.r f *j **■— MB;»M6— awMrmpcr^ojtti i i 1 i i a 1 1 ' 1 1 ; 1 1 ) ! ' 5 ' 1 » 1 ■ 1 1 1 'L j ^r^ii ■ CORRECTIONS TO H. 0. PUBLICATION NO. ^-THE AMERICAN PRACTICAL NAVIGATOR, 1914 EDITION. Page 108. In figure No. 37, on right-hand side: For M read M'. Page 171. (a) In the example (fine print), line 4: For 50° 50' read 50° 58'. (6) Line 5: For "Northward" read "Southward." Page 292. San Salvador (Cat Island) Lighthouse, longitude column: For 75.°^ 26' W. read 74° 26' W. CORRECTIONS TO THE ABOVE-NAMED BOOK AND TO THE USEFUL TABLES (BOOK NO. 9, PART II). Page 819. Log. Hav. of Oh. 28m. 10s.: For "7.75650" read "7.57650". Log. Hav. of Oh. 26m. 44s.: For "7.35119" read "7.53119". Page 831. Nat. Hav. of 26° 10' 30": Omit characteristic 1. Page 865. Log. Hav. 4h. 32m. 3s.: For ".49226" read ".49526." Page 866. Log. Hav. 4h. 37m. 54s.: For ".31147" read ".51147". Page 832, Nat. Hav. of 27° 06' 45", for .05994 read .06494. Page 896, Nat. Hav. of 107° 14' 15", for .46817 read .64817. Page 909, Log. Hav. of 8h. 29m. 40s., for .990515 read 9.90615. Page 910, Nat. Hav. of 128° 02', for 0.90806 read 0.80806. Page 915, Nat. Hav. of 149° 01', for .92666 read .92866. Page 917, Nat. Hav. of 156° 24', for .85818 read .95818. liJUlS WEULE CO. Chfnnofnetefsand Hautlcal liistrnnents BCX)KS ON NAVIGATION, MX:. AOSMCT roa U.S. GO^^NMCNT CHAHTS *n0 •U8L«C*T"^NS 9t,.iCllU»IIUSTMSilRFIIIilUtt4.UL No. 9 American Practical Navigator An Epitome of Navigation and Nautical Astronomy ORIGINALLY BY NATHANIEL BOWDITCH, LL. D. RE-EDITED AND PUBUSHED IN THE UNITED STATES HYDROGRAPHIC OFFICE BY DIRECTION OF THE SECRETARY OF THE NAVY. IN ACCORDANCE WITH THE ACTS OF CONGRESS WASHINGTON GOVERNMENT PRINTING OFTICE 1914 STATUTES OF AUTHORIZATION. There shall be a Hydrographic Office attached to the Bureau of Navigation in the Navy Department, for the improvement of the means for navigating safely the vessels of the Navy and of the mercantile marine, by providing, under the authority of the Secretary of the Navy, accurate and cheap nautical charts, sailing directions, navigators, and manuals of instructions for the use of aU vessels of the United States, and for the benefit and use of navigators generally. (R. S. 431.) The Secretary of the Navy is authorized to cause to be prepared, at the Hydro- graphic Office attached to the Bureau of Navigation in the Navy Department, maps, charts, and nautical books relating to and required in navigation, and to publish and furnish them to navigators at the cost of printing and paper, and to purchase the plates and copyrights of such existing maps, charts, navigators, sail- ing directions, and instructions, as he may consider necessary, and when he may deem it expedient to do so, and under such regulations and instructions as he may prescribe. (R. S. 432.) 37 I>A.RT I. TEXT AND APPENDICES. ZSIOHZ Digitized by the Internet Archive in 2008 with funding from Microsoft Corporation http://www.archive.org/details/epitomenavigatOObowdrich CONTENTS OF P^RT I. Page. Abbreviations 7 Chapter I. Definitions relating to Navigation 9 II. Instruments and Accessories in Navigation 11 III. The Compass Error 36 IV. Piloting 56 V. The Sailings 72 VI. Dead Reckoning 84 VII. Definitions relating to Nautical Astronomy 87 VIII. Instruments employed in Nautical Astronomy 91 IX. Time and the Nautical Almanac 102 X. Correction of Observed Altitudes 115 XI. The Chronometer Error 121 XII. Latitude 126 XIII. Longitude 140 XIV. Azimuth '. 144 XV. The Sumner Line 150 XVI. The Practice of Navigation at Sea 169 XVII. Marine Surveying 189 XVIII. Winds 206 XIX. Cyclonic Storms 212 XX. Tides 225 XXI. Ocean Currents 232 XXII. Ice and its Movements in the North Atlantic Ocean 238 Appendix I. Extracts from the American Ephemeris and Nautical Almanac for the year 1915 which have reference to examples for that year given in this work 248 II. A collection of Forms for working Dead Reckoning and various Astronomical Sights, with notes explaining their application under all circumstances 254 III. Explanation of certain Rules and Principles of Mathematics of use in the Solution of Problems in Navigation 266 IV. Maritime Positions and Tidal Data 278 Index 358 5 ABBREVIATIONS USED IN THIS WORK. Alt. (or ft) Altitude. a. m Ante meridian. Amp Amplitude. App Apparent. App. t Apparent time. Art Astronomical. Art. t Astronomical time. Aug Augmentation. Az. (orZ) Azimuth. C Coiu*se. 0. C Chronometer correction. 0— W Chronometer minus watch. Chro. t Chronometer time. Co. L Co. latitude. Col Column. Corr Correction. Cos Cosine. Cosec Cosecant. Cot Cotangent. d (or Dec.) Declination. D (or D.Lo) Difference longitude. Dep Departure. Dev Deviation. Diff Difference. Dirt Distance. DL Difference latitude. D. R Dead reckoning. E., Ely East, easterly. Elap. t Elapsed time. Eq. t Equation of time. F Longitude factor. / Latitude factor. G. (or Gr.) Greenwich. G. A. T Greenwich apparent time. G. M. T Greenwich mean time. G. S. T Greenwich sidereal time. h Altitude. H Meridian altitude. H. A. (or t) Hour angle. Hav Ilaversine. H. D Hourly difference. H. P. (or Hor. par.). .Horizontal parallax. Hr-s Hour-s. H. W High water. 1. C Index correction. L. (or Lat.) Latitude. L. A. T Local apparent time. L. M. T Local mean time. L. S. T Local sidereal time. Lo. (or Long.) Longitude. Log Logarithm. Lun. Int Lunitidal interval. L. W Low water. X Longitude. m Meridional difference. Merid Meridian or noon. Mag Magnetic . M. D Minute's difference. Mid Middle. Mid. L Middle latitude. M. T Mean time. nat Natural. N., Nly North, northerly. N. A. (orNaut. Aim.) Nautical Almanac. •Np Neap. Obs Observation. p (or P. D.) Polar distance. p. c Per compass. jP. D. (or p) Polar distance. P. L. (or Prop. Log.). Proportional logarithm, p. m Post meridian. p. & T Parallax and refraction. Par Parallax. R. A Right ascension. R. A. M. S Right ascension mean sun. Red Reduction. Ref Refraction. S., Sly South, southerly. S. D Semidiameter. Sec Secant. Sid Sidereal. Sin Sine. Spg Spring. t Hour angle. T Time. Tab Table. Tan Tangent. Tr. (or Trans.) Transit. Var Variation. Vert Vertex or vertical. W., Wly West, werterly. W. T Watch time. z Zenith distance. Z Azimuth. 6 Auxiliary angle. X Difference longitude in tima. SYMBOLS. O The Sun. • (C The Moon. * A Star or Planet. T3 C Alt. upper limb, d ^ Alt. lower limb, (t) ^ Azimuthal angle. A a ..Alpha. B ^ ..Beta. r Y .. Gamma. J d ..Delta. E e .. EpsUon. Z C ..Zeta. H 7) ..Eta. e 6 . .Theta. / e .. Iota. K K .. Kappa. A X ..Lambda. M it.MvL. GREEK LETTEBS. Degrees. Minutes of Arc. Seconds of Arc. Hours. Minutes of Time. Seconds of Time. N V Nu. S ^ Xi. o Omicron. niz PL P p Rho. 1 a (C).-. Sigma. T X Tau. Y a Upsilon. Phi. Xr Chi. 7^ Psi. Q u) Omega. CHAPTER I. DEFINITIONS EELATING TO NAVIGATION. 1. That science, generally termed Navigation, which affords the knowledge necessary to conduct a ship from point to point upon the earth, enabling the mariner to determine, with a sufficient degree of accuracy;, the position of his vessel at any time, is properly divided into two branches: Navigation and Nautical Astronomy. 2. Navigation, in its limited sense, is that branch which treats of the determina- tion of the position of the ship by reference to the earth, or to objects thereon. It comprises (a) Piloting, in which the position is ascertained from visible objects upon the earth, or from soundings of the depth of the sea, and (6) Dead Reckoning, in which the position at any moment is deduced from the direction and amount of a vessel's progress from a known point of departure. 3. Nautical Astronomy is that branch of the science which treats of the deter- mination of the vessel's place by the aid of celestial objects — the sun, moon, planets, or stars. 4. Navigation and Nautical Astronomy have been respectively termed Geo- Navigation and Celo- Navigation, to indicate the processes upon which they depend. 5. As the method of piloting can not be employed excepting near land or in moderate depths of water, the navigator at sea must fix his position either ly dead reckoning or by observation of celestial objects; the latter method is more exact, but as it is not always available, the former must often be depended upon. 6. The Earth. — The Eartn is an oblate spheroid, being a nearly spherical body slightly flattened at the poles; its longer or equatorial axis measures about 7,927 statute miles, and its El 1 h— I frrr— iw shorter axis, around which it rotates, about 7,900 statute miles. The Earth (assumed for purposes of illustra- tion to be a sphere) is represented in figure 1. The Axis of Rotation, usually spoken of simply as the Axis, is rP'. The Poles are the points, P and P', in which P' the axis intersects the surface, and are designated, fio. i. respectively, as the North Pole and the South Pole. The Equator is the great circle EQMW, formed by the intersection with the earth's surface of a plane perpendicular to the axis; the equator is equidistant from the poles, every point upon it boin^90° from each pole. Meridians are the great circles JPQP', PMP', PM'P', formed by the intersection with the earth's surface of planes secondary to the equator (that is, passing through its poles and therefore perpendicular to its plane). Parallels of Latitude are small circles NTn, N'n'T', formed by the intersection with the earth's surface of planes passed parallel to the equator. The Latitude of a place on the surface of the earth is the arc of the meridian intercepted between the equator and that place. Latitude is reckoned North and South, from the equator as an origin, through 90° to the poles; thus, the latitude of the pomt T is MT, north, and of the pomt T', MT', north. The Difference of Latitude between any two places is the arc of a meridian intercepted between their parallels of latitude, and is called North or South, according to direction; thus, the difference of latitude between T and T' is Tn' or T'n, north from T or south from T'. The Longitude of a place on the surface of the earth is the arc of the equator inter- cepted between its meridian and that of some place from which the longitude is p lr\ \ "l Ql JM M' 10 DEFISriTION RELATING TO NAVIGATION. reckoned. Longitude is measured East or West through 180° from the meridian of a designated place, such meridian being termed the Prime Meridian; the prime meridian used by most nations, including the United States, is that of Greenwich, England. If, in the figure, the prime meridian be PGQP', then the longitude of the point T is QM, east, and of T', QM', east. The Difference of Longitude oetween any two places is the arc of the equator intercepted between their meridians, and is called East or West, according to direction ; thus, the difference of longitude between T and T' is MM', east from M or west from M'. The Departure is the linear distance, measured on a parallel of latitude, between two meridians; unlike the various quanti- ties previously defined, departure is reckoned in miles; the departure between two meridians varies with the parallel of latitude upon which it is measured; thus, the departure between the meridians of T and T' is the number of mUes corresponding to the distance Tn in the latitude of T, or to ti'T' in the latitude of T'. The curved line which joins any two places on the earth's surface, cutting all the meridians at the same angle, is called the Rhumb Line, Loxodromic Curve, or Equiaiv- gular Spiral. In the figure this line is represented by TrT'. The constant angle which tnis line makes with the meridians is called the Course; and the length of tne line between any two places is called the Distance between those places. The unit of linear measure employed by navigators is the Nautical or Sea Mile, or Knot. This unit is defined in the United States of America as being 6,080.27 feet in length and equal to one-sixtieth part of a degree of a great circle of a sphere whose surface is equal in area to the area of the surface of the earth. The nautical mUe is not exactly the same in all countries, but, from the navi- gator's standpoint, the various lengths adopted do not differ materially. Since, upon the ocean, latitude has been capable of easier and more accurate determination than longitude, it might naturally be expected that there exists an intimate fixed relation between the nautical mile and the minute of latitude (or the length of that portion of a meridian which subtends at the earth's center the angular measure of one minute); but on account of the fact that the earth is not a perfect sphere, a fixed relation does not exist, and the arc of a meridian that subtends an angle of 1' at the center of the earth varies slightly in length from the Equator to the poles, being 6,045.95 feet at the Equator and 6,107.85 feet at the poles. Its average length is 1,852.201 meters, or 6,076.82 feet. Accordingly in France, Germany, and Austria the nautical mile is 1,852 meters, 2,025.41 yards, or 6,076.23 feet. For purposes of navigation the nautical mUe is assumed to be equal to a minute of latitude in all parts of the world; and, hence, when a vessel changes her position to the north or south by 1 nautical mile, it may always be considered that the latitude has changed 1'. Owing to the fact that the meridians converge toward the poles, the difference of longitude produced by a change of position of 1 mile to the east or west wUl vary with the latitude ; thus, a departure of 1 mile will equal a difference of longitude of 1' at the Eguator, but of more than 1' at any higher latitude, being in fact equal to I'.l of longitude in latitude 30° and to 2' of longitude in latitude 60°. In England the nautical mile, corresponding to the Admiralty Jcnot, is regarded as having a length of 6,080 feet. The statute mile of 5,280 feet, which is employed in land measurements, is commonly used in navigating river and lake vessels. This is notably the case on the Great Lakes of America, but with the recognition of the advantages to be gained by the practice of nautical astronomy in the navigation of these vessels, the use of the nautical mile is extending. The Great Circle Track or Course between any two places is the route between those places along the circumference of the great circle which joins them. In the figure this line is represented by Tj/T'. From the properties of a great circle (which is a circle upon the earth's surface formed by the intersection of a plane passed through its center) the distance between two points measured on a great circle track is shorter than the distance upon any other line which joins them. Except when the two points are on the same meridian or when both he upon the equator, the great circle track will always differ from the rhumb line, and the great circle track wUl intersect each intervening meridian at a different angle. CHAPTER II. INSTRUMENTS AND AOOESSOEIES IN NAYIGATION. DIVIDEBS OB COMPASSES. 7. This instrument consists of two legs movable about a loint, so that the points at the extremities of the legs may be set at any required distance from each other. It is used to take and transfer distances ana to describe arcs and circles. When used for the former purpose it is termed dividers, and the extremities of both legs are metal points; when used for describing arcs or circles, it is called a compass, and one of the metal points is replaced by a pencil or pen. PABALLEIi BULEBS. 8. Parallel rulers are used for drawing lines parallel to each other in any direc- tion, and are particularly useful in transferring the rhumb-Une on the chart to the nearest compass-rose to ascertain the course, or to lay oflF bearings and courses. PBOTBACTOB. 9. This is an instrument used for the measurement of angles upon paper; there is a wide variation in the material, size, and shape in which it may be made. (For a description of the Three Armed Protractor, see art. 428, Chap. XVII.) THE CHIP liOO. 10. This instrument, for measuring the rate of sailing, consists of three parts; viz, the log-chip, the log-line, and the log-glass. A light substance thrown from the ship ceases to partake of the motion oi the vessel as soon as it strikes the water, and wUl be left behind on the surface; after a certain interval, if the distance of the ship from this stationary object be measured, the approximate rate of sailing will be given. The log-chip is the float, the log-line is the measure of the distance, and the log-glass defines the interval of time. The log-chip is a thin wooden quadrant of about 5 inches radius, loaded with lead on the circular edge sufficiently to make it float upright in the water. There is a hole in each corner of the log-chip, and the lo^-line is knotted in the one at the apex; at about 8 inches from the end there is seized a wooden socket; a piece of line of proper length, being knotted in the other holes, has seized into its bight a wooden peg to fit snugly into the socket before the log-chip is thrown; as soon as the line is checked this peg pulls out, thus allowing the log-chip to be hauled in with the least resistance. The log-line is about 150 fathoms in length, one end made fast to the log-chip, the other to a reel upon which it is wound. At a distance of from 15 to 20 fathoms from the log-chip a permanent mark of red bunting about 6 inches long is placed to allow sufficient stray line for the log-chip to clear the vessel's eddy or wake. The rest of the fine is divided into lengths of 47 feet 3 inches called Jcnots, by pieces of fish-line thrust through the strands, with one, two, three, etc., knots, according to the number from stray-line mark; each knot is further subdivided into five equal lengths of two-tenths of a knot each, marked by pieces of white rag. The length of a knot depends upon the number of seconds which the log-glass measures; the length of each knot must bear the same ratio to the nautical mile (^ of a degree of a great circle of the earth, or 6,080 feet) that the time of the glass does to an hour. U 12 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. In the United States Navy all log-lines are marked for log-glasses of 28 seconds, for which the proportion is : 3600 : 6080 = 28" : x, X being the length of the knot. Hence, a; = 47".29, or 47" 3'«. The speed of the ship is estimated in knots and tenths of a knot. The log-glass is a sand glass of the same shape and construction as the old hour- glass. Two glasses are used, one of 28 seconds and one of 14 seconds; the latter is employed when the ship is going at a high rate of speed, the number of knots indi- cated on a Hne markea for a 28-second glass being doubled to obtain the true rate of speed. 11. The log in all its parts should be frequently examined and adjusted; the })eg must be found to fit sufficiently tight to keep the log-chip upright; the log- ine shrinks and stretches and should often be verified; the log-glass should be compared with a watch. One end of the glass is stopped with a cork, by removing which the sand may be dried or its quantity corrected. 12. A ground log consists of an ordinary log-hne, with a lead attached instead of a chip; in shoal water, where there are no well-defined objects available for fixing the position of the vessel and the course and speed are influenced by a tidal or other current, this log is sometimes used, its advantage being that the lead marks a sta- tionary point to which motion may be referred, whereas the chip would drift with the stream. The speed, which is marked in the usual manner, is the speed over the ground, and the trend of the fine gives the course actually made good by the vessel. THE PATENT LOG. 13. This is a mechanical contrivance for registering the distance actually run by a vessel through the water. There are various types of patent logs, but for the most part they act upon the same principle, consisting of a registering device, a fly or rotator, and a lo^ or towline; the rotator is a small spincue with a number of blades extending radially in such manner as to form a spiral, and, when drawn through the water in the direction of its axis, rotates about that axis after the manner of a screw propeller; the rotator is towed from the vessel by means of a log or towline from 30 to 100 fathoms in length, made fast at its apex, the line being of special make, so that the turns of the rotator are transmitted through it to the worm shaft of the register, to which the inboard end of the line is attached; the registering device is so constructed as to show upon a dial face the distance run, according to the number of turns of its worm shaft due to the motion of the rotator; the register is carried at some convenient point on the vessel's quarter; it is frequently found expedient to rig it out upon a small boom, so that the rotator will be towed clear of the wake. 14. Though not a perfect instrument, the patent log affords a means of deter- mining the vessel's speed through the water. It will usually be found that the indications of the log are in error by a constant percentage, and the amount of this error should be determined by careful experiment and applied to all readings. Various causes may operate to produce inaccuracy of working in the patent log, such as the bending of the blades of the rotator by accidental blows, fouling of the rotator by seaweed or refuse from the ship, or mechanical wear of parts of the register. The length of the towUne has much to do with the working of the log, and by varying the length the indications of the instrument may sometimes be adjusted when the percentage of error is small; it is particularly important that the line shall not be too short. The readings of the patent log can not be depended upon for accuracy at low speeds, when the rotator does not tow horizontally, nor in a head or a foUowing sea, when the effect depends upon the wave motion as well as upon the speed of the vessel. 15. Electrical registers for patent logs are in use, the distance recorded by the mechanical register being communicatea electrically to some point of the vessel which is most convenient for the purposes of those charged with the navigation. 17 fathoms from the lead, same as at 7 fathoms. 20 fathoms from the lead, with 2 knots. 25 fathoms from the lead, with 1 knot. 30 fathoms from the lead, with 3 knots. 35 fathoms from the lead, with 1 knot. 40 fathoms from the lead, with 4 knots. And so on. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 18 16. A number of instruments based upon different physical principles have been devised for recording the speed of a vessel through the water and have been used with varying degrees of success. Of these the hydrauUc speed indicator, known as the Nicholson Ship Log, affords an instance. 17. The revolutions of the screw propeller afford in a steamer the most valuable means of detennining a vessel's speed through the water. The number of revolu- tions per knot must be carefully determined for the vessel by experiment under varying conditions of speed, draft, and foulness of bottom. THE LEAD. 18. This device, for ascertaining the depth of water, consists essentially of a suitably marked line, having a lead attached to one of its ends. It is an invaluable aid to the navigator in shallow water, particularly in thick or foggy weather, and is often of service when the vessel is out of sight of land. Two leads are used for soundings — the hand-lead, weighing from 7 to 14 pounds, with a Une marked to about 25 fathoms, and the deep-sea lead, weighing from 30 to 100 pounds, the hne being 100 fathoms or upward in length. Lines are generally marked as follows : 2 fathoms from the lead, with 2 strips of leather. 3 fathoms from the lead, with 3 strips of leather. 5 fathoms from the lead, with a white rag. 7 fathoms from the lead, with a red rag. 10 fathoms from the lead, with leather having a hole in it. 13 fathoms from the lead, same aa at 3 fathoms. 15 fathoms from the lead, same as at 5 fathoms. Fathoms which correspond with the depths marked are called marks; the inter- mediate fathoms are called deeps; the only fractions of a fathom used are a half and a quarter. A practice sometimes followed is to mark the hand-lead line in feet around the critical depths of the vessel by which it is to be used. Lead lines should be measured frequently while wet and the correctness of the marking verified. The distance from the leadsman's hand to the water's edge should be ascertained in order that proper allowance may be made therefor in taking soundings at night. 19. The deep-sea lead may be armed by filling with tallow a hole hollowed out in its lower end, by which means a sample of the bottom is brought up. THE SOUNDING MACHINE. 20. This machine possesses advantages over the deep-sea lead, for which it is a substitute, in that soundings may be obtained at great depths and with rapidity and accuracy without stopping the ship. It consists essentially of a stand holding a reel upon which is wound the sounding wire, and which is controlled by a suitable brake. Crank handles are provided for reeling in the wire after the sounding has been taken. Attached to the outer end of the wire is the lead, which has a cavity at its lower end for the reception of the tallow for arming. Above the lead is a cylindrical case containing the depth-registering mechanism; various devices are in use for this purpose, aU depending, however, upon the increasing pressure of the water with increasing depths. 21. In the Lord Kelvin macMne a slender glass tube is used, sealed at one end and open at the other, and coated inside with a chemical substance which changes color upon contact with sea water; this tube is placed, closed end up, in the metal cylinder; as it sinks the water rises in the tube, the contained air being compressed with a force dependent upon the depth. The limit of discoloration is marked by a clearly defined line, and the depth oi the sounding corresponding to this Une is read off from a scale. Tubes that have been used in comparatively shallow water may be used again where the water is known to be deeper. 22. A tube whose inner surface is ground has been substituted for the chemical- coated tube, ground glass, when wet, showing clear. The advantage of these tubes 14 INSTEUMENTS AND ACCESSORIES IN NAVIGATION. is that they may be used an indefinite number of times if thoroughly dried. To facilitate drying, a rubber cap is fitted to the upper end, which, when removed, admits of a circulation of the air through the tube. 23. As a substitute for the glass tubes a mechanical depth recorder contained in a suitable case has been used. In this device the pressure of the water acts upon a piston against the tension of a spring. A scale with an index pointer records the depth reached. The index pointer must be set at zero before each soimding. 24. Since the action of the sounding machine, when glass tubes are used, depends upon the compression of the air, the barometric pressure of the atmosphere must be taken into account when accurate results are required. The correction consists in incredsing the indicated depth by a fractional amount according to the following table: Bar. reading. Increase. 1 // 29.75 30.00 30.50 30.75 One-fortieth. One- thirtieth. One-twentieth. One-fifteenth. THE MARINER'S COMPASS. 25. The Mariner's Compass is an instrument consisting either of a single magnet, or, more usually, of a group of magnets, which, being attached to a graduated circle pivoted at the center and allowed to swing freely in a horizontal plane, has a tendency, when not affected by disturbing magnetic features within the ship, to lie with its magnetic axis in the plane of the earth's magnetic meridian, thus affording a means of determiniag the azimuth, or horizontal angular distance from that meridian, of the ship's course and of all visible objects, terrestrial or celestial. 26. The circular card of the compass is divided on its periphery into 360°, frequently numbered from 0° at North and South to 90° at East and West; also into thirty-two divisions of 11 1° each, called points, the latter being further divided into half-points and quarter-points; still finer subdivisions, eighth-points, are some- times used, though not indicated on the card, A system of numbering the degrees from 0° to 360°, always increasing toward the right, is shown in figure 2. This system is in use in the United States Navy and by the mariners of some foreign nations, and its general adoption would carry with it certain undoubted advantages. 27. Boxing the Compass is the process of naming the points in their order, and is one of the first things to oe learned oy the young mariner. The four principal points are called cardinal points and are named North, South, East, and West; each differs in direction from the adjacent one by 90°, or 8 points. Midway between the cardinal points, at an angular distance of 45°, or 4 points, are the inter-cardinal pomts, named according to their position Northeast, Southeast, etc. Midway between each cardinal and inter-cardinal point, at an angular distance of 22^°, or 2 points, is a point whose name is made up of a combination of that of the cardinal with that of the inter-cardinal point: North-Northeast, East-Northeast, East-Southeast, etc. At an angular distance of 1 point, or 11 i°, from each cardinal and inter-cardinal point (and therefore midway between it and the 22i°-division last described), is a point which bears the name of that cardinal or inter-cardinal point joined by the word by to that of the cardinal point in the direction of which it lies: North by East, Northeast by North, Northeast by East, etc. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 15 In boxing by fractional points, it is evident that each division may be referred to either of the whole points to which it is adjacent; for instance, NE. by N. i N. and NNE. i E. would describe the same division. It is the custom in the United States Navy to box from North and South toward East and West, excepting that divisions adjacent to a cardinal or inter-cardinal point are always referred to that point; as Fig. 2. N. i E., N. by E. i E., NNE. ^ E., NE. ^ N., etc. Some mariners, however, make it a practice to box from each cardinal and inter-cardinal point toward a 22i°-point (NNE., ENE., etc.); as N. ^ E., N. by E. i E., NE. by N. ^ N., NE. ^ N., etc. The names of the whole points, together with fractional points (according to the nomenclature of the United States Navy), are given in the following table, which 16 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. shows also the degrees, minutes, and seconds from North or South to which each division corresponds: NORTH TO EAST. North: N.iE N.iE N.f E N.by E N.byE. iE N.byE. ^E N.byE.fE NNE NNE. iE NNE.^E NNE. JE NE. byN NE.f N NE. *N NE.IN NE NE.iE NE.iE NE.f E NE.byE NE. byE.iE.... NE. byE. iE.... NE. byE. |E.... ENE ENE. iE ENE. iE ENE. JE E.byN E.fN E.^N E-iN SOUTH TO WEST South S.iW S.iW S.f W S. byW S.byW.iW S. byW. iW S.byW.iW SSW SSW. iW SSW. iW SSW. fW SW. byS SW. JS SW. iS SW. iS SW SW.iW SW.^W SW.fW SW. by W SW. by W. iW... SW. by W. iW... SW.byW. fW... WSW WSW. iW WSW. iW WSW. JW W.byS W.|S W.iS W.iS Points. i i i I ^ 2 2i ^ 2f 3 3i 3i 3i 4 ^ 4i 4i 5 5i H 5| 6 6i 6i H 7 n 7i 16 16i 16i 16i 17 17i 17i 17i 18 18i 18^ 18J 19 19i 19i 19J 20 20i 20i 20i 21 21i 21i 21} 22 22i 22i 22} 23 23i 23i 23} Angular measure. 2 48 45 5 37 30 8 26 15 11 15 GO 14 03 45 16 52 30 19 41 15 22 30 00 25 18 45 28 07 30 30 56 15 33 45 00 36 33 45 39 22 30 42 11 15 45 00 00 47 48 45 50 37 30 53 26 15 56 15 00 59 03 45 61 52 30 64 41 15 67 30 00 70 18 45 73 07 30 75 56 15 78 45 00 81 33 45 84 22 30 87 11 15 180 00 00 182 48 45 185 37 30 188 26 15 191 15 00 194 03 45 196 52 30 199 41 15 202 30 00 205 18 45 208 07 30 210 56 15 213 45 00 216 33 45 219 22 30 222 11 15 225 00 00 227 48 45 230 37 30 233 26 15 236 15 00 239 03 45 241 52 30 244 41 15 247 30 00 250 18 45 253 07 30 255 66 15 258 45 00 261 33 45 264 22 30 267 11 15 EAST TO SOUTH. East..... E.iS E.iS E.f S E.by S ESE. }E ESE. iE ESE. iE ESE SE. byE. }E. SE. byE. iE. SE. byE. iE. SE.byE SE.}E SE.iE SE.iE Points. SE.. SE.iS SE.iS SE.}S SE.byS SSE. }E SSE.iE SSE. iE SSE S.byE.fE S.byE.iE S.byE.iE S.byE S.}E S.iE S.iE WEST TO NORTH. West W\iN W.iN W.}N W.byN WNW. } W WNW. iW^ , WNW. iW WNW NW. by W. } W. . NW. by W. i W. . NW. by W. iW.. NW.bvW NW. } W NW. iW NW. iW NW NW. iN NW. iN NW. f N NW.byN NNW. f W NNW. iW NNW. iW NNW N.by W. } W N. by W. iW N.by W. iW.... N.by W N.} W N. iW N.iW North 8 8i 8i 8} 9 9i 9} 10 lOi lOi 10} 11 ni Hi 11} 12 m 12i 12} 13 13i 13i 13} 14 14i Hi 14} 15 15i 15i 15} 21 2-li 24i 24} 25 25i 25i 25} 26 26i 26i 26} 27 27i 27i 27} 28 28i 23* 28} 29 29i 29i 29} 30 30i 30i 30} 31 31i 31i 31} 32 Angular measure. 90 00 00 92 48 45 95 57 30 98 26 15 101 15 GO 104 03 45 106 52 30 109 41 15 112 30 00 115 18 45 118 07 30 120 56 15 123 45 GO 126 33 45 129 22 30 132 11 15 135 00 GO 137 48 45 140 37 30 143 26 15 146 16 GO 149 03 45 151 52 30 154 41 15 157 30 GO 160 18 45 163 07 30 165 66 15 168 45 GO 171 33 45 174 22 30 177 11 15 270 00 00 272 48 45 275 37 30 278 26 15 281 15 GO 284 03 45 286 52 30 289 41 15 292 30 00 295 18 45 298 07 30 300 56 15 303 45 00 306 33 45 309 22 30 311 11 15 315 00 GO 317 48 45 320 37 30 323 26 15 326 15 00 329 03 45 331 52 30 334 41 15 337 30 GO 340 18 45 343 07 30 345 56 15 348 45 GO 351 33 45 354 22 30 357 11 15 360 00 00 INSTRUMENTS AND ACCESSORIES IN NAVIGATION, 17 28. The compass card is mounted in a bowl which is carried in gimhals, thus enabhng the card to retain a horizontal position while the ship is pitching and rolling. A vertical black line called the lubber's line is marked on the inner surface of the bowl, and the compass is so mounted that a line joining its pivot with the lubber's line is parallel to the keel line of the vessel; thus the lubber's line always indicates the com- pass direction of the ship's head. 29. According to the purpose which it is designed to fulfill, a compass is desig- nated as a Standard, Steering, Check, or Boat Compass. On United States naval ves- sels additional compasses are designated as follows : Maneuvering, battle, auxiliary battle, top, and conning-tower compasses. 30. There are two types of magnetic compass in use, the liquid or wet and the dry; in the former the bowl is filled with liquid, the card being thus partially buoyed with consequent increased ease of working on the pivot, and the liquid further serving to decrease the vibrations of the card when deflected by reason oi the motion of the vessel or other cause. On account of its advantages the liquid compass is used in the United States Navy. 31. The Navy Service 7^-inch Liquid Compass. — ^This consists of a skeleton card 7i inches in diameter, made of tinned brass, resting on a pivot in liquid, with provisions for two pairs of magnets syrnmetrically placed. The magnet system of the card consists of four cyHndrical bundles of steel wires; these wires are laid side by side and magnetized as a bundle between the poles of a powerful electro-magnet. They are afterwards placed in a cylindrical case, sealed, and secured to the card. Steel wires made up into a bundle were adopted because they are more homogeneous, can be more perfectly tempered, and for the same weight give greater magnetic power than a sohd steel bar. Two of the magnets are placed parallel to the north and south diameter of the card, and on the chords of 15 (nearly) of a circle passing through their extremities. These magnets penetrate the air vessel, to which tney are soldered, and are further secured to the bottom of the ring of the card. The other two magnets of the system are placed parallel to the longer magnets on the chords of 45° (nearly) of a circle passing through their extremities and are secured to the bottom of the ring of the card. The card is of a curved annular type, the outer ring being convex on the upper and inner side, and is graduated to read to one-quarter point, a card circle being adjusted to its outer edge and divided to half degrees, with legible figures at each 3°, for use in reading bearings by an azimuth circle or in laying the course to degrees. The card is provided with a concentric spheroidal air vessel, to buoy its own weight and that of the magnets, allowing a pressure of between 60 and 90 grains on the pivot at 60° F.; the weight of the card in air is 3,060 grains. The air vessel has within it a hollow cone, open at its lower end, and provided with the pivot bearing or cap, containing a sapphire, which rests upon the pivot and thus supports the card; the cap is provided with adjusting screws for accurately centering the card. The pivot is fastened to the center of the bottom of the bowl by a flanged plate and screws. Through this plate and the bottom of the bowl are two smafl holes which communicate with the expansion chamber and admit of a circulation of the liquid between it and the bowl. The pivot is of gun metal with an iridium cap. The card is mounted in a bowl of cast bronze, the glass cover of which is closely packed with rubber, preventing the evaporation or leakage of the liquid, which entirely fills the bowl. This liquid is composed of 45 per cent pure alcohol and 55 per cent distilled water, and remains liquid below —10° F. The lubber's line is a fine line drawn on an enameled plate on the inside of the bowl, the inner surface of the latter being covered with an insoluble white paint. Beneath the bowl is a metaUic self-adj^isting expansion chamber of elastic metal, by means of which the bowl is kept constantly full without the show of bubbles or the development of undue pressure caused by the change in volume of the liquid due to changes of temperature. The rim of the compass bowl is made rigid and its outer edge turned strictly to gauge to receive the azimuth circle. 32. The Dry Compass. — The Lord Kelvin Compass, which may be regarded as the standard for the dry type, consists of a strong paper card with the central parts cut away and its outer edge stiffened by a thm aluminum ring. The 21594°— 14 2 18 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. pivot is fitted with an iridium point, upon which rests a small light aluminum boss fitted with a sapphire bearing. Radiating from this boss are 32 silk threads whose outer ends are made fast to the inner edge of the compass card; these threads sustain the weight of the suspended card, and as they possess some elasticity, tend to decrease the shocks due to motion. Eight small steel wire needles, 3\ to 2 inches long, are secured normally to two parallelsilk threads, and are slung from the aluminum rim of the card by other silk threads which pass through eyes in the ends of the outer pair of needles. The needles are below the radial threads, thus keeping the center of gravity low. 33. The Gyro Compass. — This compass, which has recently been developed, consists essentially of a rapidly spinning rotor, usually driven by a three-phase alternating current of electricity, at a rate varying according to the type, from 8,000 to 21,000 revolutions per minute, and so suspended that it automatically places its axis approximately in the direction of the geographical meridian and permits of the reading of the heading of the ship, unaffected by any magnetic influ- ence, from a graduated compass card like that in use on magnetic compasses. From the "master compass," which may be located in a compartment below, electrical connections are made to "repeating compasses" on the bridge, in the conning tower, or in the steering-engine room, so that the ship's true heading may be transmitted to any desired part of the vessel. The action of the gyro compass, affected as it is by the earth's rotation under it, conforms to Foucault's general law that "a spinning body tends to swing around so as to place its axis parallel to the axis of any impressed forces, and so that its direc- tion of rotation is the same as that of the impressed forces," Small corrections, depending upon the latitude, course, and speed, can be readily computed for applica- tion to the gyro compass readings either mechanically or by reference to tables. 34. The Azimuth Circle. — This is a necessary fitting for all compasses employed for taking bearings — that is, noting the directions — of either celestial or terrestrial objects. The instrument varies widely in its different forms; the essential features which all share consist in (a) a pair of sight vanes, or equivalent device, at the extremities of the diameter of a circle that revolves concentrically with the compass bowl, the line of sight thus always passing through the vertical axis of the compass; and (&) a system, usually of mirrors and prisms, by which the point of the compass card cut by the vertical plane through the line of sight — in other words, the compass direction — is brought into the field of view of the person making the observation. In some circles, for observing azimuths of the sun advantage is taken of the brightness of that body to reflect a pencil of light upon the card in such a manner as to indicate the bearing; such an azimuth circle is used in the United States Navy. The azimuth circles should be tested occasionally for accuracy. This can best be done by mounting a standard compass on a tripod m a nonmagnetic spot on shore, in a locality where the variation has been accurately determined. The observed compass bearing of the sun should, of course, be the same as the computed magnetic bearing at any instant, the difference between the two, if any, being eo[ual to the error of the compass or, what is more likely, the error of the azimuth circle. Any doubt in the matter may be removed by the use of two or more compasses. It will be frequently found that the error of the azimuth circle varies with the sun's altitude; this is due to the fact that the axis of the mirror is not normal to the plane passing through the sun, the 5-sided prism, and the center of the mirror. 35. Binnacles. — Compasses are mounted for use in stands known as Binnacles, of which there are two principal types — the Compensating and the Noncom'pensating Binnacle, so designated according as they are or are not equipped with appliances by which the deviation of the compass, or error in its indications due to disturbing magnetic features within the ship may be compensated. Binnacles may be of wood or of some nonmagnetic metal; all contain a compass chamber within which the compass is suspended in its gimbal ring, the knife ed^es upon which it is suspended resting in V-shaped bearings; an appropriate method is supplied for centering the compass. A hood is provided for the protection of the compass and for lighting it at night. Binnacles must be rigidly secured to the deck of the vessel in such position that the lubber's line of the compass gives true indications of the direction of the ship's head. INSTRUMENTS AND ACCESSOBIES IN NAVIGATION. 19 The position of the various binnacles on shipboard and the height at which they carry the compass must be chosen with regard to the purpose which the compass is to serve, having in mind the magnetic conditions of the ship. Compensatmg binnacles contain the appliances for carrymg the various correctors used in tne compensation of the deviation of the compass. These consist of (a) a system of permanent magnets for semicircular deviation, placed in a magnetic chamber lymg immediately beneath the compass chamber, so arranged as to permit variation m the height and number of the magnets employed; (b) a pair of arms projecting horizontally from the compass chamber and supporting masses of soft iron for quadrantal deviation; (c) a central tube in the vertical axis of the binnacle for a permanent magnet used to correct the heeling error; and (d) an attachment, sometimes fitted, for securing a vertical soft-iron rod, or ''Flinders bar," used in certain cases for correction of a part of the semicircular deviation. An explanation of the various terms here used, together with the method of compensating the com- pass, will be given in Chapter III. THE PELOBTJS. 36. This instrument consists of a circular flat metallic ring, mounted in gimbals, upon a vertical standard at some point on board ship affording a clear view for taking bearings. The inner edge of this ring is engraved in degrees — the 360° and the 180° marks indicating a fore-and-aft line parallel to the keel of the ship. Within this ring a ground-glass dial is pivoted concentrically. This ground-glass dial has painted upon it a compass rose divided into points and subdivisions and into 360 . This dial is capable of revolution, but may be clamped to the outside ring. Pivoted concentrically with the flat ring and tne glass dial is a horizontal bar carrying at both of its extremes a sight vane, or, mounted upon the bar and parallel to it, a telescope containing cross wires. This sight-vane bar can be clamped in any position independently of the ground-glass dial, which can be moved freely beneatn it. An. indicator showing the direction the sight-vane bar points can be read upon the com- pass card on the glass dial. The instrument is used for taking bearings of distant objects, and, at times, may be more convenient than the standard compass for that purpose on account of the better view commanded by its position, as well as because it may be made to eliminate compass errors from observed bearings, thus reducing the bearings observed to magnetic or true bearings. If the glass dial be revolved until the degree of demarcation which is coincident with the right-ahead marking on the flat ring is the same as that which points to the lubber's line of the standard compass, then all directions indicated by the glass will be parallel to the corresponding directions of the standard compass, and all bearings taken by the pelorus will be identical with those taken by the compass (leaving out of the question the difference due to the distance which separates them). If it is known that the ship's compass has a certain error due to deviation of the compass and if the glass dial be set to allow for this deviation, then aU bearings read from the pelorus will be magnetic. If the dial be set allowing for both deviation and variation of the compass, then all bearings read will be true. It should be noted, however, that the bearings taken by pelorus will be accurate only when the ship is on her exact course by standard compass. For this reason it is usual to take a bearing by pelorus, at the same time noting the heading by standard compass, and clamping the sight vane; then, moving the glass dial until the direction opposite the dead-ahead mark is the same as that noted by the standard compass, the bearing observed (corrected for the variation and for the deviation of the heading at the instant of observation) will be the true bearing. The pelorus described above is of the most modem type and is fitted for illu- minating the glass dial from below in order to facihtate night work. Peloruses whose dials are controlled by a master gyroscopic compass of course indicate at once the true bearing of the object observed. When fitted with a telescope the pelorus may be used to take the azimuth of stars. The standard compass is usually located in the ship in the central fore-and-aft line which is established from the builders' marks placed in th^t vicinity. The; 20 INSTRUMENTS AND ACCESSOEIES IN NAVIGATION. standard compass being located, all peloruses may be oriented from it by any one of the following methods : (a) Bv making the azimuth of a celestial body, taken by the pelorus, coincide with the smiultaneous azimuth of the same body taken by the standard compass. (&) By a similar process with distant objects; and the parallax may be entirely eliminated in an apparently near object, in view of the moderate distance that usually separates the two instruments on board ship. (c) By reciprocal bearings between the correct instrument and the instrument to be estaolished; it is evident that if the lubber lines of the two instruments are both in the direction of the keel line, the bearing of the sight vane of each from the other (one being reversed) should coincide. {d) By computing the angle subtended at the pelorus by the fore-and-aft line through the pelorus and the line drawn through the pelorus to the jack staff, and setting the pelorus at this angle and sighting on the jack staff. THE CHART. 37. A nautical chart is a miniature representation upon a plane surface, in accordance with a definite system of projection or development, of a portion of the navigable waters of the world. It generally includes the outline of the adjacent land, together with the surface forms and artificial features that are useful as aids to navigation, and sets forth the depths of water, especially in the near approaches to the land, by soundings that are fixed in position by accurate determinations. Except in charts of harbors or other localities so limited that the curvature of the earth is inappreciable on the scale of construction, a nautical chart is always framed over with a network of parallels of latitude and meridians of longitude in relation to which the features to be depicted on the chart are located and drawn; and the mathematical relation between the meridians and parallels of the chart and those of the terrestrial sphere determines the method of measurement that is to be employed on the chart and the special uses to which it is adapted. 38. There are three principal systems of projection in use: {a) the Mercator, (&) the polyconic, and (c) the gnomonic; of these theMercatorisbyfarthe most generally used for purposes of navigation proper, while the polyconic and the gnomonic charts are employed for nautical purposes in a more restricted manner, as for plotting surveys or for facilitating great circle sailing. 39. The Mercator Projection. — The Mercator Projection, so called, may be said to result from the development, upon a plane surface, of a cylinder which is tangent to the earth at the equator, the various points of the earth's surface having been projected upon the cylinder in such manner that the loxodromic curve or rJiumh line (art. 6, Chap. I) appears as a right line preserving the same angle of bearing with respect to the intersected meridians as does the ship's track. In order to realize this condition, the line of tangency, which coincides with the earth's equator, being the circumference of a right section of the cylinder, will appear as a right line on the development; while the series of elements of the cylinder corresponding to the projected terrestrial meridians will appear as equidistant right lines, parallel to each other and perpendicular to the equator of the chart, main- taining the same relative positions and the same distance apart on that equator as the meridians have on the terrestrial spheroid. The scries of terrestrial parallels will also appear as a system of right lines parallel to each other and to the e(][uator, and will so intersect the meridians as to form a system of rectangles whose altitudes, for successive intervals of latitude, must be variable, increasing from the equator in such manner that the angles made by the rhumb line with the meridian on tne chart may maintain the required equality with the corresponding angles on the spheroid. 40. Meridional Parts. — At the equator a degree of longitude is equal to a degree of latitude, but in receding from the equator and approaching the pole, while the degrees of latitude remain always of the same length (save for a shght change due to the fact that the earth is not a perfect sphere), the degrees of longitude become less and less. Since, in the Mercator projection, the degrees of longitude are made to appear everywhere of the same length, it becomes necessary, in order to preserve the proper- INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 21 tion that exists at different parts of the earth's surface between degrees of latitude and degrees of longitude, that the former be increased from their natural lengths, and such increase must become greater and greater the higher the latitude. The length of the meridian, as thus increased, between the equator and any given latitude, expressed in minutes at the equator as a unit, constitutes the number of Meridional Parts corresponding to that latitude. The Table of Meridional Parts or Increased Latitudes (Table 3), computed for every minute of latitude between 0° and 80°, affords faciUties for construct'mg charts on the Mercator projection and for solving problems in Mercator saihng. 41. To Construct a Mercator Chart." — If the chart for which a projection is to be made includes the equator, the values to be measured off are given directly by Table 3. If the equator does not come upon the chart, then the parallels of latitude to be laid down should be referred to a prindpaZ parallel, preferably the lowest parallel to be drawn on the chart. The distance of any other parallel of latitude from the principal parallel is then the difference of the values for the two taken from Table 3. The values so found may either be measured off, without previous numerical conversion, by means of a diagonal scale constructed on the chart, or they may be laid down on the chart by means of any properly divided scale of yards, meters, feet, or miles, after having been reduced to the scale of proportions adopted for the chart. If, for example, it be required to construct a chart on a scale of one-quarter of an inch to five minutes of arc on the equator, a diagonal scale may first be constructed, on which ten meridional parts, or ten minutes of arc on the equator, have a length of half an inch. It may often be desirable to adapt the scale to a certain allotment of paper. In this case, the lowest and the highest parallels of latitude mav first be drawn on the sheet on which the transfer is to be made. The distance between these parallels may then be measured, and the number of meridional parts between them ascertained. Dividing the distance by this number will then give the length of one meridional part, or the quantity by which all the meridional parts taken from Table 3 must be multiplied. This quantity will represent the scale of the chart. If it occurs that the limits of longitude are a governing consideration, tne case may be similarly treated. Example: Let a projection be required for a chart of 14° extent in longitude between the parallels of latitude 20° 30' and 30° 25', and let the space allowable on the paper between these parallels measure 10 inches. Entering the column in Table 3 headed 20°, and running down to the line marked 30' in the side column, will be found 1248.9; then, entering the column 30°, and running down to the line 25', will be found 1905.5. The difference, or 1905.5 — 1248.9 = 656.6, is the value of the meridional arc between these latitudes, for which 1' of arc of the equator is taken as the unit. On the intended projection, therefore, 1' of arc of longitude will measure „_- ' =0.0152 inch, which wiU be the scale of the d5o.d chart. For the sake of brevity call it 0.015. By this quantity aU the values derived from Table 3 will have to be multiplied before laying them down on the projection, if they are to be measured on a diagonal scale of one inch. Draw in the center of the sheet a straight line, and assume it to be the middle meridian of the chart. Construct very carefully on this line a perpendicular near the lower border of the sheet, and assume this perpendicular to be the parallel of latitude 20° 30': this will be the southern inner neat line of the chart. From the intersection of tne lines lay off on the parallel, on each side of the middle meridian, seven degrees of longitude, or distances each equal to 0.015X60X7 = 6.3 inches; and through the points thus obtained draw lines parallel to the middle meridian, and these wiU be the eastern and western neat lines of the chart. In order to construct the parallel of latitude for 21° 00', find, in Table 3, the meridional parts for 21° 00', which are 1280.8. Subtracting from this number the number for 20° 30', and multiplying the difference by 0.015, we obtain 0.478 inch, which is the distance on the chart between 20° 30' and 21° 00'. On the meridians o This construction for the purpose of plotting lines of position in ordinary navigation will often be unnecessary if use is made of the Position Plotting Sheets published by the Hydrographic Office. 22 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. lay off distances equal to 0.478 inch, and through the three points thus obtained draw a straight line, which will be the parallel of 21° 00'. Proceed in the same manner to lay down all the parallels answering to full degrees of latitude; the distances wiU be respectively: O^^.OIS X (1344.9 - 1248.9) = 1.440 inches. 0*''.015 X (1409.5 - 1248.9) = 2.409 inches. O'^'.IOS X (1474.5 - 1248.9) = 3.384 inches, etc. Thus wiU be shown the parallels of latitude 22° 00', 23° 00', 24° 00', etc. FinaUy, lay down in the same way the parallel of latitude 30° 25', which will be the northern inner neat line of the chart. A degree of longitude will measure on this chart 0^".015X60 = 0*^9. Lay off, therefore, on the lowest parallel of latitude drawn on the chart, on a middle one, and on the highest parallel, measuring from the middle meridian toward each side, the distances of 0'°.9, 1'°.8, 2*°. 7, 3'°. 6, etc., in order to determine the points where meridians answering to full degrees cross the parallels drawn on the chart. Through the points thus found draw the meridians. Draw then the outer neat lines of the chart at a convenient distance outside of the inner neat lines, and extend to them the meridians and parallels. Between the inner and outer neat lines of the chart sub- divide the degrees of latitude and longitude as minutely as the scale of the chart will permit, the subdivisions of the degrees of longitude being found by dividing the degrees into equal parts, and the subdivisions of the degrees of latitude being accu- rately found in the same manner as the full degrees of latitude previously described, though it will generally be found sufficiently exact to make even subdivisions of the degrees, as in tne case of the longitude. The subdivisions between the two eastern as well as those between the two western neat lines wiU serve for measuring or estimating terrestrial distances. Dis- tances between points bearing North and South of each other may be ascertained by referring them to the subdivisions between the same parallels. Distances repre- sented by fines at an angle to the meridians (loxodromic lines) may be measured by taking between the dividers a small number of the subdivisions near the middle latitude of the line to be measured, and stepping them off on that line. If, for instance, the terrestrial length of a line running at an angle to the meridians between the parallels of latitude of 24° 00' and 29° 00' oe req[uired, the distance shown on the neat space between 26° 15' and 26° 45' ( = 30 nautical miles) may be taken between the dividers and stepped off on that line. 4:2. Coast lines and other positions are plotted on the chart by their latitude and longitude. A chart may be transferred from any other projection to that of Mercator by drawing a system of corresponding parallels of latitude and meridians over both charts so close to each other as to form minute squares, and then the lines and characters contained in each square of the map to be transferred may be copied by the eye in the corresponding squares of the Mercator projection. Since the unit of measure, the mile or minute of latitude, has a different value in every latitude, there is an appearance of distortion in a Mercator chart that covers any large extent of surface; for instance, an island near the pole will be represented as being much larger than one of the same size near the equator, due to the different scale used to preserve the character of the projection. 43. The Polyconic Projection. — ^This projection is based upon the develop- ment of the earth's surface on a series of cones, a different one for each parallel of latitude, each one having the parallel as its base, and its vertex in the point where a tangent to the earth at that latitude intersects the earth's axis. The degrees of latitude and longitude on this chart are projected in their true length, and the general distortion of the figure is less than in any other method of projection, the relative magnitudes bein^ closely preserved. A straight hne on the polyconic chart represents a near approach to a great circle, making a slightly different angle with each successive meridian as the meridians converge toward the pole and are theoretically curved lines; but it is only on charts of large extent that this curvature is apparent; the parallels are also curved, this fact being apparent to the eye upon all excepting the largest scale charts. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 23 This method of projection is especially adapted to the plotting of surveys; it is also employed to some extent in the charts of the United States Coast and Geodetic Survey. 44. Gnomonic Projection. — ^This is based upon a system in which the plane of projection is tangent to the earth at some ^iven point; the eye of the spectator is situated at the center of the sphere, where, bemg at once in the plane of every great circle, it will see all such circles projected as straight lines where the visual rays passing through them intersect the plane of projection. In a gnomonic chart, tne straight Ime between any two points represents the arc of a great circle, and is there- fore the shortest line between those points. Excepting in the polar regions, for which latitudes the Mercator projection can not be constructed, the gnomonic charts arc not used for general navigating purposes. Their greatest application is to afford a ready means of finding the course and distance at any time in great circle sailing, the method of doing wmch will be explained in Chapter V. 45. Meridians Adopted in the Construction of Charts. — ^The nautical charts published b^ the United States are based upon the meridian of Greenwich, and this meridian is also the origin of longitudes in use on the nautical charts pub- lished by the Governments of Argentina, Austria, Belgium, Brazil, Chile, Denmark, Germany, Great Britain, Holland (for all charts published at Batavia and for some pubUshed at I'he Hague), Italy, Japan, Norwav, Russia, and Sweden. In addition to the meridian of Greenwich, tlie meridian of Pulkowa Observatory, at St. Petersburg, in longitude 30° 19' 40" east of Greenwich, is sometimes referred to in the Russian charts. At one time the Royal Observatory at Naples, in longitude 14° 15' 26" east of Greenwich, was referred to in the Italian charts, and the observatory at Christiania, in longitude 10° 43' 23" east of Greenwich, was referred to in the Norwegian charts. The French charts are based upon the meridian of the Observatory at Paris, which has been determined to be in longitude 2° 20' 14.6" east of Greenwich. The longitudes of a few Dutch charts p ublished at The Hague are reckoned from the meridian of the west tower of Wester Kirk at Amsterdam, which is in longi- tude 4° 53' 01.5" east of Greenwich. All Portuguese charts constructed on a scale of 1:100,000 refer exclusively to the meridian of the observatory of Lisbon Castle, which is 9° 07' 54.86" west of Greenwich; Portuguese charts on a scale of 1:50,000 carry two ^aduations, one based on the meridian of Greenwich, the other on the meridian of Lisbon Castle. In Spain the meridian of San Fernando Observa- tory, at Cadiz, which is m longitude 6° 12' 18" west of Greenwich, is used. 46. Quality of Bottom. — The following table shows the qualities of the bottom, as expressed on charts of various nations: United States. English. French. ItAlian. Spanish. German. Clay C. Clay ..cl. Argile ...A. Argila •arg. Arcillo or Barro.arc. Lehm ....L. Coral Co. Coral ..crl. Corail .Cor. Corfillo .crl. Coral cl. Korallen ..Kor. Gravel G. Gravel ...g. Gravier ..Gr. RenaorGhiaja.gh. Cascfijo Co. Kies ....k. Mud M. Mud ..m. Vase ...V. Fango ...f. Fango or Luno...F. Schlamm .Schl. Rocky rky. Rock ..rk. Roche ...R. Roccia ...r. Piedra or Roca. P. or r. Felsig ..Fls. Sand 8. Sand ...s. Sable ...S. S£bbia or Artoa. . s. Arena A. Sand ...8d. Shells Sh. ShelLi ..sh. CoquUle .Coq. Conchiglia.... . ..c. Conchuela ca. Muacheln ....M. Stone St. Stones ..St. Pierre ...P. Pletre ..p. Piedra P. Stein ...St. Weed ....Wd. Weed .wd. Herb ...n. Alga .alg. Alga A. Gras ..Grs. Fine fne. crs. stf. sft. bk. rd. Fine Coarse Stiff Soft Black Red ...c. ..stf. ..sft. .bUc. ..rd. Fin Gros Dure MoUe Noire Rouge Jaune ..to. ....g. ....d. ...m. n. r. Fino Fina f. Gruesa g. Tenaz Fein Grob Schlick Weich Schwarz Roth f. Coarse Grosso ...gb. ....sk. Stifl T«iina«» Soft Molle Blando bdo. Negro n. Rojo r. Amarillo am. .Wch. Black Nero .schw. Red Rosse.. r. YeUow.... yi- ey. YeUow ...y. ....j. Giallo Gelb g. Gray 24 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 47. Measures of Depth. — The following table shows the units of measure employed in expressing the soundings in the more modern nautical charts of foreign nations together with their equivalents in the units of measure used in the charts published by the United States : Nationality of chart. Argentine.. . Austrian Belgian . Chilean . Danish . Dutch.. French. . German. Italian.. Unit of soundings. Metro . . . Metro . . . or faden . Metre . . . Metro . . . favn vadem... or metre. Metre . . . do... Metro . . - Equivalent in United States units. Feet. Fathoms. 3.281 3.281 6.223 281 281 176 905 281 281 3.281 3.281 0.547 0.547 1.037 0.547 0.547 1.029 0.984 0.547 0.547 0.547 0.547 Nationality of diart. Japanese . . Norwegian Portuguese Russian.. . Spanish... Swedish... British Unit of soundings. Fathom. Metre . . or favn . Metro . . Sajene.. Metro . . or braza Metre . . or famn. Fathom, Equivalent in United States units. 6.000 3.281 6.176 3. 281 6.000 3.281 5.492 3.281 5.844 6.000 Fathoms. 1.000 0.547 1.029 0.547 1.000 0.547 0.914 0. 547 0.974 1.000 FiQ. 3. the the THE BAROMETER. 48. The harometer is an instrument for measuring the pres- sure of the atmosphere, and is of great, service to the mariner in affording a knowledge of existing meteorological conditions and of the probable changes therein. There are two classes of barometer — mercurial and aneroid. 49. The Mercurial Barometer. — This instrument, in- vented by Torricelli in 1643, indicates the pressure of the atmos- phere by the height of a column of mercury. If a glass tube of uniform internal diameter somewhat more than 30 inches in length and closed at one end be com- pletely filled with pure mercury, and then placed, open end down, in a cup of mercur;^ (the open end having been tempo- rarily sealed to retain the liquid during the process of inverting), it will be found that the mercury in the tube will fall until the top of the column is about 30 inches dbove the level of that which is in the cup, leaving in the upper part of the tube a vacuum. Since the weight of the column of mercury thus left standing in the tube is equal to the pressure by which it is held in position — namely, that of the atmospheric air — it follows that the height of the column is subject to variation upon variation of that pressure; hence the mercury falls as the pressure of the atmosphere decreases and rises as that pressure increases. The mean pressure of the atmosphere is equal to nearly 15 pounds to the square inch; the mean height of the barometer is about 30 inches. 50. In the practical construction of the barometer the glass tube which contains the mercury is encased in a brass tube, the latter terminating at the top in a ring to be used for suspension, and at the bottom in a flange, to which the several parts form- ing the cistern are attached. The upper part of the brass tube is partially cut away to expose the mercurial column for observation; abreast this opening is fitted a scale for measur- ing the height, and along the scale travels a vernier for exact reading; the motion of the vernier is controlled by a rack and pinion, the latter having a milled head accessible to the observer, by which the adjustment is made. In the middle of the brass tube is fixed a thermometer, the bulb of which is covered from Fig. 4. outside but open toward the mercury, and which, bein^ nearly in contact with glass tube, inaicates the temperature of the mercury and not that of the external INSTBUMENTS AND ACCESSORIES IN NAVIGATION. 25 air; the central position of the column is selected in order that the mean temperature may be obtained — a matter of importance, as the temperature of the mercurial column must be taken into account in every accurate application of its reading. 51. In the arrangement of further details mercurial barometers are divided into two classes, according as they are to be used, as Standards (fig. 4) on shore, or as Sea Barometers (fig. 3) on shipboard. In the Standard Barometer the scale and vernier are so graduated as to enable an observer to read the height of the mercurial column to the nearest 0.002 inch, while in the Sea Barometer the reading can not be made closer than 0.01 inch. The instruments also differ in the method of obtaining the true height of the mercurial column at varying levels of the liquid in the cistern. It is evident that as the mercury in the tube rises, upon increase of atmospheric pressure, the mercury in the cistern must fall ; and, conversely, when the mercurial column falls the amount of fluid in the cistern will thereby be increased and a rise of level will occur. As the height of the mercurial column is required above the existing level in the cistern, some means must be adopted to obtain the true height under varying conditions. In the Standard Barometer the mercury of the cistern is contained in a leather bag, against the bottom of which presses tne point of a vertical screw, the milled head of the screw projecting from the bottom of the instrument and thus placing it under control of the observer. By this means the surface of the mercury in the cistern (which is visible through a glass casing) may be raised or lowered until it exactly coincides with that level which is chosen as the zero of the scale, and which is indicated by an ivory pointer in plain view. In the Sea Barometer there is no provision for adjusting the level of the cistern to a fixed point, but compensation for the variable level is made in the scale gradu- ations ; a division representing an inch On the scale is a certain fraction short of the true inch, proper allowance being thus made for the rise in level which occurs with a fall of the column, and for the reverse condition. Further modification is made in the Sea Barometer to adapt it to the special use for which intended. The tube toward its lower end is much contracted to prevent the oscillation of the mercurial column known as "pumping," which arises from the motion of the ship ; and just below this point is a trap to arrest any small bubbles of air from finding their way upward. Tne instrument aboard ship is suspended in a revolving center ring, in gimbals, supported on a horizontal brass arm which is screwed to the bulkhead; a vertical position is thus maintained by the tube at all times. 62. The vernier is an attachment for facilitating the exact reading of the scale of the barometer, and is also applied to many other instruments of precision, as, for example, the sextant and theodolite. It consists of a metal scale similar in general construction to that of the instrument to which it is fitted, and arranged to move alongside of and in contact with the main scale. The general principle of the vernier requires that its scale shall have a total length exactly equal to some whole number of divisions of the scale of the instrument and that this length shall be subdivided into a number of parts equal to 1 more or 1 less than the number of divisions of the instrument scale which are covered; thus, if a space of 9 divisions of the main scale be designated as the length of the vernier, the vernier scale would be divided into either 8 or 10 parts. Suppose that a barometer scale be divided into tenths of an inch and that a length of 9 divisions of such a scale be divided into 10 parts for a vernier (fig. 5) ; and suppose that the divisions of the vernier be numbered consecutively from zero at the origin to 10 at the upper extremity. If, now, by means of the movable rack and pinion, the bottom or zero division of the vernier be brought level with the top of the mercurial column, and that division falls into exact coincidence with a division of the main scale, then the height of the column wiU correspond with the scale reading indicated. In such a case the top of the vernier will also exactly coincide with a scale division, but none of the intermediate divisions wiU be evenly abreast of such a division; the division marked *'l" will fall short oi a scale division by one-tenth of 1 division of the scale, or by 0^01 inch; that marked "2" by two-tenths of a division, or 0.02 inch; and so on. If the vernier, instead of having Fig. 5. 26 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. the zero coincide with a scale division, has the division "1" in such coincidence, it follows that the mercurial column stands at 0.01 inch above that scale division which is next below the zero; for the division "2," at 0.02 inch; and similarly for the others. In the case portrayed in figure 5, the reading of the column is 29.81 inches, the scale division next below the zero being 29.80 inches, while the fact that the first division is abreast a mark of the scale shows that 0.01 inch must be added to this to obtain the exact reading. Had an example been chosen in which 8 vernier divisions covered 9 scale divisions — that is, where the number of vernier divisions was 1 less than the number of scale divisions covered — the principle would still have applied. But, instead of the length of 1 division of the vernier falling short of a division of the scale by one- tenth the length of the latter, it would have fallen beyond by one-eighth. ^ To read in such a case it would therefore be necessary to number the vernier divisions from up downward and to regard the subdivisions as -^ instead of 0.01 inch. It is a general rule that the smallest measure to which a vernier reads is equal to the lengm of 1 division of the scale divided by the number of divisions of the vernier; hence, by varying either the scale or the vernier, we may arrive at any subdivision that may be desired. 53. The Sea Barometer is arranged as described for the instrument assumed in the illustration; the scale divisions are tenths of an inch, and the vernier has 10 divisions, whence it reads to 0.01 inch. It is not necessary^ to seek a closer reading, as complete accuracy is not attainable in observing the height of a barometer on a vessel at sea, nor is it essential. The Standard Barometer on shore, however, is capable of very exact reading; hence each scale division is made equal to half a tenth, or 0.05 inch, while a vernier covering 24 such divisions is divided into 25 parts; hence the column may be read to 0.002 inch. 54. To adjust the vernier for reading the height of the mercurial column the eye should be brought exactly on a level with the top of the column; that is, the line of sight should be at right angles to the scale. _ When properly set, the front and rear edges of the vernier and the uppermost point of the mercury should all be in the line of sight. A piece of white paper, held at the back of the tube so as to reflect the light, assists in accurately setting the vernier by day, while a small bull's-eye lamp held behind the instrument enables the observer to get a correct reading at night. When observing the barometer it should hang freely, not being inclined by holding or even by touch, because any inclination will cause the column to rise in the tube. 55. Other things being equal, the mercury wiU stand higher in the tube when it is warm than when it is cold, owing to expansion. For the purposes of comparison, all barometric observations are reduced to a standard which assumes 32° F. as the temperature of the mercurial column, and 62° F. as that of the metal scale; it is therefore important to make this reduction, as well as that for instrumental error (art. 67), in order to be enabled to compare the true barometric pressure with the normal that may be expected for any locality. The following table gives the value of this correction for each 2° F., the plus sign showing that the correction is to be added to the reading of the ship's barometer and the minus sign that it is to be subtracted : Tempera- ture. Correction. Tempera- ture. Correction. Tempera- ture. Correction. Tempera- ture. Correction. 20 22 24 26 28 30 32 34 36 38 Inch. +0.02 +0.02 +0.01 +0.01 0.00 0.00 -0.01 -0.02 -0.02 -0.03 40 42 44 46 48 50 52 54 56 1 58 1 Inch.. -0.03 -0.04 -0.04 -0.05 -0.05 -0.06 -0.06 -0.07 -0.07 -0.08 60 62 64 66 68 70 72 74 76 78 Inch. -0.09 -0.09 -0.09 -0.10 -0.10 -0.11 -0.12 -0.12 -0.13 -0.13 o 80 82 84 86 88 90 92 94 96 98 Inch. -0.14 -0.14 -0 15 -0.15 -0. 16 -0. 16 -0.17 -0.17 -0.18 -0.18 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 27 As an example, let the observed reading of the mercurial barometer be 29.95 inches, and the temperature as given by the attached thermometer 74°; then we have: // Observed height of the mercury 29. 95 Correction for temperature (74°) —0. 12 Height of the mercury at standard temperature 29. 83 66. The Aneroid Barometer. — This is an instrument in which the pressure of the air is measured by means of the elasticity of a plate of metal. It consists of a cylindrical brass box, the metal in the sides being very thin; the contained air having been partially, though not completely, exhausted, the box is hermetically sealed. When the pressure of the atmosphere increases the inclosed air is compressed, the capacity oi the box is diminished, and the two flat ends approach each other; when the pressure of the atmosphere decreases, the ends recede from one another in conse- quence of the expansion of the inclosed air. By means of a combination of levers, wiis motion of the ends of the box is communicated to an index pointer which travels over a graduated dial plate, the mechanical an-angement being such that the motion of the ends of the box is magnified many times, a very minute movement of the box maldng a considerable difference in the indication of the pointer. The graduations of the aneroid scale are obtained by comparison with the correct readings of a standard mercurial barometer under normal and reduced atmospheric pressure. The thermometer attached to the aneroid barometer is merely for convenience in indicating the temperature of the air, but as regards the instrument itself no cor- rection for temperature can be applied with certainty. Aneroids, as now manufac- tured, are almost perfectly compensated for temperature by the use of different metals having unequal coefficients of expansion; tney ought, therefore, to show the same pressure at all temperatures. The aneroid barometer, from its small size and the ease with which it may be trans- Eorted, can often be usefully employed under circumstances where a mercurial arometer would not be available. It also has an advantage over the mercurial instrument in its greater sensitiveness, and the fact that it gives earlier indications of change of pressure. It can, however, be relied upon only when frequently com- pared with a standard mercurial barometer; moreover, considerable care is required m its handling; while slight shocks will not ordinarily affect it, a severe jar or faaock may change its indications by a large amount. Wlien in use the aneroid barometer may be suspended vertically or placed flat, but changing from one position to another ordinarily makes a sensible change in the readings; the instrument should always, therefore, be kept in the same position, and the errors determined by comparisons made while occupying its customary place. 67. Comparison of Barometers. — To determine the reliability of tne ship's barometer, whether mercurial or aneroid, comparisons should from time to time be made with a standard barometer. Nearly all instruments read either too hi^jh or too low by a small amount. These errors arise, in a mercurial barometer, from the improper placing of the scale, lack of uniformity of caliber of the glass tube, or similar causes; in an aneroid, which is less accurate and in which there is even more necessity for frequent comparisons, errors may be due to derangement of any of the various mechanical features upon which its working depends. The errors of the barometer should be determined for various heights, as they are seldom the same at all parts of the scale. In the principal ports of the world standard barometers are observed at specified times each day, and the readings, reduced to zero and to sea level, are puoUshed. It is therefore only necessary to read the barometer on shipboard at those times and, if a mercurial instrument is used, to note the attached thermometer and apply the correction for temperature (art. 55). It is evident that a comparison of the heights by reduced standard and by the ship's barometer wiU give the correction to be applied to the latter, including the instrumental error, the reduction to sea level, and the personal error of the observer. In the United States, standard barometer readings are made by the Weather Bureau. Aneroid barometers may be adjusted for instrumental error by moving the index hand, but this is usually done only in the case of errors of considerable magnitude. 28 INSTRUMENTS AND ACCESSOEIES IN NAVIGATION. 58. Determination of Heights by Barometer. — The barometer may be used to determine the difference in heights between any two stations by means of the difference in atmospheric pressure between them. An approximate rule is to allow 0.0011 inch for each difference in level of 1 foot, or, more roughly, 0.01 inch for every 9 feet. A very exact method is afforded by Babinet's formula. If Bo and B represent the barometric pressure (corrected for all sources of instrumental error) at the lower and at the upper stations respectively, and to and t the corresponding temperatures of the air; then, TJ T> Diff . in height = C X t3° . ^ ; if the temperatures be taken by a Fahrenheit thermometer, C (in feet) =52, 494 (l + ^""^qqq^^ ); if a centigrade thermometer is used, C (in meters) = 16,000(^1 +^^^)- THE THERMOMETER. 59. Tlie Thermometer is an instrument for indicating temperature. In its construction advantage is taken of the fact that bodies are expanded by heat and contracted by cold. In its most usual form the thermometer consists of a bulb filled with mercury, connected with a tube of very fine cross-sectional area, the liquid column rising or falling in the tube according to the volume of the mercury due to the actual degree of heat, and the height of the mercury indicating upon a scale the temperature; the mercury contained in the tube moves in a vacuum produced by the expulsion of the air through boiling the mercury and then closing the top of the tube by means of the blowpipe. There are three classes of thermometer, distinguished according to the method of graduating the scale as follows: the FakrenTieit, in which the freezing point of water is placed at 32° and its boUing point (under normal atmospheric pressure) at 212°; the Centigrade, in which the freezing point is at 0° and the boilmg point at 100°; and the Reaumur, in which these pomts are at 0° and 80°, respectively. The Fahrenheit thermometer is generally used in the United States and England. Tables will be found in this work for the interconversion of the various scale readings (Table 31). 60. The thermometer is a valuable instrument for the mariner, not only by reason of the aid it affords him in judging meteorological conditions from the tem- perature of the air and the amount of moisture it contains, but also for the evidences it furnishes at times, through the temperature of the sea water, of the ship's position and the probable current that is being encountered. 61. The thermometers employed in determining the temperature of the air (wet and dry bulb) and of the water at the surface, should be mercurial, and of some standard make, with the graduation etched upon the glass stem; they should be compared with accurate standards, and not accepted if their readings vary more than 1 ° from the true at any point of the scale. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 29 62. The diy-bulb thermometer gives the temperature of the free air. The wet-bulb thermometer, an exactly similar instrument, the bulb of which is surrounded by an envelope of moistened clotn, gives what is known as the temperature of evapora- tion, which is always somewhat less than the temperature of the free air. From the difference of these two temperatures the observer may determine the proximity of the air to saturation; that is, how near the air is to that point at which it will be obliged to precipitate some of its moisture (water vapor) in the form of liquid. With the envelope of the wet bulb removed, the two thermometers should read precisely the same ; otherwise they are practically useless. The two thermometers, the wet and the dry bulb, should be hung within a few inches of each other, and the surroundings should be as far as possible identical. In practice the two thermometers* are gener- ally inclosed within a small lattice case, such as that shown in figure 6 ; the case should be placed in a position on deck remote from any source of artificial heat, sheltered from the direct rays of the sun, and from the rain and spray, but freely exposed to the circulation of the air; the door should be kept closed except during the process of reading. The cloth envelope of the wet bulb should be a single thickness of fine muslin, tightly stretched over the bulb, and tied with a fine thread. The wick which serves to carry the water from the cistern to the bulb should consist of a few threads of lamp cotton, and should be of sufficient length to admit of two or three inches being coded in the cistern. The muslin envelope of the wet bulb should be at all times thoroughly moist, but not dripping. When the temperature of the air falls to 32° F. the water in the wick freezes, the capillary action is at an end, the bulb in consequence soon becomes quite dry, and the thermometer no longer shows the tem- Eerature of evaporation. At such times the ulb should be thoroughly wetted with ice- cold water shortly before the time of observation, using for this purpose a camel's hair brush or feather; by this process the temperature oithe wet bulb is temporarily raised above that of the dry, but oiJy for a brief time, as the water quickly freezes; and inasmuch as evaporation takes place from the surface of the ice thus formed precisely as from the surface of the water, the thermometer will act in the same way as if it had a damp bulb. The wet-bulb thermometer can not properly read higher than the dry, and if the reading of the wet bulb should be the higher, it may always be attributed to imperfections in the instruments. a Called a psyohrometer. 30 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 63. Knowing the temperature of the wet and dry bulbs, the relative humidity of the atmosphere at the time of observation may be found from the following table: Tempera- DifEerence between dry-bulb and wet-bulb readings. lure of the air, dry- bulb ther- 1° 2° 3° 4° 5° 6° 8° 9° 10* mometer. Per ct. Per ct. Per ct. Per a. Per ct. Per ct. Per ct. Per ct. Ptr ct. Per ct. 24 87 75 62 50 38 26 26 88 76 65 53 42 30 28 89 78 67 56 45 34 24 30 90 79 •68 58 48 38 28 32 90 80 70 61 51 41 32 23 34 90 81 72 63 53 44 35 27 36 91 82 73 64 55 47 38 30 22 38 92 83 75 66 57 50 42 34 26 40 92 84 76 68 59 52 44 37 30 22 42 92 84 77 69 61 54 47 40 33 26 44 92 85 78 70 63 56 49 43 36 29 46 93 85 79 72 65 58 51 45 38 32 48 93 86 79 73 66 60 53 47 41 35 50 93 87 80 74 67 61 55 49 43 37 52 94 87 81 75 69 63 57 51 46 40 64 94 88 82 76 70 64 69 53 48 42 56 94 88 82 77 71 65 60 55 50 44 58 94 89 83 78 72 67 61 56 51 46 60 94 89 84 78 73 68 63 58 53 48 62 95 89 84 79 74 69 64 59 54 50 64 95 90 85 79 74 70 65 60 56 51 66 95 90 85 80 75 71 66 61 57 53 68 95 90 85 81 76 71 67 63 68 64 70 95 90 86 81 77 72 68 64 60 66 72 95 91 86 82 77 73 69 65 61 67 74 95 91 86 82 78 74 70 66 62 68 76 95 91 87 82 78 74 70 66 63 59 78 96 91 87 83 79 75 71 67 63 60 80 96 92 87 83 79 75 72 68 64 61 82 96 92 88 84 80 76 72 69 65 62 84 96 92 88 84 80 77 73 69 66 63 86 96 92 88 84 81 77 73 70 67 63 88 96 92 88 85 81 77 74 71 67 64 90 96 92 88 85 81 78 74 71 68 65 The table may be readily understood. For example, if the temperature of the air (dry bulb) be 60°, and the temperature of evaporation (wet bulb) be 56°, the difference being 4°, look in the column headed ''Temperature of the air" for 60°, and for the figures on the same line in column headed 4°; here 78 will be found, which means that the air is 78 per cent saturated with water vapor; that is, that the amount of water vapor present in the atmosphere is 78 per cent of the total amount that it could carry at the given temperature (60°). This total amount, or saturation, is thus represented hj 100, and if there occurred any increase of the quantity of vapor beyond this point, the excess would be precipitated in the form of liquid. Over the ocean's surface the relative humidity is generally about 90 per cent, or even higher in the doldrums; over the land in dry wmter weather it may fall as low as 40 per cent. 64. The sea water of which the temperature is to be taken should be drawn from a depth of 3 feet below the surface, the bucket used being weighted in order to sink it. The bulb of the thermometer should remain immersed m the water at least three minutes before reading, and the reading should be made with the bulb immersed. INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 31 THE LOG BOOK. 65. The Log Book is a record of the ship's cruise, and, as such, an important accessory in the navigation. It should afford all the data from which the position of the ship is estabhshed by the method of dead reckoning; it should also comprise fl, record of meteorological observations, which should be made not only for the purpose of foretelling the weather during the voyage, but also for contribution to the general fund of knowledge of marine meteorolo^. 66. A convenient form for recordmg the data, which is employed for the log books of United States naval vessels, is shown on page 32 ; beside the tabulated matter thus arranged, to whicli one page of the book is devoted, a narrative of the miscella- neous events of the day, written and signed by the proper officers, appears upon the opposite page. 32 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. ■t39S 9V[% JO ejKjg •oiPiP5WOPhWOQPhWO •sscduioo -iBoo •iioiai\i ue^BAV 0) o CO P <»'2 ®'2 IK'S "Si?' p.Ti P.rt 3.-.' — « — •43 S^-^ PI-X3 fl rt c« O c« O c3 O £ ^^ K^l K^l tj h:i t_5 t •ra-B 8 'a'a'sqo o •uoo^ c4 o el 5 (=5 S in-d8W) fee '« INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 33 67. For the most part, the nature of the information called for, with the method of recording it, will be apparent, A brief explanation is here given of such points as seem to require it. 68. The Wind. — In recording the force of the wind the scale devised by the late Admiral Sir F. Beaufort is employed. According to this scale the wind varies from 0, a calm, to 12, a hurricane, the greatest velocity it ever attains. In the lower grades of the scale the force of the wind is estimated from the speed imparted to a man-of-war of the early part of the nineteenth century sailing full and by; in the higher grades, from the amount of sail which the same vessel could carry when close-hauled. The scale, with the estimated velocity of the wind in both statute and nautical miles per hour, is as follows : Conditions. Velocity. Mean pressure in pounds per square foot. Force of wind. Statute miles per hour. Nautical miles per hour. 0— r.filni Full-rigged ship, all sails set, no headway. . Just sufficient to give steerage way Speed of 1 or 2 knots, "full and by " Speed of 3 or 4 knots, " full and by " Speed of 5 or 6 knots, " full and by " All plain sail, " full and by " Oto 3 8 13 18 23 28 34 40 48 56 65 75 90 and over. Oto 2.6 6.9 11.3 15.6 20.0 24.3 29. r, 34.7 41.6 48.6 56.4 65.1 78. 1 and over. 0.03 1. — Light air 0.23 2.— Light breeze 3.— Gentle breeze 4.— Moderate breeze . . . 0.62 1.2 1.9 2.9 6 —Strong breeze 7.— Moderate gale 8. — Fresh gale Topgallantsails oversingle-reefed topsails. . 4.2 6.9 Treble-reefed topsails (or reefed upper topsails and courses). Close-reefed topsails and courses (or lower topsails and courses). Close-reefed main topsail and reefed fore- sail (or lower main topsail and reefed foresail). 8.4 9. — Strong gale 10.— Whole gale 11.— Storm 11.5 15.5 20.6 Under bare poles 29.6 69. Wlien steaming or sailing with any considerable speed, the apparent direc- tion and force of the wind, as determined from a vane flag, or peimant aboard ship, may differ materially from the true direction and force, the reason being that the air appears to come from a direction and with a force dependent, not only upon the wind itself, but also upon the motion of the vessel. For instance, suppose tnat the wind has a velocity of 20 knots an hour (force 4), and take the case of two vessels, eachsteaming 20 knots, the first with the wind dead aft, the second with the wind dead ahead. The former vessel will be moving with the same velocity as the air and in the same direction; the velocity of the wind relatively to the ship will thus be zero; on the vessel an apparent calm wiU prevail and the pennant wiU hang up and down. The latter vessel will be moving with the same velocity as the air, but in the opposite direction; the relative velocity of the two will thus be the sum of the two velocities, or 40 knots an hour, and on the second vessel the wind will apparently have the velocity corresponding very nearly with a fresh gale. Again, it might be shown that in the case of a vessel steaming west at the rate of 20 knots, with the wind blowing from north with the velocitv of 20 knots an hour, the velocity with which the air strikes the ship as a result oi the combined motion wiU be 28 knots an hour, and the direction from which it comes will be NW. If, therefore, the effect of the speed of the ship is neglected the wind wiU be recorded as NW., force 6, when in reahty it is north, force 4. In order to make a proper allowance for this error and arrive at the true direction and force of the wind. Table 32 may be entered with the ship's speed and the apparent direction and force of the wind as arguments, and the true direction and force will be found. 21594°— 14 3 34 INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 70. Weather. — To dssignate the weather a series of symbols devised by the late Admiral Beaufort is employed. The system employed in the United States Navy is as follows : b. — Clear blue sky. p.— Passing showers of rain, c— Clouds. 5.— Squally weather. d. — Drizzling, or light rain. r. — Rainy weather, or continuous rain. /. — Fog, or foggy weather. s. — Snow, snowy weather, or snow falling. g. — Gloomy, or dark, stormy-looking weather. t. — Thunder. h. — Hail. u. — Ugly appearances, or threatening weather. I. — Lightning. ■?;.— Variable weather, m.— Misty weather. w.— Wet, or heavy dew. o._Overcast. 2.— Hazy weather. To indicate great intensity of any feature, its symbol may be underlined; thus: r., heavy rain. ~ 71. Clouds. — The following are the principal forms of clouds, named in the order of the altitude above the earth at which they usually occur, beginning with the most elevated. The symbols by which each is designated follows its name : 1. Cirrus (Ci.). — Detached clouds, dehcate and fibrous looking, taking the form of feathers, generally of a white color, sometimes arranged in belts which cross a portion of the sky in great circles, and, by an effect of perspective, converging toward one or two opposite points of the horizon. 2. Cirro-Stratus (Ci.-S.). — A thin, whitish sheet, sometimes completely cover- ing the sky and only giving it a whitish appearance, or at others presenting, more or less distinctly, a formation hke a tangled web. This sheet often produces halos around the sun and moon. 3. CiRRO-CuMULUS (Ci.-Cu.). — Small globular masses or white flakes, having no shadows, or only very slight shadows, arranged in groups and often in lines. 4. Alto-Cumulus (A.-Cu.). — Rather large globular masses, white or grayish, partially shaded, arranged in groups or lines, and often so closely packed that their edges appear confused. The detached masses are generally larger and more compact at the center of the group; at the margin they form into finer flakes. They often spread themselves out in lines in one or two directions. 5. Alto-Stratus (A.-S.). — A thick sheet of a gray or bluish color, showing a briUiant patch in the neighborhood of the sun or moon, and which, without causing halos, may give rise to coronas. This form goes through all the changes like the Cirro-Stratus, but its altitude is only half so great. 6. Strato-Cumulus (S.-Cu.). — Large globular masses or rolls of dark cloud, frequently covering the whole skv, especially in winter, and occasionally giving it a wavy appearance. The layer of Strato-Cumulus is not, as a rule, very thick, and patches of blue sky are often visible through the intervening spaces. All sorts of transitions between this form and the Alto-Cumulus are noticeable. It may be distinguished from Nimbus by its globular or rolled appearance and also because it does not bring rain. 7. Nimbus (N.). — Rain clouds; a thick layer of dark clouds, without shape and with ragged edges, from which continued rain or snow generally falls. Through the openings of these clouds an upper layer of Cirro-Stratus or Alto-Stratus may almost invariably be seen. If the layer of Nimbus separates into shreds or if small loose clouds are visible floating at a low level underneath a large nimbus, they may be described as Fracto-Nimbus (Fr.-N.), the "scud" of sailors. 8. Cumulus (Cu.). — Wool-pack clouds; thick clouds of which the upper surface is dome-shaped and exhibits protuberances, while the base is horizontal. When these clouds are opposite the sun the surfaces usually presented to the observer have a greater brilliance than the margins of the protuberances. When the light falls aslant, they give deep shadows; when, on the contrary, the clouds are on the same side as the sun, they appear dark, with bright edges. The true Cumulus has clear superior and inferior limits. It is often broken up by strong winds, and the detached portions undergo continual changes. These may be distinguished by the name of Fracto-Cumulus (Fr.-Cu.). INSTRUMENTS AND ACCESSORIES IN NAVIGATION. 35 9, CuMULO-NiMBUS (Cu-N.). — The thunder-cloud or shower-cloud; heavy masses of clouds rising in the form of mountains, turrets, or anvils, generally having a sheet or screen of fibrous appearance above, and a mass of clouds similar to Nimbus underneath. From the base there usually fall local showers of rain or of snow (occasionally hail or soft hail). 10. Stratus (S.). — A horizontal sheet of lifted fog; when this sheet is broken up into irregular shreds by the wind or by the summits of mountains, it may be distinguished by the name of Fracto-Stratus (Fr.-S.). 72. In the scale for the amount of clouds represents a sky which is cloudless and 10 a sky which is completely overcast. 73. State of Sea. — The state of the sea is expressed by the following system of symbols : B. — Broken or irregular sea. M. — ^Moderate sea or Hwell. C. — Chopping, short, or cross sea. R. — Rough sea. G.— Ground swell. 5.— Smooth sea. //.—Heavy sea. T.— Tide-rips. L. — Long rolling sea. Note. — There are various pubhcations issued by the Hydrographic Office dealing with special features of navigation, which should be regularly consulted. Among the most important of these are : P%lot charts of the various oceans furnish information regarding the drift of derelicts, ice, and floating obstructions, the tracks of storms, average conditions of wind and weather, ocean currents, magnetic variation, etc. Hydrographic Bulletin, weekly, gives more detailed facts than the Pilot Charts regarding ice, wrecks, and derelicts; also items on port facilities, use of oil to calm the sea, and miscellaneous items of use and interest to mariners. Daily Memorandum, published at the main office at Washington, also makes public these items through the Branch Hydrographic Offices. Notice to Mariners, weekly, gives changes in aids to navigation (lights, buoyage, harbor constructions), dangers to navigation (rocks, shoals, banks, bars), important new soundings, and, in general, all such facts as affect mariners' charts, manuals, and pilots or sailing directions. * CHAPTER III. THE COMPASS EEKOE. CAUSES OF THE ERROR. 74. The properties of magnets are such that when two magnets are near enough together to exert a mutual influence, those poles which possess like magnetism repel each other, and those which possess unlike magnetism attract each other. The earth is a magnetized body, and acts like a great spherical magnet with poles of unlike magnetism situated within the Arctic and Antarctic circles close to longitudes 97° west and 155° east of Greenwich, respectively. In common with magnets, the earth is surrounded by a region in which magnetic influence is exercised upon the compass, giving the magnetic needle a definite direction in each locality and causing the end which we name the north pole of the compass to be directed in general toward the region of the magnetic pole in the. geographical north and the south end toward the region of the magnetic pole in the geographical south. The north end of the compass — north-seeking, as it is sometimes designated for clearness — will be that end which has opposite polarity to the earth's north magnetic pole, or, otherwise stated, which possesses like magnetism with the earth's south magnetic pole. 75. By reason of the fact that the magnetic pole in each hemisphere differs in geographical position by a large and unequal amount from the geographical pole, we are made aware that the earth is not magnetized symmetrically with reference to the geographical poles. Hence the directive influence of the earth's magnetism will not in general cause the compass needle to pomt in the direction of the true meridian, but each compass point will differ from the corresponding true point by an amount varying according to the geographical locality. The angle representing this difference is the Variation of the Compass, sometimes also called the Magnetic Declination. It is the angle between the plane of the true meridian and a vertical plane passing through a freely suspended magnetic needle influenced solely by the earth's magnetism. The variation not only changes as one travels from place to place on the earth, being different in different localities, but in every locahty, besides the minor periodic movements of the needle known as the diurnal, monthly, and annual variations, which are not of material concern to the mariner, there is a progressive change which extends through centuries of time and amounts to large alterations in the pointing of the compass. In taking account of the effect produced by the variation of the compass, the navigator must therefore be sure that the variation used is correct not only for the place, but also for the time under consideration. Occasionally the magnetic needle is subject to spasmodic fluctuations of the earth's magnetism lasting from a brief period to several days. These are called magnetic storms, and are due to sudden changes in the electric currents which cir- culate within the earth and in the region surrounding the earth. They come appar- entlj^ at random, and^ may occur nearly simultaneously over the whole world or be restricted to a certain region. The range of their effect upon the compass does not often exceed the half of a degree in the lower latitudes, and hence the navigator need only be concerned with them in the higher latitudes where he may look to the aurora as an indication of their occurrence. 76. Besides the error thus produced in the indications of the compass, a further one, due to Local Attraction, ma,j arise from extraneous influences due to natural magnetic attraction in the vicinity of the vessel. Instances of this are quite common 36 THE COMPASS EKROB. 37 when a ship is in port, as she may be in close proximity to vessels, docks, machinery, or other masses of iron or steel. It is also encountered in the shallow waters of the sea in localities where the mineral substances in the earth itself possess magnetic qualities — as, for example, at certain places in Lake Suj)erior and at others oflF the coast of Australia. When due to the last-named cause, it may be a source of great danger to the mariner, but, fortunately, the number of localities subject to local attraction is limited. The amount of this error can seldom be determined except by survey; if known, it might properly be included with the variation and treated as a pai't thereof. 77. In addition to the variation, the compass ordinarily has a still further error in its indications, which arises from the effect exerted upon it by masses of magnetic metal within the ship itself. This is known as the Deviation of the Compass. For reasons that will be explained later, it differs in amount for each heading of the ship, and, further, the character of the deviations undergoes modification as a vessel proceeds from one geographical locality to another. APPLYING THE COMPASS ERROR. 78. From what has been explained, it may be seen that there are three methods by which bearings or courses may be expressed: (a) true, when they refer to the angular distance from the earth's geographical meridian; (b) magnetic, when they refer to the angular distance from the earth's magnetic meridian, and must be cor- rected for variation to be converted into true; and (c) hy compass, when they refer to the angular distance from the north indicated by the compass on a given heading of the ship, and must be corrected for the deviation on that heading for conversion to magnetic, and for both deviation and variation for conversion to true bearings or courses. The process of applying the errors under all circumstances is one of which the navigator must make mmself a thorough master; the various problems of con- version are constantly arising; no course can be set nor bearing plotted without involving the application of this problem, and a mistake in its solution may produce serious consequences. The stuaent is therefore urged to give it his most careful attention. 79. When the effect of a compass error, whether arising from variation or from deviation, is to draw the north end of the compass needle to the right, or eastward, the error is named east, or is marked + ; when its effect is to draw the north end of the needle to the left or westward, it is named west, or marked — . Figures 7 and 8 represent, respectively, examples of easterly and westerly errors. In both cases consider that the circles represent the observer's horizon, N and S being the correct north and south points in each case. If N' and S' represent the corresponding points indicated by a compass whose needle is deflected by a compass error, then in the first case, the north end of the needle being drawn to the right or east, the error will be easterly or positive, and in the second case, the north end of the needle being drawn to the left or west, the compass error will be westerly or negative. 38 THE COMPASS ERROR. Considering figure 7, if we assume the easterly error to amount to one point, it will be seen that if a direction of N. by W. is indicated by the compass, the correct direction should be north, or one point farther to the right. If the compass indicates north, the correct bearing is N. by E.; that is, still one point to the right. If we follow around the whole card, the same relation wUl be found in every case, the corrected bearing being always one point to the right of the compass bearing. Conversely, if we regard figure 8, assuming the same amount of westerly error, a compass bearing of N. by E. is the equivalent of a correct bearing of north, which is one point to the left; and this rule is general throughout the circle, the corrected direction being always to the left of that shown by the compass. 80. Having once satisfied himseK that the general rule holds, the navigator may save the necessity of reasoning out in each case the direction in which the error must be applied, and need only charge his mind with some single formula which will cover all cases. Such a one is the following: When the correct direction is to the right, the error is east. The words correct-right-east, in such a case, would be the key to all of his solutions. With easterly error, if he had a compass course to change to a corrected one, he would know that to obtain the result the error must be applied to the right; and, if it were desired to change a correct course to one indicated by compass, the error would be applied to the left. If a correct bearing is to be compared with a compass bearing to find the compass error, when the correct bearing is to the right, the error is easterly; and when the correct bearing is to the left, the error is westerly. 81. It must be remembered that the word east is equivalent to right in dealing with the compass error, and west to left, even though they involve an apparent departure from the usual rules. If a vessel steers NE. by compass with one point easterly error, her corrected course is NE. by E.; but if she steers SE., the corrected course is not SE. by E., but SE. by S. Another caution may be necessary to avoid confusion; the navigator should always regard himself as facing the point under consideration when he applies an error; one point westerly error on South will bring a corrected direction to S. by E.; but if we applied one point to the left of South while looking at the compass card in the usual way — north end up- — S. by W. would be the point arrived at, and a mistake of two points would be the result. 82. In the foregoing explanation reference has been made to ' 'correct" directions and "compass errors" without specifying "magnetic" and "true" or "variation" and "deviation." This has been done in order to make the statements apply to all cases and to enable the student to grasp the subject in its general bearing without confusion of details. Actually, as has already been pointed out, directions given may be true, magnetic, or by compass. By applying variation to a magnetic bearing we correct it and make it true, by applying a aeviation to a compass bearing we correct it to magnetic, and by applying to it the combined deviation and variation we correct it to true. Wliich- ever of these operations is undertaken, and whichever of the errors is considered, the process of correction remains the same ; the correct direction is always to the right, when the error is east, by the amount of that error. Careful study of the following examples will aid in making the subject clear: Examples: A bearing taken by a compass free from deviation is 76°; variation, 5° W.; required the true bearing. 71°. A bearing taken by a similar compass is NW. by W. ^ W.; variation, \ pt. W.; required the true bearing. NW. by W. | W. A vessel steers 153° by compass; deviation on that heading, 3° W.; variation in the locality, 12° E.; required the true course. 162°. A vessel steers S. by W, ^ W.; deviation, \ pt. W.; variation, 1 pt. E.; required the true course. SSW. \ W. It is desired to steer the magnetic course 322°; deviation, 4° E.; required the course by compass. 318°. The true course between two points is found to be W. "^ N.; variation, \\ pt. E.; no deviation; required the compass course. W. f S. True course to be made, 55°; aeviation, 7° E.; variation, 14° W.; required the course by compass. 62°. THE COMPASS EBROB. 39 A vessel passing a range whose direction is known to be 200°, magnetic, observes the bearing by compass to be 178°; required the deviation. 22° E. The sun's observed bearing by compass is 91°; it is found by calculation to be 84° (true); variation, 8° W.; required the deviation. 1° E. FINDING THE COMPASS ERROR. 83. The variation of the compass for any given locality is found from the charts. A nautical chart always contains information from which the navigator is enabled to ascertain the variation for any place within the region embraced and for any year. Beside the information thus to be acquired from local charts, special charts are published showing the variation at all points on the earth's surface. 84. The deviation of the compass, varying as it does for every ship, for every heading, and for every geographical locality, must be determined by the navigator, for which purpose various metnods are available. Whatever method is used, the ship must be swung in azimuth and an observa- tion made on each of the headings upon which the deviation is required to be known. If a new iron or steel ship is being swung for the first time, observations should be made on each of the twenty-four 15° rhumbs into which the compass card is divided. At later swings, especiall}^ after correctors have been applied, or in the case of wooden ships, twelve 15° rhumbs will suffice — or, indeed, only six. In case it is not prac- ticable to make observations on exact 15° rhumbs, they should be made as near thereto as practicable and plotted on the Napier diagram (to be explained hereafter), whence the deviations on exact 15° rhumbs may be found. 85. In swinging ship for deviations the vessel should be on an even keel and all movable masses of iron in the vicinity of the compass secured as for sea, and the com- pass accurately centered in the binnacle. The vessel, upon being placed on any head- mg, should be steadied there for three or four minutes before the observation is made, in order that the compass card may come to rest and the magnetic conditions assume a settled state. To assure the greatest accuracy the ship should first be swung to starboard, then to port, and the mean of the two deviations on each course taken. Ships may be swung under their own steam, or with the assistance of a tug, or at ancnor, where the action of the tide tends to turn them in azimuth (though in this case it is difficult to get them steadied for the requisite time on each heading), or at anchor, by means of springs and hawsers. 86. The deviation of all compasses on the ship may be obtained from the same swing, it being required to make observations mth tne standard only. To accomplish this it is necessary to record the ship's head by all compasses at the time of steadying on each even rhumb of the standard; applying the deviation, as ascertained, to the heading by standard, gives the magnetic heads, with which the direction of the ship's head by each other compass may be compared, and the deviation thus obtained. Then a complete table of deviations may be constructed as explained in article 94. 87. There are four methods for ascertaining the deviations from swinging; namely, by reciprocal hearings, by hearings of the sun, by ranges, and by a distant ohject. 88. Reciprocal Bearings. — One observer is stationed on shore with a spare compass placed in a position free from disturbing magnetic influences; a second observer is at the standard compass on board ship. At the instant when ready for observation a signal is made, and each notes the bearing of the other. The bearing by the shore compass, reversed, is the magnetic bearing of the shore station from the ship, and the difference between this and the bearing by the ship's standard compass represents the deviation of the latter. In determining the deviations of compasses placed on the fore-and-aft amidship line, when the distribution of magnetic metal to starboard and port is symmetrical, the shore compass may be replaced by a dumb compass, or pelorus, or by a theodolite in which, for convenience, the zero of the horizontal graduated circle may be termed north; the reading of the shore instrument wUl, of course, not represent magnetic directions, but by assuming that they do we obtain a series of fictitious deviations, the mean value of which is the error common to all. Upon deducting this error from each of the fictitious deviations, we obtain the correct values. 40 THE COMPASS EBBOB. If ship and shore observers are provided with watches which have been com- pared with one another, the times may be noted at each observation, and thus afford a means of locating errors due to misunderstanding of signals. 89. Bearings of the Sun. — In. this method it is required that on each heading a bearing of the sun be observed by compass and the time noted at the same moment by a chronometer or watch. By means which will be explained in Chapter XIV, the true bearing of the sun may be ascertained from the known data, and this, compared with the compass bearing, gives the total comjiass error; deducting from the compass error the variation, there remains the deviation. The variation used may be that given by the chart, or, in the case of a compass affected only by symmetrically placed u'on or steel, may be considered equal to the mean of all the total errors. Other celestial bodies may be observed for this purpose in the same manner as the sun. This method is important as being the most convenient one available for deter- mining the compass error at sea. When adjusting compasses much time will be saved by this simple modification of a detail: Instead of tabulating magnetic azimuths for given stated times in advance, draw on cross-section paper a curve whose ordinates are minutes of local apparent time and whose abscissae are degrees of magnetic azimuth, that is, true azimuth corrected for variation. Then for any given instant (the navigator's watch being set to local apparent time) the magnetic azimuth may be read directly from the curve. The difference between the magnetic azimuth of the sun and its compass bearing is, of course, the deviation of the compass on that particular heading. 90. Ranges. — In many localities there are to be found natural or artificial range marks which are clearly distinguishable, and which when in line lie on a known magnetic bearing. By steaming about on different headings and noting the compass bearing of the ranges each time of crossing the line that they mark, a series of devia- tions may be obtained, the deviation of each heading being equal to the difference between the compass and the magnetic bearing. 91. Distant Object. — A conspicuous object is selected which must be at a con- siderable distance from the ship and upon which there should be some clearly defined point for taking bearings. The direction of this object by compass is observed on successive headings. Its true or magnetic bearing is then found and compared with the compass bearings, whence the deviation is obtained. The true or the magnetic bearing may be taken from the chart. The magnetic bearing may also be found by setting up a compass ashore, free from foreign magnetic disturbance, in range with the object and the ship, and observing the bearing of the object; or the magnetic bearing may be assumed to be the mean of the compass bearings. In choosing an object for use in this method care must be taken that it is at such a distance that its bearing from the ship does not practically differ as the vessel swings in azimuth. If the ship is swung at anchor, the distance should be not less than 6 miles. If swung under way, the object must be so far that the parallax (the tangent of which may be considered equal to half the diameter of swinging divided by the distance) shall not exceed about 30'. 92. In all of the methods described it will be found convenient to arrange the results in tabular form. In one column record the ship's head by standard compass, and abreast it in successive columns the observations from which the deviation is determined on that heading, and finally write the deviation itself. When the result of the swing has been worked up, another table is constructed showing simply the headings and the corresponding deviations. This is known as the Deviation Table of the compass. If compensation is to be attempted, this table is the basis of the operation; if not, the deviation tables of the standard and steering compass should be posted in such place as to be accessible to all persons concerned with the naviga- tion of the ship. THE COMPASS ERROR. 41 93. Let it be assumed that a deviation table has been found and that the values are as follows: Deviation table. Ship's head by standard compass. Deviation, North 15 30 NE 45 60 75 East : 90 105 120 SE 135 150 165 -15 29 -14 53 -13 16 -11 19 - 9 69 - 9 42 - 9 06 - 9 01 - 7 - 5 - 2 51 54 16 + 8 29 Ship's head by standard compass. South 180 195 210 SW 225 240 255 West 270 285 300 NW 315 330 345 DeviatioE . +17 52 +23 47 +27 07 +25 35 +21 57 +15 54 + 9 56 + 1 56 - 4 09 -10 20 -13 37 -16 01 We have from the table the amount of deviation on each compass heading; therefore, knowing the ship's head by compass, it is easy to pick out the corresponding deviation and thus to obtain the magnetic neading. But if we are given the magnetic direction in which it is desired to steer and have to find the corresponding compass course, the problem is not so simple, for we are not given deviations on magnetic heads, and where the errors are large it may not be assumed that thev are the same as on the corresponding compass headings. For example, with the deviation table just given, suppose it is required to determine the compass heading corresponding to 165°, magnetic. The deviation corresponding to 165°, per compass, is +8^°. If we apply this to 165°, magnetic, we have 156^ as the compass course. But, consulting tne table, it may be seen that the deviation correspondmg to 156^°, per compass, is +2\°, and therefore if we steer that course the magnetic direction will be 159°, and not 165°, as desired. A way of arriving at the correct result is to make a series of trials until a course is arrived at which fulfills the conditions. Thus, in the example given: First trial. Mag. course desired 165° Trydev. on 165° 8^° E. Trial comp. course. Dev. onl56i° 156i= 2J= Second trial. Mag. course desired 165° Try dev. on 160° 5° E. Trial comp. course 160° Dev. on 160° 5° Mag. course made good 165° This happens to be exactly the compass course required. But it often occurs that further trials may be necessary. Mag. course made good 159° Since this assumption carries the course 6° too far to the left, assume next a deviation on a course 3^° farther to the right than the one used here. 94. The Napier Diagram. — A much more expeditious method for the solution of this problem is afforded by the Napier Diagram, and as that diagram also f aciUtates a number of other operations connected with compass work it should be clearly understood by the navigator. This admits of a graphic representation of the table of deviations of the compass by means of a curve ; besides furnishing a readj means of converting compass into magnetic courses and the reverse, one of its chief merits is that if the deviation has been determined on a certain number of head- ings it enables one to obtain the most probable value of the deviation on any other course that the ship may head. The last-named feature renders it useful in making a table of deviations oi compasses other than the standard when their errors are found as described in article 86. 95. The Napier diagram (fig. 9) represents the margin of a compass card cut at the north point and straightened into a vertical line; for convenience, it is usually divided into two sections, representing, respectively, the eastern and western semi- circles. The vertical line is of a convenient length and divided into twenty-four equal parts corresponding to the 15° rhumbs of the compass, beginning at the top 42 THE COMPASS ERROR. with North and continuing around to the right; it is also divided into 360 degrees, which are appropriately marked. To obtain a complete curve, a sufficient number of observations should be taken while the ship swings through an entire circle. Generally, observations on every alternate 15° rhumb are enough to establish a good curve, but in cases where the maximum deviation reaches 40° it is preferable to observe on every 15° rhumb. CempaM eeursas en dotted liaes. Magnetic eeunes on solid Bnet. FROM 0° NORTH TO 180° SOUTH DEVIATION EAST FROM 180° SOUTH TO 360° NORTH DEVIATION DEVIATION WEST soum EAST Curv* of Total Oeviation Curve of Semicircular Component Curve of Quadraniat Component Fig. 9. ITie cfurve shown in the full line on figure 9 corresponds to the table of deviations given in article 93. From a given compass course to find the corresponding magnetic course, through the point of the vertical Hne representing the given compass course draw a line parallel to the dotted lines until the curve is intersected, and from the point of intersection draw another line parallel to the plain Hues; the point on the scale where this last THE COMPASS EEROE. 43 line cuts the vertical line is the magnetic course sought. The correctness of this solution will be apparent when we consider that the 60° triangles are equilateral, and therefore the distance measured along the vertical side will equal the distance meas- ured along the inclined sides — that is, the deviation; and the direction will be correct, for the construction is such that magnetic directions will be to the right of compass directions when the deviation is easterly and to the left if westerly. From a given magnetic course to find the corresponding compass course, the process is the same, excepting that the first line drawn should follow, or be parallel to, the plain lines, and tne second, or return Hne, should be parallel to the dotted; and a proof similar to that previously employed will show the correctness of the result. As an example, the problem given in article 93 may be solved by the diagram, and the result will be found to accord with the solution previously ^veji. The vertical line is intersected at each 15° rhumb by two Imes inclined to it at an angle of 60°, that line which is inclined upward to the right being drawn plain and the other dotted. To plot a curve on the Napier diagram, if the deviation has been observed with the ship's head on given compass courses (as is usually the case with the standard compass), measure off on the vertical scale the number of degrees corresponding to the deviation and lay it down — to the right if easterly and to the left if westerly — on the dotted line passing through the point representing the ship's head; or, if the observation was not made on an even 15° rhumb, then lay it down on a line drawn parallel to the dotted ones through that division of the vertical line which represents the compass heading; if the deviation has been observed with the ship on given magnetic courses (as when deviations by steering compass are obtained by noting the ship's head during a swing on even 15° rhumbs of the standard), proceed in the same way, excepting that the deviation must be laid down on a plain line or a line parallel thereto. ^ Mark each point thus obtained with a dot or small circle, and draw a free curve passing, as nearly as possible, through all the points. THE THEORY OF DEVIATION.a 96. Features of the Earth's Magnetism. — It has already been stated that the earth acts like a great spherical magnet, with a pole in each hemisphere which is not coincident with the geographical pole; it has also a magnetic equator which lies close to, but not coincident with, the geographical equator. A magnetic needle freely suspencled at a point on the earth's surface, and undisturbed by any other than the earth's magnetic influence, will lie in the plane of the magnetic meridian and at an an^le with the horizon depending upon the geographical position. The magnetic elements of the earth which must be considered are shown in figure 10. The earth's total force is represented in direction and intensity by the Hne AB. Since compass needles are mechanically arranged to move only in a horizontal plane, it oecomes necessary, when investigating the effect of the earth's magnetism upon them, to resolve the total force into two components which in the figure are represented by AC and AD. These are known, respectively, as the horizontal and vertical components of the earth's total force, and are usually designated as H and Z. The angle CAB, which the line of direction makes with the plane o the horizon, is called the magnetic inclination or dip, and denoted by 6. It is clear that the horizontal component will reduce to zero at the magnetic poles, where the needle points directly downward, and that it will reach a maximum o As it is probable that the student will not have practical need of a knowledge of the theory of deviation and the compensation of the compass until after he has mastered all other subjects pertaining to Navigation and Nautical Astronomy, it may be considered preferable to omit the remainder of this chapter at first and return to it later. K>rizontal Force »H 44 THE COMPASS ERROR. at the magnetic equator, where the free needle hangs in a horizontal direction. The reverse is true of the vertical conrponent and of the angle of dip. Values representing these diflferent terms may be found from special charts. 97. Induction; Hard and Soft Iron. — When a piece of unmagnetized iron or steel is brought within the influence of a magnet, certain magnetic properties are immediately imparted to the former, which itseu becomes magnetic and continues to remain so as long as it is within the sphere of influence of the permanent magnet; the magnetism that it acquires under these circumstances is said to be induced, and the properties of induction are such that that end or region which is nearest the pole of the influencing magnet will take up a polarity opposite thereto. If the magnet is withdrawn, the induced magnetism is soon dissipated. If the magnet is brought into Eroximity again, but with its opposite pole nearer, magnetism will again be induced, ut this time its polarity wiU be reversed. A further property is that if a piece of iron or steel, while temporarily possessed of magnetic qualities through induction, be subjected to blows, twisting, or mechanical violence of any sort, the magnetism is thus made to acquire a permanent nature. The softer the metal, from a physical point of view, the more c[uickly and thor- oughly will induced magnetism be dissipated when the source of influence is with- drawn; hard metal, on the contrary, is slow to lose the effect of magnetism imparted to it in any way. Hence, in regarding the different features which affect deviation, it is usual to denominate as hard iron that which possesses retained magnetism of a stable nature, and as soft iron that which rapidly acquires and parts with its mag- netic qualities under the varying influences to which it is subjected. 98. Magnetic Properties Acquired by an Iron or Steel Vessel in Building. — The inductive action of the earth's magnetism affects all iron or steel within its influence, and the amount and permanency of the magnetism so induced depends upon the position of the metal with reference to the earth's total force, upon its character, and upon the degree of hammering, bending, and twisting that it undergoes. An iron bar held in the line of the earth's total force instantly becomes magnetic; if held at an angle thereto it would acquire magnetic properties dependent for their amount upon its incHnation to the line of total force; when held at right angles to the line there would be no effect, as each extremity would be equally near the poles of the earth and aU influence would be neutraUzed. If, whUe such a bar is in a magnetic state through inductive action, it should be hammered or twisted, a certain magnetism of a permanent character is impressed upon it, which is never entirely lost unless the bar is subjected to causes equal and opposite to those that produced the first effect. A sheet of iron is affected by induction in a similar way, the magnetism induced by the earth diffusing itself over the entire plate and separating itseff into regions of opposite polarity divided by a neutral area at right angles to the earth's line of total force. If the plate is hammered or bent, this magnetism takes up a permanent character. If the magnetic mass has a third dimension, and assumes the form of a ship, a similar condition prevails. The whole takes up a magnetic character; there is a magnetic axis in the direction of the line of total force, with poles at its extremities and a zone of no magnetism perpendicular to it. The distribution of magnetism win depend upon the horizontal and vertical components of the earth's force in the locality and upon the direction of the keel in building; its permanency will depend upon the amount of mechanical violence to which the metal has been subjected by the riveting and other incidents of construction, and upon the nature of the metal employed. 99. Causes that Produce Deviation.— There are three influences that operate to produce deviation; namely, {a) sub'permanent jnagnetism; (h) transient rnagnetism induced in vertical soft iron, and (c) transient magnetisnri induced in hori- zontal soft iron. Their effect will be explained. Sub'permanent magnetism is the name given to that magnetic force which origi- nates in the ship while building, through the process explained in the preceding article; after the vessel is launched and has an opportunity to swing in azimuth, the magnetism thus induced wiU suffer material diminution until, after the lapse of THE COMPASS ERROR. 45 a certain time, it will settle down to a condition that continues practically unchanged; the magnetism that remains is denominated subpermanent. The vessel will then approximate to a permanent magnet, in which the north polarity will lie in that region which was north in building and the south polarity (that which exerts an attracting influence on the north pole of the compass needle) in the region which was south in building. Transient magnetism induced in vertical soft iron is that developed in the soft iron of a vessel through the inductive action of the vertical component only of the earth's total force, and is transient in nature. Its value or force m any given mass varies with and depends upon the value of the vertical component at the place, and is proportional to the sine of the dip, being a maximum at the magnetic pole and zero at the magnetic equator. Transient rrmgnetism induced in horizontal soft iron is that developed in the soft iron of a vessel through the inductive action oi the horizontal component oiAj of the earth's total force, and is transient in nature. Its value or force in any given mass varies with and depends upon the value of the horizontal component at the place, and is proportional to the cosine of the dip, being a maximum at the magnetic equator and reducing to zero at the magnetic pole. The needle of a compass in any position on board ship will therefore be acted upon by the earth's total force, together with the three forces just described. The Eoles of these forces do not usually lie in the horizontal plane of the compass needle, ut as this needle is constrained to act in a horizontal plane, its movements will be affected solely by the horizontal components of these lorces, and its direction will be determined by the resultant of those components. The earth's force operates to retain the compass needle in the plane of the magnetic meridian, but the resultant of the three remaining forces, when without this plane, deflects the needle, and the amount of such deflection constitutes the deviation. 100k Classes of Deviation. — Investigation has developjed the fact that the deviation produced as described is made up of tlu-ee parts, which are known respec- tively as semicircular, quadrantal, and constant deviation, the latter being the least important. A clear understanding of the nature of each of these classes is essential for a comprehension of the methods of compensation. 101. Semicircular Deviation is that due to the combined influence, exerted m a horizontal plane, of the subpermanent magnetism of a ship and of the magnetism induced in soft iron by the vertical component of the earth's force. If we regard the effect of these two forces as concentrated in a single resultant pole exerting an attractiug influence upon the north end of the compass needle, it may be seen that there wiU be some heading of the ship whereon that pole will lie due north of the needle and therefore produce no deviation; now consider that, from this position, the ship's head swings in azimuth to the right; throughout aU of the semicircle first described an easterly deviation will be produced, and, after completmg 180°, the pole will be in a position diametericaUy opposite to that from which it started, and wiU again exert no influence that tends to produce deviation. Continuing the swing, throughout the next semicircle the direction of the deviation produced wdl be always to the westward, until the circle is completed and the ship returns to her original neutral position. From the fact that this disturbing cause acts in the two semicircles with equal and opposite effect it is given the name of semicircular deviation. In figure 9 a curve is depicted which shows the deviations of a semicircular nature separated from those due to other disturbing causes, and from this the reason for the name will be apparent. 102, Returning to the two distmct sources from which the semicircular deviation arises, it may be seen that the force due to subpermanent magnetism remains constant regardless of the geographical position of the vessel; but smce the horizontal force of the earth, which tends to hold the needle in the magnetic meridian, varies with the magnetic latitude, the deviation due to subpermanent magnetism varies inversely as the horizontal force, or as yt; this may be readily understood if it is considered that the stronger the tendency to cling to the direction of the magnetic meridian the less will be the deflection due to a given disturbiug force. On the other hand, that part 46 THE COMPASS ERROR. of the semicircular force due to magnetism induced in vertical soft iron varies as the earth's vertical force, which is proportional to the sine of the dip; its effect in producing deviation, as in the preceding case, varies inversely as the earth's horizontal force — that is, inversely as the cosine of the dip; hence the ratio representing the change of deviation arising from this cause on change of latitude is ;^^^, or tan 6. If, then, we consider the change in the semicircular deviation due to a change of magnetic latitude, it will be necessary to separate the two factors of the deviation and to remember that the portion produced by subpermanent magnetism varies as i, and that due to vertical induction as tan d. But for any consideration of the effect of this class of deviation in one latitude only, the two parts may be joined together and regarded as having a single resultant. 103. Assuming that all the forces tending^ to produce semicircular deviation are concentrated in a single pole exerting an influence on the north pole of the compass, it will be seen that this can be resolved into a horizontal and a vertical component, just as the earth's magnetic force is illustrated in figure 10. It is now- evident, therefore, that the horizontal component of this single magnet may be resolved into two components — one fore-and-aft, and one athwartship; in this case, the semi- <>, circular forces wiU be represented by two magnets, one fore- / and-aft and the other athwartship, and compensation may / be made by two separate magnets lying respectively in the directions stated, but with their north or repeUing poles in the position occupied by the south or attracting poles of the ship's force. Figure 11 represents the conditions that have been described. Let O be the center of the compass, XX' and YY', respectively, the fore-and-aft and athwartship Hnes of the ship, and OS the direction in which the attracting pole of the disturbing force is exerted. Now, if OP be laid off on the line OS, representing the amount of the disturbing force according to some convenient scale, then 0& and Oc, respec- tively, represent, on the same scale, the resolved directions of that force in the keel line and in the transverse line of the ship. Each of these resolved forces will exert a maximum effect when acting at right angles to the needle, the athwart- ship one when the ship heads north or south by compass, and the longitudinal one when the heading is east or west. On any other heading than those named the deviation pro- duced by each force will be a fraction of its maximum whose magnitude will depend upon the azimuth of the ship's head. The maximum devia- tion produced, therefore, forms in each case a basis for reckoning all of the various effects of the disturbing force, and is called a coefficient. The coefficient of semicircular deviation produced by the force in the fore-and-aft line is called B, and is reckoned as positive when it attracts a north pole toward the bow, negative when toward the stern; that produced by the athwartship force is C, and is reckoned as positive to starboard and negative to port. These coefl5.cients are expressed in degrees.* 104. The coefficient B is approximately equal to the deviation on East; or to the deviation on West with reversed sign; or to the mean of these two. Thus in the ship having the table of deviations previously given (art. 93), B is equal to -9° 06', or to -9° 56', or to i (-9° 06' -9° 56') = -9° 31'. The coefficient C is approximately equal to the deviation on North; or to the deviation on South with reversed sign; or to the mean of these two. In the example C is equal to -15° 29', or to -17° 52', or to ^ (-15° 29' -17° 52') =- 16° 40'. o It should be remarked that in a mathematical analysis of the deviations, it would be necessary to distinguish between the approximate coefficients, B and C, here described, as als3 A, D, and E, to be mentioned later, and the exact coefficients denoted by the corresponding capital letters of the German alphabet, which latter are in reality the /orccs producing those deviations expressed in terms of the " mean force to north" (Ah), as unit. In the practical discussion of the subject here given, the question of the dif- ference need not be entered into further. Fig. 11. THE COMPASS ERROR. 47 105. The value of the subpermanent magnetism remaining practically constant under all conditions, it will not alter when the ship changes her latitude; but that due to induction in vertical soft iron undergoes a change when, by change of geo- graphical position, the vertical component of the earth 3 force assumes a different value, and in such case the correction by means of one or a pair of permanent magnets will not remain effective. If, however, by series of observations in two magnetic latitudes, the values of the coefficients can be determined under the diflfering cir- cumstances, it is possible, by solving equations, to determine what effect each force has in producing the semicircular deviation; having done which, the subpermanent magnetism can be corrected by permanent magnets after the method previously described, and the vertical induction in soft iron can be corrected by a piece of vertical soft iron placed in such a position near the compass as to produce an equal but opposite force to the ship's vertical soft iron. This last corrector is called a Flinders bar. Having thus opposed to each of the component forces a corrector of magnetic character identical with its own, a change of latitude will make no difference m the effectiveness of the compensation, for m every case the modified conditions will produce identical results m the disturbing and in the correcting force. 106. Quadrantal Deviation is that which arises from horizontal induction in the soft iron of the vessel through the action of the horizontal component of the earth's total force. Let us consider, in figure 12, the effect of any piece of soft iron which is symmetrical with respect to the compass — that is, which lies wholly within a plane passing through the center of the needle in either a fore-and-aft or an athwartship direction. It may be seen (a) that such iron produces no deviation on the cardinal points (for on north and south headings the fore- and-aft iron, though strongly magnetized, has no tendency to draw the needle from a north-and-south line, while the athwartship iron, being at right angles to the meridian, receives no magnetic induction, and therefore exerts no force; and on east and west headings similar conditions prevail, the athwart- ship and the fore-and-aft iron having simply ex- changed positions); and (6) the direction of the deviation produced is opposite in successive quad- rants. The action of unsymmetrical soft iron is f>«- 12. not quite so readily apparent, but investigation shows that part of its effect is to produce a deviation which becomes zero at the inter-cardinal points and is of oppo- site name in successive quadrants. From the fact that deviations of this class change sign every 90° throughout the circle, they gain the name of quadrantal devi- ations. One of the curves laid down in the Napier diagram (fig. 9) is that of quad- rantal deviations, whence the nature of this disturbance of the needle may be observed. 107. All deviations produced by soft iron may be considered as fractions of the maximum deviation due to that disturbing influence; and consequently the maximum is regarded as a coefficient, as in the case of semicircular deviations. The coefficient due to symmetrical soft iron is designated as D, and is considered positive when it produces easterly deviations in the quadrant between North and East; the coefficient of deviations arising from unsymmetrical soft iron is called E, and is reckoned as positive when it produces easterly deviations in the quadrant between NW. and NE.; this latter attains importance only when there is some marked inequality in the distribution of metal to starboard and to port, as in the case of a compass placed off the amidship line. 108. D is approximately equal to tne mean of the deviations on NE. and SW.; or to the mean of those on SE. and NW., with sign reversed; or to the mean of those means. In the table of deviations given in article 93, D is equal to ^(— 11° 19' + 25° 35')=+7°08^o^toi( + 5°54' + 10°200=+8°07';ortoi(7°08' + 8°07')7=+7°37^ By reason of the nature of the arrangement of iron in a ship, D is almost invariably positive. 48 THE COMPASS ERROK. E is approximately equal to the mean of the deviations on North and South ; or to the mean of those on East and West with sign reversed ; or to the mean of those means. In the example, E is equal to ^ (-15° 29' + 17° 52')= +1° 11'; or to i ( + 9°06'-9°560=-0°25'; or to i ( + 1° ll'-0° 25') = +0° 23'. 109. Quadrantal deviation does not, like semicircular, undergo a change upon change of magnetic latitude ; being due to induction in horizontal soft iron, the magnetic force exerted to produce it is proportional to the horizontal component of the earth's magnetism; but the directive force of the needle likewise depends upon that same component ; consequently, as the disturbing force exerted upon the needle increases, so does the power that holds it in the magnetic meridian, with the result that on any given heading the deflection due to soft iron is always the same. 110. Quadrantal deviation is corrected by placing masses of soft iron (usually two hollow spheres in the athwartship line, at equal distances on each side of the compass) , with the center of mass in the horizontal plane of the needle. The distance is made such that the force exerted exactly counteracts that of the ship's iron. As the correcting effect of this iron will, like the directive force and the quadrantal disturbing force, vary directly with the earth's horizontal component, the compen- sation once properly made will be effective in all latitudes ; provided that the compass needles are short and, consequently, exercise little or no induction on the quadrantal correctors. With compasses such as the United States Navy standard T^-inch liquid compass, the needles of which are long and powerful, it wUl usually be found that the position of the spheres must be changed wdth change of latitude. This may be accounted for by the magnetism induced in the spheres by the compass needles at the same time and in the same manner as the earth's force. In this case the quadrantal correcting force is the resultant of the constant force due to the induction of the needles in the spheres and the variable force (the earth's horizontal force, H, varying with change in magnetic latitude) due to the induction of the earth in the spheres. This resultant of these two forces is a variable force, and, after a given quadrantal deviation is corrected in one latitude by this force, the balance will be changed upon going into another latitude and the correction wUl fail to hold good. In practice, the quadrantal deviation due to unsymmetrical iron is seldom corrected; the correction may be accomplished, however, by placing the soft iron masses on a line which makes an angle to the athwartship line through the center of the card. 111. Constant Deviation is due to induction in horizontal soft iron unsym- metrically placed about the compass. It has aheady been explained that one effect of such iron is to produca a quadrantal deviation, represented by one coefficient E ; another effect is the constant deviation, so called because it is uniform in amount and direction on every heading of the ship. If plotted on a Napier diagram, it would appear as a straight line parallel with the initial line of the diagram. 112. Like other classes of deviation, the effect of the disturbing force is repre- sented by a coefficient ; this coefficient is designated as A, and is considered plus for easterly and minus for westerly errors. It is approximately equal to the mean of the deviations on any number of equidistant headings. In the case previously given, it might be found from the four headings, North, East, South, and West, and would then be equal to i (-15° 29' -9° 06' + 17° 52' + 9° 56') = +0° 48'; or from all of the 24 headings, when it would equal —0° 01'. For the same reason as in the case of E, the value of A is usually so small that it may be neglected; it only attains a material size when the compass is placed off the midship hne, or for some similar cause. 113. Like quadrantal deviation, since its force varies with the earth's horizontal force, the constant deviation will remain uniform in amount in all latitudes. (See art. 110.) No attempt is made to compensate for this class of error. 114. Coefficients. — The chief value of coefficients is in mathematical analyses of the deviations and their causes. It may, however, be a convenience to the practical navigator to find their approximate values by the methods that have been given, in order that he may gain an idea of the various sources of the error, with a view to ameliorating the conditions, when necessary, by moving the bionacle or altering the THE COMPASS EEKOK. 49 surrounding iron. The following relation exists between the coefficients and the deviation: d = A-\-B sin z' +C cos s'+D sm 20'+E cos 22', where d is the deviation, and z' the ship's heading by compass, measured from compass North. 