47169
.67566
.17387
.67705
.17605
59
2
.66966
.46737
.67168
.46955
.67369
.47173
.67569
.17390 .67768
.17391 .67772
.47608 08 1
3
.66970
.46741
.46744
.67171
9.67175
.46958
.67372
.47176
.47180
.67572
.47613
.47616
57
+ 1'
9.66973
.46963
9.67376
9.67576
.17398
9.67775
5
.66976
.46748
.67178
.46966
.67379
.47184
.67579
.17101
.67778
.47619
55
6
.66980
.46753
.67181
.46969
.67382
.47187
.67582
.17405
.67782
.47633
54
t
.66983
.46755
.46759
.67185
9.67188"
.46973
.46977
.67386
9.67389"
.47191
.47194
.67580
9.'6"7589
.47409
.47412
.67785
9.67788
.47637
.47630
5f
+ 3'
9.66986
9
.66990
.46763
.67192
.46980
.67392
.47198
.67592
.17116
.67792
.47634
51
10
.66993
.46766
.67195
.46984
.67396
.47302
.67596
.17120
.67795
.47637
50
11
.66997
.46770
.46773
.67198
9.67202
.46987
.46991
.67399
.47305
.47309
.07599
9.07002
.47423
.47137
.67798
.47641
.47645
49
48
+ 3'
9.67000
9.67402
9.67801
13
.67003
.46777
.67205
.46995
.67406
.17313
.67006
.17430
.67805
.47648
47
14
.67007
.46781
.67208
.46998
.67409
.17216
.67609
.17134
.67808
.47653
46
15
.67010
.46784
.67212
9.67215
.47003
.67412
9.67410
.17330
.17223
.67612
9.07010
.47438
.17441
.67811
.47656
.47659
45
+ 4'
9.67013
.46788
.47006
9.67815
n
.67017
.46793
.67218
.47009
.67419
.17337
.07019
.47445
.67818
.47663
43
IS
.67020
.46795
.67222
.47013
.67422
.47331
.67622
.47449
.67821
.47666
4i
19
.67023
.46799
.67225
.47017
.47030
.67426
.47334
.67620
9^07629"
.47152
.67825
.17670
.47674
41
'40
+ 5'
9.67027
.46803
9.67228
9.67429
.47338
.47456
9.07828
21
.67030
.46806
.67232
.47034
.67432
.47343
.67632
.47459
.07831
.17677
39
22
.67034
.46810
.67235
.47037
.67436
.47345
.07036
.47463
.07835
.17681
38
23
.67037
.46813
.67238
9.67242
.47031
.47035
.67439
.17219
.67639
.17467
.07838
.17685
.17688
37
36
+ 6'
9.67040
.46817
9.67443
.17252
9.67042
.17470
9.67841
25
.67044
.46831
.67245
.17038
.67446
.17256
.67646
.17174
.67844
.17692
35
26
.67047
.46834
.67249
.17043
.67449
.17260
.67649
.17178
.67848
Ann
34
27
.67050
.46838
.67252
.17016
.47049
.67452
.17263
.17367
.67652
.17181
.6785]
.17699
.17703
33
32
+ r
9.67054
.46831
9.67255
9.67456
9.67656
.17185
9.-67854
29
.67057
.46835
.672.59
.47053
.67459
.17371
.670.59
.17489
.678.58
.17706
31
SO
.67060
.46839
.67262
.17056
.67462
.17274
.07662
.47493
.07801
.17710
30
31
.67064
"9.67067
.46843
,67265
9.67269
.17060
.67466
9.67469
.47278
.47282
.67666
9.67069
.47496
.17499
.67864
9.6'7808
.17714
.17717
29
28
+ 8'
.46846
.17064
33
.67071
.46850
.67272
.47067
.07472
.47285
.67672
.47503
.07871
.17721
27
34
.67074
.46853
.67275
.47071
.07470
.47289
.67675
.47507
.07874
.47735
26
35
.67077
.46857
.67279
.47075
.07479
9.67483
.47393
.47396
.67679
.47510
.07878
.47738
.17732
25
24
+ 9'
9.67081
.46860
9.67282
.47078
9.67682
.17511
9.07881
^7
.67084
.46864
.67285
.47083
.67486
.47300
.67685
.17518
.67884
.17735
23
3S
.67087
.46868
.67289
.47086
.67489
.47303
.67689
.17531
.67887
.17739
22
39
.67091
.46871
.67292
.47089
.67493
.17307
.67692
.17535
.67891
.17713
.47746
2~1
20
+ W
9.67094
.46875
9.67295
.47093
9.67496
.17311
9.67695
.47538
9.67894
41
.67097
.46879
.67299
.17096
.67499
.17311
.67699
.17533
.67897
.47750
19
42 .
.67101
.46883
.67302
.17100
.67.503
.17318
.67702
.17536
.67901
.47754
IS
43
.67104
.46886
.46890
.67305
.17104
.67506
.17321
.17325
.67705
""9.67709
.47539
.67904
.47757
.47761
17
16
+ 11'
9.67108
9.67309
.47107
9.67509
.47543
9.07907
45
.67111
.46893
.67312
.47111
.67512
.17329
.67712
.47547
.07911
.47765
15
46
.67114
.46897
.67315
.47115
.67516
.17332
.67715
.17550
.67914
.47768
14
47
.67118
.46900
.67319
9.67322
.47118
.47133
.67519
"9.67522
.17336
.47340
.67719
9.67722
.47554
.67917
.47772
.47775
13
12
+ 12'
9.67121
.46904
.17558
9.67920
49
.67124
.46908
.67326
.17135
.67526
.47343
.67725
.17561
.67924
.47779
11
50
.67128
.46911
.67329
.47139
.67529
.17347
.67729
.17565
.67927
.47783
10
51
.67131
.46915
.67332
9.67336
.47123
.67532
.47351
.67732
.17568
.17573
.67930
.47786
.47790
9
" 8
+ 13'
9.67134
.46919
.47136
9.67530
.47;t51
9.07735
9.67934
53
.67138
.46933
.67339
.17110
.67539
.47358
.07738
.17576
.67937
.47794
1
54
.67141
.46936
.67342
.17111
.67.542
.47361
.67742
.17579
.67940
.47797
6
55
+ 14'
.67145
.46939
.46933
.67346
.17117
.17151
.67546
.47365
.47369
.07745
"9.07748
.17583
.67944
"9.67947
.47801
.47805
5
4
9.67148
9.67349
9.67549
.47587
57
.67151
.46937
.67352
.17155
.67552
.47372
.07752
.47590
.67950
.47808
3
58
.67155
.46940
.67356
.47158
.67556
.47376
.07755
.47594
.679.53
.47812
2
59
.67158
.46944
.67359
9.67362
.47163
.67559
.47380
.47383
.67758
.47597
.67957
9.67960
.47815
1
+ 15'
9.67161
.16948
.17165
9.67.562
9.67762
.47601
.17819
lS>i
14m
ISh
lo'll
ISft
1,'">
ISh
ll>"
AS'ft
mm
TABLE 45.
Haversines.
[Page 881
s
5a 50" 87° 3r
5h Sim 87° 45'
5* 52m
88° 0'
5h 53m
88° 15'
5^54™
88° 30'
s
Log. Hav
Xat. Hav
Log. Hav
Nat. Hav
Log. Hav.
Nat. Hav
Log. Hav
Nat. Hav
Log. Hav.
Nat. Hav
1
2
S
+ 1'
5
6
9.67960
.67963
.67907
.67970
.47S19
.47823
.47826
.47830
.47834
.47837
.47841
.47844
.47848
.47852
.47855
.47859
9.68158
.68161
.68104
.68167
9.68171
.68174
.68177
.68181
9.08184
.68187
.68190
.68194
.48937
.48041
.48044
.48048
.48052
.48055
.48059
.48062
.48066
.48070
.48073
.48077
.48081
.48084
.48088
.48092
.48095
.48099
.48103
.48106
.48110
.48113
.48117
.48121
.48124
.48128
.48131
.48135
.48139
.48142
.48146
.48150
9.08354
.08358
.68361
.68364
"9.68367"
.68371
.68374
.68377
9.08380
.08384
.08387
.08390
9.68393
.68397
.68400
.68403
9.68407
.08410
.68413
.68416
9.08420"
.08423
.6842(1
.68429
9.68433
.68436
.68439
.68442
9.08446
.08449
.684.52
.68456
9.68459
.68462
.68465
.68469
9.68472
.68475
.68478
.08482
9.08485
.08488
.08491
.68495
9.08498
.08.501
.08.504
.68.508
9.68511
.68514
.68517
.68.521
9.68.524
.08527
.08.531
.68534
9.68.537
.68540
.08.544
.08.547
9.08550"
.48255
.48359
.48362
.48366
.48369
.48373
.48377
.48280
".48284
.48288
.48391
.48395
9.085.50
.08553
.68557
.68560
9.68563
.68506
.68570
.68573
.48473
.48477
.48480
.48484
.48488
.48491
.48493
.48499
.4850^
.48506
.48509
.48513
.48517
.48530
.48524
.48538
9.68745
.68748
.68751
.68755
9.68758
.68761
.68764
.68768
9.68771
.68774
.68777
.68781
9.08784
.08787
.08790
.08794
9.08797
.08800
.08803
.08806
"9.68810
.68813
.68816
.68820
9.08823
.08826
.08829
.68832
.48691
.48695
.48698
.48703
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
9.67973
.67977
.67980
.67983
.48706
.48709
.48713
.48717
.48730
.48724
.48728
.48731
:48735
.48738
.48742
.48746
+ 2'
9
10
11
+ 3'
13
14
15
9.67986
.67990
.67993
.67996
9.68576
.08579
.08.583
.08580
9.68589
.68.592
.68596
.68599
9.68000
.68003
.68006
.68010
.47863
.47866
.47870
.47874
"V47877
.47881
.47884
.47888
.47893
.47895
.47899
.47903
9.68197
.68200
.68204
.68207
.48399
.48303
.48306
.48310
.48313
.48317
.48320
.48324
.48328
.48331
.4*j:«
.48339
.48342
.48346
.48350
.48353
+ 4'
17
/*■
"+ 5'
9.68013
.68016
.68019
.68023
9.68026
.68029
.68033
.08036
9.68210
.68213
.08217
.68220
9.68223
.08227
.08230
,68233
9.68236"
.08240
.08243
.08240
9.08249
.68253
.68256
.682.59
9.68002
.08605
.68609
.08012
9.08615
.68618
.68622
.68625
9:68628'
.68631
.08035
.08038
.48531
.48535
.48538
.48542
.48546
.48549
.48553
.48557
.48560
.48564
.«8568
.48571
.48749
.48753
.48757
.48760
.48764
.48767
.48771
.48775
40
39
38
37
+ 6'
25
2fi
9.68039
.08042
.08046
.6804^
.47906
.47910
.47913
.47917
.47921
.47924
.47938
.47933
.48778
.48783
.48786
.48789
36
35
34
S3
32
31
30
29
28
27
26
25
24
23
22
21
29
50
31
9.68052
.68056
.68059
.68002
.48357
.48360
.48364
.48368
.48371
.48375
.48379
.48382
.48386
.48389
.48393
.48397
.48400"
.48404
.48408
.48411
.48415
.48419
.48433
.48436
.48439
.48433
.48437
.48440
9.08041
.08644
.08648
.68651
.48575
.48578
.48583
.48586
9.68836
.68839
.68842
.68845
"!»:^68849
.68852
.68855
.68858
9.688(i2
.68865
.68808
.08871
.48793
.48797
.48800
.48804
.48807
.48811
.48815
.48818
.48833
.48836
.48839
.48833
+ ^8'
9.68006
.68069
.68072
.08075
9.6807'9'
.68082
.68085
.68089
.47935
.47939
.47943
.47946
.47950
.47953
.47957
.47961
.47964
.47968
.47972
.47975
.47979
.47983
.47986
.47990
.47993
.47997
.48001
.48004
.48008
.48012
.48015
.48019
.48022
.48026
.48030
.48033
.48037
9.08203
.08206
.08209
.08272
9.08276
.68279
.68282
.68286
.48153
.48157
.48161
.48164
.48168
.48171
.48175
.48179
".48182"
.48186
.48190
.48193
".48197
.48201
.48304
.48308
.48311
.48315
.48319
.48233
.48336
.48330
.48333
.48237
9.686.54
.68657
.68661
.68064
.48589
.48593
.48597
.48600
+ 9'
37
■18
39
9.68667
.68670
.68074
.08077
.48604
.48608
.48611
.48615
+ w
41
42
43
9.68092
.08095
.08098
.68102
9.68289
.68292
.68295
.68299
9.68302
.68.305
.68308
.68312
9.08S15
.08318
.68322
.68325
"9:68328
.68331
.08335
.08338
9.08080
.08083
.08687
.68690
9.68693
.68696
.68700
.68703
.48618
.48623
.48636
.48639
.48633
.48637
.48640
.48644
.48648
.48651
.48655
.48658
.48662
.48666
.48669
.48673
9.08875
.68878
.08881
.08884
"9"."68887
.08891
.68894
.68897
9.08900
.08904
.68907
.68910
.48837
.48840
.48844
.48847
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
S
2
1
+ 11'
45
46
47
4- 12'
49
50
51
9.08105
.68108
.08112
.68115
9.68118"
.68121
.68125
.08128
9.08131
.08135
.08138
.68141
.48851
.48855
.48858
.48863
9.68706
.68709
.68713
.68716
.48866
.48869
.48873
.48877
+ 13'
53
54
55
.48444
.48448
.48451
.48455
.48459"
.48462
.48466
.48469
.48473
9.68719
.08722
.68726
.68729
9.68732
.68735
.68739
.68742
9.68745
9.68913
.68917
.68920
.68923
9.68926
.68929
.08933 J
.68936 '
9.08939 [
.48880
.48884
.48887
.48891
.48895
.48898
.48902
.48906
.48909
+ 14'
57
58
59
"+ 15'
9.68144
.68148
.68151
.68154
9.681.58
9.08341
.68344
.68348
.68351
9.68354
.48241
.48244
.48348
.48351
.48355
.48677
.48680
.48684
.46688
.48691
Igh 9m 1
]Sh 8m 1
ISk
7m
ISliSm
18^
.5™
24972°-12~
-40
Page 882] TABLE 45.
Ilaversines.
s
5h 55m 88° 45'
5ft 56m 89° 0'
5h 57™ 89° 15'
5* oSm 89° 30'
5A dm 89° 45'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9,68939
.68942
.68946
.68949
.48909
.48913
.48917
.48920
9.69132
.69130
.69139
.69142
.49127
.49131
.49135
.49138
9.09325
.09328
.(;9331
.09334
.49346
.49349
.i9US
.49356
9.69516
.69.520
.69.523
.69.526
9.69.529
.69532
.69535
.69539
.49564
.49567
.49571
.49575
9.69707
.69710
.69713
.69717
.49783
.49785
.49789
.49793
60
59
57
+ y
5
6
7
9.68952
.68953
.68958
.68962
.48934
.48927
.48931
.48935
9.09145
.69148
.691,52
.69155
.49142
.49146
.49149
.49153
9.09338
.09341
.09344
.69347
.49360
.49364
.49367
.49371
.49578
.49583
.49585
.49589
9.09720
.09723
.69726
.69729
.49796
.49800
.49804
.49807
56-
55
54
S3
51'
SI
SO
49
48
47
46
4S
+ 2'
9
10
11
9.68965
.68908
.68971
.68975
.48938
.48943
.48946
.48949
9.09158
.69161
.09164
.69168
.49156
.49160
.49164
.49167
9.69350
.69354
.69357
.69360
.49375
.49378
.49382
.49386
.49389
.49393
.49396
.49400
9.69,542
.09545
.69,548
.69.551
.49593
.49596
.49600
.49604
9.69732
.69730
.69739
.69742
.49811
.49815
.49818
.49822
+ 3'
IS
14
15
9.68978
.68981
.68984
.68988
.48953
.48957
.48960
.48964
9.69171
.69174
.69177
.69181
.49171
.49175
.49178
.49183
9.()9303
.09366
.69370
.69373
9.09555
.69.5.58
.69.561
.69564
.49607
.49611
.49615
.49618
9.69745
.69748
.69751
.69755
9.69758
.69701
.09764
.09767
9.69770
.69774
.69777
.09780
.49825
.49829
.49833
.49836
+ 4'
17
18
19
9.68991
.68994
.68997
.69000
.48967
.48971
.48975
.48978
9.69184
.69187
.69190
.69193
.49186
.49189
.49193
.49196
9.69370
.09379
.09382
.69386
.49404
.49407
.49411
.49415
9.09507
.09570
.09574
.69577
9.09580
.09583
.09586
.09590
9. mm
.09596
.09599
.69002
.49633
.49635
.49639
.49633
.49636
.49640
.49644
.49647
.49840
.49844
.49847
.49851
.49855
.49858
.49862
.49865
44
43
42
41
40
39
3S
37
3G
35
34
33
+ 5'
21
22
23
9.69004
.69007
.69010
.69013
.48983
.48986
.48989
.48993
9.69197
.69200
.69203
.69206
.49200
.49204
.49207
.49211
9.69389
.69392
.69395
.69398
.49418
.49422
.49426
.49429
+ 6'
25
26
27
9.69017
.69020
.69023
.69026
.48997
.49000
.49004
.49007
9.09209
.09213
.09216
.09219
9.09222
.69225
.09229
.09232
9.69235
.69238
.69242
.69245
.49215
.49218
.49233
.49236
9.69402
.69405
.09408
.69411
.4943:}
.49436
.49440
.49444
.49851
.49655
.49658
.49863
9.09783
.09786
.69789
.69793
.49869
.49873
.49876
.49880
+ r
29
SO
31
9.69029
.69033
.69036
.69039
.49011
.49015
.49018
.49023
.49239
.49233
.49336
.49340
9.09414
.69417
.69421
.69424
.49447
.49451
.49455
.49458
9.09(i05
.09009
.09612
.09015
.49665
.49869
.49673
.49676
9.09796
.69799
.69802
.69805
.49884
.49887
.49891
.49895
32
31
30
^9
+ 8'
33
34
35-
9.69042
.69046
.69049
.690.52
.49036
.49039
.49033
.49036
.49344
.49347
.49351
.49355
9.09427
.09430
.69433
.69437
.49463
.49465
.49469
.49473
9.09018
.69621
.09625
.69628
.49680
.49684
.49687
.49691
9.69808
.69812
.69815
.69818
9.69821
.69824
.69827
.69831
9.69834
.69837
.69840
.69843
.49898
.49902
.49905
.49909
L'8
27
26
2S
+ 9'
37
38
39
9.690.55
.69058
.69062
.69065
.49040
.49044
.49047
.49051
9.69248
.69251
.69254
.09258
.49358
.49363
.49266
.49269
9.09440
.69443
.69446
.69449
.49476
.49480
.49484
.49487
9.09631
.69634
.69637
.09040
.49695
.49898
.49703
.49705
.49913
.49916
.49930
.49934
.49937
.49931
.49935
.49938
24
23
22
21
20
19
18
17
16
IS
14
13
12
11
10
9
1
6
S
~r
/
+ W
41
42
43
9.69068
.69071
.69074
.69078
.49055
.49058
.49063
.49066
9.09201
.09264
.09267
.69270
.49273
.49276
.49280
.49284
9.69453
.69456
.69459
.69462
.49491
.49495
.49498
.49503
9.69044
.69647
.690.50
.69653
.49709
.49713
.49716
.49730
+ 11'
45
46
47
9.69081
.69084
.69087
.69091
.49069
.49073
.49076
.49080
9.09274
.69277
.69280
.69283
.49287
.49391
.49395
.49398
9.69465
.69469
.09472
.69475
.49506
.49509
.49513
.49516
9.090.56
.690.59
.69063
.69666-
.49734
.49727
.49731
.49735
9.69846
.69850
.09853
.698-56
.49943
.49945
.49949
.49953
.49956
.49960
.49964
.49967
.49971
.49975
.49978
.49982
+ 13'
49
50
51
9.69094
.69097
.69100
.69103
.49084
.49087
.49091
.49095
.49098
.49102
.49106
.49109
9.09286
.69290
.09293
.09296
.49303
.49306
.49309
.49313
9.69478
.69481
.69484
.69488
.49530
.49524
.49527
.49531
9.69609
.69672
.69675
.69678
.49738
.49743
.49745
.49749
.49753'
.49756
.49760
.49764
9.09859
.69802
.69865
.69869
9.69872
.69875
.69878
.69881
+ 13'
53
54
55
9.69107
.69110
.69113
.69116
9.09299
.09302
.69306
.69309
.49316
.49330
.49334
.49327
9.69491
.69494
.69497
.69500
.49535
.49538
.49542
.49545
9.09682
.09685
.09688
.69691
+ 14'
57
58
59
9.69120
.69123
.69126
.69129
.49113
.49116
.49130
.49134
9.69312
.69315
.69318
.09322
.49331
.49335
.49338
.49343
9.69504
.69507
.69510
.09513
.49549
.49553
.49556
.49560
9.69694
.69698
.69701
.69704
.49767
.49771
.49775
.49778
9.69884
.69888
.69891
.69894
.49985
.49989
.49993
.49997
+ 15'
9.69132
.49127
9.09325
.49346
9.09516
.49564
9.69707
.49783
9.69897
.50000
18h 4m
18h sm
JSh I'm
jSh pn
Igh 0>n
'
PABLE 45.
Ilavcnsines.
:Page 883
s
6A0">90°0'
eh pn 90° 15'
6* 2m 90° SO'
6h sm 90° 45'
eft 4m
91° 0'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.69897
.69900
.69903
.69906
.50000
.50004
.50007
.50011
9.70086
.70089
.70092
.70096
9.70099
.70102
.70105
; 701 08
.50218
.50222
.50235
.50229
.50233
.50236
.50240
.50244
.50247
.50251
.50255
.50258
9.70274
.70277
.70281
.70284
.50436
.50440
.50444
.50447
9.70462
.70465
.70468
.70471
.50654
.50658
.50662
.50665
.50669
.50673
.50676
.50680
.50684
.50687
.50691
.50694
.50698
.50702
.50705
.50709
9.70648
.706.52
.70655
.70658
.50873
.50876
.50880
.50884
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
5
6
7
9.699J0
.69913
.69916
.69919
.50015
.50018
.50023
.50025
9.70287
.70290
.70293
.70296
.50451
.50455
.50458
.50463
9.70474
.70477
.70480
.70484
9.70661
.70664
.70667
.70670
.50887
.50891
.50894
.50898
+ r
9
10
11
9.69922
.69925
.69929
.69932
.50029
.50033
.50036
.50040
.50044
.50041
.50051
.50055
9.70111
.70114
.70118
.70121
9.70124
.70127
.70130
.70133
9.70299
.70303
.70306
.70309
.50465
.50469
.50473
.50476
.50480
.50484
.50487
.50491
9.70487
.70490
.70493
.70496
9.70673
.70676
.70679
.70683
.50902
.50905
.50909
.50913
.50916
.50920
.50924
.50937
+ 3'
13
14
15
9.69935
.69938
.69941
.69944
.50262
.50365
.50369
.50273
.50276
.50280
.50284
.50287
9.70312
.70315
.70318
.70321
9.70324"
.70328
.70331
.70334
9.70499
.70.502
.70.505
.70509
9.70686
,70689
.70692
.70695
+ in
17
IS
19
19:69948
.69951
.69954
.69957
.50058
.50062
.50065
.50069
9.70136
.70140
.70143
.7014t)
.50495
.50498
.50502
.50505
9.70512
.70515
.70518
.70.521
.50713
.50716
.50720
.50724
9.70698
.70701
.70704
.70707
.50931
.59934
.50938
.50943
+ 5'
21
22
28
9.69960
.69963
.69966
.69970
.50073
.50076
.50080
.50084
9.70149
.701.52
.701.55
.701.58
.50391
.50295
.50298
.50302
9.70337
.70340
.70343
.70346
.50509
.50513
.50516
.50520
9.70524
.70,527
.70.530
.70.533
.50727
.50731
.50734
.50738
9.70710
.70714
.70717
.70720
.50945
.50949
.50953
.50956
.50960
.50964
.50967
.50971
+ «'
25
26
27
+ r
29
30
31
9.69973
.69976
.69979
.69982
.50087
.50091
.50095
.50098
9.70161
.70165
.70168
.70171
.50305
.50309
.50313
.50316
.50320
.50324
.50327
.50331
9.70349
.70353
.70356
.70359
.50524
.50537
.50531
.50534
.50538
.50543
.50545
.50549
9.70.537
.70540
.70543
.70546
9.70549
.70552
.70.555
.70558
.50742
.50745
.50749
.50753
.50756
.50760
.50764
.50767
.50771
.50774
.50778
.50782
9.70723
.70726
.70729
.70732
9.69985
.69988
.69992
.69995
.50102
.50105
.50109
.50113
9.70174
.70177
.70180
.70183
9.70362
.70365
.70368
.70371
9.70735
.70738
.70741
.70745
.50974
.50978
.50983
.50985
+ 8'
33
34
35
9.69998
.70001
.70004
.70007
.50116
.50120
.50124
.50127
9.70187
.70190
.70193
.70196
.50335
.50338
.50343
.50345
9.70374
.70378
.70381
.70384
.50553
.50556
.50560
.50564
9.70561
.70565
.70.568
.70571
9.70748
.70751
.70754
.707.57
.50989
.50993
.50996
.51000
28
27
26
25
24
23
22
21
+ 9'
37
3S
39
9.70011
.70014
.70017
.70020
.50131
.50135
.50138
.50142
.50145
.50149
..50153
.50156
9.70199
.70202
.70205
.70209
.50349
.50353
.50356
.50360
.50364
.50367
.50371
.50375
9.70387
.70390
.70393
.70396
.50567
.50571
.50574
.50578
9.70574
.70577
.70580
.70.583
9.70586'
.70.589
.70593
.70596
.50785
.50789
.50793
.50796
9.70760
.70763
.70766
.70769
.51004
.51007
.51011
.51014
+ 10'
41
42
43
9.70023
.70026
.70029
.70033
9.70036"
.70039
.70042
.70045
9.70212
.70215
.70218
.70221
9.70399
.70402
.70406
.70409
.50582
.50585
.50589
.50593
.50800
.50804
.50807
.50811
9.70772
.70775
.70779
.70782
.51018
.51033
.51035
.51039
20
19
18
17
+ 11'
45
40
47
.50160
.50164
.50167
.50171
9.70224
.70227
.70230
.70234
.50378
.50383
.50385
.50389
9.70412
.70415
.70418
.70421
.50596
.50600
.50604
.50607
.50611
.50614
.50618
.50622
9.70599
.70602
.70605
.70608
9.70611
.70614
.70617
.70620
9:70624"
.70627
.70630
.70633
.50814
.50818
.50823
.50825
.50829
.50833
.50836
.50840
.50844
.50847
.50851
.50854
9.70785
.70788
.70791
.70794
.51033
.51036
.51040
.51043
16
15
14
13
1!
11
10
9
8
7
6,
•')
4
3
2
1
+ 12'
49
50
51
9.70048
.70051
.700.55
.70058
.50175
.50178
.50183
.50185
9.70237
.70240
.70243
.70246
.50393
.50396
.50400
.50404
9.70424
.70427
.70431
.70434
9.70797
.70800
.70803
.70806
9.70809
.70813
.70816
.70819
.51047
.51051
.51054
.51058
.51063
.51065
.51069
.51073
+ 13'
53
54
.5.5
9.70061
.70064
.70067
.70070
.50189
.50193
.50196
.50200
9.70249
.702.52
.702.56
.702.59
.50407
.50411
.50415
.50418
9.70437
.70440
.70443
.70446
.50635
.50629
.50633
.50636
+ 14'
.57
5S
59
9.70074
.70077
.70080
.70083
.50204
.50207
.50211
.50215
9.70262
.70265
.70268
.70271
.50433
.50425
.50429
.50433
9.70449
.704.52
.70456
.70459
.50640
.50644
.50647
.50651
9.70636
.70639
.70642
.70645
.50a58
.50862
.50865
.50869
9.70822
.70825
.70828
.70831
.51076
.51080
.51083
.51087
+ 15'
9.70086
.50218
9.70274
.50436
9.70462
.50654
9.70648
.50873
9.70834
.51091
17h
59"^
m
5Sm
nh.
57m
17h 56m
nh
5.5"
Page 884]
TABLE 45.
llaversincs.
s
6* .i" 91° 15'
fift 677. 91° 30'
6k7">91°^'
6**77!
92° 6'
eh ym 93° 16'
s
Log. Ilav.
Nat. Hav,
Log. Hav.
Nat. Ilav.
Log. Ilav.
Nat. Ilav,
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Hav
1
2
S
9.70834
.70837
.70840
.70843
.51091
.51094
.51098
.51102
9.71019
.71022
.71025
.71028
.51309
.51312
.51316
.51320
9,71203
.71206
.71210
.71213
.51537
.51531
.51534
.51538
.51541
.51545
.51549
.51553
9.71387
,71390
.71393
.71390
'9,71399
.71402
.71405
,71408
.51746
.51749
.51762
.51766
.51760
.51763
.51767
.61770
9.71569
.71572
.71575
.71579
.51963
.51967
.61970
.61974
60
59
58
57
56'
55
54
53
5>
51
51)
49
48
47
46
45
+ 1'
5
e
7
9.70847
.708.^0
.70853
.70S5G
.51105
.51109
.51113
.51116
.51120
.51123
.51127
.51131
.51134
.51138
.51142
.51145
9.71032
.71035
.71038
.71041
9.71044
.71047
.71050
.71053
.51323
.51327
.51331
.51334
9.71216
.71219
.71222-
. .71225
9.71582
.71585
.71588
.71591
.51978
.51981
.61985
.61988
+ -i'
9
10
11
9.70859
.70802
.70865
.70868
.51338
.51342
.51345
.51349
9.71228
,71231
,71234
.71237
.51556
.61560
.51563
.61567
9,71411
,71414
,71417
.71420
.51774
.51778
.51781
.51786
9.71594
.71.597
.71600
.71603
.61992
.61996
.51999
.52003
.53007
.52010
.53014
.52018
+ 3'
13
14
15
9.70871
.70874
.70877
.70881
9.710-56
.71059
.71062
.71065
9.71068
.71072
.71075
.71078
.51352
.51356
.51360
.51363
9.71240
.71243
.71246
.71249
.51571
.51574
.51578
.51581
.51585
.51589
.51592
.51596
.51600
.51603
.51607
.51611
.51614
.51618
.51621
.51625
9.71423
.71420
,71430
,71433
9,71436
,71439
,71442
,71445
.51789
.51792
.51796
.51799
.61803
.61807
.51810
.51814
9,71606
.71609
.71612
.71015
+ 4'
17
18
19
9.70884
.70887
.70890
.70893
.51149
.51153
.51156
.51160
.51163
.51167
.51171
.51174
.51367
.51371
.51374
.51378
9,712.52
,712.55
,712.^9
.71262
9.71018
.71021
.71624
.71627
.53021
.53025
.52028
.52032
44
43
4-1
41
40
J9
38
37
'36
35
34
33
J-2
■il
30
;i9
J8
27
26
25
24
23
22
21
+ 5'
21
22
23
9.70896
.70899
.70902
.70905
9.71081
.71084
.71087
.71090
.51382
.51385
.51389
.51392
.51396
.51400
.51403
.51407
.51411
.51414
.51418
.51422
9.71205
.71208
,71271
,71274
9,71277
,71280
,71283
,71280
9,71289
,71292
,71295
,71298
9,71448
,71451
,714.54
,71457
9,71460
,71463
.71460
.71469
.51818
.51821
.51825
.51839
9.71630
.71633
.71636
.71639
.52036
.52039
.52043
.52047
+ 6'
25
26
27
9.70908
.70911
.70914
.70918
.51178
.51182
.51185
.51189
9.71003
.71096
.71099
.71102
.51833
.51836
.51839
.51843
9.71642
.71645
.71648
.71651
.53050
.52054
.52057
.52061
+ r
29
SO
31
9.70921
.70924
.70927
.70930
.51193
.51198
.51200
.51203
.51207
.51211
.51214
.51218
9.71105
.71108
.71111
.71114
9.71118
.71121
.71124
.71127
.51639
.51633
.51636
.51640
9.71472
.71475
.71478
,71481
.51847
.51860
.61854
.51868
9.716-54
.71657
.71660
.71603
.52065
.52068
.52072
.52076
+ 8'
33
34
35
9.70933
.70936
.70935
.70942
.51425
.51429
.51432
.51436
9,71301
.71304
.71307
.71311
.51643
.51647
.51650
.61654
.51658
.51661
.51665
,51669
.51673
.51676
.51680
.51683
9,71484
,71487
,71490
,71493
9,71496
,71.500
,71.503
,71506
9,7i509
,71512
.71515
.71518
.51861
.51865
.51869
.51873
.51876
.51879
.51883
.51887
.61890
.51894
.51898
.51901
9.71066
.71070
.71073
.71070
.52079
.52083
.52087
.52090
+ 9'
37
38
39
9.70945
.70948
.70951
.70955
.51222
.51225
.51229
.51233
.51236
.51240
.51243
.51247
9.71130
.71133
.71136
.71139
.51440
.51443
.51447
.51451
9.71314
,71317
.71320
,71323
9.71079
.71082
.71685
.71688
9.71691
.71694
.71697
.71700
.52094
.52097
.52101
.53105
+ ir
42
43
9.70958
.70961
.70964
.70967
9.71142
.71145
.71148
.711.51
.51454
.51468
.51462
.51465
9,71320
,71329
,71332
,71335
.63108
.53113
.53116
.53119
20
19
18
17
16
15
14
+ U'
46
47
9.70970
.70973
.70976
.70979
.51251
.51254
.51258
.51262
9.71154
.71157
.71161
.71164
.51469
.51472
.51476
.51480
9.71338
.71341
.71344
.71347
.51687
.51690
.51694
.51698
9,71521
,71.524
,71527
,71530
.51905
.51908
.51912
.61916
9.71703
.71700
.71709
.71712
.52123
.53136
.53130
.52134
+ 12'
49
SO
51
9.70982
.70985
.70988
.70992
.51265
.51269
,51273
.51276
.51280
.51283
.51287
.51291
9,71167
.71170
.71173
.71176
.61483
.61487
.51491
.51494
9.71350
.713.53
.71350
.71359
.51701
.51705
.51709
.51712
9,71533
,71536
,71539
,71.542
9,71.545
.71.548
.71551
.71554
.51919
.51933
.51937
.51930
9.71715
.71718
.71721
.71724
.52137
.52141
.53145
.52148
1..'
11
10
9
8"
7
6
5
+ 13'
.5.i
54
' 55
9.70995
.70998
.71001
.71004
9.71179
.71182
.71185
.71188
.51498
.51601
.51605
.51508
9.71362
.71365
.71309
,71372
.51716
.51720
.51723
.51727
.51934
.51938
.51941
.51946
9.71727
.71730
.71733
.71736
.52152
.53156
.53159
.52163
+ W
57
58
59
9.71007
.71010
.71013
.71016
.51294
.51298
.51302
.51305
9.71191
.71194
.71197
.71200
.51512
.51516
.51520
.51523
9,71375
.71378
.71381
.71384
.51730
.51734
.51738
.51741
9.715.57
.71.560
.71563
.71566
.51948
.51953
.51956
.51959
9.71739
.71742
.71745
.71748
.52166
.52170
.52174
.52177
4
.1
1
4- 15'
9.71019
.51309
9.71203
.61627
9.71387
.51746
9.71569
.51963
9.71751
.52181
17h
54™
17h 53^
irh 59m
17h
5im
17h
SOm
TABLE
45.
[Page 885
Haversine.-;.
s
6h lOm 93° SC
ehlim
93° 45'
eh l»m
93° 0'
6h ism
93° 15'
eh 14m
93° sr
3
Log. llav.
Nat. Ilav,
Log. Ilav.
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Hav.
9.71751
.52181
9.71932
.53399
9.72112
.52617
9.72292
.53835
9.72471
.53052
60
1
.71754
.53185
.71935
.53403
.72115
.53630
.72295
.53838
.72474
.53056
59
'2
.71757
.52188
.71938
.53406
.72118
.53624
.72298
.53843
.72476
.53060
5fl
3
.71760
.52193
.71941
.53410
.53413
.72121
9.72124
.52638
.53631
.72301
9.72304
.53846
.53849
.72479
9.72482
.53063
.53067
57
56
+ 1'
9.71763
.53196
9.711I44
5
.71766
.53199
.71947
.53417
.72127
.53635
.72307
.53853
.72485
.53071
55
6
.71769
.53303
.71950
.53431
.72130
.53639
.72310
.53856
.72488
.53074
54
i
.71772
.53306
.71953
9.71956"
.53434
.72133
9:72136
.52642
.52646
.72313
9.72316
.53860
.52864
.72491
9.72494
.53078
.53081
53
52
+ 2'
9.71775
.53310
.53438
9
.71778
.53314
.71959
.53433
.72139
.52649
.72319
.53867
.72497
.53085
51
10
.71781
.53317
.71962
.52435
.72142
.53653
.72322
.53871
.72500
.53089
50
11
.71784
9.71787
.53331
.53335
.71965
9.71968
.52439
.52443
.72145
9.72148
.52657
.53660
.72325
9.72328
.52875
' .53878'
.72503
9.72506
.53092
.53096
49
4S
+ 3'
13
.71791
.53338
.71971
.53446
.72151
.53664
.72331
.53883
.72509
.53100
47
14
.71794
.53333
.71974
.53450
.72154
.53668
.72334
.53885
.72512
.53103
46
15
.71797
.53335
.71977
.53453
.72157
.53671
.72337
.53889
.72515
.53107
45
+ 4'
9.71800
.53339
9.71980
.53457
9.72160
.53675
9.72340
.53893
9.72518
.53110
44
;?
.71803
.53343
.71983
.53461
.72163
.52679
.72343
.53896
.72521
.53114
43
2,S
.71806
.53340
.71986
.53464
.72166
.52682
.72346
.53900
.72524
.53118
42
19
.71809
.53350
.71989
9 "7 1992
.52468
.52472
.72169
9.72172
.53688
.52689
.72349
.53904
.52907
.72527
.53121
41
+ 5'
9.71812
.53354
9.72352
9.72530
.53135
40
5i
.71815
.52257
.71995
.52475
.72175
.53693
.72354
.52911
.72533
.53129
39
;?.;
.71818
.53261
.71998
.53479
.72178
.53697
.72357
.52915
.72536
.53132
.W
;?.J
.71821
.52364
.72001
.53483
.72181
.53700
.72360
.53918
.72539
.53136
37
+ 6'
9.71824
.53368
9.72004
.53486
9.72184
.53704
9.72363
.53933
9.72.542
.53140
36
25
.•71827
.52372
.72007
.53490
.72187
.52708
.72366
.53935
.72545
.53143
35
26
.71830
.53375
.72010
.53493
.72190
.52711
.72369
.53939
.72548
.53147
34
21
.71833
.53379
.53383
.72013
9.72016
.53497
.53501
.72193
9772196
.52716
.52718
.72372
9.72375
.52933
.53936
.72551
9.72554
.53150
.53154'
33
32
+ r
9.71836
29
.71839
.53386
.72019
.52504
.72199
.53733
.72378
.53940
.72557
.53158
31
SO
.71842
.52290
.72022
.53508
.72202
.52736
.72381
.53944
.72560
.53161
30
SI
.71845
9.71848
.52294
.52397
.72025
9.72028
.53511
.53515
.72205
.52729
.72384
9..72387
.53947
.53951
.72563
9.72565
.53165
.53169
29
'28
+ 8'
9.72208
.52733
.M
.71851
.53301
.72031
.53519
.72211
.52737
.72390
.52954
.72568
.53173
2 1
•f^
.71854
.53304
.72034
.52523
.72214
.53740
.72393
.52958
.72571
.53176
>6
.J.5
.71857
.53308
.53313
.72037
9.72040
.53S36
.53530
.72217
.53744
.72396
9.72399
.52963
.53965
.72574
9.72577
.53179
.53183
25
+ »'
9.71860
9.72220
.53748
57
.71863
.53315
.72043
.53533
.72223
.53751
.72402
.53969
.72580
.53187
>3
5S
.71866
.53319
.72046
.53537
.72226
.52755
.72405
.53973
.72583
.53190
'/-)
59
.71869
.52333
.53336
.72049
9.72052"
.52541
.52544
.72229
9.72232
.53758
.53763
.72408
.53976
.52980
.72586
.53194
.53198
21
20
+ 10'
9.71872
9.72411
9.72589
41
.71875
.53330
.720.55
.52548
.72235
.53766
.72414
.52983
.72592
.53301
19
42
.71878
.53334
.720.58
.52551
.72238
.52769
.72417
.52987
.72595
.53205
18
43
.71881
.53337
.53341
.72061
9.72064
.53555
.53559
.72241
9.72244
.52773
.52776
.72420
9.72423"
.52991
.52994
.72598
9.72601
.53208
.53212
17
16'
+ 11'
9.71884
45
.71887
..53344
.72067
.53563
.72247
.52780
.72426
.52998
.72604
.53316
15
46
.71890
.53348
.72070
.53566
.72250
.52784
.72429
.53003
.72607
.53319
14
47
+ ir
.71893
9.71896
.53353
.72073
.53570
.53573
.72253
.52787
.72432
9.72435
.53005
.53009
.72610
9.72613
.53333
.53337
13
if
.52355
9.72076
9.72256
.52791
49
.71899
.52359
.72079
.53577
.72259
.52795
.72438
.53013
.72616
.53230
11
50
.71902
.53363
.72082
.53580
.72262
.52798
.72441
.53016
.72619
.53234
in
51
.71905
.53368
.53370"
.72085
'9.72088
.53.584
.53588
.72265
9.72268
.53803
.52806
.72444
9.724 47
.53030
.53033
.72622
.53238
9
+ 13'
9.71908
9.72625
.53341
8
53
.71911
.53373
.72091
.53591
.72271
.52809
.724.50
.53027
.72628
.53345
7
54
.71914
.53377
.72094
.53595
.72274
.52813
.72453
.53031
.72631
.53348
r,
55
.71917
.53381
.53384
.72097
9.72100
.53599
.53603
.72277
9.72280'
.53816
.72456
.53034
.53038
.72634
9.72637
.53253
5
+ 14'
9.71920
.52820
9.72459
.55256
4
57
.71923
.53388
.72103
.53606
.72283
.52824
.72462
.53043
.72640
.53259
3
58
.71926
.53393
.72106
.53610
.72286
.53837
.72465
.53045
.72642
.53363
2
59
.71929
.53395
.53399
.72119
.53613
.72289
.53831
.72468
.53049
.72645
9.72648
.53367
1
+ 15'
9.71932
9.72112
.52617
9.72292
.53835
9.72471
.53053
.53370
17h
49m
17k
4Sm
17h
47m
nh4em
17h
4.5™
Page 886]
TABLE 45.
Haversine,-!.
s
gft l.jm
93° 45'
eh 16m
94° 0'
6h 17m 94° 15'
eh 18m 94° 30'
eh 19m
94° 45
s
Log. Hav.
Nat. Hav.
Log. Ilav.
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
9.73177
.73180
.73183
.73186
9.73189
.73192
.73195
.73198
9,73261"
.73204
.73207
.73209
9773212
.73215
.73218
.73221
Nat. Hav.
Log. Hav.
Nat. Hav .
1
2
3
9.72648
.72651
.72654
.72657
^3270
.53274
.53277
.53281
.53285"
.53288
.53292
.53296
.53299
.53303
.53306
.53310
.53314
.53317
.53321
.53325
9.72825
.72828
.72831
.72834
9.72837
.72840
.72843
.72846
9.72849
.72852
.72855
.72858
.53488
.53491
.53495
.53499
.53502
.53506
.53510
.53513
.53517
.53520
.53524
.53528
9.73002
.73005
.73008
.73011
.53705
.53709
.53713
.53716
.53720
.53724
.53727
.53731
.53734
.53738
.53742
.53745
.53749
.53753
.53756
.53760
.53923
.53927
.53930
.53934
.53937
.53941
.53945
.53948
.53952
.53956
.53959
.53963
.53966
.53970
.53974
.53977
.53981
.53985
.53988
.53993
.53995
.53999
.54003
.54006
.54010
.54014
.54017
.54021
9.73352
.73355
.73358
.73361
9.73364
.73367
.73370
.73373
9.73375
.73378
.73381
.73384
.54140
.54144
.54148
.54151
.54155
.54159
.54162
.54166
.54169
.54173
.54177
.54180
(iO
59
58
.57
.56
55
54
53
'5J
51
50
49
'48
47
46
45
44
43
4i
41
'40
39
38
o7
36'
35
34
33
3^
31
30
.'9
['8
J6
J5
J4
23
il
iO
ta
IS
17
7«
/.5
14
13
1.;
11
10
.9
8
7
r>
5
+ 1'
5
6
7
9.72660
.72663
.72666
.72669
9.72672
.72675
.72678
.72681
9.73014
.73016
.73019
.73022
+ r
. 9
10
11
9.73025
.73028
.73031
.7.3034
+ 3'
13
14
15
9.72684
.72687
.72690
.72693
9.72861.
.72864
.72867
.72870
9.72873
.72876
.72878
.72881
.53531
.53535
.53539
.53542
9.73037
.73040
.73043
.73046
9.73387
.73390
.73393
.73396
9.73399
.73402
.73404
.73407
9.73410
.73413
.73416
.73419
.54184
.54188
.54191
.54195
.54198
.54202
.54306
.54209
.54313
.54317
.54330
.54334
+ *'
17
18
19
9.72696
.72699
.72702
.72705
9.72708
.72710
.72713
.72716
.53328
.53332
.53335
.53339
.53343
.53346
.53350
.53354
.53546
.53549
.53553
.53557
9.73049
.73052
.73055
.73057
9.73060
.73063
.73066
.73069
9.73072
.73075
.75078
.73081
9.73084
.73087
.73090
.73093
9:73096
.73098
.73101
.73104
"9:73107
.73110
.73113
.73116
9.73119
.73122
.73125
.73128
9.'7313r
.73134
.73136
.73139
9.73142
.73145
.73148
.73151
9.73154
.73157
.73160
.73163
9.73166
.73169
.73172
.73174
9.75177
.53763
.53767
.53771
.53774
.53778
.53782
.53785
.53789
.53792
.53796
.53800
.53803
.53807
.53811
.53814
.53818
.53821
.53825
.53829
.53832
.53836
.53840
.53843
.53847
.53850
.53854
.53858
.53861
.53865
.53869
.53872
.53876
.53879
.53883
.53887
.53890
..53894
.53898
.53901
.53905
.53908
.53912
.53916
.53919
.53923
9.73224
.73227
.73230
.73233
+ 5'
21
22
23
9.72884
.72887
.72890
.72893
.53560
.53564
.53568
.53571
9.73236
.73239
.73242
.73244
9.73247"
.73250
.73253
.73256
9.732.59
.73262
.73265
.73268
1).7327J
.73274
.73277
.73280
+ 6'
25
26
27
9.72719
.72722
.72725
.72728
.53357
.53361
.53364
.53368
.53372
.53375
.53379
.53383
.53386
.53390
.53394
.53397
.53401
.53404
.53408
.53412
.53415
.53419
.53423
.53426
.53430
.53433
.53437
.53441
9.72896
.72899
.72902
.72905
.53575
.53579
.53582
.53586
9.73422
.73425
.73428
.73431
9.73433
.73436
.73439
.73442
.54237
.54331
.54235
.54238
.54242
.54245
.54249
.54253
.54256
.54260
.54264
.54267
.54271
.54274
.54278
.54282
.54285
.54389
.54393
.54396
.54300
.54303
.54307
.54311
.54314
.54318
.54333
.54325
.54329
.54332
.54336
.54340
.54343
.54347
.54351
.54354
.54358
+ r
29
SO
31
9.72731
.72734
.72737
.72740
9.72908
.72911
.72914
.72917
.53589
.53593
.53597
.53600
.53604
..53608
.53611
.53615
.54024
.54038
.54033
.54035
.54039
.54043
.54046
.54050
+ 8'
33
34
35
+ 9'
37
38
39
9.72743
.72746
.72749
.72752
9772755"
.72758
.72761
.72764
9.72920
.72923
.72926
.72928
9.72931
.72934
.72937
.72940
9.73445
.73448
.73451
.73454
9.73457
.73460
.7.3462
.73465
9.73468"
.73471
.73474
.73477
9.73480
.73483
.73486
.73489
9.73491
.73494
.73497
.73500
.53618
.53622
.53626
.53629
9.73282
.73285
.73288
.73291
.54053
.54057
.54061
.54064
+ 10'
41
42
43
9.72767
.72770
.72772
.72775
9.72778
.72781
.72784
.72787
9.72790
.72793
.72796
.72799
9.72802
.72805
.72808
.72811
9.72943
.72946
.72949
.72952
9.72955
.72958
.72961
.72964
.53633
.53637
.53640
.53644
.53647
.53651
.53655
.53658
.53662
.53666
.53669
.53673
.53676
.53680
.53684
.53687
9.73294
.73297
.73300
.73303
9.73306
.73309
.73311
.73314
9.73317
.73320
.73323
.73326
9.73329
.73332
.73335
.73338
9.73341
.73343
.73346
.73349
9.73352"
.54068
.54073
.54075
.54079
.54083
.54086
.54090
.54093
.54097
.54101
.54104
.54108
+ 11'
45
46
47
+ 13'
49
50
51
.53444
.53448
.53452
.53455
.53459
.53462
.53466
.53470
.53473
.53477
.53481
.53484
.53488
9.72967
.72970
.72972
.72975
9.72978
.72981
.72984
.72987
9.72990
.72993
.72996
.72099
9.73002
+ 13'
53
54
55
.54111
.54115
.54119
.54123
.54126
.54130
.54133
.54137
.54140
9.73503
.73506
.73509
.73512
9.73515
.73517
.73520
.73523
9:73526
+ 1*'
57
58
59
9.72814
.72817
.72820
.72823
9.72825"
.53691
.53695
.53698
.53702
.53705
4
3
2
~1
+ 15'
Uh
44m
17h
43m
i7A
42'"^
17h
41m
17^4
Om
TABLE 45. [Page 887
HaversineH.
s
6'' .'0"! 95° 0'
6!t 21m 95° 15'
6* 22m 95° 30'
6h 23m 95° 45'
6h 2.'tm 96° 0'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.| Nat. Hav.
Log. Hav.
Nat. Hav.
