TO MEMORIAL
rviiis Str
Math. Dt0t>
NEW METHOD
CORRECTING LUNAR DISTANCES,
AND
IMPROVED METHOD
OF FINDING THE
ERROR AND RATE OF A CHRONOMETER
BY
EQUAL ALTITUDES.
BY WILLIAM CHAUVENET, LL. D.,
CHANCELLOE OF WASHINGTON UNIVERSITY, ST. LOUIS, LATE PEOFESSOB OF MATHEMATICS AND ASTEONOMY
IN THE U. S. NAVAL ACADEMY, ETC.
EXTRACTED FROM THE APPENDIX TO THE AMERICAN EPHEMERIS FOR 1857, BY AUTHORITY OF THE
BUREAU OF NAVIGATION, NAVY DEPARTMENT, WASHINGTON.
NEW YORK:
D. VAN NOSTRAND, 192 BROADWAY.
LONDON : TBUBNEE & CO.
1868.
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NEW METHOD
OF
CORRECTING LUNAR DISTANCES
FROM THE APPENDIX TO THE AMERICAN EPHEMERIS AND NAUTICAL
ALMANAC FOB 1855.
812165
DIRECTIONS
FOR USING
THE TABLES FOR CORRECTING LUNAR DISTANCES.
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, 1st, the parallax of the moon in the
latitude of the observer, allowing for the spherpidal figure of the earth ; 2d, the
parallax of the sun or a planet ; 3d, the true atmospheric refraction, allowing for the
actual state of the air as shown by the barometer and thermometer ; and 4th, that
effect of refraction which gives the apparent discs of the moon and sun an oval or
elliptical figure.
The longitude deduced from a iunar observation, when no attention is paid to the
spheroidal figure of the earth, to the barometer and thermometer, and the elliptical
figure of the discs, 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 10', 15', or 20'. Since lunars are now chiefly
valuable as checks upon the chronometer, 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. This is accomplished by means of these Tables, with
an amount of labor very little greater than that which is required by the inaccurate
methods in common use.
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 chro-
nometer, or its difference from mean Greenwich time.
4. The apparent distance of the moon's b *ight limb from a star or planet, or from
the nearest 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.
5
CORRECTION OF
* -
_
7, The height of the barometer and thermometer.
' :: .- 8. The hei-ght of the eye above the level of the sea.
9. The index correction of the sextant, if a sextant is used.
I *.?<[ '!J)he i indfix corrie*ction of the sextant may be supposed to be previously determined ,
but, since even in the best instruments it is not constant, its determination should be
considered a necessary part of the observation ; and when the greatest precision is
sought, it should be found both before and after the measurement of the distance, and
its mean value taken.
The error of the chronometer above alluded to is that which is obtained by apply-
ing the daily rate (multiplied by the proper 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 good or bad going of the
chronometer.
PREPARATION OF THE DATA.
Greenwich 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),
reckoning the hours in successionfrom to 24, beginning at noon.
Nautical Almanac. With the Greenwich Date enter the Almanac and take out
the moon's semidiameter and horizontal parallax ; and if the sun is observed, its semi-
diameter and horizontal parallax ; * but if a planet is observed, its horizontal parallax
only.
Apparent Altitude of the Moon. To the altitude given by the sextant apply the
index correction of the instrument and subtract the dip of the horizon, Table I. If
the lower limb is observed, add the semidiameter augmented by Table II. ; if the
upper limb is observed, subtract the augmented semidiameter. The result is the
apparent altitude of the moon's centre, denoted " <C's App. Alt."
Apparent Altitude of the Sun, Planet, or Star. To the observed altitude apply
the index correction of the sextant, and subtract the dip, Table I. ; and if the sun is
used, add its semidiameter when the lower limb is observed, or subtract it when the
upper limb is observed. The result is the apparent altitude required, denoted by
"G's or #'s App. Alt."
Apparent Distance. 1st. When the sun is used, to the observed distance (cor-
rected for index error when necessary) add the moon's augmented semidiameter and
the sun's semidiameter. 2d. When a planet or star is used, add the moon's aug-
mented semidiameter if its nearest limb is observed, but subtract it if its farthest limb
is observed. The result is " App. Dist"
Moon's Reduced Parallax and Refraction. Enter Table III. with the latitude of'
the place of observation and the moon's horizontal parallax, and take out the correc-
tion, which add -to the horizontal parallax. Call the result the moon's reduced par-
allax, or " 's Red. P."
Enter Table IV. with the moon's apparent altitude, and take out the mean reduced
" The sun's horizontal parallax may be assumed as 8".5.
6
LUNAR DISTANCES.
refraction, and apply to this mean refraction the corrections given in Tables IV. A.
and IV. B., adding or subtracting these corrections according to the directions in the
Tables. The result is the moon's reduced refraction or " d's Red. JR."
Subtract the " C's Red. R." from the " (C's Red. P." and mark the result as
""<Ts Red. P. and JR."
Reduced Parallax and Refraction of Sun, Planet, or Star.* With the apparent
altitude of the sun, planet, or star, take from Table IV. the mean reduced refraction,
which correct by Tables IV. A. and IV. B. If the sun is observed, subtract its horizontal
parallax (which may be always taken at 8".5) from its reduced refraction, and mark
the result as " Q's Red. P. <$ ." If a planet is observed subtract its horizontal
parallax, and mark the result as " jfc's Red. P. fy R." If a star is observed its
reduced refraction is at once the required " %'s Red. P. fy B."
COMPUTATION OF THE TRUE DISTANCE.
Take from Table V. the four logarithms A, B, C, D,t and place these logs, each
at the head of a column, marking the columns A, B, C, and D, respectively ; then
put the
log. of <C 's Red. P. <$ R. (Table IX.) in Columns A and B
log. of Q's Red. P. fy R. " " C " D
log. sine fs App. Alt. (Bowd. Table XXVII.) " A " D
log. sine Q's App. Alt. " " B " C
log. cotangent App. List. " " A " C
log. cosecant App. Dist. " " B " D.
The sum of the four logs, in Col. A is the log. (Table IX.) of the First Part o/<C'f
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
O's or ;fc'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 's or ^s Correction, which is always to be marked -+-.
Combine the first and second parts of the (C 's correction according to the signs
(4- or ) 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 " (C 's whole Correction."
In the same manner form the Q's or ?fc's whole Correction.
First Correction of Distance. Combine the <'s whole corr. and the 0's or >Jc'j
* The parallax of a star being zero, its " reduced parallax and refraction " become, of course,
merely its " reduced refraction"; but as no mistake can arise from marking it as " ^a P. fr R." this
designation has been retained in order to give simplicity and uniformity at once to the rules and the
tables.
t No interpolation is required in taking out these logarithms.
7
CORRECTION OF
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 -f- 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 ike Moon's Disc, or Contraction of ike
Moon's Semidiameter (Table VII.). Er.'er Table VII. A. with the <C 's App. Alt. and
<C's Red. P. & R., and take out the number. With this number and the C's whole
correction enter Table VII. B. and take the required contraction, which is to be added
to the App. Dist. when the farthest limb is observed, but subtracted when the nearest
limb is observed.
Correction for the Elliptical Figure of the Sun's Disc, or Contraction of the Sun's
Semidiameter (Table VIII.). Enter Table VIII. A. with the 0's App. Alt. and
'Q's Red. P. & R. and take out the number. With this number and the 0's whole
corr. enter Table VIII. B. and take out the required contraction, which is always to be
subtracted from the distance (the nearest limb of the sun being always observed).
Correction for Compression or for the Spheroidal Figure of the Earth. Take
from the Nautical Almanac for the Greenwich Date the value of log. N, given with
the lunar distance observed.* 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 to the distance if log. IV in the
Nautical Almanac is marked -h, or subtract it if log. N is marked ; 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 ERROR OF THE CHRONOMETER.
Fmd 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
* The values of log. N are no longer given in the Nautical Almanac. For distances of
the moon from the sun for the year 1855, they are given in Table XI. of this volume. For
other distances, at any time, log. N may be found from Table XIL by the following role :
From the Nautical Almanac take the moon's and star's (or planet's) declinations to the nearest
whole degree. With the moon's declination and apparent distance take from Table Xll. A. the fast
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 -H to or from to -K With the star's (or planet's) declination and
apparent distance, take from Table XII. B. the second part of N, and mark it -f- when the declination
is -North, and when South. 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 in Table IX., with its sign prefixed, is the required log. N, to be
used as directed in the text.
LUNAR DISTANCES.
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 dis-
tance falls. With this difference and the interval of time just found, enter Table X.
of this Appendix, and take out the seconds, which are to be added to the approx-
imate Greenwich time when the Prop. Logs, are decreasing, but subtracted when
the Prop. Logs, are increasing. The result is the true Greenwich time.
The difference between the true Greenwich time and the time shown by the chro-
nometer is the error of the chronometer as determined by the lunar observation.
i
DEGREE OF DEPENDENCE.
If the error thus determined agrees with that deduced by means of the rate ana
original error, the chronometer has run well, and its rate is confirmed ; if otherwise,
more or less doubt is thrown upon the chronometer, according to the degree of accu-
racy of the lunar observation itself. An error of 10" in the measurement of the
distance produces about 20 8> 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 8> . 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 care-
fui comparison of his several results.
CORRECTION OF
EXAMPLE L
In Lat. 35 30' N., Long. 30 W., by account, on September 7th, 1855, about 6"
A. M., the Greenwich chronometer showing 8 h- 29 m - 57 8> .5 and supposed to be fast
21 m - l'-.5 ; the observed distance of O's and C 's nearest limbs is 43 52' 10" ; ob-
served alt. _0_ 49 32' 50"; observed alt. 5 27' 10"; barometer 29.1 inches,
thermometer 75 ; height of the eye above the sea 20 feet ; index correction of the
sextant 0. What is the error of the chronometer on Greenwich time according to
these observations?
Preparation of the Data*
Chronometer
(Fast)
Greenw. date Sept. 6
h. m. B.
8 29 57.5
21 1.5
d 's semid. N. A.
Aug. Tab. II.
d 's aug. Semid.
20 8 56.0
Obs'd Alt.
Dip Tab. I.
C 's aug. semid.
C 's App. Alt.
1 II
49 32 50
4 23
+15 1
49 43 28
Obs'd alt O
Dip
0's semid
O'* App. Alt.
d'sRed.R. Tab. IV.
Barom. Tab. IV. A.
Therm. Tab. IV. B.
4'sRed.R.
4'Red.P.
i H
1 16
3
4
1 9
54 23
O's Red. R. Tab. IV.
Barom. Tab. IV. A.
Therm. Tab. IV. B.
's Par.
4 ' Red . P. &- R.
53 14
's Red. P.frR.
14 50.0
+11.2
(t'sPar.N.A.
Aug. Tab. in.
C's/fed.P.
54 19.4
+3.6
15 1.2
54 23.0
O 1 II
5 27 10
4 23
-1-15 55
Obs'd distance Ol
d 's aug. semid.
Q's semid.
App. Dist.
O 1 I/
|d 43 52 10
+ 15 1
-+-1555
5 3* 42
4423 6
8 57
16
28
8 13
T~5
Computation of the True Distance.
A.
log. A. Tab. V. 0.0021
log. d 's Bed. P.& R. TabJX. 3.5043
log. sin. a 's App. Alt. 9.8825
log. cot. App. Dist. 0.0093
C.
log. C. Tab. V. 9.9949
log.O'sRed.P.&R. TablX. 2.6857
log. sin. O's App. Alt. 8.9929
log. cot. App. Dist. 0.0093
App. Dist
1st corr.
Zdcorr. Tab. VI
Contraction of d ' )
Semid. Tab. VII. 5
Contraction of Q's >
ewm/.Tab.VIII.5
Corr. for compression
True Distance
44 fc 6
+42 18
16
20
3
C log. Tab. IX. 3.3982
\ 1st Part d 's corr. +41 ' 42"
B.
log. B. Tab. V. 9.9951
log. d 's Red. P. & R. 3.5043
log. sin. O's App. Alt. 8.9929
log. cosec. App. Dist. 0.1552
C log. Tab. IX.
\ 1st Part O'* corr.
D.
log. D. Tab. V.
log. O's Red. P & R.
log. sin. d 's App. Alt
log. cosec. App. Dist.
C log. Tab. IX.
I 2d Part Q's corr.
0's whole corr.
1.6828
0' 48"
9.9992
2.6857
9.8825
0.1552
5 log. Tab. IX. 2.6475
> 2d Part (I 's corr. 7' "24"
O whole corr. +34' 18"
log. N.* Tab. XL 0.764
log. sin. Lat 35 30' N. +9.764
log. Tab. EL 0.528
2.7226
+8' 48"
+8' 0"
45 4 45
* This log. may also be found from Table XII. by the rule in the note on p. 8.
LUNAR DISTANCES.
To find the Error of the Chronometer.
45 4' 45"
46 3 17
P.L. 0.3433 Diff. P. logs. +5
log. Tab. IX. 3.5456
log. Tab. IX. 3.8889
20
True distance
Distance N. A. at XVIII>
Difference
Approximate interval
Add
Approx. Gr. time
Corr. Tab. X.
True Gr. time
Gr. time by Chronom.
Chronom. and lunar differ only
and therefore the chronometer may be considered as going well.
This example, worked by Bowditch's First Method, gives the true distance 45 &
44", differing from the above 59", in consequence of the omission by Bowditch of
the small corrections. This difference would produce an error of 2 m * 10 s - in the
Greenwich time, and consequently the longitude in this case deduced by Bowditch's
method would be in error 32'.5 ; that is, more than half a degree.
EXAMPLE II.
In Lat. 55 20' S., Long. 120 25' W., by account, on August 29th, 1855, about
9 h - 40 ra< P. M., the Greenwich chronometer showing 5 h - 35 m - 46' .2 and from previous
rate supposed slow 5 m> 12'- ; the following distance and altitudes are found, being
the mean of six observations corrected for index errors. Observed distance of Fo-
malhaut and C 's farthest limb 46 30' 23" ; observed alt. _C_ 6 26' 10" ; observed
alt. Fomalhaut52 34' 40"; barometer 31 inches; thermometer 20 ; height of the
eye above the sea 18 feet. What is the error of the chronometer according to
these observations?
h. m. a.
Chronometer 5 35 46.2
(Slow) -H 5 12
Greenw. date Aug. 29 d - 17 40 58.2
Obs'd Alt. .1
Dip Tab. I.
d 's aug. semid.
([^ App. Alt.
d's Red. R. Tab. IV.
Barom. Tab. IV. A.
Therm. Tab. IV. B.
d'sRed. R.
CsRed.P.
O I
6 26 10
49
+16 28
6 38 29
4-16
4-32
8 36
60 20
51 44
Preparation of the Data.
<Ts semid. N. A.
Aug. Tab. II.
d 's aug. Semid.
Obs'd alt. >fc
Dip
#'s App Alt.
#'s Red. R. Tab. IV.
Barom. Tab. IV. A.
Therm. Tab. IV. B.
#'s Red. R.
#'5 Par.
#' Red. P.j-R.
11
1 H
16 26.3
-f-2.0
(TsPar.N.A.
Aug. Tab. III.
d'sRed.P.
66 if*
-1-8.3
16 28.3
60 20.1
o / //
52 34 40
4 9
52 30 31
Obs'd distance ;fc
C 's aug. semid.
App. Dist.
<[ 1 46 30 23
1628
46 13 55
Id
4- 2
4- 5
1 20
Tao
CORRECTION OF LUNAR DISTANCES.
Computation of the True Distance.
A.
log. A. Tab. V. 0.0274
log. 'sRed.P.&R.Tab.IX.3.4919
log. sin. d 's App. Alt 9.0632
log. cot. App. Dist 9.9813
c.
log. C. Tab. V. 9.9999
logo's Red. P.& R. TabJX. 1 .9031
log. sin. >f;'s App. Alt. 9.8995
log. cot. App. Dist. 9.9813
C log. Tab. IX. 1.7838
i 1st Part 5|C's dorr. 1' 1"
D.
log. D. Tab. V. 0.0267
log. #'s Red. P. & R. 1.9031
log. sin. d 's App. Alt 9.0632
log. cosec. App. Dist. 0.1414
App. Dist. 46 13
1st corr. 51
2c? corr. Tab. VI.
Contraction of d 's )
Semid. Tab. VII. 5 '
dorr, for romnrfssion -4-
55
32
22
17
14
C log. Tab. IX.
< 1st Part C 's corr.
B.
log. B. Tab. V.
log. d'sKed.P.&R.
log. sin. ^s App. Alt.
log. cosec. App. Dist.
< log. Tab. IX.
1 2d Part <[ 's corr.
<l ' whole corr.
log. N
log. sin. Lat. 55 S.
log. Tab. IX.
2.5638
-J-6' 6"
0.0001
3.4919
9.8995
0.1414
3.5329
56' 51"
50' 15"
1.230
9.913
log. Tab. IX.
J 2d Part >jc's corr.
5JC's whole corr. ' -> ^
1.1344
+0' 14"
-M)' 47"
H-1.143
True Distance 45 22
32
To find the Error of the Chronometer.
True Distance
Dist.N.A.atXV>
Difference
Approx. interval
Add
Approx. Gr. time
Corr. Tab. X.
True Gr. time
45 22' 32"
43 51 59
P.L.
log. Tab. IX.
log. Tab. IX.
0.2527 Diff. P. Logs.
3.7350
1 30 33
2^" 42 111 ' I**
15
3.9877
17 42 1
+1
17 42 2
Gr. time by chronom. 17 40 58
Chron. and lunar differ I 4
and, the distances having been observed with care, the chronometer has probably
changed its rate. A second observation confirming this, we must, from repeated
lunars, determine a new rate, which may be used until an opportunity occurs of
rating at a fixed place whose longitude is tolerably well known.
This example, worked by Bowditch's Second Method, gives the true distance 45
2V 31", which is in error I 7 1", and would produce in the longitude deduced from it
in this case an error of about 28'.
* This value of log. N. is formed from Tab. XII. by the rule in the note on page 8 of this Appea-
dix: tbus
<C's dec. 4 N., App. Dist. 46 in Tab. XII. A. gives 1st Part of N 1"
5fc's dec. 30 S., App. Dist. 46 in Tab. XII. B. gives 2d Part ofN 16
N-17
the log. of which is in Tab. IX. 1.230.
12
EXPLANATION OF THE TABLES.
TABLE I. Dip of the Sea Horizon^ computed by Delambre's formula (Astroi
mie, Vol. III., Chap. XXXVI.), which, when feet are substituted for metres, is
D = 58".8
where F = height of the eye above the level of the sea, in feet,
D == depression of the sea horizon, in seconds.
TABLE II. Augmentation of the Moon's Semidiameter ^ computed by the formula
(Francoeur, Astron. Pratique, p. 58)
x = c s* sin h + } c 2 s 3 sin 2 h 4- c 2 s 3 ,
where h = moon's apparent altitude,
s = moon's horizontal semidiameter,
x = augmentation of semidiameter for the altitude A,
log c = 5.25021.
TABLE III. Augmentation of the Moon's Horizontal Parallax^ or 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, computed by the
formulas
A,r=,r(J-l), i= y (1 _J, s . n2(/)) ,
where w =- equatorial horizontal parallax,
<f> = latitude,
e = eccentricity of the meridian, log e 3 = 7.81602,
A TT = augmentation of the horizontal parallax for the latitude cj>.
TABLE IV. Mean Reduced Refraction for Lunars^ computed by the formula
-
cos h sin h '
* Tables I., II., and IX., which are not peculiar to my method, are inserted to save a reference to
other works for them ; so that the computer requires, in connection with this volume, only a table of
logarithmic sines and tangents. These three tables have, however, been recomputed, as stated in the
u Explanation."
13
EXPLANATION
where h = the apparent altitude,
r = mean refraction, barometer 30 inches, Fahrenheit's thermometer 50,
r' = mean reduced refraction for lunars.
The refractions employed are BESSEL'S, and were taken from his table (Astro*
nomische Untersuchungen, Vol. I. p. 200), which gives directly K =z r tan h.
TABLES IV. A. AND IV. B. Corrections of the Mean Refraction for the Height
of the Barometer and Thermometer, deduced also from BessePs table above cited.
These tables serve for correcting either r or r', according as the one or the other is
taken as the argument.
TABLE V. Logs, of A, B, C, and D, for computing the First Correction of the
Lunar Distance, computed by the formulas
sin A
p _ ^sin^g-Aff) n __
'
sin 2 h '
where h = moon's apparent altitude,
H = sun's, planet's, or star's apparent altitude (denoted in the tables by O '
or ;fc's App. Alt.),
A h = difference of <C 's apparent and true altitudes,
A H = difference of Q's or jfc's apparent and true altitudes,
log K' = .000126,
and A A, A H were computed from the arguments " apparent altitude " and " re-
duced parallax and refraction " by the formulas
A h = (p r 1 ) K' cos h, &H=(R' P) cos JJ,
where p r' = <C 's reduced parallax and refraction,
R' P== O' s r sfc's reduced parallax and refraction,
p = < 's horizontal parallax -f- A tr (Table III.),
P = O's or j|c's horizontal parallax (for a star P = 0),
r' = C's reduced refraction (Table IV.),
R' = O's or #'s reduced refraction (Table IV.).
When h and H become 90, the values of B and D assume the indeterminate
forms
R n
^ = 6' J)= 6' .
and therefore, for computing their logarithms near the end of the table, the formulas
were transformed as follows :
B = C K 1 [1-*- (R 1 P) sin 1" sin H] ,
D = ^ [1 (p r') K 1 sin 1" sin h] .
By means of Logs. A , J5, C, and D, the first correction of the distance is found by
the following formulas :
14
OF THE TABLES.
if
d = apparent distance of C from or #.,
A! d = first correction,
A' = A (p r') sm h cot d,
B' = B (p r') sin Jfcosec d,
C' = C ( R' P) sin H cot d,
D' = U (' P) sin A cosec d,
then
A 1 d = (4'-h.B')-4-(C' + j)/),
and in the directions for using the tables, A 1 -+- B 1 is called the " whole correction
for <," and C' 4- D 1 the " whole correction for or #."
TABLE VI. Second Correction of the Lunar Distance^ computed by the formula
&z d = J A! <F sin I" cot d.
Strictly, this formula should be
AS d = A & sin 1" cot d,
where A <Z = whole correction of distance = A! e -H A 2 d , so that by entering the
table first with A t rf we find only an approximate value of A 2 d. But if with this ap-
proximate value we form the approximate whole correction A! d -f- A 3 d, and enter
with this as the argument in the place of Aj d, we have the true value of A 2 d. It is
evident, however, from the table itself, that, in most practical cases, this degree of
precision is unnecessary.
TABLE VII. For finding the Correction of the Lunar Distance for the Contrac*
tion of the Moon's Semidiameter (by refraction), computed by the formula.
A s = A s ^_ r ,)2 cos2
where the notation already employed is preserved, and
A $ = contraction of the moon's vertical semidiameter at the altitude h,
A * = contraction of the inclined semidiameter, or of that which lies in the dL
rection of the lunar distance.
This table is subdivided into Tables VII. A. and VII. B. If we put
* = (p
then
A* = (4'-i-#) 8 xC
where / is an arbitrary factor employed to give g convenient integral values r and m
these tables we have taken / = 18000000 ; A S Q , A s , p r', and A 1 -f- B 1 being
all expressed in seconds. Table VII. A. gives the value of g with the arguments
p r 1 and h ; and Table VII. B. gives A s with the arguments A! -H B' and g.
To find A s from the arguments p r' and 7t, the mean value of r' for the altitude
A was added to p r', so that p became known ; whence also the semidiameter,
15
EXPLANATION
and consequently, by .neans of the refraction tables, the contraction A S Q . The value
of A s given by Table VII. B. is therefore that which corresponds to a mean state of
the air, and in extreme cases may be in error 4", but in no probattle case will it be in
error more than 1". The true value of A s might, however, always be found by cor-
recting it, as refraction, by Tables IV. A. and IV. B.
TABLE VIII. For finding the Correction of the Lunar Distance for the Contra^"
lion of the Sun's Semidiameter (by refraction), computed by the formula
where, in addition to the notation already employed, A S Q = contraction of the sun's
vertical semidiameter at the altitude H; A , S = contraction of the inclined semi-
diameter. Table VIII. A., with the arguments R' P and H, gives a number
in which A S is taken for a mean value of the sun's semidiameter, P is assumed al
8".5, and F is an arbitrary factor = yfo ; jR' P, C' -4- JDf, A S , and A S being all
expressed in seconds. Table VIII. B., with the arguments O -+ D 1 and G, gives
This value of A S is that which belongs to the actual state of the air, but is fjbr a
mean value of the sun's semidiameter, the variations of which would not chang the
tabular value by more than 0".5 in any case. \
*\ < ; '\ *-** ' ' '
TABLE IX. Logarithms of Seconds. This table contains the* common loga- ,
rithm answering to the arc (either space or time) in the argument. For the con-
venience of the navigator, this table is given with the argument, degrees, minutes*
and seconds, or hours, minutes, and seconds, for every ten seconds, at the side, the^
unit figure of the seconds being found at tba top.
The logarithm is given with the proper ? caracteristic prefixed. k
TABLE X. This table contains the correction for second differences of the moon's
motion.
TABLE XI. contains the values of log. N for the distances from the sun, com-
puted by the following formula :
-^\;
sin d tan d /
where = <C 's equatorial horizontal parallax,
A = sun's declination,
d = <L 's declination,
d = angular distance of the moon and sun referred to the centre of the earth,
Q . ^
JV' = r, - o o .v i f r which the value of N 1 is taken corresponding to -
/(l e^ sin-* <p)
< = 45, or log. N' = 7.8170.
16
OF THE TABLES.
TABLE XII. For finding the Value of N. By this table an approximate value
of IV may be readily found, with sufficient accuracy for ordinary purposes. When
very great accuracy is desired, the formula given in the explanation of Table XI.
should be used. In Table XII. the moon's horizontal parallax is assumed at its
mean value == 57' 30", and the two parts of IV are separately tabulated by the
formulas
a (= first part of IV) = IV' TT sin S cotan d,
I (= second part of IV) = N 1 it sin A cosec d ;
from which IV is found by the formula
NOTE. The demonstration of most of the formulas cited in the preceding explanation is girea IB
the Astronomical Journal (Cambridge, Mass.)} Vol. II., $Tos. 3 and 4.
17
TABLES.
TABLE I.
TABLE II.
TABLE III.
Dip of the Sea
Horizon.
Augmentation of the Moon's Semidiaraeter.
Augmentation of the
Moon's Hor. Parallax.
Annar-
}>' s Semidiameter.
Lati-
}>'s Horizontal
Height
of the
Dip of the
Horizon.
Af^JBI
ent
Altitude
14'
15'
16'
17'
tude
ofOb-
serva-
Parallax.
Eye.
of J).
30"
0"
30"
0"
30"
0"
tion.
53'
57'
61'
Feet.
If
n
n
/<
n
n
o
n
I
g
00
0.1
0.1
0.1
0.1
0.2
0.2
0.0
0.0
0.0
1
59
2
0.6
0.6
0.7
0.7
0.8
0.8
2
0.0
0.0
0.0
2
1 23
4
1.0
1.1
1.2
1.3
1.4
1.5
4
0.1
0.1
0.1
3
1 42
6
1.5
1.6
1.7
1.9
2.0
2.1
6
0.1
0.1
0.1
4
1 58
8
2.0
2.1
2.3
2.4
2.6
2.7
8
0.2
0.2
0.2
5
2 11
10
2.4
2.6
2.8
3.0
3.2
3.4
10
0.3
0.3
0.4
6
2 24
12
2.9
3.1
3.3
3.6
3.8
4.0
12
0.5
0.5
0.5
7
2 36
14
3.4
3.6
3.9
4.1
4.4
4.7
14
0.6
0.7
0.7
8
246
16
3.8
4.1
4.4
4.7
5.0
5.3
16
0.8
0.9
0.9
9
2 56
18
4.3
4.6
4.9
5.2
5.6
5.9
18
1.0
1.1
1.1
10
306
20
4.7
5.1
5.4
5.8
6.1
6.5
20
1.2
1.3
1.4
11
3 15
22
5.2
5.5
5.9
6.3
6.7
7.1
22
1.5
1.6
1.7
12
3 24
24
5.6
6.0
6.4
6.8
7.3
7.7
24
1.7
1.9
2.0
13
3 32
26
6.0
6.5
6.9
7.4
7.8
8.3
26
2.0
2.2
2.3
14
3 40
28
6.5
6.9
7.4
7.9
8.4
8.9
28
2.3
2.5
2.6
15
3 48
30
6.9
7.3
7.9
8.4
8.9
9.5
30
2.6
2.8
3.0
16
3 55
32
7.3
7.8
8.3
8.9
9.4
10.0
32
2.9
3.1
3.4
17
4 02
34
7.7
8.2
8.8
9.4
10.0
10.6
34
3.3
3.5
3.8
18
09
36
8.1
8.6
92
9.8
10.5
11.1
36
3.6
3.9
4.1
19
16
38
8.4
9.0
97
10.3
10.9
11.6
38
4.0
4.3
4.6
20
23
40
8.8
9.4
10.1
10.7
11.4
12.1
40
4.3
4.6
5.0
21
29
42
9.2
9.8
10.5
11.2
11.9
12.6
42
4.7
5.0
5.4
22
36
44
9.5
10.2
10.9
11.6
12.3
13.1
44
5.0
5.4
5.8
23
42
46
9.8
10.5
11.3
12.0
12.8
13.6
46
5.4
5.8
6.2
24
48
48
10.2
10.9
11.6
12.4
13.2
14.0
48
5.8
6.2
6.6
25
4 54
50
10.5
11.2
12.0
12.8
13.6
14.4
Ufr
6.1
6.6
7.1
26
5 00
52
10.8
11.5
12.3
13.1
14.0
14.9
52
6.5
7.0
7.5
27
5 06
54
11.1
11.8
12.7
13.5
14.4
15.3
54
6.8
7.4
7.9
28
5 11
56
11.3
12.1
13.0
13.8
14.7
15.6
56
7.2
7.7
8.3
29
5 17
58
11.6
12.4
13.3
141
15.1
16.0
58
7.5
8.1
8.6
30
5 22
60
11.8
12.7
i3.5
14.4
15.4
16.3
60
7.8
8.4
9.0
35
5 48
62
12.1
12.9
13.8
14.7
15.7
16.6
62
8.1
8.8
.9.4 ;
40
6 12
64
12.3
13.2
14.1
15.0
16.0
16.9
64
8.4
9.1
9.7
45
6 34
66
12.5
13.4
14.3
15.2
16.2
17.2
66
8.7
9.4
10.0
50
6 56
68
12.7
13.6
14.5
15.5
16.5
17.5
68
9.0
9.7
10.3
55
7 16
70
12.9
13.8
14.7
15.7
16.7
17.7
70
9.2
9.9
10.6
60
7 35
72
13.0
13.9
14.9
15.9
16.9
17.9
72
9.5
10.2
10.9
65
7 54
74
13.1
14.1
15.0
16.0
17.1
18.1
74
9.7
10.4
11.1
70
8 12
76
13.3
14.2
15.2
16.2
17.2
18.3
76
9.8
10.6
11.3
75
8 29
78
13.4
14.3
15.3
16.3
17.4
18.4
78
10.0
10.8
11.5
80
846
80
13.5
14.4
15.4
16.4
17.5
18.6
80
10.1
10.9
11.7
85
9 02
82
13.5
14.5
15.5
16.5
17.6
18.7
82
10.3
11.0
11.8
90
9 18
84
136
14.6
15.6
16.6
17.6
18.7
84
10.3
11.1
11.9
95
9 33
86
13.6
14.6
15.6
16.6
17.7
18.8
86
10.4
11.2
12.0
100
9 48
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
19
TABLE IV.
Mean Reduced Refraction for Lunars. Barometer 30 inches. Fahrenheit's Thermometer fiCR
Apparent
Altitude.
Reduced
Refraction.
Biff,
to '.
Apparent
Altitude.
Reduced
Refraction.
Apparent
Altitude.
Reduced
Refraction.
Apparent
Altitude.
Reduced
Refraction.
O 1
5
i H
9 54.2
(/
.6
O 1
10
i n
5 24.1
o /
15
i //
3 41.7
27
2 7.S
5
9 46.3
.5
5
5 21.6
10
3 39.4
27 30
2 5.7
10
9 38.6
.5
10
5 19.2
20
3 37.1
28
2 3.7
15
9 31.0
.5
15
5 16.8
30
3 34.9
28 30
2 1.7
20
9 23.7
.4
20
5 14.4
40
3 32.7
29
59.8
25
9 16.5
1.4
25
5 12.1
50
3 30.6
29 30
58.0
5 30
9 9.5
1.4
10 30
5 9.8
16
3 28.5
30
56.2
35
9 2.7
1.3
35
5 7.5
10
3 26.5
30 30
54.5
40
8 56.0
1.3
40
5 5.3
20
3 24.5
31
52.8
45
8 49.5
1.3
45
5 3.1
30
3 22.6
31 30
51.2
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 58.8
50
3 18.8
32 30
1 48.2
6
8 309
1.2
11
4 56.7
17
3 16.9
33
1 46.7
5
8 24.9
1.2
5
4 54.6
10
3 15.1
33 30
1 45.3
10
8 19.1
1.1
10
4 52.5
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 48.5
40
3 9.9
35
1 41.4
25
8 2.4
1.1
25
4 46.6
50
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 5.0
36 30
1 37.8
40
7 46.7
1.0
40
4 40.8
20
3 3.4
37
36.7
45
7 41.7
1.0
45
4 38.9
30
3 1.8
37 30
35.6
50
7 36.7
1.0
50
4 37.1
40
3 0.3
38
34.5
55
7 31.9
0.9
55
4 35.3
5C
2 58.8
38 30
33.5
7
7 27.2
0.9
12
4 33.5
19
2 57.3
39
32.5
5
7 22.6
0.9
5
4 31.7
10
2 55.9
39 30
31.5
10
7 18.0
0.9
10
4 30.0
20
2 54.4
40
30.6
15
7 13.6
0.9
15
4 28.3
30
2 53.0
40 30
29.6
20
7 9.2
0.9
20
4 26.6
40
2 51.6
41
28.7
25
7 4.9
0.8
25
4 24.9
50
2 50.3
41 30
27.8
7 30
7 0.8
0.8
12 30
4 23.2
20
2 49.0
42
27.0
35
6 56.6
0.8
35
4 21.6
10
2 47.6
42 30
26.2
40
6 52.6
0.8
40
4 20.0
20
2 46.4
43
25.4
45
6 48.6
0.8
45
4 18.4
30
2 45.1
43 30
24.6
50
6 44.8
0.8
50
4 16.8
40
2 43.8
44
23.8
55
6 40.9
0.7
55
4 15.2
50
2 42.6
44 30
23.1
8
6 37.2
0.7
13
4 13.7
21
2 41.4
45
22.4
5
6 33.5
0.7
5
4 12.2
10
2 40.2
46
21.0
10
6 29.9
0.7
10
4 10.7
20
2 39.0
47
19.6
15
6 26.3
0.7
15
4 9.2
30
2 37.9
48
18.4
20
6 22.8
0.7
20
4 7.7
40
2 36.7
49
17.2
25
6 19.4
0.7
25
4 6.3
50
2 35.6
50
16.0
8 30
6 16.0
0.7
13 30
4 4.8
22
2 34.5
51
15.0
* 35
6 12.7
0.6
35
4 3.4
10
2 33.4
52
13.9
40
6 9.5
0.6
40
4 2.0
20
2 32.4
53
13.0
45
6 6.3
0.6
45
4 0.6
30
2 31.3
54
12.0
50
6 3.1
0.6
50
3 59.3
40
2 30.3
55
11.1
55
6 0.0
0.6
55
3 57.9
50
2 29.2
56
10.3
9
5 57.0
0.6
14
3 56.6
23
2 28.2
57
9.5
5
5 54.0
0.6
5
3 55.3
20
2 26.3
58
8.7
10
5 51.1
0.6
10
3 54.0
40
2 24.4
59
8.0
15
5 48.2
0.6
15
3 52.7
24
2 22.5
60
7.3
20
5 45.3
0.6
20
3 51.4
20
2 20.7
62
6.0
25
5 42.5
0.5
25
3 50.1
40
2 18.9
64
4.9
9 30
5 39.8
0.5
14 30
3 48.9
25
2 17.2
66
3.8
35
5 37.0
0.5
35
3 47.6
20
2 15.5
68
2.9
40
5 34.4
0.5
40
3 46.4
40
2 13.9
70
2.0
45
5 31.7
0.5
45
3 45.2
26
2 12.3
73
1.0
50
5 29.2
0.5
50
3 44.0
20
2 10.8
76
0.1
55
5 26.6
0.5
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
20
TABLE IV. A.
Correction of the Mean Refraction for the Height of the Barometer.
Barometer.
MEAN REFRACTION.
Barometer.
0'
1'
2'
3'
4'
5'
6'
V
8'
9'
1O
Subtract.
3('i
34
30
6
3tt
o
3fi
i
30
6'
30
30'
,!,
34
30^
t
Add.
27.50
48
a
51
2
5
7
10
12
15
17
20
23
25
28
30
33
35
38
40
43
45
27.55
2
9
7
10
12
15
17
20
22
25
27
80
32
35 37
40
42
45
47
50
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
It)
19
21
24
26
28 31
33 '36
38
40
43
45
48
27.70
2
5
7
9
11
14
16
18
21
23
25
28
30
32
35
.37
39
42
44
47
27.75
2
4
7
9
11
13
16
18
20
2.3
25
27
29
32
34
36
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
3032
34
36
38
40
43
27.95
2
4
6
8
10
12
14
16
18
21
23
25
27
29
31
33
35
-37
39
42
28.00
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
,38
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
Q
2
4
6
7
9
11
13
15
17
19
20
22
24
26
28
30
32
34
36
37
28.20
2
4
5
7
9
11
13
14
16
18
20
22
24
25
27
29
31
33
35
36
28.25
2
3
5
7
9
10
12
14
16
18
19
21
23
25
26
28
30
32
34.
35
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
2 1 J
31
32
28.45
2
3
5
G
8
9
11
12
14
16
17
19
20
22
23
25
27
28
30
31
28.50
1
3
4
6
7
9
10
12
14
15
17
18
20
21
23
24
26
27
29
30
31.50
28.55
1
3
4
6
7
9
10
12
13
15
16
17
19
20
22
23
25
26
28
29
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
1
3
4
5
7
8
9
11
12
14
15
16
18
19
20
22
23
25
26
27
31.35
28.70
1
3
4
5
6
8
9
10
12
13
14
16
17
18
20
21
22
24
25
26
31.30
28.75
1
2
4
5
6
7
9
10
11
13
14
15
16
18
19
20
21
23
24
25
31.25
28.80
1
2
4
5
6
7
8
10
11
12
13
14
16
17
18
19
21
22
23
24
31.20
2885
1
2
3
5
6
7
8
9
10
12
13
14
15
16
17
19
20
21
22
23
31.15
28.90
1
2
3
4
5
7
8
9
10
11
12
13
14
16
17
18
19
20
21
22
31.10
28.95
1
2
3
4
5
6
7
8
9
11
12
13
14
15
16
17
18
19
20
21
31.05
29.00
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
31.00
29.05
1
2
3
4
5
8
7
8
9
10
11
11
12
13
14
15
16
17
18
19
30.95
29.10
1
2
3
4
4
5
6
7
8
9
10
11
12
13
14
15
15
16
17
18
30.90
29.15
1
2
3
3
4
5
6
7
8
9
9
10
11
12
13
14
15
15
16
17
30.85
29.20
1
2
2
3
4
5
6
6
7
8
9
10
10
11
12
13
14
15
15
16
30.80
29.25
2
3
4
4
5
6
7
8
8
9
10
11
11
12
13
14
14
15
30.75
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
1
2
2
2
3
3
4
4
4
5
5
5
6
6
6
7
7
30.35
29.70
1
1
2
2
2
3
3
3
4
4
4
5
5
5
5
6
6
30.30
29.75
1
1
1
2
2
2
3
3
3
3
4
4
4
4
5
5
5
30.25
29.80
1
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
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
00
30.00
Subtract.
30'
30
&
30
30'
30
30
6'
3fl
1
30'
6'
30'
i
36
o'
Add.
0'
1'
2'
3'
4'
5'
6'
7'
8'
9'
10'
MEAN REFRACTION.
21
TABLE IV. B.
Correction of the Mean Refraction for the Height of the Thermometer.
Thermora.
MEAN REFRACTION.
Thermom.
O'
1'
2'
3'
4'
5'
6'
7'
8'
9'
10
Add.
6
36
30'
I
36
6'
30'
t
3ft
6
30
6'
3#
6'
3#
6'
sfi
& 3ft
6'
Add.