115. Mean Directive Force. — The effect of the disturbing forces is not confined to causing deviations; it is only those components acting at right angles to the needle which operate to produce deflection; the effect of those acting in the direction of the needle is exerted either in increasing or diminishing the directive force of the compass, according as the resolved component is northerly or southerly. It occurs, with the usual arrangement of iron in a vessel, that the mean effect of this action throughout a complete swing of the ship upon all headings is to reduce the directive force — that is, while it varies with the heading, the average value upon all azimuths is minus or southerly. The result of such a condition is unfavorable from the fact that the compass is thus made more "sluggish," is easily disturbed and does not return quickly to rest, and a given deflecting force produces a greater deviation when the directive force is reduced. The usual methods of compensation largely correct this fault, but do not entirely do so; it is therefore the case that the mean combined horizontal force of earth and ship to north is generaUy less than the horizontal force of the earth alone ; but it is only m extreme cases that this deficiency is serious. 116. Heeling Error. — This is an additional cause of deviation that arises when the vessel heels to one side or the other. Heretofore only those forces have been considered which act when the vessel is on an even keel; but if there is an incli- nation from the vertical certain new forces arise, and others previously inoperative become effective. These forces are (a) the vertical component of the subpermanent magnetism acquired in building; (b) the vertical component of the induced magnetism in vertical soft iron, and (c) the magnetism induced by the vertical component of the earth's total force in iron which, on an even keel, was horizontal. The first two of these disturbing causes are always present, but, when the ship is upright, have no tendency to produce deviation, simply exerting a downward pull on one of the poles of the needle; the last is a new force that arises when the vessel heels. The maximum disturbance due to heel occurs when the ship heads North or South. When heading East or West there wiU be no deviation produced, although the directive force of the needle wiU be increased or diminished. The error will increase with the amount of inclination from the vertical. 117. For the same reason as was explained in connection with semicircular deviations, that part of the heeling error due to subpermanent magnetism will vary, on change of latitude, as ^, while that due to vertical induction will vary as tan d. In south magnetic latitude the effect of vertical induction will be opposite in direction to what it is in north latitude. 118. The heeling error is corrected by a permanent magnet placed in a vertical position directly under the center of the compass. Such a magnet has no effect upon the compass when the ship is upright ; but since its force acts in an opposite direction to the force of the ship which causes heeling error, is equal to the latter in amount, and is exerted under the same conditions, it affords an effective compensation. For similar reasons to those affecting the compensation of B and C, the correction by means of a permanent magnet is not general and must be rectified upon change of latitude. PBACTICAIi COMPENSATION. 119. In the course of explanation of the different classes of deviation occasion has been taken to state generally the various methods of compensating the errors that are produced. The practical methods of applying the correctors wiU next be given. 120. Order of Correction. — The following is the order of steps to be followed in each case. It is assumed that the vessel is on an even keel, that the compass is properly centered in the binnacle, that aU surrounding masses of iron or steel are in their normal positions, all correctors removed, and that the binnacle is one in which 21594°— 14 4 50 THE COMPASS EEROB. the semicircular deviation is corrected by two sets of permanent magnets at right angles to each other. In order to ascertain if the compass is properly centered in the binnacle, the heeling corrector may be temporarily placed m its tube and drawn from its lowest to its highest position ; if no deflection is shown by the needle the compass is prop- erly centered; if not it should be adjusted by the screws provided for the purpose. 1 . Place quadrantal correctors by estimate. 2. Correct semicircular deviation. 3. Correct quadrantal deviation. 4. Swing ship for residual deviations. The heeling corrector may be placed at any time after the semicircular and quadrantal errors are corrected. A Flinders bar can be put in place only after observations in two latitudes. 121. The ship is first placed on some magnetic cardinal point. If North or South, the only force (theoretically speaking) which tends to produce deflection of the needle will be the athwartship component of the semicircular force, whose effect is represented by the coefficient C. It East or West, the only deflecting force will be the fore-and-aft component of the semicircular force, whose effect is represented by the coefficient B. This wiU be apparent from a consideration of the direction of the forces producing deviation, and is also shown by the equation connecting the terms (where A and E are zero) : d = 3 sin s' + C cos z' + D sin 2z'. If the ship is headed North or South, z' being equal to 0° or 180°, the equation becomes d = ± C. If on East or West, z' being 90° or 270°, we have d = ±B. This statement is exact if we regard only the forces that have been considered in the problem, but experience has demonstrated that the various correctors when in place create certain additional forces by their mutual action, and in order to correct the disturbances thus accidentally produced, as well as those due to regular causes, it is necessary that the magnetic conditions during correction shall approximate as closely as possible to those that exist when the compensation is completed ; therefore the quadrantal correctors should first be placed on their arms at the positions which it is estimated that they wiU occupy later when exactly located. An error in the estimate will have but slight effect under ordinary conditions. It should be under- stood that the placing of these correctors has no corrective effect while the ship is on a cardinal point. Its object is to create at once the magnetic field with which we shall have to deal when compensation is perfected. This having been done, proceed to correct the semicircular deviation. If the ship heads North or South, the force producing deflection is, as has been stated, the athwartship component of the semicircular force, which is to be corrected by perma- nent magnets placed athwartships ; therefore enter in the binnacle one or more such magnets, and so adjust their height that the heading of the ship by compass shall agree with the magnetic heading. When this is done all the deviation on that azimuth will be corrected. Similarly, if the ship heads East or West, the force producing deviation is the fore-and-aft component of the semicircular force, and this is to be corrected by entering fore-and-aft permanent magnets in the binnacle and adjusting the height so that the deviation on that heading disappears. With the deviation on two adjacent cardinal points corrected, the semicircular force has been coinpletely compensated. Next correct the quadrantal deviation. Head the ship NE., SE., SW., or NW. The coefficients B and C having been reduced to zero by compensation, and 2z% on the azimuths named, being equal to 90° or 270°, the equation becomes d = ±D. The soft-iron correctors are moved in or out from the positions in which they were placed by estimate until the deviation on the heading (aU of which is due to quadrantal force) disappears. The quadrantal disturbing force is then compensated. 122. Determination op Magnetic Headings. — To determine when a ship is heading on any given magnetic course, and thus to know when the deviation has been corrected and the correctors are in proper position, four methods are available: THE COMPASS ERROR. 51 (a) Swing the ship and obtain by the best available method the deviations on a sufficient number of compass courses to construct a curve on the Napier diagram for one quadrant, and thus find the compass headings corresponding to two adjacent magnetic cardinal points and the intermediate intercardinal point, as North, NE., and East, magnetic." Then put the ship successively on these courses, noting the corresponding headings by some other compass, and when it is desired to head on the various magnetic azimuths during the process of correction the ship may be steadied upon them by the auxiliary compass. Variations of this method will suggest themselves and circumstances may render their adoption convenient. The compass courses corresponding to the magnetic directions may be obtained from observations made with the auxiliary compass itself, or while making observations with another compass the headings "by the auxiliary may be noted and a curve for the latter constructed, as explained, in article 95, and the required headings thus deduced. (6) By the methods to be explained hereafter (Chap. XIV), ascertain in advance the true bearing of the sun at frequent intervals during the period which is to be devoted to the compensation of the compasses; apply to these the variation and obtain the magnetic Dcarings; record the times and bearings in a convenient tabular form, or, better still, plot a curve of magnetic azimuths of the sun on cross section paper, the coordinates being local apparent time and magnetic bearings of the sun, as described in article 89. Set the watch accurately for the local apparent time; then when it is required to steer any given magnetic course, set that point of the pelorus for the ship's head and set the sight vanes for the magnetic bearing of the sun corresponding to the time by watch. Maneuver the ship with the helm until the sun comes on the sight vanes, when the azimuth of the ship s head will be that which is required. The sight vanes must be altered at intervals to accord with the curve or table of times and bearings. (c) Construct a curve or table showing times and corresponding magnetic bearings of the sun, and also set the watch, as explained for the previous method. Then place the sight vanes of the azimuth circle of the compass at the proper angular distance to the right or left of the required azimuth of the ship's head ; leave them so set and maneuver the ship with the nelm until the ima^e of the sun comes on with the vanes. The course will then be the required one. As an example, suppose that the curve or table shows that the magnetic azimuth of the sun at tne time given by the watch is N. 87° E., and let it be required to head magnetic North; when placed upon this heading, therefore, the sun must bear 87° to the right or east of the direction of the ship's head; when steady on any course, turn the sight vane to the required bearing relative to the keel. Il on N. 11° W., for example, turn the circle to N. 76° E.; leave the vane undisturbed and alter course until the sun comes on. The magnetic heading is then North, and adjustment may be made accordingly. (d) When ranges are available, they may be utilized for determining magnetic headings. 123. Summary of Ordinary Corrections. — To summarize, the following is the process of correcting a compass for a single latitude, where magnets at right angles are employed for compensating the semicircular deviation and where the dis- turbances due to unsymmetrical soft iron are small enough to be neglected. First. All correctors being clear of the compass, place the quadrantal correctors in the position which it is estimated that they will occupy when adjustment is com- plete. The navigator's experience wUl serve in making the estimate, or if there seems no other means of arriving at the probable position they may be placed at the middle points of their supports. Second. Steady the ship on magnetic north, east, south, or west, and hold on that heading by such method as seems best. By means of permanent magnets alter the indications of the compass until the heading coincides with the magnetic course. If heading north, magnets must be entered north ends to starboard to correct easterly deviation and to port to correct westerly, and the reverse if heading south. If heading east, enter north ends forward for easterly and aft for westerly deviations, and the reverse if heading west. (Binnacles differ so widely in the methods of carry- ing magnets that details on this point are omitted. It may be said, however, that o This is all that is required for the purposes of compensation, but if there is opportunity it is always well to make a complete swing and obtain a full table of deviations, which may give interesting information of the existing magnetic conditions. 52 THE COMPASS EKKOR. the magnetic intensity of the correctors may be varied by altering either their number or their distance from the compass; generally speaking, several magnets at a dis- tance are to be preferred to a small number close to the compass.) Third. Steady the ship on an adjacent magnetic cardinal point and correct the compass heading by permanent magnets to accord therewith in the same manner as described for the first heading. Fourth. Steady the ship on an intercardinal point (magnetic) and move the quadrantal correctors away from or toward the compass, keeping them at equal distances therefrom, until the compass and magnetic headings comcide. Fifth. If time permits, it is very important that the ship should next be steadied on opposite cardinal and semicardinal points and one-half oi the remaining deviation corrected by changing the position or number of the correctors. The compensation being complete, the navigator should proceed immediately to swing ship and make a table of the residual deviations. Though the remain- ing errors will be small, it is seldom that they will be reduced to zero, and it must never be assumed that the compass may be relied upon without taking the devi- ation into account. Observations on eight equidistant points will ordinarily suffice for this purpose. 124, Compensation of the Compass while Cruising. — Every effort should be made to keep at least the standard and steering compasses compensated, as it is always easier to keep the compasses compensated than to keep a deviation table correct, at hand, and in use. rectangular method. By the following method the compasses may be kept practically compensated and, after the data are once obtained, it requires very little time or trouble. After the first compensation is completed, or while it is bein^ done, head the ship north or south and move the athwartship magnets up exactly 1 inch, noting by the bearing of the sun or of a distant object, the amount and direction of the effect on the coinpass. Then repeat the observation, lowering the magnets 1 inch, and noting the eflfect. Then head the ship east or west and take the same obser- vations with the fore-and-aft magnets. Then head on an intercardinal point and record the effect of moving spheres first in and then out an inch from the correct position. The record would then take this form : Date Latitude Longitude H e On North, raising B magnets (6 bundles) 1 inch (from 9.85 to 8.85) causes 12° 3(/ Easterly deviation, therefore a movement of ^i^ inch causes 1° 15'' Ely. Lowering B magnets (6 bundles) 1 inch (from 9.85 to 10.85) causes 10° 15'' Westerly deviation, therefore a movement of ^nj- inch causes 1° 2'' Wly. On East, raising magnet (2 bundles) 1 inch (from 10.45 to 9.45) causes 8° 15'' Westerly deviation, therefore a movement of ^ inch causes 0° 50' Wly. Lowering magnet (2 bundles) 1 inch (from 10.45 to 11.45) causes 6° 30^ Easterly deviation, therefore a movement of rg- inch causes 0° 39' Ely. On Northeast, moving spheres in 1 inch (from 10.6 to 9.6) causes 4° 15' Westerly deviation, therefore a movement of -rs inch causes 0° 25' Wly. Moving spheres out 1 inch (from 10.6 to 11.6) causes 3° 20^ Easterly deviation, therefore a move- ment of ^ inch causes 0° 20' Ely. If now it is found at any time that there is, say, 1° 45'' Easterly on East, it is evident that raising the C magnets -^ inch will correct it, and careful observations on two adjacent cardinal points and an inter-cardinal point are enough to recompensate. This may ordinarily be done at no expense of time and with little trouble. More confidence may be felt in the result it observations for deviations are afterwards obtained on the four cardinal points and the mean of the results on opposite courses taken for the true value; this must be done if the variation is uncertain. A new set of data observations should be taken after a large change of magnetic latitude, but it will usually be found that the changes are slight. Theoretically the quadrantal deviation, once corrected, should remain at zero. It will usually be found, however, that the position of the spheres must be changed THE COMPASS EEROE. 53 with change of latitude. A convenient way of dealing with this is to construct a curve showing the positions of the spheres for varying values of H. A similar curve showing the position of the heeling magnet is also convenient. Whenever the position of any corrector is changed, a note showing new position, date, latitude, longitude, H and 6 should be made on one of the blank leaves of the compass record. A complete record of this kind will be found of the utmost value in keeping track of the compasses. 125. Correcting the Heeling Error. — The heeling error may be corrected by a method involving computation, together with certain observations on shore. A more practical method, however, is usually followed, though its results may be less precise. The heeling corrector is placed in its vertical tube, N. end uppermost in north latitudes, as this is almost invariably the required direction; the ship being on a course near North or South and rolling, observe the vibrations of the card, which, if the error is material, will be in excess of those due to the ship's real motion in azimuth; slowly raise or lower the corrector until the abnormal vibrations disappear, when the correction will be made for that latitude; but it must be readjusted upon any considerable change of geographical position. In making this observation care must be taken to distinguish the vessel's "yawing" in a seaway from the apparent motion due to heeling error; for this reason it may be well to have an assistant to watch the ship's head and keep the adjuster informed of the real change in azimuth, by which means the latter may better judge the effect of the heeling error. In the case of a sailing vessel, or one which for any reason maintains a nearly steady heel for a continuous period, the amount of the heeling error may be exactly ascertained by obsei-ving the azimuth of the sun, and corrected with greater accuracy than is possible with a vessel which is constantly rolling. 126. Flinders Bar. — The simplest method that presents itself for the placing of the Flinders bar is one which is available only for a vessel crossing the magnetic equator. Magnetic charts of the world show the geographical positions at which the dip becomes zero — that is, where a freely suspended needle is exactly horizontal and where there exists no vertical component of the earth's total ma^etic force. In such localities it is evident that the factor of the semicircular deviation due to vertical induction disappears and that the whole of the existing semicircular deviation arises from subpermanent magnetism. If, then, when on the magnetic equator the compass be carefully compensated, the effect of the subpermanent magnetism will be exactly opposed by that of the semicircular correcting magnets. Later, as the ship departs from the magnetic equator, the semicircular deviation will gradually acquire a material value, which will be known to be due entirely to vertical induction, and if the Flinders bar be so placed as to correct it, the compensation of the compass will be general for all latitudes. In following this method it may usually be assumed that the soft iron of the vessel is symmetrical with respect to the fore-and-aft hne and that the Flinders bar may be placed directly forward of the compass or directly abaft it, disregarding the effect of components to starboard or port. It is therefore merely necessary to observe whether a vertical soft iron rod must be placed forward or abaft the compass to reduce the deviation, and, having ascertained this fact, to find by expteriment the exact distance at which it completely corrects the deviation. The Flinders bar frequently consists of a bundle of soft iron rods contained in a case, which is secured in a vertical position near the compass, its upper end level with the plane of the needles; in this method, the distance remaimng fixed, the intensity of the force that it exerts is varied by increasing or decreasing the number of rods ; this arrangement is more convenient and satisfactory than the employment of a single rod at a variable distance. The United States Navy FUnders bar, Type II, is made of carefully annealed pure soft iron, 2 inches in diameter, total length 24 inches, consisting of pieces 12 mches, 6 inches, 3 inches, 1^ inches, and f inch (2 of these) long. Hardwood blocks of the same dimensions are used to support the proper length of Flinders bar at the top of a fixed brass tube, which is secured ordinarily at the foi-ward end of the bin- nacle in the fore-and-aft hne. 64 THE COMPASS ERROK. It should be noted, however, that it is extremely difficult to get soft iron rods of a satisfactory quaUty, for, after being placed, they seldom fail to take up more or less subpermanent magnetism. This magnetism, duo to shock of gunfire, vibra- tion while cruising or on speed trials, etc., is subject to greater and more erratic changes than that of the harder portion of the hull, and its proximity to the compass intensifies the effect of the variations in its magnetic properties. 127. When it is not possible to correct the compass at the magnetic equator there is no ready practical method by which the Flinders bar may be placed; the operation will then depend entirely upon computation, and as a mathematical analysis of deviations is beyond the scope laid out for this work the details of pro- cedure will not be gone into; the general principles involved are indicated, and students seeking more must consult the various works that treat the subject fully. It has been explained that each coefficient of semicircular deviation (B and C) is made up of a subpermanent factor varying as jr and of a vertical induction factor varying as tan d. If we indicate by the subscripts s and v, respectively, the parts due to each force, we may write the equations of the coefficients: B^BsXjT + BvXtan ^; and C = a X^ + CvX tan^. Now if we distinguish by the subscripts ^ and 2 the values in the first and in the second position of observation, respectively, of those quantities that vary with the magnetic latitude, we have: Bi = B, X jj- + Bv X tan 6^, B2 = BgXtT- + BvXtan^2; and Ci = Cs X JJ- + Cv X tan di, 1^2 ^^ ^s X XT — r '^v X tan t/2- The values of the coefficients in both latitudes are found from the observations made for deviations; the values of the horizontal force and of the dip at each place are known from magnetic charts; hence we may solve the first pair of equations for Bs and By, and the second pair for Cg and Cv ; and having found the values of these various coefficients, we may correct the effects of Bg and C3 by permanent magnets in the usual way and correct the remainder — that due to By and Cy — by the Flinders bar. Strictly, the FHnders bar should be so placed that its repelhng pole is at an angular distance from ahead equal to the "starboard angle" 01 the attracting pole of the vertical induced force, this angle depending upon the coefficients By and Cy; but since, as before stated, horizontal soft iron may usually be regarded as sym- metrical, Cy is assumed as zero and the bar placed in the midship line. 128. To Correct Adjustment on Change of Latitude. — 'The compensation of quadrantal deviation, once properly made, remains effective in all latitudes, except- ing as noted in article 110; but unless a Flinders bar is used a correction of the semicircular deviation made in one latitude will not remain accurate when the vessel has materially changed her position on the earth's surface. With this in mind the navigator must make frequent observations of the compass error during a passage and must expect that the table of residual deviations obtained in the magnetic latitude of compensation will undergo considerable change as that latitude THE COMPASS ERROR. 55 is departed from. The new deviations may become so large that it will be fomid convenient to readjust the semicircular correcting magnets. This process is very simple. When correctors at nght angles are used, provide for steadying the ship, by an auxihary compass or by the pelorus, upon two adjacent magnetic cardinal points (art. 122). Put the ship on heading North or South (magnetic), and raise or lower the athwartship magnets or alter their number until the deviation disappears ; then steady on East or West (magnetic) and similarly adjust the fore-and-ait magnets. Swing ship for a new table of residual deviations. 129. It must be borne in mind that the compensation of the compass is not an exact science and that the only safeguard is unceasing watchfulness on the navi- gator's part. As the ship's iron is partly "hard" and partly "soft," the subper- manent magnetism may change appreciably from day to day, especially in a new ship as the magnetism absorbed in buildmg "shakes out." After a ship has been in service for one or two years, the magnetic conditions may be said to be "settled." They undergo changes, however, to a greater or less extent, on account of the follow- ing influences or conditions: (a) Continuous steaming on one general course for several days, especially in rough weather, or lying alongside a dock on one heading for a long period. (6) Shock of gunfire, even on a ship that has been m commission for more than a year, has been known to introduce an 8° error, which disappeared in the course of a few days. (c) Extensive alterations or repairs in the vicinity of the compass. The use of scaling hammers on a mihtary top caused a 3° change in one of the U. S. S. Con- necticufs compasses. (d) Steaming with boilers (especially under forced draft) whose funnel is near the compass has Deen known to cause a change of more than 10°, the retained mag- netism being "cooked out." (e) On the U. S. S. Oregon, a groimded searchlight circuit caused a change of 9°. (/) Ships have reported changes of as much as 7° when struck by lightning or after passing through very severe thunderstorms. The binnacle fittings must be carefully inspected from time to time, to see that the correctors have not changed position. At least once a year the quadrantal correctors should be examined for polarity. Tliis can be done by movmg them, one at a time, as close to the compass as practicable and then revolving them slowly about the vertical axis; if the compass is deflected, the magnetism should be removed by bringing the sphere to a low red heat and then letting it cool slowly. There is no excuse for large deviations in a standard or steering compass, and they should not he allowed to exist. CHAPTER IV. PILOTING. 130. Piloting, in tlie sense given the word by modern and popular usage, is the art of conducting a vessel in channels and harbors and along coasts, where landmarks and aids to navigation are available for fixing the position, and where the depth of water and dangers to navigation are such as to require a constant watch to be kept upon the vessel's course and frequent changes to be made therein. PUoting is the most important part of navigation and the part requiring the most experience and nicest judgment. An error in position on the high seas may be rectified by later observation, but an error in position while piloting usually results in disaster. Therefore the navigator should make every effort to be proficient in this important branch, bearing in mind that a modern vessel is usually safe on the high seas and in danger when approaching the land and making the harbor. 131. Requisites.' — The navigator should have ready on approaching the land the charts of the coast and the largest scale detail charts of the locality at which he expects to make his landfall, the saOing directions, and the light and buoy list, all corrected for the latest information from the Notices to Mariners and other sources. The usual instruments employed in navigation should be at hand and in good working order. The most important instrument — the sounding machine — should be in place and in order at least a day before the land is to be made. The importance of the sounding machine can not be exaggerated. The latest deviation table for the standard compass must be at hand. 132. Laying the Course. — ^Mark a point upon the chart at the ship's position; then mark another point for which it is desired to steer; join the two by a line drawn with the parallel ruler, and, maintaining the direction of the line, move the ruler until its edge passes through, the center of the compass rose and note the direction. If the compass rose indicates ^^rite directions, this will be the true course; and must be corrected lor variation and deviation (by api)lying each in the opposite direction to its name) to obtain the compass course; ii it is a magnetic rose, the course need be corrected for deviation only. Before putting the ship on any course a careful look should be taken along the line over wmch it leads to be assured that it clears all dangers. 133. Methods of Fixing Position. — ^A navigator in sight of objects whose positions are shown upon the chart may locate his vessel by anyone of the following methods: (a) cross bearings of two known objects; (b) the bearing and distance of a known object; (c) the bearing of a known object and the angle between two known objects; (d) two bearings of a known object separated by an interval of time, with the run during that interval; (e) sextant angles between three known objects. Besides the foregoing there are two methods by which, without obtaining the precise position, the navigator may assure himself that he is clear of any particular danger. These are: (f) the danger angle; (g) the danger bearing. The choice of the method wiU be governed by circumstances, depending upon which is best adapted to prevaiUng conditions. 134:, Cross Bearings of Two Known Objects. — Choose two objects whose Ttosition on the chart can be unmistakably identified and whose respective bearings from the ship differ, as nearly as possible by 90°; observe the bearing of each, either by compass or pelorus, taking one as quickly as possible after the other; see that the ship is on an even keel at the time the observation is made, and, if using the pelorus, be sure also that she heads exactly on the course for wliich the pelorus is set. Correct the bearings so that they will be either true or magnetic, according as they are to be plotted by the true or magnetic compass rose of the chart — that is, if observed by compass, apply deviation and variation to obtain the true bearing, or deviation 56 PILOTING. 57 only to obtain the magnetic ; if observed by pelorus, that instrument should be set for the true or magnetic heading, according as one or the other sort of reading is required, and no further correction will be necessary. Draw on the chart, by means of the parallel rulers, lines which shall pass thiough the respective objects in the dkection that each was observed to bear. As the ship's position on the chart is known to be at some point of each of these lines, it must be at their intersection, the only point that fulfills both conditions. In figure 13, if A and B are the objects and OA and OB the lines passing through them in the observed directions, the ship's position will be at O, their intersection. The plotting of a position from two bearings is greatly facilitated by the use of a plotter devised by Lieut. R. A. Koch, IJnited States Navy, as reference to (^A the compass rose on the chart, the use of parallel rulers, and the drawing of lines on the chart are obviated. A brief description of this plotter and its uses is as follows: All materials except bolt and washers are transparent. A sc[uare (7 by 7 mches) ruled with two series of lines ""^Q/^^ _ J 9 at nght angles about one-half inch apart, and a disk (7^ inches m diameter) marked in degrees are placed on a central hollow bolt of brass and are capable of being clamped together with any degree of friction re- quired. Three arms are placed so as to revolve around tae same hollow bolt and can be clamped together in « ■" any position. In order to plot a position from compass bearmgs of two objects, and lay off a new course, the no. is. zero mark of the disk should be revolved to the East or West of the true North and South line of the square by an amount equal to the compass error in degrees. Two of the arms are then set by the degrees on the disk to the two observed compass bearings. The plotter is then manipulated on the chart untn the two arms intersect the objects observed and the vertical lines on the square are parallel to the meridians of the chart. Mark the point of intersection of the arms by inserting a pencil in the hollow central bolt. An arm may then be swung to intersect any object on the chart and the compass course to that object read from the disk. This plotter can also be used to obtain the error of the compass from bearings of three objects by compass. 135. If it be possible to avoid it, objects should not be selected for cross bearings which subtend an angle at the ship of less than 30° or more than 150°, as, when the lines of bearing approach parallelism, a small error in an observed bearing gives a large error in the result. For a similar reason objects near the ship should be taken in preference to those at a distance. 136. When a third object is available a bearing of that may be taken and plotted. If this line intersects at the same point as the other two (as the bearing OC of the object C in the figure), the navigator may have a reasonable assurance that his "fix" is correct; if it does not, it indicates an error somewhere, and it may have arisen from inaccurate observation, incorrect determination or application of the deviation, or a fault in the chart. 137. What may be considered as a form of this method can be used when only one known object is in sight by taking, at the same instant as the bearing, an altitude of the sun or other heavenly body and noting the time; work out the sight and obtain the Sumner line (as explained in Chapter XV), and the mter- section of this with the direction line from the object will give the observer's position in the same .0 way as from two ten-estrial bearings. 138. Beaeing and Distance of a Known Object. — When only one object is available, the ship's position may be found by observing its bear- ing and distance. Follow the preceding method in j-io ■^^ the manner of taking, correcting, and plotting the bearing; then, on this fine, lay off the distance from the object, which will give the Eoint occupied by the observer. In figure 14, if A represents the object and AO the earing and distance, the position sought wiU be at O. 68 PILOTING. The stadimeter is an instrument, similar to a sextant, employed in the United States Navy, reading directly the distance of the object observed when set for the height of the object. Range-findmg instruments are used in the United States Navy for readily finding the distance of an observed object, and these instruments do not require knowledge of the height of the object. These instruments are accurate for naviga- tional purposes up to ten thousand yards. 139. It is not ordinarily easy to find directly the distance of an object at sea. The most accurate method is when its height is known and it subtends a fair-sized angle from the ship, in which case the angle may be measured by a sextant °' and the distance computed or taken from a table. Table 33 of this work gives distances up to 6 miles, corresponding to various heights and angles. Captain Lecky's ''Danger Angle and Offshore Distance Tables" carries the computation much further. The use of this method at great distances must not be too closely relied upon, as smaU errors, such as those due to refraction, may throw out the results to a material extent, but it affords an excellent approximation; and, as this method of fixing position is eroployed only when no other is available, the best possible approximation has to sumce. In measuring vertical angles, strictness requires that the observation should be so made that the angle at the foot of the object should equal 90° and that the triangle be a right triangle, as OMN, figure 15, where the line OM is truly horizontal, and not as in the triangle O'MN, where the condition is not fulfilled. This error is inappre- ciable, however, save at very close distances, when it may be sufficiently corrected by getting down as low as possible on board the vessel, so that the eye is near the water line. One condition exists, however, where the error is material — that shown in Fig. 15. Fig. 16. figure 16, where the visible shore line is at M', a considerable distance from M, the point vertically below the summit. In this case there is nothing to mark M in the observer's eye, and it is essential that aU angles be measured from a point close down to the water line. If a choice of objects can be made, the best results wall be obtained by observing that one which subtends the greatest angle, as small errors will then have the least effect. 140. There is another method, known as Buckner's method, for determining the distance of an object, which is available under certain circumstances. This consists in observing, from a position aloft, the angle between the object and the line of the sea horizon beyond. By reference to Table 34 will be found the distance in yards corresponding to different angles for various heights of the observer from 20 to 120 feet. The method is not accurate beyond moderate distances (the table being limited to 5,000 yards) and is obviously only available for finding the distance of an isolated object, such as an islet, vessel, or target, over which the horizon may be seen. In employing this method the higher the position occupied by the observer the more precise wiU be the results. 141. In observing small angles, such as those that occur in the methods just described, it is sometim.es convenient to measure them on and off the limb of the sextant. First look at the bottom of the object and reflect the top down into coin- cidence; then look through the transparentpart of the horizon glass at the top and bring the bottom up by its reflected ray. The mean of the two readings \vill be the true angle, the index correction having been eliminated by the operation. 142. When the methods of finding distance by a vertical or a horizon angle are not available, it must be obtained by such means as exist. Estimate the distance by the appearance; take a sounding, and note where the depth falls upon the line a The use of the sextant is explained in Chapter VIII. PILOTING. 59 of bearing; at night, if atmospheric conditions are normal, consider that the distance of a light when sighted is equal to its maximum range of visibiUty, remembering that its range is stated for a height of eye of 15 feet; or employ such method as suggests itself under the circumstances, regarding the result, however, as an approximation only. 143. The Bearing of a Known Object and the Angle between Two Known Objects. — This method is seldom employed, as the conditions always permit of cross bearings bemg taken, and the latter is generally considered preferable. Take a bearing of a known object by compass or pelorus and observe the sextant angle between some two known objects. The line of bearing is plotted as in former methods. In case one of the objects of the observed angle is that whose bearing is taken, the angle is applied, right or left as the case may be, to the bearing; thus giving the direction of the second object, wliich is plotted from the compass rose and parallel rulera. If the object whose bearing is taken is not one of the objects of the angle, lay off the an^le on a three-armed protractor, or piece of tracing paper, and swing it (keeping the legs or lines always over the two objects) until it passes over the line of bearing, which defines the position of the sliip; there will, except in special cases, be two points of interaection of the line with the . circle thus described, and the navigator must know his position / with sufficient closeness to judge which is correct. 144:. Two Beaeings of a Known Object. — This is a most useful method, wliich is frequently employed, certain special / cases arising thereunder being particularly easv of application. A / The process is to take a careful bearing and at tne same moment \/ read the patent log; then, after runiung a convenient distance, V take a second bearing and again read the log, the difference in A^ readings giving the intervening run; when running at a known jV speed, the time interval will also afford a means for determining j N^ the distance run. _ \. The problem is as follows: In figure 17, given OA, the direc- ^ tion of a known object. A, at the fii-st observation; PA, the direction at the second observation ; and OP, the distance trav- \ ersed between the two; to find hS^ the distance at the second \ observation. yiq. n. Knowing the angle POA, the angular distance of the object from right ahead at the first bearing; OPA, the angular distance from right astern at the second bearing; and OP, the distance run; we have by Plane Trigonometry: PAO = 180°-(POA + OPA); and AP = OP X ^f^^?^. smPAO If, as is frequently the case, we desire to know the distance of passing abeam, we have: AQ=APxsinOPA. Tables 5A and 5B give solutions for this problem, the former for intervals of bearing of quarter points, the latter for intervals of two degrees. Tlie first column of each of these tables gives the value of AP, the distance of the ship from the observed object at the time of taking the last bearing, for values of OP equal to unity; that is, for a run between bearings of 1 mile. The second column gives AQ, the distance of the object when it bears abeam, likewise for a value of OP of 1 mile. When the run between bearings is other than 1 mile, the number taken from the table must be used as a multiplier of that run to give the required distance. Example: A vessel steermg north takes a bearing of a light NW. i W.; then runs 4.3 miles, when the bearing is found to be WSW. Required the distance of the light at the time of the second bearing. Difference between course and first bearing, 4^ pts. Difference between course and second bearing, 10 pts. Multiplier from first column, Table 6A, 0.88. 4.3 miles X 0. 88 = 3.8 miles, distance at second bearing. 60 PILOTING. Example: A vessel on a course 128° takes the first bearing of an object at 154°, and the second at 182°, running in the interval 0.8 mile. Required the distance at which she will pass abeam. Difference between course and first bearing, 26° Difference between course and second bearing, 54°. Multiplier from second column. Table 5B, 0.76. 0. 8 mile X 0.76 = 0. 6 mile, distance of passing abeam. 145. As has been said, there are certain special cases of this problem where it is exceptionally easy of application; these arise when the multiplier is eq^ual to unity and the distance run is therefore equal to the distance from the object. When the angular distance on the bow at the second bearing is twice as great as it was at the first bearing, the distance of the object from the ship at second hearing is equal to the run, the multiplier being 1.0. For if, in figure 18, when the ship is in the first position, O, the object A bears a° on the bow, and at the second position, P, 2a°, we have in the triangle APO, observmg that APO = 180° - 2a, and POA = «r; PAO = 180° - (POA + APO), = 180°-(aj + 180°-2a:), = a. Or, since the angles at O and A are equal to each other, the sides OP and AP are equal or the distance at second bearing is equal to the run. This is known as doubling the angle on the how. 146. A case where this holds good is familiar to every navigator as the how and heam hearing, where the first bearing is taken when the object is broad on the bow (four points or 45° from ahead) and the second when it is abeam (eight points or 90° from ahead); in that case the distance at second bearing and the distance abeam are identical and equal to the run between bearings. 147. When the first bearing is 26^° from ahead, and the second 45°, the distance at wTiich the ohject will he passed aheam will equal the run between bearings. This is true of any two such bearings whose natural cotangents differ by unity, and the following table is a collection of solutions of this relation in which the pairs of bearings are such that, when observed in succession from ahead upon the same fixed object, the distance run between the bearings wUl be equal to the distance of the fixed object when it bears abeam, provided that a steady course has been steered, unaffected by current or drift. The marked pairs will probably be found the most convenient ones to use, as they involve whole degrees only. Bearings from ahead. Fig. 18. First. Second. First. Second. First. Second. 20 291 28 48i 37 711 21 31f *29 51 38 74i *22 34 30 53f 39 76| 23 36i 31 56i *40 79 24 38f *32 59 41 8U *25 41 33 61 i 42 83i 26 43^ 34 64i 43 85i 26J 45 35 66f *44 88 *27 46 • 36 69i *45 90 When the fixed object bears as per any entry of the first column, take the time and the reading of the patent log. Repeat this procedure on reaching the bearing of the adjacent entry in the second column. The difference of the patent-log readings will be the distance at which the fixed object will be passed abeam. PILOTING. 61 This general solution includes the 26^°-45° rule as well as the seven-tenths rule to be explained later; furthermore, it has the advantage that the approximate determination of the distance offshore, at which the fixed object will be passed, need not wait for the 45° bearmg. There are two whole-degree pairs by whidi such a determination can be made before the 45° bearing is reached. It is possible to get five whole-degree bearings or observations by the time the fixed object bears 30° forward of the beam, as follows: 22°-34°, 25°-41°, 27°-46°, 29°-51°, 32°-59°. Of these, the last three should be reasonably accurate; the acuteness of the first angle m all such observations accounts for the discrepancies noted in practice. The use of the table given above may be found to be more convenient than the methods of plotting about to be described, and the use of tables 5A and 5B; but it does not take the place of those methods. Tables 5A and 5B cover all combinations of bearings in which the first bearing is taken when the object is 20° or more on the bow. The Seven-tenths Rule. — If bearings of the fixed object be taken at two (2) and four (4) points on the bow (22^° and 45°), seven-tenths (0.7) of therun between bearings will be the distance at which the point will be passed abeam. From the combination of the seven-tenths rule and the 26i°-45° rule, there follows an interesting corollary, i. e., if bearings of an object at 22^° and 26^° on the bow be taken, then seven-thirds (f ) of the distance run in the interval will be the distance when abeam. If a bearing is taken when an object is two points (22^°) forward of the beam and the run until it bears abeam 13 measured, then its distance when abeam is seven- thirds {^) of the run. This rule, particularly, is only approximate. In case the 45° bearing on the bow is lost, in order to find the distance abeam that the object is passed, note the time when the object bears 26^° forward of the beam, and again when it has the same bearing abaft the beam; the distance run in this interval is the distance of the object when it was abeam. To steer an arc course in order to round a light, point, or other object without fixes and be sure the course itseM does not decrease the initial distance: Provided there is no current, stand on course until the light is at the required distance, deter- mined by one or more of the methods described. Immediately bring the light abeam, and do not let it get forward of the beam again, then tne course will not decrease the initial distance. When the light is one-half point abaft the beam again bring it abeam; hold course until it is again one-half point abaft the beam, repeating this pro- cedure until the light is rounded. A polygon is thus circumscribed about the circle, the nearest approach to the light being the radius of the inscribed circle. The number of sides of the polygon may be in- creased indefinitely, so that the light may be rounded, by changing the course just enough to keep the light abeam, after it is first brought abeam. 148. There is a graphic method of solving this problem that is considered by some more convenient than the use of multipliers. Draw upon the chart the lines OA and PA (fig. 19), passing through the object on the two observed bearings; set the dividers to the distance run, OP; lay down the parallel rulers in a direction parallel to the course and move them toward or away from the observed object until some point is found where the distance between the lines of bearing is exactly equal to the distance between the points of the dividers; in the figure this occurs when the rulers lie along the line OP, and therefore O represents the position of the ship at the first bearing and P at the second. For any other positions O'P', 0"P", the condition is not^ fulfilled. 149. Another graphic solution is given by the Mooring and Maneuvering Board and the various modifications of it that are in use among navigators. 150. The method of obtaining position by two bearings of the same object is one of great value, by reason of the fact that it is frequently necessary to locate the ship when there is but one landmark in sight. Careful navigators seldom, if ever. Fig. 19. 62 PILOTING. miss the opportunity for a bow and beam bearing in passing a lighthouse or other well-plotted object; it involves little or no trouble, and always gives a feeling of added security, however little the position may be in doubt. If about to pass an object abreast of which there is a danger — a familiar example of which is when a lignthouse marks a point off which are rocks or shoals — a good assurance of clearance should be obtained before bringing it abeam, either by doubling the angle on the bow, or, if the object be sighted in time, by using any of the pairs of bearings tabulated under article 147. 151. It must be remembered that, however convenient, the fix obtained by two bearings of the same object will be in error unless the course and distance are correctly estimated, the course "made good" and the distance ''over the ground" being req^uired. Difficulty will occur in estimating the exact course when there is bad steermg, a cross current, or when a ship is making leeway; errors in the allowed run will arise when she is being set ahead or back by a current or when the logging is inaccurate. A current directly with the course of the ship, if unallowed for, will give a determination of position too close to the object observed; and a current directly against the course of the ship, if unallowed for, will give a determination of position too far away from the object observed. The existence of such a current will not le revealed by taking more than two successive bearings. All such observa- tions will place the snip on the same apparent course, which course will be parallel to the course made good and to the course steered but in error in its distance from the observed object by an amount dependent upon the ratio of the speed of ship over ground to the speed of ship by log. A current oblique to the course of the ship will give a determination of position which will be erroneous. The existence of such a current but not its amount will he revealed by taking more than two observa- tions; in this case, following the usual method of plotting, the determination resulting from any two successive bearings \\dll fail to agree with the determination from any other two. If, in such a case, the observed bearings be drawn upon the chart and the distances run by log between them be laid down on the scale of the chart upon a piece of paper, a course may be found by trial, upon which course the intervals of run correspond with the intervals between the lines of bearing. The apparent course thus determined, which must always be oblique to the course steered, will be parallel to the course actually being made good, but v/ill be in error in its distance from the observed object by an amount dependent upon the ratio of the speed of ship over the ground to the speed of ship by log. If there is an apparant shortening of the distance run from earlier to later observations, or a shortening of the time if the speed is invariable, there is a component of set toward the fixed object. Therefore, if in a current of any sort, due allowance must be made, and it should be remembered that more dependence can be placed upon a position fixed by simultaneous bearings or angles, when two or more objects are available, than by two bearings of a single object. 152. Sextant Angles between Three Known Objects, — This method, involving the solution of the three-point prohlem, wiU, if the objects be well chosen, give the most accurate results of any. It is largely employed in surveying, because of its precision; and it is especially valuable in navigation, because it is not subject to errors arising from imperfect Imowledgo of the compass error, improper logging, or the effects of current, as are the methods previously described. Three objects represented on the chart are selected and the angles measured with sextants of known index error between the center one and each of the others. Preferably there should be two observers and the two angles be taken simultaneously, but one observer may first take the angle which is changing more slowly, then take the other, then repeat the first angle, and consider the mean of the first and last observations as the value of the first angle. The position is usually plotted by means of the three-armed protractor, or station-pointer (see art. 428, Chap. XVII). Set the right and left angles on the instrument, and then move it over the chart until the three beveled edges pass respectively and simultaneously through the three objects. The center of the mstrument will then mark the ship's position, which may be pricked on the chart or marked with a pencil point through the center hole. When the three-armed protractor is not at hand, the tracing-paper protractor will prove an excellent substitute, and may in some cases be preferable to it, as, for PILOTING. 63 instance, when the objects angled on are so near the observer as to be hidden by the circle of the instrument. A graduated circle printed upon tracing paper permits the angles being readily laid off, but a plain piece of tracing paper may be used and the angles marked by means of a small protractor. The tracmg-paper protractor permits the laying down, for simultaneous trial, of a number of angles, where special accuracy is sought. 163. The three-point problem, by which results are obtained in this method, is : To find a point such that three lines drawn from this point to three given points shall make given angles with each other. Let A, B, and C, in figure 20, be three fixed objects on shore, and from the ship, at D, suppose the angles CDB and ADB are found equal, respectively, to 40° and 60°. With the complement of CDB, 50°, draw the lines BE and CE; the point of intersection will be the center of a circle, on some point of whose circumference the ship must be. Then, with the complement of the angle ADB, 30°, draw the lines AF and BF, meeting at F, which pomt will be the center of another circle, on some point of whose circumference the ship must be. Then D, the point of intersection of the circumference of the two circles, will be the position of the ship. The correctness of tliis solution may be seen as follows: Take the first circle, DBC; in the triangle EBC, the angle at E, the center, equals 180° -2X50° = 2 (90° — 50°), twice the complement of 50°, which is twice the observed angle; now if the angle at the center subtended by the chord BC equals twice the observed angle, then the angle at any point on the cir- cumference subtended by that chord, which equals half the angle at the center, equals the observed angle; so the required condition is fulfilled. Should either of the angles exceed 90°, the excess of the angle over 90° must be laid off on the opposite side of the lines joining the stations. It may be seen that the intersection of the circles becomes less sharp as the centers E and F approach each other; and finally that the problem becomes indeterminate when the centers coincide, that is, when the three observed points and the observer's position all no. 20? fall upon the same circle; the two circles are then identical and there is no intersection; such a case is called a "revolver," because the protractor wUl revolve aroimd the whole circle, everywhere passing through the observed points. The avoidance of the revolver and the employment of large angles and short distances form the keys to the selection of favorable objects. Generally speaking, the observer, in judging which objects are the best to be taken, can picture in his eye the circle passing through the three points and note whether it comes near to his own position. If it does, he must reject one or more of the objects for another or others. It should be remembered that he must avoid not only the condition where the circle passes exactly through his position (when the problem is whoUy indeterminate), but also all conditions approximating thereto, for m such cases the circles will intersect at a very acute angle, and the mevitable small errors of the observation and plotting will produce large errors in the result- ing fix. Without giving an analysis of reasons, which may be found in various works that treat the problem in detail, the following may be enimierated as the general conditions whicn result in a good fix: {a) When the center object of the three lies between the observer and a line joining the other two, or Ues nearer than either of the other two. (&) When the sum of the right and left angles is equal to or greater than 180°. (c) When two of the objects are in range, or nearly so, and the angle to the third is not less than 30°. {d) When the three objects are in the same straight line. 64 PILOTING. Fig. 21. A condition that limits all of these is that angles should be large — at least as large as 30° — excepting in the case where two objects are in range or nearly so, and then the other angle must be of good size. When possible, near objects should be used rather than distant ones. The navigator should not fall into the error of assuming that objects which would give good cuts for a cross bearing are necessarily favorable for the three-point solution. In a revolver, the angle formed by lines drawn from the center object to the other two, added to the sum of the two observed angles, equals 180°. A knowledge of this fact may aid in the choice of objects. If in doubt as to the accuracy with which the angles will plot, a third angle to a fourth object may be taken. Another way to make sure oi a doubtful fix is to take one compass bearing, by means of which even a revolver may be made to give a good position. 154. The Danger Angle. — ^When sailing along a coast, to avoid sunken rocks, or shoals, or danger- ous obstructions at or below the surface of the water, and which are marked on the chart, the navigator may pass these at any desired distance by using what is known as a danger angle, of which there are two kinds, namely, the horizontal and vertical danger angles; the former requires two well-marked objects indicated on the chart, lying in the direction of the coast, and sufficiently distant from each other to give a fair-sized horizontal angle; the latter requires a well-charted object of Imown height. 155. In figure 21, let AMB be a portion of the coast along which a vessel is sailing on the course CD; A and B two prominent objects shown on the chart; S and S' are two outlying shoals, reefs, or dangers. In order to pass outside of the danger S' take the middle point of the danger as a center and the given distance from the center it is desired to pass as radius, and describe a circle. Pass a circle through A and B tangent to the seaward side of the first circle. To do this, it is only neces- sary to join A and B and draw a line perpendicular to the middle of AB, and then ascertain by trial the location of the center of the circle EAB. Measure the angle AEB, set the sextant to this angle, and remembering that AB subtends the same angle at aU points of the arc AEB, the ship will be outside the arc AEB, and clear the danger S', as long as AB does not subtend an angle greater than AEB, to which the sextant is set. At the same time in order to avoid the danger S, take the middle point of the danger S and with the desu'ed distance as a radius de- scribe a circle. Pass a second circle through A and B tangent to this circle at G, measure the angle AGB with a protractor, then, as long as the chord AB subtends an angle greater than AGB, the ship wiU be inside the cir- cle AGB. Therefore, the ship will pass between the dangers S and S' as long as the angle subtended by AB is less than AEB and greater than AGB. 156. The vertical danger angle involves the same general principle, as can be readily seen without explana- tion by reference to the figure 22 in wliich AB represents a vertical object of known height. 157. The Danger Bearing. — This is a method by which the navigator is warned by a compass bearing when the course is leading into danger. Suppose a vessel to be steering a course, as indicated in figure 23, along a coast which must not be /"' /, / / V N / \ / M T 1/^^P^;;;^^ ' \ y y^SeS^ \ \ \ ^V-^ \ \ \ \ \ c \ Fig. 22. PILOTING. 65 approached within a certain distance, the landmark A being a guide. Let the navigator draw through A the line XA, clear of the danger at all points, and note its direction by the compass rose; then let frequent bearings be taken as the ship proceeds, and so long as the bearings, YA, ZA, are to the rigM of XA he may be assured that he is on the left or safe side of the line. If, aa in the case given, there is but one object in sight and that nearly ahead, it would be very difficult to get an exact position, but this method would always show whether or not the ship was on a good course, and would, in consequence, be of the greatest value. And even if there were other objects visible by which to get an accurate fix it would be a more simple matter to note, by an occasional glance over the sightvane of the pelorus or compass, that the sliip was making good a safe course than to be put to the necessity of plotting the position each time. 158. It will occasionally occur that two natural objects will so lie that when in range they mark a danger bearing; advantage should be taken of aU such, as they are easier to observe than a compass bearing; but if in a locaUty with which the navigator has not had previous acquaintance the compass bearing of all ranges should be observed and com- | pared with that indicated on the chart in order to make sure of the identity of the objects. The utility of ranges, either artificial or natural, as guides in navigation, extends also to established lines of bearm^ giving the true or magnetic direc- tion of fixed objects, such as lines of bearing limiting the sectors of navigational Ughts. 159. Soundings. — The practice should be followed of employing one or two leadsmen to take and report soimdings continuously while in shoal water or in the vicinity of dangers. The soundings must not be regarded as fixing a position, but they afford a check upon the positions obtained by other methods. An exact agreement with the soundings on the chart need not be expected, as there may bo some little inaccu- racies in reporting the depth on a ship moving with speed through the water, or the tide may cause a discrepancy, or the chart itself mav lack perfection ; but the soundings snould agree in a general way, and a marked departure from the charac- teristic bottom shown on the chart should lead the navigator to verify his position and proceed with caution ; especially is this true if the water is more shoal than expected. 160. But if the soundings in shallow water when landmarks are in si^ht serve merely as an auxiliary guide, those taken (usually with the patent sounding machine or deep-sea lead) when there exist no other means of locatmg the position, fulfill a much more important purpose. In tliick weather, when approaching or running close to the land, and at all times when the vessel is in less than 100 fathoms of water and her position is in doubt, soundings should be taken continuously and at regular intervals, and, with the character of the bottom, systematically recorded. By laying the soundings on tracing paper, along a line which represents the track of the ship according to the scale oF the chart, and then moving the paper over the chart, keeping the various courses parallel to the correspondmg directions on the chart, until the observed soundings agree with those laid down, the ship's position wUl in general be quite well determined. While some localities, by the sharpness of the characteristics of their soundings, lend themselves better than others to accurate determinations by this method, there are few places where the mariner can not at least keep out of danger by the indications, even if they tell him no more than that the time Has come when he must anchor or he off till conditions are more favorable. 161. Lights. — Before coming within range of a light the navigator should acquaint himself with its characteristics, so that when sighted it will be recognized. The charts, sailing directions, and Ught lists give information as to the color, character, and range of visibihty of the various lights. Care should be taken to note all of these and compare them when the light is seen. If the light is of the flashing, 21594°— 14 5 66 PILOTING. revolving, or intermittent variety the duration of its periods should be noted to identify it. If a fixed light, a method that may be employed to make sure that it is not a vessel's light is to "descend several feet immediately after sighting it and observe if it disappears from view; a navigational light will usually do so, excepting in misty weather, while a vessel's light will not. The reason for this is that navigational lights are as a rule sufficiently powerful to be seen at the farthest point to which the ray can reach without being mterrupted by the earth's curvature. They are therefore seen at the first moment that the ray reaches an observer on a ship's deck, and are cut off if he lowers the eye. A vessel's light, on the other hand, is usually Hmited by its intensity and does not carry beyond a distance within which it is visible at all heights. Care must be taken to avoid being deceived on first sighting a light, as there are various errors into which the inexperienced may fall. The glare of a powerful Ii»ht is often seen beyond the distance of visibUity of its direct rays by the reflection downward from particles of mist in the air; the same mist may also cause a white light to have a distinctly reddish tinge, or it may obscure a light except within short distances. When a light is picked up at the extreme limit at which the height of the observer will permit, a fixed light may appear flashing, as it is seen when the ship is on the crest of a wave, and lost when in the hoUow. Many lights are made to show different colors in different sectors within their range, and by consulting his chart or books, the navigator may be guided by the color of the sector in which he finds himself; in such lights one color is generally used on bearings whence the approach is clear, and another covers areas where dangers are to be encountered. The visibility of lights is usually stated for an assumed height of the observer's eye of 15 feet, and must be modified accordingly for any other height. But it should be remembered that atmospheric and other conditions considerably affect thevisibihty, and it must not be positively assumed, on sighting a light, even in perfectly clear weather, that a vessel's distance is equal to the range of visibiUty; it may be either greater or less, as the path of a ray of fight near the horizon receives extraordinary deflection under certain circumstances; the conditions governing this deflection are discussed in article 296, Chapter X. 162. Buoys. — While buoys are valuable aids, the mariner should always employ a certain amount of caution in being guided by them. In the nature of things it is never possible to be certain of finding buoys in correct position, or, indeed, of finding them at all. Heavy seas, strong currents, ice, or collisions with passing vessels may drag them from their places or cause them to disappear entirely, and they are especially uncertain in unfrequented waters, or those of nations that do not keep a good lookout upon their aids to navigation. When, therefore, a buoy marks a place where a ship must be navigated with caution, it is well to have a danger angle or bearing as an additional gmde instead of placing too much dependence upon the buoy being in place. ... Different nations adopt different systems of coloring for their buoys; an important feature of many such systems, including those adopted by the tJnited States and various other great maritime nations (though not aU), consists in placing red buoys to be left on the starboard hand of a vessel entering a harbor or fairway, and black buoys on the port hand. In these various systems the color and character of the buoys are such as to denote the special purpose for which they arc employed. 163. Fogs and Fog Signals. — ^As with fights, the navigator should, in a fo^, acquaint himself with the characteristics of the various sound signals which he is fikely to pick up, and when one is heard, its periods should be timed and compared with those given in the fight lists to insure its proper identity. Experiment has demonstrated that sound is conveyed through the atmosphere in a very uncertain way; that its intensity is not always increased as its origin is approached, and that areas within its range at one time, will seem silent at another. Add to these facts the possibifity that, for some cause, the signal may not be working as it should be, and we have reason for observing the rule to proceed with the utmost caution when running near the land in a fog. Although the transmission of sound through water from the submarine bells that have been instaUed on many fight vessels and at points of danger is much more PILOTING. 67 certain than the transmission of sound through air and can be received in such a way by vessels equipped with submerged microphones on each side as to enable the direction of the submarine bell to be approximately determined, yet the lead continues to prove an ever-serviceable guide, and should accordingly be in constant use. The method of plotting soundings described in article 160 will give the most rehable position that is obtainable. Moreover, the lead will warn the navigator of the approach to shallow water, when, if his position is at all in doubt, it is wisest to to anchor before it becomes too late. When running slowly in a fog (which caution, as well as the law, requires that one should do) it must be borne in mind that the relative effect of current is increased; for instance, the angle of deflection from the course caused b}^ a cross-set is greater at low than at high speed. It is worth remembering that when in the vicinity of a bold bluff shore vessels are sometimes warned of a too close approach by having their own fog signals echoed back from the chffs; indeed, from a knowledge of the velocity of sound (art. 314, Chap. XI) it is possible to gain some rough idea of the distance in such a case. When radio-stations, equipped with fog-signahng apparatus, send out simul- taneous radio and sound signals, distances from the sending station can be found by noting the elapsed interval between the time of arrival of radio signal and sound signal, and multiplying this interval expressed in seconds by the velocity per second of sound in air, or the velocity per second of sound in water, according as the sound signals are received through air or through water. By thus determining the distance from a fog-signal station to different positions between which the course and distance are known, the position of the vessel could be approximately found in a manner analogous to that which would apply in figure 18 if the distances AO and AP were known in addition to the length and direction of OP. 164. Tides and Currents. — The information relating to the tides given on the chart and in other publications should be studied, as it is of importance for the navigator to know not only the height of the tide above the plane of reference of the chart, but also the direction and force of the tidal current. The plane of reference adopted for soundings varies with different charts; on a large number it is that of mean low water, and as no plane of reference above that of mean low water is ever employed the navigator may with safety refer his sound- ings to that level when in douot. When traversing waters in which the depth exceeds the vessel's draft by but a small margin, account must be taken of the fact that strong winds or a high barom- eter may cause the water to fall below even a very low plane of reference. On coasts where there is much diurnal inecjualitv in the tides, the amount of rise and fall can not be depended upon^ and additional caution is necessary. ' A careful distmction should be made between the vertical rise and foM of the tide, which is marked at the transition periods by a stationary height, or stand, and the tidal current, which is the horizontal transfer of water as a result of the difference of level, producing the flood and ehh, and the intermediate condition, or slack. It seldom occurs that the turn of the tidal stream is exactly coincident with the high and low water, and in some channels the current may outlast the vertical movement which produces it by as much as three hours, the effect being that when the water is at a stand the tidal stream is at its maximum, and when the current is slack the rise or fall is going on with its greatest rapidity. Care must be taken to avoid con- founding the two. The effect of the tidal wave in causing currents may be illustrated by two simple cases: (1) Where there is a small tidal basin connected with the sea by a large opening. (2) Where there is a large tidal basin connected with the sea by a small opening. In the first case the velocity of the current in the opening will have its maximum value when the height of the tide within is changing most rapidly, i. e., at a time about midway between high and low water. The water in the basin keeps at approxi- mately the same level as the water outside. The flood stream corresponds with the rising and the ebb with the falling of the tide. In the second case the velocity of the current in the opening will have its maxi- mum value when it is high water or low water without, for then there is the greatest 68 PILOTING. head of water for producing motion. The flood stream begins about three hours after low water, and the ebb stream about three hours after high water, slack water thus occurring about midway between the tides. Along most shores which lack features like bays and tidal rivers, the current usually turns soon after high water and low water. The swiftest current in straight portions of tidal rivers is usually in the middle of the stream, but in curved portions the most rapid current is toward the outer edge of the curve, and here the water will be deepest. The pilot rule for best water is to follow the ebb-tide reaches. Conntercurrents and eddies may occur near the the shores of straits, especially in bights and near points. A knowledge of them is useful in order that they may be taken advantage of or avoided. A swift current often occurs in the narrow passage connecting two large bodies of water, owing to their considerable difference of level at the same instant. The several passages between Vineyard Sound and Buzzards Bay are cases in point. In the Woods Hole Passage the maximum strength of the tidal streams occurs near high and low water. Tide rips are made by a rapid current setting over an irregular bottom, as at the edges oi banks where the change of depth is considerable. Generally speaking, the rise and fall and strength of current are at their mini- mum along straight stretches of coast upon the open ocean, while bays, bights, inlets, and large rivers operate to augment the tidal effects, and it is in the vicinity of these that one finds the highest tides and strongest currents. The navigator need there- fore not be surprised in cruising along a coast to notice that his vessel is set more strongly toward or from the shore in passing an indentation, and that the evidences of tide will appear more marked as he nears its mouth. Usually more complete data are furnished in charts and tide tables regarding the rise and fall, and it irequently occurs that the information regarding the tidal current is comparatively meager; the mariner must therefore take every means to ascertain for himself the direction and force of the tidal and other currents, either from the set shown between successive well-located positions of the ship, or by noting the ripple of the water around buoys, islets, or shoals, the direction in which vessels at anchor are riding, and the various other visible effects of the current. Current arrows on the chart must not be regarded as indicating absolutely the conditions that are to be encountered. They represent the mean of the direction and force observed, but the observations upon which they are based may not be complete, or there may be reasons that bring about a departure from the normal state. 165. Charts. — The chart should be carefully studied, and among other things all of its notes should be read, as valuable information may be given m the margm which it is not practicable to place upon the chart abreast the locality affected. The mariner will do well to consider the source of his chart and the authority upon which it is based. He will naturally feel the greatest confidence in a chart issued by the Government of one of the more important maritime nations which maintains a well-equipped office for the especial purpose of acquiring and treating hydrographic information. He should note the character of the survey from which the chart has been constructed; and, finally, he should be especially careful that the chart is of recent issue or bears correction of a recent date — facts that should always be clearly shown upon its face. It is well to proceed with caution when the chart of the locality is based upon an old survey, or one whose source does not carry with it the presumption of accu- racy. Ev^en if the original survey was a good one, a sandy bottom, in a region where the currents are strong or the seas heavy, is liable to undergo in time marked changes; and where the depth is affected by the deposit or removal of silt, as in the vicinity of the estuaries of large river systems, the behavior is sometimes most capri- cious. Large blank spaces on the chart, where no soundings are shown, may be taken as an indication that no soundings were made, and are to be regarded with suspicion, especially if the region abounds in reefs or pinnacle rocks, in which case only the closest sort of a survey can be considered as revealing all the dangers of these facts must be duly weighed. AUi J PILOTING. 69 When navigating by landmarks the chart of the locality which is on the largest scale should be used. The hydrography and topography in such charts appear in greater detail, and — a most important consideration — bearings and angles may be plotted with increased accuracy. To sum up, the navigator must know the exact draft of the ship when approaching the land. He must make himself familiar with every detail of the charts he will be required to use and must read the charts in such a way as to be able to form a mental picture of how the land and the various aids to navigation will look when sighted, remembering that the position of the sun at different times of day, or the position of the moon at night, affects the appearance of the land as presented to the navigator approaching from seaward. He must be thoroughly lamiliar with the dav, night, and fog characteristics of all aids to navigation in the locality. He must Know the state of the tide and the force and direction of the current at all times when in pilot waters. The navigator, in making his plan for entering a strange port, should give very careful previous studv to the chart, and should carefully select what appear to be the most suitable marks for use, also pro- viding himself with substitutes for use in case those selected as most suitable should prove unreliable by not being recognized with absolute certainty. It must be remembered that buoys seen at a distance, in approaching a channel, are often difficult to place or identify, because all mav appear equallv distant, though in reality far apart. Ranges should be noted, if possible, and the lines oraMm, both for leading tnrou^ the best water in channels and also for guarding against par- ticular dangers. For the latter purpose, safety bearings should in all cases be laid down where no suitable ranges oner. Tne courses to be steered in entering should also be laid down and distances marked thereon. If intending to use the sextant and danger angle in passing dangers, and especially in passing between dangers, the danger circles should be plotted and regular courses planned, rather than to run haphazard by the indications of the angle alone, with the possible trouble to be apprehended from wild steering at critical points. The ship's position should not be allowed to be in doubt at any time, even in entering ports considered safe and easy of access, and should be constantly checked by continuing to use for this purpose those marks concerning which there can be no doubt until others are unmistakably recognized. The ship should ordinarily steer exact courses and follow exact lines as planned from the chart, changing course at exact points, and, where the distances are con- siderable, her position on the line should be checked at frequent intervals, recording the time and the reading of the patent log. This is desirable, even where it may seem unnecessary for safety; because, if running by the eye alone and the ship's exact position be suddenly required, as in a sudden squall, fixing at that particular moment might be impossiole. The habit of running exact courses with precise changes of courses will be found most useful when it is desired to enter port or pass through inclosed waters during fog by means of the buoys ; here safety demands that the buoys be made successively, to do which requires, if the fog be dense, very accurate courses and careful attention to the times, rate of speed, and the set of tne current. Failure to make a buoy as expected leaves no safe alternative but to anchor at once. It is a useful point to remember that in passing between dangers where there are no suitable leading marks, as, for instance, between two islands or an island and the main shore, with dangers extending from both, a mid-channel course may be steered bj^ the eye alone with great accuracy, as the eye is able to estimate very closely the position midway between visible objects. In piloting among coral reefs or banks, a time should be chosen when the sun will be astern, conning the vessel from aloft or from an elevated position forward. The line of demarcation between the deep water and the edges of the shoals, which generally show as ^een patches, is indicated with surprising clearness. This method IS of frequent application in the numerous passages oi the Florida keys. Changes oi course should in general be made by exact amounts, naming the new course or the amount of the change desired, rather than by ordering the helm to be put over and then steadying when on the desired heading, with the possibility of the attention being diverted and so forgetting in the meantime that the ship is still 70 PILOTING. swinging. The helmsman, knowing just what is desired and the amount of change to be made, is thus enabled to act more intelligently and to avoid wild steering, which in narrow channels is a very positive source of danger. Coast 'piloting involves the same principles and requires that the ship's positions be continuously determined or checked as the landmarks are passed. On well- surveyed coasts there is a great advantage in keeping near the land, thus holding on to the marks and the soundings, and thereby knowing at all times the position, rather than keeping offshore and losing the marks, with the necessity of again making the land from vague positions, and perhaps the added inconvenience of fog or bad weather, involving a serious loss of time and fuel. The route should be planned for normal conditions of weather with suitable variations where necessary in case of fog or bad weather or making points at night, the courses and distances, in case of regular runs over the same route, being entered in a notebook for ready reference, as well as laid dowTi on the chart. The danger circles for either the horizontal or the vertical danger angles should be plotted, wherever the method can be usefully employed, and the angles marked tnereon; many a mUe may thus be saved in rounding dangerous points, with no sacrifice in safety. Ranges should also be marked in, where useful for positions or for safety, and also to use in checking the deviation of the compass by comparing, in crossing, the compass bearing of the range with its magnetic bearing, as given by the chart. Changes of course will in general be made with mark or object abeam, the posi- tion (a new "departure") being then, as a rule, best and most easily obtained. In making the land in a fog the sounding machine must be kept going at intervals of half an hour some hours before it is expected that soundings can be obtained. Several soundings taken at random will not locate a ship, but on the contrary may lead to disaster. In using the sounding machine be careful that the man handhng the tube does not invert the tube when taking it from the tube case, as this would allow water to run toward the closed end of the tube, causing a discoloration of the coating and thus bring about an incorrect sounding. It is also essential that the lead be cleanly and freshly armed for each cast. The bottom having been picked up, a graphic record of the soimdings may be laid down in the manner previously described in paragraph 160 and an approximation made of the position oi the ship. Keep a sharp lookout for any landmarks that jnight show up during a momentary lifting of the fog and have keen ears hstening for an aerial or submarine fog signal. Having picked up any such signal, make sure to ascertain exactly what landmark it is. From now on proceed with caution and determine whether it is better to anchor or to proceed through the harbor channel in the fog. If, having approached the land ana failed to hear fog signals at the time they were expected to be heard and the soundings indicate a dangerous proximity to shore, the only safe course is either to anchor or to stand off. When running slowly in a fog (which caution, as well as the law, requires that one should do) it must be borne in mind that the relative effect of current is increased; for instance, the angle of deflection from the course caused by a cross set is greater at low than at high speed. It is worth remembering that when in the vicinity of a bold bluff shore vessels are sometimes warned of a too-close, approach by having their own fog signals echoed back from the cliffs ; indeed, from a knowledge of the velocity of sound it is possible to ^ain some rough idea of the distance in such a case. Great caution must be used in approaching a bold coast in a fog and, unless soundings can be got that will reasonably assure the navigator of his distance from the coast, the only safe course is to stand off, if the depth of the water does not permit of anchoring. The best aids at the disposal of the navigator when running in a fog are the sounding machine and the hand lead, and the navigator will do well to make great use of them. Even in clear weather the sounding machine may be a great aid to the navigator in verifying his position. fl In approaching the land and entering harbors, the navigator must bear in mind ■ that rules of the road in inland waters sometimes differ from those used on the high sea, and should inform himself of the boundaries of the waters where different rules of the road obtain. 166. Records.^ — It will be found a profitable practice to pay careful attention to the recording of the various matter relating to the piloting of the ship. A notebook PILOTING. 71 should be kept at hand on deck or on the bridge, in which are to be entered all bearings or angles taken to fix the position, all changes of course, important soundings, and any other facts bearing upon the navigation. (This book should be different from the one in which astronomical sights and offshore navigation are worked.) The entries, though in memorandum form, should be complete; it should be clear whether bearings and courses are true, magnetic, or by compass; and it is especially important that the time and patent log reading should be given for each item recorded. The value of this book will make itself apparent in various directions; it will afford accurate data for the writing of the ship s lo^; it will furnish interesting information for the next run over the same ground; it will provide a means by which, if the ship be shut in by fog, rain, or darkness, or if there be difficulty in recognizing landmarl^ ahead, the last accurate fix can bo plotted and brought forward; and, finally, if there should be a mishap, the notebook would fumi^ evidence as to where the trouble has been. The chart on which the work is done should also be made an intelUgible record, and to this end the pencil marks and lines should not be needlessly numerous, heavy, or, long. In plotting bearings, draw lines only long enough to cover the probable position. Mark intersections or positions by drawing a small circle around them, and writing neatly abreast them the time and patent log reading. Indicate the courses and danger bearings by full lines and mark them appropriately, preferably giving both magnetic (or true) and compass directions. A great number of lines extending in every direction may lead to confusion; however remote the chance may seem, the responsibihties of piloting are too serious to run even a small risk. Finally, on anchoring, record and plot the position by bearings or angles taken after coming to; observe that the berth is a safe one, or, if in doubt, send a boat to sound in the vicinity of the ship to make sure. CHAPTER V. THE SAILINGS. 167. In considering a ship's position at sea with reference to any other place, either one that has been left or one toward which the vessel is bound, five terms are involved — the Course, the Distance, the Difference of Latitude, the Difference of Longitude, and the Departure."" The solutions of the various problems that arise from the mutual relation of these quantities are called Sailings. 168. Kinds of Sailings. — When the only quantities involved are the course, distance, difiFerence of latitude, and departure, tne process is denominated Plane Sailing. In this method the earth is regarded as a plane, and the operation proceeds as if the vessel sailed always on a perfectly level surface. When two or more courses are thus considered, they are combined by the method of Traverse Sailing. It is evident that the. number of miles of latitude and departure can thus be readily deduced; but, while one mile always equals one minute in difference of latitude, one mile of departure corresponds to a difference of longitude that will vary with the latitude in which the vessel is sailing. Plane sailing therefore furnishes no solution where difference of longitude is considered, and for such solution resort must be had to one of several methods, which, by reason of their taking account of the spherical figure of the earth, are called Spherical Sailings. When a vessel sails on an east or west course along a parallel of latitude, the method of converting departure into difference of longitude is called Parallel Sailing. When the course is not east or west, and thus carries the vessel through various latitudes, the conversion may be made either by Middle Latitude Sailing, in which it is assumed that the whole run has been made m the mean latitude, or by Mercator Sailing, in which the principle involved in the construction of the Mercator chart (art. 39, Chap. II) is utilized. Great Circle Sailing deals with the courses and distances between any two points when the track followed is a great circle of the terrestrial sphere. A modification of this method which is adopted under certain circumstances is called Corn- ^st. posite Sailing. PLANE SAILING. 169. In Plane Sailing, the curvature of the earth being neglected, the relation between the elements of the rhumb track joining any two points may be considered from the plane right triangle formed by the meridian of the place left, ^^' ^- the parallel of the place arrived at, and the rhumb line. In figure 24, T is the point of departure; T', the point of destination; Tn, the meridian of departure; T'n, the parallel of destination; and TT', the rhumb line between the points. Let G represent the course, T'Tn; Dist., the distance, TT'; DL, the dif- ference of latitude, Tn; and Dep., the departure, T'n. Then from the triangle TT'n, we have the following: sin c-^^- ^^ ^~Dist.' COS C = Dist. Dep. tanC = j)L- • For the definition of these tenns, see article 6, Chapter I. 72 THE SAILINGS. 73 From these equations are derived the following formulaB for working the various problems that may arise in Plane Sailing: Given. Course and distance. Difference of latitude and departure. Course and difference of latitude. Course and departure. . . Distance and difference of latitude. Distance and departure . Required. Formulae. f Difference of latitude \Departure I Course Distance Distance Departure Distance Difference of latitude f Coxu-se I Departure {Course Difference of latitude DL = Dep. = TanC= Dist. = Dist. = Dep. = Dist. = DL = CosC = Dep. : SinC = DL = =Diet. cos C. =Dist. sin C. Dep. =DL ' Dep. "sin C ' DL . "cos C =D L tan C. Dep. "sin C Dep. "tanC* DL "Dist. ■ =Dist. sia C. Dep. "Dist. ■ =Dist. cos C. Log D L =log Dist.+log cos C. Log Dep. =log Dist. -[-log sinC. Log tan C=log Dep.— log D L. Log Dist. =log Dep. —log sin C. Log Dist. =log D L —log cos C. Log Dep. =log D L -flog tan C. Log Dist, =log Dep. —log sin C. Log D L =log Dep. — l<5g tan C. Log cos C=log D L —log Dist. Log Dep. =log Dist.+log sin C. Log sin C =log Dep. —log Dist. Log D L =log Dist. -flog cos C. 170. The solution of the plane right triangle may be accompUshed either by Plane Trigonometry, by Traverse Tables, or by construction. If the former method is adopted, the logarithms of numbers may be found in Table 42, and of the functions of angles in Table 44. A more expeditious method is available, however, in the Traverse Tables, which give by inspection the various solutions. Table 1 contains values of the various parts for each unit of Dist. from 1 to 300, and for each quar- ter-point (2° 49'"), of C; Table 2 contains values for each unit of Dist. from 1 to 600, and for each de^ee of C. The method of solving by construction consists in laying down the various given terms by scale upon a chart or plain paper, and measuring thereon the terms required. 171. Of the various problems that may arise, the first two given in the foregoing table are of much the most frequent occurrence. In the first, the given quantities are course and distance, and those to be found are difference of latitude and departure; this is the case where a navigator, knowing the distance run on a given course, desires to ascertain the amount made good to north or south and to east or west. In the second case the conditions are reversed; this arises where the course and distance between two points are to be obtained from their known difference of latitude and departure. Example : A ship sails SW. by W., 244 miles. Required the difference of latitude and the departure made good. By Inspection. In Table 1, find the course SW. by W. (5 points); it occurs at the bottom of the page, therefore take the names of the columns from the bottom as well; opposite 244 in the Dist. column will be seen Lat. 135.6 and Dep. 202.9. By Computation. Dist. 244 C 56° 15' DL 135. 6 Dist. 244 C 56° ly Dep. 202. 9 log 2. 38739 log cos 9. 74474 2. 13213 log 1(^ 2. 38739 log sin 9. 91985 log 2. 30724 74 THE SAILINGS. Example: A ship sails N. 5° E., 188 miles. By CompiUation. Required the difference of latitude and the departure. By Inspection. Digt. C 188 5° log 2. 27416 log cos 9. 99834 DL 187.3 log 2. 27250 Dist. C 188 5° log log sin 2. 27416 8. 94030 In Table 2, find the course 5°; it occurs at the top of the page, therefore take the names of the columns from the top; opposite 188 in the Dist. column will be seen Lat. 187.3 and Dep. 16.4. Dep. 16.4 log 1. 21446 Example : A vessel is bound to a port which ia 136 miles to the north and 203 miles to the west of her position. Required the course and^distance. Dep. DL By Computation. 203 log 136 log 2. 30750 2. 13354 C (N.) 56" IV (W.) log tan 0. 17396 Dep. 203 log 2.30750 C 56° 11' log sin 9. 91951 Dist. 244.3 log 2.38799 By Inspection. Enter Table 1 and turn the pages until a course is found whereon the numbers 136 and 203 are found abreast each other in the columns marked respectively Lat. and Dep. This occiu-s most nearly at the course for 5 points, the angle being taken from the bottom, because the appropriate names of the columns are found there. The course ia therefore NW. by W. Interpolating for interme- diate values, the corresponding number in the Dist. column is about 244.3. Example: As a result of a day's run a vessel changes latitude 244 miles to the south and makes a departure of 171 miles to the east. What is the coiu-se and distance made good? By Inspection. Enter Table 2 and the nearest agreement will be found on course (S.) 35° (E.), the appropriate names being found at the top of the page. The nearest corresfKjnding Dist. is 298 miles. By Computation. Dep. 171 log 2.23300 DL 244 log 2.38739 C (S.) 35° 02' (E.) log tan 9. 84561 Dep. 171 C 35° 02' log 2. 23300 log sin 9. 75895 Dist. 297. 9 log 2. 47405 TRAVEBSE SAILING. 172. A Traverse is an irregular track made by a ship in sailing on several different courses, and the method of Traverse Sailing consists in finding the difference of latitude and departure corresponding to several courses and distances and reducing all to a single equivalent course and distance. This is done by determining the distance to north or south and to east or west made good on each course, taking the algebraic sum of these various differences of latitude and departure and finding the course and distance corresponding thereto. The work can be most expeditiously performed by adopting a tabular form for the computation and using the traverse tables. Example: A ship sails SSE., 15 miles; SE., 34 miles; W. by S., 16 miles; WNW., 39 miles; S. by E., 40 miles. Required the course and distance made good. Courses. Dist. N. s. E. w. SSE. SE. W. by S. WNW. S. by E. S. by W. 15 34 16 39 40 14.9 13.9 24.0 3.1 39.2 5.7 24.0 7.8 15.7 36.0 66.8 14.9 80.2 14.9 37.5 51.7 37.5 65.3 14.2 The result of the various courses is, therefore, to carry the vessel S. by W., 66.8 miles from her original position. THE SAILINGS. 75 PARALLEL SAILING. 173. Thus far the earth has been regarded as an extended plane, and its spherical fiffure has not been taken into account; it has thus been impossible to consider one of the important terms involved — namely, difference of longitude. Parallel Sailing is the simplest of the various forms of Spherical Sailing, being the method of interconverting departure and difference of longitude when the ship sails upon an east or west course, and therefore remains always on the same parallel of latitude. In figure 25, T and T' are two places in the same latitude; P, the adjacent pole; TT', the arc of the parallel of latitude through the two places; MM', the corresponding arc of the equator intercepted between their meridians PM and PM'; and TT', the departure on the parallel whose latitude is TCM=OTC, and whose radius is OT. Let D.Lo represent the arc of the equator MM', which is the measure of MPM', the difference of longitude of the me- ridians PM and PM'; R, the equatorial radius of the earth, CM = CT; r, the radius OT of the parallel TT'; and L, the latitude of that parallel. Then, since TT' and MM' are similar arcs of two circles, and are tnerefore proportions,! to the radii of the circles, we have: TT' OT CM' or Pep. _ r D.Lo~R. From the triangle COT, r = R cos L; hence Pep. _ R cos L P.Lo~ R ; or, P.Lo=Pep. sec. L; or, Pep. = P.Lo cos L. Thus the relations are expressed between minutes of longitude and miles of departure. 174. Two cases arise under Parallel Sailing: First, where the difference of longitude between two places on the same parallel is given, to find the departure; and, second, where the departure is given, to find the difference of longitude. In working these proolems, the computation can be made by logarithms; but the traverse tables may more conveniently be employed. Remembermg that those tables are based upon the formulae, PL = Pist. cos C, and Pist. = PL sec C, we may substitute for the column marked Lat. the departure, for that marked Pist. the difference of longitude, and for the courses at top and bottom of the page the latitude. The tables then become available for making the required conversions. Example: A ship in the latitude of 49° 3CK sails directly east iintil making good a difference of longitude of 3° 30'. Required the departure. By Computation. By Inspection. L 49° 3(K log COS 9. 81254 Enter Table 2 with the latitude as C and the difference D.Lo. 21(y log 2.32222 of longitude as Dist. As the table is calculated only to single degrees, we must find the numbers in the pages of 49° and 50° and take the mean. Corresponding to Dist. 210 in the former is Lat. 137.8, and in the latter Lat. 135.0. The mean, which is the required departure, is 136.4. sails due west a distance of 215.5 miles. Required the By Inspection. Entering Table 2 with the latitude, 38°, as a course, corresponding with the number 215.5 in column of Lat., is 273.5 in the column of Dist. This is therefore the required difference of longitude, being equal to 4° 33'.5. Dep. 136.4 log 2. 13476 Example: A ship difference of longituoe in the latitude of 38 By Computation. L Dep. 38° 215.5 log sec log 0. 10347 2.33345 D.Lo{4, 273'. 5 '33'. 5 log 2.43692 MIDDLE LATITUDE SAILING. 175. When a ship follows a course obUquely across the meridian the latitude is constantly changing, and the method of converting departure and difference of longitude by Parallel Sailing, just described, ceases to be applicable. 76 THE SAILINGS. In figure 26, T is the point of departure; T', the point of destination; P, the earth's pole; TT', the rhumb track; tIjIT', the course; Tn, n^T', the respective parallels of latitude; and MM', the equator. The difference of longitude between T and T' is MPM', which may be measured by the arc of the equator, MM', intercepted between their meridians. This corre- sponds to a departure Tn in the latitude of T, and to the smaller departure T'rii in the higher latitude of T'; but since the vessel neither makes all of the departure in the latitude T, nor all of it in the latitude T', the departure actually made m the passage must have some intermediate value between these extremes. Dividing the total difference of longitude into a number of equal parts MPrnj, m^'Pin^, etc., of such small extent that, for the purposes of conversion, the change of latitude corresponding to each may be neglected, we Jiave the total departure made p up of the sum of a number of small departures, each equal to the same difference of longitude, but each different from the other. These wUl be diVi in the latitude T, d^rz m the latitude r^, etc. Hence we have: MM' =diri sec MT + (?2''2> sec rriiri +d^r^, sec m^rz, + etc. Now, if LL' be a parallel of latitude lying midway between Tn and T'%, since there wiU be as many of the small parts lying above as below it, and since for moderate distances the ratio to be employed in the conversion of departure and difference of longitude may be regarded as varying directly with the latitude, it may be assumed for such distances that the sum of all of the different small departures equals the single departure between the merid- ians measured in the latitude LL', and therefore that the departure obtained by the method of plane sailing on any course maj be converted into difference of longitude by multiplying by the secant of the Middle Latitude. The method of conversion based upon this assumption is denominated Middle Latitude Sailing, and by reason of its convenience and simplicity is usually employed for short distances, such as those covered by a vessel in a day's run. 176. In Middle Latitude SaUing, having found the mean of the latitudes^ the solution is identical with that of Parallel Samng (art. 173), substituting the Middle Latitude for the single latitude therein employed. Example: A ship in Lat. 42° 30' N., Long. 58° 51' W., sails SE. by S., 300 miles, latitude and longitude arrived at. From Table 1: Course SE. by S., Dist., 300, we find Lat., 249.4 S. (4° 09'.4), Dep. Required the , 166.7 E. Latitude left, DL, 42° SO'. N. 4 09.4 S. Latitude left, 42° SO' N. Latitude arrived at, 38 21 N. Latitude arrived at, 38 20 . 6 N. Mid. latitude, 2)80 51 40 25 N. Enter Table 2 with the middle latitude, 40°, as a course; the difference of longitude (Dist.) cor- responding to the departure (Lat.) 166.7 is 217.6; entering with 41°, it is 220.9; the mean is 219.2 (3° 39'.2). Longitude left, 58° 51'.0 W. D.Lo, 3 39 .2 E. Longitude arrived at, 55 11 .8 W. Example: A ship in Lat. 39° 42' S., Long. 3° 31' E., sails S. 42° W., 236 mUes. Required the lati- tude and longitude arrived at. „^ From Table 2: Course, S. 42° W., Dist., 236 mUes; we find Lat., 175.4 S. (2° 55'.4), Dep., 157.9 W. Latitude left, DL, 39° 42'.0 S. 2 55 .4 S. Latitude left, 39° 42' S Latitude arrived at, 42 37 S. Latitude arrived at, 42 37 .4 S. Mid. latitude, 2)82 19 41 09 S. THE SAILINGS. 77 20= From Table 2: Mid. Lat. (course), 41°, Dep. (Lat.), 157.9; we find D.Ix) (Dist.), 209.3 (3° 29'.3). Longitude left, 3° SV.O E. D.Lo, 3 29 .3 W. Longitude arrived at, 01 .7 E. Example: A vessel leaves Lat. 49° 57' N., Long. 15° 16' W., and arrives at Lat. 47® 18' N., Long. lO' W. Required the course and distance made good. Latitude left 49° 57' N. Longitude left, 15° 16' W. Latitude arrived at, 47 18 N. Longitude arrived at, 20 10 W. DL, f 2° 39 \ 159 2)97'' D.Lo, 4° 54' 294' ;}w. Mid. latitude, 48 38 N. From Table 2: Mid. Lat, (course), 49°, D.Lo (Dist,), 294; we find Dep. (Lat.), 192.9. From Table 2: DL 159 S., Dep. 192.9 W., we find course S. 51° W., Dist., 251 miles. 177. It may be remarked that the Middle Latitude should not be used when the latitudes are of opposite name; if of different names and the distance is small, the departure may be assumed equal to the difference of longitude, since the meridians are sensibly parallel near the equator; but if the distance is great the two portions of the track on opposites of the equator must be treated separately. 178. The assumption upon which Middle Latitude sailing is based — that the conversion may be made as if the whole distance were sailed upon a parallel midway between the latitudes of departure and destination — while sufficiently accurate for moderate distances, may be materially in error where the distances are large. In such case, either the method of Mercator Saihng (art. 179) must bo employed, or else the correction given in the following table should be applied to the mean latitude to obtain what may be termed the latitude of conversion, being that latitude in which the required conditions are accurately fulfilled. The table is computed from the formula : cos L,=-, where Lc represents the latitude of conversion, and I and m are respectively the differ- ences of latitude and of meridional parts (art. 40, Chap. II) between the latitudes of departure and destination. <* Difference of latitude. Mid. Lat. Mid. Lat. 1" 2' «• 4" 6* 6' 7" 8* 9° 10" 12* 14* W 18' 20' 15 -86 -85 -84 -83 -81 -79 -76 -73 -69 -65 -56 -46 -34 -21 - 6 15 18 -67 -67 -66 -65 -63 -61 -59 -56 -53 -50 -43 -34 -23 -12 1 18 21 -54 -54 -53 -52 -51 -49 -47 -44 -42 -39 -32 -24 -15 - 5 7 21 24 -44 -44 -44 -42 -41 -40 -■38 -36 -33 -31 -24 -17 - 8 1 12 24 30 -31 -30 -29 -29 -28 -26 -■24 -23 -20 -18 -12 - 6 1 11 21 30 35 -23 -22 -21 -21 -19 -18 -17 -15 -12 -10 - 5 2 10 18 28 36 40 -17 -16 -15 -14 -13 -12 -10 - 8 - 6 - 4 2 8 16 25 34 40 45 -12 -11 -11 -10 - 8 - 7 - 5 - 3 - 1 1 7 14 22 31 41 45 50 - 8 - 8 - 7 - 6 - 5 - 3 - 1 1 3 6 12 20 28 38 49 50 55 -5 - 5 - 4 - 3 - 2 2 5 7 10 17 25 35 46 58 55 58 - 4 - 3 - 3 - 1 2 4 7 10 13 20 29 39 51 64 58 60 - 3 - 3 - 2 - 1 1 3 5 8 11 14 22 32 43 55 69 60 62 - 3 - 2 - 1 2 4 7 9 13 17 25 35 46 60 75 62 64 - 2 - 1 1 3 5 8 11 14 18 27 38 50 65 81 64 66 - 2 - 1 2 4 6 9 12 16 20 30 42 55 71 89 66 68 - 1 1 2 5 7 10 14 18 22 33 46 61 78 98 68 70 - 1 1 3 5 8 12 16 20 25 37 51 67 87 109 70 72 1 2 4 6 10 13 18 23 28 41 57 76 97 123 72 o The statement often made that the latitude of conversion is always greater than the middle latitude is not correct when the compression of the earth is taken into account, as an inspection of the table wiU show; that statement is based upon an assumption that the earth is a perfect sphere, and it was upon that assumption that a table which appeared in early editions of this work was computed. The value of the compression adopted for this table is ^g-jgi* 78 THE SAILINGS. Example: A vessel sails from Lat. 10° 13'' S. to Lat. 20° 21' S., making a departure of 432 milee. Required the difference of longitude. Latitude left, 10° 13' S. Latitude arrived at, 20 21 S. 2)30 34 For Mid. Lat. 15° and Diff. of Lat. 10°. Correction, -Cy. Mid. latitude, 15 17 S. Correction, — 1 05 Lc, 14 12 S. L, 14° 12' log sec .01348 Dep. 432 log 2.63548 D.Lo 445^.6 log 2.64896 MERCATOR SAILING. 179. Mercator Sailing is the method by which values of the various elements axe determined from considering them in the relation in which they are plotted upon a chart constructed according to the Mercator projection. 180. Upon the Mercator chart (art. 39, Chap. II), the meridians being parallel, the arc of a parallel of latitude is shown as equal to the corresponding arc of the equator; the length of every such arc is, therefore, expanded; and, in order that the rhumb line may appear as a straight line, the meridians are also expanded by such amount as is necessary to preserve, in any latitude, the proper proportion existing between a unit of latitude and a unit of longitude. The length of small portions of the meridian thus increased are called meridional parts (art. 40, Chap. II), and these, computed for every minute of latitude from 0° to 80°, form the TaJble of Meridional Parts (Table 3), by means of which a Mercator chart may be constructed and all problems of Mercator Sailing may be solved. In the triangle ABC (fig. 27), the angle ACB is the coui-se, C; the side AC, the distance, Dist.; the side BC, the difference of latitude, DL; and the side AB, the departure, Dep. Then corresponding to the difference of lati- tude BC in the latitude under consideration, if CE be laid off to represent the meridional difference of latitude, m, completing the right triangle CEF, EF will represent the difference of longitude, D.Lo. The triangle ABC gives the relations involved in Plane Sailing as previously described; the triangle CEF affords the means for the conversion of departure and difference of longi- tude by Mercator Sailing. 181. To find the arc of the expanded meridian intercepted between any two parallels, or the meridional difference of latitude, when both places are on the same side of the equator, subtract the meridional parts of the lesser latitude, as given by Table 3, from the meridional parts of the greater; the remainder will be the meridional difference of latitude ; but if the places are on dif- ferent sides of the equator, the sum of the meridional parts will be the meridional difference of latitude. 182. To solve the triangle CEF by the traverse tables it is only necessary to substitute meridional difference for Lat., and difference of longitude for Dep. Where long distances are involved, carrying the computation beyond the hmits of the traverse table, as frequently occurs m this method, either of two means may be adopted: the problems may be worked by trigonometrical formulae, using logarithms or tne given quantities involved may all be reduced by a common divisor until they fall within the traverse table, and the results, when obtained, correspondingly increased. The former method is generally preferable, especially when the distances are quite large and accurate results are sought. The formulae for the conversions are as follows: tanC = — ^; D.Lo = m tan C; m= D.Lo cot C. DL Fig. 27. various D.Lo THE SAILINGS. 79 Example: A ship in Lat. 42° 30^ N., Long. 58° 51^ W., sails SE. by S., 300 miles. Required the latitude and longitude arrived at. From Table 1: Coutbc, SE. by S., Dist., 300; we find Lat. 249.4 S. (4° 09^4). Latitude left, 42° 30^.0 N. Merid. parts, +2806. 4 DL, 4 09 .4 S. Latitude arrived at, 38 20 .6 N. Merid. parts, -2480.4 m, 326. By Computation. By Inspectum. m 326.0 log 2. 51322 Enter Table 1, course 3 points; since the c^uantities 33° 45^ log tan 9. 82489 involved exceed the limits of the table, divide by 2; f 217^8 log 2.33811 abreast -k- (Lat.), 163.0, find —V~(Dep.), 108.9; hence 13° 37'!8 D.Lo=217'.8 or 3° 37'.8. Longitude left, 58° 51^0 W. D.Lo, 3 37 .8 E. Longitude arrived at, 55 13 .2 W. Example: A ship in Lat. 4° 37' S., Long. 21° 05'' W., sails N. 14® W., 450 miles. Required the latitude and longituae arrived at. From Table 2: Course, (N.) 14° (W.), Dist., 450; we find Lat. 436.6 N, (7° 16'.6). Latitude left, 4° 37'.0 S. Merid. parte, +275.4 DL, 7 16 . 6 N. Latitude arrived at, 2 39 . 6 N. Merid. parts, +159. « m, 434. 4 By Computation. By Inspection. m 434.4 log 2.63789 From Table 2: Course, 14°, m (Lat.), 434.4, we find C 14° log tan 9. 39677 D.Lo (Dep.) 108'.3 W., or 1° 48'.3. D.Lojj, 108^ 3 log 2. 03466 48'. 3 Longitude left, 21° 05'. W. D.Lo, 1 48. 3 W. Longitude arrived at, 22 53 . 3 W. Example: Required the course and distance by rhumb line from a point in Lat. 42° 03' N., Long. 70° 04' W., to another in Lat. 36° 59' N., Long. 25° 10' W. Lat. departure, 42° 03' N. Merid. pts., +2770. 1 Long, departure, 70° 04' W. Lat. destination, 36 59 N, Merid. pta., -2377.3 Long, destination, 25 10 W. DL {"^;}S. », 1^ D.LO {^.>. D.Lo 2694 log 3.43040 m 392.8 log 2.59417 C (S.) 81° 42' (E.) log tan .83623 log sec. .84056 DL 304' log 2.48287 Dist. 2106 log 3.32343 The course is therefore S. 81° 42' E., and the distance is 2,106 miles. Since the figures involved are so large, it is best to employ only the method by computation. The formula by which the Dist. is obtained comes from Plane Sailing. GREAT CIRCLE SAUilNQ. 183. The shortest distance between any two points on the earth's surface is measured by the arc of the great circle which passes through those points; and the method of sailing in which the arc of a great circle is employed for the track of the vessel, taking advantage of the fact that it is the shortest route possible, is denomi- nated Great Circle Sailing. 184. It frequently happens when a great circle route is laid down that it is found to lead across the land, or to carry the vessel into a region of dangerous naviga- 80 THE SAILINGS. tion or extreme cold which it is expedient to avoid; in such a case a certain parallel should be fixed upon as a limit of jatitude, and a route laid down such that a great circle is followed as far as the limiting parallel, then the parallel itself, and finally another great circle to the port of destmation. Such a modification of the great circle method is called Composite Sailing. 185. The rhumh line (art. 6, Chap. I), also called the loxodromic curve, which cuts all the meridians at the same angle, has been largely employed as a track by navigators on account of the ease with which it may be laid down on a Mercator chart. But as it is a longer line than the great circle between the same points, intelligent navigators of the present day use the latter wherever practicable. On the Mercator chart, however, the arc of a great circle joining two points (unless both are on the equator or both on the same meridian) will not be projected as a straight line, but as a curve which seems to be longer than the rhumb line; hence the shortest route appears as a circuitous one, and this is doubtless the reason that a wider use of the great circle has not been made. It should be clearly understood that it is the rhumb line which is in fact the indirect route, and that in following the great circle the vessel is always heading for her port, exactly as if it were in sight, while on the course which is shown as a straight line on the Mercator chart the vessel never heads for her port until at the very end of the voyage. 186. The method of ^eat circle sailing is of especial value to steamers, as such vessels need not, in the choice of a route, have regard for the winds to the same extent as must a sailing vessel; but even in navigating vessels under sail a knowledge of the great circle course may prove of great value. For example, suppose a ship to be bound from Sj^dney to Valparaiso; the first great circle course is SE. by S., while the Mercator course is almost due east. The distance is 748 miles shorter by the former route (if thereat circle is followed throughout, though this would lead to a latitude of 61° S.). With the wind at E. ^ vS. the ship would he nearer to the Mercator course on the starboard tack, assuming that she sailed within six points of the wind; but if she took that tack she would be increasing her distance from the port of destination by 4^ miles in every 10 that she sailed; while on the port tack, heading one point farther from the rhumb, the gain toward the port would be 9^ miles out of every 10. An y course between East and SSW. would be better than the Mercator course; and if tne wind were anything to the eastward of SE. by S., the ship would gain by taking the port tack in preference to the starboard. 187. As the great circle makes a different angle with each meridian that is crossed, it becomes necessary to make frec[uent changes of the ship's course; in practice, the course is a series of chords joining the various points on the track line. If, while endeavoring to follow a great circle, the ship is driven from it, as by unfavorable weather, it will not serve the purpose to return to the old track at convenience, but it is required that another great circle be laid down, joining the actual position in which the ship finds herself with the port of destination. 188. The methods of determining the great circle course may be divided generally into four classes; namely, by Great Circle Sailing Charts, by Computation, by the methods of the Time Azimuth, and by Graphic ApproxiTuations. 189. Great Circle Sailing Charts. — Of the available methods, that by means of charts especially constructed for the purpose is considered greatly superior to all others. A series of great circle sailing charts covering the navigable waters of the globe is published by the United States Hydrographic Office. Being on the gnomonic projection (art. 44, Chap. II), all great circles are represented as straight Unes, and it is only necessary to join any two points by such a line to represent the great circle track between them. The courses and distance are readily obtainable by a method explained on the charts. The track may be transferred to a chart on the Mercator projection by plotting a number of its points by their coordinates and joining them with a curved line. The navigator who contemplates the use of great circle tracks will find it of the freatest convenience to be provided with these gnomonic charts for the regions which is vessel is to traverse. THE SAILINGS. 81 190. By Computation. — This method consists in determining a series of points on the great circle by their coordinates of latitude and longitude, plotting them upon a Mercator chart, and tracing the curve^ that P joins them. The first point determined is the vertex, or point of liighest latitude, even when, as sometimes occurs, it falls without that por- tion of the great circle which joins the points of departure and destination. X ^ ^g In figure 28, A represents the point of / ^ — - V departure; B, the point of destination; AVB, . the great circle joining them, with its vertex ^ ' f as at V; and P, the pole of the earth. '°' ' Let C'a = PAB, the initial course; Cb = PBA, the final course; La, Ly, IjB = the latitudes of the respective points A, V, B = (90° — PA), (90° -PV), (90° -PB). Lo^, Lo^v, LoBv = the differences of longitude between A and B, A and V, B and V, respectively, = APB, APV, BPV. D = the great circle distance between A and B; and 9? = an auxiliary angle introduced for the computation. We then have : tan ^=cos Lo^B cot Lb; cot CA = cot Lo^B cos (La + 9>) cosec fp\ cot D =cos Ca tan (Lj^ + e meridian of the observer and the hour circle passing through that point; it may also be regarded as the arc of the equinoctial intercepted between those circles. It is measured toward the west as a positive direction through the twenty-four hours, or 360 degrees, which constitute the interval between the successive returns to the meridian, due to the diurnal rotation of the earth, of any point in the celestial sphere. The hour angle of M is the angle QPD, or the arc QD. 223. The Azimuth of a point in the celestial sphere is the an^le at the zenith between the meridian of the observer and the vertical circle passing through the Fig. 29. DEFINITIONS RELATING TO NAUTICAL ASTRONOMY. 89 point; it may also be regarded as the arc of the horizon intercepted between those circles. It is measured from either the north or the south point of the horizon (usually that one of the same name as the elevated pole) to the east or west through 180°, and is named accordingly; as, N. 60° W., or S. 120° W. The azimuth of M is the angle NZH, or the arc NH, from the north point, or the angle SZH, or the arc SH, from the south point of the horizon. 224:. The Amplitude of a point is the angle at the zenith between the prime vertical and the vertical circle of the point; it is measured from the east or the west point of the horizon through 90°, as W. 30° N. It is closely allied with the azimuth and may always be deduced therefrom. In the figure, the amplitude of H is the angle WZH, or the arc WH. The amplitude is only used with reference to points in the horizon. 225. The Ecliptic is the great circle representing the path in which, bv reason of the annual revolution of the earth, the sun appears to move in the celestial sphere; the plane of the ecliptic is inclined to that of the ec[uinoctial at an angle of 23 27^', and this inclination is called the obliguity of the ecliptic. The ecliptic is represented by the great circle CVT. 226. The Equinoxes are those points at which the ecliptic and the equinoctial intersect, and when the sun occupies either of these positions the days and n^hts are of equal length throughout the earth. The Vernal Equinox is that one at which the sun appears to an observer on the earth when passing from southern to northern declination, and the Autumnal Equinox that one at which it appears when passing from northern to southern declination. The Vernal Equinox is also designated as the First Point of Aries, and is used as an origin for reckoning right ascension ; it is indicated in the ngure at V. 227. The Solstitial Points, or Solstices, are points of the ecliptic at a distance of 90° from the equinoxes, at which the sun attains its highest declination in each hemisphere. They are called respectively the Summer and the Winier Solstice, according to the season in which tne sun appears to pass these points in its path. The Summer Solstice is indicated in the figure at U. 228. The RigJit Ascension of a point is the angle at the pole between the hour circle of the point and that of the First Point of Aries; it may also be regarded as the arc of the equinoctial intercepted between those circles. It ls measured from the First Point oi Aries to the eastward as a positive direction, tlirough twenty-four hours or 360 degrees. The right ascension of the point M' is YD'. 229. Celestial Latitude is measured to the north or south of the ecliptic upon great circles secondary thereto. Celestial Longitude is measured upon the ecliptic from the First Point of Aries as an origin, being regarded as positive to the eastward throughout 360°. 230. Coordinates. — In order to define the position of a point in space, a system of lines, angles, or planes, or a combination of these, is used to refer it to* some fixed line or plane adopted as the primitive ; and the lines, angles, or planes by which it is thus referred are called H coordinates. 231. In figure 30 is shown a system of rectilinear coordinates for a plane. A fixed line FE is chosen, and D in it a definite point C, as the origin. Then the posi- tion of a point A is defined by CB = a:, the distance F C from the origin, C, to the foot of a perpendicular let fall from A on FE; and by AB=y, the length of the perpendicular. The distance x is called the ahsdssa and y the ordinate. Assuming two intersecting right fiq. 30. lines FE and HI as standard lines of reference, the location of the point A is defined by regarding the distances measured to the right hand of HI and above FE as positive; those to the left hand of HI and below FE as negative. An exemplification of this system is found in the chart, on which FE is represented by the equator, HI by the prime meridian; the coordinates x and y being the longitude and latitude of the point A. 232. The great circle is to the sphere what the straight fine is to the plane; hence, in order to define the position of a point on the surface of a sphere, some great y E B 90 DEFINITIONS RELATING TO NAUTICAL ASTRONOMY. circle must be Eelected as the primary, and some particular point of it as the origin. Thus, in figure 31, which represents the case of a sphere, some fixed great circle, CBQ, is selected as the axis and called the primary; and a point C is chosen as the origin. Then to define the position of any point A, the ab- scissa X equals the distance from C to the point B, where the secondary great circle through A intersects the primary; the ordinate y equals the distance of A from the primary measmed on the secondary — that is, a; = CB and y = AB. 233. In the case of the earth, the primary selected is the equator (its plane being perpendicular to the earth's axis), and upon this are measured the abscissae, while upon the secondaries to it are measured the ordinates of all points on the earth's surface. The initial point for refer- ence on the equator is determined by the prime meridian chosen, West lon^tudes and North latitudes being called positive, East longitudes and South latitudes, negative. 234. In the case of the celestial sphere, there are four systems of coordinates in use for defining the position of any point; these vary according to the circle adopted as the primaiy and the point used as an origin. They are as follows: 1. Altitude and azimuth. 2. Dechnation and hour angle. ^ 3. Declination and right ascension. 4. Celestial latitude and longitude. 235. In the system of Altitude and Azimuth, the primary circle is the celestial horizon, the secondaries to which are the vertical circles, or circles of altitude. The horizon is intersected by the celestial meridian in its northern and souttiern points, of which one — usually that adjacent to the elevated pole — is selected as an origin for reckoning coordinates. The azimuth indicates in which vertical circle the point to be defined is found, and the altitude gives the position of the point in that circle. In figure 29 the point M is located, according to this system, by its azimuth NH and altitude HM. 236. In the system of Declination and Hour Angle, the primaiy circle is the equinoctial, the secondaries to which are the circles of declination, or hour circles. The point of origin is that point of intersection of the equinoctial and celestial meridian wliich is above the horizon. The hour angle indicates in which declina- tion circle the point to be defined is found, and the declination gives the position of the point in that circle. In figure 29 the point M is located, according to this system, by its hour angle Q,D and declination DM. 237. In the system of Declination and Right Ascension, the primary and seconda- ries are the same as in the system just described, but the point of origin differs, being assumed to be at the First Point of Aries, or vernal equinox. The right ascension indicates in which declination circle the point to be defined may be found, and the declination gives the position in that circle. In figure 29 the point M' is located by VD', the right ascension, and D'M', the dechnation. It should be noted that this system differs from the preceding in that the position of a point is herein referred to a fixed point in the celestial sphere and is independent of the zenith of the observer as well as of the position of the earth in its diurnal motion, while, in the system of declination and hour angle, both of these are factors in determining the coordinates. 238. In the system of Celestial Latitude and Longitude, the primary, circle is the ecliptic; the point of origin, the First Point of Aries. The method of reckoning by this system, which is of only slight importance in Nautical Astronomy, will appear from the definitions of celestial latitude and longitude already given (art. 229). CHAPTER VIII. mSTEUMENTS EMPLOYED IN NAUTICAL ASTEONOMY. THE SEXTANT. 239. Tho sextant is an instrument for measuring the angle between two objects by bringing into coincidence at the eye of the observer rays of light received directly from the one and by reflection from the other, the measure bein^ afforded by the inclination of the reflecting surfaces. By reason of its small dimensions, its accuracy, and, above aU, the fact that it does not require a permanent or a stable mounting but is available for use under the conditions existing on shipboard, it is a most important instrument for the purposes of the navigator. While the sextant is not capable of the same degree of accuracy as fixed instruments, its measurements are sufficiently exact for navigation. 240. Description. — A usual form of the sextant is represented in figure 32. The frame is of brass or some similar aUoy. The graduated arc, AA, generally of silver, is marked in ai)pro- priate divisions ; in the micr _ M sextants, each division rep- resents 10', and tho vernier affords a means of reading to 10". A wooden handle, H, is provided for holding the instrument. The index mirror, M, and Twrizon mir- ror, m, are of plate glass, and are silvered, though the upper half of the horizon glass is left plain to allow direct rays to pass thi'ough unobstructed. To give greater distinctness to the images, a small telescope, E, is placed in the lino of sight ; it is supported in a ring, K, which can be moved by a screw in a direction at right angles to the plane of the sex- Pio. 32. tant, thus shifting the axis of the telescope, and therefore the plane of reflection; this plane, however, always remains parallel to that of the instrument, the motion of the telescope being intended merely to regulate the relative brightness of the direct and reflected ima^e. In the ring, K, are small screws for the purpose of adjusting the telescope by making its axis Earallel with the plane of the sextant. The vernier is carried on the end of an index ar pivoted beneath the index mirror, M, and thus travels along the graduated scale, affording a measure for any change of incUnation of the index mirror; a reading glass, R, attached to the index bar and turning upon a pivot, S, facilitates the reading of vernier and scale. The index mirror, M, is attached to the head of the index bar, with its surface perpendicular to the plane of the instrument; an adjusting screw is fitted at the back to permit of adjustment to the perpendicular plane. The fixed glass m, half silvered and half plain, is called the Jwrizon glass, as it is through this that the 91 92 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. horizon is observed in measuring altitudes of celestial bodies; it is provided with screws, by which its perpendicularity to the plane of the instrument may be adjusted. At P and Q are colored glasses of different shades, which may be used separately or in combination to protect the eye from the intense Hght oi the sun. In order to observe with accuracy and make the images come precisely in contact, a tangent screw, B, is fixed to the mdex, by means of which the latter may be moved with greater precision than by hand ; but this screw does not act until the index is fixed by the screw C at the back of the sextant; when the index is to be moved any considerable amount, the screw C is loosened; when it is brought near to ite required position the screw must be tightened, and the index may then be moved gradually by the tangent screw. Besides the telescope, E, the instrument is usually provided with an inverting telescope, I, and a tube without glasses, F ; also, with a cap carrying colored glasses, which may be put on the eye end of the telescope, thus dispensing with the necessity for the use of tlie colored shades, P and Q, and eliminating any possible errors which might arise from nonparaUelism of their surfaces. The latest type of sextant furnished to the United States Navy is fitted with an endless tangent screw which carries a micrometer drum from which the seconds of arc are read. By pressure of the thumb the tangent screw is released and the index bar may be moved to any position on the arc by hand, where the tangent screw is again thrown into gear by releasing the pressure of the thumb. The endless tangent screw is accomplished by cutting the edge of the arc with the worm teeth into which the tangent screw gears. At night the reading of this sextant is facilitated by a small electric light carried on it and supplied by a batteiy contained in the handle. 241. The vernier is an attachment for facilitating the exact reading of the scale of a sextant, by which ahquot parts of the smallest divisions of the graduated scale are measured. The principle of the sextant vernier is identical with that of the barometer vernier, a complete description of which will be found in article 52, Chapter II. The arc of a sextant is usually divided into 120 or more parts, each division representing 1°; each of these degree divisions is further subdivided to an extent dependent upon the accuracy of reading of which the sextant is capable. In the instruments lor finer work, the divisions of the scale correspond to 10' each, and the vernier covers a length corresponding to 59 such divisions, which is subdivided into 60 parts, thus permitting a reading of 10"; all sextants, however, are not so closely graduated. Whatever the limits of subdivision, all sextants are fitted with verniers which contain one more division than the length of scale covered, and in which, therefore, scale-readings and vernier-readings increase in the same direction — toward the left hand. To read any sextant, it is merely necessary to observe the scale division next F below, or to the right of, the zero of the '^ vernier, and to add thereto the angle cor- responding to that division of the vernier scale which is most nearly in exact coin- cidence with a division of the instrument scale. 242. Optical Principle. — ^When a ray of light is reflected from a plane surface, the angle of incidence is equal to the angle _ of reflection. From this it may be proved PiQ 33_ that when a ray of light undergoes two reflections in the same plane the angle be- tween its first and its last direction is equal to twice the inclination of the reflecting surfaces. Upon this fact the construction of the sextant is based. In figure 33, let B and C represent respectively the index mirror and horizon mirror of a sextant; draw EF perpendicular to B, and CF perpendicular to C; then the angle CFB represents the incUnation of the two mirrors. Suppose a ray to pro- ceed from A and undergo reflection at B and at C, its last direction being CD; then ADC is the angle between its first and last directions, and we desire to prove that ADC = 2 CFB. INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 93 From the equality of the angles of incidence and reflection: ABE=EBC, and ABC = 2 EBC; BCF = FCD, and BCD = 2 BCF. From Geometry: ADC = ABC - BCD = 2 (EBC - BCF) = 2 CFB, which is the relation that was to be proved ._ 24:3. In the sextant, since the index mirror is immovably attached to the index arm, which also carries the vernier, it follows that no change can occur in the incUna- tion between the index mirror and the horizon mirror, excepting such as is registered by the travel of the vernier upon the scale. If, when the index mirror is so placed that it is nearly parallel with the horizon mirror, an observer direct the telescope toward some weU-defined object, there wiU be seen in the field of view two separate images of the object; and if the inclination of the index mirror be slightly changed by moving the index bar, it will be seen that while one of the images remains fixed the other moves. The fixed image is the direct one seen through the unsilvered p^rt of the horizon glass, while the movable image is due to rays reflected by the index and horizon mirrors. When the two images coincide these mirrors must be parallel (assuminjj that the object is sufficiently distant to disregard the space which separates the mirrors; in this position of the index mirror the vernier indicates the true zero of the scale. If, however, instead of observing a single object, the instrument is so placed that the direct ray from one object appears in coincidence with the reflected ray of a second object, then the true angle between the objects will be twice the angle of inclination between the mirrors, or twice the angle measured by the vernier from the true zero of the scale. To avoid the necessity of doubling the angle on the scale, the latter is so marked that each half degree appears as a. whole degree, whence its indications give the whole angle directly. 244. Adjustments of the Sextant. — ^The theory of the sextant requires that, for accurate indications, the foUowing conditions be fulfilled: (a) The two surfaces of each mirror and shade glass must be parallel planes. (h) The graduated arc or limb must be a plane, and its graduations, as well as those of the vernier, must be exact. (c) The axis must be at the center of the limb, and perpendicular to the plane thereof. (d) The index and horizon glasses must be perpendicular, and the line of sight parallel to the plane of the limb. Of these, only the last named ordinarily require the attention of the navigator who is to make use of the sextant; the others, which may be called the permanent adjustments, should be made before the instrument leaves the hands of the maker, and with careful use will never be deranged. 245. The Adjustment of the Index Mirror consists in making the reflecting surface of this mirror truly perpendicular to the plane of the sextant. In order to test this, set the index near the middle of the arc, then, placing the eye very nearly in the plane of the sextant and close to the index mirror, observe whether the direct image of the arc and its image reflected from the mirror appear to form one continuous arc; if so, the glass is perpendicular to the plane of the sextant; if the reflected image appears to droop from the arc seen directly, the glass leans backward ; if it seems to rise, the glass leans forward. The adjustment is made by the screws at the back of the mirror. 246. The Adjustment of the Horizon Mirror consists in making the reflecting surface of this mirror perpendicular to the plane of the sextant. The index mirror having been adjusted, if, in revolving it by means of the index arm, there is found one position in which it is parallel to the horizon glass, then the latter must also be perpendicular to the plane of the sextant. In order to test this, put in the telescope and direct it toward a star; move the index until the reflected image appears to pass the direct image; if one passes directly over the other the mirrors must be parallel; 94 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. if one passes on either side of the other the horizon glass needs adjustment, which is accomplished b}^ means of the screws attached. The sea horizon may also be used for making this adjustment. Hold the sextant vertically and bring the du-ect and the reflected images of the horizon line into coin- cidence; then incline the sextant until its plane makes but a small angle with the horizon; if the images still coincide the glasses are parallel; if not, the horizon glass needs adjustment. 247. The Adjustment of the Telescope must be so made that, in measuring angular distances, the line of sight, or axis of the telescope, shall be parallel to the plane of the instrument, as a deviation in that respect, in measuring large angles, will occasion a considerable error. To avoid such error, a telescope is employed in which are placed two wires, parallel to each other and equidistant from the center of the telescope ; by means oi these wires the adjustment may be made. Screw on the telescope, and turn the tube containing the eyeglass tiU the wires are parallel to the plane of the instrument; then select two clearl;;/^ defined objects whose angular distance must be not less than 90°, because an error is more easily discovered when the angle is great; bring the reflected image of one object into exact coincidence with the direct image of the other at the inner wire; then, by altering slightly the position of the instrument, make the objects appear on the other wire; if the contact still remains perfect, the axis of the telescope is in its right situation ; but if the two objects appear to separate or lap over at the outer wire the telescope is not parallel, and it must be rectified by turning one of the two screws of the ring into which the telescope is screwed, having previously unturned the other screw; by repeating this operation a few times the contact will be precisely the same at both wires, and the axis of the telescope will be parallel to the plane of the instrument. Another method of making this adjustment is to place the sextant upon a table in a horizontal position, look along the plane of the limb, and make a mark upon a wall, or other vertical surface, at a distance of about 20 feet; draw another mark above the first at a distance equal to the height of the axis of the telescope above the plane of the limb; then so adjust the telescope that the upper mark, as viewed through the telescope, faUs midway between the wires. Some sextants are accom- panied by small sights whose height is exactly equal to the distance between the telescope and the plane^ of the limb ; by the use of these, the necessity for employing the second mark is avoided and the adjustment can be very accurately made. 248. The errors which arise from defects in what have been denominated the permanent adjustments of the sextant may be divided into three classes, namely: Errors due to faulty centering of the axis, called eccentricity; errors of graduation; and errors arising from lack of parallelism of surfaces in index mirror and in shade glasses. The errors due to eccentricity and faulty graduation are constant for the same angle, _ and should be determined once for all at some place where proper facilities for doing the work are at hand; these errors can only be ascertained by measuring known angles with the sextant. If angles of 10°, 20°, 30°, 40°, etc., are first laid off with a theodolite or similar instrument and then measured by the sextant, a table of errors of the sextant due to eccentricity and faulty graduation may be made, and the error at any intermediate angle found by interpolation; this table will include the error of graduation of the theodolite and also the error due to inaccurate reading of the sextant, but such errors are small. Another method for determining the combined errors of eccentricity and graduation is by measuring the angular distance between stars and comparing the observed and the computed arc between them, but this process is liable to inaccuracies by reason of the uncertainty of allow- ances for atmospheric refraction. Errors of graduation, when lar^e, may be detected by "stepping off" distances on the graduated arc with the vermer; place the zero of the vernier in exact coinci- dence with a division of the arc, and observe whether the final division of the vernier also coincides with a division of the arc; this should be tried at numerous positions of the graduated limb, and the agreement ought to be perfect in every case. The error due to a prismatic index mirror may be found by measuring a certain unchangeable angle, then taking out the glass and turning the upper edge down, and measuring the angle again; half the difference of these two measures will be the error at that angle due to the mirror. From a number of measures of angles INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 95 in this manner, a table similar to the one for eccentricity and faulty ^aduation can be made; or the two tables m.&j be combined.^ When possible to avoid it, however, no sextant should be used in which there is an index mirror which produces a greater error than that due to the probable error of reading the scale. Mirrors having a greater angle than 2" between their faces are rejected for use in the United States Navy. Index mirrors may be roughly tested by noting if there is an elongated image of a well-defined point at large angles. Since the error due to a prismatic horizon mirror is included in the index cor- rection (art. 249), and consequently applied alike to all angles, it may be neglected. Errors due to prismatic shade glasses can be determined by measuring angles with and without the shade glasses and noting the difference. They may also be determined, where the glasses are so arranged that they can be turned through an angle of 180°, by measuring the angle first with the glass in its usual position and then reversed, and taking the mean of the two as the true measure. 249. Index Error.^ — The Index Error of a sextant is the error of its indications ■ due to the fact that when the index and horizon mirrors are parallel the zero of the vernier does not coincide with the zero of the scale. Having made the adjustments of the index and horizon mirrors and of the telescope, as previously described, it is necessary to find that point of the arc at which the zero of the vernier falls when the two mirrors are parallel, for all angles measured by the sextant are reckoned from that point. If this point is to the left of the zero of the limb, aU readings will be too great; if to the right of the zero, all readings will be too small. if desirable that the reading should be zero when the mirrors are parallel, place the zero of the vernier on zero of the arc; then, by means of the adjusting screws of the horizon glass, move that glass until the direct and reflected images of the same object coincide, after which the perpendicularity of the horizon ^lass should again be verified, as it may have been deranged by the operation. This adjustment is not essential, since the correction may readily do determined and applied to the reading. In certain sextant work, however, such as surveying, it will be very convenient to be relieved of the necessity of con-ecting each angle observed. The sextant should never be relied upon for maintaining a constant index correction, and the error should be ascertained frequently. It is a good practice to verify the correction each time a sight is taken. 250. The Index Correction may be found (a) by a star, (6) by the sea horizon, and (c) by the sun. (a) Bring the direct and reflected images of a star into coincidence, and read off the arc. The index correction is numerically equal to this reading, and is positive or negative according as the reading is on the right or left of the zero. (o) The same method may be employed, substituting for a star the sea horizon, though this will be found somewhat less accurate. (c) Measure the apparent diameter of the sun by first bringing the upper limb of the reflected image to touch the lower limb of the direct image, and then cringing the lower limb of the reflected image to touch the upper limb of the direct image. Denote the readings in the two cases by r and r ; then, if S = apparent diameter of the sun, and R = the reading of the sextant when the two images are in coincidence, we have: r =R + S, r' = R-S, R = i {r + r'). As R represents the error, the correction will be — R. Hence the rule: Mark the readings when on the arc with the negative sign; when off, with the positive sign; then the index correction is one-half the algebraic sum of the two readings. Example : The sun's diameter is measured for index correction as follows : On the arc, 31' 20"; off the arc, 33' 10". Required the correction. On the arc, -31' 20" Off the arc, +33 10 2)+ 1 50 I. C, + 55 96 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 251. From the equations previously given, it is seen that: S=i (r-r'); hence, if the observations are correct, it will be found that the sun's semidiamoter, as given in the Nautical Almanac for the day of observation, is equal to one-half the algebraic difference of the readings. If required to obtain the index correction with great precision, several observations should be taken and the mean used, the accuracy being verified by comparing the tabulated with the observed semidiameter. If the sun is low, the horizontal semidiameter should be observed, to prevent the error that may arise from unequal refraction. 