1
>
"s
9.73526
.73529
.73532
.73.535
.54358
.34361
.54365
.54369
.54373
.54316
.54380
.54383
9.73699
.73702
.73705
.73708
.54575
.54579
.54582
.54586
9.73872
.73875
.73878
.73881
.54792
.54796
.54800
.54803
9.74044
.74047
.74049
.740.52
.55009
.55013
.55017
.55020
9.74215
.74218
.74220
.74223
.55336
.55330
.55234
.55337
60
59
58
57
56
55
54
5S
52
51
50
49
48
47
46
45
44
4S
42
41
40
39
■i8
37
36
35
34
33
.32
31
30
29
28
27
26
25
+ y
5
6
7
9.73538
.73541
.73544
.73546
9.73711
.73714
.73717
.73720
.54590
.54593
.54597
.54600
9.73883
.73886
.73889
.73892
.54807
.54810
.54814
.54818
9.74055
.74058
.74061
.74064
.55024
.55028
.55031
.55035
9.74226 .55341
.74229 ! .55345
.74232 .55348
.74235 .55253
9.74237 .5.5255
.74240 .55259
.74243 .55263
.74246 .(55366
+ V
9
10
11
9.73549
.73552
.73555
.73.558
.54387
.54390
.54394
.54398
.54401
.54405
.54409
.54412
9.73722
.73725
.73728
.73731
.54604
.54608
.54611
.54615
9.73895
.73898
.73901
.73903
.54821
.54825
.54828
.54832
9.74067 .55038
.74069 .55042
.74072 .55046
.74075 1 .55049
-r 3'
IS
14
1.5
9.73.561
.73564
.73567
.73570
9.73734
.73737
.73740
.73743
.54619
.54623
.54626
.54629
9.73906
.73909
.73912
.73915
9.73918
.73921
.73924
.73926
9.73929
.73932
.73935
.73938
.54836
.54839
.54843
.54847
9.74078
.74081
.74084
.74087
.55053
.55056
.55060
.55064
9.74249
.74252
.742.54
.74257
.55370
.55373
.55377
.55381
.55284
.55288
.55292
.55295
+ i'
n
18
19
9.73572
.73575
.73578
.73.581
.54416
.54419
.54423
.54427
9.73746
.73748
.73751
.73754
.54633
.54637
.54640
.54644
.54850
.54854
.54857
.54861
9.74089
.74092
.74095
.74098
.65067
.55071
.55075
.55078
9.74260
.74263
.74266
.74269
+ 5'
21
22
}~3
9.73584
.73587
.73.590
.73.593
.54430
.54434
.54437
.54441
9.73757
.73760
.73763
.73766
.54647
.54651
.54655
.54658
.54662
.54666
.54669
.54673
.54865
.54868
.54872
.54876
9.74101
.74104
.74106
,74109
.55082
.55085
.55089
.55093
9.74272
.74274
.74277
.74280
"9:74283
.74286
.74289
.74291
.55299
.55302
.55306
.55310
.55313
.55317
.55320
.55324
+ _6'
26
27
9.73596
.73598
.73601
.73604
.54445
.54448
.54452
.54456
9:73769
.73771
.73774
.73777
9.73941
.73944
.73946
.73949
.54879
.54883
.54886
.54890
9.74112
.74115
.74118
.74121
.55096
.55100
.55103
.55107
+ r
29
■¥)
■11
9.73607
.73610
.73613
.73616
.54459
.54463
.54466
.54470
9.73780
.73783
.73786
.73789
.54676
.54680
.54684
.54687
.54691
.54695
.54698
.54702
.54705
.54709
.54713
.54716
9.739.52
.739.55
.739.58
.73961
.54894
.54897
.54901
.54904
9.74124
.74126
.74129
.74132
.55111
.55114
.55118
.55122
9.74294
.74297
.74300
.74303
0.74306
.74308
.74311
.74314
.55328
.55331
.55335
.55339
.55343
.55346
.55349
.55353
+ 8'
■14
■1.5
9.73619
.73622
.73624
.73627
9.73630
.73633
.73636
.73639
.54474
.54477
.54481
.54485
9.73792
.73794
.73797
.73800
9.73803
.73806
.73809
.73812
9.73964
.73967
.73969
.73972
.54908
.54912
.54915
.54919
9.74135
.74138
.74141
.74144
.55125
.55129
.55133
.55136
+ 9'
■17
■IS
■19
.54488
.54492
.54495
.54499
9.73975
.73978
.7398]
.73984
9.73987
.73989
.73992
.73995
9.73998
.74001
.74004
.74007
9.74009^
.74012
.74015
.74018
9; 74021
.74024
.74027
.74029
0.74032
.74035
.74038
.74041
9.74044
.54923
.54926
.34930
.54933
.54937
.54941
.54944
.54948
.54953
.54955
.54959
.54963
.54966
.54970
.54973
.54977
9.74146
.74149
.74152
.74155
9.74158
.74161
.74163
.74166
.55140
.55143
.55147
.55150
.55154
.55158
.55161
.55165
9.74317
.74320
.74323
.74325
.55357
.55360
.55364
.55367
.56371
.55375
.55378
.55383
24
23
22
21
20
10
18
17
+ 10'
41
4l
■U
9.73642
.73645
.73648
.73650
.54503
.54506
.54510
.54514
.54517
.54521
.54524
.54528
.54532
.54535
.54539
.54542
9.73815
.73817
.73820
.73823
9.73826
.73829
.73832
.73835
9.73838
.73840
.73843
.73840
.54720
.54724
.54727
.54731
.54734
.54738
.54743
.54745
.54749
.54752
.54756
.54760
.54763
.54767
.54771
.54774
.54778
.54781
.54785
.54789
9.74328
.74331
.74334
.74337
4-'>
9.73653
.736.56
.73659
.73662
9.74169
.74172
.74175
.74178
9.74181
.74183
.74186
.74189
.55169
.55173
.55176
.55179
9.74340
.74342
.74345
.74348
.55386
.65389
.55393
.55396
16
15
14
13
+ 12'
■i'-l
M
■11
9.73665
.73668
.73671
.73674
.55183
.55187
.55190
.55194
9.74351
.743.54
.74357
.74350
.55400
.56404
.55407
.55411
12
11
10
9
+ 13'
9.73676
.73679
.73682
.73685
.54546
.54550
.54553
.54557
9.73849
.738.52
.738.55
.73858
.54980
.54984
.54988
.54991
.54995
.54999
.55002
.55006
9.74192
.74195
.74198
.74200
9.74203
.74206
.74209
.74212
.55197
.55201
.55305
.55308
.55313"
.55316
.55219
.55323
9.74362
.74365
.74368
.74371
.55414
.55418
.65422
.66426
8
7
6
5
+ 14'
.57
.55
.59
9.73688
.73691
.73694
.73697
.54561
.54564
.54568
.54571
9.73860
.73863
.73866
.73869
9.74374
.74376
.74370
.74382
.55429
.55433
.55436
.55440
4
3
'2
1
+ 15'
9.73699
.54575
9.73872
.54793
.55009
9.74215
.55226
9.74385
.55443
17h .39m
nhSsm
Ijh 37m
17 h Sem
n% 35m
Page 888]
TABLE 45.
Haversines.
s
6h >5m 96° 15'
6h 26m 96° W
6h 27m 96° 45'
6h 28m 97° (K
eh 29m
97° 15'
s
Log. Hav.
Nat. Hav.
Lor. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.74385
.74388
.74391
.74393
.55443
.55447
.55451
.55454
.55458
.55461
.55465
.55469
.55472
.554J6
.55479
.55483
9.74.5.54
.74.557
.74560
.74563
9.74.566
.74.569
.74571
.74574
.55660
.55664
.55667
.55671
.55675
.55678
.55682
.55685
.55689
.55693
.55696
.55700
9.74723
.74726
.74729
.74732
.55877
.55880
.55884
.55888
9.74891
.74894
.74897
.74900
.56093
.56097
.56101
.56104
.56108
.56112
.56115
.56119
9.7.50.59
.75061
.75064
.75067
.56310
.56314
.56317
.56321
60
59
5H
57
56
55
54
53
+ V
5
6
7
9.7439i)
.74399
.74402
.74405
9.74734
.74737
.74740
.74743
.55891
.55895
.55899
.55902
.55906
.55909
.55913
.55917
9.74902
.74905
.74908
.74911
9.75070
.7.5072
.75075
.75078
.56324
.56328
.56333
.56335
+ 2'
.9
10
11
9.74408
.74410
.74413
.74416
9.74577
.74.580
.74.583
.74585
9.74746
.74748
.74751
.74754
9.74914
.74916
.74919
.74922
.5«122
.56126
.56130
.56133
9.7.5081
.75084
.7.5086
.7.5089
9.7.5092
.7.5095
.7.5097
.75100
.56339
.56342
.56346
.56350
.56353
.56357
.56360
.56364
52
61
50
49
4.S'
47
46
45
U
43
42
41
40
S9
SS
37
36
35
34
S3
32
SI
30
29
+ 3'
13
14
15
9.74419
.74422
.74425
.74427
.55487
.55490
.55494
.55498
.55501
.55505
.55508
.55512
.55516
.55519
.55523
.55526
9.74.588
.74.591
.74.-J94
.74597
.55704
.55707
.55711
.55714
9.74757
.74760
.74762
.74765
.55920
.55924
.55927
.55931
9.74925
.74928
.74930
.74933
9.74936
.74939
.74941
.74944
.56137
.56140
..56144
.56147
+ *'
17
18
19
9.74430
.74433
.74436
.74439
9.74600
.74602
.74605
.74603
9.746U
.74614
.74616
.74619
9.74622
.74625
.74628
.74630
.55718
.55722
.55725
.55729
9.74768
.74771
.74774
.74776
.55935
..55938
.55942
.55945
.55949
..55953
..55956
.55960
.selsT
.56155
.56158
.56162
9.75103
.75106
.75109
.75111
.56368
.56371
.56375
.56378
+ 5'
21
22
23
9.74442
.74444
.74447
.74450
.55732
.55736
.55740
.55743
.55747
.55750
.55754
.55758
9.74779
.74782
.74785
.74788
9.74791
.74793
.74796
.74799
9.74947
.74950
.74953
.74955
.56166
.56169
.56173
.56176
9.75114
.75117
.75120
.75122
.56382
.56386
.56389
.56393
.56397
.56400
.56404
.56407
+ 6'
25
26
27
9.74453
.74456
.74458
.74461
.55530
.55534
.55537
.55541
.55964
.,55967
.55971
.55974
.55978
.55982
.55985
.55989
9.74958
.74961
.74964
.74967
9.74969
.74972
.74975
.74978
.56180
..56184
.56187
.56191
.56195
.56198
.56202
.56295
.56209
.56213
.56216
.56220
9.75125
.75128
.75131
.75134
+ r
29
30
31
9.74464
.74467
.74470
.74473
.55545
.55548
.55552
.55555
9.74633
.74636
.74639
.74642
.55761
.55765
.55769
.55772
9.74802
.74805
.74807
.74810
9.75136
.75139
.75142
.75145
9.75147
.75150
.75153
.751.56
.56411
.56415
.56418
.56423
+ 8'
33
34
35
9.74475
.74478
.74481
.74484
.55559
.55563
.55566
.55570
9.74645
.74647
.74650
.746.53
.55776
.55779
.55783
.55787
9.74813
.74816
.74819
.74821
.55992
.55996
.56000
..56003
..56007
.56010
.56014
.56018
9.74981
.74983
.74986
.74989
9.74992
.74994
.74997
.75000
.56425
.56429
.56433
.56436
'^8.
2 i
26
25
24
2S
t )
21
20
19
18
n
16
15
14
IS
12
11
1(1
9
S
6
5
+ 9^
57
38
39
9.74487
.74490
.74492
.74495
.55573
.55577
.55581
.55584
9.74656
.74659
.74661
.74664
.55790
.55794
.55797
.55801
9.74824
.74827
.74830
.74833
9.74835
.74838
.74841
.74844
9.74846
.74849
.74852
.74855
.56223
.56227
.56231
.56234
.56238
.56241
.56245
.56249
9.751.59
.75161
.75164
.75167
.56440
.56443
.56447
.56451
+ W
41
42
4.3
9.74498
.74501
.74504
.74506
.55588
.55592
.55595
.55599
.55602
.55606
.55610
.55613
9.74667
.74670
.74673
.74675
.55805
.55808
.55812
.55815
.56021
.56025
.56029
.56032
9.7.5003
.75006
.7.5008
.75011
9.75170
.75172
.75175
.75178
.56454
.56458
.56461
.56465
.56469
.56473
.56476
.56479
.56483
.56487
.56490
.56494
.56497
.56501
.56505
.56508
+ 11'
46
47
9.74509
.74512
.74515
.74518
9.74678
.74681
.74684
.74687
.55819
.55823
.55826
.55830
.56036
.56039
.56043
.56047
9.7.5014
.7."jOI7
.75020
.7-5022
.56252
.56256
.56259
.56263
9.75181
.75183
.75186
.75189
+ 12'
49
50
51
9.74521
.74523
.74526
.74529
.55617
.55620
.55624
.55628
9.74690
.74692
.74695
.74698
.55834
.55837
.55841
.55844
9.748.58
.74860
.74863
.74866
.56050
.56054
.56057
.56061
9.75025
.7.5028
.7.5031
.7.5033
.56267
.56270
.56274
.56277
9.75192
.75195
.75197
.7.5200
+ 13'
53
54
55
9.74532
.74535
.74538
.74540
9.74.543
.74546
.74549
.74552
.55631
.55635
.55638
.55642
.55646
.55649
.55653
.55657
9.74701
.74704
.74706
.74709
.55848
.55852
.55855
.55859
9.74869
.74872
.74874
.74877
.56065
.56068
.56072
.56075
9.75036
.7.5039
.7.5042
.7.5045
.56281
.56285
.56288
.56292
9.75203
.75206
.75208
.75211
+ 14'
57
58
59
9.74712
.74715
.74718
.74720
.55862
.55866
.55870
.55873
9.74880
.74883
.74886
.74888
.56079
.56083
.56086
.56090
.56093
9.7.5047
.750.50
.75053
.75056
.56296
.56299
.56303
.56306
9.75214
.75217
.75220
.75222
.56512
.56516
.56519
.56523
4
3
2
1
+ 15'
9.74.554
.55660
9.74723
.55877
9.74891
9.7.5059
.56310
9.75225
.56526
nh
34"^
17h
SSm
17h
32m
17h
Sim
17h som
TABLE 45.
Haversines.
[Page 889
s
6h30'n97°W
ehsim
97° 45'
6ft 3'2m 98° 0'
6ft 33m
98° 15'
6h spn
98° 30'
s
Log- Hav
Nat. Ilav
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
Log. Hav
Nat. Hav
1
2
3
9.75225
.75228
.75231
.75233
.56526
.56530
.56534
.56537
9.7-5391
.75394
.75396
.75399
.56743
.56746
.56750
.56753
.56757
.56761
.56764
.56768
.56771
.56775
.56779
.56783
.56786
.56789
.56793
.56797
9.75556
.75559
.75561
.75564
.56959
.56963
.56966
.56969
9.75720
.75723
.75726
.75729
.57175
.57178
.57183
.57185
9.75884
.75887
.75889
.7-5892
9.7.5895
.75898
.75900
.75903
.57390
.57394
.57398
.57401
.57405
.57408
.57413
.57416
.57419
.57433
.57436
.57430
.57434
.57437
.57441
.57444
.57448
.57453
.57455
.57459
.57462
.57466
.57470
.57473
.57477
.57480
.57484
.57488
.57491
.57495
.57498
.57502
.57506
.57509
.57513
.57516
.57530
.57534
.57537
.57531
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
36
34
S3
32
31
30
29
"28
27
26
25
'24
23
22
21
20
19
IS
17
l6
15
14
13
12
11
10
9
8
7
6
5
4
3
2
}
_
+ 1'
5
6
7
9.75236
.75239
.75242
.75244
.56541
.56544
.56548
.56552
9.7.5402
.75405
.7.5407
.7.5410
"9»»5413
.7.5416
.75418
.7.5421
9.7.5424
.7.5427
.7.5429
.75432
9.75435
.7.5438
.7.5440
.75443
9.75567
.75570
.75572
.75575
.56973
.56977
.56980
.56984
.56987
.56991
.56994
.56998
9.75T31
.75734
.75737
.75739
.57189
.57193
.57196
.57300
+ 2'
9
10
11
9.75247
.75250
.75253
.75256
.56555
.56559
.56563
.56566
.56570
.56573
.56577
.56580
.56584
.56588
.56591
.56595
9.7.5578
.75581
.75583
.75586
9J"5589
.75592
.75594
.75597
9.75742
.75745
.75748
.75750
.57303
.57307
.57311
.57314
.57318
.57321
.57335
.57339
9.75906
.75908
.75911
.75914
+ 3'
13
14
15
9.75258
.75261
.75264
.75267
.57003
.57005
.57009
.57013
.57016
.57030
.57033
.57037
.57031
.57034
.57038
.57041
9.75753
.75756
.75759
.75761
"9.75764
.75767
.75770
.75772
9.75917
.75919
.75922
.75925
9.75927
.75930
.75933
.75936
+ i'
17
18
19
9.75269
.75272
.75275
.75278
.56800
.56804
.56807
.56811
9.75600
.75603
.75605
.75608
9.75611
.75614
.75616
.75619
.57332
.57236
.57239
.57343
+ 5'
21
22
23
9.75280
.75283
.75286
.75289
.56598
.56603
.56606
.56609
9.75446
.7.5449
.754.52
.7.5454
.56815
.56818
.56833
.56835
.56839
.56833
.56836
.56840
.56843
.56847
.56851
.56854
.56858
.56861
.56865
.56869
.56873
.56876
.56879
.56883
.56887
.56890
.56894
.56897
.56901
.56905
.56908
.56913
.56915
.56919
.56933
.56936
.56930
.56933
.56937
.56941
.56944
.56948
.56951
.56955
.56959
9.75775
.75778
.75780
.75783
.57347
.57350
.57354
.57357
9.75938
.7.5941
.75944
.75947
+ 6'
25
26
27
9.75291
.75294
.75297
.75300
.56613
.56616
.56630
.56634
9.7.54.57
.7.5460
.75463
.75465
1).75468^
.7.5471
.7.5474
.7.5476
9.7.5479"
.7.5482
.75485
.7.5487
9.75622
.75625
.75627
.75630
9.75633
.75636
.75638
.75641
.57045
.57049
.57053
.57056
.57059
.57063
.57067
.57076
9.75786
.75789
.75791
.75794
9.75797
.75800
.75802
.75805
.57361
.57365
.57368
.57372
.57275
.57279
.57283
.57286
.57290
.57293
.57397
.57301
.57304
.57308
.57311
.57315
.57318
.57332
.57326
.57329
.57333
.57337
.57340
.57344
.57347
.57351
.57355
.57358
.57363
.57365
.57369
.57373
.57376
.57380
.57383
.57387
.57390
9.7.5949
-75952
-759.55
-75957
9 -75960
.7.5963
.75966
.7.5968
9.75971
.75974
.75976
.75979
9.7.5982
.7.5985
.75987
.75990
+ r
29
30
31
9.75303
.75305
.75308
.75311
.56637
.56631
.56634
.56638
.56643
.56645
.56649
.56653
+ 8'
33
34
35
9.75314
.75316
.75319
.75322
9.75644
.7.5646
.75649
.7.5652
.57074
.57077
.57081
.57085
.57088
.57093
.57095
.57099
.57i03
.57106
.57110
.57114
.57117
.57131
.57134
.57138
.57131
.57135
.57139
.57143
.57146
.57149
.57153
.57157
.57160
.57164
.57167
.57171
.57175
9.75808
.75810
.75813
.75816
9.7.5819
.75821
.75824
.75827
9.75830
.75832
.75835
.75838
+ 9'
37
38
39
+ W
41
42
4S
9.75325
.7.5327
.75330
.75333
9775336
.7.5338
.75341
.75344
9.75347
.75350
.75352
.75355
9.7.53.5^
.75361
.75363
.75366
.56656
.56660
.56663
.56667
.56670
.56674
.56678
.56681
.56685
.56689
.56693
.56696
.56699
.56703
.56707
.56710
.56714
.56717
.56731
.56735
.56738
.56733
.56735
.56739
.56743
9.75490
.75493
.7.5496
.7.5498
9.7.5501
.7.5504
.7.5507
.75.509
9.75512
.75515
.75518
.75520
9.75.523
.75526
.75529
.75531
9.75534
.75537
.7.5540
.75542
9.75655
.75657
.75660
.7.5663
¥.75666
.75668
.75671
.75674
9.75677
.7.5679
.75682
.7.5685
9.75688
.75690
.75693
.75696
9.75698
.75701
.75704
.75707
9.7:5709"
.75712
.75715
.75718
9.75720'
9.75993
.75995
.75998
.76001
9.76004
.76006
.76009
.76012
9.76014
.76017
.76020
.76023
9.76025
.76028
.76031
.76033
9.76636i
.76039 1
.76041
.76044
9.76047 1
.57534
.57538
.57541
.57545
.57549
.57552
.57556
.57559
.57563
.57567
.57570
.57574
.57577
.57581
.57585
.57588
.57592
.57595
.57599
.57603
.57606
+ 11'
45
46
47
9.7.5840
.75843
.75846
.75849
"9.7585f
.75854
.7.5857
.75859
'9.75862
.75865
.75868
.75870
9.75873"
.75876
.75879
.75881
9.75884
+ 13'
49
50
51
+ 13'
53
54
55
9.75369 1
.7.5372
.75374
.75377
9.75380 i
.7.5383 1
.7.5385
.75388
+ 14'
57
58
59
9.75545
.7.5548
.75550
.7.5553
9.75556"
+ IS'
9.75.391
/7ft
29m
nh
28m
;7A
27m
77ft
26m
77ft.
Z5m
Page 890] • TABLE 45.
Haversines.
3
6* S5"> 98° 45'
6A 36'n 99° 0'
6'* 37m 99° 15'
6h 38"> 99° 30'
6" 39>n 99° 45'
s
Log. Hav.
Nat.IIav.
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
0.76047
.700,50
.76052
.76055
.51606
.57610
.57613
.57617
.57621
.57634
.57638
.57631
9.76209
.76212
.76215
.76217
9.76220
.76223
.76225
.76228
9.76231
.76233
.76236
.76239
.57833
.57835
.57839
.57833
9.70371
.76373
.76376
.76379
.58037
.58041
.58044
.58048
.58051
.58055
.58059
.58063
.58066
.58069
.58073
.58077
9.70531
.76534
.76537
.76539
.58352
,58356
.58260
.58263
9.76691
.76094
.70697
.76699
.58467
.58471
,58475
.58478
60
59
58
.57
-5ti
55
54
53
52
51
50
49
48
41
46
45
+ 1'
.5
6
/
9.70058
.70000
.70003
.70006
9.70669
.70071
.76074
.76077
.57836
.57840
.57843
.57847
.57850
.57854
.57858
.57861
9.76381
.70384
.70387
.70389
9.70392
.76395
.76397
.76400
9.76542
.76545
.70547
.70550
.58367
.58370
.58374
.58377
.58381
.58385
.58388
.58393
.58395
.58399
.58303
.58306
9.76702
.76705
.76707
.76710
.58483
.58485
.58489
.58493
.58496
.58500
.58503
.58507
+ r
9
10
11
.57635
.57639
.57643
.57646
9.76553
.76555
.76558
.76561
9.70713
.76715
.76718
.70721
+ 3'
13
14
15
9.76079
.76082
.76085
.76088
9.76090
.76093
.76096
.76098
.57649
.57653
.57656
.57660
9.76241
.76244
.76247
.76250
.57865
.57868
.57873
.57876
9.76403
.76405
.76408
.76411
.58080
.58084
.58087
.58091
.58095
.58098
.58103
.58105
9.76-563
.76566
.76569
.76571
9.70723
.70726
.70729
.70731
9.76734
.76737
.70739
.70742
.58510
.58514
.58518
.58531
.58535
.58538
.58533
.58536
+ 4'
17
18
19
.57661
.57667
.57671
.57675
9.76252
.76255
.76258
.76200
.57879
.57883
.57886
.57890
9.76414
.76416
.76419
.76422
9.76574
.76577
.76579
.76.582
9.76585
.76587
.76590
.76593
.58310
.58313
.58317
.58331
44
43
4-:
41
40
39
38
37
36
35
34
33
+ 5'
21
22
23
9.76101
.76104
.76106
.76109
.57678
.57683
.57685
.57689
.57693
.57696
.57700
.57703
9.76263
.76266
.76268
.76271
.57894
.57897
.57901
.57904
9.76424
.76427
.76430
.76432
.58109
.58113
.58116
.58130
.58334
.58338
.58331
.58335
.58338
,58343
,58346
.58349
9.76745
.70747
.707.50
.70753
.58539
.58543
.58546
.58550
+ 6'
25
26
27
9.76112
.76115
.76117
.76120
9.76274
.76276
.76279
.76282
.57908
.57911
.57915
.57919
.57933
.57936
.57939
.57933
9.76435
.76438
.76440
.76443
.58133
.58137
.58130
.58134
9.70-595
.76598
.76601
.76603
9.70755
.70758
.70761
.76763
.58553
.58557
.58561
.58564
+ r
29
30
31
9.76123
.76125
.70128
.76131
.57707
.57710
.57714
.57718
9.76285
.76287
.76290
.76293
9.76440
.70448
.76451
.764.54
.58138
.58141
.58145
.58148
9.7660()
.76609
.70611
.76614
.58353
.58356
.58360
,58364
9.76766
.76709
.70771
.70774
.58568
.58571
.58575
.58579
.58583
.58586
.58589
.58593
.58596
.58600
.58604
.58607
3;
31
30
J9
J8
27
26
>5
24
23
r>
21
M)
19
18
77
+ 8'
33
34
35
9.76134
.76130
.76139
.76142
.57731
.57735
.57738
.57733
9.76290
.70298
.76301
.76303
.57937
.57940
.57944
.57947
9.76456
.76459
.76462
.76464
.58153
.58156
.58159
.58163
9.76617
.76619
.76622
.76625
.58367
,58371
,58374
.58378
9.70777
.70779
,76782
.76784
+ 9'
37
38
39
9.76144
.76147
.76150
.76152
.57736
.57739
.57743
.57746
9.70306
.76309
.76311
.76314
.57951
.57955
.57958
,57962
9.70407
.70470
.70473
.70475
.58166
.58170
.58173
.58177
9.76627
.76630
.76633
.76635
.58381
.58385
.58389
.58393
9.76787
.76790
.70792
.70795
+ 10'
41
42
43
9.76155
.701.58
.70101
.70103
.57750
.57753
.57757
.57761
9.76317
.76320
.70322
.76325
.57965
.57969
.57973
.57976
9.76478
.76481
.76483
.7048(i
.58181
.58184
.58188
.58191
9.76638
.76641
.76643
.70646
.58396
.58399
.58403
.58407
9.76798
.76800
.70803
.70806
.58611
.58614
.58618
.58633
.58635
.58639
.58633
.58636
.58639
.58643
.58647
.58650
+ 11'
45
46
47
9.76106
.76109
.76171
.76174
.57764
.57768
.57771
.57775
9.76328
.76330
.76333
.76336
.57980
.57983
.57987
.57990
9.76489
.70491
.70494
.76497
9.76499
.76502
. 76505
.76507
.58195
.58199
.58303
.58306
9.70649
.76651
.76654-
.76657
.58410
.58414
.58417
.58431
9.76808
.76811
.76814
.76816
9.76819
.76822
.76824
.76827
16
15
14
13
;.'
/;
10
9
8
7
6'
5
+ 13'
49
50
51
9.76177
.76179
.76182
.76185
.57779
.57783
.57786
.57789
9.76338
.76341
.76344
.76346
9.76349
.76352
.76354
.76357
.57994
.57998
.58001
.58005
.58309
.58313
.58317
.58330
.58334
.58337
.58331
.58334
9.766-59
.70602
.76665
.76667
9.76670
.76073
.76675
.76678
9.76681
.76683
.76686
.76689
9.76691
.58434
.58428
,58432
.58435
+ 13'
53
54
55
9.76188
.76190
.76193
.76196
.57793
.57797
.57800
.57804
.58008
.58013
.58016
.58019
9.70510
.70513
.70515
.70518
.58439
.58442
.58446
.58450
9.76830
.7(5832
.70835
.768.38
.58654
.58657
.58661
.58665
+ 14'
57
58
59
9.76198
.76201
.76204
.76206
.57807
.57811
.57815
.57818
9.76360
.76363
.70305
.70308
.58033
.58036
.58030
.58034
9.76521
.76523
.76526
.76529
.58238
.58343
.58345
.58349
,58353
.58453
.58457
.58460
.58464
9.76840
.76843
.76845
.76848
.58668
.58671
.58675
.58679
4
3
2
1
+ 15'
9.76209
.57833
9.703n
.58037
9.76531
.58467
9.76851
.58683
17h ^4m
17h es"!
17h 22m
;7A 21"t
17h 20m
TABLE 45.
Haversines.
[Page 891
s
eh 40m
100° c
6h 41m
100=" 15'
6h42m
100° 30'
•6 A 4-i"'
100° 45'
61^44™
101° 0'
3
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav
Log. Hav
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.76851
.70853
.76856
.76859
.58682
.58086
.58890
.58693
9.77009
.77012
.77015
.77017
9.77020
.77023
.77025
.77028
9.77031
.77033
.77030
.77038
9.77041
.77044
.77046
.77049
9.770.52
.77054
.77057
.77060
9.77002
.77005
.77007
.77070
9.77073
.77075
.77078
.77081
9.77083
.77086
.77089
.77091
9.77094
.77090
.77099
.77102
9.77104
.77107
.77110
.77112
9.77115
.77117
.77120
.77123
9.7712.5"
.77128
.77131
.77133
9.77136"
.77139
.77141
.77144
9.77146"
.77149
.77152
.771.54
9.77157
.77160
.77162
.77165
9.77167"
.58897
.58901
.58904
.58908
.589111
.58915
.58919
.58922
.58926
.^8929
.58933
.58937
.58940
.58944
.58947
.58951
.58954
.58858
.58962
.58965
.58969
.58972
.58976
.58979
9.77167
.77170
.77173
.77175
9.77178
.77181
.77183
.77186
9.77188
.77191
.77194
.77196
"9.77199
.77202
.77204
.77207
.59112
.59115
.59119
.59132
.59126
.59130
.59133
.59137
.59140
.59144
.59148
.59151
.59155
.59158
.59162
.59165
9.77325
.77327
.77330
.77333
9.77335
,77338
.77340
.77343
9.77346
.77348
.77351
.77353
9.77356
.77359
.77361
.77364
9.77300'
.77309
.77372
.77374
9.77377
.77380
.77382
.77385
9.77387
.77390
1 .77393
.77395
9.77398
.77400
.77403
.77400
"9.77408
.77411
.77413
.77410
9.77419
.77421
.77424
.77427
9.77429
.77432
.77434
.77437
9.77440
.77442
.77445
.77447
9.774.50
.774.53
.77455
,774.58
9J7406'
,77463
,77406
.77408
9.77471
.77473
.77476
.77479
9.77481
.59326
.59330
.59333
.59337
.59340
.59344
.59348
.59351
.59355
.59358
.59362
.59365
.59369
.59373
.59376
.59380
.59383
.59387
.59391
.59394
.59398
.59401
.59405
.59408
.59412
.59416
.59419
.59423
.59426
.59430
.59433
.59437
.59440
.59444
.59448
.59451
.59455
.59458
.59462
.59465
.59469
.59473
.59476
.59480
.59483
.59487
.59490
.59494
.59498
.59501
.59505
.59508
.59512
.59515
.59519
.59523
.59526
.59530
.59533
.59537
.59540
9.77481
.77484
.77486
.77489
9.77492
.77494
.77497
.77499
9.77'502
.77505
.77507
.77510
9.77512
.77515
.77518
.77520
9.77523
.77525
.77528
.77531
9.77533
.77536
.77538
.77541
9. 77544"
.77540
.77549
.77551
9777554
.77557
.77559
.77562
9.77564
.77567
.77570
.77572
9:77575
.77577
.77580
.77583
9.77585
.77588
.77590
.77593
.59540
:5»544
.59548
.59551
.59555
.59558
.59562
.59565
.59569
.59573
.59576
.59580
.59583
.59587
.59590
.59594
.59598
.59601
.59605
.59608
.59612
.59615
.59619
.59623
.59626
.59630
.59633
.59637
60
59
58
57
56
55
54
53
+ 1'
5
6
/
9.76861
.76804
.76807
.70869
9.76872
.76875
.70877
.70880
9.70883
.76885
.76888
.76891
9.76893
.76896
.76898
.76901
.58697
.58700
.58704
.58707
.58711
.58714
.58718
.5872?
.587*5
.58729
.5873:$
.58736
.58740
.58743
.58747
.58750
.58751
.58758
.58761
.58765
".58768
.58772
.58776
.58779
.58783
.58786
.58790
.58793
.58797
.58801
.58804
.58808
.58811
.58815
.58818
.58822
.58826
.58829
.58833
.58836
.58840
.58843
.58847
.58851
.58854
.58858
.58861
.58865
.58869
.58872
.58876
.58879
.58883
.58886
.58890
.58894
.58897
+ 2'
9
10
11
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
■28
27
26
25
24
23
2^2
21
20
19
18
17
16
15
14
13
12~
11
10
9
8
7
6
5
' 4
3
2
}
+ 3'
13
14
15
+ i'
17
18
19
9.77209
.77212
.77215
.77217
9.77220
.77223
.77225
.77228
.59169
.59173
.59176
.59180
.59183
.59187
.59190
.59194
,59198
.59201
.59205
..59208
.59212
.59215
.59219
.59223
.59226
.59230
.59233
.59237
.59240
.59244
.59248
.59251
.59255
.59258
.59262
.59265
+ 5'
21
22
23
9.76904
.76900
.70909
.70912
9.76914
.76917
.76920
.76922
+ 6'
25
26
27
.58983
.58987
.58990
.58994
.58997
.59001
.59005
.59008
.59012
.59015
.59019
.59022
.59026
.59030
.59033
.59037
9.77230
.77233
.77236
.77238
9.77241
.77243
.77246
.77249
9.77251
.77254
.77257
.77259
9.77262
.77264
.77267
.77270
+ r
29
30
31
9.76925
.76928
.76930
.76933
9.76936
.76938
.76941
.70943
9.70946
.70949
.76951
.76954
.59640
.59644
.59648
.59651
.59655
.59658
.59662
.59665
.59669
.59672
.59676
.59680
.59683
.59687
.59690
.59694
.59697
.59701
.59705
.59708
.59712
.59715
.59719
.59722
.59726
.59730
.59733
.59737
.59740
.59744
.59747
.59751
.59755
+ 8'
33
34
35
+ 9'
37
38
39
+ W
41
42
43
9.76957
.76959
.76962
.76965
976967
.76970
.76972
.76975
.59040
.59044
.59047
.59051
.59055
.59058
.59062
.59065
9.77272
.77275
.77278
.77280
+ 11'
45
46
47
9.77283
.77285
.77288
.77291
.59269
.59273
.59276
.59280
9,77590
.77598
.77601
.77603
9.77606
.77609
,77611
,77614
9.77616
.77619
.77622
.77624
9.77627
.77629
.77632
.77634
+ 12'
49
50
51
9.76978
.70980
.76983
.76986
.59069
.59072
.59076
.59080
.59083
.59087
.59090
.59094
.59097
.59101
.59105
.59108
9.77293
.77296
.77298
.77301
..59283
.59287
.59290
.59294
.59298
.59301
.59305
.59308
.59312
.59315
.59319
.59323
.59326
+ 13'
53
54
55'
9.76988
.76991
.70994
.70990
9.70999
.77002
.77004
.77007
9.77009
9.77304
.77306
.77309
.77312
+ 14'
57
58
59
9.77314
.77317
.77319
.77322
+ 15'
.59112
9.77325
9.77637
;7A
19m
17h
ISm
17ft
17m
17h
16™
77A
15m
Page 892]
TABLE
45.
Haversines.
s
6h 4.5m
101° 15'
6h 46m 101° W
6h 47m
101° 45'
«* 48'"
102° 0'
ah 49m
102° 15'
s
Log. Ilav.
Nat. Ilav.
Log. Hav.
Nat. Ilav.
Log. TIav.
Nat. Ilav.
Log. Ilav.
Nat. Hav.
Log. Ilav.
Nat. Hav.
9.77637
.59755
9.77792
.59968
9.77947
.60182
9.78101
.60396
9.78254
.60609
60
1
.77640
.59758
.77795
.59972
.77949
.60185
.78103
.60399
.78256
.60612
.5.9
•2
.77642
.59762
Jim
.59976
.77952
.60189
.78106
.60403
.782.59
.60616
.5.S'
S
+ 1'
.77645
9.77647
.59765
.59769
.77800
9.77803'
.59979
.77954
9.77957
.60193
.60196
.78108
9.78111
.60406
.60410
.78261
9.78264
.60620
.60623
57
~66~
.59983
5
.77650
.59772
.77805
.59986
.77960
.60200
.78113
.60414
.78266
.60627
55
6
.77653
.59776
.77808
.59990
.77962
.60203
.78116
.60417
.78269
.60630
54
7
.77655
.59779
.59783
.77810
'9.77813
.59993
.59997
.77965
9.77967
.60207
.60211
.78118
9.78121
.60420
.60424
.78271
'9.78274
.60634
.60637
53
52
+ r
9.77658
9
.77660
.59787
.77815
.60000
.77970
.60214
.78124
.60428
.78277
.60641
51
10
.77663
.59790
.77818
.60004
.77972
.60218
.78126
.60431
.78279
.60644
50
11
.77666
.59794
.77821
.60008
.77975
.60221
.78129
.60435
.78282
.60648
i9_
+ -3'
!). 77668
.59797
9.77823
.60011
9.77978
.60225
9.78131
.60438
9:78284
.60652
4S
IS
.77671
.59801
.77826
.60015
.77980
.60228
.78134
.60442
.78287
.60655
47
14
.77673
.59804
.77828
.60018
.77983
.60232
.78136
.60445
.78289
.60659
46
15
.77676
9.77679
.59808
.59812
.77831
9.77834
.60022
.60025
.77985
.60235
.60239
.78139
'9.78141
.60449
.60452
.78292
9.78294
.60662
.60666
45
'44
+ i'
9.77988
n
.77681
.59815
.77836
.60029
.77990
.60243
.78144
.60456
.78297
.60669
43
18
.77684
.59819
.77839
.600S3
.77993
.60246
.78147
.60460
.78299
.60673
4i
19
.77686
"9.77689
.59822
.59826
.77841
9.77844
.60036
.6O0iO
.77996
9.77998
.60250
.60253
.78149
9.78152'
.60463
.60467
.78302
9.78305
.60676
.60680"
41
40
+ 5'
^1
.77691
.59829
.77846
.60013
.78001
.60257
.78154
.60470
.78307
.60684
39
22
.77694
.59833
.77849
.60047
.78003
.60260
.78157
.60474
.78310
.60687
J8
23
.77697
.59837
.77852
9.77854
.60050
.60054
.78006
9.78008
.60264
.60268
.78159
9.78 162
.60477
.60481
.78312
.60691
37
+ 6'
9.77699
.59840
9.78315
.60694
25
.77702
.59844
.77857
.60057
.78011
.60271
.78164
.60484
.78317
.60698
35
26
.77704
.59847
.77859
.60061
.78013
.60275
.78167
.60483
.78320
.60701
34
27
.77707
.59851
.59854
.77862
9.77864
.60065
.60068
.78016
9.78019
.60278
,60282
.78170
9.78172
.60492
.60495
.78322
9:78325
.60705
.60708
33
32
+ V
9.77710
29
.77712
.59858
.77867
.60072
.78021
.60285
.78175
.60499
.78327
.60712
31
30
.77715
.59861
.77870
.60075
.78024
.60289
.78177
.60502
.78330
.60715
30
31
+ S'
.77717
9;77720
.59865
.59869
.77872
9. 77875
.60079
.60082
.78026
9.78029'
.60292
.602 :»6
.78 ISO
9.78182
.60506
.60509
.78332
.60719
29
28
9.78335
.60723
33
.77723
.59872
.77877
.60086
.78031
.60300
.78185
.60513
.78338
.60726
27
34
.77725
.59876
.77880
.60090
.78034
.60303
.78187
.60516
.78340
.60730
"26
35
+ 9"
.77728
^9.77730
.59879
.59883
.77882
9.77885
.60093
.60097
.78037
'9:78039
.60307
.60310
.78190
9.78192
.60520
.60524
.78343
.60733
25
9.78345
.60737
24
37
.77733
.59886
.77888
.60100
.78042
.60314
.78195
.60527
.78348
.60740
23
38
.77735
.59890
.77890
.60104
.78044
.60317
.78198
.60531
.78350
.60744
t'f
39
.77738
.59894
.59897
.77893
'9.77895
.60107
.60111
.78047
9.78049
.60321
.60324
.78200
9.78203
.60534
.60538
.78353
9:78355
.60747
21
+ W
9.77741
.60751
20
41
.77743
.59901
.77898
.60114
.78052
.60328
.78205
.60541
.783.58
.60755
19
42
.77746
.59904
.77900
.60118
.78054
.60332
.78208
.60545
.78360
.60758
18
43
.77748
9.7775T
.59908
.77903
.60122
.78057
9.78060
.60335
.60339
.78210
9.7S213'
.60548
.60552
.78363
'9.78365
.60762
.60765
17
"I6
+ 11'
.59911
9.77906
.60125
45
.77754
.59915
.77908
.60129
.78062
.60342
.78215
.60536
.78368
.60769
15
46
.77756
.59919
.77911
.60132
.78065
.60346
.78218
.6055!)
.78371
.60773
14
47
.77759
.59922
.77913
9.77916
.60136
.60139
.78067
9.78070
.60349
.60353
.78221
9.78223
.60563
.60566
.78373
9.78376
.60776
13
12
+ 12'
9.77761
.59926
.60779
49
.77764
.59929
.77918
.60143
.78072
.60356
.78226
.60570
.78378
.60783
11
50
.77766
.59933
.77921
.60146
.78075
.60360
.78228
.60573
.78381
.60786
10
51
.77769
9.77772
.59938
.59940
.77924
9.77926
.60150
.60154
.78077
9.78080
.60364
.60367
.78231
9.78233
.60577
.60580
.78383
.60790
9
+ 13'
9.78386
.60794
53
.77774
.59943
.77929
.60157
.78083
.60371
.78236
.60584
.78388
.60797
7
54
.77777
.59947
.77931
.60161
.78085
.60374
.78238
.60588
.78391
.60801
6
55
.77779
.59951
.59954
.77934
9.77936'
.60164
.60168
.78088
9.78090
.60378
.60381
.78241
'9.78243
.60591
.60595
.78393
'9.78396'
.60804
.60808
5
2f-
■+ 14'
9.77782
57
.77785
.59958
.77939
.60171
.78093
.60385
.78246
.60598
.78398
.60811
3
58
.77787
.59961
.77942
.60175
.78095
.60388
.78249
.60602
.78401
.60815
59
.77790
9,77792'
.59965
.59968
.77944
'9.77947
.60179
.60182
.78098
9.78101
.60392
.60396
.78251
9:782.54'
.60605
.78404
.60818
.60822
~1
+ 15'
.60609
9.78406
17h
14m
/7&
13m
17h
2:^m
17h
nm
nn
mm
TABLP: 45.
Haversines.
[Page 893
s
6* .50"! 103° 30' 1
6* 5lm 102° 45' 1
6ft 52™ 103° 0' 1
6* 5.3m 103° 15' 1
6ft .54™ 103° 30'
s
Log. Hav.
Nat. Hav.
Hav.Log. 1
Nat. Hav.
Ix)g. Hav.j
Nat. Hav.
lK>g. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
3
9.78400
.78409
.78411
.78414
.6082?
.60825
.60829
.60833
.60836
.60840
.60843
.60847
9.78558
.78560 1
.78563
.78565 1
9.78568
.78570
.78573 ;
.78575 ;
.61035
.61038
.61042
.61046
.61049
.61053
.61056
.61060
9.78709
.78711
.78714
.78716
.61248
.61251
.61255
.61258
9.78859
.78862
.78864
.78867
9.78869
.78872
.78874
.78877
.61460
.61464
.61467
.61471
9.79009
.79011
.79014
.79016
9.79019
.79021
.79024
.79026
.61672
.61676
.61679
.61683
.61686
.61690
.61693
.61697
.61701
.61704
.61708
.61711
.617 li
.61718
.61722
.61725
.61729
.61732
.61736
.61739
.61743
.61747
.61750
.61754
.61757
.61761
.61764
.61768
.61771
.61775
.61778
.61782
.61785
.61789
.61792
.61796
.61800
.61803
.61807
.61810
.61814
.61817
.61821
.61824
.61828
.61831
.61835
.61838
m
59
58
57
.56
55
■U
.'>■!
52
51
50
49
48
-',7
46
45
■',4
■',■3
42
41
40
■39
■38
■37
■iH
,15
■34
■3.3
+ .1'
■'J
6
7
9.7841ti
.78419
.78421
.78424
9.78719
.78721
.78724
.78726.
.61262
.61265
.61269
.61272
.61474
.61478
.61481
.61485
+ r
9
10
11
9.78426
.78429
.78431
.78434
.60850
.60854
.60857
.60861
9.78578
.78581
.78583
.78586
.61063
.61067
.61070
.61074
.61077
.61081
.61085
.61088
9.78729
.78731
.78734
.78737
9:78739
.78742
.78744
.78747
.61276
.61279
.61283
.61287
9.78879
.78882
.78884
.78887
.61488
.61492
.61495
.61499
9.79029 i
.79031 j
.79034
.79036
"9.79039 1
.79041
.79044
.79046 i
9.79049
.79051
.79054
.79056
9.79059
.79061
.79064
.79066 ;
9.79069 1
.79071
.79074
.79076
9.79079
.79081
.79084
.79086
9.79089
.79091
.79094
.79096
9.79099
.79101
.79103
.79106
977^^9108
.79111
.79113
.79116
"9.79118
.79121
.79123
.79126
+ 3'
L3
14
15
9.78436
.78439
.78442
.78444
.60865
.60868
.60872
.60875
9.78588
.78591
.78593
.78.596
.61290
.61294
.61297
.61301
9.78889
.78892
.78894
.78897
.61502
.61506
.61510
.61513
.61517
.61520
.61524
.61527
+ i'
17
18
19
9.78447
.78449
.784.52
.78454
.60879
.60882
.60886
.60889
9.78598
.78601
.78603
.78606
.61092
.61095
.61099
.61102
9.78749
.78752
.78754
.78757
.61304
.61308
.61311
.61315
9.78899
.78902
.78904
.78907
+ 5'
il
t '
9.784.57
.784.59
.78462
.78464
.60893
.60897
.60900
.60904
9.78608
.78611
.78613
.78616
.61106
.61109
.61113
.61116
9.78759
.78762
.78764
.78767
.61318
.61322
.61325
.61339
9.78909
.78912
.78914
.78917
.61531
.61534
.61538
.61541
.61545
.61548
.61552
.61556
.61559
.61563
.61566
.61570
.6157.3
.61577
.61580
.61584
.61587
.61591
.61594
.61598
2<3
27
9.78467
.78469
.78472
.78474
.60907
.60911
.60914
.60918
9.78618
.78621
.78623
.78626
9.78628
.78631
.78633
.78636
9.78638
.78641
.78643
.78646
.61120
.61124
.61127
.61131
.61104
.61138
.61111
.61145
9.78769
.78772
.78774
.78777
.81333
^.61336
.,61340
.61343
9.78919
.78922
.78924
.78927
+ ''
29
■30
SI
9.78477
.78479
.78482
.78485
.69921
.60925
.60928
.60932
.60936
.60939
.60943
.60946
9.78779
.78782
.78784
.78787
.61347
.61350
.61354
.61357
.61361
.61364
.61368
.61372
9.78929
.78932
.78934
.78937
.32
SI
.30
29
28
27
26
25
24
2S
22
21
'20
19
18
17
16
15
14
IS
+ 8'
■34
■35
9.78487
.78490
.78492
.78495
.61148
.61152
.61155
.61159
9.78789
.78792
.78794
.78797
9.78939
.78942
.78944
.78947
+ 9'
■i7
■38
■i9
9.78497
.78500
.78502
.78505
.60950
.60953
.60957
.60960
9.78649
.78651
.78654
.78()o6
.61163
.61166
.61170
.61173
9.78799
.78802
.78804
.78807
.61375
.61379
.61382
.61386
.61389
.61393
.61396
.61400
9.78949
.78952
.78954
.78957
+ 10'
41
42
4J
9.78507
.78510
.78512
.78515
.60964
.60967
.60971
.60975
.60978
.60982
.60985
.69989
.'66992
.60996
.60999
.61003
9.78(>59
.78661
.78664
.78666
9.78669
.78671
.78674
.78676
9.78679
.78681
.78684
.78686
.61177
.61180
.61184
.61187
.61191
.61194
.61198
.61201
.61205
.61209
.61212
.61216
.61219
.61223
.61226
.61230
9.78809
.78812
.78814
.78817
9.78819
.78822
.78824
.78827
9.78829
.78832
.78834
.78837
9.78839
.78842
.78844
.78847
9.78959
.78962
.78964
.78967
.61602
.61605
.61609
.61612
+ 11'
45
413
47
9.78517
.78520
.78522
.78525
.6i403
.61407
.61410
.61414
9.78969
.78972
.78974
.78977
.61616
.61619
.61623
.61626
.61630
.61633
.61637
.61640
.61644
.61648
.61651
.61655
.61658
.61662
.61665
.61669
+ IV
■'t9
50
51
9.78528
.78530
.78533
.78535
.61418
.61421
.61425
.61428
9.78979
.78982
.78984
.78987
9.79128
.79131
.79133
.79136
.61842
.61845
.61849
.61853
12
11
10
9
8
6
5
4
S
2
1
+ _13'
•';■:''
54
55
9.78538
.78540
.78543
.78545
.61007
.61010
.61014
.61017
9.78689
.78691
.78694
.78696
.61432
.61435
.61439
.61442
9.78989
.78992
.78994
.78997
9.79138
.79141
.79143
.79146
9.79148
.79151
.79153
.79156
.61856
.61860
.61863
.61867
.61870
.61874
.61877
.61881
+ _14'
57
58
59
9.78548
.78550
.78553
.78555
.61021
.61024
.61028
.61032
9.78699
.78701
.78704
.78706
.61233
.61237
.61240
.61244
9.78849
.78852
.78854
.78857
.61446
.61449
.61453
.61456
9.78999
.79002
.79004
.79007
+ 15'
9.78558
.61035
9.78709
.61248
9.78859
.61460
9.79009
.61672
9.79158
.61884
17
h^m
nhgm
77
\ 7m
77ft fim
nh
5"!