Q
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
11
15
19
22
26
30
34
38
42
47
51
55 60
64
69
74J79
84
6
i t A
4
7
11
14
18
22
25
29
33
37
41
45
49
53
57
62
66
71
76
80
4
2
3
T
10
14
17
21
24
28
31
35
39
43
47
51
55
59
64
68
72
77
2
3
7
10
13
16
20
23
27
30
34
37
41
45
49
53
57
61
65
69
74
2
a
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
59
63
67
4
6
3
6
8
11
14
17
20
23
26
29
32
36
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
2
4
6
8
10
12
14
16
18
20
22
24
27
29
31
34
36
39
41
44
19
20
2
4
6
8
9
11
13
15
17
19
22
24
26
28
30
33
35
37
40
42
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
20
22
24
26
28
30
32
34
36
24
25
2
3
5
6
8
9
11
13
14
16
18
19
21
23
25
27
29
31
33
35
25
26
3
4
6
7
9
11
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
38
30
32
27
28
3
4
5
7
8
10
11
12
14
15
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
IS
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
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
fi
8
9
10
10
11
12
13
13
40
41
2
2
3
3
4
4
5
6
6
7
8
9
9
10
11
11
12
41
42
1
2
2
3
3
4
4
5
5
e
7
7
8
8
9
9
10
11
42
43
1
2
2
3
3
3
4
4
5
je
6
6
**
7
8
8
9
9
43
44
1
1
2
2
3
3
3
4
4
4
5
5
6
6
7
7
8
8
44
45
1
1
1
1
2
2
2
3
3
3
4
4
4
5
5
6
6
6
7
45
46
1
1
1
1
2
2
2
2
2
3
3
4
4
4
4
5
5
5
46
47
1
1
1
1
1
I
2
2
2
9
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.
\
30'
II
3tf
3#
1
30'
i
30
6
30
6'
30
6'
30"
4
3ft
6'
30
*
Add.
Thermo rn.
0'
1'
2'
3'
4'
5'
6'
7'
8'
9'
10'
Tficrrnoni.
MEAN REFRACTION.
TABLE IV. B.
Correction of the Mean Refraction for the Height of the Thermometer.
Thermom.
MEAN REFRACTION.
Thermom.
O'
1'
2'
3'
4'
5'
6'
V
8'
9'
10'
Subtract.
4
36
\
30'
4
3ft
6
3ft
4
3ft
6
3 ft
6'
3ft
4
30'
6'
3ft
6'
30
6'
subtract.
o
50
/
50
51
1
i
i
i
1
1
1
i
1
i
1
i
51
52
1
1
1
1
1
i
i
i
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
1
1
1
2
2
2
2
3
3
3
3
4
4
4
5
5
5
54
55
1
1
1
2
2
2
3
3
3
4
4
4
5
5
5
6
6
6
55
56
1
1
2
2
2
3
3
4
4
4
5
5
G
6
G
7
7
8
56
57
1
2
2
2
3
3
4
4
5
5
G
6
6
7
8
8
8
9
57
58
1
2
2
3
3
4
4
5
5
6
6
7
7
8
9
9
10
10
58
59
1
1
2
2
3
3
4
4
5
5
6
6
7
8
8
9
10
10
11
12
59
60
1
1
2
2
3
3
4
5
5
6
7
7
8
9
9
10
11
11
12
13
60
61
1
1
2
3
3
4
4
5
6
7
7
8
9
9
10
11
12
12
13
14
61
62
1
1
2
3
3
4
5
6
6
7
8
9
9
10
11
12
13
14
15
15
62
63
1
1
2
3
4
5
5
6
7
8
8
9
10
11
12
13
14
15
16
17
63
64
1
2
2
3
4
5
6
7
7
8
9
10
11
12
13
14
15
16
17
18
64
65
1
2
3
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
65
66
1
2
3
4
5
6
6
7
8
9
10
11
12
14
15
16
17
18
19
20
66
67
1
2
3
4
5
6
7
8
9
10
11
12
13
14
16
17
18
19
20
22
67
68
1
2
3
4
5
G
7
8
9
11
11
13
14
15
1G
18
19
20
22
23
68
69
1
2
3
4
5
7
8
9
10
11
12
13
15
16
17
19
20
21
23
24
69
70
1
2
3
5
6
7
8
9
10
12
12
14
16
17
18
20
21
22
24
25
70
71
1
2
4
5
6
7
8
10
11
12
13
15
16
18
19
20
22
23
25
27
71
72
1
2
4
5
6
8
9
10
11
13
14
16
17
18
20
21
23
25
26
28
72
73
1
3
4
5
7
8
9
11
12
13
14
16
18
19
21
22
24
26
27
29
73
74
1
3
4
5
7
8
10
11
12
14
15
17
18
20
22
23
25
27
28
30
74
75
1
3
4
6
7
8
10
11
13
14
16
18
19
21
22
24
26
28
29
31
75
76
1
3
4
6
7
9
10
12
13
15
16
18
20
22
23
25
27
29
31
32
76
77
1
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
9
11
13
14
16
18
20
21
23
25
27
29
31
33
35
78
79
2
3
5
6
8
10
11
13
15
17
18
110
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
83
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
5
7
9
11
13
14
16
18
20
22
24
26
28
31
33
35
37
40
82
83
2
5
7
9
11
13
15
17
19
21
23
25
27
29
31
34
36
38
41
83
84
2
6
8
9
11
13
15
17
19
21
23
26
28
30
32
35
37
39
42
84
85
2
6
8
10
12
14
16
18
20
22
2426
29
31
33
36
38
40
43
85
86
2
6
8
10
12
14
16
18
20
23
25 27
29
32
34
37
39
42
44
86
87
2
6
8
10
12
14
17
19
21
23
25 28
30
32
85
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
22
24
27; 29
32
34
37
39
42
45
48
89
90
2
4
7
9
11
13
16
18
20
23
25
27 30
32
35
38
40
43
46
49
90
91
2
4
7
9
11
14
16
18
21
23
25
28|31
33
3G
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
46
49
52
93
94
2
5
7
10
12
14
17
19
22
25
27
3033
35
38
41
44
47
50
53
94
95
2
5
7
10
12
15
17
20
22
25
28
30 ! 33
3G
39
42
45
48
51
54
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
5
8
11
13
16
19
21
24
27
30
33 36
39
42
45 49
52
55
59
99
100
3
5
8
11
13
16
19
22
25
28
31
3437
40
43
46 50
53
56
60
100
Subtract.
4
3*
1
36
3ft
3ft
4
30
4
30
& 3ft
4
3ft
30
6'
3ft
6
Subtract.
JT hcrrnom.
1'
2'
3'
4'
5'
6'
7'
'
9'
10'
Thflrmnm
MEAN REFRACTION.
x nemioin >
23
TABLE V. LOG. A.
Logs A, B, C, and D, for Computing the First Correction of the lunar L/istanco.
App.
Alt
REDUCED PARALLAX AND REFRACTION O.F D.
Alt.
of J>
41'
42'
43'
44'
45'
46'
47'
4S'
49'
5O'
51
5*2'
S3'
54'
5ff
5 0'
.0288
0295
0301
0308
0315
0321
0328
0335
0341
0348
0355
0361
036&
2
.0286
0293
0299
0306
0313
0319
0326
0333 0339
0346
0352
0359
0366
4
.0284
0291
0297
0304
0311
0317
0324
0330 0337
0344
0350
0357
0363
!
1
6
.0282
0289
0296
0302
0309
0315
0322
0328
0335
0341
0348
0354
0361
8
.0281
0287
0294
0300
0307
0313
0320
0326
0333
0339
0346
0352
0359
5 10
.0279
0285
0292
0298
0305
0311
0318
0324
0331
0337
0344
0350
0356
12
.0277
0284
0290
0296
0303
0309
0316
0322
0329
0335
0341
0348
0354
14
.0275
0282
0288
0295
0301
0307
0314
0320
0327
0333
0339
0346
0352
16
.0274
0280
0286
0293
0299
0306
0312
0318
0325
0331
0337
0344
0350
18
.0272
0278
0285
0291
0297
0304
0310
0316
0323
0329
0335
0341
0348
5 20
.0270
0277
0283
0289
0296
0302
0308
0314
0321
0327
0333
0339
0346
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
0295
0301
0307
0313
0319
0325
0331
0337
0344
5 30
.0262
0268
0275
0281
0287
0293
0299
0305
0311
0317
0323
0329
0335
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 j 0270
0276
0282
0288
0294
0300
0306
0312
0318
0324
0330
'J336
38
0262
0268
0274
0280
0286
0292
0298
0304
0310
0316
0322
0328
033-1
1
5 40
0261
0267
0273
0279
0285
0290
0296
0302
0308
0314
0320
03S6
0?,32
1
42
0259
0265
0271
0277
0283
0289
0295
0301
0306
0312
0318
Of,24
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
0255
0261
0267
0272
0278
0284
0290
0296
0301
0307
0313
0319
0324
5 50
0253
0259
0265
0271
0277
0282
0288
0294
0300
0305
0311
0317
0323
' 52
0252
0258
0264
0269
0275
0281
0287
0292
0298
0304
0309
0315
0321
54
0251
0256
0262
0268
0274
0279
0280
0291
0296
0302
0308
0313
0319
56
0249
0255
0261
0266
0272
0278
0283
0289
0295
0300
0306
0312
0817
58
0248
0254
0259
0265
0271
0276
0282
0287
0293
0299
0304
0310
0316
6
0247
0252
0258
0263
0269
0275
0280
0286
0291
0297
0303
0308
0314
2
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
026'J
0274
0280
0285
0291
0296
0302
0307
,
6 10
0240
0246
0251
0256
0262
0267
0273
0278
0284
0289
0295
0300
0306
12
0239
0244
0250
0255
0261
0266
0271
0277
0282
0288
0293
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
0235
0240
0246
0251
0257
0262
0267
0273
0278
0283
0289
0294
0299
6 20
0234
0239
0245
0250
0255
0261
0266
0271
0276
0282
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
0284
0289
0295
26
0236
0241
0246
0251
0257
0262
0267
0272
0277
0283
0288
0293
28
0234
0240
0245
0250
0255
0260
0266
0271
0276
0281
0286
0292
0297
6 30
0233
0238
0244
0249
0254
0259
0264
0270
0275
0280
0285
0290
0295
32
0232
0237
0242
0248
0253
0258
0263
0268
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
0259
0264
0269
0274
0279
0284
0290
6 40
0227
0232
0238
0243
0248
0253
0258
0263
0268
0273
0278
0283
0288
42
0220
0231
0236
0241
0246
0252
0257
0262
0267
0272
0277
0282
0287
44
02?.5
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
0284
48
0223
0228
0233
0238
0243
0248
0253
0258
0263
0268
0273
0278
0283
6 50
0222
0227
0232
0237
0242
0247
0252
0257
0262
0266
0271
0276
0281
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
C243
0248
0253
0258
0263
0267
0272
0277
58
0218
0223
0227
0232 0237
0242
0247
0252
0257
0261
0266
0271
0276
7
0217"
0722
0226
0231 0236
0241
0246
0251
0255
0260
0265
0270
0275
24
TABLE V. LOG. A.
Logs. A, B, C, and D, for Lunars.
A A?f
REDUCED PARALLAX AND REFRACTION OF d.
ot }>.
44'
45'
46'
47'
4'
49'
50'
51'
52'
53'
54'
55'
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
0257
0261
0266
0271
9
.0217
0222
0226
0231
0236
0241
0245
0250
0255
0260
0264
0269
12
.0215
0220
0225
0230
0234
0239
0244
0248
0253
0258
0262
0267
7 15
.0214
0219
0223
0228
0233
0237
0242
0247
0251
0256
0261
0265
18
.0213
0217
0222
0226
0231
0236
0240
0245
0250
0254
0259
0263
21
.0211
0216
0220
0225
0230
0234
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
0236
0240
0245
0249
0254
0258
7 30
.0207
0211
0216
0220
0225
0230
0234
0239
0243
0248
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
0207
0212
0216
0221
0225
0229
0234
0238
0243
0247
0252
42
.0202
0206
0210
0215
0219
0224
0228
0232
0237
0241
0246
0250
7 45
.0200
0205
0209
0213
0218
0222
0227
0231
0235
0240
0244
0248
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
.0136
0201
0205
0209
0214
0218
0222
0227
0231
0235
0239
0244
0248
57
.0195
0200
0204
0208
0212
0217
0221
0225
0229
0234
0238
0242
0246
8
.0194
0198
0203
0207
0211
0215
0219
0224
0228
0232
0236
0241
0245
3
.0193
0197
0201
0206
0210
0214
0218
0222
0227
0231
0235
0239
0243
6
.0192
0196
0200
0204
0208
0213
0217
0221
0225
0229
0233
0238
0242
9
0195
0199
0203
0207
0211
0215
0220
0224
0228
0232
0236
0240
12
0193
0198
0202
0206
0210
0214
0218
0222
0227
0231
0235
0239
8 15
0192
0196
0201
0205
0209
0213
0217
0221
0225
0229
0233
0237
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
0196
0200
0204
0208
0212
0216
0220
0224
0228
0232
8 30
0187
0191
0195
0199
0203
0207
0211
0215
0219
0223
0226
0230
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
OJ87
0191
0195
0199
0203
0207
0211
0215
0219
0223
0226
42
0182
0186
0190
0194
0198
0202
0206
0210
0214
0217
0221
0225
8 45
0181
0185
0189
0193
0197
0201
0205
0208
0212
0216
0220
0224
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
0185
0189
0192
0196
0200
0204
0208
0211
0215
0219
9
0176
0180
0184
0188
0191
0195
0199
0203
0206
0210
0214
0218
3
0175
0179
0183
0186
0190
0194
0198
0201
0205
0209
0213
0216
6
0174
0178
0182
0185
0189
0193
0197
0200
0204
0208
0211
0215
9
0173
0177
0181
0184
0188
0192
0196
0199
0203
0207
0210
0214
12
0172
0176
0180
0183
0187
0191
0194
0198
0202
0206
0209
0213
9 15
0171
0175
0179
0182
0186
0190
0193
0197
0201
0204
0208
0212
18
0170
0174
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
0179
0182
0186
0189
0193
0196
0200
0204
U207
9 30
0170
0174
0178
0181
0185
0188
0192
0195
0199
0203
0206
33
0170
0173
0177
0180
0184
0187
0191
0194
0198
0201
0205
36
0169
0172
0176
0179
0183
0186
0190
0193
0197
0200
0204
39
0168
0171
0175
0178
0182
0185
0189
0192
0196
0199
0203
42
0167
0170
0174
0177
0181
0184
0188
0191
0195
0198
0202
9 45
0166
0169
0173
0176
0180
0183
0187
0190
0194
0197
0201
48
0165
0169
0172
0176
0179
0182
0186
0189
0193
0196
0200
0203
51
0164
0168
0171
0175
0178
0182
0185
0188
0192
0195
0199
0202
54
0163
0167
0170
0174
0177
0181
0184
0187
0191
0194
0198
0201
57
0163
0166
0169
0173
0176
0180
0183
0186
0190
0193
0197
0200
10
0162
0165
0169
0172
0175
0179
0182
0186
0189
0192
0196
0199
25
TABLE V. LOG. A,
Logs. A, B, C, and D, for Lunars.
ir
of >'
REDUCED PARALLAX AND REFRACTION OF >
46'
49"
48'
49'
50'
51'
52'
53'
54'
55'
56'
57'
58'
100'
0162
0165
0169
0172
0175
0179
0182
0186
0189
0192
0196
0199
5
0160
0164
0167
0171
0174
0177
0181
0184
0187
0191
0194
0197
10
0159
0162
0166
0169
0172
0176
0179
0182
0186
0189
0192
0196
15
0158
0161
0164
0168
0171
0174
0178
0181
0184
0187
0191
0194
20
0156
0160
0163
0166
0170
0173
0176
0179
0183
0186
0189
0192
25
0155
0158
0162
0165
0168
0171
0175
0178
0181
0184
0188
0191
1030
.0154
0157
0160
0164
0167
0170
0173
0177
0180
0183
0186
0189
35
.0153
0156
0159
0162
0166
0169
0172
0175
0178
0181
0185
0188
40
.0151
0155
0158
0161
0164
0167
0171
0174
0177
0180
0183
0186
45
.0150
0153
0157
0160
0163
0166
0169
0172
0175
0179
0182
0185
50
.0149
0152
0155
0158
0162
0165
0168
0171
0174
0177
0180
0183
55
.0148
0151
0154
0157
0160
0163
0167
0170
0173
0176
0179
0182
11
.0147
0150
0153
0156
0159
0162
0165
0168
0171
0174
0177
0181
5
.0146
0149
0152
0155
0158
0161
0164
0167
0170
0173
0176
0179
10
0148
0151
0154
0157
0160
0163
0166
0169
0172
0175
0178
15
0146
0149
0152
0155
0158
0161
0164
0167
0170
0173
0176
20
0145
0148
0151
0154
0157
0160
0163
0166
0169
0172
0175
25
0144
0147
0150
0153
0156
0159
0162
0165
0168
0171
0174
1130
0143
0146
0149
0152
0155
0158
0161
0164
0167
0170
0172
35
0142
0145
0148
0151
0154
0157
0160
0162
0165
0168
0171
40
0141
0144
0147
0150
0153
0156
0158
0161
0164
0167
0170
45
0140
0143
0146
0149
0151
0154
0157
0160
0163
0166
0169
50
0139
0142
0145
0148
0150
0153
0156
0159
0162
0165
0167
55
0138
0141
0144
0146
0149
0152
0155
0158
0161
0163
0166
12
0137
0140
0143
0145
0148
0151
0154
0157
0159
0162
0165
5
0136
0139
0142
0144
0147
0150
0153
0156
0158
0161
0164
10
0135
0138
0141
0143
0146
0149
0152
0154
0157
0160
0163
15
0134
0137
0140
0142
0145
0148
0151
0153
0156
0159
0162
20
0133
0136
0139
0141
0144
0147
0150
0152
0155
0158
0160
25
0132
0135
0138
0140
0143
0146
0148
0151
0154
0157
0159
1230
0131
0134
0137
0139
0142
0145
0147
0150
0153
0155
0158
35
0130
0133
0136
0138
0141
0144
0146
0149
0152
0154
0157
40
0129
0132
0135
0137
0140
0143
0145
0148
0151
0153
0156
45
0129
0131
0134
0136
0139
0142
0144
0147
0150
0152
0155
0158
50
0128
0130
0133
0136
0138
0141
0143
0146
0149
0151
0154
0156
55
0127
0129
0132
0135
0137
0140
0142
0145
0148
0150
0153
0155
13
0126
0129
0131
0134
0136
0139
0141
0144
0147 0149
0152
0154
5
0125
0128
0130
0133
0135
0138
0141
0143
0146i0148
0151
0153
10
0124
0127
0129
0132
0135
0137
0140
0142
0145
0147
0150
0152
15;
0123
0126
0129
0131
0134
0136
0139
0141
0144
0146
0149
0151
20
0123
0125
0128
0130
0133
0135
0138
0140
0143
0145
0148
0150
25
0122
0124
0127
0129
0132
0134
0137
0139
0142
0144
0147
0149
1330
0121
0124
0126
0129
0131
0133
0136
0138
0141
0143
0146
0148
35
0120
0123
0125
0128
0130
0133
0135
0138
0140
0142
0145
0147
40
0120
0122
0124
0127
0129
0132
0134
0137
0139
0142
0144
0146
45
0121
0124
0126
0128
0131
0133
0136
0138
0141
0143
0145
50
0120
0123
0125
0128
0130
0132
0135
0137
0140
0142
0145
55
0120
0122
0124
0127
0129
0132
0134
0136
0139 0141
0144
14
0119
0121
0124
0126
0128
0131
0133
0136
0138 0140
0143
5
0118
0121
0123
0125
0128
0130
0132
0135
0137
0139
0142
10
0117
0120
0122
0124
0127
0129
0132
0134
0136
0139
0141
15
0117
0119
0121
0124
0126
0128
0131
0133
0135
0138
0140
20
0116
0118
0121
0123
0125
0128
0130
0132
0135
0187
0139
25
0115
0118
0120
0122
0124
0127
0129
0131
0134
0136
0138
1430
0114
0117
0119
0121
0124
0126
0128
0131
0133
0135
0137
35
0114
0116
0118
0121
0123
0125
0128
0130
0132
0134
0137
40
0113
0115
0118
0120
0122
0124
0127
0129
0131
0134
0136
45
0112
0115
0117
0119
0121
0124
0126
0128
0130
0133
0135
50
0112
0114
0116
0118
0121
0123
0125
0127
0130
0132
0134
55
0111
0113
0116
0118
0120
0122
0124
0127
0129
0131
0133
15
0110
0113
0115
0117
0119
0121
0124
0126
0128
0130
0133
26
TABLE V. LOG. A.
Logs. A, B, C, and D, for Lunars.
APP
REDUCED PARALLAX AND REFRACTION OF ]>.
Alt.
of )>.
18
19
5O'
51'
52'
53
54'
55'
56'
57'
58'
59'
15
.0110
0113
0115
0117
0119
0121
0124
0126
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
I 30
.0107
0109
0111
0113
0115
0117
0119
0121
0124
0126
0128
, 40
.0105
0107
0110
0112
0114
0116
0118
0120
0122
0124
0126
50
.0104
0106
0108
0110
0112
0115
0117
0119
0121
0123
0125
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
0113
0115
0117
0119
40
.0098
0100
0102
0104
0106
0108
0110
0112
0114
0116
0118
50
.0097
0099
0101
0103
0105
0107
0109
0111
0113
0115
0117
17
.0096
0098
0100
0102
0104
0106
0108
0110
0112
0114
0116
10
.0095
0097
0099
0101
0103
0105
0107
0109
0110
0112
0114
20
.0094
0096
0098
0100
0102
0104
0106
0107
0109
0111
0113
30
0095
0097
0099
0101
0103
0104
0106
0108
0110
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
0095
0097
0098
0100
0102
0104
0105
0107
0109
20
0090
0092
0094
0096
0097
0099
0101
0103
0104
0106
0108
30
0089
0091
0093
0095
0096
0098
0100
0102
0103
0105
0107
40
0088
0090
0092
0094
0095
0097
0099
0101
0102
0104
0106
50
0088
0089
0091
0093
0094
0096
0098
0099
0101
0103
0105
19
0087
0088
0090
0092
0093
0095
0097
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
0098
0100
0102
30
0084
0086
0087
0089
0091
0092
0094
0096
0097
0099
0101
40
0083
0085
0087
0088
0090
0091
0093
0095
0096
0098
0100
50
0082
0084
0086
0087
0089
0090
0092
0094
0095
0097
0099
20
0082
0083
0085
0086
0088
0090
0091
0093
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
0088
0089
0091
0092
0094
50
0078
0079
0081
0082
0084
0085
0087
0088
0090
009JL
0093
21
0077
0079
0080
0082
0083
0085
0086
0088
0089
0091
0092
10
0076
0078
0079
0081
0082
0084
0085
0087
0088
0090
0091
20
0076
0077
0079
0980
0082
0083
0085
0086
0087
0089
0090
30
0075
0076
0078
0079
0081
0082
0084
0085
0087
0088
0090
40
0074
0076
0077
0079
0080
0082
0083
0084
0086
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
0073
0074
0076
0077
0079
0080
0081
0083
0084
0086
30
0071
0072
0074
0075
0076
0078
0079
0081
0082
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
0071
0072
0074
0075
0076
0078
0079
0080
0082
20
0068
0069
0070
0072
0073
0074
0076
0077
0078
0080
0081
30
0067
0069
0070
0071
0072
0074
0075
0076
0078
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
0068
0069
0071
0072
0073
0074
0076
0077
0078
10
0066
0067
0069
0070
0071
0073
0074
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
0066
0068
0069
0070
0071
0072
0074
0075
25
0063
0065
0066
0067
0068
0069
0071
0072
0073
0074
TABLE V. LOG. A,
Logs. A, B, C, and D, for Lunars.
ll?
REDUCED PARALLAX AND REFRACTION OF >
All.
of D-
50'
51'
52'
53'
54'
55'
56'
57'
58'
59'
oo
25 0'
0063
0065
0066
0067
0068
0069
0071
0072
0073
0074
20
0062
0064
0065
0066
0067
0068
0069
0071
0072
0073
40
0061
0062
0064
0065
0066
0067
0068
0069
0071
0072
26
0060
0061
0063
0064
0065
0066
0067
0068
0069
0071
20
0059
0060
0062
0063
0064
0065
0066
0067
0068
0069
40
0058
0059
0061
0062
0063
0064
0065
0066
0067
0068
27
0057
0058
0060
0061
0062
0063
0064
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
0055
0056
0057
0058
0059
0060
0061
0062
0063
0064
20
0054
0055
0056
0057
0058
0059
0060
0061
0062
0063
40
0053
0054
0055
0056
0057
0058
0059
0060
0061
0062
29
0052
0053
0054
0055
0056
0057
0058
0059
0060
0061
20
0051
0052
0053
0054
0055
0056
0057
0058
0059
0060
40
0050
0051
0052
0053
0054
0055
0056
0057
0058
0059
30
0050
0051
0051
0052
0053
0054
0055
0056
0057
0058
20
0049
0050
0051
0052
0052
0053
0054
0055
0056
0057
40
0048
0049
0050
0051
0052
0053
0053
0054
0055
0056
31
0047
0018
0049
0050
0051
0052
0053
0053
0054
0055
20
0047
0047
0048
0049
0050
0051
0052
0053
0054
0054
0055
40
0046
0047
0048
0048
0049
0050
0051
0052
0053
0054
0054
32
0045
0046
0047
0048
0048
0049
0050
0051
0052
0053
0054
20
0044
0045
0046
0047
0048
0049
0049
0050
0051
0052
0053
40
0044
0045 ! 0045
0046
0047
0048
0049
0049
0050
0051
0052
33
.0043
0044 0045
0045
0046
0047
0048
0049
0049
0050
0051
20
.0042
0043 ; 0044
0045
0046
0046
0047
0048
0049
0050
0050
40
.0042
0043 0043
0044
0045
0046
0046
0047
0048
0049
0050
34
.0041
0042 i 0043
0043
0044
0045
0046
0046
0047
0048
0049
20
.0040
0041 j 0042
0043
0043
0044
0045
0046
0047
0047
0048
40
.0040
'0041
0041
0042
0043
0044
0044
0045
0046
0047
0047
35
.0039
0040
0041
0041
0042
0043
0044
0044
0045
0046
0047
20
.0039 1 0039 0040
0041
0042
0042
0043
0044 0044
0045
0046
40
.0038 0039 ! 0039
0040
0041
0042
0042
0043
0044
0044
0045
36
.0037
0038 | 0039
0040
0040
0041
0042
0042
0043
0044
0044
20
.0037
0038, 0038
0039
0040
0040
0041
0042
0042
0043
0044
40
.0036
0037
0038
0038
0039
0040
0040
0041
0042
0042
0043
37
.0036
0036
0037
0038
0038
0039
0040
0040
0041
0042
0042
20
.0035
0036 i 0037
0037
0038
0039
0039
0040
0040
0041
0042
40
.0035
0035
0036
0037
0037
0038
0039
0039
0040
0040
0041
38
.0034
0035
0035
0036
0037
0037
0038
0039
0039
0040
0040
20
.0034
0034
0035
0036
0036
0037
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
0032
0033
0033
0034
0035
0035
0036
0036
0037
0037
40
0032
0032
0033
0033
0034
0035
0035
0036
0036
0037
20
0031
0032
0032
0033
0034
0034
0035
0035
04ft6
0036
I 40
0031
0031
0032
0032 0033
0034) 0034
0035
0035
0036
41
0030
0031
0031
0032 0033
0033 0034
0034
0035
0035
20
0030
0030
0031
0031
0032
0033 0033
0034
0031
0035
40
0029
0030
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
0028
0029
0029
0030
0030 0031
0031
0032
0032
20
0027
0028
0028
0029
0029
0030
0030
0031
0031
0032
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
0028
0029
0029
0030
0030
40
0026
0026
0026
0027
0027
0028
0028
0029
0029
0030
45
0025 0026
0026
0027
0027
0027 0028
0028
0029
0029
TABLE V. LOG. A.
Logs. A, B, C, and D, for Lunars.
l?t p -
REDUCED PARALLAX AND REFRACTION OF 3>. j
of >
51
52
53'
54'
55'
56'
57'
58'
59'
6O'
!
45 0'
.0025
0026
0026
0027
0027
0027
0028
0028
0029
0029
30
.0025
0025
0025
0026
0026
0027
0027
0028
0028
0028
46
.0024
0024
0025
0025
0026
0026
0027
0027
0027
0028
30
.0023
0024
0024
0025
0025
0026
0026
0026
0027
0027
47
.0023
0023
0024
0024
0025
0025
0025
0026
0026
0026
30
.0022
0023
0023
0024
0024
0024
0025
0025
0025
0026
48
.0022
0022
0023
0023
0023
0024
0024
0024
0025
0025
30
.0021
0022
0022
0022
0023
0023
0024
0024
0024
0025
49
.0021
0021
0022
0022
0022
0023
0023
0023
0024
0024
30
.0020
0021
0021
0021
0022
0022
0022
0023
0023
0023
50
.0020
0020
0020
0021
0021
0022
0022
0022
0023
0023
30
.0019
0020
0020
0020
0021
0021
0021
0022
0022
0022
51
.0019
0019
0020
0020
0020
0020
0021
0021
0021
0022
30
.0018
0019
0019
0019
0020
0020
0020
0021
0021
0021
52
.0018
0018
0019
0019
0019
0019
0020
0020
0020
0021
30
.0018
0018
0018
0018
0019
0019
0019
0020
0020
0020
53
.0017
0017
0018
0018
0018
0018
0019
0019
0019
0020
30
.0017
0017
0017
0017
0018
0018
0018
0019
0019
0019
54
.0016
0016
0017
0017
0017
0018
0018
0018
0018
0019
30
.0016
0016
0016
0017
0017
0017
0017
0018
0018
0018
55
.0015
0016
0016
0016
0016
0017
0017
0017
0017
0018
30
.0015
0015
0015
0016
0016
0016
0016
0017
0017
0017
56
.0015
0015
0015
0015
0016
0016
0016
0016
0017
0017
30
.0014
0014
0015
0015
0015
0015
0016
0016
0016
0016
57
.0014
0014
0014
0015
0015
0015
0015
0015
0016
0016
30
.0014
0014
0014
0014
0014
0015
0015
0015
0015
0015
58
.0013
0013
0014
0014
0014
0014
0014
0015
0015
0015
30
.0013
0013
0013
0013
0014
0014
0014
0014
0014
0015
59
.0012
0013
0013
0013
0013
0013
0014
0014
0014
0014
30
.0012
0012
0012
0013
0013
0013
0013
0013
0014
0014
60
.0012
0012
0012
0012
0013
0013
0013
0013
0013
0013
61
.0011
0011
0011
0012
0012
0012
0012
0012
0012
0013
62
.0011
0011
0011
0011
0011
0011
0011
0012
0012
0012
63
.0010
0010
0010
0010
0011
0011
0011
0011
0011
0011
64
.0009
0010
0010
0010
0010
0010
0010
OOlc
0010
0011
65
.0009
0009
0009
0009
0009
0009
0010
0010
0010
0010
66
.0008
0008
0009
0009
0009
0009
0009
0009
0009
0009
67
.0008
0008
0008
0008
0008
0008
0008
0009
0009
0009
68
.0007
0007
0008
0008
0008
0008
0008
0008
0008
0008
69
.0007
0007
0007
0007
0007
0007
0007
0008
0008
0008
70
.0007
0007
0007
0007
0007
0007
0007
0007
0007
0007
71
.0006
0006
0006
0006
0006
0006
0007
0007
0007
0007
72
.0006
0006
0006
0006
0006
0006
0006
0008
0006
0006
73
.0005
0005
0006
0006
0006
0006
0006
0006
0006
0006
74
.0005
0005
0005
0005
0005
0005
0005
0005
0005
0006
75
.0005
0005
0005
0005
0005
0005
0005
0005
0005
0005
76
.0004
0005
0005
0005
0005
0005
0005
0005
0005
0005
77
.0004
0004
0004
0004
0004
0004
0004
0004
0004
0004
78
.0004
0004
0004
0004
0004
0004
0004
0004
0004
0004
79
.0004
0004
0004
0004
0004
0004
0004
0004
0004
0004
80
.0004
0004
0004
0004
0004
0004
0004
0004
0004
0004
81
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
82
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
83
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
84
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
85
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
1
I
86
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
87
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
1
88
0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
89
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
!)0
.0003
0003
0003
0003
0003
0003
0003
0003
0003
0003
TABLE V. LOG. B.
Logs. A, B, C, and D, for Lunars.
|| App. Alt.
nf
REDUCED REFRACTION AND PARALLAX OF OR -)f.
OI
Oor*.
O'O"
O'iO"
I'O"
I'M"
2'0"
r so"
8'0"
I 1 80"
4/0"
4' 10"
S'O"
5' SO"
5 0'
10
20
30
40
50
6
20
9.9970
40
9.9972
7
9.9976
9.9974
20
9.9977
9.9975
40
9.9981
9.9978
9.9976
8
9.9982
9.9979
9.9977 '
20
9.9982
9.9980
9.9978
40
9.9983
9.9981
9.9979
9
9.9986
9.9984
9.9982
9.9980
20
9.9986
9.9985
9.9983
9.9981
40
9.9987
9.9985
9.9983
9.9982
10
9.9989
9.9988
9.9986
9.9984
9.9982
11
9.9992
9.9991
9.9989
9.9987
9.9986
9.9984
12
9.9993
9.9992
9.9990
9.9989
9.9987
9.9986
13
9.9995
9.9994
9.9992
9.9991
9.9990
9.9989
9.9987
14
9.9995
9.9994
9.9993
9.9992
9.9991
9.9990
15
9.9997
9.9996
9.9995
9.9994
9.9993
9.9992
9.9991
16
9.9997
9.9996
9.9995
9.9994
9.9993
9.9993
18
9.9990
9.9998
9.9997
9.9996
9.9995
9.9995
20
0.0000
9.9999 9.999S
9.9998
9.9997
9.9996
9.9996
25
0.0000
0.0000 9.9999
9.9999
9.9998
9.9998
30
00001
0.0001
0.0000 0.0000
0.0000
9.9999
50
0.0001
0.0001
0.0001
0.0001
0.0001
0.0001
90
0.0001 0.0002
0.0002
0.0002
LOG. C.
App. AH.
REDUCED REFRACTION AND PARALLAX OF Q OR #.
of
Oor*.
O'O"
0' 30"
I'O"
I'M"
I'D"
I 1 10"
S'O"
3' SO"
4/0"
4' 30"
' 0"
5' 10"
5 0'
20
40
6
20
9.9969
40
9.9970
7
9.9974
9.9972
8
9.9980
9.9978 9.9975
9
9.9984
9.9982 9.9980
9.9978
10
9.9988
9.9986
9.9984 9.9982
9.9981
11
9.9990
9.9989 9.9987
9.9986 9.9984
9.9982
12
9.9991 9.9990:9.9988
9.9987 9.9985
9.9984
13
9.9993
9.9992 9.9991 9.9989
9.998819.9987
9.9985
14
9.9994
9.9993 9.9991 9.9990
9.9989 9.9988
15
9.9995
9.9994
9.9993
9.9992 9.9991
9.9990
9.9989
16
99996
9.9995
9.9994
9.9993 9.9992
9.9990
17
9.9996
9.9995
9.9994
9.9993 9.9992
9.9991
i
18
9.9997 9.9996
9.9995
9.9994
9.9994 9.9993
20
9.9998
9.9998 9.9997
9.9996
9.9995
9.9994 9.9993
25
9.9999
9.9998 9.9998
9.9997
99996
9.9996
30
0.0000
9.9999
9.9999 9.9998
9.9998
9.9997
40
0.0000 9.9999
9.9999 99999
9.9999
, 50
0.0000 0.0000 0.0000
9.9999 9.9999
L
o.jooo o.oooo o.oooo ; o.oooo
TABLE V. LOG. B,
Logs. A, B, C, and D, for Lunars.
App. Alt.
_^
REDUCED REFRACTION AND PARALLAX OF OR ^-.
ot
6'0"
6' 10"
7'0"
1' SO"
8'0"
8' SO"
9' 0"
9' SO"
10' 0"
10' SO"
11' O 1 '
ll'IO"
5 0'
9.9951
9.9947
9.9944
9.9940
9.9937
9.9933
9.9929
9.9926
9.9922
9.9919
10
9.9953
9.9949
9.9946 '9.9942
9.9939
9.9935 9.9932
9.9928
9.9925
9.9921
20
30
9.9959
9.9954
9.9956
9.9951
9.9952
9.9948 9.9944
9.9949 9.9946
9.9941
9.9943
9.9937 9.9934
9.9939 9.9936
9.9931
9.9933
9.9927
9.9929
9.9924
40
9.9960
9.9957
9.9954
9.9951
9.9948
9.9944
9.9941
9.9938
9.9935
9.9932
50
9.9965
9.9962
9.9958
9.9955 9.9952
9.9949
9.9946
9.9943
9.9940
9.9937
6
9.9966 9.9963
9.9960
9.9957 9.9954
9.9951
9.9948
9.9945
9.9942
9.9939
20
9.9968 9.9965
9.9962
9.9959 9.9956
9.9954
9.9951
9.9948
9.9945
40
7
9.9969 9.9967
9.9971 9.9968
9.9964
9.9966
9.9961 9.9959
9.9963 9.9961
9.9956
9.9958
9.9953
9.9956
9.9951
9.9953
9.9948
I
20
9.9972 9.9970
9.9968
9.9965 9.9963
9.9960
9.9958
40
9.9974 9.9971
9.9969
9.9967 9.9965
9.9962
8
9.9975 9.9973 9.9971
9.9968
9.9966
9.9964
20
9.9976 9.9974
9.9972
9.9970
9.9968
40
9.9977
9.9975
9.9973
9.9971
9
9.9978
9.9976
9.9974
9.9972
20
9.9979 9.9977
9.9975
40
9.9980 9.9978
9.9976
10
9.9981
9.9979
9.9977
11
9.9983
9.9981
12
9.9985
13
14
15
16
18
20
25
30
50
90
LOG. C.
App. Alt.
REDUCED REFRACTION AND PARALLAX OF Q OR #.
of
or-)f
6'0"
6' 10"
7/0//
7' SO"
8'0"
8' SO"
9'0"
9' 10"
10' 0"
10' SO'
ll'O'
11' SO"
5 0'
9.9949
9.9946
9.9942
9.9938
9.9935
9.9931
9.992-7
9.9924
9.9920
9.9916
20
9.9956
9.9953
9.9949
9.9946
9.9942
9.9939
9.9936
9.9932
9.9929
9.9925
9.9922
40
9.9962
9.9959
9.9955
9.9952
9.9949
9.9946
9.9943
9.9939
9.9936
9.9933
9.9930
6
9.9964
9.9961
9.9958
9.9955
9.9952
9.9949
9.9946
9.9943
9.9940
9.9937
20
9.9966
9.9963
9.9960
9.9957
9.9955
9.9952
9.9949
9.9946
9.9943
40
9.9968
9.9965
9.9962
9.9960
9.9957
9.9954
9.9951
9.9949
9.9946
7
9.9969
9.9967
9.9964
9.9962
9.9959
9.9956
9.9954
9.9951
8
9.9973
9.9971
9.9969
9.9966
9.9964
9.9962
9.9960
9
9.9976
9.9974
9.9972
9.9970
9.9968
10
9.9979
9.9977
9.9975
11
9.9981
9.9979
12
9.9983
13
14
15
16
17
18
20
25
30
40
50
90
31
TABLE V. LOG. D.
Logs. A, B, C, and D, for Lunars.
A?F
REDUCED PARALLAX AND REFRACTION OF >
Alt.
of 2>.
41'
42'
43'
44'
45.'