252. Use of the Sextant, — ^To measure the angle between any two visible objects, point the telescope toward the lower one, if one is above the other, or toward the left-hand one, if they are in nearly the same horizontal plane. Keep this object in direct view through the unsilvcred part of the horizon glass, and move the index arm imtil the image of the other object is seen by a double reflection from the index mirror and the silvered portion of the horizon glass. Having gotten the direct image of one object into nearly exact contact with the reflected image of the other, clamp the index arm and, by means of the tangent screw, complete the adjustment so that the contact may be perfect; then read the limb. In measuring the altitude of a celestial body above the sea horizon, it is necessary that the angle shall be measured to that point of the horizon which lies vertically beneath the object. To determine this point, the observer should move the instru- ment sUghtly to the right and left of the vertical, swinging it about the line of sight as an axis, taking care to keep the object in the middle of the field of view. The object will appear to describe the arc of a circle, and the lowest point of this arc marks the true vertical. The shade glasses should be employed as may be necessary to protect the eye when observing objects of dazzling brightness, such as the sun, or the horizon when the sun is reflected from it at a low altitude. Care must be taken that the images are not too bright or the eye wiU be so affected as to interfere with the accuracy of the observations. 253. Choice of Sextants. — ^The choice of a sextant should be governed by the kind of work which is required to be done. In rough work, such as surveying, where angles need only be measured to the nearest 30'' the radius maybe as small as 6 inches, which wiU permit easy reading, and the instrument can be correspondingly lightened. Where readings to 10'' are desired, as in nice astronomical work, the radius should be about 7i inches, and the instrument, to be strongly built, should weigh about 3J pounds. The parts of an instrument should move freely, without binding or gritting. The eyepieces should move easily in the telescope tubes; the bracket for carrying tne tele- scope should be made very strong. It is frequently found that the parallehsm of the line of sight is destroyed in focusing the eyepiece, either on account of the loose- ness of the fit or because of the telescope bracket being weak. The vernier should lie close to the limbs to prevent paraUax in reading. If it is either too loose or too tight at either extremity of its travel, it may indicate that the pivot is not perpendicu- lar. The baUs of the tangent screw should fit snugly in their sockets, so that there may be no lost motion. Where possible, the sextant should always be submitted to expert exammation and test as to the accuracy of its permanent adjustments before acceptance by the navigator. 254. Kesilvering Mirrors. — Occasion may sometimes arise for resflvering the mirrors of a sextant, as they are always liable to be damaged by dampness or other causes. For this purpose some clean tin fofl and mercury are required. Upon a piece of glass about 4 mches square lay a piece of tin foil whose dimensions exceed by about a quarter of an inch in each direction those of the glass to be sflvered; smooth out the foil carefuUy by rubbing; put a small drop of mercury on the foil and spread it with the finger over the entire surface, being careful that none shall find its way under the foil; then put on a few more drops of mercury until the whole surface is fluid. The glass which is to be silvered having been carefully cleaned, it should be laid upon a piece of tissue paper whose edge just covers the edge of the foil and I INSTRUMENTS EMPLOYED IN NAUTICAL ASTEONOMY. 97 transferred carefully from the paper to the tin foil, a gentle pressure being kept upon the glass to avoid the formation of bubbles; finally, place tne mirror face downward and leave it in an inclined position to allow the surplus mercury to flow off, the latter operation being hastened bv a strip of tin foil at its lower edge. After five or six hours the tin foil around the edges may be removed, and the next day a coat of varnish made from spirits of wine and red sealing wax should be apphed. For a horizon mirror care must be taken to avoid silvermg the plain half. The mercury drawn from the foU should not be placed with clean mercury with a view to use in the artificial horizon or the whole will be spoiled. 255. Octants and Quintants. — rroperly speaking, a sextant is an instrument whose arc covers one-sixth of a complete circle, and which is therefore capable of measuring an angle of 120°. Other instruments are made which are identical in principle with the sextant as heretofore described, and which differ from that instru- ment only in the length of the arc. These are the octant, an eighth of a circle, by which angles may be measured to 90°, and the quirdant, a fifth of a circle, whicn measures angles up to 144°. The distinction between these instruments is not always carefuUy made, and in such matters as have been touched upon in the fore- going articles the sextant may be regarded as the type of all kindred reflecting mstruments. THE ABTiriCIAL HORIZON. 256. The Artificial Horizon is a small, rectangular, shallow basin of mercury, over which, to protect the mercury from agitation by the wind, is placed a roof consisting of two plates of glass at ri^ht angles to each other. The mercury affords a perfectly horizontal surface which is at tne same time an excellent mirror. The different parts of an artificial horizon are furnished in a compact form, a metal bottle being provided for containing the mercury when not in use, together with a suitable funnel for pouring. If MN, in figure 34, is the horizontal surface of the mercury; S'B a ray of light from a celestial object, inciaent to the surface atB; BA the reflected ray; then an observer at A will receive the ray BA as if it proceeded from a point S*, whose angular depression, MBS", below the horizontal plane is equal to the altitude, JMBS', of the object above that plane. If, then, SA is a direct ray from the object parallel to S'B, an observer at A can measure with the sextant the angle SAS" = S'BS" = 2 S'BM, by bringing the image of the object reflected by the index mirror into coincidence with the image S" re- flected by the mercury and seen through the horizon glass. The instrumental measure, corrected for in- dex error, will be double the apparent altitude of the fig. 34. body. The sun's altitude will be measured by bringing the lower limb of one image to touch the upper limb of the other. Half the corrected instrumental reading wfll be the apparent altitude of the sun's lower or upper limb, according as the lower or upper limb of the reflected image was the one employed in the observation. In observations of the sun with the artificial horizon, the eye is protected by a suigle dark glass over the eyepiece of the telescope through which direct and reflected rays must pass alike, thereby avoiding the errors that might possibly arise from a difference in the separate shade glasses attached to the frame of the sextant. The glasses in the roof over the mercury should be made of plate glass, with perfectly paraUel faces. If they are at all prismatic, the observed altitude will be erroneous. The error may be removed by observing a second altitude with the roof reversed, and, in general, by taking one-half of a set of observations with the roof in one position and the other half with the roof reversed. On the rare occasions when the atmosphere is so calm that the unsheltered mercury will remain undisturbed, most satisfactory observations may be made by leaving off the roof. 21594°— 14 7 98 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 257. In setting up an artificial horizon, care should be taken that the basin is free from dust and other foreign matter, as small particles floating upon the surface of the mercury interfere with a perfect reflection. The basin should be so placed that its longer edge lies in the direction in which the observed body will bear at the middle of the observations. The spot selected for taking the sights should be as free as possible from causes which will produce vibration of the mercury, and pre- cautions should be taken to shelter the horizon from the wind, as the mere placing of the roof will not ordinarily be sufficient to accomplish this. Embedding the root in earth serves to keep out the wind, while setting the whole horizon upon a thick towel or a piece of such material as heavy felt usually affords ample protection from wind, tends to reduce the vibrations from mechanical shocks, and also aids in keeping out the moisture from the ground. In damp climates the roof should be kept dry by wiping, or the moisture deposited from tne inclosed air will form a cloud upon the glass. Molasses, oil, or other viscous fluid may, when necessary, be employed as a substitute for mercury. 258. Owing to the perfection of manufacture that is required to insure accuracy of results with the artificial horizon, navigators are advised to accept only such instrument as has satisfactorily stood the necessary tests to prove the correctness of its adjustment as regards the glasses of the roof. THE CHRONOMETER. 259. The Chronometer is simply a correct time measurer, differing from an ordinary watch in having the force of its mainspring rendered uniform by means of a variable lever. Owing to the fact that on a sea voyage a chronometer is exposed to many changes of temperature, it is furnished with an expansion balance, formed of a combination of metals of different expansive qualities, which produces the required compensation. In order that its working maj^ not be deranged by the motion of the ship in a seaway, the instrument is carried in gimbals. As the re^larity of the chronometer is essential for the correct determination of a ship's position, it is of the greatest importance that every precaution be taken to insure the accuracy of its indications. There is no more certain way of doing this than to provide a vessel with several of these instruments — preferably not less than three — m order that if an irregularity develop in one, the fact may be revealed by the others. 260. Care of Chronometers on Shipboard. — ^The box in which the chro- nometers are kept should have a permanent place as near as practicable to the center of motion of the ship, and where it will be free from excessive shocks and jars, such as those that arise from the engines or from the firing of heavy guns; the location should be one free from sudden and extreme changes of temperature, and as far removed as possible from masses of vertical iron. The box should contain a separate compartment for each chronometer, and each compartment should be lined with baize cloth padded with curled hair, for the double purpose of reducing shocks and equalizing tne temperature within. An outer cover of baize cloth should be pro- vided for the box, and this should be changed or dried out frequently in damp weather. The chronometers should aU be placed with the XII mark in the same position. For transportation for short distances by hand, an instrument should be rigidly clamped in its gimbals, for if left free to swing, its performance may be deranged by the violent oscillations that are imparted to it. For transportation for a considerable distance, as by express, the chronometer should be allowed to run down, and should then be dismounted and the balance corked. 261. Since it is not possible to make a perfect instrument which will be unin- fluenced by the disturbing causes incident to a sea voyage, it becomes the duty of the navigator to determine the error and to keep watch upon the variable rate of the chronometer. The error of the chronometer is the difference between the time indicated and the standard time to which it is referred — usually Greenwich mean time. The amount the chronometer gains or loses daily is the daily rate. INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 99 The indications of a chronometer at any given instant require a correction for the accumulated error to that instant; and this can be found if the error at any given time, together with the daily rate, are known. 262. Winding. — Chi-onometers are ordinarily constructed to run for 56 hours without rewinding, and an indicator on the face always shows how many hours have elapsed since the last winding. To insure a uniform rate, they must be wound regularly every day, and, in order to avoid the serious consequences of their running down, the navigator should take some means to guard against neglecting this duty through a fault of memory. To wind, turn the chronometer gently on its side, enter the key in its hole and push it home, steadying the instrument with the hand, and wind to the left, the last half turn being made so as to bring up gently against the stop. After winding, cover the keyhole and return the instrument to its natural position. Chronometers should always be wound in the same order to prevent omissions, and the precaution taken to inspect the indicators, as a further assurance of the proper performance of the operation. After winding each day, the comparisons should be made, and, with the reading of the maximum-and-minimum thermometer and other necessary data, recorded in a book kept for the purpose.^ The maximum-and-minimum thermometer is one so arranged that its highest and lowest readings are marked by small steel indices that remain in place until reset. Every chronometer box should be provided with such an instrument, as a knowledge of the temperature to which chronometers have been subjected is essential in any analysis of the rate. To draw down the indices for the purpose of resetting, a magnet is used. This magnet should be kept at all times at a distance from the chronometers. 263. Comparison of Chronometers. — ^The instrument believed to be the best is regarded as the Standard, and each other is compared with it. It is usual to desig- nate the Standard as A, and the others as B, C, etc. Chronometers are made to boat half seconds, and any two may be compared by following the beat of one with the ear and of the other with the eye. To make a comparison, say of A and B, open the boxes of these two instruments and close all others. Get the cadence and, commencing when A has just completed the beat of some even 5-second division of the dial, count ** half-one-half -two-haK- three-haK-four-half-five," glancing at B in time to note the position of its second hand at the last count; the seconds indicated by A will be five greater than the number at the beginning of the count. The hours and minutes are also recorded for each chronometer, and the subtraction made. A good check upon the accuracy is afforded by repeating the operation, taking the tick n-om B. Where necessary for exact work, it is possible to estimate the fraction between beats, and thus make the comparison to tenths of a second; but the nearest half second is sufficiently exact for the purposes of ordinary navigation at sea. 264. The following form represents a convenient metnod of recording com- parisons : Stand. A, No. 777. Chro. B, No. 1509. Chro. 0, No. 1802. Date, 1903. Designation of comparisons. Chro. B with Stand. A. 2ddifl. Chro. C with Stand. A. 2ddifl. Therm. Bar. Rfiinarks. Max. Min. Air. January Stand. A. BandC. Difference. h. m. s. 1 13 40 1 12 2L5 s. h. m. s. 1 14 20 2 04 11 s. • 63 O 59 60 30.07 Found errors by time- ball. 1 18.5 11 10 09 2 Stand. A. B and C. Difference. 1 16 30 1 15 10 +L5 1 17 00 2 06 51. 5 -0.5 64 58 57 30.12 Left New York for San Juan, P. R. 1 20 11 10 08. 5 100 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 265. The secorid difference in the form is the difference between the comparisons of the same instruments for two successive days. When a vessel is equipped with only one chronometer there is nothing to indicate any irregularity that it may develop at sea — and even the best instruments may imdergo changes from no apparent cause. When there are two chronometers, the second difference, which is equal to the algebraic difference between their daily rates, remains uniform as long as the rates remain uniform, but changes if one of the rates undergoes a change; in such a case, there is no means of knowing which chronometer has departed from its expected performance, and the navigator must proceed with caution, giving due faith to the indications of each. If, however, there are three chronometers, an irregularity on the part of one is at once located by a comparison of the second differences. Tnus, if the predicted rates of the chronometers were such as to give for the second difference of A-B,+ 1^.5,andof A— C, — 0^5, suppose on a certain day those differences were ^-4^5and — 0^5, respectively; it would at once be suspected that the irregularity was in B, and that that chronometer had lost 3^ on its normal rate during the preceding day. Suppose, however, the second differences were +4^.5 and +2^.5; it would then be apparent that A had gained 3^. 266. Temperature Curves. — Notwithstanding the care taken to eliminate the effect of a change of temperature upon the rate of a chronometer, it is rare that an absolutely perfect compensation is attained, and it may therefore be assumed that the rates of aU chronometers vary somewhat with the temperature. Where the voyage of a vessel is a long one and marked changes of climate are encountered, the accu- mulated error from the use of an incorrect rate may be very material, amounting to several minutes' difference of longitude. Careful navigators will therefore take every means to guard against such an error. By the employment of a temperature curve in connection with the chronometer rate the most satisfactory results are arrived at. 267. There should be furnished with each chronometer a statement showing its daily rate under various conditions of temperature ; and this may be supplemented by the observations of the navigator during the time that the chronometer remains on board ship. With all available data a temperature curve should be constructed which wiU indicate graphically the performance of the instrument. It is most con- venient to employ for this purpose a piece of " profile paper," on which parallel lines are ruled at equal intervals at right angles to each other. Let each horizontal line represent, say, a degree of temperature, numbered at the left edge, from the bottom up ; draw a vertical line in red ink to represent the zero rate, and let all rates to the right be 'plus, or gaining, and those to the left minus, or losing; let the intervals between vertical lines represent intervals of rate (as one-tenth of a second) numbered at the top from the zero rate; then on this scale plot the rate corresponding to each temperature; when there are several observations covering one height of the ther- mometer, the mean mav be used. Through all the plotted points draw a fair curve, and the intersection of this curve with each temperature line gives the mean rate at that temperature. The mean temperature given by the maximum and minimum thermometer shows the rate to be used on any day. 268. Hack or Comparing Watch. — In order to avoid derangement, the chro- nometers should never be removed from the permanent box in which they are kept on shipboard. When it is desired to mark a certain instant of time, as for an astro- nomical observation or for obtaining the chronometer error by signal, the time is marked by a ''hack" (an inferior chronometer used for this purpose only), or by a comparing watch. Careful comparisons are taken — preferably both before and afterwards — and the chronometer time at the required instant is thus deduced. The correction represented by the chronometer time minus the watch time (twelve hours being added to the former when necessary to make the subtraction possible) is referred to asC-W. Suppose, for example, the chronometer and watch are compared and their indications are as follows : Chro. t., 5*^ 27'^ 30" W. T., -2 36 45.5 C-W, 2 50 44.5 INSTRUMENTS EMPLOYED IN NAUTICAL ASTRONOMY. 101 If then a sight is taken when the watch shows S** 01°° 27^.5, we have: W. T., 3^ 01" 27».5 C-W, +2 50 44.5 Chro. t., 5 52 12.0 It may occur that the values of C — W, as obtained from comparisons before and after marking the desired time, wiU vary; in that case the value to be used will be the mean of the two, if the time marked is about midway between comparisons, but if much nearer to one comparison than the other, allowance should be made accord- ingly- Thus suppose, in the case previously given, a second comparison had been taken after the sight as follows: Chro. t., 6'' 12°> 45« W. T., -3 21 59.5 C-W, 2 50 45.5 The sight having been taken at about the middle of the interval, the C — W to be used would be the mean of the two, or 2^ 50" 45*.0. Let us assume, however, that the second comparison showed the following: Chro. t., 6'' 38" 25" W. T., -3 47 39 C-W, 2 50 46 Then, the sight having been taken when onljr about one-third of the interval had elapsed between the first and second comparisons, it woidd be assumed that onlv one-third of the total change in the C — W had occurred up to the time of sight, and the value to be used would be 2'' 50" 45*.0. 269. It is considered a good practice always to subtract watch time from chronometer time, whatever the relative values, and thus to employ C — W invariably as an additive correction. It is equally correct to take the other difference, W — C, and make it sub tractive ; it may sometimes occur that a few figures will thus be saved, but a chance for en'or arises from the possibility of inadvertently using the wrong sign, which is almost impossible by the other method. Thus, the foUowmg example may be taken: (C, lO'' 57" 38" W, 11^ 42" 35" W, -11 42 35 C, -10 57 38 Comparison' Sight C-W, 11 15 03 W-C, 44 57 W, 11 50 21 W, 11 50 21 C-W, +11 15 03 W-C, - 44 57 ,C, 11 05 24 C, 11 05 24 CHAPTER IX. TIME AND THE NAUTICAL ALMANAC. 270. The subjects of Time and the Nautical Almanac are two of the most important ones to be mastered in the study of Nautical Astronomy, as they enter into every operation for the astronomical determination of a ship's position. They will be treated in conjunction, as the two are interdependent. METHODS OF BECKONING TIME. 271. The instant at which any point of the celestial sphere is on the meridian of an observer is termed the transit, culmination, or meridian passage of that point; when on that half of the meridian w^hich contains the zenith, it is designated as superior or upper transit; when on the half containing the nadir, as inferior or lower transit. 272. Three different kinds of time are employed in astronomy — (a) apparent or solar time, (6) mean time, and (c) sidereal t%me. These depend upon the hour angle from the meridian of the points to which they respectively refer. The point of reference for apparent or solar time is the Center of ike Sun; for mean time, an imaginary point called the Mean Sun; and for sidereal time, the Verrwl Equinox, also called the First Point of Aries. The unit of time is the Day, which is the period between two successive transits over the same branch of the meridian of the point of reference. The day is divided into 24 equal parts, called Hours; each hour is divided into 60 equal parts, called Minutes, and each minute into 60 equal parts, called Seconds. 273. Apparent or Solar Time. — Tne hour angle of the center of the sun affords a measure of Apparent or Solar Time. An Apparent or Solar Day is the interval of time between two successive transits over the same meridian of the center of the sun. It is Apparent Noon when the sun's hour circle coincides with the celestial meridian. This is the most natural and direct measure of time, and the unit of time adopted by the navigator at sea is the apparent solar day. Apparent noon is the time when tne latitude can be most readily determined, and the ordinary method of determining the longitude by the sun involves a calculation to deduce the apparent time first. Since, however, the intervals between the successive returns of the sun to the same meridian are not equal, apparent time can not be taken as a standard. The apparent day varies in length from two causes : first, the sun does not move in the equator, the great circle perpendicular to the axis of rotation of the earth, but in the ecliptic; and, secondly, the sun's motion in the ecliptic is not uniform. Sometimes the sun describes an arc of 57' of the ecliptic, and sometimes an arc of 61' in a day. At the points where the ecliptic and equmoctial intersect, the direction of the sun's apparent motion is inclined at an angle of 23° 27' to the equator, whUe at the solstices it moves in a direction parallel to the equator. 274. Mean Time. — ^To avoid the irregularity of time caused b;;^ the want of uniformity in the sun's motion, a fictitious sun, called the Mean Sun, is supposed to move in the equinoctial with a uniform velocity that equals the mean velocity of the true sun in the ecliptic. This mean sun is regarded as being in coincidence with the true sun at the vernal equinox, or First Point of Aries. Mean Time is the hour angle of the mean sun. A Mean Day is the interval between two successive transits of the mean sun over the meridian. Mean Noon is the instant when the mean sun's hour circle coincides with the meridian. 102 TIME AND THE NAUTICAL ALMANAC. 103 Mean time lapses uniformlv; at certain times it agrees with apparent time, while sometimes it is behind, and at other times in advance of it. It is this time that is measured by the clocks in ordinary use, and to this the chronometers used by navigators are regulated. 275. The difference between apparent and mean time is called the Equation of Time; by this quantity, the conversion from one to the other of these times may be made. Its magnitude and the direction of its application may be found for any moment from the Nautical Almanac. 276. Sidereal Time. — Sidereal Time is the hour an^le of the First Point of Aries. This point, which is identical with the vernal equinox, is the origin of all coordinates oi right ascension. Since the position of the point is fixed in the celestial sphere and does not, like the sun, moon, and planets, have actual or apparent motion therein, it shares in this respect the properties of the fixed stars. It may therefore be said that intervals of sidereal time are those which are measured by the stars. A Sidereal Day is the interval between two successive transits of tne First Point of Aries across the same meridian. Sidereal Noon is the instant at which the hour circle of the First Point of Aries coincides with the meridian. In order to interconvert sidereal and mean times an element is tabulated in the Nautical Almanac. This is the Sidereal Time of Mean Noon, which is also the Right Ascension of the Mean Sun. 277. Civil and Astronomical Time. — The Civtl Day commences at midnight and comprises the twenty-four hours until the following midnight. The hours are counted from to 12, from midnight to noon; then, again, from to 12, from noon to midnight. Thus the civil day is divided into two periods of twelve hours each, the first of which is marked a. m. (ante meridian), while the last is marked p. m. (post meridian). The Astronomical or Solar Day commences at noon of the civil day of the same date. It comprises twenty-four hours, reckoned from to 24, from noon of one day to noon of the next. Astronomical time (apparent or mean) is the hour angle of the sun (true or mean) measured to the westward throughout its entire circuit from the time of its upper transit on one day to the same instant of the next. The civil day, therefore, begins twelve hours before the astronomical day, and a clear imderstanding of this fact is all that is required for interconverting these times. For example: January 9, 2 a. m., civil time, is January 8, 14'', astronomical time. January 9, 2 p. m., civil time, is January 9, 2^, astronomical time. 278. Hour Angle. — The Tiour angle of a heavenly body is the angle at the pole of the celestial concave between the declination circle of the heavenly body and the celestial meridian. It is measured by the arc of the celestial equator between the declination circle and the celestial meridian. In figure 35 let P be the pole of the celestial sphere, of which VMQ is the equator, PQ the celestial meridian, and PM, PS, PV the declination circles of the mean sun, a heavenly body, and the First Point of Aries, respectively. Then QPM, or its arc QM, is the hour angle of the mean sun, or the mean time ; QPS, or QS, the hour angle of the fig. 35. heavenly body; QPV, or QV, the hour angle of the First Point of Aries, or the sidereal time; VPQ, or VQ, the right ascension of the meridian; VPS, or VS, the right ascension of the heavenly body; and VPM, or VM, the right ascen- sion of the mean sun. 279. Time at Different Meridians. — The hour angle of the true sun at any meridian is called the local aj^'parent time; that of the mean sun, the local mean time; that of the First Point of Anes, the local sidereal time. The hour angles of the same body and points from Greenwich are respectively the Greenwich apparent, mean, and sidereal times. The difference between the local time at any meridian and the Greenwich time is ec[ual to the longitude of that place from Greenwich expressed in time; the conversion from time to arc may be effected by a simple mathematical calculation or by the use of Table 7. In comparing corresponding times of different meridians the most easterly meridian may be distinguished as that at which the time is greatest or latest. 104 TIME AND THE NAUTICAL ALMANAC. In figure 36 PM and PM' represent the celestial meridians of two places, PS the declination circle through the sun, and PG the Greenwich meridian ; let Tq = the Greenwich time = GPS ; Tii = the corresponding local time at all places on the meridian PM = MPS; Tji' = the corresponding local time at all places on the meridian PM' = M'PS; Lo = west longitude of meridian PM = GPM ; and Lo' = east longitude of meridian PM' = GPM'. If west longitudes and hour angles be reckoned as positive, and east longitudes and hour angles as negative, we have : Lo = To-Tm; and Lo' = Tq-Tm'; therefore Lo-Lo'=Tm'-T„. Thus it may be seen that the difference of longitude be- tween two places equals the difference of their local times. Fig. 36. This relation may be shown to hold for any two meridians whatsoever. Both local and Greenwich times in the above formulae must be reckoned west- ward, always from their respective meridians and from O'* to 24^; in other words, it is the astronomical time which should be used in aU astronomical computations. The formula Lo = T^ — Tm is true for any kind of time, solar or sidereal ; or, in general terms, Tq and T^ are the hour angles of any point of the sphere at the two meridians whose difference of longitude is Lo. S may be the sun (true or mean) or the vernal equinox. 280. Finding the Greenwich Time, — Since nearly every computation made by the navigator requires a knowledge of the Greenwich date and time as a pre- liminary to the use of the Nautical Almanac, the first operation necessary is to deduce from the local time the corresponding Greenwich date, either exact or approxi- mate, and thence the Greenwich time expressed astronomically. The formula is: Tq = T^+Lo, rememDering that west longitudes are positive, east longitudes are negative. Hence the following rule for converting local to Greenwich time : Having expressed the local time astronomically, add the longitude if west, subtract it u east; the result is the corresponding Greenwich time. Example: In longitude 81** 15'' W. the local time is, April, 15"^ 10'' 17™ 30' a. m. Required the Greenwich time. Local Ast. time, April, 14'* 22'' 17° 30' Longitude, + 5 25 00 Greenwich time, 15 3 42 30 Example: In longitude 81° 15' E. the local time is, August, 5"* 2^ 10™ 30» p. m. Required the Green- wich time. Local Ast. time, August, 5"* 2'* 10™ 30' Longitude, — 5 25 00 Greenwich time, 4 20 45 30 Example: In longitude 17° 28' W. the local time is. May, 1"* 3** 10™ p. m. Required the Greenwich time. Local Ast. time. May, l-^ 3^ 10™ 00" Longitude, + 1 09 52 Greenwich time, 1 4 19 52 Example: In longitude 125° 30^ E. the local time is, May, 1^ 8'' 10™ 30» a. m. Required the Green- wich time. Local Ast. time, April, 30^ 20^ 10™ 30* Longitude, - 8 22 00 Greenwich time, 30 11 48 30 umb and the nautical almanac. 105 281. From the preceding article we have: To=Tu+Lo; hence, TM=Ta-Lo; thus it will be seen that, to find the local time corresponding to any Greenwich time, the above process is simply reversed. Since aU observations at sea are referred to chronometers regulated to Greenwich mean time, and as these instruments are usually marked on the dial from 0** to 12^, it becomes necessary to distinguish whether it is a. m. or p. m. at Gneenwich. Therefore an approximate knowledge of the longitude and local time is necessary to determine the Greenwich date. Example: In longitude &^ 00°» 00* W., about S"" 30" p. m. April 15th, the Greenwich chronometer read 8^ 25", and was fast of Gr, time 3" 15'. Required the local astronomical time. Approx. local time, 150 S^* 30" Gr. chro., 8" 25" 00» Longitude, + 5 00 Corr., - 3 15 Gr. Ast. time 15*^, 8'' 21° Longitude, —5 00 '45* 00 Approx. Gr. time, 15 8 30 Gr. Ast. time 15'', 8 21 45 Local Ast. time 15*, 3 21 45 Example: In longitude S^ 00" 00* E., about 8 a. m. May 3d, the Gr. fast of Gr. time 3" 15». Required the local astronomical time. chro. read 3" 15" 20», and was Approx. local time, May, 2'» 20'' Gr. chro., 3*" 15" 20* Longitude, — 5 Corr., — 3 15 Gr. Ast. time 2^, IS^ 12" Longitude, + 5 00 05« 00 Approx. Gr. time, 2 15 Gr. Ast. time 2^, 15 12 05 Local Ast. time 2'', 20 12 05 THE NAUTICAL AT.MANAC.a 282, The American Ephermeris and Nautical Almanac is divided into three parts as follows: Part I, Ephemeris for the meridian of Greenwich, gives the ephemerides of the sun and moon, the geocentric and heliocentric positions of the major planets, the sun's coordinates, and other fundamental astronomical data for equidistant intervals of Greenwich mean time; Part II, Ephemeris for the meridian of Washington gives the ephemerides of the fixed stars, sun, moon, and major planets for transit over the meridian of Washington, and Part III, Phenomena, contains predictions of phenomena to be observed with data for their computation. Tables are also appended for the interconversion of mean and sidereal time and for finding the latitude and azimuth by an altitude of Polaris. The American Nautical Almanac is a smaller book made up of extracts from the "Ephemeris and Almanac" just described, and is designed especially for the use of navigators, being adapted to the meridian of Greenwich. It contams the position of the sun and moon, together with the ephemerides of the planets Mercury, Venus, Mars, Jupiter, and Saturn, and the mean places of 200 fixed stars; solar and lunar echpses are described, and the tables for the interconversion of mean and sidereal time and for finding the latitude by Polaris are included. The elements dependent upon the sun and moon are placed at the beginning of the book, arranged according to the months of the year; twelve pages are devoted to each month, numbered in Roman notation from I to XII. Of these, page I con- tains the Apparent Right Ascension and Declination of the sun and the Eciuation of Time for the instant of Greenwich apparent noon; throughout the remaining eleven pages Greenwich mean time forms the basis of reckoning. Page I is used in compu- tations from observations that depend upon the time of the sun's meridian passage, at which instant the local apparent time is 0*», and the Greenwich apparent time is equal to the longitude, if west, or to 24** minus the longitude, if east; this page there- fore affords a means for reducing the elements for such observations from a knowl- edge of the longitude alone. In aU other observations the calculation is made for some definite instant of Greenwich mean time (usually as noted by the chronometer), in which case Pages II to XII are employed. See extracts from Ephemeris and Nautical Almanac for 1915, Appendix I. 106 TIME AND THE NAUTICAL ALMANAC. 283. Reduction of Elements. — The reduction of elements in the Nautical Almanac is usually accomplished by Interpolation, but in certain cases where extreme precision is necessary the method of Second Differences must be used. The Ephemeris, being computed for the Greenwich meridian, contains the right ascensions, declinations, equations of time, and other elements for given equidistant intervals of Greenwich time. Hence, before the value of any of these quantities can be found for a given local time it is necessary to determine the corresponding Green- wich time. Should that time be one for which the Nautical Almanac gives the value of the required element, nothing more is necessary than to emplojr that value. But if the time falls between the Almanac times, the required quantity must be found by interpolation. The Almanac contains the rate of change or difference of each of the principal quantities for some unit of time, and, unless great precision is required, the first differences only need be regarded. In order to use the difference columns to advan- tage, the Greenwich date should be expressed in the unit of time for which the difference is given. Thus, for using the hourly differences, the Greenwich time should be expressed in hours and decimal parts of an hour; when using the differences for one minute, the time should be in minutes and decimal parts of a minute. Instead of using decimal parts, some may prefer the use of aliquot parts. Since the quantities in the Almanac are approximate numbers, ^ven to a cer- tain decimal, any interpolation of a lower order than that decimal is unnecessary work. Moreover, since, in computations at sea, the Greenwich time is more or less inexact, too great refinement need not be sought in reducing the Almanac elements. Simple interpolation assumes that the differences of the quantities are proportional to the differences of the times; in other words, that tne differences given in the Almanac are constant; this is seldom the case, but the error arising from the assumption will be smaller the less the interval between the times in the Almanac. Hence those quantities which vary most irregularly are given for the smallest units of time; as the variations are more regular, the units for which the differences are given increase. In takmg from the Almanac the elements relating to the fixed stars the data may be found either in the table which gives the "mean place" of each star for the year or in that which gives the "apparent place" occupied by each one on every tenth day throughout the year. As the annual variation of position of the fixed stars is small, the results wiU not vary greatly whichever table may be used. Yet, as it is proper to seek always the greatest attainable accuracy, the use of the table showing the exact positions is recommended. That table is, however, published in the "Ephemeris and Nautical Almanac" only, and is omitted from tne abridged "Nautical Almanac;" hence, where the larger book is not at hand, the table of mean places must be employed. 284. To find from the Nautical Almanac a required element for any given time and place, it is first necessary to express the time astronomically and to convert it to Greenwich time and date. Then take from the Almanac, for the nearest given preceding instant, the required quantity, together with its corresponding "Diff. for 1^" or "Diff. for 1™," noting the name or sign in each case; for the sun use Page I of the proper month in the Almanac when apparent time is to be the basis for correc- tion, but otherwise use Page II. Multiply the "Diff. for 1^" by the number of hours and fraction of an hour, or the "Diff. for 1"" by the number of minutes and fraction of a minute, corresponding to the interval between the time for which the quantity is given in the Almanac and the time for which required ; apply the correction thus obtained, having regard to its sign. A modification of this rule may be adopted if the time for which the quantity is desired falls considerably nearer a subsequent time given in the Almanac than it does to one preceding; in this case the interpolation may be made backward, the sign of appHcation of the correction being reversed. 1 TIME AND THE NAUTICAL ALMANAC. 107 Example: At a place in longitude 81° 15' W., April 17, 1915, find the sun's declination and the equation of time at apparent noon. , Long.=81° 15' W. G. A. T.=17'» 6^ 25«»=17«»+5''.42. Dec., 17<» 0^, Corr., (+) + + 4- 4 10" ' 11' 32". 4 N. 4 47 .9 Eq. t., 1710", 0'»12M7 Corr., 4 3.22 Dec, 17* 5^ 25", 10 16 20 . 3 N. Eq. t., 17<»5»'25'°, 15.39 H. D., G. A. T., 53". 12 5". 42 H. D., 4- 0'.595 G. A. T., 4- 5\ 42 Corr., / 287". 91 \4' 47". 9 Corr., 4- 3V225 (Subtract from apparent time.) Example: At a place in longitude 81" 15' E., April 17, 1915, find the sun's declination and the equa- tion of time at apparent noon. Long.=81° 15' E. G. A. T.=16'» 18* 35»=17'»-5''.42. Dec., 17<» C, Corr., (+) > + 10° 11' 32". 4 N. 4 47 .9 Eq. t., 171 oh^ Qm i2». 17 Corr., - 3.22 Dec., W IS** 35» 10 06 44 .5 N. Eq. t., 16* 18" 35«, 08 . 95 H.D., G. A. T., 53". 12 5»'.42 H. D., 4- OV 595 G. A.T., - 5". 42 Corr., r 287". 91 14' 47". 9 Corr., - 3". 225 Example: April 15, 1915, at 11" 55™ 30* a. m., local mean time, in Long. 81° 15' W., required the declination and semidiameter of the sun, the equation of time, and the right ascension, declination, horizontal parallax, and semidiameter of the moon and Jupiter. Local mean time, 14* 23" 55" 30* Longitude, 4 5" 25" 00' [15<* 5" 20" 30* Greenwich mean time,] lo^ 5" 20". 5 [151 5". 34 For the Sun. Dec.,0", (4-) 9° 28' 42". 4 N. S. D., 15' 58".2 Eq. t., 0", 0* 17* . 09 Corr., 4- 4 48 .1 (Same aa at G. A. Noon.) Corr., - 3 . 33 Dec, 9 33 30 .5 N. Eqt. t.. e 13 . 76 4 48 . 1 9 33 30 .5N. 53" 5" .95 .34 H. D., 4- 53". 95 H. D., - 0«.624 G. M. T., 4 5". 34 G. M. T., 4- 5". 34 Corr., 4{ 288". 09 Corr., - 3' . 33 4' 48". 09 (Subtract from mean time.) For the Moon. R.A.,5i>, 2k 16" 39". 20 DflC., S*, (+)18'' 49* 29».4 N. Hot. Par., 0<>, 64' 13'. 9 S. D.,0«, 14' 48».2 Corr., + 40 .30 Corr., + 3 36 .5 Corr., - 2.8 Con., - .7 R. A., 2 17 19.60 Dec., 18 53 05 .9N. Hor. Par., 64 11 . 1 S. D., 14 47.5 M. D., + 1».966 M. D., + 10».66 H. D., - 0'.53 H. D., - C.W No. min., + 20". 5 No. min., + 20". 5 G. M. T., + 5*.34 G. M. T., + S«'.34 64' 13'. 2 . . 9 . 8 64 11 , , 1 + 0'.63 6>'.34 Corr., Corr., + 40«.3O r,^ j./ 216'. 48 Corr., - 2'.83 Corr., - 0».99 For Jupiter. Dec, 0", (-) 6° 13' 33". 6 S. Hor. Par., IS", 1". 5 Corr., 4 1 05 . 1 R. A., 0", Corr., 23" 11"57» 4 10 .49 .68 R. A., 23 12 08 .17 H.D., G. M. T., 4 2' 4 5" .00 .34 Dec, 6 12 28 .5 8 H. D., G. M. T., 4 12". 20 4- 5". 34 S. D., 151, 16". 4 Corr., + 10».68 Corr., 4- 60". 1 108 TIME AND THE NAUTICAL ALMANAC. 285. Should greater precision be required than that attainable by simple inter- polation, resort must be had to the reduction for second differences. The differences between successive values of the quantities given in the Nautical Almanac are called the first differences; the di£ferences between successive first differences are called the secona differences. Simple interpolation, which satisfies the necessities of sea computations, assumes the first differences to be constant; but if the variation of the first differences be regarded, a further interpolation is required for the second difference. The difference for a imit of time in the American Nautical Almanac abreast any element expresses the rate at which the element is changing at that precise instant of Greenwich time. Now, regarding the second difference as constant, the first difference varies uniformly with the Greenwich time; therefore its value may be found for any intermediate time by simple interpolation. Hence the following rule for second differences: Employ the interpolated value of the first difference which corresponds to the middle of the interval for which the correction is to be computed. Example: For the Greenwich date 1915, AprU, 10<* IS'* 25™ 30% find the moon's declination. Dec, Corr. 18^ (-)4° 56' + 6 4 50 39'^ 7 S. 09 .5 30 . 2 S. First diff., Corr., M. D., No. min., Corr., +14'^ 487 + .002 Second diff., Interval, Corr., +0'^ 009 +0^ . 213 Dec., +14 .489 +25°».5 +(/'. 002 , / 369^'. 5 +16^09^'. 5 The difference for one minute being + 14''. 487 at 18^^, and + 14 ".496 at IQ'^, the difference for one minute undergoes a change of +0''.009 during one hour. The time for which it is desired to obtain the difference is at the middle instant between 18^ 0"^ and 18^ 25'^.5— that is, at 18»^ 12'".75, or its equivalent, 18^.213. With a change of +0".009 in one hour, the change in 0^.213 is readily obtainable; correcting the minute's difference at 18^.0 accordingly, the process of correcting the declination becomes the same as in simple interpolation. CONVEBSION OF TIMES. 286. Conversion of Time is the process by which any instant of time that is defined accordiag to one system of reckoning may be defined according to some other system; and also by which any interval of time expressed in imits of one system may be converted mto units of another. 287. Sidereal and Mean Time. — ^Mean time is the hour angle of the Mean Sun; sidereal time is the hour angle of the First Point of Aries. Since the Right Ascension of the Mean Sun is the angular distance between the hour circles of the First Point of Aries and of the Mean Sun, mean time may be converted into sidereal time by adding to it the Right Ascension of the Mean Sun ; and similarly, sidereal time may be converted into mean time by subtracting from it the Right Ascension of the Mean Sun. This is explained in figure 37, which represents a projec- tion of the celestial sphere upon the equator. If P be the pole; QPQ', the meridian; V, the First Point of Aries; M, the position of the mean sun (west of the meridian) ; then QPV, or Q the arc QV, is the sidereal time ; QPM, or the arc QM, is the Fig. 37. mean time; and VPM, or the arc VM, is the Right Ascension of the Mean Sun. From this it wiQ appear that: QV = QM + VM, or Sidereal time == Mean time + Right Ascension of Mean Sun. TIME AND THE NAUTICAL ALMANAC. 109 If the mean sun be on the opposite side of the meridian, at M', then the mean time equals 24^ — M'Q. In this case: QV = yM'-M'Q, or Sidereal time = Right Ascension of Mean Sun— (24'*— Mean time), = Right Ascension of Mean Sun + Mean time — 24**. Right ascension being measured to the east and hour angle to the west, the sidereal time wiU therefore always equal the sum of these two; but 24** must be sub- tracted when the sum exceeds that amount. From the preceding equations, we also have: QM = QV-VM; and M'Q = VM'-QV, or (24''-M'Q) = (24»'+QV) - VM'. From this it may be seen that the mean time equals the sidereal time minus the Right Ascension of the Mean Sun, but the former must be increased by 24** when necessary to make the subtraction possible. 288. Apparent and Mean Times. — ^Apparent time is the angle between the meridian and the hour circle which contains the center of the sun; mean time is the angle between the meridian and the hour circle which contains the mean sun. Since the equation of time represents the angle between the hour circles of the mean and apparent suns, it is clear that the conversion of mean time to apparent time may be accomplished by the application of the equation of time, with its proper sign, to the mean time ; and the reverse operation oy the application of the same quantity, in an opposite direction, to the apparent time. The resemblance of these operations to the interconversion of mean and sidereal times may be observed if, in figure 37, we assume that PV is the hour circle of the true Sim, PM remaining that of the mean sun; tiien the arc QM will be the mean time; QV, the apparent time; and VM, the equation of time; whence we have as before : QV = QM + VM, or Apparent time = Mean time + Equation of time ; the equation of time will be positive or negative according to the relative position of the two suns. 289. Sidereal and Mean Time Intervals. — The sidereal year consists of 366.25636 sidereal days or of 365.25636 mean solar days. If, therefore, M be any interval of mean time, and S the corresponding interval of sidereal time, the relations between the two may be expressed as loUows : 8^366.25636^ M 365.25636 ^•^^^^'^^^' M 365.25636 S~366. 25636 ~"'^^^''^^^- Therefore, S = 1 . 0027379 M = M + . 0027379 M ; M = 0.9972696 S =S -.0027304 S. If M=24'*, 8 = 24'' +3™ 56'.6; or, in a mean solar day, sidereal time gains on mean time 3™ 56^.6, the gain each hour being 9^.8565. If 8 = 24**, M = 24'* — 3™ 65*.9; or, in a sidereal day, mean time loses on sidereal time 3*" 55^9, the loss each hour being 9^8296. If M and 8 be expressed in hours and fractional parts thereof, S = M + 9«.8565M; M- S-9«.8296S. Tables for the conversion of the intervals of mean into those of sidereal time and the reverse are based upon these relations. Tables 8 and 9 of this work give the values for making these conversions, and similar tables are to be foimd in the Nautical Almanac. 110 TIME AND THE NAUTICAL ALMANAC. 290. To Convert Mean Solar into Sidereal Time. — Apply to the local mean time the longitude, adding if west and subtracting if east, and thus obtain the Green- wich mean time. Take from the Nautical Almanac the Right Ascension of the Mean Sun at Greenwich mean noon, and correct it for the Greenwich mean time by Table 9 or by the hourly difference of 9*.857. Add to the local mean time this corrected right ascension, rejecting 24^ if the sum is greater than that amount. The result wSl be the local sidereal time. Example: April 22, 1915, in Long. 81° 15' W., the local mean time is 2^' 00" 00' p. m. Required the corresponding local sidereal time: L. M. T., 22 37».70, which is caUed a sidereal interval. During tliis travel of the Vernal Equinox the mean sun wUl lose a certain an- gular amount on the Vernal Equinox, depending on the travel of the latter, which travel is 16^ 02''^ 37^70. From Table 8, we find for tliis travel that the loss will be 2"" 37''.70, which is represented by the sector Ca in the figure, so that the angle QSm is V, V — 2°' 37«.70, equals IQ^ 02'° 37«.70-2'" 37«.70, equals 16'' OO"" 00*, which, from the figure, equals the desired L. M. T. Second Example of Article 291. (See Figure 41.) Draw the figure as shown, laving off the lon^tude equal to 5^ west, to the eastward, from Q, thus nnding the Greenwich meridian G. The problem is similar to the above problem except that in moving the mean sun from G to Q we see tnat the angle Smi V^ is in- creased to find Siia2 V2, as the Vernal Equinox has gained a certain amount on the mean sun during the travel of the sun to the westward from G to Q. For the travel of V2 to V, the mean sun will travel from Smj to Sm, losing a certain amount on the Vernal Equinox for the travel of V, V of the latter, and we find QS^ equals the L. M. T. 21594°— 14 8 Fig. 41. 114 TIME AND THE NAUTICAL ALMANAC. Fig. 42. First Example of Article 293. (See Figure 42.) Draw the figure as explained above, using longitude given equals 5 hours west, and L. M. T. given, 12 hours ( + ). Then G. M. T. equals 12 + 5 or 17 hours (+ ) of April 25. For this instant of time the mean sun is plotted at Sm. Now the problem is, knowing the positions of G, Q, and Sm, to find the position of the given star on the di- agram, and thence its local hour angle. If we can find the relative angles from the mean sun and from the star to some third object, we can plot this third object and find the rec[uired hour angle of the star. The third object is the First Point of Aries (the Vernal Equinox) and the angles from the mean sun and from the star are the right ascensions of the mean sun and the star. The right ascension of the mean sun is found from the Almanac, not for the instant we want, but for the Greenwich mean noon of the date. This R. A. must be increased by a correction for the angle through which the mean sun has traveled since noon, — the G. M. T. In the problem the E. A. M. S. so increased is 2 hours, so we fay off SmV from Sm to the westward 2 hours, plotting the position of the Vernal Equinox at the desired instant. From the Almanac we find the R. A. of the star to be 6 hours, and we lay off V * equal to 6 hours to the eastward. The required local hour V angle of the star is then Q * whicn equals QSni + VSm-V * equals L. M. T. + R. A. M. S.-R. A. equals 12i^+2^-6'» equals 8 hours. Second Example of Article 293. (See Figure 43.) Draw the figure as before. The problem is, know- ing the position of the star at a certain instant, to find the L. S. T., so we must plot the position of the star, then that of the Vernal Equinox. The local hour angle of the latter is the required L. S. T. The hour angle of the star is given as 2 hours, bear- ing east from the meridian, so lay off Q sfc =2 hours to the east from Q. Now find from the Almanac the R. A. of the ;ic which is 14 hours, and lay off >|c V equal to 14'' to the westward from 3\^ . The L. S. T. is then QV, equals V * — Q *, equals the R. A. * — H. A. *, equals 14^ — 2^ equals 12 hours. When doubt exists as to the Greenwich date the navigator, by plotting the data in exactly the same way as explained above, can at once remove aU doubt on the subject and can get the correct G. M. T. TVest Fig. 43. CHAPTER X. OOEEEOTION OF OBSEEVED ALTITUDES. 294. The true altitude of a heavenly body at any place on the earth's surface is the altitude of its center, as it would be measured by an observer at the center of the earth, above the plane passed through the center of the earth at right angles to the direction of the zenith. The observed altitude of a heavenly body, as measured at sea, may be converted to the true altitude by the application of the following-named corrections: Index Correction, Dip, Refraction, Parallax, and Semidiameter. The corrections for parallax and semidiameter are of inappreciable magnitude in observations of the fixed stars, and with planets are so small that they need only be regarded in refined calculations. In observations with the artificial horizon there is no correction for dip. For theoretical accuracy, the corrections should be applied in the order in which they are named, but in ordinary nautical practice the order of application makes no material difference, except in the case of the parallax of the moon as explained in article 306; and hence, instead of turning to the separate tables referred to in the following articles as containing these corrections, their combined amount, given in Table 46, may be applied to observed altitudes of the sun, the planets, and the stars, after the manner shown in article 308. INDEX CORRECTION. 295. This correction is fully explained in articles 249 and 250, Chapter VIII. REFRACTION. 296. It is known by various experiments that the rays of light deviate from their rectilinear course m passing obliquely from one medium into another of a different density; if the latter be more dense, the ray will be bent toward the per- pendicular to the line of junction of the media; if less dense, it will be bent away from that perpendicular. The ray of light before entering the second medium is called the in.ident ray; after it enters the second medium it is called the refracted ray, and the difference of direction of the two is called the refraction. The rays of li^ht from a heavenly body must pass through the atmosphere before reaching the eye of an observer upon the surface of the earth. The earth's atmos- phere is not of a uniform density, but is most dense near the earth's surface, gradu- ally decreasing in density toward its upper limit; hence the path of a ray of light, by passing from a rarer medium into one con- tinually increasing density becomes a curve, which is concave toward the earth. The last direction of the ray is that of a tangent to the curved path at the eye of the observer, and the difference of the direction of the ray before entering the atmosphere and this last direction constitutes the refraction. 297. To illustrate this, consider the earth's atmosphere as shown in figure 44; let SB be a ray from a star S, entering the atmosphere at B, and bent into the curve BA; then the apparent direction of the star is AS', the tangent to the curve at the point A, the retraction being the angle between the lines BS and AS'. If CAZ is 115 116 CORRECTION OF OBSERVED ALTITUDES. the vertical line of the observer, by a law of optics the vertical plane of the observer which contains the tangent AS' must also contain the whole curve BA and the incident ray BS. Hence refraction increases the apparent altitude of a star without affecting its azimuth. At the zenith the refraction is nothing. The less the altitude the more obliquely the rays enter the atmosphere and the greater will be the refraction. At the horizon the retraction is the greatest. 298. The refraction for a mean state of the atmosphere (barometer 30'°, Fahr. thermometer 50°) is given in Table 20 A; the combined refraction and sun's parallax in Table 20 B; and the combined refraction and moon's parallax in Table 24. Since the amount of the refraction depends upon the density of the atmosphere, and the density varies with the pressure and the temperature, which are indicated by the barometer and thermometer, the true refraction is found by applying to the mean refraction the corrections to be found in Tables 21 and 22; these are deduced from Bessel's formulae, and are regarded as the most reliable tables constructed. It should be remembered, however, that under certain conditions of the atmosphere a very extraordinary deflection occurs in rays of light which reach the observer's eye from low altitudes (that is, from points near the visible horizon), the amount of which is not covered by the ordinary corrections for pressure and temperature ; the error thus created is discussed under Di'p (art. 301) ; on account of it, altitudes less than 10° should be avoided. Example: Required the refraction for the apparent altitude 5°, when the thermometer is at 20® and the barometer at SO'^.e?. The mean refraction by Table 20 A is, 9' 52''' The correction for height of barometer is, + 13 The correction for the temperature, + 42 10 47 True refraction, 299. The correction for refraction should always be subtracted, as also that for combined refraction and parallax of the sim ; the correction for combined refrac- tion and parallax of the moon is invariably additive. DIP. 300. Dip of the Horizon is the angle of depression of the visible sea horizon below the true horizon, due to the elevation of the eye of the observer above the level of the sea. In figure 45 suppose A to be the position of an observer whose height above the level of the sea is AB. CAZ ia the true vertical at the position of the observer, and AH is the direction of the true horizon, S being an observed heavenly body. Draw ATH' tangent to the earth's surface at T. Disregardmg refraction, T will be the most distant point visible from A. Owing to refraction, however, the most distant visi- ble point of the earth's surface is more re- mote from the observer than the point T, and is to be found at a point T', in figure 46. But to an observer at A the point T' will appear to lie in the direction of AH", the tangent at A to the cm-ve AT'. If the vertical plane were revolved about CZ as an axis, the line AH would generate the plane of the true horizon, while the pomt T' would generate a small circle of the terrestrial sphere called the Visible or Sea Horizon. The Dip of the Horizon is HAH'', being the angle between the true horizon and the apparent direction of the sea horizon. Values of the dip are given m Table 14 for various heights of the observer's eye, and in the calculation of the table allowance has been made for the effect of atmospheric refraction as it exists under normal conditions. FlO. 45. CORRECTION OF OBSERVED ALTITUDES. 117 FlQ. 46. 301. The fact must be emphasized, however, that under certain conditions the deflection of the raj in its path from the horizon to the eye is so irregular as to give a value of the dip widely different from that which is tabulated for the mean state of atmosphere. These irregularities usually occur when there exists a material differ- ence between the temperature of the sea water and that of the air, and they attain a maximum value in calm or nearly cahn weather, when the lack of circulation permits the air to arrange itself in a series of horizontal strata of different densities, the denser strata being below when the air is warmer, and the reverse condition obtaining when the air is cooler. The effect of such an arrangement is that a ray of light from the horizon in passing through media of different densities, undergoes a refraction quite unlike that whicn occurs in the atmosphere of much more nearly homogeneous density that exists under normal conditions. Various methods have been suggested for computing the amount of dip for different relative values of temperature of air and water, but none of these afford a satisfactory solution, there behig so many ele- ments involved which are not susceptible of determination by an observer on shipboard that it will always be difficult to arrive at results that may be depended upon. As the amount of difference between the actual and tabulated values of the dip due to this cause may sometimes be very consider- able — reliable observations having frequently E laced it above 10', and values as high as 32' aviag been recorded — it is necessary for the navigator to be on his guard against the errors thus produced, and to reco^ze the possible inaccuracy of all results derived from observations taken under unfavorable condi- tions. Without attempting to give any method for the determination of the amount of the ex- traordinary variation in dip, the following rules may indicate to the navigator the con- ditions under which caution must be observed, and the direction of probable error: (a) A displacement of the horizon should always be suspected when there is a marked difference between the temperatures of air and sea water; this fact should be especially kept in miad in regions such as those of the Red Sea and the Gulf Stream, where the difference frequently exists. (&) The error in the tabulated value of the dip will increase with an increase in the difference of temperature, and will diminish with an increase in the force of the wind. (c) The error will decrease with the height of the observer's eye; hence it is expedient, especially when error is suspected, to make the observation from the most elevated position available. (d) When the sea water is colder than the air the visible horizon is raised and the dip is decreased; therefore the true altitude is greater than that given by the use of the ordinary dip table. When the water is warmer than the air, the horizon is depressed and the dip is increased. At such times the altitude is really less than that found from the use of the table. The same cause, it may be mentioned here, affects the kindred matter of the visibihty of objects. When the air is warmer, terrestrial objects are sighted from a greater distance and appear higher above the horizon than under ordinary conditions. When the water is warmer than the air, the distance of visibility is reduced, and terrestrial objects appear at a less altitude. 302. What has been said heretofore about the dip supposes the horizon to be free from all intervening land or other objects; but it often happens that an obser- vation is required to be taken from a ship sailing along shore or at anchor in harbor, when the sun is over the land and the shore is nearer the ship than the visible sea horizon would be if it were unconfined; in this case the dip will be different from that of Table 14, and wiU be greater the nearer the ship is to that point of the shore to which the sun's image is brought down. In such case Table 15 gives the dip at different heights of the eye and at different distances of the ship from the land. 303. The dip is always to be subtracted from the observed altitude. 118 COKEECTION OF OBSERVED ALTITUDES. PARALLAX. 304. The 'parallax of a heavenly body is, in general terms, the an^le between two straight lines drawn to the body from different points. But in Nautical Astron- omy geocentric parallax is alone considered, this being the difference between the positions of a heavenly body as seen at the same instant from the center or the earth and from a point on its surface. The zenith distance of a body, S (fig. 47), seen from A, on the surface of the earth, is ZAS; seen from C it is ZCS; the parallax is the dif- ference of these angles, ZAS — ZCS=ASC. Parallax in altitude is, then, the angle at the heavenly body subtended by the radius of the earth. If the heavenlj^ body is in the horizon as at H', the radius, being at right angles to AH', subtends the greatest possible angle at the star for the same distance, and this angle is called the horizontal parallax. The parallax is less as the bodies are farther from the earth, as will be evident from the figure. Fig. 47 Let par. = parallax in altitude, ASC; Z = SAZ, the apparent zenith distance (corrected for refraction); R=AC, the radius of the earth; and D = CS, the distance of the object from the center of the earth. Then, since SAC = 180°-SAZ, the triangle ASC gives: R sin Z sm par. = D and If the object is in the horizon at H', the ai^le AH'C is the horizontal parallax, denoting it by H. P. the right triangle AH'C gives: sinH. P.=§. R. Substituting this value of j^ in the above, sin par. = sin H. P. sin Z. If h=SAIl', the apparent altitude of the heavenly body, then Z = 90° — A; hence, sin par. =sin H. P. cos h. Since par. and H. P. are always small, the sines are nearly proportional to the angles; hence, par. = H. P. cos 7i. 306. The Nautical Almanac gives the horizontal parallax of the moon, as well as of the planets Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune. In Table 16 will be found the values of the sun's parallax for altitude intervals of 5° or 10°, while Table 20 B contains the combined values of the sun's parallax and the refraction. In Table 24 is given the parallax of the moon, combined with the refraction, at various altitudes and for various values of the horizontal parallax. COREECTION OF OBSERVED ALTITUDES. 119 I 306. Parallax is always additive; combined parallax and refraction additive in the case of the moon, but subtractive for the sun. As the correction for parallax of the moon is so large, it is essential that it be taken from the table with considerable accuracy; the corrections for index correc- tion, semidiameter, and dip should therefore be applied first, and the "approximate altitude" thus obtained snould be used as an argument in entering Table 24 for parallax and refraction. SEMTDLA TVrRTEB. 307. The semidiameter of a heavenly body is haK the angle subtended by the diameter of the visible disk at the eye of the observer. For the same body the semidiameter varies with the distance; thus, the difference of the sun's semidiameter at different times of the year is due to the change of the earth's distance from the sun; and similarly for the moon and the planets. In the case oi the moon, the earth's radius bears an appreciable and considerable ratio to the moon's distance from the center of the earth; hence the moon is materially nearer to an observer when in or near his zenith than when in or near his horizon, and therefore the semidiameter, besides having a menstrual change, has a semi- diurnal one also. The increase of the moon's semidiameter due to increase of altitude is called its augmentation. This reduction may be taken from Table 18. The semidiameters of the sun, moon, and planets are given in their appropriate places in the Nautical Almanac. The semidiameter is to be added to the observed altitude in case the lower limb of the body is brought into contact with the horizon, and to be subtracted in the case of the upper limb. When the artificial horizon is used, the limb of the reflected image is that which determines the sign of this correction, it being additive for the lower and subtractive for the upper. Example: May 6, 1915, the observed altitude of the sun's upper limb was 62* KK 40'''; I. C, + 3' 10"; height of the eye, 25 feet. Bequired Uie true altitude. Obs. alt. ^, Corr., True alt., 62° lO' 40" 18 04 I.e. + 3' 10" Required the true altitude. 61 52 36 S. D. (Naut. Aim.), dip (Tab. 14), p. & r. (Tab. 20 B), - 15' - 4 53" 54 27 - 21 14 Corr., - 18' 04" s as observed with an artificial horizon was 50" 5S ►'30* Obs. I.e. 2 alt. 9|e, 50° 59^ 30" 1 30 2)50 58 00 Obs. alt., 25 29 00 ref. (Tab. 20 A), - 2 02 True alt., 25 26 58 Example: April 16, 1915, observed altitude of Venus 53° 26' 10"; I. C, + 2' 30"; height of eye, 20 feet. Required the true altitude. Obs. alt. *, 53° 26' 10" Corr., - 2 32 53 23 38 r. (Tab. 17), + 0' 04" + 2 30 rd! Hor. Par. (Naut. Aim.), 7" + 2 34 dip (Tab. 14), - 4' 23" ref. (Tab. 20 A), - 43 Corr., - 5 06 - 2' 32" 120 CORRECTION OF OBSERVED ALTITUDES. Example: May 6, 1915, at 13'' 24"» G. M. T., the observed altitude of the moon's lower limb was 25* 3(K SO'''; I. G.,-V 30'''; height of eye, 20 feet. Required the true altitude. Obs. alt.£, 25° 30^ 30^'' S. D. (Naut. Aim.), +15' 3^ Hor. Par. (Naut. Aim.) 56' SI"' Ifit. corr., + 9 45 Aug. (Tab. 18), + 07 Approx. alt., 25 40 15 +15 38 p. & r. (Tab. 24), + 49 14 dip (Tab. 14), - 4' 23'' True alt., 26 29 29 I. C, - 1 30 - 5 53 Istcorr., + 9' 45" Or, the following modification may be adopted: Obs. alt. C, 25° 30' 30" S. D., +15' 31" H. P., 3411" log 3. 53288 1st cor., + 7 44 Aug., + 07 App. alt., 25° 38' cos 9.95500 Approx. alt., 25 38 14 +15 38 „„^ f 3075" log 3.48788 pir^, + 51 15 P^' 151' 15" ^ dip. - 4' 23" True alt., 26 29 29 ret, - 2 01 I. C, - 1 30 - 7 54 Istcorr., + 7' 44" 308. The corrections for dip, parallax, refraction, and semidiameter, which must be applied to the observed altitude of a star or of the sun's lower limb in order to obtain the true altitude, have been combined in Table 46. This is done in order to save the time and labor involved in referring to separate tables of these corrections. The tabulated correction for an observed altitude of a star combines the mean refraction and the dip; and that for the observed altitude of the sun's lower limb, the mean refraction, the dip, the parallax, and the mean semidiameter, which is taken as 16'. A supplementary table, taking account of the variation of the sun's semidiameter in the different months of the year, is given in connection with the main table. Thus, in the first example under article 324, we may, when variations from the mean state of the atmosphere (barometer 30 inches, Fahr. thermometer 50°) are left out of consideration, proceed as follows: Measured altitude Q. =40° 04' 00" I.e. =+ 3 00 Correction from Table 46, height of eye 20 feet. +10' 35" 40 07 00 Supplementary table for June 21 — 14 10 21 Truealtitude 40 17 21 CHAPTER XI. THE OHEONOMETEE EEEOE. 309. It has already been explained (art. 261, Chap. VIII) that the error of a chronometer is the difference between the time indicated by it and the correct standard time to which it is referred; and that the daily rate is the amount that it gains or loses each day. In practice, chronometer errors are usually stated with reference to Greenwich mean time. It is not required that either the error or the rate shall be zero, but in order to be enabled to determine the correct time it is essential that both rate and error be known and that the rate shall have been uniform since its last determination. 310. Determining the Rate. — Since all chronometers are subject to some variation in rate under the changeable-conditions existing on shipboard, it is desirable to ascertain a new rate as often as possible. The process of obtaining a rate involves the determination of the error on two different occasions separated by an interval of time of such length as may be convenient; the change of error during this interval, divided by the number of days, gives the daily rate. Example: On March 10, at noon, found chronometer No. 576 to be 0™ 32».5 fast of G. M. T. ; on March 20, at noon, the same chronometer waa 0™ 48''.0 fast of G. M. T. What was the rate? Error, March 10^ 0", +0» 32*. 5 Error, March 20'* 0", +0 48 . Change in 10 days, + 15 , 5 Daily rate, + 1'.55 The chronometer is therefore gaining 1^.55 per day. 311. Determining Error from Rate.— The error on any given day being known, together with the daily rate, to find the error on any other day it is only necessary to multiply the rate by the number of days that may have elapsed and to apply the product with proper sign to the given error. Example: On December 17 a chronometer is S" 27'. 5 slow of G. M. T. and losing 0'.47 daily. What is the error on December 26? Error Dec. 17, -3° 27V5 Daily rate, -0'.47 Correction, — 4 .2 No. days, 9 Error Dec. 26, -3 31.7 Corr., -4.23 The chronometer is therefore slow of G. M. T. on December 26, 3™ 3P.7. 312. It is necessary to distinguish between the signs of the chronometer correc- tion and of the chronometer error. A chronometer fast of the standard time is considered as having a positive error, since its readings are positive to (greater than) those of an instrument showing correct time; but the same chronometer has a negative correction, as the amount must be subtracted to reduce chronometer readings to correct readings. 313. Numerous methods are available for determining the error of a chronometer in port. The principal of these wiU be given. BY TIME SIGNALS. 314. In nearly all of the important ports of the world a time signal is made each day at some defined instant. In many cases this consists in the dropping of a time ball — the correct instant being given telegraphically from an observatory. In a number of places where there is no time ball a signal may be received on the instru- ments at the telegraph offices, whereby mariners may ascertain the errors of their chronometers. Such signals are to be had in almost every port of the United States, and similar signals are being sent out from Government radio stations, so that it is now possible to find the error of the chronometer on board ships fitted with 121 122 THE CHEONOMETEE EEEOE. receiving instruments when lying in port and also when underway within radio distance of these stations. The time signal may be given by a gunfire or other sound, in which case allowance must be made by the observer for the length of time necessary for the sound to travel from the point of origin to his position. Sound travels 1,090 leet per second at 32° F., and its velocity increases at the rate of 1.15 feet per second with each degree increase of temperature* If V be the velocity of sound in feet per second at the existing temperature, and D the distance in feet to be traversed, ^ is the number of seconds to be subtracted from the chronometer reading at the instant of hearing the signal to ascertain the reading at the instant the signal was made. This method of obtaining the chronometer error consists in taking the difference between the standard time and chronometer time at the time of observation and marking the result with appropriate sign. Example: A time ball drops at 5^ 0™ 0', G. M. T., and the reading of a chronometer at the same moment is 4'' 57™ 52».5. "What is the chronometer error? G. M. T., 5^ 00™ 00» Chro. t., 4 57 52.5 Chro. error, - 2 07 . 5 That is, chronometer is slow 2™ 07'. 5; chronometer correction additive. BY TRANSITS. 315. The most accurate method of finding the chronometer correction is by means of a transit instrument well adjusted in the meridian, noting the times of transit of a star or the limbs of the sun across the threads of the instrument. At the instant of the body's passage over the meridian wire, mark the time by the chronometer. The hour angle at the instant is 0^; therefore the local sidereal time is equal to the right ascension of the body in the case of a star, or the local apparent time is 0** in the case of the sun's center. By converting this sidereal or apparent time into the corresponding mean time and applj^ing the longitude, the Grreenwich mean time of transit is given. By comparing with this the time shown by chronometer the error is found. Example: 1915, May 9 (Ast. day), in Long. 44° 39'' E., observed the transit of Arcturus over the middle wire of the telescope, the time noted by a chronometer regulated to Greenwich mean time being &" 05" 33V5. Required the error. L. S. T. (R. A. *), 14" 11™ 49*. 99 Long., - 2 58 36 G. S. T., R. A. M. S.,9<»0^, 11 - 3 13 04 13 52 .99 .31 Sid. int. from O*", Reduction (Tab. 8), 8 08 1 21 20 .68 .01 G. M. T., Chro. t., 8 8 07 05 01 33 .67 .50 Chro. slow, 1 28 . 17 Example: June 25, 1915, in Long. 60° E., observed the transit of both limbs of the sun over the meridian wire of the telescope, noting the times by a chronometer. Find the error of the chronometer on G. M. T. Transit of western limb, &" 04™ 02». 5 Eq. t., 2™ 12*. 64 Transit of eastern limb, 8 06 20 . H. D., + 0».530 Chro. time, loc. app. noon, 8 05 11.25 Long., — 4'' L. A. T., loc. app. noon, 0" 00™ 00* Corr., - 2". 120 Eq. t., + 2 10.52 Eq. t., 2™ 10*. 52 L. M. T., loc. app. noon, 02 10 . 52 Add to apparent time. Long., - 4 00 00 G. M. T., loc. app. noon, 8 02 10 . 52 Chro. time, loc. app. noon, 8 05 11 . 25 Chro. fast, 3 00 . 73 THE CHRONOMETER ERROR. BY A SINGLE ALTITXTDE (TIME SIGHT). 123 316. The problem involved in this solution, by reason of its frequent application in determining the longitude at sea, is one of the most important ones in Nautical Astronomy. It consists in finding the hour angle from ^iven values of the altitude, latitude, and polar distance. The hour angle thus obtamed is converted by means of the lon^tude and equation of time in the case of the sun, or longitude and ri^ht ascension m the case of other celestial bodies, into Greenwich mean time; and this, compared with the chronometer time, gives the error. 317. It should be borne in mind that the most favorable position of the heavenly body for time observations is when near to the prime vertical. When exactly in the prime vertical a small error in the latitude produces no appreciable effect. Therefore, if the latitude is uncertain, good results may be obtained by observing the sun or other body when bearing east or west. If observations are made at the same or nearly the same altitude on each side of the meridian and the mean of the results is taken, various errors are eliminated of which it is otherwise impossible to take account, and a very accurate determination is thus afforded. 318. With a sextant and artificial horizon or good sea horizon, several altitudes of a boay should be observed in quick succession, noting in each case the time as shown by a hack chronometer or comparing watch whose error upon the standard chronom- eter is known. Condensing the observation into a brief interval justifies the assump- tion that the altitude varies uniformly with the time. A very satisfactory method is to set the sextant in advance at definite Latervals of altitude and note the time as contact is observed. 319. Correct the observed altitude for instrumental and other errors, reducing the apparent to the true altitude. If the sun, the moon, or a planet is observed, the declination is to be taken from the Nautical Almanac for the time of the observation. If the chronometer correction is not approximately known and it is therefore impossible to determine the Greenwich mean time of observation with a fair degree of accuracy, the first hour angle found will be an approximate one ; the declination corrected by this new value of the time will produce a more exact value of the hour angle, and the operation may be repeated until a sufficiently precise value is determined. 320. In figures 48 and 49 are given: AM ==^, the altitude of the body M; DM =d, the declination; and. Q'Z = L, the latitude of the place. In the astronomical triangle rMZ there may be found from the foregoing: ZM = z, the zenith distance of the body, = 90 ° - Ji; 124 THE CHRONOMETER ERROR. PM=2), the polar distance, = 90° ±(?; and PZ =co.L, tne co-latitude of the place, = 90"^ — L. From these data it is required to find the angle MPZ the hour angle of the body, = t. This is given by the formula : sm^ 1 ^_ co3 ^ (^+L + p)sin ^ (L + p — Ti) ^ cos L sin p If we let s = l (Ji + h+p), this becomes: sin ^ if = V sec L cosec p cos s sin (s — h). The polar distance is obtained by adding the declination to 90° when of different name from the latitude and subtracting it from 90° when of the same name. Like latitude and altitude, it is always positive. If the sun is the body observed, the resulting hour angle is the local apparent time and is to be taken from the a. m. or p. m. column of Table 44 according as the altitude is observed in the forenoon or afternoon. If the moon, a star, or a planet be taken, the hour angle is always found in the p. m. column. Local apparent time as deduced from an observation of the sun is converted to local mean time by the application of the equation of time; then, by adding the longitude if west and subtracting it if east, the Greenwich mean time is obtained. The hour angle of any other body, added to its right ascension when it is west of the meridian at observation or subtracted therefrom when east, gives the local sidereal time, which may be reduced to Greenwich sidereal time by the application of the longitude, and thence to Greenwich mean time by methods previously explained, A comparison of the Greenwich mean time with the chronometer time of sight gives the error of the chronometer. Example: January 20, 1915, p. m., in Lat. 48° 41' (KK' S., Long. 69° 03' 00" E., observed a series of altitudes of the sun with a sextant and artificial horizon; mean double altitude, 59° 03' IC', images approaching; mean of times by comparing watch, 4'' 40™ 66"; C — ^W, 7*^ 23"* 25»; index correction, —1' SO''; approximate chronometer correction, —0™ 10'. What was the exact chronometer error? W.T., C— W, 4'*40°'56' Obs.2alt.^, 59° 03' 10" Dec, 20° 17' 41". 9 S. Eq. t.,10™ 57«.22 7 23 25 I. C, 1 30 Chro. t., 04 21 App. CO., - 10 App.G.M.T., 04 11 Tor S. D. H. D., + 31". 8 H. D., + 0».76 0''.07 G.M.T., 0^07 29 30 50 + 14 43 + 2". 226 Corr., + 0".053 + 2)59 01 40 G.M.T., Corr., Dec, 20° 17' 39". 7 S. Eq. t., 10">57».3 29 45 33 69° 42' 20" 16' 17" (Add to apparent time.) s a — h p. & r., Corr., 29° 45' 33" 48 41 00 69 42 20 2)148 08 53 74 04 27 44 18 54 1' 34" L. A. T., 4^ SO™ 26*. 7 + sec cosec cos sin sin i { 14' 43" . 18031 . 02783 9. 43837 9. 84423 2)19. 49074 9.74537 4"* 30™ 28V 7 + 10 57 .3 L. A. T., Eq. t., L. M. T., Long., G. M. T., Chro. t., Ohro. slow, 00 51 . 4 41 24 .0 -4 36 12 .0 05 12 .0 04 21 .0 THE CHRONOMETER ERROR. 126 Example: May 18, 1915, p. m., in Lat. 8° 03' 22'^ S., Long. 34° 51' 57'' W., observed a series of altitudes of the star Arcturus, east of the meridian, using artificial horizon: mean double altitude, 60'' 10'; mean watch time, &" aO"" 32»; C— W, 2" 20"" 59V5; I. C, +2' 00". Find the true error of the I chronometer. W. T., 0— W, 6h 50™32» 2 20 59.5 Obs. 2 a LC, ref., A, sec cosec COS sin sin ^ t It. *, 60° + lO' 2 ' 00" 00 R. A. * Dec. *, S..0^ from 0", h. 8), 19° 37 "50'.0 ' 12". 8 N Chro. t. , 9 11 3L5 30" 04' 20" 8 03 22 109 37 13 2)60 30 12 06 1 00 00 40 109° 37 14* 11"" - 3 36 ' 13" h L 30 .00431 .02598 9. 44365 9. 84022 04 20 R. A. *, H. A., L. S. T., Long., G. S. T., R. A. M. Sid. int. Red. (Ta G. M. T. Chio. t., Chro. slo 50'. 01 P 10 + 2 12 - 3 35 19 55 40 49 .0 27 .8 16 .8 21 .3 s ih-h 2)147 44 55 73 52 28 43 48 08 Z^ 36"' 01* E. H. A. 2)19. 31416 9. 65708 9 14 1 55 .5 30 .9 9 9 13 11 24 .6 31 .5 1 53 .1 BT DOUBLE ALTITTrDES OB ALTTTITDES ON OPPOSITE SIDES OF THE MERIDIAN. 320. Instead of relying on a single determination of the chronometer error from altitudes on one side of the meridian, it is better to observe the same body on both sides of the meridian, and, if possible, at about the same altitude. The error of the chronometer having been found from each set of sights, the mean is taken as the correct error, and this mean wdll probably be nearer the true error than the result from either set; the effect of the constant errors of latitude, instrument, and observer, being opposite in the two cases, will be eUminated by takmg the mean. b CHAPTER XII. LATITUDE. BY MERIDIAN ALTITTJDE. 321. The latitude of a place on the surface of the earth, being its angular distance from the equator, is measured by an arc of the meridian between the zenith and the equator, and hence is equal to the declination of the zenith; therefore, if the zenith distance of any heavenly body when on the meridian be known, together with the declination of the body, the latitude can be found. Let figure 50 represent a projection of the celestial sphere on the plane of the meridian NZS; O, the center of the sphere; NS, the horizon; P and P', the poles of the sphere; QOQ', the equator; Z, the zenith of the observer.^ Then, by the above definition, ZQ will be the latitude of the observer; and NP, the altitude of the elevated pole, will also equal the latitude. Let M be the position of a heavenly body north of the ec[uator, but south of the zenith; QM = (?, its declination; MS = ^, its altitude; and ZM = 2 = 90'* — li, its zenith distance. From the figure we have: QZ = (^H-MZ, or lj = d-\-z. By attending to the names of z and d, marking Fig. 50. the zenith distance north or south according as the zenith is north or south of the body, the above equation may be considered general for any position of the body at upper transit, as M, M', M^'. In case the body is below the pole, as at M'" — that is, at its lower culmination — the same formula may be used by substituting 180° — d for d. Another solution is given in this case by observing that: NP = PM'" + NM'", or L=2) + L 322. A common practice at sea is to commence observing the altitude of the sun's lower limb above the sea horizon about 10 minutes before noon, and then, by moving the tangent-screw, to foUow the sun as long as it rises; as soon as the highest altitude is reached, the sun begins to fall and the lower hmb will appear to dip. "Wlien the sun dips the reading of the limb is taken, and this is regarded as the meridian observation. It will, however, be found more convenient, and frequently more accurate, for the observer to have his watch set for the local apparent time of the prospective noon longitude, or to know the error of the watch thereon, and to regard as the meridian altitude that one which is observed when the watch indicates noon. This wiU save time and try the patience less, for when the sun transits at a low altitude it may remain "on a stand," without appreciable decrease of altitude for several minutes after noon; moreover, this method contributes to accuracy, for when the conditions are such that the motion in altitude due to change of hour angle is a slow one, the motion therein due to change of the observer's latitude majr be very material, and tJius have considerable influence on the time of the sun's dipping. This error is large enough to take account of in a fast-moving vessel making a course in which there is a good deal of northing or southing. 126 LATITUDE. 127 In observing the altitude of any other heavenly body than the sun, the watch time of transit should previously be computed and the meridian altitude taken by time rather than by the dip. This is especially important with the moon, whose rapid motion in declination may introduce stUl another element of inaccuracy. 323. The watch time of transit for the sun, or other heavenly body, may be found by the forms given below, knowing the prospective longitude, the chronometer error, and the amount that the watch is slow of the chronometer. In this connection, article 404 describing the method of setting the watch to L. A. T. may be profitably read. For the Sun. L, A. T. noon, Long. (+if west), ± G. A. T., Eq. t., ± G. M. T., C. C. (sign reversed), T Chro. time, C— W, Watch time noon, For other Bodies. h 0^ 00" 00* L. S. T. transit, Long. (+rf -west), G. S. T., R. A. M. S., O*", Sid int. from 0^, Red. (Tab. 8), G. M. T., C. C. (sign reversed), Chro. time, O-W, Watch time transit. (Right ascension. T 324. From the observed altitude deduce the true altitude, and thence the true zenith distance. Mark the zenith distance North if the zenith is north of the body when on the meridian. South if the zenith is south of the body. Take out the declination of the body from the Nautical Almanac for the time of meridian passage, having regard for its proper sign or name. The algebraic sum of the declination and zenith distance will be the latitude. Therefore, add together the zenith distance and the declination if they are of the same name, but take their difference if of opposite names; this sum or difference will be the latitude, which will be of the same name as the greater. Example: At sea, June 21, 1915, in Long. 60° W., the observed meridian altitude of the sun's lower limb was 40° V; sun bearing south; I. C.,+3'' (f; height of the eye, 20 feet; required the latitude. Obs. alt., 40° 04' OO'' S. D., +15^46'''' Dec, 23° 26' 54'''. 3 X. Corr., + 13 21 I. C, + 3 00 H. D., + 1". 05 Long., 4''. *, 40 17 21 dip p. & r.. +18 - 4' ,- 1 46 X 49° 42' 23 26 39^ N. 59 N. 23^ 02 L. 73 09 38 N. - 5 25 Corr., + 4f. 20 Dec., 23° 26' 59" N. Corr., +13' 21" Example: At sea, April 14, 1915, in Long. 140° E., the observed meridian altitude of the sun's lower limb was 81° 15' 30"; sun bearing north; I. C.,-2' 30"; height of the eye, 20 feet. Obs. alt., 81° 15' 30" Corr., + 8 58 S. D., +15' 58" 2, 81 24 28 8° 35' 32" S. 8 58 37 N. 23 05 N. Dec, H.D., +" Long., - 9° 07' 03". 5 N. Corr., Corr., - I Dec, 54". 33 9" .33 506". 9 8' 26". 9 8° 58' 37" N. + 8' 58" Example: At sea, May 15, 1915, in Long. 0°, the observed meridian altitude of the sun's lower limb was 30° 13' 10"; sun bearing north:. I. C.,+1' 30"; height of the eye, 15 feet. Obs. alt., 30° 13' 10" + 12 02 Corr. S. D., LC, +15' 51" + 1 30 Dec, Gr. tf", 18° 40' 34" N. 30 25 12 59° 34' 48" S. 18 40 34 N. 40 54 14 8. dip, p. & r. +17 21 - 3' 48" - 1 31 Corr,; 128 LATITUDE. Example: January 1, 1915, the observed meridian altitude of Sirius was 53° 23' 4(/\ bearing bouth: I. C.,+5' 0''; height of the eye, 17 feet. Obs. alt., 53° 23' 4(/' I. C, + 5' (Xy Dec. *, 16° 35' 51" S. Corr., + 15 dip, - 4' 02" \ h, 53 23 55 ref., - 43 2, 36° 36' 05" N. d, 16 35 51 S. Corr., L, 20 00 14 N. Example: June 13, 1915, in Long. 65° W., and in a high northern latitude, the meridian altitude of the sun's lower limb was 8° 16' 10" below the pole; height of the eye, 20 feet; I. C, 0' 00". Greenwich apparent time of lower culmination, June 13, 16^ 20™ (=Long.4-12^). Obs. alt., 8° 16' 10" S. D., +15' 47" Dec, 23° 10' 20". 4 N. Corr., + 5 12 dip, - 4 23 H. D., h, 8 21 22 p. & r., - 6 12 G. M. T 2, 81° 38' 38" S. -10 35 ^ 180° -rf, 156 47 08 N. ^^"■' Corr., + 5 12 75 08 30 N. Dec. 23° 12' 52" N. Alternative method. h, 8° 21' 22" p, p, 66 47 08 180° -rf, 156° 47' 08" L, 75 08 30 N. Example: Jime 26, 1915, in Long, 80° W., the observed meridian altitude of the moon's upper limb 59° 6' 40", bearing south; I. C, +2' 0"; height of the eye, 19 feet. h, 59" 18' BO* Obs. alt., 59° 06' 40' O. M. T., Gr. trans., ll^ SO^-.g Dec. (Hi-), 26» 63' 30".0 S. — — — — — ^ Corr.forLong.(Tab.ll), + 14.5 -^— — — — Z, 30° 41' 30" N. I.e., + 2' 00" M.D., + 3''.848 4,26 51 52 S. — — — L. M. T., local trans., 12 05.4 No. min., + 25n>.4 "' Long., + 5 20 .0 ■ — L, 3 49 38 N. Aug., - 15 Corr., +| j, |p^ 23° 10' 20". 4 + 9". 29 le'^ .33 + V 151". 7 31". 7 23° 12' 52" 66° 47' 08" waa I.e., alt., lab. 2 + 2' 00" S.D., Aug., dip, - 16' 37" 15 4 16 - 21 08 1st Corr. - 19' 08" 3"" 58' !4),+ ' 47' 32" 30 68 G. M. T., local trans., +17 25.4 Dec., 26" 51' 52* S. Hor. Par., 60' 52*. 2 n, 59 18 30 Example: At sea, September 16, 1915, in Long. 75° E., the observed meridian altitude of Jupiter waa 51° 25' 24", bearing north; I. C, +3' 0"; height of the eye, 16 feet. Obs. alt., 51° 25' 24" par., +0' 01" O. M. T., Gr. trans., llh 59«'.5 Dec., 3° 58' 31". 6 S. Corr., - 1 41 I. C, +3 00 Corr. for Long., + .9 H.D., - 8". 03 h, 61 23 43 +3 01 L.M.T., local trans., 12 00.4 G. M. T., 7''. 00 ■^^— - — " Long., — 5 00 .0 . Z, 38° 36' 17" S. dip, -3' 55" Corr., - 56". 21 G. M. T., local trans., 7 00 .4 Dec., 3° 59' 28" 8. 2. 38° 36' 17" S. dip, -3' 55" d, 3 59 28 S. ref:, - 47 L, 42 35 45 8. -4 42 — — H. P., 2".2 Corr., -1' 41" par. (Tab. 17), 1' 325. Constant. — In working a meridian altitude, especially the daily noon observation of the sun, it is frequently a convenience to arrange the terms so that all computation, excepting the application of the observed altitude, is completed beforehand; then the ship's latitude will be known immediately after the sight haa been taken, it being necessary only to add or subtract the altitude. (See art. 323.) It is assumed that the^ noon longitude will be sufficiently accurately known in advance to enable the navigator to correct the declination; also the approximate meridian altitude to correct the parallax and refraction; if the latter is not known, it may readily be found from the declination and approximate latitude. Generally speaking, Lat. = Zenith distance + Dec., = 90 ° -True alt. + Dec, = 90°- (Obs. alt. + Corr.) + Dec, = (90° + Dec-Corr.) -Obs. alt., LATITUDE. 129 in which the quantity (90° + Dec. — Corr.) may be termed a Constant for the meridian altitude of the day, as it remains the same regardless of what the observed altitude may prove to be. The constant having been worked up before the observation is made, the latitude will be known as soon as the observed altitude is applied. To avoid the confusion that might arise from the necessity of combining the terms algebraically according to their diiBFerent names, it may be convenient to divide the problem into four cases and lay down rules for the arithmetical combination of the terms, disregarding their respective names as follows : Case I. Lat. and Dec. same name, Lat. greater, +90° + Dec. — Corr. — Obs. alt. Case II. Lat. and Dec, same name, Dec. greater, — 90° + Dec. + Corr. + Obs. alt. Case III. Lat. and Dec. opposite names, +90° — Dec. — Corr. — Obs. alt. Case IV. Lat. and Dec. same name, lower transit, + 90° — Dec. + Corr. + Obs. alt. The correctness of such an arrangement will become readily apparent from an inspection of figure 42. The assumption has been made that the correction to the observed altitude is positive; when this is not true the sign of the correction must be reversed. As examples of this method, the first, second, third, and fifth of the examples previously given illustrating the meridian altitude will be worked, using the constant; the details by which Corr. and Dec. are obtained are omitted, being the same as in the originals. 1st Example. Case I. + 90° 00' 00» Dec., + 23 26 69 Corr., - 13 21 2d Example. Case II. -90° 00' oof Dec., + 8 68 37 Corr., + 8 58 3d Example. Case III. +90° 00' 00» Dec., -18 40 34 Corr., - 12 02 5th Example. Case I r. +90° 00' 00* Dec., -23 12 52 Con., + 5 12 Constant, + 113 13 38 Obs. alt., - 40 04 00 Constant, —80 52 25 Obs. alt., +81 15 30 Constant, +71 07 24 Obs. alt., -30 13 10 Constant, +66 62 20 Obs. alt., + 8 16 10 Lat., 73 09 38 (N.) Lat., 23 05 (N.) Lat., 40 54 14(8.) Lat. 75 08 30 (N.) BY REDUCTION TO THE MERIDIAN. 326. Should the meridian observation be lost, owing to clouds or for other reason, altitudes may be taken near the meridian and the times noted by a watch compared with the cnronometer, from which, knowing the longitude, the hour angle may be deduced. If the observations are within 26" from the meridian, before or after, the correc- tion to be applied to the observed altitude to reduce it to the meridian altitude may be found by mspection of Tables 26 and 27. Table 26 contains the variation of the altitude for one minute from the meridian, expressed in seconds and tenths of a second. Table 27 contains the product obtained by multiplying the square of the minutes and seconds by the change of altitude in one minute. Let a = change of altitude (in seconds of arc) in one minute from the meridian : H= meridian altitude; A. = corrected altitude at observation; and < = interval from meridian passage. The value of the reduction to the meridian altitude of each altitude is found by the formula: U^h+at', a being found in Table 26, and at^ in. Table 27; hence the following rule: Find the hour angle of the body in minutes and seconds of time. Take from Table 26 the value of a corresponding to the declination and the latitude. Take from Table 27 the value of at^ corresponding to the a thus found and to the interval, in minutes and seconds, from meridian passage. This quantity will represent the amoxmt necessary to reduce the corrected altitude at the time of observation to the corrected altitude at the meridian passage; it is always additive when the body is near upper transit, and always to be subtracted when near lower transit. If tne mean of a number of sights is to be taken, determine each reduction sepa- rately, take the mean of all the reductions, and apply it to the mean of the altitudes; 21594°— 14 9 130 LATITUDE. it is incorrect, in such a case, to take the mean of the times and work the sight with this single value of t. The differences of altitude being small, the parallax and refraction will be sensibly the same for all, and one computation of the correction to the observed altitude will suffice. Knowing the meridian altitude, the latitude is to be found as previously explained. 327. When several sights are taken, the most expeditious method of calculating will be to find first the watch time of transit, and thence obtain the hour angle of each observation by comparing the watch time of observation. The watch time of transit may be found as already explained (art. 323) for computing that quantity as a guide in taking the meridian altitude, but the hour angle thus obtained is subject to a correction. The difference between watch time of transit and watch time of observa- tion gives the watch time — that is, the mean time — elapsing between transit and observation. A fixed star covers in that time an angle corresponding to the sidereal and not to the mean time interval, and a reduction should be made accordingly to give its true hour angle at the instant of observation. A planet's hour angle should be corrected in the same way (for we may disregard its very smaU change in right ascension). The correction may be entirely neglectedin the case of the sun, as the difference between mean and apparent time intervals is immaterial. The reduction of the hour angle in the case of the moon becomes rather cumbersome, so much so that it is better to find the hour angle of this body by the more usual method of converting watch time to G. M. T., and thence to L. S. T., and finding the difference between the latter and the R. A. ; an additional reason for this is that the G. M. T. of observation must be known exactly, with the moon, for the correction of the declination (art. 330). 328. Table 26 includes values of the latitude up to 60°, and those of the declina- tion up to 63°, thus taking in aU frequented waters of the globe and aU heavenly bodies that the navigator is likely to employ. No values of a are given when the altitudes are above 86 ° or below 6 °, as the method of reduction to the meridian is not accurate when the body transits very near the zenith, and the altitudes themselves are questionable when very low. In case it is desired to find the change of altitude in one minute from noon for conditions not given in the tables, it may be computed by the formula: 1''.9635 cos L cos d ~ sin (L — d) In working sights by this method where great accuracy is required, as in deter- mining latitudes on shore for surveying purposes, it is well to compute the a rather than to take it from the table, as one is thus enabled to employ the value as found to the second decimal place. Due regard must be paid to the names of the declination and latitude in working this formula; if they are of opposite names, the declination is negative, and L and a should be added together to obtain L — d. 329. Table 27 contains values of af^ up to the limits within which the method is considered to apply with a fair degree of accuracy. It must not be understood that the plan of reduction to the meridian is not available for wider limits, but it would seem preferable to employ the ^' 0" formula, described hereafter, when the hour angle falls beyond that for which the table is computed. On the other hand, the reduction is not exact in all cases covered by the table ; while sufficiently so for sea navigation, the limits given are far too wide for the precise determinations required in surveying, where the aim should be to observe bodies under such conditions that the total reduction aP shall not exceed 1'. 330. It should be kept clearly in mind when employing the method of reduction to the meridian that the resulting latitude is that of the ship at the instant of observa- tion, and to bring it up to noon the run must be applied. The declination should properly be corrected for the instant of observation; with the sun or a planet, it is sufficiently accurate to use the declination at meridian passage, unless the interval from the meridian be quite large ; but the moon's declination changes so rapidly that the exact time of observation must be used in its correction when working with this body. I LATITUDE. 131 Example: In latitude 47° S., having previously worked up the constant for meridian altitude, 78° 42' W, observed altitude of sun near meridian, 31° IV 50"; Dec. 11° N.; watch time, IP 40" 21», watch fast of L. A. T., 7". Find the latitude. Watch time, Watch fast, 11" 40™ 21* 07 Obs. alt., 31° IV 10 50" 24 L. A. T., 11 40 14 Mer. alt., 31 Constant, 78 22 42 14 10 t, igm 46» a (Tab. 26), of 2 (Tab. 27), Lat., 47 19 56 S. 1". ri".0= 6' 30" I .6=3 54 1 .6=10 24 Example: At sea, July 12, 1915, in Lat. 50° N., Long. 40° W., observed circum-mendian altitude of the sun's lower limb, 61° 48' 30", the time by a chronometer regulated to Greenwich mean time being -2™ 30'; I. C, -3' 0"; height of the eye, 15 feet. Find the latitude. 2*' 41° 39'; chro. corr. Chro. t., 2^ 41«»39' c. c, - 2 30 G.M.T., 2 Eq. t., - 39 5 09 19 G.A. T., 2 Long., - 2 33 40 50 00 L. A. T., 11 53 50 6 10 "Corr., h, S. D., dip, p. fi, I.e., + dip, ret., — Corr., P, 1 8 52 51 48 49 .4 .4 17 00 2 59 47 .0 .3 16 58 12 11 42 .7 5 10 18 53 07 .7 4 4 52 31 46 12 .7 26° 21 21 52' 34 38 00" .7 3 V 20'' 1 48" 55 6 43 5' 23" 26° 46' 4 37" 40 26 32 41 20 57 31 Watch time, C-W, Chro. t., C. C, 4h 3im 12. + 18 07 4 49 19 12 42 G. M. T. 5<» 16 36 37 R. A. M. S. Gr. 5<» 0^, + 8 51 49. 4 Red. (Tab. 9), G. S. T., Long., L. S. T., R. A. * +W + 2 43.7 1 31 10. 1 + 11 41 48 13 12 58. 1 13 34 36. 4 21 38.3 R. A. *, 1" 34» 36'.4 Dec, 57° 39' 29" S. p. 32° 20' 31" a (Tab. 26;, af (Tab. 27), 0".6 4' 40" 59 02 28 S. 331. Advantages are gained in working out meridian attitudes and reductions to the meridian, in finding the constant for a meridian altitude or a reduction to the meridian, and in predicting the approximate altitude of a body to be observed on or near the meridian, by projecting, in a quickly and roughly drawn diagram on the plane of the meridian of the observer, the known data entering into the problem. The diagram or figure will show at once how to combine the data to find the required result, and its use tends greatly to accuracy. It is ontv necessary to know the meaning of the terms already defined and to remember the single principle that the latitude of a place is equal to the declination of its zenith. In every case draw a circle (a rough approxima- tion will do) to represent the plane of the meridian, as in figure 51. The center O is the position of the ob- server. Draw a horizontal line through O, marking its intersection with the circumference on the right- hand side S, and on the left-hand side N. Erect a perpendicular to this fine at O, and mark its inter- section with the circumference Z. The line NS is the horizon; Z is the zenith. The arc ZS is that por- tion of the meridian between the zenith and the south point of the horizon; the arc ZN is that portion of the meridian between the zenith and the north point of the horizon. If the meridian altitude of a body is known (i. e., its altitude above the horizon on the meridian), and if it is known whether it bears to the southward or to the northward, its posi- FiG. 51. LATITUDE. 133 tion can be projected at once on the figure. Having the position of the heavenly body on the meridian and knowing the declination of the Dody, it is evident where to draw in the projection of the equator. Having the projection of the equator, the angular distance between the equator and the zenith (i. e., the declination of the zenith) is the latitude. Thus in figure 52, supposing the meridian alti- tude of any heavenly body, M, nas been observed, and that at the time of observation it was bearing south; also that the declination, ' and 0", the formulae are as follows: tan (f)" = tan d sec t; cos 4>' = sin h sin cj)" cosec d; The terms 0' and (j)" will have different directions of application according to the position of the body relative to the observer. From a knowledge of the approximate latitude, the method of combining them will usually be apparent ; it is better, however, to have a definite plan for so doing, and this may be based upon the following rule : Mark (p" north or south, according to the name of the declination; mark ^' north or south, according to the name of the zenith distance, it being north if the body bears south and east or south and west, and south if the body bears north and east or north and west. Then combine ^" and " ^or declination and ^' for zenith distance, the problem takes the form of a meridian altitude; indeed, the method resolves itself mto the finding of the zenith distance and declination of that point on the meridian at which the latter is intersected by a perpendicular let fall from the observed body. The time should be noted at the instant of observation, from which is foimd the local time, and thence the hour angle of the celestial object. If the sun is observed, the hour angle is the L. A. T. in the case of a p. m. sight, \oT 12'*— L. A. T. for an a. m. sight. If any other body, the hour angle may be found as hitherto explained. Example: June 7, 1915, in Lat. 30'' 25' N., Long. 81" 25' 3(K'' W., by account; chro. time, 6»» 22" 52*; oba. Q 75° 13' bearing south and west; I. C.-3' W; height of the eye, 25 feet; chro. corr.-2'» 36V i th€ " " " Find the latitude. Chro. t., c.c, 22'" 52« 2 36 G. M. T., Kq. t., O. A. T., Long., 6 20 16 + 1 29 6 21 45 - 5 25 42 Obs. alt. Q, 75' 13' 00' Corr., + 7 39 ft. S.D., 75 20 39 Dec., H. D., +' G. M. T., + 22"* 40' 44*. 9 N. Eq. t., IB 31* .84 15* .34 6^ .3 dip L.A.T.-<, {j» Oh 56»03« W. 00' 45* >r.. .C, + 15' 47" - 4' 54' - 14 - 3 00 Corr., Dec., tt 96' .6 1' 36' .6 22' 42' 22* H. D., a. M. T., Corr., Eq. t., 1" 29« . » {Add to mean time.) - 8 08 Corr., + 14*' (K/ 45'' 22 42 22 7' yy tan .01312 9. 62163 coeec . 41341 h 75 20 39 ^" 23 19 45 N. aS"" 10* 1 37.5 33 32.5 56 07.5 1 14.5 Obs. alt. ^, 68° 30' 00* S.D., Aug., 15' 40' 15 5 00 3 00 R. A. CCT*"), lOh 35m 321 .28 + Dec. (7»'), 7' 18' 28'. 2 N. 11 -10 30 54.5 36 39 - 23 55 H.A.fromGr., Long., 2 54 16 01 26 W W Ist Corr., Approx. alt., 68° 06' 05' p.*r.(Tab.24),+ 21 02 U, 68 27 07 M. D., No. min., Corr., R. A., 1« .99 33«>.54 66". 74 '06>.7 10^36»39« M. D., - No. mm., Corr., - Dec., Hor.Par., 14' .86 33". 54 / 498' \ 8' IS* - T 10' 10" N. 67' W U6° 47' 30* 136 LATITUDE, t 16° 47' 30" sec .01892 d 7 10 10 tan 9.09964 coeec .90377 h 68 27 07 Bin 9.96854 ^' 7 29 07 N. tan 9. 11856 an 9. 11485 i/ 13 51 45 S. COS 9.98716 Lat. 6 22 38 S. Example: August 6, 1915, p. m., in Lat. 52° 47' S. by D. R., Long. 146° 32' E., observed altitude of Acheraar, near lower transit, 24° 01' 20" bearing south and west; watch time, &" 48™ 22»; C— W, 9^ 4&* 27'; chro. corr. on G. M. T.,+l» 57«; height of eye, 18 feet; I. C.+l' 00". Find the latitude. Watch time, 6^ 48"' 22* Obs. alt.*, 24° 01' 20" R. A. *, l^" 34° 36' .4 C-W, +9 46 27 Oorr., - 5 19 Chro. t., 4 34 49 h, 23 56 01 CO., + 1 57 I. C, + 1' 00" Dec., 57° 39' 29" S. G. M. T., 5<', 16 36 46 R. A. M. S., + 8 51 49.4 dip, - 4' 09" Red. (Tab. 9), + 2 43. 7 ref., - 2 10 G. S. T., R. A. * Gr., t d h 180< Trfit 1 31 1 34 19.1 36.4 Corr, rHK - 6 19 coaec ein ein coe 5' 19^ see .08290 tan . 19846 H. A. from Long., 03 9 46 17 E. 08 E. H. A., 9 42 51 W. / 2'> 17« 09' [34° 17' 15" 34° 17' 15^ 57 39 29 23 56 01 '- 44'.48 20 47 41 20 -^^^— — ^ 21 14 46 10 H. D., + 33".6S H. D., - 0» .07 " " - G. M. T., - 2'>.3 G.M.T.,17d, 21 42 60.5 S. D., + 15' 50" p, 70" 38' 49" Eq.t., + 3 44.6 G. A. T., 21 4€ 35. 1 p. & r., J.r dip, . & C, 29 41 + 9 00 04 29 50 04 + 15' - 4' - 1 - 50 42' 34 30 Mean, 7 20 45.3 Mean, *» ,x w C-W, + 2 17 06 Corr., + 9 04 r^„ / 77".4 Corr., + 0« .16 ^"i - \i' 17" Chro. t., 9 37 61.3 h, 29 50 04 ———— Eq.t, 3"> 44«.6 C. C, + 4 59. 2 _— — _ Dec., 19° 21' 11" N. (.Add to mean time.) Dec., 19"' 22' 27".9 H. D., + G. M, T., - 33".6S 2h.3 Corr., - {j, Dec., 19° 21' 77".4 17" 11" Corr., + 9' 04" h 29° 50^ 04* L 41 33 00 Bee .12588 p 70 38 49 coeec .02526 cos 9. 51229 Bin 9. 81852 2)142 01 53 8 S-h 71 41 00 57 10 53 G. A. T. L. A. T. 2P 19 46" 35' 32 38.5 2)19. 48195 an it 9. 74097 T^r.^ i 2" IS'" 56*.51tt, lx)ng. "Iggo 29/ og// yN. LONGITUDE. 143 Example: At sea, April 16, 1915, p. m., in Lat. 11° 47' S., Long. 0* W E., by D. R., observed an altitude of the star Aldebaran, west oi the meridian, 23° IS' 2(K'; chronometer time, 1^ 01™ 35* ; chro- nometer fast of G. M. T., 2™ 27»; I. C, -2' m"\ height of eye, 26 feet. What was the longitude? 1^ Ol™ 35» - 2 27 Chro. t., CO., G. M. T., R. A. M. S., Red. (Tab. 9), G. S. T., R. A. *, H. A. from Gr., 4 03 15 W. 6 58 58 +1 34 11.5 + 1 08.8 8 34 18.3 4 31 03.0 Corr., 9 15 Obs.alt. *, 23° 13' 20^ R.A. *, 4" 31" 03*. Corr., 9 15 Dec, 16° 20^ 29" N *, 23 04 05 p, 106° 20^ 29" I.e., 2' 00" dip, ref., 5 00 2 15 23° 04' 05" 11 47 00 106 20 29 2)141 11 34 70 35 47 47 31 42 Or. H. A. H.A. 4" 03™ 15» W. 4 05 42 W. .00925 . 01791 9. 52143 9. 86783 2)19. 41642 sin i < 9. 70821 see cosec cos eia ^°g- t 0° 36' 45"/*^- Example: At sea, April 17, 1915, a. m., in Lat. 25° 12' S., Long. 31° 32' W., by D. R., observed an altitude of the planet Jupiter, east of the meridian, 32° 46' 10"; watch time, 5^ 48°" 02«; C-W, 2" 05» 42»; G. C, +2"» 18'; I. C, +1' 30"; height of eye, 18 feet. Required the longitude. W. T., c-w, Chro. t., C. C, Red. (Tab. 9), G. S. T., R. A. *, H.A. from Gr., 5» 48»02« 2 05 42 7 + 53 2 44 18 19 + 1 + 56 34 3 02 11.5 16.5 21 23 33 13 30.0 24.8 1 39 55 E. Obs.al1 Corr , t. *, 32* 46' - 4 10* 09 R. A. (17<> 0»), H. D., G. M. T., Corr., R.A., 23k 13m 33.. Dec.( H. D. Q.M. Corr., Dec., V, 17«l Ok), 6* 03' 51*. B. + 2".0 4''.1 - 8«.2 + T., - 12' 1 », 32 42 01 4>>.l LC, + 1' 30' 49*. « dip, ref - 4' - 1 09» 30 23'' 13- 24».8 6' 04' 41' 8. 83*65' 19* - A 39 Corr., — 32" 25 83 4' 09* 42' 12 55 01" 00 19 2)141 49 20 coeec .04343 .00245 70 38 54 12 40 39 Gr.H.A. H.A. Long. I 1" 39™ 55« E. 3 46 26 E. 2'» 06™ 31* 31° 37' 45' >) W. 008 sin 9. 51459 9. 79138 2)19. 35185 sin ^ t 9. 67592 CHAPTER XIV. AZIMUTH. 34:4:. The azimuth of a body has been defined (art. 223, Chap. VII) as the arc of the horizon intercepted between the meridian and the vertical circle passing through the body; and the amplitude (art. 224) as the arc measured between the position of the body when its true altitude is zero and the east or west point of the horizon. The amphtude is measured from the east point at rising and from the west point at setting, and, if added to or subtracted from 90°, will agree with the azimuth of the body when in the true horizon. The azimuth is usually measured from the north point of the horizon in north latitude, and from the south point in south latitude, through 180° to the east or west; thus, if a body bore N. by E., its azimuth would be named N. lli° E. in north, or S. 168f ° E. in south latitude. The determination of the azimuth of a celestial body is an operation of frequent necessity. At sea, the comparison of the true bearing with a bearing by compass affords the only means of ascertaining the error of the compass due to variation and deviation; on shore, the azimuth is required in order to furnish a knowledge of the variation, and is further essential in all surveying operations, the true direction of the base Une being thus obtained. 345. There are various methods of obtaining the true azimuth of a celestial body, which will be described as follows: (a) Amplitudes, (6) Tim^ Azimuths, (c) Altitude Azimuths, (d) Time and Altitude Azimuths. A further method, by meana of the Summer line, will be explained later (Chap. XV). Still another operation pertains to this subject, namely: (e) The determmation of the True Bearing of a Terrestrial Olject AMPLITUDES. 346. The method of obtaining the compass error by amplitudes consists in observing the compass bearing of the sun or other celestial body when its center is in the true horizon, the true bearing, under such conditions, being obtained by a short calculation. Since the true horizon is not marked by any visible line (differing as it does from the visible horizon by reason of the effects of refraction, parallax, and dip), allowance may be made for the difference by an estimate of the eye, or else the observation may be made in the visible horizon and a correction applied. 347. When the center of the sun is at a distance above the horizon equal to its own diameter it is almost exactly in the true horizon ; at such a time, note its bearing by compass, and also note (as in all observations for determining compass error) the ship's head by compass, and the angle and direction of the ship's heel. Or, note the bearing at the instant at which the center of the body is in the visible horizon; in the case of the sun and moon, the correct bearing at that time may be most accurately ascertained by taking the mean of the bearings when the upper and the lower limbs of the disk are just appearing or disappearing. 348. To find the true amplitude hy computation, there are given the latitude, L, and declination, d. The quantities are connected by the formula, sin Amp. = sec L sin d, from a solution of which the amplitude is obtained. To find the true amplitude hy inspection enter Table 39 with the declination at the top and the latitude in the side column; under the former and opposite the latter will be given the true amplitude. To obtain accurate results, interpolate for minute" of latitude and declination. 144 AZIMUTH. 145 To reduce the observed amplitude when taken in the visible horizon to what it would have been if taken in the true horizon, enter Table 40 with the latitude and declination to the nearest degree and apply the correction there found to the observed amplitude; the result will be the corrected amplitude by compass, which, by comparison with the true ampUtude, gives the compass error. When the body observed is the sun, a star, or a planet, apply the correction, at rising in north lati- tude or at setting in south latitude, to the right, and at setting in north latitude or at rising in south latitude, to the left. For the moon, apply half the correction in a contrary direction. Example: At sea, iu Lat, 11° 29^ N., the observed bearing of the sun, at the time of rising, when its center was estimated to be one diameter above the visible horizon, was E. 31° N.; corrected declination 22° 32' N. Required the compass error. By computation. By inspection ( Table 39) . L 11° 29' sec .00878 L, 11°.5N.\t, ,^ „^^ „ ooo n m d 22 32 sin 9.58345 rf/ 22 .5 N./^"^® *°^P- ^- ^S**-© N. Obs. amp. E. 31 ,0 N. True amp. E. 23° 01' N. sin 9. 59223 Obs. amp. E, 31 00 N. Error, 8°.0E. Error, 7° 59' E. Example: At sea, iu Lat, 25° 03' S., the observed bearing of Venus, when in the visible horizon at rising, was E. 18° 30' N., its declination being 21° 44' N. Required the compass error. By computation. By inspection {Table S9). L 25° 03' sec .04290 L, 25°. OS.!™. 17 0.0 n xt d 21 44 sin 9.56854 rf, 21 . 7 N.| ^rue amp. E. 24°. 1 N. Obs. amp. E. 18°.5N.\^ „ ,„ „„ True amp. E. 24° 08' N. sin 9.61144 Corr. (Tab. 40) o.3 left./ ^°™P-*™P- ■'^' ^^ -^ ^• Error, 5°. 3 W. Comp. amp. E. 18 48 N. Error, 5° 20' W. Example: At sea, in Lat. 40° 27' N., the mean of the observed bearings of the upper and lower limbs of tlie moon, when in contact with the visible horizon at setting, was W. 17° S. ; declination, 21° 12' S. What wa^ the error of the compass? By computation. By inspection {Table 39). L 40° 27' sec . 11863 L, 40°. 5 N. \ m, „ w 000 >• a d 21 12 sin 9.55826 d, 21 . 2 S. f ^"® *°^P- ^- 28". 4 S. Obs. amp. W. 17° .0 S. \p„„^ „„^ w i« t a True amp. W. 28° 22' S. sin 9.67689 Corr. (Tab. 40) 0.3 right. r^^^P'^^^P- ^'^^ •'' ^• Error, 11°. 7 W. Comp. amp. W. 16 42 S, Error, 11° 40' W. TIME AZIMUTHS. # 349. In this method are given the hour angle, t, at time of observation, the polar distance, p, and the latitude, L; to find the azimuth, Z. Any celestial body bright enough to be observed with the azimuth circle may be employed for observation; the conditions are, however, most favorable for solu- tion when the altitude is low. 350. Take a bearing of the object, bisecting it if it has an appreciable disk, and note the time with a watch of known error. Record, as usual, the ship's head by compass and the amount of heel. If preferred, a series of bearings may be taken with their corresponding times, and the means taken. 351. First prepare the data as follows: (a) Find the Greenwich time corresponding to the local time of observation. (6) Take out the declination of the body from the Nautical Almanac; if the method of computation is employed, the polar distance and the co-latitude should be noted. (c) Find the hour angle of the body by rules heretofore given. 21594°— 14 10 146 AZIMUTH. This having been done, the true azimuth may be determined either by Time Azimuth Tables, by the graphic method of an Azimuth Diagram, or by Solution of the Astronomical Triangle. Owing to the possibihty of more expeditious working, either of the first-named two is to be considered preferable to the last, and the navigator is recommended to supply himself with a copy; of a book of Azimuth Tables, such as pubhshed by the Hydrographic Office, or with an Azimuth Diagram such as Weir's or Sigsbee's; an explanation of the method of use accompanies each of these. 352. To solve the triangle: Let S = ^ sum of polar distance and co-Lat. D = ^ difference of polar distance and co-Lat. i< = i hour angle. Z = true azimuth. Then, tan X = sin D cosec S cot ^ t; tan Y = cos D sec S cot ^ t; Z=X-HY, orX~Y. First Case. — If the half -sum of the polar distance and co-Lat. is less than 90°: take the sum of the angles X and Y, if the polar distance is greater than the co-Lat. ; take the difference, if the polar distance is less than the co-Lat. Second Case. — If the half -sum of the polar distance and co-Lat. is greater than 90°: always take the difference of X and Y, which subtract from 180°, and the result will be the true azimuth. In either case, mark the true azimuth N. or S. according to the latitude, and E. or W. according to the hour angle. It may sometimes be convenient to use the supplement of the true azimuth, by subtracting it from 180° and reversing the prenx N. or S,, in order to make it correspond to the compass azimuth when the fatter is less than 90°. The cotangent of haff the hour angle may be found from Table 44 abreast the whole hour angle in the column headed ''Hour P. M." Example: At sea, in Lat. 30° 25'' N., Long. 5^ 25"* 42' W., the observed bearing of sun's center was N. 135° 30'' E., and the Greenwich mean time, December 3, 2** 36™ 11'. The corrected declination of the sun was 22° 07' S.; the equation of time (additive to mean time), 10™ 03'. Required the error of the compass. G.M.T.(Dec.3), 2i' 36™ 11' co-Lat., 59° 35' Long., - 5 25 42 p, 112 07 L,M.T.(Dec.2), 21 10 29 p+co-L, 171 42 Eq. t., -1- 10 03 S, 85 51 L.A.T., 21 20 32 t S D X Y 21139m 28* cot it .44051 85° 51' cosec .00114 26 16 50 44 88 19 sm tan 9. 64596 . 08761 cot it .44051 sec 1. 14045 cos 9. 95267 tan L 53363 t. 2^ 39™ 28' p-co-L, 52° 32' X-I-Y139 03 D, 26 16 True azimuth, Comp. azimuth. Compass error. N. 139° 03' E. N. 135 30 E. 3 33 E. Example: At sea, in Lat. 2° 16' N., the observed bearing of the sun's center waa N. 85° 15' E: sun's hour angle, 3*' 44™ 16*, and its declination, 7° 38' N. Required the compass error. co-Lat., P, 87° 82 44' 22 p-fco-L, 170 06 s, 85 03 co-L-p, 5° 22' D, 2 41 t S D X Y 3h 44m 16. 85° 03' 2 41 5 03 87 22 Y-X 82 19 True azimuth, Comp. azimuth, Compass error, cot i t cosec sin tan . 27372 .00162 8. 67039 8. 94573 N. 82° 19' E. N. 85 15 E. 2 56 W cot J t sec cos tan . 27372 1. 06406 9. 99952 1. 33730 I AZIMUTH. 147 Example: At eea, in Lat. 16° 32' S., observed bearing of Venus N. 56° OO' W., its hour angle being 4h 27ni 311^ an(j j^^g declination 23° 12'' N. What waa the error of the compass? co-Lat., 73° 28' t p, 113 12 S D p+co-L, 186 40 S, 4h 27" 31* 93° 20^ 19 52 27 16 87 40 cot it . 18022 cosec . 00074 Bin 9. 53126 tan 9. 71222 cot i t sec cos tan . 18022 1. 23549 9. 97335 L 38906 60 24 19 52 119° 36' True azimuth, Comp. azimutii, Compass error, S. 119° 36' W. S. 124 00 W. 4 24 W. AliTITTJDE AZIMUTHS. 353. This method is employed when the altitude of the body is observed at the same time as the azimuth; in such a case the hour an^le need not be known, though the time of observation should be recorded with sufficient accuracy for the correction of the declination of the sun, moon, or a planet. There are given the altitude, h, the polar distance, p, and the latitude, L; to find the azimuth, Z. 354. Take a bearing of the body by compass, bisecting it if the disk is of appreciable diameter, and simultaneously measure the altitude; note the time approximately. Observe also the ship's heading (by compass) and the heel. Or a series of azimuths, with corresponding altitudes, may be observed, and the means employed. 355. Calculate the true altitude and declination from the observed altitude and the time. Then compute the true azimuth from the following formula: cos i Z = Vcos s cos (s—p) sec L sec i^, in which s = i (h+'L-\-p). The resulting azimuth is to be reckoned from the north in north latitude and from the south in south latitude. It may occur that the term, (s — p), will have a negative value, but since the cosine of a negative angle less than 90° is positive, the result will not be affected thereby. Example: At sea, in Lat. 30° 25' N., the observed bearing of the sun's center waa N. 135° 30' E., and its corrected altitude 24° 59'; the approximate G. M. T. was 2''.6, the declination at that time being 22° 07' S. Required the compass error. h L P 24° 59' 30 25 112 07 sec sec cos COfl cos .04267 .06431 2 ) 167 31 83 45 -28 22 69 30 139 00 9. 03690 9.94445 »i 2 ) 19. 08833 9. 54416 True azimuth, N. 139° 00' E. Comp. azimuth, N. 135 30 E. Compass error, 3 30 E. TIME AND ALTITUDE AZIMUTHS. 356. When, at the time of observing the compass bearing of a celestial body, the altitude is measured and the exact time noted, the true azimuth may be very expeditiously determined, a knowledge of the latitude being unnecessary. In view of the simplicity of the computation, this method strongly commends itself to observers not provided with azimuth tables or diagram. 357. The observation is identical with that of the altitude azimuth (art. 354), with the exception that the times of observation must be exactly instead of approx- imately noted. 148 AZIMUTH. 358. Ascertain the decimation of the body at time of sight, and correct the observed altitude; compute the hour angle. We then have: sin Z = sin t cos d sec It, from which the azimuth may be found. This method has a defect in that there is nothing to indicate whether the resulting azimuth is measured from the north or the south point of the horizon; but as the approximate azimuth is always known, cases are rare when the solution will be in question. Example: At sea, in Lat. 30° 25'' N., Long. 5^ 25™ 42* W., the observed bearing of the sun's center was N. 135° 30' E.; its altitude at the time was 24° 59'; hour angle, 2^ 39™ 28* (39° 52'), and declination, 22° 07' S. Find the compass error. (See example under Altitude Azimuths and first example under Time Azimuths.) t 39° 52' sin 9. 80686 True azimuth, N. 139° 04' E. d 22 07 cos 9. 96681 Comp. azimuth, N. 135 30 E. h 24 59 sec .04267 Compass error, 3 34 E. Z S. 40° 56' E. sin 9. 81634 TBtTE BEARING OF A TERRE STRIAL OBJECT. 359. Thus far, sea observations for combined variation and deviation have been discussed, but if it becomes necessary, as in surveying, to ascertain the True Bearing of a Terrestrial Olject, or to find the variation at a shore station, more accurate methods than the foregoing must be resorted to. ' The most reliable method is that by an Astronomical Bearing. This consists in finding the true bearing of some well-defined object by taking the angle between it and the sun or other celestial body with a sextant or a theodolite, and simultaneously noting the time by chronometer, or measuring the altitude, or observing both time and altitude. It should always be noted whether the object is right or left of the sun. 360. By Sextant. — ^Measure the angular distance between the object and the sun's limb; and if there is a second observer, measure the altitude of the sun at the same moment and note the time. In the absence of an assistant, first measure the altitude of the sun; next, the an^lar distance between the sun and the object; then, a second altitude of the sun, notmg the time of each observation. Also measure the altitude of the defined point above the sea or shore horizon. By Theodolite. — This instrument is far more convenient than the sextant, for, being leveled, the horizontal angle between the sun and the object is at once given, no matter what may be the altitudes of the objects. In case the altitude of the sun is needed, it may be read accurately enough from the vertical circle, although not as finely graduated as the limb of the sextant. The error in altitude must, however, be found by the level attached to the telescope, since it will usually be found to differ from the levels of the horizontal circle. If, in directing the telescope to the sun, there is no colored eyepiece, an image of the sun may be cast on a piece of white paper held at a little distance from the eyepiece, and by adjusting the focus the shadow of the cross wires will be seen. It should be understood that any celestial body may be used as well as the sun, and there are, in fact, certain advantages in the use of the stars; the sun is chosen for illustration, because it will usually be found most convenient to employ that body. 361. Find the true azimuth of the celestial body by one of the methods pre- viously explained in this chapter, and apply to it the azimuth difference, or horizontal angle between the celestial and the terrestrial body, having regard to the direction of one from the other. To find the azimuth difference from sextant observations, change^ the observed altitudes of the bodies into apparent altitudes by correcting them for Index error of the sextant, dip, and semidiameter; change the observed an^lar distance into apparent angular distance, by correcting for index error and semidiameter. Then if S = i (App. Dist. + App. Alt.© +App. Alt. Object), we have: cos i Az. Diff . = Vsec App. Alt.© sec App. Alt. Object cos S cos (S— App. Dist.), whence the azimuth difference is deduced. AZIMUTH. 149 When the theodolite is used, the horizontal angle is given directly. If only one limb of the sun is observed, it will be necessary to apply a correction for semidiameter (S. D. Xsec h), but it is usual to eliminate this correction by taking the mean of observations of both limbs. Example : From a. m. observations, in Lat. 30° 25' 24'^ N., Long. 81° 25' 24'' W., obtained the follow- ing data for finding the true bearing of a station: Watch time, ll*' 22"" 36' C-W, 5 21 18 Chro. corr., + 2 16 Obs. Ang. Dist. 0, 117° 07' Left. Obs. 2 a, 71° 37' 20" Obe. alt. Station, 20' I. C, zero. Dec. S., 22° 56' 27" Eq. t., + 7° 00' S. D., 16' 17" Required the true bearing of the object. W. T., C-W, Chro. t., C. C, G. M. T. Eq.t., G. A. T., Long., ll^* 22"36» 5 21 18 L. A.T. t, 4 + 43 2 54 16 4 + 46 7 10 00 4 - 5 53 25 10 42 23 27 28 /O" 32™ 32' 18° 08' 00" Obs. Ans. Dist., 117» 07' 00' O's 8. D., + 16 17 App. Aag. Dist., 117 23 17 2C1, S. D., App. Alt., p. & r., h. 71° 37' 20" 35 48 40 + 16 17 36 04 57 — 1 13 36 03 44 App. Dist. App Alt. O App. Alt. Object 8 8-App. Dist. J At. Diff . Ae. Diff. 117* 23' 36 05 20 2)153 48 76 54 -40 29 62* 30' 125 00 8° 08' 00" 22 56 27 36 03 37 S. 9° 17' E. N. 170 43 E. ein 9. 15069 cos 9. 96422 sec . 09239 sin 9. 20730 seo 0.00260 see 0.00001 cos 9.35536 cos 9. 88115 True bearing O, At. Diff., 170" 43' E. 1% 00 Left. True bearing object, N. 45' 43' E. 2)19.32902 COS 9.66451 Example: Same date and place and same objects as in the preceding example; measurement made with a theodolite, angular distance (J), 123° 17'; object left of sun. Watch time, 11'' 16™ 34".5; watch slow of L. A. T., 4™ 53" .5. Dec. 0, 22° 56' S. Required the true bearing. (See article 352.) W. T., ll'' 16™34».5 W. slow, 4- 4 53.5 L. A. T., 23 21 28 .0 t, 38 32 co-Lat., 59° 35' p, 112 56 p+co-L, 172 31 s, 86 15 p— co-L, 53 21 t s D X Y 0" 38™32« 86° 15' 26 41 79° 24' 89 39 cot it 1.07435 cosec . 00093 Bin 9. 65230 tan 72758 X4-Y169 03 D, 26 41 True bearing ©, Az. Diff., N. 169° 03' E. 123 17 Left. True bearing object, N. 45 46 E. cot it 1.07436 sec 1. 18440 COB 9. 95110 tan 2. 20985 CHAPTER XV. THE SUMNER LINE. DESCRIPTION OF THE LINE. 362. The method of navigation involving the use of the Sumner line takes its name from Capt. Thomas H. Sumner, an American shipmaster, who discovered it and published it to the world. As a proof of its value, tne incident which led to its discovery may be related : " Having sailed from Charleston, S. C, 25th November, 1837, bound for Greenock, a series of heavy gales from the westward promised a quick passage; after passing the Azores the wind prevailed from the southward, with thick weather; after passing longitude 21° W. no observation was had until near the land, but soundings were had not far, as was supposed, from the bank. The weather was now more boisterous, and very thick, and the wind still southerly; arriving about midnight, 17th December, within 40 miles, by dead reckoning, of Tuskar light, the wind hauled SE. true, making the Irish coast a lee shore; the ship was then kept close to the wind and several tacks made to preserve her position as nearly as possible until daylight, when, nothing being in sight, she was kept on ENE. under short sail with heavy gales. At about 10 a. m. an altitude of the sun was observed, and the chronometer time noted; but, having run so far without observation, it was plain the latitude by dead reckoning was liable to error and could not be entirely relied upon. The longitude by chronometer was determined, using this uncertain latitude, and it was found to be 15' E. of the position by dead reckoning; a second latitude was then assumed 10' north of that by dead reckoning, and toward the danger, giving a position 27 miles ENE. of the former position; a third latitude was assumed 10' farther north, and still toward the danger, giving a third position ENE. of the second 27 miles. Upon plotting these three positions on the chart, they were seen to be in a straight Une, and this line passed through Smalls light. "It then at once appeared that the observed altitude must have happened at all the three points and at Smalls light and at the ship at the same instant." Then followed the conclusion that, although the absolute position of the ship was uncertain, she must be somewhere on that line. The ship was kept on the course ENE., and in less than an hour Smalls light was made, bearmg ENE. ^ E. and close aboard. The latitude by dead reckoning was found to be 8' in error, and if the position given by that latitude had been assumed correct, the error would have been 8 miles too far S., and 31' 30" of longitude too far W., and the result to the ship might have been disastrous had this wrong position been adopted. This represents one of the practical applications of the Sumner line. The properties of the line thus found will now be explained. 363. Chicles of Equal Altitude. — In fi^re 54, if EE'E" represent the earth projected upon the horizon of a point A, and if it be assumed that, at some particular mstant of tmie, a celestial body is in the zenith of that point, then the true altitude of the body as observed at A will be 90°. In such a case the great circle EE'E", which forms the horizon of A, wiU divide the earth into two hemispheres, and from any point on the surface of one of these hemispheres the body will be visible, while over the whole of the other hemisphere it will be invisible. The great circle EE'E", from the fact of its marking the limit of illumination of the body, is termed the circle of illumination, and from any point on its circumference the true altitude of the center of the body will be zero. If, now, we consider any small circle of the sphere, 150 THE SUMNEB LINE. 151 BB'B", CC'C, DD'D", whose plane is parallel to the plane of the circle of illumina- tion and which lies withiii the hemisphere throughout which the body is visible, it will be apparent that the true altitude of the body at any point of the circumference of one or these circles is equal to its true altitude at any other point of the same circum- ference; thus the altitude of the body at B is equal to its altitude at B' or B", and its altitude at D is the same as at D' or D". It therefore follows that at any instant of time there is a series of positions on the earth at which a celestial body appears at the same given altitude, and these positions lie in the circumference of a circle described upon the earth's surface whose center is at that position which has the body in the zemth, and whose radius depends upon the zenith distance, or — what is the same thing — upon the altitude. Such circles are termed circles of equal altUvde. It is important to note that an observer making an instantaneous transit through the latitudes and longitudes passed over by any rhumb line or loxodromic curve drawn within the hemisphere of illuniination, through the point A, will experience no astronomical difference, with reference to the observed body in the zenith of A, save an altitude difference. 364. The data for an astronomical sight comprise merely the time, declination, and altitude. The first two fix the position of the body and may be regarded as giving the latitude and lon- gitude of that point on the earth in whose zenith the body is found; the zenith distance (the complement of the altitude) indicates the distance of the observer from that point ; but there is nothing to show at which of the numerous positions ful- filling the required condi- tions the observation may have been taken. A num- ber of navigators may meas- ure the same altitude of a bod^r at the same instant of time, at places thousands position with identical data. of miles apart; and each proceeds to work out his so far as this sight is concerned. It is therefore clear that a single observation is not enough, m itself, to locate the point occu- pied by the observer, and it becomes necessary, in order to fix the position, to employ a second circle, which may be either that of another celestial body or that of the same body given by an observation when it is in the zenith of some other point than when first taken; knowing that the point of observation lies upon each of two circles, it is only possible that it can be at one of their two points of intersection; and since the position of the ship is always known within fairly close limits, it is easy to choose the proper one of the two. Figure 55 shows the plotting of observations of two bodies vertically over the points A and A' upon the earth, the zenith distances corresponding respectively to the radii AO and A'O. 365. The Sumner Line. — In practice, under the conditions existing at sea, it is never necessary to determine the whole of a circle of equal altitude, as a very small portion of it will suffice for the purposes of navigation ; tne position is always known within a distance which will seldom exceed 30 mUes under the most unfavorable conditions, and which is usually very much less; in the narrow limits thus required, the arc of the circle will practically coincide with the tangent at its middle point, 152 THE SUMNEB LINE. and may be regarded as a straight line. Such a line, comprising so much of the circle of equal altitude as covers the probable limits of position of the observer, is called a Sumner line or Line of position. The latter designation has also a more extended meaning, embracing any line, straight or curved, which forms a locus of the ship's position, whether it be obtained from observations of celestial bodies or from bearings or distances of terrestrial objects. 366. Since the direction of a circle at any point — that is, the direction of the tangent — must be perpendicular to the radius at that point, it follows that the Sunmer line always lies in a direction at right angles to that in which the body bears from the observer. Thus, in figure 55, it may be seen that m m' and n n', the extended Sumner lines corresponding to the bodies at A and A', are respectively perpendicular to the bearings of the bodies OA and OA'. This fact has a most im- portant application in the employment of the Sumner line. 367. Uses of the Sumner Line. — The Sumner line is valuable because it gives to the navigator a knowledge of all of the probable positions of his vessel, while a sight worked with a single assumed latitude or longitude gives but one of the probable positions; it must be recognized that, in the nature of things, an error in the assumed coordinate will almost invariably exist, and its possible effect should be taken into consideration; the line of position reveals the difference of longitude due to an error in the latitude, or the reverse. Since the Sumner line is at right angles to the bearing, it may be seen that when the body bears east or west — that is, when it is on the prime vertical — the resulting line runs north and south, coinciding with a meridian; if, in this case, two latitudes are assumed, the deduced longitudes will be the same. When the body bears north or south, or is on the meridian, the line runs east and west, and becomes identical with a parallel of latitude; in such a case, two assumed longitudes will give the same latitude. Any intermediate bearing gives a Sumner line inclined to both meridians and parallels; if the line agrees in direction more nearly with the meridian, latitude should generally be assumed and the longitude worked; if it is nearer a parallel, the reverse course is usually preferable. The values of the assumed coordinates may vary from 10' to 1°, according to circumstances. 368. The greatest benefit to be derived from the Sumner method is when two lines are worked and their intersection found. The two lines may be given by different bodies, which is generally preferable, or two different lines may be obtained from the same body from observations taken at different times. The position given by the intersection of two lines is more accurate the more nearly the Imes are at right angles to each other, as an error in one line thus produces less effect upon the result. When two observations of the same body are taken, the position of tne ship at the time of first sight must be brought forward to that at the second in considering the intersection ; if, for example, a certain line is determined, and the ship then runs NW. 27 mUes, it is evident that her new position is on a line parallel with tlie first and 27 mUes to the NW. of it ; a second line being obtained, the intersection of this with the first line, as corrected for the run, gives the ship's position. Besides the employment of two lines for intersection with each other, a single line may be made to serve various useful purposes for the navigator. These are described in article 389, Chapter XVI. METHODS OF DETERMINATION. 369. There are three methods in common use for determining the Sumner line: (a) The Chord Method: To assume two values of one coordinate and find the corresponding values of the other. Two values of the latitude may be assumed and THE SUMNEB LINE. 153 the longitudes determined, as was done by Capt. Sumner on the occasion that led to the discovery of his method; or else two values of the longitude may be assumed and the latitudes determined. Two points are fixed in this way, and the line joining them is the Sumner line. (&) The Tangent Method: To assume either one latitude or one longitude and determine the corresponding coordinate. This gives one point of the Sumner line. The azimuth of the observed celestial body is then ascertained, and a line is drawn through the determined point at right angles to the direction in which the body bore at the time of the sight. This will be the Sumner line. (c) In accordance with the method of Saint Hilaire, to be described in article 371, to lay off from an assumed geographical position, along the line of direction in which the body bore at the time of the sight, the determined distance to the Sumner line. 370. It follows that if the Sumner line be located by the first method and its direction thus defined, the azimuth of the observed body may be determined by finding the angle made by the line with the meridian and adding or subtracting 90 . Example: At sea, April 17, 1915, a. m., in Lat. 25° 12' S., Long. 31* 32' W., by D. R., observed an altitude of the planet Jupiter, east of the meridian, 32° 46' 10"; watch time, ^ 48™ 02»; C-W, 2" 05"» 42»; C. C, + 2™ IS"; I. C, + 1' 30"; height of eye, 18 feet. Reguired the Sumner line. From a solution of this same problem for a single longitude (art. 343, Chap. XIII), the following were found: H. A. from Or., 1" 39"" 55» E.; h, 32° 42' 01''; p, 83° 55' 19". Assume values of Lat. 25° 02' and 25° 22' S. h 32° 42' 01" L, 25 02 00 p 83 55 19 sec cosec cos sin sin i t .04284 .00245 9. 51641 9. 79057 82— h Gr.H.A. H.A.J Long.j 25° 22' 00" 70 59 40 38 17 39 sec cosec COB sin ein J i .04403 .00245 2)141 39 20 «i 70 49 40 s^-h 38 07 39 9. 51276 9. 79218 Gr.H.A. 1" 39™55'E. H. A., 3 46 33 E. 2)19. 35227 ;, 9. 67613 1" 39°55» 3 46 19 2)19. 35142 Cj 9. 67571 T^ / 2" 06™38='W Long.i| 3^0 39/ 3o//|\V. / 2" 06" 24" \^ \31° 36' 00"/ *^- A comparison of these results with those obtained by the solution with a single latitude shows that the hour angle, and consequently the longitude, corresponding to the latitude 25° 12' S. are the means of those corresponding to the latitudes here used; and therefore that the assumption that the Sumner line is a straight line is accurate. The line of the same sight might also have been found as follows : Working with the single latitude 25° 12' S., it was found that the corresponding longitude was 31° 37' 45" W. Now, by referring to an azimuth table or azimuth diagram, the azimuth corresponding to Lat. 25°.2 S., Dec., 6°.l S., H. A., 3** 46™.4 E. IS S. 99° 23' E.; therefore the Sumner line extends S. 9° 23' E. The line may therefore be defined in either of two ways, thus : . /25° 02' 00" S. i /25° 22' 00* S. ^431 39 30 W. ^131 36 00 W. ^ . /25° 12' 00" S. Line runs S. 9° 23' E. ^' ^131 37 45 W. By inspection of the coordinates of A^ and A3 it may be seen that — + 20' diff. lat. makes -3'.50 diff. long.; or + 20 miles diff. lat. makes —3.2 miles departure. Therefore by reference to Table 2 it appears that the line runs about S. 9° E., and the azimuth of the body is S. 99° E.; thus the results obtaiaed by the two methods agree. 154 THE SUMNER LINE. Example: At sea, May 18, 1915, a. m., Lat. 41° 33^ N., Long. 33° SO' W., by D, K., the mean of a series of observed altitudes of the sun's lower limb was 29° 41'' 00^''; the mean watch time, 7'' 20™ 45'. 3; C. C, +4™ 59».2; I. C, -30^^; height of the eye, 23 feet; C-W, 2^ 17™ 06». Required the Sumner line. From a solution of this same problem for a single longitude (art. 343, Chap. XIII) the following were found: G. A. T., 21'' 46™ 35»; h, 29° 50^ 04'^; p, 70° 38' 49^^ Assume values of the latitude 41° 03^ and 42° 03' N. h 29° 50' 04" L, 41 03 00 p 70 38 49 2)141 31 53 8i 70 45 57 Si-A 40 55 53 sec cosec cos sin G.A.T., 21'' 46™ 35" L.A.T.1 19 32 39 Long.i I 2" 13™56'\xx. 33° 29' 00"/"^- 4 / 41° 03' 00" N. ^4 33 29 00 W. . 12255 . 02526 9. 51776 9. 81634 2)19. 48191 sin i «i 9. 74096 A /42° 03' 00" N. ^H33 29 15 W. 42° 03' 00" *' 7. s^—n G. A. T. L. A. T.. 71 41 15 57 25 53 21'' 19 46™ 35» 32 38 . 12927 . 02526 9. 50675 9. 82068 2)19. 48196 sin i <2 9. 74098 sec cosec COS sin Long.2 jg W. 2" 13™57''U 1.33° 29' 15"/^ +60' diff. lat. makes +0'.25 long. -j-60 miles diff. lat makes +0.2 mile departure. Line runs, N. i° W. Azimuth, N. 891° E. The same sight worked with a single latitude, 41° 33' N., as was done in the original example, with azimuth taken from tables or diagram, gives : r4i° 133° 33' 00" N. Azimuth, N. 89° 52' E. 29' 08" W. Line runs, N. 0° 08' W. This example illustrates the case in which an observation is taken practically on the prime vertical; the azimuth shows the bearing to be within 0° 08' of true East, and the Sumner line is therefore within 0° 08' of the meridian; a variation of 30' in either direction from the dead reckoning latitude makes a difference of only 7". 5 in the longitude. Example: May 22, 1915, in Lat. 6° 20' S. by account. Long. 30° 21' 30" W.; chro. time, 7" 35™ 10"; observed altitude of moon's upper limb, 68° 30' 00", bearing north and east; I. 0.,— 3' 00"; height of eye, 26 feet; chro. fast of G. M. T., 1™ 37'.5. Required the Sumner line. From a solution of the same problem with a single longitude (art. 332, Chap. XII), the following values are obtained: H. A. from Greenwich, 0" 54™ 16» W.; h, 68° 27' 07"; d, 7° 10' 10" N. Assume the longitudes 30° 10' and 30° 30' W. 16° 7 68 7 14 { 36' 10 27 28 05 Sr. H. A. Long.i 00" 10 07 40 N. 30 S. 0" 54™16»W. 2 00 40 W. Gr. H. A. Long.2 cosec . 90377 sin 9. 96854 sin 9. 11442 0" 2 54™ 16» 02 00 36' 10 12' 30 5 , f 1" 06™ 24* ^H16° 36' 00" sec . 01849 tan 9.09964 1" .6° 07™ 44» 56' 00" a/ 6° a/ ^° tan 9. 11813 sec . 01925 tan 9. 09964 50" S. 00" W. \ cos 9. 98673 cosec . 90377 sin 9. 96854 sin 9. 11517 Lat.i 6 16° 7 66 7 13 36 56' 10 27 29 41 50 S. 00" 10 07 27 N. 30 S. A ^a tan 9. 11889 03" S. 00 W. 4^2 cos 9. 98748 Lat.2 6 12 03 S. THE SUMNER LINE. 155 Working by the other method, and finding the azimuth, we have : r 6° ^30 2l' SO^W LmerunsN. 38° 42' W. It might be shown that the results check with each other, as in previous cases. Example: At sea, July 12, 1915, in Lat. 50° N., Long., 40" W., observed circum-meridian altitude of the sun's lower limb, the time by a chronometer regulated to Greenwich mean time being 2'' 41" 39»; chro. corr., -2°> 30'; I. C, -3' 0^^; height of the eye, 15 feet. Find the Sumner line. From the solution of the same problem for a single latitude (art. 330, Chap. XII) the following values were obtained: G. A. T., 2'' 33°» 50'; h, 61° 57' 01'''; d, 22° 04' 57'' N.; a (Tab. 26), 2" .5. Assume longi- tudes 39° 45' and 40° 15' W. Gr H. A. 2^ 33" 50* Gr. H. A. 2" 33" 50* Long.i - 2 39 00 Long., - 2 41 00 L 7 10 h 5 10 h 61° + 57' 1 Ol'^ 06 H. 61 58 07 J 28 22 01 04 53 N 57 N h 61° 57' 01" afj* + 2 08 H, 61 59 09 L, 50 06 50 N. The line given by these coordinates is then: 4 50° 06' 50" N. 39 45 00 W. 2. 28 00 d 22 04 51 N. 57 N. L, 50 05 48 N. . /50° 05' 48" N. M40 15 00 W. This shows that the Sumner line lies so nearly in a due east-and-west direction that a difference of longitude of 30' makes a difference of latitude of only 1'. From the azimuth tables or diagram, it is found that the azimuth of the sun corresponding to Lat. 50° N. Dec. 22° N. and H. A. 6°* iq« E., is N. 177° E. Therefore, using the values given by the earlier solution, the line is defined as follows: aI^Oo' Oo'w. Line runs N. 87° E. The direction of the line thus given and of the one found from the double co- ordinates may be shown to agree as in examples before given. THE METHOD OF SAINT HIliAIBE OB. OP THE CALCULATED ALTmiDES. 371. The foregoing parts of this work have set forth that, when the purpose of the navigator is to find the latitude, the observed celestial body should be situated on or near tne meridian or at least not remote from it, and that he must apply different rules according as the body is on or near or more remote from the meridian; and again when his purpose is to find the longitude, the observed celestial body should be situated on or near or at least not remote from the prime vertical, and that he must then apply another set of rules. It is also explained in article 363 that a navi- tator, who has measured the altitude of a celestial body at a known instant of time, as really located his geographical position on the circumference of a circle whose radius is equal to the zenith distance (90° — Alt.) and whose center is the geographical position of the celestial body or that point on the earth's surface which falls vertically under the observed body at the instant of observation. It has been pointed out that practical needs are concerned only with that portion of the circumference of the circle of position which lies in the vicinity of the estimated Sosition of the ship, and, having seen how this portion may be determined and laid own by methods depending upon the computation of latitudes and longitudes, we proceed to extend our view to the accomplishment of this purpose by a method which js now rapidly growing in favor among practical navigators, because it brings the whole of astronomical navigation under a single rule by rendering the course of procedure the same, whatever the situation in the heavens of the observed bod;^ may oe, provided only that the conditions admit of accurate measurement of its altitude. 156 THE SUMNER LINE. In figure 54, the circumference of a circle of position is represented as having been laid down from A, the geographical position of the observed body, as a center, with a radius AC equal to the zenith distance of the observed celestial body; but it is evident that a small arc of the circumference, not differing sensibly from a straight line within the extent of a Sumner line, may be determined in the following manner from a neighboring geographical position, as at P, inside or outside of the circum- ference and at or near the position of the ship as given by dead reckoning: 1. Find the great-circle distance (zenith distance) and bearing (azimuth) of the geographical position of the observed body A from the observer's assumed position P. 2. Take the difference, in minutes of arc (nautical miles), between this zenith distance AP due to the observer's assumed position, and the zenith distance AC found from the true altitude resulting from observation. 