Page 894]
TABLE 45.
Haversines.
s
e* 55^ 103° 45'
eh 5&n 104° 0'
6h .57"' 104° 15'
6h asm 104° 30'
6h 59m 104° 45' 1
s
Log. llav.
Nat. Ilav.
Log. Ilav.
Xat. Uav.
Log. Ilav.
Xat. Ilav.
Log. Ilav.
Xat. Hav.
Log. Ilav.
Xat. Ilav.
1
2
3
9.79158
.79161
.79163
.79165
.61884
.61888
.61891
.61895
9.79306
.79309
.79311
.79314
.62096
.62100
.62103
.62107
9.794.34
.79457
.79459
.79462
.62308
.62311
.62315
.62318
.62322
.62325
.62329
.62332
.62336
.62339
.62343
.62346
.62350
.62353
.62357
.62361
.62364
.62368
.63371
.62375
.62378
.62382
.62385
.62389
.62392
.62.396
.62399
.62403
.62406
.62410
.62413
.62417
.62420
.62424
.62427
.62431
.62434
.62438
.62442
.62445
.62449
.62452
.63456
.63459
.63463
.63466
.62470
.63473
.62477
.62480
.62484
.62487
9. -79601
.79604
.79606
.79609
.62519
.62522
.63526
.62530
9.79748
.797-50
.79752
.79755
"9T79757
.79760
.79762
.79765
9.79767
.79770
.79772
.79774
9.79777
.79779
.79782
.79784
9779787
.79789
.79791
.79794
9.79796'
'.79799
.79801
.79804
"9.79806
.79808
.79811
.79813
9.79816
.79818
.79821
.79823
9.79825
.79828
.79830
.79833
9.79835
.79838
.79840
.79842
.62730
.62734
.62737
.62741
.62744
.62748
.62751
.63755
.63758
.63763
.62765
.62769
.62773
.62776
.62779
.62783
.62786
.62790
.62793
.62797
.62800
.62804
.62807
.62811
.62814
.63818
.63832
.63825
.63839
.63832
.62836
.62839
.62843
.63846
.63850
.63853
.63857
.63860
.63864
.63867
.63871
.63874
.62878
.62881
.62885
.62888
.62893
.62895
.62899
.62902
.62906
.62909
.62913
.63916
.63920
.63923
til)
59
oS
•ji
"51T
55
54
5i
'it
51
:>(!
49
-jS
4^
■'id
45
44
4-1
■i .
-(/
411
■i!)
,;a'
■J 4
'fi
-,7
ill
:.'9
I'd
_'.)•
21
2(1
19
IK
17
It]
15
14
1.1
12
11
10
9
G
5
4
y
1
+ 1'
5
6
7
9.79168
.79170
.79173
.79175
.61898
.61903
.61905
.61909
9.79316
.79319
.79321
.79324
.62110
.62114
.62117
.62121
9.79464
.79466
.79469
.79571
9.79474
.79476
.79479
.79481
9.79484
.79486
.79489
.79491
9.79611
.79613
.79616
.79618
'9.79621
.79623
.79626
.79628
9.79631
.79633
.79635
.79638
"9.79640
.79643
.79645
.79648
9.796-50
.796-53
.79655
.79657
9.79660
.79662
.79665
.79667
9.79670
.79672
.79674
.79677
.62533
.62537
.62540
.62544
.62547
.62551
.62554
.62558
.62561
.63565
.62568
.62572
.62575
.62579
.62582
.62586
.62589
.62593
.62596
.62600
.62603
.63607
.63611
.62614
.62618
.62621
.62625
.62628
.62632
.63635
.63639
.62642
.62646
.62649
.62653
.62656
+ r
9
10
11
9.79178
.79180
.79183
.79185
9.79188
.79190
.79193
.79195
9.79198
.79200
.79203
.79205
.61913
.61916
.61920
.61923
.61927
.61930
.61934
.61937
.61941
.61944
.61948
.61951
9.79326
.79329
.79331
.79334
9.'79336
.79339
.79341
.79343
9.79346
.79348
.79351
.79353
.62124
.62128
.62131
.62135
.62138
.62142
.62145
.62149
.62i53
.62156
.62160
.62163
+ '3'
13
14
15
+ 4'
17
18
19
9.79493
.79496
.79498
.79501
9.79503
.79506
.79:08
.79511
9.79513
.79516
.79518
.79520
9.79523"
.79525
.79528
.79530
9.79533
.79535
.79538
.79540
+ S'
21
22
23
9.79208
.79210
.79213
.79215
9.79217
.79220
.79222
.79225
9.79227
.79230
.79232
.79235
9.79237"
.79240
.79242
.79245
9.79247
.79250
.79252
.79255
.61955
.61958
,61962
.61966
.61969
.61973
.61976
.61980
.61983
.61987
.61990
.61994
.61997
.62001
.62004
.62008
.62011
.62015
.62018
.62022
.62026
.62029
.62033
.62036
.62040
.62043
.62047
.62050
.62054
.62057
.62061
.62064
.62068
.62071
.62075
.62078
.62082
.62086
.62089
.62093
.62096
9.79356
.79358
.79361
.79363
9.79366
.79368
.79371
.79373
9.79376"
.79378
.79380
.79383
.62167
.62170
.62174
.62177
.62181
.62184
.62188
.62191
.62195
.62198
.62202
.62205
+ 6'
25
26
27
+ r
29
30
31
+ 8'
33
34
35
9.79385
.79388
.79390
.79,393
9.79395
.79398
.79400
.79403
9.79405
.79407
.79410
.79412
.62209
.62213
.62216
.62220
.62223
.62227
.62230
.62234
.62237
.62241
.62244
.62248
9.79679
.79682
.79684
.79687
9.79689
.79692
.79694
.79696
9.79699
.79701
.79704
.79706
+ 9'
37
38
39
9.79542
.79545
.79547
.79550
9.79-552
.79.555
.79.557
.79560
+ 10'
41
42
43
9.79257
.79260
.79262
.79264
.62660
.62663
.62667
.62670
.62674
.62677
.62681
.62684
9.79845
.79847
.79850
.79852
+ 11'
45
46
47
9.79267
.79269
.79272
.79274
9.79415
.79417
.79420
.79422
.62251
.62255
.62258
.62262
9.79-562
.79565
.79567
.79569
9.79709
.79711
.79714
.79716
9.79718
.79721
.79723
.79726
9.79728
.79731
.79733
.79735
9.79738
.79740
.79743
.79745
9.79855
.79857
.79859
•.79862
9.79864"
.79867
.79869
.79872
9.79874
.79876
.79879
.79881
+ ir
49
50
51
9.79277
.79279
.79282
.79284
9.79425
.79427
.79430
.79432
.62265
.62269
.62272
.62276
9.79572
.79574
.79-577
.79579
9.79582
.79584
.79.587
.79589
.62688
.62691
.62695
.62698
+ 13'
53
54
55
9.79287
.79289
.79292
.79294
9.79434
.79437
.79439
.79442
9.79444
.79447
.79449
.79452
9.79454
.62279
.62283
.62287
.62290
.62294
.62297
.62301
.62304
.62308
.62491
.62494
.62498
.62501
.62703
.62706
.62709
.62713
+ w
57
58
59
9.79297
.79299
.79301
.79304
9.79591
.79-594
.79596
.79599
.62505
.62508
.62512
.62515
.62519
.62716
.62720
.62723
.62727
9.79884
.79886
.79888
.79891
9.79893
.63937
.63930
.62934
.62937
.62941
+ 15'
9.79306
9.79601
9.79748
.62730
171
I .|m
77'
•V"
17f
om
rri>
jm
i7'
i lim
TABLE
45.
Page 895
Haversines.
. s
7h0>t
105° (K
7h im 105° 15' |
7h 2m 105° 30' | 7h Sm 105° 45'
7* 4m 106° 0'
s
Log. llav.
Nat. Hav.
Log. llav.
Xat. llav.
Log. Hav.
Xat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
9.79893
.63941
9.80038
.63158
9.80183
.63368
9.80327
.63578
9.80470
.63788
60
1
.79890
.62944
.80041
.631.55
.80185
.63385
.80329
.63576
.80472
.63785
59
2
.79898
.68948
.80043
.83159
.80188
.83369
.80331
.63579
.80474
.63789
58
S
.79901
9.79903
.68951
.68955
.80046
9.80048
.63168
.63166
.80190
9:S0192
.63373
.63376
.80334
9.80330
.63583
.63586
.80477
9.80479
.63792
.63796
57
56
+ 1'
•5
.7990.5
.68958
.80050
.G3169
.80195
.63379
.80339
.63590
.80482
.63799
55
6
.79908
.62968
.800-53
.63173
.80197
.63383
.80341
.63593
.80484
.63803
54
7
.79910
9.79913
.62965
.80055
"9.80058
.63176
.63180
.80200'
9.80202"
.63386
.63390
.80343
.63597
.63600
.80486
9.80489"
.63806
.63810
53
52
+ y
.62969
9.80340
9
.79915
.62973
.80060
.63183
.80204
.6.3393
.80348
63604
.80491
.63813
51
10
.79918
.62976
.80063
.63187
.80207
.63397
.80351
.63607
.80494
.63817
50
11
.79920
.68980
.68983
.80065
9.80067
.63190
.63194
.80209
9.80212
.63400
.6.3404
^0353
9.8035:5
.63611
.83614
.80490
9.80498
.63880
.63824
49
48
+ 3'
9.79922
l.i
.79925
.68987
.80070
.63197
.80214
.63407
.80358
.63618
.80501
.63887
47
n
.79927
.62990
.80072
.63201
.80216
.63411
.80360
.63681
.80503
.63831
46
lo
.79930
9.79932"
.62994
.62997"
.80075
9:80077"
.63204
.63208
.80219
9 80221
.63414
.63418
.80362
9.80365
.63685
.63638
.80505
9.80508"
.63834
.83838
45
44
+ 4'
n
.79935
.63001
.S0079
.63811
.80224
.63431
.80367
.63633
.80510
.63841
43
18
.79937
.63004
.80082
.63815
.80220
.63435
.80370
.63635
.80513
.63845
42
19
+ 5'
.79939
9.799-42
.63008
.6.3011
.80084
9.80087"
.63218
.63282
.80228
9.80231"
.63488
.80372
.6.3639
.80515
9:80517
.63848
.63858
41
40
.63438
9.80374
.63648
L'l
.79944
.63015
.80089
.63225
.80233
.63435
.80377
.63646
.80520
.63855
39
> ;
.79947
.63018
.80091
.63329
.80236
.63439
.80379
.63649
.80522
.63859
38
23
.79949
9.79951
.63022
.63025
.80094
9.80096"
.63338
.63336
.80238
9": 80240"
.63448
.63446
.80382
9.80384
.63653
.63656
.80524
9.805i27
.63863
.63866
37
36
+ 6'
i.5
.799-54
.63029
.80099
.63339
.80243
.63450
.80386
.63660
.80529
.63869
35
J6
.79956
.63038
.80101
.63843
.80245
.6.3453
.80389
.63663
.80532
.83873
34
■21
.799-59
9.79961
.63036
.63039
.80103
9:80106
.63346
.63850
.80248
9.802.50
.63457
.80391
.63666
.63670
.80534
"9.80536
.83876
.63880
33
32
+ r
.63460
9.80393
29
.79964
.63043
.80108
.63353
.80252
.63464
.80396
.63673
.80-539
.63883
31
.10
.79966
.63046
.80111
.63357
.80255
.63467
.80398
.63677
.80541
.63887
30
■il
.79968
.63050
.80113
9.80ri6'
.63360
.6.-J864
.80257
9:80260
.63471
.63474
.80401
9.80403
.63680
.63684
.80543
9.80540
.63890
.63894
29
+ 8'
9.79971
.63053
3o
.79973
.63057
.80118
.63867
.80262
.63478
.80405
.63687
.80548
.63897
27
34
.79976
.63060
.80120
.63371
.80264
.63481
.80408
.63691
.80.551
.63901
26
35
.79978
9.79980"
.63064
.63067
.80123
9:80125"
.63874
.63378
.80267
9.80269
.63485
.63488
.80410
.63694
.80553
.63904
.63908
25
'24
+ J'
9.80413
.6.3698"
9.805.55
■J I
.79983
.63071
.80128
.63381
.80272
.63498
.80415
.63701
.80558
.63911
23
3S
.79985
.63074
.80130
.63385
.80274
.63495
.80417
.63705
.80560
.63915
22
39
+ W
.79988
9.79990"
.63078
.63081
.80132
9.80135"
.63888
.63898
.80276
9.80279
.63499
.63508
.80420
.63708
.80562
"9.80505
.63918
.63983
21
20
9.80422
.63713
41
.79993
.63085
.80137
.63895
.80281
.63506
.80424
.63715
.80507
.63985
19
42
.79995
.63088
.80140
.63899
.80284
.63509
.80427
.•3719
.80570
.63939
18
43
.79997
.63098
.80142
9.80144
.63308
.63306
.80286
9.80288
.63513
.63516
.80429
9.80432
.63733
.63736
.80572
"9.80574"
.63933
.63936
17
16
+ 11'
"9.80(H)0
.63095
•(•ii
.80002
.63099
.80147
.63309
.80291
.6.3580
.80434
.63739
.80577
.63939
15
4H
.80005
.63102
.80149
.63313
.80293
.63533
.80436
.63733
.80579
.63943
hi-
47
.80007
.63106
.80152
.63316
.80296
.63537
.80439
.63736
.80581
.63946
ts
' +"13'"
"9.80009"
.63109
9.801.54
.63330
9.80298"
.6.3530
9.80441
.63740
9.80584
.63950
12
49
.80012
.63113
.80156
.63323
.80300
.63534
.80444
.63743
.80.580
.63953
11
■W
.80014
.63116
.801.59
.63337
.80303
.63537
.80446
.63747
.80589
.63957
10
51
.80017
.63120
.63183
.80161
9.80164
.6.1330
.63.334
.80305
9.80307
.63541
.63544
.80448
.63750
.^754
.80-591
9.80593
.63960
.63964
9
8
+ 13'
9.806i9
9.80451
53
.80022
.63127
.80166
.63.337
.80310
.63548
.80453
.63757
.80590
.63967
7
54
.80024
.63131
.80168
.63.341
.80312
.63551
.80455
.63761
.80598
.83971
6
55
+ "14'"
.80026
.63134
.63138
.80171
.63344
.63348
.80315
9.80317"
.63555
.63558
.80458
9.80460
.63764
.63768
.80000
9.80603"
.63974
.63977
5
'4
9.80029
9.80173
57
.80031
.63142
.80176
.63351
.80319
.63568
.80463
.63771
.80605
.83981
3
58
.80034
.63145
.80178
.63.355
.80322
.63565
.80465
.63775
.80607
.83984
2
69
.80036
9.80038
.63148
.63152
.80180
9.80183
.63358
.6.3363
.80324
9.80327
.63569
.80467
.63778
.63788
.80610
9.80612
.63988
.63991
1
+ 15'
.63573
9.80470
16lt
59 ">
16!i
58m
leh 37m
16h
56m
16h
55m
Page 896]
TABLE 45.
Ilaversines.
7'! 5'" 106° 15'
7h am 106° 30'
7ft 7m 106° 45'
7h gm 107° 0'
7h ()m 107° 15'
s
Log. Hav
Xat.Hav.
Log. Hav.
Xat.Hav.
Log. Hav,
Nat. Hav.
Log. Hav.
Nat. Hav,
Log. Hav.
Nat. Hav
1
2
3
9.80612
.80G15
.80617
.80619
.63991
.63995
.63398
.6490'J
.64005
.64009
.6401?
.64016
.64019
.64033
.64026
.64030
.64033
.64037
.64040
.64044
.64047
.64051
.64054
.64058
.64061
.64065
.64068
.6407?
.64075
.64079
.6408?
.64086
.64089
.64093
.64096
.64109
9.80754
.80756
.80759
.80761
i), 80763
,80766
,80768
,80771
9,80773
,80775
.80778
,80780
.64201
.64204
.64208
.64211
9.80895
.80898
.80900
,80902
9,80905
,80907
,80909
.80912
,64410
.64413
.64417
.64430
.64424
.64427
.64431
.64434
.64438
.64441
.64445
.64448
9.81036
.81038
,81040
,81043
9. SI 045
,81047
.81050
.81052
9.810.54
.81057
.810-59
.81061
.64619
.64622
.64626
.64629
.64832
.64636
.64639
.64643
9.81176
.81178
.81180
.81183
.64827
.64831
.64834
.61838
60
59
58
57
56
55
54
53
5i
51
50
49
48
47
46
45
44
43
4i
41
40
39
38
'i7
35
34
33
3J
31
30
^9
28
27
J6
J5
+ 1'
5
e
7
9.80622
.80624
.80626
.80629
9.80631
.80634
.80636
.80638
.64215
.64218
.64222
.64235
9.81185
.81187
.81190
.81192
9.81194
.81197
.81199
.81201
978 1204"
.81206
.81208
.81211
.64841
.64844
.64848
.64851
.64855
.64858
.64863
.64865
.64869
.64872
.64876
.64879
+ r
9
10
11
.64229
.64232
.64236
.64239
9.80914
.80916
.80919
,80921
9.80923
.80926
.80928
.80930
.64646
.64650
.64653
.64657
.64660
.64664
.64667
.64671
+ y
13
14
15
9.80641
.80643
.80645
.80648
9.80782
.80785
.80787
.80789
9.80792
.80794
.80796
.80799
.61243
.64246
.61250
.64253
.64453
.64455
.64459
.64462
;64466
.64469
.64473
.64476
.64479
.64483
.64486
.64490
9.81061
.81066
.81068
,81071
,81073
.81075
.81078
.81080
9.81082"
.81085
.81087
,81089
+ 4'
n
18
19
9.80650
.80652
.80655
.80657
.64257
.64260
.64264
.64267
9.80933
.80935
.80937
.80940
9.80942
.80944
.80947
.80949
.64674
.64678
- .64681
.64685
.64688
.64692
.64695
.64699
9.81213
.81215
.81217
.81220
9.81222
,81224
,81227
.81229
.64883
.64886
.64890
.64893
.64897
.64900
.64903
.64907
.64910
.64914
.64917
.64921
+ 5'
21
22
23
9.80660
,80662
.80664
.80667
9.80801
.80804
,80806
,80808
9,80811
,80813
,80815
,80818
9^,80820
,80822
,S()S2,'3
,80827
9,80829
.80832
.80834
.80836
9.80839
.80841
.80844
.80846
.64270
.64274
.64277
.64281
+ 6'
25
26
27
9.80669
.80671
.80674
.80676
.64284
.64288
.64291
.64295
9.80952
.80954
.80956
.80959
.64493
.64497
.64500
.64504
9,81092
,81094
,81096
,81099
.64702
.64705
.64709
.64713
9.81231
.81234
.81236
.81238
+ T
29
30
31
9.80678
.80681
.80683
.80686
.64398
.64302
.64305
.64309
.64312
.64316
.64319
,64323
9.80961
.80963
.80966
,80968
9^80970
.80973
.80975
.80977
.64507
.64511
.64514
.64518
.64531
.64535
.64538
.64533
9,81101
,81103
,81106
.81108
9.81110
,81113
,81115
,81117
.64716
.64719
.64733
.64736
.64730
.64733
.64737
.64740
9.81241
.81243
.81245
.81248
.64924
.64938
.64931
.64935
+ 8'
33
34
35
9.80688
.80690
.80693
.80695
.64103
.64107
.64110
.64114
.64117
.64121
.64124
.64128
.64131
.64135
.64138
.64142
.64145
.64148
.64152
.64155
.64159
.64162
.64166
.64169
.64173
.64176
.64180
.64183
9.81250
.81252
.81255
.81257
.64938
.64943
.64945
.64949
+ 9'
37
38
39
9.80697
.80700
.80702
.80704
.64336
.64330
.64333
.64337
9.80980
.80982
.80984
.80987
.64535
.64539
.64543
.64546
.64.549"
.64553
.64556
.64559
.64563
.64566
.64570
.64573
9,81120
.81122
.81124
.81127
.64744
.64747
.64751
.64754
9.81259
.81262
.81264
.81266
.64952
.64956
.64959
.64962
~4
23
2J
21
+ W
41
42
43
9.80707
.80709
.80712
.80714
9.80716
.80719
.80721
.80723
9.80848
,80851
.80853
.80855
.64340
.64344
.64347
.64351
9.80989
.80991
.80994
.80996
9,81129
.81131
.81134
.81136
9.81138
,81141
,81143
,81145
9.81148
.81150
.81152
.81155
.64758
.64761
.64765
.64768
9,81269
,81271
.81273
.81276
.64966
.64969
.64973
.64976
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
~'4
3
2
1
+ 11'
45
46
47
9.80858
.80860
.80862
.80865
9:80867^
.80869
.80872
.80874
.64354
.64358
.64361
.64365
9.80998
.81001
.81003
.81005
.64773
.64775
.64778
.64782
9.81278
.81280
.81282
.81285
.64980
,64983
.64987
.64990
.64994
.64997
.65001
.65004
.65008
.65011
.65014
.65018
.65021
.65025
.65038
.65033
+ 12'
50
51
9.80726
.80728
.80730
.80733
.64368
,64372
.64375
.64378
9.81008
.81010
.81012
.81015
9.81017
.81019
.81022
.81024
.04577
.64580
.64584
.64587
.64591
.64594
.64598
.64601
.64605
.64608
.64612
.64615
.64785
.64789
.64792
.64796
9.81287
.81289
.81292
.81294
+ 13'
5^
54
• 55
9.80735
.80738
.80740
,80742
9.80876
.80879
,80881
.80883
.64382
.64385
.64389
.64392
9.81157
,81159
,81162
.81164
9.81166
.81169
.81171
.81173
.64799
.64803
.64806
.64810
.64813
.46817
.64830
.64824
9.81296
.81299
.81301
.81303
9.81306
.81308
.81310
.81313
+ 14'
57
5S
59
9.80745
.80747
.80749
.80752
.64187
.64190
.64194
.64197
9.80886
.80888
.80891
.80893
.64396
.64399
,64403
,64406
9.81026
.81029
.81031
.81033
+ 15'
9.80754
.64201
9.80895
,64410
9.81036
.64619
9.81176
.64827
9.81315
.65035
16l>
54™
lefi
5,j(m
16h
SJ'"
lefi
5/^
Jfift.
;0m
TABLE 45.
Haveraines.
[Page 897
s
7* ;0™ 107° 30'
7h iim 107° 45'
7* 12™
108° 0' 7
h l.sm
108° 15'
7hl4m
108° 3r
s
60
59
58
57
56
55
54
53
52
51
60
49
Log. Hav
Nat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav. L
3g. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
3
9.8131.5
.81317
.81320
.81322
.65035
.65030
.65042
.65046
.65040
.65053
.65056
.65060
9.81454
.81456
.81458
.81460
.65243
.65247
.65250
.65254
9.81592
.81,594
.81.596
.81.598
.65451 9
.65454
.65458
.65461
81729
81731
81733
81736
.65658
.65662
.65665
.65668
9.81866
.81868
.81870
.81872
.65865
.65869
.65872
.65876
.65879
.65882
.65886
.65889
+ 1'
S
6
7
+ 3'
9
10
11
9.81324
.81326
.81329
.81331
9.81463
.81465
.81467
.81470
.65257
.65261
.65264
.65267
9.81601
.81603
.81605
.81608
.65465 9
.65468
.65472
.65475
81738
81740
81743
81745
.65672
.65675
.65679
.65682
9.81875
.81877
.81879
.81882
9.81333
.81336
.81338
.81340
9.81343
.81345
.81.347-
.813.50
9:813.52
.813.54
.81357
.81359
.65063
.65066
.65070
.6.^073
.65077
.65080
.65084
.65087
9.81472
.81474
.81477
.81479
.65271
.65274
.65278
.65281
9.81610
.81612
.81614
.81617
.65479 9
.65482
.65485
.65489
81747
81749
817.52
817.54
.65686
.65689
.65693
.65696
9.81884
.81886
.81888
.81891
.65893
.65896
.65900
.65903
+ 3'
13
14
15
9.81481
.81483
.81486
.81488
.65285
.65288
.65292
.65295
.65299
.65302
.65306
.65309
9.81619
.81621
.81624
.81626
.65492 9
.65496
.65499
.65503
81756
81759
81761
81763
.65700
.65703
.65707
.65710
9.81893
.81895
.81897
.81900
.65907
.65910
.65914
.65917
.65920
.65924
.65927
.65931
4S
47
46
45
44
43
42
41
40
39
38
37
n
IS
19
.65091
.65094
.65098
.65101
9.81490
.81493
.81495
.81497
9.81628
.81631
.81633
.81635
.65506 9
.65510
.65513
.65516
81765
81768
81770
81772
.65713
.65717
.65720
.65724
9.81902
.81904
.81907
.81909
+ 5'
21
22
23
9.81361
.81364
.81366
.81.368
.65105
.65108
.65112
.65115
.65118
.65122
.65125
.65129
.65132
.65136
.65139
.65143
9.81500
.81.502
.81.505
.81507
9.81.509
.81511
.81513
.81516
9.81518
.81.520
.81523
.81,525
9.81.527
.81.530
.81.532
.81534
9.81.536
.81.539
.81.541
.81.543
.65312
.65316
.65319
.65323
.65326
.65330
.65333
.65337
9.81637
.81640
.81642
.81644
9.81647
.81649
. .81651
.816,53
.65520 9
.65523
.65527
.65530
81775
81777
8177!)
81781
.65727
.65731
.65734
.65738
9.81911
.81913
.81916
.81918
.65934
.65938
.65941
.65944
+ 6'
25
26
27
9.81370
.81373
.81375
.81377
.65534 9
.65537
.65541
.65544
81784
81786
81788
81791
81793
81795
81797
81800
.65741
.65744
.65748
.65751
.65755
.65758
.65762
.65765
9.81920
.81922
.81925
.81927
.65948
.65951
.65955
.65958
36
35
34
33
+ r
30
31
9.81380
.81382
.81384
.81387
.65340
.65344
.65347
.65351
9.81656
.81658
.81660
.81663
.6-5548 9
.65551
.65555
.65558
9.81929
.81931
.81934
.81936
.65962
.65965
.65969
.65972
32
St
30
29
+ 8'
J.i
.3.5
9.81389
.81,391
.81394
.81396
.65146
.65150
.65153
.65157
.65354
.65357
.65361
.65364
.65368
.65372
.65375
.65378
9.81665
.81667
.81669
.81672
.65561 9
.65565
.65568
.65572
81802
81804
81806
81809
.65769
.65772
.65776
.65779
9.81938
.81941
.81943
.81945
.65976
.65979
.65982
.65986
28
27
26
25
24
23
22
21
+ 9'
37
3S
39
9.81398
.81400
.81403
.81405
.65160
.65164
.65167
.65171
9.81674
.81676
.81679
,81681
.6.5575 9
.65579
.65582
.65586
.65589 '9
.65593
.65596
.65599
81811
81813
81816
81818
81820
81822
81825
81827
.65782
.65786
.65789
.65793
.65796
.65800
.65803
.65807
.65810
.65813
.65817
.65820
.65824
.65827
.65831
.65834
.65838
.65841
.65845
.65848
.65851
.65855
.65858
.65862
9.81947
.819,50
.81952
.819,54
.65989
.65993
.65996
.66000
+ 10'
41
42
4-i
9.81407
.81410
.81412
.81414
.65174
.65177
.65181
.65184
.65188
.65191
.65195
.65198
.65202
.65205
.65209
.65212
.65216
.6.5219
.65222
.65226
.65229
.65233
.65236
.65240
.65243
9.81,546
.81.548
.81.5.50
.81.5.52
9.81.5.55
.81.5.57
.81.5.59
.81.562
.65382
.65385
.65389
.65392
.65396
.65399
.65402
.65406
9.81683
.81685
.81688
.81690
9.81692
.81695
.81697
.81699
9.81701
.81704
.81706
.81708
9.81956
.81959
.81961
.81963
.66003
.66006
.66010
.66013
20
19
18
n
+ 11'
45
46
47
9.81417
.81419
.81421
.81424
.65603
.65606
.65610
.65613
.65617 9
.65620
.65624
.65627
.65630 9
.65634
.65637
.65641
.65644 9
.55648
.65651
.65655
81829
81832
81834
81836
818,38
81841
81843
81845
81847"
818,50
81852
818,54
81857'
818.59
81861
81863
9.81965
.81968
.81970
.81972
.66017
.66020
.66024
.66027
16
15
14
13
12
11
10
9
8
7
6
5
4
S
2
1
+ 12'
49
50
51
+ 13'
53
54
55
9.81426
.81428
.81430
.81433
9.81,564
.81,566
.81.569
.81.571
9.81573
.81,575
.81,578
.81.580
"9.8i:582
.81.585
.81.587
.81.589
9.81.592
.65409
.65413
.65416
.65420
9.81975
.81977
.81979
.81981
.66031
.66034
.66038
.66041
.66044
.66048
.66051
.66055
9.81435
.814,37
.81440
.81442
.65423
.65427
.65430
.65434
.65437
.65440
.65444
.65447
.65451
9.81711
.81713
.81715
.81717
9.81720
.81722
.81724
.81727
9.81729
9,81984
.81986
.81988
.81990
4- 14'
.57
.55
,59
9.81444
.81447
.81449
.81451
9:814.54
9.81993
.81995
.81997
.81999
.66058
.66062
.66065
.66068
.66072
+ 15'
.65658 9
81866
.65865
9.82002
16h
49^
ifiA
4Sm
16'' 4
7m
161^46™
ifiA
45m
24972°— 12-
-47
Page 898]
TABLE 45.
Haversinee.
s
7A 15m 108° 45'
Jh 16m 109° 0'
7ft 17m 109° 15'
7A ISm 109° 30'
Th 19m 109° 45'
s
Log. Hav.
Nat, Hav.
Log. Hav.
Nat, Hav,
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nal. Hav.
1
~3
9.82002
.82004
.82006
,.82009
.66073
.66015
.66079
.66083
.66086
.66089
.66093
.66096
9.82137
.82139
.82142
.82144
.66378
.66383
.66385
.66389
9.82272
.82274
.82277
,82279
9,82281
,82283
,82286
,82288
9,82290
,82292
,82294
,82297
.66485
.66488
.66491
.66495
.66498
.66503
.66505
.66508
9,82406
.82409
.82411
.82413
.66690
.66694
.66697
.66701
9.82540
.82542
.82.544
.82547
9.82549
.82551
.82553
.82555
¥.82558"
.82560
.82562
.82564
9.82567
.82569
.82571
.82573
9,82575
,82578
,82580
,82582
9,82584^
,82587
.82589
.82.591
9.82.593
.82.595
.82598
.82600
9,82602
,82604
.82606
,82609
9.82611
,82613
,82615
,82618
9.82620
.82622
,82624
,82627
9,82629
,82631
,82633
,82635
9.82638
.82640
,82642
,82644
.66896
.66899
.66903
.66906
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
-44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
+ 1'
5
6
7
9.82011
.82013
.82015
.82018
9.82146
.82148
.82151
.82153
9.82155
.82157
.82160
.82162
.66393
.66396
.66399
.66303
.66306
.66309
.66313
.66316
9.82415
.82417
.82420
.82422
.66704
.66707
.66711
.66714
.66718
.66731
.66735
.66738
.66731
.66735
.66738
.66743
.66745
.66749
.66753
.66755
.66759
.66763
.66766
.66769
.66773
.66776
.66779
.66783
.66786
.66790
.66793
.66797
.66800
.66803
.66807
.66810
.66814
.66817
.66831
.66834
.66837
.66831
.66834
.66838
.66841
.66844
.66848
.66851
.66910
.66913
.66916
.66930
.66933"
.66937
.66930
.66933
.66937
.66940
.66944
.66947
.66951
.66954
.66957
.66961
.66964
.66968
.66971
.66975
.66978
.66981
.66985
.66988
.66993
.66995
.66998
.67003
.67'0«5
.67009
.67013
.67016
+ 2'
9
10
11
9.82020
.82022
.82024
.82027
.66100
.66103
.66106
.66110
.66513
.66515
.66519
.66533
9.82424
.82426
.82429
.82431
+ 3'
14
IS
9.82029
.82031
.82033
.82036
.66113
.66117
.66130
.66131
9.82164
.82166
.82169
.82171
.66330
.66333
.66337
.66330
9,82299
,82301
.82303
.82306
9.82308
.82310
.82312
,82315
.66536
.66539
.66533
.66536
9.82433
.82435
.82438
.82440
+ *'
i7
18
19
9.82038
.82040
.82042
.82045
.66137
.66130
.66134
.66137
9.82173
.82175
.82178
.82180
.66333
.66337
.66340
.66344
.66539
.66543
.66546
.66550
9.82442
.82444
.82446
,82449
9,82451
.82453
.82455
.82458
+ 5'
22
23
9.82047
.82049
.82051
.82054
9.820.56
.82058
.82061
.82063
.66141
.66144
.66148
.66151
.66155
.66158
.66161
.66165
9.82182
.82184
.82187
.82189
9.82191
.82193
.82196
.82198
9.82200
.82202
.82205
.82207
9.82209
.82211
.82214
.82216
9.82218
.82220
.82223
.82225
9.82227
.82229
.82232
.82234
.66347
.66351
.66354
.66357
9,82317
,82319
,82321
,82324
.66553
.66557
.66560
.66563
.66567
.66570
.66574
.66577
.66581
.66584
.66587
.66591
+ 6'
25
26
27
.66361
.66364
.66368
.66371
.66375
.66378
.66383
.66385
.66388
.66393
.66395
.66399
.66403
.66406
.66409
.66413
.66416
.66419
.66433
.66436
.66430
.66433
.66436
.66440
.66443
.66447
.66450
.66454
9,82326
,82328
.82330
,82333
9,82335
,82337
,82339
,82341
9.82460
.82462
.82464
.82467
+ r
29-
30
31
9.82065
.82067
.82070
.82072
9.82074
.82076
.82079
.82081
.66168
.66173
.66175
.66179
9.82469
.82471
.82473
,82475
9,82478
.82480
.82482
.82484
9.82487
.82489
.82491
.82493
+ »'.
33
34
35
.66183
.66186
.66189
.66193
.66196
.66199
.66303
.66306
.66310
.66313
.66317
.66330
.66333
.66337
.66330
.66334
9,82344
,82346
,82348
,82350
.66594
.66598
.66601
.66605
+ 9'
.37
38
39
9.82083
.82085
.82088
.82090
9,82353
,82355
,82357
,82359
.66608
.66611
.66615
.66618
.67019
.67033
.67036
.67039
24
23
22
21
+ 10'
42
43
9.82092
.82094
.82097
.82099
9,82362
,82364
,82366
,82368
.66633
.66635
.66639
.66633
9.82495
.82498
.82500
.82502
.67033
.67036
.67039
.67043
767046
.67050
.67053
.67057
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
+ 11'
46
47
9.82101
.82103
.82106
.82108
9.82236
.82238
.82241
.82243
9.82245
.82247
.82250
.82252
9,82371
,82373
,82375
,82377
9,82380
,82382
,82384
,82386
.66635
.66639
.66643
.86646
.66649
.66653
.66656
.66659
9.82504
,82507
,82509
,82511
+ 13'
•49
50
51
9,82110
.82112
,82115
,82117
.66337
.66341
.66344
.66347
9,82513
,82515
.82518
,82520
.66855
.66858
.66863
.66865
9,82646
,82649
,82651
,82653
.67060
.67063
.67067
.67070
.67074
.67077
.67081
.67084
+ 13'
5.?
54
55
9,82119
,82121
,82124
,82126
.66351
.66354
.66358
.66361
9.82254
.82256
.82259
.82261
.66457
.66460
.66464
.66467
9,82388
,82391
* ,82393
,82395
.66663
.66666
.66670
.66673
9,82522
,82524
.82527
.82529
.66868
.66873
.66875
.66879
.66883
.66886
.66889
.66893
9,82655
,82657
.82660
,82662
+ 14'
57
58
59
9.82128
.82130
.82133
.82135
.66365
.66368
.66373
.66375
9.82263
.82265
,82268
,82270
.66471
.66474
.66478
.66481
.66485
9,82397
,82400
,82402
.82404
.66677
.66680
.66683
.66687
9.82531
.82533
.82535
.82538
9,82664
.82666
.82668
.82671
.67087
.67091
.67094
.67098
4
3
2
~1
+ 15'
9.82137
.66378
9.82272
9.82406
.66690
9.82540
.66896
9,82673
.67101
76*
44m
16h 43m
leti
4^m
16!i
41m
16h
40m
TABLE 45.
Haversines.
[Page 899
s
7ft 20™ 110° C
jh 21^
110° 15'
7ft o2jn
110° 30'
7h 23m 110° 46'
7^ 24^
111° c
s
Log. Hav.
Nat. Hav
Log. Hav.
Nat. Hav,
Lbg. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.82673
.82675
.82677
.82680
.67101
.67104
.67108
.67111
9.82805
.82807
.82810
.82812
9.82814
.82816
.82818
.82821
9.82823
.82825
.82827
.82829
.67306
.67309
.67313
.67316
.67320
.67333
.67336
.«7330
.67333
.67337
.67340
.67343
9.82937
.82939
.82941
.82944
'9.82946
.82948
.82950
.82952
9.82955
.82957
.82959
.82961
.67510
.67514
.67517
.67521
.67524
.67527
.67531
.67534
.67538
.67541
.67544
.67548
.67551
.67555
.67558
.67561
9.83068
.83070
.83073
.83075
9.83077
.83079
.83081
.83083
9.83086
.83088
.83090
.83092
9.83094
.83097
.83099
.83101
9.83103
.83105
.83107
.83110
9.83112
.83114
.83116
.83118
9.83120
.83123
.83125
.83127
9,83129
.83131
.83134
.83136
9.83138
.83140
.83142
.83144
9.83147
,83149
,83151
.83153
9,83155
.831.57
.83160
.83162
9,83164
.83166
.83168
.83170
9.83173
.83175
.83177
.83179
.67715
.67718
.67731
.67735
9.83199
.83201
.83203
.83205
.67918
.67922
.67925
.67929
60
59
58
.57
56
55
54
53
5i
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
+ 1'
5
6
7
9.82682
.82684
.82686
.82688
.67115
.67118
.67132
.67135
.67138
.67132
.67135
.67139
.67738
.67732
.67735
.67738
9.83207
.83210
.83212
.83214
.67933
.67935
.67939
.67943
+ 2'
9
10
11
9.82691
.82693
.82695
.82697
.67742
.67745
.67749
.67753
9.83216
.83218
.83220
.83223
.67946
.67949
.67952
.67956
+ 3'
13
14
15
9.82699
.82702
.82704
.82706
.67143
.67145
.67149
.67152
.67156
.67159
.67163
.67166
.67169
.67173
.67176
.67180
.67183
.67186
.67190
.67193
.67197
.67200
.67203
.67207
9.82832
.82834
.82836
.82838
9.82840
.82843
.82845
.82847
9.82849"
.82851
.828-54
.82856
9.828.58"
.82860
.82862
.82865
9.82867
.82869
.82871
.82873
¥.82876
.82878
.82880
.82882
9.82884
.82887
.82889
.82891
.67347
.67350
.67354
.67357
9.82963
.82966
.82968
.82970
.67755
.67759
.67762
.67766
.67769
.67772
.67776
.67779
.67783
.67786
.67789
.67793
.67796
.67800
.67803
.67806
.67810
.67813
.67817
.67820
.67823
.67827
.67830
.67834
.67837
.67840
.67844
.67847
9.83225
.83227
.83229
.83231
9.83233
.83236
.83238
.83240
.67959
.67963
.67966
.67969
.67973
.67976
.67979
.67983
.67986
.67990
.67993
.67996
+ 4'
n
18
19
9.82708
.82710
.82713
.82715
9.82717
.82719
.82722
.82724
.67360
.67364
.67367
.67371
.67374
.67377
.67381
.67384
9.82972
.82974
.82976
.82979
9.82981
.82983
.82985
.82987
.67565
.67568
.67572
.67575
.67578
.67582
.67585
.67589
+ 5'
21
■22
23
9.83242
.83244
.83246
.83249
+ 6'
25
26
27
9.82726
.82728
.82730
.82733
9.82735
.82737
.82739
.82741
.67388
.67391
.67395
.67398
.67401
.67405
.67408
.67413
.67415
.67418
.67433
.67425
.67429
.67433
.67435
.67439
9.82990
.82992
.82994
.82996
9.82998"
.83001
.83003
.83005
9.83007
.83009
.83011
.83014
9.83016
.83018
.83020
.83022
9.83025
.83027
.83029
.83031
'9.83033
.83035
.83038
.83040
.67592
.67595
.67599
.67603
.67606
.67609
.67613
.67616
.67619
.67623
.67626
.67630
.67633
.67636
.67640
.67643
.67647
.67650
.67653
.67657
.67660
.67661
.67667
.67670
.67674
.67677
.67681
.67684
.67687
.67691
.67694
.67698
9.83251
.83253
.83255
.83257
9.83259"
.83262
.83264
.83266
9'.83268
.83270
.83272
.83275
.68000
.68003
.68007
.68010
+ r
29
SO
31
+ 8'
33
34
35
.68013
.68017
.68030
.68034
.68037
;68030
.68034
.68037
32
31
30
29
28
27
26
25
9.82744
.82746
.82748
.827,50
.67210
.67214
.67217
• .67221
.67234
.67237
.67231
.67334
+ »'
37
38
39
9.82752
.82755
.82757
.827.59
9782761
.82763
.82766
.8:4768
9.83277
.83279
.83281
.83283
.68041
.68044
.68047
.68051
24
23
22
21
20
19
IS
n
16
15
14
13
+ W
41
42
43
.67238
.67241
.67244
.67248
.67251
.67255
.67258
.67361
.67365
.67268
.67272
.67275
9.82893
.82895
.82898
.82900
9.82902
.82904
.82906
.82909
9.82911
.82913
.82915
.82917
9.82920
.82922
.82924
.82926
9.82928
.82930
.829.33
.82935
9.82937"
.67443
.67446
.67449
.67452
.67456
.67459
.67463
.67466
.67469
.67473
.67476
.67480
.67850
.67854
.67857
.67861
9.83285
.83288
.83290
.83292
.68054
.68058
.68061
.68064
.68068
.68071
.68074
.68078
+ 11'
45
46
47
9.82770
.82772
.82774
.82777
9.82779
.82781
.82783
.82785
.67864
.67868
.67871
.67874
.67878
.67881
.67884
.67888
.67891
.67895
.67898
.67901
9.83294
.83296
.83298
.83301
9.83303"
.83305
.83307
.83309
9.83311"
.83314
.83316
.83318
+ IV
49
50
51
9.83042
.83044
.83046
.83049
9.83051
.83053
.83055
.83057
.68081
.68085
.68088
.68091
.68095
.68098
.68102
.68105
.68108
.68113
.68115
.68119
.68132
12
11
10
9
8
7
6
5
4
3
2
1
+ 13'
53
54
55
9.82788
.82790
.82792
.82794
.67279
.87383
.67385
.67389
.67292
.67296
.67299
.67302
.67306
.67483
.67487
.67490
.67493
.67497
.67500
.67504
.67507
.67510
9.83181
.83184
.83186
.83188
+ U'
57
58
59
9.82796
.82799
.82801
.82803
9.83059
.83062
.83064
.83066
9.83068
.67701
.67704
.67708
.67711
.67715
9.83190
.83192
.83194
.83197
.67905
.67908
.67913
.67915
9.83320
.83322
.83324
.83327
9.83329
+ 15'
9.82805
9.83199
.67918
16h 39m
16f^ SSm
leri
.V"
leh sem
?6* 35^^
Page 900]
TABLE 45.
Haversines.
s
7A 25m 111° 15' 1
7A 26m 111° 30' |
7ft 27m 111° 45' j
7ft 28m 113° (K 1
7lt 29m 113° 15' 1
s
Log. llav.
Nat. Hav.
Log. Hav.j
Nat. Uav.
Log, Hav,
Nat. Hav.
Log. Uav.
Nat. Hav.
Log. Hav.
Nat, Hav,
1
2
3
9.83329
.83331
.83333
.83335
.68133
.68135
.68139
.68133
9.83458
.83460
.83462
.83464
.68335
.68338
.68333
.68335
9.83587
.83589
.83591
.83593
9.83595
.83597
.83600
.83602
.68538
.68531
.68535
.68538
.68541
.68545
.68548
.68553
.68555
.68558
.68563
.68565
.68568
.68573
.68575
.68579
.68583
.68585
.68589
.68593
9.83715
.83717
.83719
.83721
9.83723
.83725
.83728
,83730
.68730
.68734
.68737
.68740
.68744
.68747
.68751
.68754
9.83842
.83844
.83847
.83849
9.83851"
.83853
.838.55
.83857
9.83859
.83861
.83864
.83866
9^83868
.83870
.83872
.83874
9.83876
.83878
.83881
.83883
9:83885
.83887
.83889
.83891
"9.83893"
.83895
.83897
.83900
9.83902
.83904
.83906
.83908
9.83910
.83912
.83914
.83916
.68933
.68936
.68939
.68943
60
59
58
.57
"56
.5,5
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
3~1
30
29
+ 1'
5
6
i
9.83337
.83339
.83342
.83344
.68135
.68139
.68143
.68146
9.83467
.83469
.83471
.83473
.68339
.68343
.68345
.68349
.68946
.68949
.68953
.68956
+ 2'
9
10
11
9.83346
.83348
.83350
.83352
9.83355"
.83357
.83359
.83361
.68119
.68153
.68156
.68159
.68163
.68166
.68169
.68173
9.83475
.83477
.83480
.83482
"9.83484
,83486
.83488
.83490
.68353
.68356
.68359
.68363
.68.366
.68369
.68373
.68376
9.83604
.83606
.83608
.83610
9.83732
.83734
.83736
.83738
.68757
.68761
.68764
.68767
.68771
.68774
.68778
.68781
.68784
.68788
.68791
.68794
.68798
.68801
.68804
.68808
.68811
.68815
.68818
.68831
.68835
.68838
.68831
.68835
.68838
.68843
.68845
.68848
.68853
.688.55
.68858
.68863
.68959
.68963
.68966
.68969
+ 3'
/J
14
15
9.83612
,83615
,83617
,83619
9.83740
.83743
.83745
.83747
.68973
.68976
.68980
.68983
+ 4'
18
19
9.833«3
.83305
.83368
.83370
9.83372
.83374
.83376
.83378
.68176
.68180
.68183
.68186
9.83492
.83495
.83497
.83499
.68379
.68383
.68386
.68389
.68393
.68396
.68399
.68403
.68406
.68410
.68413
.68416
9,83621
,83623
,83625
.83627
9.83749
.83751
.837.53
,837.55
.68986
.68990
.68993
.68996
.69000
.69003
.69006
.69010
.69013
.69017
.69030
.69033
.69037
.69030
.69033
.69037
+ s'
22
23
.68190
.68193
.68196
.68300
9.83501
.83,503
.83.505
.83507
9.83510
.83512
.83514
.83516
9,83630
-.83632
.83634
.83636
"9.83638
,83640
,83642
,83644
9.83647
.83649
.83651
.83653
.68595
.68599
.68603
.68606
.68609
.68613
.68616
.68619
.68633
.68636
.68639
.68633
9.83757
.83760
.83762
.83764
9.83766
.83768
.83770
.83772
9.83774
.83777
.83779
.83781
9.83783
.83785
.83787
.83789
+ 6'
•26
£7
9.83380
.83383
.83385
.83387
.68303
.68307
.68310
.68313
+ r
29
30
31
9.83389
.83391
.83393
.83396
.68317
.68330
.68334
.68337
.68330
.68334
.68337
.68340
9.83518
.83520
.83522
.83525
9.83.527
.83529
.83.531
.83533
.68430
.68433
.68437
.68430
.68433
.68437
.68440
.68443
+ 8'
55
34
35
+ 9'
57
38
39
9.83398
.83400
.83402
.83404
9.83406
.83409
.83411
.83413
9.83655
,83657
,83659
,83662
9.83664"
.83666
,83668
,83670
.68636
.68639
.68643
.68646
.68649
.68653
.68656
.68660
.68663
.68666
.68670
.68673
.68676
.68680
.68683
.68687
.68690
.68693
.68697
.68700
.68703
.68707
.68710
.68713
.69040
.69044
.69047
.69050
28
27
26
25
■24
23
22
~21
20
19
18
17
16
15
14
13
12
11
10
9
~F
i
6
5
.68344
.68347
.68351
.68354
9.83535
.83537
.83540
.83.542
9,83.544
.83.546
.83548
.83550
.68447
.68450
.68454
.68457
.68460
.68464
.68467
.68470
.68474
.68477
.68481
.68484
.68487
.68491
.68494
.68497
.68501
.68504
.68508
.68511
.68515
.68518
.68531
.68535
.68538
9.83791
.83794
.83796
.83798
9.83919
.83921
.83923
.83925
9.83927"
.83929
.83931
,839,33
9,8393.'f
.83938
.83940
,83942
.69054
.69057
.69060
.69064
.69067
.69070
.69074
.69077
.69080
.69084
.69087
.69091
+ W
41
42
43
+ 11'
45
46
47
9.83415
.83417
.83419
.83421
.68357
.68361
.68364
.68368
9,83672
,83674
,83676
,83679
9,83681
,83683
,83685
,83687
9."8"3689"
,83691
,83694
,83696
9,83698
,83700
.83702
,83704
9.83800
.83802
.83804
.83806
9,83808
,83811
.83813
.83815
9.83817
.83819
.83821
.83823
9.83"825
.83828
.83830
.83832
9.83834
.83836
.83838
.83840
"9.83842
.68865
.68869
.68873
.68875
.68879
.68883
.68885
.68889
.68893
.68895
.68899
.68903
9.83424
.83426
.83428
.83430
.68371
.68374
.68378
.68381
9,83.5.52
.83.5.55
.83.557
.83559
+ ir
49
50
51
9.83432
.83434
.83436
.83439
.68384
.68388
.68391
.68395
9.83.561
.83563
.83565
.83567
9.83570"
,83572
,83574
,83576
9,83578'
,83580
,83.582
.83.585
"9,83.587"
9,83944
,83946
.83948
.839.50
9.8"3"952
.83955
.83957
.83959
.69094
.69097
.69101
.69104
.69107
.69111
.69114
.69117
+ 13'
53
54
55
+ 14'
.57
58
59
9.83441
.83443
.83445
.83447
9.83449
.83452
.83454
.83456
.68398
.68301
.68305
.68308
.68313
.68315
.68318
.68333
.68335
.68906
.68909
.68913
.68916
.68919
.68933
.68936
.68939
.68933
9.83706
.83708
.83711
.83713
.68717
.68730
.68734
.68737
9.83961
.83963
.83965
.83967
9,83969"
.69131
.69134
.69137
.69131
.69134
4
3
2
1
+ 15'
9.83458
9.83715
.68730
16h 34-^
76* 33m
. /fiA 32™
16h
3im
16^30m
TABLE 45.