46'
47'
48'
49'
5O'
51'
52'
53'
54'
55'
50'
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
0352
0359
0365
6
0277
0284
0291
0297
0304
0310
0317
0323
0330
0336
0342
0349
0355
0362
9
0275
0281
0288
0294
0301
0307
0313
0320
0326
0333
0339
0345
0352
0358
12
0272
0279
0285
0291
0298
0304
0310
0317
0323
0330
0336
0342
0349
0355
5 15
0270
0276
0282
0289
0295
0301
0308
0314
0320
0326
0333
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
24
0262
0268
0274
0281
0287
0293
0299
0305
0311
0317
0324
0330
0336
0342
27
0260
0266
0272
0278
0284
0290
0296
0302
0308
0314
0321
0327
0333
0339
530
0257
0263
0269
0275
0282
0288
0294
0300
0306
0312
0318
0324
0330
0336
33
0255
0261
0267
0273
0279
0285
0291
0297
0303
0309
0315
0321
0327
0333
36
0253
0259
0265
0271
0276
0282
0288
0294
0300
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
0283
0289
0295
0301
0306
0312
0318
03*24
545
0252
0258
0263
0269
0275
0281
0287
0292
0298
0304
0310
0315
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
0249
0254
0260
0266
0271
0277
0282
0288
0294
0299
0305
0310
6
0241
0247
0252
0258
0263
0269
0275
0280
0286
0291
0297
0302
0308
3
0239
0245
0250
0256
0261
0267
0272
0278
0283
0289
0294
0300
0305
6
0237
0243
0248
0254
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
0271
0276
0282
0287
0292
0298
6 15
0231
0237
0242
0247
0253
0258
0263
0269
0274
0279
0285
0290
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
0242
0247
0252
0257
0262
0267
0273
0278
0283
0288
27
0229
0234
0240
0245
0250
0255
0260
0265
0271
0276
0281
0286
0291
630
0227
0233
0238
0243
0248
0253
0258
0263
0268
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
0240
0245
0250
0255
0260
0265
0270
0275
0280
645
0219
0224
0229
0234
0239
0244
0248
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
0250
0254 0259
0264
0269
0274
54
0214
0219
0224
0228
0233
0238
0243
0248; 0253 0257
0262
0267
1272
57
0212
0217
0222
0227
0232
0236
0241
0246 0251 0255
0260
0265
0270
7
0211
0216
0220
0225
0230
0235
0239
0244 ! 0249, 0254
0258
0263
0268
3
0209
0214
0219
0223
0228
0233
0238
0242 0247 0252
0256
0261
0266
6
0208
0212
0217
0222
0227
0231
0236
0241 0245 0250
0255
0259
0264
9
0211
0216
0220
0225
0230
0234
0239 0243 ! 0248
0253
0257
0262
12
0209
0214
0219
0223
0228
0232
0237 j 0242 0246
0251
0255
0260
7 15
0208
0212
0217
0222
0226
0231
0235 0240 0245
0249
0254
0258
18
0206
0211
0216
0220
0225
0229
0234 0238 0243
0247
0252
0256
21
0205
0209
0214
0219
0223
0228
0232 0237; 0241
0246
0250
0255
24
0204
0208
0213
0217
0222
0226
0230 0235 0239
0244
0248
0253
27
0202
0207
0211
0216
0220
0224
0229; 0233 0238
0242
0247
0251
730
0201
0205
0210
0214
0218
0223
0227 0232! 0236
0241
0245
0249
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
0208
0213
0217
0221 0225 0230
0234
0238
0243
7 45
0194
0198
0203
0207
0211
0215
0220! 0224 0228
0232
0237
0241
48
0193
0197
0201
0205
0210
0214
0218 0222; 0227
0231
0235
0239
51
019
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
0206
0210
0214
0218 0222
0226
0230
0235
*
0188
0192
0196
020C
0204
0208
0212
0217 0221
0225
0229
0233
32
TABLE V. LOG. D.
Logs. A, B, C, and D, for Lunars.
App.
A 1*
EEDUCED PARALLAX AND REFRACTION OF }>.
Alt.
of >
45'
46'
47'
48'
49'
50'
51'
52'
53'
54'
55'
56'
57'
58
8 D 0'
.0192
0196
0200
0204
0208
0212
0217
0221
0225
0229
0233
0237
5
.0190
0194
0198
0202
0206
0210
0214
0218
0222
0227
0231
0235
10
.0188
0192
0196
0200
0204
0208
0212
0216
0220
0224
0228
0232
15
.0186
0190
0194
0198
0202
0206
0210
0214
0218
0222
0226
0230
20
.0184
0188
0192
0196
0200
0204
0207
0211
0215
0219
0223
0227
25
.0182
0186
0190
0194
0197
0201
0205
0209
0213
0217
0221
0225
8 30
.0180
0184
0188
0192
0195
0199
0203
0207
0211
0215
0219
0223
35
.0178
0182
0186
0190
0193
0197
0201
0205
0209
0213
0216
0220
40
.0176
0180
0184
0188
0191
0195
0199
0203
0207
0210
0214
0218
45
.0174
0178
0182
0186
0189
0193
0197
0201
0205
0208
0212
0216
50
.0173
0176
0180
0184
0188
0191
0195
0199
0202
0206
0210
0214
55
.0171
0175
0178
0182
0186
0189
0193
0197
0200
0204
0208
0212
9
.0169
0173
0177
0180
0184
0188
0191
0195
0198
0202
0206
0209
5
.0167
0171
0175
0178
0182
0186
0189
0193
0197
0200
0204
0207
10
.0166
0169
0173
0177
0180
0184
0187
0191
0195
0198
0202
0205
15
.0164
0168
0171
0175
0179
0182
0186
0189
0193
0196
0200
0203
20
.0163
016610170
0173
0177
0180
0184
0187
0191
0194
0198
0201
25
.0161
0165
0168
0172
0175
0179
0182
0186
0189
0193
0196
0199
9 30
0163
0166
0170
0173
0177
0180
0184
0187
0191
0194
0198
35
0161
0165
0168
0172
0175
0179
0182
0185
0189
0192
0196
-
40
0160
0163
0167
0170
0174
0177
0180
0184
0187
0191
0194
45
0158
0162
0165
0169
0172
0175
0179
0182
0185
0189
0192
0195
50
0157J 0160
0164
0167
0170
0174
0177
0180
0184
0187
0190
0194
55
0156 0159
0162
0165
0169
0172
0175
0179
0182
0185
0189
0192
10
0154
0157
0161
0164
0167
0171
0174
0177
0180
0184
0187
0190
5
0153
0156
0159
0162
0166
0169
0172
0175
0179
0182
0185
0188
10
0151
0155
0158
0161.
0164
0167
0171
0174
0177
0180
0183
0187
15
0150
0153
0156
0160
0163
0166
0169
0172
0175
0179
0182
0185
20
0149
0152
0155
0158
0161
0164
0168
0171
0174
0177
0180
0183
25
0147
0150
0154
0157
0160
0163
0166
0169
0172
0175
0179
0182
1030
0146
0149
0152
0155
0158
0162
0165
0168
0171
0174
0177
0180
35
0145
0148
0151
0154
0157
0160
0163
0166
0169
0172
0175
0179
40
.
0143
0147
0150
0153
0156
0159
0162
0165
0168 0171 0174
0177
45
0142
0145
0148
0151
0154
0157
0160
0163
0166 0169 0172
0175
50
0141
0144
0147
0150
0153
0156
0159
0162
0165 0168 0171
0174
55
0140
0143
0146
0149
0152
0155
0158
0161
0164 0167 0170
0172
11
0139
0142
0145
0147
0150
0153
0156
0159
0162 0165-1)168
0171
5
0137
0140
0143
0146
0149
0152
0155
0158
0161 0164 0167
0170
10
0139
0142
0145
0148
0151
0154
0157
0159 0162 0165
0168
15
0138
0141
0144
0147
0150
0152
0155
0158 0161 0164
0167
20
0137
0140
0143
0145
0148
0151
0154
0157 0160 0163
0165
25
0136
0139
0141
0144
0147
0150
0153
0156 0158 0161
0164
1130
0135
0137
0140
0143
0146
0149
0151
0154 0157 0160
0163
35
0133
0136
0139
0142
0145
0147
0150
0153 0156 0159
0161
40
0132
0135
0138
0141
0143
0146
0149
0152 i 0154 0157
0160
45
0131
0134
0137
0140
0142
0145
0148
0150 0153 0156
0159
50
0130
0133
0136
0138
0141
0144
0147
0149 0152 0155
0157
55
0129
0132
0135
0137
0140
0143
0145
0148
0151 0153
0156
12
0128
0131
0134
0136
0139
0142
0144
0147
0150 0152
0155
5
0127
0130
0132
0135
0138
0140
0143
0146
0148 ' 0151
0154
10
0126
0129
0131
0134
0137
0139
0142
0145J 0147 0150
0152
15
0125
0128
0130
0133
0136
0138
0141
0143 0146 0149
0151
20
0124
0127
0129
0132
0135
0137
0140
0142 0145 0147
0150
25
0123
0126
0128
0131
0133
0136
0139
0141 0144J 0146
0149
1230
0122
0125
0127
0130
0132
0135
0138
0140
0143 0145
0148
.
35
0121
0124
0126
0129
0131
0134
0136
0139
0141 0144
0147
40
0120
0123
0125
0128
0130
0133
0135
0138
0140
0143
0145
45
0119
0122
0124
0127
0129
0132
0134
0137
0139
0142
0144
0147
50
0118
0121
0123
0126
0128
0131
0133
0136
0138
0141
0143
0146
55
0118
0120
0123
0125
0127
0130
0132
0135
0137
0140
0142
0145
13
0117
0119
0122
0124
0126
0129
0131
0134
0136
0139
0141
0143
33
TABLE V. LOG. D.
Logs. A, B, C, and D, for Lunars.
l?t p '
REDUCED PARALLAX AND REFRACTION OF D.
of 3>-
4T
48'
49'
.*O
51'
52'
53'
54'
55'
56'
57'
58'
59'
13 0'
.0117
0119
0122
0124
0126
0129
0131
0134
0136
0139
0141
0143
10
.0115
0117
0120
0122
0125
0127
0129
0132
0134
0137
0139
0141
20
.0113
0116
0118
0120
0123
0125
0127
0130
0132
0134
0137
0139
30
.0112
0114
0116
0119
0121
0123
0125
0128
0130
0132
0135
0137
40
0112
0114
0117
O119
0121
0124
0126
0128
0131
0133
0135
50
0111
0113
0115
0117
0120
0122
0124
0126
0129
0131
0133
14
0109
0111
0113
0116
0118
0120
0122
0125
0127
0129
0131
10
0107
0110
0112
0114
0116
0118
0121
0123
0125
0127
0129
20
0106
0108
0110
0112
0114
0117
0119
0121
0123
0125
0127
30
0104
0106
0109
0111
0113
0115
0117
0119
0121
0123
0126
40
0103
0105
0107
0109
0111
0113
0115
0118
0120
0122
0124
50
0101
0103
0106
0108
0110
0112
0114
0116
0118
0120
0122
15
0100
0102
0104
0106
0108
0110
0112
0114
0116
0118
0120
10
0099
0101
0103
0105
0107
0109
0111
0113
0115
0117
0119
20
0097
0099
0101
0103
0105
0107
0109
0111
0113
0115
0117
30
0096
0098
0100
0102
0104
0106
0108
0110
0112
0113
0115
40
0094
0096
0098
0100
0102
0104
0106
0108
0110
0112
0114
50
0093
0095
0097
0099
0101
0103
0105
0107
0108
0110
0112
16
0092
0094
0096
0098
0099
0101
0103
0105
0107
0109
0111
10
0091
0093
0094
0096
0098
0100
0102
0104
0106
0107
0109
20
0089
0091
0093
0095
0097
0099
0100
0102
0104
0106
0108
30
0088
0090
0092
0094
0096
0097
0099
0101
0103
0105
0106
40
0087
0089
0091
0092
0094
0096
0098
0100
0101
0103
0105
50
0086
0088
0089
0091
0093
0095
0096
0098
0100
0102
0104
17
0085
0087
0088
0090
0092
0093
0095
0097
0099
0100
0102
10
0084
0085
0087
0089
0091
0092
0094
0096
0097
0099
0101
20
0083
0084
0086
0088
0089
0091
0093
0094
0096
0098
0099
30
0083
0085
0086
0088
0090
0091
0093
0095
0096
0098
40
0082
0084
0085
0087
0089
0090
0092
0094
0095
0097
50
0081
0083
0084
0086
0087
0089
0091
0092
0094
0096
18
0080
0082
0083
0085
0086
0088
0090
0091
0093
0094
20
0078
0079
0081
0083
0084
0086
0087
0089
0090
0092
0093
40
0076
0077
0079
0080
0082
0083
0085
0087
0088
0090
0091
19
0074
0075
0077
0078
0080
0081
0083
0084
0086
0087
0089
20
0072
0073
0075
0076
0078
0079
0081
0082
0084
0085
0086
40
0070
0072
0073
0074
0076
0077
0079
0080
0081
0083
0084
20
0068
0070
0071
0073
0074
0075
0077
0078
0079
0081
0082
20
0067
0068
0069
0071
0072
0073
0075
0076
0077
0079
0080
40
0065
0066
0068
0069
0070
0072
0073
0074
0075
0077
0078
21
0063
0065
0066
0067
0068
0070
0071
0072
0074
0075
0076
20
0062
0063
0064
0065
0067
0068
0069
0070
0072
0073
0074
40
0060
0061
0063
0064
0065
0066
0067
0069
0070
0071
0072
22
0059
0060
0061
0062
0063
0065
0066
0067
0068
0069
0070
20
0057
0058
0059
0061
0062
0063
0064
0065
0066
0068
0069
40
0056
0057
0058
0059
0060
0061
0062
0064
0065
0066
0067
23
0054
0055
0057
0058
0059
0060
0061
0062
0063
0064
0065
20
0053
0054
0055
0056
0057
0058
0059
0060
0061
0063
0064
40
0052
0053
0054
0055
0056
0057
0058
0059
0060
0061
0062
24
0050
0051
0052
0053
0054
0055
0056
0057
0058
0059
0060
20
0050
0051
0052
0053
0054
0055
0056
0057
0058
0059
40
0049
0050
0051
0052
0053
0053
0054
0055
0056
0057
25
0047
0048
0049
0050
0051
0052
0053
0054
0055
0056
20
0046
0047
0048
0049
0050
0051
0052
0053
0053
0054
40
0045
0046
0047
0048
0049
0049
0050
0051
0052
0053
26
0044
0045
0046
0046
0047
0048
0049
0050
0051
0052
20
0043
0043
0044
0045
0046
0047
0048
0048
0049
0050
40
0041
0042
0043
0044
0045
0046
0046
0047
0048
0049
27
0040
0041
0042
0043
0044
0044
0045
0046
0047
0047
20
0039
0040
0041
0042
0042
0043
0044
0045
0045
0046
40
0038
0039
0040
0040
0041
0042
0043
0043
0044
0045
28
0037
0038
0039
0039
0040
0041
0042
0042
0043
0044
34
TABLE V. LOG. D.
Logs. A, B, C, and D, for Limars.
Apparent
Altitude
of 5-
REDUCED PARALLAX AND REFRACTION OF >
50'
51'
52'
53'
54'
55'
56'
57'
58'
59'
6O'
28 0'
0.0037
0.0038
0.0039
0.0039
0.0040
0.0041
0.0042
0.0042
0.0043
0.0044
30
0.0036
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 0.0033 0.0034
0.0035
0.0035
0.0036
0.0036
0.0037 0.0038
0.0038
30
0.003 1
0.0032 0.0032
0.0033
0.0034
0.0034
0.0035
0.0035 0.0036
0.0037
30
0.0030
0.0030 00031
0.0031
0.0032
0.0033
0.0033
0.0034 0.0034
0.0035
31
0.0028
0.0029 0.0029
00030
0.0031
0.0031
0.0032
0.0032 0.0033
0.0033
30
0.0027
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
0.0029
0.0029 0.0030
0.0030
0.0031
30
00024
0.0025 0.0025
0.0026
0.0026
0.0027
0.0027
0.0028 0.0028
0.0029
0.0029
33
0.0023
0.0024 0.0024
0.0025
0.0025
0.0025
0.0026
0.0026 0.0027
0.0027
0.0028
30
0.0022
0.0022 0.0023
0.0023
0.0024
0.0024
0.0025
0.0025
00025
0.0026
0.0026
34
0.0021
0.0021 0.0022
0.0022
0.0022
0.0023
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
00019.0.0019
0.0020
0.0020
0.0020
0.0021
0.0021
0.0021
0.0022
0.0022
30
0.0017
0.0018 0.0018
0.0018
0.0019
0.0019
0.0019
0.0020
0.0020
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
00015
0.0015
0.0015
0.0016
38
0.0012
0.0012 0.0013
0.0013
0.0013
0.0013
0.0014
0.0014
0.0014
0.0014
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
0.0010 0.0011
0.0011
0.0011
0.0011
00011
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
0.0009
0.0009
00009
0.0009
0.0010
0.0010
0.0010
41
0.0007 0.0007
0.0007
0.0007
0.0007
0.0007
0.0007
00007
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
0.0002
45
00000 0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
46
9.9998 9.9998
9.9998
9.9998
9.9998
9.9998
9.9998
9.9998
99998
9.9998
47
9.9997 9.9997
9.9997
9.9997
9.9996
9.9996
9.9996
9.9996
9.9996
9.9996
48
9.999519.9995
9.9995
9.9995
9.9995
9.9995
9.9995
9.9995
9.9994
9.9994
49
9.999419.9994
9.9994
9.9993
9.9993
9.9993
9.9993
9.9993
9.9993
9.9993
50
9.9992
9.9992
9.9992
9.9992
9.9992
9.9992
9.9992
9.9991
9.9991
9.9991
51
9.9991
9.9991
9.9991
9.9991
9.9990
9.9990
9.9990
9.9990
9.9990
9.9990
52
9.9990
9.9990
9.9990
9.9989
9.9989
9.9989
9.9989
9.9989
9.9988
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
9.9985
9.9985
9.9985
9.9984
9.9984
9.9984
56
9.9985
9.9985
9.9985
9.9984
9.9984
9.9984
9^9984
9.9983
9.9983
9.9983
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
9.9982
9.9982
9.9981
9.9981
9.9981
9.9980
9.9980
9.9980
9.9979
9.9979
60
9.9981
9.9981
9.9980
9.9980
9.9980
9.9979
9.9979
9.9979
9.9978
9.9978
61
9.9980
9.9980
9.9980
9.9979
9.9979
9.9978
9.9978
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
9.9.976
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
9.9974
9.9974
9.9973
9.9972
66
9.9976
9.9976
9.9975
9.9975
9.9974
9.9974
9.9973
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
9.9973
9.9973
9.9972
9.9972
9.9971
9.9971
9.9970
69
9.9974
9.9974
9.9973
9.9973
9.9972
9.9972
9.9971
9.9971
9.9970 9.9970
70
9.9974
9.9973
9.9973
9.9972
9.9972
9.9971
9.9970
9.9970
9.9969 9.9969
72
9.9972
9.9972
9.9971
9.9971
9.9970
9.9970
9.9969
9.9969
9.9968
9.9968
74
9.9971
9.9971
9.9970
9.9970
9.9969
9.9969
9.9968
9.9968
9.9967
9.9966
76
9.9971
9.9970
9.9969
9.9969
9.9968
9.9968
9.9967
9.9966
9.9966(9.9965
78
9.9970
9.9969
9.9969
9.9968
9.9967
9.9967
9.9966
9.9966
9.996519.9964
80
9.9969
9.9969
9.9968
9.9967
9.9967
9.9966
9.9965
9.9965
9.9964
9.9964
90
9.9968 9.9967
9.9966
9.9966
9.9965
9.9964
9.9964
9.9963
9.9963 9.9962
35
TABLE VI.
'Second Correction of the Lunar Distance.
Appar-
FIRST CORRECTION OF DISTANCE.
Appar-
ent
ent
Dis-
Dis-
tance.
8'
/
1(1 1J
IHG
18
J4
M
27; 28
29 30 7
31
3J
13
ii
Itf
X
tance.
^0
2122
2i
24
Subtr.
Add.
;i5o'
b
2
3
5
C)
8
11
13
14 16
17
19
20 22
24
'26
27 29
33
33
35
38 40
42
30
2
3
5
6
8
10
13
14
15 17
18
20 21
23
25
26 28 32
32
34
36 39 i 41
16
3
4
6| 8
10
12
13
15 16
18
19 21
22
24
26 27
31
31
33
35 37
39
30
3
4
6 8
10
12
13
14 16
17
18 20
21
23
25 27
30
30
32
34! 36
38
17
3
4
6 ! 7
9
11
13
14
15
16
18
19
21
22
24 26
29
29
31
33 35
37
30
3
4
5
7
9
11
12 13
15
16
17
19
20
22
23 25
28
28
30
32 34 36
18
3
4
5
7
9
11
12J13
14
15
17
18
20
21
23 24
28
28
29
31 33 35
30
3
4
5
7
8
10
12
13
14
15
16
18
19
20
22i23
27
27
28
30i 32
34
19
3
4
5
6
8
10
11
12
13
15
16
17
13
20
21 23
26
26
28
29 31
33
30
2
4
5
6
8
10
11
12
13
14
15
17
18
19
21
22
25
25
27
28 30
32
20
2
3
5
6
8
10
11
12
13
14
15
16
17
19
20;22
25
25
26
28
29
31
21
2
3
4
6
7
9
10
11
12
13
14
15
17
18
19 20
23
23
25
26 28 1 29
22
2
3
4
6
7
9
10
10
11
12
14
15
16
17
18 19
22
22
24
25 26
28
23
2
3
4
5
7
8
9
10
11
12
13
14
15
16
17|19
21
21
22
24
25
27
24
2
3
4
5
6
8
9
9
10
11
12
13
14
15
ie;i8
20
20
21
23
24
25
25
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
19
19
20
22 23
24
26
2
3
4
5
6
7
8
9
9
10
11
1-2
13
14
15
1G
18
18
19 21 22
23
27
2
2
3
4
6
7
8
8
9
10
11
12
12
13
14
15
18
18
19
20 i 21 22
28
2
2
3
4
5
7
7
8
9
9
10
11
12
13
14
15 17
17
18
19 20! 21
29
2
2
3
4
5
6
7
8
8
9
id
11
11
12
13
14
16
16
17
18 19 i 20
30
2
2
3
4
5
6
7
7
8
9
9
10
11
12
13
14
15
15
16
171 19 20
31
2
3
4
5
6
6
7
8
8
9
10
11
11
12
13
15
15
16
17
18
19
32
2
3
4
5
6
6
7
7
8
9
9
10
11
12
13
14
14
15
16
17
18
33
2
3
3
4
5
6
7
7
8
8
9
10
11
11
12
14
14
15
16
16
17
34
2
3
3
4
5
6
6
7
7
8
9
9
10
11
12
13
13
14
15
16
17
35
2
2
3
4
5
5
6
7
7
S
8
9
10
10
11
13
13
14
14
15
16
136
2
2
a
4
5
5
6
6
7
8
8
9 9
10
11
12
12
13
14
15
16
37
2
2
3
4
B
'i*
6
6
7
3
8
9
10
10
12
12
13
13
14
15
38
2
2
3
4
4
i?.5
5
6
6
:-?
8
8
9
9
10
11
11
12
13
14
14
39
1
2
2
a
3
4
5
5
6
6
V?
7
8
9
10
11
11
12
12
13
14
40
1
2
2
3
3
4
5
5
6
6
7
7
8
Q
9
9
11
11
,11
12
13
13
140
42
2
2
3
4
4
5
5
6
6
7
7 1 8
8
9
10
10
11
11
12
13
138
44
2
2
3
4
4
4
5
5
6
6
1
7
8
8
9
9
10J 10
11
12
136
46
2
2
3
3
4
4
4
5
5
6
6
7
7
8
9
9
9 10
10
11
134
48
2
2
3
a
3
4
4
5
5
5
r>
6
7
7
8
8
9
9
10
10
132
50
2
2
3
3
4
4
4
5
5
5
6
6
7
8
8
8
8
9
9
130
52
2
2
3
3
3
4
4
4
5
5
5
6
6
7
7
7
8
8
9
128
54
2
2
3
3
3
3
4
4
4
5
5
5
6
6
7
7
8
8
126
56
2
2
2
3 3
3
3
4
4
4
5
5
5
6
6
6
*?
7
8
124
58
1
2
2
2
3
3 3
3
4
'4
4
v'S
5
6
,6
6
6
7
7
122
60
2
2
2
2
3
3
3
3
4
4
4
5
5
5
5
6
6
7
120
62
2
2
2! 2
2
3
3
a
3
4
4
4
5
5
5
5
6
6
118
64
1
2
2 2
2
2
3
3
3
3
4
4
4
4
5
5
5
6
116
66
CO
2
2 2
20
2
2
2
3
3
3
3
3"
4
4
4
4
4
5
fi
114
bo
70
1
1
1
2
1 2
::2
2
2
2
2
3
2
2
3
3
3
3
3
4
4
5
4
110
74
1
1
1 1
1
1
2
2
2i 2
2
2
3
3
3
3
3
3
106
78
1
1
1
l 1
1
1
1
1
2
2
2
2
2
2
2
2
102
82
1
1
1 1
1
1
1
1
1
1
1
1
1
1
2
2
98
86
1
1
1
1
1
1
1
1
94
90
90
Appar-
i
7
id
iil
11
16
18
20
If
22
ii
il
25
m
2728
B
SO
si it
ii
34
36
Appar-
ent
cnt
Dis-
Dis-
tance.
FIRST CORRECTION OF DISTANCE.
tance.
36
TABLE VI.
Second Correction of the Lunar Distance.
Appar-
FIRST CORRECTION OF DISTANCE. Appar.
ent
Tii^j
ent
Tlia
ins-
tance.
H7
58
;ig'
40
41
d
43
44
4546
4)
48
d
ill
ii
i
i
4
5>
Si
57
58
flf
60'
UlS-
tance.
Subtr
,. A,W
15 0'
45
47
50
52
55
57
60
63
66
69
72
75
78
81
85
88
91
95
99
102
106
no
113
117
30
43
45
48
50
53 56 58
61
64 67
70
72
76
79
82
85
88 92
95
99
102
106
110
113
16
42|44
40
49
51 54
56
59
62 64
67
70
73
76
79
82
85 89
92
95
99
102
106
110
30
40
43
45
47
50i52
54
57
60162
65
68
71
74
77
80
83 86
89
92
96
99
103
106
17
39
4 1
43
46
48; 50
53
55
58
60
63
66
69
71
74
77
80 83
86
90
93
96
99
103
30
98
40
42
44
47|49
51
54
56 59
61
64
66
69
72
75
78
81
84
87
90
93
96
100
18
30
37
36
39
38
41
40
43
42
45147
44 46
50
48
52
50
54 57 59
53 55 58
62
60
64
63
67
65
70
68
73
71
75
73
78
76
81
79
84
82
87
85
90
88
94
91
97
94
19
35
37
.-59
41
43
45 47
49
51 54
56
58
61
63
66
69
71
74
77
79
82
85
88
91
30
34
36
.'57
.'39
41
43 46
48
50
52
54
57
59
62
64
67
69
72
75
77
80
83
86
89
20
33
35
36
38
40
42 44
4(5
49
51
53
55
58
60
62
65
67
70
73
75
78
81
83
86
21
31
33
.'55
36
38
40 42
44
46
48
50
52
55
57
59
61
64
66
69
71
74
76
79
82
22
30
31
33
35
36
38 40
42
44
46
48
50
52
54
56
58
61163
65
68
70
73
75
78
23
28
30
31
33
.'35
36
38
40
42
44
45
47
49
51
53
56
58 60
62
64
67
69
72
74
24
'27
28
.'50
31
33
.'55
3(1
38
40
41
43
45
47
49
51
53
55
57
59
61
64
66
68
71
25
26
27
28
30
.'51
33
35
3fi
38
40
41
43
45
47
49 51
53
55
57
59
61
63
65
67
26
25
26
27
29
30
32
33
35
36
38
40
41
43
45
47 48
50
52
54
56
58
60
62
64
27
33
25
26
27
29 30
32
33
35
36
38
39
41
43
45
46
48
50
52
54
56
58
60
62
28
28
24
25
26
28
29
30
32
33
35
36
38
39
41
43 44
46
48
50
51
53
55
57
59
29
22
2-'}
24
25
26
28
29
30
32
33
35
36
38
39
41 43
44
46
48
49
51
53
55
57
30
21
22
2,'!
24
25
27
28
29
31
32
33
35
36
38
39141
42
44
46
47
49
51
53
54
31
20
21
22
2.'i
24
26
27
28
29
31
32
33
35
36
38 39
41
42
44
46
47
49
51
52
32
19
20
21
22
2:5
25
26
27
28
30
31
32
.31
85
36 38
39
41
42
44
45
47
49
50
33
18
19
20
22
23
24
25
26
27
28
30
31
32
34
35 36
38
39
41
42
44
45
47
48
34
18
19
20
21
22
23
24
25
26
27
29
30
31
32
34
35
36
38
39
41
42
44
45
47
35
17
18
19
20
21
22
23
24
25
26
28
29
30
31
32
34
35
36
38
39
40
42
43
45
36
If.
17
18
19
20
21
22
2.5
24
25
27
28
29
30
31 32
34
35
36
38
39
40
42
43
37
L6
17
18
19
19
20
21
22
23
25
26
27
28
29
3031
33
34
35
36
38
39
40
42
38
15
16
17
18
19 20
21
22
23
24
25
26
27
28
29J30
31
33
34
35
36
38
39
40
39
15
16
16
17
15
19
20
21
22
23
24
25
26
27
28 29
30
31
33
34
35
36
38
39
40
14
15
16
17
17
18
L9
20
21
22
23
24
25
26
27
28
29
30
31
33
34
35
36
37
140 3
42
I.')
14
15
16
If)
17
18
19
20
21
21
22
23
24
25
26
27
28
29
30
31
33
34
35
138
44
12
13|l4
14
15
16
17
17
18
19
20 21
22
23
24 24
25
26
27
-28
29
30
31
33
136
46
12
12J13
13
14
15
16
16
17
18
19
19
20
21
2223
24
25
26
26
27
28
29
30
134 !
48
11
11
12
13
13
14
15
15
16 17
17
18
19
20
20:21
22
23
24
25
26
26
27
28
132
50
10
11
11
12
12
13
14
14
15 16 16 17
18
18
19 20
21
21
22
23
24
25
25
26
ISO
52
9
10
10
11
11
12
13 13 14 Ullo 16
16
17
18|18
19
20
21
21
22
23
24
25
128-
54
9
9
10
10
11
11
12 12 13 13 14 15
15 16
16 17
18
18
19
20
21
21
22
23
126
56
8
9
9
9
10
10
11
11
12,; 12 13! 14
14
15 15J16
17
17
18
18
19
20
20
21
124
58
7
S
8
9-
9
10
10
11
11 12 12<13
13
14
14 15
15
16
16
17
18
18
19
20
122
CO
7
7
8
8
8
9
9
10'i 10 11 ill 12
12
13
13J14
14
15
15
16
16
17
18
18
120
62
6
-7
7
7
8
8
9
9
9 10 10 11
11
12
12! 13
13
14
14
15
15
16
16
17
118
64
G
6
6
7
'7
8
8
8
9 9
9 10
10
11 11J12
12
12
13
13
14
14
15
15
116 i
66
5
6
G
7
7
7
8
8 8
9
9
9
10 10 11
11
11
12
12
13
13
14
14
114 ]
68
5
5
5
6
6
6
7
7
7 i 7
8
8
8
9 9 10
10
10
11
11
11
12
12
13
112
70
*7 A
4
5
5
5
5
6
6
6
6 I
7 7
6f
8
8
8
9
7
9
7
9
10
10
10
11
11
11
110
1 HA
/4
78
GO
8
9
3
')
3
3
.)
3
2
3
.3
.)
4 4 4
2 o Q
D
4 4
O Q
4
3
5
7
5
5
3
|
5
5
4"
6
6
6
8
6
6
9
7
lUb
102
no
OS
86
1
I
1
1
1
1
I
j
I
I
O O
i; !
1
2
2
2
.
2
2
2 2
2
2
2
2
7O
94
90
o
o
90
Appar-
ent
37
^
$0
ri
id
11
42
n
44 45 46 47
.18
49
50
51
3l
51 M
55 56; <?
$8
ri
60 Lppar
Dis-
I Dia-
tance.
FIRST CORRECTION OF DISTANCE. Itance.
37
TABLE VII.
For finding the Correction of the Lunar Distance for the Contraction of the Moon's Semidiameter.
! TABLE VII. A. GIVING THE ARGUMENT FOR TABLE VII. B.
Reduced
APPARENT ALTITUDE OF j).
P and R
i .and tv
o
-
o
o
n
o
o
o
o
c
o
o
c
o
o
o
D
r
o o
of>.
l a
(i
(i
7i
8
9
(ii
10
11
12
13
11
Li
It)
17
18
20
25
It)
40
41'
65 56
42
63| 54
47
41
43
62 53
46
40
35
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
29
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
18
17
14
12
10
9
8
7
6
49
53
45
39
35
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
9
2
51
50
43
38
33
29
26
23
21
19
17
15
13
11
in
.11
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
C
6
5
4
3
2
2
2
54
47
41
35
31
27 24
22
19
18
16
15
12
10
9
8
7
6
6
5
4
3
2
2
2
55
35
30
27
24
21
19
17
16
14
12
10
9
8
7
e
G
5
4
3
2
2
2
56
26
23
21
19
17
15
14
12
10
9
8
7
i
5
5
4
3
2
2
2
57
18
17
15
14
12
10
9
7
7
t
5
5
4
3
2
2
2
58
13
11
10
8
7
7
f
5
5
4
3
2
2
2
59
8
7
6
G
5
5
4
3
2
2
2
60
4
3
2
; 2
2
TABLE VII. B. CONTRACTION OF ]>'S SEMIDIAMETER.
Wnole
ARGUMENT = \UMBER FROM TABLE VII. A.
Correction
of }>.
2
4
6
8
10
12
M
10
13
mm
24
21)
2s
30
52
11
16
IS
40
44
48
rl
51)
se
64
o'
G
5
"0
10 -
c
i
1
1
1
1
1
1
1
l
1
i
1
1
1
15
1
1
1
1
1
1
1
i
1
1
1
'2
2
2
2
2
2
2
3
3
3
20
1
1
I
1
1
1
2
2
2
2
.2
2
3
3
3
3
3
4
4
4
4
5
5
22
d
1
1
1
1
I
2
2
*
2
2
3
3
3
3
3
3
4
4
4
5
5
5
6
6
24
1
1
I
2
2
2.2
3
3
3
3
3
4
4
4
4
5
5
6
6
6
7
7
26
1
1
1
2
2
2
2 a
3
3
4
4
4
4
5
5
5
5
6
6
7
8
8
9
28
1
1
2
2
2
3
3
a
3
4
4
4
5
5
5
6
B
6
"7
8
8
9
9
10
30
t
1
2
2
3
3
3
4
4
4
5
5
5
6
6
6
7
7
8
9
9
10
11
12
32
I
2
2
2
3
3
4
4
5
5
5
6
6
7
7
7
8
8
9
10
11
11
12
13
34
36
1
1
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
7
6
7
i
8
7
8
8
9
8
9
9
10
9
10
10
11
11
12
12
13
13
15
14 15
16 17
38
I
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
I
2 3
3
4
4
5
6
1
7
8
8 9
9
10
ll
12
12
13
14
15
17
18
19 20
42
I
2 3
4
4
5
6
6
$
8
8
9 10
11
ll
12
13
13
14
16
17
18
20
21
23
44
2
2 3
4
5
5
6
7 S
9 9
10 11 12!l2
13
14 15
15
17
19
20
22
23
45
2
2! 3
4
5
6
6
7 {
9 J 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
13114
14
15
16
17
19
20
22
24
47
2
3 4
4
5
6
*
8 9 10.11
11 12
13 14
15
16 17
18
19 21
23
25
48
2
3 4
5
667
8 9 10 ill
12 13
1415 16
17 18
18
20 22! 24
26
49
2
3! 4
5 6| 7 8
9 10 11|12
12 13
14 15
16
17118
19
21 23
25
50
2
3 4
5 6| 7 8
13 14
15
16
17
18 ; 19 20
22 24
26
51
2
3 ! 4
5
6 7
g
9 10 1I ! 12
14 15
16
17 18
19 20
21
23 25
27
52
2
3 4
5
I 8
q
10 11J12 13
14 15
16
17
18 19 2l|22
24i26
53
1
2
3
4
6
7 8
9
10 11 12113
15 16
17
18 19 20 21
22
25
27
54
2
3
5
6
"I 8 9
10 12:13114
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
3
4
5
6
8
9
10
ll 13 14 15
16
57
1 4
5
7
!
^^.
When the nvartxt limb i* observed subtract this correction ; when the farthest, add.
TABLE VIII.
For finding the Correr.tion of the Lunar Distance for the Contraction of the Sun's Semidiameter.
I TABLE VIII. A. GIVING THE ARGUMENT FOR TABLE VIII. B.
Reduced
APPARENT ALTITUDE OF 0. ||
P. and R.
of.
o
51
6
4
7
U
n
n
9
H
10
11
Q
12
Ii
o
14
if
16
17
18
10
u
10
40
sol!
1' 0"
22
18
30
30
34
24
29
2
35
37
42
46
46
30
40
42
44
47
53
59
3
44
4G
49
51
53
57
30
45
48
51
54
57
60
62
G7
4
45
49
52
55
59
G2
65
63
30
47
49
51
55
59
63
66
70
5
47
50
52
54
57
Gl
6G
70
74
30
47
50
52
55
57
GO
62
67
72
6
49
52
55
57
60
G3
6G
68
74
30
50
53
56
59
G2
65
G8
71
74
7
51
54
5S
61 64
07
70
74
30
55
58J62
65
69
72
75
8
55
59
62
56
70
73
77
30
59
63
66
70
74
78
9
6-2
66
70
74
79
30
66
70
74
79
10
69
74
78
30
73
77
11
76
81
30
80
TABLE VIII. B. CONTRACTION OF 0*8 SEMIDIAMETER.
Whole
ARGUMENT= NUMBER FROM TABLE VIII. A. |
Correction
of Q.
20
i4
28
I!
K
40
ii
46
48
;5I)
^
U
6
58
60
61
64
66
68
70
72
74
76
78
( ii
6
b
'o
It
//
II
tl
u
1
1
i
i
i
i
2
2
2
2
2
2
2
2
i
1
I
1
i
1
1
1
1
1
1
1
1
1
i
30
3
3
3
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
i
3
4
4
K
4
5
3
5
3
3
3
3
3
3
3
3
2
2
2
2
2
2
2
30
9
7
f,
g
g
g
r.
4
20
7
7
7
7
G
6
6
6
5
5
5
5
5
5
5
4
4
40
9
8
8
8
7
7
7
7
G
6
6
6
6
5
5
5
5
5 0'
10
9
11
9
1
9
10
8
8
8
8
7
7
7
7
6
6
6
6
6
20
40
12
1 \ t
12
11
11
10
10
10
9
9
9
9
8
8
8
8
r
6
13
12
12
12
11
11
10
10
10
10
9
9
9
9
8
20
14
14
13
13
12
12
12
11
11
11 10
10
10
10
9
40
16
15
15
14
14
13
13
13
12
12 11
11
11
11
10
7
18
17
16
16
15
15
14
14
13
13 13
12
12
12
'1
20
40
19
IS
20
17
19
17
18
16
18
16
17
15
17
15
16
14.14
16|l5
13
15
13
14
13
14
i >
14
8
21
21
20
19
19
18
17
17
16
1G
16
15
15
20
22
21
20
20
19
18
18
17
17
16
16
40
23
23
22
21
20
20
19
19
18
18
17
9
24
23
22
21
21
20
20
19
19
20
25
24
23
22
22
21
21
20
40
25
25
24
23
23
22
22
10
26
2G
25
24
24
23
20
28
27
26
25
25
40
28
28
27
26
11
29
28
20
.
30
Subtract this correction fronri the distance.
39
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
d
2
3
1
a
5
n
6
n
7
//
8
9
O | II
O h. Q m. p.