3. Lay off this difference, which is called the altitude-difference, or intercept^ from the assumed position P either away from or toward the observed celestial body according as the true altitude by observation is less or greater than the altitude at the assumed position, and through the point thus reached draw a line at right angles to the bearing. The line so drawn will evidently be a tangent to the circumference of the circle of position, and will be so nearly comcident with this circumference throughout such length as the Sumner line need have, in all those cases in which the zenith distance is as great as 10°, that the tangent itself may be taken as the true Hne of position. Obviously the only trigonometrical computation that occurs under this method is in calculating the lengm and bearing of the great-circle arc joining the position P, which is assumed or known from the dead reckoning, with the geographical position A, which is always in a latitude equal to the declination of the observed celestial body at the instant of observation and in a longitude equal to the hour angle of the body from the prime meridian (Greenwich). In the case of the sun the Greenwich hour angle is expressed by Greenwich apparent time, and in the case of any other celestial body the Greenwich hour angle is found as explained in article 293, using G. M. T. instead of L. M. T. 372. Being strictly in the nature of calculating the great-circle distance and course between two pomts whose latitudes and longitudes are given, these compu- tations may be made according to articles 190 and 191, Chapter V; but in practice it is unnecessary to do so, since various altitude and azimuth tables give the distance and azimuth or true bearing, on the globe or on the celestial sphere, of any place from every other place, and consequently the altitude and azimuth, or zenith distance and bearing, that any celestial body would have at any given time to an observer situated in any given geographical position. So that an observer in a geographical position as yet unknown, about to measure the altitude of a celestial body for the purpose of deducing geographical position, may assume beforehand a geographical position in the region of his station and find from the tables the altitude and azimutn which the celestial body would have if observed from the assumed position; and then, comparing the altitude so taken from the tables with the true altitude obtained by measurement, may at once find the Sumner line by laying off from the assumed geo- graphical position along the direction of the bearing an intercept, called the altitude- difference, and drawing through its extremity a line at right angles to the bearing. After finding the altitude-difference or intercept, the simplest procedure consists in laying it off on the chart from the assumed position and drawing the Sumner Une through its extremity, but if, for any reason, this process is not desirable, the latitude and longitude of the extremity of the intercept, which is a point on the Sumner line, called the "computed point," may be found by the use of the Traverse Tables, or may be computed directly. The exact position of the observer on the Sumner line is, of course, indeterminate from one observation, unless either the latitude or longitude of the observer's position be known beforehand, but the computed point will always be nearer to the actual position of the observer than the dead reckoning or assumed position is. To obtain a fix, that is, to find the actual position, it is necessary to determine the intersection of the first Sumner line with another Hne of position, which may be another Sumner line or a line of bearing or any other line containing the ship's position at the same time. THE SUMNEE LINE. 167 When, the specially prepared altitude and azimuth tables are not preferred, the required azimuth or true bearing of the observed celestial body may be taken from the time azimuth tables, and the zenith distance, and hence the altitude, that the observed body would have at the instant of observation to an observer in the assumed geographical position may be conveniently computed by the following formula : hav 2= hav (L~d)-\- cos L cos d hav t or by the formula of haversines, which is rid of all doubt as to the algebraical signs of the quantities and requires reference to only one trigonometrical table: hav = hav (Co. L-P. D.) + {hav (Co. L + P. D.)-hav (Co. L-P. D.)}hav t These are modifications of the fundamental formula: sin h = sin L sin d + cos L cOs d cos t, which is itseK often preferred for the computation of the altitude from the latitude, declination, and hour angle. In the computations which follow, the parts of the several formulae have been designated as follows : IN THE COSINE-HAVERSINE FORMULA : hav ^=co8 L COB d hav t; hence, hav 2=hav (L-^cQ+hav d IN THE HAVERSINE FORMULA: hav A=hav (Co. L+P. D.)-hav (Co. L-P. D.) hav B={hav (Co. L+P. D.)-hav (Co. L-P. D.)} hav W hence, hav 2=hav (Co. L-P. D.)+hav B. IN THE SINE-COSINE FORMULA: A=Bin L sin d, B=co8 L cob d coa t; hence, sin A=A+B. Example.— At sea, May 18, 1915, a. m,, Lat. 41° 33' N. ; Long. 33° SO' W., by D. R., the mean of a series of observed altitudes of the sun's lower limb was 29° 41' 00'''; the mean watch time, 7^ 20™ 45. 3»; C. C.+4"'69.2^; I. C.,-30"; heightof eye, 23 feet; C.-W., 2" IT-^OG'. Required the Sumner line. From a solution of the same problem under article 343, Chapter XIII, and article 368, Chapter XV, the following are taken from among the prepared data; G. A. T., 21^46'" 35"; P. D., 70° 38' 49"; /j, 29° 50' 04", and, therefore, the measured zenith distance (90° — h), 60° 09' 56". Assume a position in latitude 41° 30' N. and longitude 33° 39' 30" or 2*' 14™ 38* W., then the solution will be as follows: L 41° 30' 00" G. A. T. 21'' 46™ 35* Long. 2 14 38 W. Co. L. 48 30 00 P. D. 70 38 49 L. A. T. 19 31 57=<. Note. — ^After obtaining the G. A. T., it will be seen that the longitude of the assumed position may be so chosen aa to avoid seconds in the L. A. T. or H. A. The azimuth found from the azimuth tables is N. 89° 52' E. BY THE COSINE-HAVERSINE FORMULA: t 19" 31™ 57* log hav 9. 48392 L 41 30 00 N. log cos 9. 87446 d 19 21 11 N. log cos 9. 97474 log hav d 9. 33312 a nat hav 0. 21534 L/^d z h h 22° 08' 49". . . . 60° 17' 40".... 90° 00' 00" nat hav 0.03689 Calculated nat hav 0.25223 Calculated Observed 29 42 20 29 50 04 Altitude-difference 7' 44" o The arrangement of Table 45 Is such as to obviate the necessity of taking out the value of the angle in finding the natural haversine from the log. haversine, or vice versa. 158 THE SUMNER LINE. BY THE HAVERSINE FORMULA: Co. L+P. D. 119° 08' 49^'' nat hav 0. 74353 Co.L-P. D. 22 08 49 nat hav 0.03689 nat hav A log hav A log hav t 0. 70664 o 9. 84920 9. 48392 log hav B nat hav B nat hav (Co. L-P. D.) 9. 33312 0. 21534 0. 03689 nat hav z Calculated z 0. 25223 60° 17' 40^' 90 00 00 Calculated h Observed h 29 42 20 29 50 04 Altitude-difference BY THE SINE-COSINE FORMULA: 7/ 44// 19^^ 3]^m gy* 292° 59' 15'' log cos 9. 59165 41 30 00 N log sin 9.82126 log cos 9.87446 19 21 11 N log sin 9.52034 log cos 9.97474 log A 9.34160 A 0.21958 log B 9. 44085 B 0.27596 A 0.21958 Calculated ^=29° 42' 19" nat Bin=A+B 0. 49554 ^ Since the observed altitude is higher than the calculated altitude, the observer's position is nearer to the observed body than the assumed position. Consequently the altitude-difference should be laid off in a direction to the east and north, 89 ** 52', 7,73 nautical miles from the assumed position. Or, by the Traverse Tables: Course. Distance. Diflf. Lat. Dep. Difif. Long. 8^° 52' 7.73 0'.02 N. 7'. 73 E. lO'.S E. Assumed position, Lat. Diff. Lat. 41° 30' 00" N. 01 N. Computed point on Sumner line, 41° 30' 01" N. Long. 33° 39' 30" W. Diff. Long. 10 18 E. 33° 29' 12" W. The direction of the Sumner line, being at right angles to the azimuth or true bearing of the observed celestial body, runs N. 0° 08' W. and S. 0° 08' E. or 359° 52' and 179° 52'. Example: At sea, May 22, 1915, in Lat. 6° 20' S. by account. Long. 30° 21' 30" W.; chro. time, 7^ 35™ 10»; observed altitude of moon's upper limb, 68° 30' 00", bearing north and east; I. C.,— 3' 00"; height of eye, 26 feet; chro. fast of G. M. T., 1™ 37'. 5. Required the Sumner line. From a solution of the same problem under article 332, Chapter XII, and again under article 370, Chapter XV, the following quantities are taken from among the prepared data: H. A. from Greenwich, Qu 54m iQs -^ . corrected altitude, h, 68° 27' 07"; d, 7° 10' 10" N. and, hence, P. D., 82° 49' 50". Assume a position in Lat. 6° 00' S. and Long. 30° 16' 45" W.; then the solution will be as follows: L 6° 00' 00" S. Gr. H. A. Long. t Qh 54mi6»W 2 01 07 W Co. L P. D. 96 00 00 82 49 50 1 06 51 a The arrangement of Table 45 is such as to obviate the necessity of taking out the value of the angle in finding the natural haversine from the log. haversine, or vice versa. THE SUMNER LINE. 159 BY THE COSINE-HAVERSINE P< ( L d 3RMULA: 1" 06° 51* 6° OO' 00'' S. 7 10 ION. 13° IC^IO^ 21 14 53 90 00 00 loghav 8.32470 log C08 9. 99761 log cos 9. 99659 log hav e 8. 31890 L-^rf nat hav 6 0. 02084 nat hav 0. 01315 t nat hav 0. 03399 Calculated h Observed h 68 45 07 68 27 07 Altitude-difference BY THE HAVERSINE FORMULA : Co. L+P. D. Co. L-P. D. nat hav A log hav A log hav t log hav B 18 00 178° 49' 50" nat hav 13 10 10 nat hav nat hav B nat hav (Co. L-P. D.) nat hav z Calculated z Calculated h Observed h Altitude-difference BY THE SINE-COSINE FORMULA : t V' 06°> 51' 16° 42' 45" . . . L d 6 00 00 S. 7 10 10 N. log Bin 9.01923- log Bin 9. 09623 log A 8. 11546- A =-0.01305 0. 99989 0.01315 0. 98674 9. 99420 8. 32470 8. 31890 0. 02084 0. 01315 0. 03399 21° 14' 53" 90 00 00 68 45 07 68 27 07 18 00 log cos 9. 98126 log cos 9.99761 log cos 9.99659 log B 9. 97546 B = 0.94506 A =-0.01305 Calculated ft=68° 45' 00" nat. sih=A+B 0. 93201 The azimuth from the Azimuth Tables S. 128° 42' E. or N. 51° 18' E. Since the observed altitude is lower than the calculated altitude, the observer's position is farther removed from the observed body than the assumed position. Consequently the altitude-difference should be laid off to the south and west, 231° 18', 18.0 nautical miles from the assumed position. Or, by the Traverse Tables : Course. Distance. Difl. Lat. Dep. Difl. Long. 231i° 18 11'.27 S. 14'.04 W. 14'.12 W. Assumed position, Lat. Diff. Lat. 6° 00' 00" S. 11 16 S. Computed point on Sximner line, 6 11 16 S. Long. 30° 16' 45" W. Diff. Long. 14 07 W. 30 30 52 W. 160 THE SUMNER LINE. The direction of the Sumner line, being at right angles to the azdmuth or true bearing of the observed body, is N. 38° 42^ W. and S. 38° 42' E., or 321° 18' and 141° 18'. Example: At sea, July 12, 1915, in Lat. 50° N., Long. 40° W., observed an ex-meridian altitude of the sun's lower limb, 61° 48' 30", the time by chronometer regulated to Greenwich mean time being 2" 41™ 39'; chro. corr.,— 2°^ 30'; I. C.,— 3' 00"; height of eye, 15 feet. Find the Sumner line. From a solution of the same problem under article 330, Chapter XII, and again under article, 370 Chapter XV, the following quantities are taken from among the prepared data; G.A.T., 2^ 33™ 50'; h, 61° 57' 01"; d, 22° 04' 57" N. Assume a position in Lat. 50° N., Long. 40° 12' 30" or 2^ 40™ 50» W., then the solution will be as follows: L. 50° 00' 00" N. G. A. T. Long. L. A. T=f FORMULA : 50° 00' 00" 22° 04' 57" 2" 33™ 50* 2 40 50 W. d P. D. 6. 36774 9. 80807 9. 96691 6. 14272 90.00014 0. 05819 22° 04' 57" N. Co. L 40 00 00 P. D. 67 55 03 BY COSINE-HAVERSINE t L d 67 55 03 N. N. 07 00 E. log hav log cos log cos log hav d nat hav i nat hav nat hav L~d 27° 55' 03" 27° 57' 07" 90° 00' 00" t 0. 05833 Calculated h Observed h 62 02 53 61 57 01 Altitude-difference BY HAVERSINE FORMULA." Co. L+ P. D. Co. L-P. D. nat hav A log hav A log hav t log hav B 5 52 107* 55' 03" nat hav 27 65 03 nat hav 0. 65383 0. 05819 0. 59564 9. 77498 6. 36774 6. 14272 nat hav B nat hav (Co. L-P. D.) nat hav z Calculated z Calculated h Observed h Altitude-difference BY THE SINE-COSINE FORMULA: 0. 00014 0. 05819 0. 05833 27° 57' 90 00 07" 00 62 61 02 57 53 01 5 52 t L d {p 07™00» 1° 45' 00".... 50 00 00 N 22 04 57 N log sin log sin log A A '""9.' 88425 9. 57512 Ic^ cos log COS log COS logB B A 9. 99980 9. 80807 9. 96691 9. 45937 0. 28799 9. 77478 0. 59536 0. 28799 Calculated /i=62° 02' 56" nat sin A-fB 0. 88335 The azimuth from the Azimuth Tables: N. 176° 32' E. or S. 3° 28' E. THE SUMNER LINE. 161 Since the observed altitude is lower than the calculated altitude, the observer's position is farther removed from the observed body than the assumed position. Consequently the altitude-difference should be laid off to the north and west, 356° 32^, 5.87 nautical miles from the assumed position. Or, by the Traverse Tables: Coxirse. Distance. Difl. Lat. Dep. Difl. Long. 356i° 5.87 5. 86 N. (K. 36 W. (y. 56 W. Assumed position, Lat. Diff. Lat. 50° 0(K (XT N. 5 52 N. Long. Diff. Long. 40° 12' 30''' W. 34^ W. Computed point of Sumner line 50 05 52 N. 40° 13' 04" W. The direction of the Sumner line, being at right angles to the azimuth or true bearing of the observed body, is N. 86° 32' E. and S. 86° 32' W., or 86° 32' and 266° 32'. 373. In the first of the three foregoing examples, the observed celestial body is represented as being near the prime vertical; in the second, remote from both the Enme vertical and the meridian; and in the third, near the meridian. These examples ave been solved in the preceding chapters by three dijfferent methods known, respectively, as the time sight, the ^' 6", and the ex-meridian; but we have here treated all of them by one method, and nave determined Sumner lines which are in agreement with those determined by the various jjrecedin^ methods. And it would be likewise if we should take examples in which meridian altitudes have been observed. Inasmuch as the local hour angle of a celestial body is O'' at the time of its passage across the meridian of an observer, the second member of the right-hand side of the equation of haversines becomes zero in cases in which the meridian altitude has been observed, since the haversine of 0° is equal to zero. The equation therefore reduces to hav 3 = hav (Co. L-P. D.) or 2=(Co. L-P. D.) which leads at once to the usual formulae given in article 321, Chapter XII, for finding the latitude from a meridian altitude. By this we are taught the full inter- pretation of a meridian altitude, which is that it gives the latitude of the intersection with the local meridian of a Sumner line coinciding with a parallel of latitude. 374. In addition to the simplicity which anses from always working by the same rule, the navigator has, by this method, the further practical advantage of being able to do the most of the work of obtairdng the Sumner line before taking the observation, since, in clear weather, he may, in selecting the assumed geographical position, assume an hour angle and calculate what time the chronometer or watch ought to show at the instant when the celestial body has this hour angle, and then observe the altitude at this instant ; or, if anything should happen to make him a few seconds late in getting the altitude, he may alter the assumed longitude by a corre- sponding amount so as to make the hour angle right, and then the rest of the work will hold good. After correcting the observed altitude and obtaining from it the true altitude, no more time need subsequently elapse in determining the Sumner Une than is necessary to take the diflFerence between the altitudes found by calculation and by observation and to rule a line at right angles to the bearing oi the observed body through the point found by laying off this altitude-difference as an intercept from the assumed position. 375. It has already been remarked that the labor of performing such computa- tions as the foregoing may be saved when a book of altitude and azimuth tables is at hand. These tables are arranged to be entered with the hour angle, the declina- tion, and the latitude; and they contain the corresponding values of the altitude and azimuth. In the various books containing such tables, the special rules to be observed in their use are set forth. 21594°— 14 11 162 THE SUMNEB LINE. It has been implied that when the akitude of the observed body is greater than 80° and, therefore, the zenith distance or radius of the circle of position is less than 10°, the tangent drawn to the circumference to represent the Sumner line could no longer be regarded as coinciding throughout its proper length with the arc of the circumference. When the zenith distance is 10°, the departure of the tangent from the circumference is one-tenth of a mile at a distance of 10 miles from the theoretical point of tangency and seven-tenths of a mile at a distance of 30 miles from the theoretical point of tangency. These departures are doubled when the zenith distance is reduced to 5°, and they are nearly ten times the amounts stated for 10° when the zenith distance is shortened to 1 °. There is not, however, any occasion for resorting to the proceeding of laying down a straight line as a substitute for an arc of the actual circle of position when the zenith distance is only a few degrees in len^h. In such cases the greatest con- venience and the best results are found by drawing circles of position directly on the navigator's chart. For this purpose the polyconic chart, being issued to navigators throughout all latitudes from 20° to 60° north of the Equator in connection with the works of the United States Coast and Geodetic Survey, and therefore being available throughout a like extent of south latitude by mere inversion, is generally serviceable, because a chart embracing any certain parallels of latitude is available between these Parallels of latitude throughout all longitudes; and the Mercator projection may also e used for this purpose within the Tropics, since the length of a minute of latitude as represented on this projection varies but little within tropical limits. For instance, it happens in crossing the tropical zone that, for a day or so, the sun is very near the zenith— perhaps not more than 1° awaj on one day and 2° or 3° on another. In such circumstances, having a chart of smtable scale embracing the parallels of latitude of the region in which the ship is situated, plot the sun's geograpnical position with Greenwich hour angle as longitude and declination as latitude, take on the dividers the zenith distance, or complement of the corrected altitude, and draw in a portion of the circumference of the actual circle of position lying near the position of the ship as ^ven by dead reckoning. Then wait until the azimuth has changed 30° or so — which it does very rapidly near noon — and draw a second similar arc. The inter- section of these arcs gives the ship's position with accuracy. Of course if the ship has moved in geographical place m the interval between the two sights, it will be necessary, in order to find the geographical position at the instant of the second sight, to move the first circle of position in direction and amount equal to the course and distance made good in the interval. FINDING THE INTERSECTION OF SUMNER LINES. 376. The intersection of Sumner lines may be found either graphically or by computation. (a) Graphic METHODS. — Each line may be plotted upon the chart of the locality in which the ship is being navigated, in accordance with the data for its determination (see art. 367), and the intersection thus found. This plan will commend itself especially when the vessel is near shore, as the chart in use will then probably be one of large enough scale, and it will be an advantage to see where the Sumner lines fall with reference to the soundings and landmarks. To aid the extension of this convenient practice on the ocean, where the navigator is usually furnished only with a general chart, position-line plotting sheets have been provided for the use oi navi- gators upon an ample scale, (6) Methods by Computation. — The finding of the intersection of two Sumner lines by computation may be divided into two cases: Case I. When one line lies in a NE.-SW. direction, and the other in a NW.-SE, direction, as shown in figure 56. Case II. When both lie in a NE.-SW., or both in a NW.-SE. direction, as shown in figure 57. 377. If each Sumner line is defined by the latitude and longitude of one of its points and the azimuth of the celestial body at right angles to whose true bearing the line rims, we may then, by means of Table 47, find the longitude of any other point on such a line when its difference of latitude from the known point has been ascer- THE SUMNER LINE. 163 tained. The numbers in Table 47 are values of the longitude factor, usually denoted by the letter F. They vary with the latitude of the observer and the celestial body's azimuth at right angles to the direction of the line, and express the change in longitude due to a change of 1' in latitude along any given Sumner line. So that the difference of latitude between any two points of a line, being multiplied by the longitude factor, will give the difference of longitude between those points. Turning to figures 56 and 57 and considering the Simmer lines A^ A2 and B^ Bj there represented to be defined by the azimuth at right angles to each and the lati- tudes and longitudes of the points A^ and Bj, respectively, we proceed to show the relations which exist for determining the latitude and longitude of the fix at their intersection by means of the tabulated longitude factors. The line PO being drawn perpendicular to the parallel of latitude through the points Ai and B,, the latitude of tne intersection will be a distance OP from the common latitude of A^ and Bj, and its longitude will be a distance A^ O from A^ and B^ O from B^. Let F^ and F2 repre- sent the longitude factors from Table 47 for the Sumner lines A^ A, and B^ Bj, respectively. Then, since F^ is the difference of longitude corresponding to a change of 1' of latitude along the line Ai Aj, the difference of longitude A^ O must be equal to El multiplied into the number of minutes of latitude in uie length OP. Therefore, and likewise A, = OPxFi, BiO = OPxF,; Fio. 57. and, since the known difference of loiigitude between the points Aj and B^ is com- gosed of the sum of Aj O and Bi O in Case I, and the difference of A^ O and B^ O in ase II, we have A, + B. 0=Ai Bi = OPxFi + OPxFj = OP (F^ + F^), in Case I, and A, 0-Bi 0=Ai Bi = 0PxFi-0PxF2 = 0P (F^-Fj), in Case 11. From which, placing the known quantities on the right-hand side of the equations, thus: A B 0P = A,B, F,-F„> in Case II. Hence, we obtain the difference of latitude from the common parallel of Aj and B^ to tiie point of intersection by dividing the known difference of longitude between the points A^ and B^ by the sum of the longitude factors of the respective Sumner lines in Case I, and by their difference in Case II. Having determined OP and hence the latitude of the point of intersection of the Smnner line, we proceed to multiply OP by F^ to get the difference of longitude AjP, and apply that difference to the known longitude of A, to find the longitude of the point of intersection P; and also, as a check, to multiply OP by F, to get the difference of longitude BjO, which, being applied to the longitude of h^, gives again the longitude of the point of intersection, r. 164 THE SUMNER LINE. The following is a summary of the successive steps to be taken in following this method : 1. Make a rough sketch of the Sunmer lines whose intersection is to be fixed in latitude and longitude, classifying them under Case I or Case II. 2. Take from Table 47 the longitude factors F^ and Fj, respectively, for the Sunmer lines. 3. If the given coordinates of the points on the two lines have not a common latitude, reduce them to a common latitude by multiplying the diflFerence between the latitudes of the points on the two lines by the longitude factor of one of the lines and applying the product to the longitude of the point on that line. The sketch will show whether the difference of longitude is to be added or subtracted, and the result will be the longitude of a poiut of this line on the conamon parallel of latitude. 4. The difference between the longitudes of the points of the two Sumner lines, on the common parallel, divided by the sum of the longitude factors (Fj+Fg), wiU give the difference of latitude between the point of intersection and the common {)arallel, when the lines are classified under Case I; and the difference between the ongitudes of the points of the two Sumner lines, on the common parallel, divided by the difference of the longitude factors (F^ — Fj), will give the difference of latitude between the point of intersection and the common parallel, when the lines are classified imder Case II. The sketch wiU show whether the intersection of the Sumner lines lies to the northward or southward of the common parallel, and hence whether the difference of latitude is to be added to or subtracted from the latitude of the common parallel. 5. Having found the difference of latitude between the point of intersection of the Sunmer lines and the common parallel, multiply this difference by the longitude factor of each line and apply theproducts each to the longitude of its corresponding line on the common parallel. The products are appHed in opposite directions in Case I, and both of them must lead to the same longitude for the point of intersection ; and the products are applied in the same direction in Case II, and in this case also both of them must lead to the same longitude for the point of intersection. Example: Find the intersection of the Sumner lines defined below by the latitude and longitude of a aingle point on each and by the respective azimutlis of the celestial bodies upon which the lines depend. {25° 4(/ S "1 115 20 E f^zimuth, at right angles to line, N. 51° E. ^ {115° 33^5^ E l^zimuth at right aisles to line, N. 72° W. From Table 47: Longitude factor for line A=0.89=Fi. Longitude factor for Line B=0.36=F2. Reduce the given points to a common parallel of latitude by transferring the point on line B to the latitude of the point on line A, (25° 40' S.-25° 25' S.)XF2=15'X0.36= 5'.4 W. 115° 33'.5 E. Fig. 68. , 115° 28'.1 E. Hence we have for the point on the line B at which the latitude is the same as the latitude of the point on the line A, B Lll° ^ f-Q JAzimuth at right angles to line, N. 72° W. We now have two Sumner lines, under Case I, whose common latitude is 25° 40^ S. and whose longitudes on the common parallel are : 115° 28M E. 115 20 .OE. 8 .l=sDiff. Long, on common parallel. 81 8 18 1 Tj< ^ p = gQ ! = j--^=«6.48 DiS. Lat. between intersection and common parallel. THE SUMNEB LINE. 165 CJorrectioDB in longitude: Long. A Diff. Long. 115*> 20' .00 E. 5 .77 E. Intersection 115 25 .77 E. 6. 48XF,=6. 48X0. 89=5' 6. 48XF2=6. 48X0. 36=2 Long. B 115° 28' .10 E. Diff. Long. 2 .33 W. 115 25 .77 E. 77 33 Lat. common parallel Diff. Lat. 25° 40'.00 S. 6 .48 S. 25 46 .48 S. Example: Find the intersection of the Sumner lines defined below: a|'*5° 2 J" 8 ^" } Azimuth, at right angles to Une, N. 81° W. BJ^g" 25^ 8 W } A-zimutii. at ""ig^* angles to Une, N. 31° W. A sketch of the lines shows their classification to be under Case II. From Table 47: Longitude factor for line A=0.24=Fi, Longitude factor for line B=2.57=Fj. Diff. Long, on common parallel=5° 25' .8—5° 24' .8=1' .0. LO LO Fa-F, 2.57-0.24 2.33 tion and common parallel. Corrections in longitude: =n^o=0.429=Diff. Lat. between intersec- 0. 429XF,=0. 429X0. 24=0. 10. 0. 429XF2=0. 429X2. 57 =L 10. Long. A Diff. Long. 5° 24' .8 W. .IE. Long. B Diff. Long. 5° 25' .8 W. 1 .1 E. Lat. common parallel Diff. Lat. 49° 30' .0 N. A N. Intersection 5 24 .7 W. 5 24 .7 W. 49 30 .4 N. 378. If the two geographical positions defining two Sumner lines have a common longitude instead of a common latitude, as represented in figures 60 and 61, their intersection may be foimd by means of the latitude factors tabulated in Table 48, in a manner similar to the use of the lon- gitude factors in connection with the Sumner lines whose known points have a common latitude. The latitude factors vary with the latitude of the observer and the celestial body's azimuth at right angles to the direction of the Kne, and express the change in latitude due to a change of 1 ' in lon^tude along any given Sumner line. So that the difference of longitude between any two points of a line being multiplied by the latitude factor will give the difference of latitude be- tween those points. The latitude factors of two Sumner lines whose intersection is to be found are usually denoted by the letters f^ and fj, and the successive steps to be taken in finding the in- tersection are here summarized : 1. Make a rough sketch of the Sumner lines whose intersection is to be fixed in latitude and longitude, classifying them under Case I or Case II. 2. Take from Table 48 the latitude factors fj and f,, respectively, for the Sumner lines. 3. The difference between the latitudes of the points of the two Sumner lines, in the common longitude, divided by the sum of the latitude factors (fj + fz), will give the difference of longitude between the point of intersection and the common meridian when the lines are classified under Case I; and the difference between the latitudes of the Fig. 60. Fig. 61. 166 THE SUMNER LINE. points of the two Sumner lines, in. the common longitude, divided by the difference of the latitude factors (fi — fj), will give the difference of longitude between the point of intersection and the common meridian when the lines are classified under Case II. The sketch will show whether the intersection of the Sumner lines Hes to the eastward or westward of the common meridian, and hence whether the difference of longitude is to be added to or subtracted from the common longitude. 4. Having found the difference of longitude between the point of intersection of the Sumner lines and the common longitude, multiply this difference by the latitude factor of each line and apply the products each to the latitude of its corre- sponding line on the common meridian. The products are applied in opposite directions in Case I, and both of them must lead to the same latitude for the point of intersection; and the products are applied in the same direction in Case II, and in this case also both of tnem must lead to the same latitude for the point of intersection. Example: Find the intersection of the Sumner lines defined below: M^i° Jf '86 w*} Azinauth, at right angles to line, N. 57°. 6 W. ■^{71° if 86 W } -'Azimuth, at right angles to line, N. 77° W. A sketch of the lines shows their classification to be under Case II. From Table 48: Latitude factor for line A=l. 23=fi. Latitude factor for line B=3. 32=f,. Diff. Lat. on common meridian=7''.15. 7. 15 7. 15 7. 15 -=y. 42 Diff. Long, between intersection and common meridian. fj-fi 3.32-1.23 2.09 Corrections in latitude: 3. 42Xfi=3. 42X1. 23= 4^ 20 3. 42Xf2=3. 42X3. 32=11 . 35 Lat. A 40° 13'. 55 N. Lat. B 40° 06^. 40 N. Long, on common me- Diff. Lat. 4 . 20 N. Diff. Lat. 11 . 35 N. ridian 71° 14^ 86 W. Diff. Long. 3. 42 E. Intersection 40° 17^ 75 N. 40° 17^ 75 N. 71° ir. 44 W. 379. When a Sumner line is defined by the latitudes and longitudes of two of its points, the longitude factor for the line may be found by dividing the difference between the longitudes of the two given points by the difference between their latitudes; and the latitude factor, being the reciprocal of the longitude factor, may be found by dividing the difference between the latitudes of the two given points by their difference of longitude. The method of finding the intersection of Sumner lines by longitude and lati- tude factors, described in articles 377 and 378, may, therefore, be applied as well when the lines are defined by pairs of geographical positions as when they are defined by the azimuth and one geographical position. 380. The modification of the methods for finding the intersection of two Sumner lines, where there is a rim between the observations from which they are deduced, will be readily apparent. It is known that at the time of taking a sight the vessel is at one of the points of the Sumner line, but which of the various points represents her precise position must remain in doubt until further data are acquired. Suppose, now, that alter an observation, the vessel sails a given distance in a given direction; it is clear that while her exact position is still undetermined it must be at one of the series of points comprised in a line parallel to the Sumner line and at a distance and direction therefrom corresponding to the course and distance made good; hence, if THE SUMNEB LINE. 167 a second sight is then taken, the position of the vessel may be found from the inter- section of two lines — one, the Sumner line given by the second observation, and the other a line parallel to the first Sumner line but removed from it by the amount of the intervening run. Positions may be brought forward graphically on a chart by taking the course from the compass rose with parallel rulers, and the distance by scale with dividers. If one of the methods by computation be adopted, the point or points of the first line are brought forward by the traverse tables, using middle latitude sailing. The direction of a Sumner line as determined from the azimuth of the body always remains the same, whatever shift may be made in the position of the point by which the line is further defined. Example: Taking the Sumner lines, which are defined in the first example under article 377, by the latitude and longitude of a point of each and by the respective azimuths of the celestial bodies upon which the lines depend, as follows: a|^j5° 3i' E 1^2"""*^. a* "g^* angles to line, N. 51° E. ^{115° 33 5 E 1-A-zimuth, at right angles to line, N. 72" W. and supposing the vessel from which the observations were taken that gave these lines to have run N. 54° E. (true) 35 miles in the interval between the sights, find the position of the vessel at the time of the second sight. The point A, in 25° 4(K S. and 115° 31' E., is first transferred to the point A^ 35 miles N. 54° E. (true) Irom A, by the method of Middle Latitude Sailing (article 177) by means of the Traverse Tables, thus: From Table 2, course N. 54° E. ; Dist., 35 miles; we find Diff. Lat. 20.5 N., Dep. 28.3 E. Therefore, Lat. A 25° 4fy S. Lat. A 25° 4(K S. Difi. Lat. 20 .6 N. Lat. A' 25 19 .4 S. Lat. A' 25 19 .4 S. 2)50 59 .4 Middle Lat. 25 29 .7 From Table 2, Middle Lat. (course), 25i°, Dep. (Lat.), 28.3 E., we find Diff. Long. (Diat.), 31.3. E. Therefore, Longitude A, 116° 31' E. Diff. Long. 31 .3 E. Longitude A', 116 02 .3 E. The Sumner lines whose intersection is to be found are therefore defined as follows: A'|jjg° J^'g |- JAzimuth, at right angles to the line, N. 51* E. B l^^ 33' 5 I JAzimuth, at right angles to the line, N. 72° W. From Table 47: Longitude factor for line A''=0.90=F, Longitude factor for line B =0.36=F, Reduce the given points to a common parallel of latitude by transferring the point on line B to the latitude of the point on line A', (25° 19^.4 S-25° 25^ S.)XF2= -5.6X0.36= 2'.0 E. 115° 33 .5 E. 115 35 .5 E. Hence we have for the point on the line B at which the latitude is the same as the latitude of the point on the line A', ^A 25° 19^.4 S. " \n5 35 .5 E. 168 THE SUM NEE LINE. We now have two Sumner lines, A' and B'', under Case I, whose common latitude is 25° 19^.4 S., and whose longitudes on the common parallel are 116° 02''.3 and 115° 35^.5. Hence, the difference of longitude on the common parallel is 116° 02'.3 E. 115 35 .5 E. 26 .8=Diff, Long, on common parallel. 9fi Q 9A Q Oft Q p /p = QA_LQ M ~T^&~'^^'^~^^^' ^^^' l^®t.ween intersection and common parallel. Corrections in longitude: 21.3XF,=21.3X0.90=19.2 21.3XF2=21.3X0.36= 7.6 Long. A' 116° 02^3 E. Loi^. B' 115° 35^.5 E. Lat. common par. 25° 19^.4 S. Diff. Long. 19 .2 W. Diff. Long. 7 .6 E. Diff. Lat. 21 .3 N. Intersection 115 43 .1 E. 116 43 .1 24 58 .1 S. CHAPTER XVI. THE PRACTICE OF NAVIGATION AT SEA. 381. Having set forth in previous chapters the methods of working dead reckoning and of solving problems to find the latitude,^ longitude, chronometer correction, and azimuth from astronomical observations, it will be the aim of the present chapter to describe the conditions which govern the choice and employment of the various problems, together with certain considerations by which the navigator may be guided in his practical work at sea. 382. Departure and Dead Reckoning. — On beginning a voyage, a good departure must be taken while landmarks are still in view and lavorably located for the purpose; this becomes the origin of the dead reckoning, which, with frequent new departures from positions by observation, is kej)t up to the completion of the voyage, thus enabling the mariner to know, with a fair degree of accuracy, the posi- tion of his vessel at any instant. At the moment oi taking the departure, the reading of the patent log (which should have been put over at least long enough previously to be regularly running) must be recorded, and thereafter at the time of taking each sight and at every other time when a position is required for any purpose, the Tog reading must also be noted. It is likewise well to read the log each hour^ for general information as to the speed of the vessel as well as to observe that it is in proper running order and that the rotator has not been fouled by seaweed or by refuse thrown overboard from the ship. It is a good plan to record the time by ship's clock on each occasion that the log is read, as a supplementary means of arriving at the distance will thus be available in case of doubt. If a vessel does not use the patent lo^ but estimates her speed by the number of revolutions of the engines or the indications of the chip log, the noting of the time becomes essential. A good sight is of no value unless one knows the point in the ship's run at which it was taken, so that the position it gave may be brought forward with accuracy to any later time. 383. General Description of the Day's Work, — ^The routine of a day's work at sea consists in working the dead reckoning, an a. m. time sight and azimuth taken when the sun is in its most favorable position for the purpose, a meridian alti- tude of the sun (or, when clouds interfere at noon, a sight for latitude as near the meridian as possible), and a p. m. time sight and azimuth. This represents the minimum of work, and it may be amplified as circumstances render expedient; but no part of it should ever be omitted unless cloudy weather renders its performance impossible. 384. Morning Sights. — ^The morning time sight and azimuth should be observed, if possible, when the sun is on the prime vertical. As the body bears east at that tune, the resulting Sumner line is due north and south, and the longitude will thus be obtained without an accurate knowledge of the latitude. Another reason for so choosing the time is that near this point of the sun's apparent path the body is changing most slowly in azimuth, and an error in noting the time will have the minimum effect in its computed bearing. The time when the sun will be on the prime vertical — that is, when its azimuth is 90° — may be found from the azimuth tables or the azimuth diagram. Speaking generally, during half the year the sun does not rise until after having crossed the prime vertical, and is therefore never visible on a bearing of east. In this case it is oest to take the observation as soon as it has risen above the altitude of uncertain atmospheric effects — between 10° and 15°. A series of several altitudes should be taken, partly because the mean is more accurate than a single sight, and partly because an error in the reading of the watch or sextant may easily occur when there is no repetition. If the sextant is set in advance of the altitude on even five or ten minute divisions of the arc, and the time 169 170 THE PRACTICE OF NAVIGATION AT SEA. marked at contacts, the method will be found to possess various advantages. As the sight is being taken the patent log should be read and ship's time recorded. It is well, too, to make a practice of noting the index correction of the sextant each time that the sextant is used. The bearing of the sun by compass should immediately afterward be observed, and the heading by compass noted, as also the time (by the same watch as was used for the sight). Before working out the sight, the dead reckoning is brought up to the time of observation, and the latitude thus found used as the approximate latitude at sight. It is strongly recommended that every sight he worked for a Sumner line, either by assuming two latitudes, or by using one latitude and the azimuth, or yet more advantageously by the method, of Saint Hilaire. The compass error is next obtained. From the time sight the navigator learns that his watch is a certain amount fast or slow of L. A. T., and he need only apply this correction to the watch time of azimuth to obtain the L. A. T. at which it was observed; then he ascertains the sun's true bearing from the azimuth tables or azimuth diagram, compares it with the compass bearing, and obtains the compass error; he should subtract the variation by chart and note if the remainder, the devia- tion, agrees with that given in his deviation table; but in working the next dead reckoning, if the ship's course does not change, the total compass error thus found may be used without separating it into its component parts. It should be increased or decreased, however, as the ship proceeds, by the amount of any change of the variation that the chart may show. 385. If there is any fear of the weather bein^ cloudy at noon, the navigator should take the precaution, when the sun has changed about 30° in azimuth, to observe a second altitude and to record the appropriate data for another sight, though this need not actually be worked unless the meridian observation is lost. If it is required it may be worked for either a time sight or ^' ' (ff sight the cosine of <}>' wiU assume a value that corresponds alike to any angle within certain wide limits — the limits within which the circle of equal altitude has practically a north-and-south du-ection. In conditions approximating to this we may obtain a longitude position more easily than one for latitude, even within a few minutes of noon. ' The tables of lunar distances have been omitted from the American Ephemeris and Nautical Almanac after the volume for the year 1911. THE PBAOTICE OF NAVIGATION AT SEA. 175 As the latitude and declination separate, conditions become more favorable for finding latitude and less so for longitude; the intermediate cases cover a wide range, wherem longitude may be well determined by observations three to five hours from the meridian, and latitude by those within two hours of meridian passage. As extreme conditions are approached the accuracy of longitude determinations con- tinues to decrease; at a point in 60° north latitude, when the sun is near the southern solstice, its bearing differs only 39° from the meridian at rising; or, in other words, even if observed at the most favorable position, the resulting Sumner line is such that 1' in latitude makes a difference of 1.3 mUes of departure, or 2 '.6 of longitude, and is far better for a latitude determination than for longitude. And in nigher latitudes stiU this condition is even more marked. Having grasped these general facts, the navigator must adapt his time for taking sights to the circumstances that prevail, and when the sun does not serve for an accurate determination of either latitude or longitude the ability to utilize the stars, planets, and moon as a substitute will be of the greatest advantage. 396. USE OF Various Sights. — Except when employing the method of Saint Hilaire (Chapter XV), the navigator may sometimes be in doubt as to the best method of working a sight. No rigorous rules can be laid down, and experience alone must be his guide. In a general way it may be well, when the body is nearer to the prime vertical than to the meridian, to work it for longitude, assuming lati- tude, and using the time sight; and when nearer the meridian to work it for latitude, assuming longitude, by the (f>' ' d)" or latitude method should not ordinarily be employed beyond three hours from the meridian, and then only when the body is withm 45° of azimuth from the meridian and has a declina- tion of at least 3°; with an hour angle of 6** (90°) or a declination of 0° the trigono- metric functions assume such form that the method is not available; nor does it give definite results when the azimuth is 90° or thereabouts. When the body is close enough to the meridian for the method of reduction to the meridian to be applicable, that method is to be preferred because of its quickness and facilitjy'. It should be noted, however, that, though close enough to employ the reduction, it may not be sufficiently correct to assume that the body bears due north or south, and the sight should be worked with two longitudes, or the Sumner line determined by the azimuth, unless the bearing nearly comcides with the direc- tion of the meridian. 397. Working to Seconds and Accuracy of Determinations. — The beginner who seeks counsel from the more experienced in matters pertaining to navigation will find that he receives conflicting advice as to whether it is more expedient to carry out the terms to seconds of arc, or to disregard seconds and work with the nearest whole minute. It is a well-recognized fact that exact results are not attainable in navigation at sea; the chronometer error, sextant error, error of refraction, and error of observa- tion are all uncertain; it is impossible to make absolutely correct allowance for them, and the uncertainty increases if the position is obtained by two observations taken at different times, in which case an exactly correct allowance for the intervening run of the ship is an essential to the correctness of the determination. No navigator should ever assume that his position is not Hable to be in error to some extent, the precise amount depending upon various factors, such as the age of the chronometer rate, the quality of the various instruments, the reliability of the observer, and the conditions at the time the sight was taken; perhaps a fair allowance for this possible error, under favorable circumstances, will be 2 miles; therefore, instead of plotting a position upon the chart, and proceeding with absolute confidence in the belief that the ship's position is on the exact point, one may describe, around the point as a center, a circle whose radius is 2 miles — if we accept that as the value of tne possible error — and shape the future courses with the knowledge that the ship's position may be anywhere within the circle. It is on account of this recognized inexactness of the determination of position that some navigators assume that the odd seconds may be neglected in deamig with 176 THE PRACTICE OF NAVIGATION AT SEA. the different terms of a sight; the average possible error due to this course is probabty about one minute, though under certain conditions it may be considerably more. It is possible that, in a particular case, the error thus introduced through one term would be offset by that from others, and the result would be the same as if the seconds had been taken into account; but that does not affect the general fact that the neglect of seconds as a regular thing renders any determination liable to be in error about one minute. Those that omit the seconds argue, however, that since, in the nature of things, any sight may be in error two minutes, it is immaterial if we introduce an additional possibihty of error of one minute, because the new error is as liable to decrease the old one as to increase it; but the fallacy of the argument will be apparent when we return to the circle drawn around our plotted point. The eccentricity of the sextant may exactly offset the improper allowance for refraction, and the mistake in the chronometer error may offset the observer's personal error, but unless we know that such is the case — which we never can — we nave no justi- fication for doing otherwise than assume that the ship may be any place within the 2-mile circle. If, now, we increase the possible error by 1 mile, our radius of uncer- tainty must be increased to 3 miles, and the diameter of the circle, representing the range of uncertainty in any given direction, is thereby increased from 4 to 6 miles. It is deemed to be the duty of the navigator to put forth every effort to obtain the most prohahle position of the ship, which requires that he shall eliminate possible errors as completely as it lies within his power to do. By neglecting seconds he introduces a source of error that might with small trouble be avoided. This becomes of stiU more importance since modern instruments and modem methods constantly tend to decrease the probability of error in the observation, and to place it within the power of the navigator to determine his ship's position with greater accuracy. 398. There is a more exact way of defining the area of the ship's possible position than that of describing a circle around the most probable point, as mentioned in the preceding article, and that is to draw a line on each side of each of the Sumner lines by which the position is defined, and at a imiform distance therefrom equal to the possible error that the navigator believes it most reasonable to assume under existing conditions; the parallelogram formed by these four auxiliary lines marks the limit to be assigned for the ship's position; this method takes accoimt of the errors due to poor intersections, and warns the navigator of the direction in which his position is least clearly fixed and in which he must therefore make extra allowance for the uncertainty of his determination. It must be remembered in this connection that no position can ever be obtained, when out of sight of the land, except from the intersection of two Sumner lines, whether or not the lines are actually plotted; thus, a meridian altitude gives a Sumner line that extends due east and west, and a sight on the prime vertical a line that extends north and south, though it may not have been considered necessary to work the former with two longitudes or the latter with two latitudes. 399. The Work Book and Forms for Sights. — The navigation work book, or sight book, being the official record of all that pertains to the navigation of the ship when not running by bearings of the land, should be neatly and legibly kept, so that it wiU be intelligible not only to the person who performed the work, but also to any other who may have reason to refer to it. Each day's work should be begun on a new page, the date set forth clearly at the top, and jjreferably, also, a brief statement of the voyage upon which the ship is engaged. It is a good plan to have the dead reckoning begin the space allotted for the day, and then have the sights follow in the order in which taken. The page should be large enough to permit the whole of any one sight to be contained thereon without the necessity of carrying it forward to a second page. No work should be commenced at the bottom of a page if there is not room to complete it. Every operation pertaining to the working of the sights should appear in the book, and all irrelevant matter should be excluded. It is weU to observe a systematic form of work for each sight, always writing the different terms in the same position on the page; this practice will conduce to rapidity and lessen the chances of error. In order to facilitate the adoption of such a method, there are appended to this work (Appendix II) a series of forms that are recommended for dead reckonmg, and for the various sights of the sun, stars. THE PRACTICE OF NAVIGATION AT SEA. 177 planets, and moon, respectively. For beginners, these are deemed of especial importance, and it is recommended that, until perfect familiarity with the dif- ferent sights is acquired, the first stop in working out an observation be to write down a copy of the appropriate blank form, indicating the proper sign of appli- cation of each quantity (for which the notes wiU be a guide), and not to put in any figures until the scheme has been completely outlined; then the remainder of the work wiU consist in writing down the various quantities in their proper places and performing the operations indicated. The navigator may make up his work book by having printed forms of the various sights which can be placed in a loose-leaf binder when they have been filled in with his computations. Instead of printed forms on separate sheets, he m&y employ rubber stamps of the various forms of sights which he may stamp in his work book or on loose leaves. THE SPECIFIC STEPS FOB CABBYING OUT THE DAY'S WOBE. 400. The day's work as described herein is so laid out that the true position at noon is known some few minutes before noon, as, when cruising in company, naval vessels have to make their noon position report by signal at exactly 12 o'clock. When cruising singly the noon position need not be known until after 12 o'clock, but it is advisable to do a daj^'s work always in one way, and, therefore, the plan of getting the correct noon position before noon wiU be followed. 4:01. The Time to Take an A. M. Observation. — The navigator of a vessel cruising may, by dead reckoning or by plotting on a chart, predict the approximate position of the snip the following mornmg, and from that position may easily determine the best time to observe the sun (or other body) for longitude. Having determined his approximate 8 a. m. position, he takes from the Nautical Almanac the declination of the sun for Greenwich noon of that day. With the latitude of the 8 a. m. position and declination for the day, he enters tne Azimuth Tables and takes out tne local apparent time when the sun will bear 90°. By getting the error of his watch on local apparent time for the approximate 8 a. m. longitude, he may easily find the watch time when the sun will bear 90°, which is the time he should take his sight. Suppose on the evening of July 18, 1915, a navigator finds that at 8 a. m. the next day he will be in approximate Lat. 35° 12' N., Long, 65° 15' W., and wishes to find at what time h/ his watch the sun will be on the prime vertical. He compares his watch with the chronometer, of which he knows the correction, and which is, we will say, slow 1™ 10^ on G. M, T., and finds that when the chronometer reads, say ll** 59" SO", the watch reads 7** 15" 12^, He then does the following work: He takes from the Nautical Almanac the declination and the equation of time for Greenwich mean noon on July 19 and finds Dec. =21° 01' N.; Eq. t. 6" 03», subtractive from mean time. With Lat. 35°.2 N., Dec. 21°.0 N., enter the Azimuth Tables, and find, for a bearing of 90°, the L. A. T. is about S^ 10". Write down the reading of the chronometer face at comparison 11'' 59"* 30* Apply the chronometer correction + 1 10 G. M. T. of the time of comparison 12 00 40 Apply equation of time — 6 03 Greenwich apparent time of comparison 11 54 37 For Long. 65° 15' W., il=4'» 21°' 00*. Apply A 4 21 00 At time of comparison the L. A. T. at the 8 a. m. position was 7 33 37 At time of comparison the watch time was 7 15 12 Error of watch on L. A. T. of 8 a. m. position 18 25 slow. L. A. T. when sun is on prime vertical 8 10 Watch time to take a. m. observation 7 51 35 The observation should therefore be taken when the watch face reads. about 7-52, which will bring the sun very close to the prime vertical. When the latitude and declination are of different names the sun crosses the prime vertical before rising. In that case," the observation is taken as soon as the 21594<*— 14 12 178 THE PRACTICE OF NAVIGATION AT SEA. sun is sufficiently high to be unaffected by any peculiar condition of the atmosphere, usually about an hour after sunrise. The L. A. T. of sunrise and sunset is given at the bottom of the page in the Azimuth Tables. Suppose in the above example the approximate 8 a. m. latitude was 35°.2 S. instead of 35°.2 N. Entering the tables with Lat. and Dec. of different names, we find the time of sunrise is about 7 a. m. The observation should therefore be taken at about 8 a. m. L. A. T., the watch time of which can be found in the same way as explained above. In a similar manner Azimuth Tables may be used to find the best time to take p. m. observations for longitude. 402. The Morning Work of the Navigator. — The navigator, having deter- mined the time at which he will take his morning observation, is called sufficiently early to be ready for work about 15 minutes before the time chosen. The first thmg the navigator does is to check up his time. To save the trouble of going below to compare the watch with the standard chronometer each time that an observation is taken, most navigators keep the hack chronometer in the chart house and use it for comparisons during the day. It is necessary to check the hack with the standard chronometer each day to make sure of its error on G. M. T. and rate. This comparison is made the first thing in the morning, the date, the error on G. M. T., and the rate of the hack being written on a slip of paper that is placed in the hack case. The hack is then taken to the chart house and is used for the day's work. As hack chronometers frequently have high daily rates, an additional correction sometimes has to be made for the rate when observations have been taken some hours after the comparison. The hack is sometimes used for marking the time of observation, and. when so used, the G. M. T. is at once obtained by applying the hack error. Having checked up the hacK chronometer, the navigator then j)repares his sextant and takes it, with his watch and notebook, to the place from which he takes his observations. At about the time he has selected for his purpose, he observes altitudes of the sun, which, with the corresponding watch times are noted in his note- book. The patent log is read while the observations are being taken and the reading is entered in the notebook. The navigator then goes to the standard compass and fets a bearing of the sun, which with the watch time of the bearing and the compass eading of the ship is entered in the notebook. Either just before or just after observing the altitude of the sun with the sextant, the index correction should be found and entered in the notebook. The navigator next compares his watch with the hack chronometer and gets the C-W, which is also entered in the notebook. From the log book he gets the courses and distances run from the last "fix" and enters them m his notebook. This completes the data for his morning's work. The computations are then made in the navigator's work book. The first step is to work up the dead reckoning from the last "fix" to the time of sight. It may be well here to call the attention of the student to the fact that for "distance run" the propellers frequently are a more accurate gauge than the patent log which some- times gets foul. In a smooth sea the distance by revolutions is usually very accurate, especially if the effect of the condition of the bottom as to fouling is known. In heavy weather the patent log is a better gauge as the effects of the wind and sea on the speed of the ship are hard to determme. But for distance run both the patent log and revolutions should be considered, and, if there is a discrepancy between them, it should be investigated and the more accurate distance should be used. Having brought the dead reckoning up to the time of sight, the latitude so found is taken as the base of the computation of the longitude by observation. It is assumed that the student is familiar with the various methods of getting a line of position from an observation. Any one of the various methods gives the same line and the choice of method is naturally the choice of the individual. Having obtained the line of position, the longitude factor is next found, as explained in article 387. The longitude factor is used twice, first to find the longitude iby observation corresponding to the D. R. latitude, and again after the noon latitude is [determined, to find the true noon longitude. As soon as the longitude factor has been Rbbtained, the longitude by observation corresponding to the D. R. latitude is found, [and it is this point on*the line of position that is used for the rest of the work to noon. [This point, corrected for run, is also the point adopted as the 8 a. m. position, and THE PRACTICE OF NAVIGATION AT SEA. 179 as by using it future steps are simplified, it is advisable alwaj^s to work from this point. Of course, any other point on the line can be moved up, and the final result will be the same, but the computation will be a little more complicated. Having obtained the position at time of sight (D. R. Lat., Long, by obs.) and the longitude factor, the navigator next proceeds to get the compass error. The work he has akeady performedin getting the line of position gives him certain data that will shorten his work in finding the compass error. If the sight has been worked out as a Sumner line the navigator, by tak-ng the L. A. T. found by his computation and correcting it for the difference between the watch times of his observation for altitude and observation for azimuth, may obtain at once the L. A. T. of the time at which he took the sun's azimuth. With this L. A. T., and the Lat. and Dec. used in working out his sight, he may at once find from the Azimuth Tables the true bearing of the sun and get the compass error. If the line of position has been obtained by one of the tangent methods, the navigator has, in his computation, deter- mined the true bearing of the sun at the time of sight. All he has to do to get the true azimuth for compass error is to correct this bearing for the change in azimuth due to the difference in time between his observation for altitude and his observation for azimuth. This correction is easily found from the Azimuth Tables by inspection. This completes the morning work when the amount of work each day is a minimum. When very accurate positions are required at other times than at noon, as for instance, when a vessel is scouting, when in dangerous waters, moving at high speed, or when making a landfall, other lines of position are worked out, and the ship's position found on each line bj^ moving the next preceding line up to it for run. For instance, lines obtained from morning twilight sights of the moon, stars, or planets, may be run up to the 8 a. m. line, the 8 a. m. line may be run up to one taken at 9.30 or 10, or later, and so on. VvTien getting the position by the intersection of lines moved up for nm, it is usual to perform the work on the plotting charts supplied for this particular purpose. These charts are Mercator projections covering each 5° of latitude from 0° to 60°. The parallels are numbered for every degree of latitude, and the navigator selects the chart covering the latitude in which he is working. The meridians on these charts, not being numbered, the navigator is left free to mark them with the longitudes through which he is working. The charts are of large scale, and, being on heavy paper, ma}'- be used over and over, lines on these being drawn in lightly and erased when no longer required. Intersections of lines of position may be computed, as explained in Chap. XV, when there are no charts at hand suitable for plottmg the lines graphically. Special plotting sheets prepared by the United States Hydrographic Office are supphed to vessels of the Navy. 4:03. The Work Between 11 A. M. and Noon. — Two important steps, not usually fully explained in the text books, must be studied. These are: I'irst, to determine the exact run from the time of the a. m. sight to local apparent noon; second, to set the watches and clocks to the local apparent time of the place the ship will be at local apparent noon. If the ship has been making westing, the watches and clocks will be ahead of the local apparent time of the noon position and will have to be set back by the amount of the change in longitude. As the change of time is made between 11 a. m. and noon, it will be seen that the elapsed time between the time of the a. m. sight and the new watch time of noon will be more than the watch face shows by the amount the watch has been set back, and tliis difference must be allowed for in computing the run to noon. In the same way, if the ship has been making east- ing, the clocks and watches will have to be set ahead and the elapsed time between the time of the a. m. sight and the new watch time of noon will be less than the watch face shows bv the amount the watch has been set ahead, and must be allowed for in computing tne run to noon. It must be remembered that this time can not be computed exactly, but it can be approximated very closely in this wav. Suppose a ship has been steaming on course 66° true, and the navigator finds from his a. m. observation taken at watch time, 8^ 00™ 03^.5, that the L. A. T. for the position, Lat. by D. R. 38° 03'.2 N., Long, by obs. 72° 46' 18" W., is 8^ 17'" 45«.2. He sees at once that at 8 a. m. his watcn is already slow 17™ 41 .7" on L. A. T. Now, if he 180 THE PRACTICE OF NAVIGATION AT SEA. continues on this couree 66° true, at a speed of 11.7 knots per hour, the watch will be still slower at noon. He therefore turns to the Traverse Tables and finds that on that course and at a speed of 11.7 knots the ship will each hour go 10.69 imles to the eastward, which, in Lat. 38°, makes a change of longitude of 13'. 6 each hour. Now, from time of sight to 11 a. m. the change of longitude will be 3 X 13'.6 = 40'.8 of longitude, which is equal to a further loss of 2™ 43^.2 of time; but the watch was already slow 17*° 41^7, so that at 11 a. m. the watch will be slow 20^" 24^9, and the time to noon will be l*"— (20™ 25"), the difference due to change in longitude in 39'"35^(l*'-20"'25«). Now39°' 35^ = 0.66'^ and thechangeof longitude = 0.66 X 13'.6=» 9'.0 of long. = 36^.0 of time. Hence the total amount the time will be changed will be: Change to time of a. m. sight 17™41'. 7 Change between a. m. sight and 11 a. m 2 43 . 2 Change between 11 a. m. and L. A. noon 36 . Total change 21 00. 9 and the run to noon will be 4 hrs. minus this change = 3^ 38™ 59M =3.65 hrs. The distance run to noon will be 3.65'' X 11'^*«.7 = 42'^.7. The navigator can now run the a. m. point, determined by dead reckoning latitude and longitude by observation, up to noon, and, after that he is ready to set his watch and clocks to the time of the coming local apparent noon position. 404:. If the body observed for the a. m. sight was on or near the prune vertical, the longitude found from it would be correct for the time of observation, since an error in latitude makes no change in the longitude. This longitude when compared with the longitude by dead reckoning at the time of sight will show if there has been an easterly or westerly set of the current, and the amount of it. If a current is found and allowed for, for the time of the run from time of sight to noon, the noon longitude can be found very accurately. If the heavenly body used for the a. m. observation was not near the prime vertical, the exact easterly or westerly set can not be deter- mined; but a close approximation to it can generally be made by comparing the longitude found by observation with the D. R. longitude, and the current so found should be allowed for in rimning the a. m. point up to noon. The error will be small and will give results sufficiently accurate for ordinary work. Having allowed for easterly or westerly current and having run the a. m. position point by observa- tion up to noon, the navigator can then set his watch to local apparent tune of the noon position, and his watch can be used to set the deck clocks. A convenient waj to set the watch is as follows: Having looked at the hack face and found what it reads, say 4^* 09™ 50^, let it be determined to set the watch to the correct local apparent time of the noon position when the hack face reads 4^* 15™ 00". Write down reading of hack face at time watch is to be set 4^ 15™ 00" Apply the hack correction (in this case hack is 5™ 38' fast on G. M. T. ) (, — ) 5 38 This gives G. M. T. at which watch is to be set to L. A. T 4 09 22 Apply equation of time from Page I, Nautical Almanac, corrected for longitude of noon position (+) 11 38.6 This gives G. A. T. of time watch is to be set 4 21 00.6 Now apply longitude for noon position (in this case") 4 48 02. 8 Watch face should read 11 32 58 The watch is now to be set so that, at 4^* 15™ 00" by hack, the watch face will show as near ll'' 32™ 58' as possible. It will be found, smce the second hand of a watch can not be set, that the watch cannot be set to the exact reading. By care, however, the watch can be set so that it will be 30 seconds or less fast or slow on the desired time. The number of seconds the watch is fast or slow on L. A. T. should be noted in the work book, as it wiU be a help in taking near-noon sights to get the correct L. A. T. at once from the reading of the watch face instead of comparing the watch again with the chronometer. The watch being set as nearly as possible to the correct L. A. T. and the error being recorded, the deck clocks are set; and the navi- gator then proceeds to work up his constants for his near-noon observations for latitude, and completes aU his forms and fills them out as far as possible before taking the observations. THE PRACTICE OF NAVIGATION AT SEA. 181 405. Now suppose the navigator wishes to take his observations at 15, 10, and 5 minutes before local apparent noon and desires to get constants for these times to which he can apply his sextant altitudes and at once get his correct noon latitude. To find the watch times at which he should take these observationsj he must know the error of his watch on local apparent time of the place of observation. He knows the error of his watch on the L. A. T. of the noon position (in this case we will sup- Eose the watch is 18^ fast). He knows that on course 66° true, speed 11.7 knots, m at. 38°, that in 1 hour he changes longitude 13'.6. Therefore 15 minutes before noon the ship will be 3' A of longitude west of where it will be at noon = 13».6 of time. Hence the observation 15 minutes before noon should be taken at watch time 11" 45" 00^ + 18^ ( = amount watch is fast on L. A. T. of noon position) + 13'.6 ( = amount watch is fast on L. A. T. of place of first near-noon observation) = 11*» 45™ 31''.6. Similarly the observation taken 10™ before noon should be taken at watch time 11" 50™ 00" + 18» + 9M ( = amount watch is fast on L. A. T. of place of second observation) = 11" 50™ 27*.l. The observation taken 5 minutes before noon should be taken at watch time 11" 55™ 00»+18'' + 4''.5 ( = amount watch is fast on L. A. T. of place of third observation) = 11" 55™ 22".5. A meridian altitude would of course be taken at watch time 12" 00™ 18*. Having obtained the watch times of the observations, the navigator next works out the constants. These constants are obtained in the same way as meridian altitude constants but to each are applied two corrections to the meridian altitude constant. These are: (1 ) at^ or the correction to be applied to an observed altitude near noon to make it a meridian altitude. (2) Jh or the difference in latitude for the run from the time of observation to noon. In working out the constant, the method of obtaining a meridian altitude con- stant is followed and the two corrections mentioned above are applied to it. In getting a meridian altitude constant, one has first to ascertain the approximate altitude. If the student will in every case plot his elements roughly on the plane of the meridian, putting O, the observer, at the center, a horizontal line through the O with the right end marked S for south, and the left end N for north, to represent the horizon, and draw a vertical line upward from O (marking its intersection with the circle Z) to represent the zenith, he can by inspection write out his formulae and see exactly how to apply all corrections. A few minutes' study will make this method clear and will fully repay the very slight mental effort required to master it. Now suppose L is the latitude oi the noon position and L' the latitude of the point from wnich the near-noon observation was taken. Then L = L'±JL where JL is the change in latitude from the time of observation to noon. Suppose, by inspection of the figure we have drawn, we see that for a meridian altitude, L' = 90°-(?-obs. alt.±corr. to alt. Now when the observed altitude is taken before noon the correction aP has to be applied to it to bring it to what the meridian altitude would be. Therefore, for an altitude taken before noon, L' =90° -d- (obs. alt. + at^) ± corr. to alt. = 90°- 30'. 4 84 49 11 11" 50'^ 26'. 4 84 53 30 11" 55'" 22». 84 55 56 12" 00"» 18* 84 56 29 Noon Lat. by Oba. Mean Noon Lat. by D. R. 38° 20' 35''' DL Long, factor (Tab. 47) .65 Corr. in Long. Noon Long, by a. m. Obs. 72® 00' 42" True longitude at noon 4:06. Having obtained the correct noon position in the above manner, the navigator completes his work in his work book and plots the ship's position on the chart. Having the correct noon position, he compares it with his previous noon position (or point of departure) and ^ets the true course and distance made good. Having the position by dead reckoning and by observation, he ^ets the set and drift of the current. He then computes the total distance gone smce leaving port and the distance yet to go to his destination. Blank forms for the noon report are arranged for the following data: (1) Lat. by observation. (2) Long, by observation. (3) Lat. by D. R. (4) Long, by D. R. (5) Current: Set and Drift. (6) Course made good. (7) Distance made good since noon. (8) Distance made good since departure. (9) Distance to destination. If the course sailed is a rhumb line, and the ship is practically on the line laid out as the track, no change of course is necessary. If the ship is decidedly off the rhumb line course as laid out, or is sailing on a gi'eat circle track that requires a change in compass course, the new course is laid out as soon as the true noon position is obtained. This completes the navigator's work to noon. 4:07. The Atteenoon Work of the Navigator. — In the afternoon the navi- gator must take an observation for longitude. He selects a time when the sun is as near as possible to the prime vertical, which time is determined in the same way as explained for the a. m. observation. He runs his true noon position up to the time of his p. m. observation, making an allowance for any evident current that was found at noon. He then gets a position point on a line of position determined from his observation. This point is run up to 8 p. m. by dead reckoning, which position is plotted on the chart and completes the mmimum navigation work for any day. When -particularly accurate positions are required, especially at 8 p. m., the navigator takes an additional observation of the sun, or of some other heavenly body at twilight, and gets the intersection of two lines of position. Or he may get a line for longitude and a line for latitude by an altitude of Polaris or another star. In this way the navigator may, at either morning or evening twilight, get a very accurate fix; and this is done frequently. In fact, fixes obtained from observations of two heavenly bodies taken at about the same time are the most accurate fixes that can be obtainea at sea, as the intersection of the two lines of position give a position point that is correct at the time, no matter what the current is. Careful navigators wiU therefore take such observations and the student should prepare himself to do so. The methods of using position points obtained in this way are exactly the same as the methods of using the points already explained. THE PBACTICE OF NAVIGATION AT SEA. 183 The following example will give a good idea of the minimum day's work for the navigator at sea. The form laid out is one that can always be followed. The cosine- haversine formula is used for getting the lines of position, but any other method may be substituted for it. Example: On October 5, 1915, the U. S. S. Delaware left Hampton Roads for Lisbon. From the Chesapeake Capes the great circle course was followed. The distance to Lisbon by great circle course is 3,120 mUes. It is 25 miles from Hanapton Roads to the point from which the departure was taken. At 5 p. m., with Cape Henry Light bearing 301° (mag.), dist. 8.3 miles, took departure, set course 74° (p. s. c.) (Var. 5° W., Dev. 3° W.), and put over patent log, reading 0. (The point of de- parture is Lat. 36° 51' 59" N., Long. 75° 51' 03" W.) The next morning by comparison with the standard, the hack chronometer was found to be 5™ 38' fast on G. M. T. and gaining P.5 daily. At about 8 a. m., patent log, reading 175.0, the navigator took an a. m. observation for longitude: W. T. 8** 00™ 03«.5; obs. alt. 22° 55^10"; I. C. + l' 50"; ht. of eye 40 ft. The navigator then observed an azimuth of the sun as follows: W. T. 8** 02™ 29"; bearing of sun p. s. c. 125° 30'; ship's head 74°. He then compared his watch with the hack as follows: hack face l** 13™ 00«; watch face 8»* 10™ 11». Perform the a. m. part of the day's work. The ship continues on same course at same speed (11.7 knots). When the hack face reads 4'' 15™ 00*, at what time should the watch be set to be on local apparent time at the noon position % If the watch was set 18 seconds fast on local apparent time at the noon position, work out constants for observations for latitude to be taken 15, 10, and 5 minutes before noon and at noon. Prepare all forms for the noon work. The observed altitudes near noon were as follows : 15 minutes before, 46° 12' 30"; 10 min. before, 46° 16' 50"; 5 min. before, 46° 19' 20". The noon alt. was 46° 19' 40". The patent log read 217.5 at noon. Complete the day's work for noon. At noon the course was changed *to 86° (p. s. c), Var, 10° W., Dev. 4° W. Steamed untU 4p. m. on this course, when at W. T. 4'' 00™ 12", obs. alt. of sun 18° 32' 40"; C-W, A^ 40™ 56"; I.C, +1' 50"; ht. of eye, 40 ft.; patent log reading, 264.3. Find position of ship at 4 p. m. by observation. The course and speed remaining unchanged, find the 8 p. m. position. 184 THE PRACTICE OF NAVIGATION AT SEA. + + o Q I 1 H H o O I I W s 'ij^ V ' o 1— 1 O ca 05 w OJ lO l-H (M i?i I— 1 t^ O .3 id P i> I— 1 « u. 3 o o o fO o CO B H ^ ^ ^ p. a 00 6 F? o ft CO 1-^ ^ ^C3 t' o u C) w to 3 o a (3 ■^ ^ ^w o >3« ^^ h^Q a. Ph p; a OD '^. ' + Eh ^ o 1 tn V ^ w 1:: ^ Qc:^ + + Wo fie Oo ^ 05 (N ->tl (M «5 oo CO 0> 05 CO OO Ol 02 C2 C^ S 5 "0 goo it^ld 05 «D 00 lO 00 CO VS CO a be .t-^'a oo (MOO ■^CO CO CO s;:: COCO C0 04 CO C<1 ^>fs; r*; 13 C3 OOC ff3 fci) (-1 o .2P bCrt T— I l-l ri2 a> 0) Hrt be «.2 Jo; '•3 O !:« h^Q ^ J2; ce CO g O |a .2 o p. o o 1^ 5^ bib . .0 « a s CO ^ !z; 3 + i _ac^ "43 ^ ^' © d 2-: ^^ ^ .a -c 03 bo n •c ".2 o * fl 'C 08 © ,c ■^ &■ •£' a .£?§ S • IC a-fl 2 . 3 g Ct 10 .^ .*^ " s ^ a a 00 00 ^>A w 00 ^^ .0 ^; o J «^ •^1 SI j3 id ^•§ a a « .2 p< a a H § i S ^ OQ 00 a ci 186 THE PRACTICE OF NAVIGATION AT SEA. »0 •= d i-H I-l II II a ti ki O in li ^ cS 0) Q a p* +^00 to 00 (B , PI So c3 ■-3 2 s h5^ H W (4 p3 a Q3 33 -<}<■ .s.a s-i II i-i i-<00 _ . QOW O0*« ^ o 4- - « I- • ^ - - i . s o jJ o d O a ej fci 2 2 T3 ^^ ^ p: Ml-t rH 00 O 'I* «o II ^-^o »o-<*« vco } 6. doo ^ II i-H i-H a o g ^^ o f-1 ij II 8 33 p 3 O £ 1 :2;^ ;^ CO . II -s t^ CD r-f ■t^ "=" (3 • CO O cd ^-^ **" o eoc^ Oi .6 a,-* 00 00 S II £ ^• eoeo ■«J 00 S ♦J c4 h4 to 00 C3 II OQ g -M s^- >>,^ gx 8^ PQPQ oQ P^> P^ ^^ o h-1 s 1 00 .2 £f ^ d a fl 33 00 "5 eoo t^ ss^ 00 i^ eo cf V* 05.-I rH II o iOtT ■* •43 :^cD ■^ ^.s loeo ■"C o «ooo eoeo t-t as II 3> S ■*« a 1 CO m ?, '3'S ^ Ok -w -fc> •^ ii ** 33 «t ct o-S o o 33 d cSq HH Q 188 THE PRACTICE OF NAVIGATION AT SEA. w H a H P o ■p o o H ^ .a CO 1 s o i o o rH O S3 > o O rH 1 O CO oo o ^^ h:iO ^ ^P ^ o oo + to ''5 + HO 5C ^H ^p4 pspq ^ wo a Vl 00<» ^ m % ■p fee ' « o Oo ++ (3 r+ Oo +' LO «J t^ T^ CO Oj OS t-H 00 '^ rfi CO 05 j(3 OS CS 05 00 + eo O «i^'« S o IM 00 coo OS OS OS CO ^ > ■4-= += > m tn >■ c3 O O c« ^ o o ^ t3 ■i IQ OO O ^^ V CO ( 00^; OS c3< II +5 < XXX 00 f-H O "O T-l 00 t^r-l I CO-* ^ r-fOS.g , "=* o T5 '^ d cS 0_p P >H IH >-l >-( o o o f^OOO go OiO im i« o 00 (N 0^ «o CO oo oeo osrj 1— ( N r-l CO oo CO S^ri -* CO'-< l^CO § ^^ 00 OO CO-* ^ ^.^ 1 HO ^6 OQ o-« »-? bCbo P5 C ^ RunNE. ^'g Run ENE. oS Run East. ^ 5; Run ESE. ° ?. Run SE. g - Run SSE. a Run South, "g K.-S- Run SSW, 3-0.^ RunSW. gK§ RunWSW. £.^ S Run West. • ^.g Run WNW. S » RunNW, B-g Run NNW, g ^ Run North, ^3 Run NNE, ^ ' Run NE, ° ^ Run ENE. %-^ Run East. „ S Run ESE, ° 5-' Run SE. g a a Courses given are for wind two points on port quarter, but it is preferable to take wind broad on quarter if possible. 488. Extra-Tropical Cyclonic Storms, — On turning to the cyclones of tem- perate latitudes, we find many features in which they resemble those of the torrid zone, but certain other features in which they differ. Their fundamental resemblance to tropical cyclones is seen in their incurving winds, forming an inflowing left-handed spiral about the center of low pressure in the northern hemisphere, an inflowing right- handed spiral in the southern. The intensity of these winds varies with the depth of the barometric depression. The depression itseK, however, in place of covering a few miles, as is the case in the tropics, will frequently have a diameter of several hundred or even a thousand miles, and for some distance around the center the gradients will have a tolerably strong value. For this reason there is less concentration of violence close to the center, and the calm and clear central space, or "eye," is seldom sharply developed, although it is not uncommon to discover a gradual "weakening or faihng 224 CYCLONIC STOBMS. of the winds, and sometimes even an imperfect breaking away of the clouds as the central area passes over the observer. The form of tropical cyclones as defined by their isobaric lines is nearly circular. Extra-tropical cyclones are as a rule less symmetrical, and their isobars are often elongated mto an oval form, the longer axis of the oval trending (in the northern hemisphere) between north and east — about, therefore, in the direction of progression. Tne steepest gradients, and consequently the strongest winds, are apt to be foimd on the equatorial and westerly sides of the depression. Extra-tropical cyclones generally follow an easterly course, inclining somewhat toward the pole; but they occasionally turn to one side or the other, become sta- tionary, or even move backward. The velocity of progression varies from 15 to 40 miles an hour. If they exist as independent barometric depressions, with strong upward gradients on all sides of the center, the cyclonic circulation will be complete, the wind shifting with the sun for an observer situated in the equatorial semicircle of the storm, against the sun for an observer situated in the polar semicircle. Important among these extra-tropical cyclonic disturbances are the pamperos of the Argentine coast. These storms are primarily caused by the approach and passage eastward of an area of low pressure, around which the winds circulate spirally m a right-handed direction. They vary in strength and duration from a squall to a gale 01 great violence. Although preceded by the indications which characterize the approach of cyclonic storms m general, yet they usually break with such sudden- ness, in a shift of wind from the northward to the southwestward, that they may become particularly dangerous from this cause alone. They usually continue to blow and die out in the southwest quadrant. 489. Storms Along the Transatlantic Steamship Routes. — The storms which are so frequently met during the winter season along the steamship routes between America and Europe are not, as a rule, due to central oarometric depressions but to depressions having a trough or V shape, wliich extend southerly from the extensive permanent area of low pressure havingits center in the vicinity of Iceland. They are not attended by complete cyclonic circulations, inasmuch as tne polar gradients which would otherwise give rise to easterly winds on this polar side are lacking. Their approach is heralded by a gradual hauling of the wind to southward, which is later followed (at the time of passage of the central line of the trough) by a change to NW., accom- panied by heavy rain squalls and a rapid increase in force. The general distribution of pressure and the sur- rounding winds are shown in figure 76. The changes in wind and pressure ensue much more rapidly in the case of a westward-bound vessel than in that of one east- ward bound, tne rate at which the observer and the depression approach each other being in the former case the sum of his own westward velocity and the eastward velocity of the trough, in the latter case the difference of these velocities. Hi^h Fig. 76. CHAPTER XX. TIDES. 490. Definitions. — Tidal phenomena present themselves to the observer under two aspects — as alternate elevations and depressions of the sea, and as recur- rent inflows and outflows of streams. The word tide, in common and general usage, is made to refer without distinction to both the vertical and horizontal motions of the sea, and confusion has sometimes arisen from this double appHcation of the term ; in its strict sense, this word may be used only with reference to the changes of eleva- tion, while the recurrent streams are properly distinguished as tidal currents. The tide rises until it reaches a maximum height called high water or high tide, and then falls to a minimum level called low water or low tide; that period at high or low water marking the transition between the tides, during which no vertical change can be detected, is called stand. Of the tidal currents, that which arises from a movement of the water in a direction, generally speaking, from the sea toward the land, is called jlood, and that arising from an opposite movement, ehh; the intermediate period between the cur- rents, during which there is no horizontal motion, is distinguished as slack. Set and drift are terms appHcable to the tidal currents, the first referring to the direction and the second to the velocity. Care should be taken to avoid confusing the terms relating to tides with those which relate to tidal currents. 491. Cause. — The cause of the tides is the periodic disturbance of the ocean from its position of equihbrium brought about through the periodic differences of attraction upon the water particles of the earth, by the moon, and to lesser degree, by the sun, on account of their relative periodic movements. The tide-producing force of the moon upon a particle of unit mass on the surface of the earth is the difference between the moon's attraction upon the given unit mass and the moon's attraction upon the entire earth; and it is hkewise with the sun, only the magnitude of the mean tide-producing force is in this case reduced to about two-fiifths of the tide-producing force of the moon, because of the comparative remoteness of the sun from the earth. A particle which has a tide-producing body in its zenith or in its nadir experi- ences, as the result of the attraction of the tide-producing body, an effect only in the vertical direction as ii the intensity of gravity were momentarily lessened; and a particle which has the tide-producing body in its horizon, being then practically at the same distance from the tide-producing body as the center of the earth, experi- ences, as the result of the attraction of the tide-producing body, an effect which is practically aU in the vertical direction as if the intensity of gravity were momentarily mcreased. But when the tide-producing body is in any other situation with reference to an attracted particle, the attraction is partly directed in a vertical line toward the center of the earth and partly in a horizontal direction along the surface of the earth. The vertical components of the attractions of the tide-producing bodies can not create any sensible disturbance on the existing oceans ; but the horizontal components of such attractions, tending to produce horizontal movements oscillating back and forth on the surface of the earth, are effective in the production of the tides, and, by acting upon portions of the oceans that are susceptible of taking up stationary oscillations in approximate imison with the period oi the tide-producing forces, give rise to the dominant tides. The peculiarities that characterize the tides of many localities are caused by modifications resulting from reflections and interferences suffered by the dependent waves generated by the dominant tides. Theory is not yet sufficiently advanced to render practicable the prediction of the tides where no observations have been made; 21594°— 14 15 225 226 TIDES. but by theory, supplemented by the observation of actual tidal conditions in a given locality during a certain period of time, very accurate predictions of the time and height of the tides can be made for that locality. 4:92. Establishment. — High and low water occur, on the average of the twenty- eight days comprising a lunar month, at about the same intervals after the transit of the moon over the meridian. These nearly constant intervals, expressed in hours and miautes, are known, respectively, as the liigh water lunitidal interval and low water lunitidal interval. The interval between the moon's meridian passage at any place and the time of the next succeeding high water, as observed on the days when the moon is at fuU or change, is called the vulgar (or common) establishment of that place, or, sometimes, simply the estahlishment. This interval is frequently spoken of as the time of Jiigh water on full and change days (abbreviated ''H. W. F. & C."); for since, on such days, the moon's two transits (upper and lower) over the meridian occur about midnight and noon, the vulgar estabHshment then corresponds closely with the local times of high water. When more extended observations have been made, the average of aU high water lunitidal intervals for at least a lunar month is taken to obtain what is termed, in distinction to the vulgar estabHshment, the corrected estahlishment of the port, or mean high water lunitidal interval. In defining the tidal characteristics of a place some authorities give the corrected estabHshment, and others the vulgar establishment, or ''high water, full, and change;" calculations based upon the former will more accurately represent average conditions, though the two intervals seldom differ by a large amount. Having determined the time of high water by appljring the estabHshment to the time of moon's transit, the navigator may obtain the time of low water with a fair degree of approximation by adding or subtracting 6** 13"" (one-fourth of a mean lunar day) ; but a closer result wiH be given by applying to the time of transit the mean low water lunitidal interval, which occupies the same relation to the time of low water as the mean high water lunitidal interval, or corrected establishment, does to the time of hi^ water. 493. Range. — The range of the tide is the difference in height between low water and high water. This term is often appHed to the difference existing under average conditions, and may in such a case be designated as the mean range or mean rise and fall to distin^ish it from the spring range or neap range, which are the ranges at spring and neap tides, respectively. 4:94. Spring and Neap Tides. — ^At the times of new and full moon the relative positions of sun and moon are such that the high water produced by one of those bodies occurs at the same time as that produced by the other, and so also with the low waters; the tides then occurring, caUed s'pring tides, have a greater range than any others of the lunar month, and at such times the highest high tides as weU as the lowest low tides are experienced, the tidal range being then at its maximum. At the first and third quarters of the moon the positions are such that the hi^h tide due to one body occurs at the time of the low tide due to the other, so that the two actions are opposed; this causes the neap tides, which are those of minimum range, the high waters being lower and the low waters higher than at other periods of the month. Since the horizontal motion of the water depends directly upon the rise and fall of the tides it foUows that the currents will be greatest at springs and least at neaps. The effect of the moon's being at fuU or change is not felt at once in aU parts of the world, and the greatest range of tides does not generally occur until oncor two days thereafter; thus, on the Atlantic coast of North America, the highest tides are experienced one day, and on the Atlantic coast of Europe two days, afterwards, though on the Pacific coast of North America thev occur nearly at fuU and change. 495. The nearer the moon is to the earth the stronger is its attraction, and as it is nearest in perigee, the tides will be larger then on that account, and consequently less in apogee. For a Hke reason, the tides will be increased by the sun's action when the eartn is near its perihelion, about the 1st of January, and decreased when near its apheHon, about the 1st of July. 4:96. The height of the tides at any place may undergo modification on account of strong prevaiHng winds or abnormal barometric conditions, a wind blowing off TIDES. 227 the shore or a high barometric tending to reduce the tides, and the reverse. The effect of atmospheric pressure is to create a difference of about 2 inches in the height of tide for every tenth of an inch of difference in the barometer, 497. Priming and Lagging. — The tidal day is the variable interval, averaging 24h 50 m^ between two alternate high or low waters. The amount by which corre- sponding tides grow later day by day — that is, the amount by which the tidal day exceeds 24'' — is called the daily retardation. When the sun's tidal effect is such as to shorten the lunitidal intervals, thus reducing the length of the tidal day and causing the tides to occur earlier than usual, there is said to be a. priming of the tide; when, from similar causes, the interval is lengthened, there is saia to be a lagging. 498. Types of Tides. — The observed tide is not a simple wave; it is a compound of several elementary undulations, rising and falling from the same common plane, of which two can be distinguished and separated by a simple ^ouping of the data. These two waves are known as the semidiurnal and the diurnal tides, be- cause the first, if alone, would give two high and two low waters in a day, while the second would give but one high and one low water in an equivalent period of time. In nearly all ports these two tides coexist, but the proportion between them varies remarkably for differ- ent seas. The effect of the com- bination of these two types of tide is to produce a diurnal inequality, both in the height of two consecutive high or low waters, and in the mtervals of time between their occurrence. The height of the diurnal wave may be regarded as reaching a maximum fortnightly, soon after the moon attains its extreme dec- lination and is therefore near one of the tropics. The tides that^ then occur are denominated tropic tides. In undertaking to investi- gate the tides of a port it is im- portant to ascertain as early as possible the form of the tide ; that is^ whether it resembles the semi- diurnal, the diurnal, or the mixed type; because not only may this information be of scientific value, but the knowledge thus gained at the outset will enable the observer to fix upon the best method of keeping his record. 499. The type forms referred to are illustrated in the diagram in figure 77, where the waves are plotted in curves, using the times as abscissae and the heights as ordinates. In this diagram, the curve traced in the full line is a tide wave of the semidiurnal type; that traced by the dotted line one of the diurnal; while the broken line is one of the mixed type, in this case the compound of the two others. In order to determine the type to which the tide of any port belongs, it is usually only necessary to make hourly observations for a day or two at the date of the moon's maximum declination, and to repeat the series about a week later, when the moon crosses the equator. The reported irregularities of the rise and faU at any place should not deter persons from careful investigation. When analyzed, even the most complicated of tides are found to follow some general law. 500. Tidal Currents. — It should be clearly borne in mind by the navigator that the periods of flood and ebb currents do not necessarily coincide with those of rising and faUing tides, and that, paradoxical though it may seem at first thought, the inward set of the surface current does not always cease when the water nas attained its maximum height, nor the outward set when a minimum height has been reached. Under some circumstances it may occur that stand and slack will be V ( )^T"2"'.'»'^4~5''6''7''8""'"0'l0 n 12 13 M 15 16 17 18 39 20 21 22 23 24 | Ff, - ^ 3 5 2 1 1 2 3 4 ^ -^ r /" V~ ■N, •-- ■ ' "n. f ^ ■n] Jl / .,' \ \ / / "**> / \ 1 / \ \ / 1 - p. - / / \,' /' / / \ ,•' \ ^' - / 1 V 17 1 / \ / K X. - 7 i ^^^ 1 J — /_ .■' \^ / - V V. - /- -" f ^- V L / T U'1 ' Semidiurnal. diurnal. FiQ. 77. mixed. 228 TIDES. simultaneous, while other conditions may produce a maximum current at stand, with a maximum rate of rise or fall at slack water. The varying effects which will be produced according to local conditions may be considered by the comparison of two tidal basins, to one of which the tide wave has access from the sea by a channel of ample capacity, while the other has an entrance that is narrow and constricted. In the first case, the process of filling or emptying the basin keeps pace with the change of level in the sea and is practically completed as soon as the height without becomes stationary; in this case slack and stand occur nearly at the same time, as do flood and rise and ebb and fall. In the second case, the limited capacity of the entrance will not permit the basin to fill or empty as rapidly as the tide changes its level without ; hence there is still a difference of level to produce a current when the vertical motion in either direction has ceased on the outside, and for a considerable time after motion in the reverse direction has been in progress ; under extreme conditions it may even occur that a common level will not be established until mid-tide, and therefore the surface current at some places will ebb until three hours after low water and flow until three hours after high water. Localities that partake of the nature of the first case are those upon open coasts and wide-mouthed eights. Examples of the latter class will be found m narrow bays and long channels. TIMES OF HIGH AND LOW WATER. 501. Tide Tables. — The most expeditious, as well as most exact, method of ascertaining the times of high and low water and other features of the tides will be by reference to a Tide Table, and every navigator is recommended to provide him- self with such a pubUcation. The United States Coast and Geodetic Survey pub- lishes annuaUy, in advance, tables giving, for every day in the year, the predicted time and height of the tides at certain principal ports of the world, and from these, by a simple reduction, the times and heights at a multitude of other ports may readily be obtained; data for ascertaining the tidal currents in certain important regions are also provided. General tide tables are also published by the govern- ments of other maritime nations, and special tables are to be had for many particular localities. 502. Where no tide tables are available, the method of calculation by applying the lunitidal interval to the time of the moon's meridian passage must be resorted to. To do this, find first the time of the moon's meridian passage, upper or lower, as may be required. The Greenwich mean time of upper transit at Greenwich is given m the Nautical Almanac (page IV of the month) ; the corresponding time of lower transit is most easily found by taking the mean of the two adjacent upper transits ; to the Greenwich time of Greenwich transit apply the correction for longi- tude given in Table 11 (using the daily variation of the moon's meridian passage shown in the Almanac), adding in west and subtracting in east longitude; the result is the local mean time of local transit. Add to this the high-water or low-water lunitidal interval of the port from Appendix IV, according as the time of high or low water may be required. The result is the time sought. The astronomical date must be strictly adhered to, and in so doing it may be found necessary to employ the time of a lower transit, or the transit of a preceding day, to find the time of the tide in question. Appendix IV contains, besides the geographical positions of all the more important positions in the world, a series of tidal data relating to many of those places. In such data are comprised the mean lunitidal intervals for high and low water; also, for places where the semi-diurnal type of tide prevails, the tidal range at spring and at neap tides, and for those where the tide is of the diurnal type, the tropic range. An alphabetical index is appended to this table. The corrected establishment taken from the charts may be substituted for the high-water lunitidal interval of the table; or, with only slight variation in the results, the vulgar establishment (H. W. F. & C.) may be employed. TIDES. 229 Example: Find the times of the high and low waters at the New York Navy Yard, occurring next after noon on April 15, 1915. G. M. T. of Gr. tiansit, 22 '<^ % S 1 '-.-Si >^^s ,^......4.: ¥ « .--, ,.•-•; ^ \ ^ Srv^^kJr*^ ^ Y- o*'"* x^ \ 1 / / \ r h. 1 h \ 1"' / / v'^' ■l - \ •i • \ .... .... .... -— .... ,,|.:. ..... • 1 / / — .... ..... \ I ^ \ ^ ■\ / ^.i^ f\ \ V \ i ^ w A(Uj 1^ w^ i"* 1 \ > s \ i ;':2g i ^^ • ^ / j "- --. . __ -*-* -- \ 't'" Fig. 81. Besides the three charts of monthly limits for April, May, and June, a fourth chart is presented showing the general limits within which icebergs and field ice have been encountered during the same months. , . • i- 653. Signs of the Proximity of Ice.— The proximity of ice is mdicated by the following-described signs : Before field ice is seen from deck the ice Wink will often mdicate its presence. On a clear day over an ice field on the horizon the sky will be much paler or hghter in color and is easily distinguished from that overhead, so that a sharp lookout should be kept and changes in the color of the sky noted. ICE AND ITS MOVEMENT IN THE NORTH ATLANTIC OCEAN. 247 On a clear day icebergs can be seen at a long distance, owing to their brightness; during foggy weather they are first seen through the fog as a black object. In thick fog the first sight of a berg is apt to be a narrow streak of dark at the water line. They can sometimes oe detected hj the echo f^om the steam whistle or the fog horn. In that case, by noting the time between the blast of a whistle and the reflected sound, the distance of tne bei^ in feet may be approximately found by multiplying by 550. The absence of echo is by no means proof that no bergs are near, for unless there is a fairly vertical wall, no return of the sound waves can be expected. The presence of icebergs is often made known by the noise of their breaking up and falling to pieces. The cracking of the ice or the falling of pieces into the sea makes a noise like breakers or a distant dischai^e of guns, which may often be heard a short distance. The absence of swell or wave motion in a fresh breeze is a sign that there is land or ice on the weather side. The appearance of herds of seal or flocks of murre far from land is an indication of the proximity of ice. The temperature of the air falls as ice is approached, especially on the leeward side, but generally only at an inconsiderable distance from it. The fall of the tem- perature of the sea water has been held to indicate the nearness of ice, but in regions where there is an intermixture of cold and warm currents going on, as at the junction of the Labrador Current and the Gulf Stream, the temperature of the sea has been known to rise as the ice is approached. The special temperature studies made during the ice patrol of 1912 have not settled the question whether icebergs influence the temperature of sea water to a measurable extent at distances of a imle or so. A reliable sign of icebergs being near is the presence of calf ice. When such pieces occur in a curved line, as they may do, especially in calm weather, the parent berg is on the concave side of the curve. No ship captain can afford to trust any of the above-named signs to the exclusion of a good lookout. Current Information Regarding Ice Conditions.— The branch hydrographic offices receive daily the latest information regarding ice and other obstructions to navigation, being furnished with the reports of passing vessels and the ice-patrol ships, as long as such are in service. The^ also distribute the publications of the Hydrographic Office dealing with this topic, namely, the Hydrographic Bulletin (weekly) and the Pilot Chart (monthly), as well as the pamphlet on North Atlantic Ice Patrols (Reprint No. 24). APPENDIX I. EXTRACTS FEOM THE AMERICAN EPHEMERIS AND NAUTICAL ALMA- NAC, FOR THE YEAR 1915, WHICH HAVE REFERENCE TO THE EXAMPLES FOR THAT YEAR GIVEN IN THIS WORK. [Extracts: Page I.) AT GREENWICH APPARENT NOON. THE SUN'3 AjiparerU Right Ascension. ft. WJ. Diff. for 1 hour. A pparent Decimation. Bifl. for 1 hour. Semi- diameter. Sidereal Time of the Semi- diameter passing the Meridian. Equation of Time, to be added to subtracted from Appar- ent Time. Diff. for 1 hour. JANUARY. Tues. 19 Wed. 20 Thur. 21 20 1 51.77 20 6 6.99 20 10 21.44 10.649 10.618 10.586 20 30 7.6 +30.83 20 17 36.1 31.79 20 4 41.8 32.73 16 17.18 69.75 16 17.10 69.65 16 17.02 69.55 10 38.76 10 57.36 11 15.20 0.790 0.759 0.727 APRIL. Thur. 1 Fri. 2 Sat. 3 Tues. 13 Wed. 14 Thur. 15 Fri. 16 Sat. 17 Sun. 18 Mon. 19 Tues. 20 Wed. 21 39 17.25 9.095 42 55.58 9.100 46 34.04 9.105 1 23 9.70 9.204 1 26 50.74 9.217 1 30 32.12 9.231 1 34 13.82 9.245 1 37 55.88 9.260 1 41 38.30 9.275 1 45 21.10 9.291 1 49 4.28 9.308 1 52 47.87 9.325 N. 4 13 56.4 +57.99 4 37 6.0 57.80 5 10.7 57.59 8 45 15.1 54.70 9 7 3.5 54.33 9 28 42.7 53.94 9 50 12.4 63.54 10 11 32.4 63.12 10 32 42.2 62.69 10 53 41.5 62.25 11 14 29.9 51.79 11 35 7.2 +51.31 16 2.05 64.47 16 1.77 64.49 16 1.49 64.51 15 58.70 64.83 15 58.43 64.88 15 58.16 64.93 15 57.89 64.98 65.03 15 57.62 15 57.36 65.09 15 57.10 65.15 15 56.84 65.21 15 56.59 65.27 4 13.33 3 55.16 3 37.11 47.70 32.23 17.09 2.28 12.17 26.27 39.99 53.32 1 6.26 0.759 0.755 0.749 0.651 0.638 0. 624 0. 610 0.595 0.580 0.564 0.547 0.531 MAY. Thur. Fri. Sat. Sun. Sat. Sun. Mon. Tues. 49 37.97 9.640 53 29.62 9.664 57 21.85 9.689 1 14.67 9.713 24 43.88 9.858 28 40.76 9.882 32 38.21 9.905 36 36.22 9.928 N. 16 18 29.2 + 42.67 16 35 25.2 41.99 16 52 4.7 41.30 17 8 27.5 40.59 18 40 33.9 36.09 18 54 50.5 35.29 19 8 47.9 34.48 19 22 25.8 +33. 67 15 52.91 66.37 15 52.68 66.45 15 52.46 66.53 15 52.24 66.61 15 50.95 67.10 15 50.75 67.18 15 50.56 67.27 15 50.37 67.35 24.11 29.00 33.32 37.04 47.15 46.82 45.93 44.48 0.216 0.192 0.167 0.143 0.001 0.025 0.049 0.072 Note. — Mean Time of the Seraidiameter passing may be found by subtracting 0«.18 from the Sidereal Time. + prefixed to the hourly change of declination indicates that north declinations are increa-siug and south declina- tions are decreasing; — indicates that north declinations are decreasing and south declinations increasing. 248 EXTEACTS FROM NAUTICAL ALMANAC. 249 [Extracts: Page I.] AT GREENWICH APPARENT NOON— Continued. i •s 1 o 1 o p THE SUN'S Sidereal Time of the Semi- diameter passing the Meridian. Equation of Time, to be subtracted from Dift. for 1 hour. Apparent Right Ascension. Piff. for 1 hour. Apparent Decimation. Difl. for 1 hour. Semi- diameter. added to AppareTU Time. h. m. s. ». . , • ' ' ». m. s. s. JUNE. Mon. Tues. Sun. Mon. Tue& Mon. Fri. Sat. 7 8 13 14 15 21 25 26 4 57 40. 36 6 1 47. 98 5 22 30. 17 5 26 39. 24 5 30 48. 47 5 55 45. 61 6 12 23. 53 6 16 32. 78 10.311 10.324 10.374 ia381 10.387 10.399 10.388 10.383 N. 22 40 44. 5 22 46 40. 9 23 10 20. 4 23 13 51. 23 16 57. 1 23 26 54. 3 23 25 17. 23 23 50. 9 +15.34 14.35 9.29 8.27 7.24 + LOS - 5.07 - 4.10 15 47. 25 15 47. 13 15 46. 61 15 46. 52 15 46. 43 15 46. 04 15 45. 86 15 45. 82 68.64 68.68 68.84 68.87 68.89 68.95 68.92 68.91 1 3L85 1 20. 82 21. 59 9.11 0.453 0.466 0.516 0.623 0.529 0.541 0.530 0.525 3.53 1 21. 10 2 12. 64 2 25.31 JULY. Sat. Sun. Mon. 10 11 12 7 14 20. 54 7 18 25. 86 7 22 30. 75 10.230 10.213 iai95 N. 22 21 8. 4 22 13 41. 2 22 5 6L -18.15 19.11 -20.07 15 45. 70 15 45. 72 15 45. 75 68.36 68.30 68.24 5 0.82 5 9.56 5 17. 87 0.372 9.355 0.337 OCTOBER. Tnbetub- tracted from Apparent Time. Tues. Wed. Thur. 5 6 7 12 41 0. 28 12 44 38. 83 12 48 17. 76 9.099 9.114 9.130 S. 4 24 53. 2 4 48 L 7 5 11 6. 7 -57.92 57.78 -67.63 16 L63 16 L90 16 2.18 64.46 64.51 64.57 11 17. 06 11 35. 02 11 52. 60 0.756 0.740 0.724 NOTl t.— Me + an Time of the Sen )reflxed to the houi ions are decreasing lidiameter passing may be found by subtracting 0«.18 frc rly change of declination indicates that north declination ; — indicates that north declinations are decreasing and m the Side 3 are incres south decli real Time. ising and south declina- nations increasing. 250 EXTRACTS FROM NAUTICAL ALMANAC. [Extracts: Page II.] AT GREENWICH MEAN NOON. Day of the Week. Day of the Month. THE SUN'S Apparent Right Ascension. A. tn. «. Diff. for 1 hour. Apparent Dechnation. DiS. for 1 hour. Equation of Time, to be subtracted from added to Mean Time. Diff. for 1 hour. Sidereal Time or Right As- cension of Mean Sun. JANUARY. Tues. 19 Wed. 20 Thur. 21 20 1 49. 88 10.647 20 6 5.05 10. 616 20 10 19. 45 10.584 S. 20 30 13. 1 20 17 41. 9 20 4 48. +30. 82 31.78 +32. 72 10 38. 62 0.790 10 57. 22 0.759 11 15. 07 0.727 19 51 11. 27 19 55 7. 82 19 59 4. 38 APRIL. Thur. 1 Fri. 2 Thur. 15 Fri. 16 Sat. 17 Tuea. 20 Wed. 21 Thur. 22 Fri. 23 Sat 24 Sun. 25 Mon, 26 39 16. 61 9.097 42 54. 99 9.102 1 30 32. 07 9.232 1 34 13. 82 9.247 1 37 55. 92 9.262 1 49 4. 42 9.309 1 52 48. 04 9.326 1 56 32. 07 9.343 2 16. 52 9.361 2 4 L40 9.379 2 7 46. 73 9.398 2 11 32. 52 9.417 N. 4 13 52. 3 +58. 01 4 37 2. 2 57.81 9 28 42. 4 53.95 9 50 12. 4 53.64 63.12 10 11 32. 6 11 14 30. 7 51.79 11 35 8. 1 51.32 11 55 34. 50.83 12 15 48. 50.33 12 35 49. 9 49.82 12 55 39. 2 49.29 13 15 15. 8 + 48.75 4 13. 39 3 55. 21 17. 09 2.28 12. 17 53. 33 6.27 18.80 30.90 42.57 53.80 4.57 0.759 0.755 0.624 0.610 0.595 0.547 0.531 0.513 0.495 0.477 0.458 0.439 35 3. 22 38 59. 78 1 30 14. 98 1 34 11. 53 38 8.09 49 57. 75 53 54. 31 57 50. 86 1 47. 42 5 43. 97 9 40. 53 13 37. 08 MAY. Sun. Mon. Tues. Wed. Mon. Tues. Sun. Mon. 10 11 12 17 18 30 31 1 15. 26 9.7)4 5 8.68 9.738 9 2.68 9.762 12 57. 27 9.787 32 38. 84 9.905 36 36. 84 9.928 24 53. 17 10. 177 28 57. 65 10. 196 N. 17 8 29. 9 17 24 35. 6 17 40 23. 7 17 55 54. 2 19 8 50. 1 19 22 27. 9 21 39 9. 7 21 48 12. 1 + 40.59 39.87 39.14 38.40 34.47 33.65 23.07 + 22.13 37.05 40.18 42.74 44.71 45.92 44.48 46.84 38.91 0.143 0.118 0.094 0.070 0.049 0.072 0.321 0.339 4 52. 31 8 48. 86 12 45. 42 16 41. 98 36 24. 76 40 21. 32 27 40. 01 31 36. 56 To be added to JUNE. subtracted from Mean Time. Mon. 7 Tues. 8 Sun. 13 Mon. 14 Tuea. 15 Sun. 20 Mon. 21 4 57 40. 63 10. 310 5 1 48. 22 10.323 5 32 30. 23 10. 373 5 26 39. 27 10.380 5 30 48. 46 10. 386 5 51 35. 81 10. 399 5 55 45. 37 10.398 N. 22 40 44. 9 22 46 41. 2 23 10 20. 4 23 13 5L 23 16 57. 1 23 26 16. 7 23 26 54. 3 + 15.34 14.35 9.29 8.26 7.24 2.08 + 1.05 1 31. 84 1 20. 81 21. 59 9.11 3.53 1 8.08 1 21. 08 0.453 0.466 0.516 0.523 0.529 0.542 0.541 4 59 12. 47 5 3 9.03 5 22 51. 82 5 26 48. 38 5 30 44. 94 5 50 27. 73 5 54 24. 29 Note. — The Semidiameter for Mean Noon may be assumed the same as that for Apparent Noon. +prefixed to the hoiu-ly change of declination indicates that n#rth declinations are increasing and south declinations are decreasing; —indicates that north declinations are decreasing and south declinations increasing. Difl. for 1 hour. +9».856S. EXTRACTS FROM NAUTICAL ALMANAC. 251 [Extracts: Page 11.] AT GREENWICH MEAN NOON-Continued. Day of the Week. Day of the Month. THE sun's Kquation of Time, to be subtracted from Mean Tme. Difr. for 1 hour. Sidereal Time or Right As- cension of Mean Sun. Apparent Right Ascension. Diff. for 1 hour. Apparent Declination. Difl. for 1 hour. ft. m. s. s. O f ft " m. s. s. ft. TO. S. AUGUST. Thur. Fri Sat. 5 6 7 8 57 44.94 9 1 35.80 9 5 26.07 9.631 9.607 9.583 N. 17 12 38.8 16 56 29. 5 16 40 3. 7 -40.04 40.73 -41.41 5 55. 56 5 49. 86 5 43.58 0.225 0.250 0.274 8 51 49. 38 8 55 45. 94 8 59 42. 50 OCTOBER. Equation of Time, to be added to Mean Time. Tues. Wed. Thur. 5 6 7 12 41 2.00 12 44 40. 59 12 48 19. 56 9.100 9.116 9.132 S. 4 25 4.1 4 48 12. 9 5 11 18. 1 -57.93 57.79 -57.64 11 17.20 11 35.16 11 52.74 0.756 0.740 0. 724 12 52 19.20 12 56 15. 75 13 12.30 [Extracts: Page IV.] GREENWICH MEAN TIME. THE MOON'S Day of the Month. SEMIDIAMETER. Noon. Midnight. HORIZONTAL PARALLAX. Noon. Diff. for 1 hour. Midnight. Diff. for 1 hour. MBRIDULN FA8SA0K. Difl. for 1 hour. Noon. APRIL. 10 11 12 13 14 15 16 17 18 15 19.5 15 11.2 15 3.9 14 57.6 14 52.3 14 48. 2 14 45.4 14 44.3 14 45. 15 15.2 15 7.4 15 0.6 14 54.8 14 50. 1 14 46. 6 14 44. 6 14 44.4 14 46. 2 56 8.78 -1.841 55 38. 40 1.192 55 11.57 1.043 54 48.40 0.888 54 29.02 0.723 54 13.91 0.531 54 3.78 0.306 53 59.53 -0.041 54 2.18 +a270 55 53. 14 -1.266 55 24. 54 1.118 54 59.52 0.966 54 38. 22 0.808 54 20.89 0.631 54 8.17 0.424 54 0.86 -0.179 53 59.92 +0.109 54 6.43 0.4^0 21 50.3 1.75 22 31.7 L71 23 12.8 1.72 23 54.5 1,76 d 37.7 1.84 1 23.0 1.94 2 10.7 2.03 3 0.4 ZIO 25.7 26.7 27.7 28.7 0.0 1.0 2.0 3.0 4.0 MAY. 6 7 8 21 22 15 38. 2 15 25.5 15 14.3 15 22. 3 15 35.8 15 31.6 15 19.7 15 9.4 15 28. 9 15 43. 1 V 57 17.33 -2.049 56 30. 64 1.831 55 49. 77 -1.570 56 19. 13 +1.925 57 8.54 +2.179 56 53. 33 -1.948 56 9.42 1.704 55 31. 75 -1.432 56 43. 07 +2.062 57 35.26 +2.270 19 6.2 1.88 22.0 19 49.8 L77 23.0 20 31. 5 L71 24.0 5 52.3 1.90 7.4 6 37.6 1.88 8.4 JUNE. 18 19 20 26 27 15 23. 7 15 35. 1 15 47.7 16 39.7 16 35.2 15 29.3 15 41.3 15 54. 2 16 38.0 16 31. 1 56 24. 15 57 6.14 57 52.20 61 3.14 60 46. 43 + 1.647 1.844 + 1.981 -0.320 -1.061 56 44. 55 +1.751 57 28.76 1.923 58 16.20 +2.014 60 57.01 -0. 699 60 31. 65 -1.396 4 34.7 1.85 5 19.0 1.85 6 3.9 1.91 11 50.0 2.77 12 55.8 2.61 5.7 6.7 7.7 13.7 14.7 252 EXTRACTS FEOM NAUTICAL ALMANAC. [Extracts: Pages V-XII.J GREENWICH MEAN TIME. THE moon's right ASCENSION AND DECLINATION. Hour. Right Ascension. h. m. s. Difl. for 1 m. Declination. Did. for 1 m. Hour. Right Ascension A. m. s. Diflf. for 1 m. Declination. Diff. for 1 m. SATURDAY, APRIL 10. SUNDAY, JUNE 20. 17 18 19 22 55 22. 91 1. 8743 22 57 15. 29 1.8717 22 59 7. 51 1. 8691 s. 5 11 8. 6 4 56 39. 7 4 42 10. 2 14.476 14.487 14. 496 11 45 13. 99 1.9983 11 47 13. 97 2.0012 11 49 14. 13 2.0043 s. 1 54 54. 5 2 10 27. 9 2 26 1. 8 15.553 15. 561 15.568 THURSDAY, APRIL 15. SATURDAY, JUNE 26. 4 2 14 41. 37 5 2 16 39. 20 6 2 18 37. 24 1.9621 1.9656 1.9691 N. 18 38 53. 3 18 49 29. 4 19 0.7 10.643 10.562 10.481 16 17 18 18 18 38. 81 2. 7984 18 21 26. 59 2. 7940 18 24 14. 09 2. 7894 26 57 14. 8 26 53 30. 26 49 33. 3.643 3.848 4.052 SATURDAY, MAY 22. 10 33 32. 76 10 35 32. 26 10 37 31. 78 1.9915 1.9918 1.9923 N. 7 33 18. 1 7 18 28. 2 7 3 35. 2 14.805 14.858 14.909 [Extracts: Pages relating to Planets.] GREENWICH MEAN TIME. JUPITER. JXTPITER. AprD. September. Apparent Right Ascension. Noon. Var. of R.A. fori Hour. Noon. Apparent Declination. Noon. Var. of Dec. fori Hour. Noon. Meridian Apparent Right Ascension. Noon. Var. of R.A. fori Hour. Noon. Apparent Declination. Noon. Var. of Dec. fori Hour. Noon. Meridian 23 11 57.49 23 12 45.35 23 13 32.95 23 14 20.30 «. +2.000 1.990 1.979 +1.968 -6 13 33. 6 6 8 4L6 6 3 51. -5 59 L 9 +12.20 12.14 12.08 +12.01 h. m. 21 38. 9 21 35. 7 21 32. 6 21 29. 4 ft. m. s. 23 39 8.02 23 38 38.64 23 38 9.26 -1.223 1.224 -1.224 -3 58 31. 6 4 1 44. 1 -4 4 56. 1 -8.03 8.01 -7.99 11 59. 5 11 55. 1 11 50.7 Day of the Month. Semidiameter HorizontalParallax 6th. 16.16 L51 22d. 16.36 1.53 16.59 1.55 30th. Day of the Month. 16.86 L58 Semidiameter Horizontal Parallax 5th. 23.64 2.21 13th. 21st. 29th. 23.75 2.22 23.74 2.22 23.62 2.21 EXTRACTS FROM NAUTICAL ALMANAC. [Extracts: Pages relating to Fixed Stars.] FIXED STA.RS. MEAN PLACES FOR 1915. 0. (Jan. 0+'» .732, Washington.) 253 star's Name. Magni- tude. Right Ascension. An. Variation. Declination. An. Variation. a Ursse Min. (Polaris)* ct Eridani (Achemar) 2.1 0.6 1.1 3.2 -1.6 1.2 0.2 L2 h. m. ». 1 29 15. 60 1 34 32. 979 4 31 2. 478 6 17 49. 125 6 41 24. 147 13 20 42.776 14 11 47. 030 16 24 11. 574 +28.5356 + 2. 2364 + 3.4400 + 3. 6307 + 2. 6434 + 3. 1570 + 2. 7355 + 3. 6741 +88 51 6. 49 -57 40 6. 31 +16 20 21. 52 +22 33 29. 65 -16 35 55. 77 -10 43 4.50 +19 37 28. 04 -26 14 39. 44 +18. 547 +18. 323 + 7. 398 - 1.671 - 4. 808 -18. 848 -18. 825 - 8.166 rtr Tauri (Aldebaran) u Geminorum (X Canis Maj (Sinus) ez Virginia (Spica) r R. A. C ± .... O 1 ' n N.orS. (12) H.A.fromGr. ... , E. 0+ .... For the remainder of the work, by which the hour angles and thence the longitudes are found, employ the method given under "Form for Time Sight of a Star (Sumner Line)." FORM FOR MERIDIAN ALTITUDE OF SUN'S LOWER LIMB. o / Corr. ± .... h (18)2 d / ....N.orS. . ... N. or 8. Lat. ....N.orS. (')S. D. + (i») Dec N.orS. (♦)I.C. + + dip — p. &r. — II H. D. ± .... h. Long. ± .... 1 II Corr. ± .... ^^^_ Q I II ' " Dec N.orS. Corr. ± FORM FOR MERIDIAN ALTITUDE OF A STAR. o I II I II a I II Obs.alt.5|e («)I. C. + Dec N.orS. Corr. ± — A dip - ref. - (18) « N.orS d N.orS. - Lat. N.orS. Corr. ± FORM FOR MERIDIAN ALTITUDE OF A PLANET. Obs. alt. * (")par. + Corr. ± (^)I.C. + (•") z N.orS. dip - d N. or S. ref. — Lat. N.orS. — , I II Corr. ± h. m. G. M. T., Gr. trans Corr. for Long. ± O t If Dec N.orS. L. M. T., local trans Long. ± G. M. T., local trans H. D. ± A. G.M.T Corr. ± O 1 II Dec N.orS. FORMS FOR WORK. 257 FOBM FOB MERIDIAN ALTITUDE OF MOON'S LOWER LIMB. " ' " h. m. Obs. alt. (t (")2 d , N.orS. ('«)S.D. N. or S. Aug. (4)1. C. Lat N.orS. dip iBt corr + .. + .. G. M. T., Gr. trans. Corr. for Long. (Tab.U) ± . L. M. T., local trans. Long. ±. G. M. T., local trans. (") Dec. M. D. ± TO. No. min. ± , n Corr. ± Dec. • t ft N.orS. N.orS. Approz. Alt. p.(fcr.(Tab.24) +. ALTERNATIVE FORM FOR MERIDIAN ALTITUDE OF A BODY. (•>) ± 90» 00' 00" {n)Dec. ± Corr. ± Constant ±. Obs. Alt. ±. Lat. Rules for signs. Case I. Lat. & Dec. same name, Lat. greater +90''+Dec.— Corr.— Alt. Case II. Lut. & Dec. same name, Dec. greater — W+Dec.+Corr.+Alt. Casein. Lat. and Dec. opposite names +90°— Dec— Corr.— Alt. Case IV. Lower transit +90°— Dec.+Corr.+Alt W. T. C-W ±. Chro. t. C. C. ±. (") G. M. T. DEq. t, ±. N.orS. FORM FOR LATITUDE SIGHTS OF SUN'S LOWER LIMB (SUMNEB LINE). h. m. s. Q. A. T. Long.i ±. L. A. T.i . h. m. «. (")" Method. log sec log tan log cosec h (U)W — • 9>i' N. or log sin N.orS. log tan log sin Lat.i N.orS. log cos log sec log tan log cosec 9>i" N.orS. log tan. q>^ N.orS. Lat.| N. or S. 21594°— 14 17 log sin log sin log cos (»)a Reduction to Meridian. h h (=«)a' Haversine formula: hav z = {hay (co. L + P. D.)— hav (co. L— P.D.)}hav< + hav (co. L— P.D.) = hav B + hav (co. L— P. D.) ; where hav B=hav A hav t, and hav A=hav (co. L+ P.D.)-hav (CO. L— P.D.) * Sine— cosine formula: sin h =sin L sin d + cos L cos d cos ( = A + B 262 FOEMS FOR WORK. FORM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING DOWN THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A STAB. (COSINE-HAVERSINE FORMULA.') h. m. s. h. m. s. ° ' " W. T. C-W. +. Chro. t. C. C. ±. (») G. M. T. R. A. M.S. +. Red. (Tab. 9) + . G. 8. T. : R. A. * . (12) H. A. * r from Gr. /' («) Long, of \ assumed Pos.ll t L-d Calcu- lated log hav log cos log cos loghavO (Smu) ;■■} nat liav9... nat hav . . . nat hav (Sum) \ o / // h ) =90°-3 .E.or\V. Ohs.h .E.orW. Alt. diff. Dec. (d ) R. A. h. m. s. -N. orS. Obs. alt. * I.e. +. Corr. (Tab. 46)-. Obs. h F<^RM FOB FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING DOWN THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A STAB. (») (HAVEBSINE F0BMULA.2) h. m. I. h. m. 8. W. T. or or W, W. Dec. (6) P. D. CO. L. CO. L-)-P. D. CO.L-P.D. t CO. L— P. D. z Calculated/ =90°- z ...N. or 8. R. A. C-W + o Obs. alt. jfc Chro. t. / // I. C. + C. C. ± nat hav nat hav Corr. (Tab 46)— fii)Q. M. T ft. m. R. A. M.S. + nat hav A (Diff.) Obs. A Red.(Tab.9)+ log hav A . . . . 1 Calculated A s. G. S. T. Alt. diff. O / J R. A. 3|( log hav B (Sum) (») H.A.*fromi Gr / E. E. (W) Long, of as- \ nat hav t .. . nat hav (Sum) o / t " ^ I Cosine — ^haveraine formula: hav z =hav (L~d) + cos L cos d hav t =hav (L~d) -t- hav d » Haveraine formula: hav z = {hav (co. L -f- P. D.)— hav (eo. L— P. D.)} hav t + hav (co. L— P. D.) = hav B + hav (co. L— P. D.); where hav B=hav A hav t, and hav A==hav (co. L-f- P. D.)-hav(co. L-P.D.) FORMS FOR WORK. 263 FORM FOR FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING DOWN THE SUMNER LINE BY THE METHOD OP SAINT HILAIRE FROM A SIGHT OF A PLANET. h. m. s. W. T. C-W + . Chro. t. C. C. ± (U) Q. M. T. R. A. M. S.+ Red.(Tab.9)+ ( G.8.T ] R.A.* c C«)H.A.*from\ Gr. / E.orW. (*>) Long, of ti»-\ sumed Pes/ E. orW. h. TO. ». (SINE-COSINE FORMULA!) A. TO. 8. R. A. Dec. i. H. D. ±... h. H. D. G. M. T. G. M. T. s. COIT. ±... Corr. R. A. d .N. or S.Obs. alt. I. C. Calculated h logsin ± log sin ± (8um)logA ± A ± nat. sin Corr.(Tab.46).-. Obs. h Calculated ft Alt. Diff. log COS log COS lug cos logB B A •A+B FORM FOR FINDING THE CALCULATED ALTITUDE AND THE ALTITUDE DIFFERENCE FOR LAYING DOWN THE SUMNER LINE BY THE METHOD OF SAINT HILAIRE FROM A SIGHT OF A PLANET. A. m. ». (COSINE-HAVERSINE FORMULA.') h. m. I. h. m, 8. W. T. .... ( log hav R. A. ... Dec N. orS. o / L log cos C-W + H.D.±... 8. h. 8. H. D. ±.... G. M. T Corr. ± ri log cos G.M.T.... Chro. t. d A. C.C. ± Ioghav0 nat hav ..... (Sum) Corr. ±... I n (")G. M. T •! R. A. ... d o 1 tr Ob8.alt Jl- R.A.M.8. + L~d nat hav . . . . , (Sum) Red.(Tab.9)+ z nat hav . . . . , G. 8. T. o -W-z R. A. * Calcu-I latedAi I.e. + Corr. (Tab. 46)— E. orW. E. or W. (H) H.A.5icfrom\ Gr. / Obs. A (") Long, of as-\ sumed Pos.i Calcu- \ lated A/ t Alt. Diff. ' Sine— cosine formula: sin A =-sin L sin i + cos L cos i cos t = A + B » Cosine — haverslne formula: hav z =hav (L~r .D .D R. A. * nathav . . . (Sum) («) H.A.*froii aGr as-i OS./ E. E, h. m. s. (^)hong . of sumed P' s. ± h. o / Calculated h\ // o / Obs.ftlt " ( =90°-z / Obs.h ....1. 0. + Corr. -\ ....(Tab. 46)/ s. ± h. VI. s. Alt. Diff ... Obs. h 1 Haversine formula: hav z = {hav (co. L + P. D.)— hav (co. L— P. D.)} hav t + hav (co. L— P. D.) = hav B + hav (co. L— P. D.); where hav B=hav A hav t, and hav A=hav (co. L-l- P. D.)-haT (CO. L-P, D.) FORMS FOR WOfeK. 265 NOTES RELATING TO THE FORMS. 1. It is not necessary to convert departure Into difference of longitude for each course; it will suflBce to make one conversion for the sum of all the departures used in bringing forward the position to any^particular time. 2. In D. R. it will be found convenient to work Lat. and Long, in minutes and tenths, rather than in minutes and eeconds. 3. If upper limb is observed, the correction for 8. D. should be negative, instead of positive. 4. A positive I. C. has been assiuned for illustration throughout the forms; if negative, it should be included with the minus terms of the correction. 6. For time sights and Example II. Multiply 3. 25 by 4. 5 3.25 4.5 1625 1300 Answer : 14. 625 In one of the factors is one decimal, and in the other two ; their sum, 3, is the number of decimals of the product. 266 Multiply . 17 by .06 .17 .06 Answer : . 0102 In each of the factors are two decimals; the pro- duct ought therefore to contain 4 ; and, there being only three figures in the product, a cipher must be prefixed. RULES AND PRINCIPLES OF MATHEMATICS. 267 Example III. Example IV. Multiply 0.5 by 0.7 Multiply .18 by 24 0.5 0.7 .18 24 Ner: 0.35 72 36 Answer: 4.32 Division of Decimals. —Division of decimals is performed in the same manner as in whole num- bers. The number of decimals in the quotient must be equal to the excess of the number of decimals of the dividend above those of the divisor; when the divisor contains more decimals than the dividend, ciphers must be affixed to the right hand of the latter to make the number equal or exceed that of the divisoi. Example I. Divide 14.625 by 3.25 3.25)14.625(4.5 13 00 1625 1625 In thi» example there are two decimals in the divisor and three in the dividend; hence, there is one decimal in the quotient. Example II. Divide 3.1 by .0062 Previous to the division affix three ciphers to the right hand of 3.1, to make the number of deci- mals in the dividend equal the number in the divisor. .0062)3.1000(500 3 10 000 Example III. Divide 17.256 by 1.16 1.16)17.25600(14.875-}- 11 6 565 464 1016 928 880 812 680 580 100 By pursuing the operation further the quotient may be carried out as many decimal placea aa desired. Multiplication of Decimals by Contraction. — The operation of multiplication of decimal fractions may be very much abbreviated when it is not required to retain any figures beyond a certain order or place; this will constantly occur in reducing the elements taken from the Nautical Almanac from Green- wich noon to later or earUer instants of time. In multiplying by this method, omit writing down that part of the operation which involves decimal places below the required order, but mental note should be made of the product of the first discarded figure by the multiplying figure, and the proper number of tens should be carried over to insure accuracy in the lowest decimal place sought. Example: Required the reduction for the sun's declination for 7''. 43, the hourly difference being 58''''. 18, where the product is required to the second decimal. By ordinary method. 58'M8 7^43 By contraction. 58'M8 7\4S 17454 23272 40726 432^^2774 1.74 23.27 407.26 432.'''27 In the contracted method, for the multiplier .03 it is not necessary to record the product of any figures in the multiplicand below units; for the multiplier .4, none below tenths; but in each case observe the product of the left-hand one of the rejected figures and carry forward the number of tens. 268 EULES AND PRINCIPLES OF MATHEMATICS. RULES AND PEINCIPLES OF MATHEMATICS. Reduction op Decimals. — To reduce a vulgar fraction to a decimal, add any number of ciphers to the numerator and divide it by the denominator; the quotient will be the decimal fraction. The decimal point must be so placed that there may be as many figures to the right hand of it as there were added ciphers to the numerator. If there are not so many figures in the quotient place ciphers to the left hand to make up the number. Example I. Reduce -^ to a decimal. 50)L00 .02 Answer. Example II. Reduce | to a decimal. 8)3.000 ,375 Answer. Example III. Reduce 3 inches to the decimal of a foot. Since 12 inches=l foot this fraction is y\. 12)8.00 .25 Answer. Example IV. Reduce 15 minutes to the decimal of an hour. Since 60"^ = 1*^, this fraction is ^. 60)15.00 .25 Answer. Example V. Reduce 17"" 22" to the decimal of an hour. 22= 22* = — 60 0™.37. 17°' 37 = 17^37 =0^289+ Answer. 60 Any decimal may be reduced to lower denominations of the same quantity by multiplying it by the number representing the relation between the respective denominations. Example VI. Reduce 7.231 days to days, hours, minutes, and seconds. Answer: 7^ 5^ 32"» 38».4. 0-1.231 24 0i'.544 60 0'".640 60 924 462 32"'.640 38''.400 51^.544 GEOMETRY. Geometry is the science which treats of the description, properties, and relations of magnitudes, of which there are three kinds; viz, a line, which has only length without either breadth or thickness; a surface, comprehended by length and breadth; and a solid, which has length, breadth, and thickness. Appoint, considered mathematically, has neither length, breadth, nor thickness; it denotes position simply. A line has length without breadth or thickness. A surface has length and breadth without thickness. A solid has length, breadth, and thickness. A straight or right line is the shortest distance between two points on a plane surface. A plane surface is one in which, any two points being taken, the straight line between them lies wholly within that surface. Parallel lines are such as are in the same plane and if extended indefinitely never meet. A circle is a plane figure bounded by a curved line of which every point is equally distant from a point within called the center. The bounding curve of the circle is called the circumference. The radius of a circle, or semidiameter, is a right line drawn from the center to the circumference, as AC (fig. 82); its length is that distance which is taken between the points of the compasses to describe the circle. A diameter of a circle is a right line drawn through the center and termi- nated at both ends by the circumference, as ACB, its length being twice that of the radius. A diameter divides the circle and its circumference into two equal parts. An arc of a circle is any portion of the circumference, as DFE. The chord of an arc is a straight line joining the ends of the arc. It divides the circle into two unequal parts, called segments, and is a chord to them both; thus, DE is the chord of the arcs DFE and DGE. A semicircle, or half circle, is a figure contained between a diameter and the arc terminated by that diameter, as AGB or AFB. Fig. 82. RULES AND PRINCIPLES OF MATHEMATICS. 269 Any part of a circle contained between two radii and an arc is called a sector, aa GCH. A quadrant ia half a semicircle, or one-fourth part of a whole circle, as CAG. All circles are Bupi)08ed to have their circumferences divided into 360 equal parts, called degrees; each degree is divided into 60 equal parts, called minutes; and each minute into 60 equal parts, called seconds; an arc ia measured by the number of degrees, minutes, and seconds that it contains. A sphere is a solid bounded by a surface of which every point is equally distant from a point within, which, as in the circle, is called the center. Substituting surface for circumference, the definitions of the radius and diameter, as given for the circle, apply for the sphere. An angle is the inclination of two intersectmg lines, and is measured by the arc of a circle inter- cepted between the two lines that form the angle, the center of the circle being the point of intersection. A right angle is one that is measured by a quadrant, or 90°. An acute angle ia one which is less than a right angle. An obtuse angle is one which is greater than a right angle. A plane triangle is a figure contained by three straight lines in the same plane. When the three sides are equal, the triangle ia called equilateral; when two of them are equal, it ia called isosceles. When one of the angles is 90°, the triangle la said to be right-angled. When each angle is less than 90°, it is said to be acute-angled. When one is greater than 90°, it ia said to be obtuse-angled. Triangles that are not right-angled are generally called oblique-angled. A quadrilatercd figure is one bounded by four sides. If the opposite sides are parallel, it is called a parallelogram. A parallelogram having all its sides equal and ita angles right angles is called a square. When the angles are right angles and only the opposite sides equal, it is called a rectangle. In a right-angled triangle the side opposite the right angle is called the hypotenuse, one of the other sides is called the base, ancf the third side is called the perpendicular. In any oblique-angled triangle, one side having been assumed as a base, the distance from the intersection of the other two sides to the base or the base extended, measured at right angles to the latter, ia the perpendicular. In a parallelo- gram, one of the sides having been assumed as the base, the distance from ita opposite side, measured at right angles to ita direction, ia the perpendicular. The term oMtude ia sometimes substituted for perpendicular in this sense. Every section of a sphere made by a plane is a circle. A great circle of a sphere is a section of the surface made by a plane which passes through its center. A smaU circle ia a section by a plane which intersects the sphere without passing through the center. A great circle may be drawn through any two points on the surface of a sphere, and the arc of that circle lying between those points is shorter than any other distance between them that can be meaaured upon the surface. All great circlea of a sphere have equal radii, and all bisect each other. The extremities of that diameter of the sphere which is perpendicular to the plane of a circle are called the poles of that circle. In the case of a small circle the poles are named the adjacent pole and the remote pole. All circles of a sphere that are parallel have the same poles. All points in the circum- ference of a circle are equidistant from the poles. In the case of a great circle, the poles are 90° distant from every point of the circle. Assuming any great circle as a primary, all gre&t circlea which paaa through its poles are called ita secondaries. All secondaries cut the primary at right angles. Useful Formulae Derived from Geometry. — In these formulae the following abbreviations are adopted: b, base of triangle or parallelogram. r, radius of sphere or circle. h, perpendicular of triangle or parallelogram. d, diameter of sphere or circle. I, height of cylinder or cone. A, major axis of ellipse. It, ratio of diameter to circumference o, minor axis of ellipse. ( = 3. 141593) . «, side of a cube. Area of parallelogram = b X h. Area of triangle = i b X h. Area of any right-lined figure = sum of the areas of the triangles into which it ia divided. Sum of three angles of any triangle = 180°. Circumference of circle = 27Cr, or Ttd. ltd' Area of circle = itr^, or -j-. Angle aubtended by arc equal to radiua = 57°. 29578. TCd^ Volume of sphere = —q-. Surface of sphere = 7C(P, or 4jrr^. Area of ellipse = — t~- Volume of cube = «*. Volume of cylinder = Area of base X I. Volume of pyramid or cone = Area of base X o . 270 RULES AND PRINCIPLES OF MATHEMATICS. TRIGONOMETRIC FUNCTIONS. The trigonometric functions of the angle formed by any two lines are the ratios existing between the sides of a right triangle formed by letting fall a perpendicular from any point in one line upon the other line; no matter what point is chosen for the perpendicular nor which line, the ratios, and therefore the respective functions, will be the same for any given angle. Let ABO (fig. 83) be a plane right triangle in which C is the right angle; A and B, the other angles; c, the hypotenuse; a and b the sides opposite the angles A and B, respectively. In considering the functions of the angle A, its opposite side, a, is regarded as the perpendicular, and its adjacent side, b, as the base; for the angle B, b is the perpendicular and a the base. Then the various ratios are designated as follows: — , or I^-P-_ , is called the sine of the angle A, abbreviated sin A; c hypotenuse b bas c hypotenuse , is called the cosine of the angle A, abbreviated cos A; a ^^ perpendicular ^ j^ ^jj^^ ^^^ tangent of the angle A, abbreviated tan A; A, or ^f , — , is called the cotangent of the angle A, abbreviated cot A; a perpendicular T' ^^ h qp — ' ^^ called the secant of the angle A, abbreviated sec A; _£. or _5^P?J??"??-, is called the cosecant of the angle A, abbreviated cosec A; a perpendicular 1— cosine A, is called the versed sine of A, abbreviated vers A. 1— sine A, is called the co-versed sine of A, abbreviated covers A. i (1— cosine A) is called the haversine of A, abbreviated hav A. The following relations may be seen to exist between the various functions: -: — r = ^ "*" T = T = coeec A ; sin A c a ' sec A; tan A sin A COB A 1-^ r = ^ = cotA; = X = tan A. Hence the cosecant is the reciprocal of the sine, the secant is the reciprocal of the cosine, the cotan gent is the reciprocal of the tangent, and the tangent equals the sine divided by the cosine. The complement of an angle is equal to 90° minus that angle, and thus in the triangle ABC the angle B is the complement of A. The supplement is equal to 180° minus the angle. From the triangle ABC, regarding the angle B, we have: 6 sin B = — = cos A; tan B = — = cot A; sec B cosec A. BULES AND PRINCIPLES OF MATHEMATICS. 271 Hence it may be seen that the sine of an angle is the cosine of the complement of that angle; the tangent of an angle is the cotangent of its coniple- » ment, and the secant of an angle is the cosecant of its complement. The functions of angles vary in sign according to the quadrant in which the angles are located. Let AA^ and BB' (fig. 84) be two lines at right angles intersecting at the point O, and let that point be the center about which a radius revolves from an initial position OB, euccessively passing the points A, W, A''. In considering the angle made by this radius at any position, P^ V, V\ V'', with the line OB, its position of origin, the functions will g, depend upon the ratios existing between the sides of a right triangle whose base, fe, will always lie within BB'', Bnd whose perpendicular, a, will always be parallel to A A'', while its hypot€nuse,c (of a con- stant length equal to that of the radius) , will de- pend upon the position occupied by the radius. Kow, if OB and OA be regarded as the positive direc- tions of the base and perpendicular, respectively, and OB' and OA' as their negative directions, the sign of the hypotenuse being always positive, the sign of any function may be determined oy the signs of the sides of the triangle upon which it depends. For example, the sine of the angle P'-'OB is -, and since a is positive the quantity has a positive value; its cosine is -, and as b is measured in a n^ative direction from O the cosine must therefore be negative. In the first quadrant, between 0° and 90°, all quantities being positive, all functions will also be positive. In the second quadrant, between 90° and 180°, sin A (=-) is positive; cos A {==-) has a nega- tive value because h is negative; tan A ( =?) is also negative because of h. The cosecant, secant, and cotangent have, as in all cases, the same signs as the sine, cosine, and tangent, respectively, being the reciprocals of those quantities. In the third quadrant, between 180° and 270°, sin A (=^) and cos A { = ^ are both n^ative, because both o and h have negative values; tan A ( =r j is positive for the same reason. In the fourth quadrant, between 270° and 360°, sin A (=^) is negative, cos A ( =-) is positive, and tan A ( =-r j is also negative. From a consideration of the signs in the manner that has been indicated, the following relations will appear: sin A = sin (180° - A) = - sin (180° -f A) = - sin (360° - A) = - sin (- A) cos A = -cos (180°- A) = - cos (180° + A) = cos (360° - A) = cos (- A). tan A = -tan (180° - A) = tan (180° + A) = - tan (360° -A) = - tan (-A' sin A = cos (90° - A) = - cos (90° -H A) = - cos (270° - A) = cos (270° -{■ A \: Any similar relation may be deduced from the figure. It is of great importance to have careful regard for the signs of the functions in all trigonometrical solutions. LOGARITHMS. In order to abbreviate the tedious operations of multiplication and division with large numbers, a series of numbers, called Logarithms, was invented by Lord Napier, by means of which the operation of multiplication may be performed by addition, and that of division by subtraction. Numbers may be involved to any power by simple multiplication and the root of any power extracted by simple division. In Table 42 are given the logarithms of all numbers, from 1 to 9999; to each one must be prefixed an inde% with a period or dot to separate it from the other part, as in decimal fractions; the logarithms of the numbers from 1 to 100 are given in that table with their indices; but from 100 to 9999 the index is left out for the sake of brevity; it may be supplied, however, by the general rule that the index of the logarithm of any integer or mixed number is always one less than the number of integral places in the natural number. Thus, the index of the logarithm of any number (integral or mixed) between 10 and 272 BULES AND PRINCIPLES OF MATHEMATICS. 100 is 1; from 100 to 1000 it is 2 ; from 1000 to 10000 it is 3, etc. ; the method of finding the logarithms from this table will be evident from the rules that follow: To find the logarithm of any number less than 100, enter the first page of the table, and opposite the given number will be found the logarithm with its index prefixed. Thus, opposite 71 is 1.85126, which IS its logarithm. To find the logarithm of any number between 100 and 1000, find the given number in the left-hand col- umn of the table of logarithms, and immediately under in the next column is a number, to which must be prefixed the number 2 as an index (because the number consists of three places of figures), and the required logarithm will be found. Thus, if the logarithm of 149 was required, this number being found in the left-hand column, against it, in the column marked at the top (or bottom) is found 17319, pre- fixing to which the index 2, we have the logarithm of 149 = 2.17319. To find the logarithm of any number between 1000 and 10000, find the three left-hand figures of the given number in the left-hand column of the table of logarithms, opposite to which, in the column that is marked at the top (or bottom) with the fourth figure, is to be found the required logarithm, to which must be prefixed the index 3, because the number contains 4 places of figures. Thus, if the logarithm of 1495 was required, opposite to 149, and in the column marked 5 at the top (or bottom) is 17464, to which prefix the index 3, and we have the logarithm, 3.17464. To find the logarithm of any number above 10000, find the first three figures of the given number in the left-hand column of the table, and the fourth figure at the top or bottom, and take out the corresponding logarithm as in the preceding rule; take also the difference between this logarithm and the next greater, and multiply it by the remaining figure or figures of the number whose logarithm is sought, pointing off aa many decimal places in the product as there are figures in the multiplier. To facilitate the calcula- tion of the proportional parts several small tables are placed in the margin, which give the correction corresponding to the difference, and to the fifth figure of the proposed number. Thus, if the logarithm of 14957 was required, opposite to 149, and under 5, is 17464; the difference between this and the next greater number, 17493, is 29; this multiplied by 7 (the last figure of the given number) gives 203; pointing off the right-hand figure gives 20.3 (or 20) to be added to 17464, which makes 17484; to this, prefixing the index 4, we have the logarithm sought, 4.17484. This correction, 20, may also be found by inspection in the small table in the margin, marked at the top 29; opposite to the fifth figure of the number, 7, in the left-hand column, is the corresponding correction, 20, in the right-hand column. Again, if the logarithm of 1495738 was required, the logarithm corresponding to 149 at the left, and 5 at the top, is, as in the last example, 17464; the difference between this and the next greater is 29; multiplying this by 738 (the given number excluding the first four figures) gives 21402; crossing off the three right-hand figures of this product (because the number 738 consists of three figures) , we have the correction 21 to be added to 17464; and the index to be prefixed is 6, because the given number consists of 7 places of figures; therefore the required logarithm is 6.17485. This correction, 21, may be found aa above, by means of the marginal table marked at the top 29, taking at the side 7.38 (or 7J nearly), to which corresponds 21, as before. To find the logarithm of any mixed decimal number, find the logarithm of the number, aa if it were an integer, by the preceding rules, to which prefix the index of the integral part of the given number. Thus, if the logarithm of the mixed decimal 149.5738 was required, find the logarithm of 1495738, with- out noticing the decimal point; this, in the last example, was found to be 17485; to this prefix the index 2, corresponding to the integral part 149; the logarithm sought will therefore be 2.17485. To find the logarithm of any decimal fraction less than unity, it must be observed that the index of the logarithm of any number less than unity is negative; but, to avoid the mixture of positive and negative (juantities, it is common to borrow 10 in the index, which, in most cases, may afterwards be neglected in summing them with other indices; thus, instead of writing the index — 1, it is written + 9; instead of — 2 we may write -f 8; and so on. In this way we may find the logarithm of any decimal fraction by the following rule: Find the logarithm of a fraction as if it were a whole nvmiber; see how many ciphers precede the first figure of the decimal fraction, subtract that number from 9, and the remainder will be the index of the given fraction. Thus the logarithm of 0.0391 is 8.59218 — 10; the logarithm of 0.25 is 9.39794 — 10; the logarithm of 0.0000025 is 4.39794 - 10, etc. In most cases the writing of — 10 after the logarithm may be dispensed with, as it will be quite apparent whether the logarithm has a positive or a negative index. To find the number corresponding to any logarithm, seek in the column marked at top and bottom the next smallest logarithm, neglecting the index; write down the number in the side column abreast which this is found, and this will give the first three figures of the required number; follow the line until the logarithm next smaller than the given one is found, and the fourth figure of the required number will be at the top and bottom of the column in which this stands; take the difference between this next smaller logarithm and the next larger one in the table, and also the difference between the next smaller logarithm and the given one; entering the small marginal table which has for its heading the first-named difference, and finding in the right-hand column of that table the last-named difference, there will^ appear abreast the latter, in the left-hand column, the fifth figure of the required number. Where it is desired to determine figures beyond the fifth for the corresponding number, the difference between the next lower logarithm and the given one may be divided by the difference between the next lower and next higher ones, and the quotient (disregarding the decimal point, but retaining any ciphers that may come between the decimal point and the significant figures) will be the fifth and suc- ceeding figures of the number sought. Having found the figures of the corresponding number, point off from the left a number of figures which shall be one greater than the index number, and there place a decimal point. In this operation of placing the decimal point, proi)er account must be taken oi the negative value of any index. Thus, if the number corresponding to the logarithm 1.52634 were required, find 52634 in the column marked at the top or bottom, and opposite to it is 336; now, the index being 1, the required number must consist of two integral places; therefore it is 33.6. If the number corresponding to the logarithm 2.57345 were required, look in the column and find in it, against the number 374, the logarithm 57287, and, guiding the eye along that line, find the given BTJLES AND PRINCIPLES OF MATHEMATICS. 273 logarithm, 57345, in the column marked 5; therefore th6 mixed number sought is 3745, and since the index is 2, the integral part must consist of 3 places; therefore the number sought is 374.5. If the index be 1 the number will be 37.45, and if the index be the number will be 3.745. If the index be 8, corresponding to a number less than unity, the number will be 0.03745. Again, if the number corresponding to the logarithm 3.57811 were required, find, against 378 and under 5, the logarithm 57807, the difference between this and the next greater logarithm, 57818, being 11, and the difference between 57807 and the given logarithm, 57811, being 4; in the marginal table headed 11, find in the right-hand column the number 4, and abreast the latter appears the figure 4, which is the fifth figure of the required number; hence the figures are 37854; pointing off from the left 3+1=4 places, the number is 3785.4. If the given logarithm were 5.57811, since the index 5 requires that there shall be six places in the whole number, it is desirable to seek accuracy to the sixth figure. The logarithmic part being the same as in the example immediately preceding, it is found as before that the first four figures are 3785, the difference between the next lower and next greater logarithms is 11, and between the next lower logarithm and the given one is 4; divide 4 by 11 and the quotient is .36; drop the decimal point, annex and point off, and the number required is found to be 378536. It may be remarked that in using five-place logarithm tables it is not generally to be expected that results will be exact bej^ond the fifth figure. To show, at one view, the indices corresponding to mixed and decimal numbers, the following examples are given: Mixed number. Logarithms. 40943.0 Log. 4.61218 4094.3 Log. 3.61218 409.43 Log. 2.61218 40.943 Log. 1.61218 4.0943 Log. 0.61218 Decimal number. Logarithms. 0.40943 Log. 9. 61218-10 0.040943 Log. 8. 61218-10 0.0040943 Log. 7.61218-10 0.00040943 Log. 6.61218-10 0.000040943 Log. 5.61218-10 To perf(yrm multiplication by logarithms, add the logarithms of the two numbers to be multiplied and the sum will be the logarithm of their product. Example I. Multiply 25 by 35. 25 Log. 1.39794 35 Log. L54407 Product, 875 Log. 2.94201 Example II. Multiply 22.4 by 1.8. 22.4. 1.8. .Log. ■ Log. L 35025 0. 25527 Product, 40.32 Log. 1.60552 EXAMPLB III. Multiply 3.26 by 0.0026. 3.26 Log. 0.51322 0.0025 Log. 7.39794 Product, 0.00815 Log. 7.91116 Example IV. Multiply 0.25 by 0.003. 0.25.. 0.003. .Log. 9.39794 .Log. 7.47712 Product, 0.00075 Log. 6.87506 In the last example, the sum of the two logarithms is really 16.87506—20; this is the same as 6.87506—10, or, remembering that the quantity is less than unity, simply 6.87506. To perform division by logarithms, from the logarithm of the dividend subtract the logarithm of the divisor; the remainder will be the logarithm of the quotient. Example I. Divide 875 by 25. 875 Log. 2.94201 25 Log. 1.39794 Quotient, 35 Log. L54407 Example II. Example III. Divide 0.00815 by 0.0025. 0.00815 Log. 7.91116 0.0025 Log. 7.39794 Quotient, 3. 26 Log. 0.51322 Example IV. Divide 0.00075 by 0.025. 0.00075 Log. 6.87506 0.025 Log. 8.39794 Quotient, 0. 03 Log. 8.47712 Divide 40.32 by 22.4. 40.32 Log. 1.60552 22.4 Log. 1.35025 Quotient, 1.8 Log. 0.25527 In Example III both the divisor and dividend are fractions less than unity, and the divisor is the lesser; consequently the quotient is greater than unity. In Example IV both fractions are less than unity; and, since the divisor is the greater, its logarithm is greater than that of the dividend; for this reason it is necessary to borrow 10 in the index before making the subtraction, that is, to regard the logarithm of .00075 as 16.87506 — 20; hence the quotient is less than unity. 21594°— 14 18 274 RULES AND PRINCIPLES OF MATHEMATICS. The arithmetical complement of the logarithm of a number, usually called the cologarithm of the number, and denoted by colog, is the remainder obtained by subtracting the logarithm of the number from the logarithm of unity. It is therefore the logarithm of the reciprocal of the number; and, since the effect of dividing by any number is the same as that of multiplying by its reciprocal, it follows that, in performing division by logarithms, we may either subtract the logarithm of the divisor or add the arith- metical complement of that logarithm. As the addition of a number of quantities can be performed in a single operation, while in subtraction the difference between only two quantities can be taken at a time, it is frequently a convenience to deal with the arithmetical complements rather than with the logarithms themselves. Example III. „. ,.