Ilaversines.
[Page 901
s
7* oJO™ 113° 30'
JhSim
113° 45'
7h32m
113° 0'
7% ssm
113° 15'
7ft 34m 113° 30'
s
Log. Hav.
Xat. Hav.
Log. Ilav.
Xat. Hav.
Log. nav.
Nat. Hav.
Log. Hav.
Nat. Hav,
Ivog, Hav.
Nat. Hav.
1 .
2
3
9.83969
.83971
.83974
.83976
.69134
.69138
.69141
.69144
.69148
.69151
.69154
.69158
9.84096
.84098
.84100
.84102
.69336
.69339
.69343
.69316
.69349
.69353
.69356
.69359
.69303
.69366
.69369
.69373
9.84221
.84223
.84226
,84228
.69537
.69540
.69543
.69547
9.84346
.84349
.84351
.84353
.69737
.69741
.69744
.69747
9.84471
.84473
.84475
.84477
.69937
.69941
.69944
.69947
.69951
.69954
.69957
.69961
.69964
.69967
.69971
.69974
.69977
.69981
.69984
.69987
.69991
.69994
.69997
.70001
60
59
58
57
56
55
54
53
52
51
50
49
4S
47
46
45
U
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
+ 1'
5
6
7
9.83978
.83980
.83982
.83984
9.84104
.84106
.84108
.84110
9.84112
.84114
.84117
.84119
9.84230
.84232
.84234
.84236
.69550
.69553
.69557
.69560
9.84355
.84357
.84359
.84361
.69751
.69754
.69757
.69761
.69764
.69767
.69771
.69774
9.84479
.84481
.84483
.84485
9.84488
.84490
.84492
.84494
9.84496
.84498
.84500
.84502
9.84504
.84506
.84508
9.84512
.84514
.84517
.84519
+ 2'
9
10
11
9.83986
.83988
.83990
.83992
.69161
.69164
.69168
.69171
9.84238
.84240
.84242
.84244
.69563
.69567
.69570
.69573
9.84363
.84365
.84367
.84369
+ 3'
15
9.83995
.83997
.83999
.84001
.69174
.69178
.69181
.69185
.69188
.69191
.69195
.69198
9.84121
.84123
.84125
.84127
9.84129
.84131
.84133
.84135
9.84138
.84140
.84142
.84144
.69376
.69379
.69383
.69386
.69389
.69393
.69396
.69399
.69403
.69406
.69409
.69413
.69416
.69419
.69423
.69426
.69439
.69433
.69436
.69439
9.84246
.84248
.84251
.84253
.69577
.69580
.69583
.69587
9.84371
.84373
.84376
.84378
.69777
.69781
.69784
.69787
.69791"
.69794
.69797
.69801
+ 4'
/7
IS
19
9.84003
.84005
.84007
.84009
9.84255
.84257
.84209
.84261
9.84263
.84265
.84267
.84269
9.84271
.84274
.84276
.84278
9.84280
.84282
.84284
.84286
9.84288
.84290
.84292
.84294
.69590
.69593
.69597
.69600
9.84380
.84382
.84384
.84386
+ 5'
23
9.84011
.84014
.84016
.84018
.69201
.69205
.69208
.69211
.69603
.69607.
.69610
.69614
.69617
.69630
.69634
.69637
.69630
.69634
.69637
.69640
9.84388
.84390
.84392
.84394
.69804
.69807
.69811
.69814
.70004
.70007
.70011
.70014
+ 6'
27
9.84020
.84022
.84024
.84026
.69215
.69318
.69231
.69225
,69228
.69333
.69335
.69338
.69242
.69245
.69348
.69353
9.84146
.84148
.84150
.84152
9.84396
.84398
.84400
.84403
.69817
.69831
.69834
.69837
.69831
.69834
.69837
.69841
9.84521
.84523
.84525
.84.527
9.84529
.84531
.84533
.84535
.70017
.70021
.70034
.70037
.70031
.70034
.70037
.70041
+ J'
31
9.84028
.84030
.84033
.84035
9.84037
.84039
.84041
.84043
9.84154
.84156
.84159
.84161
9.84405
.84407
.84409
.84411
+ 8'
35
9.84163
.84165
.84167
.84169
9.84171
.84173
.84175
.84177
.69443
.69446
.69450
.69453
.69456
.69460
.69463
.69466
.69470
.69473
.69476
.69480
.69483
.69486
.69490
.69493
.69496'
.69500
.69503
.69506
.69510
.69513
.69516
.69530
.69644
.69647
.09650
.69654
9.84413
.84415
.84417
.84419
.69844
.69847
.69851
.69854
9.84.537
.84539
.84.541
.84.543
.70044
.70047
.70051
.70054
28
27
26
25
24
23
22
21
20
19
18
17
+ »'
^7
39
9.84045
.84047
.84049
.84051
.69355
.69358
.69363
.69265
9.84296
.84299
.84301
.84303
.69657
.69660
.69664
.69667
9.84421
.84423
.84425
,84427
.69857
.69861
.69864
.69867
9.84545
.84.547
.845.50
.84552
.70057
.70061
.70064
.70067
+ 10'
4^i
9.84054
.84056
.84058
.84060
.69268
.69373
.69375
.69379
9.84179
.84182
.84184
.84186
9.84188
.84190
.84192
.84194
9.84196
.84198
.84200
.84203
9.84305
.84307
.84309
.84311
9.84313
.84315
.84317
.84319
9.84321
.84324
.84326
.84328
.69670
.69674
.69677
.69680
.69684
.69687
.69690
.69694
9.84430
.84432
.84434
.84436
.69871
.69874
.69877
.69881
9.845.54
.84556
.84558
.84.560
9.84562
.84564
.84.566
.84568
9'.84570
.84572
.84574
.84576
9.84578
.84581
.84.583
.84585
9.84587
.84589
.84591
.84.593
9.84595
.70071
.70074
.70077
.70081
+ 11'
47
9.84062
.84064
.84066
.84068
.69383
.69385
.69389
.69293
.69295
.69299
.69302
.69305
9.84438
.84440
.84442
.84444
.69884
.69887
.69891
.69894
.70084
.76087
.70091
.70094
.70097
.70101
.70104
.70107
.70111
.70114
.70117
.70131
.70134
.70137
.70131
.70134
16
15
14
13
12
11
10
9
8
7
6
5
4
3
~1
+ 13'
49
50
51
9.84070
.84072
.84075
.84077
.69697
.69700
.69704
.69707
9.84446
.84448
.84450
.84452
.69897
.69901
.69904
.69907
+ 13'
5.i
•54
55
9.84079
.84081
.84083
.84085
.69309
.69313
.69315
,69319
9.84205
.84207
.84209
.84211
9,84213
.84215
.84217
.84219
9.84221
9.84330
.84332
.84334
,84336
.69710
.69714
.69717
.69730
.69734
.69737
.69731
.69734
9.84454
.84456
.84459
.84461
.69911
.69914
.69917
.69921
.69934
.69927
.69931
.69934
.69937
+ 14'
57
58
59
9.84087
.84089
.84091
.84093
.69333
.69336
.69339
.69333
.69336
.69533
.69537
.69530
.69533
.69537
9,84338
.84340
.84342
.84344
9.84463
.84465
.84467
.84469
+ 15'
9.84096
9.84346
.69737
9.84471
.70137
i6*
29m
16h
28m
16h 27m
16h
26m
16^1- 25m
Page 902] TABLE 45.
riaversines.
s
7* 35^ 113° 45' 1
7h 36m tU° 0'
7h 37m 114° 15'
7* .S5n> 114° 30'
7A agm 114° 45' |
s
60
69
68
57
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav. Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.84595
.84597
.84599
.84601
.70137
.70141
.70144
.70147
9.84718
.84720
.84722
.84724
.70337
.70340
.70343
.70347
9.84841
.84843
.84845
.84847
.70536
.70539
.70543
.70546
9.84963
.84965
.84967
.84909
.70735
.70738
.70741
.70745
9.85085
.85087
.85089
.8.5091
.70933
.70936
.70940
.70943
+ 1'
5
6
7
9.84603
.84605
.84607
.84609
.70151
.70154
.70157
.70161
9.84726
.84729
.84731
.84733
.70350
.70353
.70357
.70360
9.84849
.84851
.84853
.84855
.70549
.70553
.70556
.70559
9.84971
.84973
.84975
.84977
.70748
.70751
.70755
.70758
9.85093
.8.5095
.85097
.85099
.70946
.70950
.70953
.70956
66
65
54
53
62
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
SO
29
28
27
26
25
+ 2'
9
• 10
11
9.84611
.84613
.84616
.84618
.70164
.70167
.70171
.70174
9.84735
.84737
.84739
.84741
.70363
.70367
.70370
.70373
9.84857
.84859
.84861
.84863
.70562
.70566
.70569
.70572
9.84979
.84982
.84984
.84986
.70761
.70764
.70768
.70771
9.85101
.85103
.85105
.85107
.70959
.70963
.70966
.70969
+ 3'
13
14
15
9.84620
.84622
.84624
.84626
.70177
.70181
.70184
.70187
9.84743
.84745
.84747
.84749
.70377
.70380
.70383
.70387
9.84866
.84868
.84870
.84872
.70576
.70579
.70582
.70586
9.84988
.84990
.84992
.84994
.70774
.70778
.70781
.70784
9.85109
.85111
.85113
.85115
.70973
.70976
.70979
.70983
+ *'
17
18
19
9.84628
.84630
.84632
.84634
.70191
.70194
.70197
.70201
9.84751
.84753
.84755
.84757
.70390
.70393
.70397
.70400
9.84874
.84876
.84878
.84880
.70589
.70592
.70596
.70599
9.84996
.84998
.85000
.8.5002
.70788
.70791
.70794
.70798
9.85117
.85119
.85121
.85123
.70986
.70989
.70992
.70996
+ «'
21
22
23
9.84636
.84638
.84640
.84642
.70204
.70207
.70311
.70314
9.84759
.84761
.84763
.84765
.70403
.70407
.70410
.70413
9.84882
.84884
.84886
.84888
.70602
.70606
.70609
.70612
9.85004
.85000
.85008
.85010
.70801
.70804
.70807
.70811
9.85125
.85127
.85129
.85131
.70999
.71002
.71006
.71009
.71012
.71016
.71019
.71023
+ 6'
25
26
27
9.84644
.84646
.84648
.84651
.70217
.70231
.70224
.70237
9.84767
.84770
.84772
.84774
.70417
.70420
.70423
.70426
9.84890
.84892
.84894
.84896
.70615
.70619
.70622
.70625
9.85012
.85014
.85016
.85018
.70814
.70817
.70821
.70824
.70827
.70831
.70834
.70837
9.85133
.85135
.85137
.85139
+ r
29
30
31
9.84653
.84655
.84657
.84659
.70230
.70234
.70237
.70340
9.84776
.84778
.84780
.84782
.70430
.70433
.70436
.70440
9.84898
.84900
.84902
.84904
.70629
.70632
.70635
.70639
9.85020
.85022
.85024
.85026
9.85141
.85143
.85145
.85)47
.71025
.71029
.71032
.71035
.71039
.71042
.71045
.71049
+ 8'
33
34
35
9.84661
.84663
.84665
.84667
.70344
.70347
.70250
.70254
9.84784
.84786
.84788
.84790
.70443
.70446
.70450
.70453
9.84906
.84908
.84910
.84912
.70642
.70645
.70649
.70652
.70655
.70659
.70662
.70665
9.85028
.85030
.85032
.85034
9.85036
.85038
.85040
.85042
.70840
.70844
.70847
.70850
.70854
.70857
.70860
.70864
9.85J49
.85151
.85153
.85155
+ 9'
37
38
39
9.84669
.84671
.84673
.84675
.70357
.70360
.70364
.70267
9.84792
.84794
.84796
.84798
.70456
.70460
.70463
.70466
9.84914
.84916
.84919
.84921
9.851.58
.85160
.85162
.85164
.71053
.71055
.71058
.71063
24
23
22
Ti
20
19
18
17
16
15
14
IS
11
10
9
+ 10'
41
42
43 .
9.84677
.84679
.84681
.84683
.70270
.70274
.70257
.70280
9.84800
.84802
.84804
.84806
.70470
.70473
.70476
.70480
9.84923
.84925
.84927
.84929
.70668
.70672
.70675
.70678
.70682
.70685
.70688
.70693
9.85044
.85046
.85048
.85050
.70867
.70870
.70874
.70877
9.85166
.85168
.85170
.85172
.71065
.71068
.71073
.71075
+ 11'
45
46
47
9.84685
.84688
.84690
.84692
.70284
.70287
.70290
.70394
9.84808
.84810
.84812
.84815
.70483
.70486
.70490
.70493
9.84931
.84933
.84935
.84937
9.8.5052
.85054
.85057
.85059
.70880
.70884
.70887
.70890
9.85174
.85176
.85178
.85180
.71078
.71083
.71085
.71088
+ 13'
49
50
51
9.84694
.84696
.84698
.84700
.70297
.70300
.70304
.70307
9.84817
.84819
.84821
.84823
.70496
.70499
.70503
.70506
9.84939
.84941
.84943
.84945
.70695
.70698
.70702
.70705
9.85061
.85063
.85065
.85067
.70893
.70897
.70900
.70903
9.85182
.85184
.85186
.85188
.71091
.71095
.71098
.71101
+ ■13'
S3
54
55
9.84702
.84704
.84706
.84708
.70310
.70314
.70311
.70320
9.84825
.84827
.84829
.84831
.70509
.70513
.70516
.70519
9.84947
.84949
.84951
.84953
.70708
.70712
.70715
.70718
9.85069
.85071
.85073
.85075
.70907
.70910
.70913
.70916
9.85190
.85192
.85, 94
-.85196
.71105
.71108
.71111
.71114
8
7
6
5
4
3
2
1
+ 14'
57
58
59
9.84710
.84712
.84714
.84716
.70324
.70327
.70330
.703.33
9.84833
.84835
.84837
.84839
.70523
.70538
.70539
.70533
9.84955
.84957
.84959
.84961
.70721
.70725
.70729
.70731
9.85077
.85079
.85081
.85083
.70930
.70933
.70926
.70930
9.85198
.85200
.85202
.85204
.71118
.71131
.71134
.71128
+ 15'
li
9.84718
.70337
9.84841
.70536
9.84963
.70735
9.85085
.70933
9.85206
.71131
16fi 24m
16h 2Sm
16h 22'<n
16^ 21m
leh 20m
TABLE 45. [Page 903
Haversines.
s
7* 40^ 115° C
7A 4Jm 115° SO'
7* 42m 115° 30' 1
-A 43m 115° 45' 1
7''.«™116°0' 1
s
Log. llav. Nat.Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2-
3
9.85206
.85208
.85210
.85212
.71131
.71134
.71138
.71141
9.8-5326
.8.5328
.85330
.85332
.71328
.71332
.71335
.71338
9.85446
.85448
.85450
.85452
.71526
.71529
.71532
.71535
9.85565
.85567
.85569
.8.5571
.71722
.71726
.71729
.71732
.71735
.71739
.71742
.71745
9.8.5684
.85686
.85688
.85690
9.85692
.85694
.85696
.8.5698
9.85700
.85702
.85704
.85706
.71919
.71922
.71925
.71928
GO
59
58
57
+ 1'
5
6
7
9.85214
.85216
.85218
.85220
.71144
.71147
.71151
.71154
9.8.5334
.85336
.85338
.85340
.71342
.71345
.71348
.71351
.71355
.71358
.71361
.71365
.71368
.71371
.71374
.71378
9.85454
.85456
.85458
.85460
.71539
.71542
.71545
.71549
9.85573
.85575
.85577
.85579
.71932
.71935
.71938
.71941
.71945
.71948
.71951
.71955
56
55
54
53
52
51
50
49
+ r
9
10
11
9.85222
.85224
.85226
.85228
.71157
.71161
.71164
.71167
.71170
.71174
.71177
.71180
9.85342
.85344
.85346
.85348
9.85350
.85352
.85354
.8.5356
9.85462
.85464
.85466
.85468
.71552
.71555
.71558
.71562
9.85.581
.85583
.85585
.85587
.71748
.71752
.71755
.71758
+ 3'
13
14
15
9.85230
.85232
.85234
.85236
9.85470
.85472
.85474
.85476
9^85478
.85480
.85482
.85484
.71565
.71568
.71571
.71575
9.85589
.85591
.85593
.85.595
.71762
.71765
.71768
.71771
.71775
.71778
.71781
.71784
.71788
.71791
.71794
.71798
9.85708
.85710
.85712
.85714
9.85716
.85718
.85720
.85722
9.85724
.85726
.85727
.85729
.71958
.71961
.71964
.71968
48.
47
46
45
+ 4'
17
18
19
9.85238
.85240
.85242
.85244
.71184
.71187
.71190
.71194
.71197
.71200
.71203
.71307
.71210
.71213
.71217
.71220
9.85358
,85360
.85362
.8,5364
.71381
.71384
.71388
.71391
.71578
.71581
.71585
.71588
9.85597
.85599
.85601
.85603
9.85605
.85607
.85609
.85611
.71971
.71974
.71977
.71981
U
43
42
41
+ 5'
21
22
23
9.85246
.85248
.85250
.85252
9.85254
.85256
.85258
.85260
9.85366
.85368
.85370
.85372
.71394
.71397
.71401
.71404
9.85486
.85488
.85490
.85492
.71591
.71594
.71598
.71601
.71984
.71987
.71990
.71994
40
39
38
37
36
35
34
33
+ 6'
25
26
27
9.85374
.85376
.85378
.85380
.71407
.71411
.71414
.71417
9.85494
.85496
.85498
.85500
.71604
.71608
.71611
.71614
9.85613
.85615
.85617
.85619
.71801
.71804
.71807
.71811
.71814
.71817
.71820
.71824
9.85731
.85733
.85735
.85737
9.85739
.85741
.85743
.85745
.71997
.72000
.72003
.72007
+ r
29
30
31
9.85262
.85264
.85266
.85268
.71223
.71226
.71230
.71233
9.8.5382
.85384
.85386
.85388
.71420
.71424
.71427
.71430
9.85502
.85504
.85506
.85508
.71617
.71621
.71624
.71627
9.8.5621
.85623
.85625
.85627
.72010
.72013
.72017
.72020
32
81
SO
29
28
27
26
25
24
23
22
21
+ 8'
33
34
35
9.85270
.8.5272
.85274
.85276
.71236
.71240
.71243
.71246
9.85390
.85392
.85394
.85396
.71434
.71437
.71440
.71443
9.85510
.85512
.85514
.85516
.71631
.71634
.71637
.71640
9.85629
.85631'
.85633
.85635
.71827
.71830
.71834
.71837
9.85747
.85749
.85751
.857.53
.72023
.72026
.72030
.72033
+ y
57
38
39
9.85278
.85280
.85282
.85284
.71249
.71253
.71256
.71259
9.8.5398
.8.5400
.85402
*.8.5404
.71447
.71450
.71453
.71456
9.8.5518
.85520
.85522
.85524
.71644
.71647
.71650
.71653
9.85637
.8.5039
.85641
.85643
.71840
.71843
.71847
.71850
9.85755
.85757
.85759
.85761
.72036
.72039
.72043
.72046
+ W
41
42
43
9.85286
.85288
.85290
.85292
.71263
.71266
.71269
.71273
9.8.5406
.8.5408
.8.5410
.8.5412
.71460
.71463
.71466
.71470
.71473
.71476
.71480
.71483
9.85526
.8.5528
.85530
.85532
.71657
.71660
.71663
.71667
9.85645
.8.5647
.85649
.8.5651
.71853
.71856
9.85763
.85765
.8-5767
.85769
9.85771
.85773
.85775
.85777
9.85779
.85781
.85783
.85785
.72049
.72052
.72056
.72059
20
19
18
17
+ n'
45
46
47
9.85294
.85296
.85298
.85300
.71276
.71279
.71282
.71286
.71289
.71292
.71296
.71299
9.8.5414
.8.5416
.8.5418
.8.5420
9.85534
.85536
.85.538
.85540
.71670
.71673
.71676
.71680
.71683
.71686
.71690
.71693
9.856.53
.85654
.85656
.85658
.71866
.71870
.71873
,71876
.72062
.72066
.72069
.72072
.72075
.72079
.72082
.72085
16
15
14
13
12
11
10
9
8
6
5
4
3
2
1
+ \V
49
50
51
9.85302
.85304
.85306
.85308
9.85422
.85424
.8.5426
.8.5428
.71486
.71489
.71493
.71496
9.85542
.85544
.85546
.85548
9.85660
.8.5662
.8.5664
.85666
.71879
.71883
.71886
.71889
+ 13'
53
54
55
9.85310
.85312
.85314
.85316
.71302
.7130.5
.71309
.71312
9.8.54.30
.8.5432
.8.5434
.8.5436
.71499
.71503
.71506
.71509
9.85550
.8.5552
.85554
.85555
.71696
.71699
.71703
.71706
9.85668
.85670
.85672
.85674
.71892
.71896
.71899
.71902
9.85787
.85788
.85790
.85792
.72088
.72092
.72095
.72098
+ 14'
57
58
59
9.85318
.85320
.85322
.85324
.71315
.71319
.71323
.71325
9.85438
.8.5440
.8.5442
.85444
9.85446
.71512
.71516
.71519
.71522
.71526
9.85557
.85559
.85561
.85563
.71709
.71712
.71716
.71719
9.85676
.8.5678
.85680
.85682
9.85684
.71905
.71909
.71912
.71915
.71919
9.85794
.85796
.85798
.85800
.72101
.72105
.72108
.72111
.72114
+ 15'
9.85326
.71328
9.85565
.71722
9.8.5802
16h 19m
le^ism
leh nm
lehiem
16h 15m
Page 904]
TABLE 45.
ITaversine?.
8
S
7^ 45m 116° 15' 1
7ft 46m 116° 30'
7ft 47m 116° 45' 1
7ft 48m 1170 0'
7lt 49m 117° 15'
s
Log. Hav.
Nat. Hav.
Log. Hav.
Xat. Hav.
Log. Hav.
Nat. Hav.
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
9.85802
.85804
.85806
.85808
.72114
.72118
.72121
.72124
9.85920
.85922
.85924
.85926
.72310
.72313
.72316
.72320
9.86037
.86039
.86041
.86043
.73505
.72508
.72511
.72515
9.86153
.86155
.86157
.86159
.72700
.72703
.72706
.72709
9.86269
.86271
.86273
.86275
.72894
.72897
.72900
.72903
60
59
58
57
+ 1'
5
6
7
9.85810
.85812
.85814
.85816
.72127
.72131
.72134
.72137
9.85928
.85930
.85931
.85933
.72323
.72326
.72329
.72333
9.86045
.86046
.86048
.86050
.72518
.72521
.72524
.72528
9.86161
.86163
.86165
.86167
.73713
.73716
.73719
.73732
9.86277
.86279
.86281
.86282
.72907
.72910
.72913
.72916
56
55
54
53
52
51
50
49
+ 2'
9
10
11
9.85818
.85820
.85822
.85824
.72141
.72144
.72147
.72150
9.85935
.85937
.85939
.85941
.72336
.72339
.72342
.72346
9.86052
.86054
.86056
.86058
.72531
.72534
.72537
.72541
9.86169
.86171
.86173
.86174
.72725
.72729
.72732
.72735
9.86284
.86286
.86288
.86290
.72920
.72923
.72926
.72929
+ 3'
13
14
15
9.85826
.85828
.85830
.85832
.72154
.72157
.72160
.72163
9.85943
.85945
.85947
.85949
.72349
.72352
.72355
.72359
9.86060
.86062
.86064
.86066
.72544
.72547
.72550
.72554
9.86176
.86178
.86180
.86182
.72738
.72742
.72745
.72748
9.86292
.86294
.86296
.86298
.73933
.73930
.73939
.72942
48
47
46
45
+ i'
17
18
19
9.85834
.85836
.85838
.85840
.72167
.72170
.72173
.72176
9.85951
.85953
.85955
.8.5957
.72362
.72365
.72368
.72372
9.86068
.86070
.86072
.86074
.73557
.72560
.72563
.72567
9.86184
.86186
.86188
.86190
.72751
.72755
.72758
.72761
9.86300
.86302
.86304
.86306
.72945
.72949
.72953
.72955
44
43
42
41
40
39
38
37
+ 5'
n
n
23
+ 6'
25
26
27
9.85841
.85843
.85845
.85847
.72180
.72183
.72186
.72189
9.85959
.85961
.85963
.85965
.73375
.73378
.73381
.72385
9.86076
.86078
.86080
.86081
.72570
.72573
.72576
• .72580
9.86192
.86194
.86196
.86198
.72764
.72768
.72771
.73774
9.86307
.86309
.86311
.86313
.72958
.72963
.72965
.72968
9.85849
.85851
.85853
.85855
.72193
.72196
.72199
.72202
9,85967
.85969
.85971
.85972
.72388
.72391
.72394
.72398
9.86083
.86085
.86087
.86089
.72583
.72586
.72589
.72593
9.86200
.86201
.86203
.86205
.72777
.72780
.72784
.72787
9.86315
.86317
.86319
.86321
.72971
.72974
.72978
.72981
30
35
34
33
+ r
29
30
31
9.85857
.85859
.85861
.85863
.72206
.72209
.72212
.72215
9.85974
.85976
.85978
.85980
.72401
.72404
.72407
.72411
9.86091
.86093
.86095
.86097
.72596
.72599
.72602
.72606
9.86207
.86209
.86211
.86213
.72790
.72793
.72797
.72800
9.86323
.86325
.86327
.86329
.72984
.72987
.72991
.72994
32
31
30
29
+ 8'
33
34
35
9.85865
.85867
.85869
.85871
.72219
.72232
.72225
.72229
9.85982
.85984
.85986
.85988
.72414
.72417
.72420
.72424
9.86099
.86101
.86103
.86105
.72609
.72612
.72615
.72618
9.86215
.86217
.86219
.86221
.73803
.72806
.72810
.73813
9.86331
.86332
.86334
.86336
.72997
.73000
.73004
.73007
28
27
26
25
24
23
22
21
+ 9'
37
38
39
9.85873
.85875
.85877
.8.5879
.72232
.72235
.72238
.72242
9.85990
.85992
.85994
.85996
.72427
.72430
.72433
.72437
9.86107
.86109
.86111
.86112
.72622
.72625
.72628
.72631
9.86223
.86225
.86227
.86229
.72816
.72819
♦.72823
.72826
9.86338
.86340
.86342
.86344
.73010
.73013
.73016
.73020
+ W
41
42
43
9.85881
.85883
.85885
.85887
.72245
.72248
.72251
.72255
9.85998
.86000
.86002
.86004
.72440
.72443
.72446
.72450
9.86114
.86116
.86118
.86120
.72635
.73638
.73641
.73644
9.86230
.86232
.86234
.86236
.72839
.72833
.73835
.73839
9.86346
.86348
.86350
.86352
.73023
.73026
.73029
73033
20
19
18
17
+ 11'
45
46
47
9.85888
.85890
.85892
.85894
.72258
.72261
.72364
.72368
9.86006
.86008
.86010
.86011
.72453
.72456
.72459
.72463
9.86122
.86124
.86126
.86128
.73648
.73651
.73654
.72657
9.86238
.86240
.86242
.86244
.73843
.73845
.72848
.72852
9.86354
.86355
.86357
.86359
.73036
.73039
.73043
.73046
16
15
14
13
+ 12'
49
50
51
9.85896
.85898
.85900
.85902
.72271
.72274
.72277
.72281
9.86013
.86015
.86017
.86019
.72466
.72469
.72472
72476
9.86130
.86132
.86134
.86136
.72661
.72664
.72667
.72670
9.86246
.86248
.86250
.86252
.72855
.72858
.72861
.72865
9.86361
.86363
.86365
.86367
.73049
.73053
.73055
.73058
12
11
10
9
8
7
6
.5
+ 13'
53
54
55
9.85904-
.85906
.85908
.85910
.72284
' .72387
.73290
.73294
9.86021
.86023
.86025
.86027
.73479
.73482
.72485
.72489
9.86138
.86140
.86142
.86143
.72674
.72677
.72680
.72683
9.86254
.86256
.86257
.86259
.72868
.72871
.72874
.72878
9.86369
.86371
.86373
.86375
.73063
.73065
.73068
.73071
+ 14'
57
58
59
9.85912
.85914
.85916
.85918
.72297
.72300
.72303
72307
9.86029
.86031
.86033
.86035
.72492
.72495
.72498
.72502
9.86145
.86147
.86149
.86151
.73687
.72690
.72693
.72696
9.86261
.86263
.86265
.86267
.72881
.72884
.72887
.73890
9.86377
.86379
.86380
.86382
.73076
.73078
.73081
.73084
4
3
}
1
+ 15'
9.85920
.72310
9.86037
.72505
9.86153
.72700
9.86269
.73894
9.86384
.73087
16^
14m.
ifiA
13m
16h
12'"'
Vi't
Um
16h 10m
TABLE 45. [Page 905
Haversines.
s
7* 60m 117° W
7ft Sim 117" 45'
7ft 52m 118° (K
7ft SSm 118° 15'
7ft 54^ 118° 30'
s
Log. Ilav. Nat. Hav.
Log. Hav.
Nat. Ilav.
Log. Hav
. Nat. Hav
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
2
3
+ r
5
6
7
+ 2'
9
10
11
9.86384 i .73087
.86386 .73091
.86388 .73094
.86390 .73097
9.86499
.86501
.86503
.86505
.73281
.73284
.73387
.73390
9.86613
.86615
.86617
.86619
.73474
.73477
.73480
73483
9.86727
.86729
.86730
.86732
.73666
.73669
.73673
.73676
9.86840
.86842
.86843
.86845
.73858
.73861
.73864
.73868
60
59
58
57
56
55
54
53
52
51
50
49
48
47
46
45
U
43
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
26
25
24
23
22
~21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
'4
3
2
1
9.86392
.86394
.86396
.86398
9.86400
.86401
.86403
.86405
.73100
.73104
.73107
.73110
9.86507
.86.509
.86510
.86512
.73394
.73297
.73300
.73303
.73306
.73310
.73313
.73316
.73319
.73333
.73336
.73339
9.86621
.86623
.86025
.80026
.73486
.73490
.73493
.73496
9.86734
.86736
.86738
.80740
9.80742
.80744
.86746
.86747
9.86749
.86751
.86753
.86755
9.86757
.86759
.86761
.86763
.73679
.73683
.73685
.73688
9.86847
.86849
.86851
.86853
.73871
.73874
.73877
.73880
.73113
.73116
.73130
.73133
.73136
.73139
.73133
.73136
9.86514
.86516
.86518
.80520
9.80522
.80524
.86520
.86528
9.80628
.80630
.86632
.80054
9.80036
.80638
.86640
.86642
.73499
.73503
.73506
.73509
.73513
.73515
.73519
.73533
.73692
.73695
.73698
.73701
9.86855
.86857
.86859
.86860
9.86862
.86864
.86866
.80808
9.80870
.86872
.86874
.86875
.73884
.73887
.73890
.73893
.73896
.73899
.73903
,73906
,73909
,73912
,73915
,73919
+ 3'
IS
14
15
9.86407
.86409
.86411
.86413
.73704
.73708
.73711
.73714
+ i'
17
18
19
+ 5'
21
22
23
9.86415
.86417
.86419
.86421
9.86423
.86424
.86426
.86428
.73139
.73143
.73145
.73149
9.86529
.86531
.80533
.80535
.73333
.73335
.73339
.73343
9.86643
.86645
.86647
.86649
.73535
,73538
.73531
.73535
.73538
.73541
.73544
.73547
.73717
.73730
.73734
.73737
.73153
.73155
.73158
.73163
9.80537
.80539
.86541
.86543
.73345
.73348
.73351
.73355
9.86651
.86653
.86655
^6057
9.86059
.80061
.86662
.86664
9.86764
.86766
.86768
.86770
.73730
.73733
.73736
.73740
9.86877
.86879
.86881
.86883
9.80885
.80887
.80889
.86890
9.86892
.86894
.80896
.86898
9,86900
.86902
.86904
.86905
9.80907
.86909
.86911
.86913
9,86915
.86917
.86919
.86920
9,86922
.86924
.86926
.86928
9,86930
.86932
.86933
.86935
,73923
,73925
,73928
.73931
.73935
.73938
.73941
.73944
.73947
,73951
,73954
.73957
.73960
.73963
.73967
.73970
,73973
,73976
.73979
.73982
.73986
.73989
.73993
.73995
.73998
.74003
.74005
.74008
.74011
.74014
.74018
.74031
.74034
.74037
.74030
.74033
.74037
.74040
.74043
,74046
+ 6'
25
26
27
9.86430
.86432
.86434
.86436
.73165
.73168
.73171
.73174
9.80545
.86547
.86509
.86550
.73358
.73361
.73364
.73368
.73i371
.73374
.73377
.73380
.73384
.73387
.73390
.73393
.73396
.73400
.73403
.73406
.73409
.73413
.73416
.73419
,73551
.73554
.73557
.73560
9.86772
.86774
.86776
.86778
.73743
.73746
.73749
.73753
+ r
29
30
31
+ 8'
S3
34
35
9.86438
.86440
.86442
.86444
.73178
.73181
.73184
.73187
.73191
.73194
.73197
.73200
.73203
.73307
.73310
.73313
9.86552
.86554
.86556
.86558
9.86560
.86562
.86564
.86566
9.86568
.86569
.86571
.86573
9.86575
.86577
.86579
.86581
9.80606
.86608
.80670
.86672
.73563
.73567
.73570
.73573
9.86780
.86781
.80783
.86785
9.86787
.86789
.86791
.86793
.73756
.73759
73762
.73765
.73768
.73773
.73775
.73778
9.86446
.86447
.86449
.86451
9.86674
.86676
.86678
.80079
.73576
.73579
.73583
.73586
+ 9'
37
38
39
9.86453
.86455
.86457
.86459
9,80081
.80683
.80685
.86687
.73589
.73593
.73595
.73599
.73603
,73605
.73608
.73611
9.86795
.86796
.86798
.86800
.73781
.73784
.73788
.73791
.73794
.73797
.73800
.73804
.73807
.73810
.73813
.73816
+ W
41
42
43
9.86461
.86463
.86465
.86467
.73216
.73330
.73333
.73336
9.86689
.86691
.86693
.86695
9.86802
.86804
.86806
.86808
+ 11'
4S
46
47
+ 12'
49
60
51
9.86468
.86470
.86472
.86474
.73339
.73232
.73336
.73339
9.86-583
.86585
.86587
.80588
.73433
.73435
.73439
.73433
9.86696
.86698
.86700
.86702
.73615
.73618
.73621
.73634
9.86810
.86812
.86813
.86815
9.86476
.86478
.86480
.86482
9.86484
.86486
.86488
.86489
.73343
.73245
.73249
.73253
.73355"
.73258
.73261
.73265
9.86590
.86592
.86594
.86596
.73435
.73438
.73441
.73445
9.86704
.86706
.86708
.86710
.73638
.73631
,73634
.73637
9.86817
.86819
.86821
.86823
.73830
.73823
.73826
,73839
+ 13'
63
64
65
9.86.598
.86600
.86602
.86604
.73448
.73451
.73454
.73458
.73461
.73464
.73467
.73470
9.86712
.86713
.80715
.80717
.73640
.73644
.73647
.73650
9.86825
.86827
.86828
.86830
,73832
,73836
,73839
.73842
.73845
.73848
.73853
.73855
.73858
9,86937
.86939
.86941
.86943
+ 14'
57
58
59
9.86491
.86493
.86495
.86497
.73268
.73271
.73274
.73278
9.86000
.86607
.86609
.86611
9.80719
.80721
.80723
.80725
9.80727"
.73653
.73656
.73660
.73663
9.86832
.86834
.86836
.86838
9.86945
.86947
.86948
.86950
+ 15'
9.86499
.73281
9.86613
.73474
.73666
9.86840
9.86952
.;f4049
IGhgm
16h gm
ieh7m
16h em
IgliSm
Page 906]
TABLE 45.
Ilaversines.
s
7* 55^ 118° 45' 1
7A56">119°0' 1
7A 57m 119° 15' 1
7A 58m 1190 30'
-ft .59m 119° 45' 1
s
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
1
S
9.86952
.86954
.86956
.86958
.74049
.74053
.74056
.74059
9.87064
.87066
.87068
.87070
.74240
.74344
.74347
.74350
9.87175
.87177
.87179
.87181
.74431
.74434
.74437
.74441
9.87286
.87288
.87290
.87292
.74631
,74634
.74628
.74631
9.87396
.87398
.87400
.87402
.74811
.74814
.74817
.74830
60
59
58
,57
+ 1'
5
6
7
9.86960
.86962
.86963
.86965
.74063
.74065
.74069
.74073
9.87072
.87073
.87075
.87077
.74353
,74356
.74360
.74363
9.87183
.87185
.87187
.87188
.74444
.74447
.74450
.74453
9.87294
.87295
.87297
.87299
.74634
.74637
.74640
.74643
9.87404
.87406
.87407
.87409
.74833
.74837
.74830
.74833
56
55
54
53
+ -i'
9
10
11
9.86967
.86989
.86971
.86973
.74075
.74078
.74081
.74084
9.87079
.87081
.87083
.87085
.74266
.74269
.74272
.74275
9.87190
.87192
.87194
.87196
.74456
.74460
.74463
.74466
9.87301
.87303
.87305
.87306
.74646
.74650
.74653
.74656
9.87411
.87413
.87415
.87417
.74836
.74839
.74842
.74846
52
51
50
49
+ y
IS
14
15
9.86975
.86977
.86978
.86980
.74088
.74091
.74094
.74097
9.87086
.87088
.87090
.87092
.74379
.74383
.74385
.74388
9.87198
.87199
.87201
.87203
.74469
.74473
.74475
.74479
9.8730S
.87310
.87312
.87314
.74659
.74663
.74665
.74669
9.87418
.87420
.87422
.87424
.74849
,74852
,74855
,74858
4S
47
46
45
44
43
42
41
+ i'
n
18
19
9.86982
.86984
.86986
.86988
.74100
.74104
.74107
.74110
9.87094
.87090
.87098
.87100
.74391
.74394
.74398
.74301
9.87205
.87207
.87209
.87211
,74483
.74485
.74488
.74491
9.87316
.87318
.87319
.87321
.74672
.74675
.74678
.74681
9.87426
.87428
.87429
.87431
.74861
.74864
,74868
74871
+ 5'
'21
22
23
9.86990
.86991
.86993
.86995
.74113
.74116
.74130
.74133
9.87101
.87103
.87105
.87107
.74304
.74307
.74310
.74314
9.87212
.87214
.87216
.87218
.74494
.74498
.74501
. .74504
9.87323
.87325
.87327
.87329
.74684
.74688
.74691
.74694
9.87433
.87435
.87437
.87439
.74874
.74877
.74880
.74883
40
39
38
37
+ 6'
25
26
27
9.86997
.86999
.87001
.87003
.74136
.74139
.74133
.74135
9.87109
.87111
.87112
.87114
.74317
.74330
.74333
.74336
9.87220
.87222
.87224
.87225
.74507
.74510
.74514
.74517
9,87330
.87332
.87334
.87336
.74697
.74700
.74703
.74707
9.87440
.87442
.87444
.87446
.74887
,74890
,74893
,74896
36
35
34
33
32
31
30
29
+ r
29
30
31
9.87004
.87006
.87008
.87010
.74139
.74143
.74145
.74148
9.87116
.87118
.87120
.87122
.74339
.74333
.74336
.74339
9.87227
.87229
.87231
.87233
.74530
.74523
.74536
.74539
9.87338
.87340
.87341
.87343
.74710
.74713
.74716
.74719
9.87448
.87450
.87451
.87453
,74889
.74902
,74905
,74906
•+ 8'
S3
S4
35
9.87012
.87014
.87016
.87018
.74151
.74155
.74158
.74161
9.87124
.87125
.87127
.87129
.74343
.74345
.74349
.74353
9.87235
.87236
.87238
.87240
.74533
.74536
.74539
.74543
9.87345
.87347
.87349
.87351
.74723
.74736
.74739
.74733
9.87455
.87457
.87459
.87460
,74912
,74915
,74918
,74921
28
27
26
25
+ r
37
38
39
9.87019
.87021
.87023
.87025
.74164
.74167
.74170
.74174
9.87131
.87133
.87135
.87137
.74355
.74358
.74361
.74364
9.87242
.87244
.87246
.87248
.74545
.74548
.74553
.74555
9.87352
.87354
.87356
.87358
.74735
.74738
.74741
.74744
9.87462
.87464
.87466
.87408
.74924
,74928
.74931
.74934
24
23
22
21
+ W
41
42
43
9.87027
.87029
.87031
.87032
.74177
.74180
.74183
.74186
9.87138
.87140
.87142
.87144
.74368
.74371
.74374
.74377
9.87249
.87251
.87253
.87255
.74558
.74561
.74564
.74567
9.87360
.87362
.87363
.87365
.74748
.74751
.74754
.74757
9.87470
.87471
.87473
.87475
.74937
.74940
.74943
.74946
20
19
IS
n
+ 11'
45
46
47
9.87034
.87036
.87038
.87040
.74190
.74193
.74196
.74199
9.87146
.87148
.87149
.87151
.74380
.74383
.74387
.74390
9.87257
.87259
.87260
.87262
.74571
.74574
.74577
.74580
9.87367
.87369
.87371
.87373
.74760
.74763
.74767
.74770
9.87477
.87479
.87481
.87482
,74950
,74953
.74956
.74959
16
15
14
13
+ \V
49
50
51
9.87042
.87044
.87045
.87047
.74303
.74305
.74209
.74313
9.87153
.87155
.87157
.87159
.74393
.74396
.74399
.74403
.74406
.74409
.74413
.74415
9.87264
.87266
.87268
.87270
.74583
.74586
.74590
.74593
9.87374
.87376
.87378
.87380
9.87382
.87384
.87385
.87387
.74773
.74776
.74779
.74783
9.87484
.87486
.87488
.87490
.74963
.74965
.74969
.74973
12
11
10
9
+ 13'
53
54
55
9.87049
.87051
.87053
.87055
.74315
.74318
.74331
.74235
9.87161
.87162
.87164
.87166
9.87271
.87273
.87275
.87277
.74596
.74599
.74603
.74605
.74786
.74789
.74793
.74795
9.87492
.87493
.87495
.87497
.74975
.74978
.74981
.74984
8
7
6
5
4
3
2
1
+ 1*'
57
58
59
9.87057
.87059
.87060
.87062
.74228
.74231
.74234
.74237
9.87168
.87170
.87172
.87174
.74418
.74433
.74435
.74438
9.87279
.87281
.87283
.87284
.74609
.74613
.74615
.74618
9.87389
.87391
.87393
.87395
,74798
,74801
.74805
.74808
9.87499
.87501
.87502
.87504
.74987
.74991
,74994
,74997
+ 15'
9.87064
.74240
9.87175
.74431
9.87286
.74631
9.87396
.74811
9.87506
,75000
16''
^m
lehsm
16h2m
16f
2 m
161
I Qm
TABLE 45. [Page 907
Haversines.
s '
8h om 130° C 1
8h 2m 120° 30'
8h 4m 131<= (K
«*6"<121°30' 1
«ft5ml33°0'
s
Log. Hav.
Nat. llav.
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log, Hav,
Nat. Hav.
9.87506
0.75000
9.87724
0.75377
9.87939
0.75752
9.88153
0.76135
9,88364
0.76496
60
2
.87510
.75006
.87727
.75383
.87943
.75758
.88156
.76131
,88367
.76502
68
4+ 1
.87513
.75013
.87731
.75389
.87947
.75764
.88160
.76137
,88371
.76508
56
6
.87517
.75019
0.75025
.87735
9.87738
.75396
0.75402
.879.50
9.87954
.75771
.88163
.76144
,88374
.76514
0.76521
54
52
8+ 2
9.87521
0.75777
9.88107
0.76150
9.88378
10
.87524
.75032
.87742
.75408
.87957
.75783
.88170
.76156
.88381
.76537
SO
li+ 3
.87528
.75038
.87745
.75415
.87961
.75789
.88174
.76163
.88385
.76533
48
14
,87532
.75044
.87749
.75421
.87964
.75795
,88177
.76168
.88388
.76539
46
16+ 4
9.87535
0.75050
9.877.53
0.75437
9.87968
0.75802
9,88181
0.76175
9.88392
0.76545
U
18
.87539
.75057
.87756
.75433
.87971
.75808
.88185 .76181
.88395
.76551
42
20+ 5
.87543
.75063
.87760
.75440
.87975
.75814
.88188 i .76187
.88399
.76558
40
22
.87546
.75069
.87764
9.87767
.75446
0.75453
.87979
.75830
.88192 ] .76193
.88402
.76564
0.76570
38
36
24+ 6
9.87550
0.75075
9.87982
0.75837
9.88195 0.76199
9.88406
26
.87553
.75082
.87771
.75458
.87986
.75833
.88199 .76205
.88409
.76576
34
28+ 7
.87557
.75088
.87774
.75465
.87989
.75839
.88202 .76212
.88413
.76583
32
^0
.87561 .75094 1
.87778
.75471
.87993
.75845
.88206 ! .76218
.88416
.76588
30
.i,'+ 8
9.87564
0.75101
9.87782
0.75477
9.87996
0.75853
9.88209 0.76224
9.88420
0.76595
28
''-^
.87568
.75107
.87785
.75483
.88000
.75858
.88213
.76330
.88423
.76601
26
jv;+ 9
.87572
.75113
.87789
.75490
.88004
.75864
.88216
.76236
.88427
.76607
24
J8
.87575
.75120
0.75126
.87792
.75496
0.75502
.88007
9.88011
.75870
0.75876
.88220
9.88223
.76243
0.76249
.88430
9.88434
.76613
0.76619
22
20
40+10
9.87579
9.87796
42
.87583
.75132
.87800
.75508
.88014
.75883
. .88227
.76255
.88437
.76625
18
44+11
.87586
.75138
.87803
.75515
.88018
.75889
.88230 .76261
.88441
.76632
16
46
.87590
.75145
.87807
.75531
.88021
.75895
.88234 .76267
.88444
.76638
14
4<*+12
9.87593
0.75151
9.87810
0.75537
9.58025
0.75901
9.88237 0.76274
9.88448
0.76644
12
60
.87597
.75157
.87814
.75533
.88029
.75908
.88241 : .76380
.88451
.76650
10
6i+n
.87601
.75164
.87818
.75540
.88032
.75914
.88244
.76286
.88455
.76656
8
64
.87604
.75170
0.75176
.87821
9.87825
.75546
0.75553
.88036
9.88039
.75930
0.75926
.88248
.76292
.88458
9.88462
.76662
0.76668
6
4
.56- +14
9.87608
9.88252
0.76398
58
9.87612
0.75182
9.87828
0.75558
9.88043
0.75933
9.882.55
0.76305
9.88465
0.76675
2
ISti 59m
15h 57m
15h 55m
15h 53m
15h Sim
s '
0+15
8h jm 120° 0'
»A 3™ 120° 30'
8h 5m 131° (K
8h 7m 131° 3r
8h 9m 133° 0'
s
60
9.87615
0.75189
9.87832
0.75565
9.88046 1 0.75939
9,88259
0.76311
9.88469 0.76681
.^
.87619
.75195
.87835
.75571
.88050 .75945
,88262
.76317
.88472 .76687
58
4+16
.87623
.75201
.87839
.75577
.88053 i .75951
,88266
.76333
.88476 i .76693
56
6
.87626
.75208
0.75214
.87843
9.87846
.75583
0.75590
.88057 1 .75957
9.88001 ! 0.75964
,88269
9,88273
.76329
0.76335
.88479
9.88483
.76699
0.76705
54
,^+17
9.87630
52
10
.87633
.75220
.87850
.75596
.88064 1 .75970
,88276
.76342
.88486
.76711
SO
12 + \%
.87637
.75226
.87853
.75602
.88068 ! .75976
.88280
.76348
.88490
.76718
48
14
.87641
.75233
.87857
.75608
.88071 i .75982
.88283
.76354
.88493
.76724
46
16+\%
9.87644
0.75239
9.87861
0.75615
9.88075 ! 0.75988
9.88287
0.76360
9.88496
0.76730
44
18
.87648.