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
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
.6812
1.6902
50
1.6990
1.7076
1.7160
1.7243
1.7324
1.7404 1.7482
1.7559
.7634
1.7709
1.7782
1.7853
1.7924
1.7993
1.8062
1.8129 1.8195
1.8261
.8325
1.8388
10
1.8451
1.8513
1.8573
1.8633
1.8692
1.8751
1.8808
1.8865
.8921
1.8976
20
1.9031
1.9085
1.9138
1.9191
1.9243
1.9294
1.9345
1.9395
.9445
1.9494
30
1.9542
1.9589
1.9638
1.9685
1.9731
1.9777 1.9823
1.9868
.9912
1.9956
40
2.0000
2.0043
2.0086
2.0128
2.0170
2.0212 2.0253
2.0294
2.0334
2.0374
50
2.0414
2.0453
2.0492
2.0531
2.0569
2.0607
2.0645
2.0682
2.0719
2.0755
020
2.0792
2.0828
2.0864
2.0899
2.0934
2.0969
2.1004
2.1038
2.1072
2.1106
2 10
2.1139
2.1173
2.1206
2.1239
2.1271
2.13031 2.1335
2.1367
2.1399
2.1430
2 20
2.1461
2.1492
2.1523
2.1553
2.1584
2.1614! 2.1644
2.1673
2.1703
2.1732
2 30
2.1761
2.1790
2.1818
2.1847
2.1875
2.1903
2.1931
2.1959
2.19-87
2.2014
2 40
2.2041
2.2068
2.2095
2.2122
2.2148
2.2175
2.2201
2.2227
2.2253
2.2279
2 50
2.2304
2.2330
2.2355
2.2380
2.24.05
2.2430
2.2455
2.2480
2.2504
2.2529
030
2.2553
2.2577
2.2601
2.2625
2.2648
2.2672
2.2695
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
23617
2.3636
2.3655
2.3674
2.3692
2.3711
2.3729
2.3747
2.3766 2.3784 '
040
2.3802
2.3820
2.3838
2.3856
2.3874
2.3892
2.3909
2.3927
2.3945! 2.3962
4 10
2.3979
2.3997
2.4014
2.4031
2.4048
2.4065
2.4082
2.4099
2.4116i 2.4133
4 20
2.4150
2.4166
2.4183
2.4200
2.4216
2.4232
2.42491 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 2.4609
4 50
'2.4624
2.4639
2.4654
2.4669
2.4683
2.4698
2.4713
2.4728
2.4742
2.4757
050
2.4771
2.4786
2.4800
2.4814
2.4829
2.4843
2.4857
2.4871
2.4886
2.4900
5 10
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
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
25403
2.5416
2.5428
5 50
2.5441
2.5453
2.5465
2.5478
2.5490
2.5502
2.5514
2.5527
2.5539
2.5551
060
2.5563
2.5575
2.5587
2.5599
2.5611
2.5623
2.5635
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
2.6138
2.6149
2.6160
2.6170
2.6180
2.6191
2.6201
2.6212
2.6222
070
2.6232
2.6243
2.6253
2.6263
2.6274
2.6284
2.6294
2.6304
2.6314
2.6325
7 10
2.6335
2.6345
2.6355
2.6365
2.6375
2.6385
2.6395
2.6405
2.6415
2.6425
7 20
2.6435
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
2.6628; 2.6637
2.6646
2.6656
2.6665
2.6675
^.6684
2.6693
2.6702
2.6712
7 50
2.6721 2.6730
2.6739
2.6749
2.6758
2.6767
2.6776
2.6785
2.6794
2.6803
080
2.6812^ 2.6821
2.6830
2.68391 2.6848
2.6857
2.6866
2.6875
2.6884
2.6893
8 10
2.6902 2.6911
2.6920
2.69281 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
2.7243 2.7251
2.7259
2.7267
2.7275
2.7284
2.7292
2.7300
2.7308
2.7316
090
2.7324 2.7332
2.7340
2.7348
2.7356
2.7364
2.7372
2.7380
2.7388
2.7396
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
? 50
2.7709 2.7716 2.7723
2.7731
2.7738
2.7745
2.7752
2.7760
2.7767
2.7774
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
l^r.
n
i
2
3
n
4
5
6
7
8
n
9
O h -lO m ' 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
27924
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
2.8142
2.8149
2.8156
2.8162
2.8169
2.8176
2.8182
2.8189
11
2.8195
2.8202
2.8209
2.8215
2.8222
2.8228
2.8235 2.8241
2.8248
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
2.8519
2.8525
2.8531
2.8537
2.8543
2.8549' 2.8555
2.8561
2.8567
12
2.8573
2.8579
2.8585
2.8591
2.8597
2.8603
2.8<> '.I i.8615
2.8621
2.8627
12 10
2.8633
2.8639
2.8645
2.8651
2.8657
2.8663
2.8tit:v) 2.8675
2.8681
2.8686
12 20
2.8692
2.8698
2.8704
2.8710
2.8716
2.8722
2.S7SS7. 2.8733
2.8739
2.8745
12 30
2.8751
2.8756
2.8762
2.8768
2.8774
2.8779
2.87 S.V 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
2.8899
2.8904
2.8910
2.8915
13
2.8921
2.8927
2.8932
2.8938
2.8943
2.8949
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
2.9201
2.9206
2.9212
2.9217
2.9222
2.9227
2.9232
29238
14
2.9243
2.9248
2.9253 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
29385 2.9390
1 14 30
2.9395
2.9400
2.9405
2.9410
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
T9661
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
2.9782
2.9786
2.9791
2.9795
2.9800
2.9805
--2^809
2.9814 2.9818
16
2.9823
2.9827
2.9832
2.9836
2.9841
2.9845
2.9850
2.9854
2.9859 2.9863
16 10
2.9868
2.9872
29877
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
2.9934
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
3.0233
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
3.0306
3.0310
3.0314
3.0318
3.0322
3.0326 \ 3.0330
18
3.0334
3.0338 ; 3.0342
3.0346
3.0350
3.0354
3.0358
3.0362
3.0366 3.0370
18 10
3.0374
3.0378' 3.0382
3.0386
3.0390
3.0394
30398
3.0402
3.0406 3.0410
18 20
3.0414 3.041 8 1 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 3.04961 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
30558
3.0561
3.0565
19
3.0569 3.0573 3.0577
3.0580
3.0584
3.0588
3.0592
3.0596
3.0599
3.0603
19 10
3.0607 3.0611
3.0615
3.0618
3.0622
3.0626
3.0630
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
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
n
i
2
n
3
4
5
6
n
1
n
8
9
0, I II
O h. 20 m. QS.
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
3.0993
3.0997
3.1000
21
3.1004
3.1007
3.1011
3.1014
3.1017
3.1021
3.1024
3.1028
3.1031
3.1035
21 10
3.1038
3.1041
3.1045
3.1048
3.1052
3.1055
3.1059
3.1062
3.1065
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
31183
3.1186
3.1189
3.1193
3.1196
3.1199
3.1202
22
3.1206
3.1209
3.1212
3.1216
3.1219
3.1222
3.1225
3.1229
3.1232
3.1235
22 10
3.1239
3.1242
3.1245
3.1248
3.1252
3.1255
3.1258
3.1261
3.1265
3.1268
22 20
3.1271
3.1274
3.1278
3.1281
3.1284
3.1287
3.1290
3.1294
3.1297
3.1300
22 30
3.1303
3.1307
3.1310
3.1313
3.1316
3.1319
3.1323
3.1326
3.1329
3.1332
22 40
3.1335
3.1339
3.1342
3.1345
3.1348
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
31421
3.1424
3.1427
23 10
3.1430
3.1433
3.1436
3.1440
3.1443
3.1446
3.1449
3.1452
3.1455
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
3.1520
23 40
3.1523
3.1526
3.1529
3.1532
3.1535
3.1538
3.1541
3.1544
3.1547
3.1550
23 50
3.1553
3.1556
3.1559
3.1562
3.1565
3.1569
3.1572
3.1575
3.1578
3.1581
24
3.1584
3.1587
3.1590
3.1593
3.1596
3.1599
3.1602
3.1605
3.1608
3.1611
24 10
3.1614
3.1617
3.1620
3.1623
3.1626
3.1629
3.1632
3.1635
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
3.1752
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
3.1853
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
3.1917
3.1920
3.1923
3.1926
3.1928
26
3.1931
3.1934
3.1937
3.1940
3.1942
3.1945
3.1948
3.1951
3.1953
3.1956
26 10
3.1959
3.19G2
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
3.201 1
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
3.2074
3.2076
3.2079
3.2082
3.2084
3.2087
3.2090
3.2092
27
3.2095
3.2098
3.2101
3.2103
3.2106
3.2109
3.2111
3.2114
3.2117
3.2119
27 10
3.2122
3.2125
3.2127
3.2130
3.2133
3.2135
3.2138
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
3.2206
3.2209
3.2212
3.2214
3.2217
3.2219
3.2222
3.2225
27 50
3.2227
3.2230
3.2232
3.2235
3.2238
3.2240
3.2243
3.2245
3.2248
3.2250
28
3.2253
3.2256
3.2258
3.2261
3.2263
3.2266
3.2269
3.2271
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
3.2343
3.2345
3.2348
3.2350
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
3.2385
3.2388
3.2390
3.2393
3.2395
3.2398
3.2400
3.2403
29
3.2405
3.2408
3.2410
3.2413
3.2415
3.2418
3.2420
3.2423
3.2425
3.2428
29 10
3.2430
3.2433
3.2435
3.2438
3.2440
3.2443
3.2445
3.2448
3.2450
3.2453
29 20
3.2455
3.2458
3.2460
3.24631 3.2465
3.2467
3.2470
3.2472
3.2475
3.2477
29 30
3.2480
3.2482
3.2485
3.2487
3.2490
3.2492
3.2494
3.2497
3.2499
3.2502
29 40
3.2504
3.2507
3.2509
3.2512
3.2514
3.2516
3.2519 3.2521
3.2524
3.2526
29 50
3.2529
3.2531
3.2533 j 3.2536 3.2538
3.2541
3.2543 1 3.2545 3.2548
3.2550
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
d
n
2
n
3
I
5
6
7
9
O, 1 II
O h. 30 m. QS .
3.2553
3.2555
3.2558
3.2560
3.2562
3.2565
3.2567
3.2570
3.2572
3.2574
30 10
3.2577
3.2579
3.2582
3.2584
3.2586
3.2589
3.2591
3.2594
3.2596
3.2598
30 20
3.2601
3.2603
3.2605
3.2608
3.2610
3.2613
3.2615
3.2617
3.2620
3.2622
30 30
3.2625
3.2627
3.2629
3.2632
3.2634
3.2636
3.2639
3.2641
3.2643
3.2646
30 40
3.2648
3.2651
3.2653
3.2655
3.2658
3.2660
3.2662
3.2665
3.2667
3.2669
30 50
3.2672
3.2674
3.2676
3.2679
3.2681
3.2683
3.2686
3.2688
3.2690
3.2693
31
3.2695
3.2697
3.2700
3.2702
3.2704
3.2707
3.2709
3.2711
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
3.2828
3.2831
32
3.2833
3.2835
3.2838
3.2840
3.2842
3.2844
3.2847
3.2849
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
3.2947
3.2949
3.2951
3.2953
3.2956
3.2958
3.2960
3.2962
3.2964
33
3.2967
3.2969
3.2971
3.2973
3.2975
3.2978
3.2980
3.2982
3.2984
3.2986
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
3? 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
33077
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
3.3137
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
3.3208
3.3210
3.3212
3.3214
3.3216
3.3218
3.3220
35
3.3222
3.3224
3.3226
3.3228
3.3230
3.3233
3.3235
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
3.3328
3.3330
3.3332
3.3334
3.3336
3.3339
3.3341
3.3343
36
3.3345
3.3347
3.3349
3.3351
3.3353
3.3355
3.3357
3.3359
3.3361
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
3.3479
3.3481
37 10
3.3483
3.3485
3.3487
3.3489
3.3491
3.3493
3.3495
3.3497
3.3499
3.3501
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
33524
3.3526
3.3528
3.3530
3.3531
3.3533
3.3535
3.3537
3.3539
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
33562
3.3564
3.3566
3.3568
3.3570
3.3572
3.3574
3.3576
3.3577
38
3.3579
3.3581
3.3583
3.3585
3.3587
3.3589
3.3591
3.3593
3.3595
3.3596
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
3.3675
3.3677
3.3679
3.3681
3.3683
3.3685
3.3687
3.3688
3.3690
39
3.3692
3.3694
3.3696
3.3698
3.3700
3.3701
3.3703
3.3705
3.3707
3.3709
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
TABLE
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
d
n
2
n
3
1
a
5
6
n
7
n
8
9
O h -40 m - o',.
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
3.3938
3.3939
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
3.4004
3.4005
3.4007
3.4009
3.4011
3.4012
42
3.4014
3.4016
3.4017
3.4019
3.4021
3.4023
3.4024
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
3.4109
3.4111
3.4113
3.4115
43
3.4116
3.4118
3.4120
3.4121
3.4123
3.4125
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
34183
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
3.4209
3.4211
3.4213
3.4214
44
3.4216
3.4218
3.4219
3.4221
3.4223
3.4224
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
3.4275
3.4276
J.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
3.4350
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
3.4390
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
3.4482
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
3.45331 3.4535
3.4536
3.4538
3.45-39
3.4541
3.4542
3.4544
3.4545
3.4547
47 30
3.45481 3.4550
3.4551
3.4553
3.4555
3.4556
3.4558
3.4559 ! 3.4561
3.4562
47 40
3.4564 3.4565
3.4567
3.4568
3.4570
3. 4 5 VI
3.4573
3.4574 3.4576
3.4577
v47 50
3.4579
3.4580
3.4582
3.4583
3.4585
3.4586
3.4588
3.4589 3.4591
3.4592
48
3.4594
3.4595
3.4597
3.4598; 3.4600
3.4601
3.4603
3.4604 3.4606
3.4607
48 10
3.4609 3.4610
3.4612
3.4613
3.4615
3.4616
3.4618
3.4619 3.4621
3.4622
48 20
3.4624J 3.4625
3.4627
3.4628
3.4630
3.4631
3.4633
3.4634 3.4636
3.4637
48 30
3.46391 3.4640
3.4642
3.4643
3.4645
3.4646
3.4648
3.4649! 3.4651
3.4652
48 40
3.4654 i 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
3.4682
49
3.4683
3.4685
3.4686
.3.4688
3.4689
3.4691
3.4692
3.4694 3.4695
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
34733
3.4735! 3.4736
3.4738 3.4739 1 3.4741
49 40
3.4742 3.4744
3.4745
3.4747
3.4748
3.47491 3.4751
3.4752 3.4754| 3.4755
49 50
3.47571 3.4758
3.4760
3.4781
3.4763
34764 3.4765
3.4767 3.4768! 3.4770
44:
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
d
it
it
2
it
3
4
ii
5
6
u
7
u
8
9
O h '50 m - s -
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
3.4847
3.4849
3.4850
3.4852
3.4853
3.4854
3.4856
51
3.4857
3.4859
3.4860
3.4861
3.4863
3.4864
3.4866
3.4867
3.4869
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
34942
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
3.49 01
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
35012
3.5013
3.5015
3.5016
3.5017
3.5019
3.5020
3.5022
3.5023
53
3.5024
3.5026
3.5027
3.5028
3.5030
3.5031
3.5032
3.5034
3.5035
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
3.5095
3.5096
3.5097
3.5099
3.5100
3.5101
3.5103
35104
54
3.5105
3.5107
3.5108
3.5109
3.5111
3.5112
3.5113
3.5115
3.5116
3.5117
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
3.51431 3.5144
54 30
3.5145
3.5147
3.5148
3.5149
3.5151
3.5152
3.5153
3.5155
3.5156
3.5157
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
8.5231
3.5232
3.5234
3.5235
3.5236
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
3.5258
3.5260
3.5261
3.5262
56
3.5263
3.5265
3.5266
3.5267
3.5269
3.5270
3.5271
3.5272
3.5274
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
3.5315
3.5316 3.5317
3.5319
3.5320
3.5321
3.5322
3.5324
3.5325
3.5326
56 50
3.5328
3.5329 3.5330
3.5331
3.5333
3.5334
3.5335
3.5336
3.5338
3.5339
57
3.5340
3.5342 3.5343
3.5344
3.5345
3.5347
3.5348
3.5349
3.5350
3.5352
57 10
3.5353
3.5354 3.5355
3.5357
3.5358
3.5359
3.5361
3.5362
3.5363
3.5364
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
3.5387
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 1 3.5431
3.5432
3.5433
3.5434
35436
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
3.5484
3.5485
35486
3.5488
3.5489
59
3.5490
3.5491
3.5492
3.5494
3.5495
3.5496
3.5497
3.5499
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
3.5553
3.5555
3.5556
3.5557
3.5558
3.5559
3.5561
3.5562
45
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
E
i
2
n
3
4
5
6
7
8
n
9
I , i n
ij 1* O' n> O 3 -
3.5563
3.5564
3.5565
3.5567
3.5568
3.5569
3.5570
3.5571
3.5573
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
3.5588
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
1
3.5635
3.5636
3.5637
3.5638
3.5640
3.5641
3.5642
3.5643
3.5644
35645
10
3.5647
3.5648
3.5649
3.5650
3.5651
3.5653
3.5654
3.5655
3.5656
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
35697
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
2 10
3.5717
3.5718
3.5719
3.5721
3.5722
3.5723
3.5724
3.5725
3.5726
35728
2 20
3.5729
3.5730
3.5731
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 50
3.5763
3.5765
3.5766
3.5767
3.5768
3.5769
3.5770
3.5771
3.5773
3.5774
1 3
3.5775
3.5776
3.5777
3.5778
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 50
3.5832
3.5833
3.5834
3.5835
3.5837
3.5838
3.5839
3.5840
3.5841
3.5842
1 4
3.5843
3.5844
3.5846
3.5847
3.5848
3.5849
3.5850
3.5851
3.5852
3.5853
4 10
3.5855
3.5856
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
3.5956
3.5957
3.5958
3.5959
3.5960
3.5962
3.5963
3.5964
3.5965
5 50
3.5966
3.5967
3.5968
3.5969
3.5970
3.5971
3.5973
3.5974
3.5975
3.5976
1 6
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
3.60i8
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
3.6033
3.6034
3.6035
3.6036
3.6037
3.6038
3.6039
3.6040
3.6041
1 7
3.6042
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
3.6056
3.6057
3.6058
3.6060
3.6061
3.6062
3.6063
7 20
3.6064
3.6065
3.6066
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
3.6085
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
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
3.6133
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
3.6150
3.6151
3.6152
3.6153
3.6154
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
3.61941 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
TABLE IX.
(LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
i
&
3
//
4
5
/(
6
7
//
8
9
l_ 1 II
i h -io m - o s -
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
3.628]
3.6282
3.6283
10 50
3.6284
3.6285
3.6286
3.6287
3.6288
3.6289
3.6290
3.6291
3.6292
3.6293
1 11
3.6294
3.6295
3.6296
3.6297
3.6298
3.6299
3.6300
3.6301
3.6302
3.6303
11 10
3.6304
3.6305
3.6306
3.6307
3.6308
3.6309
3.6310
3.6311
36312
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 30
3.6325
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
3.6347
3.6348
3.6349
3.6350
3.6351
3.6352
3.6353
3.6354
1 12
3.6355
3.6356
3.6357
3.6358
3.6359
3.6360
3.6361
3.6362
3.6363
3.6364
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
3.6414
1 1,3
3.6415
3.6416
3.6417
3.6418
3.6419
3.6420
3.6421
3.6422
3.6423
3.6424
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
3.6494
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
3.6526
3.6527
3.6528
3.6529
3.6530
3.6531
1 15
3.6532
3.6533
3.6534
3.6535
3.6536
3.6537
3.6538
3.6539
3.6540
3.6541
15 10
3.6542
3.6543
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
3.6581
3.6582
3.6583
3.6584
3.6585
3.6536
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
36632
3.6633
3.6634
3.6635
3.6636
16 50
3.6637
3.6638
3.6639
3.6640
3.6641
3.6642
3.6643
3.6644
3.6645
3.6645
1 17
3.6646
3.6647
3.6648
3.6649
3.6650
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
3.6694
3.6695
3.6696
3.6697
3.6698
3.6699
3.6700
3.6701
3.6702
1 18
3.6702
3.6703
3.6704
3.6705
3.6706
3.6707
3.6708
3.6709
3.6710
3.6711
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
36743
3.6744
3.6745
3.6746
3.6747
3.6748
18 50
3.6749
3.6750
3.6750
3.6751
3.o752
3.6753
3.6754
3.6755
3.6756
3.6757
1 19
3.6758
3.6759
3.6760
3.6761
3.6761
3.6762
3.6763
3.6764
3.6765
3.6766
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
36796
3.6797
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
4:7
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
i
\
3
//
4
1
5
ii
6
7
8
9
O i ,,
lh. 20 m. Q S .
3.6812
3.6813
3.6814 3.6815
3.6816
3.6817
3.6818
3.6819
3.6820
36821
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
3.6859
3.6860
3.6861
3.6862
3.6863
3.6864
3.6865
3.6865
1 21
3.6866
3.6867
3.6868
3.6869
3.6870
3.6871
3.6872
3.6873
3.6874
3.6874
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
P.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
3.6918
3.6919
1 22
3.6920
3.6921
3.6921
3.6922
3.6923
3.6924
3.6925
3.6926
3.6927
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
3.3947
3.6948
3.6949
3.6950
3.6950
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
3.6962
3.6963
22 50
3.6964
3.6964
3.6965
3.6966
3.6967
3.6968
3.6969
3.6970
3.6971
3.6971
1 23
3.6972
3.6973
3.6974
3.6975
3.6976
3.6977
3.6978
3.6978
3.6979
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
3.7017
3.7018
3.7019
3.7020
3.7021
3.7022
3.7023
3.7023
1 24
3.7024
3.7025
3.7026 3.7027
3.7028
3.7029
3.7029
3.7020
3.7031
3.7032
24 10
3.7033
3.7034
3.7035 3.7035
37036
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
37071
3.7072
3.7073
3.7074
3.7075
1 25
3.7076
3.7077
3.7077
3.7078
3.7079
3.7080
3.7081
3.7082
3.7083
3.70S3
25 10
3.7084
3.7085
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
3.7097
3.7098 3.7099
3.7099 3.7100
25 30
3.7101
3.7102
3.7103
3.7104
3.7105
3.7105
3.7106 3.7107
3.7108! 3.7109
25 40
3.7110
3.7110
3.7111
3.7112
3.7113
3.7114
3.7115
3.7116
3.7116! 3.7117
25 50
3.7118
3.7119
3.7120
3.7121
3.7121
3.7122
3.7123
3.7124
3.7125 3.7126
1 26
3.7126
3.7127
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
3.7164
3.7165
3.7166
3.7167
3.7168
26 50
3.7168
3.7169 3.7170
3.7171
3.7172
3.7173
3.7173
3.7174
3.7175
3.7176
1 27
3.7177
3.7178 3.7178
3.7179
3.7180
3.7181
3.7182
3.7183
3.7183
3.7184
27 10
3.7185
3.7186 3.7187
3.7188
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
37198
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
3.7221
3.7222
3.7223
3.7224
3.7225 3.7226
1 28
3.7226
3.7227
3.7228
3.7229
3.7230
3.7230
3.7231
3.7232
3.7233! 3.7234
28 10
3.7235
3.7235
3.7236
3.7237
3.7238
3.7239
37239
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
3.7271
3.7271
3.7272
37273
3.7274 3.7275
1 29
3.7275
3.7276
3.7277
3.7278
3.7279
3.7279
3.7280
3.7281
3.7282 3.7283
29 10
3.7284
3.7284
3.7285
3.7286
3.7287
3.7288
3.7288
3.7289
3.7290
3.7291
29 20
3.7292
3.7292
3.7293
3.7294
3.7295
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
3.7306 3.7307
29 40
3.7308
3.7309
3.7309
3.7310
3.7311
3.7312
3.7313
3.7313
3.7314 3.7315
29 50
3.7316
3.7317
3.7317
3.7318
3.7319
3.7320
3.7321
3.7322
3.7322 ! 3.7323
TABLE X.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
,- Arc.
d
it
2
3
</
4
5
6
7
8
9
"o /
l h -30 m - 0*-
3.7324
3.7325
3.7326
3.7326
3.7327
3.7328
3.7329
3.7330
3.7330
3.7331 !
30 10
3.7332
3.7333
3.7334
3.7334
3.7335
3.7336
3.7337
3.7338
3.7338
3.7339 1
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
3.7354
3.7355
30 40
3.7356
3.7357
3.7358
3.7358
3.7359
3.7360
3.7361
3.7362
3.7362
3.7363
30 50
3.7364
3.7365
3.7366
3.7366
3.7367
3.7368
3.7369
3.7370
3.7370
3.7371
1 31
3.7372
3.7373
3.7374
3.7374
3.7375
3.7376
3.7377
3.7377
3.7378
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 j 3.7395
31 30
3.7396
3.7397
3.7397
3.7398
3.7399
3.7400
3.7400
3.7401
3.7402
3.7403 f
31 40
3.7404
3.7404
3.7405
3.7406
3.7407
3.7408
3.7408
3.7409
3.7410
3.7411
31 50
3.7412
3.7412
3.7413
3.7414
3.7415
3.7415
3.7416
3.7417
3.7418
3.7419
1 32
3.7419
3.7420
3.7421
3.7422
3.7423
3.7423
3.7424
3.7425
3.7426
3.7426
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
3.7450 :
32 40
3.7451
3.7452
3.7452
3.7453
3.7454
3.7455
3.7455
3.7456
3.7457 j 3.7458 "
32 50
3.7459
3.7459
3.7460
3.7461
3.7462
3.7462
3.7463
3.7464
3.7465
3.7466
1 33
3.7466
3.7467
37468
3.7469
3.7469
3.7470
3.7471
3.7472
3.7473
3.7473 5
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
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
3.75271 3.7527 j
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
3.7551
3.7552
3.7553
3.7553
3.7554
3.7555
3.7556
3.7556
3.7557, 3.7558
1 35
3.7559
3.7560
3.7560
3.7561
3.7562
3.7563
3.7563
3.7564
3.7565 1 3.7566
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
3.7577
3.7578
3.7579
3.7579 3.7580
3.7581
35 30
3.7582
3.7582
3.7583
3.7584
3.7585
3.7585
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
3.7598
3.7599
3.7600
3.7600
3.7601
3.7602
3.7603
3.7603
1 36
3.7604
3.7605
3.7606
3.7606
3.7607
3.7608
3.7609
3.760$
3.7610
3.7611
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
3.7637
3.7638
3.7639
3.7640
3.7640
37641 |
36 50
3.7642
3.7643
3.7643
3.7644
3.7645
3.7645
3.7646
3.7647
3.7648
3.7648
1 37 o
3.7649
3.7650
3.7651
3.7651
3.7652
3.7653
3.7654
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 2 o
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 i
38 40
3.7723
3.7724
3.7725
3.7725
3.7726
3.7727
3.7728
3.7728
3.7729
3.7730 I 1
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 3.77751 3.7776
3.7776
3.7777
3.7778J 3.7779
3.7779, 3.7780
3.7781
49
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
i
2
3
i
5
6
n
7
8
9
l h -40 in - s
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
3.7799
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
3.7814
3.7815
3.7815
3.7816
3.7817
40 50
3.7818
3.7818
3.7819
3.7820
3.7820
3.7821
3.7822
3.7823
3.7823
3.7824
1 41
3.7825
3.7825
3.7826
3.7827
3.7828
3.7828
3.7829
3.7830
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
3.7842
3.7843
3.7843
3.7844
3.7845
3.7845
41 30
3.7846
3.7847
3.7848
3.7848
3.7849
3.7850
3.7850
3.7851
3.7852
3.7853
41 40
3.7853
3.7854
3.7855
3.7855
3.7856
3.7857
3.7858
3.7858
3.7859
3.7860
41 50
3.7860
3.7861
3.7862
37863
3.7863
3.7864
3.7865
3.7865
3.7866
3.7867
1 42
3.7868
3.7868
3.7869
3.7870
3.7870
3.7871
3.7872
3.7872
3.7873
3.7874
42 10
3.7875
3.7875
3.7876
3.7877
3.7877
3.7878
3.7879
3.7880
3.7880
3.7881
42 20
3.7882
3.7882
3.7883
3.7884
3.7885
3.7885
3.7886
3.7887
3.7887
3.7888
42 30
3.7889
3.7889
3.7890
3.7891
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
1 43
3.7910
3.7911
3.7911
3.7912
3.7913
3.7913
3.7914
3.7915
3.7916
3.7916
43 10
3.7917
3.7918
3.7918
3.7919
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
3.7930
3.7930
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
3.7948
3.7949
3.7950
3.7950
3.7951
1 44
3.7952
3.7953
3.7953
3.7954
3.7955
3.7955
3.7956
3.7957
3.7957
3.7958
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
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
3.7983
3.7984
3.7984
3.7985
3.7986
44 50
3.7987
3.7987
3.7988
3.7989
3.7989
3.7990
3.7991
3.7991
3.7992
3.7993
1 45
3.7993
3.7994
3.7995
3.7995
3.7996
3.7997
3.7998
3.7998
3.7999
3.8000
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
3.8030
3.8031
3.8032
3.8033
3.8033
3.8034
1 46
3.8035
3.8035
3.8036
3.8036
3.8037
3.8038
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
3.8054
3.8054
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
3.6104
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
3.81 1
3.8117
3.8118
3.8118
3.8119
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
3.8131
3.8132
3.8132
3.8133
3.8134
3.8134
3.8135
48 30
3.8136
3.8136
3.8137
3.8138
3.8138
3.8139
3.8140
3.8140
3.8141
3.8142 i
48 40
3.8142
3.8143
3.8144
3.8144
3.8145
3.8146
3.8146
3.8147
3.8148
3.8148
48 50
3.8149
3.8150
3.8150
3.8151
3.8152
3.8152
3.8153
3.8154
3.8154
3.8155
1 49
3.8156
3.8156
3.8157
3.8158
3.8158
3.8159
3.8160
3.8160
3.8161
3.8162
49 10
3.8162
3.8163
3.8164
3.8164
3.8165
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
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
50
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
ii
2
3
4
5
6
7
8
9
0, 1 II
l h -50 m - s -
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
3.8206
50 20
3.8209
3.8209
3.8210
3.8211
38211
38212
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 i 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
1 52
3.8274
3.8274
3.8275
3.8276
3.8276
3.8277
3.8278
3.8278
3.8279
3.8280
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
38326
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
3.8345
3.8345
3.8346
3.8347
3.8347
3.8348
3.8349
3.8349
3.8350
1 54
3.8351
3.8351
3.8352
3.8352
3.8353
3.8354
3.8354
3.8355
3.8356
3.8356
54 10
3.8357
3.8358
3.8358
3.8359
3.8359
3.8360
3.8361
3.8361
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
3.8387
3.8388
1 55
3.8388
3.8389
3.8390
3.8390
3.8391
3.8392
3.8392
3.8393
3.8394
3.8394
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
3.8417
3.8417
3.8418
3.8419
3.8419
55 50
3.8420
3.8420
3.8421
3.8422
3.8422
3.8423
3.8424
3.8424
3.8425
3.8425
1 56
3.8426
3.8427
3.8427
3.8428
3.8429
3.8429
3.8430
3.8430
3.8431
3.8432
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
3.8460
3.8460
3.8461
3.8462
3.8462
3.8463
1 57
3.8463
3.8464
3.8465
3.8465
3.8466
3.8466
3.8467
3.8468
3.8468
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
38495
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
3.8521
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
3.8536 3.8536
1 59
3.8537
3.8538
3.8538
3.8539
3.8539
3.8540
3.8541
3.8541
3.8542; 3.8542
59 10
3.8543
3.8544
3.8544
3.8545
3.8545
3.8546
3.8547
3.8547
3.8548 3.8549
59 20
3.8549
3.8550
3.8550
3.8551
3.8552
3.8552
3.8553
3.8553
3.85541 3.8555
59 30
3.8555
3.8556
3.8556
3.8557
3.8558
3.8558
3.8559
3.8559
3.8560 3.8561
59 40
3.8561
3.8562
38562
3.8563
3.8564
3.8564 3.8565
3.8565
3.8566! 3.8567
59 50
3.8567
3.8568
3.8568
3.8569
3.8570
3.8570 3.8571
3.8572
3.8572 3.8573
51
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
1
2
3
n
4
H
5
6
7
M
8
9
0. / II
2 h. O m. O s.
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
30
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
3.8605
3.8606
3.8606
3.8607
3.8608
3.8608
3.8609
2
3.8609
3.8610
3.8611
3.8611
3.8612
3.8612
3.8613
3.8614
38614
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
3.8636
3.8636
3.8637
3.8637
3.8638
3.8639
50
3.8639
3.8640
3.8640
3.8641
3.8642
3.8642
3.8643
3.8643
3.8644
3.8645
220
3.8645
3.8646
3.8646
3.8647
3.8647
3.8648
3.8649
3.8649
3.8650
3.8650
2 10
3.8651
3.8652
3.8652
3.8653
3.8653
3.8654
3.8655
3.8655
3.8656
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
230
3.8681
3.8681
3.8682
3.8682
3.8683
3.8684
3.8684
3.8685
3.8685
3.8686
3 10
3.8686
3.8687
3.8688
3.8688
3.8689
3.8689
3.8690
3.8691
3.8691
3.8692
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 i
3 40
3.8704
3.8705
3.8705
3.8706
3.8706
3.8707
3.8708
3.8708
3.8700
3.8709 ;
3 50
3.8710
38710
3.8711
3.8712
3.8712
3.8713
3.8713
3.8714
3.8715
3.8715 !
24
3.8716
3.8716
3.8717
3.8717
3.8718
3.8719
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
3.8746
3.8747
3.8747
3.8748
3.8748
3.8749
3.8749
3.8750
250
3.8751 j 3.8751
3.8752
3.8752
3.8753
3.8754
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
38778
3.8779
5 50
3.8779
3.8780
3.8781
3.8781
3.8782
3.8782
3.8783
3.8783
3.8784
3.8785 1
260
3.8785
3.8786
3.8786
3.8787
3.8788
3.8788
3.8789
3.8789
3.8790
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
3.8817
3.8818
3.8818
3.8819
270
3.8820
3.8820
3.8821
3.8821
3.8822
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
3.8852
3.8853
280
3.8854
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
a 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
290
38887
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! 38911
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
52
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arp.
i
2
3
it
4
5
6
7
8
H
9
2 h -io m - o 3 -
3.8921
3.8922
3.8922
3.8923
3.8923
3.8924
3.8924
3.8925
3.8925
3.8926
10 10
3.8927 j 3.8927
3.8928
3.8928
3.8929
3.8929
3.8930
3.8930
3.8931
3.8932
10 20
3.8932 3.8933
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
3.8954
2 11
3.8954
3.8955
3.8955
3.8956
3.8956
3.8957
3.8958
3.8958
3.8959
3.8959
11 10
3.8960 1 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
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
3.8979
3.8980
3.8980
3.8981
3.8981
11 50
3.8982
3.8982
3.8983
3.8983
3.8984
3.8985
3.8985
3.8986
3.8986
3.8987
2 12
3.8987
3.8988
3.8988
3.8989
3.8989
3.8990
3.8991
3.8991
3.8992
3.8992
12 10
3.8993
3.8993
3.8994
3.8994
3.8995
3.8995
3.8996
3.8997
3.8997
3.8998
12 20
3.8998
3.8999
3.8999
3.9000
3.9000
3.9001
3.9001
3.9002
3.9003
39003
12 30
3.9004
3.9004
3.9005
3.9005
3.9006
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
3.90131 3.9013
3.9014
12 50
3.9015
3.9015
3.9016
3.9016
3.9017
3.9017
3.9018
3.9018 3.9019
3.9019
2 13
3.9020
3.9021
3.9021
3.9022
3.9022
3.9023
3.9023
3.90241 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
3.9033
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
39040
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
3.9049
3.9049
3.9050
3.9050
3.9051
3.9051
3.9052
2 14
3.9053
3.9053
3.9054
3.9054
3.9055
3.9055
3.9056
3.9056
3.9057
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
39082
3.9083
3.9083
3.9084
3.9084
2 15
3.9085
3.9085
3.9086
3.9086
3.9087
3.9088
3.9088
3.9089
3.9089
3.9090
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
3.9097
3.9098
3.9098
3.9099
3.9099
3.9100
3.9100
15 30
3.9101
3.9101
3.9102
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 50
3.9112
3.9112
3.9113
3.9113
3.9114
3.9114
3.9115
3.9115
3.9116
3.9116
1 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
3.9130
3.9131
3.9131
3.9132
3.9132
16 30
3.9133
3.9133
3.9134
3.9134
3.9135
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
3.9144
3.9145
3.9146
3.9146
3.9147
3.9147
3.9148
3.9148
2 17
3.9149
3.9149
3.9150
3.9150
3.9151
3.9151
3.9152
3.9152
3.9153
3.9153
17 10
3.9154
3.9155
3.9155
3.9156
3.9156
3.9157
3.9157
3.9158
3.9158
3.9159 l!
17 20
3.9159
3.9160
3.9160
3.9161
3.9161
3.9162
3.9162
3.9163
3.9163
3.9164 j
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
3.9179
3.9180
2 18
3.9180
3.9181
3.9181
3.9182
3.9182
3.9183
3.9183
3.9184
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
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
3.9204
3.9204
3.9205
3.9205
3.9206
18 50,
3.9206
3.9207
3.9207 3.9208
3.9209
3.9209
3.9210
3.9210
3.9211
3.9211
2 19
3.9212
3.9212
3.9213 3.9213
3.9214
3.9214
3.9215
3.9215
3.9216
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
3.92321 3.9233
3.9233 3.9234
3.9235
3.9235 3.9236
3.9236
3.9237
3.9237
19 50
3.9238 '' 3.9238 ! 3.9239 3.9239 3.9240
3.9240 3.9241
3.9241
3.9242 j 3.9242
53
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
d
i
H
2
3
i
5
6
7
8"
9
0. I
2 h -20 m - s -
3.9243
3.9243
3.9244
3.9244
3.9245
3.9245
3.9246
3.9246
3.9247
39247
20 10
3.9248
3.9248
3.9249
3.9250
3.9250
3.9251
3.9251
3.9252
3.9252i
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
3.929
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
3.9273
3.9273
2 21
3.9274
3.9274
3.9275
3.9275
3.9276
3.9276
3.9277
3.9277
3.9278
3.9278
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 40
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
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
22 10
3.9309
3.9310
3.9311
3.9311
3.9312
3.9312
3.9313
3.9313
3.9314
3.9314
22 20
3.9315
3.9315
3.9316
3.9316
3.9317
3.9317
3.9318
3.9318
3.9319
3.9319
22 30
3.9320
3.9320
3.9321
3.9321
3.9322
3.9322
3.9323
3.9323
3.9324
3.9324
22 40
3.9325
3.9325
3.9326
3.9326
3.9327
3.9327
3.9328
3.9328
3.9329
3.9329
22 50
3.9330
3.9330
3.9331
3.9331
3.9332
3.9332
3.9333
3.9333
3.9334
3.9334
2 23
3.9335
" 3.9335
3.9336
3.9336
3.9337
3.9337
3.9338
3.9338
3.9339
3.9339
23 10
3.9340
3.9340
3.9341
3.9341
3.9342
3.9342
3.9343
3.9343
3.9344
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
3.9352
3.9353
3.9353
39354
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
3.9361
3.9362
3.9362
3.9363
3.9363
3.9364
3.9364
3.9365
2 24
3.9365
3.9366
3.9366
3.9367
3.9367
3.9368
3.9368
3.9369
3.9369
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 50
3.9390
3.9391
3.9391
3.9392
3.9392
39393
3.9393
3.9394
3.9394
3.9395
2 25
3.9395
3.9396
3.9396
3.9397
3.9397
3.9398
3.9398
3.9399
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
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
3.9422
3.9422
3.9423
3.9423
3.9424
3.9424
3.9425
2 26
3.9425
3.9426
3.9426
3.9427
3.9427
3.9428
3.9428
3.9429
3.9429
3.9430
26 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
3.9450
3.9451
3.9451
3.9452
3.9452
3.9453
3.9453
3.9454
3.9454
2 27
3.9455
3.9455
3.9456
3.9456
3.9457
3.9457
3.9458
3.9458
3.9459
3.9459
27 10
3.9460
3.9460
3.9461
3.9461
3.9462
3.9462
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
27 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
3.9480
3.9480
3.9481
3.9481
3.9482
3.9482
3.9483
3.9483
3.9484
2 28
3.9484
3.9485
3.9485
3.9486
3.9486
3.9487
3.9487
3.9488
3.9488
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
3.9501
3.9501
3.9502
3.9502
3.9503
3.9503
28 40
3.9504
3.9504
3.9505
3.9505
3.9506
3.9506
3.9507
3.9507
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
3.951 9 j 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.S530
3.9531
3.9531
3.9532
3.9532
29 40
3.9533
3.9533
3.9534 3.9534
3.9535
3.9535
3.9536
3.9536
3.9537
3.9537
29 50
3.9538 3.9538
3.9539 3.9539! 3.9540
3.9540
3.9540
3.9541
3.9541
3.9542
TABLE 15.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
d
i
2
3
4
&
6
7
4
0, ( //
2 h. 30 m. QS.