- ^, . 40.32X .00815 Simplify the expression, 92 4y 0025 ' 40.32 : Log. 1.60552 .00815 Log. 7.91116 22.4 Log. 1.35025.... Colog. 8.64975 .0025 Log. 7.39794. . . .Colog. 2. 60206 Example I. Divide 875 by 25. 875 Log. 2.94201 25 Log. 1.39794.. ..Colog. 8.60206 Quotient, 35 Log. 1.54407 Example II. Divide 0.00075 by 0.025. 0.00075 Log. 6.87506 0.026.... Log. 8.39794.... Colog. 1. 60206 Quotient, 0.03 Log. 8.47712 To perform involution by logarithms, multiply the logarithm of the given number by the index of the power to which the quantity is to be raised; the product will be the logarithm of the power sought. Result, 5.868 ....Log. 0.76849 Example I. Required the square of 18. 18 Log. 1.25527 2 Answer, 324 Log. 2.51054 Example II. Required the square of 6.4. 6.4 Log. 0.80618 2 AuBwer, 40.96 Log. L 61236 Example III. Required the cube of 13. 13 Log. 1.11394 3 Answer, 2197 Log. 3.34182 Example IV. Required the cube of 0.25. 0.25 Log. 9.39794 3 Answer, 0.015625 Log. 8.19382 In the last example, the full product of the multiplication of 9.39794—10 by 3 is 28.19382—30, which is equivalent to 8.19382—10. To perform evolution by logarithms divide the logarithm of the number by the index of the power; the quotient will be the logarithm of the root sought. If the number whose root is to be extracted is a decimal fraction less than unity, increase the index of its logarithm by adding a number of tens which shall be less by one than the index of the power before making the division. Example I. Required the square root of 324. 324 Log. 2)2.51055 Answer. 18 Log. L 25527 Example II. Required the cube root of 2197. 2197 Log. 3)3. 34183 Answer, 13 Log. L 11394 Example III. Required the square root of 40.96. 40.96 Log. 2)1.61236 Answer, 6.4 Log. 0.80618 Example IV. Required the cube root of 0.015625. 0.015625 Log. 8.19382 Add 20 to the index 3)28.19382 Answer, 0.25 Log. 9. 39794 In the last example the logarithm 8. 19382—10 was converted into its equivalent form of 28. 19382—30, which, divided by 3, gives 9.39794—10. To find the logarithm of any furtction of an angle, Table 44 must be ena ployed. This table is so arranged that on every page there appear the logarithms of all the functions of a certain angle A, RULES AND PRINCIPLES OF MATHEMATICS. 275 together with those of the angles 90°— A, 90°+ A, and 180°— A; thus on each page may be found the logarithms of the functions of four different auglee. The number of degrees in the respective angles are printed in bold-faced type, one in each corner of the page; the number of minutes corresponding appear in one column at the left of the page and in anothei at the right; the names of the functions to which the various logarithms correspond are printed at the top and bottom of the columns. The invariable rule must be to take the name of the function from the top or the bottom of the page, according aa the number of degrees of the given angle is found at the top or bottom; and to take the minutes from the right or left hand column, according as the number of degrees is found at the right or left hand side of the page; or, more briefly, take names of functions and number of minutes, respectively, from the line and column nearest in position to the number of degrees. Taking, as an example, the thirty-first page of the table, it will be found that 30° appears at the upper left-hand corner, 149° at the upper ri^ht-nand, 59° at the lower right-hand, and 120° at the lower left-hand corner. Suppose that it is desired to find the log. sine of 30° 10^; following the rule given, we find lO'' in the left-hand column and Sine at the top ot the page, and abreast one and below the other is the required logarithm, 9.70115. But if the log. sine of 59° 10' were sought, as 59° appears below and at the right of the page, the logarithm 9.93382 would be taken from the column markea Sine at the bottoni and abreast 10' on the rignt. It may also be seen that log. sin 30° 10'=log. cos 59° 50''=log. cos 120° 10'=log. sin 149° 50'=9.70115, the equality of the functions agreeing with trigonometrical deductions; (in this statement numerical A-alues only are regarded, and not signs; the latter must, of course, be taken into account in all operations) . ExAMPLK I. ' Example II. Required the log. sine, cosecant, tangent, cotan- gent, secant, and cosine of 28° 37'. Log. sin 9. 68029 Log. cot 10. 26313 Log. cosec 10. 31971 Log. sec 10. 05658 Required the log. sine, cosecant, tangent, cotaO' gent, secant, and cosine of 75° 42'. Log. sin 9. 98633 Log. cot 9. 40636- Log. cosec 10. 01367 Log. sec 10. 60730 Log. tan 9. 73G87 Log. cos 9. 94342 I Log. tan 10. 59364 Log. cos 9. 39270 When the angle of which the logarithmic function is required is given to seconds, it becomes necessary to interpolate between the logarithms given for the even minutes next below and next above^ this may be done either by computation or (except in a few cases) by inspection of the table. To mterpolate by computation, let n represent the number of seconds, D the difference between the' logarithms of the next lesser and next greater even minute, and d the difference between the logarithia of the next lesser even minute and that of the required angle. Then, It should be noted when the number of seconds is 30, 20, 15, or some similar number, permitting^ the reduction of the fraction ^ to a simple value, such aa i, i, \, aa the interpolation by this method 60 may thus be made with greater facility. Haviuj? obtained the difference of the logarithm from that of the next lower even minute, it most be applied in the proper direction — that is, if the function is such that its logarithm increases aa the angle increases, the logarithmic difference must be added; but if it decreases, then that difference must be subtracted. For example, let it be required to find the log. sin and log. cosec of 30° ICX 19". The log. sin of 30° 10' is 9.70115; the difference between this logarithm and that of the sine of 30° 11' (9.70137) is + 22^ which is D. Hence, ighthouse Seldom-come-by Harbor: Ship Hill CapeFreels: Gull I Greenspond Island Cape Bona vista: Lighthouse Catalina Harbor: Green I. lighthouse Bonaventure Head Hearts Content: Lighthouse Baccalieu Island : Lighthouse Harbor Grace: Lighthouse on beach. ... Cape St. Francis: Lighthouse St. Johns Harbor: Chain Rock Battery. . Cape Race: Lighthouse Cape Pine: Lighthouse Trepassey Harbor: Shingle Neck Cape St. 'Mary: Lighthouse Little Placentia Harbor: W. side Coopers Cove Burin Island: Lighthouse Laun: Gr. Laun R. C. Church Lat. N. 63 27 00 63 06 00 62 37 00 62 35 00 62 48 00 62 50 00 62 30 00 62 07 00 61 18 00 60 10 00 60 40 00 60 52 00 60 33 00 61 21 00 61 40 00 60 00 00 59 48 00 59 07 00 57 35 00 57 00 00 56 32 45 55 27 04 55 13 33 54 55 50 54 26 55 54 00 05 53 50 00 53 42 37 53 34 25 53 26 00 52 40 07 52 21 16 52 15 36 52 06 00 51 53 00 51 38 48 50 42 10 49 59 54 49 53 00 49 45 29 49 35 40 49 41 20 49 36 50 49 15 20 49 04 20 48 42 01 48 30 15 48 16 55 47 53 10 48 08 58 47 42 45 47 48 30 47 34 02 46 39 24 46 37 04 46 43 20 46 49 34 47 17 55 47 00 26 46 56 30 Long. W. Lun. Int. H.W. 76 30 00 77 50 00 78 08 00 77 33 00 74 00 00 75 20 00 74 03 00 72 25 00 70 02 00 67 05 00 67 50 00 64 40 00 64 12 00 65 00 00 64 30 00 64 28 00 64 07 15 63 20 00 61 20 00 62 07 00 61 40 13 60 12 34 59 08 01 57 56 40 57 12 40 56 31 31 56 23 00 56 59 50 55 58 39 55 35 48 55 44 29 55 38 08 55 32 20 55 41 00 55 22 10 55 25 12 55 35 30 55 21 33 55 37 17 53 10 56 53 45 00 54 47 35 54 12 00 53 25 12 53 37 45 53 04 42 53 02 40 53 23 35 53 23 20 52 47 42 53 08 11 52 47 20 52 40 54 53 04 30 53 31 55 53 22 10 54 11 42 53 58 43 55 08 49 55 32 00 A. m. "shs 8 00 7 00 7 00 5 30 6 10 6 27 6 38 6 30 L.W. 7 23 7 15 7 12 6 50 6 50 8 20 8 05 K m. "'2'46 1 48 48 48 11 43 12 23 15 26 18 Range. 13.5 5.0 5.2 6.5 6.9 7.0 6.0 5.0 3.5 1 11 4. 1 "i 03' '*3."3 1 01 38 38 2 08 1 53 3.3 6.5 6.6 7.2 7.0 Neap. ft. 2.0 2.1 3.0 3.2 3.2 2.8 2.3 L6 L9 L5 L5 3.0 3.1 3.3 3.2 Page 280] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. I M Place. St. Pierre: U. S. Coast Survey Station... Brunet Island: Mercers Hd. lighthouse.. Boar Islands: Burgeo I. lighthouse La Poile Bay: Gr. Espic Church Cape Ray: Lighthouse. . . : Codroy Island: S. side Boat Harbor Cape St. George: Red I., SE.pt Cow Head: NW. extreme Port Saunders: Two Hills Pt Rich Point: Lighthouse F^roUe Pena: New FeroUe Pt Flower Cove: Capstan Pt Green Island: 150 fms. from NE. end. . . Cape Norman : Lighthouse Chateau Bay: S. pt. Castle I Amour Point: Lighthouse Wood Island: S. pt Greenly Island: Lighthouse Bradore Bay: Obs. Spot, Jones Pt Old Fort Island: Center Great Mekattina Island : SE. pt Mekattina Harbor: S. point of Dead Cove Little Mekattina I.: S. pt. C. McKinnon St. Mary Reefs South Makers I^edge Cape Whittle Natashquan Point: S. edge Clearwater Point: SW. extreme Carousel Island : Lighthouse Point de Monts: Lighthouse Quebec: Mann's Bastion, Citadel Quebec: Bonner's Hill Obsy Montreal: St. James Cathedral Ottawa: Dominion Observatory Father Point: Lighthouse Cape Chatte: Extreme Cape Magdalen : Lighthouse Cape Rosier: Lighthouse Cape Gasp4: Lighthouse Anticosti Island: Heath Pt. lighthouse. . SW. pt. lighthouse. . . Bonaventure Island : E. pt Leander Shoal Macquereau Point Chaleur Bay: Carlisle Dalhousie I Miscou Island: Birch Pt. lighthouse Miramichi Bay: Portage I., N. pt Point Escumenac: Lighthouse North Point: Lighthouse Malpeque Baj^: Royalty Pt East Point: Lighthouse Charlottetown: Blackhouse Pt. light.... Gt. Bird Rock: Lighthouse East Island: E. extreme Entry Island : Lighthouse Amherst Hbr.: N. side of entrance Deadman Rock: W. pt Lat. N. 46 46 51 47 15 30 47 35 13 47 39 50 47 37 00 47 52 30 48 33 48 49 55 20 50 38 30 50 41 50 51 02 00 51 17 25 51 24 10 51 38 00 51 58 00 51 27 35 51 22 45 51 22 26 51 27 22 51 21 40 50 47 30 50 46 44 50 31 10 50 14 00 50 09 30 50 11 00 50 06 00 50 12 27 50 05 40 49 19 35 46 48 23 46 47 59 45 29 57 45 23 30 48 31 25 49 06 00 49 15 40 48 51 37 48 45 15 49 05 20 49 23 45 48 29 30 48 24 00 48 12 00 48 01 00 48 04 24 48 01 07 47 14 00 47 05 00 47 03 46 46 33 56 46 27 15 46 11 36 47 50 40 47 37 40 47 16 30 47 14 23 47 16 03 Long. W. 56 10 36 55 51 40 57 36 52 58 24 10 59 18 00 59 23 40 59 13 10 57 50 00 57 17 07 57 25 00 57 03 50 56 44 45 56 33 40 55 53 52 55 50 20 56 51 05 57 08 00 57 10 04 57 13 21 57 46 00 58 51 30 58 59 20 59 20 25 59 45 00 59 57 00 60 08 00 61 44 00 63 27 03 66 22 44 67 21 55 71 12 19 71 13 10 73 34 08 75 42 59 68 27 40 66 46 00 65 19 30 64 12 00 64 09 35 61 42 30 63 35 46 64 08 00 64 18 00 64 46 30 65 19 00 66 22 10 64 29 20 65 02 00 64 47 33 63 58 49 63 41 35 61 57 35 63 06 58 61 08 32 61 24 30 61 41 20 61 49 38 62 12 25 Lun. Int. Range. H.W. h. m. 8 23 8 53 8 22 8 50 8 50 9 40 1 25 1 43 1 48 6 07 1 52 1 46 1 33 1 25 1 20 1 25 4 20 5 15 8 17 11 07 L.W. Spg. h. m. 2 11 2 41 2 10 2 38 ft. 6.6 6.5 6.2 6.0 2 32 4.3 3 13 4.9 6 45 4.0 7 05 7 18 54 8.1 10.8 14.6 7 33 7 13 6 50 6 40 12.0 10.5 6.4 5.5 6 35 6 40 3.6 4.9 7 33 8 07 9 10 8 25 10 59 4.7 4.8 8.1 4.0 2.3 11 00 11 55 2 20 4 23 2.4 1.8 1.4 6.4 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OP NORTH AMERICA— Continued. [Page 281 Place. Lat. N. Long. W, Lun. Int. Range. H. W. L.W Neap. St. Paul Island: Lighthou.se, NE. end. Lighthouse, SW. end. Cape North : Lighthouse St. Anns Harbor: E. pt. entrance.. . Sydney Harbor: Lighthouse Scatan Island: Lighthouse, NE. pt . Louisburg: Lighthouse, NE. pt Madame Island: S. pt Port Hood : Just-au-corps I Sable Island: Lighthouse, E. end. Pictou: Customhouse Cape St. George North Canso: Lighthouse, NW. entrance. Arichat Harbor: R. C. Church steeple Cape Canso: Cranberry I., lighthouse. . . , White Head Island : Lighthouse , Green Island : Lighthouse Wedge Island : Lighthouse Halifax: Dockyard observatory Sambro Island : Lighthouse Margaret Bay: Shut-in I Tancook Island Lunenburg : Battery Pt. light Cape La Have : Black Rock CoflBn Island : Lighthouse Little Hope Island: Lighthouse Shelburne Hbr.: Two lights, McNutts I. Cape Sable: Lighthouse Seal Island : Lighthouse Yarmouth : Cape Fourchu light Cape St. Mary Bryer Island : Lighthouse Annapolis Harbor: Prim Pt. light Haute Island : Lighthouse Cape Chignecto Bumtcoat Head: Lighthouse Cape Enrag^: Lighthouse Cape Quaco: Lighthouse St. Johns: Partridge I. light Cape Lepreau : Lighthouse L'Etang Harbor: S. pt. tower St. Andrew: S. pt. li^t Campo Bello Island: Lighthouse, N. pt. . Grand Manan Island: Lighthouse, NE. pt. Gannet Rock: Lighthouse, NE. pt Machias Island : Lighthouse Calais: Astronomical station Eastport: Cong. Church Quoddy Head : Lighthouse Machias: Town Hall Petit Manan Island: Lighthouse. Bakers Island : Lighthouse Mount Desert Rock: Lighthouse. Bangor: Thomas Hill Belfast: Methodist Church Rockland : Episcopal Church Matinicus Rock : Lighthouse Monhegan Island: Lighthouse. . . Seguin Island : Lighthouse 47 13 50 47 11 20 47 01 45 46 21 00 46 12 25 46 02 15 45 54 34 45 28 00 46 00 00 43 58 14 45 40 50 45 52 00 45 41 42 45 30 48 45 19 49 45 11 58 45 06 15 45 00 35 44 39 38 44 26 10 44 34 00 44 29 00 44 21 45 44 12 00 44 02 00 43 48 30 43 37 15 43 23 19 43 23 34 43 47 28 44 05 20 44 14 57 44 41 34 45 14 55 45 19 00 45 18 40 45 35 34 45 19 30 45 14 20 45 03 40 45 04 00 45 04 06 44 57 40 44 45 52 44 30 38 44 30 07 45 11 05 44 54 15 44 48 55 44 43 01 44 22 03 44 14 29 I 43 58 08 ' 44 48 23 ! 44 25 29 ! 44 06 06 i 43 47 03 43 45 53 I 43 42 26 60 08 32 60 09 50 60 23 27 60 27 00 60 12 50 59 40 25 59 59.26 61 03 00 61 36 00 59 44 15 62 42 10 61 52 00 61 29 10 61 01 47 60 55 41 61 08 14 61 32 40 61 62 45 63 35 22 63 33 30 63 54 00 64 06 00 64 17 35 64 18 00 64 37 30 64 47 15 65 15 45 65 37 11 66 00 52 66 09 21 66 12 40 66 23 38 65 47 20 65 00 45 64 57 00 63 48 30 64 46 55 65 32 00 66 03 20 66 27 40 66 49 00 67 02 52 66 54 10 66 44 00 66 47 00 67 06 13 67 16 50 66 59 14 66 57 04 67 27 22 67 51 51 68 11 58 68 07 44 68 46 59 69 00 19 69 06 52 68 51 28 69 18 59 69 45 32 8 30 8 35 8 25 8 10 7 45 7 55 9 05 9 34 9 20 9 26 7 55 7 43 7 45 7 34 "7'32 "7'39 8 17 9 35 10 00 10 29 10 49 11 07 27 11 21 11 07 11 04 11 09 11 00 11 02 io'Si 11 36 11 09 11 02 23 11 35 11 09 10 45 h. tn. 2 12 ft. 2.7 2 17 2 13 2 05 3.1 6.0 5.0 1 35 1 47 2 47 5.0 5.0 3.5 13 00 10 47 36 38 3.9 2.8 3.1 5.0 6.5 1 46 'i'36" "i"36" 5.2 "7.*i" 2 05 3 23 3 41 8.5 12.8 16.0 4 36 4 41 5 27 20.8 27.5 33.0 7 27 50.5 30.0 23.9 24.5 23.3 24.9 5 21 22.5 4 56 5 40 5 05 18.0 23.3 20.9 4 59 15.5 6 47 5 22 4 55 4 31 15.1 11.7 11.0 10.2 ft. 1.4 1.6 3.7 3.1 L8 2.0 L4 L6 3.1 4.0 4.1 3.2 '4.'4 T3 5.2 9.5 1L8 15.4 20.4 24.4 37.4 22.2 17.7 18.2 17.1 18.2 16.7 13.2 17.1 15.2 n.3 n.o 8.6 8.1 7.5 Page 282] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OP NORTH AMERICA— Continued. Place. Lat. N. Long. W. Lun. Int. Range. H.W. L.W. Spg. Bath: Winter St. Church Brunswick : College spire Augusta: Baptist Church Portland: Customhouse Portland Head lighthouse . . . Cape Elizabeth : Lighthouse (west) Wood Island : Lighthouse Boon Island : Lighthouse Whale Back; Lighthouse Portsmouth: Navy-yard flagstaff Fort Constitution Hampton: Baptist Church Isles of Shoals: White I. lighthouse Newburyport: Academy Plum I. lighthouse Ipswich: Lighthouse (rear) Annisquam Harbor: Lighthouse Cape Ann: Thatchers I. lighthouse (N.) Gloucester: Universalist Church Ten-pound I. lighthouse... Beverly: Hospital Pt. lighthouse Salem: Derbys WTiarf lighthouse Marblehead: Lighthouse Cambridge: Harvard Observatory Boston: Navy-yard flagstaff State House Little Brewster I. lighthouse. . Minots Ledge: Lighthouse Plymouth: Pierhead Gurnet lighthouse Barnstable : Lighthouse Cape Cod : Highlands lighthouse Chatham: Lighthouse (south) Monomoy Point : Lighthouse Nantucket: South Church Nantucket Shoals: Lightship Sankaty Head : Lighthouse .' Tarpaulin Cove: Lighthouse Vineyard Haven: W. Chop lighthouse. Gay Head: Lighthouse Cuttyhunk: Lighthouse New Bedford : Baptist Church Sakonnet Point : Lighthouse Beaver Tail : Lighthouse Newport: Flagstaff, torpedo station Bristol Ferry: Lighthouse Providence : Brown University Obsy . . . Point Judith: Lighthouse Block Island: Lighthouse (SE.) Watch Hill Point: Lighthouse Montauk Point: Lighthouse Stonington: Lighthouse New London : Groton Monument Little Gull Island : Lighthouse Gardners Island: Lighthouse, N. pt Plum Island : Lighthouse, W. pt Saybrook: Lighthouse, Lynde Pt New Haven: Yale University Obsy 43 54 55 43 54 29 44 18 52 43 39 28 43 37 23 43 33 51 43 27 24 43 07 17 43 03 32 43 04 56 43 04 16 42 56 15 42 58 02 42 48 30 42 48 55 42 41 07 42 39 43 42 38 21 42 36 46 42 36 07 42 32 48 42 31 00 42 30 20 42 22 48 42 22 22 42 21 28 42 19 41 42 16 11 41 58 44 42 00 12 41 43 20 42 02 23 41 40 17 41 33 34 41 16 55 40 37 05 41 17 01 41 28 08 41 25 51 41 20 55 41 24 52 41 38 10 41 26 30 41 26 58 41 29 07 41 38 34 41 50 21 41 21 40 41 09 10 41 18 14 41 04 16 41 19 31 41 21 16 41 12 23 41 08 29 41 10 25 41 16 17 41 19 22 69 49 00 69 57 44 69 46 37 70 15 18 70 12 30 70 12 11 70 19 46 70 28 37 70 41 49 70 44 22 70 42 34 70 50 12 70 37 25 70 52 28 70 49 10 70 46 00 70 40 55 70 34 31 70 39 59 70 39 58 70 51 23 70 53 03 70 50 03 71 07 46 71 03 05 71 03 50 70 53 26 70 45 35 70 39 12 70 36 04 70 16 52 70 03 40 69 57 01 69 59 39 70 05 57 69 36 33 69 57 57 70 45 29 70 36 01 70 50 08 70 57 01 70 55 36 71 13 30 71 24 00 71 19 40 71 15 39 71 23 59 71 28 55 71 33 08 71 51 32 71 51 27 71 54 49 72 04 47 72 06 26 72 08 44 72 12 43 72 20 37 72 55 09 h. m. 12 13 2 54 11 06 11 12 11 23 11 19 11 23 11 17 11 13 11 02 11 16 11 09 11 27 'ii'69 11 23 11 36 12 11 12 00 04 7 51 11 34 7 31 7 36 7 57 7 40 7 40 7 48 7 53 8 12 7 32 7 33 8 49 8 20 9 09 9 26 9 26 9 40 10 29 11 08 h. m. 6 16 10 18 4 51 4 51 5 09 4 58 5 10 5 04 5 00 4 49 5 03 4 57 5 17 '4 56 5 11 5 25 5 57 5 48 6 00 1 51 4 33 1 20 59 1 18 1 05 1 09 1 00 40 57 1 17 1 25 2 38 2 03 3 03 3 32 3 04 3 35 4 11 4 54 ft. 7.9 4.9 10.1 10.2 10.5 10.0 9.1 10.1 10.1 10.2 10. 6 10.6 11.0 16.9' 10.8 11.6 4.6 4.3 3.8 2.8 2.0 3.7 4.3 5.2 4.5 4.7 4.4 5.2 5.4 3.8 3.7 3.2 2.3 3.2 2.9 3.0 2.5 4.3 7.0 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OP NORTH AMEBIC A— Continued. [Page 283 Place. Bri('geport Harbor: Lighthouse Norwalk Island : Lighthouse Shinnecock Bay: Lighthouse Fire Island : Lighthouse Albany : New Dud ley Observatory . New York: Nav>'-yard flagstaff CityHall Fort Wadeworth: Lighthouse Sandy Hook: Lighthouse (rear) Lightship Navesink Highlands: N. lighthouse Bamegat Inlet: Lighthouse Tuckers Beach : Lighthouse Absecon Inlet: Lighthouse Five Fathom Bank: Lightship Cape May: Lighthouse Philadelphia, Pa.: University Obsy Navy-yard fla^aff, League I Wilmington, Del. : Town Hall Cape Henlopen : Lighthouse Aesateague Island : Lighthouse Hog Island: Lighthouse Cape Charles: Lighthouse Baltimore: Johns Hopkins Obsy Annapolis: Naval Academy Observatory Point Lookout: Lighthouse Washington, D. C: Navy-yard flagstaff.. Naval Observatory . . Capitol dome Old Point Comfort: Lighthouse Norfolk: Navy-yard flagstaff Richmond, Va. : Capitol Cape Henry : Lighthouse Elizabeth City: Courthouse... Eden ton: Courthouse Currituck Beach: Lighthouse., Bodie Island: Lighthouse Cape Hatteras: Lighthouse — Ocracoke : Lighthouse Newbem : Episcopal spire Cape Lookout: Lighthouse — Beaufort, N. C: Courthouse... Frying-Pan Shoals: Lightship. Georgetown : Episcopal Church Lighthouse, North I Cape Romain: Lighthouse Charleston: Lighthouse, Morris I St. Michael's Church Beaufort, S. C: Episcopal Church Port Royal: Martins Industry lightship. Tybee Island: Lighthouse.. Savannah: Exchange spire. Sapelo Island: Lighthouse. Darien: Winnowing House. St. Simon: Lighthouse Brunswick: Academy Lat. N. 41 09 24 41 02 56 40 51 03 40 37 57 42 39 13 40 42 02 40 42 44 40 36 20 40 27 42 40 28 15 40 23 48 39 45 52 39 30 22 39 21 59 38 47 20 38 55 59 39 58 02 39 53 14 39 44 27 38 46 42 37 54 40 37 23 46 37 07 22 39 17 48 38 58 53 38 02 19 38 52 30 38 55 14 38 53 20 37 00 06 36-49 33 37 32 16 36 55 35 36 17 58 36 03 24 36 22 36 35 49 07 35 15 17 35 06 32 35 06 21 34 37 22 34 43 05 33 34 26 33 22 08 33 13 21 33 01 06 32 41 43 32 46 34 32 26 02 32 05 33 32 01 20 32 04 52 31 23 28 31 21 54 31 08 02 31 08 51 Long.W. 73 10 49 73 25 11 72 30 16 73 13 08 73 46 42 73 58 51 74 00 24 74 03 15 74 00 09 73 50 09 73 59 10 74 06 24 74 17 08 74 24 52 74 34 36 74 57 39 75 16 39 75 10 32 75 33 03 75 05 03 75 21 23 75 41 59 75 54 24 76 36 30 76 29 08 76 19 20 76 59 45 77 03 57 77 00 36 76 18 24 76 17 46 77 26 04 76 00 27 76 13 23 76 36 31 75 49 51 75 33 49 75 31 .16 75 59 11 77 02 24 76 31 29 76 39 48 77 49 12 79 16 49 79 10 55 79 22 19 79 52 54 79 55 49 80 40 27 80 33 15 80 50 37 81 05 26 81 17 01 81 25 39 81 23 30 81 29 26 Lun. Int. H. W. h. m. 11 09 11 03 7 48 7 19 5 13 8 44 7 41 7 30 7 50 7 48 9 59 8J6 1 28 53 12 00 8 17 8 03 6 34 4 39 31 7 42 8.44 9 05 4 30 7 53 7 37 7 00 6 29 7 21 8 39 "659 7 20 8 10 7 10 8 13 7 30 7 40 7 30 8 00 Range. L. W, 5 04 4 56 1 38 1 20 46 2 49 1 38 1 23 1 43 1 42 3 57 1 47 8 58 8 02 6 40 1 50 2 19 44 10 53 6«2 1 56 2 17 2 47 11 55 1 43 1 26 45 20 1 08 Spg. 3 38 056' 1 10 2 06 1 04 3 07 1 24 1 44 1 27 1 57 ft. 8.4 8.2 3.0 2.2 2.8 5.3 5.4 5.6 2.7 4.2 4.7 "5.6' 6.2 7.0 6.7 5.4 3.0 L4 LO 1.7 3.5 3.0 3.2 4.3 3.2 3.4 2.2 4.4 3.3 4.3 ■5.'9" 6.0 8.5 7.9 7.6 8.4 7.5 7.5 7.8 Neap. ft. 5.9 5.7 2.0 1.4 1.8 3.4 3.5 3.6 L7 2.7 3.0 '3*6 4.4 5.2 4.9 3.5 2.0 LO 0.8 LI 2.5 2.0 2.1 2.9 2.1 2.2 L5 3.0 2.3 2.9 4.1 4.2 5.9 5.5 5.3 5.8 5.2 5.3 5.4 Page 284] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. Place. Amelia Island : Lighthouse Femandina: Astronomical station St. Johns River: Lighthouse Jacksonville: Methodist Church St. Augustine: Presbyterian Church. . . . Lighthouse Cape Canaveral : Lighthouse Jupiter Inlet: Lighthouse Fowey Rocks: Lighthouse Carysf ort Reef : Lighthouse Alligator Reef : Lighthouse Sombrero Key : Lighthouse Sand Key: Lighthouse Key West: Lighthouse Loggerhead Key : Lighthouse Sanibel Island : Lighthouse Gasparilla Island : Lighthouse Tampa Bay: Egmont Key light Cedar Keys: Ast. station, Depot Key. .. Seahorse Key light St. Marks: Fort St. Marks Apalachicola: Flagstaff Cape St. George: Lighthouse Cape San Bias: Lighthouse Pensacola: Lighthouse Navy-yard chimney Sand Island : Lighthouse (front) Mobile Point: Lighthouse Mobile: Episcopal Church Horn Island : Lighthouse East Pascagoula: Coast Survey station. . . Mississippi City : Coast Survey station . . . Ship Island: Lighthouse Cat Island : Lighthouse Chandeleur : Lighthouse Mouth Mississippi River: Pass a 1' Outre light S. Pass light (East Jetty). SW. Pass light New Orleans: United States Mint Barataria Bay: Lighthouse Timbalier Island: Lighthouse Ship Shoal : Lighthouse Southwest Reef : Lighthouse Calcasieu Pass : Lighthouse Sabine Pass: Lighthouse Galveston : Cathedral, N . spire Lighthouse, Bolivar Pt Matagorda: Coast Survey station Lighthouse Indianola: Coast Survey station Lavaca: Coast Survey station Aransas Pass : Lighthouse Brazos Santiago: Light, S. end Padre I.. Point Isabel : Lighthouse Rio Grande del Norte: Obsy. N. side of entrance Lat. N. 30 40 23 30 40 18 30 23 36 30 19 43 29 53 20 29 53 07 28 27 37 26 56 54 25 35 25 25 13 17 24 51 02 24 37 36 24 27 10 24 32 58 24 38 04 26 27 11 26 43 06 27 36 04 29 07 29 29 05 49 30 09 03 29 43 32 29 35 18 29 40 00 30 20 47 30 20 49 30 11 19 30 13 44 30 41 26 30 13 23 30 20 42 30 22 54 30 12 53 30 13 57 30 02 58 29 11 30 28 59 28 28 58 22 29 57 46 29 16 30 29 02 49 28 54 56 29 23 36 29 46 55 29 43 04 29 18 17 29 22 05 28 41 29 28 20 18 28 32 28 28 37 36 27 51 53 26 04 16 26 04 36 25 57 22 Long. W. 81 26 26 81 27 47 81 25 27 81 39 14 81 18 41 81 17 12 80 32 30 80 04 48 80 05 41 80 12 40 80 37 08 81 06 40 81 52 40 81 48 04 82 55 42 82 00 43 82 15 34 82 45 40 83 01 57 83 03 58 84 12 42 84 59 12 85 02 54 85 21 30 87 18 32 87 16 06 88 03 02 88 01 26 88 02 28 88 31 39 88 32 45 89 01 57 88 57 56 89 09 41 88 52 19 89 02 28 89 08 08 89 23 30 90 03 28 89 56 43 90 .21 25 91 04 15 91 30 14 93 20 43 93 51 00 94 47 26 94 46 00 95 57 26 96 25 28 96 31 01 96 37 21 97 03 23 97 10 00 97 12 28 97 08 57 Lun. Int. H. W. L. W ft. m. 7 39 7 36 8 12 8 00 8 00 8 20 8 21 8 22 8 24 8 40 9 20 9 44 12 17 42 11 32 42 2 00 [12 10] [11 10] iii"28"] [11 25 [1 35 [12 00 [0 20 [0 23] [11 53] [11 15] [10 55] [10 54] [11 00 [11 50 [0 18 [0 40] 2 17 3 17 [4 18] [4 07] [4 35] [4 25] [155] ft. m. 1 31 1 33 00 52 00 16 08 00 05 20 36 21 6 10 6 19 5 07 7 13 8 30 [5 35] [4 55] ■i4"26i 3 09 6 50 5 40 5 45 [6 35] [5 33] [5 00] [4 42] [4 4lj 4 47 5 38 6 33 6 56 8 41 9 36 [10 33] [10 23] [10 47] [10 35] [8 03] Range. Spg. Neap. 6.9 5.4 5.3 5.9 L8 2.6 2.7 2.6 1.9 L5 1.6 1.4 2.3 1.4 L8 3.1 2.6 [2.5] [2.1] iL7i [1-5] 2.1] '2.0] '2.3] [2.1] [L8] [L6] [1.7] [L9] 0.9 [1.6] [1-6] [1.4] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued. [Page 285 Place. Lat. N. Long. W. Lun. Int. H.W. Range. L.W, Neap. San Fernando River: Entrance Santander River: Entrance Mount Mecate: Summit Tampico: Lighthouse Cape Roxo Lobos Cav: Lighthouse Tuxpam Keefs: Middle islet Mexico: Tacubaya National Obey Bemal Chico: Middle of islet Zempoala Point : Extreme Vera Cruz : San Juan d'UUoa light Sacrificios Island Orizaba Mountain : 17,400 feet Cofre de Perote Mount: 14,000 feet Alvarado : E . side of entrance Roca Partida: Summit Tuxtla, volcano : Summit Montepio : Landing place Zapotiilan Point: Lighthouse San Juan Point : Lighthouse Puerto Mexico: Lighthouse Santa Ana Lagoon : Entranpe Tupilco River: Entrance Tabasco River: Lighthouse Carmen Island: NE. pt Laguna de Terminos: Vigia tower, W. end Carmen I Paypoton Mount: Summit Lerma: Church Campeche: Lighthouse Fort San Josd Point Palmas Sisal: Fort light Madagascar Reef : Center Progreso: Lighthouse SUan: Village Lagartoa: Village Cape Catoche: Lighthouse Areas Cays : Lighthouse Obispo Shoal : 16-foot spot New Bank : Center Triangles, E. reef: Beacon Triangles, W. reef: Cay at SW. end. Bajo N'uevo Reef: Center Arenas Cays: NW. Cay Alacran Reef: Perez Cay Contoy Island : Lighthouse Mugeres Island : Lighthouse Canciin IslanS : Nisuc Pt Cozumel Island: N. pt. lighthouse. . S. pt. lighthouse... Ascension Bay: Allen Pt Chinchorro Bank: Cayo Lobos light. Half moon Cay: Lighthouse Mauger Cay, NW. end: Lighthouse. Glover Reef: SW. Cay English Cay : Lighthouse St. Georges Cay: Center 25 23 40 23 46 20 22 38 40 22 15 50 21 35 00 21 28 12 21 03 00 19 24 18 19 39 50 19 27 26 19 12 30 19 10 10 19 04 00 19 29 30 18 49 00 18 44 00 18 29 00 18 40 00 18 34 00 18 19 45 18 08 56 18 18 49 18 26 44 18 39 30 18 47 08 18 38 44 19 38 00 19 48 24 19 50 20 19 51 36 21 02 00 21 10 06 21 26 30 21 17 00 21 23 00 21 36 30 21 35 50 20 12 45 20 29 00 20 32 00 20 54 54 20 58 00 21 50 00 22 07 10 22 23 36 21 33 00 21 12 00 21 03 00 20 35 50 20 16 20 19 46 55 18 23 20 17 12 15 17 36 15 16 42 20 17 19 30 17 33 15 97 21 25 97 46 55 98 04 55 97 49 55 97 22 00 97 13 00 97 13 35 99 11 38 96 24 39 96 20 22 96 07 57 96 05 30 97 15 55 97 07 30 95 44 48 95 11 14 95 08 00 95 05 12 94 50 00 94 38 57 94 24 47 93 51 53 93 25 25 92 42 00 91 30 50 91 50 17 90 43 27 90 36 11 90 32 20 90 30 51 90 22 00 90 02 37 90 18 27 89 39 30 88 54 27 88 10 27 87 04 10 91 57 45 92 13 27 91 52 27 92 12 47 92 18 57 92 04 26 91 24 21 89 41 45 86 48 00 86 43 39 86 46 45 86 43 55 86 59 04 87 28 27 87 23 40 87 32 30 87 46 30 87 50 .TO 88 03 20 88 04 45 A. m. A. m. [106] [7 19] [1.3] [2 49] [8 38] [2.4] [12 16] [6 00] [1-6] 2 59 9 28 2.1 1.3 10 20 4 10 1.8 0.9 9 30 3 19 [12 06] [5 50 [12 00] 9 20 8 20 L5 [1-6] 0.8 [5 45] [1.6; 3 08 L6 0.9 2 08 L5 0.8 Page 286] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— Continued . 1 8 Place. Lat. N. Long. W. Ltin Int. Range. H.W. L. W. Spg. Neap. s i « h 9 V a e H ei s « % « e ■ ** s 0" m 6 Sand-Fly Cays: Hut, S. end 16 57 50 16 48 50 17 29 20 16 57 40 16 47 45 16 48 10 16 30 54 16 14 15 15 54 00 15 49 45 15 38 00 15 24 20 15 52 20 15 57 45 16 08 00 15 47 11 15 48 45 15 38 00 15 55 45 16 03 40 15 58 00 16 18 00 16 24 20 16 28 00 18 44 00 17 24 21 15 53 00 16 00 00 15 51 50 15 48 50 15 23 40 15 00 04 16 03 30 15 52 00 15 51 00 15 08 50 15 07 00 14 21 12 16 54 00 15 47 45 14 21 33 14 08 00 14 30 00 13 34 30 13 22 54 12 31 40 12 24 00 12 10 00 12 22 35 12 20 39 11 59 00 12 17 30 12 09 17 10 56 15 10 02 00 10 00 16 O / If 88 06 05 88 05 36 88 11 20 88 13 48 88 15 15 88 37 40 88 22 13 88 35 51 88 56 20 88 46 22 89 01 36 89 09 15 88 33 22 88 38 50 88 20 15 88 04 31 87 27 46 86 55 00 85 59 18 86 59 15 86 32 09 86 34 27 86 18 41 85 55 00 84 02 00 83 56 25 85 27 10 85 03 00 84 38 33 84 17 10 83 42 36 83 09 22 83 08 20 82 23 27 82 18 07 82 42 08 82 20 00 82 45 57 80 51 27 79 50 53 80 15 20 81 08 21 81 07 21 80 05 05 81 21 26 8l 43 06 81 27 53 81 49 54 83 23 10 83 37 12 83 41 57 82 58 35 83 03 35 83 42 15 83 48 30 83 00 57 ft. TO. ft. m. ft. ft. South Water Cay: Center Belize: Fort George light 8 00 1 50 L5 0.8 North Standing Creek : Entrance Sittee Point: Cay Cockscomb Mount: Summit, 4,000 feet... Placentia Point: Huts on point Icacos Point: S. extreme Sarstoon River: Entrance Dulce Ri ver : Entrance, W . side 9 00 2 60 2.0 1.1 Dulce Gulf: Fort St. Philip Izabal Hospital Bight: Hut, N. pt. of entrance.. Cape Three Points: NW. extreme Seal Cays: S. Cav 1 Omoa: Entrance Cape Triunfo : Bluff pt 1 Congrehoy Peak: Summit, 8,040 feet Truxillo: Fort 1 Utilla Island : S. Cay Hog Islands: Highest hill on W. islet Roatan: Center of Coxen Cay ! 7 35 1 23 3.5 1.8 Port Royal, NW. pt. of Geoi^e Cay Bonacca Island: Summit, 1,200 feet Misteriosa Bank: S. Point 8 50 2 38 1.5 0.8 Swan Islands: Light on W. pt. of west island Great Rock Head : Bluff extreme Cape Camaron Brewers Lagoon: E. side of entrance. . . . Patuca River: E. side of entrance Carataska Lagoon: E. side of entrance Cape Gracias-d-Dios: Lighthouse 10 20 4 07 2.0 1.1 Caxones Reef: Great Hobby Islet Gorda Bank: Gorda Cay Farrall Rock: Center Half moon Cay: Center Alargate Reef: E. pt Mosquito Cays: S. end Rosalind Bank : N W. extreme Serranilla Bank: Beacon Cay 4 00 4 00 10 13 10 13 2.0 2.0 1.1 1.1 Serrana Bank : Little Cay Quita Sueno Bank: S. extreme of reef Spit at NW. end Roncador Cay: S. pt Old Providence: Isabel House 4 00 10 13 LO 0.5 St. Andrews Island : SW. cove, Entrance I . Courtown Cays: Middle Cay.. Albuquerque Bank: Smith Cay Pearl Cays: Colombilla Cay 1 50 8 03 2.0 LI Pearl Cays Lagoon: Mosqui,to Pt Bluefields: Schooner Pt 1 40 7 52 2.0 LI Little Com Island : Gun Pt Great Corn Island : Wells N. of Quin Bluff. Grey town : Lighthouse 1 35 1 00 7 47 7 13 2.0 L5 LI 0.8 Mount Cartago: Peak, 11,100 feet Port Limon: Monument, Park, opp. P. 0. 1 00 7 13 L6 0.9 APPENDIX IV. [Page 287 MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF NORTH AMERICA— €ontinued. S 8 Place. Lat. N. Long. W. Lun. Int. Range. H. W. L. W. Spg. Neap. i a C&rrctsi Point' Extxeme 9 r r 9 38 30 9 26 16 9 25 00 9 14 24 9 20 17 9 14 53 9 17 00 9 10 30 9 06 00 9 19 27 9 22 39 9 22 09 9 33 20 9 34 00 8 53 52 8 46 30 82 39 06 82 20 40 82 19 28 82 19 36 82 14 29 82 07 48 83 03 00 81 54 06 81 33 57 80 00 22 79 57 13 79 54 42 79 39 13 78 57 00 77 40 53 77 32 15 h. m. , h. m. //. ft. Almirante Bay: Tirbi Pt., Extreme Columbus I., Lime Pt Shepherd I., Summit Bocas del Toro, Radio Tel Sta i 42 Crawl Cay Channel: Crawl Cay Blanco Peak: Summit, 11,740 feet Chiriqui Lagoon: Valiente Peak, Summit. Escudo de Veragua: NW. Pt. of Island . . . Chaeres' San Lorenzo Castle i 1 Torn Point • T.icrht.hniisp Colon : Lighthouse 06 6 18 LI 0.6 Porto Belfo" Ft St Geronimo Gulf of San Bias • Cape San Bias Caledonia Harbor: Dobbin Cay 11 30 5 17 L5 0.8 Port Carreto • Peak WEST COAST OF NORTH AMERICA. i s i ■d s * M d £ Point Barrow: Highest lat. of Alaska Icy Cape* Extreme 71 23 30 70 16 00 68 52 00 67 09 00 66 14 30 66 32 00 65 35 30 65 33 30 65 16 40 64 26 00 63 26 00 63 34 30 61 40 00 63 16 00 60 18 00 60 13 00 60 25 22 58 48 31 57 30 24 55 54 59 56 34 23 52 56 01 51 59 04 51 23 39 51 49 18 52 10 36 57 07 19 53 52 54 54 13 30 54 26 12 55 20 45 55 19 17 55 07 36 55 03 17 54 58 25 54 55 30 156 27 00 161 47 30 166 06 00 163 34 00 161 45 00 163 36 00 168 40 00 168 00 00 166 46 30 165 05 00 162 02 30 162 42 30 166 15 00 168 41 00 172 02 00 172 36 00 166 08 30 160 50 00 157 58 30 160 34 54 169 39 50 LongE. 173 12 24 177 30 00 179 12 06 Long W. 176 52 00 174 15 18 170 17 52 166 31 44 162 38 00 162 18 00 160 38 39 160 31 14 159 56 06 159 23 05 159 22 18 159 15 03 11 41 5 33 0.6 0.2 Cape Lisbume' 849 feet Cape Krusenstem ■ Extreme ChamLsso Island : Summit 7 45 1 50 2.0 0.6 Diomede Island: Fairway Rock Cape Prince of Wales* W pt Port Clarence: Point Spencer 6 10 2 05] [8 05] 1 10 8 25] 1 20' LI [2.1] [4.5] 0.9 Cape Nome: Extreme St Michael : Fort Stuart Island ■ W pt Cape Romanzof' Extreme St Lawrence Island ■ E pt St Matttiew Island: SE. pt 4 40 11 00 3.1 L6 Pinnacle Islet* Summit 930 feet Nunivak Island' Cape Etolin Hafijenmeister Islanc Port Moller St George Island * S side Attu Island : Chichagof Harbor 3 35 3 30 9 48 9 43 5.7 5.2 2.9 2.7 Kiska Island: Kiska Harbor, Ast. sta Amchitka Island: Constantine Harbor — Adakh Island : Bay of Islands 3 25 9 38 5.0 2.6 Atka Island : Nazan Bay (church) Pribilof Island: St. Paul I., village Unalaska Island: C. S. station, Iliuliuk. . Sannakh Reefs: S edge 4 17 3 50 12 13 10 29 9 58 6 10 2.7 2.9 5.7 L4 L5 2.8 Unga Island 2 40 8 55 8.2 4.1 NE harbor Simeonof Island: Simeonof Harbor 2 20 8 33 7.5 3.8 Page 288] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMERICA— Continued. Place. Cape Strogonof : Extreme Chignik Bay: Anchorage Anowik Island: S. end Lighthouse Rocks Chirikof Island Kodiak Island, St. Paul Harbor: Cove NW. of village Port Etches Middleton Island Mount St. Elias: Summit Yakutat Bay: Port Mulgrave Lituya Bay Sitka: Middle of parade ground Juneau Wrangell: Ast. station North Island: N. pt , Cape Knox: Extreme Port Kuper : Sansum I Forsyth Point: Extreme St. James Cape: S. extreme Cumshewa Harbor: N. side of entrance.. Skidegate Bay: Rock on bar Rose Spit Point: Extreme , Masset Harbor: Masset village Cape Edenshaw: Extreme Hecate Bay: Observatory Islet Stamp Harbor: Observatory Islet Island Harbor: Observatory Islet , Cape Beale: Lighthouse Hesquiat Harbor: Boat Cove , Estevan Point: S. extreme Nootka Sound : Friendly Cove Port Langf ord : Colwood Islet. ..'. Esperanza Inlet: Observatory Rock , Kyuquot Sound : Shingle Pomt Nasparti Inlet: Head Beach Cook Cape: Solander I North Harbor: Observatory Rock Hecate Cove: Kitten Islet Cape Scott: Summit Bull Harbor, Hope Island : N . pt. Indian I Port Alexander: Islet in center Beaver Harbor : Shell Islet Cormorant I.: Yellow Bluff in Alert Bay Baynes Sound: Beak Pt Nanoose Harbor: Entrance Rock Nanaimo: Lighthouse Benson's House Victoria: Li^thouse Esquimau : Fisgard I . light Race Island : Lighthouse Port San Juan : Pinnacle Rock Port Simpson : Methodist Church Spire . . Prince Rupert Hbr. : Fairview Obs. Spot. Port Harvey : Tide Pole Islet Port Neville: Robber's Nob Knox Bay, Thurlow Island: Stream at head of bay Valdes Island: S. pt Howe Sound: Plumper Cove Lat. N. 56 48 00 56 19 20 56 05 13 55 45 24 55 48 22 57 47 57 60 20 43 59 27 22 60 20 45 59 33 42 58 36 57 57 02 52 58 18 00 56 27 00 54 15 25 54 10 30 52 56 31 52 09 07 51 54 00 53 02 00 53 22 20 54 13 00 54 02 14 54 05 50 49 15 22 49 13 46 48 54 41 48 47 23 49 27 31 49 22 07 49 35 31 49 47 20 49 52 45 49 59 55 50 11 21 50 06 31 50 29 25 50 32 26 50 46 41 50 54 47 50 50 49 50 42 36 50 35 02 49 36 29 49 15 43 49 12 50 49 10 15 48 25 26 48 25 50 48 17 53 48 33 30 54 33 20 54 17 17 50 33 58 50 31 09 •50 24 15 50 02 42 49 24 39 Long. W. 158 46 00 158 24 24 156 39 19 157 27 04 155 42 51 152 21 21 146 37 38 146 18 45 141 00 12 139 46 16 137 40 06 135 19 31 134 24 00 132 23 00 133 02 00 133 05 10 132 09 06 131 03 20 131 01 26 131 31 00 131 51 00 131 37 00 132 11 16 132 26 10 125 55 43 124 50 07 125 16 54 125 13 14 126 24 53 126 31 58 126 36 58 126 56 31 126 59 21 127 08 56 127 37 24 127 56 46 128 03 05 127 35 44 128 26 11 127 55 29 127 39 23 127 24 33 126 56 56 124 50 44 124 07 32 123 48 11 123 56 02 123 23 31 123 26 48 123 31 47 124 27 37 130 26 09 130 21 33 126 16 06 126 03 47 125 38 26 125 14 34 123 28 46 Lun. Int. H. W. A. m. 1 45 16 50 34 06 45 30 00 07 12 15 45 12 20 12 05 12 05 11 55 11 50 11 47 10 32 30 55 4 45 4 52 4 40 [2 17 [2 00 15 50 1 55 2 30 3 40 4 45 5 38 L.W. h. m. 7 58 6 24 7 05 6 41 6 17 6 56 6 39 6 12 6 19 6 08 7 20 6 15 5 56 5 55 5 45 5 38 5 34 6 22 6 44 6 42 7 08 11 00 11 18 11 05 [8 311 [8 14] 8 10 8 47 10 00 10 15 11 58 Range. Spg. ft. 9.0 10.1 9.5 9.9 18.6 17.7 1L5 12.8 10.0 12.4 9.9 10.3 9.8 9.7 9.3 9.3 10.7 1L6 1L5 12.8 10.6 10.2 m 20 24,17 14.1 16.0 15.7 7.2 9.0 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMEBIC A— Continued. [Page 289 Place. Atkinson Point: Lighthouse Vancouver, Burrard Inlet: Govt. Re- serve, English Bay Eraser River: Garry Pt New Westminster: Military barracks Point Roberts : Parallel station Semiamoo Bay : Parallel station Admiralty Head: Lighthouse Steilacoom : Methodist Church Seattle: C. S. aat. station Port Townsend : C. S. ast. station Smith Island: Lirfithouse New Dungeness: Lighthouse Port Angeles : Ediz Hook lighthouse Cape Flattery: Lighthouse Cape Shoal water : Lighthouse Cape Disappointment: Lighthouse Bremerton : Navy-yard flagstaff Tacoma: St. Luke s Church Astoria: FlagstafiP Yaquina Head : Lighthouse Cape Arago, or Gregory : Lighthouse Cape Blanco: Lighthouse Crescent City : Lighthouse Trinidad Head : Lighthouse Eureka: Methodist Church Humboldt: Lighthouse Cape Mendocino: Lighthouse Pomt Arena: Lighthouse Point Reyes: Lighthouse San Francisco: Davidson Observatory. . . Berkeley, Univ. Obsy . . . Mare Island: Chronom. and Time Sta., Navy-yard Benicia: Church Farallon Islet: Lighthouse Santa Clara: Catholic Church Mount Hamilton: Obs. peak San Jose : Spire Pigeon Point: Lighthouse Santa Cruz : Warehouse flagstaff Monterey: C. S. azimuth station Point Pinos: Lighthouse Piedras Blancas: Lighthouse Point Conception : Lighthouse Santa Barbara: N. tower, Mission Church San Buenaventura: C. S. ast. station Pt. Fermin, San Pedro Bay: Lighthouse. Los Angeles: Courthouse Point Loma : Lighthouse San Diego: C. S. ast. station Mexican Boundary: Obelisk San Miguel Island : Seal Pt Santa Rosa Island : E. pt Santa Cruz Island: NE. pt Anacapa Island : E. pt Santa Barbara Island: Summit San Nicolas Island : Summit Santa Catalina Island : Catalina Peak . . . Lat. N. 49 19 42 49 16 18 49 07 04 49 13 01 49 00 00 49 00 00 48 09 19 47 10 20 47 35 54 48 06 56 48 19 07 48 10 52 48 08 24 48 23 30 46 43 00 46 16 29 47 33 24 47 15 32 46 11 19 44 40 35 43 20 36 42 50 22 41 44 36 41 03 01 40 48 11 40 41 37 40 26 18 38 57 12 37 59 39 37 47 28 37 52 24 38 05 56 38 03 05 37 41 51 37 20 49 37 21 03 37 19 58 37 10 49 36 57 31 36 35 21 36 37 55 35 39 50 34 26 49 34 26 10 34 15 46 33 42 14 34 03 05 32 39 48 32 43 06 32 31 58 34 04 19 33 56 30 34 03 12 34 00 25 33 28 16 33 14 55 33 23 09 LODR. W. 123 15 54 123 11 26 123 11 27 123 53 52 123 04 52 122 44 56 122 40 34 122 35 51 122 19 59 122 44 58 122 50 36 123 06 31 123 24 07 124 44 06 124 04 25 124 03 11 122 37 33 122 26 26 123 49 42 124 04 40 124 22 31 124 33 30 124 12 10 124 09 03 124 09 41 124 16 26 124 24 25 123 44 27 123 01 24 122 25 43 122 15 41 122 16 24 122 09 23 123 00 07 121 56 26 121 36 40 121 53 39 122 23 39 122 01 29 121 52 59 121 56 02 121 17 06 120 28 18 119 42 42 119 15 56 118 17 41 118 14 32 117 14 37 117 09 41 117 07 32 120 21 55 119 58 29 119 33 51 119 23 04 119 02 29 119 31 19 118 24 05 Lun. Int. H.W. 5 20 5 28 5 11 4 59 08 12 22 4 27 4 32 15 11 50 11 55 11 33 11 27 11 57 11 33 11 00 10 36 11 23 12 07 11 43 1 05 1 35 10 40 10 54 10 43 9 37 9 53 9 36 9 29 9 32 9 23 *9'29" 9 20 9 28 L. w. A. m. 11 35 12 01 11 23 11 10 11 04 10 33 9 32 9 28 8 34 8 23 6 16 6 19 10 35 10 45 6 42 5 37 5 49 7 15 7 48 4 25 4 27 4 24 3 15 3 21 3 13 3 07 3 20 3 02 '306 3 04 3 08 Range. Spg. ft. 7.8 8.2 7.0 7.1 ILO 9.2 6.2 5.6 5.0 5.3 7.1 7.7 9.4 9.8 7.8 7.3 6.0 5.8 5.7 5.7 5.1 4.6 5.6 5.6 4.5 5.2 4.8 4.8 49 5.5 5.2 5.1 4.9 4.9 5.1 Neap. ft. 4.9 5.0 4.4 4.6 7.2 6.0 4.0 3.7 3.3 3.4 4.1 3.4 3.3 3.3 3.1 3.0 2.6 3.2 3.2 2.9 3.7 3.7 2.9 3.3 3.1 2.2 2.2 2.5 2.3 2.3 2.2 '2.*2 2.2 2.3 21594°— 14- -19 Page 290] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OP NORTH AMERICA— Continued. Place. Ensenada Harbor: Head of bay, close to beach San To mas: NW. shore of cove Colnett Bay: Head of bay San Martin Island: Hassler Cove Port San Quentin: Sextant Pt San Geronimo Island: Bight at E. end. . . Canoas Point: High bluff Guadeloupe: North pt La Playa Maria: Mound on W. side Santa Rosalia Bay: Obs. spot, Cairn Lagoon Head : Highest pt. of crater Cerros Island: SE. extremity San Benito Island: Summit of W. island.. San Bartolom^: N. side of entrance Asuncion Island : Summit of island San Ignacio Point: Extreme Abreojos Point: Extreme of rocky ledge. , San Domingo Point: Edge of cliff San Juanico Point: KnoU Alijos Rocks: South Rock Cape San Lazaro: Extreme Magdalena Bay: Obs. spot (post) N. of Port Magdalena Cape Tosco: Extreme El Conejo Point: Extreme Todos Santos: Foot of hill, Lobos Pt San Lucas: Steep sand beach, NW. pt. of bay San Jos6 del Cabo: NE. side of entrance. Arena Point: Extreme , Arena de la Ventana: Extreme , Pichilinque Bay: SE. pt. of San Juan, Nepomezeino I La Paz: Obs. spot, El Mogote Lupona Point: Extreme San Evaristo: 3 m. S. of S. Evaristo Hd. San Marcial Point: Extreme Salinas Bay: Beach, NE. pt. of bay Loreto: Cathedral Pulpito Point: Summit Muleje: Equipalito Pt San Marcos Island: S. sand spit Santa Maria Cove: Beach on NW. shore. San Carlos Point: Extreme Santa Teresa Bay: Beach on N. side Las Animas: Low pt Raza Island: Landing place, S. side Angeles Bay: Bight on NW. shore Remedies Bay: Beach on W, shore Mejia Island: S. side San Luis Island: SE, side San Firmin: Beach, N. of bight San Felipe Point: Peak, 1,000 feet Philips Point: Beacon Georges Island: NE. shore Cape Tepoca: Hill, 300 feet Libertad!^ Anchorage: Beach Patos Island: SE. end Tibiu-on Island: SE. end Kino Point: 0.2 mile N. 88° W. of mound. San Pedro: N. side of bay Guaymas: Lighthouse Lat. N. 31 51 10 31 33 04 30 57 39 30 28 58 30 22 16 29 47 20 29 25 29 29 10 50 28 56 06 28 40 16 28 14 26 28 03 52 28 18 08 27 39 35 27 06 10 26 45 45 26 42 49 26 18 56 26 03 18 24 58 00 24 47 31 24 38 23 24 18 12 24 20 17 23 27 14 22 53 07 23 03 35 23 32 48 24 03 52 24 15 31 24 10 10 24 24 10 24 52 03 25 29 23 25 59 37 26 00 41 26 30 44 26 53 37 27 10 21 27 26 06 28 00 07 28 25 04 28 47 40 28 49 11 28 56 39 29 13 52 29 33 08 29 57 27 30 25 16 31 02 57 31 46 10 31 00 54 30 16 05 29 54 12 29 16 12 28 45 55 28 45 28 28 03 22 27 50 28 Liin. Int. Range. Long. W. 116 38 05 116 40 51 116 17 28 116 06 46 115 59 07 115 48 12 115 12 14 118 18 30 114 31 06 114 14 15 114 06 21 115 11 32 115 36 10 114 54 27 114 17 25 113 16 25 113 35 04 112 41 44 112 17 52 115 51 54 112 18 25 112 08 54 111 42 54 111 30 21 110 14 07 109 54 50 109 40 43 109 28 57 109 50 29 110 20 34 110 20 41 110 20 35 110 41 47 111 01 43 111 06 53 111 21 03 111 27 14 111 58 04 112 05 39 112 19 56 112 47 36 112 51 59 113 12 48 113 00 05 113 34 35 113 40 00 113 35 19 114 25 49 114 39 47 114 52 10 114 43 31 113 16 30 112 53 26 112 45 04 112 28 51 112 21 46 111 58 37 111 16 00 110 54 28 H. W. i. m. 9 28 9 27 "923 9 15 9 05 "906 9 00 '8*29" 8 25 8 36 9 40 11 50 11 30 L. W. Spg. h. m. 3 06 ft. 5.0 3 05 s'oo' 5.8 4.9 2 53 7.6 2 42 "2'37" 7.8 "8.'2' 2 48 '217" 6.7 "5.*7" 2 12 5.5 2 20 4.5 3 34 5.4 5 47 11. 2 2. 6 5 26 5.0 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF NORTH AMEBIC A— Continued . [Page 291 Place. Lat. N. Long. W. Lun. Int. Range. H.W. L.W. Spg. Neap. Ciarifl Island: NW. part Santa Barbara: NW. side of bay Agiabampo: SE. side of entrance Topolobampo: SE. end of Santa Maria I. Navachista: W. side of creek Playa Colorado: N. side of entrance. . . . Altata: N. side of entrance Mazatlan: Lighthouse Palenita Village: Boca Tecapan San Bias: Customhouse Maria Madre Island: SE. extreme Mita Point: Extreme Penas Anchorage: Mouth of Rio Real Cape Corrientes: Extreme Perula Bay: Smooth Rock San Benedicto Island: S. extreme Socorro Island: SE. part Roca Partida: Summit Clarion Island: S. end Clipperton Island: Summit Navidad Bay: W. end of sandy beach. . . Manzanilla Bay: Flagstaff, U.S. consulate Sacatula River: Beach, W. side of bay. . . Isla Grande: Tripod on NW. summit — Sihuatanejo Point: Tree on beach Morro Petatlan: Junction of stony and sandy beaches Tequepa Harbor: Limekiln Acapulco: Lighthouse Maldonado: El Recordo Pt Port Angeles: Lighthouse Sacrificios Point: Highest pt. of cape. . . Port Guatulco: Cross Morro Ayuca: Summit of N. edge of cape Salina Cruz: Lighthouse Champerico: Inshore end of iron wharf. . San Jose de Guatemala: Lighthouse Acajutla: Lighthouse Libertad: Lighthouse La Union: Lighthouse Chicarene Point: Extreme Corinto: Lighthouse San Juan del Sur: Signal station Salinas Bay: Salinas Islet Port Culebra: Extremity of Mala Pt Ballena Bay: N. Estero Toussa Parida Anchorage: S. pt. of Deer Id Port Nuevo: Entrada Pt Bahia Honda: W. end of Centinela I. . . Coiba (Quibo) Island: Observation pt. . . Cocos Island: Head of Chatham Bay. . . Panama : Cathedral, S . tower Taboga Island: Church Cape Mala: Extreme Malpelo Island : Summit Point Cham6: Extreme Flamenco Island: N. Pt Chepillo Island: Center Rey Island: Cocas Pt. extreme Darien Harbor: Graham Pt 26 58 59 26 41 09 26 16 35 25 33 56 25 23 06 25 11 42 24 38 52 23 10 40 22 30 26 21 32 30 21 30 45 20 45 50 20 36 26 20 25 00 19 34 48 19 17 15 18 42 57 18 59 41 18 20 55 10 17 00 19 13 25 19 03 15 17 58 21 17 40 15 17 37 50 17 31 28 17 16 13 16 49 10 16 19 37 15 39 09 15 40 41 15 44 58 15 52 17 16 09 36 14 17 44 13 55 15 13 34 20 13 28 50 13 20 00 13 17 09 12 27 54 11 14 45 11 03 10 10 36 46 9 43 45 8 10 13 8 04 30 7 43 32 7 24 20 5 32 57 8 57 06 8 47 45 7 27 40 4 03 00 8 39 00 8 54 30 8 56 32 8 12 30 8 28 50 109 57 17 109 40 48 109 17 30 109 10 23 108 49 00 108 23 37 107 59 37 106 26 47 105 44 25 105 18 40 106 33 14 105 33 37 105 16 00 105 39 21 105 08 54 110 49 22 110 56 53 112 04 07 114 44 17 109 13 00 104 43 26 104 19 50 102 07 06 101 40 25 101 33 23 101 27 14 101 04 32 99 55 50 98 35 05 96 30 43 96 15 04 96 08 10 95 46 43 95 12 16 91 55 36 90 49 45 89 50 26 89 19 20 87 51 00 87 47 06 87 12 31 85 53 00 85 43 38 85 42 46 85 00 46 82 14 32 81 43 30 81 31 58 81 41 51 86 59 17 79 32 09 79 33 16 79 59 25 81 36 00 79 41 45 79 31 15 79 07 55 78 54 40 78 05 35 h. m. 10 07 9 08 9 08 9 07 9 07 8 50 2 50 2 50 2 55 3 05 3 15 2 55 3 00 2 50 2 45 3 15 's'io 3 00 3 00 3 10 3 30 3 05 3 00 h. m. 3 59 2 51 5.8 3.8 2 52 3.2 2 53 2.5 2 54 L9 2 38 2.0 9 02 9 02 9 08 9 18 9 28 8.5 9.0 9.5 10.0 10.5 9 08 9 12 9 02 8 58 10.5 10.0 9.5 9.0 9 28 '922' 10.5 'ii.'6" 9 14 9 13 9 22 16.0 15.4 13.0 9 42 15.0 9 18 9 13 16.0 15.7 L4 0.9 LO 1.1 L3 0.9 4.6 4.9 5.1 5.4 5.7 5.7 5.4 5.1 4.9 5.7 "5.9 8.7 8.3 7.0 8.1 8.7 8.5 Page 292] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISLANDS. Place. Memory Rock: Center Bahama Island : W. pt Abaco Island : Lighthouse Little Guana Cay: Lighthouse Walker Cay: Highest part Great Isaac Cay: Lighthouse Gun Cay: Lighthouse Ginger Cay: Center Cay Lobos: Lighthouse St. Domingo Cay: Center Cay Verde: Hill at S. end Ragged Island: Gun Pt Nairn Cay: E. pt Nurse Channel Cay: Beacon Long Island: S. pt Great Exuma Island : Beacon Clarence Harbor: Lighthouse Eleuthera Island: Lighthouse Royal Island: Eastern Pass Nassau: Lighthouse Androa Island : Lighthouse Great Stirrup Cay: Lighthouse Little Stirrup Cay: WT end San Salvador (Cat I.) : Lighthouse Concepcion Island : W. bay Watlings Island: Hinchinbroke Rock ... Rum Cay: Harbor Pt Castle Island: Lighthouse Fortune Island: S. end Crooked Island: Moss flagstaff Bird Island: Lighthouse Samana Cay: W. pt Plana Cay: NW. pt Mariguana Island: SE. pt Hogety Reef: NW. Cay Inagua Island: Lighthouse Little Inagua Island : NW. pt W. Caicos Cay: Hill, SE. end French Cay: W. pt Fort George Cay : Old magazine Caicos Island: Parsons Pt., S. islet Turk Island: Lighthouse Square Handkerchief Bank: NE. breaker Silver Bank: E. extreme Navidad Bank: Center of E. side Cape Maysi: Lighthouse Port Baraooa: Lighthouse Port Cayo Moa: Carenero Pt Nipe Bay: Extremity of Carenero Pt Lucrecia Point: Lighthouse Port Sama: E. side of entrance Peak of Sama: Summit, 885 feet Port Naranjo: E. side of entrance Gibara: Lighthouse Port Padre: Guinchos Pt Port Nuevitas: NW. corner R. R. station Matemillos Point: Lighthouse Cay Verde: NW. end Cay Confites: S. pt Paredon Grande Cay: Lighthouse San Fernando: NW, corner Old Spanish Fort No. 1 Cayo Frances: Lighthouse Lat. N. 26 56 53 26 41 18 25 51 30 26 31 10 27 15 42 26 02 00 25 34 30 22 45 10 22 22 30 21 42 00 22 01 15 22 14 02 22 20 44 22 31 15 22 51 00 23 32 15 23 06 00 25 00 00 25 31 20 25 05 37 24 43 45 25 49 40 25 49 12 24 06 15 23 50 50 23 56 40 23 37 45 22 06 40 22 32 40 22 47 30 22 51 00 23 05 30 22 34 38 22 16 30 21 40 30 20 56 00 21 30 40 21 37 30 21 30 00 21 54 00 21 29 33 21 30 55 21 06 30 20 35 00 20 02 00 20 15 00 20 21 46 20 41 41 20 47 19 21 04 24 21 09 00 21 07 00 21 07 30 21 07 15 21 18 30 21 32 44 21 40 02 22 08 45 22 11 14 22 29 10 22 09 44 22 38 41 Long. W. 79 06 54 79 00 38 77 10 45 76 57 36 78 23 48 79 06 00 79 18 26 78 06 02 77 34 26 75 44 39 75 10 34 75 45 17 75 28 20 75 51 41 74 51 54 75 46 24 74 59 00 76 13 00 76 51 48 77 21 58 77 46 45 77 53 55 77 57 06 75 26 00 75 07 27 74 28 20 74 50 08 74 20 37 74 22 54 74 20 21 74 22 48 73 49 15 73 38 03 72 47 03 73 50 29 73 40 17 73 42 33 72 28 18 72 12 51 72 07 14 71 31 12 71 07 29 70 29 54 69 21 24 68 47 24 74 08 01 74 29 13 74 53 44 75 34 21 75 36 59 75 47 18 75 47 40 75 52 18 76 06 27 76 35 34 77 15 18 77 08 04 77 37 33 77 39 23 78 09 11 78 35 54 79 13 44 Lun. Int. H. W, A. m. 7 40 20 8 20 7 00 7 20 7 40 7 00 7 20 7 50 7 30 5 40 6 20 7 00 7 20 L.W. ft. TO. 1 28 2 08 2 08 48 1 08 1 28 48 1 08 1 38 1 18 11 53 08 48 1 08 Range. Spg. ft. 3.2 3.0 4.1 4.0 4.0 3.0 4.0 3.0 3.5 3.0 2.8 2.4 2.2 2.8 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISLANDS— Continued, [Page 293 Place. Isabella deSagua: SE. corner of church .. Cay Sal: Lighthouse Bahia de Cadiz Cay : Lighthouse Piedraa Cay: Lighthouse Cardenas: Cross on Cathedral Matanzas: Summit of peak Habana: Morro lighthouse Transit pier, Casa Blanca Ob- servatory Flagstaff, Cabafias Fortress Bahia Honda : SE. comer Morillo Fort Gobemadora Pt. : Lighthouse Dimas : N W. corner of warehouse Cape San Antonio : Lighthouse Radio tower La Caloma: SW. comer of warehouse San Felipe Cays: SW. pt Isla de Pinos: Port Frances Batabano: Lighthouse Piedraa Cay: Lighthouse Cienfuegoe: Colorados Pt. light Cathedral tower Flagstaff, Punta Gorda Casilda: Observation pier Jucaro: Observation pier Santa Cruz del Sur: Observation pier Manzanillo: Observation pier Niquero: Sugar mill, smokestack Cape Cruz: Lighthouse Pomt Mota Chirivico: Damas Cay Santiago : Lighthouse Guantanamo Bay: Fisherman Pt Lighthouse Naval Station flagstaff. Port Escondido : Inner Entrance Pt Port Baitiqueri: Barlovento Pt Cayman Brae : Ej)t Little Cayman: W. pt Grand Cayman: Fort George, W. end Formigas Bank: Shoal spot Morant Point: Lighthouse Port Antonio : Folly Pt. Light Port Maria: NW. wharf St. Ann Bay: Long wharf Falmouth: Fort Montego Bay: Fort St. Lucia: Port Savanna-la-Mar: Fort Kingston: Port Royal flagstaff Port Royal: Fort Charles, flagstaff Morant Cays: NE. Cay Pedro Bank: Portland Rock, E. end. Baxo Nuevo: Sandy Cay Cape Engano: Extreme SamanaTown: Obs. spot Cape Cabron : _ East extreme . . . Port Plata: Lighthouse Monte Cristi: Cabra Island. . . Manzanillo Point CapeHaitien: Town fountain . Lat. N. 22 23 23 23 23 23 23 23 23 22 23 22 21 21 22 21 21 22 21 22 22 22 21 21 20 20 20 19 19 19 19 19 19 19 19 20 19 19 19 18 17 18 18 18 18 18 18 18 17 17 56 30 56 30 12 34 14 10 02 43 01 54 09 26 09 04 09 11 59 11 00 00 29 32 52 01 53 55 14 36 55 00 35 30 41 09 57 45 01 49 08 36 06 52 48 16 37 24 42 23 20 26 02 55 50 32 53 31 56 57 57 29 54 42 53 04 57 00 54 08 01 01 45 15 39 10 17 45 33 00 55 05 11 31 23 00 26 24 30 34 29 25 27 45 12 20 55 56 55 56 17 26 30 17 06 20 15 53 00 18 35 52 19 12 29 19 22 12 19 48 51 19 54 00 19 46 20 19 46 19 Long. W. 80 00 32 80 27 51 80 29 26 81 07 20 81 12 02 81 43 18 82 21 29 82 20 38 82 21 01 83 09 13 83 13 00 84 14 17 84 57 09 84 56 16 83 34 24 83 31 18 83 09 13 82 17 42 81 07 18 80 26 32 80 27 05 80 27 11 79 58 58 78 51 13 77 59 45 77 07 33 77 34 50 77 43 33 75 52 03 75 09 28 77 09 28 75 07 33 75 03 08 74 50 49 79 46 07 80 07 17 81 23 17 75 44 24 76 11 08 76 26 31 76 54 22 77 12 52 77 39 62 77 56 16 78 10 52 78 08 64 76 50 35 76 50 38 75 58 20 77 26 28 78 39 04 68 18 50 69 19 23 69 12 12 70 41 27 71 40 15 71 46 40 72 12 07 LuD. Int. Range. H.W. L.W. Spg. Neap. ft. m. ft. m. ft. 8 30 8 18 2 18 1 56 2.2 L3 8 30 2.18 L5 4 47 11 00 2.0 8 20 7 50 2 30 2 00 2.2 2.6 [1.3] [1.1] '[1:2] [1.1] 9 00 2 48 3.0 6 50 39 5.5 1.2 0.7 0.9 1.1 LI 1.3 L5 2.9 Page 294] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISLANDS— Continued. Place. PortPaix: Wharf St. Nicholas Mole: Fort George, flagstaff . . Gonaives: Verreur Pt Gonave Island: W. pt Arcadins Islands: Lighthouse Port au Prince: Fort Islet light Jeremie: Fort Cape Dame Marie: Extreme Navassa Island: NW. extreme Aux Cayes: Tourterelle Bat'y Jacmel: Wharf False Cape: Extreme Beata Island: NW. pt Fraile Rock: Center Alta Vela: Summit Avarena Point: Extreme Salinas Point (Caldera) : Extreme Sto. Domingo City: Lighthouse Saona Island: Pt. Catuano Mona Island: Lighthouse Mayaguez : Mouth of Mayaguez R Aguadilla: Columbus Monument San Juan: Morro lighthouse Cape San Juan : Lighthouse Guanica: Meseta Pt. lighthouse Culebrita Island : Lighthouse Vieques (Crab) Island: Port Ferro light. St. Thomas: Fort Christian, SW. bastion. St. John Island: Ram Head Tortola: Fort Burt Virgin Gorda: Vixen Pt An^ada: W. pt E. extreme of reefs St. Croix, Christiansted: SW. bastion of fort.. St. Croix, Lang's Observatory Sombrero: Lighthouse Dog Island : Center Anguilla: Customhouse St. Martin: Fort Marigot light St. Bartiiolomew: Fort Oscar Saba: Diamond Rock St. Eustatius: Fort flagstaff St. Christopher: Basseterre Church Booby Islajid: Center Nevis: Fort Charles Barbuda: Flagstaff, Martello Tower Antigua, English Harbor: Flagstaff, dock- yard Sandy Island: Lighthouse Redonda Islet: Center Montserrat: Plymouth Wharf. Guadeloupe, Basseterre: Light on mast. . Port Louis: Light on mast. Gozier Islet: Lighthouse. . . Manroux Id. : Lighthouse . . Point a Pitre: Jarry Mill. . . Desirade: E. pt Petite Terre: Lighthouse Marie Galante: Lighthouse Saintes Islands: Tower on Chameau Hill . Lat. N. 19 57 06 19 49 15 19 27 12 18 56 00 18 48 50 18 33 31 18 39 15 18 36 48 18 25 00 18 11 08 18 13 25 17 46 08 17 36 55 17 37 37 17 28 22 18 08 55 18 12 13 18 27 54 18 11 57 18 05 17 18 12 37 18 24 51 18 28 23 18 23 01 17 57 10 18 18 56 18 05 54 18 20 23 18 18 08 18 25 04 18 30 39 18 45 11 18 36 30 17 45 09 17 44 43 18 35 37 18 16 42 18 13 06 18 04 07 17 53 58 17 39 10 17 29 10 17 18 12 17 13 38 17 07 52 17 35 50 17 00 00 17 06 54 16 55 18 16 42 12 15 59 50 16 25 09 16 11 57 16 13 14 16 13 56 16 19 56 16 10 17 15 52 59 15 51 32 Long. W. 72 50 00 73 23 07 72 43 52 73 18 20 72 39 13 72 21 00 74 06 52 74 25 50 75 01 57 73 44 08 72 30 45 71 41 06 71 31 10 71 41 10 71 38 30 71 02 25 70 32 53 69 52 59 68 45 41 67 50 50 67 09 17 67 09 42 66 07 26 65 37 07 66 54 13 65 13 40 65 25 26 64 55 47 64 42 03 64 36 47 64 21 48 64 24 58 64 10 45 64 42 16 64 41 14 63 28 13 63 16 00 63 04 39 63 05 45 62 51 30 63 15 16 62 59 09 62 43 14 62 35 25 62 37 29 61 49 54 61 46 07 61 55 11 62 19 10 62 13 24 61 44 09 61 32 15 61 29 40 61 32 05 61 33 15 61 00 44 61 06 45 61 19 15 61 35 55 Lun. Int. Range. H.W. L.W. Spg. Neap. h. m. h. m. [1-2] [2.5] [2.2] 7 04 2 00 2.0 LO 8 21 2 20 L3 0.9 [7 311 [7 35] [7 11] [1 30] [140] [0 58] [LO LO' Li; [1-2] [1.5] [2.0] [1.3] APPENDIX IV. [Page 295 MARITIME POSITIONS AND TIDAL DATA. WEST INDIA ISTiAUDS— Continued. 1 Place. Lat. N. Long. \V. Lun. Int. Range. 1 H. W. L. W. Spg. Neap. Dominica, Prince Ruperts Bav: Sand beach W. of church Roseau: Flagstaff , Fort Young Aves Island : Center 15 34 34 15 17 27 15 42 00 14 35 44 14 43 54 14 46 13 14 23 23 61 28 14 61 23 52 63 37 46 61 04 30 61 11 09 60 53 20 60 52 33 61 00 48 59 37 16 59 .SI 50 h. m. 4 00 h. m. 10 12 ft. L5 ft. 0.8 Martinique, Fort de France: Fort St. Louis light St. Pierre: Ste. Marthe Bat- tery Caravelle Pen.: Lighthouse. Cabrit Islet: Summit 3 50 10 02 1.1 0.6 St. Lucia, Port Castries: Lighthouse 14 01 54 Barbados, Bridgetown: Flagstaff, Pick- ett's Battery 13 05 43 S. Point: Lighthouse 13 02 45 2 50 9 02 3.0 L5 Ragged Point: Lighthouse 13 09 40 59 26 04 St. Vincent, Kingstown: Lighthouse 13 09 19 Bequia Island, Admiralty Bay: Church. . 13 00 25 Grenada: St. George Lighthouse 12 03 02 Tobago, Rocky Bay: Lighthouse 11 10 08 Testigos Islets: Center of Testigo Grande. 11 25 02 Sola Island: Center 11 19 00 Pampatar, Margarita I.: San Carlos Castle. 10 59 43 Tortugas Island: S. end of W. Tortugillo i Islet 10 57 45 Orchila Island: S. side i 11 47 57 61 14 34 61 14 09 61 45 06 60 42 38 63 05 48 63 36 00 63 48 00 65 26 38 66 12 31 66 39 10 68 14 10 68 39 19 68 55 48 68 56 17 70 02 34 2 50 9 05 L6 0.8 2 30 3 50 8 42 10 02 1.5 2.1 6.8 1.1 Roques Islands: Pirate Cay 11 56 16 Bonaire Island : Lighthouse 12 02 06 11 59 30 12 06 58 12 06 15 12 31 05 Little Curasao Island : Lighthouse Curafao Island : Fort Nassau Lighthouse Oruba Island: Lighthouse NORTH AND EAST COASTS OF SOUTH AMERICA. 1 i s s © © s a Caribana Point: Extreme 8 37 30 9 24 00 9 24 00 10 25 50 11 00 15 10 07 00 11 15 28 11 33 30 12 12 34 76 52 55 76 10 45 Fuerte Island: N. extreme Cispata Port: Zapote Pt 75 48 00 75 32 50 74 57 55 74 49 51 74 14 33 72 54 50 72 09 42 71 45 42 71 07 55 71 37 00 70 17 21 70 04 55 70 57 00 69 34 20 68 19 55 68 22 54 68 00 55 66 56 06 66 06 15 66 04 13 66 09 25 64 44 00 64 11 33 64 17 55 Cartagena: Lighthouse Savanilla: Lighthouse Magdalena River: NW. pt. of Gomez I. . . Santa Marta: Lighthouse Rio de la Hacha: Light on church Cape La Vela: Sand beach inside cape. . . Bahia Honda: E. pt., S. side 12 23 09 Espada Point: Extreme 12 04 00 10 57 30 11 48 56 12 11 00 12 29 15 11 27 56 10 47 00 11 10 00 10 29 53 10 36 57 10 35 00 10 34 06 10 49 30 10 13 30 10 27 20 10 40 00 10 42 00 Maracaibo: Zapara I. light 5 05 11 17 2.5 1.5 Estangues Point: 500 ft. from extreme Cape San Roman : Extreme Marjes Islets: N. islet 1 Vela de Coro: Lighthouse 1 Tucacas Island : Ore house St. Juan Bay: Cay Puerto Cabello: Lighthouse La Guaira: Lighthouse 6 00 12 12 2.8 L7 Cape Codera: Morro Corsarios Bay: W. pt 1 Centinela Islet: Center \"' ' Barcelona: Morro Cumana: Lighthouse Escarceo Point; Extreme . Chacopata: Morro 63 50 25 Page 296] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. NORTH AND EAST COASTS OF SOUTH AMEBIC A— Continued. Place. Esmeralda Islet: Center Carupano: Lighthouse Pt. Herman Vasc[uez Puerto Santo Bay: Sand spit S. of Moito. Tres Puntas Cape: Extreme Unare Bay: Obs. spot, 200 yds. S. of Morro. Pena Point: Extreme Pato Island: E. pt Mocomoco Pt. : Extreme Port of Spain: King's Wharf light Chacachacare Island: Rocks off SW. pt. . Galera Point: NE. extreme, lighthouse... Icacos Point: Lighthouse San Fernando: Pierhead Demerara: Georgetown lighthouse. Nickerie River: Lighthouse Paramaribo: Stone steps Maroni River: W. lighthouse Salut Islands: Lighthouse Enfant Perdu Islet: Lighthouse. . . Cayenne: Lighthouse Connetable Islet: Center Carimare Mount: Summit Orange Cape: Extreme... Maye Mountain: Summit. North Cape: Extreme Cape Magoari: Extreme Para: Customhouse Atalaia Point: Lighthouse Itacolomi Point: Lighthouse Maranhao Island: Landing place Santa Anna Island: Lighthouse Tutoya: Entrance Paranahiba River: Amargao Village Ceara: Lighthouse. Ja^uaribe River: Pilot station Caigara: Village Cape St. Roaue: Extreme Rio Grande do Norte: Lighthouse Natal: Cathedral Parahiba River: Lighthouse at entrance. Parahiba: Cathedral Olinda: Lighthouse Pemambuco: Picao lighthouse Cape St. Augustine: Lighthouse Tamandare: Village Maceio: Lighthouse San Francisco River: Lighthouse at en- trance Cotinguiba River: Lighthouse at entrance Vaza Barris River :^ Semaphore at en- trance Real River: Lighthoiise Conde: Village Garcia d' Aviia: Tower Bahia : Santo Antonio lighthouse Itaparica: Fort on N. pt Morro de Sao Paulo: Lighthouse Camamu: Village Contas: Church Lat. N. 10 40 00 10 40 15 10 42 00 10 43 27 10 45 00 10 44 19 10 43 48 10 38 15 8 39 25 10 38 37 10 40 03 10 50 02 10 03 29 10 16 59 6 49 20 5 58 30 49 30 44 50 16 50 02 40 66 20 49 30 23 20 4 20 45 2 46 30 1 40 17 Lat. 8. 17 00 1 26 59 35 03 2 10 11 31 48 16 22 41 55 53 20 42 05 25 35 03 15 29 15 45 05 46 41 56 30 06 35 8 00 50 8 03 22 8 20 45 8 43 40 9 39 35 10 30 30 10 58 20 11 09 45 11 27 40 12 12 05 12 33 40 13 00 37 12 52 48 13 22 37 13 56 42 14 17 40 Long. W. 63 31 55 63 18 00 63 14 00 63 09 43 62 41 55 62 44 29 61 50 50 61 51 18 60 10 15 61 30 35 61 45 54 60 54 10 61 55 41 61 28 12 58 11 30 57 00 30 55 08 48 54 00 30 52 34 53 52 21 11 52 20 26 51 55 36 51 50 36 51 27 46 50 54 46 49 56 46 ! 48 23 30 48 30 01 47 20 54 44 25 56 44 18 45 43 37 30 42 18 02 41 40 35 38 28 25 37 44 55 36 02 52 35 15 52 35 11 55 35 12 43 34 49 30 34 53 04 34 50 36 34 51 57 34 56 05 35 05 06 35 44 54 36 21 51 37 04 00 37 12 36 37 24 GO 37 45 46 38 02 16 38 32 06 38 41 28 38 54 38 39 07 05 39 00 45 Lun. Int. H. W. L. W h. m. 4 20 4 18 5 50 4 27 11 50 6 50 5 35 5 05 5 25 5 50 4 05 4 33 4 20 4 17 4 10 3 50 3 50 h. m. 10 30 9 50 12 00 10 30 5 37 38 11 47 11 17 11 37 12 00 10 17 10 50 10 32 10 29 10 22 10 00 10 00 Range. Spg. Neap. 3.2 8.6 9.5 6.0 n.o 16.5 13.1 11.7 8.2 8.0 7.0 8.5 7.8 7.6 6.0 6.3 APPENDIX IV. [Page 297 MARITIME POSITIONS AND TIDAL DATA. NORTH AND EAST COASTS OP SOUTH AMERICA— Continued. 1 Place. Lat.S. Long. W. Lun. Int. Range. H.W. L.W. Spg. Neap. eg S Ilb606 : Church tin 14 47 40 14 56 40 15 13 27 15 21 00 16 17 20 16 25 38 17 21 40 17 31 45 17 43 30 17 57 31 18 06 15 20 19 23 20 38 25 20 49 00 20 57 35 21 38 40 22 02 00 22 23 45 22 26 00 22 37 00 22 46 00 23 00 42 22 53 15 23 01 43 22 54 46 22 54 24 23 03 40 22 32 00 23 03 40 23 04 20 22 57 20 23 09 20 23 00 30 23 09 50 23 12 20 23 25 55 23 32 57 23 45 15 23 58 30 23 47 20 24 03 06 23 56 00 24 06 30 24 10 32 24 28 45 24 42 35 25 06 40 25 30 55 25 31 20 25 26 30 25 44 10 25 50 15 26 14 17 26 46 45 27 01 35 27 18 00 27 25 30 27 22 55 27 50 27 27 36 00 27 56 40 28 38 00 29 20 20 32 06 40 39 03 25 39 01 45 39 01 15 39 16 45 39 02 05 39 04 15 39 13 15 39 12 00 .39 14 36 38 41 46 39 31 16 40 16 36 40 23 46 40 40 45 40 46 35 41 02 21 40 59 00 41 47 35 41 43 15 41 59 45 41 54 05 42 00 00 42 01 15 42 54 05 43 09 19 43 10 21 43 08 45 43 11 01 43 33 24 43 59 26 44 02 29 44 08 24 44 19 04 44 05 45 44 42 04 45 04 04 45 03 50 45 00 39 45 15 20 45 21 04 46 15 57 46 19 09 45 40 49 46 47 44 46 41 04 47 32 54 47 51 50 48 19 53 48 31 03 48 43 14 48 23 14 48 25 51 48 39 29 48 36 59 48 36 44 48 22 20 48 34 25 48 26 09 48 35 16 48 34 14 48 33 44 48 49 45 49 43 39 52 07 44 ft. m. 3 35 A. m. 9 47 It. 6.4 ft. 3.1 Oliven^a: Center of village Una: Center of village Comandatuba: Center of village Santa Cruz: Church 3 25 9 37 6.0 2.9 Porto Seguro: Matriz Church Prado: River entrance Alcoba^a: Center of village Caravellae: Center of village 3 10 3 15 9 23 9 27 6.4 7.5 3.1 3.6 AbrolhoB Island : LighthouBe Porto Alegre: Center of village Espiritu Santo Bay: Lighthouse 2 50 9 00 4.0 L9 Guarapiri Islets: E. islet Benevente: Village 2 40 8 52 5.0 2.4 Itapemirim: Moscaa Islet Sao Joao da Barra: Lighthouse Cape St. Thoni6: Extreme Macah6: Fort at entrance 2 20 8 30 9.2 4.4 Santa Anna Island : Summit Barra Sao Jo3o: Village Busios: Church Cape Frio: Lighthouse Port Frio: Village 2 30 8 42 4.9 2.3 Maricas Islands: S. islet Rio de Janeiro: Fort Vill^;agnon Light. . National Observatory Raza Island: Lighthouse 2 50 9 00 4.2 2.0 Petropolis: Center of town Cape Guaratiba: Summit Msu^mbaya Island: Summit of SW. end. . Mangaratiba: Village Palmafl Bay: Beach at head of bay : . Angi"a dos Reis: Landing place Ilha Grande: Lighthouse Parati: Fort 1 35 7 47 5.3 2.5 Ubatuba: Cathedral Porcos Grande Islet: Summit Busios Islets: Summit St. Sebastian Island: Boi Pt. light Villa Nova da Princessa: Center Santos: Moela I. lighthouse Quay 2 50 9 00 5.0 2.8 Alcatrazes Island: Summit, 880 ft Concei^ao: Church Quemada Grande Island: Summit, 623 ft. loruane: Ouav Bom Abrigo . [slet: Lighthouse Ilha do Mel: Lighthouse Paranagua: Quay 2 55 9 05 6.4 3.1 Antonina: Quay Coral Islet: Center Itacolomi Islet: Center Sao Francisco: Center of town Itapacaroya: Church Cambria: Church. . . Arvoredo Island : Lighthouse - Anhatomirim: Lighthouse Sta. Catherina Island : Rapa Pt 2 35 8 47 5.9 2.8 Naufragados light. Nossa Senhora do Deeerto: Quay Cape St Martha" Lighthouse Torres Point' Extreme Rio Grande do Sul : Lighthouse 4 00 10 12 1.8 0.9 Page 298] APPENDIX IV. MAKITIME POSITIONS AND TIDAL DATA. NORTH AND EAST COASTS OF SOUTH AMERICA— Continued. 1 8 Place. Lat. S. Long. W. Lun Int. Range. 1 H.W. L.W. Spg. Neap. as S a a i a "S a 9 61 h < i a Castillos: Beuna Vista Hill, 184 feet Cape Santa Maria : Lighthouse 34 21 19 34 40 01 35 01 39 34 58 15 34 56 55 34 54 33 34 28 20 34 10 50 34 36 30 34 54 30 35 15 45 35 26 50 36 18 24 36 53 00 38 05 30 38 57 00 38 43 50 39 26 30 39 57 30 40 32 52 40 36 10 41 02 00 41 11 00 40 49 00 41 41 10 42 14 15 42 46 15 42 57 00 42 45 40 43 20 45 44 30 40 45 04 00 45 03 00 45 10 10 47 06 20 47 45 05 47 57 15 49 15 20 50 08 30 50 58 27 51 33 21 52 18 35 54 40 35 54 43 24 54 45 16 54 53 45 54 48 02 55 17 00 55 19 00 55 35 30 55 48 54 55 58 41 55 51 20 55 43 15 55 52 30 56 28 50 55 24 50 54 45 40 54 24 48 53 47 16 54 09 14 54 53 16 54 57 10 55 55 04 56 12 15 57 52 27 58 15 40 58 22 14 57 54 15 57 10 45 57 05 28 56 44 15 56 38 54 57 30 01 61 59 15 62 15 27 62 03 22 62 07 46 62 09 30 62 10 12 62 45 11 63 08 16 64 54 41 65 12 29 64 27 56 63 37 16 64 28 20 64 59 00 65 03 36 65 22 10 65 36 01 65 52 30 66 32 36 65 51 46 65 54 45 65 45 40 67 42 30 68 23 00 69 09 47 69 00 31 68 22 12 65 05 53 63 47 00 64 03 00 64 45 45 65 13 48 66 49 00 67 10 00 67 19 00 66 43 48 67 16 15 67 34 00 68 04 40 69 17 30 68 41 30 70 01 30 71 36 10 72 10 20 h. m. 8 20 h. m. 2 08 ft. 2.0 ft. 0.9 Lobos Island: Center Maldonado: Lighthouse Flores Island : Lighthouse Montevideo: Cathedral, SE. tower Colonia: Lighthouse 2 00 6 30 8 12 00 3.5 4.0 2.3 2.7 Martin Garcia Island : Lighthouse Buenos Ayres: Cupola of customhouse La Plata: National University Obsy Indio Point: Lighthouse 6 43 12 15 2.1 L4 Piedras Point: Extreme Cape San Antonio: Lighthouse 9 50 3 35 5.3 3.5 Madanas Point: Lighthouse Cape Corrientes: E. summit Port Belgrano: Anchor-Stock Hill Argentina: Fort 6 00 00 15.8 8.2 Labyrinth Head : Summit Union Bay: Indian Head San Bias Harbor: SW. end of Hog Islet... San Bias Bay: Summit of Rubia Pt Rio Negro: Main Pt 10 50 4 38 14.7 7.7 Bermeja Head : E. summit Port San Antonio: Point Villarino San Antonio Sierra: Summit 10 35 4 23 23.5 12.3 Port San Jose: San Quiroga Pt Delgado Point: SE. cliff Cracker Bay: Anchorage Port Madryn: Anchorage off cave bluff. .. Chupat River: Entrance 7 05 52 13.2 6.9 Port St. Elena: St. Elena pen 3 50 10 03 16.8 8.8 Leones Island : SE. summit MeloPort: W. pt Port Malaspina: S. pt Cape Three Points: NE. pitch Port Desire: Largest ruin 00 6 12 18.3 9.6 Sea Bear Bay: Wells Pt Port San Julian: ShoU Pt 10 35 9 20 9 00 8 40 8 18 4 20 4 19 4 23 3 08 2 47 2 28 2 06 10 33 10 32 29.5 39.6 40.0 45.6 38.7 9.9 7.8 15.4 20.7 20.9 23.9 20.2 5.2 6.0 Port Santa Cruz : Mount at entrance Coy Inlet: Height S. side of entrance Gallegos River: Observation mound Cape Virgins: SE. extreme Cape San Diego: Extreme Staten Island, Cape St. John: Light- hoiise, W. pt Port Cork: Observation mark, summit Cape St. Bartholomew: Middle pt Good Success Bay: S. end of beach Lennox Cove: Bluff, N. end of beach Goree Road : Guanaco Pt 3 50 10 03 6.7 5.2 Wollaston Island : Middle Cove Bameveldt Islands : Center Cape Horn: South summit, 500 ft Hermite Island: St. Martin Cove False Cape Horn: S. extreme 4 07 10 02 4.8 3.8 Ildefonso Islands: Highest summit Diego Ramirez Island: Highest summit. . York Minster Rock: Summit, 800 ft Cape Desolation: S. summit 3 50 10 03 5.0 3.9 Mount Skyring: Summit, 3,000 ft APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH AMEBIC A. [Page 299 Place. Lat. S. Long. W. Lun. Int. Range. H. W. L.W. Spg. Neap. Noir Island: SE. extreme Landfall Island: Summit of Cape Inman. Cape Deseado : Peaked summit Apostle Rocks: W. rocks Cape Pillar: N. cliff Dungeness Point: Lighthouse CapeEspiritu Santo: NE. cliff Catharine Point: NE. extreme Cape Possession: Lighthouse Cape Orange: N. extreme Delgada Point: Lighthouse Cape Gregory : Lighthouse Cape St. Vincent: W. extreme Elizabeth Island: NE. bluff Sandy Point: Lighthouse Cape St. Valentine: Summit, at extreme. Port Famine : Observatory Cape San Isidro : Extreme Cape Fro ward : Summit of bluff Mount Pond: Summit Port Gallant: Wigwam Pt Charles Island : White rock near NW. end . Rupertlsland: Summit Mussel Bay: Entrance Tilly Bay: Sarah I Borja Bay: Bluff on W. shore Cape Quod: Extreme Barcelo Bay. Entrance Swallow Bay: Shag I Cape Notch: Extreme Playa Parda Cove: Summit of Shelter I. . Pollard Cove: Entrance Port Angosto: Hay Pt St. Anne Island: Central summit Half Port Bay: Point Upright Port: Entrance Port Tamar: Mouat Islet Port Churruca: Summit of Blanca Pen. . . Valentine Harbor: Observation mount. . . Cape Parker: W. summit Mercy Harbor: Summit of Battle I Mayne Harbor: Observation spot Port Grappler: Observation spot Port Riofrio: Vitalia I Eden Harbor: Observation spot Halt Bay: Observation islet Westminster Hall Islet: E. summit Evangelistas Island: Lighthouse Cape Victory: Extreme Cape Isabel: W. extreme Cape Santiago: Summit Molyneux Sound : Romalo I Cape Tres Puntas: Summit, 2,000 ft Port Henry: Observation spot Mount Corso: SW. summit Rock of Dundee: Summit Santa Barbara Port: N. extreme obs. ;pt. . Guaineco Islands: Speedwell Bay, hill, NE.pt Port Otway : Observation spot Cape Tres Montes: Extreme Cape Raper: Rock close to cape Christmas Cove: SE. extreme Hellyer Rocks: Middle 54 30 00 53 18 30 52 55 30 52 46 15 52 42 50 52 23 55 52 39 00 52 32 00 52 17 54 52 28 40 52 28 00 52 38 18 52 46 20 52 49 18 53 10 10 53 33 30 53 38 12 53 47 00 53 53 43 53 51 45 53 41 45 53 43 57 53 42 00 53 37 10 53 34 20 53 31 45 53 32 10 53 30 50 53 30 05 53 25 00 53 18 45 53 15 30 53 13 40 53 06 30 53 11 40 53 06 35 52 55 46 53 01 00 52 55 00 52 42 00 52 44 58 51 18 29 49 25 19 49 12 40 49 07 30 48 54 20 52 37 18 52 24 00 62 16 10 51 51 50 50 42 00 50 17 20 50 02 00 50 00 18 49 48 00 48 06 15 48 02 20 47 39 30 46 49 31 46 58 57 46 49 10 46 35 00 46 04 00 73 00 00 74 18 15 74 36 30 74 46 50 74 42 20 68 26 45 68 34 00 68 45 20 68 57 10 69 24 00 69 33 00 70 14 16 70 25 25 70 37 61 70 64 24 70 34 27 70 58 31 70 55 03 71 17 16 71 55 30 71 59 41 72 04 45 72 10 42 72 19 30 72 27 10 72 34 16 72 32 26 72 38 00 72 47 30 72 47 55 73 00 30 73 12 05 73 21 30 73 15 30 73 17 45 73 16 15 73 44 28 73 59 33 74 17 45 74 13 30 74 38 14 74 04 00 74 17 39 74 23 27 74 25 10 74 20 55 74 23 10 75 06 00 74 55 00 75 13 20 75 27 45 74 51 30 76 22 00 75 13 20 75 34 00 75 40 30 75 28 20 75 10 00 76 18 20 75 25 30 75 37 55 75 31 30 75 12 00 2 20 1 60 0.32 8 19 8 20 8 24 8 35 8 47 9 23 10 24 11 03 11 58 12 21 28 1 20 1 64 1 63 "in 'i'69 0.55 65 0.30 15 o'io' 33 03 ft. 4.8 4.7 6 45 2 07 2 08 2 12 2 25 4.0 39.4 39.0 30.0 39.0 2 40 3 20 39.0 21.0 4 24 5 03 5 58 6 21 6 53 7 40 8 11 8 08 '7"44' "7'2i' 7 07 7 08 6 45 6.30 "6'25' 8.0 6.0 6.0 8.0 7.0 8.0 6.5 6.0 4.0 6.0 4.4 4.6 5.3 '5.'3 ft. 3.7 3.7 3.1 20.6 20.4 15.7 20.4 20.4 ILO 4.2 2.6 3.1 4.2 3.7 4.2 2.9 3.9 4.5 3.5 3.1 4.6 3.4 3.5 4.1 "4.'i Page 300] APPENDIX IV. MABITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH ATVTRItlC A— Continued. 1 Place. Lat. S. Long. W. Lun. Int. Range. 1 H.W, L.w. Spg. Neap. e a A Q Cape Taytao: W. extreme t « 45 53 20 44 55 50 44 09 00 43 49 15 43 43 05 43 19 30 43 16 25 43 11 30 42 46 45 42 29 15 42 22 45 42 11 15 41 28 36 41 46 20 41 49 58 40 46 19 40 43 18 40 35 52 40 21 04 40 11 47 39 51 37 39 23 00 38 21 22 37 35 20 37 22 30 37 05 20 36 59 07 36 42 00 36 36 45 34 46 02 33 34 13 33 38 30 33 26 42 33 01 08 33 01 52 32 46 00 32 07 55 31 51 45 31 39 30 31 17 05 30 50 45 30 14 00 30 15 14 29 56 15 29 56 24 29 55 10 29 34 40 29 15 45 29 00 50 28 27 20 28 05 45 28 04 30 27 54 10 27 39 20 27 20 00 27 03 15 27 03 15 26 51 05 26 34 30 26 20 00 26 16 12 26 09 15 75 06 00 75 08 45 74 07 45 74 00 30 74 42 15 73 42 25 74 24 15 72 48 30 72 31 25 73 45 05 73 38 10 72 35 55 72 56 15 73 07 65 73 51 12 73 51 00 73 49 50 73 45 00 73 45 20 73 41 50 73 26 25 73 14 00 73 58 06 73 39 55 73 40 00 73 11 13 73 32 30 73 07 27 73 02 49 72 06 12 71 38 00 69 56 30 70 41 32 71 38 52 71 38 42 71 32 56 71 33 22 71 34 51 71 35 20 71 39 21 71 39 00 71 39 00 71 31 09 71 21 00 71 21 53 71 22 21 71 33 20 71 34 38 71 36 40 71 15 45 71 12 48 71 11 32 71 09 38 71 03 26 70 58 45 70 52 54 70 53 45 70 51 55 70 44 25 70 37 25 80 11 43 70 43 57 A. m. 00 h. m. 6 13 ft. 4.4 ft. 3.4 Socorro Island : S. extreme Mayne Mountain: Summit, 2,080 ft Port Low: Huacanec I., S. end 15 12 10 6 10 6 00 Guafo Island : S. extreme 6.1 3.1 Port San Pedro: Cove on S. shore Cape Quilan : SW. extreme Corcovado Volcano: Summit, 7,527 ft Minchinmadiva Volcano: S. summit, 8,000 feet Castro: Extreme of point 01 6 21 18.0 9.1 Dalcahue: Chapel Comau Inlet: Morro Comau Port Montt: Lt. on end of pier 31 1 10 04 ""7'35' 6 20 2L0 14.8 5.9 14.5 7.5 3.0 Port Calbuco : La Picuta Ancud : Ahui Pt. light Condor Cove: Landing Ranu Cove : Anchorage Muilcalpue Cove : Landing place Milagro Cove : Landing place Laruehuapi Cove: Landing place Valdivia : Niebla Fort light 00 10 25 10 18 10 20 10 15 10 10 10 05 10 10 10 04 10 05 9 57 9 44 6 13 4 13 4 05 5 07 4 02 3 55 3 50 3 55 3 51 3 53 3 48 3 34 7.2 5.6 4.9 3.3 4.9 5.3 4.9 6.0 5.3 5.0 4.1 4.0 3.7 2.8 2.5 L7 2.5 2.7 2.5 3.0 2.7 2.5 2.1 2.0 Queule Bay: Choros Pt Mocha Island : Lighthouse Lebu River: Tucapel Head Yanez Port: Anchorage Lota: Lighthouse Santa Maria Island : Lighthouse Talcahuano: Fort Galvez Light on Quinquina I Llico: Village Port San Antonio : Village Aconcagua Mountain : Summit Santiago : Observatory Valparaiso : Playa Ancha Pt. light Site of old Fort San Antonio. . Quintero Point: Summit 9 37 3 26 3.9 2.0 9 35 9 30 9 26 3 25 3 20 3 16 4.1 3.9 4.2 2.1 2.0 2.1 Pichidangui: SE. pt. of island Tablas Point: SW. extreme Chuapa River: S. entrance pt Maitencillo Cove: N. head Talinay Mount: Summit Lengua de Vaca: Lighthouse . Port Tongoi: Obs. spot. W. of village Cnqiiinnbf^" Tnrtnpn. Pt light 9 15 8 58 3 05 2 48 4.1 4.9 2.1 2.5 Smeltmg works, N. of town. . N. islet. Pajaros Islets : Lighthouse. . . . Choros Islands: SW. pt. of Largest island. . Chanaral Island : Lig ithouse Huasco: Light on mole 8 23 8 50 2 10 2 38 4.9 4.9 2.5 2.5 Herradm^ de Carrizal: Landing place. . . Port Carrizal : Middle Point Matamoras Cove: Outer pt. S. side Salado Bay: Summit of Caches Pt Copiapo: Landing place 8 21 8 50 2 08 2 37 5.0 4.9 2.5 2.5 Ca dera: Lighthouse Light on mole head Cabeza de Vaca Point: Extreme Flamenco: SE. comer of bay 9 00 9 05 2 47 2 52 5.0 4.9 2.5 2.5 Chanaral Bay: Observation pt St. Felix I. : Peterborough Cathedral Rock Pan de Azucar Island * Summit APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OP SOUTH A -MTHRIC A— Continued. [Page 301 1 Place. Lat. S. Long. W. Lun. Int. Range. 1 H.W. L.W. Spg. Neap. 1 2 Lavata: Cove near SW. pt 25 39 30 25 31 00 25 25 20 25 07 00 25 05 25 24 34 30 24 15 00 23 53 00 23 38 50 23 33 05 23 28 30 23 26 42 23 06 30 22 34 00 22 06 00 21 55 50 21 28 00 21 05 30 20 57 40 20 51 05 20 12 30 19 05 01 19 36 30 19 19 00 18 45 40 18 28 43 17 58 35 17 42 00 17 37 00 17 01 00 17 00 00 16 42 20 16 23 50 16 13 30 15 48 00 15 33 15 15 20 56 14 57 00 14 41 00 14 09 50 13 50 00 13 48 00 13 45 00 13 38 20 13 01 00 12 48 00 12 31 00 12 11 30 12 04 03 12 08 15 11 47 10 11 27 10 10 49 45 10 06 15 9 38 35 9 15 30 9 04 40 8 46 30 8 34 50 8 05 40 7 42 40 7 23 40 70 44 03 70 41 18 70 34 10 70 30 16 70 29 50 70 36 29 70 33 00 70 32 28 70 25 18 70 26 55 70 34 56 70 37 11 70 31 39 70 17 42 70 13 40 70 11 17 70 02 45 70 12 12 70 10 26 70 14 40 70 11 20 70 10 30 70 15 21 70 17 50 70 21 50 70 20 00 70 52 31 71 22 31 71 20 01 72 02 53 72 07 16 72 27 16 73 16 41 73 41 31 74 27 16 74 51 01 75 09 36 75 30 46 75 49 56 76 16 36 76 27 31 76 18 31 76 10 00 76 24 15 76 31 06 76 38 11 76 48 56 77 02 31 77 15 44 77 14 45 77 16 11 77 50 04 77 43 42 78 10 02 78 21 33 78 30 03 78 35 57 78 45 16 78 56 53 79 06 46 79 26 00 79 33 15 ft. m. 9 10 ft. m. 2 57 ft. 5.0 ft. 2.5 San Pedro Point: Summit Port Taltal: Lighthouse 9 20 9 35 9 30 3 07 3 22 3 17 4.9 5.0 4.9 2.5 2.5 2.5 Grande Point: Outer summit Paposo Road: Huanillo Pt Reyes Head : Extreme pitch ... Cobre Bay: Pt W, of village . Jara Head : Summit Antofagasta: Lighthouse 9 05 2 52 4.7 2.4 Chimba Bay: E. pt. of laige island Moreno Mountain: Summit... Constitution Cove: Shingle pt. of island.. Mexillones Mount: Summit 9 35 9 44 8 55 3 22 3 31 2 42 3.9 4.0 4.8 2.0 2.0 2.4 Port Cobija: Landing place Tocopilla : Extremity Point San Francisco Head : W. pitch Loa River: Mouth Lobos Point: Outward pitch 9 00 2 47 4.9 2.5 Pabellon de Pica: Summit Pa tache Point: Extreme.. .. Iquique: Lighthouse 8 35 2 22 5.0 2.5 Mexillon Bay : Landing place Pisagua: Pichalo Pt. extreme 8 32 2 20 5.0 2.5 Gorda Point: W low extreme Lobos Point: Summit Arica: Iron chiirch 7 49 1 37 5.6 2.8 Schama Mount: Highest summit Coles Point: Extreme. Ilo: Mouth of rivulet 7 55 1 43 5.3 2.7 Port Mollendo* Lighthouse. Islay : Customhouse 7 39 1 27 6.2 3.1 QuiJica: W. head of cove Pescadores Point* SW extreme Atico: E. cove Chala Point: Extreme Lomas: Flagstaff on pt San Juan Port: Needle Hammock Nasca Point: Summit. ... 6 47 35 3.9 2.0 Mesa de Dona Maria: Central summit Carre ta Mount: Summit San Gullan Island: N summit Paraca Bay: N. extreme of W. pt Pisco: Lighthouse 6 16 04 3.8 L9 Chincha Islands: Boat slip, E. side N. id. . Frayles Point: Extreme Asia Rock: Summit Chilca Point: SW. pitch Morro Solar* Summit . . San Lorenzo Island: Lighthouse. . Callao: Palominos Rock Light 5 47 i2 '^ 3.5 L8 Pescadores Islands: Summit of largest Pelado Tslanrl : Siinimit , , Sup6 * W^ end of village . Huarmey : W. end of sandy beach floliTia RfifloTifla.* SiiTTimit, 5 08 11 21 2.1 1.1 Samanco Bay Cross Pt Chimbote: Village, N. part 4 50 11 03 2.0 1.0 Chao Islet: Center Guanape Islands: Summit of highest TTnanohflnn Point* SW fffrPiTifi Malabrigo Bay: Rocks 4 19 10 32 2.1 LI Pacasmayo ■ Lighthouse Page 302] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. WEST COAST OF SOUTH AMERICA— Continued. 1 Place. Lat. S. Long. W. Lun. Int. Kange. H. W. L. w. Spg. Neap, 9 •e 9 w i a e Eten Head: Lighthouse 6 55 50 6 46 00 6 46 45 6 26 45 5 55 30 5 05 02 4 40 50 4 16 40 3 30 42 3 10 40 2 12 24 2 44 30 2 12 00 1 16 55 1 03 30 56 50 35 25 21 30 Lat N. 50 10 40 00 1 03 30 1 36 00 1 49 36 2 37 10 2 58 10 3 49 27 4 17 06 5 28 46 6 41 19 6 49 45 79 51 30 79 57 55 80 42 54 80 51 56 81 09 19 81 07 17 81 17 01 81 12 01 80 28 12 80 25 29 79 52 19 79 53 45 80 59 00 81 03 55 80 55 55 80 42 50 80 25 24 80 30 37 80 05 40 80 07 55 79 42 00 79 03 30 78 45 29 78 24 24 78 11 16 77 11 45 77 29 44 77 33 28 77 30 31 77 40 55 ft. TO. 4 04 ft. m. 10 17 ft. 2.5 ft. 1.3 Lambayeque: Beach opposite Lobos de Af uera Island : Cove on E. side . . Lobos de Tierra Island: Central summit. . Aguja Point: W. cliff summit 1 Paita Cathedral Parinas Point : Extreme Cape Blanco: Under middle of high cliff. . Tumbez : Malpelo Pt Guayaquil River: Light on Santa Clara I. Guayaquil, Concejo: S. pt. of city Puna: llandinga Pt. light 4 00 7 00 10 13 1 00 10.0 n.o 5.1 5.6 Point Santa Elena: Veintemilla light Plata Isle: E. pt 3 00 • 9 13 7.9 4.0 Cape San Lorenzo: Marlinspike Rock Manta Bay: Lighthouse 3 10 9 23 7.5 3.8 Caraques Bay: Punta Playa Cape Pasado : Extreme 3 15 9 28 9.9 5.0 Point Galera: N. extreme Cape San Francisco: SW. extreme Esmeralda River: Lighthouse Mangles Point: S. pt. of creek entrance. . . Tumaco: S. pt. of El Morro I 3 35 9 48 13.2 7.1 Guascama Point: Extreme Gorgona Island: Watering Bay Buenaventura: Basin Pt 6 00 12 13 13.2 7.1 Chirambiri Point: N. extreme Cape Corrientes: SW. extreme 3 40 3 30 9 53 9 43 13.1 13.3 7.0 7.2 Cupica Bay: Entrance to Cupica River. . Cape Marzo: SE. extreme ISLANDS IN THE ATLANTIC OCEAN. IB •0 a s Fseroe Islands, Strom Islet: Thorshaven Fort flagstaff Halderoig Islet: Halde- roig Chiu*ch 62 02 26 62 18 20 61 23 00 57 35 52 39 40 07 39 27 00 38 32 09 38 31 45 38 34 30 38 25 00 38 40 30 39 05 24 38 38 20 37 44 16 37 49 20 36 56 00 37 16 44 6 43 08 7 00 36 6 45 30 13 42 21 31 08 00 31 08 49 28 34 00 28 37 39 28 44 00 28 28 12 28 13 00 28 00 45 27 13 45 25 40 40 25 08 21 25 10 00 24 47 06 Numiken Rock Rockall Islet: Summit, 70 feet Corvo Island: S. pt Flores Island: Santa Cruz Fort Fayal Channel: N. Magdalen Rock Fayal Island, Horta: Castle of Santa Cruz. Caldera: Summit 3,351 ft. . . Pico Island t Summit.. . . 11 30 5 18 3.9 1.8 St. George Island : Lighthouse Graciosa Island: Santo Fort light Terceira Island: Monte del Brazil, near Angra 20 6 32 4.4 2.0 St. Michael Island: Customhouse, Ponta Delgada Pt. Amel light Santa Maria Island: Villa do Porto light.. Formigae Islands: Highest rock 15 6 27 5.7 2.6 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS IN THE ATIiANTIC OC5E AN— Continued. [Page 803 Si Place. Porto Santo Island : Lighthouse Desertas: Chao I., Sail Rock Madeira Island : Funchal light Fora I. lighthouse Pico Ruivo, summit, 6,056 ft Pargo jW.)Pt Salvage Islands: Lightnouse, Gran Sal- vage I Al^ranza Island: Delgada Pt. light Lanzarote Island: Port Naos light Pechinguera Pt. light. Lobos Island : Martino Pt. light Fuerta Ventura Island : Jandia Pt. light. Gran Canaria : Isleta Pt. light Palmas light Teneriffe Island: Anga Pt. light ; Santa Cruz, Br. con- sulate Summit of peak, 12,180 ft Gomera Island : Port Gomera Ferro Island: Port HieiTo Palma Island : Light, NE.pt San Antonio Island : Bull Pt. light Summit, 7,400 ft. . , St. Vincent Island : Porto Grande light. . St. Lucia Island: N. pt Raza Island: E. pt St. Nicholas Island : Lighthouse Sal Island: N. pt. light S.pt Boavista Island : NW.pt NE.pt Lighthouse Mayo Island: Engli&h Road St. Jago Island: Reta Pt. light Porto Praya, S. light. . . Fogo Island: N. S. da Luz, village Brava Island : Lighthouse Ireland Island: Dock yard clock tower.. Bastion C Hamilton Island: Gibbs Hill light St. Davids Island : Lighthouse St, Paul Rocks: Summit, 64 ft Rocas Reef: NW. sandy islet Fernando Noronha: The Pyramid Ascension Island: Fort Thornton St. Helena Island: Obs. Ladder Hill Martin Vaz Rocks: Largest islet Trinidad Island: SE.pt Inaccessible Island : Cfenter Tristan da Cunha Islands: NW. pt Gough Island: Pengxiin Islet Lat. N. 33 03 15 32 35 45 32 37 43 32 43 14 32 45 00 32 48 07 30 08 00 29 23 50 28 57 24 28 50 56 28 45 25 28 03 00 28 10 42 28 07 06 28 35 25 28 28 12 28 16 35 28 08 00 27 46 30 28 50 06 17 06 50 17 04 00 16 53 14 16 49 00 16 38 00 16 34 00 16 50 50 16 34 00 16 13 20 16 11 00 16 09 10 15 07 30 15 18 06 14 53 40 14 53 00 14 50 30 32 19 22 32 19 37 32 15 05 32 21 40 55 30 Lat. S. 3 51 30 3 50 30 7 55 20 15 55 00 20 27 42 20 30 32 37 19 00 37 02 48 40 19 11 Long. W, 16 16 20 16 33 30 16 54 53 16 39 31 16 57 30 17 16 05 15 54 00 13 29 31 13 33 07 13 52 05 13 49 13 14 31 35 15 25 11 15 2:4 56 16 08 11 16 15 09 16 38 02 17 05 55 17 54 22 17 47 01 24 59 15 25 17 00 24 59 30 24 47 08 24 38 08 24 10 00 22 54 55 22 55 42 22 55 44 22 42 00 22 57 20 23 12 42 23 47 06 23 31 45 24 30 38 24 40 00 64 49 35 64 49 15 64 49 40 64 38 40 29 22 28 33 49 29 32 25 29 14 24 35 5 43 03 28 46 57 29 14 56 12 23 00 11 18 39 9 56 11 Lun. Int. Range. H. W. L. W h. m. 40 35 50 40 1 15 20 5 50 7 30 5 50 7 04 12 50 h. m. 6 52 6 47 7 00 6 50 7 27 6 30 12 00 1 20 12 00 52 Spg. Neap. 6.6 6.6 8.5 9.3 7.8 3.3 4.4 4.8 4.0 11 18 11 13 11 30 9 10 9 48 9 53 10.0 6.0 2.0 2.8 3.5 4.0 5 40 5.2 ft. 3.0 3.0 3.9 4.3 3.6 4.0 L5 2.0 2.2 2.6 4.6 2.7 0.9 L3 L6 L8 2.4 Page 304] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS TN" TTTR ATLANTIC OCEAN— Continued. o Place.- Lat. S. Long. W. Lun. Int. Range. 1 H. W. L. w. Spg. Neap. a- Port Egmont; Observation spot 51 21 26 51 04 11 51 32 20 51 41 10 51 40 40 54 04 45 53 48 00 59 34 00 55 57 00 60 54 00 60 46 00 62 55 36 54 16 00 f 1/ 60 04 52 68 30 56 58 08 04 57 51 30 57 41 48 38 15 00 43 25 00 27 45 00 26 33 00 44 25 00 45 53 00 60 35 00 Long. E. 6 14 00 h. m. 7 20 h. m. 1 08 ft. 10.7 ft. 5.6 Maje Hsjrbor: Observation spot . . ... Port Louis: Flagstaff, govt, house Port Stanley: Governor's bouse 5 31 11 27 4.3 2.2 Cape Pembroke: Lighthouse South Georgia Island: N. cape. • --• Shag Rocks : Center Sandwich Islands: S. Thul6 Traverse I. volcano. . . New S. Orkney Is.: E. pt. Laurie I E. summit Corona- tion I., 5,397 ft.... New S. Shetland Islands, Deception Is- land ■ Port Foster Bouvets Island (Circumcision): Center. . . ATLANTIC COAST OF EUKOPE. Greenwich" Observatory Lat. N. 51 28 38 51 45 34 52 12 52 51 22 28 51 08 23 50 54 47 50 44 15 50 46 35 50 48 03 50 53 45 50 42 07 50 39 42 50 34 30 50 31 10 50 13 18 50 20 02 50 10 49 50 08 30 49 57 40 50 02 44 50 04 10 49 53 33 50 33 00 51 04 00 51 12 05 51 27 24 51 27 48 51 36 50 51 37 52 51 41 00 51 43 15 52 24 20 52 45 00 53 18 30 53 18 54 Long. W. 00 00 1 15 06 Long. E. 05 41 1 26 48 1 22 22 58 18 13 00 Long. W. 1 05 15 1 05 58 1 24 00 1 33 04 1 35 25 1 17 47 2 27 30 3 38 28 4 09 27 4 15 53 5 01 00 5 12 06 5 39 18 5 44 45 6 20 38 5 01 55 4 12 30 4 40 35 2 35 55 3 09 42 3 56 00 4 40 59 5 10 30 5 40 15 4 05 40 4 47 50 4 42 00 4 37 01 1 10 7 46 18.8 12.6 North Foreland : Lighthouse 11 24 11 09 10 35 11 10 5 53 5 43 4 23 4 58 16.8 19.8 215 19.8 8.4 10.0 11.0 10.1 South Foreland: Lighthouse Dungeness: Lighthouse Beachy Head: Lighthouse Portsmouth: Observatory 11 31 35 11 05 4 19 6 48 4 53 13.2 12.8 12.2 6.7 6.5 6.2 Southampton* Royal Pier light Hurst Castle: W. light ^Aarllpn T?nplrs' Oln lifrlithoilfift Portland • Notch Bill fight 6 29 5 25 5 20 09 11 38 11 33 6.7 14.9 15.3 LO 6.8 7.0 Start Point: Lighthouse Plymouth: Breakwater fight Falmouth- St Anthonv Pt fiffht Lizard Point: W. fighthouse 4 45 10 58 14.2 6.5 Porthcumow: SE. cor. telegraph co.'s sta. Lands End: Longships fighthouse Scilly Islands: St. Agnes fighthouse 4 15 10 28 15.9 7.3 Bideford: High lighthouse 5 45 5 00 7 00 6 45 5 45 5 40 5 41 5 40 7 25 7 24 11 58 11 13 48 33 11 58 11 53 11 54 11 53 1 13 1 12 22.7 26.9 3L3 36.2 27.1 25.3 24.0 20.9 14.2 14.9 11.4 13.5 15.7 18.1 13.6 12.7 12.0 10.5 7.1 7.5 Lundy Island: Lighthouse, N. pt Bristol: Cathedral Cardiff: Lighthouse, W. pier Swansea: Lighthouse, W. pier Caldy Island : Lighthouse St. Anns : Upper fighthouse Smalls Rocks: Lighthouse ABerystwith : Lighthouse Bardsey Island : Lighthouse South Stack: Lighthouse on rocks Holyhead : Lighthouse on old pier 10 00 3 48 15.8 7.9 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. [Page 305 Place. Skerries Rocks: Lighthouse, highest I — Bidstone : Lighthouse on hill Liverpool: Rock light Bidston Observatory Morecambe Bay: Fleetwood high light. . . Calf of Man: Upper lighthouse Isle of Man : Ayre Pt. lighthouse , St. Bees: Lighthouse White Haven: W. pierhead light Mull of Galloway: Lighthouse Ayr, Firth of Clyde: Lighthotise, N.side harbor Troon: Lighthouse, inner pier., Ardrossan: S. breakwater light. Pladda Island : Lighthouse Glasgow: Observatory 1 Can tyre: Lighthouse Rhynns of Islay : Lighthouse Oban: Lighthouse on N. pier Skerryvore Rocks: Lighthouse Barra Head: Lighthouse Glas Island: Lighthouse, Scalpay I Stomoway : Amish Pt. light Butt of Lewis: Lighthouse Cape Wrath: Lighthouse Dunnet Head: Lighthouse Kirkwall (Orkneys): New pierhead light. Startpoint (Orkneys): Lighthouse North Ronaldsay: Lighthouse Fair Isle Skroo: Lighthouse Sumburgh Head: Lighthouse Blackness (Shetland Is.): Lighthouse pier Lerwick (Shetland Is.) : Fort Hillswickne&s (Shetland Is.): S. extreme. Balta I. (Shetland Is.): Cairn on E. side. . Pentland Skerries: Upper lighthouse Tarbertness: Lighthouse Buchanness: Lighthouse Aberdeen (Girdleness): Lighthouse Buddonness: Upper lighthouse Bell Rock: Lighthouse May Island : Lighthouse Inch Keith Rock: Lighthouse Edinburgh: City observatory Berwick: Lighthouse Fam Island: NW. lighthouse Coquet Island: Lighthouse Tynemouth: Souter Point lighthouse North Shields: Lighthouse Sunderland: N. pier light Hartlepool: Lighthouse Flamborough: New lighthouse Humber River: Killingholme middle light Lat. N. Spurn Head: Upper lighthouse . Lowestoft: Lighthouse Orfordness: N. lighthouse Harwich: Landguard Pt. light. 53 25 15 53 24 02 53 26 38 53 24 05 53 55 03 54 03 14 54 24 56 54 30 50 54 33 00 54 38 10 55 28 10 55 32 55 55 38 27 55 26 00 55 52 43 55 18 39 55 40 20 56 24 50 56 19 22 56 47 08 57 51 25 58 11 28 58 30 40 58 37 30 58 40 16 58 59 15 59 16 45 59 23 24 59 33 00 59 51 15 60 08 02 60 09 22 60 27 20 60 44 25 58 41 22 57 51 54 57 28 15 57 08 33 56 28 07 56 26 03 56 11 00 56 02 09 55 57 23 55 46 00 55 37 00 55 20 06 54 58 10 55 00 30 54 55 07 54 41 51 54 07 00 53 39 00 53 34 45 52 29 14 52 05 00 51 56 05 Long. W. 36 20 10 42 02 27 04 20 00 20 49 37 22 01 37 50 36 00 51 20 4 38 10 4 41 00 4 49 28 5 07 09 4 17 38 48 00 30 46 28 20 06 32 39 09 6 38 28 6 22 10 6 16 01 4 59 41 22 25 57 33 22 25 22 45 36 30 16 20 1 16 02 1 08 41 1 29 50 47 30 2 55 25 46 30 46 22 04 06 44 53 23 06 33 22 08 05 10 47 59 00 39 00 32 00 21 30 26 00 21 30 10 19 05 00 12 00 Long. £. 07 10 1 45 24 1 34 30 1 19 10 Lun. Int. H.W. h. TO. 11 08 11 00 10 55 11 00 11 05 11 40 11 35 55 10 20 5 10 "5"35 'e'ss 9 57 10 50 9 35 10 20 9 30 10 00 24 50 1 56 1 58 2 08 Range. L.W. 3 11 3 12 3 21 4 20 5 16 9 47 11 05 11 56 ft. m. 5 27 4 48 4 43 4 48 4 53 5 28 5 23 7 08 4 08 11 22 'ii"47 "'6'22 3 44 4 37 3 22 4 17 3 17 3 47 6 36 7 02 8 08 8 11 8 28 9 31 9 32 9 43 10 36 11 29 3 35 4 53 5 44 Spg. 27.6 27.4 19.7 25.9 14.8 8.7 8.8 11.2 4.0 12.8 ii.'i' 13.' 4' 9.8 5.0 5.2 6.0 6.4 9.8 11.2 11.7 15.5 16.5 15.0 14.8 14.5 14.2 15.8 18.5 6.2 7.8 n.2 Neap. ft. 14.0 13.9 10.0 13.1 8.9 5.2 5.3 6.7 2.4 7.7 '4.8 '5.' 7 4.2 2.2 2.2 2.6 2.7 4.2 6.1 6.4 8.5 8.9 7.5 7.4 7.3 7.0 10.2 3.6 4.5 6.6 21594°— 14- -20 Page 306] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OP ETJBOPE— Continued. Place. Cape Clear: Old lighthouse Fastnet Rock : Lighthouse Mount Gabriel: Ordnance survey station. Castlehaven : Lighthouse Mizen Hill: Ordnance survey station. . . . Bantry Bay : Roancarrig light Bull Rock: Lighthouse Skelligs Rocks: Lighthouse Valentia: Lighthouse Port Magee Dingle Bay: Light at entrance Blasket Islands: Westernmost rock Smerwick: Signal tower Tralee Bay: Lighthouse Beeves Rocks: Lighthouse Limerick: Cathedral Shannon River: Loop Head light Eeragh Island: Lighthouse Arran Island: Lighthouse Galway: Mutton I. light Golam'Head: Tower Slyne Head: N. lighthouse Clifden Bay: Gortrumnagh Hill TuUy Mountain : Ordnance survey station . Inishboffin : Lyon Head light Inishturk Island: Tower Clew Bay: Inishgort light Newport: Church Clare Island: Lighthouse Blacksod Point: Lighthouse Eagle Island : W. lighthouse Broadhaven: Guba Cashel light Dounpatrick Head: Ordnance survey station Anghris Head: Ordnance survey station.. Knocknarea: Tumulus Sligo Bay: Black Rock light Knocklane: Ordnance survey station. . . . Killybegs (Donegal Bay): St. Johns Pt. light Rathlin O'Bime Islet: Lighthouse Aran Island : Rinrawros light Bloody Foreland: Ordnance survey sta- tion Tory Island: Lighthouse Horn Head: Ordnance survey station Melmore Head: Tower Fanad Point: Lighthouse Glashedy Island: Ordnance survey station Malin Head : Tower InishtrahuU : Lighthouse Inishowen Head : E. lighthouse Moville: New Pier Londonderry: Cathedral Scalp Mountain : Ordnance survey station . Benbane Head: Summit Rathlin Island : Altacarry lighthouse Maiden Rocks: W. lighthouse Lough Lame: Farres Pt. lighthouse Belfast Bay: Light, east side Mew Islands: Lighthouse Donaghadee: Lighthouse South Rock: Light vessel Lat. N. 51 26 02 51 23 18 51 33 24 51 31 00 51 27 41 51 39 10 51 35 30 51 46 14 51 56 00 51 53 08 52 07 15 52 04 30 52 13 46 52 16 14 52 39 00 52 40 04 52 33 38 53 08 55 53 07 38 53 15 13 53 13 46 53 23 58 53 29 47 53 35 00 53 36 40 53 42 27 53 49 34 53 53 06 53 49 30 54 05 45 54 17 00 54 16 00 54 19 36 54 16 33 54 15 30 54 18 00 54 20 50 54 34 08 54 39 47 55 00 52 55 08 13 55 16 26 55 12 31 55 15 14 55 16 33 55 19 07 55 22 50 55 25 55 55 13 38 55 10 20 54 59 40 55 05 23 55 15 03 55 18 05 54 55 47 54 51 07 54 40 20 54 41 50 54 38 45 54 24 04 Long. W 9 29 03 9 36 25 9 32 44 9 10 20 9 48 19 9 44 49 10 18 03 10 32 45 10 19 16 10 23 17 10 15 30 10 40 00 10 21 40 9 52 53 9 01 18 8 37 23 9 55 54 9 51 30 9 42 06 9 03 10 9 46 03 10 14 01 10 03 54 10 00 15 10 09 40 10 06 41 9 40 12 9 32 56 9 59 00 10 03 34 10 05 31 9 53 00 9 20 41 8 46 02 8 34 25 8 37 00 8 40 14 8*27 33 8 49 52 8 33 48 8 15 38 8 15 00 7 57 15 47 12 37 53 23 51 22 22 13 37 Lun. Int. 7 7 7 7 7 6 55 38 02 20 19 25 21 51 28 45 10 45 44 18 47 21 49 30 31 30 32 01 22 20 H. W, h. m. 3 50 4 10 3 30 3 40 3 40 3 50 6 00 4 15 4 19 4 16 '4"26' 4 50 5 10 5 03 L. W. 6 55 7 48 10 30 10 42 ii 66" h. TO. 10 03 10 23 9 43 9 53 9 53 10 03 13 10 28 10 19 10 29 "i6'33' 11 03 11 23 11 16 Range. 10.6 10.8 10.7 10.7 12.3 18.7 13.4 15.1 13.2 ii'i' 10.4 11.4 11.2 5 28 I 11 41 I 11. 6 43 1 35 4 18 4 06 '4"48' 7.5 8.0 6.7 9.3 ii.'i" APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EXJBOPE— Continued. [Page 307 Place. Lat. X. Long. W. Lun. Int. H.W. L.W. Range. Spg. Neap. Dundrum Bay: St. John Pt. light Carlingford Lough: Haulbowline Rk. It. . Drogheda: Lighthouse Rockabill: Lighthouse Howth Peninsula: Bailey light Dublin: Observatory N. wall light Poolbeg: Lighthouse Kingstown: E. pier light Killiney Hill: Mapae obelisk Bray BLead: Ordnance survey station Wicklow: Upper light Tara Hill: Summit Black Stairs Mountain: Ordnance survey station Tory Hill: Ordnance survey station Wexford: College Forth Mount: Ordnance survey station.., Tuskar Rock: Lighthouse Great Saltee: S. end Waterford: Hoop Pt. light Waterford: Cathedral Great Newton Head: Metal Man Tower.. Dungarvan: Ballinacourty light Knockmealdown Mount: Ordnance sur- vey station Helvick Head: Ordnance siu-vey station. Mine Head: Lighthouse Youghal: Lighthouse Capel Island: Tower Ballycottin: Lighthouse Cork Harbor: Haulbowline Coal Wharf.. Queenstown: Roches Pt. light Kinsale: Lighthouse, S. pt Seven Heads: Tower Galley Head: Light on summit Stag Rocke: Largest Alderney Harbor: Old pier light St. Heliers: Light on Victoria Pier Vardo: Fortress Vadso: Lighthouse North Cape: Extreme Fruholm: Lighthouse Hammerfest: Lighthouse Tromso: Observatory Hekkingen : Lighthouse Andenes: Lighthouse Lodingen (Hjertholm): Lighthouse. Lofoten Island: Skraaven I. light. . Glopen light Gryto: Lighthouse Stot: Lighthouse Traenen: Soe Islet light Bronnosund: Lighthouse Villa: Lighthouse Halten Island: Lighthouse Koppem Agdenes: Lighthouse Trondheim: Mumkholmen flagstaff. Grip: Chiu-ch Chnstiansund: Storvaden Freikallen 54 13 30 54 01 10 53 43 00 53 35 47 53 21 40 53 23 13 53 20 47 53 20 30 53 18 10 53 15 52 53 10 39 52 57 54 52 41 55 52 32 55 52 20 53 52 20 04 52 18 57 52 12 09 52 06 41 52 07 25 52 15 33 52 08 13 52 04 27 52 13 39 52 03 00 51 59 33 51 56 34 51 52 54 51 49 30 51 50 33 51 47 33 51 36 11 51 34 14 51 31 50 51 28 05 49 43 00 49 10 29 70 22 00 70 04 00 71 11 00 71 06 00 70 40 15 69 39 12 69 36 05 69 19 30 68 24 40 68 09 20 67 53 15 67 23 15 66 56 35 66 25 50 65 28 40 64 32 55 64 10 25 63 48 25 63 38 45 63 27 04 63 13 11 63 07 01 63 03 04 5 39 30 6 04 45 6 15 00 6 00 20 6 03 06 6 20 17 6 13 33 6 09 00 6 07 30 6 06 37 6 04 55 6 00 08 6 13 01 6 48 17 7 07 31 6 28 15 6 33 41 6 12 35 6 37 15 6 55 53 7 06 24 7 10 15 7 33 05 54 54 32 39 35 08 50 34 51 10 59 00 8 18 20 8 15 14 8 31 58 8 42 51 8 57 10 9 13 27 2 12 00 2 06 44 Long. E. 31 07 30 29 45 00 25 40 00 23 59 00 23 40 00 18 57 00 17 50 15 16 08 00 16 02 30 14 40 40 13 04 30 13 52 30 13 28 50 11 59 50 12 13 30 10 42 10 9 24 50 9 44 45 9 45 20 10 23 30 7 36 05 7 43 35 7 46 04 10 45 10 45 10 55 11 00 10 52 10 30 10 10 7 05 5 30 5 05 5 00 5 02 4 33 4 30 4 20 6 21 6 09 5 40 2 20 1 35 42 11 35 11 18 11 00 ft. 4 33 4 33 15.8 n.6 4 43 12.7 4 48 4 27 13.0 10.9 4 18 3 58 11.8 8.7 53 4.9 11 43 ii'is 8.8 i2.'3' 11 13 11 15 4 40 10 53 10 59 10 43 10 33 16 00 11 57 8 40 7 48 6 55 5 23 5 04 4 48 12.4 12.6 n.8 n.6 11.4 10.7 17.2 3L2 9.0 8.3 7.8 7.0 6.9 8.4 5.0 ft. 9.2 6.8 7.5 7.6 6.4 6.9 5.1 2.9 5.1 "6.2 6.2 6.3 5.9 5.8 5.7 5.3 7.6 13.6 5.1 4.7 4.4 4.0 3.3 4.1 2.9 Page 308] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATTiANTIC COAST OF EUROPE— Continued. 3 Place. Lat. N. Long. E. Lun. Int. Range. H.W. L.W. Spg. Neap. « 1 Hestfikjaer: Lighthouse 63 05 00 62 58 49 62 48 20 62 19 38 62 11 12 61 51 21 61 38 40 61 33 35 61 19 16 60 45 05 60 23 54 60 21 39 60 07 50 59 57 44 59 18 20 59 03 10 58 58 30 58 39 25 58 36 56 58 25 51 58 06 25 57 58 55 57 58 00 58 07 50 58 04 15 58 15 02 58 24 40 58 51 50 58 59 25 59 00 01 58 59 34 58 58 05 59 01 35 59 10 30 59 23 10 59 25 34 59 29 23 59 39 52 59 40 21 59 54 44 59 09 00 59 07 08 58 59 45 58 54 05 58 56 24 58 54 12 58 32 45 58 20 12 57 53 49 57 40 58 57 18 15 57 06 26 56 54 08 56 40 21 56 14 40 56 18 06 56 02 37 55 52 00 55 41 52 55 36 47 55 23 00 7 29 55 7 12 32 6 36 10 5 16 25 5 07 59 5 15 11 4 47 38 4 46 45 4 47 14 4 42 55 5 18 11 5 19 35 5 01 00 5 03 30 4 52 35 5 24 20 5 45 20 5 33 35 5 49 08 5 58 49 6 34 20 7 03 10 7 29 50 8 00 30 8 03 30 8 31 36 8 47 55 9 36 15 9 45 50 9 45 14 10 03 28 10 09 26 10 31 55 10 36 25 10 32 45 10 29 52 10 19 15 10 38 08 10 36 55 10 43 23 10 50 15 11 24 09 10 47 20 11 00 45 11 10 28 11 00 36 11 02 16 11 13 24 11 28 04 11 53 54 11 54 16 12 14 32 12 29 48 12 51 38 12 51 47 12 27 11 12 41 30 12 49 48 13 11 15 12 59 49 12 49 02 h. TO. h. m. ft. ft. Stemshesten Jilrstenen: Lighthouse Svinoen Islet Hjoerringa Mountain: Summit Hornelen Mountain: Summit Batalden Island: Store Kinnsund: Lighthouse Alden , Helliso: Lighthouse Bergen: Naval School Obsy 10 15 3 55 4.1 2.1 Lorstakken Mountain: Summit Marstenen Islet : Lighthouse Furen Islet Ulsire : Lighthouse - Hvidingso : Lighthouse Port Stavanger ■ Lighthouse 9 43 3 40 1.9 0.8 Obristadbroekke : Lighthouse Synesvarde Mountain: Summit Kompas Mountain: Summit Lister: Lighthouse Lindesnes: Lighthouse Ryvingen Island: Lighthouse Christianssand ■ Odderoen light 4 16 10 15 LI 0.5 Okso : Lighthouse Hamberg: Mill Arendal Inlet: Inner Torungerne light. . . Jomfruland : Lighthouse 4 17 10 10 LO 0.7 Langotangen: Lighthouse Langesund : Church Frederiksvsern: Lookout tower 4 34 10 00 1.3 1.0 Svenor: Lighthouse Foerder Islet: Lighthouse Fulehuk: Lighthouse Ilorten: Church Holmestrand : Church Drobak : Church Oscarsberg: Fort flagstaff Christiania : Observatory 5 22 10 37 1.2 0.9 Stromtangen (Torgauten): Lighthouse — Fredriksten: Fort clock tower Torbjomskjaer : Lighthouse Koster: Lighthouse Stromstad: Steeple Nord Koster Islands: Lighthouse Wadero Island : Lighthouse Hollo Island : Lighthouse Paternoster Rocks: Lighthouse Gottenbiu-g: Signal station Nidingen Islet: Lighthouse Warberg: Castle tower Falkenberg: Church Halmstad : Palace Engelholm: Church Kullen Point: Lighthouse Helsingborg : Lighthouse Landskrona : Lighthouse Lund : Royal Observatory Malmo: Lighthouse Falsterbo : Lighthouse APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. [Page 309 Place. Trelleborg: Lighthouse Ystad : Lighthouse. Sandhammaren : Lighthouse Hano Island : Lighthouse Karlshamn: Lighthouse Karlskrona: Stumholm Tower Oland Island : Light on S. pt Gottland Island: Hoburg light, S. pt. Ostergarns light Faro Island : Holmadden light Sparo Vestervik : Granso light Haradsskar Islet: Lighthouse Norrkopings Inlopp: Lighthouse Landsort: Lighthouse Stockholm: Observatory Upsala: Observatory Norrtelge: Inn Soderarm: Lighthouse S vartklubben : Lighthouse Osthammar: Church Oregrund: Clock tower Djursten: Lighthouse Foremark: Church Orskar Rock: Lighthouse Gefle: Church Eggegrund Islet: Lighthouse Hamrange: Church Soderhamm: Courthouse Enanger: Church Hudiksvalls: Courthouse Gnarp: Church Sundsvall: Church Lungo: Lighthouse Skags Head: Lighthouse Holmogadd : Lighthouse Umea: Bredekar Light Bjuroklubb : Lighthouse Pi tea Rodkallen: Lighthouse Maloren: Lighthouse Tomea: Lighthouse Uleaborg : Karlo I . light Ulko Kalla Rock: Lighthouse. Norrsher Islet: Kvarken light.. Kaske: Shelgrund I. light Biemeborg: Sebsher light Nuistad: Ensher light Abo: Observatory Aland Island: Shelsher light... Ekkere Light Logsher light... Bogsher: Beacon Ute Islet : Lighthouse Gauge : Gauge I. light Rensher : Lighthouse Helsingfors : Observatory Soder Skars : Lighthouse Kalboden Island : Light vessel . Rodsher Island: Lighthouse... Hogland Island: Lower light... Upper light. . . Lat. N. 22 00 25 42 22 58 00 54 10 04 09 45 11 50 55 18 26 29 57 24 45 38 08 52 17 55 44 26 20 33 61 29 45 24 45 15 10 35 15 19 20 26 22 15 22 26 31 41 40 29 43 48 55 57 18 22 32 54 43 57 02 51 23 30 38 35 11 55 35 34 39 33 28 50 19 10 18 53 31 30 48 30 02 20 20 05 14 08 20 06 28 29 43 10 26 57 24 45 13 20 50 50 31 11 46 30 46 00 56 10 09 43 06 40 58 45 58 08 00 40 06 22 Long. E. 13 09 20 13 49 38 14 11 10 14 50 57 14 52 02 15 36 05 16 24 04 18 11 06 18 59 27 19 22 36 16 40 36 16 59 22 16 11 28 17 52 09 18 03 30 17 37 32 18 41 34 19 24 34 18 49 49 18 22 36 18 26 33 18 24 21 18 09 49 18 22 38 17 08 29 17 33 50 17 02 57 17 04 18 17 01 51 17 07 37 17 16 22 17 19 05 18 05 05 19 02 50 20 45 35 20 18 35 21 34 45 21 30 00 22 21 55 23 34 00 24 12 00 24 34 00 23 27 00 20 37-40 21 11 24 21 22 34 21 01 00 22 17 03 19 34 00 19 31 20 19 54 05 20 25 50 21 22 00 22 58 08 24 24 43 24 67 17 25 25 51 25 37 30 26 41 05 27 01 40 26 58 44 Lun. Int. Range. H. W. L.W. h. m. Spg. Neap. ft. Page 310] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. Place. Sommer Island : Lighthouse Vieborg Bay: Nelva I. light Stirsudden: Lighthouse Kronstadt: Light on Frederikstadt bas tion Cathedral St. Petersburg: Observatory Pulkowa: Observatory Peterhof : Pier-head light Oranienbaum: Lighthouse Seskar Islet: Lighthouse Narva: Light S. pt. of entrance Stensher Rock: Lighthouse Ekholm Islet: Lighthouse Koksher: Lighthouse Revel: Light N. end of W. mole Cathedral Nargen Island: Lighthouse Surop: W. light Baltic Port: Lighthouse Odenskholm Island: Lighthouse Takhkona Point: Lighthouse Dago Island : Dagerort light Filzand Island: Lighthouse S valf erort Tzerel : Lighthouse Kuino: Lighthouse Pemau: Light at S. entrance Riga: Ust Dyinski light Cathedral of St. Peter Runo Island: Lighthouse Domesnes: Lighthouse Windau: Light on S. jetty Libau: Light at entrance of port Memel: Lighthouse HeiUgen Creutz: Church tower Brusterort: Lighthouse Pillau: Lighthouse Fischausen: City Hall tower Konigsberg: Observatory Tolkemit: Church tower Elbing: Church tower Tiegenort: Church tower Dantzig: Observatory Neufahrwasser light Weichselmunde: Fortress tower Putziger Heistemest: Church tower. . . , Oxhoft: Lighthouse Hela: Lighthouse Rixhoft: Lighthouse Leba: Church tower Stopelmunde: Church Jershoft: Lighthouse Rugenwalde: St. Mary's Church Coslin: St. Mary's Church Funkenhagen: Lighthouse Colbem: St. Mary's Church Gross-Horst: Lighthouse Cammin: Cathedral tower Wollin: Church tower Stettin: N. Castle tower Swinemunde: Lighthouse Lat. N. Long. E. 60 12 31 27 33 46 60 14 43 27 58 36 60 11 05 29 03 01 59 58 14 29 47 12 59 59 44 29 46 07 59 56 30 30 19 22 59 46 19 30 19 40 59 53 26 29 54 54 59 55 40 29 46 38 60 02 08 28 23 01 59 28 04 28 03 31 59 49 10 26 23 00 59 41 06 25 48 58 59 42 00 25 02 37 59 27 05 24 46 10 59 26 28 24 44 45 59 36 22 24 31 57 59 27 55 24 24 05 59 21 30 24 04 30 59 18 06 23 23 15 59 05 25 22 36 15 58 55 02 22 11 36 58 23 02 21 49 56 57 54 37 22 04 15 58 05 50 23 59 34 58 23 10 24 49 25 57 03 38 24 01 27 56 57 01 24 06 38 57 48 02 23 15 00 57 48 10 22 39 15 57 24 00 21 34 00 56 31 01 20 59 40 55 43 45 21 06 06 54 53 47 20 01 25 54 57 40 19 59 06 54 38 25 19 53 55 54 43 49 20 00 39 54 42 50 20 29 46 54 19 19 19 31 58 54 09 44 19 23 58 54 16 30 19 08 37 54 21 18 18 39 54 54 24 28 18 39 59 54 23 51 18 41 03 54 12 16 18 40 35 54 33 09 18 33 46 54 36 06 18 49 04 54 49 55 18 20 29 54 45 29 17 33 38 54 35 16 16 51 35 54 32 29 16 32 50 54 25 27 16 24 52 54 11 28 16 11 05 54 14 40 15 52 39 51 10 40 15 34 44 54 05 47 15 04 06 53 58 29 14 46 36 53 50 41 14 37 12 53 25 41 14 33 52 53 55 03 14 17 19 Lun. Int. Range. H.W. L.W. Neap. ft. TO. h. m. ft. /.'. APPENDIX IV. [Page 311 MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EITROPE— Continued. 3 5 Place. Lat. N. Long. E. Liin. Int. Range. H.W. L.AV. Spg. Neap, a a 1 Streckelsberg: Survey station near beacon Usedom : Church tower 54 03 08 53 52 17 53 56 59 54 03 18 54 05 49 54 15 02 54 22 56 54 25 08 54 40 53 54 18 42 54 28 28 54 20 47 54 14 42 54 10 42 54 05 27 54 06 32 54 08 00 53 53 50 53 58 54 53 57 44 54 26 16 54 29 43 54 28 54 54 19 47 54 23 52 54 27 25 54 20 28 54 28 25 54 30 55 54 39 48 54 47 05 54 54 28 54 40 23 54 56 48 54 58 05 55 02 46 55 03 52 55 05 31 55 03 04 54 54 13 54 41 51 54 41 21 54 28 43 54 19 08 54 07 52 54 10 57 53 57 15 53 55 01 53 52 25 53 36 12 53 33 43 53 32 45 53 33 07 53 32 52 52 31 31 52 29 07 53 28 30 53 42 50 53 36 20 53 32 52 53 46 57 53 42 21 o / * 14 01 17 13 55 26 13 51 13 13 46 51 13 22 53 13 55 42 13 37 54 13 26 11 13 26 12 13 05 30 12 30 23 12 24 02 12 26 04 12 05 19 12 08 10 11 46 04 11 41 54 11 28 09 11 05 54 10 52 59 11 11 59 11 14 29 11 04 18 10 32 59 10 22 24 10 12 04 10 08 53 9 50 23 9 34 23 9 56 13 9 26 20 9 45 35 10 02 23 9 52 20 9 58 41 9 25 18 9 23 35 8 39 41 8 26 50 8 22 03 8 33 13 8 33 58 9 03 21 8 56 38 8 51 53 7 53 11 8 24 35 8 29 58 8 42 43 9 28 48 9 36 40 9 56 35 9 58 27 9 58 21 13 21 52 13 28 33 9 59 37 8 14 48 8 18 30 8 34 25 8 04 47 8 01 43 h. TO. A. m. ft. ft. Lassau : Church tower Wolgast: Church tower Griefswald: St. Nicholas Church Griefswalder Oie: Lighthouse Granitz: Castle tower Bergen : Church tower Arkona: Lighthouse Stralsund: St. Mary's Church Darsserort: Lighthouse Wustrow: Church Ribnitz : Church tower Wameraunde: Church Rostock: St. Jacob's Church Diedrichshagen : Survey station Basdorf : Survey station Wismar : St Nicholas Church Hohenschonbei^: Survey station Travemunde : Lighthouse Burg: Church tower Manenleuchte : Lighthouse Petersdorf : Church tower Hessenstein: Flagstaff of lookout tower... Schonberg: Church Bulk : Lighthouse Kiel: Observatory Eckemforde: Church Schleswig: Cathedral Kappeln : Church Flensberg: Church Duppel: Survey station Schleimunde: Lighthouse Augustenbui^: C lurch Hugeberg: Survey station Apenrade: Church Skoorgaarde: Survey station Ballum: Church List: E. lighthouse 20 6 33 5.2 3.0 Keitum: Church Fohr: St. Nicholas Church 1 35 7 47 7.8 4.5 Galgenberg: Survey station Husum: Church 2 10 1 45 1 11 11 29 8 23 7 57 7 24 5 17 10.8 ILO 1L7 8.1 6.2 6.4 6.8 4.7 Tonning: Church Busum : Church Helgoland : Lighthouse Scharhom : Beacon Neuwerk: Lighthouse Cuxhaven: Lighthouse 39 6 51 10.1 5.8 Stade: Church steeple Steinkirchen : Church 4 00 10 13 8.5 4.9 Altona: Observatory Hambui^: Old Observatory 5 00 11 12 6.1 3.5 Imperial Marine Observatory . Berlin : Urania Observatory Treptow Observatory Harburg: Lighthouse Hohe Weg: Lighthouse 25 6 38 10.1 5.7 Langwarden : Church Bremerhaven: New harbor light Minsener Sand: Light vessel 54 10 7 07 6 23 10.4 9.5 5.8 5.3 Schillighom: Lighthouse Page 312] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUHOPE— Continued. Place. WiUaelmsliaven : Observatory Wangeroog: Lighthouse Spikeroog: Church Langeoog: Belvedere Balstriun: Church Nordemey : Lighthouse Juist: Church Emden: City Hall tower Falster: Gjedser light Moen Island: Stege Church spire Moen light, SE. pt Prceste: Church spire Kjorge: Church tower Amager Island: HoUcenderby Ch. spire.. Nordse Rase light Copenhagen: University Observatory Bomholm: Ronne light Christianso Island: Great tower Kronberg: High spire Nakkehooed: Upper light Hesselo leland : Lighthouse Anholt Island: Lighthouse Spodsbjerg: Lighthouse Roeskilde: Cathedral Nykjobing: Church tower Oddensby : Church tower Sejro Island: Sejro Point light Kallundborg: Church Omo Island: Church Vordingborg: Waldemar's tower Veiro Island : Lighthouse Langeland Island: Fakkebjerg light Mro Island: Church spire Lyo Island: Church tower Assens: Church tower Baago Island: Lighthouse Kolding: Castle tower Bogense: Church spire Nyborg: Church spire Turo Island: Church spire Svendborg: Frue Church Endelave Island : Church tower Samso Island: Koldby Church tower. . . . Horsens: Frelser Chiirch spire Tuno Island: Lighthouse Samsoe Island: Nordby Church tower. . . Aarhus: Cathedral spire Hjelm Islet: Lighthouse Fomaes: Lighthouse Hals: Church tower Aalborg: St. Rudolph's Church Cape Skaw, or Skagen: Old lighthouse. . . Hirtshals: Lighthouse Haustholm: Lighthouse Boobjerg: Lighthouse Ringkjobing: Church spire Loune: Church tower Blaabjerg: Summit, 100 ft Guldager: Church Fano Island: Nordby Church Mano Island: Church spire Lat. N. 53 31 52 53 47 25 53 46 19 53 45 06 63 43 46 53 42 39 53 40 45 53 22 06 33 50 59 03 56 46 07 24 29 44 35 45 38 10 41 13 05 40 19 19 02 20 07 10 11 50 44 16 58 36 38 34 55 30 57 52 55 09 40 50 09 48 00 26 02 19 44 23 51 14 02 34 16 09 17 44 29 31 34 03 18 41 03 00 03 37 45 32 48 02 51 44 56 58 57 06 09 26 08 00 26 36 59 54 02 54 43 46 35 06 06 50 30 48 05 27 47 17 44 50 31 52 26 26 16 11 Long. E. 8 08 47 54 09 41 45 35 41 22 03 13 58 6 59 53 7 12 25 11 58 03 12 17 16 12 32 40 12 03 07 12 07 36 12 38 24 12 41 26 12 34 41 14 42 00 15 11 39 12 32 02 12 20 50 11 42 50 11 39 15 11 51 36 12 05 02 11 40 29 11 24 06 11 05 07 11 05 04 11 09 32 11 54 59 11 22 23 10 42 13 10 24 11 10 09 16 9 53 50 9 48 09 9 28 40 10 05 29 10 47 47 10 40 02 10 36 48 10 16 20 10 33 37 9 51 19 10 26 51 10 33 00 10 12 50 10 48 32 10 57 40 10 18 53 9 55 22 10 36 38 9 56 44 8 36 10 8 07 23 8 14 52 8 14 36 8 14 43 8 24 12 8 24 03 8 32 38 Lun. Int. H. W. L. W ft. m. 04 11 27 11 05 24 9 33 5 46 4 18 2 35 2 35 2 34 Range. Spg. Neap. h. m. 6 17 5 15 ft. 13.2 8.0 ft. 7.4 4.5 4 53 7.3 4.1 6 36 8.9 5.0 3 21 0.6 0.3 11 58 10 30 LO L2 .05 .07 8 47 2.1 L2 47 46 4.5 4.7 2.6 2.7 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. [Page 313 Place. Lat.N. Long. £. Lun. Int. Range. H.W. L.W. Neap. ft. 2.0 Niewe Diep: Time-ball station Amsterdam : W. church tower Utrecht: Observatory Leyden: Observatory The Hague: Church tower Scheveningen : Lighthouse Brielle: Lighthouse Rotterdam : Time-ball station Ilellevoetsluis: Time-ball station Willemstadt: Lighthouse Goedereede: Light on church tower. . . . Flushing: Time-ball station Light, Westhaven bastion Brussels: New observatory Antwerp: Observatory Notre Dame Cathedral Blankenberghe: Fort lighthouse Ostend: Lighthouse Church tower Nieuport: Templars tower Paris: Observatory Dunkerque: Tower GraveUnes: Light on N. breakwater. . . . Calais: Light on old fort Cape Oris Nez : Lighthouse Boulogne, C. Alprech: Lighthouse Abbeville: Tower Cayeux: Lighthouse Dieppe: W. jetty light Ailly Point: Lighthouse St. Valery en Caux: Light on W. break- water Fecamp: N. jetty light Cape La Heve: S. light Havre: S. jetty light Honfleur : Hospital jetty light Caen: Church tower Port CorseuUes: W. jetty light Point De Ver : Ligh&ouse Cape La Hougue: Lighthouse Cape Barfleur: Lighthouse Cherbourg: Light, W. head of breakwater Naval Observatory Cape La Hague : Lighthouse Casqueta Rocks: Light on NW. rock. . . . Port St. Peter, Guernsey : Light on Castle Coonet Breakwater Douvres Rocks: Lighthouse Cape Carteret : Lighthouse Coutances: Cathedral tower Granville: L^hthouse Chausey Is . : Light on S E . end of large id . St. Malo: Rochebourne light Cape Frehel : Lighthouse Heau de Brehat: Lighthouse Morlaix, He Noire: Lighthouse De Bas Islet: Lighthoiise Abervrach : Light on Vrach Islet Ushant: Stiff Point light 52 57 50 52 22 30 52 05 10 52 09 20 52 04 40 52 06 16 51 54 29 51 54 30 51 49 19 51 41 48 51 49 08 51 26 33 51 26 24 50 47 66 61 12 28 51 13 17 51 18 47 51 14 13 51 13 50 61 07 63 48 60 11 61 02 09 61 00 18 50 57 45 50 52 10 50 41 57 50 07 05 50 11 42 49 56 06 49 55 04 49 52 28 49 46 05 49 30 04 49 29 01 49 25 32 49 11 14 49 20 18 49 20 28 49 34 19 49 41 50 49 40 29 49 38 54 49 43 22 49 43 17 49 27 13 49 06 28 49 22 27 49 02 54 48 50 07 48 62 13 48 40 18 48 41 05 48 54 33 48 40 23 48 44 45 48 36 57 48 28 31 46 36 53 01 07 45 29 03 18 30 15 10 10 46 28 50 07 40 26 26 58 35 35 48 34 32 21 44 24 44 24 12 06 54 55 51 55 22 45 34 20 15 22 31 06 34 51 07 35 02 33 47 49 56 30 46 05 01 57 35 42 34 22 12 04 08 06 22 13 43 Long. W. 21 10 27 24 31 08 16 21 15 56 43 44 38 08 57 15 22 41 31 31 48 49 48 25 26 39 36 46 49 20 58 41 19 08 05 11 52 33 01 38 34 34 03 26 h. m. 7 17 2 50 3 35 2 20 3 20 44 4 15 05 02 10 11 58 11 59 11 39 11 17 11 18 10 54 10 29 10 06 9 03 8 13 8 14 7 30 6 20 6 12 6 67' 6 50 5 55 6 43 5 35 5 00 4 35 4 00 3 36 h. m. 1 06 ft. 3.9 9 02 9 47 8 32 9 32 4.8 6.7 5.2 9.8 6 66 14.7 10 27 14.8 6 17 6 32 12.5 16.1 6 22 15.7 5 58 6 16 6 13 5 51 6 62 16.8 19.0 2L0 21.6 26.2 6 48 27.3 6 33 5 02 26.8 23.3 4 14 22.6 2 46 2 37 18.6 17.0 1 44 16 07 17.6 'is.' 5' 26.0 15 30.8 09 04 04 36.7 34.7 36.0 12 00 11 25 11 00 10 25 10 00 30.4 23.1 22.0 20.6 18.9 2.5 3.6 2.8 6.2 7.8 7.8 6.7 8.4 8.4 8.5 9.6 10.7 ILO 12.8 13.3 13.1 1L4 ILO 8.2 7.6 6.9 1L6 13.6 16.0 15.2 15.7 13.3 10.6 10.1 9.5 8.7 Page 314] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EUROPE— Continued. Place. Lat. N. Long. W. Lun. Int. Range. H.W. L.W. Spg. Brest: Observatory Brest (approach) : Quelern light De Sein Islet: Lighthouse Bee du Raz: Lighthouse Audierne : Pierhead light Penmarch Rocks: Lighthouse Glenan Islands: Light, Penfret I De Groix Island : Lighthouse Lorient : Church-tower light Belle Isle: Lighthouse Port Haliguen : Light on N . jetty Haedic Island : Lighthouse Port Navalo: Lighthouse Vannes: St. Pierre Church Le Four Rock: Lighthouse Croisic : End of breakwater Guerande: Steeple Port St. Nazaire : Lighthouse Paimboeuf : Steeple Nantes : Cathedral Noir Moutier Island : Lighthouse Le Pilier Island : Lighthouse D' Yeu Island : Lighthouse La Chaume: Lighthouse Point de Grouin du Cou: Lighthouse R6 Island: Light, NW. pt Rochelle: E. Quay l%ht Aix Island : Lighmouse Rochefort: Hospital Oleron Island : Light, NW. pt Point de la Coubre: Lighthouse Point Cordouan : Lighthouse Point de Grave : Lighthouse Bordeaux: University Obsy., Moirac Bayonne : Cathedral Biarritz : Lighthouse St. Jean deXuz: St. Barbe Point light.. Hendaye: Abbadia Observatory Fuenterrabia: Light on Cape Higuera... Port Pasages: Light at entrance San Sebastian: Monte Igueldo light Bilbao: Light on Galea Castle Castro Urdiales: Santa Ana Castle light.. Santona : Pescador Point light Santander : Cape Mayor light San Martin de la Arena: Lighthouse San Vincent de la Barquera: End of new mole Rivadesella: Mount Somos light Gijon : Santa Catalina light Aviles: Lighthouse Rivadeo: Lighthouse Estaca Point: Lighthouse Port Cedeira: Lighthouse Ferrol: Old naval observatory Priorino Chico light Coruna : Hercules Tower light Cape Finisterre : Lighthouse Vigo: Cres I. light Oporto: Light, N. S. de Luz 48 23 32 48 19 10 48 02 40 48 02 28 48 00 47 47 47 52 47 43 17 47 38 51 47 44 53 47 18 42 47 29 10 47 19 18 47 32 53 47 39 30 47 17 63 47 18 30 47 19 44 47 16 18 47 17 17 47 13 08 47 00 41 47 02 35 46 43 04 46 29 38 46 20 41 46 14 40 46 09 25 46 00 36 45 56 37 46 02 49 45 41 39 45 35 14 45 34 10 44 50 07 43 29 29 43 29 38 43 23 58 43 22 52 43 23 30 43 20 05 43 19 22 43 22 36 43 24 20 43 28 36 43 29 30 43 26 50 43 23 35 43 31 00 43 32 48 43 38 05 43 34 40 43 47 20 43 39 00 43 29 30 43 27 30 43 23 10 42 52 45 42 12 30 41 09 10 29 36 34 28 52 03 45 25 32 50 22 30 57 15 30 35 21 31 13 38 06 09 50 07 55 08 45 28 38 05 31 25 25 48 11 50 02 09 32 59 13 16 21 37 22 56 47 45 27 49 33 40 08 57 10 40 57 50 1 24 37 1 15 16 1 10 24 1 04 27 31 23 1 28 43 1 33 16 1 39 53 1 45 02 47 30 56 05 01 40 04 06 16 10 28 06 47 40 01 00 24 55 07 10 40 11 56 00 03 00 42 00 8 05 30 8 13 29 8 20 20 8 24 26 9 15 28 8 54 00 8 40 35 ft. m. 3 23 3 25 3 04 3 05 3 00 3 25 3 35 4 18 5 50 3 05 3 18 3 20 3 27 3 27 3 45 3 35 6 30 3 00 2 50 2 45 2 45 2 43 2 44 2 43 2 42 2 25 9 45 9*53' ft. 19.5 17.2 9 31 9 34 9 27 ILl 13.3 13.0 9 36 9 50 9 58 9 46 10 08 12 11 13.8 16.6 16.9 16.7 16.6 15.8 9 47 16.7 9 56 10 39 12 28 9 26 16.6 17.0 16.5 16.7 9 40 9 44 14.7 12.7 9 22 9 22 9 55 16.6 16.6 16.7 9 53 16.8 12 '914 15.3 ii's" 9 05 9 03 9 03 9 07 9 18 9 14 9 14 n.7 12.7 n.8 12.3 14.8 n.7 10.4 9 03 8 58 8 58 13.5 12.0 14.4 8 56 8 57 14.8 14.9 8 56 8 55 14.8 10.0 8 38 10.0 APPENDIX IV. [Page 315 MARITIME POSITIONS AND TIDAL DATA. ATLANTIC COAST OF EU HOPE— Continued. s A fl Place. Lat. N. Long. W. Lun. Int. Range. H.W. L.W. Spg. Neap. 40 12 25 40 10 47 39 24 49 39 21 00 38 46 49 38 42 31 38 29 15 37 01 20 37 07 48 36 58 23 37 11 00 37 15 08 36 43 58 36 27 42 36 31 30 36 10 50 35 59 53 36 07 19 36 07 10 36 06 25 8 25 47 8 54 15 9 30 29 9 22 30 9 29 46 9 11 10 8 56 00 8 58 00 8 39 53 7 51 48 7 24 00 6 57 12 6 26 30 6 12 18 6 19 00 6 02 08 5 36 31 5 26 12 5 21 17 5 20 42 h. m. h. m. ft. ft. Cape Mondego : Lighthouse 2 20 8 35 7.0 3.0 'Rorlnnof'i Tqlnnrl • T/ifhthotiaft Peniche ■ Lighthouse 2 05 8 15 7.8 3.4 Lisbon: Royal Observatory, Tapada Setubal * Lighthouse 2 20 2 10 8 05 8 20 n.i 1L6 4.8 5.0 Lagos' Church 1 55 8 08 13.0 5.6 P.ono Sta Marin* Liphthoiise San Lucar ■ Chipiona light 1 15 7 28 12.3 5.6 Cadiz : Observatory of San Fernando San Sebastian light 1 45 7 58 n.8 5.4 Pa-no Trsifdlofar* T.ichthniisfi Tarifa" Lighthouse 1 32 7 52 5.6 2.6 Europa Pt. light 1 35 7 55 3.7 L7 COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS. Malaga* Lighthouse 36 42 39 36 50 12 36 42 57 37 33 28 37 35 50 37 33 22 37 34 38 38 12 30 38 20 12 38 30 00 38 30 57 38 33 30 38 38 36 38 40 51 38 48 06 38 51 00 39 12 15 39 28 05 39 27 50 39 53 57 40 04 53 40 27 48 40 33 30 40 43 10 41 06 00 41 25 18 41 50 04 42 16 15 42 19 10 4 24 38 2 27 50 2 11 12 1 15 12 59 09 57 58 50 20 30 12 28 48 11 42 10 06 04 02 Long. E. 02 52 09 17 12 02 07 30 Long.W. 13 37 19 48 18 50 Long. E. 41 19 08 56 28 48 39 45 53 55 1 14 42 2 07 00 3 08 28 3 17 10 3 18 55 2 15 8 35 2.9 L5 riartairPTia* Arspnal patft Escombrera light Ranta Pnla. Rav* Tii&hthouse Alicante * N mole light Villaioyose* Lighthouse.. Benidonne* Tower. .......... . Altea: Lighthouse Calpe ' Church tower. , Jarea" Cape San Antonio light Deniac Mole-head light Cape Cullera' Lighthouse Valenciai Lighthouse Mole-end light 5 00 11 30 L5 0.8 Columbretes Islands* Lighthouse Oropesa Cape ■ Lighthouse Vinaroz ■ Mole-head light Port Alfapues* Bana light Cape Tortosa* Lio'hthouse 1 Tarragona* E mole light 1 Barcelona : Royal Academy Obsy Palamos Bay* Molino Pt light CaHaniipa" Cloclc towpr Canft Crwnt • TjichthonHP Page 316] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITERRANEAN, ADRIATIC, AND* BLACK SEAS— Continued. Place. Lat. N. Cape Bear: Lighthouse Port Vendres: Fort Fanal light Port Nouvelle: S. jetty light Cette: Light, St. Louis mole Aigues Mortes: Espignette Pt. light Planier Rock : Lighthouse Marseilles: Janet Cliff light National observatory Ciotat: Berouard mole light Toulon: St. Mandrien light Grand Riband Island: Lighthouse Cannes: Lighthouse Antibes: Garoupe light Nice: Lighthouse Villefranche: Mole-head light Cape Ferret light Port Ibiza: Lighthouse Cabrera Island : Lighthouse , Pi (Majorca) : Lighthouse Port Mahon (Minorca) : Lighthouse Carloforte: Int. Latitude Obey Cape Spartivento: Lighthouse Cape Sandalo: Light on San Pietro I Porte Conte: Cape Caccia light Port Torres: Lighthouse Cape Testa: Lighthouse Razzoli Island : Lighthouse Caprera Island : Galera Pt Cape Figari: Signal station Cape Tavolara : Lighthouse Cape Bella vista : Lighthouse Cape Carbonera: Cavoli I. light Cagliari: Light on mole Bonifacio: Mount Pertusato light Ajaccio: Lighthoiise Corti: Church tower Calvi: Lighthouse Cape Corso : Giraglia I . light Bastia: Lighthouse Porto Vecchio: Chiape Pt. light Cape Melle: Lighthouse Genoa: San Benigno light Hydro. Institute Obsy Spezzia: Fort Santa Maria light Florence: Arcetri Observatory Leghorn (Livomo): Light on S. end of curved breakwater Capraia Island: Cape Ferrajone light Elba Island, Porto Longone: Cape For- cado light Pianosa Island: Light on battery, W. side of fort Africa Rock: Lighthouse Monte Christo Islet: Summit Giglio Island, Cape Rosso: Lighthouse. . Civita Vecchia: Light N. end of break- water Rome: Royal Observatory at Capitol Gaeta: Orkndo tower 42 30 59 42 31 18 43 00 47 43 23 50 43 29 17 43 11 57 43 20 43 43 18 18 43 10 21 43 05 10 43 01 01 43 32 51 43 33 51 43 41 32 43 41 58 43 40 30 38 54 10 39 06 34 39 33 00 39 51 53 37 08 09 38 52 34 39 08 44 40 33 50 40 50 25 41 14 36 41 18 24 41 14 15 40 59 52 40 54 55 39 55 47 39 05 15 39 12 35 41 22 10 41 52 50 42 18 14 42 35 10 43 01 45 42 41 47 41 35 45 43 57 17 44 24 15 44 25 09 44 04 00 43 45 15 43 32 36 43 02 57 42 45 14 42 35 06 42 21 28 42 20 15 42 19 13 42 05 38 41 53 34 41 12 27 Long. E. 07 30 06 50 04 08 42 08 08 32 13 51 20 46 23 39 36 42 5 56 06 6 08 39 00 54 08 02 17 15 18 42 19 41 1 27 25 2 57 20 2 37 00 4 18 20 8 18 44 8 51 08 8 13 29 8 10 00 8 23 56 9 08 42 9 20 28 9 29 40 9 39 14 9 44 22 9 42 52 9 32 35 9 07 20 9 11 15 8 35 45 9 09 04 8 43 25 9 24 10 9 27 00 9 22 05 8 10 22 8 54 19 8 55 20 9 50 48 11 15 20 10 17 45 9 51 07 10 24 38 10 05 50 10 03 54 10 18 39 10 55 24 11 46 50 12 29 06 13 35 15 Lun. Int. H. \V. L. W. h. m. 7 31 8 22 h. m. 2 00 2 24 Range. Spg. Neap. 0.6 0.6 0.3 0.2 APPENDIX IV. [Page 317 MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITEBBANEAN, ADBIATIC, AOTJ BLACK SEAS— Continued. Place. Lat. N. Long. E. Lun. Int. n. W. L. W Range. Spg. Neap. Ponza Islet: Pun to della Guardia light. . . Naples; Observatory, Capo di Monte Light on elbow of mole Capri Island : Carena Pt. light Lipari Island: Casa Bianca light Ustica Island: NE. point light , Faro of Messina: Capo di Faro light. . . . . Milazzo: Lighthouse Palermo : Royal Observatory , lAsht on mole head Trapani : Palumbo Rock light Maritimo Island : Light on SW. pt Marsala: W. mole light Girgenti: Port Empedoche light Gozo Island: Lighten NW. pt Malta Island, Valetta Harbor: Lighthouse. Linosa Island : J^^anding Cove Lampedusa Island: Carallo Bianco light. Cape Passaro: Lighthouse Syracuse: Maniace Castle light Augusta Port: Torre d'Avola light Catania: Sciari Biscari light Royal University Observatory . Cape Taormma: Semaphore Mes.sina: San Ranieri light Cape Peloro: Lighthouse Cape Spartivento : Lighthouse Cape Colonna: Lighthouse Cotrone: Mole-head light Taranto: Cape St. Vito light Gallipoli: St. Andrea light Cape Sta. Maria di I>euca: Lighthouse. . . Cape Otranto: Lighthouse Port Otranto: Castle Brindisi: Lighthouse Bari: St. Catalolo light Viesti: Light on St. Croce Rock Manfredonia: Lighthouse Tremiti Islands: Caprara I. light Ancona: Monte Cappucini light Makmocco : Rocchetta Mole light Venice: Site of tower of St. Mark Nautical Institute Observatory. Grado: Church tower Monfalcone: Church tower Trieste: Imperial Maritime Observatory. Theresa Mole light Capo d'Istria: Lighthouse Isola: Lighthouse Pirano: Lighthouse Salvore Point: Lighthouse Citta Nuova: Lighthouse Parenzo : Cathedral tower Rovigno: St. Eufemia light Pola: Imperial Hydro. Office Obsy Promontore Point: Porer Rock light Nera Point: Lighthouse Finme: Cathedral tower Porto Re: Lighthouse Veglia: Mole nead Prestenizza Point: Lighthouse Cherso : Kimen Point light 40 52 38 40 51 46 40 50 20 40 32 07 38 28 43 38 42 40 38 16 02 38 16 10 38 06 44 38 07 56 38 00 39 37 57 13 37 47 10 37 16 55 36 04 10 35 54 00 35 51 50 35 29 37 36 41 03 37 03 04 37 12 39 37 29 35 37 30 13 37 50 25 38 11 32 38 16 03 37 55 27 39 01 29 39 04 38 40 24 41 40 02 48 39 47 43 40 06 23 40 09 06 40 39 36 41 08 19 41 53 17 41 37 39 42 08 14 43 37 14 45 20 30 45 26 02 45 26 11 45 41 06 45 48 33 45 38 45 45 38 54 45 33 00 45 32 34 45 31 54 45 29 24 45 19 16 45 13 45 45 05 00 44 51 49 44 45 30 44 57 24 45 19 36 45 16 18 45 01 30 45 07 12 44 57 36 12 57 17 14 15 26 14 15 37 14 11 40 14 51 40 13 12 00 15 39 11 15 13 42 13 21 29 13 22 29 12 29 50 12 02 55 12 25 59 13 32 27 14 12 55 14 31 80 12 52 09 12 36 12 15 07 45 15 17 37 15 13 20 15 05 19 15 m 00 15 18 30 15 34 33 15 39 15 16 03 45 17 12 09 17 08 07 17 12 23 17 56 55 18 22 17 18 31 25 18 28 45 17 59 37 16 50 52 16 11 13 15 55 34 15 31 36 13 31 18 12 19 09 12 20 24 12 20 32 13 22 54 13 32 10 13 45 44 13 45 14 13 43 18 13 39 32 13 33 48 13 29 30 13 33 42 13 35 39 13 38 00 13 50 43 13 53 36 14 08 42 14 26 41 14 33 42 14 34 36 14 16 30 14 23 30 ft. m. ft. m. 4 00 10 13 0.7 0.2 3 12 9 25 0.7 0.2 3 00 9 13 0.9 0.3 3 30 9 43 L8 0.5 10 15 4 45 3.3 0.9 9 20 3 50 2.0 0.6 9 00 8 15 3 25 2 35 3.4 L2 0.9 'o.'s Page 318] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITERRANEAN, ADRIATIC, AND BLACK SEAS— Continued. 8 Place. Lat. N. Long. E. Lun. Int. Range. H.W. L.W, Spg. Neap. i ta Galiola Rock: Lighthouse t « 44 43 36 44 37 20 44 32 11 44 27 42 44 24 42 44 59 24 44 40 06 44 31 30 44 07 05 44 09 06 43 56 16 43 51 15 43 37 36 43 45 08 43 31 00 43 27 00 43 31 02 43 30 07 43 23 50 43 19 12 43 17 46 43 05 28 43 01 43 43 04 30 43 09 24 43 09 50 43 07 30 43 02 50 42 57 42 42 54 19 42 57 37 42 45 54 42 45 05 42 45 05 42 23 30 42 47 06 42 45 30 42 39 00 42 35 08 42 27 04 42 23 36 42 25 30 42 16 42 42 11 43 42 05 15 41 55 47 41 35 10 41 23 31 41 18 40 41 08 44 41 02 12 40 47 00 40 36 14 40 25 30 40 25 17 40 12 00 40 02 57 39 54 29 14 10 36 14 14 06 14 28 06 14 33 28 14 34 06 14 53 48 14 34 42 15 04 24 15 14 05 14 49 24 15 26 21 15 12 06 15 34 24 15 58 07 15 55 00 16 08 51 16 15 09 16 26 06 16 11 10 16 24 30 17 01 36 15 27 30 15 45 29 16 12 28 16 27 14 16 41 55 17 12 00 17 00 19 17 12 44 16 51 32 16 43 07 17 08 54 16 51 45 16 29 29 16 15 12 17 22 51 17 46 48 18 03 08 18 10 49 18 25 36 18 32 00 18 46 12 18 50 36 18 56 25 19 04 19 19 12 29 19 27 15 19 24 54 19 27 14 19 26 47 19 26 30 19 20 14 19 19 14 19 27 55 19 17 45 19 38 33 19 47 53 19 54 55 A. TO. h. m. ft. ft. Unie Island: Netak Point light Lussin Piccolo: Manora Observatory St. Pietro di Nembo Island : Health office. Gruizza Rock: Lighthouse 8 10 2 25 LI 0.3 Zengg: Mole-head light Terstenik Rock: Lighthouse Carlobago: Lighthouse Zara: Church tower Blanche Point: Lighthouse Zara Vecchia : Church tpwer Port Tajer: Lestrice I. light Lucrietta Island : Lighthouse Sebenico: Mount Tartaro 6 10 20 LO 0.3 Rogosnizza Port: Mulo Rock light Zirona Gitinde Island: St. George Chiirch tower Trani: Cathedral tower ...... Port Spalato: Cathedral tower Solta I., Port OHvetto: St. Nicholas tower Spalato Passage : Spec Pt. light Makarska; Chturch tower Porno Rock : Center St. Andrea Rock: Summit Lissa Island : Hoste Rock light 4 00 10 30 2.4 0.7 Pakon jidol Rock : Lighthouse Lesina Island : Port Gelsa light St. Giorgio Pt. light Sabioncello Peninsula: Cape Gomena light Sorelle Rocks: Lighthouse Curzola Island: Porto Bema mole head. Porto Valle Grande, church tower Lagostini Island: Glavat Rock light T/flgosta Island : St. George Chapel Cazza Island : Lighthouse Pelagosa Rock : Lighthouse Meleda Island : Port Palazzo Ruin Olipa Rock : Lighthouse Pettini di Ragusa Rocks: Lighthouse Bobara Rock : Summit Molonta Peninsula: Summit Ostro Point: Lighthouse Cattaro: Health office Budua: Mole-head light Katie Rock: St. Domenica Chapel Antivari: Pt. Valovica light Dulcigno: W. windmill Cape Rodoni: Guardhouse Cape Pali: Guardhouse Durazzo : Lighthouse Cape Laghi: Ruin Skumbi River : Pyramid at mouth Semeny River: Samana Pt. light Vojazza River: Pyramid at mouth Avlona: Lighthouse CapeLinguelta: Extreme Mount Cica: Pyramid Port Palermo: Pyramid Cape Kiefali: Pyramid ' il APPENDIX IV. [Page 319 MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITEKBANEAN, ADBIATIC, AND BLACK SEAS— Continued. 1 Place. I.at. N. Long. E. Lun. Int. Range. H.W. L.W. Spg. Neap. Saseno Island : Lighthouse t 1 K 40 30 12 39 51 53 39 39 27 39 29 50 39 16 32 39 39 54 39 37 05 39 11 30 38 56 30 38 47 25 38 40 40 38 22 04 38 11 36 38 15 00 37 38 20 37 47 10 37 15 12 37 03 38 36 54 10 36 48 40 36 47 50 36 57 20 35 28 55 35 20 30 36 29 40 36 34 25 36 15 20 36 40 27 36 59 12 37 06 32 37 00 01 37 08 38 37 26 12 37 07 36 37 25 55 37 38 00 37 39 28 37 44 00 37 57 30 36 47 05 37 18 42 37 31 45 37 44 30 37 56 14 37 58 21 37 38 45 37 52 48 38 01 28 38 28 15 39 10 48 40 37 28 39 52 10 39 50 52 39 31 58 39 12 35 39 06 10 39 03 20 38 32 00 9 t n 19 16 15 19 26 06 20 07 12 20 17 09 20 24 55 19 43 09 19 56 30 20 12 34 20 45 40 20 44 16 20 42 44 20 43 37 20 29 30 21 43 50 21 18 55 20 55 26 21 01 14 21 34 35 21 40 29 21 42 40 21 58 00 21 56 42 24 09 39 25 09 44 26 59 25 26 24 28 25 13 00 24 23 15 24 40 30 25 23 00 25 14 21 25 14 08 24 56 14 24 32 23 24 23 35 24 44 32 24 19 44 24 04 12 24 42 30 23 05 40 23 08 53 23 25 45 23 25 30 23 38 10 23 43 14 24 02 15 24 03 00 24 16 42 23 36 45 23 27 07 22 58 00 25 03 20 25 14 14 24 59 13 25 50 00 26 34 54 26 31 39 25 35 00 A. TO. ft. TO. n. ft. Fano Island : Pt. Kastri light Port Pagonia: Ruin Port Gomenitza: Well Dogana Port Parga: Madonna I Port St. Spiridione: Convent Corfu: Lighthouse Paxo Island: Madonna I. light Prevesa; Fort Nuovo minaret Port Drepano: Observation island Port Vliko: Customhouse Port Vathi: Lazaretto light Port Argostoli: St. Theodore light Patras: Lighthouse 3 40 9 53 LO 0.3 Katakolo: Lighthouse Zante: Mole light Strovathi, or Strivali Island: Stamphani I. light Proti Passage: Marathon Pt Navarin : Lighthouse Mothoni : Rotmd tower Koroni Anchorage: Mole light Petalidi Bay: Petalidi Pt Candia Island, Port Suda: Lighthouse. . . Megalo Kastron: Mole &ht Kandeliusa Island : Lighthouse Stampali Island, Maltezana Port: Agios loanes Christiana Islands: N. pt Milo Island: Summit, Mt. St. Elias Siphano Island: Lighthouse Naxos Island, Naxia: Gate on Bacchus I. Pares Island, Port Trio: Trio Pt Port Nausea: St. Yanni Church Syra: Mole light Sermo Island: Amyno Pt Thermia Island: Ruins of Cythnus Jura Island : North pt Port St. Nikolo: Lighthouse St. Nikalao Island: Port Mandri Andros Island, Cape Fasse: Lighthouse... leraka: Acropolis Port Kheli: Lighthouse Poros Island : Lighthouse ^gina: Lighthouse Pira>us : Lighthouse Athens: National Observatory Cape Colonna: Extreme Port Raphti: Statue I Petali Island: Trago I. peak Skiathos Island: Moimt Stavros Salonika: S. bastion IjCmnos Island : Kastro Castle Port Moudros: Sangrada Pt Strati Island: St. Strati Church Mi tyleni Island, PortSigri: Lighthouse. Mityleni : Light on Mit- yleni Pt Portlero: Sidero Islet. Psara Island* Fort _ Page 320] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. COASTS OF THE MEDITEBRANEAN, ADBIATIC, AND BLACK SEAS— Continued. Place. Port Baklar: Cape Xeros Port Isene: Tower Samoa Island: Fonia Pt. light Tchesm^: C. Kecil light Kos: Lighthouse Marmorice Harbor: Adassi Pt. light. Makry Harbor: Kasil I Rhodes Port: Arab's Tower light Port Lindo: Tower Dardanelles: Hellas Pt. light Gallipoli: Lighthouse Bosphorus : Tofana Pt. light Scutari: Leander Tower light Constantinople: Seraglio Pt. light.. St. Sophia Mosque. Cape Kara Bumu : Lighthouse Yuiada Road : Fort Tersana Burghaz : Lighthouse Varna Bay : Lighthouse Kusterjeh: Cape Kusterjeh light. . . Danube River: Salina light Fidonisi Island : Lighthouse Odessa: University Observatory Nikolaieff : Naval Observatory Dnieper Bay: Fort Nikolaeo light. . Sebastopol : E. lidithouse Balaklava Bay : Hospital Kertch : Lighthouse Berdiansk: Breakwater light Saukhoum : Lighthouse Batoum: Lighthouse Trebizond : Lighthouse Sinope: Lighthouse Bender Erekli : Lighthouse Marmora Island : Light off E. pt Artaki Bay: Zeitijn Adasi Islet Tenedos Island: Ponente Pt. light. Port Ajano: Nikolo Rock Port Ali-Agha: W. pt. of entrance.. Smyrna: English consulate flagstaff Vourlah: Customhouse Sighajik Harbor: Beacon on islet. . Budrum : Lighthouse Adalia: Lighthouse Alexandretta: Lighthouse Latakia: Lighthouse Tripoli Roadstead : Bluff Islet light Ruad Island : Lighthouse Beirut: Lighthouse Saida (ancient Sidon) : Lighthouse. Sr Bongao Island : S. pt Keenapoussan Island : Center Bubuan Island: Lagoon entrance Cuad Basang Island : SW. pt Siassi: Town, center of old fort 5 54 -0 18 8.6 6.4 Bulipongpong Island: Center hill Tapul Island: Center hill, 1,676 ft Jolo Islands: Maimbun Anchorage, dry bank Dalrymple Harbor, Tulyan Islet Jolo lighthouse [9 38] [3 10] [5.0] Doc Can Islet: W. extreme Pangituran Island : SW. pt Basilan Island : La Isabe a Pulo Varella : Center Pulo Brala: Center Tringano River: N . pt 8 00 1 48 5.8 2.5 Great Redang Harbor: Bukit Mara Kelantan R. : Lighthouse Tanjong Patani: NE. pt Singora (Sungkla): SW. pt. of Koh Ngu. . Koh Krah Islet: SE.pt 8 20 2 08 2.8 L2 Bangkok: Wat Cheng 8 00 2 00 7.3 3.1 Cape Liant: Koh Chuen Lighthouse Chentabun River: Entrance, Bar I Koh Chang: Obsy . I. on W. side 10 00 3 50 4.5 2.1 Koh Kong R.: S. pt. of entrance Kusrovie Rock: Center Koh Tang Rocks: Veer Islet Panjang Island : West Pt Obi Islands: Lighthouse Saigon: Observatory 5 00 11 20 9.8 4.2 Mitho: S. gate of citadel Cape St. James: Lighthouse Cape Padaran: Extreme Cape Varella: Extreme Quin Hon : Battery flagstaff Canton Pulo: Lighthouse Cham-Callao Islet: Watering place Tourane Bay : Ligbihouse Hon-M6 : Summit Nam-Dinh : Citadel tower Hon Dau Island : Lighthouse 9 00 2 48 4.3 2.1 Haif ong : Observation pagoda Haiduong: Citadel tower Hanoi: Citadel tower APPENDIX IV. [Page 337 MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. 8 Place. Lat. N. Long. E. Lun. Int. Range. H.W. L.W. Spg. Neap. « . i a a Condore Islands : Lighthouse 9 r It 8 40 06 9 58 23 10 32 36 2 02 55 3 00 00 21 29 00 18 09 00 18 11 30 20 01 15 15 46 30 16 36 00 16 40 07 16 49 55 20 42 03 21 22 30 21 24 15 21 31 00 21 34 00 21 28 00 22 11 40 22 11 24 23 06 35 22 02 00 21 48 50 22 16 52 22 16 23 22 03 40 22 15 45 22 27 06 22 24 06 22 30 42 22 32 54 22 18 30 22 48 14 22 48 07 22 56 24 23 14 00 23 20 43 23 15 43 23 32 30 23 47 15 24 09 49 24 23 16 24 25 44 24 49 13 24 52 12 24 59 36 25 02 18 25 12 00 25 16 30 25 26 10 25 58 10 25 59 00 26 08 26 26 09 29 26 22 37 26 30 00 26 36 06 26 42 30 26 51 25 26 58 52 27 09 20 27 09 42 106 41 42 109 06 00 108 56 27 109 06 10 107 48 00 109 06 00 109 35 00 109 41 30 110 16 10 111 14 30 111 40 30 112 43 32 112 20 44 116 43 07 111 10 30 111 15 25 111 38 30 111 46 43 112 21 30 113 34 00 113 33 25 113 16 30 113 47 00 113 56 20 114 09 31 114 10 02 114 19 25 114 22 07 114 36 45 114 39 12 114 50 00 115 01 00 115 06 54 115 47 56 116 04 26 116 29 44 116 47 00 116 40 22 117 17 04 117 42 00 117 36 48 118 13 30 118 10 00 118 30 11 118 41 00 118 58 00 119 27 07 119 10 36 119 35 00 119 45 00 119 56 07 119 59 02 119 27 16 119 37 35 120 24 06 120 29 40 120 10 00 120 11 12 120 22 42 120 32 33 120 42 34 120 25 50 120 32 42 h. m. h. m. ft. ft- Safatu Island: Summit Ceicer de Mer Island: SW. hill Natuna Islands: Murundum I., SE. pt... Low I Pakhoi : Customhouse flagstaff 5 00 11 12 14.0 6.6 Hainan Island : Cape Bastion, extreme. . . Gaalong Bay, E. Brother. Ligh thouse .... Paracel Islands: Triton I Observation bank Lincoln I Woody I Pratas Island: NE part Ty-fung-kyoh Islanc : Center Tien-pak Harbor: Pauk PyaJi Islet Song-yui Point: Extreme 11 50 5 37 8.2 3.8 Hui-lang-san Harbor: Mamechow Islet. . . Mandarins Cap : Summet, 200 ft Macao : Fort Guia light 9 50 3 38 6.3 3.0 Fort San Francisco Canton: Dutch Folly light 2 00 800 5.1 2.4 Raleigh Rock: Center Gap Rock" Lighthouse . ...... Hongkong: Cathedral Wellington Battery 9 20 2 52 4.4 2.0 Lema Island: Lema Head Nine-pin Rock: Center.... T|ini-5».Tig TslHTid - SlimTnit Single Island: E summit .... Mendoza Island: Summit Pank Piah Rock: Summit Pedra Blanca Rock: Summit, 130 ft Chino Bay: Obs. spot Cupchi Point: Hil Breaker Point : Lighthouse ^ Cape of Good Hope : Lighthouse Swatow: British consulate 2 50 9 00 7.5 3.5 Lamock Island ■ Lio'hthouse Brothers Islets: SE. Islet Tong-sang Harbor : Fall Peak 11 20. 5 08 12.0 7.6 Chapel Island : Lighthouse Amoy: Taitan I. light 05 6 13 15.5 9.9 Dodd Island : Lio'h thouse .... Chinchin Harbor: Pisai Islet Pyramid Point: Extreme . Ockseu Island ■ Lighthouse . Sorrel Rock : Summit Lamyit Island: High Cone Peak Hungwha Channel : Sentry I Turnabout Island : Lighthouse East Dog Island : Lighthouse Min River: Pagoda, Losing I 30 9 45 7 00 3 33 19.3 19.0 12.2 12.0 Temple Pt Alligator Island: Summit Tung-yung Islands: Peak, N. end Coney Island : Summit . . Double Peak Island : Highest peak Pih-seang Island ■ Town I DaTippiriiis Rook ■ SumiTnit Tae Islands* Summit Nam-quan Harbor: Bate I 9 50 3 38 17.2 10.9 Pinp-fnTig Tslflnd • PuTI'Tn't 21594°— 14- -22 Page 338] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. (3 C9 la m Is Place. Pih-quan Peak: Summit Port Namki: E. horn Pih-ki-shan Island : Summit. Pe-ehan Islands: Summit, SW. end Tung-chuh Island : Summit Kweshan Islands: Patahecock Nimrod Sound : Middle islet Tong-ting Islet: Summit Chin-liai: Citadel Ning-po: Square I. light Chusan Islands: Ting-hai Harbor Video Island : Summit West Volcano Island : Lighthouse , Chapu: Battery Gutzlaff Island: Lighthouse , Saddle Islands: N. Saddle light. , West Barren Island: Summit. Shanghai: Eng. consulate flagstaff Woosung: Lighthouse Shaweishan Island : Lighthouse Wang-kia-tia Bay: Langwang temple Kiaochow Bay: Yunui San light Staunton Island: Landing place, N. side.. Shantung Promontory : Lighthouse Weihaiwei: Light, S. side harbor Chifoo: Lighthouse Fort flagstaff Miautao Island: Peak of N. Island Pei Ho: S. Taku Fort, S. Cavalier Tientsin: Shore opp. NE. angle of wall. . . Shaluitien Island : Lighthouse Newchwang: Lightship Hulu-shan Bay: N. side Port Adams: Entry Liao-ti-shan Promontory: SW. pt. light. , Ryojun Ko (P. Arthur): Obs. spot Dairen Wan: Isthmus on S. Sanshan I. . . Round Island : Summit , Thornton Haven, Hai-yun-tan Island: Beach opposite Temple Point , Pescadores Islands: Fisher I. light Second pt. on N. side Makung Harbor. . . South Cape: Lighthouse Takau: Saracen Head Port Heongsan Tamsui Harbor: White Fort Kiirun Ko (Kelung Hbr.): Li§:hthouse . . Soo (Sauo) Bay: Beach near village. Botel Tobago Sima: S. extreme Sakishima Gun to, Kumi I.: N. beach... (Meiaco Sima Is.) Broughton Bay: Land- ing place Port Haddington: Hamilton pt Tai-pin-san: Ilirara, Karimata Anch Raleigh Rock: Summit, 270 ft Ti-ao-usu Island: Summit, 600 ft Hoa-pin-su Island: N. face Lat. N. 27 19 18 27 26 18 27 37 36 28 05 07 28 43 45 29 22 45 29 34 20 29 51 53 29 57 08 29 59 21 30 04 30 30 08 04 30 20 50 30 36 00 30 48 37 30 51 41 30 44 07 31 14 41 31 23 18 31 25 27 35 39 00 36 02 50 36 45 29 37 24 00 37 27 41 37 34 10 37 32 51 38 23 37 38 58 16 39 09 00 38 56 00 40 35 00 39 30 46 39 16 00 38 43 17 38 47 50 38 52 38 38 40 00 39 04 00 23 32 53 23 32 54 21 55 00 22 36 14 24 46 00 25 10 24 25 09 12 24 35 28 22 01 40 24 26 00 24 21 30 24 25 00 24 48 18 25 55 00 25 58 30 25 47 07 Long. E. 120 27 14 121 06 36 121 12 09 121 30 04 121 55 21 122 13 16 121 43 15 122 35 24 121 43 06 121 45 22 122 03 47 122 45 48 121 51 25 121 03 00 122 10 12 122 40 17 123 08 27 121 28 55 121 29 36 122 14 12 119 51 30 120 17 30 122 16 48 122 42 00 122 15 05 121 31 09 121 21 27 120 55 00 117 42 48 117 11 44 118 31 00 122 00 00 121 18 03 121 35 59 121 08 26 121 15 54 121 51 59 122 11 30 123 10 34 119 28 05 119 30 12 120 51 00 120 15 54 120 55 00 121 25 00 121 44 28 121 49 20 121 39 45 122 56 00 124 17 40 124 06 40 125 17 57 124 35 00 123 40 00 123 30 31 Lun. Int. H.W. ft. m. 1 00 12 4 50 4 00 9 20 10 25 6 50 4 30 10 05 9 45 10 00 10 15 6 00 7 27 L. W. Spg. ft. m. ft. 7 12 06 9.1 11 03 114 10 12 3 08 4 13 6.8 9.0 8.1 1 00 4.5 10 50 11.7 3 53 7.5 3 32 4.0 3 47 4 03 12 13 8.0 3.0 5.8 1 14 4.9 2.1 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OP ASIA— Continued, [Page 339 Place. Nansei Shoto, Great Nansei: Nafa-Kiang. Yori-sima, 413 ft Yerabu-sima peak, 687 ft.. Kakirouma: Summit, 2,207 ft Iwo-sima: Volcano, 541ft Oho-sima: N. extreme Kikai-jima: Summit, 867 ft Kusakaki Jima: IngersoU Rocks, 530 ft. . . Kuro Sima: 2,160ft Iwo Shima: Peak, 2,469 ft Yakuno Shima: Mount Matomi, 6,252 ft. . P"'ira8e Rocks: Highest, 92 ft Kuchino Shima: Summit, 2,230 ft Guaja Shima: Summit, 1,687 ft Naka no Shima: Peak, 3,400 ft Suwanose Jima: Volcano, 2,706 ft Tokara Jima: Summit, 860 ift Yoko Shima: Summit, 1,700 ft Choda Island: S. pt Sir James Hall Islands: N. island (Chemulpo: So Wolmi Marjoribanks Harbor: Manzoc Islet Tasdefoin Islet: Center Guerin Island : Summit, 969 ft Kokoun-tau Islands: Camp Islet Barren Island : Center, 600 ft Sea Rock: Center, 160 ft Modeste Island: N. peak. 1,228 ft Ross Island: Peak, 1,920ft Kuper Harbor: NE. extreme of Josling I . . Port Hamilton: W. pt. of Obs. Island Bate Islands: Summit Tliornton Islet. . . . Montravel Island: Center, 1,041 feet Quelpart Island: Beaufort I., middle of W. side Observation Island : Point of \V. arm Sentinel Island : Summit , 400 feet Broughton Head : Extreme Tsau-ling-hai Harbor: Lighthouse Cape Clonard : Extreme Ping-hai Harbor Liancourt Rocks: Summit, 410 ft MatuSima: Peak, 4,000 ft Port Lazaref : S. IJ miles from the S. end of Bontenef I Tsu Sima: Observation rock Iki Sima: Summit, S. end of island Oro No Sima: Summit, 277ft Kosime No Osima: Summit Wilson I Yeboshi Sima: Lighthouse Yobuko Harbor : Blu ff opposite Nicoya . . . Hirado No Seto: Taske light Goto Island : Ose Saki light Pallas Rocks: S. rock Meiaco Sima: EarsPeak Nagasaki: U. S. Transit Venus Station Nezumi Jima: Obs. spot Kuchinotsu: Lighthouse Lat. N. 26 12 25 27 02 00 27 21 00 27 44 00 27 53 00 28 31 40 28 18 00 30 51 00 30 50 00 30 47 00 30 17 00 30 05 00 29 59 00 29 54 00 29 52 00 29 38 00 29 08 00 28 47 30 38 27 00 37 58 00 37 27 40 36 26 45 36 24 30 36 07 00 35 48 08 35 21 00 34 42 00 34 42 30 34 06 00 34 17 20 34 01 23 33 57 00 33 59 00 33 29 40 34 39 00 34 33 00 34 48 00 35 07 15 36 05 45 36 36 00 37 09 30 37 30 00 39 19 12 18 55 44 30 52 10 53 50 41 30 32 30 23 31 36 45 13 12 03 00 43 21 43 15 36 05 Long. E. 127 40 10 128 25 24 128 33 10 128 59 00 128 14 30 129 42 30 129 59 00 129 28 00 129 55 30 130 18 00 130 32 00 130 03 00 129 5<) 00 129 33 00 129 52 30 129 42 00 129 13 30 129 01 30 124 34 40 124 34 30 126 36 27 126 28 00 126 24 00 126 01 09 126 31 00 125 58 00 126 19 45 125 16 00 125 07 00 126 35 28 127 18 34 126 18 00 126 55 00 126 58 25 128 14 00 128 40 00 128 44 00 129 02 10 129 33 30 129 20 00 131 55 00 130 53 00 127 32 48 129 13 06 129 42 30 130 02 00 130 25 20 129 58 50 129 52 43 129 33 21 128 36 10 128 04 39 128 25 00 129 52 25 129 49 55 130 13 40 Lun. Int. H.W. L. W, Range. Spg. Neap. 6 30 h. m. 15 ft. 5.8 ft. 2.5 4 19 10 31 28.8 11.6 9 05 2 52 10.5 4.2 7 35 1 23 7.0 3.0 8 56 2 44 6.7 2.4 9 23 3 10 6.4 2.5 7 54 8 14 1 41 8.4 n.2 3.5 7.2 Page 340] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. Place. Lat. N. Long. E. Lirn. Int. H.W. L. W. Range. Spg. Kagoshima: Breakwater light Tsukarase Rocks: Summit, 96 ft Uji Shima: High Peak, 1,097 ft Yamagawa Harbor : Spit N . of town Satano Misaki : Lighthouse Shimonoseki Strait: MejiZaki, extreme. Rokuren Island : Lighthouse Shirasu Reef: Lighthouse Susaki: SW. battery Tomo Roads: Tamatau Sima Port Okayama: Take Sima temple Wusimado Pt. : Wusimado Peak, 548 ft. . Akashi-no-seto : Maico Fort Hiogo: Wada Misaki light Kobe: Lighthouse Osaka: Fort Temposan light Sakai: Pier-head light Osaki Bay: Tree Islet, S. pt Yura No Uchi: Pier Tanabe Bay: Fossil pt Oo-sima Hbr.: Kashmosaki light, E. pt. Uragami Harbor: Village pt Owashi Bay : Hikimoto Mura Harbor: Osima Islet Matoya Harbor: Anori-saki light OmoiSaki: Lighthouse Shimizu Bay: Mound on pt Mikomoto Island : Light house Simoda Harbor: Center I Yokosuka Harbor: Eyi Yania pt Yokohama: Time-ball station Tokio: University Observatory No Sima Saki: L^hthouse Vriea Island (O Sima) Volcano: Summit, 2,512 ft Kozu Shima Volcano: Summit, 2,000 ft. Mikake Jima: Summit, 2,690 ft Redfield Rocks: S. rock Mikura Jima : Summit Broughton Rock: Summit, 60 ft Fatsizio Island : Observation spot Aoga Shima: Center Bayonnaise Island: Summit, 26 ft Smith Island : Summit, 250 ft Ponafidin Island: Summit, 1,328 ft Lots Wife Rock : Summit, 300 ft Inaboye Saki: Lighthouse Kinkwosan Island: Lighthouse Kamaishi Harbor: SE. end of village — Yaraada Harbor: Ko Sima, 90 ft Siriya Saki: Lighthouse Tonwi Saki: Center of Low Islet off Aomori: Lighthouse TatsupiSaki: N. side Bittern Rocks: SW. rock Tobi Shima: Takamori Yama Awa Sima: NE. extreme Sado Island : Ya Saki Fushiki Harbor: Lighthouse Cape Rokugo: Extreme Niigata: Buddhist temple Mana Sima: Summit, 200 ft Manao Harbor: Sorenjo Pt Tsuruga: Town 31 35 39 31 20 00 31 12 00 31 12 43 30 59 30 33 57 46 33 58 53 33 59 11 33 23 19 34 22 37 34 35 58 34 37 27 34 38 05 34 39 20 34 41 18 34 39 45 34 35 12 34 07 42 33 57 34 33 41 14 33 28 15 33 33 37 34 06 10 34 13 52 34 21 57 34 35 52 35 00 51 34 34 25 34 39 49 35 17 30 35 26 41 35 39 18 34 54 17 34 43 30 34 13 15 34 05 00 33 56 50 33 52 00 33 39 00 33 04 24 32 29 00 32 00 40 31 27 00 30 28 26 29 46 28 35 42 13 38 16 57 39 16 30 39 27 17 41 25 58 41 33 34 40 50 00 41 16 17 40 31 00 39 12 02 38 29 23 38 19 55 36 47 47 37 31 45 37 55 14 37 35 00 37 02 37 35 40 24 130 33 49 129 46 20 129 29 00 130 37 00 130 39 30 130 57 50 130 52 07 130 47 36 133 17 00 133 23 23 133 59 24 134 09 21 135 01 51 135 10 56 135 11 34 135 26 00 135 27 44 135 08 19 135 07 21 135 23 04 135 51 59 135 54 25 136 14 35 136 48 51 136 54 09 138 13 49 138 31 19 138 56 30 138 57 30 139 39 43 139 39 00 139 44 30 139 53 24 139 23 00 139 08 00 139 31 00 138 48 15 139 34 00 139 17 45 139 50 24 139 43 31 140 00 00 140 02 00 140 14 02 140 19 40 140 52 22 141 35 33 141 52 50 141 59 00 141 27 32 140 56 36 140 44 40 140 22 37 139 31 00 139 32 58 139 15 31 138 27 09 137 03 15 137 19 00 139 03 01 136 54 00 136 58 24 136 01 22 ft. in. 6 40 7 20 8 30 5 55 11 16 7 30 6 23 5 52 5 52 5 25 5 04 4 30 2 30 ft. m. 1 00 ft. 10.5 1 08 9.5 2 20 6.7 12 08 5 04 5.0 10.2 1 25 4.7 10 12 04 4.7 4.3 12 04 3.9 11 30 4.9 11 17 3.7 10 45 3.4 8 42 0. 6 0. 4 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— ContiBued. [Page 341 Place. Oki Islands: N. pt Taka Yama (Cape Louisa): Extreme. Ai Sima: Summit, 300 ft Mino Sima: Summit, 492 ft Kado Sima: Tsuno Shima light Hakodate: Lightship Endermo Harbor: Hluff on E. side. . . Okishi Bay :_ Lighthouse Noshiaf Saki: Lighthouse Nemuro : Benten Sima light Notsuke Anchorage: Village Noshiaf Misaki: Lighthouse Rifiiri Islet: Peak, 5,713 ft Kunashir Island : St. Anthonys Peak . Iturup Island: NE. pt Urup Island : Cape Vanderlind Broughton Island : Siunmit Simusir Island : Prevost Peak Ketoy Island : S. pt Matana Island : Peak ' Shiash-Kotan Island : Center Kharim-Kotan Island : Peak Oune-Kotan Island: SW. pt Moukon rushi Island : Center Pore musir Island : Fool's Peak Soumshu Island : Center Karafuto (S. Sakhalin): C. Nortoro (Nifihi Notoro Mi- saki) Light C. Shiretoko (Nata Shiretoko Misaki) Sakhalin I., Cape Elizabeth: N. pt Wawoda Rock: Summit, 12 ft Expedition Bay : Lighthouse Port Novogoroa : Lighthouse Vladivostok: Cape Goldobin light Cape Povorotnyi : Lighthouse Port Olga: Lighthouse St. Vladimir Bay : Orekhera Pt Shelter Bay SybilloBay Rque Bay Bullock Bay Luke Point: Extreme Cape Disappointment: Extreme Cape Suffren: Extreme Cape St. Nikolaia: Lighthouse De Kastri: Lighthouse Nikolaevsk: Cathedral Great Shantar Island : N . pt Port Aian : Cape Vneshni St. Jona Island: Summit, 1,200 ft Okhotsk: Battery Cape Lopatka: Extreme Petropavlovsk : Rakof light Cape Shipunski: Extreme Bering Island: Cape Khitroff Mednoi, or Copper Island: SE. extreme. Cape Kamchatka: Extreme Karajinski Island: S. pt Cape Oliutorski: Extreme, 2,480 ft Cape Navarin: Extreme, 2,512 ft Lat. N. 36 30 00 34 40 00 34 32 00 34 48 00 34 21 12 41 47 36 42 19 54 42 56 52 43 22 56 43 20 22 43 33 11 45 26 30 45 11 00 44 20 00 45 38 30 45 37 00 46 42 30 47 02 50 47 17 30 48 06 00 48 52 00 49 08 00 49 19 00 49 51 00 50 15 36 50 46 00 45 53 10 46 01 20 54 24 30 42 14 30 42 38 05 42 33 40 43 05 13 42 41 00 43 22 00 43 53 40 44 30 00 44 43 45 44 46 15 45 05 00 45 19 30 45 41 30 47 20 00 48 59 30 51 28 00 53 08 05 55 11 00 56 25 28 56 22 30 59 19 45 51 02 00 52 52 37 53 04 30 54 56 00 54 32 24 56 10 00 58 26 00 59 55 GO 62 14 30 Long. E. 133 23 00 131 30 00 131 18 00 131 09 00 130 50 29 140 41 49 140 59 33 144 52 38 145 49 10 145 34 40 145 18 00 141 38 40 141 19 00 146 15 00 149 14 00 149 34 00 150 28 30 151 52 50 152 24 00 153 12 30 154 08 00 154 39 00 154 44 00 154 32 00 156 15 20 156 26 00 142 04 51 143 26 30 142 46 30 137 17 00 130 48 45 131 10 00 131 52 46 133 02 00 135 15 00 135 27 19 136 02 00 136 22 30 136 27 15 136 44 00 137 10 15 137 38 15 138 58 00 140 23 40 140 48 00 140 42 58 137 40 00 138 25 50 143 15 45 143 07 14 156 46 00 158 46 42 160 04 00 166 43 00 168 09 00 163 24 00 163 34 00 170 22 00 179 04 30 Lun. Int. H.W, h. m. 11 41 11 20 2 45 9 50 10 45 10 3 55 3 30 6 00 L. W, h. m. 5 28 10 00 9 45 9 53 10 00 9 46 11 05 5 08 9 00 3 40 4 40 Range. 10 08 9 45 Spg. ft. i.i' 12 15 3.0 3.5 3.0 3.1 2.1 3.7 4.2 L9 2.7 6.3 7 30 8.4 4.6 5.1 4.5 Neap. ft. '6.5 1.2 1.5 L4 L4 0.5 L8 1.7 0.8 LI 2.6 3.4 1.9 2.1 L8 Page 342] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. EAST COAST OF ASIA— Continued. 1 Place. Lat. N. Long. \V. Lun Int. Range. 1 n. w. L. ^\'. Spg. Neap. i £ St. Matthew Island: Cape Upright, SE. pt. St. Lawrence Island: N. pt 60 18 00 63 12 00 64 16 00 64 25 55 64 24 30 64 46 00 64 50 00 65 00 30 66 02 00 172 04 00 159 50 00 173 10 00 173 07 15 172 12 30 172 07 00 Long. E. 178 40 00 Long. W. 175 54 00 169 32 30 h. m. h. m. ft. ft. Cape Tchoukotskio : Extreme Port Providence: Emma Harbor Cape Indian: Extreme Arakam Island: Cape Kiguinin Anadir River: Mouth Cape Bering: Extreme East Cape : Extreme ISLANDS OF THE PACIFIC. a H « u el 0, X •0 fl 4 a M h .a Malpelo Island: Summit, 1,200 ft Cocos Island: Head of Chatham Bay Redondo Rock: Summit, 85 ft 4 03 00 5 32 57 13 30 20 00 18 50 34 25 1 22 55 59 00 31 00 15 20 25 00 36 30 33 25 50 30 1 19 00 1 25 00 44 15 1 57 17 3 51 26 4 41 10 5 52 15 13 30 49 00 Lat. S. 2 40 54 2 35 00 1 50 00 1 29 14 1 23 42 1 17 14 36 00 Lat. N. 11 10 20 54 51 30 1 38 45 1 44 15 2 03 00 3 01 30 81 36 00 86 59 17 91 03 00 89 58 43 90 30 08 90 44 23 91 49 43 91 29 12 91 36 00 90 52 53 90 43 30 90 41 00 90 33 58 90 06 13 90 28 13 89 40 08 89 16 58 157 27 45 159 21 50 160 24 30 162 05 00 176 32 39 176 43 09 Long. E. 177 01 13 176 07 00 175 39 00 175 12 20 176 31 33 175 57 09 174 24 00 173 32 40 173 51 14 173 03 30 173 03 00 173 07 00 173 25 30 172 45 40 Towers Island : W. cliff Bindloe Island: S. summit Abingdon Island: Summit, 1,950 ft Wenman Island: Summit, 550 ft Albemarle Island: Iguana Cove 2 00 8 13 6.2 3.1 Marlborough Island: Cape Hammond James Island: Sugarloaf, 1,200 ft 2 45 8 58 5.2 2.6 Jervis Island: Summit Duncan Island : Center hill .... Indefatigable Island : NW. bay 2 00 8 13 6.2 3.1 Barrington Island: W. summit, 900 ft Charles Island: Summit, 1,780 ft 2 10 8 23 6.0 3.0 Fatu Iluku or Hood Island: E. summit, 640 ft Chatham Island: Mount Pitt, 800 ft Christmas Island: N. pt. of Cook Islet — Fanning Island: Flagstaff, entrance to English Hbr 2 20 4 25 6 00 8 33 10 38 12 15 6.5 2.4 2.4 3.3 1.4 1.4 Washington Island Palmyra Island 5 25 11 40 L5 O.