.75245
.87864
.75621
.88078 1 .75995
.88290 i .76366
.88500
.76736
42
.'0+20
.87652
.75251
.87868
.75637
.88082
.76001
.88294
.76373
.88503
.76742
40
22
.87655
.75258
0.75264
.87871
.75633
0.75640
.88085
9.88089
.76007
.88297
.76379
.88507
9.88510
.76748
0.76754
38
36
24+91
9.876.59
9.87875
0.76013
9.88301
0.76385
26
.87662
.75270
.87879
.75646
.88092
.76019
.88304
.76391
.88514
.76761
34
28+Zi
.87666
.75277
.87882
.75653
.88096
.76026
.88308
.76397
.88517
.76767
32
SO
.87670
.75283
.87886
.75658
.88100
.76032
.88311
.76403
.88521
.76773
30
5»+23
9.87673
0.75289
9.87889
0.75665
9.88103
0.76038
9.88315
0.76410
9.88524
0.76779
28
34
.87677
.75295
.87893
.75671
.88107
.76044
.88318
.76416
.88528
.76785
26
36+U
.87680
.75302
.87896
. .75677
.88110
.76050
.88322
.76422
.88.531
.76;91
24
38
40+Z5
.87684
.75308
.87900
9.87904
.75683
.88114
.76057
.88325
.76438
.88.5.35
9.8^528
.76/97
22
20
9.87688
0.75314
0.75690
9.88117
0.76063
9.88329
0.76434
0.76804
42
.87691
.75321
.87907
.75696
,88121
.76069
.88332
.76440
.88.542
.76810
18
44+26
.87695
.75327
.87911
.75703
.88124
.76075
.88336
.76447
.88545
.76816
16
46
.87699
.75333
.87914
.75708
.88128
.76082
.88339
.76453
.88.549
.76823
14
4^+27
9.87702
0.75339
9.87918
0.75714
9,88131
0.76088
9.88343
0.76459
9.88.552
0.76838
12
SO
.87706
.75346
.87921
.75731
,88135
.76094
.88346
.76465
.88556
.76834
10
52+28
.87709
.75353
.87925
.75727
.88139
.76100
.88350
.76471
.88559
.76840
8
54
.87713
.75358
0.75364
.87929
9.87932
.75733
0.75739
.88142
9.88146
.76106
6.76113
.88353
.76477
.88562
9.88566
.76847
0.76853
6
4
56+29
9.87717
9.88357
0.76484
58
.87720
.75371
.87936
.75746
.88149
.76119
.88360
.76490
,88569
.76859
2
60+30
9.87724
0.75377
9.87939
0.75753
9.881.53
0.76125
9.88364
0.76496
9,88573
0.76865
15h 55m
15^ 56m
ISlt 54m
iS* 52m
15ft 50m
Page 908] TABLE 45. |
Haversines. 1
s '
8^ lOm 132° 30'
gh 12m 133° 0'
Sn 14m 133° 30' 1 ^ft 16m 134° Q'
gft ISm 134° 30'
s
log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav. Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
9.88573
0.76865
9.88780
0.77333
9.88984
0.77597
9.89187
0.77960
9.89387
0.78330
60
•2
.88576
.76871
.88783
.77338
.88988
.77603
.89190
.77966
.89391
.78336
58
4+ 1
.88580 1 -Jes;;
.88787
.77344
.88991
.77609
.89194
.77972
.89394
.78333
56
6
.88583 ' .76883
.88790
9.88793"
.77250
0.77256
.88995
9.88998
.77615
0.77621
.89197
9.89200"
.77978
.89397
9.89400
.78338
0.78344
54
52
8+ Z
9.88587 0.76890
0.77984
10
.88590: .76896
.88797
.77262
.89001
.77627
.89204
.77990
.89404
.783.50
50
12+ 3
.88594 1 .76902
.88800
.77269
.89005
.77633
.89207
.77996
.89407
.78356
48
14
.88597 ! .76908
.88804
.77275
.89008
.77639
.89210
.78002
.89411
.78363
46
16+ i
9.88600 , 0.76914
9.88807
0.77281
9.89012
0.77645
9.89214 0.78008
9.89414
0.78368
44
IS
.88604
.76930
.88811
.77287
.89015
.77651
.89217
.78014
.89417
.78374
42
20+ 5
.88607
.76936
.88814
.77293
.89018
.77657
.89221
.78020
.89421
.78380
40
22
.88611
.76933
.076939
.88817
.77299
.89022
.77664
0.77670
.89224
9.89227
.78026
.89424
9.89427
.78386
0.78393
38
36
24+ 6
9.88614
9.88821 i 0.77305
9.89025
0.78033
26
.88618
.76945
.88824
.77311
.89028
.77676
.89231
.78038
.89431
.78398
34
28+ 7
.88621
.76951
.88828
.77317
.89032
.77683
.89234
.78044
.89434
.78404
32
SO
.88625
.76957
.88831
,77323
, .89035
.77688
.89237
.78050
.89437
.78410
30
32+ 8
9.88628
0.76963
9.88835
0.77329
9.89039
0.77694
9.89241
0.78056
9.89441
0.78416
28
S4
.'88632
.76969
.88838
.77336
.89042
.77700
.89244
.78062
.89444
.78433
26
36+ 9
.88635
.76975
.88841
.77343
.89045
.77706
.89247
.78068
.89447
.78438
24
38
.88639
.76981
.88845
.9.88848"
.77348
0.77354
.89049
.77712
.89251
.78074
0.78080
.89450
9.89454
.78434
0.78440
22
20
40+19
9.88642
0.76988
9.89052
0.77718
9.89254
42
.88645
.76994
.88852
.77360
.89056
.77724
.89257
.78086
.89457
.78446
18
U+tL
.88649
.77000
.88855
.77366
.89059
.77730
.89261
.78092
.89460
.78453
16
46
.88652
.77006
.88858
.77373
.89062
.77736
.89264
.78098
.89464
.78458
14
4s+n
9.88656
0.77012
9.88862
0.77378
9.89066
0.77742
9.89267
0.78104
9.89467
0.78464
12
50
.88659
.77018
.88865
.77384
.89069
.77748
.89271
.78110
.89470
.78470
10
52+XZ
.88663
.77024
.88869
.77390
.89072
.77754
.89274
.78116
.89474
.78476
8
54
.88666
.77030
0.77036
.88872
9.88876
.77396
.89076
.77760
0.77766
.89277
.78122
.89477
.78483
0.78488
6
4
56+14
9.88670
0.77403
9.89079
9.89281
0.78128
9.89480
58
9.88673
0.77043
9.88879
0.77409
9.89083
0.77772
9.89284
0.78134
.9.89484
0.78494
2
75* 49™
15h 47™
ISli 45m
15h 43m
_r,5A 41m
s '
0+15
«A lim 133° 30'
Sh ism 133° (K
8^ 15m 133° 30'
Sh nm 134° 0'
Sh 19m 134° 30'
s
9.88677
0.77049
9.88882
0.77415
9.89086
0.77779
9.89287
0.78140
9.89487
0.78500
60
2
.88680
.77055
.88886
.77413
.89089
.77785
.89291
.78146
.89490
.78506
58
4+16
.88683
.77061
.88889
.77427
.89093
.77791
.89294
.78152
.89493
.78512
56
6
.88687
.77067
.88893
.77433
0.77439
.89096
9.89099
.77797
0.77803
.89298
.78158
0.78164
.89497
.78518
54
52
8+n
9.88690
0.77073
9.88896
9.89301
9.89500
0.78524
10
.88694
.77079
.88899
.77445
.89102
.77809
.89304
.78170
.89503
.78530
50
12+\%
.88697
.77085
.88903
.77451
.89106
.77815
.89303
.78176
.89507
.78536
48
14
.88701
.77092
.88906
.77457
.89110
.77821
.89311
.78182
.89510
.78542
46
16+\%
9.88704
0.77098
9.88910
0.77463
9.89113
0.77827
9.89314
0.78188
9.89513
0.78548
44
18
.88708
.77104
.88913
.77469
.89116
.77833
.89318
.78194
.89517
.78554
42
fO+20
.88711
.77110
.88916
.77475
.89120
.77839
.89321
.78200
.89520
.78560
40
22
.88714
.77116
.88920
.77482
0.77488
.89123
.77845
0.77851
.89324
9.89328
.78206
.89523
.78566
38
24+21
9.88718
0.77122
9.88923
9.89126
0.78212
9.89527
0.78573
36
26
.88721
.77128
.88927
.77494
.89130
.77857
.89331
.78218
.89530
.78577
34
28+Zt
.88725
.77134
.88930
.77500
.89133
.77863
.89334
.78324
.89533
.78583
32
30
.88728
.77140
.88933
.77506
.89137
.77869
.89338
.78230
.89536
.78589
30
32+Z3
9.88732
0.77147
9.88937
0.77513
9.89140
0.77875
9.89341
0.78236
9.89540
0.78595
28
34
.88735
.77153
.88940
.77518
.89143
.77881
.89344
.78242
.89543
.78601
26
S6+U
.88739
.77159
.88944
.77524
.89147
.77887
.89348
.78248
.8S546
.78607
24
38
.88742
.77165
.88947
9.88950
.77530
0.77536
.89150
.77893
.89351
9.89354
.78254
0.78260
.89.550
.78613
22
20
40+25
9.88745
0.77171
9.89153
0.77899
9.89553
0.78619
42
.88749
.77177
.88954
.77543
.89157
.77905
.89358
.78266
.89556
.78625
18
44+26
.88752
.77183
.88957
.77548
.89160
.77911
.89361
.78272
.89559
.78531
16
46
.88756
.77189
.88961
.77554
.89163
.77917
.89364
.78278
.89563
.78637
14
48+^^
9.88759
0.77195
9.88964
0.77560
9.89167
0.77923
9.89368
0.78284
9.89566
0.78643
12
so
.88763
.77201
.88967
.77567
.89170
.77929
.89371
.78290
.89569
.78649
10
52+2S
.88766
.77208
.88971
.77573
.89174 ! .77936
.89374
.78396
.89573
.78665
8
54
.88769
.77214
.88974
.77579
0.77585
.89177
.77942
0.77948
.89378
9789381"
.78303
0.78308
.89576
9.89"5"79
.78661
0.78667
6
4
56+39
9.88773
0.77220
9.88978
9.89180
58
.88776
.77226
.88981
.77591
.89184 .77954
.89384
.78314
.89583
.78673
2
60+30
9.88780
0.77232
9.88984
0.77597
9.89187 0.77960
9.89387
0.78330
9.89586
0.78679
loh 4Sm
15h 46m
15h44m
15h42m
15h 40m
TABLE 45. [Page 909
llaversinos.
. s '
Sft 20m 125° 0'
8^ 22m 125° 30'
SA 24'" 126° 0'
8^ 26m 126° 30'
SA 28m 1270 (K
s
Log. Hav.^ N'at. llav.
Log. Ilav
N'at. Hav.
Log. Ilav.
Nat. Ilav.
Log. Hav.' Nat. Hav.
Log. Hav.
Nat. Hav.
9.89586 0.78679
9.89782
0.79035
9.89976
0.79389
9.90168
0.79741
9.90358
0.80091
60
2
.89589 .78685
.89785
.79041
.89979
.79395
.90171
.79747
.90361
.80097
58
4+ 1
.89592 1 .78691
.89789
.79047
.89983
.79401
.90175
.79753
.90365
.80102
56
6
.89596
.78697
0.78703
.89792
9.89795
.79053
0.79059
.89986
.79407
.90178
.79759
0.79765
.90368
.80108
54
52
8+ 3
9.89.599
9.89989
0.79413
9.90181
9.90371
0.80114
10
.89602 ; .78709
.89798
.79065
.89992
.79419
.90184 i .79770
.90374
.80120
50
12+ 3
.89606 > .78715
.89802
.79071
.89995
.79425
.90187 j .79776
.90377
.80126
48
14
.89609 1 .78721
.89805
.79077
.89999
.79430
.90191 .79782
.90380
.80131
46
16+ i
9.89612 ; 0.78726
9.89808 1 0.79082
9,90002
0.79436
9.90194 ! 0.79788
9.90383
0.80137
U
18
.89615
.78732
.89811
.79088
.90005
.79442
.90197
.79794
.90387 .80143
42
20+ 5
.89619
.78738
.89815
.79094
.90008
.79448
.90200
.78800
.90390 .80149
40
22
.89622
.78744
0.78750
.89818
.79100
.90012
9.90015
.79454
.90203
.79805
0.79811
.90393 .80155
38
36
24+ 6
9.89625
9.89821
0.79106
0.79460
9.90206
9.90396 0.80160
26
.89628 I .78756
.89824 1 .79112
.90018
.79466
.90210
.79817
.90399 . .80166
34
28+ 7
.89632 : .78762
.89828! .79118
.90021
.79471
.90213
.79823
.90402 .80172
32
30 --
.89635 .78768
.89831 i .79124
.90024
.79477
.90216
.79829
.90405 : .80178
30
32+ 8
9.89638 ! 0.78774
9.89834 j 0.79130
9.90028
0.794S3
9.90219
0.79835
9.90409 0.80184
28
34 "1
.89642 ' .78780
.89837 ; .79136
.90031
.79489
.90222
.79840
.90412 ! .80189
26
36+ 9
.89645 ; .78786
.89840! .79142
.90034
.79495
.90225
.70846
.90415 .80195
24
38
,89648 i .78792
.89844
9.89847
.79148
0.79153
.90037
9.90040
.79501
0.79507
.90229
9.90232
.79853
0.79858
.90418 .80201
9.90421 1 0.80207
22
20
40+10
9.89651 ' 0.78798
42
.896-55 .78804
.898.50 .79159
.90044
.79513
.90235
.79864
.90425 .80213
18
4^+11
.89658 1 .78810
.898.53 1 .79165
.90047
.79519
.90238
.79870
.90428 .80218
16
46
.89661 1 .78816
.89857 1 .79171
.90050
.79524
.90241
.79875
.90431 .80224
14
48+n
9.89665 1 0.78822
9.89860 1 0.79177
9.90053
0.79530
9.90244
0.79881
9.90434 0.80230
12
SO
.89668
.78828
.89863 1 .79183
.90056
.79536
.90248
.79887
.90437
.80236
10
.52+13
.89671
.78834
.89866 ' .79189
.90060
.79542
.90251
.79899
.90440
.80343
8
S4
.89674
.78839
.89870 1 .79195
9.89873 ; 0.79201
.90063
.79548
.90254
9.90257
.79893
6.79905
.90443
.80247
6
4
56+14
9.89678 i 0.78845
9.90066
0.79554
9.90446 I 0.80353
S8
9.89681 ' 0.78851
9.89876 ! 0.79207
9.90069 ', 0.79560
9.90260
0.79910
.9.90449 0.80259
15>^ 39m
15h}}m
15h S5m
15h Jjm
15h .nm
B '
0+15
8h 21m 135° O'
8h 23m 125° siy
8h 25m 126° 0'
8h 27.m 126° 30'
8h 29m 137° 0'
B
60
9.89684 ! 0.78857
9.89879 1 0.79212
.9.90072 0.79565
9.90264
0.79916
9.904.52
0.80265
9
.89687 '' .78863
.89883 .79218
.90076 .79571
.90267
.79922
.90456
.80370
58
4+16
.89691 .78869
.89886 .79224
.90079 .79577
.90270
.79928
.90459
.80376
56
6
.89694 .78875
.89889
9.89892
.79230
.90082 ' .79583
.90273
.79934
.90462
.80282
54
52
8+n
9.89697 1 0.78881
0.79236
9.90085 0.79589
9.90276
0.79940
9.90465
0.80288
10
.89701 1 .78887
.89896 .79242
.90088 .79595
.90279
.79945
.90468 1 .80294
50
72+18
.89704
.78893
.89899 1 .79248
.90092 .79601
.90282
.79951
.90471 ! .80299
48
14
.89707
.78899
.89902 .79254
.90095 .79607
.90286
.79957
.90475 ; .80305
46
16+19
9.89710
0.78905
9.89905
0.79260
9.90098 0.79612
9.90289
0.79963
9.90478 ! 0.80311
44
IS
.89714
.78911
.89908
.79266
.90101 1 .79618
.90292
.79969
.90481 1 .80317
42
20+^0
.89717
.78917
.89912
.79271
.90104 ! .79624
.90295
.79974
.90484 .80323
40
22
24+ii
.89720
9.89723
.78923
.89915
.79277
0.79283
.90108
.79630
.90298
.79980
.90487
.80328
0.80334
38
36
0.78928
9.89918
9.90111
0.79636
9.90301
0.79986
9.90490
26
.89727
.78934
.89921
.79289
.90114
.79642
.90305
.79992
.90493 1 .80340
34
2S+'iZ
.89730
.78940
.89925
.79295
.90117 .79648
.90308
.79998
.90496 .80346
32
so
.89733
.78946
.89928
.79301
.90120 .79653
.90311
.80004
.90499 j .80351
30
S2+2S
9.89736
0.78952
9.89931
0.79307
9.90124 1 0.79659
9.90314
0.80009
9.90503 0.80357
28
34
.89740
.78958
.89934
.79313
.90127 .79665
.90317
.80015
.90506 : .80363
26
36+U
.89743
.78964
.89938
.79319
.90130
.79671
.90320
.80021
.90509
.80369
24
38
.89746
.78970
0.78976
.89941
.79325
.90133
.79677
.90324
.80037
.90512
.990.515
.80375
0.80380
22
20
40+15
9.89749
9.89944
0.79330
9.90136
0.79683
9.90327
0.80033
42
.897.53
.78982
.89947
.79336
.90140 ; .79688
.90330
.80038
.90518
.80386
18
44+26
.89756
.78988
.89950
.79342
.90143 ' .79694
.90333
.80044
.90521
.80392
16
46
.897.59
.78994
.89954
.79348
.90146. .79700
.90336 .80050
.90524 .80398
14
48+Z7
9.89763
0.79000
.9.89957
0.79354
9.90149 0.79706
9.90339
0.80056
9.90527 0.80403
12
50
.89766
.79006
.89960
.79360
.90152
.79712
.90342
.80062
.90531 .80409
10
52+28
.89769
.79011
.89963
.79366
.90356
.79718
.90346
.80068
.90534 .80415
8
54
.56+29"
.89772
.79017
0.79023
.89966
9.89970
.79372
0.79377
.901.59
9.90162'
.79724
6.79729
.90349
.80073
.90537 1 .80421
6
4
9.89776
9.90352
0.80079
9.90540 0.80427
58
.89779
.79029
.89973
.79383
.90165
.79735
.90355
.80085
.90543 .80432
2
60+30
9.89782 0.79035
9.89976
0.79389
9.90168
0.79741
9.90358
0.80091
9.90546 1 0.80438
75* 38m
ISh 36'"
/5'' 34m
15f^ 32m
15li SOm
Page 910] TABLE 45. |
Haversines. 1
s '
.S* SOm 137° 3r
Sft 32>n 138° 0'
S* 34m 138° 30'
Sh 36m 139° o'
8h ssm 139° 30'
s
Log. Hav.
Nat. Ilav.
Log. Ilav.
Nat. Hav.
Log. Hav.
Nat. Hav.
Lor. Hav., Nat. 3Iav.
Log. Hav. Nat. Hav.
9.90546
0.80438
9.90732
0.80783
9.90916
0.81136
9.91098 i 0.81466
9.91277 0.81804
60
^
.90549
.80444
.90735
.80789
.90919
.81131
.91101 ; .81473
.91280; .81810
58
•4+ 1
.90552
.80450
.90738
.80795
.90922
.81137
.91104 ! ,81477
.91283 ! .81815
56
6
.90556
.80455
.90741
.80800
.90925
.81143
.91107 1 .81483
.91286
.81831
54
52
s+ a
9.90559
0.80461
9.90744
0.90806
9.90928
0.81148
9.91110
0.81489
9.91289
0.81836
10
.90562
.80467
.90747
.80813
.90931
.81154
.91113
.81494
.91292
.81833
50
12+ 3
.90565
.80473
.90751
.80817
.90934
.81160
.91116
.81500
.91295
.81838
48
i-4
.90568
.80478
.90754
.30833
.90937
.81165
.91119
.81506
.91298
.81843
46
76+ 4
9.90571
0.80484
9.90757
0.80839
9.90940
0.81171
9.91122
0.81511
9.91301
0.81849
44
18
.90574
.80490
.90760
.80835
.90943
.81177
.91125
.81517
.91304
.81854
42
20+ 5
.90577
.80496
.90763
.80840
.90946
.81183
.91128
.81533
.91307
.81860
40
2-2
.90580
.80503
.90766 .80846
.90949
.81188
.91131
.81538
.91310
.81866
0.81871
38
36
24+ 6
9.90584
0.80507
9.90769 1 0.80853
9.90952
0.81194
9.91134,0.81534
9.91313
26
.90587
.80513
.90772 i .80858
.90955
.81300
.91137 ' .81539
.91316
.81877
34
2,?+ 7
.90590
.80519
.90775
.80863
.90958
,81205
.91140 .81545
.91319
.81883
32
30
.90593
.80535
.90778
.80869
.90962
.81311
.91143 : .81551
.91322
.81888
30
32+ 8
9.90596
0.80530
9.90781
0.80875
9.90965
0.81317
9.91146 0.81556
9.91325
0.81894
28
«
.90599
.80536
.90784
.80880
.90968
.81333
.91149 .81563
.91328
.81899
26
36+ 9
.90602
.80543
.90787
.80886
.90971
.81338
.91152 i .81568
.91331
.81905
24
5S
.90605
.80548
.90790
.80893
.90974
.81334
.91155 .81573
.913.34
.81910
22
.40-flO
9.90608
0.80553
9.90794
0.80898
9.90977
0.81339
9.91158 0.81579
9.91337
0.81916
20
■42
.90611
.80559
.90797
.80903
.90980
.81345
.91161 ' .81585
.91340
.81933
18
•«+ll
.90615
.80565
.90800
.80909
.90983
.81351
.91164 .81590
.91343
.81937
16
46
.90618
.80571
.90803
.80915
.90986
.81356
.91167 .81596
.91346 ! .81933
14
4S+12
9.90621
0.80576
9.90806 ' 0.80930
9.90989
0.81363
9.91170 , 0.81601
9.91349 0.81938
12
50
.90624
.80583
.90809 , .80936
.90992
.81368
.91173 .81607
.91352 : .81944
10
52+13
.90627
.80588
.90812 I .80933
.90995
.81373
.91176 .81613
.91355 j .81950
8
54
56+14
.90630
9.90633
.80594
.90815
.80938
0.80943
.90998
9.91001
.81379
0.81385
.91179 .81618
.91358 1 .81955
9.91361 0.81961
6
4
0.80599
9.90818
9.91182 1 0.81634
58
9.90636
0.80605
9.90821
0.80949
9.91004
0.81391
9.91185 0.81630
9.91364 0.81966
2
:?5ft 29m
15h «7m
75* 25m
ISh 2Sm
Uh 2m
s '
0+15
8h 3im 137° 30;
,Sh sgm 128° 0'
Sli 35m 138° 30'
8h .3pn 129° 0'
8k 39m 139° 30'
60
9.90639
0.80611
9.90824
0.80955
9.91007
0.81296
9.91188
0.81635
9.91367 : 0.81973
2
.90642
.80617
.90827
.80960
.91010
.81302
.91191
.81641
.91369 .81978
58
4+16
.90646
.80633
.90830
.80966
.91013
.81308
.91194
.81647
.91372 ! ,81983
56
6
.90646
.80638
.90833
.80973
.91016
.81313
.91197
.81653
.91375
.81989
0.81994
54
' 5>
8+n
9.90652
0.806;»4
9.90836
0.80978
9.91019
0.81319
9.91200
0.81658
9.91378
10
.90655
.80640
.90840
.80983
.91022
.81325
.91203
.81663
.91381 .83000
50
72+18
.90658
.80645
.90843
.80989
.91025
.81330
.91206
.81669
.91384 .83005
48
14
.90661
.80651
.90846
.80995
.91028
.81336
.91209
.81675
.91387 .83011
46
16+19
9.90664
0.80657
9.90849
0.81000
9.91031
0.81343
9.91212
0.81680
9.91390 0.83017
44
IS
.90667
.80663
.90852
.81006
.91034 .81347
.91215
.81686
.91393 .83033
42
20+30
.90670
.80668
.90855
.81013
.91037
.81:553
.91218
.81693
.91396
.83038
40
22
.90673
.80674
.90858
.81017
.91040
9.91043
.81359
0.81364
.91221
.81697
.91399
9.91402
.82033
0.830.39
■18
■16
24+21
9.90676
0.80680
9.90861
0.81033
9.91224
0.81703
26
.90680
.80686
.90864
.81039
.91046
.81370
.91227
,81708
.91405
.83045
■U
28+22
.90683
.80691
.90867
.81035
.91049
.81376
.91230
,81714
.91408
.83050
32
30
.90686
.80697
.90870
.81040
.91052
.81381
.91233
,81720
.91411
.83056
■10
32+23
9.90689
0.80703
9.90873
0.81046
9.91055
0.81387
9.91236
0,81725
9.91414
0.83061
28
34
.90692
.80709
.90876
.81053
.91058
.81393
.91239
.81731
.91417
,83067
26
36+2i
.90695
.80714
.90879
.81057
.91061
.81398
.91242
.81737
.91420
,83072
24
38
.90698
.80730
.90882
.81063
.91064
.81404
.91245
.81743
.91423
,82078
22
'20
40+25
9.90701
0.80736
9.90885
0.81068
9.91067
0.81409
9.91248
0.81748
9.91426
0,83084
42
.90704
.80731
.90888
.81074
.91071
.81415
.91251
.81753
.91429
,83089
18
44+26
.90707
.80737
.90892
.81080
.91074
.81431
.91254
.81759
.91432
,83095
16
46
.90710
.80743
.90895
.81086
.91077
.81436
.91257
.81765
.91435
.83100
14
48+27
9.90714
0.80749
9.90898
0.81093
9.91080
0.81433
9.91260
0.81770
9.91437
0.83106
1>
50
.90717
.80754
.90901
.81097
.91083
.81438
.91263
.81776
.91440
.82112
10
52+38
.90720
.80760
.90904
.81103
.91086
.81443
.91265
.81781
.91443
.83117
8
54
.90723
.80766
0.80773
.90907
.81109
.91089
.81449
.91268
9.91271
.81787
0.81793
.91446
.82123
0.82138
6
4
56+39
9.90726
9.90910
0.81114
9.91092
0.81455
9.91449
58
.90729
.80777
.90913
.81130
.91095
.81460
.91274
.81798
.914.52
.83134
2
60+30
9.90732
0.80783
9.90916
0.81136
9.91098
0.81466
9.91277
0.81804
9.91455
0.83139
ISh 28m
15^ 26m
15h 9^m
75* 22m
151^ 20m
TABLE 45. [Page 911
Haversines.
s '
8h 40m 130° 0'
«ft 42''> 130° 30'
8h 44m 131° Q/
Sh 46m 131° 30'
8h 4sm 132° 0'
s
Log. Hav.j Kat. Hav.
•Log. Hav. Nat. 11 av.
Log. Hav.
Nat. Hav.
Log. Ilav.
Nat. Hav,
Log. Hav.
Nat. Uav,
9.91455
0.83139
9.91631 1 0.82473
9.91805
0.83803
9.91976
0.83131
9.92146
0.83457
60
2
.91458
.83145
.91634 .83478
.91807
.83808
.91979
.83136
.92149
.83462
58
4+ 1
.91461
.82151
,91637 : .83483
.91810
.83814
.91982
.83142
.92152
.83467
56
6
.91464
.82156
.91640 1 .83489
9.91643 0.83495
.91813
9.91816
.83819
0.83835
.91985
.83147
.92154
.83473
0.83478
54
52
S+ 2
9.91467
0.82163
9.91988
0.83153
9.92157
10
.91470
.83167
.91645
.82500
.91819
.83830
.91991 1 .83158
.92160
.83484
SO
12+ 4
.91473
.83173
.91648
.82506
.91822
.83836
.91993 1 .83164
.92163
.83489
48
14
.91476
.83178
.91651
.82511
.91825
.83841
.91996 .83169
.92166
.83494
46
16+ 4
9.91479
0.SJ1S4
9.91654
0.83517
9.91828
0.83847
9.91999
0.83175
9.92169
0.83500
U
18
.91482 ' .82189
.91657
.83532
.91830
.83853
.92002
.83180
.92171
.83505
42
20+ 5
.91485 i .82195
.91660
.83528
.91833
.83858
.92005
.83185
.92174
.83511
40
22
.91488
.82200
.91663
.82533
0.82539
.91836
.83863
.92008
9.92010
.83191
.92177
.83516
38
36
24+ 6
9.91490
0.83206
9.91666
9.91839
0.83869
0.83196
9.92180 0.83521
2' 6'
.91493
.83313
.91669
.82544
.91842
.83874
.92013
.83203
.92183 .83527
34
L'«+ 7
.91496
.83317
.91672
.82550
.91845
.83880
.92016
.83307
.92185 .83532
32
30
.91499
.82233
.91674
.82555
.91848
.83885
.92019
.83213
.92188 .83538
SO
32+ 8
9.91502 : 0.82228
9.91677
0.82561
9.91851
0.83891
9.92022
0.83218
9.92191 0.83543
28
54
.91505
.82234
.91680
.82566
.918.53
.83896
.92025
.83224
.92194 .83548
26
56+ 9
.91508
.83340
.91683
.82573
.91856
.82902
.92027
.83229
.92197 .83554
24
SS
.91511
.83345
.91686
.83577
.918.59
.82907
0.83913
.92030
9.92033
.83234
0.83240
.92199
9.92202
.83559
0.83564
22
20
40+10
9.91514
0.82251
9.91689
0.83583
9.91862
42
.91517
.82256
.91692
.82588
.91865
.83918
.92036
.83245
.92205
.83570
IS
44+11
.91520
.82263
.91695
.82594
.91868
.82934
.92039
.83251
.92208
.83575
16
46
.91523
.83367
.91698
.82599
.91871
.82929
.92042
.83256
.92211
.83581
14
4S+IZ
9.91.526
0.83373
9.91701
0.82605
9.91874
0.82934
9.92044
0.83263
9.92213
0.83586
12
30
.91529
.83278
.91703
.82610
.91876
.83940
.92047
.83367
.92216
.83591
10
52 +n
.91532
.83384
.91706
.83616
.91879
.83945
.92050
.83373
.92219
.83597
8
54
.91534
.83290
.91709 .83631
.91882
9.91885^
.83951
0.83956
.92053
9.92056
.83378
0.83383
.92222
.83602
6
66+U
9.91537
0.82295
9.91712
0.83637
9.92225
0.83608
4
58
9.91.540
0.83301
9.91715
0.82632
9.91888
0.83963
9.920.59
0.83389
9.92227
0.83613
2
ISh igm
15h 17m
ISh 15m
15h 13m
15h urn
s '
0+15
8h 4im 130° 0'
8h 43m 130° 30'
Sh 45m 131° 0'
8h 47m 131° 30:
5* 49m 132° 0'
s
60
9.91543 0.83306
9.91718
0.83638
9.91891
0.82967
9.92061
0.83394
9.92230 ! 0.83618
2
.91546
.83313
.91721
.82644
.91894
.82973
.92064
.83300
.92233 .83624
58
4+16
.91549
.83317
.91724
.82649
.91896
.83978
.92067
.83305
.92236 .83629
56
6
.91552
9.91555
.83333
.91727
.82655
0.82660
.91899
9.91902
.83984
0.83989
.92070
.83310
0.83316
.9223!) .83635
9.92241 1 0.83640
.54
52
8+n
0.83338
9.91730
9.92073
10
.91.558
.83334
.91732
.83666
.91;H)5
.83995
.92076
.83331
.92244 .83645
50
i:>+n
.91-561
.83339
.91735
.82671
.91908
.83000
.92078
.83337
.92247
.83651
48
14
.91564
.83345
.91738
.82677
.91911
.83006
.92081
.83332
.922.50
.83656
46
/6'+19
9.91.567
0.83351
9.91741
0.82682
9.91914
0.83011
9.92084
0.83.337
9.92253
0.83661
44
18
.91570
.82356
.91744
.82688
.91916
.83016
.92087
.83343
.92255
.83667
42
20+2«
.91573
.82363
.91747
.82693
.91919
.83033
.92090
.83348
.92258
.83672
40
22
.91575
9.91578
.83367
0.83373
.91750
9.917.53
.83699
0.82704
.91922
9.91925
.83037
0.8:i033
.92093
9.92095
.83354
0.8335*9
.92261
9.92264
.83678
0.83683
38
36
24+Zl
26
.91.581
.83378
.917.56
.83710
,91928
.83038
.92098
.83365
.922(i6
.83688
34
i.S'+23
.91.584
.82384
.917.58
.83715
.91931
.83044
.92101
.83370
.92269
.83694
32
30
.91587
.82389
.91761
.83731
.91934
.83049
.921104
.83375
.92272
.83699
30
32+ZZ
9.91590
0.82395
9.91764
0.83736
9.919.36
0.83055
9,92107
0.83381
9.92275
0.83704
28
34
.91593
.83400
.91767
.82733
,919.39
.83060
.92109
.83386
.92278
.83710
26
36 +U
.91,596
.83406
.91770
.82737
.91942
.83066
.92112
.83392
.92280
.83715
24
38
.91.599
.83412
.91773
9.91776
.83743
0.83748
.91945
9,91948
.83071
0.83077
.92115
9.92118
.83397
0.83402
.92283
9.92286'
.83720
0.83726
22
20
40+2S
9.91602
0.83417
42
.91605
.83433
.91779
.83754
,91951
.83082
.92121
.83408
.92289
.83731
18
44+36
.91608
.83438
.91782
.82759
,919.54
.83087
.92124
.83413
,92292
.83737
16
46-
.91610
.82434
.91784
.82765
.919.56
.83093
.92126
.83419
,92294
.83743
14
4.V+37
9.91613
0.82439
9.91787
0.82770
9.919.59
0.83098
9.92129
0.83434
9,92297
0.83747
12
50
.91616
.82445
.91790
.83776
.91962
.83104
.92132
.83430
.92300
.83753
10
52+2S
.91619
.82450
.91793
.83781
.91965
.83109
.92135
.83435
.92303
.83758
8
54
.91622
9.91(^25
.82456
0.82461
.91796
9.91799
.83786
0.83793
.91968
9.91971
.83115
0.83120
.92138
9.92140"
.83440
0.83446
.92305
9.92308
.83763
0.83769
6
4
56+29
58
.91628
.83467
.91802
.82797
.91973
.83126
.92143
.83451
.92311
.83774
2
60+30
9.91631
0.83473
9.91805
0.83803
9.91976
0.83131
9.92146
0.83457
9.92314
0.83780
15^^ 18m
ISh 16m
ISh 14m
]5h 12m
ISli lam
Page 912] TABLE 45. |
Haversinea. 1
s '
S»- 50m 132° SO'
Sh 5lm 133° o'
8h 54™ 133° 30'
8li S6'» 134° 0'
8h 58m 134° 30'
s
Log. Ilav.
Nat. Ilav.
Log. Hav.' Nat. Hav.
Log. Hav.
Nat. Ilav.
Log. Hav.
Nat. Hav.
Log. Hav.
Nat. Hav.
9.92314
0.83780
9.92480 1 0.84100
9.92643
0.84418
9.92805
0.84733
9.92965
0.85045
60
2
.92317
.83785
.92482; .84105
.92646
.84423
.92808
.84738
.92968
.85051
58
4+ 1
.92319
.83790
.92485 1 .84111
.92649
.84428
.92811
.84743
.92970
.85056
56
6
.92322
.83796
0.83801
.92488 : .84116
9.9249] 0.84121
.92652
.84434
.92813
9.92816
.84749
0.84754
.92973
9.92975
.85061
0.85066
54
52
8+ 2
9.92325
9.92654
0.84439
10
.92328
.83806
.92493
.84127
.92657
.84444
.92819
.84759
.92978
.85071
50
12+ 3
.92330
.83812
.92496
.84132
.92660
.84449
.92821
.84764
.92981
.85077
48
U
.92333
.83817
.92499
.84137
.92662
.84455
.92824
.84770
.92984
.85082
46
16+ 4
9.92336
0.83822
9.92502 ; 0.84142
9 92665
0.84460
9.92827
0.84775
9.92986
0.85087
44
18
.92339
.83828
.92504 ' .84148
.92668
.84465
.92829
.84780
.92989
.85092
42
20+ 5
.92342
.83833
.92507 : .84153
.92670
.84470
.92832
.84785
.92992
.85097
40
22
.92344
.83838
0.83844
.92510 1 .84158
9.92512 0.84164
.92673
.84476
.92835
.84790
0.84796
.92994
9.92997
.85102
0.85108
38
36
24+ 6
9.92347
9.92676
0.84481
9.92837
26
.92350
.83849
.92515 : .84169
.92679
.84486
.92840
.84801
.93001
.85113
34
28+ ^
.92353
.83855
.92518 1 .84174
.92681
.84492
.92843
.84806
.93002
.85118
32
30
.92355
.83860
.92521 i .84180
.92684
.84497
.92845
.84811
.93005
.85123
30
32+ 8
9.92358
0.83865
9.92523 i 0.84185
9.92687
0.84502
9.92848
0.84817
9.93007
0.85128
28
34
.92361
.83871
.92526 .84190
.92689
.84507
.92851
.84822
.93010
.85134
26
36+ 9
.92364
.83876
. .92529
.84196
.92692
.84513
.92853
.84827
.93013
,85139
24
38
.92366
.83881
0.83887
.92532
.84301
.92695
.84518
.92856
9.92859'
.84832
0.84837
.93015
.85144
0.85149
22
20
^+10
9.92369
9.92534
0.84206
9.92698
0.84523
9.93018
42
.92372
.83892
.92537 ! .84211
.92700
.84528
.92861
.84843
.93021
.85154
18
44+n
.92375
.83897
.92540 1 .84217
.92703
.84534
.92864
.84848
.93023
.85159
16
46
.92378
.83903
.92543 i .84222
.92706
.84539
.92867
.84853
.93026
.85165
14
48+n
9.92380
0.83908
9.92545 i 0.84227
9.92708
0.84544
9.92S69
0.S4S.W
9.93029
0.S;5I70
12
SO
.92383
.83913
.92548
.84233
.92711
.84549
.92872
.84863
.93031
.85175
10
s2+n
.92386
.83919
.92551
.84238
.92714
.84555
.92875
.84869
.93034
.85180
8
54
.92389
.83924
0.83929
.92554
9.92556
.84243
0.84249
.92716
.84560
0.84565
.92877
9.92880
.84874
0.84879
.93036
9.93039
.85185
0.85190
6
4
56+14
9.92391
9.92719
58
9.92394
0.83935
9.92559
0.84254
9.92722
0.84570
9.92883
0.84884
9.93042
0.85196
2
ISh^m
Uhym
15h 5m.
IShsm
15h im
s '
8h 53'^ 133° 0'
Sh 57m 134° 0'
8h 59m 134° 30'
s
Sh 51^ 132° 30'
8h 55rr> 133° 30'
0+15
9.92397
0.83940
9.92562
0.84259
9.92725 i 0.84576
9.92885
0.84890
9.93044
0.85201
60
2
.92400
.83945
92564
.84264
.92727
.84581
.92888
.84895
.93047
.85206
58
■4+16
.92402
.83951
.92567
.84270
.92730
.84586
.92891
.84900
.93050
.85211
56
6
.92405
.83956
0.83961
.92570
.84275
0.84280
.92733
.84591
.92893
9.92896
.84905
0.84910
.93052
9.93055
.85216
0.85221
54
52
8+n
9.92408
9.92573
9.92735
0.84597
10
.92411
.83967
.92575
.84286
.92738
.84602
.92899
.84916
.93057
.85227
50
12+tS
.92413
.83972
.92578
.84291
.92741
.84607
.92901
.84921
.93060
.85232
48
14
.92416
.83977
.92581
.84296
.92743
.84612
.92904
.84926
.93063 1 .85237
46
76+19
9.92419
0.83983
9.92584
0.84302
9.92746
0.84618
9.92907
0.84931
9.93065 ! 0.85242
44
18
.92422
.83988
.92586
.84307
.92749
.84623
.92909
.84936
.93068 ; .85247
42
20+20
.92425
.83993
.92589
.84312
.92751 .84628
.92912
.84942
.93071
.85252
40
22
.92427
.83999
.92592
9.92594
.84317
0.84323
,92754
.84633
0.84639
.92915
9.92917"
.84947
0.84952
.93073
.85258
38
36
24+n
9.92430
0.84004
9.92757
9.93076
0.85263
26
.92433
.84009
.92597
.84328
.92760 1 .84644
.92920
.84957
.93079
.85268
34
28+n
.92436
.84015
.92600
.84333
.92762 1 .84649
.92923
.84962
.93081
.85273
32
30
.92438
.84020
.92603
.84339
.92765
.84654
.92925
.84968
.93084
.85278
30
32+23
9.92441
0.84025
9.92605
0.84344
9.92768
0.84660
9.92928
0.84973
9.93086
0.85283
28
34
.92444
.84031
.92608
.84349
.92770 1 .84665
.92931
.84978
.93089
.85288
26
36+1U
.92447
.84036
.92611
.84354
.92773
.84670
.92933
.84983
.93092
.85294
24
38
.92449
.84041
.92613
9.92616
.84360
0784365
.92776
9.92778
.84675
0.84681
.92936
.84988
0.84994
.93094
.85299
0.85304
22
20
40+25
9.92452
0.84047
9.92939
9.93097
42
.92455
.84052
.92619
.84370
.92781
.84686
.92941
.84999
.93100
.85309
18
44+26
.92458
.84057
.92622
.84376
.92784
.84691
.92944
.85004
.93102
.85314
16
46
.92460
.84063
.92624
.84381
.92786
.84696
.92947
.85009
.93105
.85319
14
48+21
9.92463
0.84068
9.92627
0.84386
9.92789
0.84702
9.92949
0.85014
9.93107
0.85324
12
50
.92466
.84073
.92630
.84391
.92792
.84707
.92952
.85020
.93110
.85*30
10
52+28
.92469
.84079
.92633
.84397
.92794
.84712
.92955
.85025
.93113
.85335
8
54
.92471
9.92474
.84084
0;84089
.92035
9.92638
.84402
0.84407
.92797
"9.92800
.84717
0.84722
. .92957
9.92960
.85030
0.85035
.93115
.85340
0.85345
6
4
56+29
9.93118
58
.92477
.84095
.92641
.84412
.92802
.84728
.92962
.85040
.93120
.a5350
2
60+30
9.92480
0.84100
9.92643
0.84418
9.92805 0.84733
9.92965
0.85045
9.93123
0.85355
15h8m
IShem
15h 4m
15h 2™
loh Om
TABLE 45. [Page 913
Haversines.
s
,
9A on 135°
9A 4m 136°
9h sm 137°
pA 12™ 138°
9hl6m 139°
Log. Ilav.
Nat. Ilav.
Log. Ilav.
Nat. Ilav.
Log. Ilav.
Nat, Hav.
Log. Ilav.
Nat. Hav,
0.87157
Log. Hav.
Nat. Itav.
0.87735
s
60
9.93123
0.85355
9.93433
0.85967
9.93736
0.86568
9.94030
9.94318
4
1
.93128
.85366
.93438
.85977
.93741
.86578
.940.35
.87167
.94322
.87745
56
8
3
.93134
.85376
.93443
.85987
.93746
.86588
.94040
.87177
.94327
.87755
52
12
3
.93139
.85386
.93448
.85997
.93751
.86597
.94045
.87186
.94332
.87764
48
16
4
9.93144
0.85396
9.93454
0.86007
9.93755
0.86607
9.940.50
0.87196
9.94336
0.87774
U
20
5
.93149
.85407
.93459
.86017
.93760
.86617
.94055
.87206
.94341
.87783
40
24
6
.93154
.85417
.93464
.86028
.93765
.86627
.94059
.87216
.94346
.87793
36
28
7
.93160
.85437
.93469
.86038
.93770
.86637
.94064
.87325
.94351
.87803
32
32
8
9.93165
0.85438
9.93474
0.86048
9.93775
0.86647
9.94069
0.87335
9.94355
0.87813
28
36
9
.93170
.85448
.93479
.86058
.93780
.86657
.94074
.87245
.94360
.87831
24
40
10
.93175
.85458
.93484
.86068
.93785
.86667
.94079
.87254
.94365
.87831
20
44
11
.93181
.85468
.93489
.86078
.93790
.86677
.94084
.87364
.94369
.87840
16
48
12
9.93186
0.85479
9.93494
0.86088
9.93795
0.86686
9.94088
0.S7274
9.94374
0.87850
12
52
13
.93191
.85489
.93499
.86098
.93800
.86696
.94093
.87383
.94379
.87859
8
56
14
9.93196
0.85499
9.93504
0.86108
9.93805
0.86706
9,94098
0.87293
9.94383
0.87869
4
14^ 59m
14h .5.-;m
14h Sim
14h 47m
14h 4,im ~\
s '
9l>' ;"> 135°
9A 5"" 136°
gh gm 137°
9h ISm 138°
gh 17m 139°
s
15
9.93201
0.85509
9.93509
0.86118
9.93810
0.86716
9.94103
0.87303
9.94388
0.87878
60
4
16
.93207
.85520
.93515
.86128
.93815
.86736
.94108
.87313
.94393
.87888
56
8
17
.93212
.85530
.93520
.86138
.93820
.86736
.94112
.87333
.94398
.87897
52
12
18
.93217
.85540
.93525
.86148
.93825
.86746
.94117
.87333
.94402
.87907
48
16
19
9.93222
0.85550
9.93530
0.86158
9.93830
0.86756
9.94122
0.87343
9.94407
0.87916
U
20
30
.93227
.85560
.93535
.86168
.93835
.86765
.94127
.87351
.94412
.87936
40
24
31
.93232
.85571
.93540
.86178
.93840
.86775
.94132
.87361
.94416
.87935
36
28
33
.93238
.85581
.93545
.86189
.93845
.86785
.94137
.87371
.94421
.87945
32
32
33
9.93243
0.85591
9.93550
0.86199
9.93849
0.86795
9.94141
0.87380
9.94426
0.87954
28
S6
34
.93248
.85601
.93555
.86209
.93854
.86805
.94146
.87390
.94430
.87964
24
40
35
.93253
.85613
.93.560
.86219
.93859
.86815
.94151
.87400
.94435
.87973
20
44
36
.93258
.85633
.93565
.86229
.93864
.86835
.94156
.87409
.94440
.87983
16
4S
37
9.93264
0.85633
9.93570
0.86239
9.93809
0.86834
9.94161
0.87419
9.94444
0.87993
12
52
38
.93269
.85643
.93575
.86349
.93874
.86844
.94165
.87438
.94449
.88001
8
56
39
9.93274
0.85653
9.93580
0.86259
9.93879
0.86854
9.94170
0.87438
9,94454
0.88011
4
141^58™
14h 54m
14'tS(/m
14h 46m
J4h 42m
s '
9^ 2m 135°
gh em 136°
9h lOm 137°
9A 14^ 138°
9h 18m 139°
s
30
9.93279
0.85663
9.93585
0.86396
9.93884
0.86864
9.94175
0.87448
9.94458
0.88030
60
4
31
.93284
.85673
.93590
.86379
.93889
.86874
.94180
.87457
.94463
,88030
66
8
33
.93289
.85683
.93595
.86289
.93894
.86884
.94184
.87467
.94468
.88039
62
12
33
.93295
.85693
.93600
.86299
.93899
.86893
.94189
.87477
.94472
.88049
48
16
34
9.93300
0.85703
9,93605
0.86309
9.93904
0.86903
9.94194
0.87486
9.94477
0.88058
44
20
35
.93305
.85713
.93611
.86319
.93908
.86913
.94199
.87496
.94482
.88068
40
24
36
.93310
.85734
.93616
.86339
.93913
.86933
.94204
.87505
.94486
.88077
36
28
37
.93315
.85734
.93621
.86339
.93918
.86933
.94208
.87515
.94491
.88086
32
82
38
9.93320
0.85744
9.93626
0.86349
9.93923
0.86943
9.94213
0.87535
9.94496
0.88096
28
36
39
.93326
.85754
.93631
.86359
.93928
.86953
.94218
.87534
.94500
.88105
24
40
40
.93331
.85764
.93636
.86369
.93933
.86963
.94223
.87544
.94505
.88115
20
44
41
.93336
.85774
.93641
.86379
.93938
.86973
.94227
.87554
.94509
.88134
16
48
43
9.93341
0.85785
9,93646
0.86389
9.93943
0.86983
9.94232
0.87563
9.94514
0.88133
12
52
43
.93346
.85795
.93651
.86399
.93948
.86991
.94237
.87573
.94519
.88143
8
56
44
9.93351
0.85805
9,93656
0.86409
9.93952
0.87001
9,94242
0.87583
9.94523
0.88153
4
1411 57m.
14h 5.jm
14'>- 49m
I4h 4r,m
14h 41m
s '
9h .jm 135°
9h Tm 136°
gh nm 137°
9h lorn 138°
- 9li- 19m 139°
s
~60'
45
9.93356
0.85815
9.93661
0.86419
9.93957
0.87011
9.94246
0.87593
9.94528
0.88162
4
46
.93362
.85825
.93666
.86439
.93962
.87031
.94251
.87603
.94533
.88171
66
8
47
.93367
.85835
.93671
.86438
.93967
.87030
.94256
.87611
.94537
.88180
52
12
48
.93372
.85846
.93676
.86448
.93972
.87040
.94261
.87631
.94542
.88190
48
16
49
9.93377
0.85856
9.93681
0.86458
9.93977
0.87050
9.94265
0.87630
9.94546
0.88199
44
20
50
.93382
.85866
.93686
.86468
.93982
.87060
.94270
.87640
.94551
.88309
40
24
51
.93387
.85876
.93691
.86478
.93987
.87070
.94275
.87649
.94556
.88318
36
28
53
.93392
.85886
.93096
.86488
,93991
.87079
.94280
.87659
.94560
.88337
32
32
53
9.93397
0.85896
9.93701
0.86498
9.93996
0.87089
9.94284
0.87669
9.94505
0.88337
28
36
54
.93403
.85906
.93706
.86508
.94001
.87099
.94289
.87678
.94570
.88346
24
40
55
.93408
.85916
.93711
.86518
.94006
.87109
.94294
.87688
.94574
.88355
■20
44
56
.93413
.85926
.93716
.88528
.94011
.87118
.94299
.87697
.94579
.88365
16
48
57
9.93418
0.85937
9.93721
0.86538
9.94016
0.87138
9.94303
0.87707
9.94583
0.88374
12
52
58
.93423
.85947
.93726
.86548
.94021
.87138
.94308
.87716
.94588
.88284
8
66
59
.93428
.85957
.93731
.86558
.94026
.87148
,94313
.87736
.94593
.88293
4
60
60
9.93433
0.85967
9.93736
0.86568
9.94030
0.87157
9.94318
0.87735
9.94.597
0.88303
Uh 5gm
14^ 52m 1
14>'48m
14h 44m
14h 40m 1
24972°— 12-
-48
Page 914] TABLE 45. |
Haversines. 1
s '
gh 20m 140°
Sh 24™ 141°
9A 28m 1430
gh 32m 143°
gh 36m 144°
s
hog. Uav.
Nat. Hav.
Log. ilav.
9.94869
Nat. [lav.
Log. Hav.
9.95134
Nat. Ilav.
0.89401
Log. Ilav.
"9795391
Nat. Ilav.
Log. Hav.
¥.95641"
Nat. Hav.