3.9542
3.9543
3.9543
3.9544
3.9544
3.9545
3.9545
3.9546
3.9546
3.9547
30 10
3.9547
3.9548
S.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
3.9556
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
3.9569
3.9570
3.9570
3.9571
2 31
3.9571
3.9572
3.9572
3.9573
3.9573
3.9574
3.9574
3.9575
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
39585
3.9585
31 30
3.9586
3.9586
3.9587
3.9587
3.9588
3.9588
3.9589
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
3.9697
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
3.9609
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
39623
32 50
3.9624
3.9624
3.9625
3.9625
3.9626
3.9626
3.9627
3.9627
3.9627
3.9628
2 33
3.9628
3.9629
3.9629
3.9630
3.9630
3.9631
3.9631
3.9632
3.9632
3.9633
33 10
3.9633
3.9634
3.9634
3.9634
3.9635
3.9635
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
39653
3.9653
3.9653
3.9654
3.9654
3.9655
3.9655
3.9656
3.9656
2 34
3.9657
3.9657
3.9658
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
35 10
3.9689
3.9690
3.9690
3.9691
3.9691
3.9692
3.9692
3.9693
3.9693
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
3.9709
3.9709
3.9710
3.9710
3.9710
3.9711
3.9711
3.9712
3.9712
2 36
3.9713
3.9713
3.9714
3.9714
3.9715
3.9715
3.974C
3.9716
3.9716
3.9717
36 10
3.9717
3.9718
3.9718
3.9719
3.9719
3.9720
3.9720
3.9721
3.9721
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
3.9739
3.9739
3.9740
3.9740
2 37
3.9741
3.9741
3.9741
3.9742
3.9742
3.9743
3.9743
3.9744
3.9744
3.9745
37 10
3.9745
3.9746
39746
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
39764
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
3.0779
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 1 3.9785
3.9785
3.9785
3.9786
38 40
3.9786
3.9787
3.9787
3.9788
3.9788
3.9789 3.9889
3.9790
3.9790
3.9790
38 50
3.9791
3.9791
3.9792
3.9792
3.9793
3.9793 3.9794
3.9794
3.9795
3.9795
2 39
3.9795
3.9796
3.9796
3.9797
3.9797
3.9798 3.9798
3.9799
3.9799
3.9800
39 10
3.9800
3.9800
3.9801
3.9801
3.9802
3.9802 i 3.9803
3.9803
3.9804
3.9804
39 20
3.9805
3.9805
3.9805
3.9806
3.9806
3.98071 3.9807
3.9808
3.9808
3.9809
39 30
3.9809
3.9810
3.9810
3.9810
3.9811
3.981 1 1 3.9812
3.9812
3.9813
3.98ia
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
3.9S19
3.9819
3.9820
3.9820 3.9821
3.9821
3.9822 3.9822
55
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
i
ii
2
3
4
5
n
6
8"
9
O. 1 11
2 h. 40 m. .
3.9823
3.9823
3.9824
3.9824
3.9825
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
3.9835
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
3.9845
40 50
3.9845
3.9846
3.9846
3.9^47
3.9847
3.9848
3.9848
3.9848
3.9849
3.9849
2 41
3.9850
3.9850
3.9851
3.9851
3.9852
3.9852
3.9852
3.9853
3.9853
3.9854
41 10
3.9854
3.9855
3.9855
3.9856
3.9856
3.9857
3.9857
3.9857
3.9858
3.9858
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
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
3.9874
3.9874
3.9874
3.9875
3.9875
3.9876
3.9876
2 42
3.9877
3.9877
3.9878
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
3.9885
3.9885
42 20
3.9886
3.9886
3.9886
3.9887
3.9887
3.9888
3.9888
3.9889
3.9889
3.9890
42 30
3.9890
3.9890
3.9891
3.9891
3.9892
3.9892
3.9893
3.9893 3.9894
3.9894
42 40
3.9894
3.9895
3.9895
3.9896
3.9896
3.9897
3.9897
3.9898 3.9898
3.9898
42 50
3.9899
3.9899
3.9900
3.9900
3.9901
3.9901
3.9902
3.9902
3.9903
3.9903
2 43
3.9903
3.9904
3.9904
3.9905
3.9905
3.9906
3.9906
3.9906
3.9907
3.9907
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
39920
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
3.9927
3.9927
3.9928
3.9928
3.9929
3.9929
3.9930
2 44
3.9930
3.9930
3.9931
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
3.9938
3.9938
44 20
3.9939
3.9939
3.9940
3.9940
3.9941
3.9941
3.9941
3.9942
3.9942
3.9943
44 30
3.9943
3.9944
3.9944
3.9944
3.9945
3.9945
3.9946
3.9946
3.9947
3.9947
44 40
3.9948
3.9948
3.9948
3.9949
3.9949
3.9950
3.9950
3.9951
3.9951
3.9952
44 50
3.9952
3.9952
3.9953
3.9953
3.9954
39954
3.9955
3.9955
3.9955
3.9956
2 45
3.9956
3.9957
3.9957
3.9958
3.9958
3.9959
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
3.9966
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
3.9981
3.9981
3.9982
3.9982
2 46
3.9983
3.9983
3.9983
3.9984
3.9984
3.9985
3.9985
3.9986
3.9986
3.9987
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
3.9995
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
4.0005
4.0006
4.0006
4.0007
4.0007
4.0007
4.0008
4.0008
2 47
4.0009
4.0009
4.0010
4.0010
4.0010
4.0011
4.001 1
4.0012
4.0012
4.0013
47 10
4.0013
4.0013
4.0014
4.0014
4.0015
4.0015
4.0016
4.0016
4.0016
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
4.002$
4.0029
4.0029
4.0029
4.0030
47 50
4.0030
4.0031
4.0031
4.0032
4.0032
4.0032
4.0033
4.0033
4.0034
4.0034
2 48
4.0035
4.0035
4.0035
4.0036
4.0036
4.0037
4.0037
4.0038
4.0038
4.0038
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
4.0045
4.0045
4.0045
4.0046
4.0046
4.0047
4.0047
48 30
4.0048
4.0048
4.0048
4.0049
4.0049
4.0050
4.0050
4.0051
4.0051
4.0051
48 40
4.0052
4.0052
4.0053
4.0053
4.0054
4.0054
4.0054
4.0055
4.0055
4.0056
48 50
4.0056
4.0057
4.0057
4.0057
4.0058
4.0058
4.0059
4.0059
4.0060
4.0060
2 49
4.0060
4.0061
4.0061
4.0062
4.0062
4.0063
4.0063
4.0063
4.0064
4.0064
49 10
4.0065
4.0065
4.0066
4.0066
4.0066
4.0067
4.0067
4.0068
4.0068
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
t9 50
4.0082
4.0082
4.0083
4.0083
4.0083
4.0084
4.0084
4.0085
4.0085
4.0086
56
TABLE IX.
LOGARITHMS OF SMALL ARCS IN SPACE OR TIME.
Arc.
//
1
2
3
4
5
6
n
7
8
9
0, ( II
2 h. 50 m. Q s.
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
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
40119
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
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
4.0133
4.0134
4.0134
4.0135
4.01, ']:, ' 4.0136
4.0136
4.0136
2 52
4.0137
4.0137
4.0138
4.0138
4.0138
4.0139
4.0! I'.l
4.0140
4.0140
4.0141
52 10
4.0141
4.0141
4.0142
4.0142
4.0143
4.0143
4.0.44
4.0144
4.0144
4.0145
52 20
4.0145
4.0146
4.0146
4.0146
4.0147
4.0147
4.0148
4.0148
4.0149
4.0149
52 30
4.0149
4.0150
4.0150
4.0151
4.0151
4.0152
4.0152
4.0153
4.0153
4.0153
52 40
4.0154
4.0154
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
4.0160
4.0161
4.0161
4.0162
2 53
4.0162
4.0162
4.0163
4.0163
4.0164
4.0164
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
4.0187
4.0188
4.0188
4.0189
4.01 89
4.0190
4.0190
4.0190
4.0191
54 10
4.0191
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 50
4.0208
4.0208
4.0209
4.0209
4.0209
4.0210
4.0210
4.0211
4.0211
4.0211
2 55
4.0212
4.0212
4.0213
4.0213
4.0214
4.0214
4.0214
4.0215
4.0215
4.0216
55 10
4.0216
4.0216
4.0217
4.0217
4.0218
4.0218
4.0219
4.0219
4.0219
4.0220
55 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
40225
4.0225
4.0225
4.0226
4.0226
4.0227
4.0227
4.0228
4.0228
55 40
4.0228
4.0229
4.0229
4.0230
4.0230
4.0230
4.0231
4.0231
4.0232
4.0232
55 50
4.0233
4.0233
4.0233
4.0234
4.0234
4.0235
4.0235
4.0235
4.0236
4.0236
2 56
4.0237
4.0237
4.0237
4.0238
4.0238
4.0239
4.0239
4.0240
4.0240
4.0240
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
4.0256
4.0256
4.0257
56 50
4.0257
4.0258
40258
4.0258
4.0259
4.0259
4.0260
4.0260
4.0260
4.0261
2 57
4.0261
4.0262
4.0262
4.0262
4.0263
4.0263
4.0264
4.0264
4.0265
4.0265
57 10
4.0265
4.0266
4.0266
4.0267
4.0267
4.0267
4.0268
4.0268
4.0269
4.0269
57 20
4.0269
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
4.0284
4.0284
4.0285
4.0285
2 58
4.02S6
4.0286
4.0287
4.0287
4.0287
4.0288
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
4.031 1
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
4.0330
59 50
4.0330
4.0331
4.0331
4.0331
4.0332
4.0332
4.0333
4.0333
4.0333
4.0334
TABLE X.
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.
Difference of the Proportional Logarithms in the Ephemeris.
Approximate
I
4
6
8
10
12 14 16
IS
20
2224
26
28
032
34
36
38
40
42
44 46 48
ftjfl
hn
.
3
C
C
10
2 50
1
i
1
1
1
i
i
1
2
2
2
2
2
2
2
2
3
3
3
3
8
3
3
20
2 40
1
1
1
i
2
2
2
2
2
3
3
3
3
4
4
4
4
5
5
5
5
6
6
6
6
30
2 30
1
2
2
2
2
3
3
3
4
4
5
5
5
C
G
G
7
7
7
8
8
8
9
9
40
2 20
1
2
2
3
3
3
4
4
5
5
6
6
G
7
7
8
8
9
9
10
10
10
11
11
50
2 10
1
2
2
3
3
4
4
5
5
5
G
6
7
7
8
8
9
9
10
10
11
12
12
13
13
1
2
1
2
2
3
3
4
4
B
C
6
7
7
8
8
9
9
10
10
11
12
12
13
13
14
14
1 10
1 50
I
2
2 3
4
4 5
5
G
C
7
8
8
9
9
10
11
11
12
12
13
14
14
15
15
1 20
1 40
I
2
3 3
4
4 5
C
G
7
7
8
9
9 10
10
11
12
12
13
14
14
15
15
16
1 30
1 30
1
2
3
3
4
4
5
G
G
7
8
8
9
9 10
11
11
12
12
13
14
14
15
If
16
Difference of the Proportional logarithms in the Ephemeris,
4
5553
63
63 64 65
G3
70
72
74
76 78 80
82
8486
S3
9092
91
9698
100
102
.
h. ra
Olft
3
2r:n
7!
20
2 40
7
7
7
1
8
8
8
8
9
9
9
9
10
10
10
10
11
11
11
11
12
12
12
12
13
30
2 30
9
10
10
10
11
11
12
12
12
13
13
13
14
14
14
14
15
15
1G
16
16
17
17
17
18
40
2 20
12
12
13
13
13 14 14
15 15 16
1G
1C
17
17
18
18
19
19 19
20
20
21
21
22
22
50
2 10
14
14
15
15
16 16
16
17
17
IS
19
19
20
20
21
21
22
22 22
23
23
24
24
25
26
1
2
15
16
16
17
17
18
18
19
19
20
21
21
22
22
23 23
24
24
25
25
26
27
27
28
28
1 10
1 50
10
17
17
18 18 19 19 2021 21
22 22 23
24 24 25 25
2G
27
27
28
28
29
30
30
1 20
1 40
17
17
18
19 19 20 20 21
21 22
23 23 24 25 25 26 26
27
28
28
29
29
30
31
31
1 30
1 30
17
18
18
19
19 20 21 21
22 23
23 24 24 25 25 26 27
27
28
29
29
30 31
31
32
1 1
1
Difference of the Proportional Logarithms in the Ephemeris,
W.
I 106
1(E
110
112
114
115
118
120
122 124
i:
i 128
132
132
131
136
188
.
.
3
10
2 50
7
7
7
7
7
7
8
8
8
8 8
8
8
8
9
9
9
9
20
2 40
13
13
13
14
14
14
14
15
15
15 15
15
16
10
16
1G
17
17
30
2 30
18
13
19
19
19
20
20
20
21
21 21
22
22
22
23
23
24
24
40
2 20
22
23
23
24
24
25
25
25
26
25 27
27
23
23
23
29
29
30
50
2 10
26
26
27
27
28
29
9
29
30
30 31
31
32
32
33
33
34
34
1
2
29
29
30
30
31
31
32
33
33
34 34
35
35
3G
37
37
38
38
1 10
1 50
31
31
32
32
33
34
34
35
35
36 37
37
33
33
39
40
40
41
1 20
1 40
32
33
33
34
34
35
35
36
37
33 33
39
39
43
41
41
42
42
1 30
1 30
32
33
34
34
35
35
3G
36
37
33 39
39
40
40
41
42
42
43
The Correction is to be aslded to the approximate Greenwich Time when the Proportional Logarithms in the
Epheineris are decreasing^ and subtracted when they are increasing.
58
TABLE XI.
LOG. N FOR DISTANCES FROM THE SUN.
ISff.
Qh.
f"
6 h -
gh.
ir
15 h
18 h
21 h.
18ff.
o h -
r
6 h -
9 b -
ir
IS"'
18 h -
21 h.
Jan. 7
0.76
.78
.79
.80
.81
.82
.83
.84
Apr. 10
+0.66
.69
.72
.74
.77
.79
.81
.83
8
0.85
.86
.87
.87
.88
.89
.89
.90
11
0.85
0.86
088
0.89
0.91
0.92
0.93
0.95
9
0.90
.91
.91
.91
.92
.92
.92
.92
12
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.02
10
0.92
.92
.92
.92
.92
.92
.92
.92
13
+1.03
1.04
1.04
1.05
1.06
1.06
1.07
1.07
11
0.92
.91
.91
.91
.90
.90
.89
.89
18
0.80
0.78
0.77
0.76
0.75
0.73
0.71
0.69
12
0.88
.87
.86
.85
.84
.83
.82
.81
19
0.67
.65
.63
.60
.58
.55
.52
.48
13
0.80
.78
.77
.75
.73
.71
.69
.66
20
0.46
.41
.36
.31
.25
.18
.10
.00
14
0.63
.60
.56
.52
.48
.42
.36
.28
22
+0.12
.20
.26
.32
.37
.41
.45
.49
20
0.71
.74
.76
.79
.81
.83
.84
.85
23
0.52
.55
.58
.60
.63
.65
.67
.69
21
0.87
.88
.89
.89
.90
.91
.91
.92
24
0.71
.73
.75
.76
.78
.79
.80
.82
22
0.92
.93
.93
.93
.93
.93
.93
.93
25
+0.83
.84
.85
.86
.87
.88
.89
.90
23
0.93
.93
.93
.92
.92
.91
.91
.90
26
0.91
.92
.93
.93
.94
.95
0.95
0.96
24
0.90
.89
.89
.88
.87
.86
.85
.84
27
0.97
0.97
0.98
.98
.99
.99
0.99
1.00
25
0.83
.82
.81
.80
.78
.77
.75
.74
May 6
9.77
9.96
0.10
.20
.28
.35
0.40
0.46
26
0.72
.70
.68
.66
.04
.61
.59
.56
7
0.50
0.54
0.58
.61
.04
.67
.70
.72
27
0.53
.49
.45
.41
.37
.31
.25
.18
8
+0.75
.77
.79
.80
.82
.84
.85
.87
Feb. 6
0.88
.88
.88
.89
.89
.89
.89
.89
9
0.88
.89
.90
.92
.93
.94
0.94
0.95
7
0.89
.89
.89
.89
.89
.88
.88
.88
10
0.96
0.97
0.97
0.98
0.99
0.99
0.99
LOO
8
0.87
.87
.86
.86
.85
.84
.83
.82
11
1.00
1.01
1.01
1.01
1.01
1.01
1.01
101
9
0.82
.80
.79
.78
.77
.75
.74
.72
12
1.01
1.01
1.01
1.01
1.01
1.00
1.00
1.00
10
0.70
.68
.66
.64
.61
.58
.55
.52
13
+0.99
0.09
0.98
0.97
0.97
0.96
0.95
0.94
11
0.48
.43
.38
.32
.25
.16
.05
9.89
18
0.46
.41
.35
.29
.22
.13
0.03
9.89
13
+0.43
.49
.55
.60
.64
.69
.73
.76
20
+0.23
.29
.34
.39
.43
.47
0.51
0.54
14
+0.80
.83
.87
.90
.93
.96
.99
1.02
21
0.57
.59
.62
.64
.66
.68
.70
.72
18
0.78
.80
.82
.84
.85
.86
.87
.88
22
0.73
.75
.76
.78
.79
.81
.82
.83
19
0.89
.89
.90
.90
.90
.90
.90
.90
23
+0.84
.85
.86
.87
.88
.88
.89
.90
20
0.90
.89
.89
.89
.88
.88
.87
.86
24
0.91
.91
.92
.93
.93
.94
.94
.94
21
0.86
.85
.84
.83
.82
.81
.79
.78
25
0.95
.95
.96
.96
.96
.96
.96
.97
22
0.77
.75
.74
.72
.70
.69
.67
.64
26
0.97
.97
.97
.97
.97
.97
.97
.96
23
0.62
.60
.57
.54
.51
.48
.44
.40
27
0.96
.96
.96
.95
.95
.94
.94
.98
26
+0.30
.36
.41
.45
.49
.53
.56
.60
June 3
+0.05
.18
.28
.35
.42
.47
.52
.56
Mar. 8
0.83
.82
.81
.80
.79
.78
.77
.76
4
0.60
.63
.66
.69
.72
.74
.76
.78
9
0.74
.73
.71
.70
.68
.66
.64
.60
5
0.80
.82
.83
.85
.86
.87
.88
.89
10
0.59
.56
.53
.49
.45
.41
.36
.30
6
0.90
.91
.92
.93
.94
.94
.95
.95
12
+0.91
.06
.17
.26
.34
.40
.46
.51
7
0.96
.96
.97
.97
.97
.97
.98
.98
13
+0.55
.59
.63
.67
.70
.73
.76
.78
8
+0.98
.98
.98
.98
.97
.97
.97
.97
14
0.81
0.83
0.85
0.87
0.89
0.91
0.93
0.95
9
0.96
.96
.95
.95
.94
.94
.93
.92
15
+0.97
0.99
1.00
1.02
1.03
1.05
1.06
1.08
10
0.91
.91
.90
.88
.87
.86
.85
.83
19
0.78
0.80
0.82
0.84
0.84
0.85
085
0.86 ! 11
0.82
.80
.78
.76
.73
.71
.68
.64
20
0.86
.86
.85
.85
.84
.84
.83
17
0.18
.26
.32
.38
.43
.47
.51
.54
21
0.82
.81
.80
.78
.77
.76
.74
.73
18
+0.57
.60
.63
.65
.67
.69
.71
.73
22
0.71
.69
.67
.65
.63
.61
.58
.55
19
0.74 .76! .77
.79
.80
.81
.82
.83
23
0.53
.49
.46
.42
.38
.33
.27
.21
20
0.84 ' .85 .86
.87
.87
.88
.89
.89
25
+0.84
.98
.08
.16
.23
.29
.35
.39
21
0.90
.90
.91
.91
.92
.92
.93
.93
26
0.44
.48
.51
.54
.57
.60
.63
.65
22
0.93
.93
.92
.94
.94
.94
.94
.94
27
+0.67
.69
.71
.73
75
.77
.79
.80
23
+0.94
.94
.94
.93
.93
.93
.93
.92
28
+0.82
.83
.85
.86
.87
.88 .90
.91
24
0.92
.91
.91
.90
.90
.89
.88
.88
Apr. 6
0.67
.65
.63
.61
.58
.55' .52
.48
25
0.87
.86
.85 .83
.82
.81
.79
.78
7
- 0.44
.40
.35
.29
.22' .13' .03
.88
Julv 3
0.82 .84
.85 .87
.88
.89
.90
.91
9
+0.31
.37
.43
.48
.52 .56 .60
.63
' 4
0.92
.92
.93 .93
.93
.94
.95
.95
59
TABLE XI.
LOG. N FOR DISTANCES FROM THE SUN.
184$.
Qh.
r
gh.
gh.
ir
IF'
18 h -
21 h -
18tf.
Qh.
8 h -
gh.
Qh.
ir
15 h -
18 h>
21 m
July 5
+0.95
.95
.96
.96
.96
.95
.95
.95
Oct. 3
0.40
.44
.48
.52
.55
.58
.61
.63
6
0.95
.95
.94
.94
.94
.93
.93
.92
4
0.66
.68
.70
.72
.74
.76
.77
.79
7
0.91
.91
.90
.89
.88
.87
.86
.85
5
0.80
.82
.83
.84
.86
.87
.88
.89
8
0.84
.83
.81
.80
.78
.76
.75
.73
6
0.90
.91
.92
0.93
0.94
0.95
0.96
0.96
9
0.70
.68
.66
.63
.60
0.57
0.53
0.49
7
0.97
.98
.98
0.99
1.00
1.00
1.01
1.02
10
+0.44
.39
.38
.25
.16
0.04
9.86
9.54
13
+0.84
.83
.82
0.81
0.80
0.78
0.77
0.76
16
0.47
.52
.56
.60
.63
0.66
0.68
0.70
14
0.74
.72
.71
.69
.67
.64
.62
.59
17
0.72
.74
.76
.77
.79
.80
.81
.82
15
+0.56
.53
.50
.46
.42
.37
.31
.25
18
0.83
.84
.85
.86
.86
.87
.88
.88
17
9.98
.10
.20
.28
.34
.40
.45
.50
19
0.89
.89
.90
.90
.90
.91
.91
.91
18
0.54
.58
.61
.64
.67
.70
.73
.75
20
+0.91
.91
.91
.91
.91
.91
.91
.91
19
0.77
.79
.81
.83
.85
.86
.88
.89
21
0.91
.91
.90
.90
.90
.89
.89
.88
20
0.91
.92
.93
.94
.96
.97
.98
.99
22
0.88
.87
.86
.85
.85
.84
.83
.82
30
9.99
.10
.18
.25
.31
.36
.41
.45
23
0.80
.79
.78
.76
.75
.73
.71
.69
31
0.49
.52
.55
.58
.61
.63
.65
.68
24
0.67
.64
.62
.59
.55
.52
.47
.42
Nor. 1
0.70
.72
.73
.75
.77
.78
.79
.81
Aug. 1
+0.91
.92
.92
.93
.93
.93
.94
.94
2
0.82
.83
.84
.85
.86
.87
.88
.89
2
0.94
.94
.94
.94
.93
.93
.93
.92
3
0.90
.91
.91
.92
.93
.93
.94
.94
3
0.92
.91
.91
.90
.90
.89
.88
.87
4
0.95
.95
.96
.96
.96
.97
.97
.97
4
0.86
.85
.86
.83
.82
.80
.79
.77
5
0.98
.98
.98
.98
.98
.98
.98
.98
5
0.76
.74
.72
.70
.68
.66
.63
.61
6
0.98
.98
.98
.98
.98
.97
.97
.97
6
+0.58
.55
.51
.47
.43
.38
.83
.27
12
+0.53
.48
.43
.37
.31
.23
.14
.02
8
9.93
.07
.17
.26
.33
.39
.45
.50
14
0.28
.35
.41
.46
.50
.54
.58
.61
9
0.54
.58
.62
.66
.69
.72
.75
.78
15
0.64
.67
.76
.72
.74
.77
.79
.80
15
+0.79
.81
.82
.83
.84
.85
.86
.86
16
0.82
.84
.85
.87
.88
.89
.90
.91
16
0.87
.87
.88
.88
.88
.89
.89
.89
17
0.92
.93
.94
.95
.96
0.96
0.97
0.97
17
+0.89
.89
.89
.89
.89
.88
.88
.88
18
0.98
0.98
0.99
0.99
0.99
1.00
1.00
1.00
18
0.88
.87
.87
.86
.86
.85
.84
.84
19
1.00
1.00
1.00
1.00
1.00
1.00
0.99
0.99
19
0.83
.82
.81
.80
.79
.78
.76
.75
27
0.06
0.16
0.24
0.31
0.36
0.41
.45
.49
20
0.73
.72
.70
.68
.66
.64
.61
.58
28
0.53
.56
.59
.62
.64
.66
.68
.70
21
+0.55
.52
.48
.44
.40
.34
.28
.20
29
0.72
.73
.75
.76
.78
.79
.80
.82
23
0.17
.27
.35
.42
.48
.53
.58
.63
30
0.83
.84
.85
.86
.86
.87
.88
.89
30
+0.92
.92
.92
.91
.91
.91
.90
.90
Dec. 1
0.89
.90
.91
.91
.92
.92
.93
.93
31
0.89
.88
.87
.87
.86
.85
.84
.82
2
0.93
.94
.94
.94
.94
.95
.95
.95
Sept. 1
0.81
.70
.78
.77
.75
.74
.72
.70
3
0.95
.95
.95
.95
.95
.95
.94
.94
2
0.67
.65
.63
.60
.57
.54
.51
.47
4
0.94
.94
.93
.93
.93
.92
.92
.91
3
+0.43
.38
.33
.27
.20
.12
.02
.88
5
0.90
.90
.89
,88
.87
.86
.85
.84
5
0.24
.31
.36
.41
.46
.50
.53
.57
6
0.82
.81
.79
.77
.75
.73
.70
.67
6
0.60
.63
.65
.68
.70
.73
.75
.77
12
0.38
.44
.49
.54
.58
.62
.65
.68
7
0.79
.81
.83
.84
.86
.88
.89
.71
13
0.71
.73
.75
.77
.79
.81
.83
.84
13
+0.83
.84
.85
.85
.86
.86
.86
.87
14
0.86
.87
.88
.89
.90
.91
.92
.93
14
+0.87
.87
.87
.86
.86
.86
.86
.85
15
0.93
.94
.95
.95
.96
.96
.96
.97
15
0.85
.84
.83
.83
.82
.81
.80
.79
16
0.97
.97
.97
.97
.97
.97
.97
.97
16
0.78
.77
.75
.74
.72
.71
.69
.67
17
0.97
.96
.96
.96
.95
.95
.94
.94
17
0.65
.63
.60
.58
.55
0.52
0.48
0.44
18
0.93
.92
.91
.90
.89
.88
.87
.86
18
+0.40
.35
.29
.22
.14
0.03
9.89
9.67
27
0.72
.73
.75
.76
.78
.79
.80
.81
20
0.39
.44
.49
.54
.58
0.62
0.65
0.69
28
0.83
.84
.84
.85
.86
.87
.88
.88
21
-0.71
.74
.77
.79
.82
.84
.86
.88
29
0.89
.89
.90
.90
.91
.91
.91
.92
29
+0.77
.75
.74
.72
.70
.68
.65
.63
30
0.92
.92
.92
.92
.93
.93
.93
.93
30
+0.60
0.57
0.54
0.50
.46
.42
.37
.32
31
0.93
.92
.92
.92
.92
.92
.91
.91
Oct. 2
9.58
9.81
9.97
0.08
.16
.24
.30
.35
60
TABLE XII.
For finding the valtre of N for correcting lunar distances for the compression of the earth.
TABLE XII. A. giving 1st Part of N.
TABLE XII. B. giving 2d Part of N.
ADD
J)'s Declination.
App.
j|C's Declination.
A^JJ.
Dist.
3
o
1
12
15
ft
il
24
27
30
Dist.
o
I
6
o
9
12
o
15
18
21
&
c
27
30
20
o
20
4-0
i
II
1
a
10
//
14
i?
26'
//
24
27
//
30
II
33
Si 6
10
13
16
19
22
25
28
31
22
3
6
9
12
14
17
20
23
25
28
22
3
6
9
13
16
19
22
29
27
30
24
3
5
8
11
13
16
18
21
23
25
24
a
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
4
7
9
11
13
15 17
19
21
28
3
5
8
1C)
12
15
17
20
22
24
30
2
4
6
8
10
12
14
16
18
20
30
4-0
2
5
7
9
12
14
16
18
21
23
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
y
10
12
14
15
17
34
2
4
6
8
11
13
15
10
18
20
36
2
3
5
7
8
10
11
13
14
16
36
2
4
6
8
10
12
14
10
17
19
38
2
3
6
8
9
10
12
13
14
38
2
4
6
8
10
11
13
15
17
18 ;
40
1
3
4
6
7
8
10
11
12
13
40
4-0
2
4
6
7
9
11
13
14
16
18
42
1
3
4
5
7
8
9
10
11
13
42
2
4
5
7
9
10
12
14
is
17 ,
44
1
2
4
5
6
7
8
10
11
12
44
2
3
5
7
8
10
12
13
15
16
46
1
2
3
5
6
7
8
9
10
11
46
2
3
5
6
8
10
11
ia
14
16
48
1
2
3
4
5
6
7
8
9
10
48
2
3
5
6
8
9
11
12
14
15
50
2
a
4
5
6
7
8
9
10
50
4-0
2
3
5
6
8
9
11
12
ia
15
52
2
3
4
5
5
6
7
8
9
52
2
3
4
6
7
9
10
12
13
14 i
54
2
3
3
4
5
6
7
7
8
54
1
3
4
6
7
9
10
11
13
14 |
56
2
2
3
4
5
5
6
7
8
56
1
3
4
6
7
8
10
11
i a
14 |
58
1
2
3
4
4
5
6
6
7
58
1
3
6
7
8
10
11
H
13 ,
60
1
2
3
3
4
5
5
6
7
60
4-0
3
5
7
8
9
11
12
13 !'
62
1
2
3
3
4
4
5
5
6
62
3
5
7
8
9
10
\->
13 ;
64
1
2
2
3
3
4
4
5
6
64
3
5
7
8
9
10
11
13
66
1
2
2
3
3
4
4
5
5
66
3
5
6
8
9
10
11
12 :
68
1
2
2
3
3
4
4
5
68
3
5
6
8
9
10
11
12 ;
70
1
2
2
3
3
3
4
4
70
4-0
3
4
B
6
7
9
10
11
12 !
72
]
2
2
2
3
3
3
4
72
2
4
5
6
7
9
10
11
12 i
74
1
1
2
2
2
3
3
3
74
2
4
5
6
7
8
10
11
12
76
1
1
1
2
2
2
3
3
76
2
4
5
6
7
8
9
11
12
78
1
1
1
1
2
2
2
2
78
2
4
5
6
7
8
9
11
12
80
1
1
1
1
1
2
2
2
80
4-0
2
4
5
6
7
8
9
10
11 i
82
1
1
1
1
1
]
2
82
2
4
5
6
7
8
9
10
11
84
1
1
1
1
1
1
84
2
4
5
6
7
8
9
10
11
86
1
1
1
1
86
2
4
5
6
7
8
9
10
11
88
88
2
4
5
6
7
8
9
10
11
90
90
4-0
2
4
5
6
7
8
9
10
11
92
+0
92
2
4
5
6
7
8
9
10
ll ;
94
1
1
1
1
94
2
4
5
6
7
8
9
10
11 i
96
1
1
1
1
1
1
96
2
4
5
6
7
8
9
10
11 1
98
1
1
1
1
1
1
2
98
2
4
5
6
7
8
9
10
11
100
+0
1
1
1
1
2
2
2
100
4-0
2
4
5
6
7
8
9
10
11
102
1
1
1
2
2
2
2
102
2
4
5
6
7
8
9
11
12
104
1
I
2
2
2
3
3
104
2
4
5
6
7
8
9
11
12
106
1
2
2
2
3
3
3
106
2
4
5
6
7
8
]()
!1
12 '
108
2
2
2
3
3
3
4
108
2
4
5
6
7
9
10
11
12
110
+0
1
2
2
3
3
3
4
4
110
4-0
3
4
5
6
7
9
10
11
12
112
1
2
2
3
3
4
4
5
112
3
4
5
6
8
9
10
11
12
114
1
2
2
3
3
4
4
5
5
114
3
4
5
6
8
9
10
11
12
116
1
2
2
3
3
4
4
5
6
116
3
4
5
7
8
9
10
11
13
118
1
2
3
3
4
4
5
5
6
118
3
4
5
7
8
9
10
12
13
120
+0
1
1
2
3
3
4
5
5
6
7
120
4-0
1
3
4
5
7
8
9
11
12
13
122
1
1
2
3
4
4
5
6
6
7
122
1
3
4
6
7
8
10
11
12
13
124
1
2
2
3
4
5
5
6
7
8
124
1
3
4
6
7
8
10
11
12
14
126
1
2
a
3
4
5
6
7
7
8
126
1
3
4
6
7
9
10
11
i a
14
128
1
2
3
4
5
5
6
7
8
9
128
2
3
4
6
7
9
10
12
13
14
130
+0
1
2
3
4
5
6
7
8
9
10
130
4-0
2
3
5
6
8
9
11
12
13
15
The signs in the column apply to all the numbers in the same line, and are to be used when the declination
is North. When the declination is South,, change the sign + to and to +.
61
IMPROVED METHOD
OF FINDING THE
3RROR AND HATE OF A CHRONOMETER
BY EQUAL ALTITUDES.
FROM THE APPENDIX TO THE AMERICAN EPHEMERIS AND NAUTICAL
ALMANAC FOR 1866.
METHOD
OF FINDING THE
ERROR AND RATE OF A CHRONOMETER BY EQUAL ALTITUDES.
To regulate a chronometer to Greenwich time, we must determine its error and
rate at a place whose longitude is well known. The most accurate method of doing
this is by observing the transit of the sun or a star over the meridian. For the nav-
igator, the most simple and accurate substitute for the meridian observation is that cf
equal altitudes of the same object on each side of the meridian. 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 from 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 before 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.
The method of computing this equation given below is based upon that first given
by GAUSS (Monatliche Correspondenz, Vol. XXIII. ). We do not, however, follow
him in using the doable daily change of declination, or difference between the sun's
declination on the noon preceding and the noon following that of the observation ; but
prefer to use the hourly difference, because this may be obtained directly from the
American Ephemeris, and is at the same time even more accurate. We also extend
our table so as to meet the case where one altitude is taken in the afternoon and the
corresponding equal altitude on the following morning ; in which case, the equation is
computed for apparent midnight.*
* It should be observed, as a caution to navigators, that the rule for computing the equation for mid-
night is sometimes inaccurately, or incompletely, stated in works on navigation or astronomy. The
rule in Lieut. RAPER'S Practice of Navigation is wholly erroneous. GALBRAITH'S rule (Mathematical
and Astronomical. Tables) is incomplete, in not noticing the case where the elapsed time is less than 12^.
His rule for computing the equation for noon is similarly defective, in not noticing the case where the
elapsed time is greater than 12 h *. In Professor INMAN'S rule there is a slight inaccuracy introduced,
by taking the equation of time for mean, instead of apparent noon or midnight ; and in all the books,
9 65
EQUAL ALTITUDES.
L EQUAL ALTITUDES OF THE SUN, MORNING AND EVENING.
THE OBSERVATION.
On shore, at a place whose longitude is accurately known, and whose latitude is
approximately known, observe with an artificial horizon the same altitude both in the
morning and in the afternoon, as near the prime vertical as convenient after the alti-
tude is more than 10, noting the times by the chronometer. In low latitudes, how-
ever, the method of equal altitudes will often give very accurate results, even when
the observations are quite near to the meridian. In general, a sufficiently accurate
result may be obtained if the observations are taken when the sun's change of altitude
is not less than 10" in 0"-.5, or when the change in the double altitude taken with the
artificial horizon is not less than 20" in s .5.
It is most convenient, as well as conducive to accuracy, to take the observation in
the following manner. In the morning, bring the lower limb of the sun, reflected
from the sextant-mirrors, and the upper limb of that reflected from the mercury, into
approximate contact ; move the of the vernier forward (say from 10' to 20'), and
set it on a division of the limb ; the images will be overlapped and will be separating ;
wait for the instant of contact ; note it by chronometer, and immediately set the ver-
nier on the next division of the limb, that is, 10' in advance ; note the instant of con-
tact again, and proceed in the same manner for as many observations as are thought
necessary. If the sun rises too rapidly, let the intervals on the limb be 20'. Find
(roughly) the time when the sun will be at the same altitude in the afternoon, and
just before that time set the vernier on the last altitude noted in the morning (of
course using the same sextant) ; the images of the sun will be separated, but will be
approaching ; wait for the instant of contact ; note it by chronometer ; set the vernier
back to the next division of the limb (10' or 20', as the case may be) ; note the con-
tact again, and so proceed till all the A. M. altitudes have been again noted as P, M.
altitudes.
THE COMPUTATION.
Take the mean of the A. M. times and call it the A. M. Chronometer Time. The
mean of the P. M. times call the P. M. Chronometer Time. If, instead of noting the
times by the chronometer, a watch is used (compared 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. This difference
being applied to the mean of the watch times, we have the mean chronometer time
the same as would have been found by employing the chronometer directly.
the methods given of taking out the sun's change of declination, whether for 48 ht or for 24 h> , are not
as accurate as they should be.
A perfectly accurate rule, with a special table, for the midnight correction, is given in SCHUMACHER'S
Hvlfstafeln (Ed. by WAKNSTORFF). It requires, however, one logarithm more than our method in the
text, and is otherwise not so simple.
66
EQUAL ALTITUDES.
The half sum of the A. M. and P. M. Chronometer Times is the Middle Chronom-
eter Time, their difference is the Elapsed Time; observing that when the A. M.
time is before 12 h by chronometer, while the P. M. time is after 12 h -, the latter must
be supposed to be increased by 12 h in finding this half sum and difference.
Take from the Nautical Almanac the sun's declination, the hourly difference of
decimation, and the equation of time, reducing each to the instant of local apparent
noon by applying the changes for the longitude.
Mark north latitude and north declination +-
" south latitude and south declination
" hourly diff. of decl. when towards north +
" hourly diff. of decl. when towards south .
Enter Table I. with the elapsed time, and take out log. A and log. B, prefixing to
each its proper sign given in the table at the head of the page.
To log. A add the log. of the hourly diff, Table II., and the log. tangent of the
latitude (Bowditch, Table XXVII.). Prefix to each log. the sign of the quantity it
represents and to their sum the sign which results from the algebraic combination of
the three signs.* This sum is the log. (Table II.) of the number of seconds of time
in the first part of equation of equal attitudes, to be marked -f- or like its log.
To log. B. add the log. of the hourly diff. and the log. tangent of the declination,
marking the signs as before. The sum is the log. of the second part of the equation
of equal altitudes, to be marked H- or like its log.
Apply the two parts of the equation, according to their signs, to the Middle Chro-
nometer Time ; the result is the Chronometer Time of Apparent Noon.
To this apply the equation of time (adding, when the equation of time is additive
to mean time, otherwise subtracting) ; the result is the Chronometer Time of Mean
Noon, which, if the chronometer is regulated to local time, will be 12 h O m> s - when
the chronometer is- right ; more than 12 ht when fast, less than 12 h< when slow.
If the chronometer is regulated to Greenwich time, apply the longitude (in time) to
the chronometer time of mean noon (subtracting in west, adding in east) ; the result
will be more or less than 12 h , according as the chronometer is fast or slow.
Repeat this process on a subsequent day. The difference between the chronome-
ter errors on the two days, divided by the number of days in the interval, is the daily
rate of the chronometer, gaining or losing according as the chronometer goes too
fast or too slow.
EXAMPLE 1.
May 3d, 1856. At the United States Naval Academy, Lat. 38 59' N., Long.
5 h * 5 m - 55* .1 W., suppose the following observations of equal altitudes to be taken with
an artificial horizon. Required the error of the chronometer on Greenwich time at
noon of that day ?
* The algebraic rule being, that, when there is an odd number of factors with the sign minus,
the result must have the sign minus, otherwise the sign plus. In the present application of this
rule, when there is either one or three of the logs, marked , their sum must be marked j
otherwise 4-.
67
EQUAL ALTITUDES.
A.M.
Comparisons.
h. m. 8.
Ohronom. 12 52 0.0
Watch 7 45 8.0
Diff. 5 6 52.0
A. M., watch gains l':5 in 28 m *
Interval to obs. 17 m %5
28 m. . 17 m. <5 __ p. 5 . os%9
P. M., watch gains 2'-.2 in 34 m -
Interval to obs. 21 m<
34 m. . 21 m. _ 2 s. >2 : is.,4
2 O Art. Hor.
o t
65 50
66
66 10
(Eq. T.) "'iS-ll 0.258
1.32 5.1
P.M.
Comparisons,
h. m. a.
Chronom. 8 37 0.0
Watch 3 30 31.3
Diff. 5 6 28.7
Chronom. 9 11 0.0
Watch 4 4 33.5
Chronom. 1 20 0.0
Watch 8 13 9.5
Diff. 5 6 50.5
Diff. 5 6 26.5
Watch A. M.
h. m. 8.
829.
8 2 35.5
8 3 0.5
Watch P. M.
h. m. s.