^Q Baker Islet : Center Howland Islands : Center island 7 10 1 00 6.2 3.6 Arorai or Hurds Island : S. pt Tamana Island : Center Onoatoa Island: Center Taputeuea or Drummond Island: SE.pt.. Nukunau or Byron Island: SE. pt Peru or Francis Island : N W. pt Nonuti or Sydenham Island Aranuka or Henderville Island: W. pt. of W isliind Apamama or Hoppers Island: Entrance ialet 4 30 10 45 4.7 2.7 Maiana Island' S pt... Tarawa Island ■ NE pt 4 45 11 00 4.7 2.7 Taritari Island ' S t)t APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OP THE PACIFIC— Continued. [Page 343 Place. Ebon Atoll: Rube Pt Jaluit or Bonham Islands: Jarbor Pier Burrh Island: Port Rhin, N. pt. of en- trance Majuro or Arrowsmith Islands: Anchor- age Djarrit I Amo Atoll: NE.pt Odia Islands : S. islet Namu Island : S. pt Jabwat Island : Center Aurh or Ibbetson Island: NE. end, an- chorage Maloclab Islands: NW. end Karen Islet.. Wotje or Romanzov Islands: Christmas Harbor Litkieh Island: NW. pt Ailuk Islands: Capeniur Islet Bigar Islet: Center Kongelab or Pescadores Islands: Center of group Rongerik or Radakala Islands: Observa- tion spot Ailinginae Island : Easternmost Islet Bikini or Eschholtz Islands: W. ex- treme Wottho or Schanz Island : Center Eniwetok Islands: North or Engibi I. . . Ujelang or Providence Island: Center of atoll Greenwich Island : Northern islet Lat. N. Eaatemmost of the S. Matelotas group islands Yap Island : Light in Tomil Bay Eau Island : Center Uluthi or Mackenzie Islands: Mogmog Islet Feys or Tromelin Island: E. extreme Sorol or Philip Island : Center Eauripik or Kama Islands: E. islet Oleai group: Raur Islet, N. pt Ifalik or Wilson Islets: N. end Faraulep Island : S. end W. Faiu Islet: Center Olimarao Islet: Center , Toass Island : Center Satawal Island : Center Coquille or Pikelot Island: Center Suk or Polusuk Island : S. end Los Martires: OUap Islet, N. pt Namonuito Islands: Magur Islet Hall Island: Nam nine Islet Hogolu (Hogulu) Group: N. end of Tsis Islet Namoluk Islands: NW. islet Mortlock Islands: Lukanor, Port Cha- misso Nukuor or Monteverde Islands: E. pt — Oraluk or Bordelaise Island: Center. . . . Ngatik or Valientes Islands: E. extreme.. Ponapi Island : Ponapi Harbor Mokil or Duperrey Islands: Aoura, NE. pt Pingelasp or MacAskill Islands: E. end of island XJalan or Strong Island : Chabrol Harbor. 4 35 25 5 55 07 6 14 00 7 05 30 7 09 17 7 15 00 8 14 00 8 27 00 8 19 00 8 54 21 Long. E. 168 41 31 169 39 31 171 46 00 171 24 30 171 55 51 168 46 00 168 03 00 168 26 00 171 09 00 170 49 00 9 28 09 170 16 05 10 03 40 169 01 57 10 17 25 169 59 20 11 48 00 170 07 00 11 19 21 11 24 00 11 07 00 11 40 00 10 05 00 11 40 00 9 39 00 1 04 00 8 18 30 9 29 00 9 52 30 10 06 00 9 46 00 8 06 00 6 40 00 7 21 45 7 15 00 8 35 00 8 03 00 7 43 30 7 29 30 7 22 00 8 09 00 6 40 00 7 38 00 8 59 45 8 25 30 7 18 30 5 55 00 29 18 51 00 39 00 48 00 00 35 6 41 45 6 14 00 5 20 06 167 24 57 167 35 00 166 35 00 166 24 25 166 04 00 162 15 00 161 08 30 154 47 55 137 33 30 138 04 00 139 42 00 139 46 00 140 35 00 140 52 00 143 11 00 143 57 30 144 31 00 144 36 00 146 50 00 145 55 45 146 24 30 147 06 48 147 42 00 149 21 00 149 27 30 150 14 30 151 49 15 151 56 30 153 13 30 153 58 00 155 00 54 155 05 00 157 31 30 158 17 35 159 50 00 160 38 43 163 00 45 Lun. Int. H.W. L. W h. m. 4 45 5 00 4 50 Range. Spg. Neap. h. m. 11 00 ft. 4.7 ft. 2.7 11 15 5.0 2.8 11 00 6.2 3.6 7 15 1 00 3.4 4 00 6 00 10 15 4.3 2.4 12 15 3.5 2.0 Page 344] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. 4^ 6 Place. Lat. N. Long. E. Lun. Int. Range. 1 H.W. L.W. Spg. Neap. i V s t I £ M e fl 2 •s « » d « a £ V G si » M fl « B Angaur Island: SW. pt o / 9 6 53 55 7 02 00 7 08 00 7 19 00 7 40 30 8 08 00 4 20 00 3 02 00 5 20 00 13 26 22 14 07 30 14 59 22 15 08 30 15 17 10 16 20 00 16 41 00 17 17 00 17 36 00 18 04 00 18 46 20 19 45 00 20 00 00 20 32 54 19 15 00 14 41 00 16 44 48 10 17 00 19 46 14 20 03 00 19 28 00 19 38 26 20 33 39 20 36 00 20 52 00 21 06 17 21 18 16 21 15 08 21 17 57 21 17 55 22 12 51 21 57 17 23 05 50 23 35 18 23 46 00 25 00 40 25 31 00 25 48 00 26 00 00 27 56 30 28 13 15 28 24 45 24 14 00 134 05 24 133 18 03 134 27 00 134 32 30 134 39 30 134 17 00 132 21 00 131 11 00 132 16 00 144 39 42 145 13 04 145 36 20 145 43 55 145 42 50 145 39 00 145 47 00 145 57 00 145 55 00 145 52 00 145 41 45 145 30 00 145 21 00 144 54 00 166 31 30 168 54 28 Long. W. 169 32 24 109 13 00 155 05 31 155 48 00 155 55 00 156 00 15 156 35 04 156 26 00 156 35 00 157 18 32 157 39 07 157 48 44 157 51 34 157 51 54 159 30 47 159 40 08 161 58 17 164 40 47 166 17 57 168 00 52 170 39 20 171 44 00 173 57 00 175 46 00 177 21 30 178 27 45 Long. E. 154 00 00 ! A. 7n. 1 h, 7n. ft- ft. Pililu Island : S. pt 1 Earakong or Akamokan Islands: Center.. Korro Islands: Korror Harbor, Malakal pier Baubeltaub Island: Cape Artingal Kyangle Islets: Center of largest Warren Hastings Island: Center Nevil or Lord North Island: Center Sonserol Island: Approx. Guam: Fort Sta. Cruz, Harbor of Apra.. . Rota Island: Summit 7 20 1 20 2.6 L5 Tinian Island: Sunharon village Saipan Island: Magicienne Bay, landing. Tanapag Hbr., Garapag... Anataxan Island: Center 7 00 50 2.0 LI Sariguan Island: Center Guguan Island: Center Alamaguan Island: Center Pagan Island: SW. pt Agrigan Island: SE. pt Asuncion Island: Crater, 2,600 ft Urracas Islands: Largest islet Farralon de Pajaros: S. end Wake Island: Obs. spot Gaspar Rico Reef: N. clump of rocks .... Johnston or Comwallis Islands: Flagstaff on W. island Clipperton Island : Center Hawaii Island: Hilo, Kanaha Pt. light Kawaihae light 3 09 9 08 2.3 L3 Kealakeakua Bay light. Kailua, stone chiirch. . . Kahoolawe Island: Summit 2 20 8 10 L6 0.9 Maui Island : Kanahena Pt. light Lahaina light 3 32 2 38 9 58 8 56 2.2 2.1 L2 LI Molokai Island: Lighthouse Oahu Island: E. pt Makapuu station .... Diamond Head Honolulu, Tr. of V. Obs. . . . Honolulu, Reef light Kauai Island: Hanalei, Black Head Waimea, stone church .... Bird Island: Center 3 46 9 59 L5 0.8 4 00 10 20 2.0 LI Necker Island: Center French Frigate Shoal: Islet (120 ft.) Gardiner Island: Center Marc Reef: NW. pt Laysan Island: Lighthouse Lisiansky Island: Lighthouse Pearl and Hermes Reef: NE. extreme Midway Islands: Lighthouse, Sand I Ocean Island: Sand Islet 3 30 9 45 LI 0.6 Marcus Island : Center I APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIPIC— Continued. [Page 345 Place. Ogasawara Is. (Benin Is.), Parrys Group: N. rock Kater Island: N. rock Peel Island: Port Lloyd, observatory Volcano Is., San Alessandro or North Is- land: Center Sulphur Island San Augustine Island : Center Rosario Island : Center, 148 ft Douglass Rocks: Center Borodino Islands: Center of N. island.. Center of S. island.. Rasa Island: Center Fatu Hiva Island: S. pt Motane Island: SSE. pt Tahuata Island: Port Resolution, water- ing place Hiva-Oa Island: C. Balguerie Fatu Huku Island: Center Roa Poua Island: Obelisk Islet Nuka-Hiva Island: Port Tai-o-hae light. Iliaou Island: S. pt Motu-ili Island: Summit, 130 ft Ua-Huka or Ua-Una Island: N. pt Fetouhouhou Island: NE. pt Caroline Islands: Solar Eclipse Transit Pier Voetok Island: Center Flint Island: S. extremity Maiden Island: Flagstaff, W. side Starbuck Island: Flagstaff, W. side Penfhyn or Tongarewa Island: NNW. pt Jarvis Island: Center Reirson Island: Church Humphrey Island: N. pt Union or Tokelau Islands: Spot N. of Fakaofu or Bowditch Islet Union or Tokelau Islands: Nuku-nono, or SE. island, Duke of Clarence I Union or Tokelau Islands: Clump on S. island, Oatafu or Duke of York I Canton or Mary Island: N. pt. Enderbury Island: W. pt Phoenix Island, N. pt Bimeys Island: S. pt Gardners Island : Center McKean Island: Center Hulls Island: W. pt Mukulaelae or Mitchells Island: S. pt Fimafuti or EUice Island: E. pt , Nukufetau or De Peysters Island: S. pt. , Vaitupu Island: S. end Nui or Netherland Island: S. pt Nauomaga Island: Center Niutao Island: Church Nanomea Island : Center Lat. N. Long. E. 27 45 00 142 06 53 27 31 00 27 05 37 25 14 00 24 48 00 24 14 00 27 15 32 20 30 00 25 59 38 25 52 45 24 27 00 Lat. S. 10 32 00 10 01 40 9 56 00 9 45 00 9 27 30 9 29 30 8 55 13 8 03 30 8 44 00 8 54 00 7 55 00 10 00 01 10 06 00 11 25 23 4 03 00 5 37 00 8 55 15 22 33 10 02 00 10 20 30 9 23 02 9 13 06 8 39 40 44 25 08 30 42 28 34 15 37 42 35 10 30 95 9 18 00 8 25 19 8 04 02 7 32 00 7 15 45 6 12 00 6 06 00 5 39 00 142 11 53 142 11 23 141 11 00 141 13 00 141 20 00 140 50 28 136 10 00 131 19 30 131 12 17 131 01 50 Long. W . 138 39 20 138 48 30 139 09 00 138 47 40 138 55 10 140 04 45 140 04 00 140 44 00 140 38 30 139 33 30 140 34 40 150 14 30 152 23 00 151 48 34 155 01 00 155 56 00 158 07 00 159 54 11 161 05 30 161 01 12 171 14 46 171 44 40 172 28 10 171 45 29 171 10 00 170 42 37 171 32 07 174 40 18 174 17 26 172 13 28 Long. E. 179 50 00 179 07 25 178 28 51 178 41 01 177 16 50 176 16 30 177 20 01 176 06 15 Lun. Int. H.W. L.W. Range. Spg. Neap. h, m. h. tn. 6 10 00 2.4 L4 2 30 8 45 3.1 L9 3 50 10 05 3.5 2.1 4 00 10 14 LI 0.7 00 12 15 L5 0.9 6 00 12 13 2.4 L4 5 00 11 15 4.6 2.7 Page 346] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. Place. Ocean or Paanopa ^sland: Center (appx.) Pleasant Island : Center Indispensable Reefs: S. pt. of S. reef Rennel Island: SE. extreme W. end San Cristoval Island : Point Wangalaha. . Guadalcanal Island: Wanderer Bay, mouth of Boyd Creek , Florida Island: Mboli Harbor, Tree Islet. Malaita Island: Village, Mary I., Port Adam Stewart Islands: Largest islet Isabel Island: N. side of Cockatoo Islet. . , Gizo or Shark Island: N. point village Choiseul Island: Choiseul Bay entrance Treasury Islands: Observation Islet Bougainville Island: Husker Pt., Gazelle Harbor Buka Island : Cape North Lord Howe Group: Center, small SW. islet Center, small NE. islet NW. pt. of Ham- mond I Neu Pommem (New Britain), Blanche Bay: Matupil. N.pt Duke of York Island: Makada Harbor, SpitPt Neu Mecklenburg (New Ireland): Car- teret Harbor, Cocoa- nut I Katharine Haven Holz Haven, E. side. . New Hanover Island: Water Haven, creek mouth . . . North Haven an- chorage St. Matthias Island: SW. extreme Admiralty Island: Nares Harbor, obs. islet St. Andrew Island: Violet Islet, 60 ft Jesus Maria Island : SE. pt Commerson Island : Center of largest islet . Anchorite Island: N. pt Hermit or Loaf Island : Peme Islet Purdy Island: Mole Islet Point d'Urville: extreme Drei Cap Peninsula: Wass Islet Triton Bay: Fort Dubus, Dubus Haven. . Cape Walsche: Extreme Fly River: Free Islet, S. pt Port Moresby: N. end of Jane I Cape Rodney: Extreme South Cape: S. pt. Su Au I Hayter Island: W. end Cape Cretin: Cretin Islets 52 00 25 00 12 50 15 11 52 15 11 33 45 10 17 32 9 41 47 9 01 30 9 30 00 8 23 00 8 30 50 8 05 40 6 42 40 7 24 30 6 35 00 5 00 00 5 38 00 5 18 00 5 18 GO 4 14 12 4 06 25 41 26 11 00 47 30 2 33 43 26 30 35 00 1 55 10 2 25 40 2 22 00 45 00 53 15 1 28 00 2 51 00 1 25 40 2 44 00 3 47 00 8 22 00 8 41 00 9 25 30 10 14 30 10 43 35 10 37 00 6 43 00 Long. E. 169 35 00 167 05 00 160 26 00 160 40 15 159 55 00 161 33 30 159 39 30 160 27 20 161 27 40 162 58 15 159 38 20 156 50 15 156 23 16 155 34 00 155 05 00 154 35 00 159 21 00 159 34 00 159 17 00 152 11 35 152 06 15 152 42 25 151 35 30 150 57 35 150 04 33 149 55 36 149 37 00 146 40 56 147 28 35 147 55 00 145 17 00 145 33 04 145 08 00 146 15 00 135 28 12 132 04 00 134 06 00 137 40 00 143 36 04 147 07 04 148 30 30 150 14 20 150 40 34 147 53 20 Lun. Int. H. W. L. W. 6 45 5 00 12 00 9 00 2 50 2 30 55 8 50 9 15 8 25 Spg. Neap. ft. m. ft. 33 11 15 5 47 2 45 9 03 8 43 7 08 2 38 3 00 2 12 3.3 3.5 2.7 2.1 2.4 2.4 7.3 8.0 8.1 5.8 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLAHUS OF THE PACIFIC— Continued. [Page 347 is N s , Place. Trobriand Islands: NE. pt. Cape Denis. . Woodlark Islands: N. pt D'Entrecasteaux Is.: Ferj^uson I., S\V. extreme Well Island, E. pt. Normanby I.,ob8. islet St. Aignan Island: Summit Renard Islands: W. pt Rossel Island: E. pt Adele Island: S. extreme Coringa Islands: Chilcott Islet. Herald Cays: NE. Cay Tregosse Islands: S. islet Lhou Reef: Observation Cay. . Mellish Reef: Cay beacon Bampton Island Renard Island: Center Wreck Reef: Bird Islet i Cato Island: Center Duff or Wilson Group: N . island Matema or Sw^low Group: Nimanu Islet . Tinakula Island: Summit, 2,200 ft Nitendi Island: NE. pt., Cape Byron Tapua Island: Basilislc Harbor, S. pt. of entrance Vanikoro: Ocili village i Torres or Ababa island: Hayter Bay, Middlel Vanua Lava Island: Port Patterson, NusaPt Santa Maria Island: Lasolara Anchorage. Aurora Island : Laka-rere MallicoUo Island: Port Sandwich, pt. on E . side Vate or Sandwich Island: Havannah Harbor, Matapou Bay flagstaff Erromaugo Island: Dillon Bay, Pt. Wil- liams Tanna Island: Port Resolution, Mission. Erronan or Futuna Island: NW. pt Aneityum Island: Port Anatom, Sand Islet Matthew Island: Peak, 465 feet Hunter Island: Peak, 974 feet Walpole Island: S. pt Mitre Island : Center Rotumah Island: Epipigi Peak. Kandavu Island: N. rock Astrolabe Reef light Mt. Washington, N. peak Ngaloa Harbor, outer beacon Vatu Lele Island: S. pt Ovalau Island: Levuka lighthouse Lat. s. 8 24 00 9 03 30 9 38 00 9 41 00 9 43 53 10 42 00 10 52 40 11 23 25 11 29 10 16 50 00 16 55 50 17 43 00 17 07 20 17 24 39 19 08 00 19 14 00 22 10 30 23 15 02 9 48 00 10 21 00 10 23 30 10 40 00 11 17 30 11 40 24 13 15 00 13 48 00 14 11 00 14 58 00 16 26 00 17 44 58 18 47 30 19 31 17 19 31 20 20 15 17 22 20 12 22 24 02 22 38 07 11 55 00 12 30 10 18 38 15 19 07 09 19 05 30 18 36 00 17 40 45 Long. E. 151 01 24 152 47 00 150 30 00 150 58 00 150 44 43 152 42 04 152 47 12 154 08 00 154 25 14 149 58 00 149 11 54 150 42 04 152 06 20 155 52 24 158 40 00 159 00 00 155 28 24 155 33 04 166 53 15 166 17 15 165 47 30 166 00 30 166 32 14 166 57 45 166 33 00 167 30 31 167 30 00 168 02 00 167 47 15 168 18 50 168 58 00 169 27 30 170 11 15 169 44 45 171 20 30 172 05 15 168 56 45 170 10 00 177 07 15 178 32 15 177 57 09 178 10 24 177 38 00 178 49 00 Lim. Int. H.W. L. W ft. m. 4 45 7 05 4 50 6 40 4 38 5 15 5 10 6 15 6 40 ft. tn. 10 58 53 11 05 30 10 50 11 27 11 23 00 25 Range. Spg. Neap. ft. 3.0 4.2 ft. L8 2.5 3.8 2 3 3.8 2.3 3.8 3.0 L9 L8 3.1 L9 4.2 2.5 4.0 2.4 Page 348] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF TTTF. PACIFIC— Continued. 1 Place. Lat. S. Long. E. Lun. Int. Range. 1 H. W. h. m. L. W. Spg. Neap. i •0 H S <£ M « 9 a ei Viti Levu Island: Summit of Malolo Islet. Suva Harbor, low light . Mbega or Mbengha Island: Swan Harbor, Leaven Pt 17 44 45 18 06 50 18 22 00 19 09 38 18 32 49 17 59 32 17 37 11 17 27 14 17 15 21 16 42 01 16 57 53 16 49 19 16 08 00 16 46 00 15 44 45 17 03 00 17 25 33 17 17 20 17 10 00 17 25 26 17 44 12 17 39 33 17 59 00 18 14 10 18 25 46 18 38 56 18 46 00 18 56 15 18 58 57 19 03 00 19 04 00 19 49 11 20 39 10 21 00 09 21 01 39 14 14 20 13 23 35 15 34 00 15 52 00 15 58 00 13 45 00 13 48 56 14 18 06 14 19 00 14 32 00 19 10 00 10 52 47 13 14 30 18 05 50 16 28 00 15 48 00 16 52 00 177 09 00 178 24 40 178 06 53 179 44 27 179 56 25 179 14 08 178 59 29 178 57 46 179 20 44 178 54 15 178 48 32 179 16 08 Long. W. 179 58 46 179 51 00 179 54 26 179 17 00 179 32 17 179 10 00 179 05 45 179 10 33 179 19 49 178 50 27 179 04 00 178 52 00 178 27 04 178 30 54 178 44 00 178 59 05 179 52 58 178 47 25 178 33 25 178 13 38 178 43 27 178 44 03 178 49 47 178 06 45 176 11 47 175 40 40 173 52 00 173 52 00 172 17 00 171 44 56 170 42 14 169 32 00 168 09 00 169 50 00 165 51 30 163 04 10 163 10 00 154 30 00 154 31 00 154 OOOO h. m. ft. ft. 6 30 15 3.6 2.2 Matuku Island: N. side of Matuku en- trance Moala Island: Rocks off N. pt Ngau Island: Herald Bay, E. side Wakaya Island : Rocky Peak Makongai Island: Dilliendreti Peak Goro Island: NW. pt Vanua Levu Island: Mount Dana Nandi, observation islet Savu Savu Pt., ex- treme 6 00 12 13 4.3 2.6 NE.Pt Taoiuni Island: Somu-Somu town Thikombia Island: E. hummock Naitamba Island : Center Vatu Vara Island: N. end, summit Kanathea Island : S. pt Vanua Mbalavu Island : NW. pt ...« Mango Island : Pier end 6 10 00 3.1 L9 Thithia Island : Highest peak Tuvutha Island : Peak Naian Island : Summit, 580 ft. Oneata Island : Summit of Loa I Mothe Island : Summit Mamuka Island: Center, 260 feet Kambara Island : Highest peak Totoya Island: Black Rock Bay, W. side. Fulanga Island: W. bluff 6 35 20 3.5 2.1 Ongea Levu Island : Center Vatoa or Turtle Island: Hummock Ono Islands: Peak 6 10 00 3.1 L9 Michaeloff Island : Center Simonoff Island : Center Fatuna or Home Island: Mt. Schouten. . . Uea or Wallis Island: Fenua-fu Islet Niua-fu or Good Hope Island: NW. ex- treme 6 40 28 4.4 2.7 Keppel Island : Center Boscawen Island : Center Savaii Island : Paluale village IJpulo Is. : Apia Harbor, obs. spot Tutuila Island: Pago-Pago, obs. pt Manua Island: Village, NW. side Rose Island: Center Niue or Savage Island : S. pt 6 25 7 00 6 00 13 45 12 13 3.1 2.7 4.6 L9 L6 2.7 Danger, or Bernardo, Is.: Middle rock... Suwarrow or Souwaroff Island: Cocoanut Islet 3 10 9 23 2.4 1.4 Palmerston Islands : W. islet Scilly Islands: E. islet ::: 1 Bellingshausen Island: Center 1 Mopelia (Lord Howe) Island: Center 1 I APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. [Page 349 Place. Maitea Island : Summit Tahiti Island : Lighthouse Tubuai-Manu or Maia-iti I.: NW. Eimeo Island: Talu Hbr., Vincennes Pt.. Huaheine Island : Lighthouse Ulietea Island : Regent Pt Tahoa Island: Center Bola-Bola Island: Otea-Vanua village.. Tubai or Motu-iti Island: N. pt. of reef. Marua or Maupili Island : Center Ducie Island: NE. entrance Pitcaim Island : Village Henderson or Elizabeth Island: Center. . Oeno Island: N. pt Mangareva or Gambier Island: Flagstaff.. Marutea or Lord Hood Island: Center Maria or Moerenhout Island : Center Vahanga Island: W. pt Morane or Cadmus Island: Center Tureia or Carysfort Island: E. pt Miu-uroa or Osnabrug Island: Obs. spot. . Tematangi or Bligh Island: N. pt Nukutipipi: SW. pt Hereheretue or St. Paul Island: Center.. Vanavana or Barrow Island: Center Nukutavake or Queen Charlotte I. : N. pt Reao or Clermont Tonnere Island: NW. point Puka-ruha or Series Island: NW. pt. Vahitahi Island: W. pt Ahunui or Byam Martin Island: NW. pt. Pinaki or Whitsunday Island: E. pt Tatakoto or Gierke Island: Flagstaff on western coast Hao or La Harpe Island: NW. pass Paraoa or Gloucester Island: Center Ravahere Island: S. pt Reitoru or Bird Island : N . beach Hikueru or Melville Island: E. pt Tauere Island: NW^t Puka-puka Island: E. pt Napuka Island: W. pt Angatau or Araktcherf Island: W. pt. . . Tukume or Wolkonsky Island: NW. pt. . Tuanske Island: NW. pt Nihiru Island (Tuanake): SW. pt Anaa Island: Islet in N. pass Tepoto Island: N. pt Haraiki or Crocker Island: SW. pt Makemo or Phillips Island: W. pass. . . . Fakarana or Wittgenstein Island: SE. pass Taiaro or Kings I.: Middle of W. shore. . Aratika Island: E. pt Toaii or Elizabeth Island: Amyot Bay. . Takapoto Island: S. pt Aheu Island : Lagoon Entrance Rangiroa Island : E. pt Makatea Island : W. pt Matahiva Island: W. pt Lat. S. 17 53 00 17 29 10 17 36 39 17 29 23 16 42 30 16 50 00 16 35 00 16 31 35 16 11 00 16 26 00 24 40 20 25 03 50 24 21 20 24 01 20 23 07 36 21 31 30 22 01 00 21 20 00 23 07 50 20 46 20 21 50 00 21 38 00 20 43 00 19 53 17 20 46 07 19 16 30 18 00 29 18 16 00 18 43 30 19 37 00 19 25 00 17 19 30 18 05 20 19 08 45 18 18 30 17 49 35 17 35 28 17 20 30 14 49 00 14 12 00 15 50 00 15 44 20 16 39 10 16 44 29 17 20 20 16 47 49 17 28 41 16 26 09 16 31 00 15 43 15 15 30 00 15 50 00 14 43 00 14 29 10 15 14 30 15 50 30 14 53 00 Long. W. 148 05 00 149 29 00 150 36 56 149 50 30 151 01 28 151 27 21 151 35 00 151 46 00 151 48 00 152 12 00 124 48 00 130 08 30 128 19 00 130 41 00 134 57 54 135 33 05 136 10 15 136 38 53 137 06 15 138 27 45 138 56 30 140 38 45 143 03 15 144 57 00 139 08 45 138 48 30 136 26 30 137 03 30 138 53 15 140 15 45 138 40 45 138 26 26 140 59 30 141 41 10 142 11 31 143 05 23 142 35 16 141 29 43 138 46 45 141 15 37 140 53 35 142 08 40 144 14 45 142 53 34 145 30 54 144 17 18 143 31 17 143 57 59 145 22 45 144 38 34 145 24 45 146 02 45 145 11 00 146 20 00 147 11 00 148 15 00 148 39 45 Lun. Int. Range. H.W. L.W. Spg. Neap. A. m. h. m. ft. 12 00 5 48 LO 0.6 12 10 6 00 L4 0.8 1 50 8 03 2.4 L4 2 40 8 55 2.4 L4 4 30 10 43 2.1 L3 Page 360] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ISLANDS OF THE PACIFIC— Continued. 9t« Place. Juan Fernandez Island: Fort S. Juan Batista Mas Afuera Island : Summit, 4,000 ft St. Ambrose Island : N. part creek St. Felix Island: Center Sala y Gomez: N\V. pt Easter Island: Cooks Bay, mission Rapa or Oparo Island: Tauna Islet Bass Islets (Morotiri): SE. islet, 344 ft. . . Tubuai or Austral Is., Vavitoal.: Center. Tubuai I.: Flag- staff, N, side Rurutu I.: N. pt.. Rimitara I. : Center. Hull Island: NW. pt Mangaia Island: Center Rarotonga Island: NW. pt Mauki or Parry Island: Center Mitiero Island: Center Vatiu or Atiu Island: Center Hervey Islets: Center Aitutaki Island: Center Vavau Island: Port Valdes, Sandy Pt Kao Island: Summit, 5,000 ft Tofua Island: Summit, 2,800 ft Tongatabu Island: Lighthouse Minerva Reefs, N. Minerva: NE. side S. Minerva: S. side of en- trance Kermadec Is., Raoul or Sunday I.: Den- ham B. flagstaff Macauley I. : Center CiurtisL: Center Conway Reef: Center • Loyalty Is., Uvea or Halgan I.: Uvea Church Lifu I.: Wreck Bay, NW. shore Mare or Britannia I. : S. pt . . . Port Kanala: Observatory St. Vincent Bay: Marceau I Noumea: Lighthouse Balari Pass: Amed6e I. light Port Alcmeme: Alcmene I Norfolk Island: Inner end of jetty Elizabeth Reef: Center Lord Howe Island : S. end of middle beach Balls Pyramid: Summit, 1,816 ft Macquarie Island: N. pt Auckland Is.: Port Ross, Terror Cove Campbell Island: S. harbor. Shoal Pt Antipodes Island: Summit, 600 ft Bounty Islands: Anchorage N. I., West Group Chatham Island, Whare-Kauri Island: Port Waitangi, Pt. Hanson Chatham Island, Whare-Kauri Island: Port Hutt, Gordon Pt Lat. S. 33 37 36 33 46 00 26 18 07 26 16 00 26 27 41 27 10 00 27 35 46 27 55 30 23 55 00 23 21 45 22 29 00 22 45 00 21 47 00 21 49 00 21 11 35 20 17 00 20 01 00 20 04 00 19 18 00 18 54 00 18 39 02 19 41 35 19 45 00 21 08 00 23 37 06 23 55 00 29 15 30 30 15 00 30 35 00 21 44 45 20 27 06 20 46 00 21 42 00 21 29 12 22 00 10 22 16 22 22 28 44 22 42 30 29 03 45 29 56 00 31 31 38 31 45 10 54 19 00 50 32 15 52 33 26 49 42 00 47 43 00 43 57 24 43 49 03 Long. W. 78 50 02 80 46 00 79 54 56 80 06 56 105 28 00 109 26 00 144 17 20 143 28 21 147 48 00 149 35 35 151 23 41 152 55 00 154 51 00 157 56 00 159 47 00 157 23 00 157 34 00 158 08 00 158 54 00 159 32 00 174 01 00 174 59 50 175 03 00 175 12 00 178 55 45 179 07 45 177 55 40 178 31 45 178 37 00 Long. E. 174 37 45 166 35 25 167 02 30 168 00 00 165 58 50 166 03 30 166 25 52 166 28 51 167 27 55 167 58 06 159 04 30 159 05 58 159 16 10 158 56 00 166 13 20 169 08 41 178 43 05 179 00 27 Long. W. 176 32 15 176 42 00 Lun. Int. Range. H. W. ft. m. 4 00 40 10 3 00 6 00 6 20 6 20 7 50 6 00 6 30 5 40 8 25 7 55 7 30 "8'26 11 50 11 45 3 20 5 22 L. W. ft. m. 10 15 6 53 6 25 9 13 12 15 10 10 1 35 12 13 18 11 52 2 13 1 45 1 17 '2'68' 5 38 5 33 9 30 Spg. 23 ft. 3.3 2.8 2.4 2.4 2.7 3.8 3.8 5.5 3.3 4.2 3.3 3.1 3.6 4.7 '5.4' 3.2 3.5 5.3 2.5 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. ATJSTRAUA. [Page 351 Place. Groate Eylandt: SE. pt Bickerton Island: Summit Cape Arnheim: Extreme Cape Wilberiorce: E. extreme Cape Wessel: Extreme Dale Point: Extreme Cape Stewart: Extreme Liverpool River: W. pt. entrance. . Cape Croker: Extreme Port Essington: Govermnent house . Melville Island: Cape Van Diemen. . Bathurst Island : CapeFourcroy Adelaide River: E. entrance pt Port Darwin: Charles Pt. light Port Patterson: Quail Islet Port Keate: Tree Pt Pearce Point; Extreme Victoria River: Water Valley Cape Dussejour: Rock off cape Cape Londonderry: Extreme Cape Bougainville: Extreme Caseini Island: S. pt Cape Voltaire: Flat Hill Barker Islets: Center Montalivet Islands: W. islet Maret Islets: N. islet Colbert Islet: Center Prince Regent River: Mount Trafalgar. . Port Nelson : Careening beach De Freycinet Islets: Beacon on summit. . . Red Islet: Center Cockell Islet: W. pt MacLeay Islets: Rock off N. end Port Usbome: S. pt Fitz Roy River: Escape Pt Cape L'Ev^nue: Extreme Lacepede Island: N\V. islet Cape Baskerville: Extreme Cape Latouche Tr^ville: Extreme Turtle Isles: Center of N. isle Cape Lamljert: Extreme Legendre Island: NW. extreme , Rosemary Island: W. summit Enderby Island: Rocky Head Monte bello Island : N . extreme of reef Barrow Island: N. pt Northwest Cape: Extreme Cape Cuvier: Extreme Cape Inscription: Extreme Houtman Rocks: N. islet Port Gregory Cape Leschenault: Extreme Rottnest Island : Lighthouse Perth (Frenxantle) : Arthur Head light. . . State Observatory . . . Peel: Robert Pt Cape Naturaliste: Extreme Cape Leeuwin : Lighthouse D'Entrecasteaux Point: Extreme Nuyts Point: Extreme West Cape Howe: Extreme Eclipse Islets: Summit of largest King George Sound: Commissariat house near Albany jetty Lat. s. 14 16 00 13 45 00 12 14 00 11 53 00 10 59 00 11 36 00 11 57 00 11 54 00 10 57 00 11 22 02 11 08 00 11 51 00 12 13 20 12 23 20 12 30 58 13 59 00 14 25 50 15 13 45 14 42 00 13 44 00 13 52 00 13 57 07 14 15 00 13 55 00 14 14 00 14 23 00 14 51 00 15 16 36 15 06 00 14 59 20 15 13 15 15 46 00 15 52 00 15 39 25 17 24 25 16 23 00 16 50 00 17 09 00 18 29 00- 19 54 00 20 36 00 20 19 00 20 27 00 20 35 00 20 16 45 20 40 40 21 46 41 24 00 00 25 29 19 28 18 05 28 12 00 31 18 00 32 00 20 32 03 12 31 57 09 32 27 00 33 31 45 34 21 55 34 52 00 35 05 00 35 09 00 35 11 54 35 02 20 Long. E. 136 58 00 136 15 00 137 00 00 136 34 00 136 46 00 136 07 00 134 45 00 134 12 00 132 36 30 132 09 18 130 19 00 129 58 00 131 16 30 130 37 00 130 27 00 129 37 00 129 20 42 129 48 14 128 10 00 126 57 00 126 12 00 125 38 45 125 39 00 124 55 00 125 12 00 125 00 00 124 42 00 125 07 00 125 01 00 124 32 11 124 14 00 124 04 00 123 45 00 123 36 27 123 39 47 122 55 45 122 05 30 122 15 00 121 54 00 118 48 00 117 11 00 116 45 00 116 30 00 116 23 00 115 22 00 115 27 45 114 10 08 113 21 00 112 57 09 113 35 33 114 14 30 115 30 00 115 30 12 115 43 48 115 50 26 115 44 00 115 00 15 115 08 00 116 01 00 116 38 00 117 40 00 117 53 45 117 54 04 Lun. Int. H.W. h. m. 8 00 6 17 5 15 4 57 3 50 5 45 6 45 11 30 L.W. ft. m. 1 48 05 11 27 11 18 10 00 11 58 27 [10 16] [10 53] Range. 8pg. Neap. ft. ft. 9.8 5.8 12.0 7.1 16.8 17.0 16.7 21.9 23.0 9.9 10.0 9.9 12.9 13.6 5 10 17.6 10.4 [3 43] [2.1] [4 40] [2.6] Page 362] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. AUSTRALIA— Continued. Place. Bald Isle: Center Hood Point: Doubtful Isles Recherche Archipelago: Termination Isle Culver Point: Extreme Dover Point: Extreme Fowler Point: Extreme Streaker Bay: Port Blanche Coffin Bay: Mount Dutton Cape Catastrophe: W. pt Neptune Isles: SE. islet Port Lincoln: English Church Franklin Harbor: Observation spot Port Augusta: Flagstaff Port Victoria: Wardang Island hut Cape Spencer: S. pt Investigator Strait: Troubridge light.. . Port Wakefield: Lighthouse Port Adelaide : Wonga Shoal light Observatory Cape Jervis: Lighthouse Cape Borda: Lighthouse Cape Willoughby : Lighthouse Port Victor: Flagstaff Cape Jaffa: Margaret Brock lighthouse. Cape Northumberland: Lighthouse Cape Nelson: S. extreme Portland Bay: Lawrence Rock Port Fairy: Griffith Island summit Cape Otway : Lighthouse King Island: Cape Wickham light Port Phillip: Point Lonsdale light Geelong: Customhouse Melbourne: Observatory Cape Schanck: Lighthouse Port Western: Extreme of W. head Wilson Promontory: Light, SE. pt Kent Island : Deal Island light Flinders Is.: Strzelecki Peaks, SE. peak Groose Island : Light on S. end Banks Strait: Swan Island light Port Albert: Lighthouse Gabo Island: Lighthouse Cape Howe: East extreme Cape Green: SE. pt Twofold Bay: Lookout Pt. light Dromedary Mountain: Summit Montagu Island : Lighthouse Bateman Bay: Observation head UUaduUa : Inner end of pier Jervis Bay: Lighthouse Kiama Harbor: Outer extreme of S. head Wollongong : Summit of head Sydney: Observatory Port Jackson: Outer S. Head light Broken Bay: Baranjo Head light Newcastle : Nobb jr Head light Port Stephens : Lighthouse Sugar Loaf Point: Lighthouse Port Macquarie : Entrance. Solitary Islands: S. Isle light Clarence River: S. Head light Lat. S. 34 55 00 34 24 00 34 30 00 32 57 00 32 34 00 32 01 30 32 48 00 34 29 29 35 00 15 35 20 15 34 43 22 33 44 08 32 29 42 34 28 25 35 18 21 35 07 31 34 12 00 34 50 25 34 55 38 35 36 45 35 45 30 35 51 00 35 34 06 36 57 00 38 04 18 38 26 00 38 24 39 38 23 47 38 51 45 39 35 38 38 18 00 38 08 52 37 49 53 38 29 42 38 29 15 39 08 00 39 25 45 40 11 45 40 18 40 40 43 40 38 45 06 37 34 15 37 30 10 37 15 40 37 04 18 36 18 30 36 14 30 35 43 58 35 21 41 35 09 15 34 40 25 34 25 30 33 51 41 33 51 30 33 35 00 32 55 15 32 45 10 32 26 20 31 25 30 30 12 00 29 25 30 Long. E. 118 27 00 119 34 00 121 58 00 124 39 00 125 30 00 132 33 00 134 13 40 135 24 56 135 56 09 136 06 24 135 51 03 136 57 22 137 45 24 137 22 21 136 53 30 137 49 39 138 09 00 138 26 58 138 35 05 138 05 29 136 34 39 138 07 45 138 37 09 139 39 39 140 39 40 141 32 39 141 40 02 142 14 37 143 30 39 143 57 03 144 37 00 144 21 47 144 58 35 144 52 51 145 01 34 146 25 16 147 18 39 148 04 00 147 47 39 148 07 24 146 37 43 149 55 10 149 58 39 150 03 04 149 54 45 150 01 34 150 13 34 150 12 34 150 29 29 150 46 26 150 52 19 150 55 14 151 12 23 151 18 15 151 20 30 151 48 19 152 13 20 152 33 40 152 55 19 153 17 00 153 23 10 Lun. Int. Range. H.W. h. TO. 11 50 35 20 4 31 4 04 4 00 11 52 " '6'26 10 43 2 02 2 19 10 38 8 40 8 05 8 20 '8'26 8 40 8 35 8 15 9 00 's'is L.w. Spg. h. m. 9 35 5.1 6 55 5.5 2 15 11.4 10 45 10 22 10.2 6.3 10 15 5 40 '635 4 30 8 20 8 41 4 25 2 27 1 52 2 07 '2'67' 2 27 2 23 2 00 2 46 '2 bo' 5.8 4.2 2.5 3.0 1.9 8.1 4.5 5.2 5.3 '5.'4' 4.2 4.7 5.8 4.1 '4.'6" APPENDIX IV. [Page 353 MARITIME POSITIONS AND TIDAL DATA. AUSTRALIA— Continued . 8 Place. Lat. s. Long. E. Liuulnt. Range. H.W. L. w. Spg. Neap. •6 a « a S 9 9 Richmond River: N. Head light 28 51 30 27 23 22 27 28 00 27 26 20 27 02 10 25 56 00 25 00 15 24 43 20 24 45 00 24 07 00 24 01 20 24 01 20 23 53 00 23 29 30 22 31 40 21 39 00 21 19 15 21 32 00 20 32 20 20 18 50 20 15 30 20 00 50 19 57 30 19 41 50 19 19 20 19 11 25 18 45 30 18 09 30 17 40 40 17 09 45 16 04 20 15 45 00 15 29 45 15 16 30 14 37 15 14 10 00 14 07 45 14 00 30 13 24 45 12 51 00 11 58 15 11 55 00 11 46 30 11 36 30 10 41 30 10 37 45 10 22 00 10 46 00 10 36 05 17 36 40 17 35 10 17 06 50 153 35 55 153 10 31 153 01 36 153 33 50 153 28 04 153 13 00 153 23 00 153 13 40 152 25 00 152 45 15 151 41 04 151 37 15 151 23 50 151 14 04 150 45 44 150 14 00 149 43 30 149 31 04 148 58 00 148 53 15 149 00 00 148 16 54 148 27 34 148 23 00 147 27 40 147 01 10 146 42 50 146 11 04 146 11 00 146 02 30 145 29 34 145 28 30 145 17 30 145 23 15 144 57 30 144 32 34 144 15 19 143 42 15 143 36 19 143 34 00 143 15 15 143 29 00 143 06 00 142 56 19 142 32 24 142 39 20 142 21 19 142 10 50 141 53 49 140 37 06 139 45 56 139 38 36 ft. tn. ft. m. ft. ft. Brisbane: Signal station, Fisherman la... Observatory 10 45 4 30 6.4 3.9 Lookout Point: Extreme Cape Moreton: Lighthouse ■ Double Island Point : Lighthouse Indian Head : Extreme Sandy Cape: Lighthouse Burnett River: S. Head light Lady Elliot Islet: Lighthouse Bustard Head: Lighthouse Rodd Bay: Spit end Port Curtis: Gatcombe Head light Cape Capricorn: Lighthouse Port Bo wen: Observation rock Percy Isles: Pine I. light Northumberland Isles: Summit of Prud- hoe I Cape Palmeraton: N. extreme Cape Conway: SE. pt : . . . Port Molle: S. side of entrance Cumberland Island: Whitsunday I., sum- mit on W. side Port Denison: Obs. pt., W. side of Stone Isle '. 10 05 3 53 9.0 5.4 Gloucester Island: Summit near N. end.. Holbome Islet: Center Cape Bowling Green: Lighthouse Cape Cleveland: Lighthouse Palm Islands: SE. point of SE. island. . . Rockingham Bay: Peak of Goold Isle Barnard Island: Lighthouse Frankland Island: High islet Cape Tribulation: Extreme Hope Island: S. islet Cook Mountain: Summit 8 55 2 43 7.5 4,5 Cape Bedford: SE. extreme Murdock Point: Extreme Cape Melville: NE. extreme Flinders Island: N. extreme of N. island. Claremont Point: Extreme Cape Sidmouth: Extreme 9 00 2 47 9.6 5.8 Cape Direction: NE. extreme Cape Grenville: Extreme Sir Charles Hardy Island: N. extreme of SE. isle Bird Island: NW. isle Hannibal Isles: E. isle Cape York: Sextant Rock i 66 1 7 in 8.0 4.7 Mount Adolphus: Summit Travers Isles: Center Prince of Wales Island: Cape Cornwall, extreme Booby Island: Center 4 20 10 30 7.8 4.7 Flinders River: Entrance Albert River: Kangaroo Pt Sweers Island: Inscription Pt 21594°— 14- -23 Page 354] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. TASMANIA. Place. Cape Portland: NW. pt Port Dalrymple: Low Head light Port Sorrell: NW. entrance head Port Frederick: Entrance Leven River: W. entrance head Emu Bay: Blackman Pt Hunter Island: N. pt Cape Grim: Outer Doughboy Islet .... Albatross Islet: N. pt Arthur River: Entrance Pieman River: Rocks close to entrance Macquarie Harbor: Entrance Islet Cape Sorrell : Lighthouse Port Davey : Pollard Head Southwest Cape: Extreme pt Mewetone Rock: Center Cape Bruny : Lighthouse Bruny Island: Penguin Islet HobartTown: Transit of Venus station. Cape Pillar: Tasman Islet Cape Frederik Hendrik: Extreme Freycinet Peninsula: Summit St. Patrick Head: N. pt Eddystone Point: Extreme Lat. S. 40 44 15 41 03 25 41 07 05 41 10 00 41 08 30 41 02 50 40 23 40 40 40 10 40 22 00 41 04 00 41 41 00 42 11 37 42 11 00 43 19 00 43 33 30 43 44 30 43 29 40 43 21 00 42 53 25 43 14 00 42 52 00 42 13 00 41 34 00 40 59 40 Long. E. 147 56 09 146 47 54 146 33 30 146 24 30 146 12 00 145 56 39 144 47 45 144 39 44 144 39 19 144 44 00 144 57 00 145 12 34 145 10 30 145 53 00 146 01 04 146 22 04 147 08 49 147 23 40 147 20 07 148 02 00 148 00 00 148 18 04 148 19 30 148 20 50 Lun. Int. Range. n. W. L. W h. TO. 11 10 7 20 8 05 Spg. h, TO. 5 00 1 07 1 52 ft. 9.0 2.7 4.2 NEW ZEALAND. Three Kings Islands: NE. extreme of NE. island North Cape: Cape Islet Parenga-renga Harbor: Kohan Pt Maunganui Harbor: White Pt Wangaroa Harbor: Peach Islet Bay of Islands: Motu Mea Islet Wangaruru Harbor: Grove Pt Wangari Harbor: Loot Pt Great Barrier Island : Needles Pt Auckland Harbor: Lighthouse Coromandel Harbor: Tulinia I Cape Colville: N. pt Cuvier Island: Lighthouse Tauranga Harbor: Mount Maunganui, 860 ft White Island: Summit, 863 ft Cape Runaway: Extreme East Cape: Islet, 420 ft Tolaga Bay: Matu-heka Islet Mahia Peninsula: S. extreme of Port- land I Ahuriri Harbor: Lighthouse Kidnappers Cape: Extreme Cape Palliser: Lighthouse Port Nicholson: Pencarrow light Wellington: Queens Wharf light New Observatory Mana-watu River: Lighthouse Wanganui River: N, head Egmont Mountain: Summit, 8,270 ft New Plymouth: Flagstaff Kawhia Harbor: S. head 34 06 20 34 25 07 34 31 00 35 00 20 35 01 44 35 17 00 35 23 48 35 51 09 36 01 15 36 50 06 36 48 35 36 28 20 36 26 20 37 36 25 37 30 00 37 30 45 37 40 00 38 20 50 39 18 00 39 28 30 39 38 00 41 36 45 41 21 40 41 17 17 41 17 04 40 27 10 39 57 00 39 18 00 39 03 35 38 04 50 172 08 49 173 03 34 173 00 54 173 32 39 173 45 48 174 06 06 174 21 24 174 31 14 175 25 34 174 51 00 175 24 34 175 21 04 175 49 00 176 10 14 177 10 49 177 59 34 178 35 09 178 20 14 177 53 15 176 54 14 177 06 44 175 18 45 174 51 04 174 47 25 174 46 04 175 14 40 174 59 44 174 03 59 174 04 35 174 48 04 7 40 7 26 7 15 7 05 7 20 7 05 7 05 8 10 8 00 6 05 4 40 '4'52' 9 40 9 15 9 10 1 30 1 55 1 05 55 6.4 5.9 6.5 6.7 1 10 55 10.8 10.7 55 6.1 2 00 1 50 6.6 12 15 3.5 10 50 1654' 3 30 5.7 3.6' 6.3 3 05 3 00 n. 6 IL 9 APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. NEW ZEALAND— Continued. [Page 366 22 Place. Aotea llarbor: S. head Whaingaroa Harbor: S. entrance pt Manukau Harbor: Paratutai flagstaff Kaipara Harbor: Lighthouse Hokianga River: Flagstaff at entrance Cape Campbell : Lighthouse Port Cooper: Lyttleton customhouse Akaroa Island : Lighthouse Ashburton River: N. entrance pt Waitangi River: N. entrance head Otago Harbor: Taivoa Head light Molyneux Bay: Landing place Nugget Point: Lighthouse Bluff Harbor: Lighthouse Tewaewae Bay: Pahia Pt Solander Islands: Summit, 1,100 ft Preservation Inlet: Lighthouse West Cape: Extreme Queenetown: U. S. Tr. of Venus station . . . Milford Sound : Freshwater Basin Cascade Point: N. extreme Grey River: Entrance Hokitika: Entrance light Cape Foulwind: Lighthouse Ca|)e Farewell: Extreme Nelson: Bowlder Bank liglit D'Urville Island: Port Hardy Port Gore: Head of Melville Cove Port Underwood : Flag Pt Port William: HoweU's house Paterson Inlet: Glory Cove Port Adventure: White Beach, S. end Port Pegasus: Cove abreast Anchorage I . . Codfish Island: NW. extreme Snares Islands: SW. islet Lat. S. Long. E. Liin. Int. Range. H.W. L.W. Spg. Neap. 37 59 35 37 46 22 37 03 00 36 23 00 35 32 05 41 44 00 43 46 40 43 54 00 44 04 50 44 54 50 45 46 55 46 24 05 46 27 10 46 37 00 46 20 40 46 36 00 46 10 00 45 54 50 45 02 07 44 40 20 44 00 30 42 26 20 42 42 20 41 45 40 40 29 50 41 16 05 40 46 35 41 01 55 41 20 28 46 50 30 46 58 30 47 03 52 47 11 40 46 45 45 48 06 43 174 50 04 174 52 19 174 31 14 174 08 00 173 21 59 174 17 14 172 44 17 173 00 20 171 48 34 171 11 14 170 44 02 169 47 53 169 50 04 168 23 00 167 42 19 166 54 04 166 38 15 166 25 49 168 40 06 167 54 45 168 21 34 171 11 54 170 59 30 171 27 44 172 41 04 173 17 30 173 54 04 174 11 22 174 08 24 168 05 34 168 09 54 168 10 57 167 40 51 167 36 49 166 27 44 A. m. h. m. ft. ft. 9 08 9 05 9 00 8 40 4 45 3 45 2 55 2 50 2 50 2 30 11 00 10 00 12.3 12.6 10.0 9.2 7.5 7.4 8.7 9.0 7.1 6.5 6.5 5.8 3 31 9 39 5.6 4.4 1 05 7 15 7.8 6.2 11 10 5 00 7.5 5.9 "* 10 10 10 20 4 00 4 10 9.8 9.5 7.7 7.5 L. 9 55 9 45 3 45 3 36 12.0 11.6 9.4 9.2 6 00 12 15 7.6 6.6 1 00 9 15 7.8 6.2 11 45 5 40 7.9 6.2 THE ARCTIC REGIONS. Cape Walsingham: Extreme Mile Island: N.pt Marble Island: E. end Cape Kendall: Extreme Iglooik Island : E. pt Victoria Harbor: N. shore Elizabeth Harbor: Entrance. . . . Magnetic Pole, 1831 PortNeill: N. pt. of entrance... Port Bowen: N. cove Batty Bay: S. pt. of entrance... Port Leopold: Whaler Pt Careys Islands Discovery Harbor Alert's Winter Quarters Cape Joseph Henry: N. extreme Cape Hecla: N. extreme Cape Columbia: Extreme Melville Island: Winter Harbor. North Cape 00 00 04 00 33 00 42 00 21 00 09 17 38 14 05 00 09 13 13 39 13 00 50 05 49 00 04 40 27 00 40 00 54 00 07 00 47 10 55 00 69 28 77 50 91 06 87 15 81 31 91 30 92 10 96 47 89 00 88 54 91 08 90 12 73 10 64 45 61 18 63 38 64 45 70 20 110 48 179 57 4 00 'o"56' 11 38 10 35 1 20 10 15 40 5 29 4 20 7 40 12.0 8.0 5.5 2.6 3.8 5.1 4.2 2.9 1.0 L9 Page 356] APPENDIX IV. MARITIME POSITIONS AND TIDAL DATA. THE ARCTIC REGIONS— Continued. Place. Liakhov Islands: E. pt. of New Siberia. . . Cape Tscheljuskin: E. pt Nova Zembia: Vaigats I., N. pt Cape Costin (Kostina) NE. pt., Cape Desire Franz Josef Land: Wilczek I Mezen: Epiphany Church Morjovetz Island: Lighthouse Archangel: Trinity Church Jighinsk Island : Lighthouse Onega: St. Michael's Church Salovetski: Lighthouse Cape Sviatoi Nos: Lighthouse Bear Island Spitzbergen Island : S . cape Cloven Cliff Danes I., Robbe Bay Cape Morris Jesup Thank God Harbor Cape York: Extreme Upemivik: Flagstaff Proven: Village Omenak Island : Village Godhavn: Village Jacobshavn : Village Claushavn : Village Christianshaab : Village Egedesmunde: Village Whalefish Island: Boat Inlet. Holsteinberg : Village Kangamint Ny Sukkertop: Village Godthaab : Flagstaff Sermelik Fjord : Kasuk Peak. Fiskemaes: Village Jensen Nunatak: Peak Ravn Storo: Peak Frederikshaab: Church. Kangarssuk Havn : Village Arsuk: Pingo Beacon Kajartalik Island: Summit... Ivigtuk: House Bangs Havn : Anchorage Aurora Harbor Julianshaab : Village Neunortalik: Village Frederiksthal: Village Cape Farewell: Statenlluk.. Aleuk Islands: Center Cape Tordenskjold: Extreme. Cape Bille: Extreme , CapeJuul: Extreme Cape Lowenorn: Extreme Dannesbrog Island : Beacon . . Ingolsfjeld Rigny Mount: Summit Pendulum Islands Cape Philipp Broke Cape Bismarck: Extreme Lat. S. 75 10 00 77 41 00 70 25 00 70 55 00 76 58 00 79 55 00 65 50 18 66 45 50 64 32 06 65 12 17 63 53 36 65 07 00 68 08 51 74 30 00 76 35 00 79 50 00 79 42 00 Lat. N. 83 39 00 81 38 00 75 55 00 72 47 48 72 20 42 70 40 00 69 14 04 69 13 12 69 07 30 68 49 06 68 42 30 68 58 30 66 55 54 65 48 42 65 24 30 64 10 36 63 29 12 63 05 12 62 50 00 62 42 36 61 59 36 61 28 20 61 10 24 61 09 42 61 12 12 60 47 30 60 48 36 60 43 07 60 08 12 60 00 00 59 49 00 60 09 00 61 25 00 62 01 00 63 14 00 64 30 00 65 18 00 66 19 02 69 00 12 74 40 00 74 55 00 76 47 00 Long. E. 150 30 00 104 01 00 59 10 00 53 01 50 65 40 00 58 45 00 44 17 00 42 30 00 40 33 30 36 51 30 38 08 30 35 37 00 39 48 54 20 00 00 17 23 00 11 40 30 11 07 00 Long. W. 30 40 00 61 44 00 65 30 00 55 53 42 55 20 00 51 59 00 53 24 07 50 56 30 50 55 30 51 00 00 52 46 00 53 27 00 53 40 18 53 23 00 52 54 00 51 45 48 51 10 48 50 43 36 48 57 00 50 20 48 49 44 00 48 51 00 48 26 00 48 30 42 48 10 30 47 52 00 47 46 48 46 01 00 45 16 00 44 40 00 44 01 42 42 55 00 42 15 00 42 00 00 40 50 00 39 30 00 38 30 00 35 11 00 26 10 24 18 17 00 17 33 00 18 40 00 Lun. Int. n. W. L. W 10 00 7 18 5 05 9 02 9 05 14 (approx) 12 14 10 50 8 05 6 20 6 40 6 12 6 15 4 56 5 33 2 55 4 00 11 05 11 10 h. m. 3 50 2 00 11 30 3 10 2 55 6 25 5 58 4 38 1 52 07 27 Range. g. Neap. ft- 7.0 2.2 3.8 9.1 13.9 5.3 5.4 8.0 7.5 10.0 12.5 00 9.0 03 12.0 11 09 11 46 9 10 10 13 7.0 8.6 9.4 7.5 4 53 4 58 6.7 3.7 APPENDIX IV. [Page 357 MARITIME POSITIONS AND TIDAL DATA. TTTK ARCTIC REGIONS— Continued. Place. Lat. S. Long. W. Lun. Int. Range. H.W. L.W. Spg. Neap. 1 a ed g M Jan Mayen Island: Mt. Beerenberg, 6,870 ft Youngs Foreland, or Cape Northeast Mary Muss Bay Langanaes Point 71 04 00 71 08 00 71 00 00 66 22 45 66 32 40 66 33 42 66 07 30 66 27 29 66 26 30 65 30 15 64 48 04 64 08 40 64 04 09 63 48 06 63 48 19 64 35 42 64 55 27 65 16 14 65 45 00 n r 7 36 00 7 26 00 8 28 00 14 30 46 16 10 24 17 57 36 20 05 26 22 23 04 23 08 00 24 31 26 23 45 08 21 55 00 22 39 04 22 39 00 16 36 13 14 08 31 13 41 10 13 32 22 14 23 35 ft. TO. A. m. /'. ft. 11 21 5 06 3.8 2.2 Rissnaes Point Grimsey Norddranger: Tr. Station Skagataaa Point North Cape : Kalfatindr Straumness Point Fugle or Staabierg Huk: Point Snaefells Yokul : Tiw Station Reykiavik: Observatory 6 io ii 25 14.5 8.4 Cape Skagi : Lighthouse Reykianaes: Lighthouse 1 Ingolfshofde: Tr. Station ) Papey Island : Tr. Station i Rev thur Fjeld : Tr. Station 1 Balatangi: Lighthouse 1 Dia Fjefd: Tr. Station 1 1 Page 358] INDEX TO APPENDIX IV. Page. Admiralty Islands 346 Adriatic Sea 315-321 Africa, east coast 323-325 north coast 320, 321 west coast 321-323 Alabama 284 Alaska 287,288 Albania 318 Aleutian Islands 287 Algeria 321 Arabia 327 Arctic regions 355-357 Argentina 298 Asia, east coast 331-342 islands. 332 south coast 327-330 Atlantic Ocean, islands 302-304 Australia 351-353 Austria 317,318 Azores Islands 302 Bahama Islands 292 Balearic Islands 316 Baluchistan 328 Banka Strait 331 Belgium 313 Belize 285,286 Bermuda Islands 303 Black Sea 315-321 Borneo 333 Brazil 295,297 British Columbia 288, 289 Burma 329 California 289 Canary Islands 303 Cape Breton Island 281 Verde Islands 303 Caroline Islands 343 Celebes Island 333 Central America, east coast 285-287 west coast 291 Ceylon 329 Chile 298-801 China 337,338 Sea 337 Entrance 331 Chosen 339 Cochin China 336 Colombia, north coast. . 295, 302 west coast Connecticut 282, 283 Cook Islands 350 Coral Sea Archipelago 347 Corsica 316 Costa Rica 280 Crozet Islands 327 Cuba 292,293 Cyprus 320 Delaware 283 Denmark 312 REGIONS AND COASTS. Page. East Indian Is., smaller Dutch 332 Ecuador 302 E,^ypt 320 Eliice Islands 345 Europe, Atlantic coast. 304-315 Falkland Islands 304 Fiji Islands 347,348 Florida 284 Formosa Island 338 France, north and west coasta 313,314 France, south coast 316 Galapagos Islands 342 Gaspar Strait 331 Georgia 283 Germany 310-312 Gilbert Islands 342 Great Britain 304-307 Greece 319 Greenland 356 Guatemala 286 Guiana 296 Haiti, island of 293, 294 Hawaiian Islands 344 Holland 313 Honduras 286 Iceland 357 India 328,329 Indian Ocean, islands.. 325-327 Italy 316,317 Jamaica 293 Japan 339-341 Java 331 Kergueleii Islands 327 Korea 339 Kuril Islands 341 Labrador 279, 280 Laccadive Islands 325 Ladrone Islands 344 Louisiade Archipelago 347 Louisiana 284 Lower California 290 Mad£^ascar 326 Madeira Islands 303 Magdalen Islands 280 Maine 281, 282 Malaysia 329, 330 Maldive Islands 325 Mariana Islands 344 Marquesas Islands 345 Marshall Islands 343 Maryland 283 Massachusetts 282 Mauritius Island 325 Mediterranean Sea. . . . 315-321 Mexico, east coast 285 west coast 290, 291 Mississippi 284 Molukka Islands 332, 333 Morocco 321 Mosquito Coast 286 New Brunswick 280, 281 Caledonia 350 Newfoundland 279, 280 New Guinea Island 346 Hampshire 282 Hebrides Islands 347 Jersey 283 South Wales 352 York 282, 283 Zealand 354, 355 Nicaragua 286 North America, east coast 279-287 west coast. . . . 287-291 Australia 351 Carolina 283 l8land,NewZealand 354, 355 Norway 307, 308 Nova Scotia 281 Oregon 289 Pacific Ocean, Lilands. . 342-350 Panama 287 Pelew Islands 344 Pennsylvania 283 Persia 328 Peru 301,302 Philippine Islands 333-336 Phoenix Islands 345 Porto Rico 294 Portugal 314,315 Prince Edward Island 280 Queen Charlotte Islands 288 Queensland 353 Red Sea 324,325 Rhode Island 282 Russia, south coast 320 west coast 309, 310 St. Lawrence, River and Gulf 280 Samoan Islands 348 Santa Cruz Islands 347 Sardinia 316 Siam, Gulf 336 Siberia 341,342 Society Islands 349 Solomon Islands 346 South America, north and east coasts 295-298 South America, W.coast 298-302 Australia 352 Carolina 283 INDEX TO APPENDIX IV. [Page 359 Page. South Island, New Zealand 355 S. AV. Is. of Japan 338, 339 Spain, north and west coasta 314,315 south and east coasts. . 315 Stewart Island 355 Sumatra 330 Sweden 308, 300 Taiwan ( Formosa) 338 A.alborg 312 Aarhus 312 Ababa Island 347 Abaco Island 292 A bang Besar Island 330 Abbeville 313 Abd-al-Kuri Island 324 Aberdeen 305 Abervrach 313 Aberystwith 304 Abingdon Island 342 Abo 309 AboukirBav 320 Abreojos Point 290 Abrolhos Island 297 Absecon Inlet 283 Acajutla 291 Acapulco 291 Accra 322 AcheenHead 330 Aconcagua Mountain 300 Acre 320 Adakh Island 287 Adalia 320 Adams, Port 338 Addu Atoll 325 Adelaide, Port 352 River 351 Ad^le Island 347 Aden 327 Adenara Island 332 Admiralty Head 289 Islands 346 Adolphus Mountain. ... 353 Adventure, Port 355 Mgina....- 319 Aero Island 312 iErstenen 308 Africa Rock 316 Agalegaa Island 326 Agdenes • 307 Agiabampo 291 Agrigan Island 344 AguadillaBay 294 Aguia Point 302 Agulhaa, Cape 323 Agutaya Islet 334 Aheu Island 349 Ahunui Island 349 Ahuriri 354 Ai Sima 341 Aian 341 Aignan, St., Island 347 Aigues Alortes 316 Ailinginae Islands 343 Aillick Harbor 279 AiUy Point 313 REGIONS AND COASTS — Continued. Page. Tasmania 354 Texas 284 Tokara Islands 339 Tonga Islands 350 Trinidad 296 Tuamotu Archipels^o 349 Tunis 321 Turkey 320 Uruguay 298 PLACES. Ailuk Islands 343 Aitutaki Island 350 Aix Island 314 Aiaccio 316 Aiano 320 Akamokan Island 344 Akaroa Island 355 Akashi-no-seto 340 Akpatok Island 279 Akyab 329 Alacran Reef 285 Alamaguan Island 344 Aland Island 309 Alargate Reef 286 Albany 283 Albatross Islet 354 Albemarle Island 342 Albert, Port 352 River 353 Alboran Island 321 Albuquerque Bank 286 Alcatrazes Island 297 Alcmene 350 Alcobaga 297 Aldabra Island 327 Alden 308 Alderney Harbor 307 Alegranza Island 303 Alegre, Porto 297 Alert 's Winter Quarters 355 Alessandro, San, Island 345 Aleuk Islands 356 Alexander, Port 322 Vancouver 288 Alexandretta 320 Alexandria 320 Alfaques, Port 315 Alfred, Port 323 Algeciras 315 Algiers 321 AH-Agha, Port 320 Alicante 315 Alijos Rocks 290 Alipee 328 Alligator Island 337 Reef 284 Almadie Point 321 Almeria 315 Almirante Bay 287 Alphonse Island 325 AltaVela 294 Altata 291 Altea 315 Altona 311 Alvarado 285 Amager Island 312 Amber, Cape 326 Page. Vancouver Island 288 Venezuela 295,296 Victoria 352 Virginia 283 Washington 289 Western Aiistralia 351,352 West India Islands 292-295 Yucatan 285 Amboina Island 332 Ambrose, St., Island 350 Amchitka Island 287 Amelia Island 284 Ameni Islet 325 Amherst Harbor 280 Amirante Islands 325 Amour Point 280 Amoy 337 Amsterdam 313 Island 327 Ana, Sta., Lagoon 285 Anaa Island 349 Anacapa Island 289 Anadir River 342 Analaboe 330 Anamba Islands 331 Anataxan Island 344 Anchorite Island 346 Ancona 317 Ancud 300 Andaman Islands 329 Andenes 307 AndravaBay 326 Andrea, St., Rock 318 Andrew, St 281 Cape 326 Island 346 Andrews, St., Island 286 Androa Island, Bahamas. . . 292 Grecian Arch .... 319 Ane^da 294 Aneityum Island 347 Angatau 349 Angaur Island 344 Angeles Bay 290 Los 289 Port, Mexico 291 , Washington 289 AnghrisHead 306 Angosto, Port 299 Angoxa Island 323 Angra dos Reis 297 Pequena 322 Anguilla 294 Anhatomirim 297 Anholt Island 312 Animas, Las 290 Anjer 331 Anjoe, Cape 331 Ann, Cape 282 St., Bay 293 Anna, Sta., Island, N. Brazil 297 S. Brazil. . . . 296 Annapolis, Maryland 283 Nova Scotia 281 Anne, St., Island 299 Page 360] INDEX TO APPENDIX IV. Page. Annisquam 282 Anno Bon Island 322 Anns, St., C. Breton 1 281 England 304 Anowik Island 288 Antareh, Eas 324 Antibes 316 Anticosti Island 280 Antigua 294 Antipodes Island 350 Antivari 318 Antofagasta 301 Antonina 297 Antonio, Port 293 San, Cape, Argentina. . 298 Cuba 293 Mt. and Island... 303 Port, Argentina. . 298 —-Chile 300 Sierra Antwerp 313 Aoga Shima 340 Aomori 340 Aor, Pulo 331 Aotea 355 Apaiang Island 342 Apalachicola 284 Apamama 342 Aparri 334 Apenrade 311 Apo Islet 334 Apostle^Rocks 299 Arago Cape 289 Araish, El 321 Arakam Island 342 Araktcheff Island 349 Aran Island 306 Aransas Pass 284 Aranuka Island 342 Aratika Island 349 Arcadins Islands 294 Areas Cays 285 Archangel 356 Ardassier Islands 332 Ardrossan 305 Arena de la Ventana 290 Point, California 289 L. California 290 Arenas Cay 285 Arendal Inlet 308 Arentes Island 332 Argentina 298 Aigostoli, Port 319 Anca 301 Arichat Harbor 281 Arkona 311 Armeghon 329 Amheim, Cape 351 Amo Atoll 343 Arorai Island 342 Arran Island 306 Arrowsmith Islands 343 Arsuk 356 ArtakiBay 320 Arthur River 354 Port 338 Am Islands 332 Arvoredo Island 297 Ascension Bay 285 Island 303 PLACES — continued. Page. Ashburton River 355 Ashrafi Island 324 Asia Rock 301 Assateague Island 283 Assens 312 Assumption Island 326 Astoria 289 Asuncion Island, Ladroues. 344 L. Caliiomia 290 Atalaia Point 296 Athens 319 Atico 301 Atiu Island 350 Atka Island 287 Atkinson Point 289 Attu Island 287 Auckland 354 Islands 350 Audieme 314 Augusta 282 Port, Australia 352 Sicily 317 Augustenberg 311 Augustin, St., Cape, Brazil. 296 Philippines . 335 Augustine, San, Island 345 St., Bay 326 Harbor 284 Aurh Island 343 Aurora Harbor 356 Island 347 Austral Islands 350 Aux Cayes 294 Avarena Point 294 Aves Island 295 Aviles 314 Avlona 318 AximBay 322 Awa Sima 340 Ayamonte 315 Ayer Bangis 330 Ayr 305 Baago Island 312 Babayan Claro Island 334 Baccalieu Island 279 Bagamoyo 324 Bahaltolis Island 336 Bahama Island 292 Bahia, Brazil 296 Colombia 295 de Cadiz Cay 293 Honda, C. Ainerica 291 Honda 293,295 Bahrein Harbor 327 Baitiqueri, Port 293 Bajo Nuevo 285 Baiuren Island 333 Baker Islet 342 Bakers Island 281 Baklar 320 Balilbac Island 333 Balaklava Bay 320 BalariPass 350 Balasor River 329 Balatangi 357 Balayan 334 Bald Isle 352 Balfour Rock 327 Bali Island 332 Balingtang Islands 334 Ballena Bay 291 Balls Pyramid 350 Ballum 311 Ballycottin 307 Balstrum 312 Balta Island 305 Baltic Port 310 Baltimore 283 Bampton Island 347 Banda Island 332 Banderburum 327 Bandjermasin 333 Bangkaru Islands 330 Bangkok 336 Bangor 281 Bangs Havn 356 Banjuwangi 331 Banka Island 331 Strait 331 Bankot 328 Banks Strait 352 Bantal 330 Bantam 331 Bantenan 331 Banton Island 335 Bantry Bay 306 Baracoa 292 Barataria Bay 284 Baratoube Bay 326 Barbados Island 295 Barbara, Santa, California. . 289 Island 289 Mexico 291 Port 299 Barbe, St., Island . ' .'. .'.' .' .' '. 331 Barbuda 294 BarceloBay 299 Barcelona, Spain 315 Venezuela 295 Bardsey Island 304 Barfleur, Cape 313 Bari 317 Barker Islets 351 Barnard Island 353 Bamegat Inlet 283 Bameveldt Islands 298 Barnstable 282 Barrallead 305 SaoJoao 297 Barren Island 339 West 338 Barrier, Great, Island 354 Barrington Island 342 Barrow Island, Australia. . . 351 Tuamotu Arch. . . 349 Point 287 Bartholomew, St 294 Cape 298 Bartolom^, San 290 Barton, Port 334 Baru, Point 330 Barung Island 331 Bas, De, Island 313 Basdorf 311 Basianang Bay 335 Bdsidu 328 Basilan Island 336 INDEX TO APPENDIX IV. [Page 361 Page. Baskerville, Cape 351 Basrah 327 Bass Islets. . .- 350 Bassa, Grand 322 Bassas Rocks 329 da India 326 Bassein, Burma 329 India 328 River 329 Basseterre 294 Bastia 316 Bastion, Cape 337 Basto 308 Batabano 293 Batalden Island 308 Batan Island 334 Port 335 Batangas 334 Batavia 331 Batbatan Island 335 Bate Islands 339 BatemanBay 352 Bath 282 Bathurst 321 Island 351 Batian Island 333 Batoe Islands 330 BatoeToetong 330 Batoiim 320 Batticaloa 329 Battle Islands 279 Batty Bay 355 Baubeltaub Island 344 Bauld Cape 279 BaxoNuevo 293 Bay of Islands 354 Baynes Sound 288 Bayonnaise Islajid 340 Bayonne 314 Bazanito Island 323 Beachy Head 304 BealeCape 298 Bear Island 356 Cape 316 Beata Island 294 Beaufort, N. Carolina 283 S. Carolina 283 Port 323 Beaver Harbor 288 Beaver-tail Light 282 BecduRaz 314 Beda'a, Al 327 Bedford, Cape 353 Bees, St 305 BeevesRocks 306 Beirut 320 Bel Air 326 Belfast 281 Bay 306 Belgrano 298 Belize 286 BeUIsland 279 Rock, Scotland 305 Bellavista Cape 316 Belle Isle, France 314 Belle Isle, Labrador 279 Bellingshausen Island 348 Bellone, Cape 326 BenGhazi 321 Benbane Head 306 PLACES — continued. Page. Bender Erekli 320 Benedict©, San, Island 291 Benevente 297 Benguela 322 Benicia 289 Benidonne 315 Benia River 322 Benito, San, Island 290 Benkulen 330 Bento, San, River 322 Benzert 321 Bequia Island 295 Berbera 324 Berdiansk 320 Bergen, Germany 311 •^i Norway 308 Berikat 331 Bering, Cape 342 Island 341 Berlanga Island 315 Berlin 311 Bermejallead 298 Bermudas 303 BemalChico 285 Bernardo Islands 348 Berwick 305 Besuki 331 Betrapar Islet 325 Beverly 282 Beyt. 328 Bhaunagar 328 Blanche Point 318 Biarritz 314 Bickerton Island 351 Bideford 304 Bidstone 305 Bierneborg 309 Bigar Islet. 343 Bikini Islands 343 Bilbao 314 Bille, Cape 356 Billiton Island 331 Bindloe Island 342 BintangHill 330 Bintoean 330 Bird Island, Australia 353 Bahamas 292 BandaSea 332 N.Pacific 344 Seychelle Islands. 325 Tuamotu Arch . . . 349 W. Africa 321 Islands 323 Bimeys Island 345 Bismarck, Cape 356 Bittern Rocks 340 Bjuroklubb 309 Blaabjerg 312 Black Head 279 Point Bay 322 Stairs Motmtain 307 Blackness 305 Blacksod Point 306 Blair, Port Blaize, St 323 Blanco Cape, N., Africa 321 Oregon 289 Peru 302 Africa 321 Peak 287 Page. Blankenbei^he 313 Blaa, San, Argentina 298 Cape, Florida 284 Mexico 291 Blasket Islands 306 Bligh Island 349 BlighsCape 327 Blimbing Bay 330 Blinyu 331 Block Island 282 Bloody Foreland 306 Bluefields 286 Bluff Harbor 355 Boar Islands 280 Boavista Island 303 Bobara Rock 318 Bocas del Tore 287 Bodie Island 283 Bogense 312 Bc^sher 309 Bohol Island 335 Bojador, Cape 321 Boieador, Cape 334 Bola-Bola Island 349 Bom Abrigo Islet 297 Bombay 328 Bon, Cape 321 Pomt 330 Bona 321 Bonacca Island 286 Bonaire Island 295 Bonaventure Head 279 Island 280 Bonaviflta Cape 279 Bongao Island 336 Bonham Islands 343 Bonifacio 316 Bonin Islands 345 Boobjerg 312 Booby Island, Leeward Is. . 294 Queensland 353 Boompjeo Island 331 Boon Island 282 Borda, Cape 352 Bordeaux 314 Bordelaise Island 343 BorjaBay 299 Bomholm 312 Borodino Islands 345 Boscawen Island 348 Bosphorus 320 Boston 282 Botel Tobago Sima 338 Bougainville, Cape 351 Island 346 Bougaroni, Cape 321 Boulogne 313 Bounty Islands 350 Bourbon, Cape 327 Bouro Island 332 Bouton Island 333 Bouvets Island 304 Bowditch Islet 345 Bowen, Port, Australia 353 -BaflBnsBay 355 Bowling Green, Cape 353 Boyanna Bay 326 BradoreBay 280 Brala, Pulo 336 Bras, Pulo 330 Page 362] INDEX TO APPENDIX IV. Brass River 322 Brava Island, C. Verde Is. . 303 E.Africa 324 Brazos Santiago 284 Bray Head 307 Breaker Point 337 Bremerhaven 311 Bremerton 289 Brest 314 Brewers Lagoon 286 Brid£;eport 283 Brieile 313 Brill Reef 332 Brindisi 317 Brisbane 353 Bristol, England 304 Rhode Island 282 Britannia Island 350 Broadhaven 306 Broken Bay 352 Bronnosimd 307 Brothers Island, Red Sea. . 324 Islets, China 337 Broughton Bay 338 Head 339 Island 341 Rock 340 Brunet Island 280 Bruni River 333 Brunswick, Georgia 283 Maine 282 Bruny, Cape 354 Island 354 Brussels 313 Brusterort 310 Bryer Island 281 Bubuan Island 336 -Bucaa Island 335 Buchanness 305 Buddonness 305 Budrum 320 Buliluyan, Cape 333 Budua 318 Buenaventura 302 San :.... 289 Buenos Ayres 298 Bu|:ui Point 335 Buitenzorg 331 Bukalsland 346 Bulipongj)ong Island 336 Bulk 311 BuU Harbor 288 Rock 306 Bullock Bay 341 Burg 311 Burghaz 320 Bunas Island 335 Burin Harbor 279 Burnett River 353 Burntcoat Head 281 Burrh Island 343 Busios 297 Islets 297 Bustard Head 353 Busuanga Island 334 Biisum 311 Butt of Lewis 305 Button Islands 279 Byam Martin Island 349 Byron Island 342 PLACES — continued. Page. Caballo Island 334 Cabeceira, Cape 323 Cabeza de Vaca 300 Cabrera Island 316 Cabron Cape 293 Cabrut Islet 325 Cadaques 315 Cadiz 315 Cadmus Island 349 Caen 313 Cagayan Jolo Island 336 Cagayanes Islands 336 Cagliari 316 Caigara 296 Caicos Island 292 West, Cay 292 Calaan, Point 335 Calais, France 313 Maine 281 Calavite, Monte 334 Calayan Island 334 Calbuco 300 Calcasieu Pass 284 Calcutta 329 Caldera 300 Caldy Island 304 Calebar River, New 322 Old 322 Caledonia Har1x)r 287 Calf of Man 305 Calicut 328 Calimere Point 329 Callao 301 Calpe 315 Caluya Island 334 Calvi 316 Camamu 296 Camaron Cape 286 Camasusu Island 335 Cambay 328 Cambria 297 Cambridge, England 304 United States 282 Camiguin Island, Luzon 334 Mindanao 336 Cammin 310 Campbell, Cape 355 Island 350 Campeche 285 Campobello Island 281 Canaria, Gran, Island 303 Canaveral Cape 284 Cancun Island 285 Candia Island 319 Candon 334 Cannes. 316 Cannonier Point 325 Canoas Point 290 Canso, Cape 281 North 281 Canton 337 Island 345 Pulo 336 Cantyre 305 CapeHaitien 293 Cape Town 323 Cape Verde Islands 303 Capel Island 307 Caped'Istria 317 Capones Islet 334 Page. Capraia Island 316 Caprera Island 316 Capri Island 317 Capricorn, Cape 353 CarNicobar 330 Carabane 321 Carabao Island 335 Caraques Bay 302 Carataska Lagoon 286 Caravellas 297 Carbon, Cape 321 Carbon era Cape 316 Cardamum Islet 325 Cardenas 293 Cardiff 304 Careys Islands 355 Cargados Carajos 325 Caribana Point 295 Carimare Moimtain 296 Carimata Island 331 Carlingford Lough 307 Carlobago 318 Carloforte 316 Carlos, San £00 Point 290 Carmen Island 285 Caroline Islands, N. Pacific. 343 S. Pacific 345 Carousel Island 280 Carre ta Mountain 301 Point 287 Carreto, Port 287 Carrizal, Port 300 Carta^na, Colombia 295 Spain 315 Cartage Mountain 286 Carteret Cape 313 Harbor 346 Car twright Harbor 279 Carupano 295 Carysf ort Island 349 Reef 284 Cascade Point 355 Casilda 293 Casqueta Rocks 313 Cassmi Island 351 Castilloa 298 Castle Island 292 Castlehaven 306 Castro 300 Urdiales 314 Cat Island 284 Catalina Harbor 279 Sta., Island 289 Catanduanes Islands 335 Catania 317 Catastrophe, Capo 352 Catbalogan 335 Catharine Point 299 St 304 Catherina, Sta. , Island 297 Cato Island 347 Catoche Cape 285 Cattaro 318 Cavite 334 Caxones 286 Cayenne 296 Cayeux 313 Caymans 293 Cazza Island 318 INDEX TO APPENDIX IV. [Page 363 Page. Ceard 296 Cebu Island 335 Cedar Keys 284 Cedeira 314 Ceicer de Mer Islar.d 337 Celebes 333 Centinela Islet 295 Ceram Island 332 Cerros Island 290 Cestos 322 Cette 316 Ceuta 321 Ceylon 329 Chacachacare Island 296 Chacopata 295 Chagos Arch 325 Chagres 287 Chahbar Bay 328 Chala Point 301 ChaleurBay 280 Challenger, Cape 327 Chama Bay 322 Cham-Callao Island 336 Cham6, Point 291 Chamisso Island 287 Champerico 291 Chunaral Bav. 300 Island." 300 Chandeleur Islands 284 Chao Islet 301 Chapel Island 337 Chapu 338 Charles Cape 283 Island, Chile 299 Galapagos Group . 342 Hudson Strait 279 Charleston 283 Charlottetown 280 Chateau Bay 280 Chatham Harbor 282 Island, Galapagos Group 342 S.Pacific 350 ChatteCape 280 Chaume, La 314 Chausey Islands 313 Chedubah Island 329 Chemulpo 339 Chentabun River 336 Chepillo Island 291 Cherbourg 313 Cheribon 331 Cherso 317 Chicarene Point 291 Chidleigh Cape 279 Chifoo 338 Chignecto Cape 281 Chignik Bay 288 Chilca Point 301 ChimbaBay 301 Chimbote 301 Chincha Islands 301 Chinchin Harbor 337 Chinchorro Bank 285 Chin-hai 338 ChinoBay 337 Chirambiri Point 302 Chirikof Island 288 Chiriqui Lagoon 287 Chirivico 293 PLACES — continued. Page. Chitlac Islet 325 Chittagong River 329 Choda Island 339 Choiseul Island 346 Port 326 ChoroB Islands 300 Christiana Islands 319 Christiania 308 Christianshaab 356 Christianso Island 372 Christianssand 308 Christiansund 307 Christmas Cove 299 Harbor 327 I . , Indian Ocean 327 N. Pacific 342 Christopher, St 294 Chuapa River 300 Chuluwan Island 323 Chupat River 298 Churruca, Port 299 Chusan Islands 338 Claris Island...: 201 Cica, Mount 318 Cienfuegos 293 Ciotat 316 Cispata, Port 295 CittaNuova 317 Civita Vecchia 316 Clara, Sta 289 Clare Island 306 Claremont Point 353 Clarence Harbor, Bahamas. 292 Port, Alaska 287 River 352 Clarion Island 291 Claushavn 356 Clear Cape 306 Clearwater Point 280 Clerke Island 349 Clermont Tonnere Island... 349 Cleveland, Cape 353 Clew Bay 306 ClifdenBay 306 Clipperton Island, Mexico. . 291 N.Pacific 344 Clonard, Cape 339 Coast Castle, Cape 322 Cobija 301 CobreBay 301 Cochin 328 Cockell Islet 351 Cockscomb Mountain 286 Coconada 329 Cocos Island, C. America. . . 291 N.Pacific 342 Cod, Cape 282 CoderaCape 295 Codfish Island 355 Codroy Island 280 Coetivy Island 326 Coffin Bay 362 Island, Madagascar 326 Nova Scotia 281 Cofre de Perote Mt 285 Coiba Island 291 Coimbra 315 Colberg 310 Colbert Islet 351 Coles Point 301 Page. Colina Redonda 301 Colnett Bay 290 Colombo 329 Colon 287 Colonia 298 Colonna, Cape, Greece 319 Italy 317 Columbia, Cape 355 Columbretes Islands 315 Coliunbus Island 287 Colville, Cape 354 Comau Inlet 300 Comandatuba 297 Commerson Island 346 Comorin, Cape 328 Comoro Island 326 Concei^-ao 297 Conception Island 292 Point 289 Conde 296 Condor Cove 300 Condore Islands 337 Conducia 323 Conejo, El, Point 290 Coney Island 337 ConfitesCay 292 Congo River 322 Congrehoy Peak 286 Conn^table Islet 296 Constantinople 320 Constitution Cove 301 Contas 296 Conte, Port 316 Contoy Island 285 Conway, Cape 353 Reef 350 Cook Cape 288 Mountain 353 Cooper, Port 355 Copenhagen 312 Copiapo 300 Copper Island 341 Coquet Island 305 Coquille Island 343 Coquimbo 300 Coral Island 297 Islet 297 Corcovado Volcano 300 Cordouan, Point 314 Corfu 319 Coringa Islands 347 Corinto 291 Cork, Ireland 307 Port, Staten Island. . . 298 Cormorant Island 288 Com Islands 286 Comwallis Islands 344 Port 329 Coro, Velade 295 Coromandel Harbor 354 Coronation Island 304 Corregidor Island 334 Corrientes, Cape, Argentina. 298 Colombia 302 Mexico 291 S. Africa 323 Corsarios Bay 295 Corseulles, Port 313 Corso, Cape 316 Mountain 299 Page 364] INDEX TO APPENDIX IV. Page. Corti 316 Corufia 314 Corvo Island 302 Coslin 310 Cosmoledo Island 327 Cotinguiba 296 Cotrone 317 Coubre, Point de la 314 Courtown Cays 286 Coutances 313 Cove Rock 323 Cow Head 280 Coy Inlet 298 Cozumel Island 285 Cracker Bay 298 Crassok Point 331 Crawl Cay 287 Crescent City 289 Cretin, Cape 346 Creux, Cape 315 Cristoval, San, Island 346 Crocker Island 349 Croisic 314 Croix, St 294 Croker, Cape 351 Crooked Island 292 Crozet Islands 327 Cruz Cape 293 Sta., Brazil 297 California 289 Island 289 Islands, Philip- pines 335 S. Pacific... 347 Luzon 334 Port 298 Cuad Basang Island 336 Cuba Culebra 291 Culebrita Island 294 Culion Island 334 Cullera, Cape 315 Culver Point 352 Cumana 295 Cumberland Island 353 Cumshewa Harbor 288 Cupchi Point 337 Cupica Bay 302 Cwcagao Island 295 Little 295 Currimao 334 Currituck Beach 283 Curtis Island 353 Port 353 Curzola Island 318 Cuttyhunk Light 282 Cuvier, Cape 351 Island 354 Cuxhaven 311 Cuyo Island 334 Cyprus 320 Daedalus Shoal 324 Dago Island 310 Dairen Wan 338 Dakar, Port 321 Dalcahue 300 Dale Point 351 Dalrymple Harbor 336 Port 354 PLACES — continued. Page. Dalupiri Island 334 Dame Marie, Cape 294 Damghot 327 Damma Island 332 Danger Islands 348 Dangerous Rock 337 Dannesbrog Island 356 Danube River 320 Dantzig 310 Dapitan 336 Dardanelles 320 Dar el Beida, Cape 321 Dar-es-Salaam 324 Darien Harbor 291 Georgia, U. S 283 Darsserort 311 Darwin, Port 351 Dato Island 331 Datu, Point 330 Dauphin, Fort 326 Davao 335 Davey, Port 354 Davids, St., Island 303 De Freycinet Islets 351 De Kastri 341 De Peysters Island 345 Deadman Rock 280 Deception Island 304 Deimaniyeh 327 Delagoa Bay 323 Delgada Point 299 Delgado, Cape 324 Point 298 Demerara 296 Denia 315 Denis, St 326 Denison, Port 353 D'Entrecasteaux Islands. . . 347 Point 351 D'Urville Island 355 — Point 346 Deseado, Cape 299 Desert, Mt., Rock 281 Desertas 303 Desirade 294 Desire, Port 298 Desolation, Cape 298 DiaFjeld 357 Diamond Harbor 329 —;- Point 330 Diedrichshagen 311 Diego Garcia 325 Ramirez Island 298 San 289 Cape 298 Dieppe 313 Digges Islands 279 Dimas 293 Dimasalasan, Port 334 Dinding Channel 329 Dingle Bay 306 Diomede Island 287 Direction, Cape 353 Island 331 Disappointment, Cape, Sib. 341 — ; Washington. ..... 289 Discovery Harbor 355 Diseilsland 324 DiuHead 328 DixCove 322 Page. Djabon, Point 330 Djambi 330 Djursten 309 Dnieper Bay 320 Doc Can Islet 336 Dodd Island 337 Dog Island 294 Domar, Pulo 331 Demesnes 310 Domingo, San, Point 290 St., Cay 292 Dominica 295 Donaghadee 306 Dondra Head 329 Donegal Bay 306 Double Island 329 Point 353 Peak Island 337 Douglass Rocks 345 Dounpatrick Head 306 Douvres Rocks 313 Dover Point.. 352 Drei Cap Peninsula 346 Drepano, Port 319 Drobak 308 Drogheda 307 Dromedary Mountain 352 Drummond Island 342 Dublin 307 Ducie Island 349 Duff Islands 347 Duke of Clarence Island 345 York I., N.Britain. 346 — S.Pac. 346 DulceGulf 286 River 286 Dulcigno 318 Dumaguete 335 Dumaly Point 334 Dumford Poiat 323 Duncan Island 342 Dundee, Rock of 299 DundrumBay 307 Dungarvan 307 Dungeness 304 New 289 Point 299 Dunkerque 313 Dunnet Head 305 Duperrey Islands 343 Duppel 311 Durazzo 318 Dumford, Port 324 Dussejour, Cape 351 Dwarka 328 Eagle Island 306 Earakong Island 344 East Cape, Madagascar 326 New Zealand 354 Siberia 342 Dog Island 337 Island, Crozet Is 327 Magdalen Is 280 Easter Island 350 Eastport 281 Eau Island 343 Eauripik Islands 343 Ebon Atoll 343 INDEX TO APPENDIX IV. [Page 365 Page. Eckemforde 311 Eclipse Harbor 279 Islands 351 Eddystone 304 Point 354 Eden Harbor 299 Edenshaw Cape 288 Edenton 283 Edinburgh 305 Eeragh Island 306 Egedesmunde 356 Eggegrund Islet 309 Egmont Mountain 354 Port 303 Eimeo Island 349 Ekholra Islet 310 Elba Island 316 Elbing 310 Elena, St., Port 298 Sta., Point 302 Elephant Bay 322 Eleuthera Island 292 Eliaa, St., Mount 288 Elizabeth Bay 322 Cape 282 City 283 Harbor 355 Island, Chile 299 Tuamotu Arch . . . 349 Port 323 Elizabeth Reef 350 Ellice Islands 345 Emden 312 Emu Bay 354 Endnger 309 Endelave Island 312 Enderbury Island 345 Enderby Island 351 Endermo 341 Enfant Perdu Island 296 Engano, Cape 293 Engano, Cape 334 Engano Island 330 Engelholm 308 English Cay 285 Eniwetok Islands 343 Enrag^, Cape 281 Ensenada 290 Entry Island 280 Erromango Island 347 Erronan Island 347 Escarceo Point, Phil. Is... 334 , Venezuela 295 Eschholtz Islands 343 Escondido, Port 293 Escudo de Veragua 287 Escumenac Point 280 Esdu Island 325 Esmeralda Islet 296 River 302 Espada Point, Colombia. . . 295 Espenberg, Cape 287 Esperanza Inlet 288 Espiritu Santo Bay 297 Cape 299 Esc^uimalt 288 Eaemgton, Port 351 Estaca Point 314 Estangues Point 295 Estevan Point 288 Etches, Port 288 PLACES — continued. Page. EtenHead 302 Eu, Pulo 331 Eureka 289 Euripo Strait 319 Europa Island 326 Eustatius, St 294 Evangelistas Island 299 Evaristo, San 290 Expedition Bay 341 Exuma, Great, Island 292 Faero Islands 302 Fair Isle Skroo 305 Fairy, Port 352 Faiu, W., Met 343 Fakaofu Islet 345 Fakarana Island 349 Falkenberg 308 Falkland Islands 304 Falmouth, England 304 Jamaica 293 False, Cape 294 False Cape Horn 298 Point 329 Falster Island 312 Falsterbo 308 Famagusta 320 Famine, Port 299 Fanad Point 306 Fanning Island 342 Fano Island, Adriatic 319 Denmark 312 Farallon Islet 289 Faraulep Island 343 Farewell, Cape, Greenland. 356 New Zealand 355 Farina, Cape 321 Farisan Island 325 Earn Island 305 Faro Island, Sweden 309 of Messina 317 Farquhar Islands 326 FarrallRock 286 Farralon de Pajaros 344 Fartak, Ras 327 Fastnet Rock 306 Father Point 280 Fataizio Island 340 Fatu Hiva Island 345 Huku Island,Galapagos 342 Marquesas . . 345 Fatuna Island 348 Fayal Channel 302 Island 302 Fecamp 313 Felipe, San, Cays 293 Point 290 Felix, St., Island, Chile.... 300 S. Pacific... 350 Fenerive Point 326 Fermin Point 289 Femandina 284 Fernando Noronha 303 Po Island 322 San, Cuba 292 River 285 Port, P. 1 334 Trinidad 296 F^roUe Pena. , New 280 Ferro Island 303 Ferrol 314 Page. Fetouhouhou Island 345 Feys Island 343 Fidonisi Island 320 Figari Cape 316 Filzand Island 310 Finisterre, Cape 314 Firase Rocks 339 Fire Island 283 Firmin, San 290 Fischausen 310 Fish, Great, Bay 322 Little, Bay 322 Fiskemaes 356 Fitz Roy River 351 Fiume 317 Five Fathom Bank 283 Flamborough 305 Flamenco 300 Island 291 Fiat Island 325 Flattery, Cape 289 Flensberg 311 Flesko, Cape 333 Flinders Island 352 Islands 353 River 353 Flint Island 345 Florence 316 Flores Island, Azores 302 Indian Arch 332 Uruguay 298 Florida Island 346 Flower Cove 280 Flushing 313 Fly River 346 Foerder Islet 308 Fogo Island 303 Fohr 311 Foreland, North 304 South 304 Formigaa Islands 302 Shoal 293 Formosa Island 338 Fomaes 312 Forsmark 309 Forsyth Point 288 Forth Mountain 307 Fortune Island 292 Foulwind, Cape 355 Four, Le, Rock 314 Fowey Rocks 284 Fowler Point 352 Frances, Cayo 292 Francis Island 342 St., Cape, C. Colony... 323 ; Newf'drd... 279 Francisco, San 289 Cape 302 Head 301 River 296 Sao 297 Frankland Island 353 Franklin Harbor 352 Franz Josef Land 356 Eraser River 289 FraileRock i 294 Frayles Point 301 Frederick, Port 354 Frederik Hendrik, Cape. . . 354 Frederikshaab 356 Frederiksthal 356 Page 366] INDEX TO APPENDIX IV. Page. Frederiksvaem 308 Fredriksten 308 FreelaCape 279 Frehel, Cape 313 Freikallen 307 Fremantle 351 French Cay 292 Frigate Shoal 344 Freycinet, De, Islets 351 Peninsula 354 Frio, Cape, Brazil 297 W.Africa 322 Port 297 Froward Cape 299 Fruholm 307 Frying Pan Shoals 283 Fuenterrabia 314 Fuerta Ventura Island 303 Fiierte Island 295 Fuga Island 334 Fugle Huk 357 Fuianga Island 348 Fulehuk 308 Funafuti Island 345 Funk Island 279 Funkenhagen 310 Furen Islet 308 Fushiki 340 Futuna Island 347 GaalongBay 337 Gabo Island 352 Gabriel Mountain 306 Gaeta 31G Gafor Island 325 Galapagos Islands 342 Galera Point, Ecuador 302 Trinidad 296 Galgenbeig 311 GaliolaRock 318 Galita Island 321 Gallant, Port 299 Galle, Point de 329 Gallegos River 298 Galley Head 307 Gallinas River 322 Gallipoli, Italy 317 Turkey 320 Galloway, Mull of 305 Galveston 284 Galway 306 Gambler Island 349 Gauge 309 Gannet, Outer, Island 279 Rock 281 Gap Rock 337 Garcia d'Avila 296 Gardiner Island 344 Gardners I., Long Island... 282 S.Pacific 345 Garrafi, Little 330 Caspar, Island and Strait. . 331 Rico Reef 344 Gasparilla Island 284 Gasp6 Cape 280 Gata, Cape, Cyprus 320 de, Spain 315 Gaujam 329 Gay Head 282 Gebey Islands 333 PLACES — continued. Page. Geelong 352 Gefle 309 Genoa 316 George, Fort, Cay 2J2 St., Cape, Florida 234 Newf'dl'd... 280 Nova Scotia. 281 Island, Alaska. . . 287 Azores 302 Georges Island 290 St., Cay 285 Geoi^etown 283 Georgia, South, Island 304 Geronimo, San, Island 290 Geyser Reef 326 Gharib, Ras 324 Ghir, Cape 321 Gibara 292 Gibdo Island 335 Gibraltar 315 Giglio Island 316 Gijon 314 Gilbert Islands 342 Gillolo Island 333 Ginger Cay 292 Giigenti 317 Gizau 325 Gizo Island 346 Glas Island 305 Glasgow 305 Glashedy Island 306 Glenan Islands 314 Glorioso Islands 326 Gloucester Island, Aus 353 TuamotuArch... 349 Massachusetts 282 Glover Reef 285 Gnarp 309 Goa 328 Grobernadora 293 Godhavn 356 Godthaab 356 Goedereede 313 GolamHead 306 Gomenitza 319 Gomera Island 303 Gonaives 294 Gonave Island 294 Good Hope, Cape, Africa... 323 China 337 Island 348 Success Bay 298 Goose Island 352 Gopalpur 329 Coram Islands 332 Gorda Cay 286 Point 331 Gore, Port 355 Goree Island 321 Road 298 Goi^ona Island 302 Goro Island 348 Gorontalo 333 Goto Island 339 Gottenburg 308 Gottland Island 309 Gough Island 303 Cozier Islet 294 Gozo Island 317 Graciaa d Dios, Cape 286 Graciosa Island 302 Grade 317 Grand Manan Island 281 Port 325 Riband Island 316 Grande Point 301 Granitz 311 Granville 313 Crappler, Port 299 Grave, Point de 314 Gravelines 313 Gready Harbor 279 Great Bird Rock 280 Rock Head 286 Green, Cape 352 Island, Labrador 279 Newfoundland... 280 Nova Scotia 281 Greenly Island 280 Greenspond Island 279 Greenwich 304 Island 343 Gregory, Cape 299 Port 351 Grenada 295 Grenville, Cape 353 Grey River 355 Greytown 286 Griefswald 311 Griefswalder Oie 311 Grim, Cape 354 Grimsey Norddranger. 357 Grip 307 GrisNezCape 313 Groate Evlandt 351 Groix, Island de 314 Gross-Horst 310 Grouin du Cou, Point de. . . 314 Gruizza Rock 318 Gryto 307 Guadalcanal Island 346 Guadeloupe, L. California.. 290 West Indies 294 Guafo 1 300 Guaineco Islands 299 Guaira, La 295 Guaja Shima 339 Guam Island 344 Guana, Little, Cay 292 Guanape Islands 301 Guanica 294 Guantanamo 293 Guarapiri Islets 297 Guaratiba, Cape 297 Guardafui, Cape 324 Guascama Point 302 Guatulco, Port 291 Guayaquil 302 Guaymas 290 Guerande 314 Guerin Island 339 Guguan Island 344 Guimaras Island 335 Guiuan 335 Guldager 312 Gull Island, Little 282 Gullan, San, Island 301 Gun Cay 292 Gunong Api Island 332 GutzlaS Island 338 INDEX TO APPENDIX IV. [Page 367 Page. GwadarBay 328 GwatarBay 328 Habana 293 Habibas Island 321 Hacha, Rio de la 295 Haddington, Port 338 Haedic Island 314 Hafun, Rae 324 Hagenmeister Island 287 Hague, Cape la 313 The 313 Haiduong 336 Haifong 336 Haifa 320 Hainan Island 337 Hai-yun-tan Island 338 Hakodate 341 Half Port Bay 299 Halfmoon Cay, Belize 285 Nicaragua 286 Halgan Island 350 HalSax 281 Haliguen, Port 314 Hall Island 343 Islands, Sir James. . . . 339 Halmahera 1 333 Halmstad 308 Hals 312 Halt Bay 299 Halten Island 307 Hamberg 308 Hamburg 311 Hamilton Island 303 Mountain 289 Port 339 Hammamet Bay 321 Hammerfest 307 Hampton 282 Hamrange 309 Hanalei 344 Hanfelah Bay 324 Hangklip, Cape 323 Hanjam Islet 328 Hannibal Isles 353 Hano Island 309 Hanoi 336 Hao Island 349 Haradsskar Islet 309 Haraiki Island 349 HarborGrace 279 Harburg 311 Hardy, Sir C, Island 353 Harpe, La, Island 349 Harrison Cape 279 Hartlepool 305 Harvey, Port 288 Harwich 305 Hatteras Cape 283 Haustholm 312 Haute Island 281 Have, Cape la 281 Havre 313 Hawaii 344 Hayter Island 346 Heard Island 327 Hearts Content 279 HeaudeBrehat 313 Heawandu Island 325 Hecate Bay 288 PLACES — continued. Page. Hecate Cove 288 Hecla.Cape 355 Hed, Kaaal 327 Hee-tah-doo Island 325 Hegadis Island 332 Heili^en Creutz 310 Hekkingen 307 Hela 310 Helena, St., Island 303 Helgoland 311 Hehers, St 307 Hellevoetsluis 313 Helliso 308 Hellyer Rocks 299 Helsmborg 308 Helsingfors 309 Helvick Head 307 Hendaye 314 Hend erson Island 349 Henderville Island 342 Henlopen Cape 283 Henry Cape 283 Port 299 Ileongsan, Port 338 Herald Cays 347 Hereheretue Island 349 Hermes, Cape 323 Hermit Island 346 Hermite Island 298 Herradura de Carrizal 300 Hervey Islets 350 Hesquiat Harbor 288 HesselS Island 312 Hessenstein 311 Hestskjaer 308 Heve, Cape La 313 Hiaou Island 345 Hikueru Island 349 Hillswickness 305 Hilo 344 Himmittee Island 325 Hindwar 328 Hiogo 340 HiradoNoSeto 339 Hirtshala 312 Hiva-Oa Island 345 Hielm Islet 312 Hjertholm 307 Hjoerringa Mountain 307 Hoa-pin-su Island 338 HobartTown 354 Hodeidah Road 325 Hog Island, Indian Ocean. . 327 Virginia 283 Islands 286 Hogland Island 309 Hogolu Islands 343 Hogsty Reef 292 Hogulu Islands 343 HoheWeg 311 Hohenschonberg 311 Hokianga River 355 Hokitika 355 Holbome Islet 353 Hole-in-the-Wall 323 Hollo Island' 308 Holmestrand 308 Holmogadd 309 Holsteinberg 356 Holyhead 304 Page. Hon Dau Island 336 Hondeklip Bay 323 Honfleur 313 Hongkong 337 Hon-M6 336 Honolulu 344 Hood Island 342 Lord, Island. 349 Point, Australia 352 Port, Cape Breton I... 281 Hope Island 353 Hopedale Harbor 279 Hopes Advance, Cape 279 Hoppers Island 342 Horn, Cape 298 False Cape 298 Head 306 Island 284 Home Island 348 Hornelen Mountain 308 Horsens 312 Horten 308 Hospital Bight 286 Hougue, Cape La 313 Houtman Rocks 351 Howaiyuh 327 Howe, Cape, East 352 West 351 Lord, Island 348, 350 Islands 346 Sound 288 Howland Islands 342 Howth Peninsula 307 Huaheine Island 349 Huanchaco Point 301 Huarmey 301 Huasco 300 Hudiksvalls 309 Huelva 315 Iliigeberg 311 Hui-Iang-san 337 Hull Island 360 Hulls Island 345 Ilulu-shan Bay. . .-. 338 Humber River 305 Humboldt 289 Humphrey Island 345 Hungwha Channel 337 Hunter Island, N. Hebrides 347 Tasmania 354 Hurds Island 342 Hurst Castle 304 Husum 311 Hvidingso 308 Iba 334 Ibayat Island 334 Ibbetson Island 343 Ibiza, Port 316 Icacos Point, Belize 286 Trinidad 296 Ichabo Island 322 Icy Cape 287 leraka 319 Ifalik Islands 343 Iglooik Island 355 Ignacio, San, Point 290 Iguape 297 IkiSima 339 Ildefonso Islands 298 Page 368] INDEX TO APPENDIX IV. Page. Ilha Grande 297 Ilheos 297 Ilo 301 Iloilo 335 InaboyeSaki 340 Inaccessible Island 303 I nagua Islands 292 Inch Keith Kocks 305 Indefatigable Island 342 Indian, Cape 342 Harbor 279 Head 353 Tickle 279 Indianola 284 Indio Point 298 Indispensable Keefs 346 Indrapura Point 330 Ingolfshofde 357 IngoMjeld 356 ImshboffiQ 306 Inishowen Head 306 InishrahuU 306 Inishturk Island 306 Iniue Island Innamban Bay 323 Inscription, Cape 351 Investigator Strait 352 Ipswich 282 Iquape 297 Iquique 301 Ireland Island 803 Isaac, Great, Cay 291 Isabel, Cape 299 Island 346 Point 284 Isabella de Sagua 293 Isene 320 Isidro, San, Cape 299 Isla Grande 291 Island Harbor 288 Islay 301 IsleofMan 305 Isola 317 Isolette, Cape 327 Istria, Cape d' 317 Itacolomi Islet 297 Point 296 Itapacaroya Point 297 Itaparica 296 Itapemirim 297 Iturup Island 341 Ivigtuk 356 IwoShima 339 Iwo-sima 339 Jabwat Island 343 Jackson, Port 352 Jacksonville 284 Jacmel 294 Jacobshavn 356 Jaffa, Cape 352 Jago, St., Island 303 Jaguaribe River 296 Jaluit Island 343 Jamaica 293 James Island 342 St., Cape, 0. China.... 336 Vancouver I. 288 Jan Mayen Island 357 JaraHead 301 PLACES — continued. Page. Jarea 315 Jarvis Island 345 Jask Bay 328 Java 331 Head 331 Jean, St., de Luz 314 Jebel Zukur Island 325 Jelaka, Pulo 331 JelaUl 324 Jensen Nunatak 356 Jeremie 294 Jershoft 310 Jervis Bay 352 Cape 352 Island 342 Jesus Maria Island 346 Jiddah 324 Jighinsk Island 356 Johanna Island 326 John, St., Cape, Newf'dl'd. 279 Staten Island 298 Island 294 Johns, St., Island, Red Sea. 324 New Brunswick. . 281 Newfoundland... 279 River 284 Johnston Islands 344 Jolo Islands 336 Jomfruland 308 Jona, St., Island 341 Jos6, San, California 289 de Guatemala 291 delCabo 290 Port 298 Joseph Henry, Cape 355 Juan Fernandez Island 350 San 294 Cape 294 delSur 291 Point 285 Port, Peru 301 Vancouver I. 288 St., Bay 295 Juanico, San, Point 290 Juby, Cape 321 Jucaro 293 Judith Point 282 Juggemath 329 Juist 312 Julian, San, Port 298 St., Island 331 Julianshaab 356 Juneau 288 Jupiter Inlet t 284 Jura Island 319 Juul, Cape 356 Kabenda Bay 322 ICabuli Island 334 ICadoSima 341 Kagoshima ^ 340 Kaiioolawe Island 344 Kahrig Islet 328 Kaipara Harbor 355 Kais Islet 328 KaiartaUk Island 356 Kaldrouma 339 Kal Farun Islet 324 Kalboden Island 309 KaHbia 321 Page. Kalingapatam 329 Kallundborg 312 Kalpeni Islet 325 ICama Islands 343 Kamaishi 340 Kamardn Bay 325 Kambangan Island 331 Kambara Island 348 Kamchatka, Cape 341 Kanala, Port 350 Kanathea Island 348 Kandavu 347 KandeUusa Island 319 Kangamint 356 Kangarssuk Ha vn 356 Kannanur 328 Kao Island 350 Kappeln , 311 Kara Bumu, Cape 320 Karachi 328 Karafuto 341 Karajinski Island 341 Karimon Djawa Island 332 Karlshamn 309 Karlskrona 309 Kaske 309 Kasm 328 KatakoloBay 319 Kater Island 345 Katiagam 330 Katie Rock 318 Kauai Island 344 Kawhia Harbor 354 Keats, Port 351 Kee-lah Island 325 Keeling Islands 327 Keenapoussan Island 336 Keitum 311 Kelantan River 336 Kendall, Cape 355 Kent Island 352 Keppel Island 348 Kermadec Islands 350 Kertch 320 Ketoy Island 341 Key West 284 Kharig Islet 328 Kharim-Kotan Island 341 Kheli t319 Khor Nohud 324 Nowarat 324 Fakan Bay 327 Ki Islands 332 Kiaochow Bay 338 Kiama Harbor 352 IGdnappers Cape 354 Kiefali, Cape 318 Kiel 311 Kiirun Ko .• 338 Kikai-jima 339 Kiliman 323 KillineyHUl 307 Killybegs 306 Kilwa Kisiwani 323 Kimbeedso Island 325 King George Sound 351 Island, Australia 352 Kings Island 349 Kingston 293 Kingstown 307 Kinkwosan Island 340 INDEX TO APPENDIX IV. [Page 369 Page. Kinnstind 308 Kino Point 290 Kinsale 307 Kirkwall 305 KisimayuBay 324 Kiska Island 287 Kietna 329 Kiflwere 324 Kittan Islet 325 Kjorge 312 Knocklane 306 Knockmealdown Mountain. 307 Kjiocknarea 306 Knox Bay 288 Cape 288 Knysna 323 Kobe 340 Kodiak Island 288 Koh Chang 336 Kong River 336 Krah Islet 336 Tang Rocks 336 Kokoun-tan Islands 339 Koksher 310 Kolding 312 Komba Island... 332 Kompaa Mountain 308 Kongelab Islands 343 Konigsbere 310 Koniushi tslajad 287 Koppem 307 Koroni Anchorage 319 Korror Islands 344 Koa 320 Koeair, Arabia 327 Red Sea 324 Koeime No Osima 339 Koster 308 Kottaringin Bay 333 Kovra Ry thi Point 326 Kozu Shima Mountain 340 Krakatoa Island 331 Krishna Shoal 329 Kroe 330 Kronberg 312 Kronstadt 310 Kxusenstem Cape 287 Kub Kalat 328 Kuchino Shima 339 Kuchinotsu 339 Kuino 310 Kullen Point 308 Kumi Island 338 Kumpta 328 Kunashir Island 341 Kundapur 328 Kunfidah 324 Kuper Harbor 339 Port 288 Kiuia Maria Islands 327 KuroSima 339 Kusakaki Jima 339 Kusrovie Rock 336 Kusterjeh 320 Kutpur 328 Kuweit 327 Kweshan Islands 338 Kyangle Islets 344 Kyuquot Sound 288 PLACES — continued. Pago. Labuan Island 333 Labyrinth Head 298 LaCaloma 293 Laccadive Islands 325 Lacepede Island 351 Lady Elliot Island 353 Frances, Port 326 Lagartos 285 Laghi, Cape 318 Lagoon Head 290 Lagos 315 River 322 Lagosta Island 318 Lagostini Island 318 Laiemba Island 348 Lamaka 320 Lambayeque 302 Lambert, Cape 351 LamoBay 324 Lamock Island 337 Lampedusa Island 317 Lampong Bay 330 Lamyit Island 337 Landfall Island 299 Lands End 304 Landskrona 308 Landsort 309 Langanaes Point 357 Langeland Island 312 Langeoog 312 Langesund 308 Langford, Port 288 Langkuas Island 331 Langotangen 308 Langwarden 311 Lanzarote Island 303 LaPaz 290 La Plata 298 Laruehuapi Cove 300 Lassa, Cape 333 Laesau 311 Latakia 320 Latouche Tr^ville, Cape — 351 Laun 279 Laurie Island 304 Laut, Pulo 333 Lavaca 284 Lavata 301 Lawrence, St., Island, Alaska 287 Siberia 342 Laykan, Port 333 Laysan Island 344 Lazaref, Port 339 Lazaro, San, Cape 290 Leander Shoal 280 Leba 310 Lebu River 300 Leeuwin, Cape 351 Legendre Island 351 Leghorn 316 Lema Island 337 Lemnos Island 319 Lengua de Vaca Point 300 Lennox Cove 298 Leones Island 298 Leopold, Port 355 Lepar, Pulo 331 Le Pilier Island 314 Page. Lepreau Cape 281 Lerma 285 Lerwick 305 Leschenault, Cape 351 Lesina Island 318 L'Etang Harbor 281 Leven Island 326 Port 326 River 354 L'Evdque, Cape 351 Lewis, St., Cape 279 Leyden 312 Leyte Island 335 LhouReef 347 Liakhov Islands 356 Liancourt Rocks 339 Liant, Cape 336 Liao-ti-shan 338 Libau 310 Libertad, C. America 291 Mexico 290 Lifu Island 350 Lighthouse Rocks 288 Limerick 306 Limon, Port 286 Lincoln Island 337 Port 352 Lindesnes 308 Lindi River 324 Lindo, Port 320 Linga Island 330 Linguelta, Cape 318 Linosa Island 317 Lipari Island 317 Lisbon 315 Lisbume Cape 287 Lisiansky Island 344 Lissa Island 318 List 311 Lister 308 Lith 324 Litkieh Island 343 Little Hope Island 281 Lituya Bay 288 Liverpool 305 Port 326 River 351 Livomo 316 Lizard Point 304 LUco 300 Loa River 301 Loaf Island 346 Loango Bay 322 Lobito Point 322 Lobos Cay, Bahamas 292 Mexico 285 de Afuera Island 302 Tierra 302 Island, Canaries 303 Uruguay 298 Point, N. Chile 301 S.Chile 301 Lodingen 307 Lofoten Island 307 Loggerhead Key 284 Loheiyah 325 ^ Loma Point 289 Lomaa Point 301 Lombata Island 332 21594°— 14- -24 Page 370] INDEX TO APPENDIX IV. Lombok Island 332 London, East 323 Londonderry 306 Cape 351 Long Island, Bahamas 292 United States 282 Look6, Port 326 Lookout Cape, N . CaroHna. . 283 Point, Australia 353 Maryland 283 Lopatka, Cape 341 Lopez, Cape 322 Lorenzo, San, Cape 302 Island 301 Loreto 290 Lorient 314 Loro, Mount 334 Lorstakken Mountain 308 Los, Isles do 321 Lota 300 Lots Wife Rock 340 Lough Larne 306 Louis, Port, Falkland Is 304 Guadeloupe 294 Mauritius Island . 325 St 321 Louisburg 281 Louisiade Archipelago 347 Loune 312 Low Island 337 Port 300 Lowenom, Cape 356 Lowestoft 305 Loyalty Islands 350 Lubang Island 334 Lucar, San 315 Lucas, San 290 Lucia, Santa 326 St 293 Cape 323 I., C. Verde Is. . . 303 Windward Is. 295 Lucipara Island 332 Lucipari Islands 331 Lucrecia Point 292 Lucrietta Island 318 Ltiis, San, Island 290 Luk6 Point 341 Lund 308 Lundy Island 304 Lunenburg 281 Lungo 309 Lupona Point 290 LurioBay 323 Lussin Piccolo 318 Luzon Island 334 Lyo Island 312 Maasin 335 Macah6 297 Macao 337 MacAskill Islands 343 Macauley Island 350 Maceio 296 Machias 281 — Island 281 Machikora 326 Mackenzie Islands 343 MacLeay Islets 351 Macquarie Harbor 354 Island 350 PLACES — continued . Page. Macquarie, Port 352 Macquereau Point 280 Madagascar 323 Eeef , Africa 323 ■ • Yucatan 285 Madame Island 281 Madanas Point 298 Madeira Island 303 Madras 329 Madryn, Port 298 Madura Island 331 Maestro de Campo Island. . 335 Mafamale Island 323 Mafialsland 324 Magadoxa 324 Magdalen Cape 280 Islands 280 Magdalena Bay 290 River 295 Magnetic Pole 355 Magoari Cape 296 Mah Kundu Island 325 Mahanuru 326 Mah6 328 Mahia Peninsula 354 Mahon, Port 316 Maiana Island 342 MaidenRocks 306 Mairaira Point 334 Mdit Island 324 Maitea Island 349 Maitencillo Cove 300 Majamba Bay 326 Majorca 316 Majunga 326 Maiiu"o Islands 343 MakallehBay 327 Makarska 318 Makassar 333 Makatea Island 349 Makaua Island 324 Makemo Island 349 Makers Ledge, South 280 Makkian Island (Makjan I.). 333 Makongai Island 348 Makry 320 Mala Cape 291 MalabrigoBay 301 Malaga 315 Malaita Island 346 Malakka 330 Malamocco 317 Malaspina, Port 298 Maiden Island 345 Maldonado, Mexico 291 Uruguay 298 Mal6 Island 325 Malemba Bay 322 MalinHead 306 Mallicollo Island 347 Malmo 308 Malo, St 313 Maloclab Islands 343 Maloren 309 Malpelo Island, Galapagos.. 342 Panama 291 Malpeque Bay 280 Malta 317 Mamuka Island 348 Manaar 329 Mana Sima 340 Page. Manado Bay 333 Manao 340 Mana-watu River 354 Manda Roads 324 Mandarins Cap 337 Mandavi 328 Manfredonia,. 317 Mangaia Island 350 Mangalore 328 Mangaratiba 297 Mangareva Island 349 Mangarin Point 334 Mangarol 328 Mangles Point 302 Mango Island 348 Manila 334 Mano Island, Asia 332 — Denmark 312 Manoel, Cape 321 Manroux 1 294 Manta Bay 302 Manua Island 348 Manukau Harbor 355 Manvers, Port 279 Manzanillo, Cuba 293 Manzanillo Bay, Mexico 291 ■ Point, Haiti 293 Maracaibo 295 Maraki Island 342 Marambaya Island 297 Maranliiio Island 296 Marble Island 355 Marblehead 282 Marcial, San, Point 290 Marcos, San, Island 290 Marcus Island 344 Mare Harbor 304 • Island, CaUfomia 289 —S.Pacific 350 Maret Islets 351 Margaret Bay 281 Margate Head 322 Maria Island 349 Madre Island 291 Port 293 ■ Sta., Cape, Portugal.. . 315 — Uruguay... 298 Cove 290 di Leuca, Cape. . - 317 Island, Azores 302 Chile 300 S. Pacific... 347 ■ Port 335 Marianas 344 Maricas Islands 297 Marie Galante 294 Marienleuchte 311 Mariguana Island 292 Marinduque Island 335 Marion Island 327 Maripipi Island 335 Maritimo Island 317 Marjes Islets 295 Marjoribanks 339 Mark8,St 284 Marlborough Island 342 Mai-mora Island 320 Marmorice 320 MaroReef 344 Maroni River 296 INDEX TO APPENDIX IV. [Page 371 Page. Marsala 317 Marseilles 316 Marshall 322 Islands 343 Marstenen Islet 308 Marta.Sta 295 Martha, St., Cape 297 Martin de la Arena, San .... 314 Garcia Island 298 San, Island, L. Cal. . . . 290 St., I., Leeward Is 294 Vaz Rocks 303 Martinique 294 Martires, Los 343 Mama Island 349 Marutea Island 349 Mary Island 345 St., Bay 322 Cape, Madagascar. 326 Newfound- land.... 279 Nova Scotia. 281 Reefs 280 Marys, St., Island 326 Marzo Cape 302 Mas Afuera Island 350 Masbate Island 335 Mafiinloc 334 Masirah Island 327 Maskat 327 Massaua Harbor 324 Masset Harbor 288 Masulipatam 329 Matabella Islands 332 Matacong Island 321 Matagorda 284 Matahiva Island 349 Matamoras Cove 300 Matana Island 341 Matanzas Peak 293 Matatane 326 Matelotas Islands 343 Matema Islands 347 Maternillos Point 292 Matinicus Rock 281 Matova 340 Matthew Island 347 ■ St., Island, Alaska ... 287 Burma 329 Siberia 342 Matthias, St., Island 346 Matu Sima 339 Matuku Island 348 Mauger Cay 285 Maui Island 344 Mauki Island 350 Maun^auui Harbor 354 Maupili Island 349 Mauritius 325 May, Cape 283 Island 305 Mayaguez 294 May6 Mountain 296 Mayne Harbor 299 Mountain 300 Mayo Island 303 Mayotta Island 326 Maysi Cape 292 Mayumba Bay 322 Mazarron 315 PLACES — continued . Page. Mazatlan 291 Mazemba River 323 Mbega Island 348 MchingaBay 324 McKean Island 345 Mecate Mountain 285 Mednoi Island 341 Mega Island 330 Megalo Kaatron 319 Mehediah 321 Meiaco Sima 338 Meiaco-sima Islands 339 Mejia Island 290 Mekattina Islands 280 Mel, Ilhado 297 Melbourne 352 Meleda Island 318 Melinda 324 Melle, Cape 316 MellishReef 347 Melmore Head 306 Melo, Port 298 Melville, Cape, BalAbac I.. 333 Queensland 353 Island, Australia 351 Barrows Strait. . . 355 Tuamotu Arch... 349 Memel 310 Memory Rock 292 Menali Island 330 Menchikof Cape 287 Mendocino Cape 289 Mendoza Island 337 Merbat 327 Mercy Harbor 299 Mergui 329 Mesa de Dofia Maria 301 Messina 317 Meeurado, Cape 322 Meurka 323 Mew Islands 306 Mewstone Rock 354 Mexican Boundary 289 Mexico, City of 285 MexillonBay 301 Mexillones Mountain 301 Mezen 356 Miautao Island 338 Michael, St., Fort 287 Island 302 Michaeloff Island 348 Middleton Island 288 Midway Islands 344 Miguel, San, Island 289 — ^ Islands 336 Mikake Jima 340 Mikindini 324 Mikomoto Island 340 Mikura Jima 340 Milagro Cove 300 Milazzo 317 Mile Island 355 Milford Sound 355 Milo Island 319 Min River 337 MinaBay, El 322 Minchinmadiva Mountain . . 300 Mindanao Island 335 Mindoro Island 334 Mine Head 307 Page. Minerva Reefs 350 Minikoi Island 325 Mine Sima 341 Minorca 316 Minots Ledge 282 Minow 326 MinsenerSand 311 Mintok 331 Miramichi Bay 280 Misamis 336 Miscou Island 280 Mississippi River, mouth. . . 284 City 284 Misteriosa Bank 286 Mita Point 291 Mitchells Island 345 Mitho 336 Mitiero Island 350 Mitre Island 347 Mityleni Island 319 MizenHill 306 MoaCayo, Port 292 Island 332 Moala Island 348 Mobile 284 Mocha Island 300 Mocomoco Point 296 Modeste Island 339 Moeara Kompehi 330 Moen Island 312 Moerenhout Island 349 Mogador 321 Mohilla Island 326 Moianga Mokambo, Port 823 Mokatein 327 Mokha 325 Mokil Islands 343 MoUe, Port 353 Mollendo, Port 301 MollerPort 287 Molloy 327 Molokai Islands 344 Molonta PeninsiUa 318 Moluk Island 325 Molukka Islands 333 Molyneux Bay 355 Sound 299 Mombasa 324 Mona Island 294 Monastir 321 Mondego, Cape 315 Monfalcone 317 Monhegan Island 281 Monomoy Point 282 Monrovia 322 Montagu Island 352 Montalivet Islands 351 Montauk Point 282 Monte Christo Islet 316 Monte Cristi 293 Montebello Island 351 Montego Bay 293 Montepio 285 Monterey 289 Monteverde Islands 343 Montevideo 298 Montravel Island 339 Montreal 280 Monts, Point de 280 Page 372] INDEX TO APPETNDIX IV. Montserrat 249 Montt, Port 300 Monze, Cape 328 Mopelia Island 348 Morane Island 349 MorantCaya 293 Point 293 Morayva 315 Morecambe Bay 305 Moreno Mountain 301 Moresby, Port 346 Moreton, Cape 353 Morgan, Cape 323 Morjovetz Island 356 Morlaix 313 Morotirilslands 350 Morria Jesup, Cape 356 Morro Ayuca 291 de Sao Paulo 296 'Petatlan 291 Solar 301 Mortlock Islands 343 Mosquito Cays 286 Mota, Point 293 Motane Island 345 Mothe Island 348 Mothoni 319 Motu-ili Island 345 Motu-iti Island 349 MoudroB 319 Moukon ruflhi Island 341 Moulmein 329 River 329 Mount, Cape 322 Mourondava 326 Moville 306 Mozambique 323 Msimbati 324 Mugan Mwania 324 Mugeres Island 285 Mmlcalpue Cove 300 Mukulaelae Island 345 Muleje 290 Mulu Island 332 Mura Harbor 340 MuratHill 324 Murderers Bay 326 Murdock Point 353 Murundum Island 337 Mururoa Island 349 Muscat 327 Musendum, Ras 327 Mussel Bay 299 Mysole Island 332 NachvackBay 279 Nafa-Kiang 339 Nagai Island 287 Nagasaki 339 Naian Island 348 Nain 279 Nairn Cay 292 Naitamba Island 348 NakanoShima 339 Nakkehooed 312 Nam-Dinh 336 Namki, Port 338 Namoluk Islands 343 Namonuito Islands 343 Nam-quan 337 PLACES — continued. Page. Namu Island 343 Nanaimo 288 Nancowry Harbor 330 Nanka Island 331 Nanomea Island 345 Nanoose Harbor 288 Nansei Shoto 339 Nantes 314 Nantucket Island 282 Shoals 282 Naples 317 Napuka Island 349 Nar Foree Island 325 Naranjo, Port 292 Narendri Bay 326 Nargen Island 310 Narva 310 Nasca Point 301 Nasparti Inlet 288 Nassau 292 Natal, Brazil 296 ^ Port, Africa 323 -Sumatra 330 Natashquan Point 280 Natuna Islands 331, 337 Naturaliflte, Cape 351 Nauomaga Island 345 Navachista 291 Navalo, Port 314 Navarin 319 Cape 341 Navassa Island 294 Navesink Highlands 283 Na\idadBank 292 Bay 291 NavireBay 327 Naxos Island 319 Nazaire, St., Port 314 Necker Island 344 Needles Rocks 304 N^apatam 329 Negrais, Cape 329 Negro, Rio 298 Negros Island 335 Neill, Port 355 Nelson 355 Cape 352 Port 351 Nemuro 341 Neptune Isles 352 Nera Point 317 Netherland Island 345 Neunortalik 356 Neuwerk 311 Nevil Island 344 Neville, Port 288 Nevis 294 New Bank 285 Bedford 282 Britain 346 Caledonia 350 Guinea 346 Hanover 346 Haven 282 Hebrides 347 Ireland 346 London 282 Mecklenburg 346 Orleans 284 Plymouth 354 Page. NewPommem 346 South Orkneys 304 Shetland 304 Westminster 289 York 283 Newbem 283 Newburyport 282 Newcastle 352 Newchwang 338 Newfoxindland 279 Newport, Ireland 306 Rhode Island 282 Newton Head, Great 307 Nezumi Jima 339 Ngatik Islands 343 Ngau Island 348 Nias Island 330 Nice 316 Nicholas, St., Island 303 Nicholson, Port 354 Nickerie River 296 Nicobar, Great, Island 330 Islands 330 San, Island 289 Nidingen Islet 308 Nieuport 313 NieweDiep 313 Nihiru Island 349 Niigata 340 Nikalao, St., Island 319 Nikolaevsk 341 Nikolaia, St., Cape 341 Nikolaieff 320 Nikolo, St., Port 319 Nila Island 332 Nile River 320 Nimrod Sound 338 Nine-pin Rock 337 Ning-po 338 NipeBay 292 Niquero 293 Nitendi Island 347 Niua-fu 348 Nine Island 348 Niutao Island 345 No Sima Saki 340 Noir Island....^ 299 Noir Moutier Island 314 NoUoth, Port 323 Nome Cape 287 Nonuti Island 342 Nootka Sound 288 Nord Koster Islands 308 Nordemey 312 Norfolk 283 Island 350 Norman Cape 280 Norrkopings Inlopp 309 Norrsher Islet 309 Norrtelge 309 North Cape, Arctic Amer. . 355 Brazil 296 C. Breton 1 281 Iceland 357 New Zealand 354 Norway 307 Harbor 288 Island, Vancouver 288 Volcano Islands. . 345 Lord, Island 344 INDEX TO APPENDIX IV. [Page 373 Page. North Standing Creek 286 Northumberland, Cape 352 Isles 353 Northwest Cape 351 Norwalk Island 283 Noshiaf Misaki 341 Saki 341 NosiB^ 326 NossaSenhoradoDeserto... 297 Notch Cape 299 Notsuke 341 Nottingham Island 279 Noumea 350 Noun, Cape 321 Nouvelle, Port 316 Nova Zembla 356 Novogorod, Port 341 Nuevitas, Port 292 Nuevo, Port 291 Nugget Point 355 Nui Island 345 Nuistad 309 Nuka-Hivi 345 Nukufetau Island 345 Nukunau Island 342 Nuku-nono 345 Nukuor Islands 343 Nukutavake Island 349 Nukutipipi Island 349 Numbalsland 323 Nunez River 321 Nunivak Island 287 Nurse Channel Cay 292 Nuyte Point 351 Ny Sukkertop 356 Nybotg 312 Nykjobing 312 Oahu 344 Oatafu Island 345 Oban 305 Obi Islands 336 Obi Major Island 332 Obispo Shoal 285 Obristadbroekke 308 Observation Island 339 Occasional Harbor 279 Ocean Island, N. Pacific. . . 344 S.Pacific 346 Ockseu Island 337 Ocracoke 283 Oddensby 312 Odenskholm 310 Odessa 320 Odia Islands 343 Oeno Island 349 Offer Wadham 279 Ogasawara Islands 345 Oho-sima 339 Okayama, Port 340 Okhotsk 341 Oki Islands 341 OkishiBay 341 Okso 308 Oland Island 308 Old Fort Island 280 Point Comfort 283 ProvicTonce 286 Olcai Islands 343 Oleron Island 314 I'LACES — continued . Page. Olga, Port 341 Olimarao Islet 343 Olinda 296 OlipaRock 318 Oliutorski, Cape 341 Olivenja 297 Omapui Island 336 Omenak Island 356 Omo Island 312 Omoa 286 OmoiSaki 340 One Fathom Bank 329 Oneata Island 348 Onega 356 Ongea Levu Island 348 One Islands 348 Onoatoa Islands 342 06-Sima Harbor 340 Oparo Island 350 Opobo River 322 Oporto 314 Oraluk Island 343 Oran 321 Orange Cape, Brazil 296 Magellan Strait. . 299 Oranienbaum 310 Orchila Island 295 Oregrund 309 Orfordness 306 Orizaba Mountain 286 Orkney Islands 306 Ormarah 328 Ormoc 336 Ombay Island 332 Ore No Sima 339 OropesaCape 316 OrskarRock 309 Oruba Island 295 Osaka..... 340 OsakiBay 340 Oscarsberg 308 Osnabrug 349 Oetend 313 Osthammar 309 Ostro Point 318 Otago Harbor 365 Otranto, Cape and Port 317 Ottawa 280 Otway, Cape 352 Port 299 Oune-Kotan Island 341 Ouro River 321 Ovalau Island 347 Owaahi Bay 340 Oxford 304 Oxhoft 310 Paanopa Island 346 Pabellon de Pica 301 Pacasmayo 301 Padang 330 Tikar 333 Padaran, Cape 336 Padre, Port 292 Pagan Island 344 Pa^nia, Port 319 Paimboeuf 314 Paix, Port 294 Pajaros Islets 300 Pak Chan River 329 Pago. Pakhoi 337 Pakonjidol Rock 318 PalamosBay 315 Palanog 335 Paldwan Island 333 Palembang 330 Palenita 291 Palermo 317 Port 318 Pali, Cape 318 Pallaa Rocks 339 Palliser, Cape 354 Palm Islands 353 Palma Island 303 PalmasBay 297 Cape 322 Point 285 Palmerston, Cape 353 Islands 348 Palmyra Island 342 Palompon 335 PalosBay 333 Pamaroong Island 333 Pamban Pass 328 Pampatar Island 296 Pan de Azucar Island 300 Panama -. 291 Panay Island , 336, Pangituran 336 Paniang Island 336 PankPiahRock 337, Pantar Island 332 Papey Island 367 Paposo Road 301 Para 296 ParacaBay 301 Paracel Islands '337 ParahibaRiver and Port... 296 Paramaribo..... 296 Paranagua 297 Paranahiba River 296 Paraoa Island 349 Parati .Tr. 297 Paredon Grande Cay 292 Parenga-renga 354 Parenzo 317 Parga 319 Panda T. 291 Parinas Point 302 Paris 313 Parker Cape 299 Pares Island 319 Parry Island 360 Parrys Group 345 PasadoCape 302 Pasages, Port 314 Pascagoula, East 284 Pasni 328 Passaro, Cape 317 Pasuruao 331 Patache Point 301 Patani, Tanjong 336 Paternoster Rocks 308 Paterson Inlet 355 Pato Island 296 PatucaRiver 286 Patoslsland 290 Patras 319 Patrick, St., Head 354 Patterson, Port 351 Page 374] INDEX TO APPENDIX IV. Paul, St., de Loando 322 Island, N. Amer. 281 Tuamotu.... 349 K^union Island.. 326 Rocks 303 Paula, St., Island 327 Paxo Island 319 Paypoton Mountain 285 Pearce Point 351 Pearl and Hermes Beef. . . . 344 Cays 286 Pedra Blanca Rock 337 •Branca 330 deGalha 321 Pedro Bank 293 San 290 Point 301 ZZ^ort 300 Peel. .1?:^.r. 351 ■Island.- 345 Pegasus, Port, .t: 355 PeiHo..'.rrr...::. 338 Pekalongan. 331 IPelado Island 301 rPelagosaRock 318 j Peloro, Cape 317 [PembaBay..: 323 I Pembroke Cape 304 i Pena Point 296 jPenang, Pulo 329 j Pefias Anchorage 291 j Pendulum Islands 356 Penguin Islands 327 iPenha Grande 321 IPeniche 315 Penmarch Rocks 314 iPenrhyn Island 345 Pensacola 284 Pentland Skerries 305 Percy Isles 353 Perim Island, Africa 324 ■ India 328 Pernambuco 296 Pemau 310 Peroa Banhoa Islands 325 Perth 351 Peru Island 342 PerulaBay 291 Pescadores Islands, Asia, E. coast 338 ^N. Pacific 343 Peru 301 Point 301 Pe-shan Islands 338 Petali Island 319 Petalidi Bay 319 Peter St., Port 313 Peterhof 310 Petersburg, St 310 Petersdorf 311 Petit Manan Island 281 Petite Terre 294 Petropavlovsk 341 Petropolis 297 Pha-li-du Island 325 Philadelphia 283 Philip Island 343 Philipp Broke, Cape 356 Philips Point 290 Phmlp, Port 352 PLACES — continued . Page. Phillii>8 Island 349 Phoenix Island 345 H 316 Pianosa Island 316 Pichidanqui 300 Pichilinque Bay 290 Pico Island 302 Pictou Harbor 281 PiedraBlanca 336 Piedraa Blancas 289 Cay, Cuba, N. coast. . . 293 • S. coast 293 Point 298 Pieman River 354 Pierre, St., Newf'dl'd 280 Reunion 1 326 • Rock 331 Pietro di Nembo, St., Island 318 Pigeon Point 289 Pih-ki-shan Island 338 Pih-quan Peak 338 Pih-seang Island 337 Pikelot Island 343 Pililu Island 344 Pillau 310 Pillar, Cape, Chile 299 Tasmania 354 Pinaki Island 349 Pine, Cape 279 Pingelasp Islands 343 Ping-fonglsland 337 Ping-hai Harbor 339 Pinnacle Islet 287 Pinos, Isla de 293 Pinos Point 289 Pique Bay 341 Piraeus 319 Pirano 317 Pisagua 301 Pisang 330 Pisco 301 Pitcairn Island 349 Pitea 309 Pitong Island 330 Pitre Point 294 Placentia Harbor 279 Point 286 Pladda Island 305 Plana Cay 292 PlanierRock 316 Plata, Isle 302 Platte Island 325 Playa Colorado 291 Maria, La 290 ■PardaCove 299 Pleasant Island 346 Plettenburg Bay 323 Plum Island 282 Plymouth, England 304 U.S 282 Poile,La, Bay 280 Pola 317 Sta., Bay 315 Polillo Island 335 Pollard Cove 299 Police 335 Polusuk Island 343 PomoRock 318 Ponafidin Island 340 Ponapi Island 343 Page. Pond Mountain 299 Pondicherri 329 Ponga River 321 Ponza Islet 317 Poolbeg 307 Popalsland 332 Popof Island 287 Porcos Grande Islet 297 Porbandar 328 Porman 315 Poro musir Island 341 Poros Island 319 Portau Prince 294 Montt 300 of Spain 296 Plata 293 Royal, Jamaica 293 S. Carolina 283 Said 320 Portendik 321 Porthcumow 304 Portland, Bay 352 Cape 354 England 304 Maine 282 Porto Bello 287 R^ 317 Rico 294 Santo 303 Seguro 297 Vecchio 316 Portsmouth, England 304 U.S 282 Possession, Cape 299 Island 327 Postilion Islands 332 Povorotnyi, Cape 341 Prado 297 Prataa Island 337 Premeira Islands 323 Preservation Inlet 355 Prestenizza Point 31 7 Prevesa 319 Pribilof Islands 287 Prince Edward Island 280 Edwards Islands 327 Prince of Wales Cape 287 Island 353 Sound 279 Regent River 351 Rupert Hbr 288 Princes Island 322 Proeste 312 Progreso 285 Promontore Point 317 Proti Passage 319 Proven 356 Providence 282 Island 343 Port 342 Psara Island 319 Pucio Point 335 Puerto Cabello 295 Mexico 285 Santo Bay 295 Puka-puka Island 349 Puka-ruha Island 349 Pulicat 329 Pulkowa 310 Pulpito Point 290 INDEX TO APPENDIX IV. [Page 376 t Page. Puna 302 Purdy Island 346 Putziger Heistemest 310 Pyramid Point 337 Pyramidal Rocks 331 Quaco, Cape 281 Quaebo River 322 Quebec 280 Queen Charlotte Island 349 Queenstown, Ireland 307 N.Zealand 355 Quelpart Island 339 Quemada Grande Island . . . 297 Quentin, San, Port 290 Querimba Islands 323 QueuleBay 300 Quilan, Cape 300 Quilca 301 Quilon 328 QuinHon 336 Quiniluban Islet 334 Quintero Point 300 Quita Sueiio Bank 286 Quod, Cape 299 QuoddyHead 281 Quoin Great, Island 327 Point 323 Race, Cape 279 Island 288 Rachado, Cape 330 Radakala Islands 343 Radama Islands 326 Port 326 Ragged Island 292 Ragiisa Rocks, Pettini di. . . 318 Rakkin, Ras 327 Raleigh Rock, China 337 Formosa 338 Ramas, Cape 328 RameHead 323 Ramree Island 329 Rangiroa Island 349 Rangoon 329 River 329 RaiiuCove 300 Raoul Island Rapa Island 350 Raper Cape 299 Raphti, Port 319 Rarotonga Island 350 Rasa Island 345 Rathlin Island 306 O'Bime Island 306 Ratnagherry 328 Ravahere Island 349 Ravn Store 356 Rawean Island 332 Ray Cape 280 Raza Island, Brazil 297 C. Verde la 303 L. California 290 Razzoli Island 316 Re Island 314 Real River 296 Reao Island 349 Recherche Archipelago 352 Recife Cape 323 Red Islet 351 FLACES — continued. Page. Redang, Great, Harbor 336 Redfield Rocks 340 Redonda Islet 294 Redondo Rock 342 Reirson Island 345 Reitoru 349 Rembang 331 Remedies Bay 290 Renard Island 347 Islands 347 Rennel Island 346 Rensher 309 Repon, Pulo 331 Resolution Island 279 Reunion Island 326 Revel 310 Rey Island 291 ReyesHead 301 Point 289 Reykianaes 357 Reykiavik 357 ReythurFjeld 357 Rhio 330 Rhodes, Port 320 Rhynns of Islay 305 Ribnitz 311 Rich Point 280 Richmond 283 River 353 Riga 310 Rigny Mount 356 Rimitara Island 350 Ringkjobin 312 Rio Grande del Norte 284 do Norte 296 Sul 297 Janeiro 297 Riofrio, Port 299 Risiri Islet 341 Rissnaes Point 357 Rivadeo 314 Rivadesella 314 Rivers, Cape 333 Rixhoft 310 Roa Poua Island 345 Roatan 286 Roberts Point 289 Roca, Cape 315 Partida, Mexico, E. coast 285 W. coast 291 Rocas Reef 303 Rochefort 314 Rochelle 314 Rockabill 307 Rockall Islet 302 Rockingham Bay 353 Rockland 281 Rodd Bay. . .- 353 Rodkallen... ;. 309 Rodney, Cape 346 Rodoni, Cape 318 Rodriguez Island 325 Rodsher Island 309 Roeskilde 312 Rogosnizza 318 Rokugo, Cape 340 Rokuren Island 340 Roma Island 332 Romain, Cape 283 Page. Roman, San, Cape 295 RomanzofCape 287 Romanzov Islands 343 Romblon Island 335 Rome 316 Ronaldsay, North 305 Roncador Cay 286 Rongerik Islands 343 Roodewal Bay 323 Roque, St., Cape 296 Roques Islands 295 Rosa, Sta., Island 289 Rosalia, Sta., Bay 290 Rosalind Bank 286 Rosario Island 345 Rose Island 348 Spit Point 288 Rosenoary Island 351 Rosier Cape 280 Ross Island 339 Rossel Island 347 Rostock 311 Rota Island 344 Rotterdam 313 Rotti Island 332 Rottnest Island 351 Rotumah Island 347 Round Island 338 Roundhill Island 279 Rovigno 317 Roxo Cape 285 Royal Island 292 Royalist, Port 333 Ruad Island 320 Rugenwalde 310 Rum Cay 292 Runaway, Cape 354 Runo Island 310 Rupert Island 299 Rurutu Island 350 Ry vingen Island 308 Ryojun Ko 338 Saba 294 Sabine Pass 284 Sabioncello Peninsula 318 Sablayan Point 334 Sable Cape 281 Island 281 Sacatula River 291 Sacrificios Island 285 Point 291 Saddle Group 338 Island 279 Sado Island 340 Safajah Island 324 Safatu Island 337 Sagua, Isabello de Saida 320 Saigon 336 Saintes Islands 294 Saipan Island 344 Sakai 340 Sakhalin Island 341 Sakishima Gunto 338 Sakonnet Point 282 Sal Cay 293 Island 303 Sala y Gomez 350 SaladoBay 300 Page 876] INDEX TO APPENDIX IV. » Page. Salayar Island 333 Saldanha Bay 323 Salem 282 Sail 321 Salina Cruz 291 Salinas Bay, C. America. . . 291 L. California 290 Point 294 Salisbury Island 279 Salomague Island 334 Salonika 319 Salovetsld 356 Saltee, Great 307 Salut Islands 296 Salvador, San 292 Salvage Islands 303 Salvore Point 317 Sama, Port and Peak 292 Samana 293 Cay 292 Samanco Bay 301 Samar Islana 335 Samarang 331 Sambro Island 281 Samoa Islands Samos Island 320 Sampit Bay 333 Samso Island 312 Samsoe Island 312 San Bias, Gulf 287 Sand Island 284 Key 284 Sandakan Harbor 333 Sandalo, Cape 316 Sandalwood Island 332 Sandfly Cay 286 Sandiiammaren 309 Sandwich Island 347 Islands 304 Sandy Cape 353 Hook 283 Point 299 Sangwin River 322 Sanibel Island 284 Sankaty Head 282 Sannakhlsland 287 Santa Cruz del Sur 293 Santander 314 River 285 Santiago Cape 299 de Chile 300 Cuba 293 Port 334 Santo Domingo City 294 Santona 314 Santos 297 Sao JoSo da Barra 297 Saona Island 294 Sapelo Island 283 Sarang^uni Islands 335 Sarawak 333 River 333 Sariguan Island 344 Sarstoon River 286 Sarulsland 332 Saseno Island 319 Satano Misaki 340 Satawal Island 343 Saugor Island 329 Sauguir Island 333 PLACE 8 — continu ed . Sauh, Pulo 330 Saukhoum 320 Saunders, Port 280 SauoBay 338 Savage Island 348 Savaii Island 348 SavanUla 295 Savannah 283 Savanna-la-Mar 293 Saybrook 282 Scalp Mountain 306 Scarcies River 321 Scatari Island : 281 Schama Mountain 301 Schanck, Cape 352 Schanz Island 343 Scharhom 311 Scheveningen 313 Schillighom 311 Schleimunde 311 Schleswig 311 Schonberg 311 Scilly Islands, England .... 304 S.Pacific 348 Scott Cape 288 Scutari 320 Sea Bear Bay 298 Rock 339 Seal Cays 286 Island 281 Seao Island 333 Seattle 289 Seba8tian,San,Cape,M'g'8c'r 326 Spain 314 St., Cape, S. Africa. ... 323 Island 297 Sebastopol 320 Sebenico 319 Sedano, Cape 331 SedashigarBay 328 Seguin Island 281 Sem, I. de 314 Sejro Island 312 Selatan Point 333 Seldom-come-by Harbor 279 Semeny River 318 Semerara Island 334 Semiamoo Bay 289 Semione Island 331 Sentinel Island 339 Series Island 349 Sermata Island 332 Sermelik Fjord 356 Sermo Island 319 Serrana Bank 286 Serxanilla Bank 286 Seskar Islet 310 Setubal 315 SeuheliPar 325 Seven Heads 307 Seychelles 325 Sfax 321 Shag Rocks 304 Shahah 327 Shahr, Abu 328 Shaikh Shu'aib Islet 328 Shaluitien Island 338 Shanghai 338 Shannon River 306 Shantar Islands 341 Shantung 338 Sharjah 327 Shark Island 346 Sharmoh 327 Shaweishan Island 338 Shelbume Harbor 281 Shelter Bay 341 Shepherd Island 287 Sherbedat, Ras 327 Sherbro Island 322 River 322 Sherm Hassey 324 Joobbah 324 Rabegh 324 Wej 324 Yahar 324 Shetland Islands 305 Shiash-Kotan Island 341 Shields, North 305 Shimizu Bay 340 Shimonoseki Strait 340 Shinnecock Bay 283 Ship Island 284 Shoal 284 Shipunski, Cape 341 ShirasuReef 340 Shoals, Isles of 282 Shoalwater Cape 289 Island 331 Siargao Island 335 Siassi 336 Siberoet Island 330 Siboga 330 SibucoBay 336 Sibutu Island 336 Sibuyan Island 335 Sidmouth, Cape 353 Sierra Leone 322 Sighajik 320 Sigri, Port 319 Sihuatanejo Point 291 Sihut 327 Silan 285 Silaqui Islet 334 Silver Bank 292 Simaloe Island 330 Simeonof Island 287 Simoda 340 Simon, St., Island 283 Simonoff Island 348 Simonor Island 336 Simons Bay 323 Simpson, Port 288 Simusir Island 341 Singapore 330 Singkel Island 330 Singkep Island 330 Single Island 337 Singora (Sungkla) 336 Sinon 322 Sinope 320 Siphano Island 319 Siquijor Island 335 Sink, Cape 333 SiriyaSaki 340 Sisal 285 Sitka 288 Sittee Point 286 Skagataas Point 357 Skagi, Cape 357 INDEX TO APPENDIX IV. [Page 377 Page. SkagsHead 309 Skaw, Cape 312 Skelligs Rocks 306 Skerries Rocks 305 Skerry vore Rocks 305 Skiathos Island 319 SkidegateBay 288 Skoorgaarde 311 Skumbi River 318 Skyring Mountain 298 SligoBay 306 SlyneHead 306 Smalls Rocks 304 Smerwick 306 Smith Island, Japan 340 Washington 289 Smyrna 320 Snaefells Yokul 357 Snares Islands 355 Socorro Island , Chile 300 Mexico 291 SoderSkars 309 Soderarm 309 Soderhamm 309 Sofala 323 Sohar 327 Sokotra Island 324 Sola Island 295 Solander Islands 355 Solitary Islands 352 Solombo, Great, Island 332 Solomon Islands 346 Solta Island 318 Sombrero 294 Key 284 Rock 336 Sommer Island 310 Song-yui Point 337 Sonserol Island 344 SooBay 338 Sorelle Rocks 318 Sorol Island 343 Sorrel Rock 337 Sorrell, Cape 354 Port 354 Sorsogon, Port 335 Soumshu Island 341 Souwaroff Island 348 South Cape, Formosa 338 N. Guinea 346 Rock 306 Water Cay 286 Southampton 304 Southsea Castle 304 Southwest Cape 354 Reef 284 Spalato Passage 318 Port 318 Sparo Vestervik 309 Spartel, Cape 321 Spartivento Cape, Italy 317 Sardinia 316 Spencer, Cape 352 Spezzia 316 Spikeroog 312 Spiridione, St., Port 319 Spitzbergen 356 Spodsbjei^ 312 Spurn Head 305 Square Handherchief Bank. 292 L PLACES — continued. Page. StaabiergHuk 357 Stack, South 304 Stade 311 Stag Rocks 307 Stamp Harbor 288 Stampali Island 319 Stanley, Port 304 Starbuck Island 345 Start Point 304 Startpoint 305 Staten Island 298 Staunton Island 338 Stavanger 308 Steilacoom 289 Steinkirchen 311 Stemshesten 308 StensherRock 310 Stephens, Port 352 Stettin 310 Stewart, Cape 351 Stewart Islands 346 Stirrup Cays 292 Stirsudden 310 Stockholm 309 Stonington 282 Stopelmiinde 310 Stora 321 Stomoway 305 Stot 307 Stralsund 311 Strati Island 319 Straumness Point 357 Streaker Bay 352 Streckelsberg 311 Strogonof Cape 288 Stromstad 308 Stromtangen 308 Strong Island 343 Strovathi Island 319 Stuart Island 287 Suakin 324 Sual 334 Subic 334 Succadana 333 Suda, Port 319 Sueik 327 Suez 324 Suffren, Cape 341 Sugar Loaf Point 352 Sughrah 327 Suk Island 343 Sula Islands 332 Sulphur Island 345 Sumbawa Island 332 Sumburgh Head 305 Sunda Strait 331 Sunday Island 350 Sunderland 305 Sundsvall 309 Sunmiyani 328 Sup6 301 Sur 320 Surabaya 331 Surat 328 River 328 Sxuigao 335 Surop 310 Susaki 340 SuwanoseJima 339 Suwarrow Island 348 Page. Svalferort Tzerel 310 Svartklubben 309 Svendborg 312 Svenor 308 SviatoiNos 356 Svinoen 308 Swallow Bay 299 Islands 347 Swan Islands 286 Swansea 304 Swatow 337 Sweers Island 353 Swinemunde 310 SybilloBay 341 Sydenham Island 342 Sydney, Australia 352 Harbor, C. Breton I . . . 281 Synesvarde Mountain 308 Syra 319 Syracuse 317 Tabaco 335 Tabasco River 285 Tabertness. 305 Tablaa Island 335 Point 300 Table Bay 323 Head 279 Island 329 Taboga Island 291 Tabou River 322 Tacloban 335 Tacoma 289 TacoradyBay 322 Tae Islands 337 Tagulanda Island 333 Tahiti 349 Tahoa Island 349 Tahuata Island 345 Taiaro Island 349 Tai-pin-san 338 Tajer, Port 318 Taka Yama 341 Takapoto Island 349 Takau 338 Takhkona Point 310 Talabo, Cape 333 Talcahuano 300 Talinay Mountain 300 Taltal, Port 301 Taluat Island 333 Tamana Island 342 Tamandar6 296 TamarPort 299 Tamatave 326 Tambelan Island 331 Tampa Bay 284 Tampat Toewon Point 330 Tampico 285 TamsuiHarbof 338 Tanabe Bay 340 Tancook Island 281 TangaBay 324 Tangier 321 Tanjong Barram 333 Datu 333 Mangkalihat 333 Pandan 331 Patani 336 Tanna Island 347 Page 378] INDEX TO APPENDIX IV. Page. Tantang, Port 326 Taoiunu 348 Taormina Cape 317 Tapua Island 347 Tapul Island 336 Taputeuea 342 TaraHill 307 Taranto 317 Tarawa Island 342 Tarbertness 305 Tarifa 315 Taritari Island 342 Tarpaulin Cove 282 Tarragona 315 Tas de Foin Islet 339 Tatakoto 349 TatsupiSaki 340 Tauere Island 349 Tauranga Harbor 354 Tauzon, Cape 326 Tavolara Cape 316 Tavoy River 329 TaytaoCape 300 TaytayFort 333 Tchesm6 320 Tchoukotskoi, Cape 342 Tegal 331 Tehor Island 332 Tellicherri 328 Telle Islands 332 Tematangi Island 349 Tenasserim 329 Tenedoa Island 320 Teneriff e Island 303 Tenez, Cape 321 TepocaCape 290 Tepoto Island 349 Tequepa 291 Terceira Island 302 Teresa, Sta., Bay 290 Terkolei 330 Terminos Lagoon 285 Temate Island 333 Terstenik Rock 318 Testa, Cape 316 Testigos Islets 295 Tewaewae Bay 355 Thabi, Abu 327 Thank God Harbor 356 Thermia Island 319 Thikombia Island 348 Thithia Island 348 Thomas, St., I., B. of Biafra 322 West Indies. 294 Thom^, St., Cape 297 Thorton Haven 338 Three Kings Islands 354 Points Cape, Africa. . . 322 Argentina . . . 298 Honduras... 286 Ti-ao-usu Island 338 Tiburon Island 290 Tiegenort 310 Tien-pak 337 Tientsin 338 Tilly Bay 299 Timbalier Island 284 Timor Island 332 Laut Island 332 Tinakula Island 347 Tinian Island 344 PLACES — continued. Page. Tintolo Point 335 Tirby Point 287 Tiruchendore 328 Toasa Island 343 Toau 349 Tobago 295 TobiShima 340 TobolAli 331 Tocopilla 301 Todos Santos 290 To-du Island 325 Tofua Island 350 Tokara Jima 339 Tokelau Islands 345 Token Bessi Island 332 Tokio 340 Tolaga Bay 354 Tolkemit 310 Tomas, San 290 Tomo Roads 340 Tongarewa Island 345 Tonga tabu Island 350 Tongka Harbor 329 Tongoi 300 Tong-sang Harbor 337 Tong-ting Islet 338 Tonning 311 Topolobampo 291 Tor 324 Torbjomskjaer 308 Tordenskjold, Cape 356 Torgauten 308 TonwiSaki 340 Tomea 309 Toro Point 287 Torres Island 347 Point 297 Port 316 Tortola 294 Tortosa, Cape 315 Tortugas Island 295 Tory Hill 307 Island 306 Tosco Cape 290 Totoya Island 348 Toulinguet Islands 279 Toulon 316 Tourane Bay 336 Towers Island 342 Townsend, Port 289 Trsenen 307 Trafalgar, Cape 315 TraleeBay 306 Trani 318 Trapani 317 Travemunde 311 Travers Islands 353 Treasury Islands 346 Trebizond 320 Tregosse Islands 347 Trelleborg 309 Tremiti Islands 317 Trepassey Harbor 279 Trea Montes Cape 299 Puntaa Cape, Chile. ... 299 Venezuela... 296 Trevose Head 304 Triangles 285 Tribulation, Cape 353 Trieste 317 Trincomali 329 Page. Tringano River 336 Trinidad Head 289 Island 303 Tripoli, Africa 321 Turkey 320 Tristan da Cunha 303 Triton Bay 346 Island 337 Triunfo Cape 286 Trivandrum 328 Trobriand Islands 347 Tromelin Island, Caroline Is. 343 Indian Ocean 326 Tromso 307 Trondheim 307 Troon 305 Truxillo 286 Tsau-liang-hai 339 Tscheljuskin, Cape 356 Tsmano 326 Tsu Sima 339 Tsukarase Rocks 340 Tsuruga 340 Tuanske Island 349 Tubailsland 349 Tubuai Islands 350 Tubuai-Manu Island 349 Tucacas Island 295 Tuckers Beach 283 Tukume Island 349 TuUy Mountain 306 Tumaco 302 Tumbez 302 Tung-chuh Island 338 Tung-yung Islands 337 Tuni-ang Island 337 Tunis 321 Tuno Island 312 Tupilco River 285 Tureia Island 349 Turk Island 292 Turnabout Island 337 Turo Island 312 Turtle Island 348 Isles 351 Tuskar Rock 307 Tuticorin 328 Tutoya 296 Tutuila Island 348 Tuvutha Island 348 Tuxpam Reefs 285 Tuxtla Volcano 285 Twelve Islands 327 Twofold Bay 352 Tybee Island 283 Ty-fung-kyoh Island 337 Tynemouth 305 Ua-Huka Island 345 Ualan Island 343 Ubatuba 297 Uea Island 348 Ujelang Island 343 Uji Shima 340 Uleaborg 309 Ulietea Island 349 IJlko Kalla Rock 309 UlladuUa 352 Ulsire 308 Uluthi Islands 343 Umea 309 INDEX TO APPENDIX IV. [Page 379 Page. Una 297 Unalaska Island 287 UnareBay 296 Underut Islet 325 Underwood, Port 355 Unga Island 287 Unie Island 318 Union Bay 298 Islands 345 Portdela 291 Unsan^ 333 Upemivik 356 Upright Port 299 Upsala 309 Upulo Islands 348 Uragami 340 Urracaa Islands 344 Urup Island 341 Usbome, Port 351 Usedom 311 Ushant 313 Ustica Island 317 Ute Islet 309 Utillalsland 286 Utrecht 313 Uvea Island 350 Vadao 307 Vahanga Island 349 Vahitahi Island 349 Vaitupu Island 345 Valdea Island 288 Valdivia 300 Valencia 315 Valentia 306 Valentine Harbor 299 St., Cape 299 Valery en Caux, St 313 ValientePeak 287 Valientes Islands 343 Valparaiso 300 Vanavana Island 349 Vancouver 289 Vanikoro 347 Vannes 314 Vanua Lava Island 347 Levu Island 348 Mbalavu Island 348 Vardo 307 VarellaCape 336 Pulo 336 Varna Bay 320 Vat6 Island 347 Vathi, Port 319 Vatiu Island 350 Vatoa Island 348 Vatu Lele Island 347 Vara Island 348 Vavau Island 350 Vavitoa Island 350 Vaza Barria River 296 Veglia 317 Veiro Island 312 Vela, La, Cape 295 Venangue B6 Bay 326 Vendres, Port 316 Venice 317 Ver, Pointde 313 Vera Cruz 285 Verde Cape 321 PLACES — continued. Page. Verd Cay, Bahamas 292 Cuba 292 Vicente, San, Cape 299 Port 334 Victor- Port 352 Victoria 288 Harbor 355 Port, Australia 352 Sey chelle Islands. 325 River 351 Victory Cape 299 Island 331 Vidal, Cape 323 Video Island 338 VieborgBay 310 Vieques Island 294 Vieste 317 Vigan 334 Vigo 314 Villa 307 Nova da Princessa. . . . 297 Villajoyose 315 Villefranche 316 Vinaroz 315 Vincent, San, de la Barquera 314 St. Cape, Chili 299 Madagascar . 326 Portugal 315 I., C. Verde Is . . . 303 Windward Is. 295 Bay, S. Pacific ... 350 Vineyard Haven 282 Vingorla 328 Rocks 328 Virgin Gorda 294 Virgins, Cape 298 VitiLevu 348 Vizagapatam 329 Viziadiug 328 Vladimir, St., Bay 341 Vladivostok 341 Vliko, Port 319 Vohemar 326 Voiazza River 318 Volcano Island, West 338 Islands 345 Volta River 322 Voltaire, Cape 351 Vordate Island 332 Vordingborg 312 Vostok Island 345 Vourlah 320 Vriea Island 340 Wadero Island 308 Wadsworth, Fort 283 Wahdu Island 325 Waimea 344 Waitangi River 355 Wakaya Island 348 Wake Island 344 Wakefield, Port 352 WalfischBay 322 Walker Cay 292 Wallis Island 348 Walpole Island 347 Walsche, Cape 346 Walsingham, Cape 355 Wanganui River 354 Wangari Harbor 354 Page. Wangajoa Harbor 364 Wangaruru 354 Wangeroog 312 Wang-kia-tia Bay 338 Warberg 308 Wamemunde 311 Warren Hastings Island 344 Washingtoji 283 Island 342 Watch Hill Point 282 Watcher, North, Island 331 Waterfall Bluff 323 Waterford 307 Waterloo Bay 323 Watlings Island 292 WawodaRock 341 Wedge Island 281 Weggs Cape 279 Weichselmunde 310 Weihaiwei 338 Wellington 354 Wenman Island 342 Wessel, Cape 351 West Cape 355 Western, Port 352 Westminster Hall Islet 299 Wetta Island 332 Wexford 307 Whaingaroa Harbor 355 WhaleBack 282 Whalefiah Island 356 Wliare-Kauri 350 White Haven 305 Head Island 281 Island 354 Rock Wliitsunday Island 349 WHiittle Cape 280 Wicklow 307 Wilberforce, Cape 351 Wilhelmsliaven 312 Willemstadt 313 William. Port 355 Willoughby, Cape 352 Wilmington 283 Wilson Islands 347 Islets 343 Promontory 352 Windau 310 Winter Harbor 355 Wismar 311 Wittgenstein Island 349 Wolgast 311 Wolkonsky Island 349 Wollaston Island 298 Wollin 310 Wollongong 352 Wood Island, Labrador. . . . 280 Maine 282 Woodlark Islands 347 Woody Island 337 Woosung 338 Wostenholme Cape 279 Wotje Islands 343 Wottho Island 343 Wowoni Island 333 Wrangell 288 Wrath, Cape 305 Wreck Reef 347 Wusimado Point 340 Wustrow 311 Page 380] INDEX TO APPENDIX IV. Page. Yakuno Shima 339 YakutatBay 288 Yamada 340 Yamagawa 340 Yami Island 334 Yafiez 300 Yap Island 343 Yaquina Head 289 Yarmouth 281 Yeboshi Sima 339 Yemb6 324 Yerabu-sLma 339 Yeu, Island de 314 Ylin Island 334 PLACES — continued. Yobuko 339 Yoko Shima 339 Yokohaina 340 Yokosuka 340 Yori-eima 339 York, Cape, Greenland. . . . 356 Queensland 353 Minister Rock 298 Youghal 307 Ystad 309 Ytapere Bay 326 Point 326 Yuiada Road 320 Yura No Uchi 340 Page. Zafarana 324 Zafarin Islands 321 Zambesi River 323 Zamboanga 335 Zante 319 Zanzibar 324 Zapotitlan Point 285 Zara 318 Vecchia 318 Zempoala Point 285 Zengg 318 Zeyla 324 Zirona Grande Island 318 INDEX TO PART T. Subject. Abbreviations Account. {See Dead reckoning.) Adjustments, horizon mirror index mirror plane table sextant permanent. . . theodolite or transit. Afternoon sights AguUias Current Airy 'a method for great circle sailing. . . Alidade, plane table Almanac, Nautical, (-Se« Nautical Al- manac.) Altitude and azimuth time azimuth azimuth calculated, method of circle, definition circum-meridian forms for computed, method of definition ex-meridian forms for meridian, constant form for. . . forms for latitude by observation of reduction to forms . observed, how corrected of Polaris for latitude single, for chronometer error . . latitude longitude ashore at sea true, definition Altitudes, doubloj for chro. error Amplitude, definition determination of Anchor^e, position to be plotted Angle, danger. (5ee Danger angle.) hour. {See Hour angle.) ' to repeat Angles, between three known objects. . horizon, for finding distance. . . round of sextant and theodolite in hy- drography vertical terrestrial, to measure 26i°-45° on bow Anticyclonic regions, features of Apparent day, definition variation in length noon, definition time, conversion to mean . . . definition inequab'ty of Art. 246 245 413 244 248 410 389 544 194 412 235 356 353 371 217 326 371 220 326 325 321 322 326 294 333 316 332 340 341 294 320 224 347 166 411 152 139 411 452 139 147 476 273 273 273 292 273 273 Page. 93 93 192 93 94 190 171 237 82 192 90 147 147 155 88 129 257 155 88 129 257 128 257 256 126 126 129 257 115 136 123 134 141 142 115 125 89 144 71 191 62 58 191 202 58 60 214 102 102 102 110 102 102 Subject. Art. Page. Apparent time, relation to mean Arctic Current Aries, first point of, definition Arming of lead Artificial horizon, description method of use should be tested — Ascension, right. {See Right ascen- sion.) Astronomical base. bearing time transit instruments work of survey Atlantic Ocean, currents storms Attraction, local Australia Current Axis of rotation, definition Azimuth, altitude and altitude circle definition from Sumner line how deterijained named of body determines use terrestrial object time and altitude determination dit^am for compass errors in great circle sailing. . tables Barometer, aneroid comparisons definition effect of, on tides mercurial sea standard temperature correction to determine height vernier Base, astronomical line, description Beam compass, description Bearing and angle, position by distance, position by danger method of observing and plot- ting of terrestrial object Bearings, bow and beam cross sun, for compass error two, of object, with run be- tween Beaufort's scale for wind Bench mark, definition 288 530 226 19 256 257 258 441 359 277 427 445 523 489 76 540 6 353 235 34 223 370 345 344 395 359 356 349 351 89 191 351 56 57 48 496 49 51 51 55 58 52 441 434 430 143 138 157 134 359 146 134 89 144 68 511 109 235 89 13 97 98 98 200 148 103 196 201 233 224 36 236 9 147 90 18 88 153 144 144 174 148 147 145 145 40 82 145 27 27 24 226 24 25 26 26 28 25 200 198 197 59 57 64 56 148 60 56 40 59 33 230 381 382 INDEX TO PART I. Subject. Binnacles, description Bottom, quality of, on chart Boxing the compass Brazil Cxirrent Buoys C — W, definition Calculated Altitude Method Cape Horn Current Celestial coordinates equator, definition horizon, definition latitude and longitude definition meridian , definition sphere or concave, definition . . Celo-Navigation, definition Chart. {See also Projection.) as record of piloting employment in piloting general features great circle for composite sailing. isobaric measures of depth on Mercator, to construct quality of bottom on standard meridians on Chilean Current Chronometer, advantage of more than one C— W, definition care on shipboard comparison record correction. {See Chro- nometer error.) description error, by double alts single altitude . time sight signals transits definition differs from corr. . . from rate hack, use of max. and min. ther- mometer minus watch, definition. second difference eight . {See Time eight . ) temperature curve transportation of winding Circle, declination, definition hour, definition of altitude, definition equal altitude illumination vertical definition Circum-meridian altitude forms Civil time Clouds, description and symbols Coefficients, constant quadrantal semicircular value and relation Collimation, line of, definition Comparing watch, use of Art. Page. 35 18 46 23 27 14 532 235 162 66 268 100 371 155 541 236 234 90 215 88 213 87 238 90 229 89 216 88 210 87 4 9 166 71 165 68 37 20 189 80 197 83 460 270 47 24 41 21 46 23 45 23 541 236 265 100 268 100 260 98 263 99 264 99 259 98 320 125 316 123 316 123 314 121 315 122 261 98 312 121 311 121 268 100 262 99 268 100 265 100 266 100 260 98 262 99 216 88 216 88 217 88 363 150 363 150 217 88 326 129 257 103 277 71 34 111 48 107 47 103 46 114 48 410 190 268 100 Subject. Comparison, barometer chronometer, method record Compass, beam, description boxing compensation. {See Devia- tion.) declination definition deviation. {See Deviation.) divisions on card dry error. {See Error, compass.) local attraction Lord Kelvin Navy service, 7i-inch variation wet Compasses (drawing) Compensation, compass. {See Devia- tion.) Composite sailing, computation definition graphic approxima- tion shortest course for. . terrestrial globe . . . . Computed altitude method Concave, celestial, definition Constant deviation. {See Deviation.) for meridian altitude form . . . Conversion of time, apparent to mean. . definition mean to apparent . sidereal. . . sidereal to mean. . . Coordinates, celestial definition Correction, chro. {See Chronometer.) index, sertant of observed altitude Course, definition to lay Culmination, definition Current, Agulhas , allowance for Arctic Australia Brazil Cape Horn Chilean determined at noon effect in piloting equatorial, Atlantic Indian Pacific Guinea Gulf Stream Humboldt Japan Stream Kamchatka Kuroshiwo Labrador ocean, Atlantic cause of definition determination of drift, definition of Atlantic 232 INDEX TO PAET I. 383 Subject. Art. Current, ocean, Indian Pacific fitream, definition... Bubmarine Oyaehiwo Peruvian Rennells Rossel _ Southern connecting tidal, definitions description of observation of to find Ourve, temperature, chronometer — Cyclones and cyclonic circulations... Cyclonic regions, features of stormfl, description maneuvering in . . . Bummary of rules. . . tropicJil character. . Danger angle, horizontal vertical bearing Data, useful, miscellaneous Day's work, routine Dead reckoning, always kept definition form for method of working. value of Decimal fractions Declination and hour angle right ascension circle, definition definition of compass Declinatoire, plane table Definitions, nautical astronomy navigation Departure, definition on beginning voyj^e .... to take Depth, measures of, on charts. ..... recorder, sounding machine. Deviation, causes of classes of compensation of constant, coefficient definition definition heeling error, compensation definition Napier diagram for quadrantal, coefficients definition recompensation semicircular, coefficients — definition table theory of to apply find Diagram, time azimuth Difference, second. (See Second dif- ference.^ Dip of horizon, definition how applied none with artificial horizon variation in when land intervenes. , 542 535 516 518 538 541 531 540 533 490 500 506 207 266 475 476 477 486 487 478 481 155 156 157 Page. 383 882 202 205 203 236 237 216 218 75 412 209 1 6 382 204 47 23 99 100 119 112 111 77 125 116 94 107 106 128 103 101 92 96 78 84 351 300 303 294 301 302 237 235 232 232 236 236 235 236 235 225 227 230 86 100 213 214 214 221 222 214 218 64 64 64 277 169 169 84 254 84 84 266 90 90 88 88 36 192 87 10 10 169 84 24 14 44 45 49 48 48 37 53 49 41 47 47 54 46 45 40 43 37 39 145 116 117 115 117 117 Subject. Art. Page. Distance and \)earing by horizon angle definition of objects of known height. polar, definition zenith. (5ce Zenith distance.) Distant object for comjjass error Diurnal inequality of tide type of tide Dividers, description pntportional, description . . . Doldrums Doubling angle on bow Drift currents, Atlantic Earth, definitions relating to Eccentricity, sextant Ecliptic, definition Elevated pole Ephemeris. (5ee Nautical Almanac.) Equation of time, definition in conversion of time Equator, celestial, definition earth's Equatorial currents. (See Current.) Equiangular spiral Equinoctial, definition Equinox, definition vernal. (See First jwint of Aries.) Error, chro. (See Chronometer.) compass, causes to apply find heeling. {See Deviation.) index, sextant, description probable, of position, how shown sextant. (See Sextant.) Establishment, tidal, definitions Ex-meridian altitudes forms Extraordinary refraction near horizon.. Extra- tropical cj^clonic storms First point of Aries, definition hour angle is si- dereal time Flinders bar, definition to place Fogs and fc^ signals Forms for sights, etc notes on use recommended . Fractions, decimal Gauges, tide, description Geodetic surveying Geometry formulae derived from Geo-Navigation, definition Gimbals, compass chronometer Glasses, shade. (See Shade glasses.) Globe, terrestrial, for comp. sailing. . . gt. circle sailing. Graduation, sextant, error Great circle charts for comp. sailing . . . course sailing, advantages Airy's method computation definition graphic approx — 138 139 6 139 219 91 498 498 7 431 465 145 527 6 248 225 214 275 288 215 6 6 215 226 74 78 83 250 398 492 326 301 488 226 276 105 127 163 399 513 408 4 28 259 200 193 248 189 197 6 186 194 190 183 192 57 58 9 58 88 40 227 227 11 197 209 60 234 10 94 89 87 103 109 88 9 10 88 89 36 37 39 «5 176 226 129 257 117 223 103 47 54 66 254 265 176 266 231 189 268 269 9 17 98 83 82 94 80 83 10 80 82 81 79 82 384 INDEX TO PART I. Subject. Great circle sailing methods terrestrial globe. . . time azimuth methods Greenwich adopted as prime meridian. time, to find Guinea Current Gulf Stream, description extraordinary dip in ... . Gyro-compaae Hack chronometer, use of Heading, magnetic, determination of. . Heeling error. {See Deviation . ) Height, determination by barometer. . . Hehograph, use in surveying Heliotrope, use in surveying Horizon angle, distance by artificial, description method of use no dip with should be tested — celestial, definition dip of, definition how applied none with artificial horizon variation in when land intervenes. . mirror, adjustment description prismatic visible or sea, definition Horse latitudes Hour angle and declination time, coavession definition how measured circle, definition Humboldt Current Hydrographic survey j method of surveying, definition Hydrography in survey, description. . . to plot Ice and its movements in the North Atlantic Ocean Identification of unknown bodies Index correction, sextant, to find error, sextant, description minor, adjustment description prismatic Indian Ocean, currents Induction, magnetic Instruments, astronomical transit nautical astronomy navigation surveying Interpolation, Nautical Almanac Intersection, Sumner. (See Sumner.) Intervals, lunitidal, definitions list of mean and sidereal time Iron, hard and soft. Isobars, chart showing Japan Stream E[amchatka Current Knot, length of Kuroshiwo Current Labrador Current Lagging of tide Land and sea breezes Art. 188 193 191 336 280 529 526 301 33 268 122 58 426 426 139 256 257 294 258 213 300 303 294 301 302 246 240 248 213 466 236 293 222 278 216 541 432 408 451 452 392 250 249 245 240 248 542 97 427 239 7 409 283 492 289 97 460 436 637 6 536 530 497 469 Page. 80 82 82 140 104 235 233 117 18 100 50 28 195 195 58 97 98 115 98 87 116 117 115 117 117 93 91 95 87 209 90 111 88 103 88 236 197 189 202 202 238 172 95 95 93 91 94 237 44 196 91 11 189 106 226 279 109 44 270 235 236 10 235 235 227 211 Subject. Latitude, by meridian altitude forms . . Polaris reduction to meridian reduction to meridian, forms single altitude forms 9/ g/^ method forms celestial, definition definition difference, of definition horse Lead, arming description line, marking of Level of bench mark surveying, use of description Lights, employment in piloting Line, base, description of of coUimation, definition , position. (-Sffi Sumner line.) sight, definition Sumner. (See Sumner line.) Local attraction time, to find Log book chip ground patent electric registers. revolutions as substitute . . Logarithms, explanation Longitude, by single altitude ashore. at sea. . time sights, forms transit observations. . . celestial, definition definition difference of of secondary meridians. . . tertiary meridians Loxodromic Curve Lubber's line Lunitidal intervals, definitions Ustof Magnetic observations in survey Magnetism, acquired in building vessel features of earth's subpermanent transient Main triangulation Maneuvering, cyclonic storms . summary of rules Marine surveying Mean day, definition directive force noon, definition sun, definition Mean time, conversion to apparent. . . sidereal definition intervals, relation to side- real time, relation to apparent sidereal Mercator projection, description to construct sailing INDEX TO PABT I. 385 Subject. Meridian altitude, constant forma for latitude by observation of reduction to celestial, definition of earth, definition passage, definition prime, Greenwich adopted... secondary, definition determination of.. standard, on charts tertiary, definition determination of Meridional parts Method of Saint Hilaire or of the com- puted altitudes Middle latitude sailing correction Mile, nautical or sea, length of Mirror, horizon. (yiSec Horizon mirror.), index. (See Index mirror.) sextant, resilvering Monsoon winds Moon, correction of observed altitude.. form for latitude sights meridian altitude time sight planets, and stars, use of value of observations of Morning sights Nadir, definition Napier diagram Nautical Almanac, description for 1915, extracts . . gives horizontal parallax interpolation reduction of ele- ments second differences. Astronomy, definitions instnunents mile, length of Navigation, definitions instrimients and accessories Neap tides Noon sights Notes on forms for sights, etc Occupying a station Ocean current. (See Current, ocean.) Octant, description Optical principal of sextant Orient, to, a plane table Oyashiwo current Parallax, definition horizontal, in Nautical Al- manac how applied of planet or star Parallel of latitude, definition rulers, description sailing, description Passage, meridian, definition Pelorus, description Peruvian Current Piloting, definition requisites Plane of reference, tidal sailing..." table, adjustments description Art. Page. 235 321 322 326 216 6 271 336 336 337 45 336 339 40 371 175 178 6 254 468 294 391 394 384 212 94 282 305 283 283 285 209 239 6 1 7 494 386 411 255 242 414 538 304 305 306 294 6 8 173 271 36 541 130 131 509 169 413 412 128 256 126 126 129 88 9 102 140 140 140 23 140 141 20 155 75 77 10 96 210 115 259 257 256 172 174 169 87 41 105 248 118 106 106 108 87 91 10 9 11 226 170 265 190 97 92 192 236 118 118 119 115 9 11 75 102 19 236 56 56 230 72 192 191 Subject. Plane table, to improvise use of. Planet, correction of observed altitude. form for latitude sights meridian altitude .... time sight identification of unknown Planets, stars, and moon, use of Polar distance, definition Polaris, latitude by Pole, elevated star, latitude by Poles of earth Portable transit Position by angles between 3 objects. . 26i°-45'' on bow . . . bearing and angle distance bow and beam bearings. . . cross bearings doubling angle on bow two bearings and run methods of fixing of anchorage to be plotted body determines its use soundings in survey probable error of by Sumner lines, how shown Pressure, effect in wind progressive areas of seasonal variations in variation of atmospheric Prime meridian, Greenwich adopted . . vertical, definition Priming of tide Projection, gnomonic Mercator polyconic systems in use Proportional dividers, description Prosection method, plane table Protractor, ordinary three armed, description. . . substitute use of Quadrantal deviation. (See Deviation.) Quintant, description Range of tide at various places definitions Ranges for finding compass error in piloting Rate, chronometer. (See Chronometer rate.) Reciprocal bearings for compass error. . Reckoning, dead. (See Dead reckon- ing-) Record of astronomical work chronometer comparisons piloting tidal Red Sea, extraordinary dip in Reduction to meridian forms for Reference, planes of, tidal Refraction, correction for definition effect on dip extraordinary, near horizon how applied Relative humidity Rennells Current Repeat, to, an angle Art. Page. 416 413 294 392 391 219 333 214 333 6 427 152 147 143 138 146 134 145 144 133 166 395 452 398 460 474 461 471 336 217 497 44 39 43 38 431 414 9 428 429 152 255 493 90 158 88 399 263 166 507 301 326 509 298 296 301 301 299 63 531 411 193 193 115 258 256 255 172 172 88 136 87 136 9 196 62 60 59 57 60 66 60 59 56 71 174 202 176 207 212 207 212 140 88 227 23 20 22 20 197 192 11 196 196 62 97 279 226 40 65 39 176 99 70 230 117 129 257 230 116 115 117 117 116 30 235 191 21594°— 14- -25 386 INDEX TO PAKT I. Subject. Resection method, plane table Residual deviation Rhumb line, definition not shortest course Right ascension and declination definition Roaring forties Rossel Current Round of angles Run, calculation of determined at noon Running survejr, description Sailing, composite. (See Composite.) great circle. (See Great circle.) Mercator middle latitude correction parallel plane spherical traverse Sailings, definition kinds of Saint Hilaire's method Sargasso sea Sea and land breezes mile, length of pymbols for state of water temperature Second difference, chronometer Nautical Almanac . Secondary meridian, definition determination of. triangulation Seconds, employment in naut. sights. . Semicircles, storm Semicircular deviation. (See Devia- tion. ) Semidiameter, definition how applied measured of planet or star Semidiurnal type of tide Seztant adjustments permanent angles for plotting soundings. . choice of definition description eccentricity graduation errors index correction, to find error, description ..'... method of use optical principle prismatic mirrors shade glasses resilVering mirrors surveying vernier Shade glasses, for artificial horizon . . . sextant, description . . . prismatic Sidereal day, definition noon, definition ! time, conversion to mean definition intervals, relation to mean relation to mean Sight, chronometer. (See Time sight.) latitude. (See Latitude.) Art. Page. 414 192 123 52 6 10 185 80 237 90 237 90 467 210 540 236 411 191 208 86 388 171 457 204 186 80 179 78 175 75 178 77 173 75 169 72 168 72 172 74 167 72 les 72 371 155 528 235 469 211 6 10 73 35 64 30 265 100 285 108 336 140 337 140 444 201 397 179 485 221 307 119 308 120 251 96 294 115 498 227 244 93 248 94 452 202 253 96 239 91 240 91 248 94 248 94 250 95 249 95 252 96 242 92 248 94 248 94 254 96 423 195 241 92 256 97 240 91 248 94 276 103 276 103 291 110 276 103 289 109 287 108 Subject. Sight, line of, definition longitude. (See Longitude.) time. (See Time sight.) Sights, afternoon employment of various morning noon Signals, surveying, description time, for chronometer error Silvering sextant mirrors Solar time. (See Apparent time.) Solstice, definition Sound J velocity of Sounding machine, barometric corr depth recorder .... description tubes Soundings, surveying, how plotted use in piloting Southern connecting current Sphere, celestial, definition Spherical sailing Spring tides Stadia. (See Telemeter.) Star, correction of observed altitude. . . form for latitude sights meridian altitude time sight identification observations in surveying Stars, planets, and moon, use of Station pointer. (See Protractor, three armed.) Storm center, motion of rate of ])rogres8 to avoid fix bearing distance semicircles tables Storms, along transatlantic routes cyclonic. (See Cyclonic storms.) Submarine ocean currents Sumner line, always recommended. . applications of choice of bodies description determination uses lines, intersection, computation graphically, when run in- tervenes. Sun, correction of observed altitude. . form for latitude sights meridian altitude time sight mean, definition observations in surveying Survey, astronomical work of hydrographic, method of running, description to plot soundings in Surveying, hydrographic, definition.. instruments marine, definition topographic, definition transit, description Symbols for clouds sea .'.. weather Table, plane. (See Plane table.) INDEX TO PAST I. 387 Subject. Table, tide time azimuth Telemeter, description substitute for use of Telescope, direct and reversed sextant, adjustment description zenith Temperature curve, chronometer Terrestrial object, true bearing of Tertiary meridian, definition determination of. . . Theodolite, adjustments angles for plotting sound- ings.. . description method of use Thermometer, classes of description dry and wet bulb max. and min., chro Three-armed protractor. (See Pro- tractor.) point problem, conditions explanation Tidal current. (See Current, tidal.) day, definition establishment, definitions observations in survey instructions for record Tide, bench mark, deSnition cause of definitions relating to diurnal inequality type effect of, in piloting wind and barometer on. gauges, description observation of planes of reference of priming and lading of range of, at various places definitions semidiurnal type spring and neap tables time of high and low form for tropic types of Time and altitude azimuth hour angle, conversion of . . . apparent. (See Apparent time.) astronomical at different meridians azimuth. (See Azimuth, time.) civil conversion of. (See Conversion.) equation of. (See Equation of time.) Greenwich, to find local, to find mean. (See Mean time.) of high and low water form for. . . Art. 501 351 417 422 417 411 247 240 427 266 359 336 339 410 451 409 411 59 59 61 262 153 152 497 492 503 503 507 511 491 490 498 498 164 496 513 504 509 497 493 498 494 501 501 498 498 356 293 277 279 277 280 279 501 228 145 194 195 194 191 94 91 190 100 148 140 141 190 203 189 190 28 28 28 99 63 62 227 226 229 229 230 230 225 226 227 227 67 226 231 229 230 227 279 226 227 226 228 228 259 227 227 147 111 103 103 103 104 103 228 259 Subject. Time of transit, how found sidereal. (See Sidereal time.) signals for chronometer error eight for chronometer error longitude ashore at sea forms for solar. (See Apparent time.) Topographic surveving, definition Topojgraphy in hyarographic survey. . . Tracing paper to plot soundings 3-point problem. Trade wind Transit, astronomical definition observations for chronometer error longitude . . . portable surveying. (See Theodolite.) time of, how found Traverse sailing tables, use of Triangulation, main secondary Trigonometric functions logarithms Tropic tide Tropical cyclonic storms character Tubes, sounding machine Unknown bodies, identification of Useful data, miscellaneous Variation of compass, definition to apply find Variations, atmospheric nonperiodic . . . periodic Vernier, barometer sextant theodolite Vertical angles, terrestial, to measure. . circle, definition prime Visible horizon, definition Watch, comparing, use of Weather symbols Wind, Beaufort's scale causes of definition doldrums effect of, on tides land and sea breezes monsoon normal pressure prevailing westerly "Roaring forties " storms. (See Cyclonic storms.) Trade true direction and force wire drag Zenith, definition distance, definition how named telescope Art. Page. 323 314 316 340 341 408 450 160 429 464 427 271 315 338 427 323 172 170 443 444 498 478 481 21 392 75 78 83 471 473 472 52 241 409 139 217 217 213 268 70 68 459 458 465 496 469 468 460 462 467 467 464 69 454 212 221 321 427 127 121 123 141 142 254 189 202 65 1&6 209 196 102 122 140 196 127 74 73 201 201 270 271 227 214 218 13 172 277 36 37 39 212 212 212 26 92 189 58 88 88 87 100 34 33 206 206 209 226 211 210 207 207 210 210 209 33 203 87 88 126 196 I PA.RT II. TABLES. 601 PREFACE. The following tables comprise Part II of the American Phactical Navioator, by the late Nathaniel Bowditch, LL. D., as revised in 1880 and in 1903, and again in 1914, under the direction of the Bureau of Navigation, Navy Department. In the present edition, former tables 28A, 28B, 28C and 28D, Latitude by Polaris; 37, Logarithms for Equal Altitude Sights; 37A, Equation of Equal Altitudes near Noon, have been omitted, but the former assignment of table numbers and page numbers has not been disturbed, the pages on which these tables were printed being simply dropped from the book and the tables and pages not renumbered consecutively. This edition has been extended by incorporating Table 45, Logarithmic and Natural Haversines; Table 46, Consolidated Altitude Corrections; Table 47, Longitude Factor, and Table 48, Altitude Factor. Hydrographic Office, WasMngUm, D. C, 19 U. 503 CONTENTS OF PART 11. Page. Explanation of the Tables 507 Table 1. Traverse Table, Quarter Points 515 2. Traverse Table, Degrees 531 3. Meridional Parte 621 4. Length of Degrees of Latitude and Longitude 629 5A. Distance of an Object by Two Bearings, Quarter Points 631 5B. Distance of an Object by Two Bearings, Degrees 634 6. Distance of Visibility of Objects of different Heights 640 7. Conversion of Arc and Time 641 8. Conversion of Sidereal into Mean Solar Time 642 9. Conversion of Mean Solar into Sidereal Time 645 10. Local mean time of Sun's visible Rising and Setting 648 11. Reduction of Moon's Meridian Passage for Longitude 672 12. Reduction of Quantities from Nautical Almanac 673 13. Change of Sun's Right Ascension : 683 14. Dip of Sea Horizon 685 15. Dip at Distances short of Horizon 685 16. Parallax of Sun 685 17. Parallax of Planet 686 18. Augmentation of Moon's Semidiameter 687 19. Augmentation of Moon's Horizontal Parallax 687 20A. Mean Refraction 688 20B. Mean Refraction and Parallax of Sun 689 21 . Correction of Refraction for Barometer 690 22. Correction of Refraction for Thermometer 691 23. Mean Refraction and Mean Parallax of Moon 693 24. Mean Refraction and Parallax of Moon 693 25. Variation of Altitude due to change of Declination 702 26. Variation of Altitude in one minute from Meridian 704 27. Variation of Altitude in given time from Meridian 714 28A. 1 ^g^- [omitted. 28D. J 29. Nautical and Statute Miles 725 30. Conversion of Metric and English Linear Measure 726 31. Fahrenheit, Centigrade, and Reaumur Temperatures 727 32. True Force and Direction of Wind 728 33. Distance by Vertical Angle 729 34. Distance by Horizon Angle. 731 35. Speed Table for Measured Mile 732 36. Local Mean and Standard Meridian Times 733 fy-j^ jOmitted. 38. Error in Longitude produced by Error in Latitude 739 39. Amplitudes 740 40. Correction for Amplitude observed in Apparent Horizon 745 41. Natural Sines and Cosines 746 42. L^arithms of Numbers 755 43. Logarithms of Trigonometric Fimctions, Quarter Points 771 44. Ix^arithms of Trigonometric Functions, Degrees 772 45. Logarithmic and Natural Haversines 817 46. Consolidated table of Altitude Corrections 922 47. The Longitude Factor 938 48. The Latitude Factor 941 505 I EXPLANATION OF THE TABLES. TABLES 1, 2: TRAVERSE TABLES. Tables 1 and 2 were originally calculated by the natural sinea taken from the fourth edition of Sherwin's Logarithms, which were previously examined, by differences; when the proof sheets of the first edition were examined the numbers were again calculated by the natural sines in the second edition »f Button's Logarithms; and if any difference was found, the numbers were calculated a third time by Taylor's Logarithms. The first table contains the difference of latitude and departure corresponding to distances not exceeding 300 miles, and for courses to every quarter point of the compass. Table 2 is of the same nature, but for courses consisting of whole degrees; it was originally of the same extent as Table 1, but has been extended to include distances up to 600 miles. The manner of using these tables is particularly explained under the different problems of Plane, Middle Latitude, and Mercator Sailing in Chapter V. The tables may be employed in the solution of any right triangle. TABLE 3: MERIDIONAL PARTS. Thia table contains the meridional parts, or increased latitudes, for every degree and minute to 80°, calculated by the following formula: m in which =^ log tan ^45° + g^ J — a (e* sin L + J e* sm* L + ^ c« sin* L -f . . . 10800'' the Equatorial radius a = ^ = 3437'. 74677 (log 3.5362739); M, the modulus of common logarithms = 0.4342945; ^= 2.3025851 ( log 0.3622157 ) ; C, the compression or meridional eccentricity of the earth according to Clarke (1880) = ggg^ = 0.003407562 (log 7.5324437); from which e=s/2c — c' =0.0824846 (log 8.9163666); ^ = 7915^7044558 (log 3.8984895) ; a«» = 23^38871 (log 1.3690072); Jae* = 0^053042 (log 8.7246192) ; |ae«= 0^000216523 (log 6.3355038). The results are tabulated to one decimal place, which is sufficient for the ordinary problems of navigation. The practical application of this table is illustrated in Chapters II and V, in articles treating of the Mercator Chart and Mercator Sailing. TABLE 4: LENGTH OF DEGREES OF LATITTTDE AND LONGITXTDE. This table gives the length of a degree in both latitude and longitude at each parallel of latitude on the earth's surface, in nautical and statute miles and in meters, based upon Clarke's value (1866) of the earth's compression, "SqqT^" ^^ *^^® ^^^^ ^^ latitude, the length relates to an arc of which the given degree is the center. TABLES 5 A, 5B: DISTANCE BY TWO BEARINGS. These tables have been calculated to facilitate the operation of finding the distance from an object by two bearings from a given distance run and course. In Table 5A the arguments are given in points, in Table 5B in degrees; the first column contains the multiplier of the distance run to give the distance of observed object at second bearing; the second, at time of passing abeam. The method is explained in article 143, Chapter IV. 507 508 EXPLANATION OF THE TABLES. TABIiE 6: DISTANCE OF VISIBrLITT OF OBJECTS. This table contains the distances, in nautical and statute miles, at which any object is risible at sesL It is calculated by the formulae: _ _ * . d = 1, 15 ^x, and d' = 1.32 x/a;, in which d is the distance in nautical miles, d' the distance in statute miles, and x the height of the eye or the object in feet. To find the distance of visibility of an object, the distance given by the table corresponding to its height should be added to that corresponding to the height of the observer's eye. Example: Required the distance of visibility of an object 420 feet high, the observer being at an elevation of 15 feet. Dist. corresponding to 420 feet, 23.5 naut. miles. Dist. corresponding to 15 feet, 4.4 naut. miles. Dist. of visibility. 27.9 naut. miles. TABLE 7: CONVERSION OF ARC AND TIME. In the first column of each pair in this table are contained angular measures expressed in arc (degrees, minutes, or seconds), and in the second column the corresponding angles expressed in time (hours, minutes, or seconds). As will be seen from the headings of columns, the time corresponding to degrees (") is given in hours and minutes; to minutes of arc (''), in minutes and seconds of time; and to seconds of arc (''''), in seconds and sixtieths of a second of time. The table will be especially convenient in dealing with longitude and hour angle. The method of ite employment is best illustrated by examples. Example I. Required the time corresponding to 50° 31' 21''''. 50° 00' OO'' = 3" 20'° 00^ 31 00 = 2 04 21 = m 50 31 21 =3 22 05.4 Example II. Required the arc corresponding to &" 33° 6" 32" 00» = 98° 00' 00" 1 24 = 21 00 2#S= 37.6 26'.5. 6 33 26.5 = 21 37.5 TABLES 8 AND 9: SIDEREAL AND MEAN SOLAR TIMES. These tables give, respectively, the reductions necessary, to convert intervals of sidereal time into those of mean solar time, and intervals of mean solar into those of sidereal time. The reduction for any interval is found by entering with the number of hours at the top and the number of minutes at the side, adding the reduction for seconds aa given in the margin. The relations between mean solar and sidereal time intervals, and the methods of conversion of these times, are given in articles 289-291, Chapter IX. TABLE 10: SXTN'S RISING AND SETTING. This table gives the local mean time of the sun's visible rising and setting — that is, of the appearance and disappearance of the sun's upper limb in the unobstructed horizon of a person whose eye is 15 feet above the level of the earth's surface, the atmospheric conditions being normal. The local apparent times of rising and setting were determined from the formula for a time sight, the altitude employed being —0° 56' 08", made up of the following terms: Refraction, — 36' 29"; semi- diameter, - 16' 00"; dip, — 3' 48"; and parallax, + 9". To ascertain the time of rising or setting for any given date and place, enter the table with the latitude and declination, interpolating if the degrees are not even. In the line R will be found the time of rising; in the line S, the time of setting. Be careful to choose the page in which the latitude is of the correct name, and in which the "approximate date" corresponds, nearly or exactly, with the given date. This table is computed with the intention that, if accuracy is desired, it will be entered with the declination as an argument — not the date — as it is impossible to construct anv table based upon dates whose application shall be general to all years. But as a given degree of declination will, in the majority of years, fall upon the date given in the table as the "approximate date," and as, when it dops not do so, it can never be more than one day removed therefrom, it will answer, where a slight inaccuracy may be admitted, to enter the table with the date as an argument, thus avoiding the neces- sity of ascertaining the declination. Example: Find the local mean time of sunset at Rio de Janeiro, Brazil (lat. 22° 54' S., long. 43° 10' W.), on January 1, 1903 (dec. 23° 04' S.). Eacact method. Lat. 22° \ Dec. 23°; Corr. for + 54' lat . Corr. for -f 04' dec. &" 48- + 02 00 Approximate method. Lat. 22°.. -I January 2 j Corr. for + 64' lat +02 Corr. for 1 dav — 01 gh 48m L. M. T. sunset 6 50 L. M. T. sunset , 6 49 EXPLANATION OF THE TABLES. 