9.94597
0.88302
0.88857
0.89932
0.90451
60
4 1
.94602
.88312
.94874
,88866
.95138
.89409
.95396
.89941
.95645
.90459
66
8 2
.94606
.88321
.94878
.88876
.95143
.89418
.95400
.89949
.95649
.90468
52
12 3
.94611
.88330
.94883
.88885
.95147
.89427
.95404
.89958
.95654
.90476
48
16 4
9.94616
0.88340
9.94887
0.88894
9.95151
0.89436
9.9.5408
0.89967
9.95658
0.90485
44
20 5
.94620
.88349
.94892
.88903
.95156
.89445
.95412
.89976
.95662
.90494
40
24 ' 6
.94625
.88358
.94896
.88912
.95160
.89454
.95417
.89984
.95666
.90503
36
28 7
.94629
.88368
.94901
.88921
.95164
.89463
.95421
.89993
.95670
.90511
32
5^ 8
9.94634
O.K.S.177
9.94905
0.88930
9.95169
0.89472
9.95425
0.90002
9.95674
0.90519
28
56 9
.94638
.88386
.94909
.88940
.95173
,89481
.95429
.90010
.95678
.90538
24
40 10
.94643
.88396
.94914
.86949
.95177
.89490
.95433
.90019
.95682
.90537
20
u n
.94648
.88405
.94918
.88958
.95182
.89499
.95438
.90028
.95686
.90545
16
4S 12
9.94652
0.XH4U
9.94923
0.88967
9.95186
0,89508
9.95442
0.!HMt37
9.95690
0.90553
12
52 13
.94657
.88423
.94927
.88976
.95190
,89517
.95446
.90045
.95694
.90563
3
56 14
9.94661
0.88433
9.94932
0.88985
9.95195
0.89526
9.95450
0.90054
9.9.5699
0.90570
4
14h S9m
Uh 35m
I4h Sim
14h 27m
14^ 2Sm
s '
15
gh oim 140°
9h 25m 141°
gh 29m 142°
9h 33m 143°
gh 37m 144°
s
60
9.94666
0.88442
9.94936
0.88994
9.95199
0.89534
9.95454
0.90063
9.95703
0.90579
4 16
.94670
.88451
.94941
.89003
.95203
.89543
.95459
.90071
.97507
.90588
56
S 17
.94675
.88461
.94945
.89012
.95208
.89552
.95463
.90080
.95711
.90596
52
12 18
.94680
.88470
.94950
.89023
.95212
.89561
.95467
.90089
.95715
.90604
48
J6 19
9.94684
0.88479
9.94954
0.89031
9.95216
O.S!»570
9.95471
0.90097
9.95719
0.90613
44
20 20
.94689
.88489
.949.58
.89040
.95221
.89579
.95475
.90106
.95723
.90631
40
24 21
.94693
.88498
.94963
.89049
.95225
.89588
.95480
90115
.95727
.90630
36
2S 23
.94698
.88507
.94967
.89058
.95229
.89597
.95484
.90134
.95731
.90638
32
32 23
9.94702
0.88516
9.94972
0.89067
0.95234
0.89606
9.95488
0.90132
9.95735
0.90647
28
56 24
.94707
.88526
.94976
.89076
.95238
,89614
.95492
.90141
.95739
.90655
24
40 25
.94711
.88535
.94981
.89085
.95242
.89633
.9.5496
.90150
.9574a
.90664
20
44 26
.94716
.88544
.94985
.89094
.95246
,89632
.95501
.90158
.95747
.90672
16
4S 27
9.94721
0.88553
9.94989
0.89103
9.95251
0.89641
9.95.505
0.90167
9.95751
0.90680
12
52 28
.94725
.88563
.94994
.89112
.95255
.89650
.95509
.90176
.95755
.90689
8
56 29
9.94730
0.88572
9.94998
0.89131
9.952.59
0.89659
9.95513
0.90184
9.95759
0.90697
4
14h 38m
Uh 34m
14>^ SOm
14h 26m
]4h 22m
s '
30
Qh 22m 140°
9A 26m 141°
gh 30m 14a°
gh 34m 143°
gh 38m 144°
60
9.94734
0.88581
9.95003
0.89130
9.95264
0.89668
9.95517
0.90193
9.95763
0.90706
4 31
.94739
.88590
.95007
.89139
.95268
.89677
.95521
.90201
.95768
.90714
56
8 32
.94743
.88600
.95011
,89149
.95272
.89685
.95526
.90310
.95772
.90723
52
72 33
.94748
.88609
.95016
,89158
.95276
.89694
.95530
,90319
.95776
.90731
48
16 34
9.94752
0.88618
9.95020
0.89167
9.95281
0.89703
9.9.5534
0.90337
9.95780
0.90740
44
20 35
.94757
.88627
.95025
.89176
.95285
.89712
.95538
.90336
.95784
.90748
40
24 36
.94761
.88637
.95029
.89185
.95289
.89721
.95542
.90345
.95788
.90756
36
28 37
.94766
.88646
.95033
.89194
.95294
.89730
.95546
.90353
.95792
.90765
32
52 38
9.94770
0.88655
9.95038
0.89203
9.95298
0.»97*S
9.95.550
0.90362
9.95796
0.90773
28
36 39
.94774
.88664
.95042
.89212
.95302
.89747
.95555
.90371
.95800
.90792
24
40 40
.94779
.88674
.95047
.89221
.95306
.89756
.95559
.90379
.95804
.90790
20
44 41
.94784
.88683
.95051
.89230
.95311
.89765
.95563
.90388
.95808
.90798
16
48 42
9.94788
0.88692
9.9.5055
0.89239
9.95315
0.89774
9.95567
0.90396
9.95812
0.90807
12
52 43
.94793
.88701
.95060
.89248
.95319
.89783
.95571
.90305
.95816
.90815
8
56 44
9.94797
0.88710
9.95064
0.89357
9.9.5323
0.89791
9.9.5575
0.90314
9.95820
0.90824
4
14h. 37m
J4ft 5.5m
14h 29m
14h 25m
14h 21m
s '
45
gh 23m 140°
9h 27m 141°
yh 3im 142°
gh 35m 143°
gh 39m 144°
s
60
9.94802
0.88720
9.9.5069
0.89266
9.95328
0.89800
9.95.579
0.90332
9.9.5824
0.90832
4 46
.94806
.88729
.95073
.89275
.95332
.89809
.95584
.90331
.95828
.90840
56
S 47
.94811
.88738
.95077
.89284
.95336
.89818
.95588
.90339
.95832
.90849
52
12 48
.94815
.88747
.95082
.89293
.95340
.89837
.95592
.90348
.9.5836
.90857
48
i6 49
9.94820
0.88756
9.95086
0.89302
9.75345
0.89835
9.95596
0.90357
9.9.5840
0.90866
44
20 50
.94824
.88766
.95090
.89311
.95349
.89844
.95600
.90365
.9.5844
.90874
40
24 51
.94829
,88775
.95095
.89320
.95353
.89853
.95604
.90374
.95848
.90882
36
25 52
.94833
.88784
.95099
.89329
.9.5357
.89862
.95608
.90382
.95852
.90891
32
32 53
9.94838
0.88793
9.95104
0.89338
9.95362
0.89870
9.9.5613
0.90391
.9 95856
0.90899
28
56 64
.94842
.88802
.95108
.89347
.95366
,89879
.9.5617
.90399
.95860
.90907
24
40 55
.94847
.88811
.95112
.89356
.95370
,89888
.95621
.90408
.95864
.90916
20
U 56
.94851
.88821
.95117
.89365
.95374
,89897
.95625
.90417
.95868
.90934
16
45 57
9.94856
0.88830
9.95121
0.89374
9.95379
0,89906
9.9.5629
0.90425
9.95872
0.90933
12
52 58
.94860
.88839
.95125
,89383
.95383
.89914
.95633
.90434
.9.5876
.90941
8
56 59
.94865
.88848
.95130
.89392
.95387
.89933
.9.5637
.90442
.95880
.90949
4
60 66
9.94869
0.88857
9.95134
0.89401
9,9.5391
0.89932
9.95641
0.90451
9.95884
0.90958
14h 36m
14h 32m
14h 28m
14h 24'^
14h 20m
TABLE 45. [Page 916
Haversines.
s '
9ft 40^ 145°
9h44m 146°
9ft 4*™ 147°
9ft 52m 148°
9ft 56m 149°
s
60
Log. llav.
9.95884
Nat. Ilav.
0.90958
Log. Ilav.
9.96119
Nat. Ilav.
Loi!. Hav.; Nat. Ilav.
Los;. Ilav.
Nat. Ilav.
Log. Hav.
Nat. Hav.
0.92858
0.91452
9.96347
0.91934
9.96568
0.92403
9.96782
4 1
.95888
.90966
.96123
.91469
.96351
.91941
.96572
.93410
.96786
, .92666
56
8 2
.95892
.90974
.96127
.91468
.96355
.91949
.96576
.92418
.96789
.92873
52
12 3
.95896
.90983
.96131
.91476
.96359
.91957
.96579
.92426
.96793
.92881
48
16 i
9.95900
0.90991
9.96135
0.91484
9.96362
0.91965
9.96583
0.93433
9.96796
0.92888
44
20 5
.95904
.90999
.96139
.91493
.96366
.91973
.96586
.92441
.96800
.92896
40
24 6
.95908
.91008
.96142
.91501
.96370
.91981
.96590
.92449
.96803
.92903
56
28 7
.95912
.91016
.96146
.91509
.96374
.91989
.96594
.93456
.96807
.92911
32
52' 8
9.95916
0.91024
9.96150
0.91517
9.96377
0.91997
9.96597
0.92464
9.96810
0.92918
28
36 9
.95920
.91033
.96154
.91525
.96381
.92005
.96601
.92472
.96814
.93936
24
40 10
.95924
.91041
.96158
.91533
.96385
.92013
.96604
.92479
.90817
.92933
20
•^4 11
.95928
.91049
.96162
.91541
.96388
.92020
.96608-
.93487
.96821
.92941
16
4S 12
9.95932
0.91057
9.96165
0.91549
9.96392
0.92028
9.96612
0.92495
9.96824
0.92948
12
5:;^ 13
.95936
.91066
.96169
.91557
.96396
.92036
.96615
.93503
.96827
.92955
8
36 14
9.9.5939
0.91074.
9.96173
0.91565
9.96400
0.92044
9.96619
0.92510
9.96831
0.93963
4
14h 19m
14h 15m
14h 11m
14h 7m
14h jm
15
9h 41m 145°
9ft 45m 146°
9ft 49"^ 147°
9ft 53m 148°
9ft 57™ 149°
s
60
9.95943
0.91082
9.96177
0.91674
9.96403
0.92053
9.96622
0.92518
9.96834
0.93970
i 16
.95947
.91091
.96181
.91582
.96407
.92060
.96626
.92525
.96837
.93978
56
8 17
.95951
.91099
.96185
.91590
.96411
.92068
.96630
.92533
.96841
.92985
52
J;^ 18
.95955
.91107
.96188
.91598
.96412
.93076
.96633
.92541
.96845
.92993
4S
16 19
9.95959
0.91115
9.96192
0.91606
9.96418
0.93083
9.96637
0.92548
9.96848
0.93000
44
:i?0 20
.95963
.91124
.96196
.91614
.96422
.92091
.96640
.92556
.96852
.93007
40
24 21
.95967
.91132
.96200
.91632
.96426
.92099
.96644
.92563
.96855
.93015
36
28 22
.95971
.91140
.96204
.91630
.96429
.92107
.96648
.93571
.968.59
.93022
32
5« 23
9.95975
0.91149
9.96208
0.91638
9.96433
0.92115
9.96651
0.93579
9.96862
0.93030
28
S6 24
.95979
.91157
.96211
.91646
.96437
.92123
.96655
.92586
.96866
.93037
24
40 25
.95983
.91165
.96215
.91654
.96440
.92130
.96658
.93594
.96869
.93045
20
44 26
.95987
.91173
.96219
.91662
.96444
.92138
.96662
.92603
.96873
.93053
16
48 27
9.95991
0.91182
9.96223
0.91670
9.96448
0.93146
9.96665
0.92609
9.96876
0.93059
12
5? 28
.95995
.91190
.96227
.91678
.96451
.93154
.96669
.92617
.96879
.93067
8
56 29
9.95999
0.91198
9.96230
0.91686
9.964.55
0.92162
9.96673
0.92624
9.96883
0.93074
4
14h ism
14h 14m
Wi 10m
14h em
14h 2m
30
9ft 42m 145°
9h 46m 146°
yh som 147°
9ft 54m 148°
gh 5Sm 149°
s
60
9.96002
0.91206
9.96234
0.91694
9.964.59
0.93170
9.96676
0.92632
9.96886
0.93081
4 31
.96006
.91215
.96238
.91703
.96462
.93177
.96680
.92640
.96890
.93089
56
8 32
.96010
.91233
.96242
.91710
.96466
.93185
.96683
.93647
.96894
.93096
52
;2 33
.96014
.91231
.96246
.91718
.96470
.92193
.96687
.92655
.96897
.93104
48
16 34
9.96018
0.91239
9.96249
0.91736
9.90473
0.92201
9.96690
0.92662
9.96900
0.93111
44
fO 35
.96022
.91247
.96253
.91734
.96477
.92209
.96994
.92670
.96904
.93118
40
24 36
.96026
.91256
.96257
.91742
.96481
.92316
.90697
.92678
.96907
.93136
36
28 37
.96030
.91264
.96261
.91750
.96484
.92224
.96701
.92685
.96910
.93133
32
52 38
9.96034
0.91272
9.96265
0.91758
9.96488
0.92232
9.96705
0.92693
9.96914
0.93140
28
56 39
.96038
.91280
.96268
.91766
.96492
.92240
.90708
.92700
.96917
.93148
24
40 40
.96042
.91289
.96272
.91774
.96495
.92248
.96712
.93708
.96921
.93155
20
44 41
.96046
.91297
.96276
.91782
.96499
.92255
.96715
.92715
.96924
.93162
16
48 42
9.96049
0.91305
9.96280
0.91790
9.96503
0.92263
9.96719
0.92723
9.96928
0.93170
12
52 44
.96053
.91313
.96283
.91798
.96506
.92271
.96722
.92731
.96931
.93177
8
56 44
9.96057
0.91321
9.96287
0.91806
9.96510
0.92279
9.96726
0.92738
9.96934
0.93184
4
14h nm
14h ism
14h gm
14h ,5m
14h im
s '
45
9ft 45m 145°
9h 47m 146°
9h Sim 147°
gh ssm 148°
9ft 59m 149°
s
60
9.96061
0.91329
9.96291
0.91814
"9.96514
0.92386
9.96729
0.93746
9.96938
0.93192
4 46
.96065
.91338
.96295
.91822
.96517
.92394
.96733
.93753
.96941
.93199
56
S 47
.96069
.91346
.96299
.91830
.96521
.92302
.96736
.92761
.96945
.93206
52
12 48
.96073
.91354
.96302
.91838
.96525
.92310
.96740
.92768
.96948
.93214
48
J6 49
9.96077
0.91362
9.96306
0.91846
9.96528
0.92317
9.96743
0.92776
9.96951
0.93221
u
20 50
.96081
.91370
.96310
.91854
.96532
.92325
.96747
.92783
.96955
.93228
40
U 51
.96084
.91379
MViii
.91862
.96536
.92333
.967.50
.92791
.96958
.93236
36
2« 52
.96088
.91387
.96317
.91870
.96539
.92341
.967.54
.92798
.96962
.93343
32
52 53
9.96092
0.91395
9.96321
0.91878
9.96S43
0.93348
9.96758
0.92806
9.96965
0.93350
28
36 54
.96096
.91403
.96325
.91886
.96547
.92356
.98761
.92813
.96968
.93358
24
40 55
.96100
.91411
.96329
.91894
.96550
.92364
.96765
.92821
.96972
.93365
20
44 56
.96104
.91419
.96332
.91902
.96554
.92372
.96768
.92828
.96975
.93372
16
4« 57
9.96108
0.91427
9.96336
0.91910
9.96557
0.92379
9.96772
0.92836
9.96979
0.93279
12
52 58
.96112
.91436
.96340
.91918
.96561
.92387
.96775
.92843
.96982
.93287
8
50 59
.96115
.91444
.96344
.91926
.96565
.92394
.96779
.92^51
.96985
.93294
4
60 60
9.96119
0.91452
9.96347
0.91934
9.96568
0.92402
9.96782
0.92858
9.96989
0.93301
14h 16m
14h 12m
14hSm'
14h 4m
Uhffm
Page 916] TABLE 45. |
Havereines. 1
s
Whom 150° 1
inh4m 151° 1
IQh 8m 152° 1
lOhnm 153° 1
lOhiem 154° 1
s
60
Log, Hav.'
Nat, Hav,
l^g, Ilav,
"9:97188
.Mat. Hav.
0.93731
Log. Hav.
9.97381
Nat, Ilav.
0.94147
Log, Hav,
Nat. Hav.
0.94550
Log. Hav.
9.97745
Nat. Hav.
0.94940
9.96989
0.93301
9,97566
4
1
.96992
.93309
,97192
.93738
.97384
.94154
.97569
.95557
.97748
.94946
56
8
3
.96996
.93316
,97195
.93745
.97387
.94161
,97572
.94564
.97751
.94952
62
n
3
.96999
.93333
.97198
.93752
.97390
.94168
.97575
.94570
.97754
.94959
48
16
4
9.97002
0,93330
9,97201
0.93759
9.97393
0.94175
9.97578
0.94577
9.977.56
0.94965
44
W
5
,97006
.93338
.97205
.93766
.97397
.94181
.97581
.94583
.97759
.94972
40
U
6
.97009
.93345
,97208
.93773
.97400
.94188
.97584
.94590
.97762
.94978
36
28
7
.97012
.93353
.97211
.93780
.97403
.94195
.97587
.94596
.97765
.94984
32
32
8
9.97016
0.93359
9.97214
0.93787
9.97406
0.94203
9.97591
0.94603
9.97768
0.94991
28
36
9
.97019
.93367
.97218
.93794
.97409
.94209
.97594
.94610
.97771
.94997
24
40
10
.97022
.93374
,97221
.93801
.97412
.94215
.97597
.94616
.97774
.95003
20
44
11
.97026
.93381
,97224
.93808
.97415
.94232
.97600
.94623
.97777
.95010
16
48
n
9,97029
0.93388
9,97227 0.93815
9.97418
0.94229
9.97603
0.94639
9.97780
0.95016
12
52
13
.97033
.93395
.97231 .93823
.97422
.94236
.97606
.94636
.97783
.95033
8
56
14
9,97036
0.93403
9.97234 , 0.93839
9.97425
0.94343
9.97609
0.94643
9.97785
0.95039
4
13l> 59m
13>> 55m
ISh Sim
13h 4Tm
13h4sm
s
15
lOh. im 150°
IQh 5m 151°
lOh gm 162°
lOh 13m 153°
IQh nm 154°
s
60
9,97039
0.93410
9,97237
0.93836
9.97428
0.94249
9.97612
0.94649
9.97788
0.95035
4
16
,97043
.93417
.97240
.93843
.97431
.94356
.97615
.94655
.97791
.95041
56
8
17
,97046
.93434
,97244
.93850
.97434
.94363
.97618
.94662
.97794
.95048
52
12
18
,97049
.93433
,97247
.93857
.97437
.94370
.97621
.94669
.97797
.95054
48
16
19
9,97052
0,93439
9,97250
0.93864
9.97440
0.94276
9.97624
0.94675
9.97800
0.95060
44
20
30
,97056
.93446
,97253
.93871
.97443
.94383
.97627
.94682
.97803
.95066
40
24
21
,97059
.93453
,97257
.93878
.97447
.94390
.97630
.94688
.97806
.95073
36
28
32
,97063
.93460
,97260
.93885
.97450
.94397
.97633
.94695
.97808
.95079
32
32
33
9,97066
0,93468
9,97263
0.93892
9.97453
0.94303
9.97636
0.94701
9.97811
0.95085
28
36
34
,97069
.93475
,97266
.93899
.97456
.94310
.97639
.94708
.97814
.95093
24
40
35
,97073
.93483
,97269
.93906
.97459
.94317
.97642
.94714
.97817
.95098
20
U
36
.97076
.93489
,97273
.93913
.97462
.94334
.97645
.94721
.97820
.95104
16
48
37
9.97079
0.93496
9,97276
0.93930
9.97465
0.94330
9.97647
0.94727
9.97823
0.95111
12
52
38
,97083
.93503
.97279
.93937
.97468
.94337
.976.50
.94734
.97826
.95117
8
56
39
9,97086
0.93511
9,97282
0.93934
9.97471 : 0.94344
9.97653
0.94740
9.97829
0.95133
4
13h 58m
13h S4m
13h 50m
ISh 46m
ISh 42m
s
30
IQh 2™ 150°
lOh 6-m 151°
mh lOm 152°
lOh 14m 153°
IQh ism 154°
s
60
9,97089
0.93518
9.97285
0.93941
9.97474
0.94351
9.97656
0.94747
9.97831
0.95129
4
31
.97093
.93535
.97289
.93948
.97478
.94357
.97659
.94753
.97834
.95136
56
8
33
,97096
.93532
.97292
.93955
.97481
.94364
.97662
.94760
.97837
.95142
52
12
33
,97099
.93539
,97295
.93962
.97484
.94371
.97665
.94766
.97840
.95148
48
16
34
9,97103
0.93546
9,97298
0.93969
9.97487
0.94377
9.97668
0.94773
9.97843
0.95154
44
20
35
,97106
.93554
.97301
.93976
.97490
.94384
.97671
.94779
.97846
.95161
40
U
36
.97109
.93561
.97305
.93983
.97493
.94391
.97674
.94786
.97849
.95167
36
28
37
.97113
.93568
.97308
.93989
.97496
.94397
.97677
.94792
.97851
.95173
32
32
38
9.97116
0,93575
9.97311
0.93996
9.97499
0.94404
9.97680
0.94799
9.978.54
0.95179
28
36
39
.97119
.93583
.97314
.94003
.97502
.94411
.97683
.94805
.97857
.95185
24
40
40
,97123
.93589
.97317
.94010
.97505
.94418
.97686
.94811
.97860
.95192
20
44
41
.97126
.93596
.97321
.94017
.97508
.94434
.97689
.94818
.97863
.95198
16
48
42
9.97129
0.93603
9.97324
0.94024
9.97511
0.94431
9.97692
0.94824
9.97866
0.95204
12
52
43
.97132
.93611
.97327
.94031
.97514
.94438
.97695
.94831
.97868
.95210
8
56
44
9,97136
0.93618
9.97,330
0.94038
9.97518
0.94444
9.97698
0.94837
9.97871
0.95217
4
ISh 57m
13h 5sm
13h 49m
13h 45m
13h 41m
s
45
IQh 3m 150°
l()h 7771 151°
lOh im 153°
lOh ir,m 153°
l()>t 19'
> 154°
s
60
9,97139
0.93625
9.97333
0.94045
9.97521
0.94451
9.97701
0.94844
lK97874^
0.95233
4
46
,97142
.93633
.97337
.94051
.97524
.94458
.97704
.94850
.97877
.95339
56
8
47
,97146
.93639
.97340
.94058
.97527
.94464
.97707
.94857
.97880
.95335
52
12
48
,97149
.93646
.97343
.94065
.97530
.94471
.97710
.94863
.97883
.95341
48
16
49
9,97152
0.93653
9.97346
0.94073
9.97533
0.94477
9.97713
0.94869
9.97885
0.95348
44
20
50
.97156
.93660
.97349
.94079
.97536
.94484
.97716
.94876
.97888
.95354
40
24
51
,97159
.93667
.973.52
.94086
.97539
.94491
.97718
.94882
.97891
.95360
36
28
53
,97162
.93674
.97356
.94093
.97542
.94497
.97721
.94889
.97894
.95366
32
32
53
9.97165
0.93683
9.97359
0.94099
9.97545
0.94504
9.97724
0.94895
9.97897
0.95372
28
36
54
.97169
.93689
.97362
.94106
.97548
.94511
.97727
.94901
.97899
.95278
24
40
55
.97172
.93696
.97365
.94113
.97551
.94517
.97730
.94908
.97902
.95385
20
44
56
.97175
.93703
.97368
.94120
.97554
.94524
.97733
.94914
.97905
.95391
16
48
57
9.97179
0.93710
9.97371
0.94127
9.97557
0.94531
9.97736
0.94921
9.97908
0.95397
12
52
58
.97182
.93717
.97575
.94134
.97560
.94537
.97739
.94927
.97911
.95303
8
66
59
.97185
.93734
.97378
.94141
.97563
.94544
.97742
.94933
.97914
.95309
4
60
60
9.97188
0,93731
9.97381
0.94147
9.97566
0.94550
9.97745
0.94940
9.97916
0.95315
ISk S6m
ISh 52m
ISh 48m
ISh 44m
ISh 40m
TABLE 45. [Page 917
Haversines.
s '
10^20^ 155° 1 10^24^ 156°
IQh 28^ 157°
70ft 32™ 158°
70* 36m 159°
Log. Hav.
Nat. llav.
kLog. Hav. Nat.Hav.
Log. Hav.
Nat.ltav.
0.96025
Log. Hav.
9.98389"
Nat. Hav.
0.96359
Log. Hav.
Nal. llav.
s
9.97916
0.95315
9.98081
0.95677
97982159"
9.98533
0.96679
60
•4 1
.97919
.95322
.98084
.95683
.98241
.96031
.98392
.96365
.98536
.96684
56
8 2
.97922
.95328
.98086
.95689
.98244
.96037
.98394
.96370
.98538
.96689
52
12 3
.97925
.95334
.98089
.95695
.98246
.96043
.98397
.96376
.98540
.96695
48
16 i
9.97927
0.95340
9.98092
0.95701
9.98249
0.96048
9.98399
0.96381
9.98543
0.96700
44
20 5
.97930
.95346
.98094
.95707
.98251
.96054
.98402
.96386
.98545
.96705
40
«4 6
.97933
.95352
.98097
.95713
.98254
.96059
.98404
.96393
.98547
.96710
36
28 7
.97936
.95358
.98100
.95719
.98256
.96065
.98406
.96397
.98550
.96715
32
.32 8
9.97939
0.95364
9.98102
0.95724
9.98259
0.96071
9.98409
0.96403
9.98552
0.96721
28
36 9
.97941
.95371
.98105
.95730
.98262
.96076
.98411
.96408
.98554
.96726
24
40 10
.97944 ' .95377
.98108
.95736
.98264
.96083
.98414
.96413
.98557
,96731
20
44 11
.97947 : .95383
.98110
.95742
.98267
.96088
.98416
.96419
.98559
.96736
16
48 12
9.979.50 0.95389
9.98113
0.95748
9.98269
0.96093
9.98419
0.96434
9.98561
0.96741
12
5;? 13
.97953 i .95395
.98116
.95754
.98272
.9(i099
.98421
.96430
.98564
.96746
8
56- U
9.97955 0.95401
9.98118
0.95760
9.98274
0.96104
9.98424
0.96435
9.98566
0.96752
4
13h 39m
13h 35m
75ft 3im
jSh 27m
75ft 23m
15
lOh 21m 155°
IQh 25m 156°
lOh 29m 157°
lOh 33m 158°
IQh Sim 159°
S
60
9.97958
0.95407
9.98121
0.95766
9.98277
0.96110
9.98426
0.96440
9.98568
0.96757
4 16
.97961
.95413
.98124
.95771
.98279
.96116
.98428
.96446
,98570
.96762
56
8 17
.97964
.95419
.98126
.95777
.98282
.96131
.98431
.96451
.98573
.96767
52
72 18
.97966
.95425
.98129
.95783
.98285
.96137
.98433
.96457
.98575
.96772
48
16 19
9.97969
0.95431
9.98132
0.95789
9.98287
0.96133
9.98436
0.96462
9.98577
0.96777
44
20 20
.97972
.95438
.98134
.95795
.98290
.96138
.98438
.96467
.98580
.96782
40
24 21
.97975
.95444
.98137
.95801
.98292
.96144
.98440
.96473
.98582
.96788
36
28 23
.97977
.95450
.98139
.95806
.98295
.96149
.98443
.96478
.98584
.96793
32
.32 23
9.97980
0.95456
9.98142
0.95812
9.98297
0.96155
9.98455
0.96483
9.98587
0.96798
28
36 24
.97983
.95462
.98145
.85818
.98300
.96161
.98448
.96489
.98589
.96803
24
40 25
.97986
.95468
.98147
.95824
.98302
.96166
.98450
.96494
.98591
.96808
20
44 26
.97988
.95474
.98150
.95830
.98305
.96173
.984,53
.96500
.98593
.96813
16
48 27
9.97991
0.95480
9.98153
0.95836
9.98307
0.96177
9.98455
0.96505
9.98596
0.96818
12
52 28
.97994
.95486
.98155
.95841
.98310
.96183
.98457
.96510
.98598
.96823
8
56 29
9.97997
0.95493
9.98158
0.95847
9.98312
0.96188
9.98460
0.96516
9.98600
0.96839
4
13'i 38m
ISh 34m
75ft 30m
75ft 26m
7.3ft 22m
30
101^ 22m 155°
lOh 26m 156°
70ft 30"' 157°
lOh 34m 158°
10l> 38m 159°
60
9797999
0.95498
9.98161
0.95853
9.98315"
0.96194
9.98462
0.96531
9.98603
0.96834
4 31
.98002
.95504
.98163
.95859
.98317
.96300
.98465
.96526
.98605
.96839
56
8 33
.98005
.95510
.98166
.95865
.98320
.96205
.98467
.96532
.98607
.96844
52
72 33
.98008
.95516
.98168
.95870
.98322
.96311
.98469
.96537
.98009
.96849
48
16 U
9.98010
0.95523
9.98171
0.95876
9.98325
0.96316
9.98472
0.96543
9.98612
0.96854
44
20 35
.98013
.95528
.98174
.95882
.98327
.96333
.98474
.96547
.98614
.96859
40
24 36
.98016
.95534
,98176
.95888
.98330
.96337
.98476
.96553
.98616
.96864
36
28 37
.98019
.95540
,98179
.95894
.98332
.96233
.98479
.96.558
.98619
.96869
32
52 38
9.98021
0.9,5546
9.98182
0.95899
9.98335
0.96338
9.98481
0.96563
9.98621
0.96874
28
36 39
.98024
.95552
.98184
.95905
.98337
.96344
.98484
.96569
.98623
.96879
24
40 40
.98027
.95558
.98187
.95911
.98340
.96249
.98486
.96574
.98625
.96884
20
44 41
.98030
.95564
.98189
.95917
.98342
.96355
.98488
.96579
.98628
.96889
16
48 42
9.98032
0.95570
9.98192
0.95922
9.98345
0.96260
9.98491
0.96585
9.98630
0.96894
12
.5? 43
.98035
.95576
.98195
.95928
.98347
.96266
,98493
.96590
.98632
.96899
8
.56 44
9.98038
0.95583
9.98197
0.959.34
9.983.50
0.96373
9.98496
0.96595
9.98634
0.96905
4
13h 37'n
13h 33m
7.3ft 2.9'"
75ft 2.5"!
75ft 2;m
s '
45
l()li 23"
» 155°
I()h 2~m
156°
70ft 3im 157°
70ft 5.5m 158°
70ft 39m 159°
s
60
9.98040
0.95588
9;982()0"
0.95940
9.98352
0.96377
9.98498
0.96600
9.98637
0.96910
4 46
.98043
.95594
.98202
.95945
.98355
.96383
.98500
.96606
.98639
.96915
56
.? 47
.98046
.95600
.98205
.95951
.98357
.96388
.98,503
.96611
.98641
.96930
52
12 48
.98049
.95606
.98208
.95957
.98360
.96394
.98505
.96616
.98643
.96935
48
76 49
9.98051
0.95612
0.98210
0.95962
9.98362
0.96399
9.98,507
0.96631
9.98646
0.96930
44
20 50
.980,54
.95618
.98213
.95968
.98365
.96305
.98510
.96637
.98648
.96935
40
24 51
.98057
.95034
.98215
.95974
.98367
.96310
.98512
.96633
.98650
.96940
36
/5 52
.98059
.95630
.98218
.95980
.98370
.96315
.98514
.96637
.98652
.96945
32
32 53
9.98062
0.95636
9.98221
0.95985
9.98372
0.96331
9.98517
0.96643
9.986,55
0.96950
28
56 54
.98065
.95643
.98223
.95991
.98375
.96336
.98519
.96648
.98657
.96955
24
40 55
.98067
.95648
.98226
.95997
.98377
.96.333
.98521
.96653
.98659
.96960
20
44 56
.98070
.95654
.98228
.96002
.98379
.96337
.98524
.96653
.98661
.96965
16
4S 57
9.98073
0l95660
9.98231
0.96008
9.98382
0.96343
9.98526
0.96663
9.98664
0.96970
12
52 58
.98076
.95665
.98233
.96014
.98384
.96348
.98529
.96669
,98666
.96975
8
.56 59
.98078
.95671
.98236
.96030
.98387
.96354
.98531
.96674
.98668
.96980
4
60 60
9.98081
0.95677
9.98239
0.96035
9.98389
0.96359
9.98533
0.96679
9.98670
0.96985
/.3ft 36m
7.3ft .32"*
7.3 ft 28m
ISh 24m
7,3ft 20m
Page 918] TABLE 45.
Haversines.
s '
70'» 40m 160°
lOh 44m 161°
IQh 48m 162° |
70'» 52^ 163°
70*56™ 164° 1
3
Log. llav. Nat.IIav.
Log. Hav.' Nat. Hav,
Log. Hav.
Nat. llav.
Log, llav. Nat, llav.
Log. Hav,
Nat. Hav.
9.98670
0.96985
9. 98801
0.97276
9.98924
0.97553
9.99041 , 0.97815
9,99151
0.98063
60
4 1
.98673
.96990
,98803
.97281
,98926
.97557
,99043
.97819
.99152
.98067
56
8 2
.98675
.96995
,98805
.97285
.98928
.97562
.99044
.97834
.99154
.98071
52
12 3
.98677
.97000
,98807
.97290
,98930
.97566
.99046
.97828
.99156
.98075
48
16 4
9.98679
0.97005
9,98809
0.97295
9,98932
0.97571
9.99048
0.97832
9.99158
0.98079
U
20 5
.98681
.97009
,98811
.97300
,98934
.97575
.99050
.97836
.99159
.98083
40
« 6
.98684
.97014
,98813
.97304
,98936
.97580
.99052
.97841
,99161
.98087
36
28 7
.98686
.97019
,98815
.97309
,98938
.97584
.99054
.97845
.99163
.98091
32
5:? 8
9.98688 1 0.97024
9,98817
0.97314
9,98940
0.97589
9.99056
0.97849
9.99165
0.98095
28
36 9
.98690 .97029
.98819
.97318
.98942
.97593
.99058
.97853
.99166
.98099
24
40 10
.98692 .97034
.98822
.97323
,98944
.97598
.99059
.97858
.99168
.98103
20
^ 11
.98695 1 .95'«39
.98824
.97328
.98946
.97602
.99061
.97862
.99170
.98107
16
48 n
9.98697
0.97044
9,98826
0.97332
9.98948
0.97606
9.99063
0.97866
9.99172
0.98111
12
52 13
.98699
.97049
.98828
.97337
.98950
.97611
.99065
.97870
.99173
.98115
8
56 14
9.98701
0.97054
9.98830
0.97342
9.98952
0.97613
9.99067
0.97874
9.99175
0.98119
4
13h igm
l-ili 15m
l.jh nm
ISh 7m
ISh sm
s '
lOh 4im 160°
10h4.im 161°
lOli 49m 163°
70ft 5Sm 163°
lOh 57m 164°
s
60
15
9.98703
0.97059
9.98832
0.97347
9,989.54
0.97620
9.99069
0.97879
9.99177
0.98123
4 16
.98706
.97064
,98834
.97351
,98956
.97624
.99071
.97883
.99179
.98127
56
S 17
.98708
.97069
,98836
.97356
,98958
.97629
.99072
.97887
.99180
.98131
52
12 18
.98710
.97074
,98838
.97361
,98960
.97633
.99074
.97891
.99182
.98135
48
J6 19
9.98712
0.97078
9,98840
0.97365
9.98962
0.97637
9.99076
0.97895
9.99184
0.98139
44
;20 20
.98714
.97083
,98842
.97370
,98964
.97642
.99078
.97899
.99186
.98142
40
24 21
.98717
.97088
.98845
.97374
,98966
.97646
.99080
.97904
.99187
.98146
36
2S 2?
.98719
.97093
,98847
.97379
,98968
.97651
.99082
.97908
.99189
.98150
32
32 23
9.98721
0.97098
9,98849
0.97384
9,98970
0.97655
9.99084
0.97913
9.99191
0.98154
28
56 24
.98723
.97103
.98851
.97388
,98971
.97660
.99085
.97916
.99193
.98158
24
40 25
.98725
.97108
,98853
.97393
,98973
.97664
.99087
.97920
,99194
.98162
20
44 26
.98728
.97113
.98855
.97398
.98975
.97668
.99089
.97924
,99196
.98166
16
4* 27
9.98730
0.97117
9,98857
0.97403
9.98977
0.97673
9.99091
0.97939
9,99198
0.98170
12
52 28
.98732
.97122
,98859
.97407
,98979
.97677
.99093
.97933
,99200
.98174
8
.56 29
9.98734
0.97127
9,98861
0.97412
9,98981
0.97681
9.99095
0.97937
9,99201
0.98178
4
13K ism
ISh 14m
7.^* lOm
Ighem
JSh gm
s '
lOli 42™- 160°
IQh 46m 161°
lOh 50m 162°
lOh 54m 163°
70* 5Sm 164°
s
30
9.98736
0.97132
9.98863
0.97416
9.98983
0.97686
9.99096
0.97941
9,99203
0.98182
60
4 31
.98738
.97137
.98865
.97421
.98985
.97690
.99098
.97945
.99205
.98185
56
8 32
.98741
.97142
.98867
.97435
.98987
.97695
.99100
.97949
.99206
.98189
52
i2 33
.98743
.97147
.98869
.97430
.98989
.97699
.99102
.97953
.99208
.98193
48
76 34
9.98745
0.97151
9.98871
0.97435
9.98991
0.97703
9.99104
0.97957
9.99210
0.9«<I97
44
20 35
.98747
.97156
.98873
.97439
.98993
.97708
.99106
.97963
.99212
.98201
40
24 36
.98749
.97161
.98875
.97444
.98995
.97713
.99107
.97966
.99213
.98205
36
28 37
.98751
.97166
.98877
.97448
,98997
.97716
.99109
.97970
.99215
.98209
32
.32 38
9.98754
0.97171
9.98880
0.97453
9,98999
0.97731
9.99111
0.97974
9,99217
0.98212
28
36 39
.98756
.97176
.98882
.97458
.99001
.97735
.99113
.97978
,99218
.98216
24
40 40
.98758
.97180
.98884
.97462
.99003
.97729
.99115
.97982
,99220
.98220
20
44 41
.98760
.97185
.98886
.97467
,99004
.97734
.99116
.97986
,99222
.98234
16
48 42
9.98762
0.97190
9.98888
0.97471
9,99006
0.97738
9,99118
0.97990
9.99223
0.98338
12
52 43
.98764
.97195
,98890
.97476
.99008
.97742
,99120
.97994
.99225
.98232
8
.56 44
9.98766
0.97200
9.98892
0.97480
9.99010
0.97747
9.99122
0.97998
9.99227
0.98236
4
ISh 17m
7.?'' 13m
ISh gm
7,S* 5m
ISh pn
s '
IQh 43m 160°
lOh 47m 161°
lOli 5im 162°
IQh 55m 163°
lOh 59m 164°
s
45
9.98769
0.97204
9.98894
0.97485
9:99012
0.97751
9,99124
0.98002
9.99229
0.98239
60
4 46
.98771
.97209
.98896
.97490
.99014
.97755
,99126
.98007
.99230
.98243
56
« 47
.98773
.97214
.98898
.97494
.99016
.97760
,99127
.98011
.99232
.98347
52
72 48
.98775
,97219
.98900
.97499
.99018
.97764
,99129
.98015
.99234
.98351
48
76 49
9.98777
0.97224
9.98902
0.97503
9.99020
0.97768
9,99131
0.98019
9.99235
0.98355
44
20 50
98779
.97238
.98904
.97508
.99022
.97773
,99133
.98023
.99237
.98258
40
24 51
.98781
.97233
.98906
.97512
.99024
.97777
,99135
.98027
.99239
.98362
36
2/? 52
.98784
.97238
.98908
.97517
.99026
.97781
,99136
.98031
.99240
.98366
32
52 53
9.98786
0.97243
9.98910
0.97521
9.99027
0.97785
9,99138
0.98035
9.99242
0.98370
28
36 54
.98788
.97247
.98912
.97526
.99029
.97790
,99140
.98039
.99244
.98274
.24
40 55
,98790
.97253
.98914
.97530
.99031
.97794
,99142
.98043
.99245
.98277
20
44 56
.98792
.97357
.98916
.97535
,99033
.97798
,99143
.98047
.99247
.98281
16
4S 57
9.98794
0.97363
9.98918
0.97539
9,99035
0.97803
9,99145
0.98051
9.99249 : 0.98285
12
52 58
.98796
.97366
.98920
.97544
.99037
.97807
.99147
.98055
.99250 .98289
8
56 59
,98798
.97371
.98922
.97548
.99039
.97811
,99149
.98059
.99252 1 .98293
4
60 60
9.98801
0.97376
9.98924
0.97553.
9,99041
0.97815
9,99151
0.98063
9.99254 j 0.98296
ISh 16m
ISh 12m
ISh sm
ISh 4m
IShom
TABLE 45. [Page 919
Haversines.
s '
77'>0m 165°
77ft 4"' 166°
77ft 5m 167°
77ft 72m 168°
77ft 16m 169°
s
~~60
Log.Hav. Nat. Ilav
Log. llav
9:99350
Nat. llav.
¥.98515"
Log. Hav
9.99440
Nat. Hav
0.98719
Ix)g. Hav.
Nat. Hav
Log. Hav.
Nat. Hav
0.99081
9.99254 ' 0.98296
9.99523
0.98907
9.99599"
4 1
.99255 .98300
.99352
.98518
.99441
.98722
.99524
.98910
.99600
.99084
56
8 2
.99257 .98304
.99353
.98522
.99443
.98725
.99526
.98913
.99602
.99087
52
12 3
.99259 .98308
.99355
.98525
.99444
.98728
.99527
.98916
.99603
.99090
48
16 i
9.99260 0.98311
9.99356
0.98529
9.99446
0.98732
9.99528
0.98919
9.99604
0.99092
44
20 5
.99262 : .98315
.99358
.98532
.99447
.98735
.99529
.98922
.99605
.99095
40
24 6
.99264 ! .98319
.99359
.98536
.99448
.98738
.99531
.98925
.99606
.99098
36
28 7
.99265 .98323
.99361
.98539
.99450
.98741
.99532
.98938
.99608
.99101
32
32 8
9.99267 ' 0.98326
9.99362
0.98543
9.99451
0.98745
9.99533
0.98931
9.99609
0.99103
28
36 9
.99269 ' .98330
.99364
.98546
.99453
.98748
.99535
.98934
.99610
.99106
24
>#0 10
.99270 1 .98334
.99366
.98550
.99454
.98751
.99536
.98937
.99611
.99109
20
•4-^ 11
.99272 : .98337
.99367
.98553
.99456
.98754
.99537
.98940
.99612
.99112
16
48 12
9.99274 ' 0.98341
9.99369
0.98557
9.99457
0.98757
9.99539
0.98943
9.99614
0.99114
12
52 13
.99275 1 .98345
.99370
.98560
.99458
.98761
.99540
.98946
.99615
.99117
8
56 U
9.99277 1 0.98349
9.99372
0.98564
9.99460
0.98764
9.99541
0.98949
9.99616
0.99120
4
72'» 59m
72ft 5,~>™
72ft 57™
72ft 47"!
72* 4.^™
s '
iih m 165°
llhsm _ 166°
77 ft S"! 167°
llh ism 168°
77* nm 169°
s
15
9.99278
0.98352
9.99373
0.98567
9.99461
0.98767
9.99543
0.98952
9.99617
0.99123
60
4 16
.99280
.98356
.99375
.98571
.99463
.98770
.99544
.98955
.99618
.99125
56
5 17
.99282
.98360
.99376
.98574
.99464
.98774
.99545
.98958
.99620
.99128
52
12 18
.99283
.98363
.99378
.98577
.99465
.98777
.99546
.98961
.99621
.99131
48
76 19
9,99285
0.98367
9.99379
0.98581
9.99467
0.98780
9.99548
0.98964
9.99622
0.99133
44
20 20
.99287
.98371
.99381
.98584
.99468
.98783
.99549
.98967
.99623
.99136
40
24 21
.99288
.98374
.99382
.98588
.99470
.98786
.99550
.98970
.99624
.99139
36
25 22
.99290
.98378
.99384
.98591
.99471
.98789
.99552
.98973
.99626
.99141
32
32 23
9.99291
0.98382
9.99385
0.98595
9.99472
0.98793
9.99553
0.98976
9.99627
0.99144
28
56 24
.99293
.98385
.99387
.98598
.99474
.98796
.99554
.98979
.99628
.99147
24
^ 25
.99295
.98389
.99388
.98601
.99475
.98799
.99555
.98982
.99629
.99149
20
^4 26
.99296
.98393
.99390
.98605
.99477
.98802
.99557
.98985
.99630
.99152
16
45 27
9.99298
0.98396
9.99391
0.98608
9.99478
0.98805
9.99558
0.98987
9.99631
0.99155
12
52 28
.99300
.98400
.99393
.98611
.99479
.98809
.99559
.98990
.99633
.99157
8
56 29
9.99301
0.98404
9.99394
0.98615
9.99481
0.98812
9.99561
0.98993
9.99634
0.99160
4
72ft 58i>
72ft 54"'
72ft 5<m
72* 46m
72* 42m
s '
llh2m 165°
llhem 166°
llh lorr
167°
llh urn 168°
llh 18m 169°
s
60
30
9.99303
0.98407
9.99396
0.98619
9.99482"
0.98815
9799562
0.98996
9.99635
o:99163
4 31
.99304
.98411
.99397
.98622
.99484
.98818
.99563
.98999
.99636
.99165
56
8 32
.99306
.98415
.99399
.98625
.99485
.98821
.99564
.99002
.99637
.99168
52
/2 33
.99308
.98418
.99400
.98629
.99486
.98824
.99566
.99005
.99638
.99171
48
76 34
9.99309
0.98422
9.99402
0.98632
9.99488
0.98827
9.99567
0.99008
9.99639
0.99173
44
20 35
.99311
.98426
.99403
.98635
.99489
.98830
.99568
.99011
.99641
.99176
40
24 36
.99312
.98429
.99405
.98639
.99490
.98834
.99569
.99014
.99642
.99179
36
28 37
.99314
.98433
.99406
.98642
.99492
.98837
.99571
.99016
.99643
.99181
32
52 38
9.99316
0.98436
9.99408
0.98646
9.99493
0.98840
9.99572
0.99019
9.99644
0.99184
28
56 39
.99317
.98440
.99409
.98649
.99495
.98843
.99573
.99022
.99645
.99186
24
40 40
.99319
.98444
.99411
.98652
.99496
.98846
.99575
.99025
.99646
.99189
20
44 41
.99320
.98447
.99412
.98656
.99497
.98849
.99576
.99028
.99648
.99192
16
48 42
9.99322
0.98451
9.99414
0.98659
9.99499
0.98852
9.99577
0.99031
9.99649
0.99194
12
52 43
.99324
.98454
.99415
.98662
.99500
.98855
.99578
.99034
.99650
.99197
8
56 44
9.99325
0.98458
9.99417
0.98666
9.99501
0.98858
9.99580
0.99036
9.99651
0.99199
4
72ft .57'"
72*
53™
72ft 49m
72* 4om
72ft 47"'
s
"45
ll^Sm
165°
77ft 7™ 166°
nhllm 167°
llh 15m 168°
77 ft 79™ 169°
s
9.99327
0.98462
9.99418
0.98669
9.99503
0.98862
9.99581
0.99039
9.99652
0.99202
60
4 46
.99328
.98465
.99420
.98672
.99504
.98865
.99582
.99042
.99653
.99205
56
8 47
.99330
.98469
.99421
.98676
.99505
.98868
.99583
.99045
.99654
.99207
52
72 48
.99331
.98472
.99422
.98679
.99507
.98871
.99584
.99048
.99655
.99210
48
76 49
9.99333
0.98476
9.99424
0.98682
9.99508
0.98874
9.99586
0.99051
9.99657
0.99212
44
20 50
.99335
.98479
.99425
.98686
.99510
.98877
.99587
.99053
99658
.99215
40
24 51
.99336
.98483
.99427
.98689
.99511
.98880
.99588
.99056
.99659
.99217
36
28 52
.99338
.98487
.99429
.98692
.99512
.98883
.99589
.99059
.99660
.99220
32
52 53
9.99339
0.98490
9.99430
.0.98696
9.99514
0.98886
9.99591
0.99062
9.99661
0.99223
28
56 54
.99341
.98494
.99431
.98699
.99515
.98889
.99592
.99065
.99662
.99225
24
40 55
.99342
.98497
.99433
.98702
.99516
.98892
.99593
.99067
.99663
.99228
20
44 56
.99344
.98501
.99434
.98705
.99518
.98895
.99594
.99070
.99664
.99230
16
48 57
9.99345
0.98504
9.99436
0.98709
9.99519
0.98898
9.99596
0.99073
9.99666
0.99233
12
52 58
.99347
.98508
.99437
.98712
.99520
.98901
.99597
.99076
.99667
.99235
8
56 59
.99349
.98511
.99438
.98715
.99522
.98904
.99598
.99079
.99668
.99238
4
60 60
9.99350
0.98515
9.99440
0.98719
9.99523
0.98907
9.99599
0.99081
9.99669
0.99240
72ft 56m
72ft 52m 1
72ft 45™ 1
72ft 44m i
72* 40m
Page 920] TABLE 45.
Haversines.
s '
llh2ff<n 170°
77A24™ 171°
77*25™ 172° 1
77*52™ 173° 1
77*56™ 174° 1
s
60
Log. Hav.
9.99669
Nat. Hav.
0.99240
Log. Hav.' Xar. Hav.
9:9973Y "0.99384
Log. Hav.
¥.99788
Nat. Hav.
0.99513
Log. Hav.
9.99838
Nat. Hav.
0.99637
Log. Hav.
9.9988r
Nat. Hav.