3 52 10.7
3 51 44.0
3 51 18.5
Mean 8 2 35.0
Comparison 5 6 51.1
Mean 3 51 44.4
Comparison 5 6 27.3
P. M. Chro. Time 8 58 11.7
A. M. Chro. Time 1 9 26.1
Elapsed Time 7 48 45.6
* V
A. M. Chro. Time 1 9 26.1
P. M. Chro. Time 8 58 11.7
2)10 7 37.8
Eq. T. 3 19.43 1.32
(D.) +15 48 50.5 (H. D.) +43.82
3 42.8 0.14
Middle Chro. T. 53 48.9
Equat. of Eq. Alts. 8.8
Chro. T. App. N. 5 3 40.1
Equat. of Time H-3 19.4
Decrease in 5.1 = 0.14
log. B. Tab. I. +9.201!
+1 6403
D. +155233.3 H. D. +43.68
5.1
Chro. T. Mean N. 5 6 59.5
Longitude 5 5 55.1 W.
222.8
log.A.Tab.I. 9.4846
H.D.+43".68 log. Tab. II. +1.6403
Lat. + 38 59' log. tan. +9.9081
Chro./orf 1 4.4
D. + 15 53' log. tan. +9.4542
1st Pt. Eq. 10*-.79 log. 1.0330
2d Pt. Eq. + l f -.98 log. +0.2956
By similar observations on May 15th, suppose the chronometer is found to be fast
I2 \5; we have
May 3d, fast
May 15th, fast
Loses in 12 days
Daily rate
4.4
12.5
_51.9
~4.33~ losing.
H. EQUAL ALTITUDES OF THE SUN, EVENING AND MORNING.
THE OBSERVATION.
Take a set of altitudes, in the manner already explained, in the afternoon of one
day, and the same altitudes in reverse order on the morning of the next, noting the
times by the chronometer, or by a watch compared with it.
THE COMPUTATION.
The half sum of the P. M. and A. M. Chronometer Times is the Middle Chronom-
eter Time ; their difference is the Elapsed Time ; observing that when the P. M.
time is before 12 h by chronometer, while the A. M. time is after 12 h , the latter must
be supposed to be increased by 12 h - in finding this half sum and this difference.
Take from the Nautical Almanac the sun's declination, the hourly difference of
declination, and the equation of time, reducing them each to the instant of local flp-
parent midnight.
68
EQUAL ALTITUDES.
Mark the sign of each quantity as before, and compute the two parts of the equa-
tion of equal altitudes precisely as in the preceding case, observing to mark the signs
of log. A and log. B as given in the table for midnight.
Apply the two parts of the equation to the middle chronometer time, according to
their signs ; the result is the Chronometer Time of Apparent Midnight.
To this apply the equation of time (adding, when the equation of time is additive
to mean time, otherwise subtracting) ; the result is the Chronometer Time of Mean
Midnight, which, if the chronometer is regulated to local time, will be 12 hi O ra O" 1
when the chronometer is right ; more than 12 hl when fast ; less than 12 h> when slow.
If the chronometer is regulated to Greenwich time, apply the longitude, in time, to
the chronometer time of mean midnight (subtracting in west, adding in east) ; the re-
sult will be more or less than 12 h> (or 24 h- ) according as the chronometer is fast or slow.
A repetition of this process at a subsequent day will give another error, whence the
rate will be found as before. Or the rate may be found by comparing the results of
an A. M. P. M., and a P. M. A. M. observation, remembering that the interval
elapsed between two such observations is equal to the difference between the two
dates plus or minus half a day.
EXAMPLE 2.
May 3d, 1856, Lat. 43 21' S., Long. 9 h - 50 m - 8 s - E., suppose the altitude of the
sun to be observed in the afternoon and the same altitude again on the morning of
the 4th, as below. Required the error of the chronometer on Greenwich time at mid-
night of the 3d ?
Chronom., P. M. 2 Art. Hor. Chronom., A. M.
6 h. 54 m. 10 s. 3 ~3 8 o Q, gh. 9 m. 17 s. 5
The A. M. time must be called 21 h - 9 m 17 8> .5. The Greenwich time of midnight
for which the declination, &c. must be found, is May 3 d - 2 h - 9 m> 52 s - (= 3 d - 2 h .16.).
P. M. Chro. T. 6' 54 H).3
A.M. Chro. T. 21 9 17.5
m s. s.
(Eq. T.) 3 18.11 0.258
0.56 2.15
h. m. s.
A. M. Chro. T. 21 9 17.5
P. M. Chro. T. 6 54 10.3
2)28 3 27.8
Eq.T. 3 18.67 0.56
(D.) +15 48 50.5 (H. D.) +43.82
1 34.1 0.06
Elapsed T. 14 15 7.2
h.
Decrease in 24.0 = 0.66
Decrease in 2.16 = 0.06
log. B. Tab. I. 9.1586
. . . . . +1 6411
Middle Chro. T. 14 1 43.9
Eq. of Eq. Alts. 22.3
Chro.T.App.Midn. 14 1 21.6
Eq. of Time -1-3 18.7
D. +15 50 24.6 H. D +43.76
2.15
Chro.T.M'n Midn. 14 440.3
Longitude 9 50 8.0 E.
23 54^48.3
24 0.0
94.1
log.A.Tab.L +9.6958
H.D.+43".76 log. Tab. II. +1.6411
Lat, 43 21' log. tan. 9.9750
1st Pt. Eq. 20*-.51 log. T.s!l9
Chronom. slow 5 1 1 .7
D + 15 50' log. tan. +9.4527
2dPt.Eq. P-.79 log. (X2524
By an A. M. P. M. observation on May 20th, suppose this chronometer is found
to be slow 8 m - 14 8> ,6 ; we have
d. h. m. s.
May 3 12 slow 5 11.7
May 20 slow 8 14.6
Loses in 16 d -.5 ~3~2.9~
Daily rate
69
11.09 losing.
EQUAL ALTITUDES.
III. EQUAL ALTITUDES OF A FIXED STAR.
THE OBSERVATION.
In selecting stars for this observation, it is to be observed that the nearer the zenitri
the star passes, the less may the elapsed time be ; and when the star passes exactly
through the zenith, the two altitudes may be taken within a few minutes of each
other. But with the ordinary sextants, altitudes near 90 cannot be taken with the
artificial horizon, as the double altitude is then nearly 180. The prismatic sextants,
or still better, the prismatic circles of Pistor and Martin, are adapted for measuring
angles of all magnitudes up to 180, and are therefore especially suitable for this ob-
servation.
Set the sextant and wait for the coincidences of the two images of the star, as in
the case of the sun's limb, noting the times by chronometer or watch.
THE COMPUTATION.
Take the mean of the times before the meridian passage as the A. M. Chronome-
ter Time, and the mean of those after the meridian passage as the P. M. Chronome*
ter Time.
The mean of the A. M. and P. M. Chronometer Times is the Chronometer Time of
Star's Transit. This time, if the chronometer is right, will agree with the true mean
time of star's transit, which is to be computed as follows.
To the right ascension of the star apply the longitude of the place of observation
(adding in west, subtracting in east) ; the result is the Greenwich Sidereal Time of
Star's Transit, from which subtract the sidereal time at the preceding mean noon
Greenwich (Nautical Almanac, page II. of the month) ; the remainder is the Sidereal
Interval since mean noon. From Table IV. with the argument Sidereal Interval, take
out the correction, which subtract from the sidereal interval ; the remainder is the
Greenwich Mean Time of the Star's Transit. The chronometer time will be more
or less than this according as the chronometer is fast or slow.
If the chronometer is regulated to local time, apply the longitude to the Greenwich
mean time of star's transit (subtracting in west, adding in east) ; the result is the
Local Mean Time of Star's Transit, and the chronometer is fast or slow according as
it shows more or less than this time.
EXAMPLE 3.
July 15th, 1856, at the Cape of Good Hope, Lat. 33 56' S., Long. l h - 13 re - 56 s - E.,
observed equal altitudes of Antares as follows :
70
EQUAL ALTITUDES.
Chronom. A. M. 2 Alt. Antares. Chronom. P. M
h- m. 8. o i h. m. s
5 32 10.5 125 30 9 34 20.3
5 32 35.0 40 9 33 56.0
5 32 59.3 50 9 33 32.0
A. M. Chr.. T. 5 32 34.9 . P. M. wnro. T. 9 33 56.f
P. M. Chro. T. 9 33 56.1
2 ) 15 6 31.0 Antares R. A, 16 20 37.58
Chro. T. # Transit 7 33 15.5 Longitude 1 13 56.00 E
Gr. T. * Transit 7 31 22.1 Gr. Sid. T. 15 641.58
Chro. fast 1 53.4 July 15, Gr. Sid. T. Mean Noon 7 34 5.25
Sid. Interval 7 32 36.33
Correction, Table IV. 1 14.15
Gr. M. T. >fc Transit 7 31 22.18
IV. TO CORRECT FOR SMALL INEQUALITIES IN THE ALTITUDES
Although the sextant readings are the same at the A. M. and P. M. observations, it
may happen that neither the true nor even the apparent altitudes are the same.
1st. Supposing the sextant to remain unchanged, the atmospheric refraction may be
different at the two observations in consequence of changes in the density and tem-
perature of the air as shown by the barometer and thermometer. In this case, the
apparent altitudes are equal, but the true altitudes are not so. 2d. The sextant may
be affected by changes of temperature, particularly in day observations in the sun, so
as to make the sextant readings the same for apparent altitudes slightly different. I
do not think these changes in the sextant are to be eliminated by determining the
index error at each observation, as has been supposed by some, since it is quite pos-
sible that the expansion and contraction of the various parts might leave the index
correction unchanged while it affected the readings of the altitudes, or the reverse.
The only course appears to be to guard the instrument as much as possible from
changes of temperature, exposing it to the sun's rays only during the few minutes re-
quired for fiach observation.
But the correction for changes of refraction may be satisfactorily made as follows.
Note the barometer and thermometer both A. M. and P. M. ; take out the correspond-
ing refractions for each observation from Tables III., III. A., and III. B., and find the
difference of these refractions. Also take the difference between any two sextant
readings and the difference between the two corresponding chronometer times. Then
the correction of either noon or midnight will be found by the following proportion.
The difference of the sextant readings is to the difference of the refractions as the dif-
ference of the chronometer times is to the renuired correction.
Apply this correction to the Chronometer Time of Noon or Midnight (obtained by
the preceding rules) as follows : add it when the A. M. refraction is the greater ;
subtract it when the P. M. refraction is the greater. The result is the true Chronom-
eter Time of Noon or Midnight.
EXAMPLE. Suppose, in Example 1, we have in the morning, Barometer 30 inches,
Thermometer 55 ; in the afternoon, Barometer 29.5 inches, Thermometer 85. The
apparent altitude of sun's lower limb 33 0' ; the apparent altitude of sun's centre
33 16'. We have
71
EQUAL ALTITUDES.
A M. P. M.
Mean refraction 1 29 Mean refraction 1 29
Barom. 30 in. Barorn. 29.5 in. 1
Therm. 55 1 Therm. 85 6
True refraction 1 28 True refraction 1 22
Then the difference of the sextant readings is 10' (=600") and the corresponding
diff. of chronometer times is about 26* ; whence
II U 8. B
600 : 6 = 26 : 0.26
h. m. B.
The (approximate) Chronometer Time of Mean Noon was found to be 5 6 59.5
Correction for change of refraction -1-0.3
True Chronometer Time of Mean Noon 5 6 59.8
NOTE. This correction may be found by the following rule, which we should have to resort to
when but one altitude was taken at each observation. Add together the log. of the diff. of refractions
(Tab. II.), log. cosine of the altitude, log. secant of the latitude, log. secant of the declination, log.
cosecant of half elapsed time (or if the elapsed time is greater than 12 h> , half its supplement to 24 h '),
and the constant log. 8.523 ; the sum is the log. (Table II.) of the required correction. Thus in the
preceding example we have
Diff.refr. 6" log. 0.778
Alt. 33 16' log. cos. 9.922
Lat. 38 59' log. sec. 0.109
Dec. 15 53' log. sec. 0.017
El. T. 7 h - 49 m> log. cosec.* 0.069
const, log. 8.523
Correction 8 \26 log. 9.418
DEGREE OF DEPENDENCE.
An error of 5' in the latitude would not affect the corresponding part of the equa-
tion of equal altitudes by more than one hundredth of its amount in the most unfavor-
able 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 plain that errors in the longitude affecting the declination
and its hourly difference produce but small proportionate 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 con-
clude 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 most practised observers
with the sextant cannot depend on the noted time of a single contact within 0" .5, 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 s -. 2,
provided the rate of the chronometer between the observations is uniform.
Errors resulting from changes in the refraction may be almost wholly removed by
computation as above.
* Enter BOWDITCH'S Table XXVII., column P. M., with the whole elapsed time and take out the
corresponding cosecant.
72
EXPLANATION OF THE TABLES
TABLE I. Logarithms of A and B, for computing the Equation of Equal Alfo
tudes, are calculated by the formulas
A -= E R - _E
1800 sin i E ' 1800 tan 4 E '
where E = elapsed time in minutes, and E in the denominator is the elapsed time
expressed in arc.
If we put
$ = latitude of the place of observation, H- north, south,
b = declination of the sun, H- north, south,
A = hourly change of declination, +- north, south,
X = correction to reduce the middle chronometer time to chronometer time of ap-
parent noon, algebraically additive,
tf = the same for midnight,
we have
X = A A tan <f> 4- B A tan d
X I = A A tan < -+ B A tan 8.
TABLE II. Logarithms of Numbers to four decimal places. The first two fig-*
ures of the number are found in the left-hand column, the third at the top, and the
corresponding logarithm opposite and under these respectively. The proportional
part for the fourth figure is found on the side in the same line with the logarithm taken
out. The proper characteristic of the logarithm is to be supplied by the usual rule.
TABLE III. Mean Refraction, reduced from BESSEL'S Tables, to barometer 30
inches, and thermometer 50.
TABLES III. A. and III. B. Corrections of the Mean Refraction for the Height
of the Barometer and Thermometer, also deduced from BESSEL'S Tables. These are
the same as Tables IV. A. and IV. B., given in the Appendix to the Nautical Alma-
nac for 1855, where they are used for finding the corrections of the Mean Reduced
Refraction for Lunars. It is for the purpose of having the same table for correct-
ing both these mean refraction tables, that the argument in Tables III. A. and III. B*
is the mean refraction instead of the apparent altitude.
TABLE IV. For converting Sidereal into Mean Solar Time. This table gives
the correction required to reduce a sidereal interval to its equivalent solar interval.
10 73
TABLE I. LOG. A. AND LOG. B.
For Computing the Equation of Equal Altitudes.
KSS3&TA+} ARGUMENT = ELAPSED TIME. { ^Lfg h t?B+'
|l
Q h.
l h '
r
f-
4 h -
h.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
Log. A.
Log. B.
9.4059
9.4059
9.4072
9.4034
9.4109
9.3959
9.4172
9.3828
9.4260
9.3635
9.4374
9.3369
i
.4059
.4059
.4072
.4034
.4110
.3957
.4173
.3825
.4261
.3631
.4376
.3364
2
.4059
.4059
.4073
.4033
.4111
.3955
.4174
.3822
.4263
.3627
.4378
.3358
3
.4059
.4059
.4073
.4032
.4112
.3953
.4175
.3820
.4265
.3624
.4380
.3353
4
.4059
.4059
.4074
.4031
.4113
.3952
.4177
.3817
.4266
.3620
.4383
.3348
5
9.4059
9.4059
9.4074
9.4030
9.4113
9.3950
9.4178
9.3814
9.4268
9.3616
9.4385
9.3S43
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
.3332
8
.4060
.4059
.4075
.4027
.4116
.3944
.4182
.3806
.4273
.3604
.4391
.3327
9
.4060
.4059
.4076
.4026
.4117
.3943
.4183
.3803
.4275
.3600
.4393
.3321
10
9.4060
9.4059
9.4076
9.4025
9.4118
9.3941
9.4184
9.3800
9.4277
9.3596
9.4396
9.3316
11
.4060
.4059
.4077
.4024
.4119
.3939
.4186
.3797
.4279
.3592
.4398
.3311
12
.4060
.4058
.4077
.4023
.4120
.3937
.4187
.3794
.4280
.3588
.4400
.3305
13
.4060
.4058
.4078
.4022
.4121
.3935
.4188
.3792
.4282
.3584
.4402
.3300
14
.4060
.4058
.4078
.4021
.4121
.3933
.4190
.3789
.4284
.3580
.4405
.3294
15
9.4060
9.4058
9.4079
9.4020
9.4122
9.3931
9.4191
9.3786
9.4286
9.3576
9.4407
9.3289
16
.4060
.4058
.4079
.4019
.4123
.3929
.4193
.3783
.4288
.3572
.4409
.3283
17
.4060
.4057
.4080
.4018
.4124
.3927
.4194
.3780
.4289
.3568
.4411
.3278
18
.4061
.4057
.4080
.4017
.4125
.3925
.4195
.3777
.4291
.3564
.4414
.3272
19
.4061
.4057
.4081
.4016
.4126
.3923
.4197
.3774
.4293
.3559
.4416
.3266
20
9.4061
9.4057
9.4081
9.4015
9.4127
9.3921
9.4198
9.3771
9.4295
9.3555
9.4418
9.3261
21
.4061
.4056
.4082
.4014
.4128
.3919
.4199
.3768
.4297
.3551
.4420
.3255
22
.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
.4061
.4055
.4084
.4010
.4131
.3913
.4204
.3759
.4302
.3538
.4427
.3238
25
9.4062
9.4055
9.4084
9.4009
9.4132
9.3911
9.4205
9.3756
9.4304
9.3534
9.4430
9.3232
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
.4062
.4054
.4087
.4004
.4136
.3903
.4211
.3743
.4312
.3516
.4439
.3208
30
9.4062
9.4053
9.4087
9.4003
9.4137
9.3900
9.4212
9.3740
9.4314
9.3512
9.4441
9.3203
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
.3499
.4448
.3185
34
.4063
.4051
.4090
.3998
.4141
.3892
.4218
.3727
.4321
.3494
.4451
.3178
35
9.4064
9.4051
9.4091
9.3997
9.4142
9.3889
9.4220
9.3723
9.4323
9.3490
9.4453
9.3172
36
.4064
.4050
.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
.4065
.4049
.4093
.3991
.4147
.3880
.4226
.3710
.4331
.3471
.4463
.3148
40
9.4065
9.4048
9.4094
9.3990
9.4148
9.3878
9.4227
9.3707
9.4333
9.3467
9.4465
9.3142
41
.4065
.4048
.4095
.3988
.4149
.3875
.4229
.3703
.4335
.3462
.4468
.3135
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
.4066
.4046
.4097
.3984
.4152
.3868
.4234
.3693
.4341
.3448
.4475
.3116
45
9.4066
9.4045
9.4097
9.3982
9.4154
9.3866
9.4235
9.3690
9.4343
9.3443
9.4477
9.3110
46
.4067
.4045
.4098
.3981
.4155
.3863
.4237
.3686
.4345
.3438
.4480
.3103
47
.4067
.4044
.4099
3979
.4156
.3861
.4238
.3683
.4347
.3433
.4482
.3097
48
.4067
.4043
.4100
.3978
.4157
.3859
.4240
.3679
.4349
.3429
.4485
.3091
49
.4068
.4043
.4100
.3976
.4158
.3856
.4242
.3675
.4351
.3424
.4487
.3084
50
9.4068
9.4042
9.4101
9.3975
9.4159
9.3854
9.4243
9.3672
9.4353
9.3419
9.4490
9.3078
51
.4068
.4041
.4102
.3973
.4161
.3851
.4245
.3668
.4355
.3414
.4492
.3071
52
.4069
.4041
.4103
.3972
.4162
.3849
.4246
.3665
.4357
.3409
.4494
.3064
53
.4069
.4040
.4103
.3970
.4163
.3846
.4248
.3661
.4359
.3404
.4497
.3058
54
.4069
.4039
.4104
.3969
.4164) .3843
.4250
.3657
.4361
.3399
.4500
.3051
55
9.4070
9.4038
9.4105
9.3967
9.4165
9.3841
9.4251
9.3654
9.4363
9.3394
9.4503
9.3044
56
.4070
.4038
.4106
.3965
.4167
.3838
.425a
.3650
.4366
.3389
.4505 .3038
57
.4071
.4037
.4107
.3964
.4168
.3836
.4255
.3646
.4368
.3384
.4508
.3031
58
.4071
.4036
.4107
.3962
.4169' .3833
.4256
.3643
.4370
.3379
.4510
.3024
59
.4071
.4035
.4108
.3960
.4170 .3830
.4258
.3639
.4372
.3374
.4513
.3017
60
9.4072
94034
9.4109
9.3959
9.4172 9.3828
9.4260 9.3635
9.4374
9.3369
9.4515: 9.3010
74
TABLE I. LOG. A. AND LOG. B
For Computing the Equation of Equal Altitudes.
forSgtt7A + } ARGUMENT = ELAPSED TIME. {Mia m *?B+
1 s
o< a
B e
gh.
7 b.
8 h -
gh.
io b -
U h.
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
9.4515
9.3010
9.4685
9.2530
9.4884
9.1874
9.5115
9.0943
95379
8.9509
9.5680
8.6837
1
.4518
.3003
.4688
.2520
.4888
.1861
.5119
.0925
.5384
.9478
.5685
.6770
2
.4521
.2996
.4691
.2511
.4892
.1848
.5123
.0906
.5389
.9447
.5691
.6701
3
.4523
.2989
.4694
.2502
.4895
.1835
.5127
.0887
.5393
.9416
.5696
.6632
4
.4526
.2982
.4697
.2492
.4899
.1822
.5132
.0867
.5398
.9384
.5701
.6560
5
9.4528
9.2975
9.4701
9.2483
9.4902
9.1809
9.5136
9.0848
9.5403
8.9352
9.5707
8.6488
6
.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
8
.4536
.2954
.4710
.2454
.4913
.1769
.5148
.0789
.5417
.9254
.5723
.6262
9
.4539
.2947
.4713
.2444
.4917
.1756
.5153
.0769
.5422
.9221
.5728
.6183
10
9.4542
9.2940
9.4716
9.2434
9.4921
9.1742
9.5157
9.0749
9.5427
8.9187
9.5734
8.6103
11
.4544
.2932
.4719
.2425
.4924
.1728
.5161
.0729
.5432
.9153
.5739
.6021
12
.4547
.2925
.4723
.2415
.4928
.1715
.5165
.0708
.5436
.9118
,5745
.5937
13
.4550
.2918
.4726
.2405
.4932
.1701
.5169
.0688
.5441
.9083
.5750
.5852
14
.4552
.2911
.4729
.2395
.4935
.1687
.5174
.0667
.5446
.9048
.5756
.5764
15
9.4555
9.2903
9.4732
9.2385
9.4939
9.1673
9.5178
9.0646
9.5451
8.9013
9.5761
8.5674
16
.4558
.2896
.4735
.2375
.4943
.1659
.5182
.0625
.5456
.8977
.5767
.5583
17
.4561
.2888
.4738
.2365
.4946
.1645
.5186
.0604
.5461
.8940
.5772
.5488
18
.4563
.2881
.4742
.2355
.4950
.1630
.5191
.0583
.5466
.8903
.5778
.5392
19
.4566
.2873
.4745
.2344
.4954
.1616
.5195
.0561
.5470
.8866
.5783
.5293
20
9.4569
9.2866
9.4748
9.2334
9.4958
9.1602
9.5199
9.0540
9.5475
8.8829
9.5789
8.5192
21
.4572
.2858
.4751
.2324
.4961
.1587
.5204
.0518
.5480
.8791
.5794
.5088
22
.4574
.2850
.4755
.2313
.4965
.1573
.5208
.0496
.5485
.8752
.5800
.4981
23
.4577
.2843
.4758
.2303
.4969
.1558
.5212
.0474
.5490
.8713
.5806
.4871
24
.4580
.2835
.4761
.2292
.4973
.1543
.5217
.0452
.5495
.8674
.5811
.4758
25
9.4583
9,2827
9.4764
9.2282
9.4977
9.1528
9.5221
9.0429
9.5500
8.8634
9.5817
8.4641
26
.4585
.2819
.4768
.2271
.4980
.1513
.5225
.0406
.5505
.8594
.5822
.4521
27
.4588
.2812
.4771
.2261
.4984
.1498
.5230
.0383
.5510
.8553
.5828
.4397
28
.4591
.2804
.4774
.2250
.4988
.1483
.5234
.0360
.5515
.8512
.5834
.4270
29
.4594
.2796
.4778
.2239
.4992
.1468
.5238
.0337
.5520
.8470
.5839
.4138
30
9.4597
9.2788
9.4781
9.2228
9.4996
9.1453
9.5243
9.0314
9.5525
8.8427
9.5845
8.4001
31
.4600
.2780
.4784
.2217
.5000
.1437
.5217
.0290
.5530
.8384
.5851
.3860
32
.4602
.2772
.4788
.2206
.5003
.1422
.5252
.0266
.5535
.8341
.5856
.3713
33
.4605
.2764
.4791
.2195
.5007
.1406
.5256
.0242
.5540
.8297
.5862
.3561
34
.4608
.2756
.4794
.2184
.5011
.1390
.5261
.0218
.5545
.8253
.5868
.3403
35
9.4611
9.2747
9.4798
9.2173
9.5015
9.1375
9.5265
9.0194
9.5550
8.8208
9.5874
8.3239
36
.4614
.2739
.4801
.2162
.5019
.1359
.5269
.0169
.5555
.8162
.5879
.3067
37
.4617
.2731
.4804
.2151
.5023
.1343
.5274
.0144
.5560
.8115
.5885
.2888
38
.4620
.2723
.4808
.2140
.5027
.1327
.5278
.0119
.5565
.8068
.5891
.2701
39
.4622
.2714
.481 1
.2128
.5031
.1310
.5283
.0094
.5570
.8020
.5897
.2505
40
9.4625
9.2706
9.4815
9.2117
9.5035
9.1294
9.5287
9.0069
9.5576
8.7972
9.5902
8.2299
41
.4628
.2698
.4818
.2105
.5038
.1278
.5292
.0043
.5581
.7923
.5908
.2082
42
.4631
.2689
.4821
.2094
.5042
.1261
.5296
.0017
.5586
.7873
.5914
.1853
43
.4634
.2681
.4825
.2082
.5046
.1244
.5301
8.9991
.5591
.7823
.5920
.1611
44
.4637
.2672
.4828
.2070
.5050
.1228
.5305
.9965
.5596
.7772
.5926
.1354
45
9.4640
9.2664
9.4832
9.2059
9.5054
9.1211
9.5310
8.9938
9.5601
8.7720
9.5931
8.1080
46
.4643
.2655
.4835
.2047
.5058
.1194
.53 ! 5
.9911
.5606
.7668
.5937
.0786
47
.4646
.2646
.4839
.2035
.5062
.1177
.5319
.9884
.5612
.7614
.5943
.0470
48
.4649
.2638
.4842
.2023
.5066
.1159
.5324
.9857
.5617
.7560
.5949
.0128
49
.4652
.2629
.4846
.2011
.5070
.1142
.5328
.9830
.5622
.7505
.5955
7.9756
50
9.4655
9.2620
9.4849
9.1999
9.5074
9.1125
9.5333 89802
9.5827
8.7449
9.5961
7.9348
51
.4658
.2611
.4853
.1987
.5078
.1107
.5337 .9774
.5632
.7392
.5967
.8897
52
.4661
.2602
.4856
.1974
.5082
.1089
.53421 .9745
.5638
.7335
.5973
.8391
53
.4664
.2593
.4860
.1962
.50861 .1072
.5347 .9717
.5643
.7276
.5979
.7817
54
.4667
.2584
.4863
.1950
.5091 j .1054
.5351 .9688
.5648
.7217
.5985
.7154
55
9.4670
9.2575
9.4867
9.1937
9.5095 9.1036
9.5356 8.9659
9.5654
8.7156
9.5991
7.6368
56
.4673
.2566
.4870
.1925
.5099
.1017
.5361) .9630
.5659
.7094
.5997
.5405
57
.4676
.2557
.4874
.1912
.5103
.0999
.5365 .9600
.5664
.7032
.6003
.4162
58
.4679
.2548
.4877
.1900
.5107 .0981
.5370 .9570
.5669
.6968
.6009
.2407
59
.4682
.2539
.4881) .1887
.51111 .0962
.5375 - .9540
.5675
.6903
.6015
6.9591
60
9.4685
92530
9.4884 9.1874
9.5115 9.0943
9.5379 8.9509
9.5680
8.6837
9.6021
/n/.
75
TABLE 1. LOG. A. Ai\D LOG.
For Computing the Equation of Equal Altitudes.
foJ SSS g ttTA + } ARGUMENT = ELAPSED TIME. { Sdnfg^B-
Elapsed
Time.
If"
If"
14 h -
is h -
16"'
1? h.
Log. A.
Log. B.
Log. A.
Log.B
1
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
2
.6033
7.2431
.6419
.7718
.6856
.1057
.7351
.3225
.7915
.4937
.8562
.6431
3
.6039
.4198
.6426
.7794
.6864
.1099
.7360
.3256
.7925
.4963
.8573
.6455
4
.6045
.5453
.6433
.7868
.6872
.1141
.7369
.3287
.7935
.4990
.8585
.6478
5
9.6051
7.6428
9.6440
8.7942
9.6879
9.1183
9.7378
9.3319
9.7945
9.5016
9.8597
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
8
.6069
.8488
.6461
.8158
.6903
.1306
.7404
.3411
.7975
.5094
.8632
.6573
9
.6075
.9005
.6467
.8227
.6911
.1347
.7413
.3442
.7986
.5120
.8644
.6597
10
9.6082
7.9469
9.6474
8.8296
9.6919
9.1387
9.7422
Q.3472
9.7996
9.5146
9.8655
9.6621
11
.6088
.9889
.6481
.8364
.6926
.1428
.7431
.3503
.8006
.5171
.8667
.6644
12
.6094
8.0273
.6488
.8432
.6934
.1468
.7440
.3533
.8016
.5197
.8679
.6668
13
.6100
.0627
.6495
.8498
.6942
.1507
.7449
.3563
.8027
.5223
.8691
.6691
14
.6106
.0955
.6502
.8564
.6950
.1547
.7458
.3593
.8037
.5248
.8703
.6715
15
9.6112
8.1260
9.6509
8.8628
9.6958
9.1586
9.7467
9.3623
9.8047
9.5274
9.8715
9.6738
16
.6119
.1547
.6516
.8692
.6966
.1625
.7476
.3653
.8058
.5300
.8727
.6762
17
.6125
.1816
.6523
.8756
.6974
.1664
.7485
.3683
.8068
.5325
.8739
.6785
18
.6131
.2071
.6530
.8818
.6982
.1703
.7494
.3713
.8078
.5351
.8751
.6809
19
.6137
.2312
.6538
.8880
.6990
.1741
.7503
.3742
.8089
.5376
.8763
.6832
20
9.6144
8.2541
9.6545
8.8941
9.6998
9.1779
9.7512
9.3772
9.8099
9.5401
9.8775
9.6856
21
.6150
.2759
.6552
.9002
.7006
.1817
.7522
.3801
.8110
.5427
.8787
.6879
22
.6156
.2967
.6559
.9062
.7014
.1855
.7531
.3831
.8120
.5452
.8799
.6903
23
.6163
.3166
.6566
.9121
.7022
.1893
.7540
.3860
.8131
.5477
.8812
.6926
24
.6169
.3357
.6573
.9180
.7030
.1930
.7549
.3889
.8141
.5502
.8824
.6949
25
9.6175
8.3540
9.6580
8.9238
9.7038
9.1967
9.7558
9.3918
9.8152
9.5528
9.8836
9.6973
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
.7586
.4005
.8184
.5603
.8873
.7043
29
.6201
.4210
.6609
.9464
.7071
.2114
.7595
.4033
.8194
.5628
.8885
.7066
30
9.6207
8.4363
9.6616
8.9519
9.7079
9.2150
9.7605
9.4062
9.8205
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
.4796
.6638
.9681
.7104
.2258
.7633
.4147
.8237
.5727
.8935
.7159
34
.6233
.4932
.6645
.9734
.7112
.2293
.7642
.4175
.8248
.5752
.8948
.7182
35
9.6239
8.5064
9.6653
8.9787
9.7121
9.2329
9.7652
9.4204
9.8259
9.5777
9.8961
9.7205
36
.6246
.5192
.6660
.9839
.7129
.2364
.7661
.4232
.8270
.5801
.8973
.7228
37
.9252
.5318
.6667
.9891
.7137
.2399
.7671
.4260
.8281
.5826
.8986
.7251
38
.6259
.5440
.6675
.9942
.7146
.2434
.7680
.4288
.8292
.5850
.8999
.7275
39
.6265
.5559
.6682
.9993
.7154
.2468
.7690
.4316
.8303
.5875
.9011
.7298
40
9.6272
8.5675
9.6690
9.0043
9.7162
9.2503
9.7699
9.4343
9.8314
9.5900
9.9024
9.7321
41
.6279
.5788
.6697
.0093
.7171
.2537
.7709
.4371
.8325
.5924
.9037
.7344
42
.6285
.5899
.6704
.0142
.7179
.2571
.7718
.4399
.8336
.5948
.9050
.7367
43
.6292
.6008
.6712
.0191
.7187
.2605
.7728
.4426
.8347
.5973
.9063
.7390
44
.6298
.6114
.6719
.0240
.7196
.2639
.7738
.4454
.8358
.5997
.9075
.7413
45
9.6305
8.6218
9.6727
9.0288
9.7204
9.2673
9.7747
9.4481
9.8369
9.6022
9.9088
9.7436
46
.6311
.6320
.6734
.0336
.7213
.2706
.7757
.4509
.8380
.6046
.9101
.7459
47
.6318
.6419
.6742
.0384
.7221
.2740
.7767
.4536
.8391
.6070
.9114
.7482
48
.6325
.6517
.6749
.0431
.7230
.2773
.7776
.4563
.8402
.6094
.9127
.7505
49
.6331
.6613
.6757
.0478
.7238
.2806
.7786
.4590
.8414
.6119
.9140
.7529
50
9.6338
8.6707
9.6764
9.0524
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
.6365
.7067
.6795
.0707
.7281 .2970
.7835
.4725
.8470
.6239
.9206
.7644
55
9.6372
8.7153
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
.3034
.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
.6359
.9273 .7759
60
9.6406
8 7563
9.68411 9.0971
9.7333 9.3162
9.7895 9.4884
9.8539
9.6383
9.9287 9.7782
76
TABLE I. LOG. A. AND LOG. B,
For Computing the Equation of Equal Altitudes.
lorSSgttTA-f} ARGUMENT = ELAPSED TIME. {SSSi5?B-
!|
S H
18 h -
19 h -
20 h -
21 h -
2f-
ir
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
9.9287
9.7782
0.0172
9.9167
0.1249
0.0625
0.2623
0.2279
04523
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
.0727
.2729
.2401
.4680
.4540
.8000
.7967
5
9.9355
9.7896
0.0253
9.9284
0.1351
0.0753
0.2756
0.2431
0.4720
0.4582
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
.1433
.0856
.2865
.2556
.4884
.4755
.8420
.8393
10
9.9424
9.8011
0.0336
9-9402
0.1454
0.0882
0.2893
0.2587
0.4926
0.4799
0.8508
0.8483
11
.9437
.8034
.0353
.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
.9497
.1538
.0987
.3005
.2714
.5097
.4980
.8882
.8860
15
9.9493
9.8126
0.0420
9.9520
0.1559
0.1013
0.3034
0.2746
0.5140
0.5026
0.8980
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
.9550
.8218
.0489
.9616
.1645
.1119
.3150
.2876
.5319
.5213
.9396
.9378
20
9.9564
9.8241
0.0506
9.9640
0.1667
0.1146
0.3179
0.2909
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
.9622
.8333
.0576
.9735
.1755
.1253
.3298
.3041
.5553
.5457
.9975
.9961
25
9.9636
9.8356
0.0593
9.9760
0.1777
0.1280
0.3328
0.3075
0.5601
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
.1389
.3451
.3211
.5798
.5712
.0638
.0628
30
9.9709
9.8471
0.0682
9.9880
0.1889
0.1417
0.3482
0.3245
0.5848
0.5764
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
.9769
.8563
.0754
.9977
.1981
.1527
.3609
.3385
.605^
.5979
.1416
.1409
35
9.9784
9.8586
0.0772
0.0002
0.2004
0.1555
0.3641
0.3420
0.6110
0.6034
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
.1667
.3772
.3563
.6329
.6261
.2359
.2354
40
9.9859
9.8701
0.0864
0.0124
0.2122
0.1695
0.3805
0.3599
0.6386
0.6319
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
.6501
.6438
.3037
.3033
43
.9904
.8771
.0920
.0198
.2194
.1780
.3907
.3710
.6560
.6498
.3288
.3285
44
.9920
.8794
.0939
.0223
.2218
.1808
.3941
.3747
.6619
.6559
.3554
.3552
45
9.9935
9.8817
0.0958
0.0248
0.2243
0.1837
0.3975
0.3784
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
.3936
.6928
.6876
.5196
.5195
50
0.0013
9.8933
0.1053
0.0372
0.2366
0.1982
0.4151
0.3974
0.6993
0.6942
1.5613
1.5612
51
.0029
.8956
.1072
.0397
.2391
.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
.0076
.9026
.1131
.0473
.2467
.2099
.4297
.4130
.7259
.7214
.7844
.7843
55
0.0092
9.9050
0.1150
0.0498
0.2493
0.2129
0.4334
0.4170
0.7328
0.7284
1.8638
1.8638
56
.0108
.9073
.1170
.0523
.2518
.2159
.4371
.4210
.7398
.7355
.9610
.9610
57
.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 .4331
.7615
.7576
2.5640
2.5640
60
0.0172
99167
0.1249
0.0625
0.2623
0.2279
0.4523 ! 0.4372
0.7689
0.7652
Inf. 7n/_J
77
TAKLE II.
LOGARITHMS OF NUMBERS.
1
Proportional Parts,
la
1
2
3
4
5
6
7
8
9
i*
1
2 3
4
7
8
9
10
0000
0043
0086
0128
0170
0212
0253
0294
0334
0374
4
8 12
17
21
25
29
33
37
11
0414
0453
0492
0531
0569
0607
0645
0682
0719
0755
4
8
11
15
19
23
26
30
34
12
0792
0828
0864
0899
0934
0969
1004
1038
1072
1106
3
7
10
14
17
21
24
28
31
13
1139
1173
1206
1239
1271
1303
1335
1367
1399
1430
3
6
10
13
16
19
"21.