509 TABLE 11: REDUCTION FOR MOON'S TRANSIT. This table was calculated by proportioning the daily variation of the time of the moon's passing the meridian. The numbers taken from the table are to be added to the Greenwich time of moon's txansit in west longitude, but subtracted in east longitude. TABLE 12: REDUCTIONS FOR NAUTICAL ALMANAC. This is a table of proportional parts for finding the variation of the sun' s right ascension or declination, or of the equation oftime, in any number of minutes of time, the horary motion being given at the top of the page in seconds, and the number of minutes of time in the side column; also for finding the variation of the moon's declination or right ascension in any number of seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. TABLE 13: CHANOE OF SUN'S RIGHT ASCENSION. This is a table that may be employed for finding the change of the sun's right ascension for any given number of hours, the hourly change, as taken from the Nautical Almanac, being gfiven in the marginal columns. TABLE 14: DIP OF SEA HORIZON. This table contains the dip of the sea horizon, calculated by the formula: in which F = height of the eye above the level of the sea in feet. It is explained in article 300, Chapter X. TABLE 16: DIP SHORT OF HORIZON. This table contains the dip for various distances and heights, calculated by the formula: D = ? d -f 0.56514 X K 7 a in which D represents the dip in miles or minutes, d, the distance of the land in sea miles, and h, the height of the eye of the observer in feet. TABLE 16: PARALLAX OF SUN. This table contains the sun's parallax in altitude calculated by the formula: par. = sin z X 8^.75, in which z = apparent zenith distance, the sun's horizontal parallax being S'^.TS. It is explained in article 304, Chapter X. TABLE 17: PARALLAX OF PLANET. Parallax in altitude of a planet is found by entering at the top with the planet's horizontal parallax, and at the side with the altitude. TABLE 18: AUGMENTATION OF MOON'S SEMIDIAMETER. This table gives the augmentation of the moon's semidiameter calculated by the formula: x = c 8* siD.h-\- ^ c^^ sin* ^ -f i c* »*, where ?i = moon's apparent altitude; 8 = moon's horizontal semidiameter; X = augmentation of semidiameter for altitude h; and log c = 5.25021. TABLE 10: AUGMENTATION OF MOON'S HORIZONTAL PARALLAX. This table contains the augmentation of the moon's horizontal parallax, or the correction to reduce the moon's equatorial horizontal parallax to ^hat point of the earth's axis which lies in the vertical of the observer m any given latitude; it is computed by the formulae: A'r = «r(6-1), ^ =,^(1 - e»8in« L)' where it = equatorial horizontal parallax; L= latitude; e = eccentricity of the meridian; log e* = 7.81602; and A Jf = augmentation of the horizontal parallax for the latitude li. 510 EXPLANATION OF THE TABLES. TABLE 20 A: MEAN REFRACTION. This table gives the refraction, reduced from Bessel's tables, for a mean atmospheric condition in which the barometer is 30.00 inches, and thermometer 50° Fahr. TABLE SOB: MEAN REFRACTION AND PARALLAX OF SUN. This table contains the correction to be applied to the sun's apparent altitude for mean refraction and parallax, being a combination of the quantities for the altitudes given in Tables 16 and 20A. TABLES 21, 22: CORRECTIONS OF REFRACTION FOR BAROMETER AND THERMOMETER. These are deduced from Bessel's tables. The method of their employment will be evident. TABLE 23: MEAN REFRACTION AND MEAN PARALLAX OF MOON. This table contains the correction of the moon's altitude for refraction and parallax corresponding to the mean refraction (Table 20A), and a horizontal parallax of the mean value of 57^ 30^^. TABLE 24: MEAN REFRACTION AND PARALLAX OF MOON. This table contains the correction to be applied to the moon's apparent altitude for each minute of horizontal parallax, and for every 10'' of altitude from 5°, with height of barometer 30.00 inches, and thermometer 50° Fahr. For seconds of parallax, enter the table abreast the approximate correction and find the seconds of horizontal parallax, the tens of seconds at the side and the units at the top. Under the latter and opposite the former will be the seconds to add to the correction. For minutes of altitude, take the seconds from the extreme right of the page, and apply them as there directed. TABLE 26: CHANGE OF ALTITUDE DUE TO CHANGE OF DECLINATION. This table gives the variation of the altitude of any heavenly body arising from a change of 100''' in the declination. It is useful for finding the equation of equal altitudes by the approximate method explained in article 324, Chapter XI, and for other purposes. If the change move the body toward the elevated pole, apply the correction to the altitude with the eigne in the table; otherwise change the signs. TABLE 26: CHANGE OF ALTITUDE IN ONE MINUTE FROM MERIDIAN. This table gives the variation of the altitude of any heavenly body, for one minute of time from meridian passage, for latitudes up to 60°, declinations to 63°, and altitudes between 6° and 86°. It is based upon the method set forth in article 334, Chapter XII, and the values may be computed by the formula: 1^^9635 cos L cos d ~ sin (L— d) where a = variation of altitude in one minute from meridian, L = latitude, and d = declination — positive for same name and negative for opposite name to latitude at upper transit, and negative for same name at lower transit. The limits of the table take in all values of latitude, declination, and altitude which are likely to be required. In its employment, care must be taken to enter the table at a place where the declination is appropriately named (of the same or opposite name to the latitude) ; it should also be noted that at the bottom of the last three pages values are given for the variation of a body at lower transit, which can only be observed when the declination and latitude are of the same name, and in which case the reduc- tion to the meridian is subtractive; the limitations in this case are stated at the foot of the page, and apply to all values below the heavy rules. TABLE 27: CHANGE OF ALTITUDE IN GIVEN TIME FROM MERIDIAN. This table gives the product of the variation in altitude in one minute of a heavenly body near the meridian, by the square of the number of minutes. Values are given for every half minute between 0" 30' and 26'" 0", and for all variations likely to be employed in the method of "reduction to the meridian." The formula for computing is: Red. = a X f^_ where a — variation in one minute (Table 26) , and t — number of minutes (in units and tenths) from time of meridian passage. The table is entered in the column of the nearest interval of time from meridian, and the value taken out corrresponding to the value of a found from Table 26. The units and tenths are picked out separately and combined, each being corrected by interpolation for intermediate intervals of time. The result is the amount to be applied to the observed altitude to reduce it to the meridian altitude, which is always to be added for upper transits and subtracted for lower. EXPLANATION OF THE TABLES. 511 TABLE 28, A, B, C, D: LATITUDE BY POLARIS. [Omitted.] TABLES 29, 30, 31: CONVEBSION TABLES. These are self-explanatory. TABLE 32: TB-UE FOBCE AND DIRECTION OF WIND. This table enables an observer on board of a moving vessel to determine the true force and direction of the wind from its apparent force and direction. Enter the table with the apparent direction of the wind (number of points on the bow) and force (Beaufort scale) as arguments, and pick out the direc- tion relatively to the ship's head and the force corresponding to the known speed of the ship. Example: A vessel steaming SE. at a speed of 15 knots appears to have a wind blowing from three points on the starboard bow with a force of 6, Beaufort scale. What is the true direction and force? In the column headed 3 (meaning three points on bow, apparent direction) and in the line 6 (apparent force, Beaufort scale), we find abreast 15 (knots, speed of vessel) that the true direction is 5 points on starboard bow, i. c, S. by W., and true force 4. TABLE 33: VERTICAL ANGLES. This table gives the distance of an object of known height by the vertical angle that it subtends at the position of the observer. It was computed by the formula: h tan <^ = ^> where a = the vertical angle; h = the height of the observed object in feet; and d = the distance of the object, also converted into feet. The employment of this method of finding distance is explained in article 139, chapter IV. TABLE 34: HORIZON ANGLES. This shows the distance in yards corresponding to any observed angle between an object and the sea horizon beyond, the observer being at a known height. The method of use is explained in article 139, chapter IV. TABLE 35: SPEED TABLE. k This table shows the rate of speed, in nautical miles per hour, of a vessel which traverses a measured mile in any given number of minutes and seconds. It is entered with the number of minutes at the top and the number of seconds at the side; under one and abreast the other is the number of knots of speed- 512 EXPLANATION OF THE TABLES. TABLE 36: LOCAL AND STANDARD TIMES. This table contains the reduction to be applied to the local time to obtain the corresponding time at any other meridian whose time is adopted as a standard. The results are given to the nearest minute of time only; being intended for the reduction of such approximate quantities as the time of high water or time of sunset. More exact reductions, when required, may be made by Table 7. TABLE 37: LOGARITHMS FOR EQUAL ALTITUDE SIGHTS. [OlOTTBD.] TABLE 37A: EQUATION OF EQUAL ALTITUDES NEAR NOON. [Omitted.] I EXPLANATION OF THE TABLES. 513 TABLE 38: EFFECT UPON LONGITUDE OF EBBOB IN LATITUDE. Table 38 shows, approximately, the error in longitude in miles and tenths of a mile, occasioned by an error of one mile in the latitude. Thus, when the sun's altitude is 30°, the latitude 30°, and the polar distance 100°, the error is eight- tenths of a mile. The effect of an increase of latitude is as follows: In West longitude, / East "1 of meridian, the f decreased \ except where marked f increased "1 the body being \ West ) longitude is \ increased j ' by *, when it is \ decreased ) ' In East longitude, / East "I of meridian, the f increased ) except where marked / decreased \ the body being \ West J longitude is \ decreased / ' by *, when it is \ increased / " A deo'ease of latitude has the contrary effect. The direction of error may readily be seen by drawing the Sumner line in a direction at right angles to the approximate bearing oi the body. TABLE 30: AMPLITUDES. This table contains amplitudes of heavenly bodies, at rising and setting, for various latitudes and declinations, computed by the formula: sin amp.=8ec Lat Xsin dec. It is entered with the declination at the top and the latitude at the side. Its use is explained in article 358, Chapter XIV. TABLE 40: COBBECTION FOB AMPLITUDES. This table gives a correction to be applied to the observed amplitude to counteract the vertical displacement due to refraction, parallax, and dip, when the body is observed with its center in the visible horizon. The correction is to be applied for the sun, a planet, or a star, as follows: "^^ tSginl. ^t }^PP»y ^b« '^o"^*^^" t° ^^« "g^*- ^^^ttlnl/nl: i2t }*ppiy *h« «*>"««««° ^ *^« i«^*- For the moon, apply half the correction in the contrary manner. TABLE 41: NATUBAL SINES AND COSINES. This table contains the natural sine and cosine for every minute of the quadrant, and is to be entered at the top or bottom with the degrees, and at the side marked M., with the minutes; the corresponding numbers will be the natural sine and cosine, respectively, observing that if the degrees are found at the top, the name sine, cosine, and M. must also be found at the top, and the contrary if the degrees are found at the bottom. It should be understood that all numbers given in the table should be divided by 100,000 — that is, pointed off to contain five decimal places. Thus, .43366 is the natural sine of 25° 42'', or the cosine of 64° 18'. In the outer columns of the margin are given tables of proportional parts, for the purpose of finding, approximately, by inspection, the proportional part corresponding to any number of seconds in the proposed angle, the seconds being found in the marginal column marked M., and the correction in the adjoining column. Thus, if we suppose that it were required to find tlie natural sine corresponding to 25° 42' W^, the difference of the sines of 25° 42' and 25° 43' is 26, being the same as at the top of the left-hand column of the table; and in this column, and opposite 19 in the column M., is the correc- tion 8. Adding this to the above number .43366, because the numbers are increasing, we get .43374 for the sine of 25° 42' 19". In like manner, we find the cosine of the same angle to be .90108— 4=. 90104, using the right-hand columns, and subtracting hecauae the numbers are decreasing; observing, however, that the number 14 at the top of this column varies 1 from the difference between the cosines of 25° 42' and 25° 43', which is only 13; so that the table may give in some cases a unit too much between the angles 25° 42' and 25° 43'; but this is, in general, of but little importance, and when accuracy is required, the usual method of proportional parts is to be resorted to, using the actual tabular difference. TABLE 42: LOGABITHMS OP NUMBEBS. This table, containing the common logarithms of numbers, was compared with Sherwin's, Hutton's, and Taylor's logarithms; its use is explained in an article on Logarithms in Appendix III. TABLE 43: LOGABITHMS OF TBIGONOMETBIC FUNCTIONS, QUABTEB POINTS. This table contains the logarithms of the sines, tangents, etc., corresponding to points and quarter points of the compass. This was compared with Sherwin's, Hutton's, and Taylor's logarithms. 21594°— 14 26 514 EXPLANATION OF THE TABLES. TABLE 44: LOaARITHMS OF TRIGONOMETRIC FUNCTIONS, DEGREES. This table contains the common logarithms of the sines, tangents, secants, etc. It was compared with Sherwin's, Hutton's, and Taylor's tables. Two additional columns are given in this table, which are very convenient in finding the time from an altitude of the sun; also, three columns of proportional parts for seconds of space, and a small table at the bottom of each page for finding the proportional parts for seconds of time. The degrees are marked to 180°, which saves the trouble of subtracting the given angle from 180° when it exceeds 90°. The use of this table is fully explained in Appendix III in an article on Logarithms. TABLE 45: LOGARITHMIC AND NATURAL HAVERSINES. The haversine is defined by the following relation: hav. A=^ vers. A=K1— cos A)=sin2 ^A. It is a trigonometric function which simplifies the solution of many problems in nautical astronomy as well as in plane trigonometry. To afford the maximum facility in carrying out the processes of solution, the values of the natural haversine and its logarithm are set down together in a single table for all values of angle ranging from 0° to 360°, expressed both in arc and in time. TABLE 46: CORRECTIONS TO BE APPLIED IN ORDER TO FIND THE TRUE ALTI- TUDE OF A STAR AND ALSO OF THE SUN FROM THE OBSERVED ALTITUDE ABOVE THE HORIZON. This is a consolidated table in which the tabulated correction for an observed altitude of a star combines the mean refraction and the dip, and that for an observed altitude of the sun's lower limb combines the mean refraction, the dip, the parallax, and the mean semidiameter, which is taken as 16''. A supplementary table at the foot of the main table takes account of the variation of the sun's semidiameter in the different months of the year. TABLE 47: THE LONGITUDE FACTOR. The change in longitude due to a change of V in latitude, called the longitude factor, F, is given in this table at suitable intervals of latitude and azimuth. The quantities tabulated are computed from the formula — F=sec. Lat. Xcot. Az. When a time sight is solved with a dead-reckoning latitude, the resulting longitude is only true if the latitude be correct. This table, by setting forth the number of minutes of longitude due to each minute of error in latitude, gives the means of finding the correction to the longitude for any error that may subsequently be disclosed in the latitude used in the calculation. Regarding the azimuth of the observed celestial body as less than 90° and as measured from either the North or the South point of the horizon towards East or West, the rule for determining whether the correction in longitude is to be applied to the eastward or to the westward will be as follows: If the change in latitude is of the same name as the first letter of the bearing, the change in longitude is of the contrary name to that of the second letter, and vice versa. Thus, if the body bears S. 45° E. and the change in latitude is to the southward, the change in longitude will be to the westward; and, if the change in latitude is to the northward, the change in longitude will be to the eastward. The convenient application of the longitude factor in finding the intersection of Sumner lines is explained in article 389. TABLE 48: THE LATITUDE FACTOR. The change in latitude due to a change of V in the longitude, called the latitude factor, f, is given in this table at suitable intervals of latitude and azimuth. The quantities tabulated, being the reciprocals of the values of the longitude factor, are computed from the formula — ^=F=sec. Lat.Xcot.Az.==^««- Lat.Xtan. Az. When an ex-meridian sight is solved with a longitude afterwards found to be in error, this table, by setting forth the number of minutes of latitude due to each V of error in longitude, gives the means of finding the correction in the latitude for the amount of error in the longitude used in the calculation. Regarding the azimuth of the observed celestial body as less than 90° and as measured from either tiie North or the South point of the horizon towards East or West, the rule for determining whether the correction in latitude is to be applied to the northward or to the southward is as follows: If the change in longitude ia of the same name as the second letter of the bearing, the change in latitude is of the contrary name to the first letter, and vice versa. Thus, if the body bears S. 14° E. and the change in longitude ia to the westward, the change in latitude will be to the southward, and, if the change in longitude is to the eastward, the change in latitude will be to the northward. The convenient application of the latitude factor in finding the intersection of Sumner lines is explained in article 390. TABLE 1. [Page 516 | Difference of Latitude and Departure for J Point. N. JE. N. i W. S. iE. S. \W. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.0 61 60.9 3.0 121 120.9 5.9 181 180,8 8.9 241 240.7 11,8 2 2.0 0.1 62 61.9 3.0 22 121.9 6.0 82 181.8 8.9 42 241.7 11.9 3 3.0 0.1 63 62.9 3.1 23 122.9 6.0 83 182.8 9.0 43 242.7 11.9 4 4.0 0.2 64 63.9 3.1 24 123.9 6.1 84 183.8 9.0 44 243.7 12.0 5 5.0 0.2 65 64.9 3.2 25 124.8 6.1 85 184.8 9.1 45 244.7 12.0 6 6,0 0.3 66 65.9 3.2 26 125.8 6.2 86 185.8 9.1 46 245.7 12.1 7 7.0 0.3 67 66.9 3.3 27 126.8 6.2 87 186.8 9.2 47 246.7 12.1 8 8.0 0.4 68 67.9 3.3 28 127.8 6.3 88 187.8 9.2 48 247.7 12.2 9 9.0 0.4 69 68.9 3.4 29 128.8 6.3 89 188.8 9.3 49 248.7 12.2 10 10.0 0.5 70 69.9 3.4 30 129.8 6.4 90 189.8 9.3 50 249.7 250.7 12.3 11 11.0 0.5 71 70.9 3.5 131 130.8 6.4 191 190.8 9.4 251 12.3 12 12.0 0.6 72 71.9 3.5 32 131.8 6.5 92 191.8 9.4 52 251.7 12,4 13 13.0 0.6 73 72.9 3.6 33 132.8 6,5 93 192.8 9.5 53 252.7 12,4 14 14.0 0.7 74 73.9 3.6 34 133.8 6.6 94 193.8 9.5 54 253.7 12,5 15 15.0 0.7 75 74.9 3.7 35 134.8 6.6 95 194.8 9.6 55 254.7 12.5 16 16.0 0.8 76 75.9 3.7 36 135.8 6.7 96 195.8 9.6 56 255.7 12.6 17 17.0 0.8 77 76.9 3.8 37 136.8 6.7 97 196.8 9.7 57 256.7 12.6 18 18.0 0.9 78 77.9 3.8 38 137.8 6.8 98 197.8 9.7 58 257.7 12.7 19 19.0 0.9 79 78.9 3.9 39 138.8 6.8 99 198.8 9.8 59 258.7 12.7 20 20.0 1.0 80 79.9 80.9 3.9 4.0 40 141 139.8 6.9 200 199.8 9.8 60 259.7 260.7 12.8 12.8 21 21.0 1.0 81 140.8 6.9 201 200.8 y.9 261 22 22.0 1.1 82 81.9 4.0 42 141.8 7.0 02 201.8 9.9 62 261.7 12.9 23 23.0 1.1 83 82.9 4.1 43 142.8 7.0 03 202.8 10.0 63 262.7 12.9 24 24.0 1.2 84 83.9 4.1 44 143.8 7.1 04 20.3.8 10.0 64 263. 7 13.0 25 25.0 1.2 85 84.9 4.2 45 144.8 7.1 05 204.8 10.1 65 264.7 13.0 26 26.0 1.3 86 85.9 4.2 46 145.8 7.2 06 205.8 10.1 66 265.7 1.3.1 27 27.0 1.3 87 86.9 4.3 47 146.8 7.2 07 206.8 10.2 67 266.7 13.1 28 28.0 1.4 88 87.9 4.3 48 147.8 7.3 08 207.7 10.2 68 267.7 13.2 29 29.0 1.4 89 88.9 4.4 49 148.8 7.3 09 208.7 10.3 69 268.7 13.2 30 31 30.0 31.0 1.5 90 89.9 4.4 50 149.8 7.4 7.4 10 209.7 10.3 70 269.7 13,2 1.5 91 90.9 4.5 151 150.8 211 210.7 10.4 271 270.7 13,3 32 32.0. 1.6 92 91.9 4.5 52 151.8 7.5 12 211.7 10.4 72 271.7 13,3 33 33.0 1.6 93 92.9 4,6 53 152.8 7.5 13 212.7 10.5 73 272.7 13,4 34 34.0 1.7 94 93.9 4.6 54 153.8 7.6 14 213.7 10.5 74 273. 7 13.4 35 35.0 1.7 95 94.9 4.7 55 154.8 7,6 15 214.7 10.5 75 274. 7 13.5 36 36.0 1.8 96 95.9 4,7 56 155.8 7.7 16 215.7 10.6 76 275. 7 13.5 37 37.0 1.8 97 96.9 4,8 57 156.8 7,7 17 216.7 10.6 77 276.7 13.6 38 38.0 1.9 98 97.9 4.8 58 157.8 7,8 18 217.7 10.7 78 277.7 13.6 39 39.0 1.9 99 98.9 4.9 59 158.8 7.8 19 218.7 10.7 79 278.7 13.7 40 40.0 2.0 100 99.9 4,9 60 159.8 7.9 20 219.7 10.8 80 279.7 280.7 13.7 41 41.0 2.0 101 100.9 5,0 161 160.8 7.9 221 220.7 10.8 281 13.8 42 41.9 2.1 02 101.9 5,0 62 161.8 7.9 22 221.7 10.9 82 281.7 13.8 43 42.9 2.1 03 102.9 5,1 63 162.8 8.0 23 222.7 10.9 83 282.7 13.9 44 43.9 2.2 04 103.9 5.1 64 163.8 8.0 24 223.7 11.0 84 283.7 13.9 45 44.9 2.2 05 104.9 5.2 65 164.8 8.1 25 224.7 11.0 85 284.7 14.0 46 45.9 2.3 06 105.9 5.2 66 165.8 8.1 26 225. 7 11.1 86 285.7 14.0 47 46.9 2.3 07 106.9 5.3 67 166.8 8.2 27 226.7 11.1 87 286.7 14.1 48 47.9 2.4 08 107.9 5.3 68 167.8 8.2 28 227.7 11.2 88 287.7 14.1 49 48.9 2.4 09 108.9 5.3 69 168.8 8.3 29 228.7 11.2 89 288.7 14.2 50 49.9 2.5 10 109.9 5.4 70 169.8 8.3 30 229.7 11.3 90 289.7 14.2 51 50.9 2.5 111 110.9 5.4 171 170.8 8.4 231 230.7 11.3 291 290.6 14.3 52 51.9 2.6 12 111.9 5.5 72 171.8 8.4 32 231. 7 11.4 92 291.6 14.3 53 52.9 2.6 13 112.9 5.5 73 172.8 8.5 33 232.7 11.4 93 292.6 14.4 54 53.9 2.6 14 113.9 5.6 74 173.8 8.5 34 233. 7 11.5 94 293.6 14.4 55 54.9 2.7 15 114.9 5.6 75 174.8 8.6 35 234.7 11.5 95 294.6 14.5 56 55.9 2.7 16 115.9 5.7 76 175. 8 8.6 36 235.7 11.6 96 295. 6 14.5 57 56.9 2.8 17 116.9 5.7 77 176.8 8.7 37 236,7 11.6 97 296.6 14.6 58 57.9 2.8 18 117.9 5.8 78 177.8 8.7 38 237,7 11.7 98 297.6 14.6 59 58.9 2.9 19 118.9 5.8 79 178.8 8.8 39 238,7 11.7 99 298.6 14.7 60 59.9 2.9 20 119.9 5.9 80 179.8 8.8 40 239.7 11.8 300 299.6 14.7 Dist. Dep. Lat. Dist. Dep. I^t. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. E. iN. E. iS W. iN. W. \ S, [Fc )r 7i Po ints. Page 616] TABLE 1. Difference of Latitude and Depart ure for J Point. N. JE. N. ^W. S. iE. S. i w. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.1 61 60.7 6.0 121 120.4 11.9 181 180.1 17.7 241 239.8 23.6 2 2.0 0.2 62 61.7 6.1 22 121.4 12.0 82 181.1 17.8 42 240.8 23.7 3 3.0 0.3 63 62.7 6.2 23 122.4 12.1 83 182.1 17.9 43 241.8 23.8 4 - 4.0 0.4 64 63.7 6.3 24 123.4 12.2 84 183.1 18.0 44 242.8 23.9 5 5.0 0.5 65 64.7 6.4 25 124.4 12.3 85 184.1 18.1 45 243.8 24.0 6 6.0 0.6 66 65.7 6.5 26 125.4 12.4 86 185.1 18.2 46 244.8 24.1 7 7.0 0.7 67 66.7 6.6 27 126.4 12.4 87 186.1 18.3 47 245.8 24.2 8 8.0 0.8 68 67.7 6.7 28 127.4 12.5 88 187.1 18.4 48 246.8 24.3 9 9.0 0.9 69 68.7 6.8 29 128.4 12.6 89 188.1 18.5 49 247.8 24.4 10 10.0 1.0 1.1 70 71 69.7 70.7 6.9 30 129.4 12.7 90 189.1 18.6 50 248.8 24.5 11 10.9 7.0 131 130.4 12.8 191 190.1 18.7 251 249.8 24.6 12 11.9 1.2 72 71.7 7.1 32 131.4 12.9 92 191.1 18.8 52 250.8 24.7 13 12.9 1.3 73 72.6 7.2 33 132.4 13.0 93 192.1 18.9 53 251. 8 24.8 14 13.9 1.4 74 73.6 7.3 34 133.4 13.1 94 193.1 19.0 54 252.8 24.9 15 14.9 1.5 75 74.6 7.4 35 134.3 13.2 95 194.1 19.1 55 253.8 25.0 16 15.9 1.6 76 75.6 7.4 36 135.3 13.3 96 195.1 19.2 56 254.8 25.1 17 16.9 1.7 77 76.6 7.5 37 136.3 13.4 97 196.1 19.3 57 255.8 25.2 18 17.9 1.8 78 77.6 7.6 38 137.3 13.5 98 197.0 19.4 58 256.8 25.3 19 18.9 1.9 79 78.6 7.7 39 138.3 13.6 99 198.0 19.5 59 257.8 25.4 20 19.9 2.0 80 79.6 7.8 40 139.3 13.7 200 199.0 19.6 60 258.7 25.5 21 20.9 2.1 81 80.6 7.9 141 140.3 13.8 201 200.0 19.7 261 259.7 25.6 22 21.9 2.2 82 81.6 8.0 42 141.3 13.9 02 201.0 19.8 62 260.7 25.7 23 22.9 2.3 83 82.6 8.1 43 142.3 14.0 03 202.0 19.9 63 261.7 25.8 24 23.9 2.4 84 83.6 8.2 44 143.3 14.1 04 203.0 20.0 64 262.7 25.9 25 24.9 2.5 85 84.6 8.3 45 144.3 14.2 05 204.0 20.1 65 263.7 26.0 26 25.9 2.5 86 85.6 8.4 46 145.3 14.3 06 205.0 20.2 66 264.7 26.1 27 26.9 2.6 87 86.6 8.5 47 146.3 14.4 07 206.0 20.3 67 265.7 26.2 28 27.9 2.7 88 87.6 8.6 48 147.3 14.5 08 207.0 20.4 68 266.7 26.3 29 28.9 2.8 89 88.6 8.7 49 148. 3 14.6 09 208.0 20.5 69 267.7 26.4 30 29.9 2.9 90 89.6 90.6 8.8 50 149.3 14.7 10 209.0 20.6 70 268.7 26.5 31 30.9 3.0 91 8.9 151 150.3 14.8 211 210.0 20.7 271 269.7 26.6 32 31.8 3.1 92 91.6 9.0 52 151.3 14.9 12 211.0 20.8 72 270.7 26.7 33 32.8 3.2 93 92.6 9.1 53 152.3 15.0 13 212.0 20.9 73 271.7 26.8 34 33.8 3.3 94 93.5 9.2 54 153.3 15.1 14 213.0 21.0 74 272.7 26.9 35 34.8 3.4 95 94.5 9.3 55 154.3 15.2 15 214.0 21.1 75 273.7 27.0 36 35.8 3.5 96 95.5 9.4 56 155.2 15.3 16 215.0 21.2 76 274.7 27.1 37 36.8 3.6 97 96.5 9.5 57 156.2 15.4 17 216.0 21.3 77 275.7 27.2 38 37.8 3.7 98 97.5 9.6 58 157.2 15.5 18 217.0 21.4 78 276.7 27.2 39 38.8 3.8 99 98.5 9.7 59 158.2 15.6 19 217.9 21.5 79 277.7 27.3 40 39.8 3.9 100 99.5 9,8 60 159.2 15.7 20 218.9 21.6 80 278.7 27.4 41 40.8 4.0 101 100.5 9.9 161 160.2 15.8 221 219.9 21.7 281 279.6 27.5 42 41.8 4.1 02 101.5 10.0 62 161.2 15.9 22 220.9 21.8 82 280.6 27.6 43 42.8 4.2 03 102.5 10.1 63 162.2 16.0 23 221.9 21.9 83 281.6 27.7 44 43.8 4.3 04 103.5 10.2 64 163.2 16.1 24 222.9 22.0 84 282.6 27.8 45 44.8 4.4 05 104.5 10.3 65 164.2 16.2 25 223.9 22.1 85 283.6 27.9 46 45.8 4.5 06 105.5 10.4 66 165.2 16.3 26 224.9 22.2 86 284.6 28.0 47 46.8 4.6 07 106.5 10.5 67 166.2 16.4 27 225.9 22.2 87 285.6 28.1 48 47.8 4.7 08 107.5 10.6 68 167.2 16.5 28 226.9 22.3 88 286.6 28.2 49 48.8 4.8 09. 108.5 10.7 69 168.2 16.6 29 227.9 22.4 89 287.6 28.3 50 49.8 4.9 10 109.5 10.8 70 169.2 16.7 30 228.9 22.5 90 288.6 28.4 28.5 51 50.8 5.0 111 110.5 10.9 171 170.2 16.8 231 229.9 22.6 291 289.6 52 51.7 5.1 12 111.5 11.0 72 171.2 16.9 32 230.9 22.7 92 290.6 28.6 53 52.7 5.2 13 112.5 11.1 73 172.2 17.0 33 231.9 22.8 93 291.6 28.7 54 53.7 5.3 14 113.5 11.2 74 173.2 17.1 34 232.9 22.9 94 292.6 28.8 55 54.7 5.4 15 114.4 11.3 75 174.2 17.2 35 233.9 23.0 95 293.6 28.9 56 55.7 5.5 16 115.4 11.4 76 175.2 17.3 36 234.9 23.1 96 294.6 29.0 57 56.7 5.6 17 116.4 11.5 77 176.1 17.3 37 235.9 23.2 97 295.6 ,29.1 58 57.7 5.7 18 117.4 11.6 78 177.1 17.4 38 236.9 23.3 98 296.6 29.2 59 58.7 5.8 19 118.4 11.7 79 178.1 17.5 39 237.8 23.4 99 297.6 29.3 60 59.7 5.9 20 119.4 11.8 80 179.1 17.6 40 238.8 23.5 300 298.6 29.4 Dist. Dep. Lat. Di8t. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. E. JN. E. JS. W. JN WJS. "liv )r 7i Po nts. TABLE 1. [Page 617 Difference of Latitude and Departure for J Point. ^T. }E. N. |W • S. 1 E. S. fW Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.1 61 60.3 9.0 121 119.7 17.8 181 179.0 26.6 241 238.4 35.4 2 2.0 0.3 62 61.3 9.1 22 120.7 17.9 82 180.0 26.7 42 239.4 35.5 3 3.0 0.4 63 62.3 9.2 23 121.7 18.0 83 181.0 26.9 43 240.4 35.7 4 4.0 0.6 64 63.3 9.4 24 122.7 18.2 84 182.0 27.0 44 241.4 35.8 5 4.9 0.7 65 64.3 9.5 25 123.6 18.3 85 183.0 27.1 45 242.3 35.9 6 5.9 0.9 66 65.3 9.7 26 124.6 18.5 86 184.0 27.3 46 243.3 36.1 7 6.9 1.0 67 66.3 9.8 27 125.6 18.6 87 185.0 27.4 47 244.3 36.2 8 7.9 1.2 68 67.3 10.0 28 126.6 18.8 88 186.0 27.6 48 245.3 36.4 9 8.9 1.3 69 68.3 10.1 29 127.6 18.9 89 187.0 27.7 49 246.3 36.5 10 9.9 1.5 1.6 70 71 69.2 10.3 30 128.6 19.1 90 187.9 27.9 50 247.3 36.7 11 10.9 70.2 10.4 131 129.6 19.2 191 188.9 28.0 251 248.3 36.8 12 11.9 1.8 72 71.2 10.6 32 130.6 19.4 92 189.9 28.2 52 249.3 37.0 13 12.9 1.9 73 72.2 10.7 33 131.6 19.5 93 190.9 28.3 53 250.3 37.1 14 13.8 2.1 74 73.2 10.9 34 132.5 19.7 94 191.9 28.5 54 251.3 37.3 15 14.8 2.2 75 74.2 11.0 35 133.5 19.8 95 192.9 28.6 55 252.2 37.4 16 15.8 2.3 76 75.2 11.2 36 134.5 20.0 96 193.9 28.8 .16 253.2 37.6 17 16.8 2.5 77 76.2 11.3 37 135.5 20.1 97 194.9 28.9 57 254.2 37.7 18 17.8 2.6 78 77.2 11.4 38 136.5 20.2 98 195.9 29.1 58 255.2 37.9 19 18.8 2.8 79 78.1 11.6 39 137. 5 20.4 99 196.8 29.2 59 256.2 38.0 20 19.8 2.9 80 79.1 11.7 40 138.5 20.5 200 197.8 29.3 60 257.2 38.1 21 20.8 3.1 81 80.1 11.9 "141 139.5 20.7 201 198.8 29.5 261 258.2 38.3 22 21.8 3.2 82 81.1 12.0 42 140.5 20.8 02 199.8 29.6 62 259.2 38.4 23 22.8 3.4 83 82.1 12.2 43 141.5 21.0 03 200.8 29.8 63 260.2 38.6 24 23.7 3.5 84 83.1 12.3 44 142.4 21.1 04 201.8 29.9 64 261.1 38.7 25 24.7 3.7 85 84.1 12.5 45 143.4 21.3 05 202.8 30.1 65 262.1 38.9 26 25.7 3.8 86 85.1 12.6 46 144.4 21.4 06 203.8 30.2 66 263.1 39.0 27 26.7 4.0 87 86.1 12.8 47 145.4 21.6 07 204.8 30.4 67 264.1 39.2 28 27.7 4.1 88 87.0 12.9 48 146.4 21.7 08 205.7 30.5 68 265.1 39.3 29 28.7 4.3 89 88.0 13.1 49 147.4 21.9 09 206.7 30.7 69 266.1 39.6 30 29.7 4.4 4.5 90 91 89.0 13.2 50 148.4 22.0 10 207.7 30.8 70 267.1 39.6 39.8 31 30.7 90.0 13.4 151 149.4 22.2 211 208.7 31.0 271 268.1 32 31.7 4.7 92 91.0 13.5 52 150.4 22.3 12 209.7 31.1 72 269.1 39.9 33 32.6 4.8 93 92.0 13.6 53 151.3 22.4 13 210.7 31.3 73 270.0 40.1 34 33.6 5.0 94 93.0 13.8 54 152.3 22.6 14 211.7 31.4 74 271.0 40.2 35 34.6 5.1 95 94.0 13.9 55 153.3 22.7 15 212.7 31.5 75 272.0 40.4 36 35.6 5.3 96 95.0 14.1 56 154.3 22.9 16 213.7 31.7 76 273.0 40.5 37 36.6 5.4 97 96.0 14.2 57 155.3 23.0 17 214.7 31.8 77 274.0 40.6 38 37.6 5.6 98 96.9 14.4 58 156.3 23.2 18 215.6 32.0 78 275. 40.8 39 38.6 5.7 99 97.9 14.5 59 157.3 23.3 19 216.6 32.1 79 276.0 40.9 40 39.6 5.9 100 98.9 14.7 60 158.3 23.5 20 1 217.6 32.3 80 277.0 278.0 41.1 41 40.6 6.0 101 99.9 14.8 161 159.3 23.6 221 218.6 32.4 281 41.2 42 41.5 6.2 02 100.9 15.0 62 160.2 23.8 22 219.6 32.6 82 278.9 41.4 43 42.5 6.3 03 101.9 15.1 63 161.2 23.9 23 220.6 32.7 83 279.9 41.5 44 43.5 6.5 04 102.9 15.3 64 162.2 24.1 24 221.6 32.9 84 280.9 41.7 45 44.5 6.6 05 103.9 15.4 65 163.2 24.2 25 222.6 33.0 85 281.9 41.8 46 45.5 6.7 06 104.9 15.6 66 164.2 24.4 26 223.6 33.2 86 282.9 42.0 47 46.5 6.9 07 105.8 15.7 67 165.2 24.5 27 224.5 33.3 87 283.9 42,1 48 47.5 7.0 08 106.8 15.8 68 166.2 24.7 28 225.5 33.5 88 284.9 42.3 49 48.5 7.2 09 107.8 16.0 69 167.2 24.8 29 226.5 33.6 89 285.9 42.4 50 49.5 7.3 10 108.8 16.1 70 168.2 24.9 30 227.5 33.7 33.9 90 286.9 42.6 51 50.4 7.5 111 109.8 16.3 171 169.1 25.1 231 228.5 291 287.9 42.7 52 51.4 7.6 12 110.8 16.4 72 170.1 25.2 32 229.5 34.0 92 288.8 42.8 53 52.4 7.8 13 111.8 16.6 73 171.1 25.4 33 230.5 34.2 93 289.8 43.0 54 53.4 7.9 14 112.8 16.7 74 172.1 25.5 34 231.5 34.3 94 290.8 43.1 55 54.4 8.1 15 113.8 16.9 75 173.1 25.7 35 232.5 34.5 95 291.8 43.3 56 55.4 8.2 16 114.7 17.0 76 174.1 25.8 36 233.4 34.6 96 292.8 43.4 57 56.4 8.4 17 115.7 17.2 77 175.1 26.0 37 234.4 34.8 97 293.8 43.6 58 57.4 8.5 18 116.7 17.3 78 176.1 26.1 38 235.4 34.9 98 294.8 43.7 59 58.4 8.7 19 117.7 17.5 79 177.1 26.3 39 236. 4 35.1 99 295.8 43.9 60 59.4 8.8 20 118.7 17.6 80 178.1 26.4 40 237.4 35.2 300 296.8 44.0 Dist Dep. L«t. Dist. Dep. Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. E. JN E. |S. W. JN. W. |S [For 7k V ointa. Page 618] TABLE 1. Difference of Latitude and Departure for 1 Point . N. byE N. by w. S. by E. 3. by w. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.2 61 59.8 11.9 121 118.7 23.6 181 177.5 35.3 241 236.4 47.0 2 2.0 0.4 62 60.8 12.1 22 119.7 23.8 82 178.5 35.5 42 237.4 47.2 3 2.9 0.6 63 61.8 12.3 23 120.6 24.0 83 179.5 35.7 43 238.3 47.4 4 3.9 0.8 64 62.8 12.5 24 121.6 24.2 84 180.5 35.9 44 239.3 47.6 5 4.9 1.0 65 63.8 12.7 25 122.6 24.4 85 181.4 36.1 45 240.3 47.8 6 5.9 1.2 66 64.7 12.9 26 123.6 24.6 86 182.4 36.3 46 241.3 48.0 7 6.9 1.4 67 65.7 13.1 27 124.6 24.8 87 183.4 36.5 47 242.3 48.2 8 7.8 1.6 68 66.7 13.3 28 125.5 25.0 88 184.4 36.7 48 243.2 48.4 9 8.8 1.8 69 67.7 13.5 29 126.5 25.2 89 185.4 36.9 49 244.2 48.6 10 9.8 2.0 70 68.7 13.7 30 127.5 25.4 90 186.3 37.1 50 245.2 48.8 49.0 11 10.8 2.1 71 69.6 13.9 131 128.5 25.6 191 187.3 37.3 251 246.2 12 11.8 2.3 72 70.6 14.0 32 129.5 25.8 92 188.3 37.5 52 247.2 49.2 13 12.8 2.5 73 71.6 14.2 33 130.4 25.9 93 189.3 37.7 53 248.1 49.4 14 13.7 2.7 74 72.6 14.4 34 131.4 26.1 94 190.3 37.8 54 249.1 49.6 15 14.7 2.9 75 73.6 14.6 35 132.4 26.3 95 191.3 38.0 55 250.1 49.7 16 15.7 3.1 76 74.5 14.8 36 133.4 26.5 96 192.2 38.2 56 251.1 49.9 17 16.7 3.3 77 75.5 15.0 37 134.4 26.7 97 193.2 38.4 57 252.1 50.1 18 17.7 3.5 78 76.5 15.2 38 135.3 26.9 98 194.2 38.6 58 253.0 50.3 19 18.6 3.7 79 77.5 15.4 39 136.3 27.1 99 195.2 38.8 59 254.0 50.5 20 19.6 3.9 80 78.5 15.6 40 137.3 27.3 200 196.2 39.0 60 255.0 50.7 21 20.6 4.1 81 79.4 15.8 141 138.3 27.5 201 197.1 39.2 261 256.0 50.9 22 21.6 4.3 82 80.4 16.0 42 139.3 27.7 02 198.1 39.4 62 257.0 51.1 23 22.6 4.5 83 81.4 16.2 43 140.3 27.9 03 199.1 39.6 63 257.9 51.3 24 23.5 4.7 84 82.4 16.4 44 141.2 28.1 04 200.1 39.8 64 258.9 51.5 25 24.5 4.9 85 83.4 16.6 45 142.2 28.3 05 201.1 40.0 65 259.9 51.7 26 25.5 5.1 86 84.3 16.8 46 143.2 28.5 06 202.0 40.2 66 260.9 51.9 27 26.5 5.3 87 85.3 17.0 47 144.2 28.7 07 203.0 40.4 67 261.9 52.1 28 27.5 5.5 88 86.3 17.2 48 145.2 28.9 08 204.0 40.6 68 262.9 52.3 29 28.4 5.7 89 87.3 17.4 49 146.1 29.1 09 205.0 40.8 69 263.8 52.5 30 29.4 5.9 90 88.3 17.6 50 147.1 29.3 10 206.0 206.9 41.0 70 264.8 52.7 31 30.4 6.0 91 89.3 17.8 151 148.1 29.5 211 41,2 271 265.8 52.9 32 31.4 6.2 92 90.2 17.9 52 149.1 29.7 12 207.9 41.4 72 266.8 53.1 33 32.4 6.4 93 91.2 18.1 53 150.1 29.8 13 208.9 41.6 73 267.8 53.3 34 33.3 6.6 94 92.2 18.3 54 151.0 30.0 14 209.9 41.7 74 268.7 53.5 35 34.3 6.8 95 93.2 18.5 55 152.0 30.2 15 210.9 41.9 75 269.7 53.6 36 35.3 7.0 96 94.2 18.7 56 153.0 30.4 16 211.8 42.1 76 270.7 53.8 37 36.3 7.2 97 95.1 18.9 57 154.0 30.6 17 212.8 42.3 77 271.7 54.0 38 37.3 7.4 98 96.1 19.1 58 155.0 30.8 18 213.8 42.5 78 272.7 54.2 39 38.3 7.6 99 97.1 19.3 59 155.9 31.0 19 214.8 42.7 79 273.6 54.4 40 39.2 7.8 100 98.1 19.5 60 156.9 31.2 20 215.8 42.9 80 274.6 275.6 54.6 41 40.2 8.0 101 99.1 19.7 161 157.9 31.4 221 216.8 43.1 281 54.8 42 41.2 8.2 02 100.0 19.9 62 158.9 31.6 22 217.7 43.3 82 276.6 55.0 43 42.2 8.4 03 101.0 20.1 63 159.9 31.8 23 218.7 43.5 83 277.6 55.2 44 43.2 8.6 04 102.0 20.3 64 160.8 32.0 24 219.7 43.7 84 278.5 55.4 45 44.1 8.8 05 103.0 20.5 65 161.8 32.2 25 220.7 43.9 85 279.5 55.6 46 45.1 9.0 06 104.0 20.7 66 162.8 32.4 26 221.7 44.1 86 280.5 55.8 47 46.1 9.2 07 104.9 20.9 67 163.8 32.6 27 222.6 44.3 87 281.5 56.0 48 47.1 9.4 08 105.9 21.1 68 164.8 32.8 28 223.6 44.5 88 282.5 56.2 49 48.1 9.6 09 106.9 21.3 69 165.8 33.0 29 224.6 44.7 89 283.4 56.4 50 49.0 9.8 10 107.9 21.5 70 166.7 33.2 30 225.6 44.9 90 284.4 56.6 51 50.0 9.9 111 108.9 21.7 171 167.7 33.4 231 226.6 45.1 291 285.4 56.8 52 51.0 10.1 12 109.8 21.9 72 168.7 33.6 32 227.5 45.3 92 286.4 57.0 53 52.0 10.3 13 110.8 22.0 73 169.7 33.8 33 228.5 45.5 93 287.4 57.2 54 53.0 10.5 14 111.8 22.2 74 170.7 33.9 34 229.5 45.7 94 288.4 57.4 55 53.9 10.7 15 112.8 22.4 75 171.6 34.1 35 230.5 45.8 95 289.3 57.6 56 54.9 10.9 16 113.8 22.6 76 172.6 34.3 36 231.5 46.0 96 290.3 57.7 57 55.9 11.1 17 114.8 22.8 77 173.6 34.5 37 232.4 46.2 97 291.3 57.9 58 56.9 11.3 18 115.7 23.0 78 174.6 34.7 38 233.4 46.4 98 292.3 58.1 59 57.9 11.5 19 116.7 23.2 79 175.6 34.9 39 234.4 46.6 99 293.3 58.3 60 58.8 11.7 20 117.7 23.4 80 176.5 35.1 40 235.4 46.8 300 294.2 58.5 DIst. |Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. E. by N. E. I )yS. W. b> N. W. byS 3. 1 Tor 7 p oints. TABLE 1. [Page 619 Difference of Latitude and Departure for li Points. N. by E. i E. N. by W. i W. S. by E. i E. S. by W. i W. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.2 61 59.2 14.8 121 117.4 29.4 181 175.6 44.0 241 233.8 58.6 2 1.9 0.5 62 60.1 15.1 22 118.3 29.6 82 176.5 44.2 42 234.7 58.8 3 2.9 0.7 63 61.1 15.3 23 119.3 29.9 83 177.5 44.5 43 235.7 59.0 4 3.9 1.0 64 62.1 15.6 24 120.3 30.1 84 178.5 44.7 44 236.7 59.3 5 4.9 1.2 65 63.1 15.8 25 121.3 30.4 85 179.5 45.0 45 237.7 59.5 6 5.8 1.5 66 64.0 16.0 26 122.2 30.6 86 180.4 45.2 46 238.6 59.8 7 6.8 1.7 67 65.0 16.3 27 123.2 30.9 87 181.4 45.4 47 239.6 60.0 8 7.8 1.9 68 66.0 16.5 28 124.2 31.1 88 182.4 45.7 48 240.6 60.3 9 8.7 2.2 69 66.9 16.8 29 125.1 31.3 89 183.3 45.9 49 241.5 60.5 10 11" 9.7 2.4 70 67.9 17.0 30 126.1 31.6 90 184.3 46.2 50 242.5 243.5 60.7 10.7 2.7 71 68.9 17.3 131 127.1 31.8 191 185.3 46.4 251 61.0 12 11.6 2.9 72 69.8 17.5 32 128.0 32.1 92 186.2 46.7 52 244.4 61.2 13 12.6 3.2 73 70.8 17.7 33 129.0 32.3 93 187.2 46.9 53 245.4 61.5 14 13.6 3.4 74 71.8 18.0 34 130.0 32.6 94 188.2 47.1 54 246.4 61.7 15 14.6 3.6 75 72.8 18.2 35 131.0 32.8 95 189. 2 47.4 55 247.4 62.0 16 15.5 3.9 76 73.7 18.5 36 131.9 33.0 96 190.1 47.6 56 248.3 62.2 17 16.5 4.1 77 74.7 18.7 37 132.9 33.3 97 191.1 47.9 57 249.3 62.4 18 17.5 4.4 78 75.7 19.0 38 133.9 33.5 98 192.1 48.1 58 250.3 62.7 19 18.4 4.6 79 76.6 19.2 39 134.8 33.8 99 193.0 48.4 59 251.2 62.9 20 19.4 4.9 80 77.6 19.4 40 135.8 34.0 200 194.0 48.6 60 261 252.2 63.2 21 20.4 5.1 81 78.6 19.7 141 136.8 34.3 201 195.0 48.8 253.2 63.4 22 21.3 5.3 82 79.5 19.9 42 137.7 34.5 02 195.9 49.1 62 254.1 63.7 23 22.3 5.6 83 80.5 20.2 43 138.7 34.7 03 196.9 49.3 63 255.1 63.9 24 23.3 5.8 84 81.5 20.4 44 139.7 35.0 04 197.9 49.6 64 256.1 64.1 25 24.3 6.1 85 82.5 20.7 45 140.7 35.2 05 198.9 49.8 65 257.1 64.4 26 25.2 6.3 86 83.4 20.9 46 141.6 35.5 06 199.8 50.1 66 258.0 64.6 27 26.2 6.6 87 84.4 21.1 47 142.6 35.7 07 200.8 50.3 67 259.0 64.9 28 27.2 6.8 88 85.4 21.4 48 143.6 36.0 08 201.8 50.5 68 .260.0 65.1 29 28.1 7.0 89 86.3 21.6 49 144.5 36.2 09 202.7 50.8 69 260.9 65.4 30 29.1 7.3 90 87.3 21.9 50 145.5 36.4 10 203.7 51.0 70 261.9 65.6 31 30.1 7.5 91 88.3 22.1 151 146.5 36.7 211 204.7 51.3 271 262.9 65.8 32 31.0 7.8 92 89.2 22.4 52 147.4 36.9 12 205.6 51.5 72 263.8 66.1 33 32.0 8.0 93 90.2 22.6 53 148.4 37.2 13 206.6 51.8 73 264.8 66.3 34 33.0 8.3 94 91.2 22.8 54 149.4 37.4 14 207.6 52.0 74 265.8 66.6 36 34.0 8.5 95 92.2 23.1 55 150.4 37.7 15 208.6 52.2 75 266.8 66.8 36 34.9 8.7 96 93.1 23.3 56 151.3 37.9 16 209.5 52.5 76 267.7 67.1 37 35.9 9.0 97 94.1 23.6 57 152.3 38.1 17 210. 5 52.7 77 268.7 67.3 38 36.9 9.2 98 95.1 23.8 58 153. 3 38.4 18 211.5 53.0 78 269.7 67.5 39 37.8 9.5 99 96.0 24.1 59 154.2 38.6 19 212.4 53.2 79 270.6 67.8 40 38.8 9.7 100 97.0 24.3 60 155.2 38.9 20 213.4 53.5 80 271.6 68.0 41 39.8 10.0 101 98.0 24.5 161 156.2 39.1 221 214.4 53.7 281 272.6 68.3 42 40.7 10.2 02 98.9 24.8 62 157.1 39.4 22 215.3 63.9 82 273.5 68.5 43 41.7 10.4 03 99.9 25.0 63 158.1 39.6 23 216.3 54.2 83 274.5 68.8 44 42.7 10.7 04 100.9 25.3 64 159.1 39.8 24 217.3 54.4 84 275.5 69.0 45 43.7 10.9 05 101.9 25.5 65 160.1 40.1 25 218.3 54.7 85 277.5 69.2 46 44.6 11.2 06 102.8 25.8 66 161.0 40.3 26 219.2 54.9 86 277.4 69.5 47 45.6 11.4 07 103.8 26.0 67 162.0 40.6 27 220.2 55.2 87 278.4 69.7 48 46.6 11.7 08 104.8 26.2 68 163.0 40.8 28 221.2 56.4 88 279.4 70.0 49 47.5 11.9 09 105.7 26.5 69 163.9 41.1 29 222.1 55.6 89 280.3 70.2 50 51 48.5 12.1 10 106.7 26.7 70 164.9 41.3 30 223.1 55.9 90 281.3 70.5 49.5 »12.4 111 107.7 27.0 171 165.9 41.5 231 224.1 56.1 291 282.3 70.7 52 50.4 12.6 12 108.6 27.2 72 166.8 41.8 32 225.0 56.4 92 283.2 71.0 53 51.4 12.9 13 109.6 27.5 73 167.8 42.0 33 226.0 56.6 93 284.2 71.2 54 52.4 13.1 14 110.6 27.7 74 168.8 42.3 34 227.0 56.9 94 285.2 71.4 55 53.4 13.4 15 111.6 27.9 75 169.8 42.5 35 228.0 57.1 95 286.2 71.7 56 54.3 13.6 16 112.5 28.2 76 170.7 42.8 36 228.9 57.3 96 287.1 71.9 57 55.3 13.8 17 113.5 28.4 77 171.7 43.0 37 229.9 57.6 97 288.1 72.2 58 56.3 14.1 18 114.5 28.7 78 172.7 43.3 38 230.9 57.8 98 289.1 72.4 59 57.2 14.3 19 115.4 28.9 79 173.6 43.5 39 231.8 58.1 99 290.9 72.7 60 58.2 14.6 20 116.4 29.2 80 174.6 43.7 40 232.8 58.3 300 291.0 72.9 Dist. Dep. Lat. DLst. Dep. Lat. Dist. Dep. Lat. DiHt. Dep. Lat. Dist. Dep. Lat. B NE. f E Ee 5E. i E. WNW. i W. WSW. f W. [For 6J Points. 1 Page 520] TABLE 1. Difference of Latitude and Departure for IJ Points. N . byE. iE. N. by w. ^ w. S. by E. ^ E. S. by W. i W. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 241 Lat. Dep. 1 1.0 0.3 61 58.4 17.7 121 115.8 35.1 181 173.2 52.5 230.6 70.0 2 1.9 0.6 62 59.3 18.0 22 116.7 35.4 82 174.2 52.8 42 231.6 70.2 3 2.9 0.9 63 60.3 18.3 23 117.7 35.7 83 175.1 53.1 43 232.5 70.5 4 8.8 1.2 64 61.2 18.6 24 118.7 36.0 84 176.1 53.4 44 233. 5 70.8 5 4.8 1.5 65 62.2 18.9 25 119.6 36.3 85 177.0 53.7 45 234.5 71.1 6 5.7 1.7 66 63.2 19.2 26 120.6 36.6 86 178.0 54.0 46 235.4 71.4 7 6.7 2.0 67 64.1 19.4 27 121.5 36.9 87 178.9 54.3 47 236.4 71.7 8 7.7 2.3 68 65.1 19.7 28 122.5 37.2 88 179.9 54.6 48 237.3 72.0 9 8.6 2.6 69 66.0 20.0 29 123.4 37.4 89 180.9 54.9 49 238.3 72.3 10 11 9.6 2.9 70 67.0 20.3 20.6 30 124.4 37.7 90 181.8 182.8 55.2 50 239.2 72.6 10.5 3.2 71 67.9 131 125.4 38.0 191 55.4 251 240.2 72.9 12 11.5 3.5 72 68.9 20.9 32 126.3 38.3 92 183.7 55.7 52 241.1 73.2 13 12.4 3.8 73 69.9 21.2 33 127.3 38.6 93 184.7 56.0 53 242.1 73.4 14 13.4 4.1 74 70.8 21.5 34 128.2 38.9 94 185.6 56.3 54 243.1 73.7 15 14.4 4.4 75 71.8 21.8 35 129.2 39.2 95 186.6 56.6 55 244.0 74.0 16 15.3 4.6 76 72.7 22.1 36 130.1 39.5 96 187.6 56.9 56 245.0 74.3 17 16.3 4.9 77 73.7 22.4 37 131.1 39.8 97 188.5 57.2 57 245.9 74.6 18 17.2 5.2 78 74.6 22.6 38 132.1 40.1 98 189.5 57.5 58 246.9 74.9 19 18.2 5.5 79 75.6 22.9 39 133.0 40.3 99 190.4 57.8 59 247.8 75.2 20 19.1 5.8 80 76.6 23.2 40 134. 40.6 200 191.4 58.1 60 248.8 75.5 21 20.1 6.1 81 77.5 23.5 141 134.9 40.9 201 192.3 58.3 261 249.8 75.8 22 21.1 6.4 82 78.5 23.8 42 135.9 41.2 02 193.3 58.6 62 250.7 76.1 23 22.0 6.7 83 79.4 24.1 43 136.8 41.5 03 194. 3 58.9 63 251.7 76.3 24 23.0 7.0 84 80.4 24.4 44 137.8 41.8 04 195.2 59.2 64 252.6 76.6 25 23.9 7.3 85 81.3 24.7 45 138.8 42.1 05 196.2 59.5 65 253.6 76.9 26 24.9 7.5 86 82.3 25.0 46 139.7 42.4 06 197.1 59.8 66 254.5 77.2 27 25.8 7.8 87 83.3 25.3 47 140.7 42.7 07 198.1 60.1 67 255.5 77.5 28 26.8 8.1 88 84.2 25.5 48 141.6 43.0 08 199.0 60.4 68 256.5 77.8 29 27.8 8.4 89 86.2 25.8 49 142.6 43.3 09 200.0 60.7 69 257.4 78.1 30 28.7 8.7 90 86.1 26.1 50 143.5 43.5 10 201.0 201.9 61.0 70 258.4 78.4 31 29.7 9.0 91 87.1 26.4 151 144.5 43.8 211 61.3 271 259.3 78.7 32 30.6 9.3 92 88.0 26.7 52 145.5 44.1 12 202.9 61.5 72 260.3 79.0 33 31.6 9.6 93 89.0 27.0 53 146.4 44.4 13 203.8 61.8 73 261.2 79.2 34 32.5 9.9 94 90.0 27.3 54 147.4 44.7 14 204.8 62.1 74 262.2 79.5 35 33.5 10.2 95 90.9 27.6 55 148. 3 45.0 15 205.7 62.4 75 263.2 79.8 36 34.4 10.5 96 91.9 27.9 56 149.3 45.3 16 206.7 62.7 76 264.1 80.1 37 35.4 10.7 97 92.8 28.2 57 150.2 45.6 17 207.7 63.0 77 265.1 80.4 38 36.4 11.0 98 93.8 28.4 58 151.2 45.9 18 208.6 63.3 78 266.0 80.7 39 37.3 11.3 99 94.7 28.7 59 152.2 46.2 19 209. 6 63.6 79 267.0 81.0 40 38.3 11.6 100 95.7 29.0 60 153.1 46.4 20 210.5 63.9 80 267.9 81.3 41 39.2 11.9 101 96.7 29.3 161 154.1 46.7 221 211.5 64.2 281 268.9 81.6 42 40.2 12.2 02 97.6 29.6 62 155.0 47.0 22 212.4 64.4 82 269.9 81.9 43 41.1 12.5 03 98.6 29.9 63 156. 47.3 23 213.4 64.7 83 270.8 82.2 44 42.1 12.8 04 99.5 30.2 64 156. 9 47.6 24 214.4 65.0 84 271.8 82.4 45 43.1 13.1 05 100.5 30.5 65 157.9 47.9 25 215.3 65.3 85 272.7 82.7 46 44.0 13.4 06 101.4 30.8 66 158.9 48.2 26 216.3 65.6 86 273.7 83.0 47 45.0 13.6 07 102.4 31.1 67 159.8 48.5 27 217.2 65.9 87 274.6 83.3 48 45.9 13.9 08 103.3 31.4 68 160.8 48.8 28 218.2 66.2 88 275.6 83.6 49 46.9 14.2 09 104.3 31.6 69 161.7 49.1 29 219.1 66.5 89 276.6 83.9 50 47.8 14.5 10 105.3 31.9 70 162.7 49.3 30 220.1 66.8 90 277.5 84.2 51 48.8 14.8 111 106.2 32.2 171 163.6 49.6 231 221.1 67.1 291 278. 5 84.5 52 49.8 15.1 12 107.2 32.5 72 164.6 49.9 32 222.0 67.3 92 279.4 84.8 53 50.7 15.4 13 108.1 32.8 73 165.6 50.2 33 223.0 67.6 93 280.4 85.1 54 51.7 15.7 14 109.1 33. 1 74 166.5 50.5 34 223.9 67.9 94 281.3 85.3 55 52.6 16.0 15 110.0 33.4 75 167.5 50.8 35 224.9 68.2 95 282.3 85.6 56 53.6 16.3 16 111.0 33.7 76 168. 4 51.1 36 225. 8 68.5 96 283.3 85.9 57 54.5 16.5 17 112.0 34.0 77 169.4 51.4 37 226.8 68.8 97 284.2 86.2 58 55.5 16.8 18 112.9 34.3 78 170.3 51.7 38 227.8 69.1 98 285.2 86.5 59 56.5 17.1 19 113.9 34.5 79 171.3 52.0 39 228.7 69.4 99 286.1 86.8 60 57.4 17.4 20 114.8 34.8 80 172.2 52.3 40 229. 7 69.7 300 287.1 87.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. E> FE. i E. ES] E. ^E. WN^ ^V. J W WSW. i ^\ [For 6J P< ■)ints. TABLE 1. [Page 521 | Difference of Latitude and Departure for If Points. N. by E. |E. N. by w. 1 W. S. by E. f E. S. by W. J W. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.3 61 57.4 20.6 121 113.9 40.8 181 170.4 61.0 241 226.9 81.2 2 1.9 0.7 62 58.4 20.9 22 114.9 41.1 82 171.4 61.3 42 227.9 81.5 3 2.8 1.0 63 59.3 21.2 23 115.8 41.4 83 172.3 61.7 43 228,8 81.9 4 3.8 1.3 64 60.3 21.6 24 116.8 41.8 84 173.2 62.0 44 229.7 82.2 5 4.7 1.7 65 61.2 21.9 25 117.7 42.1 85 174.2 62.3 45 230.7 82.5 6 5.6 2.0 66 62.1 22.2 26 118.6 42.4 86 175.1 62.7 46 231.6 82.9 7 6.6 2.4 67 63.1 22.6 27 119.6 42.8 87 176.1 63.0 47 232.6 83.2 8 7.5 2.7 68 64.0 22.9 28 120.5 43.1 88 177.0 63.3 48 1 233.5 83.5 9 8.5 3.0 69 65.0 23.2 29 121.5 43.5 89 178.0 63.7 49 i 234.4 83.9 10 9.4 3.4 70 65.9 23.6 23.9 30 122.4 123.3 43.8 90 178.9 64.0 50 ! 235.4 84.2 11 10.4 3.7 71 66.8 131 44.1 191 179.8 64.3 251 ! 236.3 84.6 12 11.3 4.0 72 67.8 24.3 32 124.3 44.5 92 180.8 64.7 52 237.3 84.9 13 12.2 4.4 73 68.7 24.6 33 125.2 44.8 93 181.7 65.0 53 238.2 85.2 14 13.2 4.7 74 69.7 24.9 34 126.2 45.1 94 182.7 65.4 54 239.2 85.6 15 14.1 5.1 75 70.6 25.3 35 127.1 45.5 95 183.6 65.7 55 240.1 85.9 16 15.1 5.4 76 71.6 25.6 36 128.0 45.8 96 184. 5 66.0 56 241.0 86.2 17 16.0 5.7 77 72.5 25.9 37 129.0 46.2 97 185.5 66.4 57 242.0 86.6 18 16.9 6.1 78 73.4 26.3 .38 129.9 46.5 98 186.4 66.7 58 242.9 86.9 19 17.9 6.4 79 74.4 26.6 39 130.9 46.8 99 187.4 67.0 59 243.9 87.3 20 18.8 6.7 80 75.3 27.0 27.3 40 141 131.8 47.2 200 201 188.3 189.3 67.4 60 244.8 245.7 87.6 21 19.8 7.1 81 76.3 132.8 47.5 67.7 261 87.9 22 20.7 7.4 82 77.2 27.6 42 133.7 47.8 02 190.2 68.1 62 246.7 88.3 23 21.7 7.7 83 78.1 28.0 43 134.6 48.2 03 191.1 68.4 63 247.6 88.6 24 22.6 8.1 84 79.1 28.3 44 135.6 48.5 04 192.1 68.7 64 248.6 88.9 25 23.5 8.4 85 80.0 28.6 45 136.5 48.8 05 193.0 69.1 65 249.5 89.3 26 24.5 8.8 86 81.0 29.0 46 137.5 49.2 06 194.0 69.4 66 250.5 89.6 27 25.4 9.1 87 81.9 29.3 47 138.4 49.5 07 194.9 69.7 67 251.4 89.9 28 26.4 9.4 88 82.9 29.6 48 139.3 49.9 08 195.8 70.1 68 252.3 90.3 29 27.3 9.8 89 83.8 30.0 49 140.3 50.2 09 196.8 70.4 69 1 253.3 90.6 30 28.2 10.1 90 84.7 30.3 50 141.2 50.5 10 197.7 198.7 70.7 70 254.2 91.0 31 29.2 10.4 91 85.7 30.7 151 142.2 50.9 211 71.1 271 255.2 91.3 32 30.1 10.8 92 86.6 31.0 52 143.1 51.2 12 199.6 71.4 72 256.1 91.6 33 31.1 11.1 93 87.6 31.3 53 144.1 51.5 13 200.5 71.8 73 257.0 92.0 34 32.0 11.5 94 88.5 31.7 54 145.0 51.9 14 201.5 72.1 74 258.0 92.3 35 33.0 11.8 95 89.4 32.0 55 145.9 52.2 15 202.4 72.4 75 258.9 92.6 36 33.9 12.1 96 90.4 32.3 56 146.9 52.6 16 203.4 72.8 76 259.9 93.0 37 34.8 12.5 97 91.3 32.7 57 147.8 52.9 17 204.3 73.1 77 260.8 93.3 38 35.8 12.8 98 92.3 33.0 58 148.8 53.2 18 2a5.3 73.4 78 261.7 93.7 39 36.7 13.1 99 93.2 33.4 59 149.7 53.6 19 206.2 73.8 79 262.7 94.0 40 37.7 13.5 100 94.2 33.7 60 150.6 53.9 20 207.1 74.1 80 26:^.6 264.6 94.3 94.7 41 38.6 13.8 101 95.1 34.0 161 151.6 54.2 221 208.1 74.5 281 42 39.5 14.1 02 96.0 34.4 62 152.5 54.6 22 209.0 74.8 82 265.5 95.0 43 40.5 14.5 03 97.0 34.7 63 153.5 54.9 23 210.0 75.1 83 266.5 95.3 44 41.4 14.8 04 97.9 35.0 64 154.4 55.2 24 210.9 75.5 84 267.4 95.7 45 42.4 15.2 05 98.9 35.4 65 155.4 55.6 25 211.8 75.8 85 268.3 96.0 46 43.3 15.5 06 99.8 35.7 66 156.3 55.9 26 212.8 76.1 86 269.3 96.4 47 44.3 15.8 07 100.7 36.0 67 157.2 56.3 27 213.7 76.5 87 270.2 96.7 48 45.2 16.2 08 101.7 36.4 68 158.2 56.6 28 214.7 76.8 88 271.2 97.0 49 46.1 16.5 09 102.6 36.7 69 159.1 56.9 29 215.6 77.1 89 272.1 97.4 50 51 47.1 48.0 16.8 10 103.6 37.1 70 160.1 57.3 30 I 216.6 77.5 90 273.0 97.7 17.2 111 104.5 37.4 171 161.0 57.6 231 217.5 77.8 291 274. 98.0 52 49.0 17.5 12 105.5 37.7 72 161.9 57.9 32 218.4 78.2 92 274. 9 98.4 53 49.9 17.9 13 106.4 38.1 73 162.9 58.3 33 219.4 78.5 93 275.9 98.7 54 50.8 18.2 14 107.3 38.4 74 163.8 58.6 34 220.3 78.8 94 276.8 99.0 55 51.8 18.5 15 108.3 38.7 75 164.8 59.0 35 221.3 79.2 95 277.8 99.4 56 52.7 18.9 16 109.2 39.1 76 165.7 59.3 36 222.2 79.5 96 278.7 99.7 57 53.7 19.2 17 110.2 39.4 77 166.7 59.6 37 223.1 79.8 97 279.6 100.1 58 54.6 19.5 18 111.1 39.8 78 167.6 60.0 38 224.1 80.2 98 280.6 100.4 59 55.6 19.9 19 112.0 40.1 79 168.5 60.3 39 225.0 80.5 99 281.5 100.7 60 56.5 20.2 20 113.0 40.4 80 169.5 60.6 40 226.0 80.9 300 282.5 101.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ENE. \ E. I :sE. \ I ]_ M ^NW. i W. WSW. i W. [For 6k Po ints. Page 622] TABLE 1. Differenca of Latitude and Departure for 2 Points. NNE. NNW. SSE. ssw. DiBt. Lat. Dep. Dlfit. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 56.4 23.3 121 111.8 46.3 181 167.2 69.3 241 222.7 92.2 2 1.8 0.8 62 57.3 23.7 22 112.7 46.7 82 168.1 69.6 42 223.6 92.6 3 2.8 1.1 63 58.2 24.1 23 113.6 47.1 83 169.1 70.0 43 224.5 93.0 4 3.7 1.5 64 59.1 24.5 24 114.6 47.5 84 170.0 70.4 44 225.4 93.4 5 4.6 1.9 65 60.1 24.9 25 115.5 47.8 85 170.9 70.8 45 226.4 93.8 6 5.5 2.3 66 61.0 25.3 26 116.4 48.2 86 171.8 71.2 46 227.3 94.1 7 6.5 2.7 67 61.9 25.6 27 117.3 48.6 87 172.8 71.6 47 228.2 94.5 8 7.4 3.1 68 62.8 26.0 28 118.3 49.0 88 173.7 71.9 48 229.1 94.9 9 8.3 3.4 69 63.7 26.4 29 119.2 49.4 89 174.6 72.3 49 230.0 95.3 10 9.2 3.8 70 64.7 26.8 30 120.1 49.7 90 175.5 72.7 50 231.0 95.7 11 10.2 4.2 71 65.6 27.2 131 121.0 50.1 191 , 176. 5 73.1 251 231.9 96.1 12 11.1 4.6 72 66.5 27.6 32 122.0 50.5 92 177.4 73.5 52 232.8 96.4 13 12.0 5.0 73 67.4 27.9 33 122.9 50.9 93 178.3 73.9 53 233.7 96.8 14 12.9 5.4 74 68.4 28.3 34 123.8 51.3 94 179.2 74.2 54 234.7 97.2 15 13.9 5.7 75 69.3 28.7 35 124.7 51.7 95 180.2 74.6 55 235.6 97.6 16 14.8 6.1 76 70.2 29.1 36 125.6 52.0 96 181.1 75.0 56 236.5 98.0 17 15.7 6.5 77 71.1 29.5 37 126.6 52.4 97 182.0 75.4 57 237.4 98.3 18 16.6 6.9 78 72.1 29.8 38 127.5 52.8 98 182.9 75.8 58 238.4 98.7 19 17.6 7.3 79 73.0 30.2 39 128.4 53.2 99 183.9 76.2 59 239.3 99.1 20 18.6 7.7 80 ' 73.9 30.6 31.0 40 129.3 53.6 200 184.8 76.5 60 240.2 99.5 21 19.4 8.0 81 74.8 141 130.3 54.0 201 185.7 76.9 261 241.1 99.9 22 20.3 8.4 82 75.8 31.4 42 131.2 54.3 02 186.6 77.3 62 242.1 100.3 23 21.2 8.8 83 76.7 31.8 43 132.1 54.7 03 187.5 77.7 63 243.0 100.6 24 22.2 9.2 84 77.6 32.1 44 133.0 55.1 04 188.5 78.1 64 243.9 101.0 25 23.1 9.6 85 78.5 32.5 45 134.0 55.5 05 189.4 78.5 65 244.8 101.4 26 24.0 9.9 86 79.5 32.9 46 134.9 55.9 06 190.3 78.8 66 245.8 101.8 27 24.9 10.3 87 80.4 33.3 47 135.8 56.3 07 191.2 79.2 67 246.7 102.2 28 25.9 10.7 88 81.3 33.7 48 136.7 56.6 08 192.2 79.6 68 247.6 102.6 29 26.8 11.1 89 82.2 34.1 49 137.7 57.0 09 193.1 80.0 69 248.5 102.9 30 27.7 11.5 90 83.1 34.4 50 138.6 139.5 57.4 10 194.0 80.4 70 249.4 103.3 31 28.6 11.9 91 84.1 34.8 151 57.8 211 194.9 80.7 271 250.4 103.7 32 29.6 12.2 92 85.0 35.2 52 140.4 58.2 12 195.9 81.1 72 251.3 104.1 33 30.5 12.6 93 85.9 35.6 53 141.4 58.6 13 196.8 81.5 73 252.2 104.5 34 31.4 13.0 94 86.8 36.0 54 142.3 58.9 14 197.7 81.9 74 253.1 104.9 35 32.3 13.4 95 87.8 36.4 55 143.2 59.3 15 198.6 82.3 75 254.1 105.2 36 33.3 13.8 96 88.7 36.7 56 144.1 59.7 16 199.6 82.7 76 255.0 105.6 37 34.2 14.2 97 89.6 37.1 57 145.0 60.1 17 200.5 83.0 77 255.9 106.0 38 35.1 14.5 98 90.5 37.5 58 146.0 60.5 18 201.4 83.4 78 256.8 106.4 39 36.0 14.9 99 91.5 37.9 59 146.9 60.8 19 202.3 83.8 79 257.8 106.8 40 37.0 15.3 100 92.4 38.3 60 147.8 61.2 20 203.3 84.2 80 258.7 107.2 41 37.9 15.7 101 93.3 38.7 161 148.7 61.6 221 204.2 84.6 281 259.6 107.5 42 38.8 16.1 02 94.2 39.0 62 149.7 62.0 22 205.1 85.0 82 260.5 107.9 43 39.7 16.5 03 95.2 39.4 63 150.6 62.4 23 206.0 85.3 83 261.5 108.3 44 40.7 16.8 04 96.1 39.8 64 151.5 62.8 24 206.9 85.7 84 262.4 108.7 45 41.6 17.2 05 97.0 40.2 65 152.4 63.1 25 207.9 86.1 85 263.3 109.1 46 42.5 17.6 06 97.9 40.6 66 153.4 63.5 26 208.8 86.5 86 264.2 109.4 47 43.4 18.0 07 98.9 40.9 67 154.3 63.9 27 209.7 86.9 87 265.2 109.8 48 44.3 18.4 08 99.8 41.3 68 155.2 64.3 28 210.6 87.3 88 266.1 110.2 49 45.3 18.8 09 100.7 41.7 69 156.1 64.7 29 211.6 87.6 89 267.0 110.6 50 46.2 19.1 10 101.6 42.1 70 157.1 65.1 30 212.5 88.0 90 267.9 111.0 51 47.1 19.5 111 102.6 42.5 171 158.0 65.4 231 213.4 88.4 291 268.8 111.4 52 48.0 19.9 12 103.5 42.9 72 158.9 65.8 32 214.3 88.8 92 269.8 111.7 63 49.0 20.3 13 104.4 43.2 73 159.8 66.2 33 215.3 89.2 93 270.7 112.1 54 49.9 20.7 14 105.3 43.6 74 160.8 66.6 34 216.2 89.5 94 271.6 112.5 55 50.8 21.0 15 106.2 44.0 75 161.7 67.0 35 217.1 89.9 95 272.5 112.9 56 51.7 21.4 16 107.2 44.4 76 162.6 67.4 36 218.0 90.3 96 273.5 113.3 57 52.7 21.8 17 108.1 44.8 77 163.5 67.7 37 219.0 90.7 97 274.4 113.7 58 53.6 22.2 18 109.0 45.2 78 164.5 68.1 38 219.9 91.1 98 275.3 114.0 59 54.5 22.6 19 109.9 45.5 79 165.4 68.5 39 220.8 91.5 99 276.2 114.4 60 55.4 23.0 20 110.9 45.9 80 166.3 68.9 40 221.7 91.8 300 277.2 114.8 Dist. Dep. Lat. Dist. Dep. Lat, Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ENE. ESE. WNW WSW [F or 6 Poi] its. TABLE 1. [Page 623 j Difference of Latitude and Departure for 2J- Points. NNE. iE. NNW . i W. SSE. iE. ssw. iW. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 55.1 26.1 121 109.4 51.7 181 163.6 77.4 241 217.9 103.0 2 1.8 0.9 62 56.0 26.5 22 110.3 52.2 82 164.5 77.8 42 218.8 103.6 3 2.7 1.3 63 57.0 26.9 23 111.2 52.6 83 165.4 78.2 43 219.7 103.9 4 3.6 1.7 64 57.9 27.4 24 112.1 53.0 84 166.3 78.7 44 220.6 104.3 5 4.5 2.1 65 58.8 27.8 25 113.0 53.4 85 167. 2' 79.1 45 221.5 104.8 6 5.4 2.6 66 59.7 28.2 26 113.9 53.9 86 168.1 79.5 46 222.4 105.2 7 6.3 3.0 67 60.6 28.6 27 114.8 54.3 87 169.0 80.0 47 223.3 105.6 8 7.2 3.4 68 61.5 29.1 28 115.7 54.7 88 169.9 80.4 48 224.2 106.0 9 8.1 3.8 69 62.4 29.5 29 116.6 55.2 89 170.9 80.8 49 226.1 106.5 10 9.0 4.3 70 63.3 29.9 30 117.5 118.4 55.6 90 191 171.8 81.2 50 261 226.0 106.9 11 9.9 4.7 71 64.2 30.4 131 56.0 172.7 81.7 226.9 107.3 12 10.8 5.1 72 65.1 30.8 32 119.3 56.4 92 173.6 82.1 52 227.8 107.7 13 11.8 5.6 73 66.0 31.2 33 120.2 56.9 93 174.5 82.6 53 228.7 108.2 14 12.7 6.0 74 66.9 31.6 34 121.1 57.3 94 175.4 82.9 54 229.6 108.6 15 13.6 6.4 75 67.8 32.1 35 122.0 57.7 95 176.3 83.4 65 230.6 109.0 16 14.5 6.8 76 68.7 32.5 36 122.9 58.1 96 177.2 83.8 56 231.4 109.5 17 15.4 7.3 77 69.6 32.9 37 123.8 58.6 97 178.1 84.2 57 232. 3 109.9 18 16.3 7.7 78 70.5 33.3 38 124.8 59.0 98 179.0 84.7 58 233.2 110.3 19 17.2 8.1 79 71.4 33.8 39 125.7 59.4 99 179.9 85.1 59 234.1 110.7 20 18.1 8.6 80 81 72.3 34.2 40 126.6 59.9 200 180.8 85.6 60 235.0 236.9 111.2 21 19.0 9.0 73.2 34.6 141 127.5 60.3 201 181.7 85.9 261 111.6 22 19.9 9.4 82 74.1 35.1 42 128.4 60.7 02 182.6 86.4 62 236.8 112.0 23 20.8 9.8 83 75.0 35.5 43 129.3 61.1 03 183.5 86.8 63 237.7 112.4 24 21.7 10.3 84 75.9 35.9 44 130.2 61.6 04 184.4 87.2 64 238.7 112.9 25 22.6 10.7 85 76.8 36.3 45 131.1 62.0 05 185.3 87.6 65 239.6 113.3 26 23.5 11.1 86 77.7 36.8 46 132.0 62.4 06 186.2 88.1 66 240.5 113.7 27 24.4 11.5 87 78.6 37.2 47 132.9 62.9 07 187.1 88.5 67 241.4 114.2 28 26.3 12.0 88 79.6 37.6 48 133.8 63.3 08 188.0 88.9 68 242. 3 114.6 29 26.2 12.4 89 80.5 38.1 49 134.7 63.7 09 188.9 89.4 69 243.2 115.0 30 31 27.1 12.8 90 81.4 38.5 50 136.6 64.1 10 189.8 89.8 70 244.1 115.4 28.0 13.3 91 82.3 38.9 151 136.5 64.6 211 190.7 90.2 271 245.0 116.9 32 28.9 13.7 92 83.2 39.3 52 137.4 65.0 12 191.6 90.6 72 246.9 116.3 33 29.8 14.1 93 84.1 39.8 53 138.3 65.4 13 192.5 91.1 73 246.8 116.7 34 30.7 14.5 94 85.0 40.2 54 139.2 65.8 14 193.5 91.5 74 247.7 117.2 35 31.6 15.0 95 85.9 40.6 55 140.1 66.3 16 194.4 91.9 76 248.6 117.6 36 32.5 15.4 96 86.8 41.0 56 141.0 66.7 16 195.3 92.4 76 249.6 118.0 37 33.4 15.8 97 87.7 41.5 57 141.9 67.1 17 196.2 92.8 77 260.4 118.4 38 34.4 16.2 98 88.6 41.9 58 142.8 67.6 18 197.1 93.2 78 261.3 118.9 39 35.3 16.7 99 89.5 42.3 59 143.7 68.0 19 198.0 93.6 79 252.2 119.3 40 41 36.2 17.1 100 90.4 42.8 60 144.6 68.4 20 198.9 94.1 80 253.1 119.7 37.1 17.5 101 91.3 43.2 161 145.5 68.8 221 199.8 94.6 281 254.0 120.1 42 38.0 18.0 02 92.2 43.6 62 146.4 69.3 22 200.7 94.9 82 254.9 120.6 43 38.9 18.4 03 93.1 44.0 63 147.4 69.7 23 201.6 96.3 83 266.8 121.0 44 39.8 18.8 04 94.0 44.5 64 148.3 70.1 24 202.5 95.8 84 256.7 121.4 45 40.7 19.2 05 94.9 44.9 65 149.2 70.5 25 203.4 96.2 86 257.6 121.9 46 41.6 19.7 06 95.8 45.3 66 150.1 71.0 26 204.3 96.6 86 268.6 122.3 47 42.5 20.1 07 96.7 45.7 67 151.0 71.4 27 205.2 97.1 87 259.4 122.7 48 43.4 20.5 08 97.6 46.2 68 151.9 71.8 28 206.1 97.5 88 260.3 123.1 49 44.3 21.0 09 98.5 46.6 69 152.8 72.3 29 207.0 .97.9 89 261.3 123.6 50 45.2 21.4 10 99.4 100. 3" 47.0 70 153.7 154.6 72.7 73.1 30 231 207.9 98.3 90 291 262.2 124.0 51 46.1 21.8 111 47.5 171 208.8 98.8 263.1 124.4 52 47.0 22.2 12 101.2 47.9 72 155.5 73.5 32 209.7 99.2 92 264.0 124.8 53 47.9 22.7 13 102.2 48.3 73 156.4 74.0 33 210.6 99.6 93 264.9 126.3 54 48.8 23.1 14 103.1 48.7 74 157.3 74.4 34 211.5 100.0 94 265.8 126.7 55 49.7 23.5 15 104.0 49.2 75 158.2 74.8 35 212.4 100.5 95 266.7 126.1 56 50.6 23.9 16 104.9 49.6 76 159.1 75.2 36 213.3 100.9 96 267.6 126.6 57 51.5 24.4 17 105.8 50.0 77 160.0 75.7 37 214.2 101.3 97 268.5 127.0 58 52.4 24.8 18 106.7 50.5 78 160.9 76.1 38 215.1 101.8 98 269.4 127.4 59 53.3 25.2 19 107.6 50.9 79 161.8 76.5 39 216.1 102.2 99 270.3 127.8 60 54.2 25.7 20 108.5 51.3 80 162.7 77.0 40 217.0 102.6 300 271.2 128.3 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. m ]. by E. fE. SI :. by E. 1 E. NW. by AV. 1 W. SW . by W. |W. [For 6| P oints. Page 524] TABLE 1. Difference of Latitude and Departure for 2J Points. Diet. NNE . iE. NNW. i W. SSE i E. SSW ^ w. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 63.8 28.8 121 106.7 57.0 181 159.6 86.3 241 212.5 113.6 2 1.8 0.9 62 54.7 29.2 22 107.6 57.5 82 160. 5 86.8 42 213.4 114.1 3 2.6 1.4 63 66.6 29.7 23 108.5 58.0 83 161.4 86.3 43 214.3 114.5 4 3.5 1.9 64 66.4 30.2 24 109.4 58.5 84 162.3 86.7 44 216.2 115.0 5 4.4 2.4 65 67.3 30.6 26 110.2 58.9 85 163. 2 87.2 45 216.1 115.6 6 5.3 2.8 66 58.2 31.1 26 111.1 59.4 86 164.0 87.7 46 217.0 116.0 7 6.2 3.3 67 69.1 31.6 27 112.0 69.9 87 164.9 88.2 47 217.8 116.4 8 7.1 3.8 68 60.0 32.1 28 112.9 60.3 88 165.8 88.6 48 218.7 116.9 9 7.9 4.2 69 60.9 32.6 29 113.8 60.8 89 166.7 89.1 49 219.6 117.4 10 8.8 4.7 70 61.7 33.0 30 114.6 61.3 61.8 90 191 167.6 89.6 50 220.6 117.8 11 9.7 5.2 71 62.6 33.6 131 116.6 168.4 90.0 251 221.4 118.3 12 10.6 5.7 72 63.5 33.9 32 116.4 62.2 92 169.3 90.6 52 222.2 118.8 13 11.5 6.1 73 64.4 34.4 33 117.3 62.7 93 170.2 91.0 53 223.1 119.3 14 12.3 6.6 74 65.3 34.9 34 118.2 63.2 94 171.1 91.6 64 224.0 119.7 15 13.2 7.1 76 66.1 36.4 35 119.1 63.6 96 172.0 91.9 65 224.9 120.2 16 14.1 7.5 76 67.0 35.8 36 119.9 64.1 96 172.9 92.4 56 225.8 120.7 17 15.0 8.0 77 67.9 36.3 37 120.8 64.6 97 173.7 92.9 57 226.7 121.1 18 15.9 8.5 78 68.8 36.8 38 121.7 65.1 98 174.6 93.3 58 227.5 121.6 19 16.8 9.0 79 69.7 37.2 39 122.6 65.5 99 176.5 93.8 59 228.4 122.1 20 17.6 9.4 80 70.6 37.7 38.2 40 123.5 66.0 66.6 200 201 176.4 94.3 60 229.3 122.6 21 18.5 9.9 81 71.4 141 124.4 177.3 94.8 261 330.2 123.0 22 19.4 10.4 82 72.3 38.7 42 125.2 ; 66.9 02 178.1 95.2 62 231.1 123.5 23 20.3 10.8 83 73.2 39.1 43 126.1 ; 67.4 03 179.0 95.7 63 231.9 124.0 24 21.2 11.3 84 74.1 39.6 44 127.0 67.9 04 179.9 96.2 64 232.8 124.4 25 22.0 11.8 85 75.0 40.1 45 127.9 68.4 06 180.8 96.6 65 233.7 124.9 26 22.9 12.3 86 75.8 40.6 46 128.8 68.8 06 181.7 97.1 66 234.6 125.4 27 23.8 12.7 87 76.7 41.0 47 129.6 69.3 07 182. 6 97.6 67 235.5 125.9 28 24.7 13.2 88 77.6 41.6 48 130.5 69.8 08 183.4 98.1 68 236.4 126.3 29 25.6 13.7 89 78.5 42.0 49 131.4 70.2 09 184.3 98.5 69 237.2 126.8 30 26.5 14.1 90 79.4 42.4 60 132.3 70.7 10 185. 2 99.0 70 238.1 127.3 127.7 31 27.3 14.6 91 80.3 42.9 151 133.2 71.2 211 186.1 99.6 271 239.0 32 28.2 15.1 92 81.1 43.4 52 134.1 71.7 12 187.0 99.9 72 239.9 128.2 33 29.1 15.6 93 82.0 43.8 63 134.9 72.1 13 187.8 100.4 73 240.8 128.7 34 30.0 16.0 94 82.9 44.3 54 135.8 72.6 14 188.7 100.9 74 241.6 129.2 35 30.9 16.5 95 83.8 44.8 65 136.7 73.1 15 189.6 101.4 76 242.5 129.6 36 31.7 17.0 96 84.7 46.3 56 137.6 73.5 16 190.5 101.8 76 243.4 130.1 37 32.6 17.4 97 86.6 46.7 67 138.5 74.0 17 191.4 102.3 77 244.3 130.6 38 33.5 17.9 98 86.4 46.2 68 139.3 74.5 18 192.3 102.8 78 245.2 131.0 39 34.4 18.4 99 87.3 46.7 69 140.2 76.0 19 193.1 103.2 79 246.1 131. 5 40 36.3 18.9 100 88.2 47.1 60 141.1 75.4 20 194.0 103.7 80 246.9 132.0 132.6 41 36.2 19.3 101 89.1 47.6 161 142.0 75.9 221 194. 9 104.2 281 247.8 42 37.0 19.8 02 90.0 48.1 62 142.9 76.4 22 195.8 104.7 82 248.7 132.9 43 37.9 20.3 03 90.8 48.6 63 143.8 76.8 23 196. 7 105.1 83 249.6 133.4 44 38.8 20.7 04 91.7 49.0 64 144.6 77.3 24 197.6 105.6 84 260.5 133.9 45 39.7 21.2 05 92.6 49.5 65 145.5 77.8 26 198.4 106.1 86 251.3 134.3 46 40.6 21.7 06 93.6 50.0 66 146.4 78.3 26 199.3 106.5 86 252.2 134.8 47 41.6 22.2 07 94.4 50.4 67 147.3 78.7 27 200.2 107.0 87 253.1 135. 3 48 42.3 22.6 08 96.2 50.9 68 148.2 79.2 28 201.1 107.5 88 254.0 135.8 49 43.2 23.1 09 . 96.1 61.4 69 149.0 79.7 29 202.0 107.9 89 264.9 136.2 50 44.1 23.6 24.0 10 97.0 61.9 70 149.9 80.1 30 202.8 108.4 90 255.8 136. 7 61 46.0 111 97.9 52.3 171 160.8 80.6 231 203.7 108.9 291 256.6 137.2 52 46.9 24.5 12 98.8 52.8 72 151.7 81.1 32 204.6 109.4 92 267.5 137. 6 53 46.7 25.0 13 99.7 63.3 73 152.6 81.6 33 205.5 109.8 93 268.4 138. 1 54 47.6 25.5 14 100.5 63.7 74 153.5 82.0 34 206.4 110.3 94 259. 3 138.6 55 48.5 25.9 16 101.4 54.2 75 164.3 82.5 36 207.3 110.8 96 260.2 139.1 56 49.4 26.4 16 102.3 64.7 76 166.2 83.0 36 208.1 111.2 96 261.0 139.6 57 50.3 26.9 17 103.2 55.2 77 166.1 83.4 37 209.0 111.7 97 261.9 140.0 58 51.2 27.3 18 104.1 56.6 78 157.0 83.9 38 209.9 112.2 98 262.8 140.5 59 52.0 27.8 19 104.9 56.1 79 157.9 84.4 39 210.8 112.7 99 263.7 140.9 60 52.9 28.3 20 105.8 56.6 80 168.7 84.9 40 211.7 113.1 300 264.6 141.4 Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. NE . by E. i E. SE . by E. i E. NW. by W. ^ W. SW. by W. i W. [For 5J P( jintfi. TABLE 1. [Page 625 Difference of Latitude and Departure for 2J Points. NNE.' J E. NNW. i W. SSE. 1 E SSW. f w. Dist. Lat. Dep. Dist. Lat. Dep. Diat. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 52.3 31.4 121 103.8 62.2 181 155.2 93.1 241 i 206.7 123.9 2 1.7 1.0 62 53.2 31.9 22 104.6 62.7 82 156.1 93.6 42 207.6 124.4 3 2.6 1.5 63 54.0 32.4 23 105.5 63.2 83 157.0 94.1 43 208.4 124.9 4 3.4 2.1 64 54.9 32.9 24 106.4 63.7 84 157.8 94.6 44 209.3 125.4 5 4.3 2.6 65 55.8 33.4 25 107.2 64.3 85 158.7 95.1 45 210.1 126.0 6 5.1 3.1 66 56.6 33.9 26 108.1 64.8 86 159.5 95.6 46 211.0 126.5 7 6.0 3.6 67 57.5 34.4 27 108.9 65.3 87 160.4 96.1 47 211.9 127.0 8 6.9 4.1 68 58.3 35.0 28 109.8 65.8 88 161.3 96.7 48 212.7 127.5 9 7.7 4.6 69 59.2 35.5 29 110.6 66.3 89 162.1 97.2 49 213.6 128.0 10 8.6 5.1 70 60.0 36.0 30 131 111.5 66.8 90 163.0 97.7 50 214.4 215.3 128.5 11 9.4 5.7 71 60.9 36.5 112.4 67.3 191 163.8 98.2 251 129.0 12 10.3 6.2 72 61.8 37.0 32 113.2 67.9 92 164.7 98.7 52 216.1 129.6 13 11.2 6.7 73 62.6 37.5 33 114.1 68.4 93 165.5 99.2 53 217.0 130.1 14 12.0 7.2 74 63.5 38.0 34 114.9 68.9 94 166.4 99.7 54 217.9 130.6 15 12.9 7.7 75 64.3 38.6 35 115.8 69.4 95 167.3 100.3 55 218.7 131.1 16 13.7 8.2 76 65.2 39.1 36 116.7 69.9 96 168.1 100.8 56 ! 219.6 131.6 17 14.6 8.7 77 66.0 39.6 37 117.5 70.4 97 169.0 101.3 57 i 220.4 132.1 18 15.4 9.3 78 66.9 40.1 38 118.4 70.9 98 169.8 101.8 58 221.3 132.6 19 16.3 9.8 79 67.8 40.6 39 119.2 71.5 99 170.7 102.3 59 222.2 133.2 20 17.2 10.3 80 68.6 41.1 40 120.1 120.9 72.0 200 171.5 102.8 60 223.0 133.7 21 18.0 10.8 81 69. S 41.6 141 72.5 201 172.4 103.3 261 223.9 134.2 22 18.9 11.3 82 70.3 42.2 42 121.8 73.0 02 173.3 103.8 62 224.7 134.7 23 19.7 11.8 83 71.2 42.7 43 122.7 73.5 03 174.1 104.4 63 225.6 135.2 24 20.6 12.3 84 72.0 43.2 44 123.5 74.0 04 175.0 104.9 64 226.4 135.7 25 21.4 12.9 85 72.9 43.7 45 124.4 74.5 05 175.8 105.4 65 227.3 136.2 26 22.3 13.4 86 73.8 44.2 46 125.2 75.1 06 176.7 106.9 66 228.2 136.8 27 23.2 13.9 87 74.6 44.7 47 126.1 75.6 07 177.5 106.4 67 229.0 137.3 28 24.0 14.4 88 75.5 45.2 48 126.9 76.1 08 178.4 106.9 68 229.9 137.8 29 24.9 14.9 89 76.3 45.8 49 127.8 76.6 09 179.3 107.4 69 230.7 138.3 30 31 25.7 15.4 90 77.2 46.3 50 128.7 77.1 10 180.1 108.0 70 231.6 138.8 26.6 15.9 91 78.1 46.8 151 129.5 77.6 211 181.0 108.5 271 232.4 139.3 32 27.4 16.5 92 78.9 47.3 52 130.4 78.1 12 181.8 109.0 72 233.3 139.8 33 28.3 17.0 93 79.8 47.8 53 131.2 78.7 13 182.7 109.5 73 234.2 140.4 34 29.2 17.5 94 80.6 48.3 54 132.1 79.2 14 183.6 110.0 74 235.0 140.9 35 30.0 18.0 95 81.5 48.8 55 132.9 79.7 15 184.4 110.5 75 235.9 141.4 36 30.9 18.5 96 82.3 49.4 56 133.8 80.2 16 185.3 lll.O 76 236.7 141.9 37 31.7 19.0 97 83.2 49.9 57 134.7 80.7 17 186.1 111.6 77 237.6 142.4 38 32.6 19.5 98 84.1 50.4 58 135.5 81.2 18 187.0 112.1 78 238.4 142.9 39 33.5 20.1 99 84.9 50.9 59 136.4 81.7 19 187.8 112.6 79 239.3 143.4 40 34.3 20.6 100 85.8 51.4 60 137.2 82.3 20 188.7 113.1 80 240.2 143.9 41 35.2 21.1 101 86.6 51.9 161 138.1 82.8 221 189.6 113.6 281 241.0 144.5 42 36.0 21.6 02 87.5 52.4 62 139.0 83.3 22 190.4 114.1 82 241.9 145.0 43 36.9 22.1 03 88.3 53.0 63 139.8 83.8 23 191.3 114.6 83 242.7 145.5 44 37.7 22.6 04 89.2 53.5 64 140.7 84.3 24 192.1 115.2 84 243.6 146.0 45 38.6 23.1 05 90.1 54.0 65 141.5 84.8 25 193.0 115.7 85 244.5 146.5 46 39.5 23.6 06 90.9 54.5 66 142.4 85.3 26 193.8 116.2 86 245.3 147.0 47 40.3 24.2 07 91.8 55.0 67 143.2 85.9 27 194.7 116.7 87 246.2 147.5 48 41.2 24.7 08 92.6 55.5 68 144.1 86.4 28 195.6 117.2 88 247.0 148.1 49 42.0 25.2 09 93.5 56.0 69 145.0 86.9 29 196.4 117.7 89 247.9 148. 6 50 42.9 25.7 10 94.4 56.6 70 171 145.8 146.7 87.4 30 197.3 118.2 90 248.7 149.1 51 43.7 26.2 111 95.2 57.1 87.9 231 198.1 118.8 291 249.6 149.6 52 44.6 26.7 12 96.1 57.6 72 147.5 88.4 32 199.0 119.3 92 250.5 150.1 53 45.5 27.2 13 96.9 58.1 73 148.4 88.9 33 199.9 119.8 93 251.3 150.6 54 46.3 27.8 14 97.8 58.6 74 149.2 89.5 34 200.7 120.3 94 252.2 151.1 55 47.2 28.3 15 98.6 59.1 75 150.1 90.0 35 201.6 120.8 95 253.0 151.7 56 48.0 28.8 16 99.5 59.6 76 151.0 90.5 36 202.4 121.3 96 253.9 152.2 57 48.9 29.3 17 100.4 60.2 77 151.8 91.0 37 203.3 121.8 97 254.7 152.7 58 49.7 29.8 18 101.2 60.7 78 152.7 91.5 38 204.1 122.4 98 255.6 153.2 59 50.6 30.3 19 102.1 61.2 79 153.5 92.0 39 205.0 122.9 99 256.5 153.7 60 51.5 30.8 20 102.9 61.7 80 154.4 92.5 40 205.9 123.4 300 257.3 154.2 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. N] E. by E. i E. SI 5. by E. t E. NW. by W. i W. sw . by VV. i W. [For 5J^ PoL nt8. Page 526] TABLE 1. Difference of Latitude and Departure for 3 Points. NE. by N. NW. by N. SE. by S. SW. by S. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 50.7 33.9 121 100.6 67.2 181 160.6 100.6 241 200.4 133.9 2 1.-7 1.1 62 51.6 34.4 22 101.4 67.8 82 151.3 101.1 42 201.2 134.4 3 2.5 1.7 63 62.4 36.0 23 102.3 68.3 83 152.2 101.7 43 202.0 135.0 4 3.3 2.2 64 53.2 35.6 24 103.1 68.9 84 153.0 102.2 44 202.9 135.6 5 4.2 2.8 65 54.0 36.1 25 103.9 69.4 85 163.8 102.8 46 203.7 136.1 6 5.0 3.3 66 64.9 36.7 26 104.8 70.0 86 164.7 103.3 46 204.5 136.7 7 5.8 3.9 67 55.7 37.2 27 106.6 70.6 87 155.5 103. 9 47 206.4 137.2 8 6.7 4.4 68 66.6 37.8 28 106.4 71.1 88 156. 3 104.4 48 206.2 137.8 9 7.5 5.0 69 67.4 38.3 29 107.3 71.7 89 157.1 105.0 49 207.0 138.3 10 8.3 5.6 70 58.2 38.9 30 108.1 72.2 72.8 90 191 158.0 105.6 60 207.9 138.9 11 9.1 6.1 71 59.0 39.4 131 108.9 158.8 106.1 251 208.7 139.4 12 10.0 6.7 72 59.9 40.0 32 109.8 73.3 92 159.6 106.7 52 209.6 140.0 13 10.8 7.2 73 60.7 40.6 33 110.6 73.9 93 160.5 107.2 63 210.4 140.6 14 11.6 7.8 74 61.5 41.1 34 111.4 74.4 94 161.3 107.8 54 211.2 141.1 15 12.5 8.3 75 62.4 41.7 35 112.2 75.0 96 162.1 108.3 55 212.0 141.7 16 13.3 8.9 76 63.2 42.2 36 113.1 75.6 96 163.0 108.9 56 212.9 142.2 17 14.1 9.4 77 64.0 42.8 37 113.9 76.1 97 163.8 109.4 57 213.7 142.8 18 15.0 10.0 78 64.9 43.3 38 114.7 76.7 98 164.6 110.0 58 214.5 143.3 19 15.8 10.6 79 65.7 43.9 39 115.6 77.2 99 166.5 110.6 59 215.4 143.9 20 16.6 11.1 80 66.5 44.4 40 116.4 77.8 200 166.3 111.1 60 216.2 144.4 21 17.5 11.7 81 67.3 45.0 141 117.2 78.3 201 167.1 111.7 261 217.0 145.0 22 18.3 12.2 82 68.2 45.6 42 118.1 78.9 02 168.0 112.2 62 217.8 145.6 23 19.1 12.8 83 69.0 46.1 43 118.9 79.4 03 168.8 112.8 63 218.7 146.1 24 20.0 13.3 84 69.8 46.7 44 119.7 80.0 04 169.6 113.3 64 219.6 146.7 26 20.8 13.9 85 70.7 47.2 45 120.6 80.6 05 170.6 113.9 65 220. 3 147.2 26 21.6 14.4 86 71.5 47.8 46 121.4 81.1 06 171.3 114.4 66 221.2 147.8 27 22.4 15.0 87 72.3 48.3 47 122.2 81.7 07 172.1 116.0 67 222.0 148.3 28 23.3 15.6 88 73.2 48.9 48 123.1 82.2 08 172.9 115.6 68 222.8 148.9 29 24.1 16.1 89 74.0 49.4 49 123.9 82.8 09 173.8 116.1 69 223.7 149.4 30 24.9 16.7 90 74.8 50.0 60 124.7 83.3 10 174.6 116.7 70 224.5 225.3 160.0 160.6 31 25.8 17.2 91 75.7 50.6 161 126.6 83.9 211 175.4 117.2 271 32 26.6 17.8 92 76.5 51.1 52 126. 4 84.4 12 176.3 117.8 72 226.2 151.1 33 27.4 18.3 93 77.3 51.7 53 127.2 85.0 13 177.1 118.3 73 227.0 161.7 34 28.3 18.9 94 78.2 52.2 64 128.0 85.6 14 177.9 118.9 74 227.8 162.2 35 29.1 19.4 95 79.0 52'. 8 65 128.9 86.1 15 178.8 119.4 75 228.7 152.8 36 29.9 20.0 96 79.8 53.3 56 129.7 86.7 16 179.6 120.0 76 229.5 163. 3 37 30.8 20.6 97 80.7 53.9 67 130.5 87.2 17 180.4 120.6 77 230.3 163.9 38 31.6 21.1 98 81.5 54.4 68 131.4 87.8 18 181.3 121.1 78 231.1 164.4 39 32.4 21.7 99 82.3 65.0 69 132.2 88.3 19 182.1 121.7 79 232.0 155.0 40 33.3 22.2 100 83.1 55.6 60 133.0 88.9 20 182.9 122.2 80 232.8 233.6 156.6 41 34.1 22.8 101 84.0 56.1 161 133.9 89.4 221 183.8 122.8 281 166.1 42 34.9 23.3 02 84.8 56.7 62 134.7 90.0 22 184.6 123.3 82 234. 5 166.7 43 35.8 23.9 03 85.6 67.2 63 135.5 90.6 23 185.4 123.9 83 235.3 167.2 44 36.6 24.4 04 86.5 57.8 64 136.4 91.1 24 186.2 124.4 84 236.1 157.8 45 37.4 25.0 05 87.3 58.3 65 137.2 91.7 25 187.1 125.0 85 237.0 158.3 46 38.2 25.6 06 88.1 68.9 66 138.0 92.2 26 187.9 125.6 86 237.8 168.9 47 39.1 26.1 07 89.0 69.4 67 138.9 92.8 27 188.7 126.1 87 238.6 159.4 48 39.9 26.7 08 89.8 60.0 68 139.7 93.3 28 189.6 126.7 88 239.5 160.0 49 40.7 27.2 09 90.6 60.6 69 140.5 93.9 29 190.4 127.2 89 240.3 160.6 50 41.6 27.8 10 91.5 61.1 70 141.3 94.4 30 191.2 127.8 90 241. 1 161.1 51 42.4 28.3 111 92.3 61.7 171 142.2 95.0 231 192.1 128.3 291 242.0 161.7 52 43.2 28.9 12 93.1 62.2 72 143.0 95.6 32 192.9 128.9 92 242.8 162.2 53 44.1 29.4 13 94.0 62.8 73 143.8 96.1 33 193.7 129.4 93 243.6 162.8 54 44.9 30.0 14 94.8 63.3 74 144.7 96.7 34 194.6 130.0 94 244.6 163.3 65 45.7 30.6 15 95.6 63.9 75 146.5 97.2 36 195.4 130.6 95 246.3 163.9 56 46.6 31.1 16 96.5 64.4 76 146.3 97.8 36 196.2 131. 1 96 246.1 164.4 57 47.4 31.7 17 97.3 65.0 77 147.2 98.3 37 197.1 131.7 97 246.9 165.0 58 48.2 32.2 18 98.1 65.6 78 148.0 98.9 38 197.9 132.2 98 247.8 166.6 59 49.1 32.8 19 98.9 66.1 79 148.8 99.4 39 198.7 132.8 99 248.6 166.1 60 49.9 33.3 20 99.8 66.7 80 149.7 100.0 40 199.6 133.3 300 249.4 166.7 Dlst Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat Dist. Dep. Lat. Dist. Eep. Lat NE. by E. g 5E. by E. NW. by W. SW. by W. [For 5 Points. 1 TABLE 1. [Page 527 1 Difference of Latitude and Departure for S\ Points. NE. IN . NW. 1 N. SE. 1 S. SW. 1 S. Dist Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 49.0 36.3 121 97.2 72.1 181 145.4 107.8 241 193.6 143.6 2 1.6 1.2 62 49.8 36.9 22 98.0 72.7 82 146.2 108.4 42 194.4 144.2 3 2,4 1.8 63 50.6 37.5 23 98.8 73.3 83 147.0 109.0 43 195.2 144.8 4 3.2 2.4 64 51.4 38.1 24 99.6 73.9 84 147.8 109.6 44 196.0 145.4 5 4.0 3.0 65 52.2 38.7 25 100.4 74.5 85 148.6 110.2 45 196.8 145.9 6 4.8 3.6 66 53.0 39.3 26 101.2 75.1 86 149.4 110.8 46 197.6 146.5 7 5.6 4.2 67 53.8 39.9 27 102.0 75.7 87 150.2 111.4 47 198.4 147.1 8 6.4 4.8 68 54.6 40.5 28 102.8 76.2 88 151.0 112.0 48 199.2 147.7 9 7.2 5.4 69 55.4 41.1 29 103.6 76.8 89 151.8 112.6 49 200.0 148.3 10 8.0 6.0 70 56.2 41.7 30 104.4 77.4 90 152.6 113.2 50 200.8 148.9 149.5 11 8.8 6.6 71 57.0 42.3 131 105.2 78.0 191 153.4 113.8 251 201.6 12 9.6 7.1 72 57.8 42.9 32 106.0 78.6 92 154.2 114.4 52 202.4 150. 1 13 10.4 7.7 73 58.6 43.5 33 106.8 79.2 93 155.0 115.0 53 203.2 150.7 14 11.2 8.3 74 59.4 44.1 34 107.6 79.8 94 155.8 115.6 54 204.0 151.3 15 12.0 8.9 75 60.2 44.7 35 108.4 80.4 95 156.6 116.2 55 204.8 151.9 16 12.9 9.5 76 61.0 45.3 36 109.2 81.0 96 157.4 116.8 56 205.6 152.5 17 13.7 10.1 77 61.8 45.9 37 110.0 81.6 97 158.2 117.4 57 206.4 153.1 18 14.5 10.7 78 62.7 46.5 38 110.8 82.2 98 159.0 117.9 58 207.2 153.7 19 15.3 11.3 79 63.5 47.1 39 111.6 82.8 99 159. 8 118.5 59 208.0 154.3 20 16.1 11.9 80 64.3 47.7 40 112.4 83.4 200 160.6 119.1 60 208.8 154.9 21 16.9 12.5 81 65.1 48.3 141 113.3 84.0 201 161.4 119.7 261 209.6 155. 5 22 17.7 13.1 82 65.9 48.8 42 114.1 84.6 02 162.2 120.3 62 210.4 156.1 23 18.5 13.7 83 66.7 49.4 43 114.9 85.2 03 163.1 120.9 63 211.2 156.7 24 19.3 14.3 84 67.5 50.0 44 115.7 85.8 04 163. 9 121.5 64 212.0 157. 3 25 20.1 14.9 85 68.3 50.6 45 116.5 86.4 05 164.7 122.1 66 212.8 157.9 26 20.9 15.5 86 69.1 51.2 46 117.3 87.0 06 165.5 122.7 66 213.7 158.5 27 21.7 16.1 87 69.9 51.8 47 118.1 87.6 07 166.3 123.3 67 214.5 159.1 28 22.5 16.7 88 70.7 52.4 48 118.9 88.2 08 167.1 123.9 68 215.3 159.6 29 23.3 17.3 89 71.5 53.0 49 119.7 88.8 09 167.9 124.5 69 216.1 160.2 30 24.1 17.9 90 72.3 53.6 50 120,5 89.4 10 168.7 125.1 70 216.9 160.8 31 24.9 18.5 91 73.1 54.2 151 121.3 90.0 211 169.5 125.7 271 217.7 161.4 32 25.7 19.1 92 73.9 54.8 52 122.1 90.5 12 170.3 126.3 72 218.5 162.0 33 26.5 19.7 93 74.7 55.4 53 122.9 91.1 13 171.1 126.9 73 219.3 162.6 34 27.3 20.3 94 75.5 56.0 54 123.7 91.7 14 171.9 127.5 74 220.1 163.2 35 28.1 20.8 95 76.3 56.6 55 124.5 92.3 15 172.7 128.1 75 220.9 163.8 36 28.9 21.4 96 77.1 57.2 56 125.3 92.9 16 173.5 128.7 76 221.7 164.4 37 29.7 22.0 97 77.9 57.8 57 126.1 93.5 17 174.3 129.3 77 222.5 165.0 38 30.5 22.6 98 78.7 58.4 58 126. 9 94.1 18 175.1 129.9 78 223.3 165.6 39 31.3 23.2 99 79.5 59.0 59 127.7 94.7 19 175.9 130.5 79 224.1 166.2 40 32.1 23.8 100 80.3 59.6 60 128.5 95.3 20 176.7 131.1 80 224.9 166.8 41 32.9 24.4 101 81.1 60.2 161 129.3 95.9 221 177.5 131.6 281 225.7 167.4 42 33.7 25.0 02 81.9 60.8 62 130.1 96.5 22 178.3 132.2 82 226.5 168.0 43 34.5 25.6 03 82.7 61.4 63 1.30.9 97.1 23 179.1 132.8 83 227.3 168.6 44 35.3 26.2 04 83.5 62.0 64 131.7 97.7 24 179.9 133.4 84 228.1 169.2 45 36.1 26.8 05 84.3 62.5 65 132.5 98.3 25 180.7 134.0 85 228.9 169.8 46 36.9 27.4 06 85.1 63.1 66 133.3 98.9 26 181. 5 134.6 86 229.7 170.4 47 37.8 28.0 07 85.9 63.7 67 134.1 99.5 27 182.3 135.2 87 230.5 171.0 48 38.6 28.6 08 86.7 64.3 68 134.9 100.1 28 183.1 135.8 88 231.3 171.6 49 39.4 29.2 09 87.5 64.9 69 135.7 100.7 29 183.9 136.4 89 232.1 172.2 50 40.2 29.8 10 88.4 65.5 70 136.5 101.3 30 184.7 137.0 90 232.9 172.8 51 41.0 30.4 111 89.2 66.1 171 137.3 101.9 231 185.5 137.6 291 233.7 173.3 52 41.8 31.0 12 90.0 66.7 72 138.2 102.5 32 186.3 138.2 92 234.5 173.9 53 42.6 31.6 13 90.8 67.3 73 139.0 103.1 33 187.1 138.8 93 235.3 174.5 54 43.4 32.2 14 91.6 67.9 74 139.8 103.7 34 188.0 139.4 94 236.1 175.1 55 44.2 32.8 15 92.4 68.5 75 140.6 104.2 35 188.8 140,0 95 236.9 175.7 56 45.0 33.4 16 93.2 69.1 76 141.4 104.8 36 189.6 140.6 96 237.7 176.3 57 45.8 34.0 17 94.0 69.7 77 142.2 105.4 37 190.4 141.2 97 238.6 176.9 68 46.6 34.6 18 94.8 70.3 78 143.0 106.0 38 191.2 141.8 98 239.4 177.5 69 47.4 35.1 19 95.6 70.9 79 143.8 106.6 39 192.0 142.4 99 240.2 178.1 60 48.2 35.7 20 96.4 71.5 80 144.6 107.2 40 192.8 143.0 300 241.0 178.7 Wst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. NE. ^ ^E. SE. 1 E. NW. 1 W. SW. f W. [For 4| Points. 1 Page 628] TABLE 1. Difference of Latitude and Departure for 3J Points. NE. J N. NW . ^N. SE . ^S. SW. i s. 1 Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 47.2 38.7 121 93.6 76.8 181 139.9 114.8 241 186.3 152.9 2 1.5 1.3 62 47.9 39.3 22 94.3 77.4 82 140.7 116.6 42 187. 1 163.5 3 2.3 1.9 63 48.7 40.0 23 95.1 78.0 83 141.6 116.1 43 187.8 154.2 4 3.1 2.5 64 49.6 40.6 24 95.9 78.7 84 142.2 116.7 44 188.6 164.8 5 3.9 3.2 65 60.2 41.2 25 96.6 79.3 85 143.0 117.4 46 189.4 155.4 6 4.6 3.8 66 51.0 41.9 26 97.4 79.9 86 143.8 118.0 46 190.2 166.1 7 5.4 4.4 67 51.8 42.5 27 98.2 80.6 87 144.6 118.6 47 190.9 166.7 8 6.2 5.1 68 62.6 43.1 28 98.9 81.2 88 145.3 119.3 48 191.7 157.3 9 7.0 5.7 69 63.3 43.8 29 99.7 81.8 89 146.1 119.9 49 192. 5 158.0 10 7.7 6.3 70 54.1 44.4 30 100.5 82.5 90 146.9 147.6 120.5 50 193.3 168.6 11 8.5 7.0 71 54.9 45.0 131 101.3 83.1 191 121.2 261 194.0 159.2 12 9.3 7.6 72 55.7 45.7 32 102.0 83.7 92 148.4 121.8 62 194.8 159.9 13 10.0 8.2 73 56.4 46.3 33 102.8 84.4 93 149.2 122.4 53 196.6 160.5 14 10.8 8.9 74 57.2 46.9 34 103.6 85.0 94 150.0 123.1 54 196.3 161.1 15 11.6 9.5 75 58.0 47.6 35 104.4 85.6 95 150.7 123.7 56 197.1 161.8 16 12.4 10.2 76 58.7 48.2 36 105.1 86.3 96 151.6 124.3 56 197.9 162.4 17 13.1 10.8 77 59.6 48.8 37 105.9 86.9 97 162.3 126.0 67 198.7 163.0 18 13.9 11.4 78 60.3 49.5 38 106.7 87.5 98 163.1 125.6 58 199.4 163.7 19 14.7 12.1 79 61.1 50.1 39 107.4 88.2 99 153.8 126.2 69 200.2 164.3 20 15.5 12.7 80 61.8 60.8 40 108.2 109.0 88.8 89.4 200 201 154.6 126.9 60 201.0 164.9 21 16.2 13.3 81 62.6 61.4 141 156.4 127.6 261 201.8 165.6 22 17.0 14.0 82 63.4 52.0 42 109.8 90.1 02 166.1 128.1 62 202.6 166.2 23 17.8 14.6 83 64.2 52.7 43 110.6 90.7 03 166.9 128.8 63 203.3 166.8 24 18.6 15.2 84 64.9 63.3 44 111.3 91.4 04 157.7 129.4 64 204.1 167.5 25 19.3 15.9 85 65.7 63.9 45 112.1 92.0 05 168.5 130.1 66 204.8 168.1 26 20.1 16.5 86 66.6 64.6 46 112.9 92.6 06 169.2 130.7 66 206.6 168.7 27 20.9 17.1 87 67.3 55.2 47 113.6 93.3 07 160.0 131.3 67 206.4 169.4 28 21.6 17.8 88 68.0 56.8 48 114.4 93.9 08 160.8 132.0 68 207.2 170.0 29 22.4 18.4 89 68.8 66.6 49 116.2 94.5 09 161.6 132.6 69 207.9 170.7 30 23.2 19.0 90 69.6 57.1 60 116.0 95.2 10 162.3 133.2 70 208.7 171.3 31 24.0 19.7 91 70.3 67.7 151 116.7 96.8 211 163.1 133.9 271 209.5 171.9 32 24.7 20.3 92 71.1 58.4 62 117.5 96.4 12 163.9 134.5 72 210.3 172.6 33 25.5 20.9 93 71.9 59.0 63 118.3 97.1 13 164.7 136.1 73 211.0 173.2 34 26.3 21.6 94 72.7 59.6 64 119.0 97.7 14 166.4 136.8 74 211.8 173.8 36 27.1 22.2 95 73.4 60.3 55 119.8 98.3 15 166.2 136.4 75 212.6 174.5 36 27.8 22.8 96 74.2 60.9 66 120.6 99.0 16 167.0 137.0 76 213.4 176.1 37 28.6 23.5 97 75.0 61.6 57 121.4 99.6 17 167.7 137.7 77 214.1 176.7 38 29.4 24.1 98 75.8 62.2 68 122.1 100.2 18 168.6 138.3 78 214.9 176.4 39 30.1 24.7 99 76.5 62.8 59 122.9 100.9 19 169.3 138.9 79 215.7 177.0 40 30.9 25.4 100 77.3 63.4 60 123.7 101.5 20 170.1 170.8 139.6 80 216.4 177.6 41 31.7 26.0 101 78.1 64.1 161 124.5 102. 1 221 140.2 281 217.2 178.3 42 32.5 26.6 02 78.8 64.7 62 125.2 102.8 22 171.6 140.8 82 218.0 178.9 43 33.2 27.3 03 79.6 66.3 63 126.0 103.4 23 172.4 141.5 83 218.8 179.5 44 34.0 27.9 04 80.4 66.0 64 126.8 104.0 24 173.2 142.1 84 219.5 180.2 45 34.8 28.5 05 81.2 66.6 65 127.5 104.7 25 173.9 142.7 85 220.3 180.8 46 35.6 29.2 06 81.9 67.2 66 128.3 105.3 26 174.7 143.4 86 221.1 181.4 47 36.3 29.8 07 82.7 67.9 67 129.1 105.9 27 175.5 144.0 87 221.9 182.1 48 37.1 30.5 08 83.5 68.5 68 129.9 106.6 28 176.2 144.6 88 222.6 182.7 49 37.9 31.1 09 84.3 69.1 69 130.6 107.2 29 177.0 145.3 89 223.4 183.3 50 38.7 31.7 10 85.0 69.8 70 131.4 107.8 30 177.8 146.9 90 224.2 184.0 51 39.4 32.4 111 86.8 70.4 171 132.2 108.5 231 178.6 146.6 291 224.9 184.6 52 40.2 33.0 12 86.6 71.1 72 133.0 109.1 32 179.3 147.2 92 226.7 186.2 53 41.0 33.6 13 87.4 71.7 73 133.7 109.8 33 180.1 147.8 93 226.5 185.9 54 41.7 34.3 14 88.1 72.3 74 134.5 110.4 34 180.9 148.4 94 227.3 186.6 55 42.5 34.9 15 88.9 73.0 75 135.3 111.0 35 181.7 149.1 95 228.0 187.1 56 43.3 35.5 16 89.7 73.6 76 136.0 111.7 36 182.4 149.7 96 228.8 187.8 57 44.1 36.2 17 90.4 74.2 77 136.8 112.3 37 183.2 160.4 97 229.6 188.4 58 44.8 36.8 18 91.2 74.9 78 137.6 112.9 38 184.0 161.0 98 230.4 189.0 59 45.6 37.4 19 92.0 75.6 79 138.4 113.6 39 184.7 161.6 99 231.1 189.7 60 46.4 38.1 20 92.8 76.1 80 139.1 114.2 40 186.5 162.3 300 231.9 190.3 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. NE. i] E. SE. JE N W. JW. sw. ^^ V. [For 4J Points. 1 i^ >• — =^ 1 TABLE 1. [Page 629 Difference of Latitude and Departure for 3| Points. NE. i N. NW. tN. SE. } S. 8W. i 8. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 241 Lat. Dep. 1 0.7 0.7 61 45.2 41.0 121 89.7 81.3 181 134.1 121.6 178.6 161.8 2 1.5 1.3 62 45.9 41.6 22 90.4 81.9 82 134.9 122.2 42 179.3 162.5 3 2.2 2.0 63 46.7 42.3 23 91.1 82.6 83 135.6 122.9 43 180.1 163.2 4 3.0 2.7 64 47.4 43.0 24 91.9 83.3 84 136.3 123.6 44 180.8 163.9 5 3.7 3.4 65 48.2 43.7 25 92.6 83.9 85 137.1 124.2 45 181.5 164.5 6 4.4 4.0 66 48.9 44.3 26 93.4 84.6 86 137.8 124.9 46 182.3 165.2 7 5.2 4.7 67 49.6 45.0 27 94.1 85.3 87 138.6 125.6 47 183.0 165.9 8 5.9 5.4 68 50.4 45.7 28 94.8 86.0 88 139.3 126.3 48 183.8 166.5 9 6.7 6.0 69 51.1 46.3 29 95.6 86.6 89 140.0 126.9 49 184.5 167.2 10 7.4 6.7 70 51.9 47.0 30 96.3 87.3 90 140.8 127.6 50 251 185.2 167.9 11 8.2 7.4 71 52.6 47.7 131 97.1 88.0 191 141.5 128.3 186.0 168.6 12 8.9 8.1 72 53.3 48.4 32 97.8 88.6 92 142.8 128.9 52 186.7 169.2 13 9.6 8.7 73 54.1 49.0 33 98.5 89.3 93 143.0 129.6 53 187.5 169.9 14 10.4 9.4 74 54.8 49.7 34 99.3 90.0 94 143.7 130.3 54 188.2 170.6 15 11.1 10.1 75 55.6 50.4 35 100.0 90.7 95 144.5 131.0 55 188.9 171.2 16 11.9 10.7 76 56.3 51.0 36 100.8 91.3 96 145.2 131.6 56 189.7 171.9 17 12.6 11.4 77 57.1 51.7 37 101.5 92.0 97 146.0 132.3 57 190.4 172.6 18 13.3 12.1 78 57.8 52.4 38 102.3 92.7 98 146.7 133.0 58 191.2 173.3 19 14.1 12.8 79 58.5 53.1 39 103.0 93.3 99 147.4 133.6 59 191.9 173.9 20 14.8 13.4 80 59.3 53.7 40 103.7 94.0 200 148.2 148.9 134.3 60 192.6 174.6 21 15.6 14.1 81 60.0 54.4 141 104.5 94.7 201 135.0 261 193.4 175.3 22 16.3 14.8 82 60.8 55.1 42 105.2 95.4 02 149.7 135.7 62 194.1 175.9 23 17.0 15.4 83 61.5 55.7 43 106.0 96.0 03 150.4 136.3 63 194.9 176.6 24 17.8 16,1 84 62.2 56.4 44 106.7 96.7 04 151.2 137.0 64 195.6 177.3 25 18.5 16.8 85 63.0 57.1 45 107.4 97.4 05 151.9 137.7 65 196.4 178.0 26 19.3 17.5 86 63.7 57.8 46 108.2 98.0 06 152.6 138.3 66 197.1 178.6 27 20.0 18.1 87 64.5 58.4 47 108.9 98.7 07 153.4 139.0 67 197.8 179.3 28 20.7 18.8 88 65.2 59.1 48 109.7 99.4 08 154.1 139.7 68 198.6 180.0 29 21.5 19.5 89 65.9 59.8 49 110.4 100.1 09 154.9 140.4 69 199.3 180.6 30 22.2 20.1 90 66.7 60.4 50 111.1 100.7 10 155.6 141,0 70 200.1 200.8 181.3 31 23.0 20.8 91 67.4 61.1 151 111.9 101.4 211 156.3 141.7 271 182.0 32 23.7 21.5 92 .68.2 61.8 52 112.6 102.1 12 157.1 142.4 72 201.5 182.7 33 24.5 22.2 93 68.9 62.5 53 113.4 102.7 13 157.8 143.0 73 202.3 183.3 34 25.2 22.8 94 69.6 63.1 54 114.1 103.4 14 158.6 143.7 74 203.0 184.0 35 25.9 23.5 95 70.4 63.8 55 114.8 104.1 15 159.3 144.4 75 203.8 184.7 36 26.7 24.2 96 71.1 64.5 56 115.6 104.8 16 160.0 145.1 76 204.5 185.4 37 27.4 24.8 97 71.9 65.1 57 116.3 105.4 17 160.8 145.7 77 205.2 186.0 38 28.2 25.5 98 72.6 65.8 58 117.1 106.1 18 161.5 146.4 78 206.0 186.7 39 28.9 26.2 99 73.4 66.5 59 117.8 106.8 19 162.3 147.1 79 206.7 187.4 40 29.6 26.9 100 101 74.1 67.2 60 118.6 107.4 20 163.0 147.7 80 207.5 188.0 41 30.4 27.5 74.8 67.8 161 119.3 108.1 221 163.8 148.4 281 208.2 188.7 42 31.1 28.2 02 75.6 68.5 62 120.0 108.8 22 164.5 149.1 82 208.9 189.4 43 31.9 28.9 03 76.3 69.2 63 120.8 109.5 23 165.2 149.8 83 209.7 190.1 44 32.6 29.5 04 77.1 69.8 64 121.5 110.1 24 166.0 150.4 84 210.4 190.7 45 33.3 30.2 05 77.8 70.5 65 122.3 110.8 25 166.7 151.1 85 211.2 191.4 46 34.1 30.9 06 78.5 71.2 66 123. 111.5 26 167.5 151.8 86 211.9 192.1 47 34.8 31.6 07 79.3 71.9 67 123.7 112.2 27 168.2 152.4 87 212.7 192.7 48 35.6 32.2 08 80.0 72.5 68 124.5 112.8 28 168.9 153.1 88 213.4 193.4 49 36.3 32.9 09 80.8 73.2 69 125.2 113.5 29 169.7 153.8 89 214.1 194.1 50 37.0 33.6 10 81.5 73.9 70 126.0 114.2 30 170.4 154. 5 90 214.9 215.6 194.8 51 37.8 34.2 111 82.2 74.5 171 126.7 114.8 231 171.2 155.1 291 195.4 52 38.5 34.9 12 83.0 75.2 72 127.4 115.5 32 171.9 155. 8 92 216.4 196.1 53 39.3 35.6 13 83.7 75.9 73 128.2 116.2 33 172.6 156.5 93 217. 1 196.8 54 40.0 36.3 14 84.5 76.6 74 128.9 116.9 34 173.4 157.1 94 217.8 197.4 55 40.8 36.9 15 85.2 77.2 75 129.7 117.5 35 174.1 157.8 95 218.6 198.1 56 41.5 37.6 16 86.0 77.9 76 130.4 118.2 36 174.9 158.5 96 219.3 198.8 57 42.2 38.3 17 86.7 78.6 77 131.1 118.9 37 175.6 159.2 97 220.1 199.5 58 43.0 39.0 18 87.4 79.2 78 131.9 119.5 38 176.3 159.8 98 220.8 200.1 59 43.7 39.6 19 88.2 79.9 79 132.6 120.2 39 177.1 160.5 99 221.5 200.8 60 44.5 40.3 20 88.9 80.6 80 133.4 120.9 40 177.8 161.2 300 222.3 201.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. NE. i E. S E. } E. N^ W. J W. SW. } W. [For 4} Points. 1 21594°— 14- -27 Page 630] TABLE 1. Difference of Latitude and Depart are for 4 Points. NE. NW. SE. SW. Diet. Lat. bep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.7 0.7 61 43.1 43.1 121 85.6 85.6 181 128.0 128.0 241 170.4 170.4 2 1.4 1.4 62 43.8 43.8 22 86.3 86.3 82 128.7 128.7 42 171.1 171.1 3 2.1 2.1 63 44.5 44.5 23 87.0 87.0 83 129.4 129.4 43 171.8 171.8 4 2.8 2.8 64 45.3 45.3 24 87.7 87.7 84 130.1 130.1 44 172.5 172.5 5 3.5 3.5 65 46.0 46.0 25 88.4 88.4 85 130.8 130.8 45 173.2 173.2 6 4.2 4.2 66 46.7 46.7 26 89.1 89.1 86 131.5 131.5 46 173.9 173.9 7 4.9 4.9 67 47.4 47.4 27 89.8 89.8 87 132.2 132.2 47 174.7 174.7 8 5.7 5.7 68 48.1 48.1 28 90.5 90.5 88 132.9 132.9 48 175.4 175.4 9 6.4 6.4 69 48.8 48.8 29 91.2 91.2 89 133.6 133.6 49 176.1 176.1 10 7.1 7.1 70 49.5 49.5 50.2 30 91.9 91.9 90 134.4 134.4 50 176.8 176.8 11 7.8 7.8 71 50.2 131 92.6 92.6 191 135.1 135.1 251 177.5 177.5 12 8.5 8.5 72 50.9 50.9 32 93.3 93.3 92 135.8 135.8 52 178.2 178.2 13 9.2 9.2 73 51.6 51.6 33 94.0 94.0 93 136.5 136.5 53 178.9 178.9 14 9.9 9.9 74 52.3 52.3 34 94.8 94.8 94 137.2 137.2 54 179.6 179.6 15 10.6 10.6 75 53.0 53.0 36 95.5 95.5 95 137.9 137.9 55 180.3 180.3 16 11.3 11.3 76 53.7 53.7 36 96.2 96.2 96 138.6 138.6 56 181.0 181.0 17 12.0 12.0 77 54.4 54.4 37 96.9 96.9 97 139.3 139.3 57 181.7 181.7 18 12.7 12.7 78 55.2 55.2 38 97.6 97.6 98 140.0 140.0 58 182.4 182.4 19 13.4 13.4 79 55.9 55.9 39 98.3 98.3 99 140.7 140.7 59 183.1 183.1 20 14.1 14.1 80 56.6 56.6 40 99.0 99.0 200 141.4 141.4 60 183.8 183.8 21 14.8 14.8 81 57.3 57.3 141 99.7 99.7 201 142.1 142.1 261 184.6 184.6 22 15.6 15.6 82 58.0 58.0 42 100.4 100.4 02 142.8 142.8 62 185.3 185.3 23 16.3 16.3 83 58.7 58.7 43 101.1 101.] 03 143.5 143.5 63 186.0 186.0 24 17.0 17.0 84 59.4 59.4 44 101.8 101.8 04 144.2 144.2 64 186.7 186.7 25 17.7 17.7 85 60.1 60.1 45 102.5 102.5 05 145.0 145.0 65 187.4 187.4 26 18.4 18.4 86 60.8 60.8 46 103.2 103.2 06 145.7 145.7 66 188.1 188.1 27 19.1 19.1 87 61.5 61.5 47 103.9 103.9 07 146.4 146.4 67 188.8 188.8 28 19.8 19.8 88 62.2 62.2 48 104.7 104.7 08 147.1 147.1 68 189.5 189.5 29 20.5 20.5 89 62.9 62.9 49 105.4 105.4 09 147.8 147.8 69 190.2 190.2 30 21.2 21.2 90 63.6 63.6 50 106.1 106.1 10 148.5 148.5 70 190.9 190.9 31 21.9 21.9 91 64.3 64.3 151 106.8 106.8 211 149.2 149.2 271 191.6 191.6 32 22.6 22.6 92 65.1 65.1 52 107.5 107.5 12 149.9 149.9 72 192.3 192.3 33 23.3 23.3 93 65.8" 65.8 53 108.2 108.2 13 150.6 150.6 73 193.0 193.0 34 24.0 24.0 94 66.5 66.5 54 108.9 108.9 14 151.3 151.3 74 193.7 193.7 35 24.7 24.7 95 67.2 67.2 55 109.6 109.6 15 152.0 152.0 75 194.5 194.5 36 25.5 25.5 96 67.9 67.9 56 110.3 110.3 16 152.7 152.7 76 195.2 195.2 37 26.2 26.2 97 68.6 68.6 57 111.0 111.0 17 153.4 153.4 77 195.9 195.9 38 26.9 26.9 98 69.3 69.3 58 111.7 111.7 18 154.1 154.1 78 196.6 196.6 39 27.6 27.6 99 70.0 70.0 59 112.4 112.4 19 154.9 154.9 79 197.3 197.3 40 28.3 28.3 100 70.7 70.7 60 113.1 113.8 113.1 20 155.6 155.6 156.3 80 198.0 198.0 41 29.0 29.0 101 71.4 71.4 161 113.8 221 156.3 281 198.7 198.7 42 29.7 29.7 02 72.1 72.1 62 114.6 114.6 22 157.0 157.0 82 199.4 199.4 43 30.4 30.4 03 72.8 72.8 63 115.3 115.3 23 157.7 157.7 83 200.1 200.1 44 31.1 31.1 04 73.5 73.5 64 116.0 116.0 24 158.4 158.4 84 200.8 200.8 45 31.8 31.8 05 74.2 74.2 65 116.7 116.7 25 159.1 159.1 85 201.5 201.5 46 32.5 32.5 06 75.0 75.0 66 117.4 117.4 26 159.8 159.8 86 202.2 202.2 47 33.2 33.2 07 75.7 75.7 67 118.1 118.1 27 160.5 160.5 87 202.9 202.9 48 33.9 33.9 08 76.4 76.4 68 118.8 118.8 28 161.2 161.2 88 203.6 203.6 49 34.6 34.6 09 77.1 77.1 69 119.5 119.5 29 161.9 161.9 89 204.4 204.4 50 35.4 35.4 10 77.8 77.8 70 120.2 120.2 30 162.6 162.6 90 205.1 205.1 51 36.1 36.1 111 78.5 78.5 171 ]20.9 120.9 231 163.3 163.3 291 205.8 205.8 52 36.8 36.8 12 79.2 79.2 72 121.6 121.6 32 164.0 164.0 92 206.5 206.5 53 37.5 37.5 13 79.9 79.9 73 122.3 122.3 33 164.8 164.8 93 207.2 207.2 54 38.2 38.2 14 80.6 80.6 74 123.0 123.0 34 165.5 165.5 94 207.9 207.9 55 38.9 38.9 15 81.3 81.3 75 123.7 123.7 35 166.2 166.2 95 208.6 208.6 56 39.6 39.6 16 82.0 82.0 76 124.5 124.5 36 166.9 166.9 96 209.3 209.3 57 40.3 40.3 17 82.7 82.7 77 125.2 125.2 37 167.6 167.6 97 210.0 210.0 58 41.0 41.0 18 83.4 83.4 78 125.9 125.9 38 168. 3 168.3 98 210.7 210.7 59 41.7 41.7 19 84.1 84.1 79 126.6 126.6 39 169.0 169.0 99 211.4 211.4 60 42.4 42.4 20 84.9 84.9 80 127.3 127.3 40 169.7 169.7 300 212.1 212.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. . NE. NW. ] 3E. SW. [For 4 Points. 1 Page 632] TABLE 2. Difference of Latitude and Departure for 1° (179°, 181' ', 359°] . Dist. Lat. Dep. Dist. 61 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.0 61.0 1.1 121 121.0 2.1 181 181.0 3.2 241 241.0 4.2 2 2.0 0.0 62 62.0 1.1 22 122.0 2.1 82 182.0 3.2 42 242. 4.2 3 3.0 0.1 63 63.0 1.1 23 123.0 2.1 83 183.0 3.2 43 243.0 4.2 4 4.0 0.1 64 64.0 1.1 24 124.0 2.2 84 184.0 S.2 44 244.0 4.3 5 5.0 0.1 65 65.0 1.1 25 125.0 2.2 85 185.0 3 2 45 245.0 4.3 6 6.0 0.1 66 66.0 1.2 26 126.0 2.2 86 186.0 3.2 46 246.0 4.3 7 7.0 0.1 67 67.0 1.2 27 127.0 2.2 87 187.0 3.3 47 247.0 4.3 8 8.0 0.1 68 68.0 1.2 28 128.0 2.2 88 188.0 3.3 48 248.0 4.3 9 9.0 0.2 69 69.0 1.2 29 129.0 2.3 89 189.0 3.3 49 249.0 4.3 10 10.0 0.2 70 70.0 1.2 30 130.0 2.3 90 190.0 3.3 50 250.0 4.4 11 11.0 0.2 71 71.0 1.2 131 131.0 2.3 191 191.0 3.3 251 251.0 4.4 12 12.0 0.2 72 72.0 1.3 32 132.0 2.3 92 192.0 3.4 52 252.0 4.4 13 13.0 0.2 73 73.0 1.3 33 133.0 2.3 93 193.0 3.4 53 253.0 4.4 14 14.0 0.2 74 74.0 1.3 34 134.0 2.3 94 194.0 3.4 54 254.0 4.4 15 15.0 0.3 75 75.0 1.3 35 135.0 2.4 95 195.0 3.4 55 255. 4.5 16 16.0 0.3 76 76.0 1.3 36 136.0 2.4 96 196.0 3.4 56 256.0 4.5 17 17.0 0.3 77 77.0 1.3 37 137.0 2.4 97 197.0 3.4 57 257.0 4.5 18 18.. 0.3 78 78.0 1.4 38 138.0 2.4 98 198.0 3.5 58 258.0 4.5 19 19.0 0.3 79 79.0 1.4 39 139.0 2.4 99 199.0 3.5 59 259.0 4.5 20 20.0 0.3 80 80.0 1.4 40 140.0 2.4 200 200.0 3.5 60 260.0 4.5 21 21.0 0.4 81 81.0 1.4 141 141.0 2.5 201 201.0 3.5 261 261.0 4.6 22 22.0 0.4 82 82.0 1.4 42 142.0 2.5 02 202.0 3.5 62 262.0 4.6 23 23.0 0.4 83 83.0 1.4 43 143.0 2.5 03 203.0 3.5 63 263.0 4.6 24 24.0 0.4 84 84.0 1.5 44 144.0 2.5 04 204.0 3.6 64 264.0 4.6 25 25.0 0.4 85 85.0 1.5 45 145.0 2.5 05 205.0 3.6 65 265.0 4.6 26 26.0 0.5 86 86.0 1.5 46 146.0 2.5 06 206.0 3.6 66 266.0 4.6 27 27.0 0.5 87 87.0 1.5 47 147.0 2.6 07 207.0 3.6 67 267.0 4.7 28 28.0 0.5 88 88.0 1.5 48 148.0 2.6 08 208.0 3.6 68 268.0 4.7 29 29.0 0.5 89 89.0 1.6 49 149.0 2.6 09 209.0 3.6 69 269.0 4.7 30 31 30.0 0.5 90 90.0 1.6 50 150.0 151.0 2.6 10 210.0 3.7 70 270.0 4.7 31.0 0.5 91 91.0 1.6 151 2.6 211 211.0 3.7 271 271.0 4.7 32 32.0 0.6 92 92.0 1.6 52 152.0 2.7 12 212.0 3.7 72 272.0 4.7 33 33.0 0.6 93 93.0 1.6 53 153.0 2.7 13 213.0 3.7 73 273.0 4.8 34 34.0 0.6 94 94.0 1.6 54 154.0 2.7 14 214.0 3.7 74 274.0 4.8 35 35.0 0.6 95 95.0 1.7 55 155.0 2.7 15 215.0 3.8 75 275. 4.8 36 36.0 0.6 96 96.0 1.7 56 156.0 2.7 16 216.0 3.8 76 276.0 4.8 37 37.0 0.6 97 97.0 1.7 57 157. 2.7 17 217.0 3.8 77 277.0 4.8 38 38.0 0.7 98 98.0 1.7 58 158.0 2.8 18 218.0 3.8 78 278.0 4.9 39 39.0 0.7 99 99.0 1.7 59 159.0 2.8 19 219.0 3.8 79 279.0 4.9 40 40.0 0.7 100 100.0 101.0 1.7 60 160.0 2.8 20 220.0 3.8 80 280.0 4.9 41 41.0 0.7 101 1.8 161 161.0 2.8 221 221.0 3.9 281 281.0 4.9 42 42.0 0.7 02 102.0 1.8 62 162.0 2.8 22 222.0 3.9 82 282.0 4.9 43 43.0 0.8 03 103.0 1.8 63 163.0 2.8 23 223.0 3.9 83 283.0 4.9 44 44.0 0.8 04 104.0 1.8 64 164.0 2.9 24 224.0 3.9 84 284.0 5.0 45 45.0 0.8 05 105.0 1.8 65 165.0 2.9 25 225.0 3.9 85 285.0 5.0 46 46.0 0.8 06 106.0 1.8 66 166.0 2.9 26 226.0 3.9 86 286.0 5.0 47 47.0 0.8 07 107.0 1.9 67 167.0 2.9 27 227.0 4.0 87 287.0 5.0 48 48.0 0.8 08 108.0 1.9 68 168.0 2.9 28 228.0 4.0 88 288.0 5.0 49 49.0 0.9 09 109. 1.9 69 169.0 2.9 29 229.0 4.0 89 289.0 5.0 50 50.0 0.9 10 110.0 1.9 70 170.0 3.0 30 230.0 4.0 90 290.0 5.1 51 51.0 0.9 111 111.0 1.9 171 171.0 3.0 231 231.0 4.0 291 291.0 5.1 52 52.0 0.9 12 112.0 2.0 72 172.0 3.0 32 232.0 4.0 92 292.0 5.1 53 53.0 0.9 13 113.0 2.0 73 173.0 3.0 33 233.0 4.1 93 293.0 5.1 54 54.0 0.9 14 114.0 2.0 74 174.0 3.0 34 234.0 4.1 94 294.0 5.1 55 55.0 1.0 15 115.0 2.0 75 175.0 3.1 35 235.0 4.1 95 295.0 5.1 56 56.0 1.0 16 116.0 2.0 76 176.0 3.1 36 236.0 4.1 96 296.0 5.2 57 57.0 1.0 17 117.0 2.0 77 177.0 3.1 37 237.0 4.1 97 297.0 5.2 58 58.0 1.0 18 118.0 2.1 78 178.0 3.1 38 238.0 4.2 98 298.0 5.2 59 59.0 1.0 19 119.0 2.1 79 179.0 3.1 39 239.0 4.2 99 299.0 5.2 60 60.0 1.0 20 120.0 2.1 80 180.0 3.1 40 240.0 4.2 300 300.0 5.2 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 89° (( )1°, 269°, 271° )• 1 TABLE 2. [Page 533 Difference of Latitude and Departure for 1° (179°, 181°, 369° ). Diet. Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. DiBt Lat. Dep. Dist. Lat. Dep. 301 301.0 5.3 361 360.9 6.3 421 420.9 7.3 481 480.9 8.4 541 540.9 9.6 02 302.0 6.3 62 361.9 6.3 22 421.9 7.4 82 481.9 8.4 42 541.9 9.5 03 303.0 5.3 63 362. 9 6.3 23 422.9 7.4 83 482.9 8.6 43 542.9 9.5 04 304.0 5.3 64 363.9 6.4 24 423.9 7.4 84 483.9 8.5 44 543.9 9.5 06 305.0 5.3 66 364.9 6.4 25 424.9 7.4 85 484.9 8.5 46 544.9 9.5 06 306.0 5.3 66 365.9 6.4 26 425.9 7.4 86 485.9 8.5 46 546.9 9.6 07 307.0 5.4 67 366.9 6.4 27 426.9 7.4 87 1 486.9 8.5 47 646.9 9.6 08 308.0 5.4 68 367.9 6.4 28 427.9 7.5 88 487.9 8.6 48 547.9 9.6 09 309.0 5.4 69 868.9 6.4 29 428.9 7.6 89 488.9 8.6 49 548.9 9.6 10 310.0 5.4 70 369.9 370! 9 6.5 30 429.9 7.5 90 489.9 8.6 50 549.9 9.6 311 311.0 5.4 371 6.6 431 430.9 7.5 491 490.9 8.6 551 550.9 9.6 12 312.0 6.4 72 371.9 6.5 32 431.9 7.6 92 491.9 8.6 62 561.9 9.6 13 313.0 5.5 73 372.9 6.5 33 432.9 7.5 93 492.9 8.7 53 652.9 9.7 14 314.0 5.5 74 373.9 6.5 34 433.9 7.6 94 493.9 8.7 64 653.9 9.7 15 315.0 6.6 75 374.9 6.5 36 434.9 7.6 95 1 494.9 8.7 55 554.9 9.7 16 316.0 5.5 76 376.9 6.6 36 435.9 7.6 96 495.9 8.7 66 566.9 9.7 17 317.0 5.5 77 376.9 6.6 37 436.9 7.6 97 496.9 8.7 67 556.9 9.7 18 318.0 5.5 78 377.9 6.6 38 437.9 7.6 98 497.9 8.7 58 557.9 9.7 19 319.0 5.6 79 378.9 6.6 39 438.9 7.7 99 498.9 8.8 69 658.9 9.8 20 320.0 5.6 80 379.9 6.6 40 439.9 7.7 500 i 499.9 8.8 60 559. 9 9.8 321 321.0 5.6 381 380.9 6.7 441 440.9 7.7 501 500.9 8.8 661 560.9 9.8 22 322.0 6.6 82 381.9 6.7 42 441.9 7.7 02 601.9 8.8 62 561.9 9.8 23 323.0 5.6 83 382. 9 6.7 43 442.9 7.7 03 602.9 8.8 63 662.9 9.8 24 324.0 5.6 84 383.9 6.7 44 443.9 7.7 04 503.9 8.8 64 563.9 9.8 25 325.0 6.7 85 384.9 6.7 45 444.9 7.8 05 604.9 8.8 66 564.9 9.9 26 326.0 6.7 86 385.9 6.7 46 445.9 7.8 06 505.9 8.9 66 665.9 9.9 27 327.0 5.7 87 386.9 6.8 47 446.9 7.8 07 506.9 8.9 67 666.9 9.9 28 328.0 5.7 88 387.9 6.8 48 447.9 7.8 08 607.9 8.9 68 567.9 9.9 29 329.0 6.7 89 388.9 6.8 49 448.9 7.8 09 608.9 8.9 69 668.9 9.9 30 330.0 5.8 90 389.9 6.8 50 449.9 7.8 10 609.9 8.9 70 569.9 9.9 331 331.0 5.8 391 390.9 6.8 451 450.9 7.9 611 610.9 9.0 571 570.9 10.0 32 332.0 5.8 92 391.9 6.8 52 451.9 7.9 12 511.9 9.0 72 671.9 10.0 33 333.0 6.8 93 392.9 6.9 63 452.9 7.9 13 512.9 9.0 73 572.9 10.0 34 333.9 5.8 94 393.9 6.9 54 453.9 7.9 14 513.9 9.0 74 573.9 10.0 35 334.9 6.8 95 394.9 6.9 55 464.9 7.9 15 614.9 9.0 76 674. 9 10.0 36 335.9 5.9 96 395.9 6.9 56 466.9 8.0 16 515.9 9.0 76 576.9 10.0 37 336.9 6.9 97 396.9 6.9 57 456.9 8.0 17 516.9 9.1 77 676.9 10.1 38 337.9 5.9 98 397.9 6.9 68 457.9 8.0 18 517.9 9.1 78 577.9 10.1 39 338.9 6.9 99 398.9 7.0 69 458.9 8.0 19 618.9 9.1 79 678.9 10.1 40 339.9 6.9 400 399.9 7.0 60 459.9 8.0 20 519.9 9.1 80 679.9 10.1 341 340.9 6.0 401 400.9 7.0 461 460.9 8.0 621 520.9 9.1 581 680.9 10.1 42 341.9 6.0 02 401.9 7.0 62 461.9 8.1 22 621.9 9.1 82 581.9 10.1 43 342. 9 6.0 03 402.9 7.0 63 402.9 8.1 23 622.9 9.2 83 582.9 10.2 44 343.9 6.0 04 403.9 7.1 64 463.9 8.1 24 523.9 9.2 84 683.9 10.2 45 344.9 6.0 05 404.9 7.1 66 464.9 8.1 26 524. 9 9.2 85 584.9 10.2 46 345.9 6.0 06 405.9 7.1 66 465.9 8.1 26 625. 9 9.2 86 586.9 10.2 47 346.9 6.1 07 406.9 7.1 67 466.9 8.1 27 526.9 9.2 87 586.9 10.2 48 347.9 6.1 08 407.9 7.1 68 467.9 8.2 28 527.9 9.2 88 587.9 10.2 49 348.9 6.1 09 408.9 7.1 69 468.9 8.2 29 628.9 9.3 89 688.9 10.3 50 349.9 6.1 10 411 409.9 7.2 70 471 469.9 8.2 30 631 529.9 9.3 90 589.9 590.9 10.3 351 350.9 6.1 410.9 7.2 470.9 8.2 630.9 9.3 591 10.3 52 351.9 6.1 12 411.9 7.2 72 471.9 8.2 32 531.9 9.3 92 591.9 10.3 53 352.9 6.2 13 412.9 7.2 73 472.9 8.2 33 532.9 9.3 93 692. 9 10.3 54 353.9 6.2 14 413.9 7.2 74 473.9 8.3 34 533.9 9.3 94 693.9 10.3 55 354.9 6.2 15 414.9 7.2 76 474.9 8.3 35 534.9 9.4 95 594.9 10.4 56 355.9 6.2 16 416.9 7.3 76 475.9 8.3 36 536.9 9.4 96 595.9 10.4 57 356.9 6.2 17 416.9 7.3 77 476.9 8.3 37 636.9 9.4 97 696.9 10.4 58 357.9 6.2 18 417.9 7.3 78 477.9 8.3 38 537.9 9.4 98 697.9 10.4 69 368.9 6.3 19 418.9 7.3 79 478.9 8.4 39 638.9 9.4 99 598.9 10.4 60 369.9 6.3 20 419.9 7.3 80 479.9 8.4 40 539.9 9.4 600 599.9 10.5 Di8t. Dep. Lat. DSst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat 89° (9 1°, 269° , 271°) Page 534] TABLE 2. Difference of Latitude and Depart ure for 2° (178°, 182 °, 358° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.0 61 61.0 2.1 121 120.9 4.2 181 180.9 6.3 241 240.9 8.4 2 2.0 0.1 62 62.0 2.2 22 121.9 4.3 82 181.9 6.4 42 241.9 8.4 3 3.0 0.1 63 63.0 2.2 23 122.9 4.3 83 182.9 6.4 43 242.9 8.5 4 4.0 0.1 64 64.0 2.2 24 123.9 4.3 84 183.9 6.4 44 243.9 8.5 5 5.0 0.2 65 65.0 2.3 25 124.9 4.4 85 184.9 6.5 45 244.9 8.6 6 6.0 0.2 66 66.0 2.3 26 125.9 4.4 86 185.9 6.5 46 245.9 8.6 7 7.0 0.2 67 67.0 2.3 27 126.9 4.4 87 186.9 6.5 47 246.8 8.6 8 8.0 0.3 68 68.0 2.4 28 127.9 4.5 88 187.9 6.6 48 247.8 8.7 9 9.0 0.3 69 69.0 2.4 29 128.9 4.5 89 188.9 6.6 49 248.8 8.7 10 10.0 0.3 70 70.0 2.4 30 129.9 4.5 90 189.9 6.6 50 249.8 8.7 11 11.0 0.4 71 71.0 2.5 131 130.9 4.6 191 190.9 6.7 251 250.8 8.8 12 12.0 0.4 72 72.0 2.5 32 131.9 4.6 92 191.9 6.7 52 251.8 8.8 13 13.0 0.5 73 73.0 2.5 33 132.9 4.6 93 192.9 6.7 53 252.8 8.8 14 14.0 0.5 74 74.0 2.6 34 133.9 4.7 94 193.9 6.8 54 253.8 8.9 15 15.0 0.5 75 75.0 2.6 35 134.9 4.7 95 194.9 6.8 55 254.8 8.9 16 16.0 0.6 76 76.0 2.7 36 135.9 4.7 96 195.9 6.8 56 255.8 8.9 17 17.0 0.6 77 77.0 2.7 37 136.9 4.8 97 196.9 6.9 57 256.8 9.0 18 18.0 0.6 78 78.0 2.7 38 137.9 4.8 98 197.9 6.9 58 257.8 9.0 19 19.0 0.7 79 79.0 2.8 39 138.9 4.9 99 198.9 6.9 59 258.8 9.0 20 20.0 0.7 80 80.0 2.8 40 139.9 4.9 200 199.9 7.0 60 259.8 9.1 21 21.0 0.7 81 81.0 2.8 141 140.9 4.9 201 200.9 7.0 261 260.8 9.1 22 22.0 0.8 82 82.0 2.9 42 141.9 5.0 02 201.9 7.0 62 261.8 9.1 23 23.0 0.8 83 82.9 2.9 43 142.9 5.0 03 202.9 7.1 63 262.8 9.2 24 24.0 0.8 84 83.9 2.9 44 143.9 5.0 04 203.9 7.1 64 263.8 9.2 25 25.0 0.9 85 84.9 3.0 45 144.9 5.1 05 204.9 7.2 65 264.8 9.2 26 26.0 0.9 86 85.9 .3.0 46 145.9 5.1 06 205.9 7.2 66 265.8 9.3 27 27.0 0.9 87 86.9 3.0 47 146.9 5.1 07 206.9 7.2 67 266.8 9.3 28 28.0 1.0 88 87.9 3.1 48 147.9 5.2 08 207.9 7.3 68 267.8 9.4 29 29.0 1.0 89 88.9 3.1 49 148.9 5.2 09 208.9 7.3 69 268.8 9.4 30 30.0 1.0 90 89.9 3.1 50 149.9 5.2 10 211 209.9 7.3 70 269.8 9.4 31 31.0 1.1 91 90.9 3.2 151 150.9 5.3 210.9 7.4 271 270.8 9.5 32 32.0 1.1 92 91.9 3.2 52 151.9 5.3 12 211.9 7.4 72 271.8 9.5 33 33.0 1.2 93 92.9 3.2 53 152.9 5.3 13 212.9 7.4 73 272.8 9.5 34 34.0 1.2 94 93.9 3.3 54 153.9 5.4 14 213.9 7.5 74 273.8 9.6 35 35.0 1.2 95 94.9 3.3 55 154.9 5.4 15 214.9 7.5 75 274.8 9.6 36 36.0 1.3 96 95.9 3.4 56 155.9 5.4 16 215.9 7.5 76 275.8 9.6 37 37.0 1.3 97 96.9 3.4 57 156.9 5.5 17 216.9 7.6 77 276.8 9.7 38 38.0 1.3 98 97.9 3.4 58 157.9 5.5 18 217.9 7.6 78 277.8 9.7 39 39.0 1.4 99 98.9 3.5 59 158.9 5.5 19 218.9 7.6 79 278.8 9.7 40 40.0 1.4 100 99.9 3.5 60 159.9 5.6 20 219.9 7.7 80 279.8 9.8 41 41.0 1.4 101 100.9 3.5 161 160.9 5.6 221 220.9 7.7 281 280.8 9.8 42 42.0 1.5 02 101.9 3.6 62 161.9 5.7 22 221.9 7.7 82 281.8 9.8 43 43.0 1.5 03 102.9 3.6 63 162.9 5.7 23 222.9 7.8 83 282.8 9.9 44 44.0 1.5 04 103.9 3.6 64 163.9 5.7 24 223.9 7.8 84 283.8 9.9 45 45.0 1.6 05 104.9 3.7 65 164.9 5.8 25 224.9 7.9 85 284.8 9.9 46 46.0 1.6 06 105.9 3.7 66 165.9 5.8 26 225.9 7.9 86 285.8 10.0 47 47.0 1.6 07 106.9 3.7 67 166.9 5.8 27 226.9 7.9 87 286.8 10.0 48 48.0 1.7 08 107.9 3.8 68 167.9 5.9 28 227.9 8.0 88 287.8 10.1 49 49.0 1.7 09 108.9 3.8 69 168.9 5.9 29 228.9 8.0 89 288.8 10.1 50 50.0 1.7 10 109.9 3.8 70 169.9 5.9 30 229.9 8.0 90 289.8 10.1 10.2 51 51.0 1.8 111 110.9 3.9 171 170.9 6.0 231 230.9 8.1 291 290.8 52 52.0 1.8 12 111.9 3.9 72 171.9 6.0 32 231.9 8.1 92 291.8 10.2 53 53.0 1.8 13 112.9 3.9 73 172.9 6.0 33 232.9 8.1 93 292.8 10.2 54 54.0 1.9 14 113.9 4.0 74 173.9 6.1 34 233.9 8.2 94 293.8 10.3 55 55.0 1.9 15 114.9 4.0 75 174.9 6.1 35 234.9 8.2 95 294.8 10.3 56 56.0 2.0 16 115.9 4.0 76 175.9 6.1 36 235.9 8.2 96 295.8 10.3 57 57.0 2.0 17 116.9 4.1 77 176.9 6.2 37 236.9 8.3 97 296.8 10.4 58 58.0 2.0 18 117.9 4.1 78 177.9 6.2 38 237.9 8.3 98 297.8 10.4 59 59.0 2.1 19 118.9 4.2 79 178.9 6.2 39 238.9 8.3 99 298.8 10.4 60 60.0 2.1 20 119.9 4.2 80 179.9 6.3 40 239.9 8.4 300 299.8 10.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 88° (92°, 268° , 272°) . TABLE 2. [Page 535 [ Difference of Latitude and Departure for 2° (178°, 182°, 358°] . Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 Dist. Lat. Dep. 301 300.8 10.5 361 360.8 12.6 421 420.8 14.7 481 480.7 16.8 541 540.7 18.9 02 301.8 10.5 62 361.8 12.6 22 421.8 14.7 82 481.7 16.8 42 541.7 18.9 03 302.8 10.6 63 362.8 12.7 23 422.8 14.7 83 482.7 16.8 43 542.7 18.9 04 303.8 10.6 64 363.8 12.7 24 423.8 14.8 84 483.7 16.9 44 543.7 19.0 05 304.8 10.6 65 364.8 12.7 25 424.8 14.8 85 484.7 16.9 45 544.7 19.0 06 305.8 10.7 66 365.8 12.8 26 425.7 14.9 86 485.7 16.9 46 545.7 19.0 07 306.8 10.7 67 366.8 12.8 27 426.7 14.9 87 486.7 17.0 47 546.7 19.1 08 307.8 10.7 68 367.8 12.8 28 427.7 14.9 88 487.7 17.0 48 547.7 19.1 09 308.8 10.8 69 368.8 12.9 29 428.7 15.0 89 488.7 17.0 49 548.7 19.1 10 309.8 10.8 70 369.8 12.9 30 429.7 15.0 90 489.7 17.1 50 549.7 19.2 311 310.8 10.8 371 370.8 12.9 431 430.7 15.0 491 490.7 17.1 551 550.7 19.2 12 311.8 10.9 72 371.8 13.0 32 431.7 15.1 92 491.7 17.1 52 551.7 19.2 13 312.8 10.9 73 372.8 13.0 33 432.7 15.1 93 492.7 17.2 53 552.7 19.3 14 313.8 10.9 74 373.8 13.0 34 433.7 15.1 94 493.7 17.2 54 553.7 19.3 15 314.8 11.0 75 374.8 13.1 35 434.7 15.2 95 494.7 17.2 55 554.7 19.3 16 315.8 11.0 76 375.8 13.1 36 435.7 15.2 96 495.7 17.3 56 555.7 19.4 17 316.8 11.0 77 376.8 13.1 37 436.7 15.2 97 496.7 17.3 57 556.7 19.4 18 317.8 11.1 78 377.8 13.2 38 437.7 15.3 98 497.7 17.3 58 557.7 19.4 19 318.8 11.1 79 378.8 13.2 39 438.7 15.3 99 498.7 17.4 59 558.7 19.5 20 321 319.8 11.2 80 379.8 13.2 40 439.7 15.3 500 499.7 17.4 60 559.7 19.5 320.8 11.2 381 380.8 13.3 441 440.7 15.4 501 500.7 17.5 561 560.7 19.5 22 321.8 11.2 82 381.8 13.3 42 441.7 15.4 02 501.7 17.5 62 561.7 19.6 23 322.8 11.3 83 382.8 13.3 43 442.7 15.4 03 502.7 17.5 63 562.7 19.6 24 323.8 11.3 84 383.8 13.4 44 443.7 15.5 04 503.7 17.6 64 563.7 19.6 25 324.8 11.3 85 384.8 13.4 45 444.7 15.5 05 504.7 17.6 65 564.7 19.7 26 325.8 11.4 86 385.8 13.5 46 445.7 15.6 06 505.7 17.6 66 565.7 19.7 27 326.8 11.4 87 386.8 13.5 47 446.7 15.6 07 506.7 17.7 67 566.7 19.7 28 327.8 11.4 88 387.8 13.5 48 447.7 15.6 08 507.7 17.7 68 567.7 19.8 29 328.8 11.5 89 388.8 13.6 49 448.7 15.7 09 508.7 17.7 69 568. 7 19.8 30 329.8 11.5 90 389.8 13.6 50 449.7 15.7 10 509.7 17.8 70 569.7 19.9 331 330.8 11.5 391 390.8 13.6 451 450.7 15.7 511 510.7 17.8 571 570.7 19.9 32 331.8 11.6 92 391.8 13.7 52 451.7 15.8 12 511.7 17.8 72 571.7 19.9 33 332.8 11.6 93 392.8 13.7 53 452.7 15.8 13 512.7 17.9 73 572.7 20.0 34 333.8 11.6 94 393.8 13.7 54 453.7 15.8 14 513.7 17.9 74 573.6 20.0 35 334.8 11.7 95 394.8 13.8 55 454.7 15.9 15 514.7 17.9 75 574.6 20.0 36 335.8 11.7 96 395.8 13.8 56 455.7 15.9 16 515.7 18.0 76 575.6 20.1 37 336.8 11.7 97 396.8 13.8 57 456.7 15.9 17 516.7 18.0 77 576.6 20.1 38 337.8 11.8 98 397.8 13.9 58 457.7 16.0 18 517.7 18.1 78 577.6 20.1 39 338.8 11.8 99 398.8 13.9 59 458.7 16.0 19 518.7 18.1 79 578.6 20.2 40 339.8 11.9 400 399.8 13.9 60 459.7 16.0 20 519.7 18.1 80 579.6 20.2 341 340.8 11.9 401 400.8 14.0 461 460.7 16.1 521 520.7 18.2 581 580.6 20.2 42 341.8 11.9 02 401.8 14.0 62 461.7 16.1 22 521.7 18.2 82 581.6 20.3 43 342.8 12.0 03 402.8 14.0 63 462.7 16.1 23 522.7 18.2 83 582.6 20.3 44 343.8 12.0 04 403.8 14.1 64 463.7 16.2 24 523.7 18.3 84 583.6 20.3 45 344.8 12.0 05 404.8 14.1 65 464.7 16.2 25 524.7 18.3 85 584.6 20.4 46 345.8 12.1 06 405.8 14.2 66 465.7 16.2 26 525.7 18.4 86 585.6 20.4 47 346.8 12.1 07 406.8 14.2 67 466.7 16.3 27 526.7 18.4 87 586.6 20.4 48 347.8 12.1 08 407.8 14.2 68 467.7 16.3 28 527.7 18.4 88 587.6 20.5 49 348.8 12.2 09 408.8 14.3 69 468.7 16.4 29 528.7 18.5 89 588.6 20.5 50 351 349.8 12.2 10 409.8 14.3 70 469.7 16.4 30 529.7 18.5 90 589.6 20.5 350.8 12.2 411 410.8 14.3 471 470.7 16.4 531 530.7 18.5 591 590.6 20.6 52 351.8 12.3 12 411.8 14.4 72 471.7 16.5 32 531.7 18.6 92 591.6 20.6 53 352.8 12.3 13 412.8 14.4 73 472.7 16.5 33 532.7 18.6 93 592.6 20.6 54 353.8 12.3 14 413.8 14.4 74 473.7 16.5 34 533.7 18.6 94 593.6 20.7 55 354.8 12.4 15 414.8 14.5 75 474.7 16.6 35 534.7 18.7 95 594.6 20.7 56 355. 8 12.4 16 415.8 14.5 76 475.7 16.6 36 535.7 18.7 96 595.6 20.7 57 356.8 12.4 17 416.8 14.5 77 476.7 16.6 37 536.7 18.7 97 596.6 20.8 58 357.8 12.5 18 417.8 14.6 78 477.7 16.7 38 537.7 18.8 98 597.6 20.8 59 358.8 12.5 19 418.8 14.6 79 478.7 16.7 39 538.7 18.8 99 598.6 20.8 60 359.8 12.5 20 419.8 14.6 80 479.7 16.7 40 539.7 18.8 600 599.6 20.9 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 88° (92°, 268 ^ 272° ). Page 636] TABLE 2. Difference of Latitude and Depart ure for 3° (177°, 183 % 357° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.1 61 60.9 3.2 121 120.8 6.3 181 180.8 9.6 241 240.7 12.6 2 2.0 0.1 62 61.9 3.2 22 121.8 6.4 82 181.8 9.6 42 241.7 12.7 3 3.0 0.2 63 62.9 3.3 23 122.8 6.4 83 182.7 9.6 43 242.7 12.7 4 4.0 0.2 64 63.9 3.3 24 123.8 6.5 84 183.7 9.6 44 243.7 12.8 5 5.0 0.3 65 64.9 3.4 26 124.8 6.5 85 184.7 9.7 45 244.7 12.8 6 6.0 0.3 66 65.9 3.5 26 125.8 6.6 86 185.7 9.7 46 245.7 12.9 7 7.0 0.4 67 66.9 3.5 27 126.8 6.6 87 186.7 9.8 47 246.7 12.9 8 8.0 0.4 68 67.9 3.6 28 127.8 6.7 88 187.7 9.8 48 247.7 13.0 9 9.0 0.5 69 68.9 3.6 29 128.8 6.8 89 188.7 9.9 49 248.7 13.0 10 10.0 0.5 70 69.9 3.7 30 129.8 6.8 90 189.7 9.9 60 249.7 13.1 11 11.0 0.6 71 70.9 3.7 131 130.8 6.9 191 190.7 10.0 251 260.7 13.1 12 12.0 0.6 72 71.9 3.8 32 131.8 6.9 92 191.7 10.0 52 251.7 13.2 13 13.0 0.7 73 72.9 3.8 33 132.8 7.0 93 192.7 10.1 53 262.7 13.2 14 14.0 0.7 74 73.9 3.9 34 133.8 7.0 94 193.7 10.2 54 253.7 13.3 15 15.0 0.8 75 74.9 3.9 36 134.8 7.1 95 194.7 10.2 55 254.7 13.3 16 16.0 0.8 76 75.9 4.0 36 136.8 7.1 96 195.7 10.3 56 255.6 13.4 17 17.0 0.9 77 76.9 4.0 37 136.8 7.2 97 196.7 10.3 57 256.6 13.6 18 18.0 0.9 78 77.9 4.1 38 137.8 7.2 98 197.7 10.4 58 267.6 13.5 19 19.0 1.0 79 78.9 4.1 39 138.8 7.3 99 198.7 10.4 69 268.6 13.6 20 20.0 1.0 80 79.9 4.2 40 139.8 7.3 200 199.7 10.5 60 259.6 13.6 21 21.0 1.1 81 80.9 4.2 141 140.8 7.4 201 200.7 10.5 261 260.6 13.7 22 22.0 1.2 82 81.9 4.3 42 141.8 7.4 02 201.7 10.6 62 261.6 13.7 23 23.0 1.2 83 82.9 4.3 43 142.8 7.5 03 202.7 10.6 63 262.6 13.8 24 24.0 1.3 84 83.9 4.4 44 143.8 7.5 04 203.7 10.7 64 263.6 13.8 25 26.0 1.3 85 84.9 4.4 45 144.8 7.6 05 204.7 10.7 65 264.6 13.9 26 26.0 1.4 86 85.9 4.5 46 146.8 7.6 06 206.7 10.8 66 266.6 13.9 27 27.0 1.4 87 86.9 4.6 47 146.8 7.7 07 206.7 10.8 67 266.6 14.0 28 28.0 1.5 88 87.9 4.6 48 147.8 7.7 08 207.7 10.9 68 267.6 14.0 29 29.0 1.5 89 88.9 4.7 49 148.8 7.8 09 208.7 10.9 69 268.6 14.1 30 30.0 1.6 90 89.9 4.7 60 149.8 7.9 10 209.7 11.0 70 269.6 270.6 14.1 31 31.0 1.6 91 90.9 4.8 161 160.8 7.9 211 210.7 11.0 271 14.2 32 32.0 1.7 92 91.9 4.8 62 151.8 8.0 12 211.7 11.1 72 271.6 14.2 33 33.0 1.7 93 92.9 4.9 63 152.8 8.0 13 212.7 11.1 73 272.6 14.3 34 34.0 1.8 94 93.9 4.9 54 153.8 8.1 14 213.7 11.2 74 273.6 14.3 35 36.0 1.8 95 94.9 5.0 56 164.8 8.1 15 214.7 11.3 75 274.6 14.4 36 36.0 1.9 96 95.9 5.0 66 155.8 8.2 16 215.7 11.3 76 275.6 14.4 37 36.9 1.9 97 96.9 5.1 57 166.8 8.2 17 216.7 11.4 77 276.6 14.5 38 37.9 2.0 98 97.9 6.1 58 167.8 8.3 18 217.7 11.4 78 277.6 14.5 39 38.9 2.0 99 98.9 5.2 59 168.8 8.3 19 218.7 11.5 79 278.6 14.6 40 39.9 2.1 100 99.9 5.2 60 159.8 8.4 20 221 219.7 11.5 80 279.6 14.7 41 40.9 2.1 101 100.9 5.3 161 160.8 8.4 220.7 11.6 281 280.6 14.7 42 41.9 2.2 02 101.9 6.3 62 161.8 8.6 22 221.7 11.6 82 281.6 14.8 43 42.9 2.3 03 102.9 5.4 63 162.8 8.6 23 222.7 11.7 83 282.6 14.8 44 43.9 2.3 04 103.9 6.4 64 163.8 8.6 24 223.7 11.7 84 283.6 14.9 45 44.9 2.4 05 104.9 6.5 65 164.8 8.6 26 224.7 11.8 86 284.6 14.9 46 45.9 2.4 06 105.9 5.6 66 165.8 8.7 26 225.7 11.8 86 286.6 15.0 47 46.9 2.5 07 106.9 5.6 67 166.8 8.7 27 226.7 11.9 87 286.6 16.0 48 47.9 2.5 08 107. 9 5.7 68 167.8 8.8 28 227.7 11.9 88 287.6 15.1 49 48.9 2.6 09 108.9 6.7 69 168.8 8.8 29 228.7 12.0 89 288.6 15.1 50 49.9 2.6 10 109.8 5.8 70 169.8 8.9 30 229.7 12.0 90 289.6 16.2 51 50.9 2.7 111 110.8 6.8 171 170.8 8.9 231 230.7 12.1 291 290.6 16.2 52 51.9 2.7 12 111.8 6.9 72 171.8 9.0 32 231.7 12.1 92 291.6 15.3 53 52.9 2.8 13 112.8 5.9 73 172.8 9.1 33 232.7 12.2 93 292.6 16.3 54 53.9 2.8 14 113.8 6.0 74 173.8 9.1 34 233.7 12.2 94 293.6 16.4 55 54.9 2.9 15 114.8 6.0 75 174.8 9.2 35 234.7 12.3 95 294.6 16.4 56 55.9 2.9 16 115.8 6.1 76 175.8 9.2 36 236.7 12.4 96 296.6 16.5 67 56.9 3.0 17 116.8 6.1 77 176.8 9.3 37 236.7 12.4 97 296.6 15.6 58 57.9 3.0 18 117.8 6.2 78 177.8 9.3 38 237.7 12.5 98 297.6 16.6 59 68.9 3.1 19 118.8 6.2 79 178.8 9.4 39 238.7 12.5 99 298.6 15.6 60 59.9 3.1 20 119.8 6.3 80 179.8 9.4 40 239.7 12.6 300 299.6 15.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. 87° ( 93°, 267 °, 273° )• TABLE 2. . [Page 637 | Difference of Latitude and Departure for 3° (177°, 183°, 357° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 300.6 15.7 361 360.5 18.9 421 420.4 22.0 481 480.3 26.2 641 540.2 28.3 02 301.6 15.8 62 361.5 19.0 22 421.4 22.1 82 481.3 25.2 42 641.2 28.4 03 302.6 15.9 63 362.5 19.0 23 422.4 22.2 83 482.3 25.3 43 642.2 28.4 04 303.5 15.9 64 363.5 19.1 24 423.4 22.2 84 483.3 1 25.3 44 543.2 28.6 05 304.5 16.0 65 364.5 19.1 25 424. 4 22.3 85 484.3 1 26.4 45 544.2 28.6 06 305.5 16.0 66 365.5 19.2 26 425. 4 22.3 86 485.3 26.4 46 546.2 28.6 07 306.5 16.1 67 366.5 19.2 27 426. 4 22.4 87 486.3 26.5 47 546.2 28.6 08 307.5 16.1 68 367.5 19.3 28 I 427.4 22.4 88 487.3 25.6 48 647.2 28.7 09 308.5 16.2 69 368.5 19.3 29 1 428.4 22.5 89 488.3 25.6 49 548.2 28.7 10 311 309.5 310.5 16.2 70 369.5 19.4 30 431 429.4 22.5 90 489.3 25.6 50 549.2 28.8 16.3 371 370.5 19.4 430.4 22.6 491 490.3 26.7 551 550.2 28.8 12 311.5 16.3 72 371.5 19.5 32 431.4 22.6 92 491.3 26.7 52 561.2 28.9 13 312.5 16.4 73 372.5 19.5 33 432.4 22.7 93 492.3 25.8 53 552.2 28.9 14 313.5 16.4 74 373.5 19.6 34 433.4 22.7 94 493.3 25.9 54 553.2 29.0 15 314.5 16.5 75 374.5 19.6 36 434.4 22.8 96 494.3 26.9 55 654.2 29.1 16 315.5 16.6 76 375.5 19.7 36 435.4 22.8 96 495.3 26.0 66 665.2 29.1 17 316.5 16.6 77 376.5 19.8 37 436.4 22.9 97 496.3 26.0 67 566.2 29.2 18 317.5 16.7 78 377.4 19.8 38 437.4 22.9 98 497.3 26.1 68 667.2 29.2 19 318.5 16.7 79 378.4 19.9 39 438.4 23.0 99 498.3 26.1 59 558.2 29.3 20 319.5 16.8 80 379.4 19.9 40 439.4 23.0 500 501 499.3 500.3 26.2 26.2 60 561 559.2 29.3 29.4 321 320.5 16.8 381 380.4 20.0 441 440.4 23.1 560.2 22 321.5 16.9 82 381.4 20.0 42 441.4 23.1 02 501.3 26.3 62 561.2 29.4 23 322.5 16.9 83 382.4 20.1 43 442.4 23.2 03 502.3 26.3 63 662.2 29.6 24 323.5 17.0 84 383.4 20.1 44 443.4 23.3 04 503.3 26.4 64 563.2 29.6 25 324.5 17.0 85 384.4 20.2 45 444.4 23.3 05 604.3 26.4 65 564.2 29.6 26 325. 5 17.1 86 385.4 20.2 46 445.4 23.4 06 605.3 26.6 66 666.2 29.6 27 326.5 17.1 87 386.4 20.3 47 446.4 23.4 07 506.3 26.6 67 666.2 29.7 28 327.5 17.2 88 387.4 20.3 48 447.4 23.5 08 507.3 26.6 68 567.2 29.7 29 328.5 17.2 89 388.4 20.4 49 448.4 23.5 09 508.3 26.6 69 568.2 29.8 30 329.5 17.3 90 389.4 20.4 50 449.3 23.6 10 509.3 26.7 70 569. 2 29.8 331 330.5 17.3 391 390.4 20.5 451 450.3 23.6 511 510.3 26.7 571 570.2 29.9 32 331.5 17.4 92 391.4 20.5 52 461.3 23.7 12 511.3 26.8 72 571.2 29.9 33 332.5 17.5 93 392.4 20.6 53 452.3 23.7 13 612.3 26.8 73 572.2 30.0 34 333.5 17.5 94 393.4 20.6 54 453.3 23.8 14 513.3 26.9 74 573.2 30.0 35 334.5 17.6 95 394.4 20.7 55 454.3 23.8 15 514.3 27.0 76 674.2 30.1 36 335.5 17.6 96 395.4 20.7 56 455.3 23.9 16 515.3 27.0 76 575.2 30.1 37 336.5 17.7 97 396.4 20.8 57 456.3 23.9 17 516.3 27.1 77 576.2 30.2 38 337.5 17.7 98 397.4 20.8 58 457.3 24.0 18 517.3 27.1 78 677.2 30.2 39 338.5 17.8 99 398.4 20.9 59 458.3 24.0 19 618.3 27.2 79 678.2 30.3 40 339.5 17.8 400 399.4 20.9 60 459.3 24.1 20 519.3 27.2 80 679.2 30.3 341 340.5 17.9 401 400.4 21.0 461 460.3 24.1 621 520.3 27.3 681 580.2 30.4 42 341.5 17.9 02 401.4 21.1 62 461.3 24.2 22 621.3 27.3 82 581.2 30.4 43 342.5 18.0 03 402.4 21.1 63 462.3 24.2 23 522.3 27.4 83 582.2 30.5 44 343.5 18.0 04 403.4 21.2 64 463.3 24.3 24 523. 3 27.4 84 583.2 30.5 45 344.5 18.1 05 404.4 21.2 65 464.3 24.4 26 624.3 27.6 85 584.2 30.6 46 345.5 18.1 06 405.4 21.3 66 465.3 24.4 26 626.3 27.5 86 685.2 30.6 47 346.5 18.2 07 406.4 21.3 67 466.3 24.6 27 526.3 27.6 87 586.2 30.7 48 347.5 18.2 08 407.4 21.4 68 467.3 24.5 28 527.3 27.6 88 587.2 30.7 49 348.5 18.3 09 408.4 21.4 69 468.3 24.6 29 528.3 27.7 89 588.2 30.8 50 349.5 18.3 18.4 10 411 409.4 21.5 70 469.3 24.6 30 529.3 27.7 90 589.2 590.2 30.9 351 350.5 410.4 21.5 471 470.3 24.7 631 630.3 27.8 591 30.9 52 351.5 18.4 12 411.4 21.6 72 471.3 24.7 32 631.3 27.8 92 591.2 31.0 53 352.5 18.5 13 412.4 21.6 73 472.3 24.8 33 532.3 27.9 93 592.2 31.0 54 353. 5 18.5 14 413.4 21.7 74 473.3 24.8 34 533.3 27.9 94 593.2 31.1 55 354.5 18.6 15 414.4 21.7 75 474.3 24.9 36 534.3 28.0 95 594.2 31.1 56 355.5 18.6 16 415.4 21.8 76 476.3 24.9 36 635.3 28.1 96 696.2 31.2 57 356.5 18.7 17 416.4 21.8 77 476.3 25.0 37 536.3 28.1 97 696.2 31.2 58 357.5 18.8 18 417.4 21.9 78 477.3 25.0 38 537.3 28.2 98 697.2 31.3 59 358.5 18.8 19 418.4 21.9 79 478.3 25.1 39 538.3 28.2 99 598.2 31.3 60 359.5 18.9 20 419.4 22.0 80 479.3 25.1 40 539.3 28,3 600 599.2 31.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 87° (93*, 267°, 273°). 1 Page 638] TABLE 2. Difference of Latitude and Departure for 4° (176°, 184 °, 356° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.1 61 60.9 4.3 121 120.7 8.4 181 180.6 12.6 241 240.4 16.8 2 2.0 0.1 62 61.8 4.3 22 121.7 8.5 82 181.6 12.7 42 24J.4 16.9 3 3.0 0.2 63 62.8 4.4 23 122.7 8.6 83 182.6 12.8 43 242.4 17.0 4 4.0 0.3 64 63.8 4.5 24 123.7 8.6 84 183.6 12.8 44 243.4 17.0 5 5.0 0.3 65 64.8 4.5 25 124.7 8.7 85 184.5 12.9 45 244.4 17.1 6 6.0 0.4 66 65.8 4.6 26 125.7 8.8 86 185.5 13.0 46 245.4 17.2 7 7.0 0.5 67 66.8 4.7 27 126.7 8.9 87 186.5 13.0 47 246.4 17.2 8 8.0 0.6 68 67.8 4.7 28 127.7 8.9 88 187.5 13.1 48 247.4 17.3 9 9.0 0.6 69 68.8 4.8 29 128.7 9.0 89 188.5 13.2 49 248.4 17.4 10 10.0 0.7 70 69.8 4.9 30 129.7 9.1 90 189.5 13.3 50 249.4 17.4 11 11.0 0.8 71 70.8 5.0 131 130.7 9.1 191 190.5 13.3 251 250.4 17.5 12 12.0 0.8 72 71.8 5.0 32 131.7 9.2 92 191.5 13.4 52 251.4 17.6 13 13.0 0.9 73 72.8 5.1 33 132.7 9.3 93 192.5 13.5 53 252.4 17.6 14 14.0 1.0 74 73.8 5.2 34 133.7 9.3 94 193.5 13.5 54 253.4 17.7 15 15.0 1.0 75 74.8 5.2 35 134.7 9.4 95 194.5 13.6 55 254.4 17.8 16 16.0 1.1 76 75.8 5.3 36 135.7 9.5 96 195.5 13.7 56 255.4 17.9 17 17.0 1.2 77 76.8 5.4 37 136.7 9.6 97 196.5 13.7 57 256.4 17.9 18 18.0 1.3 78 77.8 5.4 38 137.7 9.6 98 197.5 13.8 58 257.4 18.0 19 19.0 1.3 79 78.8 5.5 39 138.7 9.7 99 198.5 13.9 59 258.4 18.1 20 20.0 1.4 80 79.8 5.6 40 139.7 9.8 200 199.5 14.0 60 259.4 18.1 21 20.9 1.5 81 80.8 5.7 141 140.7 9.8 201 200.5 14.0 261 260.4 18.2 22 21.9 1.5 82 81.8 5.7 42 141.7 9.9 02 201.5 14.1 62 261.4 18.3 23 22.9 1.6 83 82.8 5.8 43 142.7 i 10.0 03 202.5 14.2 63 262. 4 18.3 24 23.9 1.7 84 83.8 5.9 44 143.6 10.0 04 203.5 14.2 64 263.4 18.4 25 24.9 1.7 85 84.8 5.9 45 144.6 10.1 05 204.5 14.3 65 264.4 18.5 26 25,9 1.8 86 85.8 6.0 46 145.6 10.2 06 205.5 14.4 66 265.4 18.6 27 26.9 1.9 87 86.8 6.1 47 146.6 10.3 07 206.5 14.4 67 266.3 18.6 28 27.9 2.0 88 87.8 6.1 48 147.6 10.3 08 207.5 14.5 68 267.3 18.7 29 28.9 2.0 89 88.8 6.2 49 148.6 10.4 09 208.5 14.6 69 268.3 18.8 30 31 29.9 2.1 90 89.8 90.8 6.3 6.3 50 149.6 10.5 10 209.5 14.6 70 269.3 18.8 30.9 2.2 91 151 150.6 10.5 211 210.5 14.7 271 270.3 18.9 32 31.9 2.2 92 91.8 6.4 52 151.6 10.6 12 211.5 14.8 72 271.3 19.0 33 32.9 2.3 93 92.8 6.5 53 152.6 10.7 13 212.5 14.9 73 272.3 19.0 34 33.9 2.4 94 93.8 6.6 54 153.6 10.7 14 213.5 14.9 74 273.3 19.1 35 34.9 2.4 95 94.8 6.6 55 154.6 10.8 15 214.5 15.0 75 274.3 19.2 36 35.9 2.5 96 95.8 6.7 56 155.6 10.9 16 215.5 15.1 76 275.3 19.3 37 36.9 2.6 97 96.8 6.8 57 156.6 11.0 17 216.5 15.1 77 276.3 19.3 38 37.9 2.7 98 97.8 6.8 58 157.6 11.0 18 217.5 15.2 78 277.3 19.4 39 38.9 2.7 99 98.8 6.9 59 158.6 11.1 19 218.5 15.3 79 278.3 19.5 40 39.9 2.8 100 99.8 7.0 60 159.6 160.6 11.2 20 219.5 15.3 80 279.3 19.5 41 40.9 2.9 101 100.8 7.0 161 11.2 221 220.5 15.4 281 280.3 19.6 42 41.9 2.9 02 101.8 7.1 62 161.6 11.3 22 221.5 15.5 82 281.3 19.7 43 42.9 3.0 03 102.7 7.2 63 162.6 11.4 23 222.5 15.6 83 282.3 19.7 44 43.9 3.1 04 103.7 7.3 64 163.6 11.4 24 223.5 15.6 84 283.3 19.8 45 44.9 3.1 05 104.7 7.3 65 164.6 11.5 25 224.5 15.7 85 284.3 19.9 46 45.9 3.2 06 105.7 7.4 66 165.6 11.6 26 225.4 15.8 86 285.3 80.0 47 46.9 3.3 07 106.7 7.5 67 166.6 11.6 27 226.4 15.8 87 286.3 20.0 48 47.9 3.3 08 107.7 7.5 68 167.6 11.7 28 227.4 15.9 88 287.3 20.1 49 48.9 3.4 09 108.7 7.6 69 168.6 11.8 29 228.4 16.0 89 288.3 20.2 50 49.9 3.5 10 109.7 7.7 70 169.6 11.9 30 229.4 16.0 90 289.3 20.2 51 50.9 3.6 111 110.7 7.7 171 170.6 11.9 231 230.4 16.1 291 290.3 20.3 52 51.9 3.6 12 111.7 7.8 72 171.6 12.0 32 231.4 16.2 92 291.3 20.4 53 52.9 3.7 13 112.7 7.9 73 172.6 12.1 33 232.4 16.3 93 292.3 20.4 54 53.9 3.8 14 113.7 8.0 74 173.6 12.1 34 233.4 16.3 94 293.3 20.5 55 54.9 3.8 15 114.7 8.0 75 174.6 12.2 35 234.4 16.4 95 294.3 20.6 56 55.9 3.9 16 115.7 8.1 76 175.6 12.3 36 235.4 16.5 96 295.3 20.6 57 56.9 4.0 17 116.7 8.2 77 176.6 12.3 37 236.4 16.5 97 296.3 20.7 58 57.9 4.0 18 117.7 8.2 78 177.6 12.4 38 237.4 16.6 98 297.3 20.8 59 58.9 4.1 19 118.7 8.3 79 178.6 12.5 39 238.4 16.7 99 298.3 20.9 60 69.9 4.2 20 119.7 8.4 80 179.6 12.6 40 239.4 16.7 300 299.3 20.9 Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. J !6°; ( H°, 266°, 274° )• TABLE 2. [Page 639 Difference of Latitude and Depart are for 4° (176°, 184°, 356° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist Lat. Dep. Dist. Lat. Dep. Dist Lat Dep. 301 300.3 21.0 361 360.1 25.2 421 420.0 29.4 481 479.8 33.5 541 539.7 37.7 02 301.3 21.1 62 361. 1 25.2 22 421.0 29.4 82 480.8 33.6 42 540.7 37.8 03 302.2 21.1 63 362.1 25.3 23 422.0 29.5 83 481.8 33.7 43 541.7 37.9 04 303.2 21.2 64 363.1 25.4 24 423.0 29.6 84 482.8 33.7 44 542.7 37.9 05 304.2 21.3 65 364.1 25.5 25 424.0 29.6 85 483.8 33.8 45 543.7 38.0 06 305. 2 21.3 66 365.1 25.5 26 424.9 29.7 86 484.8 33.9 46 544.7 38.1 07 306.2 21.4 67 366.1 25.6 27 425.9 29.8 87 485.8 33.9 47 545.7 38.1 08 307.2 21.5 68 367.1 25.7 28 426.9 29.9 88 486.8 34.0 48 546.7 38.2 09 308.2 21.6 69 368.1 25.7 29 427.9 29.9 89 487.8 34.1 49 547.7 38.3 10 309.2 21.6 70 369.1 25.8 30 428.9 30.0 90 488.8 34.2 50 548.7 38.3 311 310.2 21.7 371 370.1 25.9 431 429.9 30.1 491 489.8 34.2 551 549.7 38.4 12 311.2 21.8 72 371.1 25.9 32 430.9 30.1 92 490.8 34.3 52 550.7 38.5 13 312.2 21.8 73 372.1 26.0 33 431.9 30.2 93 491.8 34.4 53 551.7 38.5 14 313.2 21.9 74 373.1 26.1 34 432.9 30.3 94 492.8 34.4 54 552.7 38.6 15 314.2 22.0 75 374.1 26.2 35 433.9 30.3 95 493.8 34.5 55 553.6 38.7 16 315.2 22.1 76 375.1 26.2 36 434.9 30.4 96 494.8 34.6 56 554.6 38.7 17 316.2 22.1 77 376.1 26.3 37 435.9 30.5 97 495.8 34.6 57 555.6 38.8 18 317.2 22.2 78 377.1 26.4 38 436.9 30.6 98 496.8 34.7 58 556.6 38.9 19 318.2 22.3 79 378.1 26.4 39 ^37.9 30.6 99 497.8 34.8 59 557.6 38.9 20 319.2 22.3 80 379.1 26.5 40 438.9 30.7 500 498.8 34.8 60 558.6 39.0 321 320.2 22.4 381 380.1 26.6 441 439.9 30.8 501 499.8 34.9 561 559.6 39.1 22 321.2 22.5 82 381.1 26.6 42 440.9 30.8 02 500.8 35.0 62 560. 6 39.2 23 322.2 22.5 83 382.1 26.7 43 441.9 30.9 03 501.8 35.0 63 561.6 39.2 24 323.2 22.6 84 383.1 26.8 44 442.9 31.0 04 502.8 35.1 64 562.6 39.3 25 324.2 22.7 85 384.0 26.9 45 443.9 31.0 05 503.8 35.2 65 563.6 39.4 26 325.2 22.7 86 385.0 26.9 46 444.9 31.1 06 504.8 35.2 66 564.6 39.4 27 326.2 22.8 87 386.0 27.0 47 445.9 31.2 07 505.8 35.3 67 565.6 39.5 28 327.2 22.9 88 387.0 27.1 48 446.9 31.2 08 506.8 35.4 68 566.6 39.6 29 328.2 23.0 89 388.0 27.1 49 447.9 31.3 09 507.8 35.5 69 567.6 39.7 30 329.2 23.0 90 389.0 27.2 50 448.9 31.4 10 508.8 35.6 70 568.6 39.8 331 330.2 23.1 391 390.0 27.3 451 449.9 31.5 511 509.8 35.6 571 569.6 39.8 32 331.2 23.2 92 391.0 27.3 52 450.9 31.5 12 510.8 35.7 72 1 570. 6 39.9 33 332.2 23.2 93 392.0 27.4 53 451.9 31.6 13 511.8 35.8 73 i 571.6 40.0 34 333.2 23.3 94 393.0 27.5 54 452.9 31.7 14 512.7 35.8 74 1 572.6 40.0 35 334.2 23.4 95 394.0 27.6 55 453.9 31.7 15 513.7 36.9 75 573.6 40.1 36 335.2 23.4 96 395.0 27.6 56 454.9 31.8 16 514.7 36.0 76 574.6 40.2 37 336.2 23.5 97 396.0 27.7 57 455.9 31.9 17 515.7 36.0 77 575.6 40.2 38 337.2 23.6 98 397.0 27.8 58 456.9 31.9 18 516.7 36.1 78 576.6 40.3 39 338.2 23.6 99 398.0 27.8 59 457.9 32.0 19 517.7 36.2 79 577.6 40.4 40 339.2 23.7 400 399.0 27.9 60 458.9 32.1 20 518.7 36.2 80 578.6 40.5 341 340.2 23.8 401 400.0 28.0 461 459.9 32.2 521 519.7 36.3 581 579.6 40.5 42 341.2 23,9 02 401.0 28.0 62 460.9 32.2 22 520.7 36.4 82 580.6 40.6 43 342.2 23.9 03 402.0 28.1 63 461.9 32.3 23 521.7 36.4 83 581.6 40.7 44 343.1 24.0 04 403.0 28.2 64 462.9 32.4 24 522.7 36.5 84 582.6 40.7 45 344.1 24.1 05 404.0 28.2 65 463.9 32.4 25 523.7 36.6 85 583.6 40.8 46 345.1 24.1 06 405.0 28.3 66 464.9 32.5 26 524.7 36.7 86 584.6 40.9 47 346.1 24.2 07 406.0 28.4 67 465.8 32.6 27 525.7 36.8 87 585.6 40.9 48 347.1 24.3 08 407.0 28.5 68 466.8 32.6 28 526.7 36.8 88 586.6 41.0 49 348.1 24.3 09 408.0 28.5 69 467.8 32.7 29 527.7 36.9 89 587.6 41.1 50 349.1 24.4 10 409.0 28.6 70 468.8 32.8 30 531 528.7 529.7 37.0 90 588.6 41.2 351 350. 1 24.5 411 410.0 28.7 471 469.8 32.9 37.0 591 589.6 41.3 52 a51. 1 24.6 12 411.0 28.7 72 470.8 32.9 32 530.7 37.1 92 590.6 41.3 53 352.1 24.6 13 412.0 28.8 73 471.8 33.0 33 531.7 37.2 93 591.6 41.4 54 353. 1 24.7 14 413.0 28.9 74 472.8 33.1 34 532.7 37.2 94 592.6 41.5 55 354.1 24.8 15 414.0 28.9 75 473.8 33.1 35 533.7 37.3 95 593.6 41.5 56 355.1 24.8 16 415.0 29.0 76 474.8 33.2 36 534.7 37.4 96 594.6 41.6 57 356.1 24.9 17 416.0 29.1 77 475.8 33.3 37 535.7 37.5 97 595.6 41.7 58 357.1 25.0 18 417.0 29.2 78 476.8 33.3 38 536.7 37.5 98 596.6 41.7 59 358. 1 25.0 19 418.0 29.2 79 477.8 33.4 39 537.7 37.6 99 597.6 41.8 60 359.1 25.1 20 419.0 29.3 80 478.8 35.5 40 538.7 37.7 600 598.6 41.9 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat Dist. Dep. Lat. Dist Dep. Lat i }6»; ( 94°, 266 % 274° . 1 Page 540] TABLE 2. Difference of Latitude and Departure for 5° (175°, 185 °, 355° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.1 61 60.8 5.3 121 120.5 10.5 181 180.3 15.8 241 240.1 21.0 2 2.0 0.2 62 61.8 5.4 22 121.5 10.6 82 181.3 15.9 42 241.1 21.1 3 3.0 0.3 63 62.8 5.5 23 122.5 10.7 83 182.3 15.9 43 242. 1 21.2 4j 4.0 0.3 64 63.8 5.6 24 123.5 10.8 84 183.3 16.0 44 243. 1 21.3 5 5.0 0.4 65 64.8 5.7 25 124.5 10.9 85 184.3 16.1 45 244.1 21.4 6 6.0 0.5 66 65.7 5.8 26 125.5 11.0 86 185.3 16.2 46 245.1 21.4 7 7.0 0.6 67 66.7 5.8 27 126.5 11.1 87 186.3 16.3 47 246.1 21.5 8 8.0 0.7 68 67.7 5.9 28 127.5 11.2 88 187.3 16.4 48 247.1 21.6 9 9.0 0.8 69 68.7 6.0 29 128.5 11.2 89 188.3 16.5 49 248.1 21.7 10 10.0 0.9 70 69.7 6.1 30 129.5 11.3 90 189.3 16.6 50 249.0 250. 0" 21.8 21.9 11 11.0 1.0 71 70.7 6.2 131 130.5 11.4 191 190.3 16.6 251 12 12.0 1.0 72 71.7 6.3 32 131.5 11.5 92 191.3 16.7 52 251.0 22.0 13 13.0 1.1 73 72.7 6.4 33 132.5 11.6 93 192.3 16.8 53 252.0 22.1 14 13.9 1.2 74 73.7 •6.4 34 133. 5 11.7 94 193.3 16.9 54 253.0 22.1 15 14.9 1.3 75 74.7 6.5 35 134.5 11.8 95 194.3 17.0 55 254.0 22.2 16 15.9 1.4 76 75.7 6.6 36 135.5 11.9 96 195.3 17.1 56 255.0 22.3 17 16.9 1.5 77 76.7 6.7 37 136.5 11.9 97 196.3 17.2 57 256.0 22.4 18 17.9 1.6 78 77.7 6.8 38 137.5 12.0 98 197.2 17.3 58 257.0 22.5 19 18.9 1.7 79 78.7 6.9 39 138.5 .12.1 99 198. 2 17.3 59 258.0 22.6 20 19.9 1.7 80 79.7 7.0 40 139.5 12.2 200 199.2 17.4 60 259.0 22.7 21 20.9 1.8 81 80.7 7.1 141 140.5 12.3 201 200.2 17.5 261 260.0 22.7 22 21.9 1.9 82 81.7 7.1 42 141.5 12.4 02 201.2 17.6 62 261.0 22.8 23 22.9 2.0 83 82.7 7.2 43 142.5 12.5 03 202.2 17.7 63 262.0 22.9 24 23.9 2.1 84 83.7 7.3 44 143.5 12.6 04 203.2 17.8 64 263.0 23.0 25 24.9 2.2 85 84.7 7.4 45 144.4 12.6 05 204.2 17.9 65 264.0 23.1 26 25.9 2.3 86 85.7 7.5 46 145.4 12.7 06 205.2 18.0 66 265.0 23.2 27 26.9 2.4 87 86.7 7.6 47 146.4 12.8 07 206.2 18.0 67 266.0 23.3 28 27.9 2.4 88 87.7 7.7 48 147.4 12.9 08 207.2 18.1 68 267.0 23.4 29 28.9 2.5 89 88.7 7.8 49 148.4 13.0 09 208.2 18.2 69 268.0 23.4 30 29.9 2.6 90 89.7 7.8 50 149.4 13.1 10 209.2 18.3 18.4 70 271 269.0 270.0 23.5 31 30.9 2.7 91 90.7 7.9 151 150.4 13.2 211 210.2 23.6 32 31.9 2.8 92 91.6 8.0 52 151.4 13.2 12 211.2 18.5 72 271.0 23.7 33 32.9 2.9 93 92.6 8.1 53 152.4 13.3 13 212.2 18.6 73 272.0 23.8 34 33.9 3.0 94 93.6 8.2 54 153.4 13.4 14 213.2 18.7 74 273.0 23.9 35 34.9 3.1 95 94.6 8.3 55 154.4 13.5 15 214.2 18.7 75 274.0 24.0 36 35.9 3.1 96 95.6 8.4 56 155.4 13.6 16 215.2 18.8 76 274.9 24.1 37 36.9 3.2 97 96.6 8.5 57 156. 4 13.7 17 216.2 18.9 77 275.9 24.1 38 37.9 3.3 98 97.6 8.5 58 157.4 13.8 18 217.2 19.0 78 276.9 24.2 39 38.9 3.4 99 98.6 8.6 59 158.4 13.9 19 218.2 19.1 79 277.9 24.3 40 39.8 3.5 100 99.6 8.7 60 159.4 13.9 20 219.2 19.2 80 278.9 24.4 41 40.8 3.6 101 100.6 8.8 161 160.4 14.0 221 220.2 19.3 281 279.9 24.5 42 41.8 3.7 02 101.6 8.9 62 161.4 14.1 22 221.2 19.3 82 280.9 24.6 48 42.8 3.7 03 102.6 9.0 63 162.4 14.2 23 222.2 19.4 83 281.9 24.7 44 43.8 3.8 04 103.6 9.1 64 163.4 14.3 24 223.1 19.5 84 282.9 24.8 45 44.8 3.9 05 104.6 9.2 65 164.4 14.4 25 224.1 19.6 85 283.9 24.8 46 45.8 4.0 06 105.6 9.2 66 165.4 14.5 26 225.1 19.7 86 284.9 24.9 47 46.8 4.1 07 106.6 9.3 67 166.4 14.6 27 226.1 19.8 87 285.9 25.0 48 47.8 4.2 08 107.6 9.4 68 167.4 14.6 28 227.1 19.9 88 286.9 25.1 49 48.8 4.3 09 108.6 9.5 69 168.4 14.7 29 228.1 20.0 89 287.9 25.2 50 49.8 50.8 4.4 10 109.6 9.6 70 169.4 14.8 30 231 229.1 20.0 90 288.9 289.9 25.3 51 4.4 111 110.6 9.7 171 170.3 14.9 230.1 20.1 291 25.4 52 51.8 4.5 12 111.6 9.8 72 171.3 15.0 32 231.1 20.2 92 290.9 25.4 53 52.8 4.6 13 112.6 9.8 73 172.3 15.1 .33 232.1 20.3 93 291.9 25.5 54 53.8 4.7 14 113.6 9.9 74 173.3 15.2 34 233.1 20.4 94 292.9 25.6 55 54.8 4.8 15 114.6 10.0 75 . 174. 3 15.3 35 234.1 20.5 95 293.9 25.7 56 55.8 4.9 16 115.6 10.1 76 175.3 15.3 36 235.1 20.6 96 294.9 25.8 57 56.8 5.0 17 116. 6 10.2 77 176.3 15.4 37 236.1 20.7 97 295.9 25.9 58 57.8 5.1 18 117.6 10.3 78 177.3 15.5 38 237.1 20.7 98 296.9 26.0 59 58.8 5.1 19 118.5 10.4 79 178.3 15.6 39 238.1 20.8 99 297.9 26.1 60 59.8 5.2 20 119.5 10.5 80 179.3 15.7 40 239.1 20.9 300 298.9 26.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 85° (95°, 265°, 275°) 1 TABLE 2. [Page 641 Difference of Latitude and Departure for 5° (175°, 185 °, 356° )• Dist. Lat. } Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 299.9 26.2 361 359.6 31.5 421 419.4 36.7 481 479.2 41.9 641 538.9 47.2 02 300.8 26.3 62 360.6 31.6 22 420.4 36.8 82 480.2 42.0 42 539.9 47.3 03 301.8 26.4 63 361. 6 31.6 23 421.4 36.9 83 481.2 42.1 43 540.9 47.4 04 1 302.8 26.5 64 362. 6 31.7 24 422.4 37.0 84 482.2 42.2 44 541.9 47.5 05 303.8 26.6 65 363.6 31.8 25 423.4 37.1 86 483.2 42.3 46 542.9 47.6 06 304.8 26.7 66 364.6 31.9 26 424.4 37.1 86 484.1 42.4 46 543.9 47.7 07 305. 8 26.8 67 365.6 32.0 27 425.4 37.2 87 485.1 42.4 47 544.9 47.7 08 306.8 26.9 68 366.6 32.1 28 426.4 37.3 88 486.1 42.5 48 545.9 47.8 09 i 307. 8 26.9 69 367.6 32.2 29 427.4 37.4 89 487.1 42.6 49 546.9 47.9 10 i 308.8 311 ! 309.8 27.0 27.1 70 368.6 '369.6 32.3 30 428.4 37.5 90 488.1 489.1 42.7 60 647.9 48.0 371 32.3 431 429.4 37.6 491 42.8 551 548.9 48.1 12 310. 8 27.2 72 370.6 32.4 32 430.4 37.7 92 490.1 42.9 52 549.9 48.2 13 311.8 27.3 73 371.6 32.5 .33 431.3 37.7 93 491.1 43.0 53 650.9 48.3 14 312.8 27.4 74 372.6 32.6 34 432.3 37.8 94 492.1 43.1 54 551.9 48.4 15 313.8 27.5 75 373.6 32.7 35 433.3 37.9 95 493.1 43.1 56 552.9 48.4 16 314. 8 27.5 76 374.6 32.8 36 434.3 38.0 96 494.1 43.2 66 653.9 48.5 17 315. 8 27.6 77 375.6 32.9 37 436.3 38.1 97 495.1 43.3 57 554.9 48.6 18 316. 8 27.7 78 376.6 33. 38 436.3 38.2 98 496.1 43.4 68 566.9 48.7 19 317. 8 27.8 79 377.6 33.0 39 437. 3 38.3 99 497.1 43.5 69 556. 9 48.8 20 318. 8 319. 8 27.9 80 378.6 33.1 40 438.3 38.4 500 498.1 43.6 60 557.9 48.8 321 28.0 381 379. 5 33.2 441 439.3 38.4 501 499.1 43.7 561 568.8 48.9 22 320.8 28.1 82 380. 5 33.3 42 440.3 38.5 02 500.1 43.8 62 559.8 49.0 23 .321.8 28.2 83 381.5 33.4 43 441.3 38.6 03 501.1 43.8 63 560.8 49.1 24 322.8 28.2 84 382.5 33.5 44 442.3 38.7 04 502.1 43.9 64 561.8 49.2 25 323. 8 28.3 85 383.5 33.6 45 443.3 38.8 05 503.1 44.0 65 562.8 49.3 26 324.8 28.4 86 384. 5 33.7 46 444.3 38.9 06 504.1 44.1 66 563.8 49.4 27 325.8 28.5 87 385. 5 33.7 47 445.3 39.0 07 605.1 44.2 67 564.8 49.5 28 326.7 28.6 88 386. 5 33.8 48 446.3 39.1 08 606.1 44.3 68 565.8 49.6 29 327.7 1 28.7 89 387.5 33.9 49 447.3 39.1 09 507.1 44.4 69 566.8 49.7 30 328. 7 1 28. 8 90 391 388.5 389.5 34.0 50 448.3 39.2 10 508.1 44.5 70 571 667.8 49.7 331 329.7 28.9 34.1 451 449.3 39.3 511 509.0 44.5 568.8 49.8 32 330.7 28.9 92 390.5 34.2 52 450.3 39.4 12 510.0 44.6 72 569.8 49.9 33 331. 7 29. 93 391. 5 34.3 53 451.3 39.5 13 511.0 44.7 73 570.8 50.0 34 332.7 29.1 94 392.5 34.3 54 452.3 39.6 14 512.0 44.8 74 571.8 50.1 35 333. 7 29.2 95 393.5 34.4 55 453.3 39.7 16 513.0 44.9 75 672.8 50.2 36 334.7 29.3 96 394.5 34.5 56 454.3 39.8 16 514.0 46.0 76 573.8 60.3 37 335. 7 29.4 97 395.5 34.6 57 465.3 39.8 17 515.0 45.1 77 574.8 50.4 38 336. 7 29.5 98 396.5 34.7 58 456.3 39.9 18 516.0 45.2 78 575.8 50.4 39 337.7 29.6 99 397.5 34.8 59 457.3 40.0 19 517.0 45.2 79 676.8 50.5 40 338.7 29.6 400 398.5 34.9 60 458.2 40.1 20 518.0 519.0 46.3 80 577.8 50.6 341 339.7 29.7 401 399.5 35.0 461 459.2 40.2 521 46.4 581 578.8 50.7 42 340. 7 29.8 02 400.5 35.0 62 460.2 40.3 22 520.0 46.5 82 579.8 50.8 43 341.7 29.9 03 401.5 35.1 63 461.2 40.4 23 521.0 45.6 83 580.8 50.9 44 342. 7 30.0 04 402.5 35.2 64 462.2 40.4 24 622.0 46.7 84 681.8 60.9 45 343.7 30.1 05 403.5 35.3 65 463.2 40.5 25 523.0 46.8 86 582.8 51.0 46 344.7 30.2 06 404.5 35.4 66 464. 2 40.6 26 524.0 45.9 86 583. 8 51.1 47 345.7 30.3 07 405.4 35.5 67 466.2 40.7 27 625.0 46.9 87 584.8 61.2 48 ;M6.7 30.3 08 406.4 35.6 68 466.2 40.8 28 626.0 46.0 88 585.8 51.3 49 347. 7 30.4 09 407.4 35.7 69 467.2 40.9 29 527.0 46.1 89 586.8 51.4 50 348.7 349.7 30.5 10 408.4 35.7 70 468.2 41.0 30 528.0 529.0 46.2 90 587.8 61.6 351 30.6 411 409.4 35.8 471 469.2 41.1 531 46.3 591 688.7 51.6 52 350. 7 30.7 12 410.4 35.9 72 470.2 41.1 32 530.0 46.4 92 589.7 61.6 53 351. 7 30.8 13 411.4 36.0 73 471.2 41.2 33 531.0 46.6 93 590.7 51.7 54 352. 6 30.9 14 412.4 36.1 74 472.2 41.3 34 532. 46.6 94 591.7 51.8 55 353.6 30.9 15 413.4 36.2 75 473.2 41.4 35 533.0 46.6 95 592.7 51.9 56 354.6 31.0 16 414.4 36.3 76 474.2 41.5 36 533.9 46.7 96 693.7 52.0 57 355.6 31.1 17 415.4 36.4 77 475.2 41.6 37 534.9 46.8 97 694.7 62.1 58 356.6 31.2 18 416.4 36.4 78 476.2 41.7 38 536. 9 46.9 98 595.7 52.2 59 357.6 31.3 19 417.4 36.5 79 477.2 41.8 39 536.9 47.0 99 596.7 52.3 60 358.6 31.4 20 418.4 36.6 80 478.2 41.8 40 537.9 47.1 600 597.7 52.3 Diet. Dep. Lat. Diat. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 85° (95°, 265°, 275°). 1 Page 542] TABLE 2. Difference of Latitude anc Departure for 6° (174°, 186°, 354° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 25.2 1 1.0 0.1 61 60.7 6.4 121 120.3 12.6 181 180.0 18.9 241 239.7 2 2.0 0.2 62 61.7 6.5 22 121.3 12.8 82 181.0 19.0 42 240.7 25.3 3 3.0 0.3 63 62.7 6.6 23 122.3 12.9 83 182.0 19.1 43 241.7 2.5.4 4 4.0 0.4 64 63.6 6.7 24 123.3 13.0 84 183.0 19.2 44 242.7 25.5 5 5.0 0.5 65 64.6 6.8 25 124.3 13.1 85 184.0 19.3 45 243.7 25.6 6 6.0 0.6 66 65.6 6.9 26 125.3 13.2 86 185.0 19.4 46 244.7 25.7 7 7.0 0.7 67 66.6 7.0 27 126.3 13.3 87 186.0 19.6 47 245.6 25.8 8 8.0 0.8 68 67.6 7.1 28 127.3 13.4 88 187.0 19.7 48 246.6 25.9 9 9.0 0.9 69 68.6 7.2 29 128.3 13.5 89 188.0 19.8 49 247.6 26.0 10 9.9 1.0 70 69.6 7.3 30 129.3 13.6 90 189.0 19.9 50 248.6 26.1 11 10.9 1.1 71 70.6 7.4 131 130.3 13.7 191 190.0 20.0 251 249.6 26.2 12 11.9 1.3 72 71.6 7.5 32 131.3 13.8 92 190.9 20.1 52 250.6 26.3 13 12.9 1.4 73 72.6 7.6 33 132.3 13.9 93 191.9 20.2 53 251.6 26.4 14 13.9 1.5 74 73.6 7.7 34 133.3 14.0 94 192.9 20.3 54 252.6 26.6 15 14.9 1.6 75 74.6 7.8 35 134.3 14.1 95 193.9 20.4 55 253.6 26.7 16 15.9 1.7 76 75.6 7.9 36 135.3 14.2 96 194.9 20.5 56 254.6 26.8 17 16.9 1.8 77 76.6 8.0 37 136.2 14.3 97 195.9 20.6 57 255.6 26.9 18 17.9 1.9 78 77.6 8.2 38 137.2 14.4 98 196.9 20.7 58 256.6 27.0 19 18.9 2.0 79 78.6 8.3 39 138.2 14.5 99 197.9 20.8 59 257.6 27.1 20 19.9 2.1 80 79.6 8.4 40 139.2 140.2 14.6 14.7 200 201 198.9 20.9 60 261 258.6 27.2 21 20.9 2.2 81 80.6 8.5 141 199.9 21.0 259.6 27.3 22 21.9 2.3 82 81.6 8.6 42 141.2 14.8 02 200.9 21.1 62 260.6 27.4 23 22.9 2.4 83 82.5 8.7 43 142.2 14.9 03 201.9 21.2 63 261.6 27.5 24 23.9 2.5 84 83.5 8.8 44 143.2 15.1 04 202.9 21.3 64 262.6 27.6 25 24.9 2.6 85 84.5 8.9 45 144.2 15.2 05 203.9 21.4 65 263.5 27.7 26 25.9 2.7 86 85.5 9.0 46 145.2 15.3 06 204.9 21.5 66 264.5 27.8 27 26.9 2.8 87 86.5 9.1 47 146.2 15.4 07 205.9 21.6 67 265. 5 27.9 28 27.8 2.9 88 87.5 9.2 48 147.2 15.5 08 200. 9 21.7 68 266.5 28.0 29 28.8 3.0 89 88.5 9.3 49 148.2 15.6 09 207.9 21.8 69 267.5 28.1 30 29.8 3.1 90 89.5 9.4 50 149.2 15.7 10 208.8 22.0 70 268.5 28.2 31 30.8 3.2 91 90.5 9.5 151 150. 2 15.8 211 209.8 22.1 271 269. 5 28.3 32 31.8 3.3 92 91.5 9.6 52 151.2 15.9 12 210.8 22.2 72 270. 5 28.4 33 32.8 3.4 93 92.5 9.7 53 152.2 16.0 13 211.8 22.3 73 271.5 28.6 34 33.8 3.6 94 93.5 9.8 54 153.2 16.1 14 212.8 22.4 74 272.5 28.6 35 34.8 3.7 95 94.5 9.9 55 154.2 16.2 15 213.8 22.5 75 273.5 28.7 36 35.8 3.8 96 95.5 10.0 56 155.1 16.3 16 214.8 22.6 76 274.5 28.8 37 36.8 3.9 97 96.5 10.1 57 156.1 16.4 17 215. 8 22.7 77 275.5 29.0 38 37.8 4.0 98 97.5 10.2 58 157.1 16.5 18 216.8 22.8 78 276.5 29.1 39 38.8 4.1 99 98.5 10.3 59 158.1 16.6 19 217.8 22.9 79 277.5 29.2 40 39.8 4.2 100 99.5 10.5 60 159.1 160.1 16.7 20 218.8 23.0 23.1 80 278.6 29.3 29.4 41 40.8 4.3 101 100.4 10.6 161 16.8 221 219.8 281 279.5 42 41.8 4.4 02 101.4 10.7 62 161.1 16.9 22 220.8 23.2 82 280.5 29.5 43 42.8 4.5 03 102.4 10.8 63 162.1 17.0 23 221.8 23.3 83 281.4 29.6 44 43.8 4.6 04 103.4 10.9 64 163.1 17.1 24 222.8 23.4 84 282.4 29.7 45 44.8 4.7 05 104.4 11.0 65 164.1 17.2 25 223.8 23.5 85 283.4 29.8 46 45.7 4.8 06 105.4 11.1 66 165.1 17.4 26 224.8 23.6 86 284.4 29.9 47 46.7 4.9 07 106.4 11.2 67 166.1 17.5 27 225.8 23.7 87 285.4 30.0 48 47.7 5.0 08 107.4 11.3 68 167.1 17.6 28 226.8 23.8 88 286.4 30.1 49 48.7 5.1 09 108.4 11.4 69 168.1 17.7 29 227.7 23.9 89 287.4 30.2 50 49.7 5.2 10 109.4 11.5 70 169.1 17.8 30 228.7 229.7 24.0 90 288.4 30.3 51 50.7 5.3 111 110.4 11.6 171 170.1 17.9 231 24.1 291 289.4 30.4 52 51.7 5.4 12 111.4 11.7 72 171.1 18.0 32 230.7 24.3 92 290.4 30.5 53 52.7 5.5 13 112.4 11.8 73 172.1 18.1 33 231. 7 24.4 93 291.4 30.6 54 53.7 5.6 14 113.4 11.9 74 173.0 18.2 34 232.7 24.5 94 292.4 30.7 55 54.7 5.7 15 114.4 12.0 75 174.0 18.3 35 233.7 24.6 95 293.4 30.8 56 55.7 5.9 16 115.4 12.1 76 175.0 18.4 36 234.7 24.7 96 294.4 30.9 57 56.7 6.0 17 116.4 12.2 77 176.0 18.5 37 235.7 24.8 97 295.4 31.0 58 57.7 6.1 18 117.4 12.3 78 177.0 18.6 38 236.7 24.9 98 296.4 31.1 59 58.7 6.2 19 118.3 12.4 79 178.0 18.7 39 237.7 25.0 99 297.4 31.3 60 59.7 6.3 20 119.3 12.5 80 179.0 18.8 40 238.7 25.1 300 298.4 31.4 Diet. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 84° (« >6°, 264^ , 276°) TABLE 2. [Page 543 Difference of Latitude and Departure for 6° (174°, 186°, 354°) Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 299.3 31.5 361 369.0 37.7 421 418.7 44.0 481 478.4 50.3 541 538.0 56.5 02 300.3 31.6 62 360.0 37.8 22 419.7 44.1 82 479.4 50.4 42 539.0 56.6 03 301.3 31.7 63 361.0 37.9 23 420.7 44.2 83 480.4 50.5 43 540.0 56.7 04 302.3 31.8 64 362.0 38.0 24 421.7 44.3 84 481.3 50.6 44 541.0 56.8 05 303.3 31.9 65 363.0 38.1 25 422.7 44.4 85 482.3 50.7 45 542.0 56.9 06 304.3 32.0 66 364.0 38.3 26 423.7 44.5 86 483.3 50.8 46 543.0 57.0 07 305.3 32.1 67 365.0 38.4 27 424.7 44.6 87 484.3 50.9 47 544.0 57.1 08 306.3 32.2 68 366.0 38.5 28 425.7 44.7 88 485.3 51.0 48 545.0 57.2 09 307.3 32.3 69 367.0 38.6 29 426.6 44.8 89 486.3 51.1 49 546.0 57.3 10 308.3 32.4 70 368.0 38.7 30 427.6 44.9 90 487.3 51.2 50 547.0 57.4 311 309.3 32.5 371 369.0 38.8 431 428.6 45.0 491 488.3 51.3 551 548.0 57.5 12 310.3 32.6 72 370.0 38.9 32 429.6 45.2 92 489.3 51.4 52 549.0 57.6 13 311.3 32.7 73 371.0 39.0 33 430.6 45.3 93 490.3 51.5 53 550.0 57.7 14 312.3 32.8 74 371.9 39.1 34 431.6 45.4 94 491.3 51.6 54 551.0 57.9 15 313.3 32.9 75 372.9 39.2 35 432.6 45.5 95 492.3 51.7 55 552.0 58.0 16 314.3 33.0 76 373.9 39.3 36 433.6 45.6 96 493.3 51.8 56 553.0 58.1 17 315.3 33.1 77 374.9 39.4 37 434.6 45.7 97 494.3 51.9 57 554.0 58.2 18 316.3 33.2 78 375.9 39.5 38 435.6 45.8 98 495.3 52.0 58 555.0 58.3 19 317.3 33.3 79 376.9 39.6 39 436.6 45.9 99 496.3 52.1 59 556.0 58.4 20 318.2 33.4 80 377.9 39.7 40 437. 6 46.0 500 497.3 52.3 60 556.9 58.5 321 319.2 33.6 381 378.9 39.8 441 438.6 46.1 501 498.3 52.4 561 557.9 58.6 22 320.2 33.7 82 379.9 39.9 42 439.6 46.2 02 499.3 52.5 62 558.9 58.7 23 321.2 33.8 83 380.9 40.0 43 440.6 46.3 03 500.2 52.6 63 559. 9 58.8 24 322.2 33.9 84 381.9 40.1 44 441.6 46.4 04 501.2 52.7 64 560.9 59.0 25 323.2 34.0 85 382.9 40.2 45 442.6 46.5 05 502.2 52.8 65 561.9 59.1 26 324.2 34.1 86 383.9 40.3 46 443.6 46.6 06 503.2 52.9 6& 562.9 59.2 27 325.2 34.2 87 384.9 40.5 47 444.5 46.7 07 504.2 53.0 67 563.9 59.3 28 326.2 34.3 88 385.9 40.6 48 445.5 46.8 08 505. 2 53.1 68 564.9 59.4 29 327.2 34.4 89 386.9 40.7 49 446.5 46.9 09 506.2 53.2 69 565.9 59.5 30 328.2 34.5 90 387.9 40.8 50 447.5 47.0 10 507.2 53.3 70 566.9 59.6 331 329.2 34.6 391 388.9 40.9 451 448.5 47.1 511 508.2 53.4 571 567.9 59.7 32 330.2 34.7 92 389.9 41.0 52 449.5 47.2 12 509.2 53.5 72 568.9 59.8 33 331.2 34.8 93 390.8 41.1 53 450.5 47.3 13 510.2 53.6 73 569.9 59.9 34 332.2 34.9 94 391.8 41.2 54 451.5 47.5 14 511.2 53.7 74 570.9 60.0 35 333.2 35.0 95 392.8 41.3 55 452.5 47.6 15 512. 2 53.8 75 571.9 60.1 36 334.2 35.1 96 393.8 41.4 56 453.5 47.7 16 513.2 53.9 76 572.9 60.2 37 335.2 35.2 97 394.8 41.5 57 454.5 47.8 17 514.2 54.0 77 573.9 60.3 38 336.1 35.3 98 395.8 41.6 58 455.5 47.9 18 515.2 54.1 78 574.9 60.4 39 337.1 35.4 99 396.8 41.7 59 456.5 48.0 19 516.2 54.2 79 575.8 60.5 40 338.1 35.5 400 397.8 41.8 60 457.5 48.1 20 517.2 54.3 80 576.8 60.6 341 339.1 35.6 401 398.8 41.9 461 458.5 48.2 521 518.1 54.5 581 577.8 60.7 42 340.1 35.7 02 399.8 42.0 62 459.5 48.3 22 519.1 54.6 82 578.8 60.8 43 341.1 35.8 03 400.8 42.1 63 460.5 48.4 23 520.1 54.7 83 579.8 60.9 44 342.1 36.0 04 401.8 42.2 64 461.5 48.5 24 521.1 54.8 84 580.8 61.1 45 343.1 36.1 05 402.8 42.3 65 462.5 48.6 25 522.1 54.9 85 581.8 61.2 46 344.1 36.2 06 403.8 42.4 66 463.4 48.7 26 523.1 55.0 86 582.8 61.3 47 345.1 36.3 07 404.8 42.5 67 464.4 48.8 27 524.1 55.1 87 583.8 61.4 48 346.1 36.4 08 405.8 42.6 68 465.4 48.9 28 525.1 55.2 88 584.8 61.5 49 347.1 36.5 09 406.8 42.7 69 466.4 49.0 29 526.1 55.3 89 585.8 61.6 50 348.1 349.1 36.6 36.7 10 407.8 42.9 43.0 70 467.4 49.1 30 527.1 55.4 90 586.8 61.7 351 411 408.7 471 468.4 49.2 531 528.1 55.5 591 587.8 61.8 52 350.1 36.8 12 409.7 43.1 72 469.4 49.3 32 529.1 55.6 92 588.8 61.9 53 351.1 36.9 13 410.7 43.2 73 470.4 49.4 33 530.1 55.7 93 589.8 62.0 54 352.1 37.0 14 411.7 43.3 74 471.4 49.5 34 531.1 55.8 94 590.8 62.1 55 353.1 37.1 15 412.7 43.4 75 472.4 49.6 35 532.1 55.9 95 591.8 62.2 56 354.0 37.2 16 413.7 43.5 76 473.4 49.8 36 533.1 56.0 96 592.8 62.3 57 355.0 37.3 17 414.7 43.6 77 474.4 49.9 37 534.1 56.1 97 593.8 62.4 58 356.0 37.4 18 415.7 43.7 78 475.4 50.0 38 535.1 56.2 98 594.7 62.5 59 357.0 37.5 19 416.7 43.8 79 476.4 50.1 39 536.1 56.3 99 595.7 62.6 60 358.0 37.6 20 417.7 43.9 80 477.4 50.2 40 537.1 56.4 600 596.7 62.7 DlBt. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 84° (96°, 264°, 276° ). 1 Page 644 TABLE 2. Difference of Latitude and Departure for 7° (173°, 187°, 353°) • Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.1 61 60.5 7.4 121 120.1 14.7 181 179.7 22.1 241 239. 2 29.4 2 2.0 0.2 62 61.5 7.6 22 121.1 14.9 82 180.6 22.2 42 240.2 29.5 3 3.0 0.4 63 62.5 7.7 23 122.1 15.0 83 181.6 22.3 43 241.2 29.6 4 4.0 0.5 64 63.5 7.8 24 123.1 15.1 84 182.6 22.4 44 242.2 29.7 5 6.0 0.6 65 64.5 7.9 25 124.1 15.2 85 183.6 22.5 45 243.2 29.9 6 6.0 0.7 66 65.5 8.0 26 125.1 15.4 86 184.6 22.7 46 244.2 30.0 7 6.9 0.9 67 66.5 8.2 27 126.1 15.5 87 185.6 22.8 47 245.2 30.1 8 7.9 1.0 68 67.5 8.3 28 127.0 15.6 88 186.6 22.9 48 246.2 30.2 9 8.9 1.1 69 68.5 8.4 29 128.0 15.7 89 187.6 23.0 49 247.1 30.3 10 9.9 1.2 70 69.5 8.5 30 129.0 15.8 90 188.6 23.2 50 248.1 30.5 11 10.9 1.3 71 70.5 8.7 131 130.0 16.0 191 189.6 23.3 251 249.1 30.6 12 11.9 1.5 72 71.5 8.8 32 131.0 16.1 92 190.6 23.4 52 250.1 30.7 13 12.9 1.6 73 72.5 8.9 33 132.0 16.2 93 191.6 23.5 53 251.1 30.8 14 13.9 1.7 74 73.4 9.0 34 133.0 16.3 94 192.6 23.6 54 252.1 31.0 15 14.9 1.8 75 74.4 9.1 35 134.0 16.5 95 193.5 23.8 55 253.1 31.1 16 15.9 1.9 76 75.4 9.3 36 135.0 16.6 96 194.5 23.9 56 254.1 31.2 17 16.9 2.1 77 76.4 9.4 37 136.0 16.7 97 195.5 24.0 57 255.1 31.3 18 17.9 2.2 78 77.4 9.5 38 137.0 16.8 98 196.5 24.1 58 256.] 31.4 19 18.9 2.3 79 78.4 9.6 39 138.0 16.9 99 197.5 24.3 59 257.1 31:6 20 19.9 2.4 2.6 80 79.4 9.7 40 139.0 17.1 200 198.5 24.4 60 258.1 259.1 31.7 21 20.8 81 80.4 9.9 141 139.9 17.2 201 199.5 24.5 261 31.8 22 21.8 2.7 82 81.4 10.0 42 140.9 17.3 02 200.5 24.6 62 260.0 31.9 23 22.8 2.8 83 82.4 10.1 43 141.9 17.4 03 201.5 24.7 63 261.0 32.1 24 23.8 2.9 84 83.4 10.2 44 142.9 17.5 04 202.5 24.9 64 262.0 32.2 25 24.8 3.0 85 84.4 10.4 45 143.9 17.7 05 203.5 25.0 65 263.0 32.3 26 25.8 3.2 86 85.4 10.5 46 144.9 17.8 06 204.5 25.1 66 264.0 32.4 27 26.8 3.3 87 86.4 10.6 47 145.9 17.9 07 205.5 25.2 67 265.0 32.5 28 27.8 3.4 88 87.3 10.7 48 146.9 18.0 08 206.4 25.3 68 266.0 32.7 29 28.8 3.5 89 88.3 10.8 49 147.9 18.2 09 207.4 25.5 69 267.0 32.8 30 29.8 3.7 90 89.3 11.0 50 148.9 18.3 10 208.4 25.6 70 268.0 32.9 31 30.8 3.8 91 90.3 11:1 151 149. 9 18.4 211 209.4 25.7 271 269.0 33.0 32 31.8 3.9 92 91.3 11.2 52 150.9 18.5 12 210.4 25.8 72 270.0 33.1 33 32.8 4.0 93 92.3 11.3 53 151.9 18.6 13 211.4 26.0 73 271.0 33.3 34 33.7 4.1 94 93.3 11.5 54 152.9 18.8 14 212.4 26.1 74 272.0 33.4 35 34.7 4.3 95 94.3 11.6 55 153.8 18.9 15 213.4 26.2 75 273.0 33.5 36 35.7 4.4 96 95.3 11.7 56 154.8 19.0 16 214.4 26.3 76 273.9 33.6 37 36.7 4.5 97 96.3 11.8 57 155. 8 19.1 17 215.4 26.4 77 274.9 33.8 38 37.7 4.6 98 97.3 11.9 58 156.8 19.3 18 216.4 26.6 78 275.9 33.9 39 38.7 4.8 99 98.3 12.1 59 157. 8 19.4 19 217.4 26.7 79 276.9 34.0 40 41 39.7 40.7 4.9 100 101 99.3 12.2 60 158.8 19.5 20 218.4 26.8 80 277.9 34.1 5.0 100.2 12.3 161 159.8 19.6 221 219.4 26.9 281 278.9 34.2 42 41.7 5.1 02 101.2 12.4 62 160.8 19.7 22 220.3 27.1 82 279.9 34.4 43 42.7 5.2 03 102.2 12.6 63 161.8 19.9 23 221.3 27.2 83 280.9 34.5 44 43.7 5.4 04 103.2 12.7 64 162.8 20.0 24 222. 3 27.3 84 281.9 34.6 45 44.7 5.5 05 104.2 12.8 65 163.8 20.1 25 223.3 27.4 85 282.9 34.7 46 45.7 5.6 06 105.2 12.9 66 164.8 20.2 26 224 3 27.5 86 283.9 34.9 47 46.6 5.7 07 106.2 13.0 67 165. 8 20.4 27 225.3 27.7 87 284.9 35.0 48 47.6 5.8 08 107.2 13.2 68 166.7 20.5 28 226.3 27.8 88 285.9 35.1 49 48.6 6.0 09 108.2 13.3 69 167.7 20.6 29 227.3 27.9 89 286.8 35.2 50 49.6 6.1 6.2 10 109.2 13.4 70 168.7 20.7 30 228.3 28.0 90 287.8 288.8 35.3 51 50.6 111 110.2 13.5 171 169.7 20.8 231 229.3 28.2 291 35.5 52 51.6 6.3 12 111.2 13.6 72 170.7 21.0 32 230.3 28.3 92 289.8 35.6 53 52.6 6.5 13 112.2 13.8 73 171.7 21.1 33 231.3 28.4 93 290.8 35.7 54 53.6 6.6 14 113.2 13.9 74 172.7 21.2 34 232.3 28.5 94 291.8 35.8 55 54.6 6.7 15 114.1 14.0 75 173.7 21.3 35 233.2 28.6 95 292.8 36.0 56 55.6 6.8 16 115.1 14.1 76 174.7 21.4 36 234.2 28.8 96 293.8 36.1 57 56.6 6.9 17 116.1 14.3 77 175.7 21.6 37 235.2 28.9 97 294.8 36.2 58 57.6 7.1 18 117.1 14.4 78 176.7 21.7 38 236.2 29.0 98 295.8 36.3 59 58.6 7.2 19 118.1 14.5 79 177.7 21.8 39 237.2 29.1 99 296.8 36.4 60 59.6 7.3 20 119.1 14.6 80 178.7 21.9 40 238.2 29.2 300 297.8 36.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 83° (97°, 263°, 277°, . TABLE 2. [Page 546 Difference of Latitude and Departure for 7° (173°, 187°, 353°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 298.7 36.7 361 358.3 44.0 421 417.9 51.3 481 477.4 58.6 541 537.0 65.9 02 299.7 36.8 62 359.3 44.1 22 418.8 51.4 82 478.4 58.7 42 537.9 66.0 03 300.7 36.9 63 360.3 44.2 23 419.8 51.5 83 479.4 58.8 43 538.9 66.2 04 301.7 37.0 64 361.3 44.4 24 420.8 51.7 84 480.4 59.0 44 539. 9 66.3 05 302. 7 37.2 65 362.3 44.5 25 421.8 51.8 85 481.4 59.1 45 540.9 66.4 06 303.7 37.3 66 363.3 44.6 26 422.8 51.9 86 482.4 59.2 46 541.9 66.6 07 304.7 37.4 67 364.3 44.7 27 423.8 52.0 87 483.4 59.4 47 542.9 66.7 08 305.7 37.5 68 365.2 44.8 28 424.8 52.2 88 484.3 59.5 48 543.9 66.8 09 306.7 37.7 69 366.2 45.0 29 425.8 52.3 89 485.3 59.6 49 544.9 66.9 10 307.7 37.8 70 367.2 45.1 30 426.8 52.4 90 486.3 59.7 50 545.9 67.0 311 308.7 37.9 371 368.2 45.2 431 427.8 52.5 491 487.3 59.8 551 546.9 67.1 12 309.7 38.0 72 369.2 45.3 32 428.8 52.6 92 488.3 59.9 52 547.9 67.2 13 310.7 38.1 73 370.2 45.5 33 429.8 52.8 93 489.3 60.1 53 548.9 67.4 14 311.7 38.3 74 371.2 45.6 34 430.8 52.9 94 490.3 60.2 54 549.9 67.5 15 312.6 38.4 75 372.2 45.7 35 431.7 53.0 95 491.3 60.3 55 550.8 67.6 16 313.6 38.5 76 373.2 45.8 36 432.7 53.1 96 492.3 60.5 56 551.8 67.8 17 314.6 38.6 77 374.2 45.9 37 433.7 53.3 97 493.3 60.6 57 552.8 67.9 18 315.6 38.7 78 375.2 46.1 38 434.7 53.4 98 494.3 60.7 58 553.8 68.0 19 316.6 38.9 79 376.2 46.2 39 435.7 53.5 99 495.3 60.8 59 554.8 68.1 20 317.6 39.0 80 377.2 46.3 40 436.7 53.6 500 496.3 61.0 60 555.8 68.3 321 318.6 39.1 381 378.1 46.4 441 437.7 53.7 501 497.2 61.1 561 556.8 68.4 22 319.6 39.2 82 379.1 46.5 42 438.7 53.9 02 498.2 61.2 62 557.8 68.5 23 320.6 39.4 83 380.1 46.7 43 439.7 54.0 03 499.2 61.3 63 558.8 68.6 24 321.6 39.5 84 381.1 46.8 44 440.7 54.1 04 500.2 61.4 64 559.8 68.7 25 322.6 39.6 85 382.1 46.9 45 441.7 54.2 05 501.2 61.5 65 560.8 68.9 26 323.6 39.7 86 383.1 47.0 46 442.7 54.3 06 502.2 61.6 66 561.8 69.0 27 324.6 39.8 87 384.1 47.2 47 443.7 54.5 07 503.2 61.8 67 562.8 69.1 28 325.5 40.0 88 385.1 47.3 48 444.7 54.6 08 504.2 61.!) 68 563.8 69.2 29 326.5 40.1 89 386.1 47.4 49 445.6 54.7 09 505.2 62.0 69 564.8 69.3 30 327.5 40.2 90 387.1 47.5 50 446.6 54.8 10 506.2 62.1 70 571 565.8 69.4 331 328.5 40.3 391 388.1 47.6 451 447.6 55.0 511 507.2 62.3 566.7 69.6 32 329.5 40.5 92 389.1 47.8 52 448.6 55.1 12 508.2 62.4 72 567.7 69.7 33 330.5 40.6 93 390.1 47.9 53 449.6 55.2 13 509.2 62.5 73 568.7 69.8 34 331.5 40.7 94 391.1 48.0 54 450.6 55.3 14 510.2 62.6 74 569.7 69.9 35 332.5 40.8 95 392.0 48.1 55 451.6 55.4 15 511.1 62.7 75 570.7 70.1 36 333.5 40.9 96 393.0 48.3 56 452.6 55.6 16 512.1 62.9 76 571.7 70.2 37 334.5 41.1 97 394.0 48.4 57 453.6 55.7 17 513.1 63.0 77 572.7 70.3 38 335.5 41.2 98 395.0 48.5 58 454.6 55.8 18 514.1 63.1 78 573.7 70.4 39 336.5 41.3 99 396.0 48.6 59 455.6 55.-9 19 515.1 63.2 79 574.7 70.5 40 337.5 41.4 400 397.0 48.7 60 456.6 56.1 20 516.1 63.4 80 575.7 70.7 341 338.4 41.6 401 398.0 48.9 461 457.6 56.2 521 517.1 63.5 581 576.7 70.8 42 339.4 41.7 02 399.0 49.0 62 458.5 56.3 22 518.1 63.6 82 577.6 70.9 43 340.4 41.8 03 400.0 49.1 63 459.5 56.4 23 519.1 63.7 83 578.6 71.0 44 341.4 41.9 04 401.0 49.2 64 460.5 56.5 24 520.1 63.8 84 579.6 71.2 45 342.4 42.0 05 402.0 49.4 65 461.5 56.7 25 521.1 64.0 85 580.6 71.3 46 343.4 42.2 06 403.0 49.5 66 462.5 56.8 26 522.1 64.1 86 581.6 71.4 47 344.4 42.3 07 404.0 49.6 67 463.5 56.9 27 523.1 64.2 87 582.6 71.5 48 345.4 42.4 08 405.0 49.7 68 464.5 57.0 28 524.1 64.3 88 583.6 71.6 49 346.4 42.5 09 405.9 49.8 69 465.5 57.2 29 525.0 64.5 89 584.6 71.8 50 347.4 42.6 10 406.9 50.0 70 466.5 57.3 30 526.0 64.6 90 585.6 71.9 351 348.4 42.8 411 407.9 50.1 471 467.5 57.4 531 527.0 64.7 591 586.6 72.0 52 349.4 42.9 12 408.9 50.2 72 468.5 57.5 32 528.0 64.8 92 587.6 72.1 53 350.4 43.0 13 409.9 50.3 73 469.5 57.6 33 529.0 64.9 93 588.6 72.2 54 351.4 43.1 14 410.9 50.4 74 470.5 57.8 34 530.0 65.1 94 589.6 72.4 55 352.3 43.3 15 411.9 50.6 75 471.5 57.9 35 531.0 65.2 95 590.6 72.5 56 353.3 43.4 16 412.9 50.7 76 472.4 58.0 36 532.0 65.3 96 591.5 72.6 57 354.3 43.5 17 413.9 50.8 77 473.4 58.1 37 533.0 65.4 97 592.5 72.7 58 355.3 43.6 18 414.9 50.9 78 474.4 58.2 38 534.0 65.6 98 593.5 72.9 59 356.3 43.7 19 415.9 51.1 79 475.4 58.4 39 535.0 65.7 99 594.5 73.0 60 357.3 43.9 20 416.9 51.2 80 476.4 58.5 40 536.0 65.8 600 595.5 73.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 83° (97°, 263°, 277° 1 21594°— 14- -28 Page 646] TABLE 2. Difference of Latitude and Departure for 8° (172°, 188 °, 352° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.1 61 60.4 8.5 121 119.8 16.8 181 179.2 25.2 241 238.7 33.5 2 2.0 0.3 62 61.4 8.6 22 120.8 17.0 82 180.2 25.3 42 239.6 33.7 3 3.0 0.4 63 62.4 8.8 23 121.8 17.1 83 181.2 25.5 43 240.6 33.8 4 4.0 0.6 64 63.4 8.9 24 122.8 17.3 84 182.2 25.6 44 241.6 34.0 5 5.0 0.7 65 64.4 9.0 25 123.8 17.4 85 183.2 25.7 45 242.6 34.1 6 5.9 0.8 66 65.4 9.2 26 124.8 17.5 86 184.2 25.9 46 243.6 34.2 7 6.9 1.0 67 66.3 9.3 27 125.8 17.7 87 185.2 26.0 47 244.6 34.4 8 7.9 1.1 68 67.3 9.5 28 126.8 17.8 88 186.2 26.2 48 245.6 34.5 9 8.9 1.3 69 68.3 9.6 29 127.7 18.0 89 187.2 26.3 49 246.6 34.7 10 9.9 1.4 70 69.3 9.7 9.9 30 128.7 18.1 90 188.2 26.4 50 247.6 34.8 11 10.9 1.5 71 70.3 131 129.7 18.2 191 189.1 26.6 251 248.6 34.9 12 11.9 1.7 72 71.3 10.0 32 130.7 18.4 92 190.1 26.7 52 249.5 35.1 13 12.9 1.8 73 72.3 10.2 33 131.7 18.5 93 191.1 26.9 53 250.5 35.2 14 13.9 1.9 74 73.3 10.3 34 132.7 18.6 94 192.1 27.0 54 251. 5 35.3 15 14.9 2.1 75 74.3 10.4 35 133.7 18.8 95 193.1 27.1 55 252.5 35.5 16 15.8 2.2 76 75.3 10.6 36 134.7 18.9 96 194.1 27.3 56 253.5 35.6 17 16.8 2.4 77 76.3 10.7 37 135.7 19.1 97 195.1 27.4 57 254.5 35.8 18 17.8 2.5 78 77.2 10.9 38 136.7 19.2 98 196.1 27.6 58 255.5 35.9 19 18.8 2.6 79 78.2 11.0 39 137.7 19.3 99 197.1 27.7 59 256.5 36.0 20 19.8 2.8 80 79.2 11.1 40 138.6 19.5 200 198.1 27.8 60 257.5 36.2 21 20.8 2.9 81 80.2 11.3 141 139.6 19.6 201 199.0 28.0 261 258.5 36.3 22 21.8 3.1 82 81.2 11.4 42 140.6 19.8 02 200.0 28.1 62 259.5 36.5 23 22.8 3.2 83 82.2 11.6 43 141.6 19.9 03 201.0 28.3 63 260.4 36.6 24 23.8 3.3 84 83.2 11.7 44 142.6 20.0 04 202.0 28.4 64 261.4 36.7 26 24.8 3.5 85 84.2 11.8 45 143.6 20.2 05 203.0 28.5 65 262.4 36.9 26 25.7 3.6 86 85.2 12.0 46 144.6 20.3 06 204.0 28.7 66 263.4 37.0 27 26.7 3.8 87 86.2 12.1 47 145.6 20.5 07 205.0 28.8 67 264.4 37.2 28 27.7 3.9 88 87.1 12.2 48 146.6 20.6 08 206.0 28.9 68 265.4 37.3 29 28.7 4.0 89 88.1 12.4 49 147.5 20.7 09 207.0 29.1 69 266.4 37.4 30 29.7 4.2 90 89.1 12.5 50 148.5 20.9 10 208.0 29.2 70 267.4 37.6 31 30.7 4.3 91 90.1 12.7 151 149.5 21.0 211 208.9 29.4 271 268.4 37.7 32 31.7 4.5 92 91.1 12.8 52 150.5 21.2 12 209.9 29.5 72 269.4 37.9 33 32.7 4.6 93 92.1 12.9 53 151.5 21.3 13 210.9 29.6 73 270.3 38.0 34 33.7 4.7 94 93.1 13.1 54 152.5 21.4 14 211.9 29.8 74 271.3 38.1 35 34.7 4.9 95 94.1 13.2 55 153.5 21.6 15 212.9 29.9 75 272.3 38.3 36 35.6 5.0 96 95.1 13.4 56 154. 