0.99736
4 1
.99670
.99343
.99733
.99387
.99789
.99515
.99839
.99639
,99882
.99728
56
* 3
.99671
.99345
.99734
.99389
.99790
.99517
.99839
.99631
.99882
.99729
52
1^ 3
.99672
.99348
.99735
.99391
.99791
.99519
' .99840
.99633
,99883
.99731
48
16 i
9.99673
0.99350
9.99736
0.99393
9.99792
0.99521
9.99841
0.99634
9.99884
0.99732
44
go 5
.99674
.99353
.99737
.99396
.99793
.99523
.99842
.99636
.99884
.99734
40
U 6
.99675
.99356
.99738
.99398
.99793
.99525
.99842
.99638
.99885
.99735
36
^8 7
.99677
.99358
.99739
.99400
.99794
.99527
.99843
.99640
.99885
.99737
32
5;? 8
9.99678
0.99360
9.99740
0.99403
9.99795
0.99629
9.99844
0.99641
9.99886
0.99738
28
S6 9
.99679
.99263
.99741
.99405
.99796
.99631
.99845
.99643
.99887
.99740
24
40 10
,99680
.99265
.99742
.99407
.99797
.99633
.99845
.99645
.99887
.99741
20
44 11
.99681
.99268
.99743
.99409
.99798
.99535
.99846
.99647
.99888
.99743
16
48 13
9.99682
0.99270
9.99744
0.99411
9.99799
0.99537
9.99847
0.99648
9.99889
0.99744
12
5:? 13
.99683
.99273
.99745
.99414
.99800
.99539
.99848
.99650
.99889
.99746
8
56 14
9.99684
0.99275
9.99746 0.99416
9.99800
0.99541
9.99848
0.99663
9.99890
0.99747
4
72'' 39™
72* 5.5 '«
72* 57™
72*27™
72* 23m
s '
llh2im 170°
77*25™ 171°
77*29™ 172°
77*55™ 173°
JlhsTm 174°
s
16
9.99685
0.99278
9.99747
0.99418
9.99801
0.99543
9.99849
0.99653
9.99891
0.99748
60
4 16
.99686
.99280
.99748
.99420
.99802
.99546
.998.50
.99656
.99891
.99750
56
S 17
.99687
.99283
,99748
.99433
.99803
.99547
.99851
.99667
.99892
.99751
52
12 18
.99688
.99285
.99749
.99425
.99804
.99549
.99851
.99669
.99893
.99763
48
76 19
9.99690
0.99288
9.99750
0.99427
9.99805
0.99551
9.99852
0.99660
9.99893
0.99754
44
20 20
.99691
.99390
.99751
.99429
.99805
.99553
.998.53
.99663
.99894
.99756
40
24 31
.99692
.99393
.99752
.99431
.99806
.99555
.99854
.99664
.99894
.99767
36
gS 33
.99693
.99396
.99753
.99433
.99807
.99557
.99854
.99666
.99895
.99769
32
32 33
9.99694
0.99397
9.99754
0.99436
9.99808
0.99559
9.99855
0.99667
9.99896
0.99760
28
56 34
.99695
.99300
.99755
.99438
.99809
.99561
.99856
.99669
.99896
.99761
24
40 35
.99696
.99302
.99756
.99440
.99810
.99563
.99857
.99670
.99897
.99763
20
44 26
.99697
.99305
.99757
.99442
.99811
.99565
.99857
.99673
.99897
.99674
16
45 27-
9.99698
0.99307
9.99758
0.99444
9.99811
0.99567
9.99858
0.99674
9,99898
0.99766
12
52 28
.99699
.99309
.997.59
.99446
.99812
.99568
.998.59
.99675
,99899
.99767
5
56 29
9.99700
0.99312
9.99760
0.99449
9.99813
0.99670
9,99859
0.99677
9,99899
0.99768
4
72'* 55™
72* .34™
72* 50™
72* 26™
72* 2>m
s. '
77 A 22m 170°
77*26™ 171°
77*50™ 172°
77*54™ 173°
llhSSm 174°
s
60
30
9.99701
0.99314
9.99761
0.99451
9.99814
0.99572
9,99860
0.99679
9,99900
0.99770
4 31
.99702
.99317
.99762
.99453
.99815
.99574
.99861
.99680
,99901
.99771
56
8 32
.99703
.99319
.99763
.99455
.99815
.99576
.99862
.99683
,99901
.99773
52
72 33
.99704
.99321
.99764
.99457
.99816
.99678
.99862
.99684
,99902
.99774
48
76 34
9.99705
0.99324
9.99765
0.99459
9.99817
0.99680
9.99863
0.99685
9,99902
0.99775
44
20 35
.99706
.99326
.99766
.99461
.99818
.99582
.99864
.99687
,99903
.99777
40
24 36
.99707
.99329
.99766
.99464
.99819
.99684
.99864
.99688
,99904
.99778
36
28 37
.99708
.99331
.99767
.99466
.99820
.99686
.99865
.99690
.99904
.99780
32
52 38
9.99710
0.99333
9.99768
0.9«4«s
9.99820
0.995H7
9.99866
0.99693
9.99905
0.99781
28
56 39
.99711
.99336
.99769
.99470
.99821
.99689
.99867
.99693
.99905
.99782
24
40 40
.99712
.99338
.99770
.99473
.99822
.99691
.99867
.99696
.99906
.99784
20
44 41
.99713
.99340
.99771
.99474
.99823
.99593
.99868
.99696
.99906
.99785
16
48 42
9.99714
0.99343
9.99772
0.99476
9.99824
0.99595
9.99869
0.99698
9.99907
0.99786
12
52 43
.99715
.99345
.99773
.99478
.99824
.99697
.99869
.99700
.99908
.99788
8
56 44
9.99716
0.99347
9.99774
0.99480
9.99825
0.99698
9,99870
0.99701
9.99908
0.99789
4
72ft 57m
72* -j.i™
72* 29™
72* 25™
72*27™
s '
11'' 23m 170°
77* 27m 171°
77*57™
172°
7 7 A. 35™ 173°
77*59™ 174°
s
60
4S
9.99717
0.99350
9.99774
0.99483
l)M$2n
0.99600
9.99871
0.99703
9.99909
0.99790
4 46
.99718
.99353
.99775
.99485
.99827
.99602
.99871
.99704
.99909
.99792
56
« 47
.99719
.99354
.99776
.99487
.99828
.99604
.99872
.99706
.99910
.99793
52
72 48
.99720
.99357
.99777
.99489
.99828
.99606
.99873
.99708
.99911
.99794
48
76 49
9.99721
0.99359
9.99778
0.99491
9.99829
0.99608
9.99874
0.99709
9.99911
0.99796
44
20 60
.99722
.99361
.99779
.99493
.99830
.99609
.99874
.99711
.99912
.99797
40
24 61
.99723
.99364
.99780
.99495
.99831
.99611
.99875
.99712
.99912
.99798
36
2S 62
.99724
.99366
.99781
.99497
.99832
.99613
.99876
.99714
.99913
.99799
32
52 63
9.99725
0.99368
9.99782
0.99499
9.99832
0.99615
9.99876
0.99715
9.99913
0.99801
28
36 64
.99726
.99371
.99783
.99501
.99833
.99617
.99877
.99717
.99914
.99802
24
40 56
.99727
.99373
.99784
.99503
.99834
.99618
.99878
.99719
.99915
.99803
20
44 56
.99728
.99375
.99785
.99505
.99835
.99630
.99878
.99720
.99915
.99805
16
45 57
9.99729
0.99378
9.99786
0.99507
9.99836
0.99633
9.99879
0.99722
9.99916
0.99806
12
52 58
.99730
.99380
.99786
.99509
.99836
.99624
.99880
.99723
.99916
.99807
8
56 59
.99731
.99383
.99787
.99511
.99837
.99636
.99880
.99725
.99917
.99808
4
60 60
9.99732
0.99384
9.99788
0.99513
9.99838
0.99637
9.99881
0.99736
9.99917
0.99810
12h 36m
72* 52"'
72* 25™
72* 24™
72* 20™
TABLE 45. [Page 921
Haversines.
8
i;*40'» 175°
UhW" 176°
lilt 48m 177°
llh 52m 178°
llh 56m 179°
s
60
lyOK. Havj Nat. Uav.
Log. Iliiv.
9.99947
Nat.Hav.
0.99878
Ixjj;. Hav.
9.99970
Xat,Uav.
0.99931
Log, Ilav,
9,99987
Nat. Hav.
0.99970
Log. Ilav.
».99997
Nat, Hav.
9.99917
0.99810
0.99993
4 1
.99918
.99811
.99948
.99879
.99971
.99933
,99987
.99971
.99997
.99993
56
8 2
.99918
.99812
.99948
.99880
.99971
.99933
,99987
.99971
.99997
.99993
52
12 3
.99919
.99814
.99948
.99881
,99971
.99934
,99987
.99971
.99997
.99993
48
16 4
9.99919
0.99815
9.99949
0.99883
9.99972
0.99934
9.99988
0.99972
9.99997
0.99994
44
20 5
.99920
.99816
.99949
.98883
.99972
.99935
.99988
.99972
.99997
.99994
40
24 6
.99921
.99817
.99950
.99884
.99972
.99936
.99988
.99973
.99997
.99994
36
28 7
.99921
.99819
.99950
.99885
.99973
.99937
.99988
.99973
.99997
.99994
32
•32 8
9.99922
0^820
9.99951
0.99886
9.99973
0.99937
9.99988
0.99973
9.99998
0.99994
28
56 9
.99922
.99821
.99951
.99887
.99973
.99938
.99989
.99974
.99998
.99995
24
40 10
.99923
.99822
.99951
.99888
.99973
.99939
.99989
.99974
.99998
.99995
20
-« 11
.99923
.99823
.99952
.99889
.99974
.99940
.99989
.99975
.99998
.99995
16
48 12
9.99924
0.99825
9.99952
0.99890
9.99974
0.99940
9.99989
0.99975
9.99998
0.99995
12
52 13
.99924
.99836
.99953
.99891
.99974
.99941
.99989
.99976
.99998
.99995
8
56 14
9.99925
0.99827
9.99953
0.99892
9.99975
0.99943
9.99990
0.99976
9.99998
0.99996
4
12h 19m
121^ lorn
12k 11m
12h ym
12h3'm
s '
Uh4im 175°
111145m 176°
llh 49m 177
llh 53m 178°
llh 57m 179°
3
60
15
9.99925
0.99828
9.99953
0.99893
9.99975
0.99942
9.99990
0.99977
9.99998
0.99996
4 16
.99926
.99829
.99954
.99894
.99975
.99943
.99990
.99977
.99998
.99996
56
,y 17
.99926
.99831
.99954
.99895
.99976
.99944
.99990
.99978
,99998
.99996
52
7J 18
.99927
.99832
.99954
.99896
.99976
.99944
.99990
.99978
,99998
.99996
48
16 19
9.99927
0.99833
9.99955
0.99897
9.99976
0.99945
9.99991
0.99978
9.99998
0.99996
44
20 20
.99928
.99834
.99955
.99898
.99976
.99946
.99991
.99979
.99999
.99997
40
24 21
.99928
.99835
.99956
.99899
.99977
.99947
.99991
.99979
.99999
.99997
36
2,s' 22
.99929
.99837
.99956
.99900
.99977
.99947
.99991
.99980
.99999
.99997
32
52 23
9.99929
0.99838
9.99957
0.99900
9.99977
0.99948
9.99991
0.99980
9.99999
0.99997
28
36 24
.99930
.99839
.99957
.99901
.99978
.99949
.99992
.99981
.99999
.99997
24
40 25
.99931
.99840
.99958
.99902
.99978
.99949
.99992
.99981
.99999
.99997
20
44 26
.99931
.99841
.99958
.99903
.99978
.99950
.99992
.99981
.99999
.99998
16
4.V 27
9.99932
0.99843
9.999.58
0.99904
9.99978
0.99950
9.99992
0.99982
9.99999
0.99998
12
.;.' 28
.99932
.99844
.99959
.99905
.99979
.99951
.99992
.99982
.99999
.99998
8
56 29
9.99933
0.99845
9.99959
0.99906
9.99979
0.99952
9.99992
0.99983
9.99999
0.99998
4
12h igm
12h 14m
12h 10m
12h6m
12h2m
s '
2lh42m 175°
llh46m 176°
llhSOm 177°
llh 54m 178°
llh 58m 179°
s
30
9.99933
0.99846
9.99959
0.99907
9.99979
0.99952
9.99993
0.99983
9.99999
0.99998
60
4 31
.99934
.99847
.99960
.99908
.99980
.99953
.99993
.99983
.99999
56
« 32
.99934
.99848
.99960
.99909
.99980
.99954
.99993
.99984
.99999
.99998
52
n 33
.99935
.99849
.99961
.99909
.99980
.99954
.99993
.99984
.99999
.99998
48
i6 34
9.99935
0.99850
9.99961
0.99910
9.99980
0.99955
9.99993
0.99984
9.99999
44
20 35
.99935
.99851
.99961
.99911
.99981
.99956
.99993
.99985
.99999
.99999
40
24 36
.99936
.99853
.99962
.99913
.99981
.99956
.99994
.99985
9.99999
.99999
36
2,s' 37
.99936
.99854
.99962
.99913
.99981
,99957
.99994
.99985
0.00000
.99999
32
32 38
9.99937
0.99855
9.99963
0.99914
9.99981
0.99957
9.99994
0.99986
0.00000
0.99999
28
56 39
.99937
.99856
.99963
.99915
.99982
.99958
.99994
.99986
.00000
24
40 40
.99938
.99857
.99963
.99915
.99982
.99959
.99994
.99986
.00000
.99999
20
4-4 41
.99938
.99858
.99964
.99916
.99982
.99959
.99994
.99987
.00000
.99999
16
4.'? 42
9.99939
0.99859
9.99964
0.99917
9.99983
0.99960
9.99994
0.99987
0.00000
0.99999
12
52 43
.99939
.99860
.99964
.99918
.99983
.99960
.99995
.99987
.00000
.99999
8
56 44
9.99940
0.99861
9.99965
0.99919
9.99983
0.99961
9.99995
0.99988
0.00000
0.99999
4
12h nm
12^ 13m
12h gm
12h 5m
12h im
s '
llh4.3m 175°
nh47m 176°
llh. Mm 177°
llh 55m 178°
llh 59m 179°
s
45
9.99940
0.99863
9.99965
0.99920
9.99983
0.99961
9.99995
0.99988
0.00000
1.00000
60
4 46
.99941
.99864
.99965
.99920
.99983
.99962
.99995
.99988
.00000
.00000
56
8 47
.99941
.99865
.99966
.99931
,99984
.99963
.99995
.99989
.00000
.00000
52
i2 48
.99942
.99866
.99966
.99923
,99984
.99963
,99995
.99989
,00000
.00000
48
16 49
9.99942
0.99867
9.99966
0.99933
9.99984
0.999G4
9,99995
0.99989
0,00000
1.00000
44
fO 50
.99943
.99868
.99967
.99934
.99984
.99964
,99996
.99990
,00000
.00000
40
24 51
.99943
.99869
.99967
.99934
.99985
.99965
,99996
.99990
,00000
.00000
36
28 52
.99943
.99870
.99968
.99935
.99985
.99965
,99996
.99990
,00000
.00000
32
52 S3
9.99944
0.99871
9.99968
0.99926
9.99985
0.99966
9,99996
0.99991
0,00000
1.00000
28
S6 54
.99944
.99872
.99968
.99927
.99985
.99966
,99996
.99991
,00000
.00000
24
40 55
.99945
.99873
.99969
.99938
.99986
.99967
,99996
.99991
,00000
.00000
20
44 5«
.99945
.99874
.99969
.99938
.99986
.99967
.99996
.99991
,00000
.00000
16
48 57
9.99946
0.99875
9.99969
0.99939
9.99986
0.99968
9.99996
0.99992
0.00000
1.00000
12
52 58
,99946
.99876
.99970
.99930
.99986
.99969
.99996
.99992
,00000
.00000
8
56 59
.99947
.99877
.99970
.99931
,99987
.99969
.99997
.99992
.00000
.00000
4
60 60
9.99947
0.99878
9,99970
0.99931
9,99987
0.99970
9.99997
0.99993
0,00000
1.00000
72* 16m 1
12^ 12m
12h sm
12h 4m
12hom
Page 922]
TABLE 46.
Corrections* to be Applied to the Observed Altitude of a Star
or of the Sun's
Lower Limb, to Find
the True Altitude.
HEIGHT OF THK EYE. 1
8 Feet.
9 Feet.
10 Feet. 1
11 Feet.
12 Feet.
13 Feet.
Obs. Alt.
O
*
O
*
O
*
O
*
O
*
O
*
Sun's
Star's
Sun's
Star's
Sun's
Star's
Sun'#
star's
Sun's
star's
Sun's
star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
( + )
(-)
( + )
(-)
( + )
(-)
( + )
(-)
(+)
(-)
(+)
(-)
o /
6 30
5 29
10 40
5 19
10 50
5 09
11 00
5 00
11 09
4 51
11 18
/ //
4 43
11 26
40
5 39
10 30
5 29
10 40
5 19
10 50
5 10
10 59
5 01
11 08
4 53
11 16
50
5 49
10 20
5 39
10 30
5 29
10 40
5 20
10 49
5 11
10 58
5 03
11 06
7 00
5 59
10 10
5 49
10 20
5 39
10 30
5 30
10 39
5 21
10 48
5 13
10 56
10
6 08
10 01
5 58
10 11
5 48
10 21
5 39
10 30
5 30
10 39
5 22
10 47
20
6 17
9 52
6 07
10 02
5 57
10 12
5 48
10 21
5 39
10 30
5 31
10 38
7 30
6 26
9 43
6 16
9 53
6 06
10 03
5 57
10 12
5 48
10 21
5 40
10 29
40
6 34
9 35
6 24
9 45
6 14
9 55
6 05
10 04
5 56
10 13
5 48
10 21
50
6 42
9 27
6 32 , 9 37
6 22
9 47
6 13
9 56
6 04
10 05
5 56
10 13
8 00
6 50
9 19
6 40 j 9 29
6 30
9 39
6 21
9 48
6 12
9 57
6 04
10 05
10
6 57
9 12
6 47 ! 9 22
6 37
9 32
6 28
9 41
6 19
9 50
6 11
9 58
20
7 04
9 05
6 54
9 15
6 44
9 25
6 35
9 34
6 26
9 43
6 18
9 51
8 30
7 11
8 58
7 01
9 08
6 51
9 18
6 42
9 27
6 33
9 36
6 25 9 44
40
7 18
8 51
7 08
9 01
6 58
9 11
6 49
9 20
6 40
9 29
6 32 i 9 37
50
7 24
8 45
7 14
8 55
7 04
9 05
6 55
9 14
6 46
9 23
6 38
9 31
9 00
7 30
8 39
7 20
8 49
7 10
8 59
7 01
9 08
6 52
9 17
6 44
9 25
20
7 42
8 27
7 32
8 37
7 22
8 47
7 13
8 56
7 04
9 05
6 56
9 13
40
7 53
8 16
7 43
8 26
7 33
8 36
7 24
8 45
7 15
8 54
7 07
9 02
10 00
8 04
8 05
7 54
8 15
7 44
8 25
7 35
8 34
7 26
8 43
7 18
8 51
20
8 14
7 55
8 04
8 05
7 54
8 15
7 45
8 24
7 36
8 33
7 28
8 41
40
8 23
7 46
8" 13
7 56
8 03
8 06
7 54
8 15
7 45
8 24
7 37
8 32
11 00
8 32
7 37
8 22
7 47
8 12
7 57
8 03
8 06
7 54
8 15
7 46
8 23
30
8 44
7 25
8 34
7 35
8 24
7 45
8 15
7 54
8 06
8 03
7 58
8 11
12 00
8 55
7 14
8 45
7 24
8 35
7 34
8 26
7 43
8 17
7 52
8 09
8 00
30
9 06
7 03
8 56
7 13
8 46
7 23
8 37
7 32
8 28
7 41
8 20
7 49
13 00
9 16
6 53
9 06
7 03
8 56
7 13
8 47
7 22
8 38
7 31
8 30
7 39
30
9 25
6 44
9 15
6 54
9 05
7 04
8 56
7 13
8 47
7 22
8 39
7 30
14 00
9 33
6 36
9 23
6 46
9 13
6 56
9 04
7 05
8 55
7 14
8 47
7 22
15 00
9 49
6 20
9 39
6 30
9 29
6 40
9 20
6 49
9 11
6 58
9 03
7 06
16 00
10 02
6 07
9 52
6 17
9 42
6 27
9 33
6 36
9 24
6 45
9 16
6 53
17 00
10 15
5 54
10 05
6 04
9 55
6 14
9 46
6 23
9 37
6 32
9 29
6 40
18 00
10 25
5 44
10 15
5 54
10 05
6 04
9 56
6 13
9 47
6 22
9 39 i 6 30
19 00
10 35
5 34
10 25
5 44
10 15
5 54
10 06
6 03
9 57
6 12
9 49
6 20
20 00
10 43
5 25
10 33
5 35
10 23
5 45
10 14
5 54
10 05
6 03
9 57
6 11
22 00
10 59
5 09
10 49
5 19
10 39
5 29
10 30
5 38
10 21
5 47
10 13
5 55
24 00
11 12
4 56
.11 02
5 06
10 52
5 16
10 43
5 25
10 34
5 34
10 26
5 42
26 00
11 23
4 45
11 13
4 55
11 03
5 05
10 54
5 14
10 45
5 23
10 37
5 31
28 00
11 33
4 35
11 23
4 45
11 13
4 55
11 04
5 04
10 55
5 13
10 47
5 21
30 00
11 41
4 27
11 31
4 37
11 21
4 47
11 12
4 56
11 03
5 05
10 55
5 13
32 00
11 49
4 19
11 39
4 29
11 29
4 39
11 20
4 48
11 11
4 57
11 03
5 05
34 00
11 56
4 12
11 46
4 22
11 36
4 32
11 27
4 41
11 18
4 50
11 10
4 58
36 00
12 02
4 06
11 52
4 16
11 42
4 26
11 33
4 35
11 24
4 44
11 16
4 52
38 00
12 07
4 01
11 57
4 11
11 47
4 21
11 38
4 30
11 29
4 39
11 21
4 47
40 00
12 12
3 55
12 02
4 05
11 52
4 15
11 43
4 24
11 34
4 33
11 26
4 41
45 00
12 23
3 44
12 13
3 54
12 03
4 04
11 54
4 13
11 45
4 22
11 37
4 30
50 00
12 31
3 35
12 21
3 45
12 11
3 55
12 02
4 04
11 53
4 13
11 45
4 21
55 00
12 38
3 27
12 28
3 37
12 18
3 47
12 09
3 56
12 00
4 05
11 52
4 13
60 00
12 44
3 20
12 34
3 30
12 24
3 40
12 15
3 49
12 06
3 58
li 58
4 06
65 00
12 51
3 13
12 41
3 23
12 31
3 33
12 22
3 42
12 13
3 51
12 05
3 59
70 00
12 56
3 07
12 46
3 17
12 36
3 27
12 27
3 36
12 18
3 45
12 10
3 53
75 00
13 00
3 02
12 50
3 12
12 40
3 22
12 31
3 31
12 22
3 40
12 14
3 48
80 00
13 06
2 56
12 56
3 06
12 46
3 16
12 37
3 25
12 28
3 34
12 20
3 42
85 00
13 10
2 51
13 00
3 01
12 50
3 11
12 41
3 20
12 32
3 29
12 24
3 37
90 00
13 14
2 46
13 04
2 56
12 54
3 06
12 45
3 15
12 36
3 24
12 28
3 32
Additioi
dAL CORB.
Day of Month.
Jan.
Feb.
Mar.
Apr
May.
June
July. Aug.
Sept.
Oct.
Nov.
Dec.
//
tt
//
//
/'
"
/'
"
"
ft
rt
"
FOR SU
N's Alt.
l8ttol5th....
+18
+15
f8
- 8
-13
-14
-11
-5
+3
+ 11
+16
16th to 31st. . .
+17
+12
f-4
-4
-11
-14
-13
- 9
-1
+7
+14
+18
*The(
K)rrections for theobserved altitude of a
star or Pi
met involves the di
>and the refraction;
and for the observed altitude
of the Sun
s lower limii, tlie dip, refraction, paraila
X, and me
an semidiameter, w
lich is iaken as 16'.
A supplementary correction
taking aec
sunt of ttie variation of ttie Sun's semidi
ameter in
the different month
sot the year is given
at the foot of the main table
TABLE 46.
[Page 923 1
Corrections to be Applied to the Observed Altitude of a Star or of the Sun's
the True Altitude — Continued.
Lower Limb, to Find
HEIGHT OF THE EYE. »
14 Feet.
15 Feet.
16 Feet.
17 Feet.
18 Feet.
19 Feet. 1
Obi. .\LI.
o
Sun's
Corr.
( + )
*
! star's
Corr.
Sun's
Corr.
( + )
*
star's
Corr.
(-)
^un's
Corr.
( + )
*
Star's
Corr.
(-)
Sun's
Corr.
(+)
Star's
Corr.
(-)
Sun's
Corr.
( + )
star's
Corr.
(-)
Sun's
Corr.
(+)
*
Star's
Corr.
(-)
6 30
4 35
11 34
4 27
11 42
4 20
11 49
4 13
11 56
4 06
12 03
3 59
12 10
40
4 45
11 24
4 37
11 32
4 30
11 39
4 23
11 46
4 16
11 53
4 09
12 00
50
4 55
11 14
4 47
11 22
4 40
11 29
4 33
11 36
4 26
11 43
4 19
11 50
7 00
5 05
11 04
4 57 i 11 12
4 50
11 19
4 43
11 26
4 36
11 33
4 29
11 40
10
5 14
10 55
5 06 11 03
4 59 i 11 10
4 52
11 17
4 45
11 24
4 38
11 31
20
5 23
10 46
5 15 10 54
5 08 ; 11 01
5 01
11 08
4 54
11 15
4 47
11 22
7 30
5 32
10 37
5 24 10 45
5 17
10 52
5 10
10 59
5 03
11 06
4 56 i 11 13 1
40
5 40
10 29
5 32 10 37
5 25
10 44
5 18
10 51
5 11
10 58
5 04 i 11 05 1
•50
5 48
10 21
5 40 10 29
5 33 ' 10 36
5 26
10 43
5 19
10 50
5 12
10 57
8.00
5 56
10 13
5 48 10 21
5 41 i 10 28
5 34
10 35
5 27
10 42
5 20
10 49
10
6 03
10 00
5 55 10 14
5 48
10 21
5 41
10 28
5 34
10 35
5 27
10 42
20
6 10
9 59
6 02 , 10 07
5 55
10 14
5 48
10 21
5 41
10 28
5 34
10 35
8 30
6 17
9 52
6 09 j 10 00
6 02
10 07
5 55
10 14
5 48
10 21
5 41
10 28
40
6 24
9 45
6 16 i 9 53
6 09 10 00
6 02
10 07
5 55
10 14
5 48
10 21
50
6-30
9 39
6 22 9 47
6 15 i 9 54
6 08
10 01
6 01
10 08
5 54
10 15
9 00
6 36
9 33
6 28 9 41
6 21 1 9 48
6 14
9 55
6 07
10 02
6 00
10 09
20
6 48
9 21
6 40 9 29
6 33 ; 9 36
6 26
9 43
6 19
9 50
6 12
9 57
40
6 59
9 10
6 51
9 18
6 44
9 25
6 37 ; 9 32
6 30
9 39
6 23 1 9 46
10 00
7 10
8 59
7 02
9 07
6 55
9 14
6 48 i 9 21
6 41
9 28
6 34 I 9 35
20
7-20
8 49
7 12
8 57
7 05
9 04
6 58 ; 9 11
6 51
9 18
6 44 : 9 25
40
7 29
8 40
7 21
8 48
7 14
8 55
7 07 ; 9 02
7 00
9 09
6 53 9 16
11 00
7 38
8 31
7 30
8 39
7 23
8 46
7 16 ! 8 53
7 09
9 00
7 02 I 9 07
30
7 50
8 19
7 42
8 27
7 35
8 34
7 28 1 8 41
7 21
8 48
7 14 1 8 55
12 00
8 01
8 08
7 53
8 16
7 46
8 23
7 39 8 30
7 32
8 37
7 25 8 44
30
8 12
7 57
8 04
8 05
7 57
8 12
7 50 ! 8 19
7 43
8 26
7 36 8 33
13 00
8 22
7 47
8 14
7 55
8 07
8 02
8 00 8 09
7 53
8 16
7 46 1 8 23
30
8 31
7 38
8 23
7 46
8 16
7 53
8 09 8 00
8 02
.8 07
7 55 1 8 14
14 00
8 39
7 30
8 31
7 38
8 24
7 45
8 17 : 7 52
8 10
7 59
8 03 1 8 06
15 00
8 55
7 14
8 47
7 22
8 40
7 29
8 33 : 7 36
8 26
7 43
8 19 . 7 50
16 00
9 08
7 01
9 00
7 09
8 53
7 16
8 46 ! 7 23
8 39
7 30
8 32 : 7 37
17 00
9 21
6 48
9 13
6 56
9 06
7 03
8 59 : 7 10
8 52
7 17
8 45 : 7 24
18 00
9 31
6 38
9 23
6 46
9 16
6 53
9 09 7 00
9 02
7 07
8 55 7 14
19 00
9 41
6 28
9 33
6 36
9 26
6 43
9 19
6 50
9 12
6 57
9 05
7 04
20 00
9 49
6 19
9 41
6 27
9 34
6 34
9 27
6 41
9 20
6 48
9 13
6 55
22 00
10 05
6 03
9 57
6 11
9 50
6 18
9 43
6 25
9 36
6 32
9 29 6 39 1
24 00
10 18
5 50
10 10
5 58
10 03
6 05
9 56
6 12
9 49
6 19
9 42
6 26
26 00
10 29
5 39
10 21
5 47
10 14
5 54
10 07
6 01
10 00
6 08
9 53
6 15
28 00
10 39
5 29
10 31
5 37
10 24
5 44
10 17
5 51
10 10
5 58
10 03 6 05
30 00
10 47
5 21
10 39
5 29
10 32
5 36
10 25
5 43
10 18
5 50
10 11 ; 5 57
32 00
10 55
5 13
10 47
5 21
10 40
5 28
10 33 5 35
10 26
5 42
10 19 , 5 49
34 00
11 02
5 06
10 54
5 14
10 47
5 21
10 40
5 28
10 33
5 35
10 26 1 5 42
30 00
11 08
5 00
11 00
5 08
10 53
5 15
10 46
5 22
10 39
5 29
10 32 5 36
38 00
11 13
4 55
11 05
5 03
10 58
5 10
10 51
5 17
10 44
5 24
10 37 5 31
40 00
11 18
4 49
11 10
4 57
11 03
5 04
10 56
5 11
10 49
5 18
10 42 5 25
45 00
U 29
4 38
11 21
4 46
11 14
4 53
11 07
5 00
11 00
5 07
10 53 5 14
50 00
11 37
4 29
11 29
4 37
11 22
4 44
11 15
4 51
11 08
4 58
11 01 I 5 05
55 00
11 44
4 21
11 36
4 29
11 29
4 36
11 22
4 43
11 15
4 50
11 08 4 57
60 00
11 50
4 14
11 42
4 22
11 35
4 29
11 28
4 36
11 21
4 43
11 14 4 50
65 00
11 57
4 07
11 49
4 15
11 42
4 22
11 35 1 4 29
11 28
4 36
11 21 1 4 43
70 00
12 02
4 01
11 54
4 09
11 47
4 16
11 40 j 4 23
11 33
4 30
11 26 4 37
75 00
12 06
3 56
11 58
4 04
11 51
4 11
11 44 ! 4 18
11 37
4 25
11 30 4 32
80 00
12 12
3 50
12 04
3 58
11 57
4 05
11 50 4 12
11 43
4 19
11 36 4 26
85 00
12 16
3 45
12 08
3 53
12 01
4 00
11 54 4 07
11 47
4 14
11 40 4 21
90 00
12 20
3 40 12 12
3 48
12 05
3 55
11 58 4 02 11 51 1
4 09
11 44 i 4 16
1
1
Additional Coke.
Day of Month.
Jan. Feb.
Mar.
Apr.
May. i
Fune.
July.
Aug.
Sept. C
)ot.
Nov.
Dec.
„ „
//
/,
,,
//
„
n
"
„
„
„
FOR Sun's Alt.
lattol5th...
16th to 31st..
. +18 +15
.+17 +12
+8
+4
-4
-8 -
-11 -
-13
-14
-14
-13
-11
- 9
-5 -
-1 -
f3
f7
+ 11
+ 14.
+16
+18
* The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; t
of the Sun's lower limb, the dip, refraction, paralla.\, and mean semidiameter, which is taken as 16'.
taljing account of the variation of the Sun's semidiameter in the different months of the year is given i
ind for th(
A supplei
It the foot
! observed altitude
nentary correction
of the main table.
Page 924]
TABLE 46.
Corrections to be Applied to the ObBerved Altitude of a Star or of the Sun's
the True Altitude— Continued.
Lower Limb, to Find
Ob?. Alt.
•
HEIGHT OF THE EYE.
20 Feet.
21 Feet.
22 Feet.
23 Feet.
24 Feet.
25 Feet.
Sun's
Corr.
(+)
+
star's
Corr.
C-)
O
Sun's
Corr.
(+)
*
Star's
Corr.
(-)
O
Sun's
Corr.
(+)
*
Star's
Corr.
(-)
Sun's
Corr.
(+)
*
Star's
Corr.
(-)
Sun's
Corr.
(+)
*
Star's
Corr.
(-)
1 ■*
Sun's 1 Star's
Corr. Corr.
(+) (-)
O 1
6 30
3 52
12 17
/ //
3 46
12 23
3 39
12 30
3 33
12 36
3 27
12 42
3 21 ' 12 48
40
4 .2
12 07
3 56
12 13
3 49
12 20
3 43
12 26
3 37
12 32
3 31 12 38
50
4 12
11 57
4 06
12 03
3 59
12 10
3 53
12 16
3 47
12 22
3 41 12 28
7 00
4 22
11 47
4 16
11 53
4 09
12 00
4 03
12 06
3 57
12 12
3 51 12 18
10
4 31
11 38
4 25
11 44
4 18
11 51
4 12
11 57
4 06
12 03
4 00 : 12 09
20
4 40
11 29
4 34
11 35
4 27
11 42
■4 21
11 48
4 15
11 54
4 09
12 00 1
7 30
4 49
11 20
4 43
11 26
4 36
11 33
4 30
11 39
4 24
11 45
4 18
11 51 1
40
4 57
11 12
4 51
11 18
4 44
11 25
4 38
11 31
4 32
11 37
4 26 j 11 43
5&
5 05 i 11 04
4 59
11 10
4 52
11 17
4 46
11 23
4 40
11 29
4 34 ! 11 35
8 00
5 13
10 56
5 07
11 02
5 00
11 09
4 54
11 15
4 48
11 21
4 42 i 11 27
10
5 20
10 49
5 14
10 55
5 07
11 02
5 01
11 08
4 55
11 14
4 49
11 20
20
5 27
10 42
5 21
10 48
5 14
10 55
5 08
11 01
5 02
11 07
4 56
11 13
8 30
5 34
10 35
5 28
10 41
5 21
10 48
5 15
10 54
5 09
11 00
5 03
11 06
40
5 41
10 28
5 35
10 34
5 28
10 41
5 22
10 47
5 16
10 53
5 10 10 59
50
5 47
10 22
5 41
10 28
5 34
10 35
5 28
10 41
5 22
10 47
5 16 j 10 53
9 00
5 53
10 16
5 47 i 10 22
5 40
10 29
5 34
10 35
5 28
10 41
5 22 ' 10 47
20
6 05
10 04
5 59 1 10 10
5 52
10 17
5 46
10 23
5 40
10 29
5 34 10 35
40
6 16
9 53
6 10
9 59
6 03
10 06
5 57
10 12
5 51
10 18
5 45
10 24
10 00
6 27
9 42
6 21
9 48
6 14
9 55
6 08
10 01
6 02
10 07
5 56
10 13
20
6 37
9 32
6 31
9 38
6 24
9 45
6 18
9 51
6 12
9 57
6 06
10 03
40
6 46
9 23
6 40
9 29
6 33
9 36
6 27
9 42
6 21
9 48
6 15
9 54
11 00
6 55
9 14
6 49
9 20
6 42
9 27
6 36
9 33
6 30
9 39
6 24
9 45
30
7 07
9 02
7 01
9 08
6 54
9 15
6 48
9 21
6 42
9 27
6 36
9 33
12 00
7 18
8 51
7 12
8 57
7 05
9 04
6 59
9 10
6 53
9 16
• 6 47
9 22
30
7 29
8 40
7 23
8 46
7 16
8 53
7 10
8 59
7 04
9 05
6 58
9 11
13 00
7 39
8 30
7 33
8 36
7 26
8 43
7 20
8 49
7 14
8 55
7 08
9 01
30
7 48
8 21
7 42
8 27
7 35
8 34
7 29
8 40
7 23
8 46
7 17
8 52
14 00
7 56
8 13
7 50
8 19
7 43
8 26
7 37
8 32
7 31
8 38
7 25
8 44
15 00
8 12
7 57
8 06
8 03
7 59
8 10
7 53
8 16
7 47
8 22
7 41
8 28
16 00
8 25
7 44
8 19
7 50
8 12
7 57
8 06
8 03
8 00
8 09
7 54
8 15
17 00
8 38
7 31
8 32'
7 37
8 25
7 44
8 19
7 50
8 13
7 56
8 07
8 02
18 00
8 48
7 21
8 42
7 27
8 35
7 34
8 29
7 40
8 23
7 46
8 17
7 52
19 00
8 58
7 11
8 52
7 17
8 45
7 24
8 39
7 30
8 33
7 36
8 27
7 42
20 00
9 06
7 02
9 00
7 08
8 53
7 15
8 47
7 21
8 41
7 27
8 35
7 33
22 00
9 22
6 46
9 16
6 52
9 09
6 59
9 03
7 05
8 57
7 11
8 51
7 17
24 00
9 35
6 33
9 29
6 39
9 22
6 46
9 16
6 52
9 10
6 58
9 04
7 04
26 00
9 46
6 22
9 40
6 28
9 33
6 35
9 27
6 41
9 21
6 47
9 15
6 53
28 00
9 56
6 12
9 50
6 18
9 43
6 25
9 37
6 31
9 31
6 37
9 25
6 43
30 00
10 04
6 04
9 58
6 10
9 51
6 17
9 45
6 23
9 39
6 29
9 33
6 35
32 00
10 12
5 56
10 06
6 02
9 59
6 09
9 53
6 15
9 47
6 21
9 41
6 27
34 00
10 19
5 49
10 13
5 55
10 06
6 02
10 00
6 08
9 54
6 14
9 48
6 20
36 00
10 25
5 43
10 19
5 49
10 12
5 56
10 06
6 02
10 00
6 08
9 54
6 14
38 00
10 30
5 38
10 24
5 44
10 17
5 51
10 11
5 57
10 05
6 03
9 59
6 09
40 00
10 35
5 32
10 29
5 38
10 22
5 45
10 16
5 51
10 10
5 57
10 04
6 03
45 00
10 46
5 21
10 40
5 27
10 33
5 34
10 27
5 40
10 21
5 46
10 15
5 52
50 00
10 54
5 12
10 48
5 18
10 41
5 25
10 35
5 31
10 29
5 37
10 23
5 43
55 00
11 01
5 04
10 55
5 10
10 48
5 17
10 42
5 23
10 36
5 29
10 30
5 35
60 00
11 07
4 57
11 01
5 03
10 54
5 10
10 48
5 16
10 42
5 22
10 36
5 28
65 00
11 14
4 50
11 08
4 56
11 01
5 03
10 55
5 09
10 49
5 15
10 43
5 21
70 00
11 19
4 44
11 13
4 50
11 06
4 57
11 00
5 03
10 54
5 09
10 48
5 15
75 00
11 23
4 39
11 17
4 45
11 10
4 52
11 04
4 58
10 58
5 04
10 52
5 10
80 00
11 29
4 33
11 23
4 39
11 16
4 46
11 10
4 52
11 04
4 58
10 58
5 04
85 00
11 33
4 28
11 27
4 34
11 20
4 41
11 14
4 47
11 08
4 53
11 02
4 59
90 00
11 37
4 23
11 31
4 29
11 24
4 36
11 18
4 42
11 12
4 48
11 06
4 54
1
Additional Ookr.
Day of Month.
Jan.
Feb.
Mar.
Apr
May.
June. July. Aug.
Sept.
Oct.
Nov.
Dec.
//
„
//
//
//
// // ti
//
It
It
It
FOE Sun's Alt.
1st to 15th....
16th to 31st...
+18
+17
+15 -
+12 -
f8
f4
-4
-8
-11
-13 -14
-14 -13
-11
- 9
-5
-1
+3
+ 11
+14
+16
+18
* The corrections for the observed altitude of a
of the Sun's lower limb, the dip, refraction, paralU
taking account of the variation of the Sun's semid
Star or PI
IX, and m
ameter in
met involves the dii
3an semid lamp ter, w
the dilTerent month
) and the refraction;
hich is taken as 16'.
s of the year is given
and for the observed altitude
.\ suppleraentarv correction
at the root of the main table.
TABLE 46.
[Page 925
Corrections*
to be Applied to the Observed Altitude of a Star or of the Sun's Lo-wer Limb,
to Find
the True Altitude — Continued.
Obs. Alt.
HEIGHT OF THE EYE. ^
26 Feet.
27 Feet.
28 Feet.
29 Feet.
30 Feet. 1
*
G
*
O
*
o
*
O
*
Sun's
star's
Sun's
star's
Sun's
star's
Sun's
star's
.Sun's
star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
(+)
(-)
(+)
(-)
(+)
(-)
(+)
(-)
( + )
(-)
6 30
3 15
12 54
3 09
13 00
3 04
13 05
2 58
13 11
/ //
2 53
13 16
40
3 25
12 44
3 19
12 50
3 14
12 55
3 08
13 01
3 03
13 06
50
3 35
12 34
3 29
12 40
3 24
12.45
3 18
12 51
3 13
12 56
7 00
3 45
12 24
3 39
12 30
3 34
12 35
3 28
12 41
3 23
12 46
10
3 54
12 15
3 48
12 21
3 43
12 26
3 37
12 32
3 32
12 37
20
4 03
12 06
3 57
12 12
3 52
12 17
3 46
12 23
3 41
12 28
7 30
4 12
11 57
4 06
12 03
4 01
12 08
3 55
12 14
3 50
12 19
40
4 20
11 49
4 14
11 55
4 09
12 00
4 03
12 06
3 58
12 11
50
4 28
11 41
4 22
11 47
4 17
11 52
4 11
11 58
4 06
12 03
8 00
4 36
11 33
4 30
11 39
4 25
11 44
4 19
11 50
4 14
11 55
10
4 43
11 26
4 37
11 32
4 32
11 37
4 26
11 43
4 21
11 48
20
4 50
11 19
4 44
11 25
4 39
11 30
4 33
11 36
4 28
11 41
8 30
4 57
11 12
4 51
11 18
4 46
11 23
4 40
11 29
4 35
11 34
40
5 04
11 05
4 58
11 11
4 53
11 16
4 47
11 22
4 42
11 27
50
5 10
10 59
5 04
11 05
4 59
11 10
4 53
11 16
4 48
11 21
9 00
5 16
10 53
5 10
10 59
5 05
11 04
4 59
11 10
4 54
11 15
20
5 28
10 41
5 22
10 47
5 17
10 52
5 11
10 58
5 06
11 03
40
5 39
10 30
5 33
10 36
5 28
10 41
5 22
10 47
5 17
10 52
10 00
5 50
10 19
5 44
10 25
5 39
10 30
5 33
10 36
5 28
10 41
20
6 00
10 09
5 54
10 15
5 49
10 20
5 43
10 26
5 38
10 31
40
6 09
10 00
6 03
10 06
5 58
10 11
5 52
10 17
5 47
10 22
11 00
6 18
9 51
6 12
9 57
6 07
10 02
6 01
10 08
5 56
10 13
30
6 30
9 39
6 24
9 45
6 19
9 50
6 13
9 56
6 08
10 01
12 00
6 41
9 28
6 35
9 34
6 30
9 39
6 24
9 45
6 19
9 50
30
6 52
9 17
6 46
9 23
6 41
9 28
6 35
9 34
6 30
9 39
13 00
7 02
9 07
6 56
9 13
6 51
9 18
6 45
9 24
6 40
9 29
30
7 11
8 58
7 05
9 04
7 00
9 09
6 54
9 15
6 49
9 20
14 00
7 19
8 50
7 13
8 56
7 08
9 01
7 02
9 07
6 57
9 12
15 00
7 35
8 34
7 29
8 40
7 24
8 45
7 18
8 51
7 13
8 56
16 00
7 48
8 21
7 42
8 27
7 37
8 32
7 31
8 38
7 26
8 43
17 00
8 01
8 08
7 55
8 14
7 50
8 19
7 44
8 25
7 39
8 30
18 00
8 11
7 58
8 05
8 04
8 00
8 09
7 54
8 15
7 49
8 20
19 00
8 21
7 48
8 15
7 54
8 10
7 59
8 04
8 05
7 59
8 10
20 00
8 29
7 39
8 23
7 45
8 18
7 50
8 12
7 56
8 07
8 01
22 00
8 45
7 23
8 39
7 29
8 34
7 34
8 28
7 40
8 23
7 45
24 00
8 58
7. 10
8 52
7 16
8 47
7 21
8 41
7 27
8 36
7 32
26 00
9 09
6 59
9 03
7 05
8 58
7 10
8 52
7 16
8 47
7 21
28 00
9 19
6 49
9 13
6 55
9 08
7 00
9 02
7 06
8 57
7 11
30 00
9 27
6 41
9 21
6 47
9 16
6 52
9 10
6 58
9 05
7 03
32 00
9 35
6 33
9 29
6 39
9 24
6 44
9 18
6 50
9 13
6 55
34 00
9 42
6 26
9 36
6 32
9 31
6 37
9 25
6 43
9 20
6 48
36 00
9 48
6 20
9 42
6 26
9 37
6 31
9 31
6 37
9 26
6 42
38 00
9 53
6 15
9 47
6 21
9 42
6 26
9 36
6 32
9 31
6 37
40 00
9 58
6 09
9 52
6 15
9 47
6 20
9 41
6 26
9 36
6 31
45 00
10 09
5 58
10 03
6 04
9 58
6 09
9 52
6 15
9 47
6 20
50 00
10 17
5 49
10 11
5 55
10 06
6 00
10 00
6 06
9 55
6 11
55 00
10 24
5 41
10 18
5 47
10 13
5 52
10 07
5 58
10 02
6 03
60 00
10 30
5 34
10 24
5 40
10 19
5 45
10 13
5 51
10 08
5 56
65 00
10 37
5 27
10 31
5 33
10 26
5 38
10 20
5 44
10 15
5 49
70 00
10 42
5 21
10 36
5 27
10 31
5 32
10 25
5 38
10 20
5 43
75 00
10 46
5 16
10 40
5 22
10 35
5 27
10 29
5 33
10 24
5 38
80 00
10 52
5 10
10 46
5 16
10 41
5 21
10 35
5 27
10 30
5 32
85 00
90 00
10 56
5 05
10 50
5 11
10 45
5 10
10 39
5 22
10 34
5 27
11 00
5 00
10 54
5 06
10 49
5 11
10 43
5 17
10 38
5 22
1
Additional Cc
RR.
Day of Month.
Jan.
Feb.
Mar.
Apr.
May.
June
. July.
Aug.
Sept.
Oct.
Nov.
Dec.
/,
,/
//
„
//
//
„
n
„
„
//
/,
POK Son's Ai
-T.
1st
to 15th....
+18
+15
+8
-
- 8
-13
-14
-11
-5
+3
+
11
+16
16
thto3lBt...
+17
+12 +4
-4 -
-11
-14
-13
- 9
-1
+7
14
+18
♦The correct
ons for the
observed altitude of a S
jtaror Planet Involves the dip and the refraction; and for
c, and mean semidiameter, wnieh is talcen as 16'. A supi
imeter in the different months of the year is given at the i
the observe
d altitude
of the Sun's lowe
rlimb, the
clip, refraction, paralla
)lementary
correction
taking account of
the varlati
on of the Sun'ssemidis
oot of the n
lain table.
Page 926]
TABLE 46.
Oorrrections to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb,
to Find
the True Altitude — Continued.
HEIGHT OF THE EYE. 1
31 Feet.
32 Feet.
33 Feet.
34 Feet.
35 Fept. 1
Obs. Alt.
O
*
o
*
Q
*
O
*
o
*
Sun's
Star's
Sun's
star's
Sun's
star's
Sun's
star's
Sun's
Star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
( + )
(-)
(+)
(-)
(+)
(-)
(+)
(-)
(+)
(-)
6 30
2 48
13 21
2 42
13 27
/ //
2 37
13 32
/ //
2 32
13 37
2 27
13 42
40
2 58
13 11
2 52
13 17
2 47
13 22
2 42
13 27
2 37
13 32
50
3 08
13 01
3 02
13 07
2 57
13 12
2 52
13 17
2 47
13 22
7 00
3 18
12 51
3 12
12 57
3 07
13 02
3 02
13 07
2 57
13 12
10
3 27
12 42
3 21
12 48
3 16
12 53
3 11
12 58
3 06
13 03
20
3 36
12 33
3 30
12 39
3 25
12 44
3 20
12 49
3 15
12 54
7 30
3 45
12 24
3 39
12 30
3 34
12 35
3 29
12 40
3 24
12 45
40
3 53
12 16
3 47
12 22
3 42
12 27
3 37
12 32
3 32
12 37
50
4 01
12 08
3 55
12 14
3 50
12 19
3 45
12 24
3 40
12 29
8 00
4 09
12 00
4 03
12 06
3 58
12 11
3 53
12 16
3 48
12 21
10
4 16
11 53
4 10
11 59
4 05
12 04
4 00
12 09
3 55
12 14
20
4 23
11 46
4 17
11 52
4 12
11 57
4 07
12 02
4 02
12 07
8 30
4 30
11 39
4 24
11 45
4 19
11 50
4 14
11 55
4 09
12 00
40
4 37
11 32
4 31
11 38
4 26
11 43
4 21
11 48
4 16
11 53
50
4 43
11 26
4 37
11 32
4 32
11 37
4 27
11 42
4 22
11 47
9 00
4 49
11 20
4 43
11 26
4 38
11 31
4 33
11 36
4 28
11 41
20
5 01
11 08
4 55
11 14
4 50
11 19
4 45
11 24
4 40
11 29
40
5 12
10 57
5 06
11 03
5 01
11 08
4 56
11 13
4 51
11 18
10 00
23
10 46
5 17
10 52
5 12
10 57
5 07
11 02
5 02
11 07
20
5 33
10 36
5 27
10 42
5 22
10 47
5 17
10 52
5 12
10 57
40
5 42
10 27
5 36
10 33
5 31
10 38
5 26
10 43
5 21
10 48
11 00
5 51
10 18
5 45
10 24
5 40
10 29
5 35
10 34
5 30
10 39
30
6 03
10 06
5 57
10 12
5 52
10 17
5 47
10 22
5 42
10 27
12 00
6 14
9 55
6 08
10 01
6 03
10 06
5 58
10 11
5 53
10 16
30
6 25
9 44
6 19
9 50
6 14
9 55
6 09
10 00
6 04
10 05
13 00
6 35
9 34
6 29
9 40
6 24
9 45
6 19
9 50
6 14
9 55
30
6 44
9 25
6 38
9 31^
6 33
9 36
6 28
9 41
6 23
9 46
14 00
6 52
9 17
6 46
9 23
6 41
9 28
6 36
9 33
6 31
9 38
15 00
7 08
9 01
7 02
9 07
6 57
9 12
6 52
9 17
6 47,
9 22
16 00
7 21
8 48
7 15
8 54
7 10
8 59
7 05
9 04
7 00
9 09
17 00
7 34
8 35
7 28
8 41
7 23
8 46
7 18
8 51
7 13
8 56
18 00
7 44
8 25
7 38
8 31
7 33
8 36
7 28
8 41
7 23
8 46
19 00
7 54
8 15
7 48
8 21
7 43
8 26
7 38
8 31
7 33
8 36
20 00
8 02
8 06
7 56
8 12
7 51
8 17
7 46
8 22
7 41
8 27
22 00
8 18
7 50
8 12
7 56
8 07
8 01
8 02
8 06
7 57
8 11
24 00
8 31
7 37
8 25
7 43
8 20
7 48
8 15.