&
29
14
1461
1492
1523
1553
1584
1614
1644
1673
1703
1732
3
6
9
12
15
18
21
SM
27
15
1761
1790
1818
1847
1875
1903
1931
1959
1987
2014
3
6
8
11
14
17
20
22
25
16
2041
2068
2095
2122
2148
2175
2201
2227
2253
2279
3
5
S
11
13
16
18
21
24
17
2304
2330
2355
2380
2405
2430
2455
2480
2504
2529
2
5
7
10
12
15
17
20
22
18
2553
2577
2601
2625
2648
2672
2695
2718
2742
2765
2
5
7
9
12
14
16
19
21
19
2788
2810
2833
2856
2878
2900
2923
2945
2967
2989
2
4
7
9
11
13
16
18
20
20
3010
3032
3054
3075
3096
3118
3139
3160
3181
3201
2
4
6
8
11
13
15
17
19
21
3222
3243
3263
3284
3304
3324
3345
3365
3385
3404
2
4
6
8
10
12
14
16
18
22
3424
3444
3464
3483
3502
3522
3541
3560
3579
3598
2
4
6
8
10
12
14
15
17
23
3617
3636
3655
3674
3692
3711
3729
3747
3766
3784
2
4
6
7
9
11
13
15
17
24
3802
3820
3838
3856
3874
3892
3909
3927
3945
3962
2
4
5
7
9
11
12
14
16
25
3979
3997
4014
4031
4048
4065
4082
4099
4116
4133
2
3
5
7
9
10
12
14
15
26
4150
4166
4183
4200
4216
4232
4249
4265
4281
4298
2
3
5
7
8
10
11
13
15
27
4314
4330
4346
4362
4378
4393
4409
4425
4440
4456
2
3
5
6
8
9
11
13
14
28
4472
4487
4502
4518
4533
4548
4564
4579
4594
4609
2
3
5
6
8
9
11
12
14
29
4624
4639
4654
4669
4683
4698
4713
4728
4742
4757
1
3
4
6
7
9
10
12
13
30
4771
4786
4800
4814
4829
4843
4857
4871
4886
4900
3
4
6
7
9
10
11
13
31
4914
4928
4942
4955
4969
4983
4997
5011
5024
5038
3
4
6
7
8
10
11
12
32
5051
5065
5079
5092
5105
5119
5132
5145
5159
5172
3
4
5
7
8
9
11
12
33
5185
5198
5211
5224
5237
5250
5263
5276
5289
5302
3
4
5
6
8
9
10
12
34
5315
5328
5340
5353
5366
5378
5391
5403
5416
5428
3
4
5
6
8
9
10
11
35
5441
5453
5465
5478
5490
5502
5514
5527
5539
5551
2
4
5
6
7
9
10
11
36
5563
5575
5587
5599
5611
5623
5635
5647
5658
5670
2
4
5
6
7
8
10
11
37
5682
5694
5705
5717
5729
5740
5752
5763
577
5786
2
3
5
6
7
8
9
10
38
5798
5809
5821
5832
5843
5855
5866
5877
5888
5899
2
3
5
6
7
8
9
10
39
5911
5922
5933
5944
5955
5966
5977
5988
5999
6010
2
3
4
5
7
8
9
10
40
6021
6031
6042
6053
6064
6075
6085
6096
6107
6117
2
3
4
5
6
8
9
10
41
6128
6138
6149
6160
6170
6180
6191
6201
6212
6222
2
3
4
5
6
7
8
9
42
6232
6243
6253
6263
6274
6284
6294
6304
6314
6325
2
3
4
5
G
7
8
9
43
6335
6345
6355
6365
6375
6385
6395
6405
6415
6425
2
3
4
5
6
7
8
9
44
6435
6444
6454
6464
6474
6484
6493
6503
6513
6522
2
3
4
5
6
7
8
9
45
6532
6542
6551
6561
6571
6580
6590
6599
6609
6618
2
3
4
5
6
7
8
9
46
6628
6637
6646
6656
6665
6675
6684
6693
6702
6712
2
3
4
5
6
'7
7
8
47
6721
6730
6739
6749
6758
6767
6776
6785
6794
6803
2
3
4
5
5
G
7
8
48
6812
6821
6830
6839
6848
6857
6866
6875
6884
6893
2
3
4
4
5
6
7
8
49
6902
6911
6920
6928
6937
6946
6955
6964
6972
6981
2
3
4
4
5
G
7
8
50
6990
6998
7007
7016
7024
7033
7042
7050
7059
7067
2
3
3
4
5
G
7
8
51
7076
7084
7093
7101
7110
7118
7126
7135
7143 7152
2
3
3
4
5
6
7
8
52
7160
7168
7177
7185
7193
7202
7210
7218
7226 7235
2j 2
3
4
5
6
7
7
53
7243
7251
7259
7267
7275
7284
7292
7300
7308 7316
2 2
3
4
5
6
6
7
54
7324
7332
7340
7348
7356
7364
7372
7380 j 7388 7396
1
2 2! 3
4
5
6
6j 7
78
TASLE SI.
LOGARITHMS OF NUMBERS.
Natural
Numbers.
1
2
3
4
5
6
7
8
9
Proportional Parts,
1
2 3
4
i
6
7
8
9
.55
7404
7412
7419
7427
7435
7443
7451
7459
7466
7474
!
2
3
..
5
j
6
7
56
7482
7490
7497
7505
7513
7520
7528
7536
7543
7551
]
2
4
5
5
6
7
57
7559
7566
7574
7582
7589
7597
7604
7612
7619
7627
]
f
3
4
5
5
6
7
58
7634
7642
7649
7657
7664
7672
7679
7686
7694
7701
1
1
3
4
..
|
6
7
59
7709
7716
7723
7731
7738
7745
7752
7760
7767
7774
]
1
3
4
4
5
6
7
60
7782
7789
7796
7803
7810
7818
7825
7832
7839
7846
1
3
4
5
6
6
61
7853
7860
7868
7875
7882
7889
7896
7903
7910
7917
1
3
4
4
u
G
6
62
7924
7931
7938
7945
7952
7959
7966
7973
7980
7987
1
3
4
5
6
6
63
7993
8000
8007
8014
8021
8028
8035
8041
8048
8055
1
3
3
4
5
5
6
64
8062
8069
8075
8082
8089
8096
8102
8109
8116
8122
1
2
3
3
4
5
5
6
65
"8129
8136
8142
8149
8156
8162
8169
8176
8182
8189
1
2
3
3
4
5
5
6
66
8195
8202
8209
8215
8222
8228
8235
8241
8248
8254
1
3
*
4
5
5
6
67
8261
8267
8274
8280
8287
8293
8299
8306
8312
8319
1
3
4
5
5
6
68
8325
8331
8338
8344
8351
8357
8363
8370
8376
8382
1
3
4
4
5
6
69
8388
8395
8401
8407
8414
8420
8426
8432
8439
8445
1
1
2
4
4
5
6
70
8451
8457
8463
8470
8476
8482
8488
8494
8500
8506
1
1
2
4
4
5
6
71
8513
8519
8525
8531
8537
8543
8549
8555
8561
8567
1
1
2
4
i
5
5
72
8573
8579
8585
8591
8597
8603
8609
8615
8621
8627
1
1
2
4
4
5
5
73
8633
8639
8645
8651
8657
8663
8669
8675
8681
8686
1
1
2
4
4
5
5
74
8692
8698
8704
8710
8716
8722
8727
8733
8739
8745
1
1
2
4
4
5
5
75
8751
8756
8762
8768
8774
8779
8785
8791
8797
8802
1
1
2
2
3
4
5
5
76
8808
8814
8820
8825
8831
8837
8842
8848
8854
8859
1
1
2
2
o
4
5
5
77
8865
8871
8876
8882
8887
8893
8899
8904
8910
8915
1
1
2
2
8
3
4
4
5
78
8921
8927
8932
8938
8943
8949
8954
8960
896^
8971
1
1
2
2
3
8
4
4
5
79
8976
8982
8987
8993
8998
9004
9009
9015
9020
9025
1
1
2
2
2
3
4
4
5
80
9031
9036
9042
9047
9053
9058
9063
9069
9074
9079
1
2
2
3
3
4
4
5
81
9085
9090
9096
9101
9106
9112
9117
9122
9128
9133
1
2
2
3
3
4
4
5
82
9138
9143
9149
9154
9159
9165
9170
9175
9180
9186
1
2
2
3
3
4
4
5
S3
9191
9196
9201
9206
9212
9217
9222
9227
9232
9238
1
2
2
3
3
4
4
5
84
9243
9248
9253
9258
9263
9269
9274
9279
9284
9289
1
2
2
8
8
4
4
5
85
9294
9299
9304
9309
9315
9320
9325
9330
9335
9340
1
2
2
8
3
4
4
5
86
9345
9350
9355
9360
9365
9370
9375
9380
9385
9390
1
2
2
3
3
4
4
5
87
9395
9400
9405
9410
9415
9420
9425
9430
9435
9440
1
2
2
3
3
4
4
88
9445
9450
9455
9460
9465
9469
9474
9479
9484
9489
1
2
2
3
8
4
4
89
9494
9499
9504
9509
9513
9518
9523
9528
9533
9538
1
2
2
3
8
4
4
90
9542
9547
9552
9557
9562
9566
9571
9576
9581
9586
1
2
2
8
3
4
4
91
9590
9595
9600
9605
9609
9614
9619
9624
9628
9633
1
2
2
3
3
4
4
92
9638
9643
9647
9652
9657
9661
9666
9671
9675
9680
1
2
2
8
3
4
4
93
9685
9689
9694
9699
9703
9708
9713
9717
9722
9727
1
2
2
3
3
4
4
94
9731
9736
9741
9745
9750
9754
9759
9763
9768
9773
1
2
2
3
8
4
4
95
9777
9782
9786
9791
9795
9800
9805
9809
9814
9818
1
2
2
3
3
4
4
96
9823
9827
9832
9836
9841
9845
9850
9854
9859
9863
1
2
2
3
3
4
4
97
9868
9872
9877
9881
9886
9890
9894
9899
9903
9908
1
2
2
8
3
4
4
98
9912
9917
9921
9926
9930
9934
9939
9943
9948
9952
1
2
2
3
3
4
4
99
9956
9961
9965
9969
9974
9978
9983
9987
99911
9996
' 1 2
2
3
3
3
4
79
TABLE III. MEAN REFRACTION.
Barometer 30 inches. Fahrenheit's Thermometer 50.
Apparent
Altitude.
Mean
Refraction.
.pparent
Altitude.
Mean
Refraction.
Apparent
Altitude.
Mean
Refraction.
Apparent
Altitude.
Mean
.Refraction.
Apparent
Altitude.
Mean
Refraction.
(
/ ii
1
9 30
; n
5 35.1
O 1
15
i //
3 34.1
o /
25
i ii
2 4.4
1
42
i ii
1 4.7
36 29.4
35
5 32.4
10
3 31.7
10
2 3.4
20
1 3.9
1
24 53.6
40
5 29.6
20
3 29.4
20
2 2.5
40
1 3.2
2
18 25.5
45
5 27.0
30
3 27.1
30
2 1.6
43
1 2.4
3
14 25.1
50
5 24.3
40
3 24.8
40
2 0.7
20
1 1.7
4
11 44.4
55
5 21.7
50
3 22.6
50
1 59.8
40
1 1.0
5
9 52.0
10
5 19.2
16
3 20.5
26
1 58.9
44
1 0.3
5
9 44.0
5
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
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
3 8.3
27
1 53.9
46
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
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
8 28.0'
11
4 51.2
18
2 57.5
28
1 49.2
48
52.5
5
8 22.1
5
4 49.1
10
2 55.8
20
1 47.7
49
50.6
10
8 16.2
10
4 47.0
20
2 54.1
40
1 46.2
50
48.9
15
8 10.5
15
4 44.9
30
2 52.4
29
1 44.8
51
47.2
20
8 4.8
20
4 42.9
40
2 50.8
20
1 43.4
52
45.5
25
7 59.3
25
4 40.9
50
2 49.2
40
1 42.0
53
43.9
6 30
7 53.9
11 30
4 38.9
19
2 47.7
30
1 40.6
54
42.3
35
7 48.7
35
4 36.9
10
2 46.1
20
1 39.3
55
40.8
40
7 43.5
40
4 35.0
20
2 44.6
40
1 38.0
56
39.3
45
7 38.4
45
4 33.1
30
2 43.1
31
1 36.7
57
37.8
50
7 33.5
50
4 31.2
40
2 41.6
20
1 35.5
58
36.4
55
7 28.6
55
4 29.4
50
2 40.2
40
1 34.2
59
35.0
7
7 23.8
12
4 27.5
20
2 38.8
32
1 33.0
60
33.6
5
7 19.2
5
4 25.7
10
2 37.4
20
1 31.8
61
32.3
10
7 14.6
10
4 23.9
20
2 36.0
40
1 30.7
62
31.0
15
7 10.1
15
4 22.2
30
2 34.6
33
1 29.5
63
29.7
20
7 5.7
20
4 20.4
40
2 33.3
20
1 28.4
64
28.4
25
7 1.4
25
4 18.7
50
2 32.0
40
1 27.3
65
27.2
7 30
6 57.1
12 30
4 17.0
21
2 30.7
34
1 26.2
66
25.9
35
6 53.0
35
4 15.3
10
2 29.4
20
1 25.1
67
24.7
40
6 48.9
40
4 13.6
20
2 28.1
40
1 24.1
68
23.6
45
6 44.9
45
4 12.0
30
2 26.9
35
1 23.1
69
22.4
50
6 41.0
50
4 10.4
40
2 25.7
20
1 22.0
70
21.2
55
6 37.1
55
4 8.8
50
2 24.5
40
1 21.0
71
20.1
8
6 33.3
13
4 7.2
22
2 23.3
36
1 20.1
72
18.9
5
6 29.6
5
4 5.6
10
2 22.1
20
1 19.1
73
17.8
10
6 25.9
10 4 4.1
20
2 20.9
40
1 18.2
74
16.7
15
6 22.3
15
4 2.6
30
2 19.8
37
1 17.2
75
15.6
20
6 18.8
20
4 1.0
40
2 18.7
20
1 16.3
76
14.5
25
6 15.3
25
3 59.6
50
2 17.5
40
1 15.4
77 '0
13.5
8 30
6 11.9
13 30
3 58.1
23
2 16.4
38
1 14.5
78
12.4
35
6 8.5
35
3 56.6
10
2 15.4
20
1 13.6
79
11.3
40
6 5.2
40
3 55.2
20
2 14.3
40
1 12.7
80
10.3
45
6 2.0
45
3 53.7
30
2 13.3
39
1 11.9
81
9.2
50
5 58.8
50
3 52.3
40
2 12.2
20
1 11.0
82
8.2
55
5 55.7
55
3 50.9
50
2 11.2
40
1 10.2
83
7.2
9
5 52.6
14
3 49.5
24
2 10.2
40
1 9.4
84
6.1
p
5 49.6
10
3 46.8
10
2 9.2
20
1 8.6
85
5.1
10
5 46.6
20
3 44.2
20
2 8.2
40
1 7.8
86
4.1
15
5 43.6
30
3 41.6
30
2 7.2
41
1 7.0
87
3.1
20
5 40.7
40
3 39.0
40
2 6.2
20
1 6.2
88
2.0
25
5 37.9
50
3 36.5
50
2 5.3
40
1 5.4
89
1.0
9 30
5 35.1
15
3 34.1
25
2 4.4
42
1 4.7
90
0.0
TABLE III. A.
Correction of the Mean Refraction for the Height of the Barometer.
Barometer.
MEAN REFRACTION.
Barometer.
O'
1'
2'
3'
4'
5'
6'
y,
'
9'
10'
Subtract.
"I
(
I
II
Add.
30
31)
30
3
30
6'
a'i
:*o
o so'
6'
30
6 3O
6
27.50
51
2
5
7
10
12
15
17
20
23
25
28
30
33
35 38
40
43
45 48
27.55
2
5
7
10
12
15
17
20
7!
25
27
30
32
35 37
40
42
45
47
50
27.60
2
5
7
10
12
14J17
19
24 27
29
31
34 36
39
41
44
40
49
27.65
2
5
7
9
12
14|l6
19
21
24! 26
28
31
33! 36
88
40
4,3
45
48
27.70
2
5
7
9
11
14
10
18
21
23
25
28
30
32 35
.37
39
42
44
47
27.75
2
4
7
9
11
13
16
18
20
23
25
27
29
32 ! 34
36
39
41
43
46
27.80
2
4
7
9
11
13 15
18
20
22
24
27
29
31i33
.35
38
4!)
42
45
27.85
2
4
G
9
11
13 15
17
19
22
24
26
28
3032
35
.37
39
41
44
27.90
2
. 4
6
8
10
13
15
17
19
21
23
25
27
30 32
34
.30
38
40
43
27.95
2
4
8
10
12
14
16
18
21
23
25
27
.29
31
33
35
37
39
42
28.00
2
4
6
8
10
12
14
16
18
20
22
24
26
28
.30
32
34
30
38
41
28.05
o
2
4
6
8
10
12
14
16
18
20
'2'2
24
25
27
29
31
33
,35
37
39
28.10
2
4
6
8
9
11
13
15
17
14
21
23
25
27
29
31
.3.3
34
30
38
28.15
2
4
7
9
11
1.3
15
17
19
20
22
24
546
28
30
32
34
30
37
28.20
2
4
5
7
9
11
1,3
14
10
18
20
22
24
25
27
29
.31
3,3
35
36
28.25
2
a
5
7
9
10
12
14
16
18
19
21
2,3
25
20
28
30
32
34
35
28.30
2
3
5
7
8
10
12
14
15
17
19
21
22
24
20
27
29
31
33
34
28.35
2
.3
5
7
8
10
12
1.3
15
17
18
20
22
2
25
27
28
30
32
33
28.40
2
3
5
8
10
11
13
14
16
18
19
21
23J24
20
27
29
31
32
28.45
2
9
5
6
8
9
11
12
14
10
17
19
20
22
23
25
27
28
30
31
28.50
1
3
4
6
7
9
10
12
14
15
17
18
20
21
23
24
26
27
29
30
31.50
28.55
1
3
4
6
7
9
10
12
13
15
10
37
19
20
22
2.3
25
20
28
29
31.45
28.60
1
9
4
6
7
8
10
11
1.3
14
15
17
18
20
21
23
24
25
27
28
31.40
28.65
9
4
5
7
8
9
11
12
14
15
16
18
19
20
22
23
25
20
27
31.35
28.70
3
4
5
G
8
9
10
12
13
14
16
17
18
20
21
22
24
25
26
31.30
28.75
2
4
5
G
7
9
10
11
13
14
15
10
18
19
20
21
23
24
25
31.25
28.80
2
4
5
G
7
8
10
11
12
13
14
10
17
18
19
21
22
2.3
24
31.20
2885
2
8
5
7
8
9
10
12
1,3
14
15
10
17
19
20
21
22
23
31.15
28.90
2
3
4
9
7
8
9
10
11
12
1,3
14
16
17
18
19
20
21
22
31.10
28.95
2
8
4
5
6
7
8
9
11
12
13
14
15
10
17
18
19
20
21
31.05
29.00
2
,3
4
5
6
7
8
9
10
11
Vt
1,3
14
15
10
17
18
19
20
31.00
29.05
2
8
4
5
6
7
8
9
10
11
11
12
13
14
15
10
17
18
19
30.95
29.10
2
a
4
4
5
G
7
8
9
10
11
12
1,3
14
15
15
16
17
18
30.90
29.15
2
3
3
4
5
6
7
8
9
9
10
11
12
1.3
14
15
15
10
17
30.85
29.20
2
2
3
4
5
G
6
7
8
9
10
10
11
12
1,3
14
15
15
16
30.80
29.25
2
a
4
4
5
6
7
8
8
9
10
11
11
12
13
14
14
15
30.75
29.30
2
3
3
4
5
6
G
7
8
8
9
10
11
11
12
13
13
14
30-70
29.35
2
3
a
4
5
5
G
7
7
8
9
9
10
10
11,
12
13
13
30.65
29.40
1
2
2
3
4
4
5
5
G
7
7
8
8
9
10
10
11
12
12
30.60
29.45
1
2
2
a
3
4
4
5
G
6
7
7
8
8
9
9
10
11
11
30.55
29.50
I
1
2
2
3
3
4
5
5
G
G
7
7
8
8
9
9
10
10
30.50
29.55
1
1
2
2
3
3
4
4
5
5
5
6
G
7
7
8
8
9
9
30.45
29.60
1
1
2
2
2
3
3
4
4
4
5
5
G
6
G
7
7
8
8
30.40
29.65
1
1
1
2
2
2
3
a
4
4
4
5
5
5
G
G
6
7
7
30.35
29.70
1
1
1
1
2
2
2
3
3
a
4
4
4
5
5
5
5
6
6
30.30
29.75
1
1
1
1
2
2
2
3
3
3
3
4
4
4
4
5
5
5
30.25
29.80
1
1
1
1
1
2
2
2
2
2
3
3
a
8
3
4
4
4
30.20
29.85
1
1
1
1
1
1
2
2
2 2
2
2
2
3
3
3
3
30.15
29.90
1
I
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
00
30.00
Subtract,
6'
30'
6'
30
6'
30
6'
36"
H
30*
o
ai
6' 30
6'
30
6'
30
6'
3
6'
Add.
Barometer.
0'
I'
2'
3'
4'
5'
6'
7'
8'
9'
10'
MEAN REFRACTION.
11
81
TABLE III. B.
Correction of the Mean Refraction for the Heisht of the Thermometer.
Thermom.
MEAN REFRACTION.
Thermom.
0'
1'
2'
3'
4'
5'
6'
'
8'
9'
10
Add.
36
<S
30
3*
\
3j
30
30*
6'
aft
&
3/>
;;ft
o 36
Add.
10
i
4
6
II
12
ii
90
i
24
a
28
33
87
41
J
-l8
46
5C
55
GO
05
70
75
80 85
-90
8
4
s
12
15
19
28
27
31
36
40
44
48
53
58
62
07
72
77
82
87
8
6
4
7
11
Ifi
19
22
26
30
34
38
42
47
51
55
60
04
09
74
79
84
6
- 4
4
7
11
14
18
22
25
29
33
37
41
45
49
53
57
62
00
71
70
80
4
2
o
3
7
10
14
17
21
24
28
31
35
39
43
47
51
55
59
04
OS
72
77
. . o
Q
3
7
10
13
10
20
23
27
30
34
37
41
45
49
53
57
01
05
69
74
2
3
6
9
12
16
19
22
25
29
32
36
39
43
47
50
54
58
62
GO
70
2
4
3
G
9
12
15
18
21
24
28
31
34
37
41
44
48
52
55
59
03
67
4
6
3
6
B
11
H
17
20
23
20
29
32
30
39
42
40
49
53
50
00
64
6
8
3
5
S
11
14
10
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
20
29
32
35
38
41
44
48
51
54
58
10
11
2
5
7
10
13
15
18
20
23
20
28
31
34
37
40
43
40
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
10
19
21
24
26
29
31
34
37
40
42
15
48
51
14
15
2
4
7
9
11
13
16
18
20
|S
25
28
30
3
30
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
It
15
17
19
21
24
20
2;
31
33
36
'39
41
44
47
17
18
2
4
G
8
10
12
14
16
19
21
23
25
28
80
32
35
37
40
43
45
18
19
2
4
6
8
10
12
14
16
18
20
22
24
27
29
31
34
36
39
41
44
19
20
2
4
6
8
9
11
13
15
17
19
22
24
20
28
SO
33
35
37
40
42
20
21
2
4
5
7
9
11
13
15
17
19
21
23
25
27
29
31
34
30
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
30
38
23
24
2
3
5
G
8
10
11
13
15
17
18
20
22
24
20
28
30
32
34
36
24
25
2
3
5
G
8
g
11
13
14
1C
18
19
21
23
25
27
29
31
33
35
25
26
3
4
6
7
9
11
12
14
15
17
19
20
22
24
20
28
29
31
33
26
27
3
4
6
7
9
10
12
13
15
10
18
19
21
23
25
20
38
30
32
27
28
3
4
5
7
8
10
11
12
14
15
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
20
27
29
29
30
2
4
5
6
7
9
10
11
13
14
15
17
IS
20
21
23
24
20
28
30
31
Q
2
3
5
G
7
8
9
11
12
13
15
10
17
19
20
22
23
25
26
31
32
1
2
3
4
6
7
8
9
10
11
13
14
15
16
18
19
20
22
23
25
32
33
1
2
3
4
5
G
7
8
10
11
12
13
14
15
17
18
19
21
22
23
33
34
1
2
3
4
5
G
7
8
9
10
11
12
13
14
16
17
18
19
21
22
34
35
2
3
4
5
6
G
7
8
9
10
11
13
14
15
10
17
18
19
20
35
36
2
3
3
4
5
6
7
8
9
10
11
12
13
14
15
10
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
7
8
9
10
11
12
13
13
14
15
16
38 '
39
2
3
a
4
5
5
6
7
8
8
9
10
11
11
12
13
14
15
39
40
2
2
a
4
4
5
G
6
7
8
S
9
10
10
11
12
13
13
40
41
2
2
3
3
4
4
5
6
G
7
7
8
9
9
10
11
11
12
41
42
1
2
2
3
3
4
4
5
5
6
7
7
8
8
9
9
10
11
42
43
1
2
2
3
3
3
4
4
5
5
6
6
7
7
8
8
9
9
43
44
1
1
2
2
a
3
3
4
4
4
5
5
6
6
7
7
8
8
44
45
1
1
1
1
2
2
2
a
3
3
4
4
4
5
5
G
6
7
45
46
1
1
1
1
2
2
2
2
2
3
3
4
4
4
4
5
5
5
46
47
1
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.
<s
30
3ft
II
3ft
3ft
6 1
3ft
6'
3ft
6'
3ft
30
6 3#
o'
30
Add.
i
|
Xftcrinom.
O'
1'
2'
3'
4'
5'
6'
7'
8'
'
10'
Tlicrnioro*
MEAN REFRACTION.
TABLE III. B.
Corrector of the Mean Refraction for the Height of the Thermometer.
Thermom.
MEAN REFRACTION.
Thermom.
1'
2'
3'
4'
5'
6'
7'
8'
9'
10'
Subtract. '
1
30
d
s
6
9&
3<'l
3&
II
30
3l
o'
:w
6'
3&
6' 36
6'
Subtract.
o
(
50
6'j 6
c
50
51
i)
1
l
1
1
i
1
1
1
1
ij i
i
51
52
1
I
1
]
1
1
1
1
2
2
2
2
2
2! 2
3
52
53
1
i
1
1
1
I
2
2
2
2
2
2
a
3
3
3
4
4
53
54
1
i
1
1
2
2
2
2
3
3
a
8
4
4
4
5
5
5
54
55
1
1
i
1
2
2
2
3
3
3
4
4
4
5
5
',
6
G
6
55
.56
1
1
i
2
2
2
3
3
4
4
4
5
5
6
G
G
7
7
8
56
57
1
1
2
2
2
3
a
4
4
5
5
G
6
G
7
8
8
8
9
57
58
1
1
2
2
3
3
4
4
5
5
6
G
7
7
8
9
9
10
10
58
59
1
1
2
2
3
3
4
4
5
5
6
6
7
8
8
9
10
10
11
12
59
60
1
2
2
3
3
4
5
5
6
7
7
8
9
9
10
11
11
12
13
60
61
.0
1
2
3
3
4
4
5
6
7
7
8
9
9
10
1 !
12
12
13
14
61
62
1
2
3
3
4
5
G
6
7
8
9
9
10
11
12
13
14
15
15
62
63
1
2
3
4
5
5
6
7
8
8
9
10
11
12
13
14
15
16
17
63
64
2
2
3
4
5
6
7
7
8
9
10
11
12
13
14
15
1G
17
18
64
65
2
3
3
4
5
G
7
8
9
10
11
12
13
14
15
1G
17
18
19
65
66
2
3
4
B
6
C)
7
8
9
10
11
12
14
15
1G
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
3
4
5
G
7
8
9
11
11
13
14
15
16
18
19
20
22
23
68
69
2
3
4
r,
7
8
9
10
11
12
13
15
1C,
17
19
20
21
23
24
69
70
2
3
B
6
7
8
9
10
12
12
14
1G
17
18
20
21
22
24
25
70
71
2
4
5
r,
7
8
10
11
12
13
15
1G
IS
19
20
22
23
25
27
71
72
2
4
5
G
8
9
id
11
13
14
16
17
18
20
21
23
25
26
28
72
73
1
3
4
5
7
8
9
11
12
13
14
16
IS
19
21
22
24
2G
27
29
73
74
1
3
4
5
7
8
10
11
12
14
15
17
18
20
22
2,".
25
27
28
30
74
75
1
3
4
6
7
8
10
11
13
14
16
IS
19
21
22
24
26
28
29
31
75
76
1
3
4
8
7
9
10
12
13
15
16
18
20
22
23
25
27
29
31
32
76
77
1
3
5
6
8
9
11
12
14
16
17
19
21
22
24
26
28
30
32
34
77
78
2
3
5
r,
8
9
11
13
14
16
18
20
21
23
25
27
29
31
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
83
85
37
80
81
2
3
5
7
9
10
12
14
16
18
20
21
24
2G
28
30
32
34
36
38
81
82
2
4
5
7
9
11
13
14
16
18
20
22 24
2G
28
31
33
35
37
40
82
83
2
4
5
7
9
11
13
15
17
19
21
23125
27
29
31
34
36
88
41
83
84
2
4
6
8
9
11
13
15
17
19
21
23 26
1
28
30
32
35
37
39
42
84
85
2
4
6
8
10
12
14
1G
IS
20
22
24 26
29
31
33
3G
33
40
43
85
86
2
4
6
8
10
12
14
16
IS
20
28
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
f,
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
22
24
27 29
32
34
37
39
4-2
45
48
89
90
2
4
7
9
11
13
1G
18
20
23
25
27 ! 30
32
35
38
40
43
46
49
90
91
2
4
7
9
11
14
1G
18
21
23
25
28 31
33 36
39
41
H
47
50
91
92
2
5
7
9
11
14
16
19
21
24
26
29 31
3437
39
42
45
48
51
92
93
2
5
7
9
12
14
17
19
22
24
27
29 32
35 37
40
43
4C,
49
52
93
94
2
5
7
10
12
14
17
19
22
25
27
30 33
35J38
41
44
47
50
53
94
95
2
5
7
10
12
15
17
20
22
25
28
30 33
3G ! 39
42
45
48
51
54
95
96
2
5
7
10
12
IS
18
20
23
2G
28
31 34
37 40
'43
4G
49 52
55
96
97
3
5
8
10
13
15
18
21
23
2G
29
32 35
38 41
44 47
50 j 53
56
97
98
3
5
8
10
13
16
18
21
24
27
29
32 35
38141
44 48
51 54
58
98
99
3
5
8
11
13
16
19
21
24
27
30
33 36
39
42
45 49
52
55
59
99
100
3
5
8
11
13
16
19
22
25
23
31
34 37
40
43
46 50
53
56
60
100
Subtract.
4
30
d
3('i
30
30
6'
3/i
o'
30
3(J
6'
30
6' 30
n
.
30
6
Subtract.
o
1'
2'
3'
4'
5'
6'
V
8'
9'
1O'
HPViai-YV*rtv
Tnerrnom.
MEAN REFRACTION.
i nerinoni
TABLE IF. SIDEREAL INTO MEAN SOLAR TIME.
Sidd-
real.
o h
l h '
2 h.
3*
41,
5 h.
6 h.
7 h.
For
^Arnnrta
m.
m. a.
m. .
m. B.
m. s.
m.
m. g.
m. s.
u.
OUCOQU3.
00.000
09.830
19.659
29.489
39.318
49.148
58.977
08.807
g
1
00.164
09.993
19.823
29.653
39.482
49.312
59.141
08.971
1
oioos
2
00.323
10.157
19.987
29.816
39.646
49.475
59.305
09.185
2
.005
3
00.491
10.321
20.151
29.980
39.810
49.639
59.4G9
09.298
3
.008
4
00.655
10.485
20.314
30.144
39.974
49.803
59.633
09.462
4
.Oil
5
00.819
10.649
20.478
30.308
40.137
49.967
59.796
09.626
5
.014
6
00.983
10.813
20.642
30.472
40.301
50.131
59.960J 09.790
<3
.016
7
01.147
10.976
20.806
30.635
40.405
5U.2U5
1 00.124
09.954
7
.019
8
01.311
11.140
20.970
30.799
40.629
5U.458
1 00.288
10.118
8
.022
9
01.474
11.304
21.134
30.963
40.793
50.022
1 00.452
10.281
c
.025
10
01.638
11.468
21.297
31.127
40.956
50.786
1 00.616
10.445
14
.027
11
01.802
11.632
21.461
31.291
41.120
50.950 i 1 00.779
10.609
11
.030
12
01.966
11.795
21.625
31.455
41.284
51.114
1 00.943
10.773
12
.033
13
02.130
11.959
21.789
31.618
41.448
51.278
01.107
10.937
13
.035
14
0^2.294
12.123
21.953
31.782
41.612
51.441
1 01.271
11.100
14
.038
15
02.457
12.287
22.117
31.946
41.776
51.605
1 01.435
11.264
15
.041
16
02.621
12.451
22.280
32.110
41.939
51.769
1 01.599
11.428
16
.044
17
02.785
12.615
22.444
32.274
42.103
51.933J 1 01.762
11.592jj 17
.040
18
02.949
12.778
22.608
32.438
42.267
52.U97 1 01.926
11.756
18
.049
19
03.113
12.942
22.772
32.601
42.431
52.260
1 02.090
11.920
19
.052
20
03.277
13.106
22.936
32.765
42.595
52.424
1 02.254
12.083
20
.055
21
03.440
13.270
23.099
32.929
42.759
52.588
1 02.418
12.247
21
.057
22
03.604
13.434
23.263
33.093
42.922
52.752 1 02.582
12.411
22
.060 i
23
03.768
13.598
23.427
33.257
43.086
52.916 1 02.745
12.fi 75 !| 23
.063
24
03.932
13.761
23.591
33.420
43.250
53.080 1 02.909
1 2.739 J 24
.066
25
04.096
13.925
23.755
33.584
43.414
53.243i 1 03.073
12.G03JJ 25
.068
26
04.259
14.089
23.919
33.748
43.578
53.407
1 03.237
13.066 | 26
.071
27
04.423
14.253
24.082
33.912
43.742
53.571
1 03.401
13.230
27
.074
28
04.587
14.417
24.246
34.076
43.905
53.735
1 03.564
13.394
28
.076 !
29
04.751
14.581
24.410
34.240
44.069
53.899
1 03.728
13.558
29
.079
30
04.915
14.744
24.574
34.403
44.233
54.063
1 03.892
13.722
30
.082
31
05.079
14.908
24.738
34.567
44.397
54.226
1 04.056
13.886
31
.085
32
05.242
15.072
24.902
34.731
44.561
54.390
1 04.220
14.049
32
.087
33
05.406
15.236
25.065
34.895
44.724
54 554
04.384
14.213
33
.090
34
05.570
15.400
25.229
35.059
44.888
54.718
04.547
14.377
34
.093
35
05.734
15.563
25.393
35.223
45.052
54.882
04.711
14.541
35
.096
36
05.898
15.727
25.557
35.386
45.216
55.046
04.875
14.705
36
.098
37
06.062
15.891
25.721
35.550
45.380
55.209
05.039
14.868
37
.101
38
06.225
16.055
25.885
35.714
45.544
55.373
05.203
15.032
38
.104
39
06.389
16.219
26.048
35.878
45.707
55.537
05.367
15.196
39
.106
40
06.553
16.383
26.212
36.042
45.871
55.701
05.530
1 15.360
40
.109
41
06.717
16.546
26.376
36.206
46.035
55.865
05.694
1 15.524
41
.112
42
06.881
16.710
26.540
36.369
46.199
56.028
1 05.858
1 15.088
42
.115
43
07.045
16.874
26.704
36.533
46.363
56.192
1 06.022
1 15.851
43
.117
44
07.208
17.038
26.867
36.697
46.527
56.356
1 06.186
1 16.015
44
.120
45
07.372
17.202
27.031
36.861
46.690
56.520
1 06.350
16.179
45
.123
46
07.536
17.366
27.195
37.025
46.854
56.684
1 06.513
16.343
46
.126
47
07.700
17.529
27.359
37.188
47.018
56.848
1 06.677
16.507
47
.128
48
07.864
17.693
27.523
37.352
47.182
57.011
1 08.841
16.671
48
.131
49
08.027
17.857
27.687
37.516
47.346
57.175
1 07.005
16.834
49
.134
50
08.191
18.021
27.850
37.680
47.510
57.339
1 07.160
16.998
50
.137
51
08.355
18.185
28.014
37.844
47.673
57.503
1 07.332
17.162
51
.139
52
08.519
lb.349
28.178
38.008
47.837
57.667
1 07.496
1 7.326
52
.142
53
08.683
18.512
28.342
38.171
48.001
57.831
1 07.660
17.490
53
.145
54
08.847
18.676
28.506
38.335
48.165
57.994
1 07.824
17.654
54
.147
55
09.010
18.840
28.670
38.499
48.329
58.158
1 07.988
1 17.817
55
.150
56
09.174
19.004
28.833
38.663
48.492
58.322
I 08.152
1 17.981
56
.153
57
09.338
19.168
28.997
38.827
48.656
58.486
1 08.315
1 18.145
57
.156
58
09.502
19.331
29.161
38.991
48.820
58.650
1 08.479
I 18.309
58
.158
59
09.666
19.495
29.325
39.154
48.984
58.814
1 08.643
1 18.473
59
.161 |]
TABLE IV. SIDEREAL INTO MEAN SOLAR TIME.
Side
real
8"-
9 h.
10 "
ll*
12 h -
13 L
14*.
15 s -
For
Soconds.
m
m. t.
m. s.
m. i.
in. <
m. i.
m. s.
m. 8.
m.
o
1 18.636
1 28.466
38.296
1 48,125
57.955
2 07.784
2 17.61
2 27.443
8
i.
i
1 18.800
1 28.630
38.459
1 48.289
58.119
2 07.948
2 17.77
2 27.607
1
0.003
t
1 18.964
1 28.794
38.623
1 48.453
58.282
2 08.112
2 17.94
2 27.771
j
.005
<
1 19.128
1 28.958
38.787
1 48.617
58.446
2 08.276
2 18.10
2 27.935
.008
4
1 19.292
1 29.121
38.951
1 48.780
58.610
2 08.440
2 18.26
2 28.099
4
.011
K
I
1 19.456
1 29.285
39.115
1 48.944
58.774
2 08.603
2 18.433
2 28.263
r
.014
6
1 19.619
1 29.449
39.279
I 49.108
58.938
2 08.767
2 18.59
2 28.426
i
.016
j
1 19.783
1 29.613
39.442
1 49.272
59.101
2 08.931
2 18.76
2 28.590
-
.019
8
1 19.947
1 29.777
39.606
1 49.436
59.265
2 09.095
2 18.924
2 28.754
i
.022
fj
1 20.111
1 29.940
39.77?
1 49.600
59.429
2 09.259
2 19.088
2 28.918
j
.025
10
1 20.275
1 30.104
1 39.934
1 49.763
59.593
2 09.423
2 19.252
2 29.082
10
.027
11
1 20.439
I 30.268
1 40.098
1 49.927
59.757
2 09.586
2 19.416
2 29.245
11
.030
12
1 20.602
1 30.432
1 40.261
1 50.091
59.921
2 09.750
2 19.580
2 29.409
12
.033
13
1 20.766
1 30.596
1 40.425
1 50.255
2 00.084
2 09.914
2 19.744
2 29.573
13
.035
14
1 20.930
1 30.760
1 40.589
1 50.419
2 00.248
2 10.078
2 19.907
2 29.737
14
.038
15
1 21.094
1 30.923
40.753
1 50.583
2 00.412
2 10.242
2 20.071
2 29.901
15
.041
16
1 21.258
1 31.087
40.917
1 50.746
2 00.576
2 10.405
2 20.235
2 30.065
16
.044
17
1 21.422
1 31.251
41.081
1 50.910
2 00.740
2 10.569
2 20.399
2 30.228
17
.046
18
1 21.585
1 31.415
41.244
1 51.074
2 00.904
2 10.733
2 20.563
2 30.392
18
.049
19
1 21.749
1 31.579
41.408
1 51.238
2 01.067
2 10.897
2 20.727
2 30.556
19
,052
20
1 21.913
1 31.743
41.572
1 51.402
2 01.231
2 11.061
2 20.890
2 30.720
20
.055
21
1 22.077
1 31.906
41.736
1 51.565
2 01.395
2 11.225
2 21.054
2 30.884
21
.057
22
1 22.241
1 32.070
41.900
1 51.729
2 01.559
2 11.388
2 21.218
2 31.048
22
.060
23
1 22.404
1 32.234
42.064
1 51.893
2 01.723
2 11.552
2 21.382
2 31.211
23
.063
24
1 22.568
1 32.398
42.227
1 52.057
2 01.887
2 11.716
2 21.546
2 31.375
24
.066
25
1 22.732
1 32.562
42.391
1 52.221
2 02.050
2 11.880
2 21.709
2 31.539
25
.068
26
1 22.896
1 32.726
42.555
1 52.385
2 02.214
2 12.044
2 21.873
2 31.703
26
.071
27
1 23.060
1 32.889
42.719
1 52.548
2 02.378
2 12.208
2 22.037
2 31.867
27
.074
28
1 23.224
1 33.053
42.883
1 52.712
2 02.542
2 12.371
2 22.201
2 32.031
28
.076
29
1 23.387
1 33.217
43.047
1 52.876
2 02.706
2 12.535
2 22.365
2 32.194
29
.079
30
1 23.551
1 33.381
43.210
1 53.040
2 02.869
2 12.699
2 22.529
2 32.358
30
.082
31
1 23.715
1 33.545
43.374
1 53.204
2 03.033
2 12.863
2 22.692
2 32.522
31
.085
32
1 23.879
1 33.708
43.538
1 53.368
2 03.197
2 13.027
2 22.856
2 32.686
32
.087
33
1 24.043
1 33.872
43.702
1 53.531
2 03.361
2 13.191
2 23.020
2 32.850
33
.090
34
1 24.207
1 34.036
43.866
1 53.695
2 03.523
2 13.354
2 23.184
2 33.013
34
.093
35
1 24.370
1 34.200
44.029
1 53.859
2 03.689
2 13.518
2 23.348
2 33.177
35
.096
36
1 24.534
1 34.364
44.193
1 54.023
2 03.852
2 13.682
2 23.512
2 33.341
36
.098
37
1 24.698
1 34.528
44.357
1 54.187
2 04.016
2 13.846
2 23.675
2 33.505
37
.101
38
1 24.862
1 34.691
44.521
1 54.351
2 04.180
2 14.010
2 23.839
2 33.669
38
.104
39
1 25.026
1 34.855
44.685
1 54.514
2 04.344
2 14.173
2 24.003
2 33.833
39
JOG i
40
1 25.190
1 35.019
44.849
1 54.678
2 04.508
2 14.337
2 24.167
2 33.996
40
.109
41
1 25.353
1 35.183
45.012
1 54.842
2 04.672
2 14.501
2 24.331
2 34.160
41
.112
42
1 25.517
1 35.347
45.176
1 55.006
2 04.835
2 14.665
2 24.495
2 34.324
42
.115
43
1 25.681
1 35.511
45.340
1 55.170
2 04.999
2 14.829
2 24.658
2 34.488
43
.117
44
1 25.845
1 35.674
45.504
1 55.333
2 05.163
2 14.993
2 24.822
2 34.652
44
.120
45
1 26.009
1 35.838
45.668
1 55.497
2 05.327
2 15.156
2 24.986
2 34.816
45
.123
46
1 26.172
36.002
45.832
1 55.661
2 05.491
2 15.320
2 25.150
2 34.979
46
.126
47
1 26.336
36.166
1 45.995
1 55.825
2 05655
2 15.484
2 25.314
2 35.143
47
.128
48
1 26.500
36.330
1 46.159
1 55.989
2 05.818
2 15.b48
2 25.477
2 35.307
48
.131
49
1 26.664
36.493
1 46.323
1 56.153
2 05.982
2 15.812
2 25.641
2 35.471
49
.134
50
1 26.828
36.657
1 46.487
1 56.316
2 06.146
2 15.976
2 25.805
2 35.635
50
.137
51
1 26.992
36.821
1 46.651
1 56.480
2 06.310
2 16.139
2 25.969
2 35.798
51
.139
52
1 27.155
36.985
1 46.815
1 56.644
2 06.474
2 16.303
2 26.133
2 35.962
52
.142
53
1 27.319
37.149
46.978
1 56.808
2 06.637
2 16.467
2 26.297
2 36.126
53
.145 H
54
1 27.483
37.313
47.142
1 56.972
2 06.801
2 16.631
2 26.460
2 36.290 j
54
.147 I!
55
1 27.647
1 37.476
47.306
1 57.136
2 06.965
2 16.795
2 26.624
2 36.454
55
.150
56
1 27.811
1 37.640
47.470
1 57.299
2 07.129
2 16.959
2 26.788
2 36,618
56
.153 i
57
1 27.975
1 37.804
47.634
1 57.463
2 07.293
2 17.122
2 26.952
2 36.781
57
.156
58
1 28.138
I 37.968
47.797
1 57.627
2 07.457
2 17.286
2 27.116
2 36.945
58
.158
59
1 28.302
1 38.132
47.961
1 57.791
2 07.620
2 17.450
2 27.280
2 37.109
59
.161
85
TABLE IV. SIDEREAL INTO MEAN SOLAR TIME.
Side-
real.
16 h -
17 h
IS*
19 h -
20 h -
21 b
22 h -
23 h
For
Seconds.
ID.
in. .
m. s
m. s.
m. s.
m. s.
m. s.
m. 8.
m. r
2 37.273
2*47.102
2 56.932
3 06.762
3 16.591
3 26.421
3 36.250
3 46.080
B.
1
2 37.437
2 47.266
2 57.096
3 06.925
3 16.755
3 26.585
3 36.414
3 46.244
i
0.003
2
2 37.601
2 47.430
2 57.260
3 07.089
3 16.919
3 26.748
3 36.578
3 46.407
2
.005
3
2 37.764
2 47.594
2 57.424
3 07.253
3 17.083
3 26.912
3 36.742
3 46.571
3
.008
4
2 37.928
2 47.758
2 57.587
3 07.417
3 17.246
3 27.076
3 36.906
3 46.735
4
.011
5
2 38.092
2 47.922
2 57.751
3 07.581
3 17.410
3 27.240
3 37.069
3 46.899
5
.014
6
2 38.256
2 48.085
2 57.915
3 07.745
3 17.574
3 27.404
3 37.233
3 47.063
6
.016
7
2 38.420
2 48.249
2 58.079
3 07.908
3 17.738
3 27.568
3 37.397
3 47.227
7
.019
8
2 38.584
2 48.413
2 58.243
3 08.072
3 17.902
3 27.731
3 37.561
3 47,390
8
.022
9
2 38.747
2 48.577
2 58.406
3 08.236
3 18.066
3 27.895
3 37.725
3 47.554
9
.025
10
2 38.911
2 48.741
2 58.570
3 08.400
3 18.229
3 28.059
3 37.889
3 47.718
10
.027
11
2 39.075
2 48.905
2 58.734
3 08.564
3 18.393
3 28.223
3 38.052
3 47.882
11
.030
12
2 39.239
2 49.068
2 58.898
3 08.728
3 18.557
3 28.387
3 38.216
3 48.046
12
.033
13
2 39.403
2 49.232
2 59.062
3 08.891
3 18.721
3 28.550
3 38.380
3 48.210
13
.035
14
2 39.566
2 49.396
2 59.226
3 09.055
3 18.885
3 28.714
3 38.544
3 48.373
14
.038
15
2 39.730
2 49.560
2 59.389
3 09.219
3 19.049
3 28.878
3 38.708
3 48.537
15
.041
16
2 39.894
2 49.724
2 59.553
3 09.383
3 19.212
3 29.042
3 38.871
3 48.701
16
.044
17
2 40.058
2 49.888
2 59.717
3 09.547
3 19.376
3 29.206
3 39.035
3 48.865
17
.046
18
2 40.222
2 50.051
2 59.881
3 09.710
3 19.540
3 29.370
3 39.199
3 49.029
18
.049
19
2 40.386
2 50.215
3 00.045
3 09.874
3 19.704
3 29.533
3 39.363
3 49.193
19
.052
20
2 40.549
2 50.379
3 00.209
3 10.038
3 19.868
3 29:697
3 39.527
3 49.356
20
.055
21
2 40.713
2 50.543
3 00.372
3 10.202
3 20.032
3 29.861
3 39.691
3 49.520
21
.057
22
2 40.877
2 50.707
3 00.536
3 10.366
3 20.195
3 30.025
3 39.854
3 49.68-1
22
.060
23
2 41.041
2 50.870
3 00.700
3 10.530
3 20.359
3 30.189
3 40.018
3 49.848
23
.063
24
2 41.205
2 51.034
3 00.864
3 10.693
3 20.523
3 30.353
3 40.182
3 50.012
24
.066
25
2 41.369
2 51.198
3 01.028
3 10.857
3 20.687
3 30.516
3 40.346
3 50.175
25
.068
26
2 41.532
2 51.362
3 01.192
3 11.021
3 20.851
3 30.680
3 40.510
3 50.339
26
.071
27
2 41.696
2 51.526
3 01.355
3 11.185
3 21.014
3 30.844
3 40.674
3 50.503
27
.074
28
2 41.860
2 51.690
3 01.519
3 11.349
3 21.178
3 31.008
3 40.837
3 50.667
28
.076
29
2 42.024
2 51.853
3 01.683
3 11.513
3 21.342
3 31.172
3 41.001
3 50.831
29
.079
30
2 42.188
2 52.017
3 01.847
3 11.676
3 21.506
3 31.336
3 41.165
3 50.995
30
.082
31
2 42.352
2 52.181
3 02.011
3 11.840
3 21.670
3 31.499
3 41.329
3 51.158
31
.085
32
2 42.515
2 52.345
3 02.174
3 12.004
3 21.834
3 31.663
3 41.493
3 51.322
32
.087
33
2 42.679
2 52.509
3 02,338
3 12.168
3 21.997
3 31.827
3 41.657
3 51.486
33
.090
34
2 42.843
2 52.673
3 *2.502
3 12.332
3 22.161
3 31.991
3 41.820
3 51.650
34
.093
! 35
2 43.007
2 52.836
3 02.666
3 12.496
3 22.325
3 32 155
3 41.984
3 51.814
35
.096
36
2 43.171
2 53.000
3 02.830
3 12.659
3 22.489
3 32.318
3 42.148
3 51.978
36
.098
37
2 43.334
2 53.164
3 02.994
3 12.823
3 22.653
3 32.482
3 42.312
3 52.141
37
.101
38
2 43i498
2 53.328
3 03.157
3 12.987
3 22.817
3 32.646
3 42.476
3 52.305
38
.104
39
2 43.662
2 53.492
3 03.321
3 13.151
3 22.980
3 32.810
3 42.639
3 52.469
39
.106
40
2 43.826
2 53.656
3 03v485
3 13.315
3 23.144
3 32.974
3 42.803
3 52.633
40
.109
41
2 43.990
2 53.819
3 03,649
3 13.478
3 23.308
3 33.138
3 42.967
3 52.797
41
.112
42
2 44.154
2 53.983
3 03.813
3 13.642
3 23.472
3 33.301
3 43.131
3 52.961
42
.115
43
2 44.317
2 54.147
3 03.977
3 13.06
3 23.636
3 33.465
3 43.295
3 53.124
43
.117
44
2 44.481
2 54.311
3 04.140
3 13.970
3 23.800
3 33.629
3 43.459
3 53.288
44
.120
45
2 44.645
2 54.475
3 04.304
3 14.134
3 23.963
3 33.793
3 43.622
3 53.452
45
.123
46
2 44.809
2 54.638
3 04.468
3 14.298
3 24.127
3 33.9:37
3 43.786
3 53.616
46
.126
47
2 44.973
2 54.802
3 04.632
3 14.461
3 24.291
3 34.121
3 43.950
3 53.780
47
.128
48
2 45.137
2 54.966
3 04.796
3 14.625
3 24.455
3 34.284
3 44.114
3 53.943
48
.131
49
2 45.300
2 55.130
3 04.960
3 14.789
3 24.619
3 34.448
3 44.278
3 54.107
49
.134
50
2 45.464
2 55.294
3 05.123
3 14.953
3 24.782
3 34.612
3 44.442
3 54.271
50
.137
51
2 45.628
2 55.458
3 05.287
3 15.117
3 24.946
3 34.776
3 44.605
3 54.435
51
.139
52
2 45.792
2 55.621
3 05.451
3 15.281
3 25.110
3 34.940
3 44.769
3 54.599
52
.142
53
2 45.956
2 55.785
3 05.615
3 15.444
3 25.274
3 35.104
3 44.933
3 54.763
53
.145
54
2 46.120
2 55.949
3 05.779
3 15.608
3 25.438
3 35.267
3 45.097
3 54.926
54
.147
55
2 46.283
2 56.113
3 05.942
3 15.772
3 25.602
3 35.431
3 45.261
3 55.090
55
.150
56
2 46.447
2 56.277
3 06.106
3 15.936
3 25.765
3 35.595
3 45.425
3 55.254
56
.153
57
2 46.611
2 56.441
3 06.270
3 16.100
3 25.929
3 35.759
3 45.588
3 55.418
57
.156
58
2 46,775
2 56.604
3 06.434
3 16.264
3 26.093
3 35.923
3 45.752
3 55.582
58
.158
59
2 46.939J
8 fifi,768i 3 06.598
8 16.427
3 26.257
3 36.Q86
3 45.916
3 55.746
59
.161
86
D. Van Nostrantf s Publications.
Barre Duparcq' Military Art and History. Elements of
Military Art and History: comprising the History and Tactics of the
separate Arms ; the Combination of the Arms ; and the minor operations
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Ben ton's Ordnance and Gunnery. A Course of Instruction
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2
D. Van No str and' s Publications.
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Barnard and Barry's Peninsular Campaign. Report of
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4
D. Van No sir and} s Publications.
Simpson's Ordnance and Naval Gunnery. A Treatise on
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*' I'; 3 scarcely necessary for us to say, that a work prepared by a writer so practically
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Holley's Ordnance and Armor. Embracing Descriptions,
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trations. 1 vol. 8vo, 948 pages. Half roan, $10.00.
Luce's Naval Light Artillery. Instructions for Naval Light
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troops, and must handle their guns like the artillery soldiers of a battery. ' The Exercise
of the Howitzer Afloat 1 was prepared and arranged by Captain Dahlgren, whose name
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also given. The Plates are numerous and exceedingly clear, and the whole typography ijj
excellent." Philadelphia Inquirer.
Ward's Waval Ordnance and Gunnery. Elementary In-
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mander U. S. Navy ; author of " Naval Tactics," and " Steam for the
Million." New edition, revised and enlarged. 8vo, cloth. $2.00.
u It conveys an amount of information in the same space to be found nowhere else, and
given with a clearness which renders it useful as well to the general as the professional
inquirer." N. Y. Evening Post.
" The whole detail of Ordnance, In ts history, philosophy, and application, is glvea
by Commander "Ward in such a manner (with occasional diagrams) as to convey to the
student accurate notions for practical use." New Yorker.
5
D. Van No sir and} s Publications.
I
lance's Seamanship. Compiled from various authorities, and Illus-
trated with numerous original and selected Designs. For the use of the
United States Naval Academy. By S. B. Luce, Lieut.-Commander U. S. N.
j In two parts. Second Edition. , One royal octavo volume, cloth. $10.00.
Squadron Tactics Under Steam. By Foxhall A. Parker,
Commander U. S. Navy. Published by authority of the Navy Depart-
ment. 1 voL 8vo, with numerous Plates. $5.00.
"In this useful work to Navy officers, the author demonstrates by the aid of profuse
diagrams and explanatory text a new principle for manoeuvring naval vessels in action.
The author contends that the winds, waves, and currents of the ocean oppose no more
serious obstacles to the movements of a steam fleet, than do the inequalities on the sur-
face of the earth to the manoeuvres of an army. It is in this light, therefore, that he
views a vast fleet simply as an army ; the regiments, brigades, and divisions of which
are represented by a certain ship or ships." Scientific American.
Nautical Routine and Stowage. With Short Rules in Navi-
gation. By John McLeod Murphy and "Wm. N. Jeffers, Jr., U. S. Navy.
1 vol. 8vo, blue cloth. $2.50.
Obon' Hand-Book of the United States Navy. Be-
ing a Compilation of all of the Principal Events in the History of every
Vessel of the United States Navy, from April, 1861, to May, 1864.
Compiled and arranged by B. S. Osbon. 1 vol. 12mo, blue cloth. $2.50.
" Ae a condensed and compact history, as well as a work containing a vast amount of
Information, this work cannot be surpassed." Boston Traveller.
Brandt's Gunnery Catechism. Gunnery Catechism, as applied
to the Service of Naval Ordnance. Adapted to the Latest Official Regu-
lations, and approved by the Bureau of Ordnance, Navy Department.
By J. D. Brandt, formerly of the U. S. Navy. 1 vol. 18mo, illustrated,
blue cloth. $1.50.
"This manual is very full of information and instruction, and shows the 'chief end' of
Gunnery, and the aim of those who follow that profession. It is indispensable to all
those who are suddenly introduced to a gun-deck, and will be found a valuable aid also
to experienced officers." Commercial Advertiser .
Barrett's Gunnery Instructions. Gunnory Instruction^, sim-
plified for the Volunteer Officers of the United States Navy, with Hints
to Executive and other Officers. By Lieut. Edward Barrett, U. S. N.,
Instructor of Gunnery, Navy Yard, Brooklyn. 1 vol. 12mo, cloth. $1.25.
"It is a thorough work, treating plainly on its subject and contains also somfi valu-
able hints to executive officers. No officer In the volunteer navy should be without a
coj y "Boston Evening Traveller.
D. Van No sir and? s Publications.
Totten's Naval Text-Book. Naval Text-Book and Dictionary,
compiled for the use of the Midshipmen of the U. S. Navy. By Com
mander B. J. Totten, U. S. N. Second and revised edition. 1 vol. 12mo.
$3.00.
Calculated Tables of Ranges for Navy and Army
Guns. With a Method of Finding the Distance of an Object at Sea.
By Lieut. W. P. Buckner, U. S N. 1 vol. 8vo, cloth. $1.50.
JUanual of Internal Rules and Regulations for Men-
of- War. By Commodore U. P. Levy, U. S. N., late Flag Officer com-
manding U. S. Naval Force in the Mediterranean, &c. Flexible blue
cloth. Third Edition, revised and enlarged. 50 cents.
"Among the professional publications for which we are indebted to the war, we will-
ingly give a prominent place to this useful little Manual of Eules and Regulations to be
observed on board of ships of war. Its authorship is a sufficient guarantee for its accu-
racy and practical value ; and as a guide to young officers in providing for the discipline,
police, and sanitary government of the vessels under their command, we know of nothing
superior." N. Y. Herald.
King's Lessons and Practical Notes on Steam, The
Steam Engine, Propellers, &c., &c., for Young Marine Engineers, Stu-
dents, and others. By the late W. H. King, U. S. Navy. Revised by
Chief Engineer J. W. King, U. S. Na\/. Ninth Edition, enlarged. 8vo,
cloth. $2.00.
" This is the ninth edition of a valuable work of the late W. HTKing, U. S. Navy. It
contains lessons and practical notes on Steam and the Steam-Engine, Propellers, &c. It
is calculated to be of great use to young marine engineers, students, and others. The
text is illustrated and explained by numerous diagrams and representations of machi-
nery. This new edition has been revised and enlarged by Chief Engineer J. W. King,
U. 8. Navy, brother to the deceased author of the work." Boston Daily Advertiser.
Ward's Steam for the Million. A popular Treatise on Steam
and its Application to the Useful Arts, especially to Navigation. By
J. H. "Ward, Commander U. S. Navy. New and revised Edition. 1 vol.
8vo, cloth. $1.00.
The Naval Howitzer Ashore. By Foxhall A. Parker, Com-
mander U. S. Navy. 1 vol. 8vo, with Plates. Cloth. $4.00.
D. Van No sir and} s Publications.
Gillmore's Fort S muter. Official Report of Operations against
the Defences of Charleston Harbor, 18G3. Comprising the Descent upon
Morris Island, the Demolition of Fort Sumter, and the Siege and Reduc-
tion of Forts Wagner and Gregg. By Major-Gen. Q. A. GILLMORE, U. S.
Volunteers, and Major U. S. Corps of Engineers. With Maps and Litho-
graphic Plates, Views, &c. 1 vol. 8vo. cloth. $10.
Gillmore's Siege and Reduction Of Fort Pulaski,
Georgia. Papers on Practical Engineering. No. 8. Official Report
to the U. S. Engineer Department of the Siege and Reduction of Fort
Pulaski, Ga., February, March, and April, 1862. By Brig.-Gen. Q. A.
GILLMORE, U. S. A. Illustrated by Maps and Views. 1 vol. 8vo, cloth.
$2.50.
"This Is an official history of the siege of Fort Pulaski, from the commencement, with
all the details in full, made up from a daily record, forming a most valuable paper for
future reference. The situation and construction of the Fort, the position of the guns,
both of the rebels and the Federals, and their operation, are made plain by maps and
engraved views of different sections. Additional reports from other officers are fur-
nished in the appendix, and every thing has been done to render the work full and reli-
able." Boston Journal.
Gill in ore's Treatise on Limes, Hydraulic Cements, and
Mortars. Papers on Practical Engineering, U. S. Engineer Depart-
ment, No. 9, containing Reports of numerous Experiments conducted in
New York City, during the years 1858 to 1861, inclusive. By Q. A.
GILLMORE, Brig.-Gen. U. S. Volunteers, and Major U. S. Corps of Engi-
neers. With numerous Illustrations. One vol. 8vo. $4.00.
" This work contains a record of certain experiments and researches made under the
authority of the Engineer Bureau of the War Department from 1858 to 1861, upon the
various hydraulic cements of the United States, and the materials for their manufacture.
The experiments were carefully made, and are well reported and compiled.'' Journal
Franklin Institute.
Tbe Volunteer Quartermaster. Containing a Collection and
Codification of the Laws, Regulations, Rules, and Practices governing the
Quartermaster's Department of the United States Army, and in force
March 4, 1865. By Captain ROELIFP BRINKERHOFF, Assistant Quarter-
master U. S. Volunteers, and Post Quartermaster at "Washington. 1
vol. 12mo, cloth. $2.50.
This work embraces all the laws of Congress, and all the orders and circulars of the
War Office and its bureaus, bearing upon the subject It also embodies the decisions of
the Second Comptroller of the Treasury, so far as they affect the Quartermaster's Depart-
ment These decisions have the force of law in the adjustment of accounts, and are there-
fore invaluable to all disbursing officers.
D. Van No sir and} s Publications.
1 ill hnii's Military Bridges. Systems of Military Bridges in Use
by the United States' Army; those adopted by the Great European
Powers ; and such as are employed in British India. "With Directions
for the Preservation, Destruction, and Re-establishment of Bridges. By
Brig.-Gen. GEORGE "W. CULLUM, Lieut.-Col. Corps of Engineers, U. S. A.
1 vol. 8vo. "With numerous Illustrations, cloth. $3.50.
44 We have no man more competent to prepare such a work than Brig.-Gen. Cullum,
who had the almost exclusive supervision, devising, building, and preparing for service
of the various bridge-trains sent to our armies in Mexico during our war with that
country. The treatise before us is very complete, and has evidently been prepared with
scrupulous care. The descriptions of the various systems of military bridges adopted
by nearly all civilized nations are very interesting even to the non-professional reader,
and to those specially interested in such subjects must be very instructive, for they are
evidently the work of a master of the art of military bridge-building." Washington
Chronicle.
llaupt's Military Bridges. For the Passage of Infantry, Artil-
lery, and Baggage-Trains ; with Suggestions of many new Expedients
and Constructions for Crossing Streams and Chasms ; designed to utilize
the Resources ordinarily at command, and reduce the amount and cost of
Army Transportation. Including also Designs for Trestle and Truss
Bridges for Military Railroads, adapted especially to the wants of the
Service of the United States. By HERMAN HAUPT, Brig.-Gen. in charge
of the Construction and Operation of the U. S. Military Railways, Author
of " General Theory of Bridge Construction," &c. Illustrated by sixty-
nine Lithographic Engravings. 8vo, cloth. $6.50.
"This elaborate and carefully prepared, thouth thoroughly practical and simple work,
is peculiarly adapted to the military service of the United States. Mr. Haupt has added
very much to the ordinary facilities for crossing streams and chasms, by the instructions
afforded in this work." Boston Courier.
Holley's Railway Practice. American and European Railway
Practice, in the Economical Generation of Steam, including the Materials
and Construction of Coal-burning Boilers, Combustion, the Variable
Blast, Vaporization, Circulation, Superheating, Supplying and Heating
Feed- water, &c., and the Adaptation of "Wood and Coke-burning Engines
to Coal-burning ; and in permanent "Way, including Road-bed, Sleepers,
Rails, Joint Fastenings, Street Railways, &c., &c. By Alexander L.
Holley, B. P. "With 77 lithographed plates. 1 vol. folio, cloth. $12.00.
* * * " All these subjects are treated by the author in both an intelligent and in-
telligible manner. The facts and ideas are well arranged, and presented in a clear and
simple style, accompanied by beautiful engravings, and we presume the work will be
regarded as indispensable by all who are interested in a knowledge of the construction
of railroads, and rolling stock, or the working of locomotives. 11 Scientific American.
9
D. Van Nostrand? s Publications.
Authorized U. S. Infantry Tactics. For the Instruction,
Exercise, and Manoeuvres of the Soldier, a Company, Line of Skirmish,
ers, Battalion. Brigade, or Corpa d'Armee. By Brig.-Gen. SILAS CASEY,
U S. A. 3 vols 24mo. Cloth, lithographed plates. $2.50.
Vol. I. School of the Soldier; School of the Company; Instruction for
Skirmishers.
Yol. II. School of the Battalion.
Yol. III. Evolutions of a Brigade ; Evolutions of a Corps d'Armee.
"WAR DEPARTMENT, WASHINGTON, August 11, 1S62.
" The System of Infantry Tactics prepared by Brig.-Gen. Silas Casey, U. 8. A., having
been approved by the President, is adopted for the instruction of the Infantry of the
Armies of the United States, whether Regular, Volunteer, or Militia.
"EDWIN M. STANTON, Secretary of Far."
U. S. Tactics for Colored Troops. U. S. Infantry Tactics,
for the Instruction, Exercise, and Manoeuvres of the Soldier, a Company,
Line of Skirmishers, and Battalion, for the use of the Colored Troops of
the United States Infantry. Prepared under the direction of the War
Department. I vol., plates. $1.50.
"WAR DEPARTMENT, WASHINGTON, March 9, 1863.
" This system of United States Infantry Tactics, prepared under the direction of the
War Department, for the use of the Colored Troops of the United States Infantry, having
been approved by the President, is adopted for the instruction of such troops.
"EDWIN M. STANTON, Secretary of War."
Keltoii's Bayonet Exercise. A New Manual of the Bayonet,
for the Army and Militia of the United States. By Colonel J. C. KELTON,
U. S. A. With forty beautifully engraved plates. Red cloth. $2.00.
"This Manual was prepared for the use of the Corps of Cadets, and has been introduced
at the Military Academy with satisfactory results. It is simply the theory of the attack
and defence of the sword applied to the bayonet, on the authority of men bkilled in the
use of arms." New York Times.
JBcrriniau's Sword-Play. The Militiaman's Manual and Sword-
Play without a Master. Rapier and Broad-Sword Exercises copiously
Explained and Illustrated ; Small- Arm Light Infantry Drill of the United
States Army ; Infantry Manual of Percussion Muskets ; Company Drill
of the United States Cavalry. By Major M. \V. BEftRiMAN, engaged for
the last thirty years in the practical instruction of Military Students.
Fourth edition. 1 vol. 12mo, red cloth. $1.00.
"This work will be found very valuable to all persons seeking military instruction;
but it recommends itself most especially to officers, and those who have to .ise the sword
or sabre. We believe it is the only work on the use of the sword published in ,nis
country." New York Tablet.
10
D. Van No sir and} s Publications.
i
Heavy Artillery Tactics. 1863. Instruction for Heavy Ar.
tillery ; prepared by a Board of Officers, for the use of the Army of the
United States. With service of a gun mounted on an iron carriage. In
one volume, 12 mo, with numerous illustrations, cloth. $2.50.
"WAR DEPARTMENT, >
"WASHINGTON, D. C., Oct. 20, 1862. )
"This system of Heavy Artillery Tactics, prepared under direction of the War De-
partment, having been approved by the President, is adopted for the instruction of
troops when acting as heavy artillery. EDWIN M. STANTON, Secretary of War,"
w The First Part consists of sixteen lessons relating to the service of the single piece, in-
cluding the gun, howitzer, mortar, and columbiad ; also, the formation of batteries, the art
of aiming pieces and firing hot-shot. Part Second relates entirely to mechanical manoeu-
vres, and appliances for handling, mounting, dismounting, and transporting heavy pieces.
Part Third is of a miscellaneous cnaracter, containing directions for embarking and disem-
barking artillery and ordnance stores; also, tables of dimensions and weights of guns,
carriages, shot, shell, machines, and implements, with charges for, and ranges of heavy
artillery. These instructions are not only copious in detail, but aptly illustrated with
thirty-nine elegant steel-plate engravings." Bulletin.
Roberta's Hand-Book of Artillery. For the Service of the
United States Army and Militia. New revised and greatly enlarged
edition. By Major JOSEPH ROBERTS, U. S. A. 1 vol. ISmo, cloth.
$1.25.
"A complete catechism of gun practice, covering the whole ground of this branch of
military science, and adapted to militia and volunteer drill, as well as to the regular
army. It has the merit of precise detail, even to the technical names of all parts of a
gun, and how the smallest operations connected with its use can be best performed. It
has evidently been prepared with great care, and with strict scientific accuracy."
New York Century.
Duauc's Manual for Engineer Troops. Consisting of Part
I., Pontoon Drill ; II., Practical Operations of a Siege ; III , School of
the Sap ; IV., Military Mining ; V., Construction of Batteries. By
Major J. C. DUANE, Corps of Engineers, U. S. Army. 1 vol. 12mo,
cloth. $2.50.
"I have carefully examined Capt. J. C. Duane's 'Manual for Engineer Troops," 1 and do
not hesitate to pronounce it the very best work on the subject of which it treats.
"H. W. HALLECK, Major- General, U. S. A:" 1
Diifoiir's Principles of Strategy and Grand Tactics.
Translated from the French of General G. H. Dufour. By WILLIAM P.
CRAIGHILL, Capt. of Engineers, U. S. Army, and Assistant Professor of
Engineering, U. S. Military Academy, West Point. From the last
French Edition. Illustrated. In one volume 12mo. cloth. $3.00.
" In all military matters General Dufour is recognized as one of the first authorities fa
Europe, and consequently the translation of this very valuable work is a most acceptable
addition to our military libraries." London Naval and Military Gazette.
11
D. Van Nostrandl s Publications.
Iiitructions for Field Artillery. Prepared by a Board of
Artillery Officers. 1 voL 12mo, illustrated by 122 pages of Engravings.
Cloth. $3.00.
"WAR DEPARTMENT, WASHINGTON, March, 1, 1868.
"This system of Instruction for Field Artillery, prepared under direction of the War
Department, having been approved by the President, is adopted for the instruction of
troops when acting as field artillery.
" Accordingly, instruction in the same will be given after the method pointed out
therein ; and all additions to or departures from the exercise and manoeuvres laid dowu
in the system, are positively forbidden.
"EDWIN M. STANTON, Secretary of War."
Anderson's Evolutions of Field Batteries of Artil-
lery. Translated from the French, and arranged for the Army and
Militia of the United States. By Gen. ROBERT ANDERSON, U. S. A.
Published by order of the War Department. 1 vol., cloth, 32 plates. $1.
" WAR DEPARTMENT, Nov. 2d, 1859.
"The system of 'Evolutions of Field Batteries,' translated from the French, and ar-
ranged for the service of the United States, by Major Kobert Anderson, of the 1st Begi-
ment of Artillery, having been approved by the President, is published for the informa-
tion and government of the army.
"All Evolutions of Field Batteries not embraced in this system are prohibited, and
those herein prescribed will be strictly observed. J. B. FLOYD,
"Secretary of War."
Mendel 1's Treatise on Military Surveying. Theoretical
and Practical, including a Description of Surveying Instruments. By
G. H. MENDELL, Captain of Engineers. 1 vol. 8vo, with numerous illus-
trations, cloth. $2.50.
"The author is a Captain of Engineers, and has for his chief authorities Salneuve, Lalo-
bre, and Simms. He has presented the subject in a simple form, and has liberally illus-
trated it with diagrams, that it may be readily comprehended by every one who is liable
to be called upon to furnish a military sketch of a portion of country." N&io York
Evening Post.
Viele's Hand-book. Hand-Book for Active Service, containing
Practical Instructions in Campaign Duties. For the use of Volunteers.
By Brigadier-General Egbert L. Viele, U. S. A. 12mo, cloth. $1.
M It is a thorough treatise, copiously illustrated, and embraces a complete drill by com-
pany, regiment, &c. It also embraces instructions in regard to the camp, fortifications,
rations, and mode of cooking them, and has a manual for light and heavy artillery."
New Haven Palladium.
A Treatise on the Camp and March. "With which is
connected the Construction of Field- Works and Military Bridges ; with an
Appendix of Artillery Ranges, &c. For the use of Volunteers and Militia
in the United States. By Captain Henry D. Grafton, U. S. A. 1 voL
12mo. cloth. 75 cents.
12
D. Van Nostrand? s Publications.
It i
The Automaton Regiment; or, Infantry Soldier's
Practical Instructor. For all Regimental Movements in the
Field, By G-. Douglas Brewerton, U. S. Army. Neatly put up in boxes,
price $1 ; when sent by mail, $1.40.
The "Automaton Regiment" is a simple combination of blocks and counters, so
arranged and designated, by a carefully considered contrast of colors, that it supplies the
student with a perfect miniature regiment, in which the position in the battalion of each
company, and of every officer and man in each division, company, platoon, and section,
is clearly indicated. It supplies the studious soldier with the means whereby he can
consult his "tactics," and at the same time join practice to theory by manoeuvring a
mimic regiment.
I hereby certify that I have examined the " Automaton Regiment," invented by GL
Douglas Brewerton, late of the United States Regular Army, and now serving as a Vol-
unteer Aide upon my military staff, and believe that his invention will prove a useful
and valuable assistant to every student of military tactics. I take pleasure in recom-
mending it accordingly. B. SAXTON,
Brigadier- General Volunteers.
The Automaton Company; or, Infantry Soldier's
Practical Instructor. For all Company Movements in the Field.
By G-. Douglas Brewerton, U. S. A. Price in boxes, $1.25 ; when sent
by mail, $1.95.
The Automaton Battery; or, Artillerist's Practical
Instructor. For all Mounted Artillery Manoeuvres in the Field.
By G-. Douglas Brewerton, U. S. A. Price in boxes, $1 ; when sent by
mail, $1.40.
These productions are of a similar character, and cannot fail to be of great value to the
military student. They are object lessons, that will teach more in an hour than mere
rerbal instruction could in a month. They cannot be too highly commended to both
officers and men. Commercial Advertiser.
Monroe's Company and Skirmish Drill. The Company
Drill of the Infantry of the Line, together with the Skirmish Drill' of the
Company and Battalion, after the method of G-eneral Le Louterel. Bayonet
Fencing ; with a Supplement on the Handling and Service of Light In-
fantry. By J. Monroe, Colonel 22d Regiment, N. G-., N. Y. S. M., for-
merly Captain U. S. Infantry. 1 vol. 32mo, cloth. 75 cents.
This is a most valuable and timely little manial. It should be in the hands of every
new recruit. Chicago Tribune.
School of the Guides. Designed for the use of the Militia of the
United States. By Colonel Eugene Le Gal, 55th Regiment, N. Y. S.
M. cloth, 60 cents.
" This excellent compilation condenses into a compass of less than sixty pages all the
Instruction necessary for the guides, and the information being disconnected with other
matters, is more readily referred to and more easily acquired." Louisville Journal.
L- i?
D. Van Nostrarid? s Publications.
Craighill's Army Officer's Pocket Companion. Princi-
pally designed for Staff Officers in the Field. Partly translated from the
French of M. DE ROUVRE, Lieutenant- Colonel of the French Staff Corps,
with Additions from standard American, French, and English Authorities.
By T\ r M. P. CRAIGHILL, First Lieutenant U. S. Corps of Engineers, Assist.
Prof, of Engineering at the U. S. Military Academy, West Point. 1 vol.
18mo, full roan. $2.00.
" I have carefully examined Capt. Craighill's Pocket Companion. I find it one of the
very best works of the kind I have ever seen. Any Army or Volunteer officer who will
make himself acquainted with the contents of this little book, will seldom be ignorant
of his duties in camp or field. II. W. HALLECK, Major- General U. S. A."
Hunter's Manual for Quartermasters and Commis-
saries. Containing Instructions in the Preparation of Touchers, Ab-
stracts, Returns, etc., embracing all the recent changes in the Army
Eegulations, together with instructions respecting Taxation of Salaries,
etc. By Captain R. F. HUNTER, late of the U. S. Army. 12mo, cloth,
$1.25. Flexible morocco, $1.50.
"This is the only work of the kind extant. It is based on the latest regulations of the
War Department, and will be regarded as authority by those officers for whose use it is
designed." Saturday Evening Gazette.
Ordronaux's manual of Instructions for Military
Surgeons, in the Examination of Recruits and Discharge of Sol-
diers. With an Appendix, containing the Official Regulations of the
Provost-Marshal General's Bureau, and those for the formation of the In-
valid Corps, etc., etc. Prepared at the request of the United States
Sanitary Commission. By JOHN ORDRONAUX, M. D., Professor of Medical
Jurisprudence in Columbia College, New York. 12mo. Half morocco.
$1.50.
" In a condensed form, it is an admirable treatise on the important subjects of which it
treats. The author has aimed to be brief without being obscure, to omit nothing of real
importance, and to draw his materials from the best sources. He treats of the physical
disabilities which have relation to the military service, and of these alone. Medical Ex-
aminers are instructed in their duties, and the method of discovering feigned, artificially
produced, and concealed diseases is pointed out The book will prove valuable to all
who are concerned in the manipulation of recruits or conscripts. An Appendix contains
official regulations and instructions relative to the Provost-Marshal's office, the Invalid
j Corps, etc." Commercial Advertiser.
\ Ordronaux's Hints on the Preservation of Health in
Armies. For the use of Volunteer Officers and Soldiers. By JOHN
ORDRONAUX, M. D. New edition, 18mo, cloth. 75 cents.
14
D. Van No sir and? s Publications.
Thomas's Rifled Ordnance. A Practical Treatise on the Ap-
plication of the Principle of the Rifle to Guns and Mortars of every
Calibre. To which is added, a new theory of the initial action and force
of Fired Gunpowder. By LYNALL THOMAS, F. R. S. L. Fifth edition,
revised. One volume, octavo, illustrated, cloth- $2.00.
"At a time when the manufacture of guns engrosses the attention of thousands on
thousands, any practical treatise which may suggest desirable alterations or innovations
is of importance, and deserves that attention we doubt not will be extended to the pres-
ent volume." Boston Evening Gazette.
Wilcox's Rifles and Rifle Practice. An Elementary Trea-
tise on the Theory of Rifle Firing ; explaining the causes of Inaccuracy
of Fire and the manner of correcting it ; with descriptions of the Infan-
try Rifles of Europe and the United States, their Balls and Cartridges.
By Captain C. M. WILCOX, U. S. A. New edition, with engravings and
cuts. Green cloth. $2.00.
! " The book will be found intensely interesting to all who are watching the changes in
the art of war arising from the introduction of the new rifled arms. We recommend to
our readers to buy the book." Military Gazette.
Lcmly's Maxims and Instructions on the Art of War.
Maxims, Advice, and Instructions on the Art of War ; or, A Practical
Military Guide for the use of Soldiers of all Arms and of all Countries.
Translated from the French by Captain LENDY, Director of the Practical
Military College, late of the French Staff, etc., etc. 1 vol. 18mo, cloth.
75 cents.
"This book treats generally of the art of war and the conduct of campaigns, and with-
out going into all the details of a soldier's business, aims to explain the principles on
which an army may be well established in camp, or successfully led and mano3uvred on
the field." Providence Journal.
Andrews's Hints to Company Officers oil their Mili-
tary Duties. By Captain C. C. ANDREWS, Third Regiment Minne-
sota Volunteers. 1 vol. 18rno, cloth. 60 cents.
"This is a hand-book of good practical advice, which officers of all ranks may study
with advantage.'' Philadelphia Press.
Ileth's System of Target Practice. For the use of Troops
when armed with the Musket, Rifle-Musket, Rifle, or Carbine. Prepared
principally from the French, by Captain Henry Heth, 10th Infantry, TJ S.
A. 18mo, cloth. 75 cents.
15
D. Van No sir and} s Publications.
Miiiifie's Mechanical Drawing. A Text-Book of Geometrical
Drawing, for the Use of Mechanics and Schools, in which the Definitions
and Rules of Geometry are familiarly explained; the Practical Prob-
lems are arranged from the most simple to the more complex, and in their
description technicalities are avoided as much as possible. With Illus-
trations for Drawing Plans, Sections, and Elevations of Buildings and
Machinery; an introduction to Isometrical Drawing, and an Essay on
Linear Perspective and Shadows. Illustrated with over 200 Diagrams
engraved on Steel. By WILLIAM MINIFIE, Architect. Seventh edition.
With an Appendix on the Theory and Application of Colors. 1 vol. 8vo,
cloth. $4.00.
" It is the best work on Drawing that we have ever seen, and is especially a text-book
of Geometrical Drawing for the use of Mechanics and Schools. No young Mechanic, such
as a Machinist, Engineer, Cabinet-Maker, Millwright, or Carpenter, should be without it. 1 '
Scientific American.
"One of the most comprehensive works of the kind ever published, and cannot but
possess great value to builders. The style is at once elegant and substantial." Penn-
sylvania Inquirer.
"We think this the best work on this subject, which is saying very much ; as much
attention has been given to the science of Drawing. There is nothing in the range of
drawing that cannot be found in this book, and which is not well explained." Ohio
Teacfter.
u Whatever is said is rendered perfectly intelligible by remarkably well executed dia-
grams on steel, leaving nothing for mere vague supposition ; and the addition of an
introduction to isometrical drawing, linear perspective, and the projection of shadows,
winding up with a useful index to technical terms." Glasgow Mechanic's Journal.
Minified Geometrical Drawing. Abridged from the Octavo
edition, for the use of Schools. Illustrated with 48 Steel Plates. Fifth
edition. 1 vol. 12mo, half roan. $1.50.
Peirce' System of Analytic Mechanics. Physical and Ce-
lesrial Mechanics, by BENJAMIN PEIRCE, Perkins Professor of Astronomy
and Mathematics in Harvard University, and Consulting Astronomer of
the American Ephemeris and Nautical Almanac. Developed in four sys-
tems of Analytic Mechanics, Celestial Mechanics, Potential Physics, and
Analytic Morphology. 1 vol 4to ( cloth. $10.00.
Dictionary of Weights and Measures. Universal Dictionary
of Weights and Measures, Ancient and Modern, reduced to tie standards
of the United States of America. By J. H. ALEXANDER. New edition,
enlarged. 1 vol. 8vo, cloth. $2 .50
16
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