7 53
8 10
7 58
26 00
8 42
7 26
8 36
7 32
8 31
7 37
8 26
7 42
8 21
7 47
28 00
8 52
7 16
8 46
7 22
8 41
7 27
8 36
7 32
8 31
7 37
30 00
9 00
7 08
8 54
7 14
8 49
7 19
8 44
7 24
8 39
7- 29
32 00
9 08
7 00
9 02
7 06
8 57
7 11
8 52
7 16
8 47
7 21
34 00
9 15
6 53
9 09
6 59
9 04
7 04
8 59
7 09
8 54
7 14
36 00
9 21
6 47
9 15
6 53
9 10
6 58
9 05
7 03
9 00
7 08
38 00
9 26
6 42
9 20
6 48
9 15
6 53
9 10
6 58
9 05
7 03
40 00
9 31
6 36
9 25
6 42
9 20
6 47
9 15
6 52
9 10
6 57
45 00
9 42
6 25
9 36
6 31
9 31
6 36
9 26
6 41
9 21
6 46
50 00
9 50
6 16
9 44
6 22
9 39
6 27
9 34
6 32
9 29
6 37
55 00
9 57
6 08
9 51
6 14
9 46
6 19
9 41
6 24
9 36
6 29
60 00
10 03
6 01
9 57
6 07
9 52
6 12
9 47
6 17
9 42
6 22
65 00
10 10
5 54
10 04
6 00
9 59
6 05
9 54
6 10
9 49
6 15
70 00
10 15
5 48
10 09
5 54
10 04
5 59
9 59
6 04
9 54
6 09
75 00
10 19
5 43
10 13
5 49
10 08
5 54
10 03
5 59
9 58
6 04
80 00
10 25
5 37
10 19
5 43
10 14
5 48
10 09
5 53
10 04
5 58
85 00
10 29
5 32
10 23
5 38
10 18
5 43
10 13
5 48
10 08
5 53
90 00
10 33
5 27
10 27
5 33
10 22
5 38
10 17
5 43
10 12
5 48
ADDITIONAL CC
)RR.
Day of Month.
Jan.
Feb.
Mar.
Apr.
May.
June
. July.
Aug.
Sept.
Oct.
Nov.
Dec.
„
//
//
/'
'/
It
"
"
/f
"
"
tr
FOE Sun's A
LT.
Is
t to 15th....
+18
+15
+8
-
- 8
-13
-14
-11
-5
+3
+
11
+16
16
th to 31st...: +17
+12
+4
-4 -
-11
-14
-13
- 9
-1
+7
+
14
+18
* Thecorroct
onsforthec
jbserved altitude of a S
tar or Planet involves the dip and the refraction; and for
, and mean semidiameter, which is taken as 16'. .\ sup
the observ<
!d altitude
of the Sun's lowe
limb, the
lip. refraction, paralla^i
Dlemeutarj^
oot of the II
correction
taking account of
the variati(
)n of the Sun's semidia
meter in the different months of the year is given at the f
lain table.
TABLE 46.
[Page 927 1
Corrections*
to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb,
to Find
the True Altitude — Continued.
Ob.=. Alt.
HEIGHT OF THE EYE. 1
36 Feet.
37 Feet.
38 Feet.
39 Feet.
40 Feet. |
O
*
o
*
*
O
*
O
*
.Sun's
Star's
Sun's
star's
Sun's
star's
Sun's
star's
Sun's
star's
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
Corr.
(+)
(-)
(+)
(-)
(+)
(-)
(+)
(-)
(+)
(-)
o /
6 30
2 22
13 47
2 17
13 52
2 13
13 56
2 08
14 01
2 03
14 06
40
2 32
13 37
2 27
13 42
2 23
13 46
2 18
13 51
2 13
13 56
50
2 42
13 27
2 37
13 32
2 33
13 36
2 28
13 41
2 23
13 46
7 00
2 52
13 17
2 47
13 22
2 43
13 26
2 38
13 31
2 33
13 36
10
3 01
13 08
2 56
13 13
2 52
13 17
2 47
13 22
2 42
13 27
20
3 10
12 59
3 05
13 04
3 01
13 08
2 56
13 13
2 51
13 18
7 30
3 19
12 50
3 14
12 55
3 10
12 59
3 05
13 04
3 00
13 09
40
3 27
12 42
3 22
12 47
3 18
12 51
3 13
12 56
3 08
13 01
50
3 35
12 34
3 30
12 39
3 26
12 43
3 21
12 48
3 16
12 53
8 00
3 43
12 26
3 38
12 31
3 34
12 35
3 29
12 40
3 24
12 45
10
3 50
12 19
3 45
12 24
3 41
12 28
3 36
12 33
3 31
12 38
20
3 57
12 12
3 52
12 17
3 48
12 21
3 43
12 26
3 38
12 31
8 30
4 04
12 05
3 59
12 10
3 55
12 14
3 50
12 19
3 45
12 24
40
4 11
11 58
4 06
12 03
4 02
12 07
3 57
12 12
3 52
12 17
50
4 17
11 52
4 12
11 57
4 08
12 01
4 03
12 06
3 58
12 11
9 00
4 23
11 46
4 18
11 51
4 14
11 55
4 09
12 00
4 04
12 05
20
4 35
11 34
4 30
11 39
4 26
11 43
4 21
11 48
4 16
11 53
40
4 46
11 23
4 41
11 28
4 37
11 32
4 32
11 37
4 27
11 42
10 00
4 57
11 12
4 52
11 17
4 48
11 21
4 43
11 26
4 38
11 31
20
5 07
11 02
5 02
11 07
4 58
11 11
4 53
11 16
4 48
11 21
40
5 16
10 53
5 11
10 58
5 07
11 02
5 02
11 07
4 57
11 12
11 00
5 25
10 44
5 20
10 49
5 16
10 53
5 11
10 58
5 06
11 03
30
5 37
10 32
5 32
10 37
5 28
10 41
5 23
10 46
5 18
10 51
12 00
5 48
10 21
5 43
10 26
5 39
10 30
5 34
10 35
5 29
10 40
30
5 59
10 10
5 54
10 15
5 50
10 19
5 45
10 24
5 40
10 29
13 00
6 09
10 00
6 04
10 05
6 00
10 09
5 55
10 14
5 50
10 19
30
6 18
9 51
6 13
9 56
6 09
10 00
6 04
10 05
5 59
10 10
14 00
6 26
9 43
6 21
9 48
6 17
9 52
6 12
9 57
6 07
10 02
15 00
6 42
9 27
6 37
9 32
6 33
9 36
6 28
9 41
6 23
9 46
16 00
6 55
9 14
6 50
9 19
6 46
9 23
6 41
9 28
6 36
9 33
17 00
7 08
9 01
7 03
9 06
6 59
9 10
6 54
9 15
6 49
9 20
18 00
7 18
8 51
7 13
8 56
7 09
9 00
7 04
9 05
6 59
9 10
19 00
7 28
8 41
7 23
8 46
7 19
8 50
7 14
8 55
7 09
9 00
20 00
7 36
8 32
7 31
8 37
7 27
8 41
7 22
8 46
7 17
8 51
22 00
7 52
8 16
7 47
8 21
7 43
8 25
7 38
8 30
7 33
8 35
24 00
8 05
8 03
8 00
8 08
7 56
8 12
7 51
8 17
7 46
8 22
26 00
8 16
7 52
8 11
7 57
8 07
8 01
8 02
8 06
7 57
8 11
28 00
8 26
7 42
8 21
7 47
8 17
7 51
8 12
7 56
8 07
8 01
30 00
8 34
7 34
8 29
7 39
8 25
7 43
8 20
7 48
8 15
7 53
32 00
8 42
7 26
8 37
7 31
8 33
7 35
8 28
7 40
8 23
7 45
34 00
8 49
7 19
8 44
7 24
8 40
7 28
8 35
7 33
8 30
7 38
36 00
8 55
7 13
8 50
7 18
8 46
7 22
8 41
7 27
8 36
7 32
38 00
. 9 00
7 08
8 55
7 13
8 51
7 17
8 46
7 22
8 41
7 27
40 00
9 05
7 02
9 00
7 07
8 56
7 11
8 51
7 16
8 46
7 21
45 00
9 16
6 51
9 11
6 56
9 07
7 00
9 02
7 05
8 57
7 10
50 00
9 24
6 42
9 19
6 47
9 15
6 51
9 10
6 56
9 05
7 01
55 00
9 31
6 34
9 26
6 39
9 22
6 43
9 17
6 48
9 12
6 53
60 00
9 37
6 27
9 32
6 32
9 28
6 36
9 23
6 41
9 18
6 46
65 00
9 44
6 20
9 39
6 25
9 35
6 29
9 30
6 34
9 25
6 39
70 00
9 49
6 14
9 44
6 19
9 40
6 23
9 35
6 28
9 30
6 33
75 00
9 53
6 09
9 48
6 14
9 44
6 18
9 39
6 23
9 34
6 28
80 00
9 59
6 03
9 54
6 08
9 50
6 12
9 45
6 17
9 40
6 22
85 00
10 03
5 58
9 58
6 03
9 54
6 07
9 49
6 12
9 44
6 17
90 00
10 07
5 53
10 02
5 58
9 58
6 02
9 53
6 07
9 48
6 12
1
Additional Cc
)RK.
Di
>y of Montt
. 1 Jan.
Feb.
Mar.
Apr.
May.
June
. July.
Aug.
Sept.
Oct.
Nov.
Dec.
i "
,/
//
//
'»
II
/'
II
"
"
"
FOB Sun's A
LT.
ls(
-to 15th.
..+18
+15
+8
-
- 8
-13
-14
-11
-5
+3
+
11
+16
16
th to 31st
-1+17
+12 +4
-4 -
-11
-14
-13
- 9
-1
+7
+
14
+18
* The correct
ions for the
observed a
titudeofa
star or Planet involves the dip and the refraction; and foi
s, and mean semidlameter, which is talcen as 16'. A sup
theobserv
ed altitude
of the Sun's lowe
r limb, the
lip, refract
on, paralla
jlementary
oot of the 11
correction
taking account ot
the varlatic
n of the Su
n's semidla
meter in the different months of the year is given at the
aain table.
Page 928] TABLE 47.
Longitude Factors.
F is the Correction (in Minutes) to Long., due to each Mile of Error in Lat.
Latitude.
Az.
o
17.3
24.4
29.4
33.7
37°.4
40.7
43.6
46.2
O
48.6
50^9
52°.9
54.9
56.7
Az.
1°.0
2.0
57
29
60
30
63
32
66
33
69
35
72
36
76
38
79
40
83
42
87
44
91
46
95
48
100
50
105
52
i!o
2.0
3.0
4.0
5.0
19
14
11
20
15
12
21
16
13
22
17
13
23
17
14
24
18
14
25
19
15
26
20
16
28
21
17
29
22
17
30
23
18
32
24
19
33
25
20
35
26
21
3.0
4.0
5.0
6.0
7.0
8.0
9.5
8.1
7.1
10
8.7
7.6
10
9.1
7.9
11
9.5
8.3
7.2
11
10
8.7
12
10
9.1
13
11
9.5
13
11
10
14
12
10
14
13
11
15
13
11
16
14
12
17
14
13
17
15
13
6.0
7.0
8.0
9.0
6.3
6.6
6.9
7.6
7.9
8.3
8.7
9.1
9.6
10.0
10.0
11.0
11.0
9.0
9.4
9.9
6.03'
5.75
6.31
6.03
6.61
6.31
6.92
6,61
7.24
6.92
7'.24
7.95
7.59
8.32
7.95
7.59
7.24
6.92
s.n
8.32
9.12
8.71
9.12
10.0
9.55
10.5
10.0
11.0
10.5
9.4
9.9
10.3
10.8
11.3
5.50
5.25
5.01
5.75
5.50
5.25
5.01
4.79
4.57
6.03
5.75
5.50
5.25
5.01
4.79
6.31
6.03
5.75
6.61
6.31
6.03
6.92
6.61
6.31
7.24
6.92
6.61
7.95
7.59
7.24
8.32
7.95
7.59
8.71
8.32
7.95
9.12
8.71
8.32
9.55
9.12
8.71
10.0
9.55
9.12
10.3
10.8
11.3
11.8
12.3
12.9
4.79
4.57
4.37
5.50
5.25
5.01
5.75
5.50
5.25
6.03
5.75
5.50
6.31
6.03
5.75
6.61
6.31
6.03
6.92
6.61
6.31
7.24
6.92
6.61
7.59
7.24
6.92
7.95
7.59
7.24
8.32
7.95
7.59
8.71
8.32
7.95
11.8
12.3
12.9
13.5
14.1
14.7
4.17
3.98
3.80
4.37
4.17
3.98
4.57
4.37
4.17
4.79
4.57
4.37
5.01
4.79
4.57
5,25
5.01
4.79
5.50
5.25
5.01
5.75
5.50
5.25
6.03
5.75
5.50
6.31
6.03
5.75
6.61
6.31
6.03
6.92
6.61
6.31
7.24
6.92
6.61
7.59
7.24
6.92
13.5
14.1
14.7
15.4
16.1
16.8
15.4
16.1
16.8
3.63
3.47
3.31
3.80
3.63
3.47
3.98
3.80
3.63
4.17
3.98
3.80
4.37
4.17
3.98
4.57
4.37
4.17
4.79
4.57
4.37
5.01
4.79
4.57
5.25
5.01
4.79
5.50
5.25
5.01
5.75
5.50
5.25
6.03
5.75
5.50
6.31
6.03
5.75
6.61
6.31
6.03
17.5
18.3
19.1
3.16
3.02
2.88
3.31
3.16
3.02
3.47
3.31
3.16
3.63
3.47
3.31
3.80
3.63
3.47
3.98
3.80
3.63
4.17
3.98
3.80
4,37
4,17
3,98
3.80
3.63
3.47
4.57
4.37
4.17
4.79
4.57
4.37
5.01
4.79
4.57
5.25
5.01
4.79
5.50
5.25
5.01
5.75
5.50
5.25
17.5
18.3
19.1
20.0
20.8
21.7
22.6
23.6
24.6
2.75
2.63
2.51
2.88
2.75
2.63
3.02
2.88
2.75
3.16
3.02
2.88
3.31
3.16
3.02
3.47
3.31
3.16
3.63
3.47
3.31
3.98
3.80
3.63
4.17
3.98
3.80
4.37
4.17
3.98
4.57
4.37
4.17
4.79
4.57
4.37
5.01
4.79
4.57
20.0
20.8
21.7
2.40
2.29
2.19
2.51
2.40
2.29
2.63
2,51
2.40
2.75
2.63
2.51
2.88
2.75
2.63
3.02
2.88
2.75
3.16
3.02
2.88
3.31
3.16
3.02
3.47
3.31
3.16
3.63
3.47
3.31
.3.80
3.63
3.47
3.98
3.80
3.63
4.17
3.98
3.80
4.37
4.17
3.98
22.6
23.6
24.6
25.6
26.6
27.7
2.09
2.00
1.91
2.19
2.09
2.00
2.29
2.19
2.09
2.40
2.29
2.19
2.51
2.40
2.29
2.63
2.51
2.40
2.75
2.63
2.51
2.88
2.75
2.63
3.02
2.88
2.75
3.16
3.02
2.88
3.31
3.16
3.02
3.47
3.31
3.16
3.63
3.47
3.31
3.80
3.63
3.47
25.6
26.6
27.7
28.8
29.9
31.1
1.82
1.74
1.66
1.91
1.82
1.74
2.00
1.91
1.82
2.09
2.00
1.91
2.19
2.09
2.00
2.29
2.19
2.09
2.40
2.29
2.19
2.51
3-.40
2.29
2.63
2.51
2.40
2.75
2.63
2.51
2.88
2.75
2.63
3.02
2.88
2.75
3.16
3.02
2.88
3.31
3.16
3.02
28.8
29.9
31.1
32.2
33.5
34.7
1.58
1.51
1.45
1.66
1.58
1.51
1.74
1.66
1.58
1.82
1.74
1.66
1.91
1.82
1.74
2.00
1.91
1.82
2.09
2.00
1.91
2.19
2.09
2.00
2.29
2.19
2.09
2.40
2.29
2.19
2.51
2.40
2.29
2.63
2.51
2.40
2.75
2.63
2.51
2.88
2.75
2.63
32.2
33.5
34.7
35.9
37.2
38.5
39.8
41.1
42.4
1.38
1.32
1.26
1.45
1.38
1.32
1.51
1.45
1.38
1.58
1.51
1.45
1.66
1.58
1.51
1.74
1.66
1.58
1.82
1.74
1.66
1.91
1.82
1.74
2.00
1.91
1.82
2.09
2.00
1.91
2.19
2.09
2.00
2.29
2.19
2.09
2.40
2.29
2.19
2.09
2,00
1.91
2.51
2.40
2.29
35.9
37.2
38.5
1.20
1.15
1.10
1.26
1.20
1.15
1.32
1.26
1.20
1.38
1.32
1.26
1.45
1.38
1.32
1.51
1.45
1.38
1.58
1.51
1.45
1.66
1.58
1.51
1.74
1.66
1.58
1.82
1.74
1.66
1.58
1.51
1.91
1.82
1.74
2.00
1.91
1.82
2.19
2.09
2.00
39.8
41.1
42.4
43.7
45.0
1.05
1.00
1.10
1.05
1.15
1.10
1.20
1.15
1.26
1.20
1.32
1.26
1.38
1.32
1.45
1.38
1.51
1.45
1.66
1.58
1.74
1.66
1.82
1.74
1.91
1.82
43.7
45.0
8
17°.3
O
24.4
29.4
33.7
O
37.4
o
40.7
43.6
46.2
48.6
50.9
52.9
5I.9
56.7
Corr. toLong.=Errorin Lat.XF. 1
TABLE
47.
[Page 929 |
L
ongitude Factors
F is the Correction (in Minutes) to Long.
due to each Mile of Error in Lat.
Latitude
Az.
O
17.3
2I.4
29.4
33.7
37.4
40.7
43.6
46.2
48.6
50.9
52.9
5I.9
56.7
Az.
45°.0
1,00
1.05
1.10
1.15
1,20
1.26
1.32
1.38
1.45
1.51
1.58
1.66
1.74
1.82
45.0
46.3
.95
1.00
1.05
1.10
1.15 1 1.20
1.26
1.32
1.38
1.45
1,51
1.58
1.66
1.74
46.3
47.6
.91
.95
1.00
1.05
1.10
1.15
1.20
1.26
1.32
1.38
1.45
1.51
1.58
1.66
47.6
48.9
.87
.91
.95
1.00
1.05
1.10
1.15
1.20
1.26
1.32
1.38
1.45
1.51
1.58
48.9
50.2
.83
.87
.91
.95
1.00
1.05
1.10
1.15
1.20
1.26
1.32
1.38
1.45
1.51
50.2
51.5
.79
.83
.87
.91
.95
1.00
1.05
1.10
1.05
1.15
1.10
1.20
1.26
1.32
1.38
1.45
51.5
53.8
,76
.79
.83
.87
.91
.95
1.00
1.15
1.20
1.26
1.32
1.38
52.8
54.1
.72
.76
.79
.83
.87
.91
.95
1.00
1.05
1.10
1.15
1.20
1.26
1.32
54.1
55.3
.69
.72
.76
.79
.83
.87
.91
.95
1.00
1.05
1.10
1.15
1.20
1.26
55.3
56.5
.66
.69
.72
.76
.79
.83
.87
.91
.95
1.00
1.05
1.10
1.15
1.20
56.5
57.7
.63
.66
.69
.72
.76
.79
.83
.87
.91
.95
1.00
1.05
1.10
1.15
57.7
58.9
.60
.63
.66
.69
.72
.76
.79
.83
.87
.91
.95
1.00
1.05
1.10
58.9
60.1
.58
.60
.63
.66
.69
.72
.76
.79
.83
.87
.91
.95
1.00
1.05
60.1
61.2
.55
.58
.60
.63
.66
.69
.72
.76
.79
.83
.87
.91
.95
1.00
61.2
62.3
.52
.55
.58
.60
.63
.66
.69
.72
.76
.79
.83
.87
.91
.95
62.3
63.4
.50
.52
.55
.58
.60
.63
.66
.69
.72
.76
.79
.83
.87
.91
63.4
64.4
.48
.50
.52
.55
.58
.60
.63
.66
.69
.72
.76
.79
.83
.87
64.4
65.4
,45
.48
.50
.52
.55
.58
.60
.63
.66
.69
.72
.76
.79
.83
65.4
66.4
.44
.46
.48
.50
.52
.55
.58
.60
.63
.66
.69
.72
.76
.79
66.4
67.4
.42
.44
.46
.48
.50
.52
.55
.58
.60
.63
.66
.69
.72
.76
67.4
68.3
.40
.42
.44
.46
.48
.50
.52
.55
.58
.60
.63
.66
.69
.72
68.3
69.2
.38
.40
.42
.44
.46
.48
.50
.52
.55
.58
.60
.63
.66
.69
69.2
70.0
.36
.38
.40
.42
.44
.46
.48
.50
.52
.55
.58
.60
.63
.66
70.0
70.9
71.7
,35
.36
.38
.40
.42
.44
.46
.48
.50
.52
.55
.58
.60
.63
70.9
.33
.35
.36
.38
.40
.42
.44
.46
.48
.50
.52
.55
.58
.60
71.7
72.5
.32
.33
.35
.36
.38
.40
.42
.44
.46
.48
.50
.52
.55
.58
72.5
73.2
73.9
.30
.32
.33
.a5
.36
.38
.40
.42
.44
.46
.48
,46
.50
.52
.55
73.2
.29
.30
.32
.33
.35
.36
.38
.40
.42
.44
.48
.50
.52
73.9
74.6
.28
.29
.30
.32
.33
.35
.36
.38
.40
.42
.44
.46
.48
.50
74.6
75.3
.26
.28
.29
.30
.32
.33
.35
.36
.38
.40
.42
.44
.46
.48
75.3
75.9
,25
.26
.28
.29
.30
.32
.33
.35
.36
.38
.40
.42
.44
.46
75.9
76.5
,24
.25
.26
.28
.29
.30
.32
.33
.35
.36
.38
.40
.42
.44
76.5
77.1
,23
.24
.25
.26
.28
.29
.30
.32
.33
.35
.36
.38
.40
.42
77.1
77.7
.22
.23
.24
.25
.26
.28
.29
.30
.32
.33
.35,-
' .36
.38
.40
77.7
78.2
.21
.22
.23
.24
.25
.26
.28
.29
.30
.32
.33
.35
.36
.38
78.2
78.7
79.2
.20
.21
.22
.23
.24
.25
.26
.28
.29
.30
.32
.33
.35
.36
78.7
.19
.20
.21
.22
.23
.24
.25
.26
.28
.29
.30
.32
.33
.35
79.2
79.7
.18
.19
.20
.21
.22
.23
.24
.25
.26
,28
.29
.30
.32
.33
79.7
80.1
.17
.18
.19
.20
.21
.22
.23
.24
.25
.26
.28
.29
.30
.32
80.1
80.6
80.6
.17
.17
.18
.19
.20
.21
.22
.23
,24
.25
.26
,28
.29
.30
81.0
.16
.17
.17
.18
.19
.i6
.21
.22
.2^
.24
.in
.26
.28
.29
81.0
82.0
.14
.14
.15
.16
.17
.17
.18
.19
.20
.21
.22
.23
.24
.25
82.0
83.0
.12
.12
.13
.14
.14
.15
.16
.17
.17
.18
.19
.20
.21
.22
83.0
84.0
.10
.11
.11
.12
.13
.13
.14
.14
.15
.16
.17
.17
.18
.19
84.0
8.5.0
86.0
.09
.09
.09
.10
.10
.11
.11
.12
.13
.13
.14
.14
.15
.16
85.0
86.0
.07
,07
,08
.08
.08
.09
.09
.09
.10
.10
.11
.11
.12
.13
87.0
.05
.05
.06
.06
.06
.07
.07
.08
.08
.08
.09
.09
.09
.10
87.0
88.0
.03
.04
.04
.04
.04
.04
.05
.05
.05
.05
.05
.06
.06
.06
88.0
89.0
.02
.02
.02
.02
.02
.02
.02
.02
.03
.03
.03
.03
.03
.03
89.0
O
17.3
24.4
29.4
33.7
37.4
40.7
43.6
46.2
48.6
50.9
52.9
54.9
56.7
Corr.tc
Long.
= Error
in Lat
XF.
24972°— 12 49
Page 930] TABLE 47.
Longitude Factors.
F is the Correction (in Minutes) to Long., due to eacii Mile of Error in Lat.
Latitude.
Latitude.
Az.
i!o
3.0
58.3
59.9
61.4
63.8
64.1
Az.
o
45.0
46.3
47.6
58.3
59.9
61.4
62.8
64.1
110
55
115
58
120
60
126
63
132
66
1.91
1.82
1.74
2.00
1.91
1.82
2.09
2.00
1.91
2,19
2,09
2,00
2.29
2.19
2,09
3.0
4.0
5.0
36
28
22
38
29
23
40
30
24
42
32
25
44
33
26
48.9
50.3
51.5
1.66
1.58
1.51
1.74
1.66
1.58
1.82
1.74
1.66
1,91
1,82
1,74
2.00
1,91
1.82
6.0
7.0
8.0
18
16
14
19
17
14
20
17
15
21
18
16
22
19
17
14
53.8
54.1
55.3
1.45
1.38
1.32
1.51
1.45
1.38
1.58
1.51
1.45
1,66
1,58
1,51
1,74
1.66
1,58
9.0
12
13
13
14
9.4
9.9
11.5
11.0
12.0
11.5
12.6
12.0
13.2
12.6
13.8
13.2
56.5
57.7
58.9
60.1
61.3
63.3
1.26
1.20
1.15
1.32
1.26
1.20
1.38
1.32
1.26
1,45
1.38
1.32
1,51
1,45
1,38
10.3
10.8
U.3
10.5
10.0
9.55
11.0
10.5
10.0
11.5
11.0
10.5
12,0
11.5
11.0
12.6
12.0
11.5
1.10
1.05
1.00
1.15
1.10
1.05
1.20
1.15
1.10
1.26
1.20
1.15
1,32
1,26
1,20
11.8
13.3
13.9
9.12
8.71
8.32
9.55
9.12
8.71
10.0
9.55
9.12
10.5
10.0
9.55
11.0
10.5
10.0
63.4
64.4
65.4
.95
.91
.87
1.00
.95
.91
1.05
1.00
.95
1.10
1.05
1.00
1,15
1,10
1,05
13.5
14.1
14.7
7.95
7.59
7.24
8.32
7.95
7.59
• 8.71
8.32
. 7.95
9.12
8.71
8.32
9.55
9.12
8.71
66.4
67.4
68.3
.83
.79
.76
.87
.83
.79
.91
.87
.83
.95
.91
.87
1,00
,95
,91
15.4
16.1
16.8
17.5
18.3
19.1
6.92
6.61
6.31
7.24
6.92
6.61
7.59
7.24
6.92
7.95
7.59
7.24
8.32
7.95
7.59
69.3
70.0
70.9
.72
.69
.66
.76
.72
.69
.79
.76
.72
.83
.79
.76
,87
,83
,79
6.03
5.75
5.50
6.31
6.03
5.75
6.61
6.31
6.03
6.92
6.61
6.31
7.24
6.92
6.61
71.7
73.6
73.2
73.9
74.6
75.3
.63
.60
.58
.66
.63
.60
.69
.66
.63
.72
.69
.66
.76
.72
,69
30.0
30.8
31.7
5.25
5.01
4.79
5.50
5.25
5.01
5.75
5.50
5.25
6.03
5.75
5.50
6.31
6.03
5.75
.55
.52
.50
.58
.55
.52
.60
.58
.55
.63
.60
.58
,66
,63
,60
33.6
33.6
34.5
4.57
4.37
4.17
4.79
4.57
4.37
5.01
4.79
4.57
5.25
5.01
4.79
5.50
5.25
5.01
75.9
76.5
77.1
.48
.46
.44
.50
.48
.46
.52
.50
.48
.55
.52
.50
,58
,55
,52
35.6
36.6
37.7
3.98
3.80
3.63
4.17
3.98
3.80
4.37
4.17
3.98
4.57
4.37
4.17
4.79
4.57
4.37
77.7
78.3
78.7
.42
.40
.38
.44
.42
.40
.46
.44
.42
.48
.46
.44
.50
.48
.46
38.8
39.9
31.1
33.3
33.5
34.7
3.47
3.31
3.16
3.02
2.88
2.75
3.63
3.47
3.31
3.80
3.63
3.47
3.98
3.80
3.63
4.17
3.98
3.80
79.2
79.7
80.1
80.6
.36
.35
.33
.38
.36
.35
.40
.38
.36
.42
.40
.38
.44
,42
,40
,38
3.16
3.02
2.88
3.31
3.16
3.02
3.47
3.31
3.16
3.63
3.47
3.31
.32
.33
.35
.36
81.0
83.0
83.0
84.0
85.0
.30
.26
.32
.28
.33
.29
.35
.30
,36
,35
35.9
37.3
38.5
2.63
2.51
2.40
2.75
2.63
2.51
2.88
2.75
2.63
3.02
2,88
2.75
3.16
3,02
2.88
.23
.20
.17
.24
.21
.17
.25
.22
.18
.26
.23
.19
,28
,24
.20
39.8
41.1
43.4
2.29
2.19
2.09
2.40
2.29
2.19
2.51
2.40
2.29
2.63
2.51
2.40
2.75
2.63
2.51
86.0
87.0
88.0
89.0
.13
.10
.07
.14
.11
.07
.14
.11
.08
.15
.12
.08
.16
.13
.08
43.7
45.0
2.00
1.91
2.09
2.00
2.19
2.09
2.29
2.19
2.40
2.29
.03
.03
.04
.04
.04
58.3
59.9
61.4
6§.8
64.1
o
58.3
59.9
O
61.4
6^.8
6l.l
Corr. to Long.- Error in Lat. XF. 1
TABLE 48.
[Page 931
Latitude Factors.
F is the Correction (
in Miles) to Lat.,
due to each Minute of Error in Long.
LaUtude.
Latitude.
Az.
O
17'.3
24.4
29.4
33.7
37.4
40.7
Az.
s
17.3
24.4
29.4
33.7
37.4
40°.7
i!o
.02
.02
.02
.01
.01
.01
.01
o
45.0
1.00
.95
.91
.87
.83
.79
.76
2.0
.03
.03
.03
.03
.03
.03
.03
46.3
1.05
1.00
.95
.91
.87
.83
.79
3.0
.05
.05
.05
.05
.04
.04
.04
47.6
1.10
1.05
1.00
.95
.91
.87
.83
1.0
.07
.07
.06
.06
.06
.06
.05
48.9
1.15
1.10
1.05
1.00
.95
.91
.87
5.0
.09
.08
.08
.08
.07
.07
.07
50.2
1.20
1.15
1.10
1.05
1.00
.95
.91
6.0
.11
.10
.10
.09
.09
.08
.08
51.5
1.26
1.20
1.15
1.10
1.05
1.00
.95
7.0
.12
.12
.11
.11
.10
.10
.09
52.8
1.32
1.26
1.20
1.15
1.10
1.05
1.00
8.0
.14
.13
.13
.12
.12
.11
.11
54.1
1.38
1.32
1.26
1.20
1.15
1.10
1.05
9.0
.16
.15
.14
.14
.13
.13
.12
55.3
1.45
1.38
1.32
1.26
1.20
1.15
1.10
9.4
.17
.16
15
.14
.14
.li
:ii
56.5
1.51
1.45
1.38
1.32
1.26
1.20
1.15
9.9
.17
.17
.16
.15
.14
.14
.13
57.7
1.58
1.51
1.45
1.38
1.32
1.26
1.20
10.3
.18
.17
.17
.16
.15
.14
.14
58.9
1.66
1.58
1.51
1.45
1.38
1.32
1.26
10.8
.19
.18
.17
.17
.16
.15
.14
60.1
1.74
1.66
1.58
1.51
1.45
1.38
1.32
11.3
.20
.19
.18
.17
.17
.16
.15
61.2
1.82
1.74
1.66
1.58
1.51
1.45
1.38
11.8
.21
.20
.19
.18
.17
.17
.16
62.3
1.91
1.82
1.74
1.66
1.58
1.51
1.45
12.3
.22
.21
.20
.19
.18
.17
.17
63.4
2.00
1.91
1.82
1.74
1.66
1.58
1.51
12.9
.23
.22
.21
.20
.19
.18
.17
64.4
2.09
2.00
1.91
1.82
1.74
1.66
1.58
13.5
.24
.23
.22
.21
.20
.19
.18
65.4
2.19
2.29
2.09
2.00
1.91
1.82
1.74
1.66
14.1
.25
.24
.23
.22
.21
.20
.19
66.4
2.19
2.09
2.00
1.91
1.82
1.74
14.7
.26
.25
.24
.23
.22
.21
.20
67.4
2.40
2.29
2.19
2.09
2.00
1.91
1.82
15.4
.28
.26
.25
.24
.25
.23
.22
.21
68.3
2.51
2.40
2.29
2.19
2.09
2.00
1.91
16.1
.29
.28
.26
.24
.23
.22
69.2
2.63
2.51
2.40
2.29
2.19
2.09
2.00
16.8
.30
.29
.28
.26
.25
.24
.23
70.0
2.75
2.63
2.51
2.40
2.29
2.19
2.09
17.5
.32
.30
.32
.29
.28
.26
.25
.24
-70.9
2.88
2.75
2.63
2.51
2.40
2.51
2.29
2.40
2.19
2.29
18.3
.33
.30
.29
.28
.26
.25
71.7
3.02
2.88
2.75
2.63
19.1
.34
.33
.32
.30
.29
.28
.26
72.5
3.16
3.02
2.88
2.75
2.63
2.51
2.40
20.0
.36
.34
.33
.32
.30
.29
.28
73.2
3.31
3.16
3.02
2.88
2.75
2.63
2.51
20.8
.38
.36
.34
.33
.32
.30
.29
73.9
3.47
3.31
3.16
3.02
2.88
2.75
2.63
21.7
.40
.38
.36
.34
.33
.32
.30
74.6
3.63
3.47
3.31
3.16
3.02
2.88
2.75
22.6
23.6
.42
.40
.38
.36
.34
.33
.32
75.3
3.80
3.63
3.80
3.47
3.63
3.31
3.47
3.16
3.02
2.88
.44
.42
.40
.38
.36
.34
.33
75.9
3.98
3.31
3.16
3.02
24.6
.46
.44
.42
.40
.38
.36
.34
76.5
4.17
3.98
3.80
3.63
3'.47
3,31
3.16
25.6
26.6
.48
.46
.44
.42
.40
.42
.38
.40
.36
.38
77.1
4.37
4.57
4.17
4,37
3.98
3.80
3.63
3147
3.31
.50
.48
.46
.44
77.7
4.17
3.98
3.80
3.63
3.47
27.7
.52
.50
.48
.46
.44
.42
.40
78.2
4.79
4.57
4.37
4.17
3.98
3.80
3.63
28.8
.55
.52
.50
.48
.46
.48
.44
.42
78.7
5.01
5.25
4.79
5.01
4.57
4.79
4.37
4.17
3.98
3.80
29.9
.58
.55
.52
.50
.46
.44
79.2
4..57
4.37
4.17
3.98
31.1
.60
.58
.55
.52
.50
.48
.46
79.7
5.50
5.25
5.01
4.79
4.57
4.37
4.17
32.2
.63
.60
.58
.55
.52
.50
.48
80.1
5.75
5.50
5.25
5.01
4.79
4.57
4.37
33.5
.66
.63
.60
.58
.55
.52
.50
81.0
6..^
6.0
5.8
5.5
5.2
S.O
4.8
34.7
.69
.66
.63
.60
.58
.55
.52
82.0
7.2
6.9
6.6
6.3
6.0
~5.8
5.5
35.9
37.2
.72
.76
.69
.66
.63
.60
.63
.58
.60
.55
83.0
8.3
7.9
7.6
7.2
6.9
6.6
6.3
.72
.69
.66
.58
84.0
9.5
9.1
8.7
8.3
7.9
7.6
7.2
38.5
.79
.76
.72
.69
.66
.63
.60
85.0
n
11
10
10
9.5
9.1
8.7
39.8
41.1
.83
.79
.76
.72
.76
.69
.72
.66
.63
86.0
14
14
13
12
12
11
11
.87
.83
.79
.69
.66
87.0
19
18
17
17
16
15
14
42.4
.91
.87
.83
.79
.76
.72
.69
88.0
29
27
26
25
24
23
22
43.7
.95
.91
.87
.83
.79
.76
.72
.76
89.0
57
55
52
50
48
46
43
45.0
1.00
.95
.91
.87
.83
.79
17.3
o
24.4
o
29.4
o
33.7
o
37.4
O
40.7
o
o
17.3
o
24.4
o
39.4
31.7
o
37.4
O
40.7
Corr. to
Lat.-E
Tor in Long.XF.
Page
932]
TABLE 48.
Latitude Factors.
F is the Correction (
01 Miles) to Lat.,
due to each Minute of Error in Long.
Latitude.
Latitude.
Az.
43.6
O
46.3
48.6
50.9
51.9
54.9
56.7
Az.
43.6
46.3
48.6
50.9
o
52.9
54.9
o
56.7
o
1.0
.01
.01
.01
.01
.01
.01
.01
45.0
.72
.69
.66
.63
.60
.58
.55
3.0
.03
.02
.02
.02
.02
.02
.02
46.3
.76
.72
.69
.66
.63
.60
.58
3.0
4.0
.04
.05
.04
.03
.03
.03
.03
.03
47.6
.79
.76
.72
.69
.66
.63
.60
.05
.05
.04
.04
.04
.04
48.9
.83
.79
.76
.72
.69
.66
.63
5.0
.06
.06
.06
.06
.05
.05
.05
50.3
.87
.83
.79
.76
.72
.69
.66
6.0
.08
.07
.07
.07
.06
• .06
.06
51.5
.91
.87
.83
.79
.76
.72
.69
7.0
.09
.08
.08
.08
.07
.07
.07
53.8
.95
.91
.87
.83
.79
.76
.72
8.0
.10
.10
.09
.09
.08
.08
.08
54.1
1.00
.95
.91
.87
.83
.79
.76
9.0
.11
.11
.10
.10
.09
.09
.09
55.3
1.05
1.00
.95
,91
.87
.91"
.83
.79
9.4
.12
.11
.11
.10
.10
.09
.09
56.5
1,10
1.05
1.00
.95
.87
.83
9.9
.13
.12
.11
.11
.10
.10
.09
57.7
1.15
1.10
1.05
1.00
.95
.91
.87
10.3
.13
.13
.12
.11
.11
.10
.10
58.9
1.20
1.15
1.10
1.05
1.10
1.00
.95
1.00
.91
10.8
.14
.13
.13
.12
.11
.11
.10
60.1
1.26
1.20
1.15
.95
11.3
.14
.14
.13
.13
.12
.11
.11
61.3
1.32
1.26
1.20
1.15
1.10
1.05
1.00
11.8
.15
.14
.14
.13
.13
.12
.11
63.3
1.38
1.32
1.26
1.32
1.20
T.26
1,15
1.10
1.05
13.3
.16
.15
.14
.14
.13
.13
.12
63.4
1.45
1.38
1,20
1.15
1.10
13.9
.17
.16
.15
.14
.14
.13
.13
64.4
1.51
1.45
1.38
1.32
1.26
1.20
1.15
13.S
.17
.17
.16
.15
.14
.14
.13
65.4
1.58
1.51
1.45
1.38
1.32
i:38"
1.26
1.32
1.20
1.26
14.1
.18
.17
.17
.16
.15
.14
.14
66.4
1.66
1.58
1.51
1.45
14.7
.19
.18
.17
.17
.16
.15
.14
67.4
1.74
1.66
1.58
1.51
1.45
1.38
1.32
15.4
.20
.21
.19
.20
.18
.17
.17
.16
.15
68.3
1.82
1.74
1.82
1.66
1.74
1.58
1.66"
1.51
1.58
1.45
1.51
1.38
1.45
16.1
.19
.18
.17
.17
.16
69.3
1.91
16.8
.22
.21
.20
.19
.18
.17
.17
70.0
2.00
1.91
1.82
1.74
1.66
1.58
1.51
17.5
18.3
.23
.22
.21
.20
.19
.18
.17
70.9
2.09
2.19
2.00
2.09
1.91
1.82
1.74
1.66
1.58
.24
.23
.22
.21
.20
.19
.18
71.7
2.00
1.91
1.82
1.74
1.66
19.1
.25
.24
.23
.22
.21
.20
.19
72.5
2.29
2.19
,2.09
2.00
1.91
1.82
1.74
30.0
.26
.25
.24
.23
.22
.21
.20
73.3
2.40
2.29
2.40
2.19
2.09
2.00
1.91
1.82
1.91
30.8
.28
.26
.25
.24
.23
.22
.21
73.9
2.. 51
2.29
2.19
2.09
2.00
31.7
.29
.28
.26
.25
.24
.23
.22
74.6
2.63
2.51
2.40
2.29
2.19
2.09
2.00
33.6
.30
.29
.30
.28
.29
.26
.28
.25
.24
.23
75.3
2.75
2.63
2.51
2.40
2.29
2.40
2.19
2.29
2.09
2.19
33.6
.32
.26
.25
.24
75.9
2.88
2.75
2.63
2.51
34.6
.33
.32
.30
.29
.28
.26
.25
76.5
3.02
2.88
2.75
2.63
2.51
2,40
2.29
35.6
.34
.33
.32
.30
.29
.28
.26
77.1
3.16
3.02
2,88
2.75
2.63
2,51
2,63
2.40
2,51
36.6
.36
.34
.33
.32
.30
.29
.28
77.7
3.31
3.16
3.02
2.88
2.75
27.7
.38
.36
.34
.33
.32
.30
.29
78.3
3.47
3.31
3.16
3.02
2.88
2,75
2,63
38.8
.40
.38
.36
.34
.33
.32
.30
78.7
3.63
3.80
3.47
3.63
3.31
3.16
3.02
2.88
2.75
39.9
.42
.40
.38
.36
.34
.33
.32
79.2
3.47
3.31
3.16
3,02
2.88
31.1
.44
.42
.40
.38
.36
.34
.33
79.7
3.98
3,80
3.63
3.47
3.31
3,16
3.02
33.3
.46
.44
.42
.40
.42
.38
.36
.34
80.1
4.17
3,98
3.80
3.63
3.47
3,31
3.16
33.5
.48
.46
.44
.40
.38
.36
81.0
4.6
4.4
4,2
4,0
3.8
3,6
3.5
34.7
.50
.48
.46
.44
.42
.40
.38
83.0
5.2
5.0
4.8
4.6
4.4
4,2
4,0
35.9
.52
.50
.48
.46
.44
.42
.40
83.0
6.0
5.8
5.5
5.2
5.0
4,8
4,6
5,2
37.3
.55
.52
.50
.48
.46
.44
.42
84.0
6.9
6.6
6.3
6.0
5.8
5,5
38.5
.58
.55
.52
.50
.48
.46
.44
85.0
8.3
7.9
7.6
7.2
6.9
6.6
6,3
39.8
.60
.58
.55
.52
.50
.48
.46
86.0
11
10
9.9
13
9.4
12
9.0
ll
8.6
11
8,2
10
41.1
.63
.60
.58
.55
.52
.50
.48
87.0
14
13
43.4
.66
.63
.60
.58
.55
.52
.50
88.0
21
20
19
18
17
16
16
43.7
.69
.66
.63
.60
.58
.55
.52
89.0
41
40
38
36
35
33
31
45.0
.72
.69
.66
.63
.60
.58
.55
O
43.6
46.3
48.6
50.9
53°.9
54.9
O
56.7
O
43.6
o
46.3
48.6
o
50.9
O
54.9
56°.7
Corr. to
Lat.= Ei
Tor in H-ong.xF.
TABLE 48. [Page 933
Latitude Factors.
F is the Correction (in Miles) to Lat., due to each Minute of Error in Long.
Latitude.
Latitude.
Az.
58.3
D
59.9
O
61.4
63.8
6l.l
Az.
58.3
o
59.9
61.4
63.8
64.1
i!o
3.0
3.0
.01
.02
.03
.01
.02
.03
.01
.02
.03
.03
.04
.05
.01
.02
.03
.03
.04
.05
.01
.02
.02
.03
.04
.05
45.0
46.3
47.6
.52
.55
.58
.50
.52
.55
.48
.50
.52
.46
.48
.50
.44
.46
.48
1.0
5.0
6.0
.04
.05
.06
.04
.04
.05
48.9
50.3
51.5
.60
.63
.66
.58
.60
.63
.55
.58
.60
.52
.55
.58
.50
.52
.55
7.0
8.0
9.0
.06
.07
.08
.06
.07
.08
.06
.07
.08
.06
.06
.07
.05
.06
.07
53.8
54.1
55.3
.69
.72
.76
.66
.69
.72
.63
.66
.69
.60
.63
.66
.58
.60
.63
9.4
9.9
10.3
.09
.09
.09
.08
.09
.09
.08
.08
.09
.08
.08
.08
.07
.08
.08
56.5
57.7
58.9
.79
.83
.87
.76
.79
.83
.72
.76
.79
.69
.72
.76
.66
.69
.72
10.8
11.3
11.8
.10
.10
.11
.09
.10
.10
.09
.09
.10
.09
.09
.09
.08
.09
.09
60.1
61.3
63.3
.91
.95
1.00
.87
.91
.95
.83
.87
.91
.79
.83
.87
.76
.79
.83
13.3
13.9
13.5
.11
.12
.13
.11
.11
.12
.10
.11
.11
.10
.10
.11
.09
.10
.10
63.4
64.4
65.4
1.05
1.10
1.15
1.00
1.05
1.10
.95
1.00
1.05
.91
.95
1.00
.87
.91
.95
14.1
14.7
15.4
.13
.14
.14
.13
.13
.14
.12
.13
.13
.11
.12
.13
.11
.11
.12
66.4
67.4
68.3
1.20
1.26
1.32
1.15
1.20
1.26
1.10
1.15
1.20
1.05
1.10
1.15
1.00
X.05
1.10
16.1
16.8
17.5
.15
.16
.17
.14
.15
.16
.14
.14
.15
.13
.14
.14
.13
.13
.14
69.3
70.0
70.9
1.38
1.45
1.51
1.32
1.38
1.45
1.26
1.32
1.38
1.20
1.26
1.32
1.15
1.20
1.26
18.3
19.1
30.0
.17
.18
.19
.17
.17
.18
.16
.17
.17
.15
.16
.17
.14
.15
.16
71.7
73.5
73.3
1.58
1.66
1.74
1.51
1.58
1.66
1.45
1.51
1.58
1.38
1.45
1.51
1.32
1.38
1.45
30.8
31.7
33.6
.20
.21
.22
.19
.20
.21
.18
.19
.20
.17
.18
.19
.17
.17
.18
73.9
74.6
75.3
1.82
1.91
2.00
1.74
1.82
1.91
1.66
1.74
1.82
1.58
1.66
1.74
1.51
1.58
1.66
33.6
34.6
35.6
.23
.24
.25
.22
.23
.24
.21
.22
.23
.20
.21
.22
.19
.20
.21
.22
.23
.24
75.9
76.5
77.1
2.09
2.19
2.29
2.00
2,09
2.19
1.91
2.00
2.09
1.82
1.91
2.00
1.74
1.82
1.91
36.6
37.7
38.8
.26
.28
.29
.25
.26
.28
.24
.25
.26
.23
.24
.25
77.7
78.3
78.7
2.40
2.51
2.63
2.29
2.40
2.51
2.19
2.29
2.40
2.09
2.19
2.29
2.40
2.51
2.63
2.00
2.09
2.19
2.29
2.40
2.51
39.9
31.1
33.3
.30
.32
.33
.29
.30
.32
.28
.29
.30
.26
.28
.29
.25
.26
.28
79.3
79.7
80.1
2.75
2.88
3.02
2.63
2.75
2.88
2.51
2.63
2.75
33.5
34.7
35.9
37.3
38.5
39.8
.34
.36
.38
.33
.34
.36
.32
.33
.34
.30
.32
.33
.29
.30
.32
81.0
83.0
83.0
3.3
3.8
4.4
3.2
3.6
4.2
3.0
3.5
4.0
2.9
3.3
3.8
2.8
3.2
3.6
.40
.42
.44
.38
.40
.42
.36
.38
.40
.34
.36
.38
.33
.34
.36
84.0
85.0
86.0
5.0
6.0
7.9
4.8
5.7
7.5
4.6
5.5
7.2
4:4
5.2
6.8
4.2
5.0
6.5
41.1
43.4
43.7
.46
.48
.50
.44
.46
.48
.42
.44
.46
.40
.42
.44
.38
.40
.42
87.0
88.0
89.0
10
15
30
9.6
14
29
9.1
14
27
8.7
13
26
8.3
12
25
45.0
.52
.50
.48
.46
.44
58.3
59.9
61.4
63.8
O
64.1
58.3
59.9
6i.4
63.8
O
64.1
Corr. to Lat.- Error in Long.XF.
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