5 21.7 16 213.9 30.1 76 273.3 38.4 37 36.6 5.1 97 96.1 13.5 57 155.5 21.9 17 214.9 30.2 77 274.3 38.6 38 37.6 5.3 98 97.0 13.6 58 156.5 22.0 18 215.9 30.3 78 275.3 38.7 39 38.6 5.4 99 98.0 13.8 59 157.5 22.1 19 216.9 30.5 79 276.3 38.8 40 39.6 5.6 100 99.0 13.9 60 158.4 22.3 20 217.9 30.6 80 277.3 39.0 41 40.6 5.7 101 100.0 14.1 161 159.4 22.4 221 218.8 30.8 281 278.3 39.1 42 41.6 5.8 02 101.0 14.2 62 160.4 22.5 22 219.8 30.9 82 279.3 39.2 43 42.6 6.0 03 102.0 14.3 63 161.4 22.7 23 220.8 31.0 83 280.2 39.4 44 43.6 6.1 04 103.0 14.5 64 162.4 22.8 24 221.8 31.2 84 281.2 39.5 45 44.6 6.3 05 104.0 14.6 65 163.4 23.0 25 222.8 31.3 85 282.2 39.7 46 45.6 6.4 06 105.0 14.8 66 164.4 23.1 26 223.8 31.5 86 283.2 39.8 47 46.5 6.5 07 106.0 14.9 67 165.4 23.2 27 224.8 31.6 87 284.2 39.9 48 47.5 6.7 08 106.9 15.0 68 166.4 23.4 28 225.8 31.7 88 285.2 40.1 49 48.5 6.8 09 107.9 15.2 69 167.4 23.5 29 226.8 31.9 89 286.2 40.2 50 49.5 7.0 10 108.9 15.3 70 168.3 23.7 30 227.8 32.0 90 287.2 40.4 51 50.5 7.1 111 109.9 15.4 171 169.3 23.8 231 228.8 32.1 291 288.2 40.5 52 51.5 7.2 12 110.9 15.6 72 170.3 23.9 32 229.7 32.3 92 289.2 40.6 53 52.5 7.4 13 111.9 15.7 73 171.3 24.1 33 230.7 32.4 93 290.1 40.8 54 53.5 7.5 14 112.9 15.9 74 172.3 24.2 34 231.7 32.6 94 291.1 40.9 55 54.5 7.7 15 113.9 16.0 75 173.3 24.4 35 232.7 32.7 95 292.1 41.1 56 55.5 7.8 16 114.9 16.1 76 174.3 24.5 36 233.7 32.8 96 293.1 41.2 57 56.4 7.9 17 115.9 16.3 77 175.3 24.6 37 234.7 33.0 97 294.1 41.3 58 57.4 8.1 18 116.9 16.4 78 176.3 24.8 38 235.7 33.1 98 295.1 41.5 59 58.4 8.2 19 117.8 16.6 79 177.3 24.9 39 236.7 33.3 99 296.1 41.6 60 59.4 8.4 20 118.8 16.7 80 178.2 25.1 40 237.7 33.4 300 297.1 41.8 Dist. Dep. Lat. Di8t. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat. 82° (< )8°, 262°, 278° . TABLE 2. [Page 647 Difference of Latitude and Departure for 8° (172°, 188°, 352° ). DiBt. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 298.0 41.9 361 357.5 50.2 421 416.9 58.6 481 476.3 66.9 641 535.7 75.2 U2 299.0 42.0 62 358.5 50.4 22 417.9 68.7 82 477.3 67.1 42 536.7 75.4 03 300.0 42.2 63 ■359.4 50.5 23 418.9 58.9 83 478.3 67.2 43 537.7 75.5 04 301.0 42.3 64 360.4 50.7 24 419.8 59.0 84 479.3 67.4 44 538.7 75.7 05 302.0 42.5 65 361.4 50.8 25 420.8 69.2 85 480.3 67.5 46 539.7 75.8 06 303.0 42.6 66 362.4 50.9 26 421.8 59.3 86 481.2 67.6 46 540.6 76.9 07 304.0 42.7 67 363.4 51.1 27 422.8 59.4 87 482.2 67.8 47 541.6 76.1 08 305.0 42.9 68 364.4 51.2 28 423.8 59.6 88 483.2 67.9 48 542.6 76.2 09 306.0 43.0 69 365.4 51.4 29 424.8 59.7 89 484.2 68.1 49 543. 6 76.4 10 307.0 43.1 70 366.4 51.5 30 425.8 59.8 90 485.2 68.2 68.3 50 551 544.6 545.6 76.6 76.6 311 307.9 43.3 371 367.4 51.6 431 426.8 60.0 491 486.2 ^?, 308.9 43.4 72 368.4 51.8 32 427.8 60.1 92 487.2 68.5 52 546.6 76.8 13 309.9 43.6 73 369.3 51.9 33 428.8 60.3 93 488.2 68.6 53 547.6 76.9 14 310.9 43.7 74 370.3 52.1 34 429.8 60.4 94 489.2 68.8 54 548.6 77.1 15 311.9 43.8 75 371.3 52.2 35 430.7 60.6 95 490.2 68.9 56 549.6 77.2 16 312.9 44.0 76 372.3 52.3 36 431.7 60.7 96 491.2 69.0 56 560.6 77.4 17 313.9 44.1 77 373.3 52.5 37 432.7 60.8 97 492.1 69.2 67 551.5 77.6 18 314.9 44.3 78 374. 3 52.6 38 433.7 61.0 98 493.1 69.3 58 552.6 77.6 19 315.9 44.4 79 375.3 52.7 39 434.7 61.1 99 494.1 69.6 59 553.5 77.8 20 321 316.9 44.5 80 376.3 52.9 40 436.7 61.2 500 501 495.1 69.6 60 564.6 77.9 317.9 44.7 381 377.3 53.0 441 436.7 61.4 496.1 69.7 561 665.5 78.1 22 318.8 44.8 82 378.3 53.2 42 437.7 61.5 02 497.1 69.9 62 556.6 78.2 23 319.8 45.0 83 379.2 53.3 43 438.7 61.7 03 498.1 70.0 63 557.5 78.3 24 320.8 45.1 84 380.2 53.4 44 439.7 61.8 04 499.1 70.2 64 558.6 78.5 25 321.8 45.2 85 381.2 53.6 45 440.6 61.9 06 500.1 70.3 65 659.6 78.6 26 322.8 45.4 86 382.2 53.7 46 441.6 62.1 06 501.0 70.4 66 560.6 78.8 27 323.8 45.5 87 383.2 53.9 47 442.6 62.2 07 502.0 70.6 67 561.5 78.9 28 324.8 45.7 88 384.2 54.0 48 443.6 62.4 08 503.0 70.7 68 562.5 79.0 29 325.8 45.8 89 385.2 54.1 49 444.6 62.6 09 504.0 70.8 69 563.6 79.1 30 326.8 45.9 90 386.2 54.3 50 446.6 62.6 10 505.0 70.9 70 564.5 79.3 331 327.8 46.1 391 387.2 54.4 451 446.6 62.8 511 506.0 71.1 571 565.4 79.4 32 328.7 46.2 92 388.2 54.6 52 447.6 62.9 12 507.0 71.2 72 566.4 79.6 33 329.7 46.3 93 389.1 54.7 53 448.6 63.0 13 508.0 71.4 73 667.4 79.7 34 330.7 46.5 94 390.1 54.8 54 449.6 63.2 14 609. 71.5 74 568.4 79.8 35 331.7 46.6 95 391.1 55.0 55 460.5 63.3 16 610.0 71.6 75 569.4 80.0 36 332.7 46.8 96 392.1 55.1 56 451.6 63.5 16 610.9 71.8 76 670.4 80.1 37 333.7 46.9 97 393.1 55.3 57 452.6 63.6 17 611.9 71.9 77 571.4 80.2 38 334.7 47.0 98 394.1 55.4 58 463.6 63.7 18 512.9 72.0 78 572.4 80.4 39 335.7 47.2 99 395.1 55.5 59 464.6 63.9 19 513.9 72.2 79 573.4 80.5 40 336.7 47.3 400 396.1 55.7 60 456.6 64.0 20 614.9 72.3 80 574.4 80.6 341 337.7 47.5 401 397.1 55.8 461 466.5 64.2 521 515.9 72.4 581 575.4 80.8 42 338.6 47.6 02 398.1 56.0 62 467.6 64.3 22 516.9 72.6 82 676.4 80.9 43 339.6 47.7 03 399.1 56.1 63 468.5 64.4 23 517.9 72.8 83 677.4 81.1 44 340.6 47.9 04 400.0 56.2 64 469.6 64.6 24 518.9 73.0 84 678.4 81.3 45 341.6 48.0 05 401.0 56.4 65 460.4 64.7 25 519.9 73.1 86 679.4 81.4 46 342.6 48.2 06 402.0 56.5 66 461.4 64.9 26 520.9 73.2 86 580.3 81.6 47 343.6 48.3 07 403.0 56.6 67 462.4 65.0 27 521.8 73.4 87 581.3 81.7 48 344.6 48.4 08 404.0 56.8 68 463.4 65.1 28 622.8 73.5 88 682.3 81.8 49 345.6 48.6 09 405.0 56.9 69 464.4 66.3 29 523.8 73.7 89 683.3 82.0 50 346.6 48.7 10 406.0 57.1 70 466.4 65.4 30 524.8 73.8 90 584.3 82.1 351 347.6 48.9 411 407.0 57.2 471 466.4 66.6 631 626.8 73.9 591 685.3 82.2 52 348.5 49.0 12 408.0 57.3 72 467.4 66.7 32 526.8 74.1 92 686.3 82.4 53 349.6 49.1 13 409.0 57.5 73 468.4 65.8 33 527.8 74.2 93 587.3 82.5 54 350.5 49.3 14 409.9 57.6 74 469.4 66.0 34 628.8 74.3 94 588.3 82.6 55 351.5 49.4 15 410.9 57.8 75 470.4 66.1 36 629.8 74.6 95 589.3 82.8 56 352.5 49.5 16 411.9 57.9 76 471.3 66.2 36 530.8 74.6 96 690.3 83.0 57 353.5 49.7 17 412.9 58.0 77 472.3 66.4 37 531.7 74.7 97 591.2 83.1 58 354.5 49.8 18 413.9 58.2 78 473.3 66.6 38 532.7 74.9 98 592.2 83.2 59 355.5 50.0 19 414.9 58.3 79 474.3 66.7 39 533.7 75.0 99 593.2 83.3 60 356.5 50.1 20 415.9 58.5 80 475.3 66.8 40 534.7 76.1 600 594.2 83.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat 82° (98°, 262°, 278° )• Page 648] TABLE 2. ^ Difference of Latitude and Departure for 9° (171°, 189°, 351°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.2 61 60.2 9.5 121 119.5 18.9 181 178.8 28.3 241 238.0 37.7 2 2.0 0.3 62 61.2 9.7 22 120.5 19.1 82 179.8 28.5 42 239.0 37.9 3 3.0 0.5 63 62.2 9.9 23 121.5 19.2 83 180.7 28.6 43 240.0 38.0 4 4.0 0.6 64 63.2 10.0 24 122.5 19.4 84 181.7 28.8 44 241.0 38.2 5 4.9 0.8 65 64.2 10.2 25 123.5 19.6 85 182.7 28.9 45 242.0 38.3 6 5.9 0.9 66 65.2 10.3 26 124.4 19.7 86 183.7 29.1 46 243.0 38.5 7 6.9 1.1 67 66.2 10.5 27 125.4 19.9 87 184.7 29.3 47 244.0 38.6 8 7.9 1.3 68 67.2 10.6 28 126.4 20.0 88 185.7 29.4 48 244.9 38.8 9 8.9 1.4 69 68.2 10.8 29 127.4 20.2 89 186.7 29.6 49 245.9 39.0 10 11 9.9 10.9 1.6 70 71 69.1 11.0 30 128.4 20.3 90 191 187.7 29.7 50 246.9 247.9 39.1 1.7 70.1 11.1 131 129.4 20.5 188.6 29.9 251 39.3 12 11.9 1.9 72 71.1 11.3 32 130.4 20.6 92 189.6 30.0 52 248.9 39.4 13 12.8 2.0 73 72.1 11.4 33 131.4 20.8 93 190.6 30.2 53 249.9 39.6 14 13.8 2.2 74 73.1 11.6 34 132. 4 21.0 94 191.6 30.3 54 250.9 39.7 15 14.8 2.3 75 74.1 11.7 35 133.3 21.1 95 192.6 30.5 55 251.9 39.9 16 15.8 2.5 76 75.1 11.9 36 134.3 21.3 96 193.6 30.7 56 252.8 40.0 17 16.8 2.7 77 76.1 12.0 37 135.3 21.4 97 194.6 30.8 57 253.8 40.2 18 17.8 2.8 78 77.0 12.2 38 136.3 21.6 98 195.6 31.0 58 254.8 40.4 19 18.8 3.0 79 78.0 12.4 39 137.3 21.7 99 196.5 31.1 59 255.8 40.5 20 19.8 3.1 80 79.0 12.5 40 138.3 21.9 200 201 197.5 31.3 60 256.8 40.7 21 20.7 3.3 81 80.0 12.7 141 139.3 22.1 198.5 31.4 261 257.8 40.8 22 21.7 3.4 82 81.0 12.8 42 140.3 22.2 02 199.5 31.6 62 258.8 41.0 23 22.7 3.6 83 82.0 13.0 43 141.2 22.4' 03 200.5 31.8 63 259.8 41.1 24 23.7 3.8 84 83.0 13.1 44 142.2 22.5 04 201.5 31.9 64 260.7 41.3 25 24.7 3.9 85 84.0 13.3 45 143.2 22.7 05 202.5 32.1 65 261.7 41.5 26 25.7 4.1 86 84.9 13.5 46 144.2 22.8 06 203.5 32.2 66 262.7 41.6 27 26.7 4.2 87 85.9 13.6 47 145.2 23.0 07 204.5 32.4 67 263.7 41.8 28 27.7 4.4 88 86.9 13.8 48 146.2 23.2 08 205.4 32.5 68 264.7 41.9 29 28.6 4.5 89 87.9 13.9 49 147.2 23.3 09 206.4 32.7 69 265.7 42.1 30 29.6 4.7 90 88.9 14.1 50 148. 2 23.5 10 207.4 32.9 70 266.7 42.2 31 30.6 4.8 91 89.9 14.2 151 149.1 23.6 211 203.4 33.0 271 267.7 42.4 32 31.6 5.0 92 90.9 14.4 52 150.1 23.8 12 209.4 33.2 72 268.7 42.6 33 32.6 5.2 93 91.9 14.5 53 151.1 23.9 13 210.4 33.3 73 269.6 42.7 34 33.6 5.3 94 92.8 14.7 54 152.1 24.1 14 211.4 33.5 74 270.6 42.9 35 34.6 5.5 95 93.8 14.9 55 153. 1 24.2 15 212.4 33.6 75 271.6 43.0 36 35.6 5.6 96 94.8 15.0 56 151.1 24.4 16 213.3 33.8 76 272.6 43.2 37 36.5 5.8 97 95.8 15.2 57 155.1 24.6 17 214.3 33.9 77 273.6 43.3 38 37.5 5.9 98 96.8 15.3 58 156.1 24.7 18 215.3 34.1 78 274.6 43.5 39 38.5 6.1 99 97.8 15.5 59 157.0 24.9 19 216.3 34.3 79 275.6 43.6 40 39.5 6.3 100 98.8 15.6 15.8 60 158.0 25.0 20 217.3 34.4 80 281 276.6 43.8 44.0 41 40.5 6.4 101 99.8 161 159.0 25.2 221 218.3 34.6 277.5 42 41.5 6.6 02 100.7 16.0 62 160.0 25.3 22 219.3 34.7 82 278.5 44.1 43 42.5 6.7 03 101.7 16.1 63 161. 25.5 23 220.3 34.9 83 279.5 44.3 44 43.5 6.9 04 102.7 16.3 64 162.0 25.7 24 221.2 35.0 84 280.5 44.4 45 44.4 7.0 05 103.7 16.4 65 163.0 25.8 25 222.2 35.2 85 281.5 44.6 46 45.4 7.2 06 104.7 16.6 66 164.0 26.0 26 223.2 35.4 86 282.5 44.7 47 46.4 7.4 07 105.7 16.7 67 164.9 26.1 27 224.2 35.5 87 283.5 44.9 48 47.4 7.5 08 106.7 16.9 68 165.9 26.3 28 225.2 35.7 88. 284.5 45.1 49 48.4 7.7 09 107.7 17.1 69 166.9 26.4 29 226.2 35.8 89 285.4 45.2 50 49.4 50.4 7.8 10 108.6 17.2 70 167.9 168.9 26.6 30 231 227.2 36.0 90 286.4 45.4 51 8.0 111 109.6 17.4 171 26.8 228.2 36.1 291 287.4 45.5 52 51.4 8.1 12 110.6 17.5 72 169.9 26.9 32 229.1 36.3 92 288.4 45.7 53 52.3 8.3 13 111.6 17.7 73 170.9 27.1 33 230.1 36.4 93 289.4 45.8 54 53.3 8.4 14 112.6 17.8 74 171.9 27.2 34 231.1 36.6 94 290.4 46.0 55 54.3 8.6 15 113.6 18.0 75 172.8 27.4 35 232.1 36.8 95 291.4 46.1 56 55.3 8.8 16 114.6 18.1 76 173.8 27.5 36 233.1 36.9 96 292.4 46.3 57 56.3 8.9 17 115.6 18.3 77 174.8 27.7 37 234.1 37.1 97 293.3 46.5 58 57.3 9.1 18 116.5 18.5 78 175.8 27.8 38 235.1 37,2 98 294.3 46.6 59 58.3 9.2 19 117.5 18.6 79 176.8 28.0 39 236.1 37.4 99 295.3 46.8 60 59.3 9.4 20 118.5 18.8 80 177.8 28.2 40 237.0 37.5 300 296.3 46.9 DUt. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat 81° (99°, 261°, 279°). TABLE 2 [Page 549 Difference of Latitude and Departure for 9° (171°, 189°, 351°) Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 297.3 47.1 361 356.6 56.5 421 415.8 65.9 481 475.1 75.2 541 534.4 84.6 02 298.3 47.2 62 357.5 56.7 22 416.8 66.0 82 476.1 75.3 42 535.4 84.7 03 299.3 47.4 63 358.5 56.8 23 417.8 66.2 83 477.1 75.5 43 536.3 84.9 04 300.3 47.6 64 359.5 56.9 24 418.8 66.3 84 478.0 75.6 44 537.3 85.1 05 301.2 47.7 65 360.5 57.1 25 419.8 66.5 85 479.0 75.8 45 538.3 85.3 06 302.2 47.9 66 361.5 57.3 26 420.8 66.6 86 480.0 75.9 46 539.3 85.4 07 303.2 48.0 67 362.5 57.4 27 421.7 66.8 87 481.0 76.1 47 540.3 85.6 08 304.2 48.2 68 363.5 57.6 28 422.7 67.0 88 482.0 76.2 48 541.3 85.7 09 305.2 48.3 69 364.5 57.7 29 423.7 67.1 89 483.0 76.4 49 542.3 85.9 10 311 306.2 307.2 48.5 70 365.4 57.9 30 424.7 67.3 90 484.0 76.5 50 543.3 86.0 48.7 371 366.4 58.1 431 425.7 67.4 491 485.0 76.7 551 544.3 86.2 12 308.2 48.8 72 367.4 58.2 32 426.7 67.6 92 485.9 76.8 52 545.2 86.3 13 309.1 49.0 73 368.4 58.4 33 427.7 67.7 93 486.9 77.0 53 546.2 86.5 14 310.1 49.1 74 369.4 58.5 34 428.7 67.9 94 487.9 77.1 54 547.2 86.6 15 311.1 49.3 75 370.4 58.7 35 429.6 68.1 95 488.9 77.3 55 548.2 86.8 16 312.1 49.4 76 371.4 58.8 36 430.6 68.2 96 489.9 77.5 56 549.2 87.0 17 313.1 49.6 77 372.4 59.0 37 431.6 68.4 97 490.9 77.7 57 550.2 87.1 18 314.1 49.8 78 373.3 59.1 38 432.6 68.5 98 491.9 77.9 58 551.2 87.3 19 315.1 49.9 79 374.3 59.3 39 433.6 68.7 99 492.9 78.0 59 552.2 87.4 20 316.1 50.1 80 375.3 59.5 40 434.6 68.8 500 493.8 78.2 60 553.1 87.6 321 317.0 50.2 381 376. 3 59.6 441 435.6 69.0 501 494.8 78.4 561 554.1 87.7 22 318.0 50,4 82 377.3 59.8 42 436.6 69.1 02 495.8 78.5 62 555.1 87.9 23 319.0 50.5 83 378.3 59.9 43 437.5 69.3 03 496.8 78.7 63 556.1 88.0 24 320.0 50.7 84 379.3 60.1 44 438.5 69.5 04 497.8 78.8 64 557.1 88.2 25 321.0 50.8 85 380.3 60.2 45 439.5 69.6 05 498.8 79.0 65 558.1 88.3 26 322.0 51.0 86 381.2 60.4 46 440. 5 69.8 06 499.8 79.1 66 559.1 88.5 27 323.0 51.2 87 382.2 60.5 47 441.5 69.9 07 500.8 79.2 67 560.1 88.6 28 324.0 51.3 88 383.2 60.7 48 442.5 70.1 08 501.7 79.4 68 561.0 88.8 29 324.9 51.5 89 384.2 60.9 49 443.5 70.2 09 502.7 79.5 69 562.0 88.9 30 325.9 51.7 90 385.2 61.0 50 444.5 70.4 10 503.7 79.7 70 563.0 89.1 331 326.9 51.8 391 386.2 61.2 451 445.4 70.6 511 504.7 79.8 571 564.0 89.2 32 327.9 51.9 92 387.2 61.3 52 446.4 70.7 12 505.7 80.1 72 565.0 89.4 33 328.9 52.1 93 388.2 61.5 53 447.4 70.9 13 506.7 80.2 73 566.0 89.5 34 329.9 52.3 94 389.1 61.6 54 448.4 71.0 14 507.7 80.3 74 567.0 89.7 35 330. 9 52.4 95 390.1 61.8 55 449.4 71.2 15 508.7 80.5 75 568.0 89.9 36 331.9 52.6 96 391.1 62.0 56 450.4 71.3 16 509.6 80.6 76 568.9 90.1 37 332.8 52.7 97 392.1 62.1 57 451.4 71.5 17 510.6 80.8 77 569.9 90.2 38 333.8 52.9 98 393.1 62.3 58 452.4 71.7 18 511.6 80.9 78 570.9 90.3 39 334.8 53.0 99 394.1 62.4 59 453.3 71.8 19 512.6 81.1 79 571.9 90.5 40 335.8 53.2 400 395.1 62.6 60 454.3 72.0 20 513.6 81.3 80 572.9 90.7 341 336.8 53.3 401 396.1 62.7 461 455.3 72.1 521 514.6 81.4 581 573.9 90.9 42 337. 8 53.5 02 397.0 62.9 62 456.3 72.3 22 515.6 81.6 82 574.9 91.0 43 338.8 53.7 03 398.0 63.0 63 457.3 72.4 23 516.6 81.8 83 575.9 91.2 44 339.8 53.8 04 399.0 63.2 64 458.3 72.6 24 517.6 81.9 84 576.9 91.3 45 340.8 54.0 05 400.0 63.4 65 459.3 72.7 25 518.6 82.1 85 577.9 91.5 46 341.7 54.1 06 401.0 63.5 66 460.3 72.9 26 519.5 82.3 86 578.8 91.7 47 342.7 54.3 07 402.0 63.7 67 461.2 73.1 27 520.5 82.4 87 579.8 91.8 48 343. 7 54.4 08 403.0 63.8 68 462.2 73.2 28 521.5 82.6 88 580.8 92.0 49 344.7 54.6 09 404.0 64.0 69 463.2 73.4 29 522.5 82.7 89 581.8 92.1 50 345.7 54.8 10 405.0 64.1 70 464.2 73.5 30 523.5 82.9 90 582.8 92.2 351 346.7 54.9 411 405.9 64.3 471 465.2 73.7 531 524.5 83.1 591 583.8 92.4 52 347.7 55.1 12 406.9 64.5 72 466.2 73.8 32 525.5 83.2 92 584.8 92.5 53 348.7 55.2 13 407.9 64.6 73 467.2 74.0 33 526.5 83.4 93 585.7 92.7 54 349.6 55.4 14 408.9 64.8 74 468.2 74.2 34 527.5 83.5 94 586.7 92.9 55 350.6 55.5 15 409.9 64.9 75 469.2 74.3 35 528.4 83.7 95 587.7 93.1 56 351.6 55.7 16 410.9 65.1 76 470.1 74.5 36 529.4 83.8 96 588.7 93.2 57 352.6 55.9 17 411.9 65.2 77 471.1 74.6 37 530.4 84.0 97 589.7 93.4 58 353.6 56.0 18 412.9 65.4 78 472.1 74.8 38 531.4 84.1 98 590.7 93.5 59 354.6 56.2 19 413.8 65.6 79 473.1 74.9 39 532.4 84.3 99 591.7 93.7 60 355.6 56.3 20 414.8 65.7 80 474.1 75.0 40 533.4 84.4 600 592.6 93.8 Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 81° (99°, 261 °, 279° )• Page 650] TABLE 2. Difference of Latitude and Departure for 10° (170°, 19C °, 350°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.2 61 60.1 10.6 121 119.2 21.0 181 178.3 31.4 241 237.3 41.8 2 2.0 0.3 62 61.1 10.8 22 120.1 21.2 82 179.2 31.6 42 2.38. 3 42.0 3 3.0 0.5 63 62.0 10.9 23 121.1 21.4 83 180.2 31.8 43 239.3 42.2 4 3.9 0.7 64 63.0 11.1 24 122.1 21.5 84 181.2 32.0 44 240.3 42.4 6 4.9 0.9 65 64.0 11.3 25 123.1 21.7 85 182.2 32.1 45 241.3 42.5 6 5.9 1.0 66 65.0 11.5 26 124.1 21.9 86 183.2 32.3 46 242.3 42.7 7 6.9 1.2 67 66.0 11.6 27 125.1 22.1 87 184.2 32.5 47 243.2 42.9 8 7.9 1.4 68 67.0 11.8 28 126.1 22.2 88 185.1 32.6 48 244.2 43.1 9 8.9 1.6 69 68.0 12.0 29 127.0 22.4 89 186.1 32.8 49 245.2 43.2 10 9.8 1.7 70 68.9 12.2 30 128.0 22.6 90 187.1 33.0 50 246.2 43.4 11 10.8 1.9 71 69.9 12.3 131 129.0 22.7 191 188.1 33.2 251 247.2 43.6 12 11 8 2.1 72 70.9 12.5 32 130.0 22.9 92 189.1 33.3 52 248.2 43.8 13 12.8 2.3 73 71.9 12.7 33 131.0 23.1 93 190.1 33.5 53 249.2 43.9 14 13.8 2.4 74 72.9 12.8 34 132.0 23.3 94 191.1 33.7 54 250.1 44.1 15 14.8 2.6 75 73.9 13.0 35 132.9 23.4 95 192.0 33.9 55 251.1 44.3 16 15.8 2.8 76 74.8 13.2 36 133.9 23.6 96 193.0 34.0 56 252.1 44.5 17 16.7 3.0 77 75.8 13.4 37 134.9 23.8 97 194.0 34.2 57 253.1 44.6 18 17.7 3.1 78 76.8 13.5 38 135.9 24.0 98 195.0 34.4 58 254.1 44.8 19 18.7 3.3 79 77.8 13.7 39 136.9 24.1 99 196.0 34.6 59 255.1 45.0 20 19.7 3.5 80 78.8 13.9 40 137.9 24.3 200 197.0 34.7 60 256.1 45.1 21 20.7 3.6 81 79.8 14.1 141 138.9 24.5 201 197.9 34.9 261 257.0 45.3 22 21.7 3.8 82 80.8 14.2 42 139.8 24.7 02 198.9 35.1 62 258.0 45.5 23 22.7 4.0 83 81.7 14.4 43 140.8 24.8 03 199.9 35.3 63 259.0 45.7 24 23.6 4.2 84 82.7 14.6 44 141.8 25.0 04 200.9 35.4 64 260.0 45.8 25 24.6 4.3 85 83.7 14.8 45 142.8 25.2 05 201.9 35.6 65 261.0 46.0 26 25.6 4.5 86 84.7 14.9 46 143.8 25.4 06 202.9 35.8 66 262.0 46.2 27 26.6 4.7 87 85.7 15.1 47 144.8 25.5 07 203.9 35.9 67 262.9 46.4 28 27.6 4.9 88 86.7 15.3 48 145.8 25.7 08 204.8 36.1 68 263.9 46.5 29 28.6 5.0 89 87.6 15.5 49 146.7 25.9 09 205.8 36.3 69 264.9 46.7 30 29.5 5.2 90 88.6 15.6 50 147.7 148.7 26.0 10 206.8 36.5 70 265.9 46.9 31 30.5 5.4 91 89.6 15.8 151 26.2 211 207.8 36.6 271 266.9 47.1 32 31.5 5.6 92 90.6 16.0 52 149.7 26.4 12 208.8 36.8 72 267.9 47.2 33 32.5 5.7 93 91.6 16.1 53 150.7 26.6 13 209.8 37.0 73 268.9 47.4 34 33.5 5.9 94 92.6 16.3 54 151.7 26.7 14 210.7 37.2 74 269.8 47.6 35 34.5 6.1 95 93.6 16.5 55 152.6 26.9 15 211.7 37.3 75 270.8 47.8 36 35.5 6.3 96 94.5 16.7 56 153.6 27.1 16 212.7 37.5 76 271.8 47.9 37 36.4 6.4 97 95.5 16.8 57 154.6 27.3 17 213.7 37.7 77 272.8 48.1 38 37.4 6.6 98 96.5 17.0 58 155.6 27.4 18 214.7 37.9 78 273.8 48.3 39 38.4 6.8 99 97.5 17.2 59 156.6 27.6 19 215.7 38.0 79 274.8 48.4 40 39.4 6.9 7.1 100 98.5 17.4 60 157.6 27.8 20 216.7 38.2 80 275.7 48.6 41 40.4 101 99.5 17.5 161 158.6 28.0 221 217.6 38.4 281 276.7 48.8 42 41.4 7.3 02 100.5 17.7 62 159.5 28.1 22 218.6 38.5 82 277.7 49.0 43 42.3 7.5 03 101.4 17.9 63 160.5 28.3 23 219.6 38.7 83 278.7 49.1 44 43.3 7.6 04 102.4 18.1 64 161.5 28.5 24 220.6 38.9 84 279.7 49.3 45 44.3 7.8 05 103.4 18.2 65 162.5 28.7 25 221.6 39.1 85 280.7 49.5 46 45.3 8.0 06 104.4 18.4 66 163.5 28.8 26 222.6 39.2 86 281.7 49.7 47 46.3 8.2 07 105.4 18.6 67 164.5 29.0 27 223.6 39.4 87 282.6 49.8 48 47.3 8.3 08 106.4 18.8 68 165.4 29.2 28 224.5 39.6 88 283.6 50.0 49 48.3 8.5 09 107.3 18.9 69 166.4 29.3 29 225.5 39.8 89 284.6 50.2 50 49.2 8.7 10 108.3 19.1 70 167.4 29.5 30 226.5 39.9 90 285.6 50.4 51 50.2 8.9 111 109.3 19.3 171 168.4 29.7 231 227.5 40.1 291 286.6 50.5 52 51.2 9.0 12 110.3 19.4 72 169.4 29.9 32 228.5 40.3 92 287.6 50.7 53 52.2 9.2 13 111.3 19.6 73 170.4 30.0 33 229.5 40.5 93 288.5 50.9 54 53.2 9.4 14 112.3 19.8 74 171.4 30.2 34 230.4 40.6 94 289.5 51.1 55 54.2 9.6 15 113.3 20.0 75 172.3 30.4 35 231.4 40.8 95 290.5 51.2 66 55.1 9.7 16 114.2 20.1 76 173.3 30.6 36 232.4 41.0 96 291.5 51.4 ■ 57 56.1 9.9 17 115.2 20.3 77 174. S 30.7 37 233.4 41.2 97 292.5 51.6 I 58 57.1 10.1 18 116.2 20.5 78 175.3 30.9 38 234.4 41.3 98 293.5 51.7 I 59 58.1 10.2 19 117.2 20.7 79 176.3 31.1 39 235.4 41.5 99 294.5 51.9 ■ 60 59.1 10.4 20 118.2 20.8 80 177.3 31.3 40 236.4 41.7 300 295.4 52.1 ■ Diat. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. , f iO" (1( )0°, 260 =, 280° )• , TABLE 27 [Page 551 Difference of Latitude and Departure for 10° (170°, 190°, 350°) Dist. Lat. Dep. Dist. Lat. j Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. 1 Lat. Dep. 301 296.4 52.3 361 355.5 62.7 421 414.6 73.1 481 473.7 83.5 541 532.8 93.9 02 297.4 52.5 62 356.5 62.9 22 415.6 73.3 82 474.7 83.7 42 533.8 94.1 03 298.4 52.6 63 357.5 63.0 23 416.6 73.5 83 475.7 83.9 43 534.8 94.3 04 299.4 52.8 64 358.5 63.2 24 417.6 73.6 84 476.6 84.1 44 535.7 94.5 05 300.4 53.0 65 359. 5 63.4 25 418.5 73.8 85 477.6 84.2 45 536.7 94.6 06 301.4 53.1 66 360. 4 63.6 26 419.5 74.0 86 478.6 84.4 46 537.7 94.8 07 302.3 53.3 67 361.4 63.7 27 420.5 74.2 87 479.6 84.6 47 538.7 95.0 08 303.3 53.5 68 362.4 63.9 28 421.5 74.3 88 480.6 84.7 48 539.7 95.1 09 304.3 53.7 69 363.4 64.1 29 422.5 74.5 89 481.6 84.9 49 540.7 95.3 10 305.3 53.8 70 364.4 64.3 30 423.5 74.7 90 482.6 85.1 50 541.6 95.5 311 306.3 54.0 371 365.4 64.4 431 424.5 74.9 491 483.5 85.2 551 542.6 95.6 12 307.3 54.2 72 366.4 64.6 32 425.4 75.0 92 484.5 85.4 52 543.6 95.8 13 308.2 54.3 73 367. 3 64.8 33 426.4 75.2 93 485.5 85.6 53 544.6 96.0 14 309.2 54.5 74 368. 3 65.0 34 427.4 75.4 94 486.5 85.8 54 545.6 96.2 15 310.2 54.7 75 369.3 65.1 35 428.4 75.5 95 487.5 85.9 55 546.6 96.3 16 311.2 54.9 76 370.3 65.3 36 429.4 75.7 96 488.5 86.1 56 547.5 96.5 17 312.2 55.1 77 371.3 65.5 37 430.4 75.9 97 489.4 86.3 57 548.5 96.7 18 313.2 55.2 78 372.3 65.6 38 431.3 76.1 98 490.4 86.5 58 549.5 96.9 19 314.2 55.4 79 373.2 65.8 39 432.3 76.2 99 491.4 86.6 59 550.5 97.0 20 321 315.1 55.6 80 374.2 66.0 40 433.3 76.4 500 492.4 86.8 60 551.5 97.2 316.1 55.8 381 375.2 66.2 441 434.3 76.6 501 493.4 87.0 561 552.5 97.4 22 317.1 55.9 82 376.2 66.3 42 435.3 76.8 02 494.4 87.2 62 553.5 97.6 23 318.1 56.1 83 377.2 66.5 43 436.3 76.9 03 495.3 87.3 63 554.4 97.7 24 319.1 56.3 84 378.2 66.7 44 437.3 77.1 04 496.3 87.5 64 555.4 97.9 25 320.1 56.4 85 379.2 66.9 45 438.2 77.3 05 497.3 87.7 65 556.4 98.1 26 321.0 56.6 86 380.1 67.0 46 439.2 77.5 06 498.3 87.9 66 557.4 98.3 27 322.0 56.8 87 381.1 67.2 47 440.2 77.6 07 499.3 88.0 67 558. 4 98.4 28 323.0 57.0 88 382. 1 67.4 48 441.2 77.8 08 500.3 88.2 68 559.4 98.6 29 324.0 57.1 89 383.1 67.6 49 442.2 78.0 09 501.3 88.4 69 560.3 98.8 30 331 325.0 57.3 90 384. 1 67.7 50 443.2 78.2 10 502.2 88.6 70 561.3 99.0 326.0 57.5 391 385.1 67.9 451 444.2 78.3 511 503.2 88.7 571 562.3 99.1 32 327.0 57.7 92 386.0 68.1 52 445.1 78.5 12 504.2 88.9 72 563.3 99.3 33 327.9 57.8 93 387.0 68.2 53 446.1 78.7 13 505.2 89.1 73 564.3 99.5 34 328.9 58.0 94 388.0 68.4 54 447.1 78.8 14 506.2 89.2 74 565.3 99,6 35 329.9 58.2 95 .389. 68.6 55 448.1 79.0 15 507.2 89.4 75 566.3 99.8 36 330.9 58.4 96 390.0 68.8 56 449.1 79.2 16 508.2 89.6 76 567.2 100.0 37 331.9 58.5 97 391.0 68.9 57 450.1 79.4 17 509.1 89.8 77 568.2 100.2 38 332.9 58.7 98 392.0 69.1 58 451.0 79.5 18 510.1 89.9 78 569.2 100.3 39 333.9 58.9 99 392.9 69.3 59 452.0 79.7 19 511.1 90.1 79 570.2 100.5 40 334.8 59.1 400 393.9 69.5 60 453.0 79.9 20 512.1 90.3 90.5 80 571.2 100.7 341 335.8 59.2 401 394.9 69.6 461 454.0 80.1 521 513.1 581 572.2 100.9 42 336.8 59.4 02 395.9 69.^ 62 455. 80.2 22 514.1 90.6 82 573.2 101.0 43 337.8 59.6 03 396.9 70.0 63 456.0 80.4 23 515.1 90.8 83 574.1 101.2 44 338.8 59.8 04 397.9 70.2 64 457.0 80.6 24 516.0 91.0 84 575.1 101.4 45 339.8 59.9 05 398.9 70.3 65 457.9 80.8 25 517.0 91.2 85 576.1 101.6 46 340.7 60.1 06 399.8 70.5 66 458.9 80.9 26 518.0 91.3 86 577.1 101.7 47 341.7 60.3 07 400.8 70.7 67 459.9 81.1 27 519.0 91.5 87 578.1 101.9 48 342.7 60.4 08 401.8 70.9 68 460.9 81.3 28 520.0 91.7 88 579.1 102.1 49 343.7 60.6 09 402.8 71.0 69 461.9 81.5 29 521.0 91.9 89 580.0 102.3 50 344.7 60.8 10 403.8 71.2 70 462.9 81.6 30 521.9 92.0 90 581.0 102.4 351 345.7 61.0 411 404.8 71.4 471 463.8 81.8 531 522.9 92.2 591 582.0 102.6 52 346.7 61.1 12 405.7 71.6 72 464.8 82.0 32 523.9 92.4 92 583.0 102.8 53 347.6 61.3 13 406.7 71.7 73 465.8 82.1 33 524.9 92,5 93 584.0 102.9 54 348.6 61.5 14 407.7 71.9 74 466.8 82.3 34 525.9 92.7 94 585.0 103.1 55 349.6 61.7 15 408.7 72.1 75 467.8 82.5 35 526.9 92.9 95 586.0 103.3 56 350.6 61.8 16 409.7 72.2 76 468.8 82.7 36 527.9 93.1 96 586.9 103.5 57 351.6 62.0 17 410.7 72.4 77 469.8 82.8 37 528.8 93.2 97 587.9 103.6 58 352.6 62.2 18 411.7 72.6 78 470.7 83.0 38 529.8 93.4 98 588.9 103.8 59 353.5 62.4 19 412.6 72.8 79 471.7 83.2 39 530.8 93.6 99 589.9 104.0 60 354.5 62.5 20 413.6 72.9 80 472.7 83.4 40 531.8 93.8 600 590.9 104.2 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. i 50° (100°, 260°, 280°). Page 552] TABLE 2. Difference of Latitude and Departure for 11° (169°, 191°, 349" )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.2 61 59.9 11.6 121 118.8 23.1 181 177.7 34.5 241 236.6 46.0 2 2.0 0.4 62 60.9 11.8 22 119.8 23.3 82 178.7 34.7 42 237.6 46.2 3 2 9 0.6 63 61.8 12.0 23 120.7 23.5 83 179.6 34.9 43 238.5 46.4 4 3.9 0.8 64 62.8 12.2 24 121.7 23.7 84 180.6 35.1 44 239.5 46.6 5 4.9 1.0 65 63.8 12.4 25 122.7 23.9 85 181.6 35.3 45 240.5 46.7 6 5.9 1.1 66 64.8 12.6 26 123.7 24.0 86 182.6 35.5 46 241.5 46.9 7 6.9 1.3 67 65.8 12.8 27 124.7 24.2 87 183.6 35.7 47 242.5 47.1 8 7.9 1.5 68 66.8 13.0 28 125.6 24.4 88 184.5 35.9 48 243.4 47.3 9 8.8 1.7 69 67.7 13.2 29 126.6 24.6 89 185.5 36.1 49 244.4 47.5 10 9.8 1.9 70 68.7 13.4 30 127.6 24.8 90 186.5 36.3 50 245.4 47.7 11 10.8 2.1 71 69.7 13.5 131 128.6 25.0 191 187.5 36.4 251 246.4 47.9 12 11.8 2.3 72 70.7 13.7 32 129.6 25.2 92 188.5 36.6 52 247.4 48.1 13- 12.8 2.5 73 71.7 13.9 33 130.6 25.4 93 189.5 36.8 53 248.4 48.3 14 13.7 2.7 74 72.6 14.1 34 131.5 25.6 94 190.4 37.0 54 249.3 48.5 15 14.7 2.9 75 73.6 14.3 35 132.5 25.8 95 191.4 37.2 55 250.3 48.7 16 15.7 3.1 76 74.6 14.5 36 133.5 26.0 96 192.4 37.4 56 251.3 48.8 17 16.7 3.2 77 75.6 14.7 37 134.5 26.1 97 193.4 37.6 57 252.3 49.0 18 17.7 3.4 78 76.6 14.9 38 135.5 26.3 98 194.4 37.8 58 253.3 49.2 19 18.7 3.6 79 77.5 15.1 39 136.4 26.5 99 195.3 38.0 59 254.2 49.4 20 19.6 3.8 80 78.5 15.3 40 137.4 26.7 200 196.3 38.2 60 255.2 49.6 21 20.6 4.0 81 79.5 15.5 141 138.4 26.9 201 197.3 38.4 261 256.2 49.8 22 21.6 4.2 82 80.5 15.6 42 139.4 27.1 02 198.3 38.5 62 257.2 50.0 23 22.6 4.4 83 81.5 15.8 43 140.4 27.3 03 199.3 38.7 63 258.2 50.2 24 23.6 4.6 84 82.5 16.0 44 141 4 27.5 04 200.3 38.9 64 259.1 50.4 25 24.5 4.8 85 83.4 16.2 45 142.3 27.7 05 201.2 39.1 65 260.1 ' 50.6 26 25.5 5.0 86 84.4 16.4 46 143.3 27.9 06 202.2 39.3 66 261.1 50.8 27 26.5 5.2 87 85.4 16.6 47 144.3 28.0 07 203.2 39.5 67 262.1 50.9 28 27.5 5.3 88 86.4 16.8 48 145.3 28.2 08 204.2 39.7 68 263.1 51.1 29 28.5 5.5 89 87.4 17.0 49 146.3 28.4 09 205.2 39.9 69 264.1 51.3 30 29.4 5.7 90 88.3 17.2 50 147.2 28.6 10 206.1 40.1 70 265.0 51.5 31 30.4 5.9 91 89.3 17.4 151 148.2 28.8 211 207.1 40.3 271 266.0 51.7 32 31.4 6.1 92 90.3 17.6 52 149.2 29.0 12 208.1 40.5 72 267.0 51.9 33 32.4 6.3 93 91.3 17.7 53 150.2 29.2 13 209.1 40.6 73 268.0 52.1 34 33.4 6.5 94 92.3 17.9 54 151.2 29.4 14 210.1 40.8 74 269.0 52.3 35 34.4 6.7 95 93.3 18.1 55 152.2 29.6 15 211.0 41.0 75 269.9 52.5 36 35.3 6.9 96 94.2 18.3 56 153.1 29.8 16 212.0 41.2 76 270.9 52.7 37 36.3 7.1 97 95.2 18.5 57 154.1 30.0 17 213.0 41.4 77 271.9 52.9 38 37.3 7.3 98 96.2 18.7 58 155.1 30.1 18 214.0 41.6 78 272.9 53.0 39 38.3 7.4 99 97.2 18.9 59 156.1 30.3 19 215.0 41.8 79 273.9 53.2 40 39.3 7.6 100 98.2 19.1 60 157.1 30.5 20 216.0 42.0 80 274.9 53.4 41 40.2 7.8 101 99.1 19.3 161 158.0 30.7 221 216. 9 42.2 281 275.8 53.6 42 41.2 8.0 02 100.1 19.5 62 159.0 30.9 ^2 217.9 42.4 82 t 276. 8 53.8 43 42.2 8.2 03 101.1 19.7 63 160.0 31.1 23 218.9 42.6 83 277. 8 54.0 44 43.2 8.4 04 102.1 19.8 64 161.0 31.3 24 219.9 42.7 84 278. 8 54.2 45 44.2 8.6 05 103. 1 20.0 65 162.0 31.5 25 220.9 42.9 85 279.8 54.4 46 45.2 8.8 06 104.1 20.2 66 163.0 31.7 26 221.8 43.1 86 280.7 54.6 47 46.1 9.0 07 105.0 20.4 67 163.9 31.9 27 222.8 43.3 87 281.7 54.8 48 47.1 9.2 08 106.0 20.6 68 164.9 32.1 28 223.8 43.5 88 282.7 55.0 49 48.1 9.3 09 107.0 20.8 69 165.9 32.2 29 224.8 43.7 89 283.7 55.1 50 49.1 9.5 10 108.0 21.0 70 166.9 32.4 30 225.8 43.9 90 284.7 55.3 51 50.1 9.7 111 109.0 21.2 171 167.9 32.6 231 226.8 44.1 291 285.7 55.5 52 51.0 9.9 12 109.9 21.4 72 168.8 32.8 32 227.7 44.3 92 286 6 55.7 53 52.0 10.1 13 110.9 21.6 73 169.8 33.0 33 228.7 44.5 93 287.6 55.9 54 53.0 10.3 14 111.9 21.8 74 170.8 33.2 34 229.7 44.6 94 288.6 56.1 55 54.0 10.5 15 112.9 21.9 75 171.8 33.4 35 230.7 44.8 95 289.6 56.3 56 55.0 10.7 16 113.9 22.1 76 172.8 33.6 36 231.7 45.0 96 290.6 56.5 57 56.0 10.9 17 114.9 22.3 77 173.7 33.8 37 232.6 45.2 97 291.5 56.7 58 56.9 11.1 18 115.8 22.5 78 174.7 34.0 38 233.6 45.4 98 292.5 56.9 59 57.9 11.3 19 116.8 22.7 79 175.7 34.2 39 234.6 45.6 99 293.5 57.1 60 58.9 11.4 20 117.8 22.9 80 176.7 34.3 40 235.6 45.8 300 294.5 57.2 Diet. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat 79° (1 01°, 259 °, 281°). TABLE 2. [Page 653 | . Difference of Latitude and Departure for 11° (169°, 191°, 349° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 295.4 57.4 361 354.3 68.9 421 413.2 80.3 481 472.1 91.8 541 531.0 103.2 02 296.4 57.6 62 355.3 69.1 22 414.2 80.5 82 473.1 92.0 42 532.0 103.4 03 297.4 57.8 63 356.3 69.3 23 415.2 80.7 83 474.1 92.2 43 533.0 103.6 04 298.4 58.0 64 357.3 69.5 24 416.2 80.9 84 475.1 92.4 44 534.0 103.8 05 299.4. 58.2 65 358.3 69.6 25 417.2 81.1 85 476.1 92.6 45 535.0 104.0 06 300.3 58.4 66 359.2 69.8 26 418.1 81.3 86 477.0 92.8 46 535.9 104.2 07 301.3 58.6 67 360.2 70.0 27 419.1 81.5 87 478.0 93.0 47 536. 9 104.4 08 302.3 58.8 68 361.2 70.2 28 420.1 81.7 88 479.0 93.2 48 537.9 104.6 09 303.3 59.0 69 362.2 70.4 29 421.1 81.9 89 480.0 93.3 49 538.9 104.8 10 304.3 305.3 59.2 70 363.2 70.6 30 422.1 82.1 90 481.0 93.5 50 539.9 105.0 311 59.3 371 364.1 70.8 431 423. 82. 2 491 481.9 93.6 551 540.8 105.1 12 306.2 59.5 72 365.1 71.0 32 424.0 82.4 92 482.9 93.8 52 541.8 105.3 13 307.2 59.7 73 366.1 71.2 33 425.0 82.6 93 483.9 94.0 53 542.8 105.5 14 308.2 59.9 74 367.1 71.4 34 426.0 82.8 94 484.9 94.2 54 543.8 106.7 15 309.2 60.1 75 368.1 71.6 35 427.0 83.0 95 485.9 94.4 55 544.8 106.9 16 310.2 60.3 76 369.1 71.7 36 428.0 83.2 96 486.9 94.6 56 545.8 106.1 17 311.1 60.5 77 370.0 71.9 37 428.9 83.4 97 487.8 94.8 57 546.7 106.3 18 312.1 60.7 78 371.0 72.1 38 429.9 83.6 98 488.8 95.0 58 547.7 106.5 19 313.1 60.9 79 372.0 72.3 39 430.9 83.8 99 489.8 95.2 59 548.7 106.7 20 314.1 61.1 80 373.0 72.5 40 431.9 432.9 84.0 500 490.8 95.4 60 549.7 550.7 106.9 321 315.1 61.3 381 374.0 72.7 441 84.1 501 491.8 95.6 561 107.1 22 316.1 61.4 82 374.9 72.9 42 433.8 84.3 02 492.7 95.8 62 551.6 107.2 23 317.0 61.6 83 375.9 73.1 43 434.8 84.5 03 493.7 96.0 63 552.6 107.4 24 318.0 61.8 84 376.9 73.3 44 435.8 84.7 04 494.7 96.2 64 553.6 107.6 25 319.0 62.0 85 377.9 73.5 45 436.8 84.9 05 495.7 96.4 65 554.6 107.8 26 320.0 62.2 86 378.9 7.3.7 46 437.8 85.1 06 496.7 96.6 66 555.6 108.0 27 321.0 62.4 87 379.9 73.8 47 438. 8 85.3 07 497.7 96.8 67 556.6 108.2 28 321.9 62.6 88 380.8 74.0 48 439.7 85.5 08 498.6 97.0 68 557.6 108.4 29 322.9 62.8 89 381.8 74.2 49 440.7 85.7 09 499.6 97.2 69 558.6 108.6 30 323.9 63.0 90 382.8 74.4 50 441.7 86.9 10 500.6 97.3 70 571 559.5 108.8 331 324.9 63.2 391 383.8 74.6 451 442.7 86.1 511 501.6 97.5 560.5 109.0 32 325.9 63.4 92 384.8 74.8 52 443.7 86.2 12 502.6 97.6 72 561.5 109.1 33 326.8 63.5 93 385.7 75.0 53 444.6 86.4 13 503.5 97.8 73 562.5 109.3 34 327. 8 63.7 94 386.7 75.2 54 445.6 86.6 14 504.5 98.0 74 563.5 109.5 35 328.8 63.9 95 387.7 75.4 55 446.6 86.8 15 505.5 98.2 75 564.5 109.7 36 329.8 64.1 96 388.7 75.6 56 447.6 87.0 16 506.5 98.4 76 565.4 109.9 37 330.8 64.3 97 389.7 75.8 57 448.6 87.2 17 507.5 98.6 77 666.4 110.1 38 331.8 64.5 98 390.7 75.9 58 449.6 87.4 18 508.5 98.8 78 667.4 110.3 39 332.7 64.7 99 391.6 76.1 59 450.5 87.6 19 509.4 99.0 79 568.3 110.5 40 333. 7 64.9 400 401 392.6 76.3 76.5 60 461 451.5 87.8 20 510.4 99.2 80 569.3 110.7 341 334.7 65.1 393.6 452.5 88.0 521 511.4 99.4 581 570.3 110.9 42 335.7 65.3 02 394.6 76.7 62 453. 5 88.2 22 512.4 99.6 82 571.3 111.1 43 336.7 65.5 03 395.6 76.9 63 454.5 88.3 23 513.4 99.8 83 572.3 111.3 44 337.6 65.6 04 396. 5 77.1 64 455.4 88.5 24 514.3 100.0 84 573.2 111.5 45 338.6 65.8 05 397.5 77.3 65 456.4 88.7 25 515.3 100.2 85 574.2 111.7 46 339.6 66.0 06 398.5 77.5 66 457. 4 88.9 26 516.3 100.4 86 575.2 111.8 47 340.6 66.2 07 399.5 77.7 67 458.4 89.1 27 517.3 100.6 87 576.2 112.1 48 341.6 66.4 08 400.5 77.9 68 459.4 89.3 28 518.3 100.8 88 577.2 112.3 49 342.6 66.6 09 401.5 78.1 69 460.4 89.5 29 519.3 101.0 89 578.2 112.4 50 343.5 66.8 67.0 10 411 402.4 403.4 78.2 70 461. 3 89.7 30 520.2 521.2 101.2 90 579.1 580.1 112.6 351 344.5 78.4 471 462.3 89.9 531 101.4 591 112.8 52 345.5 67.2 12 404.4 78.6 72 463.3 90.1 32 522.2 101.6 92 581.1 113.0 53 346.5 67.4 13 405.4 78.8 73 464.3 90.3 33 523.2 101.7 93 582.1 113.2 54 347.5 67.5 14 406.4 79.0 74 465.3 90.4 34 524.2 101.8 94 583. 1 113.3 55 348.4 67.7 15 407.3 79.2 75 466.2 90.6 35 525.1 102.0 95 584.0 113.5 56 349.4 67.9 16 408.3 79.4 76 467.2 90.8 36 526.1 102.2 96 585. 113.7 57 350.4 68.1 17 409.3 79.6 77 468.2 91.0 37 527.1 102.4 97 586.0 113.9 58 351.4 68.3 18 410.3 79.8 78 469.2 91.2 38 .528. 1 102.6 98 587.0 114.1 59 352.4 68.5 19 411.3 80.0 79 470.2 91.4 39 529.1 102.8 99 688.0 114.3 60 353.4 68.7 20 412.3 80.1 80 471.1 91.6 40 530.1 103.0 600 589.0 114.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat 79° (101°, 259°, 281° ). Page 554] TABLE 2. Difference of Latitude and Departure for 12° (168°, 192°, 348°). Dist. Lat. Dep Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.2 61 59.7 12.7 121 118.4 25.2 181 177.0 37.6 241 235.7 50.1 2 2.0 0.4 62 60.6 12.9 22 119.3 25.4 82 178.0 37.8 42 236.7 50.3 3 2.9 0.6 63 61.6 13.1 23 120.3 25.6 83 179.0 38.0 43 237.7 50.5 4 3.9 0.8 64 62.6 13.3 24 121.3 25.8 84 180.0 38.3 44 238.7 50.7 5 4.9 1.0 65 63.6 13.5 25 122.3 26.0 85 181.0 38.5 45 239.6 50.9 6 6.9 1.2 66 64.6 13.7 26 123.2 26.2 86 181.9 38.7 46 240.6 51.1 7 6.8 1.5 67 65.5 13.9 27 124. 2 26.4 87 182.9 38.9 47 241.6 51.4 8 7.8 1.7 68 66.5 14.1 28 125.2 26.6 88 183.9 39.1 48 242.6 51.6 9 8.8 1.9 69 67.5 14.3 29 126.2 26.8 89 184.9 39.3 49 243.6 51.8 10 9.8 2.1 70 68.5 14.6 30 127. 2 j 27. 90 185.8 39.5 50 244.5 52.0 11 10.8 2.3 71 69.4 14.8 131 128.1 27.2 191 186.8 39.7 251 245.5 52.2 12 11.7 2.5 72 70.4 15.0 32 129.1 27.4 92 187.8 39.9 52 246.5 52.4 13 12.7 2.7 73 71.4 15.2 33 130.1 27.7 93 188.8 40.1 53 247.5 52.6 14 13.7 2.9 74 72.4 15.4 34 131.1 27.9 94 189.8 40.3 54 248.4 52.8 15 14.7 3.1 75 73.4 15.6 35 132. 28. 1 95 190.7 40.5 55 249.4 53.0 16 15.7 3.3 76. 74.3 15.8 36 133.0 1 28.3 96 191.7 40.8 56 250.4 53.2 17 16.6 3.5 77 75.3 16.0 37 134.0 28.5 97 192.7 41.0 57 251.4 53.4 18 17.6 3.7 78 76.3 16.2 38 135.0 28.7 98 193.7 41.2 58 252.4 53.6 19 18.6 4.0 79 77.3 16.4 39 136.0 28.9 99 194.7 41.4 59 253.3 53.8 20 19.6 4.2 80 78.3 16.6 40 136.9 29.1 200 195.6 41.6 60 254.3 54.1 21 20.5 4.4 81 79.2 16.8 141 137.9 29.3 201 196.6 41.8 261 255.3 54.3 22 21.5 4.6 82 80.2 17.0 42 138.9 29.5 02 197.6 42.0 62 256.3 54.5 23 22.5 4.8 83 81.2 17.3 43 139.9 29.7 03 198.6 42.2 63 257.3 54.7 24 23.5 5.0 84 82.2 17.5 44 140.9 29.9 04 199.5 42.4 64 258.2 54.9 25 24.5 5.2 85 83.1 17.7 45 141.8 30.1 05 200.5 42.6 65 259.2 55.1 26 25.4 5.4 86 84.1 17.9 46 142.8 30.4 06 201.5 42.8 66 260.2 55.3 27 26.4 5.6 87 85.1 18.1 47 143.8 30.6 07 202.5 43.0 67 261.2 55.5 28 27.4 5.8 88 86.1 18.3 48 144.8 30.8 08 203.5 43.2 68 262.1 55.7 29 28.4 6.0 89 87.1 18.5 49 145.7 31.0 09 204.4 43.5 69 263.1 55.9 30 29.3 6.2 90 88.0 18.7 50 146.7 31.2 10 205.4 43.7 70 264.1 56.1 31 30.3 6.4 91 89.0 18.9 151 147.7 31.4 211 206.4 43.9 271 265.1 56.3 32 31.3 6.7 92 90.0 19.1 52 148.7 31.6 12 207.4 44.1 72 266.1 56.6 33 32.3 6.9 93 91.0 19.3 53 149.7 31.8 13 208.3 44.3 73 267.0 56.8 34 33.3 7.1 94 91.9 19.5 54 150.6 32.0 14 209.3 44.5 74 268.0 57.0 35 34.2 7.3 95 92.9 19.8 55 151.6 32.2 15 210.3 44.7 75 269.0 57.2 36 35.2 7.5 96 93.9 20.0 56 152.6 32.4 16 211.3 44.9 76 270.0 57.4 37 36.2 7.7 97 94.9 20.2 57 153.6 32.6 17 212.3 45.1 77 270.9 57.6 38 37.2 7.9 98 95.9 20.4 58 154.5 32.9 18 213.2 45.3 78 271.9 57.8 39 38.1 8.1 99 96.8 20.6 59 155.5 33.1 19 214.2 45.5 79 272.9 58.0 40 39.1 8.3 100 97.8 20.8 60 156. 5 33.3 20 215.2 45.7 80 273.9 58.2 41 40.1 8.5 101 98.8 21.0 161 157.5 33.5 221 216.2 45.9 281 274.9 58.4 42 41.1 8.7 02 99.8 21.2 62 158.5 33.7 22 217.1 46.2 82 275.8 58.6 43 42.1 8.9 03 100.7 21.4 63 159.4 33.9 23 218.1 46.4 83 276.8 58.8 44 43.0 9.1 04 101.7 21.6 64 160.4 34.1 24 219.1 46.6 84 277.8 59.0 45 44.0 9.4 05 102.7 21.8 65 161.4 34.3 25 220.1 46.8 85 278.8 59.3 46 45.0 9.6 06 103.7 22.0 66 162.4 34.5 26 221.1 47.0 86 279.8 59.5 47 46.0 9.8 07 104.7 22.2 67 163.4 34.7 27 222.0 47.2 87 280.7 59.7 48 47.0 10.0 08 105.7 22.5 68 164.3 34.9 28 223.0 47.4 88 281.7 59.9 49 47.9 10.2 09 106.6 22.7 69 165.3 35.1 29 224.0 47.6 89 282.7 60.1 50 48.9 10.4 10 107.6 22.9 70 166.3 35.3 30 231 225.0 226.0 47.8 48.0 90 283.7 60.3 51 49.9 10.6 111 108.6 23.1 171 167.3 35.6 291 284.6 60.5 52 50.9 10.8 12 109.6 23.3 72 168.2 35.8 32 226.9 48.2 92 285.6 60.7 53 51.8 11.0 13 110.5 23.5 73 169.2 36.0 33 227.9 48.4 93 286.6 60.9 54 52.8 11.2 14 111.5 23.7 74 170.2 36.2 34 228.9 48.7 94 287.6 61.1 55 53.8 11.4 15 112.5 23.9 75 171.2 36.4 35 229.9 48.9 95 288.6 61.3 56 54.8 11.6 16 113.5 24.1 76 172. 2 36.6 36 230.8 49.1 96 289.5 61.5 57 55.8 11.9 17 114.4 24.3 77 173.1 36.8 37 231.8 49.3 97 290.5 61.7 58 56.7 12.1 18 115.4 24.5 78 174.1 37.0 38 232.8 49.5 98 291.5 62.0 59 57.7 12.3 19 116.4 24.7 79 175.1 37.2 39 233.8 49.7 99 292.5 62.2 60 58.7 12.5 20 117.4 24.9 80 176.1 37.4 40 234.8 49.9 300 293.4 62.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat rs" (1 02°, 258°, 282° )• TABLE 2. [Page 655 Difference of latitude and Departure for 12° (168°, 192°, 348 °). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 294.4 62.6 361 353.1 75.0 421 411.8 87.5 481 470.5 100.0 541 529.2 112.5 02 295.4 62.8 62 354. 1 75.2 22 412.8 87.7 82 471.5 100.2 42 530.2 112.7 03 296.4 63.0 63 355.1 75.4 23 413.8 87.9 83 472.5 100.4 43 531.1 112.9 04 297.4 63.2 64 356.0 75.7 24 414.7 88.1 84 473.4 100.6 44 532. 1 113.1 05 298.3 63.4 65 357.0 75.9 25 415.7 88.3 85 474.4 100.8 45 533.1 113.3 06 299.3 63.6 66 358.0 76.1 26 416.7 88.6 86 475.4 101.0 46 534.1 113.5 07 300.3 63.8 67 359.0 76.3 27 417.7 88.8 87 476.4 101.2 47 535.1 113.7 08 301.3 64.0 68 360.0 76.5 28 418.6 89.0 88 477.3 101.4 48 536.0 113.9 09 302.2 64.2 69 360.9 76.7 29 419.6 89.2 89 478.3 101.6 49 537.0 114.1 10 303.2 64.4 70 361.9 76.9 30 420.6 89.4 90 479.3 101.9 50 538.0 114.4 311 304. 2 64.6 371 362.9 77.1 431 421.6 89.6 491 480.3 102.1 551 538.9 114.6 12 305.2 64.8 72 363.9 77.3 32 422.6 89.8 92 481.2 102.3 52 539.9 114.3 13 306.2 65.1 73 364.8 77.5 77.7 33 423.5 90.0 93 482.2 102.5 53 540.9 115.0 14 307.1 65.3 74 365.8 34 424.5 90.2 94 483.2 102.7 54 541.9 115.2 15 308.1 65.5 75 366.8 77.9 35 425.5 90.4 95 484.2 102.9 55 542.9 115.4 16 309.1 65.7 76 367.8 78.2 36 426. 5 90.6 96 485.2 103.1 56 543.8 115.6 17 310.1 65.9 77 368.8 78.4 37 427.5 90.8 97 486.1 103.3 57 544.8 115.8 18 311.1 66.1 78 369.7 78.6 38 428.4 91.0 98 487.1 103.5 58 545.8 116.0 19 312.0 66.3 79 370.7 78.8 39 429.4 91.3 99 488.1 103.8 59 546.8 116.2 20 313.0 66.5 80 371.7 79.0 40 430.4 91.5 500 489.1 104.0 60 547.8 116.4 321 314.0 66.7 381 372.7 79.2 441 431.4 91.7 501 490.0 104.2 561 548.7 116.6 22 315.0 66.9 82 373.7 79.4 42 432.3 91.9 02 491.0 104.4 62 549.7 116.8 23 315.9 67.1 83 374.6 79.6 43 433.3 92.1 03 492.0 104.6 63 550.7 117.0 24 316.9 67.3 84 375.6 79.8 44 434.3 92.3 04 493.0 104.8 64 551.7 117.2 25 317.9 67.6 85 376.6 80.0 45 435.3 92.5 05 494.0 105.0 65 552.7 117.4 26 318.9 67.8 86 377.6 80.2 46 436.3 92.7 06 495.0 105.2 66 553.7 117.6 27 319.9 68.0 87 378.5 80.4 47 437.2 92.9 07 495.9 105.4 67 554.6 117.8 28 320.8 68.2 88 379.5 80.7 48 438.2 93.1 08 496.9 105.6 68 555.6 118.0 29 321.8 68.4 89 380.5 80.9 49 439.2 93.3 09 497.9 105.8 69 556.6 118.2 30 331 322.8 323.8 68.6 68.8 90 391 381.5 382.5 81.1 50 440.2 93.5 10 498.9 106.0 70 557.5 118.5 81.3 451 441.1 93.7 511 499.8 106.2 571 558.5 118.7 32 324.7 69.0 92 383.4 81.5 52 442.1 93.9 12 500.8 106.4 72 559.5 118.9 33 325.7 69.2 93 384.4 81.7 53 443.1 94.1 13 501.8 106.6 73 560.5 119.1 34 326.7 69.4 94 385.4 81.9 54 444.1 94.4 14 502.8 106.8 74 561.5 119.3 35 327.7 69.6 95 386.4 82.1 55 445.1 94.6 15 503.7 107.0 75 562.4 119.5 36 328.7 69.8 96 387. 3 82.3 56 446.0 94.8 16 504.7 107.2 76 563.4 119.7 37 329.6 70.0 97 388.3 82.5 57 447.0 95.0 17 505.7 107.4 77 564.4 119.9 38 330.6 70.3 98 389.3 82.7 58 448.0 95.2 18 506.7 107.6 78 565.4 120.1 39 331. 6 70.5 99 390.3 82.9 59 449.0 95.4 19 507.7 107.8 79 566.4 120.3 40 332.6 70.7 400 391.3 83.1 60 450.0 95.6 20 508.7 108.1 80 567.4 120.6 341 333.5 70.9 401 392. 2 83.4 461 450.9 95.8 521 509.6 108.3 581 568.3 120.8 42 334.5 71.1 02 393.2 83.6 62 451.9 96.0 22 510.6 108.5 82 569.3 121.0 43 335.5 71.3 03 394.2 83.8 63 452.9 96.2 23 511.6 108.7 83 570.3 121.2 44 336.5 71.5 04 395.2 84.0 64 453.9 96.5 24 512.5 108.9 84 571.2 121.4 45 337.5 71.7 05 396.2 84.2 65 454.8 96.7 25 513.5 109.2 85 572.2 121.6 46 338.4 71.9 06 397.1 84.4 66 455.8 96.9 26 514.5 109.4 86 573.2 121.8 47 339.4 72.1 07 398.1 84.6 67 456. 8 97.1 27 515.5 109.6 87 574.2 122.0 48 340.4 72.3 08 399.1 84.8 68 457.8 97.3 28 516.5 109.8 88 575.2 122.2 49 341.4 72.5 09 400.1 85.0 69 458.8 97.5 29 517.5 110.0 89 576.2 122.4 50 342.4 72.7 10 401.0 85.2 70 459.7 97.7 30 518.4 110.2 90 577.1 122.6 351 343.3 73.0 411 402.0 85.4 471 460.7 97.9 531 519.4 110.4 591 578.1 122.8 52 344.3 73.2 12 403.0 85.6 72 461.7 98.1 32 520.4 110.6 92 579.1 123.0 53 345.3 73.4 13 404.0 85.8 73 462.7 98.3 33 521.3 110.8 93 580.0 123.2 54 346.3 73.6 14 405. 86.1 74 463.6 98.5 34 522.3 111.0 94 581.0 123.4 55 347.2 73.8 15 405.9 86.3 75 464.6 98.7 35 523.3 111.2 95 582.0 123.6 56 348.2 74.0 16 406.9 86.5 76 465.6 98.9 36 524.3 111.4 96 583.0 123.9 57 349.2 74.2 17 407.9 86.7 77 466.6 99.1 37 525.3 111.6 97 584.0 124.1 58 350.2 74.4 18 408.9 86.9 78 467.6 99.4 38 526.2 111.8 98 584.9 124.3 59 351.2 74.6 19 409.8 87.1 79 468.5 99.6 39 527.2 112.0 99 585.9 124.5 60 352.1 74.8 20 410.8 87.3 80 469.5 99.8 40 528.2 112. 3 600 586.9 124.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 78° (1 02°, 258 °, 282° )■ Page 656] TABLE 2. Difference of Latitude and Departure for 13° (167°, 193°, 347° )• Dist. J^t. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.2 61 59.4 13.7 121 117.9 27.2 181 176.4 40.7 241 234.8 54.2 2 1.9 0.4 62 60.4 13.9 22 118.9 27.4 82 177.3 40.9 42 235.8 54.4 3 2.9 0.7 63 61.4 14.2 23 119.8 27.7 83 178.3 41.2 43 236.8 54.7 4 3.9 0.9 64 62.4 14.4 24 120.8 27.9 84 179.3 41.4 44 237.7 54.9 5 4.9 1.1 65 63.3 14.6 25 121.8 28.1 85 180.3 41.6 45 238.7 55.1 6 5.8 1.3 66 64.3 14.8 26 122.8 28.3 86 181.2 41.8 46 239.7 55.3 7 6.8 1.6 67 65.3 15.1 27 123.7 28.6 87 182.2 42.1 47 240.7 55.6 8 7.8 1.8 68 66.3 15.3 28 124.7 28.8 88 183.2 42.3 48 241.6 55.8 9 8.8 2.0 69 67.2 15.5 29 125.7 29.0 89 184.2 42.5 49 242.6 56.0 10 9.7 2.2 70 68.2 15.7 30 126.7 29.2 29.5 90 185.1 42.7 50 243. 6 56.2 11 10.7 2.5 71 69.2 16.0 131 127.6 191 186.1 43.0 251 244.6 56.5 12 11.7 2.7 72 70.2 16.2 32 128.6 29.7 92 187.1 43.2 52 245.5 56.7 13 12.7 2.9 73 71.1 16.4 33 129.6 29.9 93 188.1 43.4 53 246.5 56.9 14 13.6 3.1 74 72.1 16.6 34 130.6 30.1 ^4 189.0 43.6 54 247.5 57.1 15 14.6 3.4 75 73.1 16.9 35 131.5 30.4 95 190.0 43.9 55 248.5 57.4 16 15.6 3.6 76 74.1 17.1 36 132.5 30.6 96 191.0 44.1 56 249.4 57.6 17 16.6 3.8 77 75.0 17.3 37 133.5 30.8 97 192.0 44.3 57 250. 4 57.8 18 17.5 4.0 78 76.0 17.5 38 134.5 31.0 98 192.9 44.5 58 251.4 58.0 19 18.5 4.3 79 77.0 17.8 39 135.4 31.3 99 193.9 44.8 59 252.4 58.3 20 19.5 4.5 80 77.9 18.0 40 136.4 31.5 200 194.9 195.8 45.0 60 253.3 58.5 21 20.5 4.7 81 78.9 18.2 141 137.4 31.7 201 45.2 261 254.3 58.7 22 21.4 4.9 82 79.9 18.4 42 138.4 31.9 02 196.8 45.4 62 255.3 58.9 23 22.4 5.2 83 80.9 18.7 43 139.3 32.2 03 197.8 45.7 63 256.3 59.2 24 23.4 5.4 84 81.8 18.9 44 140.3 32.4 04 198.8 45.9 64 257.2 59.4 25 24.4 5.6 85 82.8 19.1 45 141.3 32.6 05 199.7 46.1 65 258.2 59.6 26 25.3 5.8 86 83.8 19.3 46 142.3 32.8 06 200.7 46.3 66 259.2 59.8 27 26.3 6.1 87 84.8 19.6 47 143.2 33.1 07 201.7 46.6 67 260.2 60.1 28 27.3 6.3 88 85.7 19.8 48 144.2 33.3 08 202.7 46.8 68 261.1 60.3 29 28.3 6.5 89 86.7 20.0 49 145.2 33.5 09 203. 6 47.0 69 262.1 60.5 30 29.2 6.7 90 87.7 20.2 50 146.2 33.7 10 204.6 47.2 70 263.1 60.7 31 30.2 7.0 91 88.7 20.5 151 147.1 34.0 211 205.6 47.5 271 264.1 61.0 32 31.2 7.2 92 89.6 20.7 62 148.1 34.2 12 206.6 47.7 72 265.0 61.2 33 32.2 7.4 93 90.6 20.9 53 149.1 34.4 13 207.5 47.9 73 266. 61.4 34 33.1 7.6 94 91.6 21.1 54 150. 1 34.6 14 208.5 48.1 74 267.0 61.6 35 34.1 7.9 95 92.6 21.4 55 151.0 34.9 15 209.5 48.4 75 268.0 61.9 36 35.1 8.1 96 93.5 21.6 56 152.0 35.1 16 210.5 48.6 76 268.9 62.1 37 36.1 8.3 97 94.5 21.8 57 153.0 35.3 17 211.4 48.8 77 269.9 62.3 38 37.0 8.5 98 95.5 22.0 58 154.0 35.5 18 212.4 49.0 78 270.9 62.5 39 38.0 8.8 99 96.5 22.3 59 154.9 35.8 19 213.4 49.3 79 271.8 62.8 40 39.0 9.0 100 97.4 22.5 60 155.9 36.0 20 214.4 49.5 80 272.8 63.0 41 39.9 9.2 101 98.4 22.7 161 156.9 36.2 221 215.3 49.7 281 273.8 63.2 42 40.9 9.4 02 99.4 22.9 62 157.8 36.4 22 216.3 49.9 82 274.8 63.4 43 41.9 9.7 03 100.4 23.2 63 158.8 36.7 23 217.3 50.2 83 275.7 63.7 44 42.9 9.9 04 101.3 23.4 64 159.8 36.9 24 218.3 50.4 84 276.7 63.9 45 43.8 10.1 05 102.3 23.6 65 160.8 37.1 25 219.2 50.6 85 277.7 64.1 46 44.8 10.3 06 103.3 23.8 66 161.7 37.3 26 220.2 50.8 86 278.7 64.3 47 45.8 10.6 07 104.3 24.1 67 162.7 37.6 27 221.2 51.1 87 279.6 64.6 48 46.8 10.8 08 105.2 24.3 68 163.7 37.8 28 222.2 51.3 88 280.6 64.8 49 47.7 11.0 09 106.2 24.5 69 164.7 38.0 29 223.1 51.5 89 281.6 65.0 50 48.7 49.7 11.2 10 107.2 24.7 70 165. 6 38.2 30 224.1 51.7 90 282.6 65.2 51 11.5 111 108.2 25.0 171 166.6 38.5 231 225.1 52.0 291 283.5 65.5 52 50.7 11.7 12 109.1 25.2 72 167. 6 38.7 32 226.1 52.2 92 284.5 65.7 53 51.6 11.9 13 110.1 25.4 73 168.6 38.9 33 227.0 52.4 93 285.5 65.9 54 52.6 12.1 14 111.1 25.6 74 169.5 39.1 34 228.0 52.6 94 286.5 66.1 55 53.6 12.4 15 112.1 25.9 75 170. 5 39.4 35 229.0 52.9 95 287.4 66.4 56 54.6 12.6 16 113.0 26.1 76 171.5 39.6 36 230.0 53.1 96 288.4 66.6 57 55.5 12.8 17 114.0 26.3 77 172.5 39.8 37 230.9 53.3 97 289.4 66.8 58 56.5 13.0 18 115.0 26.5 78 173.4 40.0 38 231.9 53.5 98 290.4 67.0 59 57.5 13.3 19 116.0 26.8 79 174.4 40.3 39 232.9 53.8 99 291.3 67.3 60 58.5 13.5 20 116.9 27.0 80 175.4 40.5 40 233.8 54.0 300 292.3 67.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 77° (1 03°, 257 °, 283°). TABLE 2. [Page 657 | Difference of Latitude and Departure for 13° (167°, 193 °, 347° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 293. 3 67.7 361 351.8 81.2 421 410.2 94.7 481 468.7 108.2 541 527.2 121.7 02 294.3 67.9 62 352.7 81.4 22 411.2 94.9 82 469.7 108.4 42 528.1 121.9 03 295. 2 68.1 63 353.7 81.6 23 412.2 95.1 83 470.6 108.6 43 529.1 122.1 04 296.2 68.4 64 354.7 81.9 24 413.1 95.3 84 471.6 108.8 44 530.1 122.3 05 297.2 68.6 65 355.6 82.1 25 414.1 95.6 85 472.6 109.0 45 531.1 122.5 06 298.2 68.8 66 356. 6 82.3 26 415.1 95.8 86 473.6 109.3 46 532.0 122.8 07 299.1 69.0 67 357.6 82.5 27 416.1 96.0 87 474.5 109.5 47 533.0 123.0 08 300.1 69.3 68 358.6 82.8 28 417.0 96.2 88 475.5 109.7 48 534.0 123.2 09 301.1 69.5 69 359.5 83.0 29 418.0 96.5 89 476.5 109.9 49 535.0 123.4 10 302.1 69.7 70 360.5 83.2 30 419.0 96.7 90 477.5 110.1 50 535.9 123.7 311 303.0 69.9 371 361.5 83.4 431 420.0 96.9 491 478.4 110.4 551 536. 9 123.9 12 304.0 70.2 72 362.5 83.7 32 420.9 97.1 92 479.4 110.6 52 537.9 124.1 13 305.0 70.4 73 363. 4 83.9 33 421.9 97.4 93 480.4 110.9 53 538.9 124.4 14 306.0 70.6 74 364.4 84.1 34 422.9 97.6 94 481.4 111.1 54 539.8 124.6 15 306.9 70.8 75 365.4 84.3 35 423.9 97.8 95 482.3 111.3 55 540.8 124.9 16 307.9 71.1 76 366.4 84.6 36 424.8 98.0 96 483.3 111.5 56 541.8 125. 1 17 308.9 71.3 77 367.3 84.8 37 425.8 98.3 97 484.3 111.8 57 542.8 125.3 18 309.9 71.5 78 368.3 85.0 38 426.8 98.5 98 485.3 112.0 58 543.7 125.5 19 310.8 71.7 79 369.3 85.2 39 427.8 98.7 99 486.2 112.2 59 544.7 125.8 20 311.8 72.0 80 370.3 85.5 40 428.7 98.9 500 487.2 112.4 60 545.7 126.0 321 312.8 72.2 381 371.2 85.7 441 429.7 99.2 501 488.2 112.6 561 546.7 126.2 22 313.8 72.4 82 372.2 85.9 42 430.7 99.4 02 489.2 112.9 62 547.6 126.4 23 314.7 72.6 83 373.2 86.1 43 431.6 99.6 03 490.1 113.1 63 548.6 126.7 24 315.7 72.9 84 374.2 86.4 44 432.6 99.8 04 491.1 113.3 64 549.6 126.9 25 316.7 73.1 85 375.1 86.6 45 433.6 100.1 05 492.1 113.5 65 550.6 127.1 26 317.6 73.3 86 376.1 86.8 46 434.6 100.3 06 493.1 113.8 66 551.5 127.3 27 318.6 73.5 87 377.1 87.0 47 435.5 100.5 07 494.0 114.0 67 552.5 127.6 28 319.6 73.8 88 378.1 87.3 48 436.5 100.7 08 495.0 114.2 68 553.5 127.8 29 320.6 74.0 89 379.0 87.5 49 437.5 101.0 09 496.0 114.5 69 554.5 128.0 30 821.5 74.2 90 380.0 87.7 50 438.5 101.2 10 496.9 114.7 70 555.4 128.3 331 322.5 74.4 391 381.0 87.9 451 439.4 101.4 511 497.9 114.9 571 556.4 128.5 32 323.5 74.7 92 382.0 88.2 52 440.4 101.6 12 498.9 115.1 72 557.4 128.7 33 324.5 74.9 93 382.9 88.4 53 441.4 101.9 13 499.9 115.4 73 558.4 128.9 34 325. 4 75.1 94 383.9 88.6 54 442.4 102.1 14 500.8 115.6 74 559.3 129.2 35 326,4 75.3 95 384.9 88.8 55 443.3 102.3 15 501.8 115.8 75 560.3 129.4 36 327.4 75.6 96 385.9 89.1 56 444.3 102.5 16 502.8 116.0 76 561.3 129.6 37 328.4 75.8 97 386.8 89.3 57 445.3 102.8 17 503.8 116.3 77 562.3 129.8 38 329.3 76.0 98 387.8 89.5 58 446.3 103.0 18 504.7 116.5 78 563.2 130.0 39 330.3 76.2 99 388.8 89.7 59 447.2 103.2 19 505.7 116.7 79 564.2 130.2 40 331.3 76.5 400 389.8 90.0 60 448.2 103.4 103.7 20 521 506.7 116.9 80 565.2 566.2 130.4 341 332.3 76.7 401 390.7 90.2 461 449.2 507.7 117.2 581 130.7 42 333.2 76.9 02 391.7 90.4 62 450.2 103. 9 22 508.6 117.5 82 567.1 131.0 43 334.2 77.1 03 392.7 90.6 63 451.1 104.1 23 509.6 117.7 83 568.1 131.2 44 335.2 77.4 04 393.6 90.8 64 452.1 104.3 24 510.6 117.9 84 569.1 131. 4 45 336.2 77.6 05 394.6 91.1 65 453.1 104.6 25 511.6 118.1 85 570.1 131.6 46 337.1 77.8 06 395.6 91.3 66 454.1 104.8 26 512.5 118.3 86 571.0 131.8 47 338.1 78.0 07 396.6 91.5 67 455.0 105.0 27 513.5 118.5 87 572.0 132. 48 339.1 78.3 08 397.5 91.7 68 456.0 105.2 28 514.5 118.7 88 573.0 132.3 49 340.1 78.5 09 398.5 92.0 69 457.0 105.5 29 515.5 119.0 89 573.9 132.5 50 341.0 78.7 10 399.5 92.2 70 458.0 105.7 30 516.4 119.2 90 574.9 132.8 351 342.0 78.9 411 400.5 92.4 471 458.9 105.9 531 517.4 119.4 591 575.9 133.0 52 343.0 79.2 12 401.4 92.6 72 459.9 106.1 32 518.4 119.6 92 576.9 133.2 53 344.0 79.4 13 402.4 92.9 73 460.9 106.4 33 519.4 119.9 93 577.8 133.4 54 344.9 79.6 14 403.4 93.1 74 461.9 106.6 34 520.3 120.1 94 578.8 133.6 55 345.9 79.8 15 404.4 93.3 75 462.8 106.8 35 521.3 120.3 95 579.8 133.8 56 346.9 80.1 16 405.3 93.5 76 463.8 107.0 36 522.3 120.5 96 580.8 134.0 57 347.9 80.3 17 406.3 93.8 77 464.8 107.3 37 523.3 120.8 97 581.7 134.3 58 348.8 80.5 18 407.3 94.0 78 465.8 107.5 38 524.2 121.0 98 582.7 134.5 59 349.8 80.7 19 408.3 94.2 79 466.7 107.7 39 525.2 121.2 99 583.7 134.8 60 350.8 81.0 20 409.2 94.4 80 467.7 107.9 40 526.2 121.5 600 584.6 135.0 Dist. Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 77° (103°, 257 °, 283° )• 1 Page 668] TABLE 2. Difference of Latitude and Departure for 14° (166°, 194°, 346° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. 1 Dep. Dist. Lat. Dep. 1 10 0.2 61 59.2 14.8 121 117.4 29.3 181 175.6 43.8 241 233.8 58.3 2 1.9 0.5 62 60.2 15.0 22 118.4 29.5 82 176.6 44.0 42 234.8 58.5 3 2.9 0.7 63 61.1 15.2 23 119.3 29.8 83 177.6 44.3 43 235.8 58.8 4 3.9 1.0 64 62.1 15.5 24 120.3 30.0 84 178.5 44.5 44 236.8 59.0 5 4.9 1.2 65 63.1 15.7 25 121.3 30.2 85 179.5 44.8 45 237.7 59.3 6 5.8 1.5 66 64.0 16.0 26 122.3 30.5 86 180.5 45.0 46 238.7 59.5 7 6.8 1.7 67 65.0 16.2 27 123.2 30.7 87 181.4 45.2 47 239.7 59.8 8 7.8 1.9 68 66.0 16.5 28 124.2 31.0 88 182.4 45.5 48 240.6 60.0 9 8.7 2.2 69 67.0 16.7 29 125.2 31.2 89 183.4 45.7 49 241.6 60.2 10 9.7 2.4 70 67.9 16.9 30 126.1 31.4 90 184.4 46.0 50 242.6 60.5 11 10.7 2.7 71 68.9 17.2 131 127.1 31.7 191 185. 3 46.2 251 243.5 60.7 12 11.6 2.9 72 69.9 17.4 32 128.1 31.9 92 186.3 46.4 52 244.5 61.0 13 12.6 3.1 73 70.8 17.7 33 129.0 32.2 93 187.3 46.7 53 245.5 61.2 14 13.6 3.4 74 71.8 17.9 34 130.0 32.4 94 188.2 46.9 54 246.5 61.4 15 14.6 3.6 75 72.8 18.1 35 131.0 32.7 95 189.2 47.2 55 247.4 61.7 16 15.5 3.9 76 73.7 18.4 36 132.0 32.9 96 190.2 47.4 56 248.4 61.9 17 16.5 4.1 77 74.7 18.6 37 132.9 33.1 97 191.1 47.7 57 249.4 62.2 18 17.5 4.4 78 75.7 18.9 38 133.9 33.4 98 192..1 47.9 58 250.3 62.4 19 18.4 4.6 79 76.7 19.1 39 134.9 33.6 99 193.1 48.1 59 251.3 62.7 20 19.4 4.8 80 77.6 19.4 40 135.8 33.9 200 194.1 48.4 60 252.3 62.9 21 20.4 5.1 81 78.6 19.6 141 136.8 34.1 201 195.0 48.6 261 253.2 63.1 22 21.3 5.3 82 79.6 19.8 42 137.8 34.4 02 196.0 48.9 62 254.2 63.4 23 22.3 5.6 83 80.5 20.1 43 138.8 34.6 03 197.0 49.1 63 255.2 63.6 24 23.3 5.8 84 81.5 20.3 44 139.7 34.8 04 197.9 49.4 64 256.2 63.9 25 24.3 6.0 85 82.5 20.6 45 140.7 35.1 05 198.9 49.6 65 257.1 64.1 26 25.2 6.3 86 83.4 20.8 46 141.7 35.3 06 199.9 49.8 66 258.1 64.4 27 26.2 6.5 87 84.4 21.0 47 142.6 35.6 07 200.9 50.1 67 259.1 64.6 28 27.2 6.8 88 85.4 21.3 48 143.6 35.8 08 201.8 50.3 68 260.0 64.8 29 28.1 7.0 89 86.4 21.5 49 144. 6 36.0 09 202.8 50.6 69 261.0 65.1 30 29.1 7.3 90 87.3 21.8 50 145. 5 36.3 36.5 10 211 203.8 204.7 50.8 51.0 70 271 262.0 65.3 31 30.1 7.5 91 88.3 22.0 151 146.5 263.0 65.6 32 31.0 7.7 92 89.3 22.3 52 147.5 36.8 12 205.7 51.3 72 263.9 65.8 33 32.0 8.0 93 90.2 22.5 53 148.5 37.0 13 206.7 51.5 73 264.9 66.0 34 33.0 8.2 94 91.2 22.7 54 149.4 37.3 14 207.6 51.8 74 265.9 66.3 35 34.0 8.5 95 92.2 23.0 55 150.4 37.5 15 208.6 52.0 75 266.8 66.5 36 34.9 8.7 96 93.1 23.2 56 151.4 37.7 16 209.6 52.3 76 267.8 66.8 37 35.9 9.0 97 94.1 23.5 57 152.3 38.0 17 210.6 52.5 77 268.8 67.0 38 36.9 9.2 98 95.1 23.7 58 153.3 38.2 18 211.5 52.7 78 269.7 67.3 39 37.8 9.4 99 96.1 24.0 59 154.3 38.5 19 212.5 53.0 79 270.7 67.5 40 38.8 9.7 100 97.0 24.2 60 155.2 38.7 20 213.5 53.2 80 271.7 67.7 41 39.8 9.9 101 98.0 24.4 161 156.2 38.9 221 214.4 53.5 281 272.7 68.0 42 40.8 10.2 02 99.0 24.7 62 157.2 39.2 22 215.4 53.7 82 273.6 68.2 43 41.7 10.4 03 99.9 24.9 63 158.2 39.4 23 216.4 53.9 83 274.6 68.5 44 42.7 10.6 04 100.9 25.2 64 159.1 39.7 24 217.3 54.2 84 275.6 68.7 45 43.7 10.9 05 101.9 25.4 65 160.1 39.9 25 218.3 54.4 85 276.5 68.9 46 44.6 11.1 06 102.9 25.6 66 161.1 40.2 26 219.3 54.7 86 277.5 69.2 47 45.6 11.4 07 103.8 25.9 67 162.0 40.4 27 220.3 54.9 87 278.5 69.4 48 46.6 11.6 08 104.8 26.1 68 163.0 40.6 28 221.2 55.2 88 279.4 69.7 49 47.5 11.9 09 105.8 26.4 69 164.0 40.9 29 222.2 55.4 89 280.4 69.9 50 48.5 12.1 10 106.7 26.6 70 165.0 41.1 30 223.2 55.6 90 281.4 282.4 70.2 51 49.5 12.3 111 107.7 26.9 171 165.9 41.4 231 224.1 65.9 291 70.4 52 50.5 12.6 12 108.7 27.1 72 166.9 41.6 32 225.1 56.1 92 283.3 70.6 53 51.4 12.8 13 109.6 27.3 73 167.9 41.9 33 226.1 56.4 93 284.3 70.9 54 52.4 13.1 14 110.6 27.6 74 168.8 42.1 34 227.0 56.6 94 285.3 71.1 55 53.4 13.3 15 111.6 27.8 75 169.8 42.3 35 228.0 56.9 95 286.2 71.4 56 54.3 13.5 16 112.6 28.1 76 170.8 42.6 36 229.0 57.1 96 287.2 71.6 57 55.3 13.8 17 113.5 28.3 77 171.7 42.8 37 230.0 57.3 97 288.2 71.9 58 56.3 14.0 18 114.5 28.5 78 172.7 43.1 38 230.9 57.6 98 289.1 72.1 59 57.2 14.3 19 115.5 28.8 79 173.7 43.3 39 231.9 57.8 99 290.1 72.3 60 58.2 14.5 20 116.4 29.0 80 174.7 43.5 40 232.9 58.1 300 291.1 72.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. / '6° (1( )4°, 256 \ 284° . TABLE 2. [Page 669 | Difference of Latitude and Departure for 14° (166°, 194°, 346° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 292.0 72.8 361 350.2 87.3 421 408.5 101.8 481 466.7 116.3 541 525.0 130.9 02 293.0 73.0 62 351.2 87.6 22 409.4 102.1 82 467.7 116.6 42 525.9 131.2 03 294.0 73.3 63 352.2 87.8 23 410.4 102.3 83 468.6 116.8 43 526.9 131.4 04 294.9 73.5 64 ■ 353. 2 88.0 24 411.4 102.6 84 469.6 117.1 44 527.9 131.6 05 295.9 73.8 65 354.1 88.3 25 412.3 102.8 85 470.6 117.3 45 528.8 131.9 06 296.9 74.0 66 355.1 88.5 26 413.3 103. 86 471.5 117.6 46 529.8 132.1 07 297.8 74.2 67 356.1 88.8 27 414.3 103.3 87 472.5 117.8 47 530.8 132.3 08 298.8 74.5 68 357.0 89.0 28 415.3 103.5 88 473.5 118.0 48 531.7 132.6 09 299.8 74.7 69 358.0 89.2 29 416.2 103.8 89 474.5 118.3 49 532.7 132.8 10 300.8 75.0 70 359.0 89.5 30 417.2 104.0 90 475.4 118.5 50 533.7 133.0 311 301.7 75.2 371 359.9 89.7 431 418.2 104.2 491 476.4 118.8 551 534.6 133.3 12 302.7 75.5 72 360.9 90.0 32 419.1 104.5 92 477.4 119.0 52 535.6 133.6 13 303.7 75.7 73 361.9 90.2 33 420.1 104.7 93 478.3 119.2 53 536.6 133.8 14 304.6 75.9 74 362.9 90.5 34 421.1 105.0 94 479.3 119.5 54 537.5 134.0 15 305.6 76.2 75 363.8 90.7 35 422.0 105. 2 95 480.3 119.7 55 538.5 134.3 16 306.6 76.4 76 364.8 90.9 36 423.0 105.5 96 481.3 120.0 56 539.5 134.5 17 307.6 76.7 77 365.8 91.2 37 424.0 105.7 97 482.2 120.2 57 540.5 134.8 18 308.5 76.9 78 366.7 91.4 38 425.0 105.9 98 483.2 120.4 58 541.4 135.0 19 309.5 77.2 79 367.7 91.7 39 425.9 106.2 99 484.2 120.7 59 542.4 135.2 20 310.5 77.4 80 368.7 91.9 40 426.9 106.4 500 485.1 121.0 60 543.4 135.5 135.7 321 311.4 77.6 381 369.6 92.2 441 427.9 106.7 501 486.1 121.2 561 544.3 22 312.4 77.9 82 370.6 92.4 42 428.8 106.9 02 487.1 121.4 62 545.3 135.9 23 313.4 78.1 83 371.6 92.6 43 429.8 107.1 03 488.0 121.7 63 546.3 136.2 24 314.3 78.4 84 372.6 92.9 44 430.8 107.4 04 489.0 122.0 64 547.2 136.5 25 315.3 78.6 85 373.5 93.1 45 431.7 107.6 05 490.0 122.1 65 548.2 136.6 26 316.3 78.8 86 374.5 93.4 46 432.7 107.9 06 491.0 122.4 66 549.2 136.9 27 317.3 79.1 87 375.5 93.6 47 433.7 108.1 07 491.9 122.6 67 550.1 137.1 28 318.2 79.3 88 376.4 93.8 48 434.7 108.4 08 492.9 122.9 68 551.1 137.4 29 319.2 79.6 89 377.4 94.1 49 435.6 108.6 09 493.9 123.1 69 552.1 137.6 30 320.2 79.8 90 378.4 94.3 50 436.6 108.8 10 494.9 123.4 70 553.1 137.9 331 321.1 80.1 391 379.4 94.6 451 437.6 109.1 511 495.8 123.6 571 554.0 138.1 32 322.1 80.3 92 380.3 94.8 52 438,5 109.3 12 496.8 123.8 72 555.0 138.3 33 323.1 80.5 93 381.3 95.1 53 439.5 109.6 13 497.8 124.1 73 556.0 138.6 34 324.0 80.8 94 382.3 95.3 54 440.5 109.8 14 498.7 124.3 74 557.0 138.8 35 325.0 81.0 95 383.2 95.5 55 441.5 110.1 15 499.7 124.6 75 557.9 139.1 36 326.0 81.3 96 384.2 95.8 56 442.4 110.3 16 500.7 124.8 76 558.9 139.3 37 327.0 81.5 97 385.2 96.0 57 443.4 110.5 17 501.7 125.0 77 559.9 139.5 38 327.9 81.7 98 386.1 96.3 58 444.4 110.8 18 502.6 125.3 78 560.9 139.8 39 328.9 82.0 99 387.1 96.5 59 445.3 111.0 19 503.6 125.6 79 561.8 140.0 40 341 329.9 82.2 400 388.1 96.7 60 446.3 111.3 20 504.6 125.8 80 562.8 140.3 330.8 82.5 401 389.1 97.0 461 447.3 111.5 521 505.5 126.0 581 563.8 140.5 42 331.8 82.7 02 390.0 97.2 62 448.2 111.7 22 506.5 126.2 82 564.7 140.8 43 332.8 83.0 03 391.0 97.5 63 449.2 112.0 23 507.5 126.5 83 565.7 141.0 44 333.7 83.2 04 392.0 97.7 64 450.2 112.2 24 508.4 126.8 84 566.7 141.3 45 334.7 83.4 05 392.9 98.0 65 451.2 112.5 25 509.4 127.0 85 567.6 141.5 46 335.7 83.7 06 393. 9 98.2 66 452.1 112.7 26 510.4 127.2 86 568.6 141.8 47 336.7 83.9 07 394.9 98.4 67 453.1 113.0 27 511.4 127.5 87 569.6 142.0 48 337.6 84.2 08 395.8 98.7 68 454.1 113.2 28 512.3 127.8 88 570.6 142.3 49 338.6 84.4 09 396.8 98.9 69 455.0 113.4 29 513.3 128.0 89 571.5 142.5 50 339.6 84.7 10 397.8 99.2 70 456.0 113.7 30 514.3 128.2 90 572.5 142.8 351 340.5 84.9 411 398.8 99.4 471 457.0 113.9 531 515.3 128.5 591 573.5 143.0 52 341.5 85.1 12 399.7 99.7 72 457.9 114.2 32 516.2 128.8 92 574.4 143.3 53 342.5 85.4 13 400.7 99.9 73 458.9 114.4 33 517.2 129.0 93 575.4 143.5 54 343.5 85.6 14 401.7 100.1 74 459.9 114.6 34 518.2 129.2 94 576.4 143. 8 55 344.4 85.9 15 402.6 100.4 75 460.9 114.9 35 519.1 129.4 95 577.3 144.0 56 345.4 86.1 16 403.6 100.6 76 461.8 115.1 36 520.1 129.7 96 578.3 144.2 57 346.4 86.3 17 404.6 100.9 77 462.8 115.4 37 521.1 129.9 97 579.3 144.5 58 347.3 86.6 18 405.5 101.1 78 463.8 115.6 38 522.1 130.2 98 580.3 144.7 59 348.3 86.8 19 406.5 101.3 79 464.7 115.9 39 523.0 130.4 99 581.2 144.9 60 349.3 87.1 20 407.5 101.6 80 465.7 116.1 40 524.0 130.6 600 582.2 145.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 76° (104°, 256°, 284°). Page 560] TABLE 2. Difference of Latitude and Departure for 15° (165°, 195°, 345°) Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.3 61 58.9 15.8 121 116.9 31.3 181 174.8 46.8 241 232.8 62.4 2 1.9 0.5 62 59.9 16.0 22 117.8 31.6 82 175.8 47.1 42 233.8 62.6 3 2.9 0.8 63 60.9 16.3 23 118.8 31.8 83 176.8 47.4 43 234.7 62.9 4 3.9 1.0 64 61.8 16,6 24 119.8 32.1 84 177.7 47.6 . 44 235.7 63.2 5 4.8 1.3 65 62.8 16.8 25 120.7 32.4 85 178.7 47.9 45 236.7 63.4 6 5.8 1.6 66 63.8 17.1 26 121.7 32.6 86 179.7 48.1 46 237.6 63.7 7 6.8 1.8 67 64.7 17.3 27 122.7 32.9 87 180.6 48.4 47 238.6 63.9 8 7.7 2.1 68 65.7 17.6 28 123.6 33.1 88 181.6 48.7 48 239.5 64.2 9 8.7 2.3 69 66.6 17.9 29 124.6 33.4 89 182.6 48.9 49 240.5 64.4 10 9.7 2.6 70 67.6 18.1 30 125.6 33.6 90 183.5 184.5 49.2 50 241.5 64.7 65.0 11 10.6 2.8 71 68.6 18.4 131 126.5 33.9 191 49.4 251 242.4 12 11.6 3.1 72 69.5 18.6 32 127.5 34.2 92 185.5 49.7 52 243.4 65.2 13 12.6 3.4 73 70.5 18.9 33 128.5 34.4 93 186.4 50.0 53 244.4 65.5 14 13.5 3.6 74 71.5 19.2 34 129.4 34.7 94 187.4 50.2 54 245.3 65.7 15 14.5 3.9 75 72.4 19.4 35 130.4 34.9 95 188.4 50.5 55 246.3 66.0 16 15.5 4.1 76 73.4 19.7 36 131.4 35.2 96 189.3 50.7 56 247.3 66.3 17 16.4 4.4 77 74.4 19.9 37 132.3 35.5 97 190.3 51.0 57 248.2 66.5 18 17.4 4.7 78 75.3 20.2 38 133.3 35.7 98 191.3 51.2 58 249.2 66.8 19 18.4 4.9 79 76.3 20.4 39 134.3 36.0 99 192.2 51.5 59 250.2 67.0 20 19.3 5.2 80 77.3 20.7 40 135.2 36.2 200 193.2 51.8 60 251.1 67.3 67.6 21 20.3 5.4 81 78.2 21.0 141 136.2 36.5 201 194. 2 52.0 261 252.1 22 21.3 5.7 82 79.2 21.2 42 137.2 36.8 02 195.1 52.3 62 253.1 67.8 23 22.2 6.0 83 80.2 21.5 43 138. 1 37.0 03 196.1 52.5 63 254.0 68.1 24 23.2 6.2 84 81.1 21.7 44 139.1 37.3 04 197.0 52.8 64 255.0 68.3 25 24.1 6.5 85 82.1 22.0 45 140.1 37.5 05 198.0 53.1 65 256.0 68.6 26 25.1 6.7 86 83.1 22.3 46 141.0 37.8 06 199.0 53.3 66 256.9 68.8 27 26.1 7.0 87 84.0 22.5 47 142.0 38.0 07 199.9 53.6 67 257.9 69.1 28 27.0 7.2 88 85.0 22.8 48 143.0 38.3 08 200.9 53.8 68 258.9 69.4 29 28.0 7.5 89* 86.0 23.0 49 143.9 38.6 09 201.9 54.1 69 259.8 69.6 30 29.0 7.8 90 86.9 23.3 50 151 144.9 38.8 10 202.8 54.4 70 260.8 69.9 31 29.9 8.0 91 87.9 23.6 145.9 39.1 211 203.8 54.6 271 261.8 70.1 32 30.9 8.3 92 88.9 23.8 52 146.8 39.3 12 204.8 54.9 72 262.7 70,4 33 31.9 8.5 93 89.8 24.1 53 147.8 39.6 13 205. 7 55.1 73 263.7 70.7 34 32.8 8.8 94 90.8 24.3 54 148.8 39.9 14 206.7 55.4 74 264.7 70.9 35 33.8 9.1 95 91.8 24.6 55 149.7 40.1 15 207.7 55.6 75 265.6 71.2 36 34.8 9.3 96 92.7 24.8 56 150.7 40.4 16 208.6 55.9 76 266.6 71.4 37 35.7 9.6 97 93.7 25.1 57 151.7 40.6 17 209.6 56.2 77 267.6 71.7 38 36.7 9.8 98 94.7 25.4 58 152.6 40.9 18 210.6 56.4 78 268.5 72.0 39 37.7 10.1 99 95.6 25.6 59 153.6 41.2 19 211.5 56.7 79 269.5 72,2 40 38.6 10.4 100 96.6 25.9 60 154.5 41.4 20 212.5 56.9 80 281 270.5 72.5 41 39.6 10.6 101 97.6 26.1 161 155.5 41.7 221 213.5 67.2 271.4 72.7 42 40.6 10.9 02 98.5 26.4 62 156.5 41.9 22 214.4 57.5 82 272.4 73.0 43 41.5 11.1 03 99.5 26.7 63 157.4 42.2 23 215.4 57.7 83 273.4 73.2 44 42.5 11.4 04 100.5 26.9 64 158.4 42.4 24 216.4 58.0 84 274.3 73.5 45 43.5 11.6 05 101.4 27.2 65 159.4 42.7 25 217.3 58.2 85 275.3 73.8 46 44.4 11.9 06 102.4 27.4 66 160.3 43.0 26 218.3 58.5 86 276.3 74.0 47 45.4 12.2 07 103.4 27.7 67 161.3 43.2 27 219.3 58.8 87 277.2 74.3 48 46.4 12.4 08 104.3 28.0 68 162.3 43.5 28 220.2 59.0 88 278.2 74.5 49 47.3 12.7 09 105.3 28.2 69 163.2 43.7 29 221.2 59.3 89 279.2 74.8 50 48,3 12.9 10 106.3 107.2 28.5 70 164.2 44.0 30 222.2 59.5 90 280.1 75.1 51 49.3 13.2 111 28.7 171 165.2 44.3 231 223.1 59.8 291 281,1 75.3 52 50.2 13.5 12 108.2 29,0 72 166.1 44.5 32 224.1 60.0 92 282.1 75.6 53 51.2 13.7 13 109.1 29.2 73 167.1 44.8 33 225.1 60.3 93 283.0 75.8 54 52.2 14.0 14 110.1 29.5 74 168.1 45.0 34 226.0 60.6 94 284.0 76.1 55 53.1 14.2 15 111.1 29.8 75 169.0 45.3 35 227.0 60.8 95 284.9 76.4 56 54.1 14.5 16 112.0 30.0 76 170.0 45.6 36 228.0 61.1 96 285.9 76.6 57 55.1 14.8 17 113.0 30.3 77 171.0 45.8 37 228.9 61.3 97 286.9 76.9 58 56.0 15.0 18 114.0 30.5 78 171.9 46.1 38 229.9 61.6 98 287.8 77.1 59 57.0 15.3 19 114.9 30.8 79 172.9 46.3 39 230.9 61.9 99 288.8 77.4 60 58.0 15.5 20 115,9 31.1 80 173.9 46.6 40 231.8 62.1 300 289.8 77.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 75° (105°, 25{ )°, 285' '). • .... - ^ TABLE 2. [Page 561 Difference of Latitude and Departure for 15° (165°, 195 °, 345° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 290.7 77.9 361 348.7 93.4 421 406.6 109.0 481 464.6 124.5 541 522.6 140.0 02 291.7 78.2 62 349.6 93.7 22 407.6 109.2 82 465.6 124.8 42 523.5 140.3 03 292.7 78.4 63 350.6 94.0 23 408.6 109.5 83 466.5 125.0 43 524.5 140.5 04 293.6 78.7 64 351.6 94.2 24 409.5 109.7 84 467.5 125.3 44 525.5 140.8 05 294.6 78.9 65 352.5 94.5 25 410.5 110.0 85 468.5 125.6 45 526.4 141.1 06 295.6 79.2 66 353.5 94.7 26 411.5 110.3 86 469.4 125.8 46 527.4 141.4 07 296.5 79.5 67 354.5 95.0 27 412.4 110.5 87 470.4 126.1 47 528.4 141.6 08 297.5 79.7 68 355.4 95.3 28 413.4 110.8 88 471.4 126.4 48 529.3 141.9 09 298.4 80.0 69 356.4 95.5 29 414.4 111.0 89 472.3 126.6 49 530.3 142.1 10 299.4 80.2 70 357.4 95.8 30 415.3 416.3 111.3 111.6 90 473.3 126.9 50 531.3 142.4 311 300.4 80.5 371 358.3 96.0 431 491 474.3 127.1 551 532.2 142.6 12 301.3 80.8 72 359.3 96.3 32 417.3 111.8 92 475.2 127.4 52 533.2 142.9 13 302.3 81.0 73 360.3 96.5 33 418.2 112.1 93 476.2 127.6 53 534.2 143.1 14 303. 3 81.3 74 361.2 96.8 34 419.2 112.3 94 477.2 127.9 54 535.1 143.4 15 304.2 81.5 75 362.2 97.1 35 420.2 112.6 95 478.1 128.1 55 536.1 143.7 16 305.2 81.8 76 363.2 97.3 36 421.1 112.9 96 479.1 128.4 56 537.1 143.9 17 306.2 82.1 77 364.1 97.6 37 422.1 113.1 97 480.1 128.6 57 538.0 144.2 18 307.1 82.3 78 365.1 97.8 38 423.1 113.4 98 481.0 128.9 58 539.0 144.4 19 308.1 82.6 79 366.1 98.1 39 424.0 113.6 99 482.0 129.1 59 540.0 144.7 20 309.1 82.8 80 367.0 98.4 40 425,0 113.9 500 483.0 129.4 60 540.9 144.9 321 310. 83.1 381 368.0 98.6 441 426.0 114.1 501 483.9 129. 7 561 541.9 145.2 22 311.0 83.3 82 369.0 98.9 42 426.9 114.4 02 484.9 129.9 62 542.9 145.4 23 312.0 83.6 83 369.9 99.1 43 427.9 114.7 03 485.9 130.2 63 543.8 145.7 24 312.9 83.9 84 370.9 99.4 44 428.8 114.9 04 486.8 130.4 64 544.8 146.0 25 313.9 84.1 85 371.9 99.6 45 429.8 115.2 05 487.8 130.7 65 545.8 146.2 26 314.9 84.4 86 372.8 99.9 46 430.8 115.4 06 488.8 131.0 66 546.7 146.5 27 315.8 84.6 87 373.8 100.2 47 431.7 115.7 07 489.7 131.2 67 547.7 146.7 28 316.8 84.9 88 374.8 100.4 48 432.7 116.0 08 490.7 131.5 68 548.7 147.0 29 317.8 85.1 89 375.7 100.7 49 433.7 116.2 09 491.7 131.7 69 549.6 147.2 30 331 318. 7 85.4 90 376.7 100.9 50 434.6 116.5 10 492.6 132.0 70 550.6 147.5 319.7 85.7 391 377.7 101.2 451 435.6 116.7 511 493.6 132.3 571 551.6 147.8 32 320. 7 85.9 92 378.6 101.5 52 436.6 117.0 12 494.5 132.5 72 552.5 148.0 33 321.6 86.2 93 379.6 101.7 53 437.5 117.3 13 495.5 132.8 73 553.5 148.3 34 322. 6 86.5 94 380.6 102.0 54 438.5 117.5 14 496.5 133.0 74 554.4 148.5 35 323.6 86.7 95 381.5 102.2 55 439.5 117.8 15 497.4 133.3 75 555.4 148.8 36 324.5 87.0 96 382. 5 102.5 56 440.4 118.0 16 498.4 133.5 76 556.4 149.0 37 325.5 87.2 97 383.4 102.8 57 441.4 118.3 17 499.4 133.8 77 557.3 149.3 38 326.5 87.5 98 384.4 103.0 58 442.4 118.5 18 500.3 134.0 78 558.3 149.5 39 327. 4 87.7 99 385.4 103.3 59 443.3 118.8 19 501.3 134.3 79 559.3 149.8 40 328.4 88.0 400 386.3 103.5 60 444.3 119.1 20 502.3 134.6 80 560.2 150.1 150. 3 341 329.4 88.3 401 387.3 103.8 461 445.3 119.3 521 503.2 134.8 581 561.2 42 330.3 88.5 02 388.3 104.1 62 446.2 119.6 22 504.2 135.1 82 562.2 150.6 43 331.3 88.8 03 389.2 104.3 63 447.2 119.8 23 505.2 135.3 83 563.1 150.8 44 332.3 89.0 04 390.2 104.6 64 448.2 120.1 24 506.1 135.6 84 564.1 151.1 45 333.2 89.3 05 391.2 104.8 65 449.1 120.4 25 507.1 135.9 85 565.1 151.4 46 334.2 89.6 06 392.1 105.1 66 450.1 120.6 26 508.1 136.1 86 566.0 151.6 47 335.2 89.8 07 393.1 105.3 67 451.1 120.9 27 509.0 136.4 87 567.0 151.9 48 336.1 90.1 08 394.1 105.6 68 452.0 121.1 28 510.0 136.6 88 568.0 152.2 49 337.1 90.3 09 395.0 105.9 69 453.0 121.4 29 511.0 136.9 89 568.9 152.4 50 338.1 339. 90.6 10 396.0 106.1 70 454.0 121.7 30 511.9 137.2 90 569.9 152.7 351 90.9 411 397.0 106.4 471 454.9 121.9 531 512.9 137.4 591 570.9 153.0 52 340.0 91.1 12 397.9 106.6 72 455.9 122.2 32 513.9 137.7 92 571.8 153.2 53 340.9 91.4 13 398.9 106.9 73 456.9 122.4 33 514.8 137.9 93 572.8 153.5 54 341.9 91.6 14 399.9 107.2 74 457.8 122.7 34 515.8 138.2 94 573.8 153.7 55 342.9 91.9 15 400.8 107.4 75 458.8 122.9 35 516.8 188.4 95 574.7 154.0 56 343.8 92.1 16 401.8 107.7 76 459.8 123.2 36 517.7 138.7 96 575.7 154.2 57 344.8 92.4 17 402.8 107.9 77 460.7 123.5 37 518.7 139.0 97 576.7 154.5 58 345.8 92.7 18 403.7 108.2 78 461.7 123.7 38 519.7 139.2 98 577.6 154.8 59 346.7 92.9 19 404.7 108.5 79 462.7 124.0 39 520.6 139.5 99 578.6 155.0 60 347.7 93.2 20 405.7 108.7 80 463.6 124.2 40 521.6 139.7 600 579.5 155.3 Dist. Dep. Lav. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 75° (1 05°, 255 °, 285° ). 21594°— 14r- -29 Page 662] TABLE 2. Difference of Latitude and Departure for 16° (] L64°, 196°, 344°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 66.4 1 1.0 0.3 61 58.6 16.8 121 116.3 33.4 181 174.0 49.9 241 231.7 2 1.9 0.6 62 59.6 17.1 22 117.3 33.6 82 174.9 50.2 42 232.6 66.7 3 2.9 0.8 63 60.6 17.4 23 118.2 33.9 83 175.9 50.4 43 233.6 67.0 4 3.8 1.1 64 61.5 17.6 24 119.2 34.2 84 176.9 50.7 44 234.5 67.3 5 4.8 1.4 65 62.5 17.9 25 120.2 34.5 85 177.8 51.0 45 235.5 67.5 6 5.8 1.7 66 63.4 18.2 26 121.1 34.7 86 178.8 51.3 46 236.5 67.8 7 6.7 1.9 67 64.4 18.5 27 122.1 35.0 87 179.8 51.5 47 237.4 68.1 8 7.7 2.2 68 65.4 18.7 28 123.0 35.3 88 180.7 51.8 48 238.4 68.4 9 8.7 2.5 69 66.3 19.0 29 124.0 35.6 89 181.7 52.1 49 239.4 68.6 10 9.6 2.8 70 67.3 19.3 30 125.0 35.8 90 182.6 52.4 50 240.3 68.9 11 10.6 3.0 71 68.2 19.6 131 125.9 36.1 191 183.6 52.6 251 241.3 69.2 12 11.5 3.3 72 69.2 19.8 32 126.9 36.4 92 184.6 52.9 52 242.2 69.5 13 12.5 3.6 73 70.2 20.1 33 127.8 36.7 93 185.5 53.2 53 243.2 69.7 14 13.5 3.9 74 71.1 20.4 34 128.8 36.9 94 186.5 53.5 54 244.2 70.0 15 14.4 4.1 75 72.1 20.7 35 129.8 37.2 95 187.4 53.7 55 245.1 70.3 16 15.4 4.4 76 73.1 20.9 36 130.7 37.5 96 188.4 54.0 56 246.1 70.6 17 16.3 4.7 77 74.0 21.2 37 131.7 37.8 97 189.4 54.3 57 247.0 70.8 18 17.3 5.0 78 75.0 21.5 38 132.7 38.0 98 190.3 54.6 58 248.0 71.1 19 18.3 5.2 79 75.9 21.8 39 133.6 38.3 99 191.3 54.9 59 249.0 71.4 20 19.2 5.5 80 76.9 22.1 40 141 134.6 38.6 38.9 200 201 192.3 55.1 60 249.9 250.9 71.7 21 20.2 5.8 81 77.9 22.3 135.5 193.2 55.4 261 71.9 22 21.1 6.1 82 78.8 22.6 42 136.5 39.1 02 194. 2 55.7 62 251.9 72.2 23 22.1 6.3 83 79.8 22.9 43 137.5 39.4 03 195.1 56.0 63 252.8 72.5 24 23.1 6.6 84 80.7 23.2 44 138.4 39.7 04 196.1 56.2 64 253.8 72.8 25 24.0 6.9 85 81.7 23.4 45 139.4 40.0 05 197.1 56.5 65 254.7 73.0 26 25.0 7.2 86 82.7 23.7 46 140.3 40.2 06 198.0 56.8 66 255.7 73.3 27 26.0 7.4 87 83.6 24.0 47 141.3 40.5 07 199.0 57.1 67 256.7 73.6 28 26.9 7.7 88 84.6 24.3 48 142.3 40.8 08 199.9 57.3 68 257.6 73.9 29 27.9 8.0 89 85.6 24.5 49 143.2 41.1 09 200.9 57.6 69 258.6 74.1 30 28.8 8.3 90 86.5 24.8 50 144.2 41.3 10 201.9 57.9 70 271 259.5 260.5 74.4 74.7 31 29.8 8.5 91 87.5 25.1 151 145.2 41.6 211 202.8 58.2 32 30.8 8.8 92 88.4 25.4 52 146.1 41.9 12 203.8 58.4 72 261.5 75.0 33 31.7 9.1 93 89.4 25.6 53 147.1 42.2 13 204.7 58.7 73 262.4 75.2 34 32.7 9.4 94 90.4 25.9 54 148.0 42.4 14 205.7 59.0 74 263.4 75.5 35 33.6 9.6 95 91.3 26.2 55 149.0 42.7 15 206.7 59.3 75 264.3 75.8 36 34.6 9.9 96 92.3 26.5 56 150.0 43.0 16 207.6 59.5 76 265.3 76.1 37 35.6 10.2 97 93.2 26.7 57 150.9 43.3 17 208.6 59.8 77 266.3 76.4 38 36.5 10.5 98 94.2 27.0 58 151.9 43.6 18 209.6 60.1 78 267.2 76.6 39 37.5 10.7 99 95.2 27.3 59 152.8 43.8 19 210. 5 60.4 79 268.2 76.9 40 38.5 11.0 100 96.1 27.6 60 153.8 44.1 20 211.5 60.6 80 269.2 77.2 41 39.4 11.3 101 97.1 27.8 161 154.8 44.4 221 212.4 60.9 281 270.1 77.5 42 40.4 11.6 02 98.0 28.1 62 155.7 44.7 22 213.4 61.2 82 271.1 77.7 43 41.3 11.9 03 99.0 28.4 63 156.7 44.9 23 214.4 61.5 83 272.0 78.0 44 42.3 12.1 04 100.0 28.7 64 157.6 45.2 24 215. 3 61.7 84 273.0 78.3 45 43.3 12.4 05 100.9 28.9 65 158.6 45.5 25 216.3 62.0 85 274.0 78.6 46 44.2 12.7 06 101.9 29.2 66 159.6 45.8 26 217.2 62.3 86 274.9 78.8 47 45.2 13.0 07 102.9 29.5 67 160.5 46.0 27 218.2 62.6 87 275.9 79.1 48 46.1 13.2 08 103.8 29.8 68 161.5 46.3 28 219.2- 62.8 88 276.8 79.4 49 47.1 13.5 09 104.8 30.0 69 162.5 46.6 29 220.1 63.1 89 277.8 79.7 50 48.1 13.8 10 105.7 30.3 70 163.4 46.9 30 221.1 63.4 90 278.8 79.9 51 49.0 14.1 111 106.7 30.6 171 164.4 47.1 231 222.1 63.7 291 279.7 80.2 52 50.0 14.3 12 107.7 30.9 72 165.3 47.4 32 223.0 63.9 92 280.7 80.5 53 50.9 14.6 13 108.6 31.1 73 166. 3 47.7 33 224.0 64.2 93 281.6 80.8 54 51.9 14.9 14 109.6 31.4 74 167.3 48.0 34 224.9 64.5 94 282.6 81.0 55 52.9 15.2 15 110.5 31.7 75 168.2 48.2 35 225.9 64.8 95 283.6 81.3 56 53.8 15.4 16 111.5 32.0 76 169.2 48.5 36 226.9 65.1 96 284.5 81.6 57 54.8 15.7 17 112.5 32.2 77 170.1 48.8 37 227.8 65.3 97 285.5 81.9 58 55.8 16.0 18 113.4 32.5 78 171.1 49.1 38 228.8 65.6 98 286.5 82.1 59 56.7 16.3 19 114.4 32.8 79 172.1 49.3 39 229.7 65.9 99 287.4 82.4 60 57.7 16.5 20 115.4 33.1 80 173.0 49.6 40 230.7 66.2 300 288.4 82.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 74° (1 06°, 254°, 286°). TABLE 2. [Page 563 Difference of Latitude and Departure for 16° (164°, 19€ °, 344* ). DIst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. 1 Dep. Dist. 1 Lat. Dep. Dist. Lat. 1 Dep. 1 301 289.3 82.9 361 347.0 99.5 421 404.7 116.0 481 462.4 132.6 541 520.1 149.1 02 290.3 83.2 62 348.0 99.7 22 405.6 116.3 82 463.3 132.8 42 521.0 149.4 03 291.2 83.5 63 348.9 100.0 23 406.6 116.6 83 464.3 133.1 43 522.0 149.7 04 292.2 83.8 64 349.9 100.3 24 407.6 116.8 84 465.2 133.4 44 523.0 150.0 05 293.2 84.0 65 350.8 100.6 25 408.5 117.1 85 466.2 133.6 46 523.9 150.2 06 294.1 84.3 66 351.8 100.8 26 409.5 117.4 86 467.2 133.9 46 524.9 150.4 07 295.1 84.6 67 352.8 101.1 27 410.4 117.7 87 468.1 134.2 47 526.9 150.7 08 296.0 84.9 68 353.7 101.4 28 411.4 117.9 88 469.1 134.5 48 526.8 151.0 09 297.0 85.1 69 354.7 101.7 29 412.4 118.2 89 470.1 134.8 49 527.8 151.3 10 298.0 85.4 70 355. 6 101.9 30 413.3 118.5 90 471.0 135.0 50 628.7 151.6 311 298.9 85.7 371 356.6 102.2 431 414.3 118.8 491 472.0 135.3 561 629.7 151.9 12 299. 9 86.0 72 357.6 102.5 32 416.2 119.0 92 472.9 136. 6 62 630.6 152.2 13 300.9 86.2 73 358.5 102.8 33 416.2 119.3 93 473.9 136.9 53 631.6 152.6 14 301.8 86.5 74 359.5 103.1 34 417.2 119.6 94 474.9 136.2 54 532.6 152.8 15 302.8 86.8 75 360.4 103.3 35 418.1 119.9 95 475.8 136.4 55 536.5 153.0 16 303.7 87.1 76 361.4 103.6 36 419.1 120.1 96 476.8 136.7 66 534.5 153.2 17 304.7 87.3 77 362.4 103. 9 37 420.0 120.4 97 477.7 137. 57 636.4 153.6 18 305.7 87.6 78 363.3 104.2 38 421.0 120.7 98 478.7 137.3 58 536.4 163.8 19 306.6 87.9 79 364.3 104.4 39 422.0 121.0 99 479.7 137.5 59 537.4 154,1 20 307.6 88.2 80 365.3 104.7 40 422.9 121. 2 500 480.6 137.8 60 638.3 154.4 321 308.5 88.4 381 366.2 105. 441 423.9 121.6 601 481.6 138.1 561 539.3 154.7 22 309. 5 88.7 82 367.2 105.3 42 424.9 121.8 02 482.6 138.3 62 540.3 154.9 23 310.5 89.0 83 368.1 105.5 43 425.8 122.1 03 483.5 138.6 63 541.2 166.2 24 311.4 89.3 84 369.1 105.8 44 426.8 122. 3 04 484.5 138. 9 64 542.2 155.4 25 312.4 89.5 85 370.1 106.1 45 427.7 122.6 06 486.4 139. 2 65 543.1 155.7 26 313.3 89.8 86 371.0 106.4 46 428.7 122.9 06 486.4 139.4 66 644.1 166.0 27 314.3 90.1 87 372.0 106.6 47 429.7 123.2 07 487.3 139'. 7 67 546.1 166. 3 28 315.3 90.4 88 372.9 106.9 48 430.6 123.4 08 488.3 140.0 68 546.0 166.6 29 316.2 90.6 89 373.9 107.2 49 431.6 123.7 09 489.3 140.3 69 547.0 156.9 30 317.2 90.9 90 374.9 107.5 50 432.6 124.0 10 490.2 140.6 70 547.9 157.1 331 318.2 91.2 391 375. 8 107.7 451 433.6 124.3 511 491.2 140.8 571 548.9 157.3 32 319.1 91.5 92 376.8 108.0 52 434.5 124.6 12 492.1 141.1 72 549.8 157.6 33 320.1 91.8 93 377.8 108.3 63 435. 4 124. 8 13 493.1 141.4 73 660.8 157.9 34 321.0 92.0 94 378.7 108.6 54 436.4 125.1 14 494.1 141.7 74 551.8 168.2 35 322. 92.3 95 379.7 108.8 55 437.4 125.4 15 495.0 141.9 75 662.7 168.4 36 323.0 92.6 96 380.6 109.1 56 438.3 125.7 16 496.0 142.2 76 653.7 158.7 37 323.9 92.9 97 381.6 109.4 57 439.3 125.9 17 496.9 142.5 77 664.6 159.0 38 324.9 93.1 98 382.6 109.7 58 440.2 126.2 18 497.9 142.8 78 666.6 159.3 39 325.8 93.4 99 383.5 109.9 69 441.2 126.6 19 498.9 143.0 79 556.6 159.5 40 326.8 93.7 400 384.5 110.2 60 442.2 126.8 127. 20 521 499.8 143.3 80 557.6 159.8 341 327.8 94.0 401 385.4 110.5 461 443.1 500.8 143.6 581 658.4 160.1 42 328.7 94.2 02 386.4 110.8 62 444.1 127.3 22 601.7 143.9 82 659.4 160.4 43 329.7 94.5 03 387.4 111.0 63 445.0 127.6 23 602.7 144.1 83 560.4 160.6 44 330.7 94.8 04 388.3 111.3 64 446.0 127.9 24 603.7 144.4 84 661.3 161.0 45 331.6 95.1 05 389.3 111.6 65 447.0 128.1 25 504.6 144.7 86 662.3 161.3 46 332. 6 95.3 06 390.2 111.9 66 447.9 128.4 26 505.6 145.0 86 5a3.2 161.6 47 333. 5 95.6 07 391.2 112.1 67 448.9 128.7 27 506.6 145.3 87 564.2 161.8 48 334. 5 95.9 08 392.2 112.4 68 449.8 129.0 28 507.6 145.6 88 666.2 162.1 49 335.5 96.2 09 393.1 112.7 69 450.8 129.2 29 508.5 145.8 89 666.1 162.4 50 351 336.4 96.4 10 394.1 113.0 70 451.8 129.5 30 531 509.4 146.1 90 567.1 162.7 337. 4 96.7 411 395.1 113.3 471 452.7 129.8 610.4 146.4 691 568.1 162.9 52 338. 3 97.0 12 396.0 113. 5 72 453.7 130.1 32 611.4 146.7 92 569.0 163.2 53 339.3 97.3 13 397.0 113.8 73 454.7 130.3 33 512.3 146.9 93 670.0 163.5 54 340.3 97.5 14 397.9 114.1 74 456.6 130.6 34 613.3 147.2 94 671.0 163.8 55 341.2 97.8 15 398.9 114.4 75 466.6 130.9 35 514.3 147.5 95 671.9 164.0 56 342.2 98.1 16 399.9 114.6 76 467.6 131.2 36 516.2 147.8 96 572.9 164.3 57 343.1 98.4 17 400.8 114.9 77 458.5 131.4 37 516.2 148.0 97 573.9 164.6 58 344.1 98.6 18 401.8 115.2 78 459.5 131.7 38 517.2 148.2 98 574.8 164.9 59 345.1 98.9 19 402.7 115.5 79 460.4 132.0 39 518.1 148.5 99 575.8 166.1 60 346.0 99.2 20 403.7 115.8 80 461.4 132.3 40 519.1 148.8 600 576.8 165.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. H° (106°, 254°, 286° )• 1 Page 664] TABLE 2. Difference of Latitude and Departure for 17° (163°, 197°, 343° ). Dist. Lat. 1.0 Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.3 61 58.3 17.8 121 115.7 35.4 181 173.1 52.9 241 230.5 70.5 2 1.9 0.6 62 59.3 18.1 22 116.7 35.7 82 174.0 53.2 42 231.4 70.8 3 2.9 0.9 63 60.2 18.4 23 117.6 36.0 83 175.0 53.5 43 232.4 71.0 4 3.8 1.2 64 61.2 18.7 24 118.6 36.3 84 176.0 53.8 44 233.3 71.3 5 4.8 1.5 65 62.2 19.0 25 119.5 36.5 85 176.9 54.1 45 234.3 71.6 6 5.7 1.8 66 63.1 19.3 26 120.5 36.8 86 177.9 54.4 46 235.3 71.9 7 6.7 2.0 67 64.1 19.6 27 121.5 37.1 87 178.8 54.7 47 236.2 72.2 8 7.7 2.3 68 65.0 19.9 28 122.4 37.4 88 179.8 55.0 48 237.2 72.5 9 8.6 2.6 69 66.0 20.2 29 123.4 37.7 89 180.7 55.3 49 238.1 72.8 10 9.6 2.9 70 66.9 20.5 30 124. 3 125.3 38.0 90 181.7 55.6 55.8 50 251 239.1 240.0 73.1 11 10.5 3.2 71 67.9 20.8 131 38.3 191 182.7 73.4 12 11.5 3.5 72 68.9 21.1 32 126.2 38.6 92 183.6 56.1 52 241.0 73.7 13 12.4 3.8 73 69.8 21.3 33 127.2 38.9 93 184.6 56.4 53 241.9 74.0 14 13.4 4.1 74 70.8 21.6 34 128.1 39.2 94 185.5 56.7 54 242.9 74.3 15 14.3 4.4 75 71.7 21.9 35 129.1 39.5 95 186.5 57.0 55 243.9 74.6 16 15.3 4.7 76 72.7 22.2 36 130. 1 39.8 96 187.4 57.3 56 244.8 74.8 17 16.3 5.0 77 73.6 22.5 37 131.0 40.1 97 188.4 57.6 57 245.8 75.1 18 17.2 5.3 78 74.6 22.8 38 132.0 40.3 98 189.3 57.9 58 246.7 75.4 19 18.2 5.6 79 75.5 23.1 39 132.9 40.6 99 190.3 58.2 59 247.7 75.7 20 19.1 5.8 6.1 80 76.5 23.4 40 133.9 40.9 200 191.3 58.5 60 248.6 76.0 21 20.1 81 77.5 23.7 141 134. 8 41.2 201 192.2 58.8 261 249.6 76.3 22 21.0 6.4 82 78.4 24.0 42 135.8 41.5 02 193.2 59.1 62 250. 6 76.6 23 22.0 6.7 83 79.4 24.3 43 136.8 41.8 03 194.1 59.4 63 251.5 76.9 24 23.0 7.0 84 80.3 24.6 44 137.7 42.1 04 195.1 59.6 64 252.5 77.2 25 23.9 7.3 85 81.3 24.9 45 138.7 42.4 05 196.0 59.9 65 253.4 77.5 26 24.9 7.6 86 82.2 25.1 46 139.6 42.7 06 197.0 60.2 66 254.4 77.8 27 25.8 7.9 87 83.2 25.4 47 140.6 43.0 07 198. 60.5 67 255.3 78.1 28 26.8 8.2 88 84.2 25.7 48 141.5 43.3 08 198.9 60.8 68 256.3 78.4 29 27.7 8.5 89 85.1 26.0 49 142.5 43.6 09 199.9 61.1 69 257.2 78.6 30 28.7 8.8 90 86.1 26.3 50 143. 4 43.9 10 211 200.8 61.4 70 258.2 78.9 31 29.6 9.1 91 87.0 26.6 151 144. 4 44.1 201.8 61.7 271 259.2 79.2 32 30.6 9.4 92 88.0 26.9 52 145.4 44.4 12 202.7 62.0 72 260.1 79.5 33 31.6 9.6 93 88.9 27.2 53 146.3 44.7 13 203.7 62.3 73 261.1 79.8 34 32.5 9.9 94 89.9 27.5 54 147.3 45.0 14 204.6 62.6 74 262.0 80.1 35 33.5 10.2 95 90.8 27.8 55 148.2 45.3 15 205.6 62.9 75 263.0 80.4 36 34.4 10.5 96 91.8 28.1 56 149.2 45.6 16 206.6 63.2 76 263.9 80.7 37 35.4 10.8 97 92.8 28.4 57 150.1 45.9 17 207.5 63.4 77 264.9 81.0 38 36.3 11.1 98 93.7 28.7 58 151.1 46.2 18 208.5 63.7 78 265.9 81.3 39 37. 3 11.4 99 94.7 28.9 59 152.1 46.5 19 209.4 64.0 79 266.8 81.6 40 38.3 11.7 100 101 95.6 29.2 60 153.0 154. 46.8 20 210.4 64.3 80 267.8 81.9 41 39.2 12.0 96.6 29.5 161 47.1 221 211.3 64.6 281 268.7 82.2 42 40.2 12.3 02 97.5 29.8 62 154.9 47.4 22 212.3 64.9 82 269.7 82.4 43 41.1 12.6 03 98.5 30.1 63 155.9 47.7 23 213.3 65.2 83 270.6 82.7 44 42.1 12.9 04 99.5 30.4 64 156.8 47.9 24 214.2 65.5 84 271.6 83.0 45 43.0 13.2 05 100.4 30.7 65 157.8 48.2 25 215.2 65.8 85 272.5 83.3 46 44.0 13.4 06 101.4 31.0 66 158.7 48.5 26 216.1 66.1 86 273.5 83.6 47 44.9 13.7 07 102.3 31.3 67 159.7 48.8 27 217.1 66.4 87 274.5 83.9 48 45.9 14.0 08 103.3 31.6 68 160.7 49.1 28 218.0 66.7 88 275.4 84.2 49 46.9 14.3 09 104.2 31.9 69 161.6 49.4 29 219.0 67.0 89 276.4 84.5 50 47.8 14.6 10 105.2 32.2 70 162.6 49.7 30 220.0 67.2 90 277.3 84.8 51 48.8 14.9 111 106.1 32.5 171 163.5 50.0 231 220.9 67.5 291 278.3 85.1 52 49.7 15.2 12 107.1 32.7 72 164.5 50.3 32 221.9 67.8 92 279.2 85.4 53 50.7 15.5 13 108.1 33.0 73 165.4 50.6 33 222.8 68.1 93 280.2 85.7 54 51.6 15.8 14 109.0 33.3 74 166.4 50.9 34 223.8 68.4 94 281.2 86.0 55 52.6 16.1 15 110.0 33.6 75 167.4 51.2 35 224.7 68.7 95 282.1 86.2 56 53.6 16.4 16 110.9 33.9 76 168.3 51.5 36 225.7 69.0 96 283.1 86.5 57 54.5 16.7 17 111.9 34.2 77 169.3 51.7 37 226.6 69.3 97 284.0 86.8 58 55.5 17.0 18 112.8 34.5 78 170.2 52.0 38 227.6 69.6 98 285.0 87.1 59 56.4 17.2 19 113.8 34.8 79 171.2 52.3 39 228.6 69.9 99 285.9 87.4 60 57.4 17.5 20 114.8 35.1 80 172.1 52.6 40 229.5 70.2 300 286.9 87.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 73° (1 07°, 252 °, 287° ). i TABLE 2. [Page 565 Difference of Latitude and Departure for 17° (163°, 197°, 343 °). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 287.8 88.0 361 345.2 105.5 421 402.6 123.1 481 460.0 140.6 541 517.3 158.2 02 288.8 88.3 62 346.1 105.8 22 403.5 123.4 82 460.9 140.9 42 518.3 158.5 03 289.7 88.6 63 347.1 106.1 23 404.5 123.7 83 461.9 141.2 43 519.2 158.8 04 290.7 88.9 64 348.1 106.4 24 405.4 124.0 84 462.8 141.5 44 520.2 159.1 05 291.6 89.2 65 349.0 106.7 25 406.4 124.3 85 463.8 141.8 45 521.2 159.3 06 292.6 89.5 66 350.0 107.0 26 407.3 124.6 86 464.7 142.1 46 522.1 159.6 07 293.5 89.8 67 350.9 107.3 27 408.3 124.8 87 465.7 142.3 47 523.1 159.9 08 294.5 90.1 68 351.9 107.6 28 409.3 125.1 88 466.7 142.6 48 524.0 160.2 09 295. 5 90.3 69 352. 8 107.9 29 410.2 125.4 89 467.6 142.9 49 525.0 160.5 10 296.4 90.6 70 353.8 108.2 30 411.2 125.7 90 468.6 143.2 50 526.0 160.8 311 297.4 90.9 371 354.8 108.5 431 412.1 126.0 491 469.5 143.5 551 526.9 161.1 12 298.3 91.2 72 355. 7 108.8 32 413.1 126.3 92 470.5 143.8 52 527.9 161.4 13 299.3 91.5 73 356.7 109.1 33 414.0 126.6 93 471.4 144.1 53 528.8 161.7 14 300.2 91.8 74 357.6 109.4 34 415.0 126.9 94 472.4 144.4 54 529.8 162.0 15 301.2 92.1 75 358.6 109.6 35 416.0 127.2 95 473.4 144.7 55 530.8 162.3 16 302.2 92.4 76 359.5 109.9 36 416.9 127.5 96 474.3 145.0 56 531.7 162.6 17 303.1 92.7 77 360.5 110.2 37 417.9 127.8 97 475.3 145.3 57 532.7 162.9 18 304.1 93.0 78 361.4 no. 5 38 418.8 128.1 98 476.2 145.6 58 533.6 163.2 19 305.0 93.3 79 362.4 110.8 39 419.8 128.4 99 477.2 145.9 59 534.6 163.5 20 306,0 93.6 80 363.4 111.1 40 420.7 128.6 500 478.1 146.2 60 535.5 163.8 321 306.9 93.9 381 364. 3 111.4 441 421.7 128.9 501 479.1 146.5 561 536.5 164.1 22 307.9 94.1 82 365. 3 111.7 42 422.7 129.2 02 480.1 146.8 62 537.5 164.4 23 308.8 94.4 83 366.2 112.0 43 423.6 129.5 03 481.0 147.1 63 538.4 164.6 24 309.8 94.7 84 367.2 112.3 44 424.6 129.8 04 482.0 147.4 64 539.4 164.8 25 310.8 95.0 85 368.1 112.6 45 425. 5 130.1 05 482.9 147.7 65 540.3 165.1 26 311.7 95.3 86 369.1 112.9 46 426.5 130.4 06 483.9 148.0 66 541.3 165.4 27 312.7 95.6 87 370.1 113.2 47 427.4 130.7 07 484.8 148.3 67 542.2 165.7 28 313.6 95.9 88 371.0 113.4 48 428.4 131.0 08 485.8 148.6 68 543.2 166.0 29 314.6 96.2 89 372.0 113.7 49 429.3 131.3 09 486.7 148.9 69 544.1 166.4 30 315.5 96.5 90 372.9 373.9 114.0 50 430.3 131.6 10 487.7 149. 1 70 545.1 166.7 331 316.5 96.8 391 114.3 451 431.3 131.9 511 488.7 149.4 571 546.1 167.0 32 317.5 97.1 92 374.8 114.6 52 432.2 132.2 12 489.6 149.7 72 547.0 167.2 33 318.4 97.4 93 375.8 114.9 53 433.2 132.4 13 490.6 150.0 73 548.0 167.5 34 319.4 97.7 94 376.7 115.2 54 434.1 132.7 14 491.5 150.2 74 548.9 167.8 35 320.3 97.9 95 377.7 115. 5 5.5 435.1 133.0 15 492.5 150.5 75 549.9 168.1 36 321.3 98.2 96 378.7 115.8 56 436.0 133.3 16 493.4 150.8 76 550.8 168.4 37 322.2 98.5 97 379.6 116.1 57 437.0 133.6 17 494.4 151.1 77 551.8 168.7 38 323.2 98.8 98 380.6 116.4 58 438.0 133.9 18 495. 3 151.4 78 552.7 169.0 39 324.2 99.1 99 381.5 116.7 59 438.9 134.2 19 496.3 151. 7 79 553.7 169.3 40 325.1 99.4 400 382. 5 117.0 60 439.9 134.5 20 497.2 152. 80 554.6 169.6 341 326.1 99. 7 401 383.4 117.2 461 440.8 1.34. 8 521 498.2 152.3 581 555. 6 169.9 42 327.0 100.0 02 384.4 117.5 62 441.8 135.1 22 499.2 152.6 82 556. 5 170.2 43 328.0 100.3 03 385.4 117.8 63 442.7 135. 4 23 500.1 152.9 83 557.5 170.5 44 328.9 100.6 04 386.3 118.1 64 443.7 135.7 24 501.1 153.2 84 558.4 170.8 45 329.9 100.9 05 387.3 118.4 65 444.6 136.0 25 502.0 153. 5 85 559.4 171.1 46 330. 8 101.2 06 388.2 118.7 66 445.6 136.2 26 503.0 153.8 86 560.4 171.3 47 331.8 101.5 07 389.2 119.0 67 446.6 136.5 27 503. 9 154.1 87 561.3 171.6 48 332.8 101.8 08 390.1 119.3 68 447.5 136.8 28 504.9 154.4 88 562.3 171.9 49 333.7 102.0 09 391.1 119.6 69 448.5 137.1 .29 505. 9 154.7 89 563.2 172.2 50 334. 7 102.3 10 392.0 119.9 70 449.4 137.4 30 506.8 155.0 90 564.2 172.5 351 335.6 102.6 411 393.0 120.2 471 450.4 137.7 531 507.8 155. 3 591 565. 1 172.8 52 336.6 102.9 12 394.0 120.5 72 451.3 138.0 32 508.7 155.6 92 566.1 173.1 53 337.5 103.2 13 394.9 120.8 73 452.3 138.3 33 509.7 155,9 93 567.1 173.4 54 338.5 103.5 14 395.9 121.0 74 453.3 138.6 34 510.6 156.2 94 568.0 173.7 55 339.5 103.8 15 396.8 121.3 75 454.2 138.9 35 511.6 156.5 95 569.0 174.0 56 340.4 104.1 16 397.8 121.6 76 455.2 139.2 36 512.6 156.8 96 569.9 174.3 57 341.4 104.4 17 398.7 121.9 77 456.1 139.5 37 513.5 157.1 97 570.9 174.6 58 342.3 104.7 18 399.7 122.2 78 457.1 139.8 38 514.5 157.3 98 571.8 174.9 59 343.3 105.0 19 400.7 122.5 79 458.0 140.0 39 515.4 157.6 99 572.8 175.2 60 344.2 105.3 20 401.6 122.8 80 459.0 140.3 40 516.4 157.9 600 573.8 175.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 73° (107°, 253°, 287° )• 1 Page 566] TABLE 2. Difference of Latitude and Departure for 18° (162°, 198 °, 342° ). Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 1.0 0.3 61 58.0 18.9 121 115.1 37.4 181 172.1 55.9 241 229.2 74.5 .2 1.9 0.6 62 59.0 19.2 22 116.0 37.7 82 173.1 56.2 42 230.2 74.8 3 2.9 0.9 63 59'. 9 19.5 23 117.0 38.0 83 174.0 56.6 43 231.1 75.1 4 3.8 1.2 64 60.9 19.8 24 117.9 38.3 84 175.0 56.9 44 232.1 75.4 5 4.8 1.5 65 61.8 20.1 25 118.9 38.6 85 175.9 57.2 45 233.0 75.7 6 5.7 1.9 66 62.8 20.4 26 119.8 38.9 86 176.9 57.5 46 234.0 76.0 7 6.7 2.2 67 63.7 20.7 27 120. 8 39.2 87 177.8 57.8 47 234.9 76.3 8 7.6 2.5 68 64.7 21.0 28 121.7 39.6 88 178.8 58.1 48 235.9 76.6 9 8.6 2.8 69 65.6 21.3 29 122.7 39.9 89 179.7 58.4 49 236.8 76.9 10 9.5 3.1 70 66.6 21.6 30 123.6 40.2 90 180.7 181.7 58.7 50 237.8 77.3 11 10.5 3.4 71 67.5 21.9 131 124.6 40.5 191 59.0 251 238.7 77.6 12 11.4 3.7 ■ 72 68.5 22.2 32 125. 5 40.8 92 182. 6 59.3 52 239.7 77.9 13 12.4 4.0 73 69.4 22.6 33 126.5 41.1 93 183.6 59.6 53 240.6 78.2 14 13.3 4.3 74 70.4 22.9 34 127.4 41.4 94 184.5 59.9 54 241.6 78.5 15 14.3 4.6 75 71.3 23.2 35 128.4 41.7 95 185.5 60.3 55 242.5 78.8 16 15.2 4.9 76 72.3 23.5 36 129.3 42.0 96 186.4 60.6 56 243. 5 79.1 17 16.2 5.3 77 73.2 23.8 37 130.3 42.3 97 187.4 60.9 57 244.4 79.4 18 17.1 5.6 78 74.2 24.1 38 131.2 42.6 98 188. 3 61.2 58 245.4 79.7 19 18.1 5.9 79 75.1 24.4 39 132.2 43.0 99 189.3 61.5 59 246.3 80.0 20 19.0 6.2 80 81 76.1 24.7 40 133. 1 43.3 200 190.2 61.8 60 247.3 80.3 21 20.0 6.6 77.0 25.0 141 134.1 43.6 201 191.2 62.1 261 248.2 80.7 22 20.9 6.8 82 78.0 25.3 42 135.1 43.9 02 192.1 62.4 62 249.2 81.0 23 21.9 7.1 83 78.9 25.6 43 136.0 44.2 03 193.1 62.7 63 250.1 81.3 24 22.8 7.4 84 79.9 26.0 44 137.0 44.5 04 194.0 63.0 64 251.1 81.6 25 23.8 7.7 85 80.8 26.3 45 137.9 44.8 05 195.0 63.3 65 252.0 81.9 26 24.7 8.0 86 81.8 26.6 46 138.9 45.1 06 195.9 63.7 66 253.0 82.2 27 25.7 8.3 87 82.7 26.9 47 139.8 45.4 07 196.9 64.0 67 253.9 82.5 28 26.6 8.7 88 83.7 27.2 48 140.8 45.7 08 197.8 64.3 68 254.9 82.8 29 27.6 9.0 89 84.6 27.5 49 141.7 46.0 09 198.8 64.6 69 255.8 83:1 30 28.5 9.3 90 85.6 27.8 50 142.7 46.4 10 199.7 64.9 70 256.8 257.7 83.4 83.7 31 29.5 9.6 91 86.5 28.1 151 143.6 46.7 211 200.7 65.2 271 32 30.4 9.9 92 87.5 28.4 52 144.6 47.0 12 201.6 65.5 72 258.7 84.1 33 31.4 10.2 93 88.4 28.7 53 145.5 47.3 13 202.6 65.8 73 259.6 84.4 34 32.3 10.5 94 89.4 29.0 54 146.5 47.6 14 203.5 66.1 74 260.6 84.7 35 33.3 10.8 95 90.4 29.4 55 147.4 47.9 15 204.5 66.4 75 261.5 85.0 36 34.2 11.1 96 91.3 29.7 56 148.4 48.2 16 205.4 66.7 76 262.5 85.3 37 35.2 11.4 97 92.3 30.0 57 149.3 48.5 17 206.4 67.1 77 263.4 85.6 38 36.1 11.7 98 93.2 30.3 58 150.3 48.8 18 207.3 67.4 78 264.4 85.9 39 37.1 12.1 99 94.2 30.6 59 151.2 49.1 19 208.3 67.7 79 265.3 86.2 40 38.0 12.4 100 95.1 30.9 60 152.2 49.4 20 209.2 210.2 68.0 80 266.3 86.5 41 39.0 12.7 101 96.1 31.2 161 153.1 49.8 221 68.3 281 267.2 86.8 42 39.9 13.0 02 97.0 31.5 62 154.1 50.1 22 211.1 68.6 82 268.2 87.1 43 40.9 13.3 03 98.0 31.8 63 155.0 50.4 23 212.1 68.9 83 269.1 87.5 44 41.8 13.6 04 98.9 32.1 64 156.0 50.7 24 213.0 69.2 84 270.1 87.8 45 42.8 13.9 05 99.9 32.4 65 156.9 51.0 25 214.0 69.5 85 271.1 88.1 46 43.7 14.2 06 100.8 32.8 66 157.9 51.3 26 214.9 69.8 86 272.0 88.4 47 44.7 14.5 07 101.8 33.1 67 158.8 51.6 27 215.9 70.1 87 273.0 88.7 48 45.7 14.8 08 102.7 33.4 68 159.8 51.9 28 216.8 70.5 88 273.9 89.0 49 46.6 15.1 09 103.7 33.7. 69 160.7 52.2 29 217.8 70.8 89 274.9 89.3 50 47.6 15.5 10 104.6 34.0 70 161.7 52.5 52.8 30 218.7 71.1 90 275.8 89.6 51 48.5 15.8 111 105.6 34.3 171 162.6 231 219.7 71.4 291 276.8 89.9 52 49.5 16.1 12 106.5 34.6 72 163.6 53.2 32 220.6 71.7 92 277.7 90.2 53 50.4 16.4 13 107.5 34.9 73 164.5 53.5 33 221.6 72.0 93 278.7 90.5 54 51.4 16.7 14 108. 4 35.2 74 165.5 53.8 34 222.5 72.3 94 279.6 90.9 55 52.3 17.0 15 109.4 35.5 75 166.4 54.1 35 223.5 72.6 95 280.6 91.2 56 53.3 17.3 16 110.3 35.8 76 167.4 54.4 36 224.4 72.9 96 281.5 91.5 . 57 54.2 17.6 17 111.3 36.2 77 168.3 54.7 37 225.4 73.2 97 282.5 91.8 ■ 58 55.2 17.9 18 112.2 36.5 78 169. 3 55.0 38 226.4 73. 5 98 283.4 92.1 ■ 59 56.1 18.2 19 113. 2 36.8 79 170.2 55.3 39 227.3 73.9 99 284.4 92.4 ■ 60 57.1 18.5 20 114.1 37.1 80 171.2 55.6 40 228.3 74.2 300 285.3 92.7 ■ Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. I i '2° (108°, 252 °, 288° )• 1 1 TABLE 2. [Page 567 Difference of Latitude and Departure for 18° (162°, 198°, 342° )• DIst. Lat. Dep. Dist. Lat. Dep. Dist. l.at. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 286.3 93.0 361 343.3 111.6 421 400.4 130.1 481 457.5 148.6 541 514.5 .167. 2 02 287.2 93.3 62 344.3 111.9 22 401.4 130.4 82 458.5 148.9 42 515.5 167.5 03 288.2 93.7 63 345.2 112.2 23 402.3 130.7 83 459.4 149.3 43 516.4 167.9 04 289.1 94.0 64 346.2 112.5 24 403.3 131.0 84 460.4 149.6 44 517.4 168.2 05 290.1 94.3 65 347.1 112.8 25 404.2 131.3 85 461.3 149.9 45 518.3 168.5 06 291.0 94.6 66 348.1 113.1 26 405.2 131.7 86 462.3 150.2 46 519.3 168.8 07 292.0 94.9 67 349.0 113.4 27 406.1 132.0 87 463.2 150.5 47 520.2 169.1 08 292.9 95.2 68 350.0 113.7 28 407.1 132.3 88 464.2 150.8 48 521.2 169.4 09 293.9 95.5 69 350.9 114.0 29 408.0 132.6 89 465.1 151.1 49 522.1 169.7 10 311 294.8 295.8 95.8 70 351.9 114.3 30 409.0 409.9 132.9 90 466.1 151.4 50 551 523.1 524. 170.0 96.1 371 352.9 114.7 431 133.2 491 467.0 151.7 170.3 12 296.7 96.4 72 353.8 115.0 32 410.9 133.5 92 468.0 152.0 52 525.0 170.6 13 297.7 96.7 73 354.8 115.3 33 411.8 133.8 93 468.9 152.3 53 525.9 170.9 14 298.6 97.0 74 355.7 115.6 34 412.8 134.1 94 469.8 152.6 54 526.9 171.2 15 299.6 97.4 75 356.7 115.9 35 413.7 134.4 95 470.8 153.0 55 527.8 171.5 16 300.5 97.7 76 357.6 116.2 36 414.7 134.7 96 471.7 153.3 56 528.8 171.8 17 301. 5 98.0 77 358.6 116.5 37 415.6 135.1 97 472.7 153.6 57 529.7 172.1 18 302.4 98.3 78 359.5 116.8 38 416.6 135.4 98 473.6 153.9 58 530.7 172.4 19 303.4 98.6 79 360.5 117.1 39 417.5 135.7 99 474.6 154.2 59 531.6 172.7 20 304.3 98.9 80 361.4 117.4 40 418.5 136.0 500 475.5 154.5 60 532.6 173.0 321 305.3 99.2 381 362.4 117.7 441 419.4 136.3 501 476.5 154.8 561 533. 5 173.3 22 306.2 99.5 82 363.3 118.1 42 420.4 136.6 02 477.4 155.1 62 534.5 173.6 23 307.2 99.8 83 364.3 118.4 43 421.3 136.9 03 478.4 155.4 63 535. 4 173.9 24 308.2 100.1 84 365.2 118.7 44 422.3 137.2 04 479.3 155.7 64 536.4 174.2 25 309.1 100.4 85 366.2 119.0 45 423.2 137.5 05 480.3 156.1 65 537.3 174.6 26 310.1 100.7 86 367.1 119.3 46 424.2 137.8 06 481.2 156.4 66 538.3 174.9 27 311.0 101.1 87 368.1 119.6 47 425.1 138.1 07 482.2 156.7 67 539.2 175.2 28 312.0 101.4 88 369.0 119.9 48 426.1 138.4 08 483.2 157. 68 540.2 175.5 29 312.9 101.7 89 370.0 120.2 49 427.0 138.8 09 484.1 157.3 69 541.1 175.8 30 313.9 102.0 102. 3 90 391 370.9 120.5 50 428.0 139.1 10 485.1 157.6 70 542.1 176.1 331 314.8 371.9 120.8 451 428.9 139.4 511 486.0 157.9 571 543.0 176.4 32 315.8 102.6 92 372.8 121.1 52 429.9 139.7 12 487.0 158.2 72 544.0 176.7 33 316.7 102.9 93 373.8 121.5 53 430.8 140.0 13 487.9 158.5 73 544.9 177.0 34 317.7 103.2 94 374.7 121.8 54 431.8 140.3 14 488.9 158. 8 74 545.9 177.3 35 318.6 103.5 95 375.7 122.1 55 432.7 140.6 15 489.8 159.1 75 546.8 177.6 36 319.6 103.8 96 376.6 122.4 56 433.7 140.9 16 490.8 159.4 76 547.8 178.0 37 320.5 104.1 97 377.6 122. 7 57 434. 6 141.2 17 491.7 159.7 77 548.7 178.3 38 321.5 104.5 98 378.5 123.0 58 435.6 141.5 18 492.7 160.0 78 549.7 178.6 39 322.4 104.8 99 379. 5 123.3 59 436.5 141.8 19 493.6 160.3 79 550.6 178.9 40 323. 4 105.1 400 380.4 123.6 60 437.5 142.2 20 494.6 160.7 80 551.6 179.2 341 324.3 105.4 401 381.4 123.9 461 438.4 142.5 521 495.5 161.0 581 552.5 179.5 42 325.3 105.7 02 382.3 124.2 62 439.4 142.8 22 496.5 161.3 82 553.5 179.8 43 326.2 106.0 03 383.3 124.5 63 440.3 143.1 23 497.4 161.6 83 554.4 180.1 44 327.2 106.3 04 384.2 124.9 64 441.3 143.4 24 498.4 161.9 84 555.4 180.4 45 328.1 106.6 05 385.2 125.2 65 442.2 143.7 25 499.3 162.2 85 556.3 180.7 46 329.1 106.9 06 386.1 125.5 66 443.2 144.0 26 500.3 162.5 86 557. 3 181.1 47 330.0 107.2 07 387.1 125.8 67 444.2 144.3 27 501.2 162.9 87 558.2 181.4 48 331.0 107.5 08 388.0 126.1 68 445.1 144.6 28 502.2 163.2 88 559.2 181.7 49 331.9 107.9 09 389.0 126.4 69 446.1 144.9 29 503.1 1 163.5 89 560.1 182.0 50 351 332.9 108.2 10 389.9 390.9 126.7 70 447.0 145.2 30 504.1 163. 8 90 561.1 182.3 333.8 108.5 411 127.0 471 448.0 145.6 531 505. 164.1 591 562.0 182.7 52 334.8 108.8 12 391.8 127.3 72 448.9 145.9 32 506.0 164.4 92 563.0 J 83.0 53 335.7 109.1 13 392.8 127.6 73 449.9 146.2 33 506.9 164.7 93 563.9 183.3 54 336.7 109.4 14 393.7 127.9 74 450.8 146.5 34 507.9 165.0 94 564.9 183.6 55 337.6 109.7 15 394.7 128.3 75 451. 8 146.8 35 508.8 165.3 95 565.8 183.9 56 338.6 110.0 16 395.6 128.6 76 452.7 147.1 36 509.8 165.6 96 566.8 184.2 57 339.5 110.3 17 396.6 128.9 77 453.7 147.4 37 510.7 165.9 97 567.7 184.5 58 340.5 110.6 18 397.5 129.2 78 454.6 147.7 38 511.7 166.2 98 568.7 184.8 59 341.4 110.9 19 398.5 129.5 79 455.6 148.0 39 512.6 166. 5 99 569.6 185.1 60 342.4 111.3 20 399.5 129.8 80 456.5 148.3 40 513.6 166.9 600 570.6 185.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 72° (108, 252°, 288° . Page 668] TABLE 2. Difference of Latitude and Departure for 19° (161°, 199 °, 341° )• Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.3 61 57.7 19.9 121 114.4 39.4 181 171.1 58.9 241 227.9 78.5 2 1.9 0.7 62 58.6 20.2 22 115.4 39.7 82 172.1 59.3 42 228.8 78.8 3 2.8 1.0 63 59.6 20.5 23 116.3 40.0 83 173.0 59.6 43 229.8 79.1 4 3.8 1.3 64 60.5 20.8 24 117.2 40.4 84 174.0 59.9 44 230. 7 79.4 5 4.7 1.6 66 61.5 21.2 25 118.2 40.7 85 174.9 60.2 45 231.7 79.8 6 5.7 2.0 66 62.4 21.5 26 119.1 41.0 86 175.9 60.6 46 232.6 80.1 7 6.6 2.3 67 63.3 21.8 27 120.1 41.3 87 176.8 60.9 47 233.5 80.4 8 7.6 2.6 68 64.3 22.1 28 121.0 41.7 88 177.8 61.2 48 234.5 80.7 9 8.5 2.9 69 65.2 22.5 29 122.0 42.0 89 178.7 61.5 49 235.4 81.1 10 9.5 3.3 70 66.2 22.8 30 122.9 42.3 90 179.6 61.9 50 236.4 81.4 11 10.4 3.6 71 67.1 23.1 131 123.9 42.6 191 180.6 62.2 251 237.3 81.7 12 11.3 3.9 72 68.1 23.4 32 124.8 43.0 92 181.5 62.5 52 238.3 82.0 13 12.3 4.2 73 69.0 23.8 33 125.8 43.3 93 182.5 62.8 53 239.2 82.4 14 13.2 4.6 74 70.0 24.1 34 126.7 43.6 94 183.4 63.2 54 240.2 82.7 15 14.2 4.9 75 70.9 24.4 35 127.6 44.0 95 184.4 63.5 55 241.1 83.0 16 15.1 5.2 76 71.9 24.7 36 128.6 44.3 96 185.3 63.8 56 242.1 83.3 17 16.1 5.5 77 72.8 25.1 37 129.5 44.6 97 186.3 64.1 57 243.0 83.7 18 17.0 5.9 78 73.8 25.4 38 130.5 44.9 98 187.2 64.5 58 243.9 84.0 19 18.0 6.2 79 74.7 25.7 39 131.4 45.3 99 188.2 64.8 59 244.9 84.3 20 18.9 6.5 80 75.6 26.0 40 132.4 45.6 200 189.1 65.1 60 245.8 84.6 21 19.9 6.8 81 76.6 26.4 141 133.3 45.9 201 190.0 65.4 261 246.8 85.0 22 20.8 7.2 82 77.5 26.7 42 134.3 46.2 02 191.0 65.8 62 247.7 85.3 23 21.7 7.5 83 78.5 27.0 43 135.2 46.6 03 191.9 66.1 63 248.7 85.6 24 22.7 7.8 84 79.4 27.3 44 136.2 46.9 04 192.9 66.4 64 249.6 86.0 25 23.6 8.1 85 80.4 27.7 45 137.1 47.2 05 193.8 66.7 65 250.6 86.3 26 24.6 8.5 86 81.3 28.0 46 138.0 47.5 06 194.8 67.1 66 251.5 86.6 27 25.5 8.8 87 82.3 28.3 47 139.0 47.9 07 195.7 67.4 67 252.5 86.9 28 26.5 9.1 88 83.2 28.7 48 139.9 48.2 08 196.7 67.7 68 253.4 87.3 29 27.4 9.4 89 84.2 29.0 49 140.9 48.5 09 197.6 68.0 69 254.3 87.6 30 28.4 9.8 90 85.1 29.3 50 141.8 48.8 10 198.6 68.4 70 255.3 87.9 31 29.3 10.1 91 86.0 29.6 151 142.8 49.2 211 199.5 68.7 271 256.2 88.2 32 30.3 10.4 92 87.0 30.0 52 143.7 49.5 12 200.4 69.0 72 257.2 88.6 33 31.2 10.7 93 87.9 30.3 53 144.7 49.8 13 201.4 69.3 73 258.1 88.9 34 32.1 11.1 94 88.9 30.6 54 145.6 50.1 14 202.3 69.7 74 259.1 89.2 35 33.1 11.4 95 89.8 30.9 55 146.6 50.5 15 203.3 70.0 75 260.0 89.5 36 34.0 11.7 96 90.8 31.3 56 147.5 50.8 16 204.2 70.3 76 261.0 89.9 37 35.0 12.0 97 91.7 31.6 57 148.4 51.1 17 205.2 70.6 77 261.9 90.2 38 35.9 12.4 98 92.7 31.9 58 149.4 51.4 18 206.1 71.0 78 262.9 90.5 39 36.9 12.7 99 93.6 .32.2 59 150.3 51.8 19 207.1 71.3 79 263.8 90.8 40 37.8 13.0 100 94.6 32.6 60 151.3 52.1 20 208.0 209.0 71.6 80 264.7 91.2 41 38.8 13.3 101 95.5 32.9 161 152.2 52.4 221 72.0 281 265.7 91.5 42 39.7 13.7 02 96.4 33.2 62 153.2 52.7 22 209.9 72.3 82 266.6 91.8 43 40.7 14.0 03 97.4 33.5 63 154.1 53.1 23 210.9 72.6 83 267.6 92.1 44 41.6 14.3 04 98.3 33.9 64 155.1 53.4 24 211.8 72.9 84 268.5 92.5 45 42.5 14.7 05 99.3 34.2 65 156.0 53.7 25 212.7 73.3 85 269.5 92.8 46 43.5 15.0 06 100.2 34.5 66 157.0 54.0 26 213.7 73.6 86 270.4 93.1 47 44.4 15.3 07 101.2 34.8 67 157.9 54.4 27 214.6 73.9 87 271.4 93.4 48 45.4 15.6 08 102.1 35.2 68 158.8 54.7 28 215.6 74.2 88 272.3 93.8 49 46.3 16.0 09 103.1 35.5 69 159.8 55.0 29 216. 5 74.6 89 273.3 94.1 50 47.3 16.3 10 104.0 35.8 70 160.7 55.3 30 217.5 74.9 90 274.2 94.4 51 48.2 16.6 111 105.0 36.1 171 161.7 55.7 231 218.4 75.2 291 275.1 94.7 52 49.2 16.9 12 105.9 36.5 72 162.6 56.0 32 219.4 75.5 92 276.1 95.1 53 50.1 17.3 13 106.8 36.8 73 163.6 56.3 33 220.3 75.9 93 277.0 95.4 54 51.1 17.6 14 107.8 37.1 74 164.5 56.6 34 221.3 76.2 94 278.0 95.7 55 52.0 17.9 15 108.7 37.4 75 165.5 57.0 35 222.2 76.5 95 278.9 96.0 56 52.9 18.2 16 109.7 37.8 76 166.4 57.3 36 223.1 76.8 96 279.9 96.4 57 53.9 18.6 17 110.6 38.1 77 167.4 57.6 37 224.1 77.2 97 280.8 96.7 58 54.8 18.9 18 111.6 38.4 78 168.3 58.0 38 225.0 77.5 98 281.8 97.0 59 55.8 19.2 19 112.5 38.7 79 169.2 58.3 39 226.0 77.8 99 282.7 97.3 60 56.7 19.5 20 113.5 39.1 80 170.2 58.6 40 226.9 78.1 300 283.7 97.7 Dlst. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Diet. Dep. Lat. ri° (1 09°, 251 °, 289° ). TABLE 2. [Page 569 Difference of Latitude and Departure for 19° (161°, 199°, 341° )• Dist. ; Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 Dist. Lat. Dep. Dist. Lat. Dep. 301 284.6 98.0 361 341.3 117.5 421 398.1 137.0 481 454.8 156.6 541 511.5 176.1 02 285.5 1 98.3 62 342.3 117.8 22 399.0 137.4 82 455.7 156.9 42 512.4 176.4 03 286.5 98.6 63 343.2 118.2 23 400.0 137. 7 83 456.7 157.2 43 513.4 176.8 04 287.4 99.0 64 344.2 118.5 24 400.9 138.0 84 457.6 157.6 44 514.3 177.1 05 288.4 99.3 65 345.1 118.8 25 401.8 138.4 85 458.6 157.9 45 515.3 177.4 06 289.3 99.6 66 346.1 119.1 26 402.8 138.7 86 459.5 158.2 46 516.2 177.7 07 290.3 99.9 67 347.0 119.5 27 403.7 139.0 87 460.5 158.5 47 517.2 178.1 08 291.2 100.3 68 348.0 119.8 28 404.7 139.3 88 461.4 158.9 48 518.1 178.4 09 292.2 100.6 69 348.9 120.1 29 405.6 139.7 89 462.4 159.2 49 519.1 178.7 10 293.1 100.9 70 349.8 120.4 30 406.6 140.0 90 463.3 159.5 50 520.0 179.0 311 294.1 101.2 371 350.8 120.8 431 407.5 140.3 491 464.3 159.8 551 521.0 179.4 12 295.0 101.6 72 351.7 121.1 32 408.5 140.6 92 465.2 160.2 52 521.9 179.7 13 295.9 101.9 73 352.7 121.4 33 409.4 141.0 93 466.1 160.5 53 522.8 180.0 14 296.9 102.2 74 353.6 121.7 34 410.4 141.3 94 467.1 160.8 54 523.8 180.3 15 297.8 102.5 75 354.6 122.1 35 411.3 141.6 95 468.0 161.1 55 524.7 180.7 16 298.8 102.9 76 355.5 122.4 36 412.2 141.9 96 469.0 161.5 56 525.7 181.0 17 299.7 103.2 77 356.5 122.7 37 413.2 142.3 97 469.9 161.8 57 526.6 181.3 18 300.7 103.5 78 357.4 123.0 38 414.1 142.6 98 470.9 162.1 58 527.6 181.6 19 301.6 103.8 79 358.4 123.4 39 415.1 142.9 99 471.8 162.4 59 528.5 182.0 20 321 302.6 104.2 80 359.3 123.7 124. 40 441 416.0 143.2 500 472.8 162.8 60 529.5 182.3 182.6 303.5 104.5 381 360.2 417.0 143.6 501 473.7 163.1 561 530.4 22 304.5 104.8 82 361.2 124.4 42 417.9 143.9 02 474.7 163.4 62 531.4 182.9 23 305.4 105. 1 83 362.1 124.7 43 418.9 144.2 03 475.6 163.7 63 532.3 183.3 24 306.3 105. 5 84 363.1 125.0 44 419.8 144.5 04 476.5 164.1 64 533.2 183.6 25 307.3 105.8 85 364.0 125.3 45 420.8 144.9 05 477.5 164.4 65 534.2 183.9 26 308.2 106.1 86 365.0 125.7 46 421.7 145.2 06 478.4 164.7 66 535.1 184.2 27 309.2 106.4 87 365. 9 126.0 47 422.6 145.5 07 479.4 165.0 67 536.1 184.6 28 310.1 106.8 88 366.9 126.3 48 423.6 145.8 08 480.3 165.4 68 537.0 184.9 29 311.1 107.1 89 367.8 126.6 49 424.5 146.2 09 481.2 165.7 69 538.0 185.2 30 312.0 107.4 90 368.8 127.0 50 425.5 146.5 10 482.2 166.1 70 538.9 185.6 331 313.0 107.7 391 369.7 127.3 451 426.4 146.8 611 483.1 166.4 571 539.9 185.9 32 313.9 108.1 92 370.6 127.6 52 427.4 147.1 12 484.1 166.7 72 540.8 186.2 33 314.9 108.4 93 371.6 127.9 53 428.3 147.5 13 485.0 167.0 73 541.7 186.5 34 315.8 108.7 94 372.5 128.3 54 429.3 147.8 14 486.0 167.4 74 542.7 186.9 35 316.7 109.1 95 373.5 128.6 55 430.2 148.1 15 486.9 167.7 75 543.6 187.2 36 317.7 109.4 96 374.4 128.9 56 431.2 148.4 16 487.9 168.0 76 544.6 187.5 37 318.6 109.7 97 375.4 129.2 57 432.1 148.8 17 488.8 168.3 77 545.5 187.8 38 319.6 110.0 98 376.3 129.6 58 433.0 149.1 18 489.7 168.7 78 546.5 188.2 39 320.5 110.4 99 377.3 129.9 59 434.0 149.4 19 490.7 169.0 79 547.4 188.5 40 321.5 110.7 400 378.2 130.2 60 434.9 149.7 20 491.6 169.3 80 548.4 188.8 341 322.4 111.0 401 379.2 130.5 461 435.9 150.1 521 492.6 169.6 581 549.3 189.1 42 323. 4 111.3 02 380.1 130.9 62 436.8 150.4 22 493.5 170.0 82 550.3 189.5 43 324.3 111.7 03 381.0 131. 2 63 437.8 150.7 23 494.5 170.3 ^3 551.2 189.8 44 825.3 112.0 04 382.0 131.5 64 438.7 151.0 24 495.4 170.6 84 552.2 190.1 45 326.2 112.3 05 382.9 131.8 65 439.7 151.4 25 496.4 170.9 85 553. 1 190.4 46 327.1 112.6 06 383.9 132.2 66 440.6 151.7 2a 497.3 171.2 86 554. 1 190.8 47 328.1 113.0 07 384.8 132.5 67 441.6 152.0 27 498.3 171.6 87 555.0 191.1 48 329.0 113.3 08 385.8 132.8 68 442.5 152.4 28 499.2 171.9 88 555. 9 191.4 49 330. 113.6 09 386.7 133.1 69 443.4 152.7 29 500.1 :172.2 89 556.9 191.7 50 330.9 113.9 10 387.7 133.5 70 444.4 153.0 30 501.1 502.0 172.5 90 557.8 192.1 351 331.9 114.3 411 388.6 133.8 471 445.3 153.3 531 172.9 591 558.8 192.4 52 332.8 114.6 12 389.6 134.1 72 446.3 153.7 32 503.0 173.2 92 559.7 192.7 53 333.8 114.9 13 390.5 134.4 73 447.2 154.0 33 503.9 173.5 93 560.7 193.0 54 334.7 115.2 14 391.4 134.8 74 448.2 154.3 34 504.9 173.8 94 561.6 193.4 55 335. 7 115.6 15 392.4 135.1 75 449.1 154.6 35 505.8 174.2 95 562.6 193.7 56 336.6 115.9 16 393.3 135.4 76 450.1 155. 36 506.8 174.5 96 563.5 194.0 57 337.5 116.2 17 394. 3 135.7 77 451.0 155.3 37 507.7 174.8 97 564.5 194.3 58 338. 5 116.5 18 395.2 136.1 78 452.0 155.6 38 508.7 175.1 98 565.4 194.7 59 339.4 116.9 19 396.2 136.4 79 452.9 155.9 39 509.6 175. 5 99 566.4 195.0 60 340.4 117.2 20 397.1 136.7 80 453.8 156.3 40 510.6 175.8 600 567.3 195.3 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 71° (109°, 251°, 289° )• Page 670] TABLE 2. Difference of Latitude and Departure for 20° (160°, 200 °, 340° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.3 61 57.3 20.9 121 113.7 41.4 181 170.1 61.9 241 226.5 82.4 2 1.9 0.7 62 58.3 21.2 22 114.6 41.7 82 171.0 62.2 42 227.4 82.8 3 2.8 1.0 63 59.2 21.5 23 115.6 42.1 83 172.0 62.6 43 228.3 83.1 4 3.8 1.4 64 60.1 21.9 24 116.5 42.4 84 172.9 62.9 44 229.3 83.5 5 4.7 1.7 65 61.1 22.2 25 117.5 42.8 85 173.8 63.3 45 230.2 83.8 6 5.6 2.1 66 62.0 22.6 26 118.4 43.1 86 174.8 63.6 46 231.2 84.1 7 6.6 2.4 67 63.0 22.9 27 119.3 43.4 87 175.7 64.0 47 232.1 84.5 8 7.5 2.7 68 63.9 23.3 28 120.3 43.8 88 176.7 64.3 48 233.0 84.8 9 8.5 3.1 69 64.8 23.6 29 , 121.2 44.1 89 177.6 64.6 49 234.0 85.2 10 9.4 3.4 70 65.8 23.9 30 122.2 44.5 90 178.5 65.0 50 234.9 235. 9 85.5 11 10.3 3.8 71 66.7 24.3 131 123.1 44.8 191 179.5 65.3 251 85.8 12 11.3 4.1 72 67.7 24.6 32 124.0 45.1 92 180.4 65.7 52 236.8 86.2 13 12.2 4.4 73 68.6 25.0 33 125.0 45.5 93 181.4 66.0 53 237.7 86.5 14 13.2 4.8 74 69.5 25.3 34 125.9 45.8 94 182.3 66.4 54 238.7 86.9 15 14.1 5.1 75 70.5 25.7 35 126.9 46.2 95 183.2 66.7 55 239.6 87.2 16 15.0 5.5 76 71.4 26.0 36 127.8 46.5 96 184.2 67.0 56 240.6 87.6 17 16.0 5.8 77 72.4 26.3 37 128.7 46.9 97 185.1 67.4 57 241.5 87.9 18 16.9 6.2 78 73.3 26.7 38 129.7 47.2 98 186.1 67.7 58 242.4 88.2 19 17.9 6.5 79 74.2 27.0 39 130.6 47.5 99 187.0 68.1 59 243.4 88.6 20 18.8 6.8 80 81 75.2 27.4 40 131.6 47.9 200 187.9 68.4 60 244.3 88.9 21 19.7 7.2 76.1 27.7 141 132.5 48.2 201 188.9 68.7 261 245.3 89.3 22 20.7 7.5 82 77.1 28.0 42 133.4 48.6 02 189.8 69.1 62 246.2 89.6 23 21.6 7.9 83 78.0 28.4 43 134.4 48.9 03 190.8 69.4 63 247.1 90.0 24 22.6 8.2 84 78.9 28.7 44 135.3 49.3 04 191.7 69.8 64 248.1 90.3 25 23.5 8.6 85 79.9 29.1 45 136.3 49.6 05 192.6 70.1 65 249.0 90.6 26 24.4 8.9 86 80.8 29.4 46 137. 2 49.9 06 193.6 70.5 66 250.0 91.0 27 25.4 9.2 87 81.8 29.8 47 138.1 50.3 07 194.5 70.8 67 250.9 91.3 28 26.3 9.6 88 82.7 30.1 48 139.1 50.6 08 195.5 71.1 68 251.8 91.7 29 27.3 9.9 89 83.6 30.4 49 140.0 51.0 09 196.4 71.5 69 252.8 92.0 30 28.2 10.3 90 84.6 30.8 50 140.9 51.3 10 197.3 71.8 70 253. 7 254.7 92.3 31 29.1 10.6 91 85.5 31.1 151 141.9 51.6 211 198.3 72.2 271 92.7 32 30.1 10.9 92 86.5 31.5 52 142.8 52.0 12 199.2 72.5 72 255.6 93.0 33 31.0 11.3 93 87.4 31.8 53 143.8 52.3 13 200.2 72.9 73 256.5 93.4 34 31.9 11.6 94 88.3 32.1 54 144.7 52.7 14 201.1 73.2 74 257.5 93.7 35 32.9 12.0 95 89.3 32.5 55 145.7 53.0 15 202.0 73.5 75 258.4 94.1 36 33.8 12.3 96 90.2 32.8 56 146.6 53.4 16 203.0 73.9 76 259.4 94.4 37 34.8 12.7 97 91.2 33.2 57 147.5 53.7 17 203.9 74.2 77 260.3 94.7 38 35.7 13.0 98 92.1 33.5 58 148.5 54.0 18 204.9 74.6 78 261.2 95.1 39 36.6 13.3 99 93.0 33.9 59 149.4 54.4 19 205. 8 74.9 79 262.2 95.4 40 37.6 13.7 100 94.0 34.2 60 150.4 151.3 54.7 20 206.7 75.2 80 281 263.1 95.8 41 38.5 14.0 101 94.9 34.5 161 55.1 221 207.7 75.6 264.1 96.1 42 39.5 14.4 02 95.8 34.9 62 152.2 55.4 22 208.6 75.9 82 265.0 96.4 43 40.4 14.7 03 96.8 35.2 63 153.2 55.7 23 209.6 76.3 83 265.9 96.8 44 41.3 15.0 04 97.7 35.6 64 154.1 56.1 24 210.5 76.6 84 266.9 97.1 45 42.3 15.4 05 98.7 35.9 65 155.0 56.4 25 211.4 77.0 85 267.8 97.5 46 43.2 15.7 06 99.6 36.3 66 156.0 56.8 26 212.4 77.3 86 268.8 97.8 47 44.2 16.1 07 100.5 36.6 67 156.9 57.1 27 213.3 77.6 87 269.7 98.2 48 45.1 16.4 08 101.5 36.9 68 157.9 57.5 28 214.2 78.0 88 270.6 98.5 49 46.0 16.8 09 102.4 37.3 69 158.8 57.8 29 215.2 78.3 89 271.6 98.8 50 47.0 17.1 10 103.4 37.6 70 159.7 58.1 30 216.1 78.7 90 272.5 99.2 99.5 51 47.9 17.4 111 104.3 38.0 171 160.7 58.5 231 217.1 79.0 291 273.5 52 48.9 17.8 12 105.2 38.3 72 161.6 58.8 32 218.0 79.3 92 274.4 99.9 53 49.8 18.1 13 106.2 38.6 73 162.6 59.2 33 218.9 79.7 93 275.3 100.2 54 50.7 18.5 14 107.1 39.0 74 163.5 59.5 34 219.9 80.0 94 276.3 100.6 55 51.7 18.8 15 108.1 39.3 75 164.4 59.9 35 220.8 80.4 95 277.2 100.9 56 52.6 19.2 16 109.0 39.7 76 165.4 60.2 36 221.8 80.7 96 278.1 101.2 57 53.6 19.5 17 109.9 40.0 77 166.3 60.5 37 222.7 81.1 97 279.1 101.6 58 54.5 19.8 18 110.9 40.4 78 167.3 60.9 38 223.6 81.4 98 280.0 101.9 59 55.4 20.2 19 111.8 40.7 79 168.2 61.2 39 224.6 81.7 99 281.0 102.3 60 56.4 20.5 20 112.8 41.0 80 169.1 61.6 40 225.5 82.1 300 281.9 102.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. '0° (110°, 250 °, 290° ). TABLE 2. [Page 571 Difference of Latitude and Depart are for 20° (160°, 200°, 340 ')• Dlst. Lat. Dep. Dist. Lat. Dep. Dlst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 282.9 103.0 361 339.2 123.5 421 395.6 144.0 481 452.0 164.5 541 508.4 185.0 02 283.8 103. 3 62 340. 2 123.8 22 396.6 144.3 82 453.0 164.8 42 509.3 185.4 03 284.7 103. 6 63 341.1 124.2 23 397.5 144.7 83 453.9 165.2 43 510.3 185.7 04 285. 7 104.0 64 342.1 124.5 24 398.4 145.0 84 454.8 165.5 44 511.2 186.0 05 286.6 104.3 65 343.0 124.8 25 399.4 145.4 85 455.8 165.9 45 512.1 186.4 06 287.6 104.7 66 343.9 125.2 26 400.3 145.7 86 456.7 166.3 46 513.1 186.8 07 288.5 105.0 67 344.9 125.5 27 401.3 146.1 87 457.7 166.6 47 514.0 187.1 08 289.4 105.4 68 345.8 125.9 28 402.2 146.4 88 458.6 166.9 48 515.0 187.4 09 290.4 105.7 69 346.8 126.2 29 403.1 146.7 89 459.5 167. 3 49 515.9 187.8 10 291.3 106.0 70 347.7 126.6 30 404.1 147.1 90 460.5 167.7 50 516.8 188.2 311 292.3 106.4 371 348.6 126.9 431 405.0 147.4 491 461.4 168.0 551 517.8 188.5 12 293.2 106.7 72 349.6 127. 2. 32 406.0 147.8 92 462.4 168.3 52 518.7 188.8 13 294.1 107.1 73 350.5 127.6 33 406.9 148.1 93 463.3 168.6 53 519.7 189.1 14 295.1 107.4 74 351.5 127.9 34 407.8 148.4 94 464.2 168.9 54 520.6 189.4 15 296.0 107.7 75 352.4 128.3 35 408.8 148.8 95 465.2 169.3 55 521.5 189.8 16 297.0 108.1 76 353. 3 128.6 36 409.7 149.1 96 466.1 169.6 56 522.5 190.2 17 297.9 108.4 77 354. 3 129.0 37 410.7 149.5 97 467.0 170.0 57 523.4 190.5 18 298.8 108.8 7^ 355.2 129.3 38 411.6 149.8 98 468.0 170.3 58 524.4 190.8 19 299.8 109.1 79 356. 2 129.6 39 412.5 150.2 99 468.9 170.7 59 525.3 191.2 20 321 300.7 109.5 80 357.1 130.0 40 413.5 150.5 500 469.9 171.0 171.3 60 .561 526.2 191.6 301.6 109.8 381 358.0 130.3 441 414.4 150.8 501 470.8 527.2 191.9 22 302.6 110.1 82 359. 130.7 42 415.4 151.2 02 471.7 171.7 62 528.1 192.2 23 303.5 110.5 83 359.9 131.0 43 416.3 151.5 03 472.7 172.0 63 529.0 192.0 24 304.5 110.8 84 360.8 131.3 44 417.2 151.9 04 473.6 172.4 64 530.0 192.9 25 305.4 111.2 85 361.8 131.7 45 418.2 152.2 05 474.5 172.7 65 530.9 193.2 26 306.3 111.5 86 362.7 132.0 46 419.1 152.5 06 475.4 173.0 66 531.8 193.6 27 307.3 111.8 87 363.7 132.4 47 420.0 152.9 07 476.4 173.4 67 532.8 193.9 28 308.2 112.2 88 364.6 132.7 48 421.0 153.2 08 477.3 173.7 68 533.7 194.2 29 309.2 112.5 89 365.5 133.1 49 421.9 153.6 09 478.3 174.1 69 534.7 194.6 30 310.1 112.9 90 366.5 133.4 50 422.9 153.9 10 479.2 174.4 70 535.6 195.0 331 311.0 113.2 391 367.4 133.7 451 423.8 154.3 511 480.2 174.8 571 536. 6 195.3 32 312.0 113.6 92 368.4 134.1 52 424.7 154.6 12 481.1 175.1 72 537.5 195,6 33 312.9 113.9 93 369. 3 134.4 53 425.7 154.9 13 482.1 175.4 73 538.5 195.9 34 313.9 114.2 94 370.2 134.8 54 426.6 155.3 14 483.0 175.8 74 539.4 196.3 35 314.8 114.6 95 371.2 135.1 55 427.6 155.6 15 484.0 176.1 75 540. 3 196.6 36 315.7 114.9 96 372.1 135.4 56 428.5 156.0 16 484.9 176.5 76 541.3 197.0 37 316.7 115.3 97 373.1 135.8 57 429.4 156.3 17 485. 8 176.8 77 542.2 197.3 38 317.6 115.6 98 374.0 136.1 58 430.4 156.7 18 486.8 177.2 78 543.2 197.7 39 318.6 116.0 99 374.9 136.5 59 431.3 157.0 19 487.7 177.5 79 544.1 198.0 40 341 319.5 116.3 400 375.9 136.8 60 432. 3 157.4 20 488.7 177.9 80 545.0 198.4 320.4 116.6 401 376.8 137.2 461 433.2 157.7 521 489.6 178.2 581 546.0 198.7 42 321.4 117.0 02 377.8 137.5 62 434.1 158.0 22 490.5 178.5 82 546.9 199.0 43 322. 3 117.3 03 378.7 137.8 63 435.1 158.4 23 491.5 178.9 83 547.9 199.4 44 323.3 117.7 04 379.6 138.2 64 436.0 158.7 24 492.4 179.2 84 548.8 199.8 45 324.2 118.0 05 380.6 138.5 65 437.0 159.0 25 493.4 179.6 85 549.8 200.1 46 325.1 118.4 06 381.5 138.9 66 437.9 159.4 26 494.3 179.9 86 550.7 200.4 47 326. 1 118.7 07 382.5 139.2 67 438. 8 159.7 27 495.3 180.2 87 551.7 200.8 48 327.0 119.0 08 383.4 139.6 68 439.8 160.1 28 496.2 180.6 88 552. 6 201.2 49 328. 119.4 09 384. 3 139.9 69 440.7 160.4 29 497.1 181.0 89 553.5 201.5 50 328. 9 119.7 10 385.3 140.2 70 441.7 160.8 30 498.1 181.3 90 554.4 201.8 351 329. 8 120.1 411 386.2 140.6 471 442.6 161.1 531 499.0 181.6 591 555. 4 202.1 52 1 330.8 120.4 12 387.2 140. 9 72 443.5 161.4 32 499.9 181.9 92 556.3 202.4 53 1 331.7 120.7 13 388.1 141.3 73 444.5 161.8 33 500.9 182.3 93 557.3 202.8 54 j 332. 7 121.1 14 389.0 141.6 74 445.4 162.1 34 501.8 182.6 94 558.2 203.2 55 333.6 121.4 15 390.0 141.9 75 446.4 162.5 35 502.7 183.0 95 559. 1 203.5 56 334.5 121.8 16 390.9 142.3 76 447.3 162.8 36 503.7 183.3 96 560.0 203.8 57 335.5 122.1 17 391.9 142.6 77 448.2 163.2 37 504.6 183.7 97 561.0 204.2 58 336. 4 122.5 18 392.8 143.0 78 449.2 163.5 38 505.5 184.0 98 561.9 204.6 59 337.4 122.8 19 393.7 143.3 79 450.1 163.8 39 506.5 184.3 99 562.9 204.9 60 338.3 123.1 20 394.7 143.7 80 451.1 164.2 40 507.4 184.7 600 563.8 205.2 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dlst. Dep. Lat. 70° (1 10°, 25C »°, 290' ). Page 572] TABLE 2. Difference of Latitude and Departure for 21° (159°, 201 °, 339°). Diet 1 Lat. Dep. Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 0.9 0.4 61 56.9 21.9 121 113.0 43.4 181 169.0 64.9 241 225.0 86.4 2 1.9 0.7 62 57.9 22.2 22 113.9 43.7 82 169.9 65.2 42 225.9 86.7 3 2.8 1.1 63 58.8 22.6 23 114.8 44.1 83 170.8 65.6 43 226.9 87.1 4 3.7 1.4 64 59.7 22.9 24 115.8 44.4 84 171.8 65.9 44 227.8 87.4 5 4.7 1.8 65 60.7 23.3 25 116.7 44.8 85 172.7 66.3 45 228.7 87.8 6 5.6 2.2 66 61.6 23.7 26 117.6 45.2 86 173.6 66.7 46 229.7 88.2 7 6.5 2.5 67 62.5 24.0 27 118.6 45.5 87 174.6 67.0 47 230.6 88.5 8 7.5 2.9 68 63.5 24.4 28 119.5 45.9 88 175.5 67.4 48 231.5 88.9 9 8.4 3.2 69 64.4 24.7 29 120.4 46.2 89 176.4 67.7 49 232.5 89.2 10 9.3 3.6 70 65.4 25.1 30 121.4 46.6 90 177.4 68.1 50 233.4 89.6 11 10.3 3.9 71 66.3 25.4 131 122.3 46.9 191 178.3 68.4 251 234.3 90.0 12 11.2 4.3 72 67.2 25.8 32 123.2 47.3 92 179.2 68.8 52 235.3 90.3 13 12.1 4.7 73 68.2 26.2 33 124.2 47.7 93 180.2 69.2 53 236.2 90.7 14 13.1 5.0 74 69.1 26.5 34 125.1 48.0 94 181.1 69.5 54 237.1 91.0 15 14.0 5.4 75 70.0 26.9 35 126.0 48.4 95 182.0 69.9 55 238.1 91.4 16 14.9 5.7 76 71.0 27.2 36 127.0 48.7 96 183.0 70.2 56 239.0 91.7 17 15.9 6.1 77 71.9 27.6 37 127.9 49.1 97 183.9 70.6 57 239.9 92.1 18 16.8 6.5 78 72.8 28.0 38 128.8 49.5 98 184.8 71^0 58 240.9 92.5 19 17.7 6.8 79 73.8 28.3 39 129.8 49.8 99 185.8 71.3 59 241.8 92.8 20 18.7 7.2 80 74.7 28.7 40 130.7 50.2 200 186.7 71.7 60 242.7 93.2 21 19.6 7.5 81 75.6 29.0 141 131.6 50.5 201 187.6 72.0 261 243.7 93.5 22 20.5 7.9 82 76.6 29.4 42 132.6 50.9 02 188.6 72.4 62 244.6 93.9 23 21.5 8.2 83 77.5 29.7 43 133.5 51.2 03 189.5 72.7 63 245.5 94.3 24 22.4 8.6 84 78.4 30.1 44 134.4 51.6 04 190.5 73.1 64 246.5 94.6 25 23.3 9.0 85 79.4 30.5 45 135.4 52.0 05 191.4 73.6 65 247.4 95.0 26 24.3 9.3 86 80.3 30.8 46 136.3 52.3 06 192.3 73.8 66 248.3 95.3 27 25.2 9.7 87 81.2 31.2 47 137.2 52.7 07 193.3 74.2 67 249.3 95.7 28 26.1 10.0 88 82.2 31.5 48 138.2 53.0 08 194.2 74.5 68 250.2 96.0 29 27.1 10.4 89 83.1 31.9 49 139.1 53.4 09 195.1 74.9 69 251.1 96.4 30 28.0 10.8 11.1 90 84.0 32.3 50 140.0 53.8 10 196.1 75.3 75.6 70 252.1 258.0 96.8 31 28.9 91 85.0 32.6 151 141.0 54.1 211 197.0 271 97.1 32 29.9 11.5 92 85.9 33.0 52 141.9 54.5 12 197.9 76.0 72 253.9 97.5 33 30.8 11.8 93 86.8 33.3 53 142.8 54.8 13 198.9 76.3 73 254.9 97.8 34 31.7 12.2 94 87.8 33.7 54 143.8 55.2 14 199.8 76.7 74 255.8 98.2 35 32.7 12.5 95 88.7 34.0 55 144.7 55.5 15 200.7 77.0 75 256.7 98.6 36 33.6 12.9 96 89.6 34.4 56 145.6 55.9 16 201.7 77.4 76 257.7 98.9 37 34.5 13.3 97 90.6 34.8 57 146.6 56.3 17 202.6 77.8 77 258.6 99.3 38 35.5 13.6 98 91.5 35.1 58 147.5 56.6 18 203.5 78.1 78 259. 5 99.6 39 36.4 14.0 99 92.4 35.5 59 148.4 57.0 19 204.5 78.5 79 260.5 100.0 40 37.3 14.3 100 93.4 35.8 60 149.4 57.3 20 205.4 78.8 80 261.4 100.3 41 38.3 14.7 101 94.3 36.2 161 150.3 57.7 221 206.3 79.2 281 262.3 100.7 42 39.2 15.1 02 95.2 36.6 62 151.2 58.1 22 207.3 79.6 82 263.3 101.1 43 40.1 15.4 03 96.2 36.9 63 152.2 58.4 23 208.2 79.9 83 264.2 101.4 44 41.1 15.8 04 97.1 37.3 64 153.1 58.8 24 209.1 80.3 84 265.1 101.8 45 42.0 16.1 05 98.0 37.6 65 154.0 59.1 25 210.1 80.6 85 266.1 102.1 46 42.9 16.5 06 99.0 38.0 66 155.0 59.5 26 211.0 81.0 86 267.0 102.5 47 43.9 16.8 07 99.9 38.3 67 155.9 59.8 27 211.9 81.3 87 267.9 102.9 48 44.8 17.2 08 100.8 38.7 68 156.8 60.2 28 212.9 81.7 88 268.9 103.2 49 45.7 17.6 09 101.8 39.1 69 157.8 60.6 29 213.8 82.1 89 269.8 103.6 50 46.7 17.9 10 102.7 39.4 70 158.7 60.9 30 214.7 82.4 90 270.7 103.9 51 47.6 18.3 111 103.6 39.8 171 159.6 61.3 231 215.7 82.8 291 271.7 104.3 52 48.5 18.6 12 104.6 40.1 72 160.6 61.6 32 216.6 83.1 92 272.6 104.6 53 49.5 19.0 13 105.5 40.5 73 161.5 62.0 33 217.5 83.5 93 273.5 105.0 54 50.4 19.4 14 106.4 40.9 74 162.4 62.4 34 218.5 83.9 94 274.5 105.4 55 51.3 19.7 15 107.4 41.2 75 163.4 62.7 35 219.4 84.2 95 275.4 105.7 56 52.3 20.1 16 108.3 41.6 76 164.3 63.1 36 220.3 84.6 96 276.3 106.1 57 53.2 20.4 17 109.2 41.9 77 165.2 63.4 37 221.3 84.9 97 277. 3 106.4 58 54.1 20.8 18 110.2 42.3 78 166.2 63.8 38 222.2 85.3 98 278.2 106.8 59 55.1 21.1 19 111.1 42.6 79 167.1 64.1 39 233.1 85.6 99 279.1 107.2 60 56.0 21.5 20 112.0 43.0 80 168.0 64.5 40 224.1 86.0 300 280.1 107.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 69° ( 111°, 249°, 291 °)- TABLE 2. [Page 673 Difference of Latitude and Departure for 21° (159°, 201°, 339 '). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 281.0 107.9 361 337.0 129.4 421 393.0 150.9 481 449.0 172.4 541 505.1 193.9 02 281.9 108.2 62 337.9 129.7 22 394.0 151.2 82 450.0 172.7 42 506.0 194.2 03 282.9 108.6 63 338.9 130.1 23 394.9 151.6 83 450.9 173.1 43 507.0 194.6 04 283.8 108.9 64 339.8 130.4 24 395.8 152.0 84 451.8 173.5 44 507.9 195.0 05 284.7 109.3 65 340.7 130.8 25 396.8 152.3 85 452.8 173.8 45 508.8 195.3 06 285.7 109.7 66 341.7 131.2 26 397.7 152.7 86 453.7 174.2 46 509.8 195.7 07 286.6 110.0 67 342.6 131.5 27 398.6 153.0 87 454.6 174.5 47 510.7 196.0 08 287.5 110.4 68 343. 5 131.9 28 399.6 153.4 88 455.6 174.9 48 511.6 196.4 09 288.5 110.7 79 344.5 132.2 29 400.5 153.7 89 456.5 175.2 49 512.6 196.8 10 289.4 290.3 111.1 111.5 70 345.4 132.6 30 401.4 154.1 90 457.4 175.6 50 551 513.5 514.4 197.1 311 371 346.3 133. 431 402.4 154.5 491 458.4 176.0 197.5 12 291.3 111.8 72 347.3 133.3 32 403.3 154.8 92 459.3 176.3 52 515.4 197.8 13 292.2 112.2 73 348.2 133.7 33 404.2 155.2 93 460.2 176.7 53 516.3 198.2 14 293.1 112.5 74 349.1 134.0 34 405.2 155. 5 94 461.2 177.0 54 517.2 198.6 15 294.1 112.9 75 350.1 134.4 35 406.1 155.9 95 462.1 177.4 55 518.2 198.9 16 295.0 113.2 76 351.0 134.7 36 407.0 156.3 96 463.0 177.8 56 519.1 199.3 17 295.9 113.6 77 351.9 135.1 37 408.0 156.6 97 464.0 178.1 57 520.0 199.6 18 296.9 114.0 78 352.9 135.5 38 408.9 157.0 98 464.9 178.5 58 521.0 200.0 19 297.8 114.3 79 353.8 135.8 39 409.8 157.3 99 465.8 178.8 59 521.9 200.3 20 298.7 299.7 114.7 80 354.7 136.2 40 410.8 157.7 500 466.8 179.2 60 522.8 200.7 321 115.0 381 355.7 136. 5 441 411.7 158.0 501 467.7 179.5 561 523.8 201.0 22 300.6 115.4 82 356.6 136.9 42 412.6 158.4 02 468.6 179.9 62 524.7 201.4 23 301.5 115.8 83 357. 5 137.3 43 413.6 158.8 03 469.6 180.3 63 525.6 201.8 24 302.5 116.1 84 358.5 137.6 44 414.5 159.1 04 470.5 180.6 64 526.6 202.1 25 303.4 116.5 85 359.4 138.0 45 415.4 159.5 05 471.5 181.0 65 527.5 202.5 26 304.3 116.8 86 360.3 138.3 46 416.4 159.8 06 472.4 181.3 66 528.4 202.8 27 305.3 117.2 87 361.3 138.7 47 417.3 160.2 07 473.3 181.7 67 529.4 203.2 28 306.2 117.5 88 362.2 139. 1 48 418.2 160.5 08 474.3 182.0 68 530.3 203.5 29 307.1 117.9 89 363.1 139.4 49 419.2 16*0. 9 09 475.2 182.4 69 531.2 203.9 30 331 308.1 118.3 90 364.1 139. 8 50 420.1 161.3 10 476.1 182.8 70 532.2 204.3 309.0 118.6 391 365.0 "140. 1 451 421.0 161.6 511 477.1 183.1 571 533.1 204.6 32 309.9 119.0 92 365.9 140.5 52 422.0 162.0 12 478.0 183.5 72 534.0 205.0 33 310.9 119.3 93 366.9 140.8 53 422.9 162.3 13 478.9 183.8 73 535.0 205. 4 34 311.8 119.7 94 367.8 141.2 54 423.8 162.7 14 479.9 184.2 74 535.9 205.7 35 312.7 120.1 95 368.7 141.6 55 424.8 163.1 15 480.8 184.6 75 536.8 206.1 36 313.7 120.4 96 369.7 141.9 56 425.7 163.4 16 481.7 184.9 76 537.8 206.4 37 314.6 120.8 97 370.6 142.3 57 426.6 163.8 17 482.7 185.3 77 538.7 206.8 38 315.5 121.1 98 371.5 142.6 58 427.6 164.1 18 483.6 185.6 78 539.6 207.1 39 316.5 121.5 99 372.5 143.0 59 428.5 164.5 19 484.5 186.0 79 540.6 207.5 40 317.4 121.8 400 373.4 143.4 60 429.4 164.9 20 485.5 186.4 80 541.5 207.9 341 318.3 122.2 401 374.3 143.7 461 430.4 165.2 521 486.4 186.7 581 542.4 208.2 42 319.3 122.6 02 375.3 144.1 62 431.3 165.6 22 487.3 187.1 82 543.4 208.6 43 320.2 122.9 03 376.2 144.4 63 432.2 165.9 23 488.3 187.4 83 544.3 208.9 44 321.1 123.2 04 377.1 144.8 64 433.2 166.3 24 489.2 187.8 84 545.2 209.3 45 322.1 123.6 05 378.1 145.1 65 434.1 166.6 25 490.1 188.1 85 546.2 209.6 46 323.0 124.0 06 379.0 145.5 66 435.0 167.0 26 491.1 188.5 86 547.1 210.0 47 323.9 124.4 07 379.9 145.9 67 436.0 167.4 27 492.0 188.9 87 548.0 210.4 48 324.9 124.7 08 380.9 146.2 68 436.9 167.7 28 492.9 189.2 88 549.0 210.7 49 325.8 125.1 09 381.8 146.6 69 437.8 168.1 29 493.9 189.6 89 549.9 211.1 50 326.7 125.4 10 382.7 146.9 70 438.8 168.4 30 494.8 189.9 90 550.8 211.4 351 327.7 125.8 411 383.7 147.3 471 439.7 168.8 531 495.7 190.3 591 551.8 211.8 52 328.6 126.1 12 384.6 147.7 72 440.6 169.2 32 496.7 190.7 92 552. 7 212.2 53 329.5 126.5 13 385.5 148.0 73 441.6 169.5 33 497.6 191.0 93 553.6 212.5 54 330.5 126.9 14 386.5 148.4 74 442.5 169.9 34 498.5 191.4 94 554.6 212.9 55 331.4 127.2 15 387.4 148.7 75 443.4 170.2 35 499.5 191.7 95 555.5 213.2 56 332.3 127.6 16 388.4 149.1 76 444.4 170.6 36 500.4 192.1 96 556.4 213.6 57 333.3 127.9 17 389.3 149.4 77 445.3 170.9 37 501.3 192.4 97 557.4 213.9 58 334.2 128.3 18 390.2 149.8 78 446.2 171.3 38 502.3 192.8 98 558.2 214.3 59 335.1 128.7 19 391.2 150.2 79 447.2 171.7 39 503.2 193.2 99 559.2 214.7 60 336.1 129.0 20 392.1 150.5 80 448.1 172.0 40 504.1 193.5 600 560.1 215.0 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. t 59° (1 11°, 249°, 291° )• 1 Page 674] TABLE 2. Difference of Latitude and Departure for 22° (158°, 202, 338°; . Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 56.6 22.9 121 112.2 45.3 181 167.8 67.8 241 223.5 90.3 2 1.9 0.7 62 57.5 23.2 22 113.1 45.7 82 168. 7 68.2 42 224.4 90.7 3 2.8 1.1 63 58.4 23.6 23 114.0 46.1 83 169.7 68.6 43 225.3 91.0 4 3.7 1.5 64 59.3 24.0 24 115.0 46.5 84 170.6 68.9 44 226.2 91.4 5 4.6 1.9 65 60.3 24.3 25 115.9 46.- 8 85 171.5 69.3 45 227.2 91.8 6 5.6 2.2 66 61.2 24.7 26 116.8 47.2 86 172.5 69.7 46 228.1 92.2 7 6.5 2.6 67 62.1 25.1 27 117.8 47.6 87 173.4 70.1 47 229.0 92.5 8 7.4 3.0 68 63.0 25.5 28 118.7 47.9 88 174.3 70.4 48 229.9 92.9 9 8.3 3.4 69 64.0 25.8 29 119.6 48.3 89 175.2 70.8 49 230.9 93.3 10 9.3 3.7 70 64.9 26.2 30 120.5 48.7 90 176.2 71.2 50 231.8 93.7 11 10.2 4.1 71 65.8 26.6 131 121.5 49.1 191 177.1 71.5 251 232.7 94.0 12 11.1 4.5 72 66.8 27.0 32 122.4 49.4 92 178.0 71.9 52 233.7 94.4 13 12.1 4.9 73 67.7 27.3 33 123.3 49.8 93 178.9 72.3 53 234.6 94.8 14 13.0 5.2 74 68.6 27.7 34 124.2 50.2 94 179.9 72.7 54 2.35. 5 95.2 15 13.9 5.6 75 69.5 28.1 35 125.2 50.6 95 180.8 73.0 55 236.4 95.5 16 14.8 6.0 76 70.5 28.5 36 126.1 50.9 96 181.7 73.4 56 237.4 95.9 17 15.8 6.4 77 71.4 28.8 37 127.0 51.3 97 182.7 73.8 57 238.3 96.3 18 16.7 6.7 78 72.3 29.2 38 128.0 51.7 98 183.6 74.2 58 239.2 96.6 19 17.6 7.1 79 73.2 29.6 39 128.9 52.1 99 184.5 74.5 59 240.1 97.0 20 18.5 7.5 80 74.2 30.0 40 129.8 130.7 52.4 200 185.4 74.9 60 241.1 97.4 21 19.5 7.9 81 75.1 30.3 141 52.8 201 186.4 75.3 261 242.0 97.8 22 20.4 8.2 82 76.0 30.7 42 131.7 53.2 02 187.3 75.7 62 242.9 98.1 23 21.3 8.6 83 77.0 31.1 43 132.6 53.6 03 188.2 76.0 63 243.8 98.5 24 22.3 9.0 84 77.9 31.5 44 133.5 53.9 04 189.1 76.4 64 244.8 98.9 25 23.2 9.4 85 78.8 31.8 45 134.4 54.3 05 190.1 76.8 65 245.7 99.3 26 24.1 9.7 86 79.7 32.2 46 135.4 54.7 06 191.0 77.2 66 246.6 99.6 27 25.0 10.1 87 80.7 32.6 47 136.3 55.1 07 191.9 77.5 67 247.6 100.0 28 26.0 10.5 88 81.6 33.0 48 137.2 55.4 08 192.9 77.9 68 248.5 100.4 29 26.9 10.9 89 82.5 33.3 49 138.2 55.8 09 193.8 78.3 69 249.4 100.8 30 27.8 11.2 90 83.4 33.7 50 139.1 56.2 10 194.7 78.7 70 250.3 251.3 101.1 31 28.7 11.6 91 84.4 34.1 151 140.0 56.6 211 195.6 79.0 271 101.5 32 29.7 12.0 92 85.3 34.5 52 140.9 56.9 12 196.6 79.4 72 252.2 101.9 33 30.6 12.4 93 86.2 34.8 53 141.9 57.3 13 197.5 79.8 73 253.1 102.3 34 31.5 12.7 94 87.2 35.2 54 142.8 57.7 14 198.4 80.2 74 254.0 102.6 35 32.5 13.1 95 88.1 35.6 55 143.7 58.1 15 199.3 80.5 75 255.0 103.0 36 33.4 13.5 96 89.0 36.0 56 144.6 58.4 16 200.3 80.9 76 255.9 103.4 37 34.3 13.9 97 89.9 36.3 57 145.6 58.8 17 201.2 81.3 77 256.8 103.8 38 35.2 14.2 98 90.9 36.7 58 146.5 59.2 18 202.1 81.7 78 257.8 104.1 39 36.2 14.6 99 91.8 37.1 59 147.4 59.6 19 203.1 82.0 79 258.7 104.5 40 41 37.1 15.0 100 92.7 37.5 60 148.3 59.9 60.3 20 204.0 82.4 80 259.6 260.5 104.9 38.0 15.4 101 93.6 37.8 161 149.3 221 204.9 82.8 281 105.3 42 38.9 15.7 02 94.6 38.2 62 150.2 60.7 22 205.8 83.2 82 261.5 105.6 43 39.9 16.1 03 95.5 38.6 63 151.1 61.1 23 206.8 83.5 83 262.4 106.0 44 40.8 16.5 04 96.4 39.0 64 152. 1 61.4 24 207.7 83.9 84 263.3 106.4 45 41.7 16.9 05 97.4 39.3 65 153.0 61.8 25 208.6 84.3 85 264.2 106.8 46 42.7 17.2 06 98.3 39.7 66 153.9 62.2 26 209.5 84.7 86 265.2 107.1 47 43.6 17.6 07 99.2 40.1 67 154.8 62.6 27 210.5 85.0 87 266.1 107.5 48 44.5 18.0 08 100.1 40.5 68 155.8 62.9 28 211.4 85.4 88 267.0 107.9 49 45.4 18.4 09 101.1 40.8 69 156.7 63.3 29 212.3 85.8 89 268.0 108.3 50 51 46.4 47.3 18.7 10 102.0 102.9 41.2 70 157.6 63.7 30 213.3 214.2 86.2 90 268.9 269.8 108.6 19.1 111 41.6 171 158.5 64.1 231 86.5 291 109.0 52 48.2 19.5 12 103.8 42.0 72 159.5 64.4 32 215.1 86.9 92 270.7 109.4 53 49.1 19.9 13 104.8 42.3 73 160.4 64.8 33 216.0 87.3 93 271.7 109.8 54 50.1 20.2 14 105.7 42.7 74 161.8 65.2 34 217.0 87.7 94 272.6 110.1 55 51.0 20.6 15 106.6 43.1 75 162.3 65.6 35 217.9 88.0 95 273.5 110.5 56 51.9 21.0 16 107.6 43.5 76 163.2 65.9 36 218.8 88.4 96 274.4 110.9 57 52.8 21.4 17 108.5 43.8 77 164.1 66.3 37 219.7 88.8 97 275.4 111.3 58 53.8 21.7 18 109.4 44.2 78 165.0 66.7 38 220.7 89.2 98 276.3 111.6 59 54.7 22.1 19 110.3 44.6 79 166.0 67.1 39 221.6 89.5 99 277.2 112.0 60 55.6 22.5 20 111.3 45.0 80 166.9 67.4 40 222.5 89.9 300 278.2 112.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 68° (] L12°, 24{ i°, 292°). TABLE 2. [Page 676 Difference of l^atitude and Departure for 22° (158°, 202°, 338' '). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 279.1 112.7 361 334.7 135.2 421 390.3 157.7 481 446.0 180.2 641 601.6 202.7 02 280.0 113.1 62 335.6 135.6 22 391.3 158.1 82 446.9 180.6 42 602.6 203.1 03 280.9 113.5 63 336.6 136.0 23 392. 2 158.4 83 447.8 180.9 43 503.4 203.5 04 281.9 113.9 64 337.5 136.3 24 393.1 158.8 84 448.8 181.3 44 604.4 203.8 05 282.8 114.2 65 338.4 136.7 25 394.1 159.2 85 449.7 181.7 45 605.3 204.2 06 283.7 114.6 66 339.3 137.1 26 395.0 159.6 86 450.6 182.1 46 506.2 204.6 07 284.6 115.0 67 340.3 137.5 27 395.9 159.9 87 451.6 182.4 47 507.2 205.0 08 285.6 115.4 68 341.2 137.8 28 396.8 160.3 88 452.5 182.8 48 508.1 205.3 09 286.5 115.7 69 342.1 138.2 29 397.8 160.7 89 453.4 183.2 49 509.0 205.7 10 287.4 116.1 70 343.1 138.6 30 398.7 161.1 90 464.3 183.6 50 510.0 206.1 311 288.4 116.5 371 344.0 139.0 431 399.6 161.4 491 465.3 184.0 551 610.9 206.5 12 289.3 116.8 72 344.9 139.3 32 400.5 161.8 92 456.2 184.3 52 511.8 206.8 13 290.2 117.2 73 345. 8 139.7 33 401.5 162.2 93 457.1 184.7 53 512.7 207.2 14 291.1 117.6 74 346.8 140.1 34 402.4 162.6 94 458.0 185.1 54 613.6 207.6 15 292.1 118.0 75 347.7 140.5 35 403.3 162.9 95 459.0 185.4 56 514.6 208.0 16 293.0 118.3 76 348.6 140.8 36 404.3 163.3 96 459.9 185.8 66 516.5 208. 3 17 293.9 118.7 77 349.5 141.2 37 405.2 163.7 97 460.8 186.2 57 616.4 208.7 18 294.8 119.1 78 350.5 141.6 38 406.1 164.1 98 461.8 186.6 68 517.4 209.1 19 295.8 119.5 79 351.4 141.9 39 407.0 164.4 99 462.7 186.9 69 518.3 209.4 20 321 296.7 297.6 119.8 80 352.3 142.3 40 408.0 164.8 500 463.6 187.3 60 519.2 209.8 120.2 381 353.3 142.7 441 408.9 165.2 501 464.6 187.7 661 620.1 210.2 22 298.6 120.6 82 354.2 143.1 42 409.8 166.5 02 466.4 188.0 62 621.0 210.5 23 299.5 121.0 83 355.1 143.4 43 410.7 165.9 03 466.4 188.4 63 522.0 210.9 24 300.4 121.3 84 356.0 143.8 44 411.7 166.3 04 467.3 188.8 64 622.9 211.3 25 301.3 121.7 85 357.0 144.2 45 412.6 166.7 05 468.2 189.2 66 523.8 211.7 26 302.3 122.1 86 357.9 144.6 46 413.5 167.0 06 469.2 189.6 66 524.8 212.0 27 303. 2 122.5 87 358.8 144.9 47 414.5 167.4 07 470.1 189.9 67 526.7 212.4 28 304.1 122.8 88 359.7 145.3 48 415.4 167.8 08 471.0 190.3 68 626.6 212.8 29 305.0 123.2 89 360.7 145.7 49 416.3 168.2 09 471.9 190.7 69 627.5 213.2 30 306.0 123.6 90 361.6 146.1 50 417.2 168.5 10 472.9 191.1 70 628.6 213.5 331 306.9 124.0 391 362.5 146.4 451 418.2 168.9 511 473.8 191.4 671 629.4 213.9 32 307.8 124.3 92 363.5 146.8 52 419.1 169.3 12 474. 7 191.8 72 530.3 214.3 33 308.8 124.7 93 364.4 147.2 53 420.0 169.7 13 475.6 192.2 73 631.2 214.7 34 309.7 125. 1 94 365.3 147.6 54 420.9 170.0 14 476.6 192.6 74 532.2 215.0 35 310.6 125.5 95 366.2 147.9 55 421.9 170.4 15 477.5 192.9 76 633.1 215.4 36 311.5 125. 8 96 367.2 148.3 56 422.8 170.8 16 478.4 193.3 76 534.0 215.8 37 312.5 126.2 97 368.1 148.7 57 423.7 171.2 17 479.3 193.7 77 534.9 216.2 38 313.4 126.6 98 369.0 149.1 58 424.6 171.5 18 480.3 194.0 78 536.9 216.6 39 314.3 127.0 99 369.9 149.4 59 425.6 171.9 19 481.2 194.4 79 636.8 216.9 40 341 315.2 316.2 127.3 400 370.9 149.8 60 426.5 172.3 20 482.1 194.8 195.2 80 537.7 217.3 127.7 401 371.8 150.2 461 427.4 172.7 521 483.0 681 538.6 217.7 42 317.1 128.1 02 372.7 150.6 62 428.4 173.0 22 484.0 195.5 82 539.6 218.0 43 318.0 128.5 03 373.7 150.9 63 429.3 173.4 23 484.9 195.9 83 640.6 218.4 44 319.0 128.8 04 374.6 151.3 64 430.2 173.8 24 485.8 196.3 84 641.4 218.8 45 319.9 129.2 05 375.5 151.7 65 431.1 174.2 25 486.7 196.7 86 642.4 219.2 46 320.8 129.6 06 376.4 152.1 66 432.1 174.5 26 487.7 197.0 86 543.3 219.6 47 321.7 130.0 07 377.4 152.4 67 433.0 174.9 27 488.6 197.4 87 544.2 219.9 48 322.7 130.3 08 378.3 152.8 68 433.9 175.3 28 489.5 197.8 88 646.1 220.3 49 323. 6 130.7 09 379.2 153.2 69 434.8 175.7 29 490.4 198.2 89 546.1 220.7 50 324.5 131.1 10 380.1 153.6 70 435.8 176.0 30 491.4 198.5 90 547.0 221.0 351 325.4 131.5 411 381.1 153.9 471 436.7 176.4 631 492.3 198.9 591 547.9 221.4 52 326.4 131.8 12 382.0 154.3 72 437.6 176.8 32 493.2 199.3 92 548.9 221.8 53 327. 3 132.2 13 382.9 154.7 73 438.6 177.2 33 494.2 199.7 93 549.8 222.2 54 328.2 132.6 14 383.9 155.1 74 439.5 177.5 34 495.1 200.0 94 650.7 222.5 55 329.2 133.0 15 384.8 155.4 75 440.4 177.9 35 496.0 200.4 95 651.7 222.9 56 330.1 133.3 16 385.7 155.8 76 441.3 178.3 36 496.9 200.8 96 552.6 223.3 57 331.0 133.7 17 386.6 156.2 77 442.3 178.7 37 497.9 201.2 97 553.5 223.7 58 332.0 134.1 18 387.6 156.6 78 443.2 179.0 38 498.8 201.6 98 554.4 224.0 59 332.9 134.5 19 388.5 156.9 79 444.1 179.4 39 499.7 201.9 99 655.4 224.4 60 333.8 134.8 20 389.4 157.3 80 445.0 179.8 40 500.7 202.3 600 556.3 224.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. . Lat. 68° (112°, 248°, 292° . Page 676] TABLE 2. Difference of Latitude and Departure for 23° (157°, 203°, 337 °)- Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 56.2 23.8 121 111.4 47.3 181 166.6 70.7 241 221.8 94.2 2 1.8 0.8 62 57.1 24.2 22 112.3 47.7 82 167.5 71.1 42 222.8 94.6 3 2.8 1.2 63 58.0 24.6 23 113.2 48.1 83 168.5 71.5 43 223.7 94.9 4 3.7 1.6 64 58.9 25.0 24 114.1 48.5 84 169.4 71.9 44 224.6 95.3 4.6 2.0 65 59.8 25.4 25 115.1 48.8 85 170.3 72.3 45 225.5 95.7 6 5.5 2.3 66 60.8 25.8 26 116.0 49.2 86 171.2 72.7 46 226.4 96.1 7 6.4 2.7 67 61.7 26.2 27 1 116.9 49.6 87 172.1 73.1 47 227.4 96.5 8 7.4 3.1 68 62.6 26.6 28 117.8 50.0 88 173.1 73.5 48 228.3 96.9 9 8.3 3.5 69 63.5 27.0 29 118.7 50.4 89 174.0 73.8 49 229,2 97.3 10 11 9.2 3.9 70 64.4 27.4 30 119.7 50.8 90 174.9 74.2 50 230.1 97.7 10.1 4.3 71 65.4 27.7 131 120.6 51.2 191 175.8 74.6 251 231.0 98.1 12 11.0 4.7 72 66.3 28.1 32 121.5 51.6 92 176.7 75.0 52 232.0 98.5 13 12.0 5.1 73 67.2 28.5 33 122.4 52.0 93 177.7 75.4 53 232.9 98.9 14 12.9 5.5 74 68.1 28.9 34 123.3 52.4 94 178.6 75.8 54 233.8 99.2 15 13.8 5.9 75 69.0 29.3 35 124.3 52.7 95 179.5 76.2 55 234.7 99.6 16 14.7 6.3 76 70.0 29.7 36 125.2 53.1 96 180.4 76.6 56 235.6 100.0 17 15.6 6.6 77 70.9 30.1 37 126.1 53.5 97 181.3 77.0 57 236.6 100.4 18 16.6 7.0 78 71.8 30.5 38 127.0 53.9 98 182.3 77.4 58 237.5 100.8 19 17.5 7.4 79 72.7 30.9 39 128.0 54.3 99 183.2 77.8 59 238.4 101.2 20 18.4 7.8 80 73.6 31.3 40 128.9 54.7 200 184.1 78.1 60 239.3 101.6 21 19.3 8.2 81 74.6 31.6 141 129.8 55.1 201 185.0 78.5 261 240.3 102.0 22 20.3 8.6 82 75.5 32.0 42 130.7 55.5 02 185.9 78.9 62 241.2 102.4 23 21.2 9.0 83 76.4 32.4 43 131.6 55.9 03 186.9 79.3 63 242.1 102.8 24 22.1 9.4 84 77.3 32.8 44 132.6 56.3 04 187.8 79.7 64 243.0 103.2 25 23.0 9.8 85 78.2 33.2 45 133.5 56.7 05 188.7 80.1 65 243.9 103.5 26 23.9 10.2 86 79.2 33.6 46 134.4 57.0 06 189.6 80.5 66 244.9 103.9 • 27 24.9 10.5 87 80.1 34.0 47 135.3 57.4 07 190.5 80.9 67 245.8 104.3 28 25.8 10.9 88 81.0 34.4 48 136.2 57.8 08 191.5 81.3 68 246.7 104.7 29 26.7 11.3 89 81.9 34.8 49 137.2 58.2 09 192.4 81.7 69 247.6 105.1 30 27.6 11.7 90 82.8 35.2 50 138.1 58.6 10 193.3 82.1 70 248.5 105.5 105.9 31 28.5 12.1 91 83.8 35.6 151 139.0 59.0 211 194.2 82.4 271 249.5 32 29.5 12.5 92 84.7 35.9 52 139.9 59.4 12 195.1 82.8 72 250.4 106.3 33 30.4 12.9 93 85.6 36.3 53 140.8 59.8 13 196.1 83.2 73 251.3 106.7 34 31.3 13.3 94 86.5 36.7 54 141.8 60.2 14 197.0 83.6 74 252.2 107.1 35 32.2 13.7 95 87.4 37.1 55 142.7 60.6 15 197.9 84.0 75 253.1 107.5 36 33.1 14.1 96 88.4 37.5 56 143.6 61.0 16 198.8 84.4 76 254.1 107.8 37 34.1 14.5 97 89.3 37.9 57 144.5 61.3 17 199.7 84.8 77 255.0 108.2 38 35.0 14.8 98 90.2 38.3 58 145.4 61.7 18 200.7 85.2 78 255.9 108.6 39 35.9 15.2 99 91.1 38.7 59 146.4 62.1 19 201.6 85.6 79 256.8 109.0 40 36.8 15.6 100 92.1 39.1 60 147.3 62.5 20 202.5 86.0 80 257.7 109.4 41 37.7 16.0 101 93.0 39.5 161 148.2 62.9 221 203.4 86.4 281 258.7 109.8 42 38.7 16.4 02 93.9 39.9 62 149.1 63.3 22 204.4 86.7 82 259.6 110.2 43 39.6 16.8 03 94.8 40.2 63 150.0 63.7 23 205.3 87.1 83 260.5 110.6 44 40.5 17.2 04 95.7 40.6 64 151.0 64.1 24 206.2 87.5 84 261.4 111.0 45 41.4 17.6 05 96.7 41.0 65 151.9 64.5 25 207.1 87.9 85 262.3 111.4 46 42.3 18.0 06 97.6 41.4 66 152.8 64.9 26 208.0 88.3 86 263.3 111.7 47 43.3 18.4 07 98.5 41.8 67 153.7 65.3 27 209.0 88.7 87 264.2 112.1 48 44.2 18.8 08 99.4 42.2 68 154.6 65.6 28 209.9 89.1 88 265.1 112.5 49 45.1 19.1 09 100.3 42.6 69 155.6 66.0 29 210.8 89.5 89 266.0 112.9 50 46.0 19.5 10 101.3 43.0 70 156.5 66.4 30 211.7 89.9 90 266.9 113.3 51 46.9 19.9 111 102.2 43.4 171 157.4 66.8 231 212.6 90.3 291 267.9 113.7 52 47.9 20.3 12 103.1 43.8 72 158.3 67.2 32 213.6 90.6 92 268.8 114.1 53 48.8 20.7 13 104.0 44.2 73 159.2 67.6 33 214.5 91.0 93 269.7 114.5 54 49.7 21.1 14 104.9 44.5 74 160.2 68.0 34 215.4 91.4 94 270.6 114.9 55 50.6 21.5 15 105.9 44.9 75 161.1 68.4 35 216.3 91.8 95 271.5 115.3 56 51.5 21.9 16 106.8 45.3 76 162.0 68.8 36 217. 2 92.2 96 272.5 115.7 57 52.5 22.3 17 107.7 45.7 77 162.9 69.2 37 218.2 92.6 97 273.4 116.0 58 53.4 22.7 18 108.6 46.1 78 163.8 69.6 38 219.1 93.0 98 274.3 116.4 59 54.3 23.1 19 109.5 46.5 79 164.8 69.9 39 220.0 93.4 99 275.2 116.8 60 55.2 23.4 20 110.5 46.9 80 165.7 70.3 40 220.9 93.8 300 276.2 117.2 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 67° (113°, 24* ^°, 293' ')• TABLE 2. [Page 677 Difference of Latitude and Departure for 23° (157°, 203 .°, 337" )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 277.1 117.6 361 332.3 141.1 421 387.5 164.5 481 442.7 188.0 541 498.0 211.4 02 278.0 118.0 62 333.2 141.5 22 388. 5 164.9 82 443.7 188.4 42 498.9 211.8 03 278.9 118.4 63 334.1 141.8 23 389.4 165.3 83 444.6 188.8 43 499.8 212.2 04 279.8 118.8 64 335. 1 142.2 24 390.3 165.7 84 445.5 189.2 44 500.7 212.6 05 280.8 119.2 65 336. 142.6 25 391.2 166.1 85 446.4 189.5 45 501.7 213.0 06 281.7 119.6 66 336.9 143.0 26 392.1 166.5 86 447.3 189.9 46 502.6 213.4 07 282.6 120.0 67 337.8 143.4 27 393.1 166.8 87 448.3 190.2 47 503.5 213.8 08 283.5 120.4 68 338. 7 143.8 28 394.0 167.2 88 449.2 190.6 48 504.4 214.2 09 284.4 120.8 69 339.7 144.2 29 394.9 167.6 89 450.1 191.0 49 505.3 214.6 10 285. 4 121.2 70 340.6 144.6 30 395.8 168.0 90 451.0 191.4 50 506.3 507.2 215.0 215.3 311 286.3 121.6 371 341.5 145.0 431 396.7 168.4 491 451.9 191.8 551" 12 287.2 121.9 72 342.4 145.4 32 397.7 168.8 92 452.9 192.2 52 508.1 215.6 13 288. 1 122.3 73 343.4 145.7 33 398.6 169.2 93 453.8 192.6 53 509.0 216.0 14 289.0 122.7 74 344. 3 146.1 34 399.5 169.6 94 454.7 193.0 54 509.9 216.4 15 290. 123.1 75 345.2 146.5 35 400.4 170.0 95 455.6 193.4 55 510.9 216.8 16 290.9 123.5 76 346.1 146.9 36 401.3 170.4 96 456.6 193.8 56 511.8 217.2 17 291. 8 123.9 77 347.0 147.3 37 402.3 170.8 97 457.5 194.2 57 512.7 217.6 18 292.7 124.3 78 348. 147.7 38 403.2 171.1 98 458.4 194.6 58 513.6 218.0 19 293.6 124.6 79 348.9 148.1 39 404.1 171. 5 99 459. 3 195. 59 514.5 218.4 20 294.6 125.0 80 349.8 148.5 40 405.0 171.9 500 460.2 195.4 60 515.5 218.8 321 295.5 125.4 381 350.7 148.9 441 405.9 172.3 501 461.2 195. 8 561 516.4 219.2 22 296.4 125.8 82 351.6 149.3 42 406.9 172.7 02 462.1 196.2 62 517.3 219.6 23 297.3 126.2 83 352.6 149.7 43 407.8 173.1 03 463.0 196.6 63 518.2 220.0 24 298.2 126.6 84 353.5 150.0 44 408.7 173.5 04 463.9 197.0 64 519.2 220.4 25 299.2 127.0 85 354.4 150.4 45 409.6 173.9 05 464.9 197.4 65 520.1 220.8 26 300.1 127.4 86 355.3 150.8 46 410.5 174.3 06 465.8 197.8 66 521.0 221.2 27 301.0 127.8 87 356.2 151.2 47 411.5 174.7 07 466.7 198.1 67 521.9 221.6 28 301.9 128.2 88 357.2 151.6 48 412.4 175.1 08 467.6 198.5 68 522.8 222.0 29 302.8 128.6 89 358.1 152.0 49 413.3 175. 4 09 468.5 198.8 69 523.8 222.3 30 303.8 128.9 90 359.0 152.4 50 414.2 175.8 10 469.5 199.3 70 524.7 222.7 331 304.7 129.3 391 359.9 152.8 451 415.2 176.2 611 470.4 199.7 571 525.6 223.1 32 305.6 129. 7 92 360.8 153.2 52 416.1 176.6 12 471.3 200.0 72 526.5 223.4 33 306.5 130.1 93 361.8 153.6 53 417.0 177.0 13 472.2 200.4 73 527.4 223.8 34 307.5 130.5 94 362.7 154.0 54 417.9 177.4 14 473.1 200.8 74 528.4 224.2 35 308.4 130.9 95 363.6 154.3 55 418.8 177.8 15 474.0 201.2 75 529.3 224.6 36 309.3 131.3 96 364.5 154.7 56 419.8 178.2 16 475.0 201.6 76 530.2 225.0 37 310.2 131.7 97 365.4 155.1 57 420.7 178.6 17 475.9 202.0 77 531.1 225.4 38 311.1 132.1 98 366.4 155.5 58 421.6 179.0 18 476.8 202.4 78 532.0 225.8 39 312.1 132.5 99 367.3 155.9 59 422.5 179.4 19 477.7 202.8 79 533.0 226.2 40 313.0 132.9 400 368.2 156.3 60 423.4 179.7 20 478.6 203.2 80 533.9 226.6 341 313.9 133.2 401 369.1 156.7 461 424.4 180.1 521 479.6 203.6 581 534.8 227.0 42 314. 8 133.6 02 370.0 157.1 62 425.3 180.5 22 480.5 204.0 82 535.7 227.4 43 315.7 134.0 03 371.0 157.5 63 426.2 180.9 23 481.4 204.4 83 536.6 227.8 44 316.7 134.4 04 371.9 157.9 64 427.1 181.3 24 482.3 204.8 84 537.6 228.2 45 317.6 134.8 05 372.8 158.3 65 428.0 181.7 25 483.2 205.2 85 538.5 228.6 46 318.5 135.2 06 373.7 158.6 66 429.0 182.1 26 484.2 205.5 86 539.4 229.0 47 319.4 135.6 07 374.6 159.0 67 429.9 182.5 27 485. 1 205. 9 87 540.3 229.4 48 320.3 136.0 08 375.6 159.4 68 430.8 182.9 28 486.0 206.3 88 541.2 229.8 49 321.3 136.4 09 376.5 159.8 69 431.7 183.3 29 486.9 206.7 89 542.2 230.2 50 322.2 136.8 10 377.4 160.2 70 432.6 183.7 30 487.8 207.1 90 543.1 230.6 351 323.1 137.2 411 378.3 160.6 471 433.6 184.0 531 488.8 207.4 591 544.0 231.0 52 324.0 137.5 12 379.3 161.0 72 434.5 184.4 32 489.7 207.8 92 544.9 231.3 53 324.9 137.9 13 380.2 161.4 73 435.4 184.8 33 490.6 208.2 93 545.8 231.7 54 325.9 138.3 14 381.1 161.8 74 436.3 185.2 34 491.5 208.6 94 546.8 232.0 55 326.8 138.7 15 382.0 162.2 75 437.2 185. 6 35 492.5 209.0 95 547.7 232.4 56 327.7 139.1 16 382.9 162.5 76 438.2 186.0 36 493.4 209.4 96 548.6 232.8 57 328.6 139.5 17 383.9 162.9 77 439.1 186.4 37 494.3 209.8 97 549.5 233.2 58 329.5 139.9 18 384.8 163.3 78 440.0 186.8 38 495.2 210.2 98 550.4 233.6 59 330.5 140.3 19 385.7 163.7 79 440.9 187.2 39 496.1 210.6 99 551.3 234.0 60 331.4 140.7 20 386.6 164.1 80 441.8 187.6 40 497.1 211.0 600 552.3 234.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. S7°(l] 3°, 247°, 293°] . 21594°— 14- -30 Page 678] TABLE 2. Difference of Latitude and Departure for 24° ( 156 °, 204°, 336°). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat, Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 55.7 24.8 121 110.5 49.2 181 165.4 73.6 241 220.2 98.0 2 1.8 0.8 62 56.6 25.2 22 111.5 49.6 82 166.3 74.0 42 221.1 98.4 3 2.7 1.2 63 57.6 25.6 23 112.4 50.0 83 167.2 74.4 43 222.0 98.8 4 3.7 1.6 64 58.5 26.0 24 113.3 60.4 84 168.1 74.8 44 222.9 99.2 5 4.6 2.0 65 59.4 26.4 25 114.2 50.8 85 169.0 75.2 45 223.8 99.7 6 5.5 2.4 66 60.3 26.8 26 115.1 51.2 86 169.9 75.7 46 224.7 100.1 7 6.4 2.8 67 61.2 27.3 27 116.0 51.7 87 170.8 76.1 47 225.6 100.5 8 7.3 3.3 68 62.1 27.7 28 116.9 52.1 88 171.7 76.5 48 226.6 100.9 9 8.2 3.7 69 63.0 28.1 29 117.8 52.5 89 172.7 76.9 49 227.5 101.3 10 9.1 4.1 70 63.9 28.5 30 118.8 52.9 90 173.6 77.3 50 228.4 101.7 11 10.0 4.5 71 64.9 28.9 131 119.7 53.3 191 174.5 77.7 251 229.3 102.1 12 11.0 4.9 72 65.8 29.3 32 120.6 53.7 92 175.4 78.1 52 230.2 102.5 13 11.9 5.3 73 66.7 29.7 33 121.5 54.1 93 176.3 78.5 53 231.1 102.9 14 12.8 5.7 74 67.6 30.1 34 122.4 54.5 94 177.2 78.9 54 232.0 103.3 15 13.7 6.1 75 68.5 30.5 35 123.3 54.9 95 178.1 79.3 55 233.0 103.7 16 14.6 6.5 76 69.4 30.9 36 124.2 55.3 96 179. 1 79.7 56 233.9 104.1 17 15.5 6.9 77 70.3 31.3 37 125.2 55.7 97 180.0 80.1 57 234.8 104.5 18 16.4 7.3 78 71.3 31.7 38 126.1 56.1 98 180.9 80.5 58 235.7 104.9 19 17.4 7.7 79 72.2 32.1 39 127.0 56.5 99 181.8 80.9 59 236.6 105.3 20 18.3 8.1 80 73.1 32.5 40 127.9 56.9 200 182.7 81. 3 60 261" 237.5 105.8 21 19.2 8.5 81 74.0 32.9 141 128.8 57.3 201 183.6 81.8 238.4 106.2 22 20.1 8.9 82 74.9 33.4 42 129.7 57.8 02 184.5 82.2 62 239.3 106.6 23 21.0 9.4 83 75.8 33.8 43 130.6 58.2 03 185.4 82.6 63 240.3 107.0 24 21.9 9.8 84 76.7 34.2 44 131.6 58.6 04 186.4 83.0 64 241.2 107.4 25 22.8 10.2 85 77.7 34.6 45 132.5 59.0 05 187.3 83.4 65 242.1 107.8 26 23.8 10.6 86 78.6 35.0 46 133.4 59.4 06 188.2 83.8 66 243.0 108.2 27 24.7 11.0 87 79.5 35.4 47 134.3 59.8 07 189.1 84.2 67 243.9 108.6 28 25.6 11.4 88 80.4 35.8 48 135.2 60.2 08 190.0 84.6 68 244.8 109.0 29 26.5 11.8 89 81.3 36.2 49 136.1 60.6 09 190.9 85.0 69 245.7 109.4 30 27.4 12.2 90 82.2 36.6 50 137.0 61.0 10 191.8 85.4 70 246.7 109.8 31 28.3 12.6 91 83.1 37.0 151 137.9 61.4 211 192.8 85.8 271 247.6 110.2 32 29.2 13.0 92 84.0 37.4 52 138.9 61.8 12 193.7 86.2 72 248.5 110.6 33 30.1 13.4 93 85.0 37.8 53 139.8 62.2 13 194.6 86.6 73 249.4 111.0 34 31.1 13.8 94 85.9 38.2 54 140.7 62.6 14 195.5 87.0 74 250.3 111.4 35 32.0 14.2 95 86.8 38.6 55 141.6 63.0 15 196.4 87.4 75 251.2 111.9 36 32.9 14.6 96 87.7 39.0 56 142.5 63.5 16 197.3 87.9 76 252.1 112.3 37 33.8 15.0 97 88.6 39.5 57 143.4 63.9 17 198.2 88.3 77 253.1 112.7 38 34.7 15.5 98 89.5 39.9 58 144.3 64.3 18 199.2 88.7 78 254.0 113.1 39 35.6 15.9 99 90.4 40.3 59 145.3 64.7 19 200.1 89.1 79 254.9 113.5 40 36.5 16.3 100 91.4 40.7 60 146.2 65.1 20 201.0 89.5 80 255.8 113.9 114.3 41 37.5 16.7 101 92.3 41.1 161 147.1 65.5 221 201.9 89.9 281 256.7 42 38.4 17.1 02 93.2 41.5 62 148.0 65.9 22 202.8 90.3 82 257.6 114.7 43 39.3 17.5 03 94.1 41.9 63 148.9 66.3 23 203.7 90.7 83 258.5 115.1 44 40.2 17.9 04 95.0 42.3 64 149.8 66.7 24 204.6 91.1 84 259.4 115.5 45 41.1 18.3 05 95.9 42.7 65 150.7 67.1 25 205.5 91.5 85 260.4 115.9 46 42.0 18.7 06 96.8 43.1 66 151.6 67.5 26 206.5 91.9 86 261.3 116.3 47 42.9 19.1 07 97.7 43.5 67 152.6 67.9 27 207.4 92.3 87 262.2 116.7 48 43.9 19.5 08 98.7 43.9 68 153. 5 68.3 28 208.3 92.7 88 263.1 117.1 49 44.8 19.9 09 99.6 44.3 69 154.4 68.7 29 209.2 93.1 89 264.0 117.5 50 45.7 20.3 10 100. 5 44.7 70 155.3 69.1 30 210.1 93.5 90 264.9 118.0 51 46.6 20.7 111 101.4 45.1 171 156.2 69. 6 231 211.0 94.0 291 265.8 118.4 52 47.5 21.2 12 102.3 45.6 72 157.1 70.0 32 211.9 94.4 92 266.8 118.8 53 48.4 21.6 13 103.2 46.0 73 158.0 70.4 33 212.9 94.8 93 267.7 119. 2 1 54 49.3 22.0 14 104.1 46.4 74 159.0 70.8 34 213.8 95.2 94 268.6 119.6 55 50.2 22.4 15 105.1 46.8 75 159.9 71.2 35 214.7 95.6 95 269.5 120.0 56 51.2 22.8 16 106.0 47.2 76 160.8 71.6 36 215.6 96.0 96 270.4 120.4 57 52.1 23.2 17 106.9 47.6 77 161.7 72.0 37 216.5 96.4 97 271.3 120.8 58 53.0 23.6 18 107.8 48.0 78 162.6 72.4 38 217.4 96.8 98 272.2 121.2 59 53.9 24.0 19 108.7 48.4 79 163.5 72.8 38 218.3 97.2 99 273.2 121.6 60 54.8 24.4 20 109.6 48.8 80 164.4 73.2 40 219.3 97.6 300 274.1 122.0 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ( )6° (1 14°, 246 °, 294° ). TABLE 2. [Page 579 Difference of Latitude and Departure for 24° (156°, 204 °, 336°). Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat Dep. 301 275.0 122.4 361 329.8 146.8 421 384.6 171.2 481 439.4 195.6 541 494.2 220. 02 275.9 122.8 62 330.7 147.2 22 385. 5 171.6 82 440.3 196.0 42 495.1 220.4 03 276.8 123.2 63 331.6 147.6 23 386.4 172.1 83 441.2 196.5 43 496.0 220.9 04 277.7 123.7 64 332.5 148.1 24 387.3 172.5 84 442.1 196.9 44 496.9 221.3 05 278.6 124.1 65 33l4 148.5 25 388.2 172.9 85 443.0 197.3 45 497.8 221.7 06 279.5 124.5 66 334.3 148.9 26 389.2 173.3 86 444.0 197.7 46 498.8 222.1 07 280.4 124.9 67 335.3 149.3 27 390.1 173.7 87 444.9 198.1 47 499.7 222.5 08 281.4 125.3 68 336.2 149.7 28 391.0 174.1 88 445.8 198.5 48 500.6 222.9 09 282.3 125.7 69 337.1 150.1 29 391.9 174.5 89 446.7 198.9 49 501.5 223.3 10 283.2 126.1 70 338.0 150.5 30 392.8 174.9 90 447.6 199.3 50 502. 4 223.7 224.1 311 284.1 126.5 371 338.9 150.9 431 393.7 175.3 491 448.6 199.7 551 503.4 12 285.0 126.9 72 339.8 151.3 32 .394. 6 175.7 92 449.5 200.1 52 504.3 224.5 13 285.9 127.3 73 340.7 151.7 33 395.6 176.1 93 450.4 200.5 53 505. 2 224.9 14 286.8 127.7 74 341.7 152.1 34 396.5 176.5 94 451.3 200.9 54 506.1 225.3 15 287.8 128.1 75 342.6 152.5 35 397.4 176.9 95 452.2 201.3 55 507.0 225.7 16 288.7 128.5 76 343. 5 152.9 36 398.3 177.3 96 453.1 201.7 56 507.9 226.1 17 289.6 128.9 77 344.4 153. 3 37 399.2 177.7 97 454.0 202.2 57 508.8 226.6 18 290.5 129.3 78 345.3 153.7 38 400.1 178.2 98 454.9 202.6 58 509.7 227.0 19 291.4 129.8 79 346.2 154.2 39 401.0 178.6 99 455.8 203.0 59 510.6 227.4 20 292.3 130.2 130.6 80 381 347.1 348.1 154.6 40 402.0 179.0 500 456.8 203.4 60 511.6 512.5 227.8 321 293.2 155. 441 402.9 179.4 501 457.7 203.8 561 228.2 22 294.2 131.0 82 349.0 155.4 42 403.8 179.8 02 458.6 204.2 62 513.4 228.6 23 295.1 131.4 83 348.9 156.8 43 404.7 180.2 03 459.5 204.6 63 514.3 229.0 24 296.0 131.8 84 350.8 156.2 44 405.6 180.6 04 460.4 205. 64 515.2 229.4 25 296.9 132.2 85 351.7 156.6 45 406.5 181.0 05 461.3 205.4 65 516.1 229.8 26 297.8 132.6 86 352.6 157.0 46 407.4 181.4 06 462.2 205. 8 66 517.0 230.2 27 298.7 133.0 87 353.5 157.4 47 408.3 181.8 07 463.2 206.2 67 518.0 230. 6 28 299.6 133.4 88 354.4 157.8 48 409.3 182.2 08 464.1 206.6 68 518.9 231.0 29 300.5 133.8 89 355.4 158.2 49 410.2 182.6 09 465.0 207.0 69 519.8 231.4 30 301.5 134. 2 90 356.3 158.6 50 411.1 183.0 183.4 10 511 465.9 207.4 70 520.7 231.8 232. 2 331 302.4 134.6 391 357.2 159.0 451 412.0 466.8 207.8 571 521.6 32 303.3 135.0 92 358.1 159.4 52 412.9 183.8 12 467.7 208.2 72 522.5 232.7 33 304.2 135,4 93 359.0 159.8 53 413.8 184.3 13 468.6 208.7 73 523.4 233.1 34 305. 1 135.9 94 359.9 160.3 54 414.7 184.7 14 469.5 209.1 74 524.3 233.5 35 306.0 136.3 95 360.8 160.7 55 415.7 185.1 15 470.5 209.5 75 525.3 233.9 36 306.9 136.7 96 361.8 161.1 56 416.6 185.5 16 471.4 209.9 76 526.2 234.3 37 307.9 137.1 97 362.7 161.5 57 417.5 185.9 17 472.3 210.3 77 527.1 234.7 38 308.8 137.5 98 363.6 161.9 58 418.4 186.3 18 473.2 210.7 78 528.0 235.1 39 309.7 137.9 99 364.5 162.3 59 419.3 186.7 19 474.1 211.1 79 528. 9 235.5 40 310.6 138.3 400 365.4 366.3" 162.7 60 420.2 187.1 20 475. 211.5 211.9 80 581 529.8 235.9 236. 3 341 311.5 138.7 401 163.1 461 421.1 187.5 521 475.9 530.8 42 312.4 139.1 02 367.2 163.5 62 422.0 187.9 22 476.8 212.3 82 531.7 236.7 43 313.3 139.5 03 368.2 163.9 63 423.0 188.3 23 477.8 212.7 83 532. 6 237.1 44 314. 3 139.9 04 369.1 164.3 64 423.9 188.7 24 478.7 213.1 84 533.5 237.5 45 315.2 140.3 05 370.0 164.7 65 424.8 189.1 25 479.6 213.5 85 534. 4 237. 9 46 316.1 140.7 06 370.9 165.1 66 425.7 189.5 26 480.5 213.9 86 535.3 238.3 47 317.0 141.1 07 371.8 165. 5 67 426.6 189.9 27 481.4 214.4 87 536.2 238.8 48 317.9 141.5 08 372.7 165.9 68 427.5 190.4 28 482.3 214.8 88 537. 1 239.2 49 318.8 142.0 09 373.6 166.4 69 428.4 190.8 29 483.2 215.2 89 538.0 239.6 50 319. 7 320.6 142.4 10 374.5 166.8 70 429.4 191.2 30 484.2 215.6 90 539.0 539.9 240.0 351 142.8 411 375.5 167.2 471 430.3 191.6 531 485.1 216.0 591 240.4 52 321.6 143.2 12 376.4 167.6 72 431.2 192.0 32 486.0 216.4 92 540.8 240.8 53 322.5 143.6 13 377.3 168.0 73 432.1 192.4 33 486.9 216.8 93 541.7 241.2 54 323.4 144.0 14 378.2 168.4 74 433.0 192.8 34 487.8 217.2 94 542.6 241.6 55 324.3 144.4 15 379.1 168.8 75 433.9 193.2 35 488.7 217.6 95 543.5 242.0 56 325.2 144.8 16 380.0 169.2 76 434.8 193.6 36 489.6 218.0 96 544.4 242.4 57 326.1 145.2 17 380.9 169.6 77 435.8 194.0 37 490.6 218.4 97 545.4 242.8 58 327.0 145.6 18 381.9 170.0 78 436.7 194.4 38 491.5 218.8 98 546.3 243.2 59 328.0 146.0 19 382.8 170.4 79 437.6 194.8 39 492.4 219.2 99 547.2 243.6 60 328.9 146.4 20 383.7 170.8 80 438.5 195.2 40 493.3 219.6 600 548.1 244.0 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. 1 Lat. ( J6° (1 14°, 246 =,294° ). Page 680] TABLE 2. Difference of Latitude and Departure for 25° (155°, 205°, 335° )• Bist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 55.3 25.8 121 109.7 51.1 181 164.0 76.5 241 218.4 101.9 2 1.8 0.8 62 56.2 26.2 22 110.6 51.6 82 164.9 76.9 42 219.3 102.3 3 2.7 1.3 63 57.1 26.6 23 111.5 52.0 83 165.9 77.3 43 220.2 102.7 4 3.6 1.7 64 58.0 27.0 24 112.4 52.4 84 166.8 77.8 44 221.1 103.1 5 4.5 2.1 65 58.9 27.5 25 113.3 52.8 85 167.7 78.2 45 222.0 103.5 6 5.4 2.5 66 59.8 27.9 26 114.2 53.2 86 168.6 78.6 46 223.0 104.0 7 6.3 3.0 67 60.7 28.3 27 115.1 53.7 87 169.5 79.0 47 223.9 104.4 8 7.3 3.4 68 61.6 28.7 28 116.0 54.1 88 170.4 79.5 48 224.8 104.8 9 8.2 3.8 69 62.5 29.2 29 116.9 54.5 89 171.3 79.9 49 225.7 105.2 10 9.1 4.2 70 63.4 29.6 30 117.8 54.9 90 172.2 80.3 50 226.6 105.7 11 10.0 4.6 71 64.3 30.0 131 118.7 55.4 191 173.1 80.7 251 227.5 106.1 12 10.9 5.1 72 65.3 30.4 32 119.6 55.8 92 174.0 81.1 52 228.4 106.5 13 11.8 5.5 73 66.2 30.9 33 120.5 56.2 93 174.9 81.6 53 229.3 106.9 14 12.7 5.9 74 67.1 31.3 34 121.4 56.6 94 175.8 82.0 54 230.2 107.3 15 13.6 6.3 75 68.0 31.7 35 122.4 57.1 95 176.7 82.4 55 231.1 107.8 16 14.5 6.8 76 68.9 32.1 36 123.3 57.5 96 177.6 82.8 56 232.0 108.2 17 15.4 7.2 77 69.8 32.5 37 124.2 57.9 97 178.5 83.3 57 232.9 108.6 18 16.3 7.6 78 70.7 33.0 38 125.1 58.3 98 179.4 83.7 58 233.8 109.0 19 17.2 8.0 79 71.6 33.4 39 126.0 58.7 99 180.4 84.1 59 234.7 109.5 20 18.1 8.5 80 72.5 73.4 33.8 34.2 40 141 126.9 59.2 200 201 181.3 182.2 84.5 60 235.6 236.5 109.9 110.3 21 19.0 8.9 81 127.8 59.6 84.9 261 22 19.9 9.3 82 74.3 34.7 42 128.7 60.0 02 183.1 85.4 62 237.5 110.7 23 20.8 9.7 83 75.2 3.5.1 43 129.6 60.4 03 184.0 85.8 63 238.4 111.1 24 21.8 10.1 84 76.1 35.5 44 130.5 60.9 04 184.9 86.2 64 239.3 111.6 25 22.7 10.6 85 77.0 35.9 45 131.4 61.3 05 185.8 86.6 65 240.2 112.0 26 23.6 11.0 86 77.9 36.3 46 132.3 61.7 06 186.7 87.1 66 241.1 112.4 27 24.5 11.4 87 78.8 36.8 47 133.2 62.1 07 187.6 87.5 67 242.0 112.8 28 25.4 11.8 88 79.8 37.2 48 134.1 62.5 08 188.5 87.9 68 242.9 113.3 29 26.3 12.3 89 80.7 37.6 49 135.0 63.0 09 189.4 88.3 69 243.8 113.7 30 27.2 12.7 90 81.6 38.0 50 135.9 63.4 10 190.3 88.7 70 244.7 114.1 31 28.1 13.1 91 82.5 38.5 151 136.9 63.8 211 191.2 89.2 271 245.6 114.5 32 29.0 13.5 92 83.4 38.9 52 137.8 64.2 12 192.1 89.6 72 246.5 115.0 33 29.9 13.9 93 84.3 39.3 53 138.7 64.7 13 193.0 90.0 73 247.4 115.4 34 30.8 14.4 94 85.2 39.7 54 139.6 65.1 14 193.9 90.4 74 248.3 115.8 36 31.7 14.8 95 86.1 40.1 55 140.5 65.5 15 194.9 90.9 75 249.2 116.2 36 32.6 15.2 96 87.0 40.6 56 141.4 6.5.9 16 195.8 91.3 76 250.1 116.6 37 33.5 15.6 97 87.9 41.0 57 142. 3 66.4 17 196.7 91.7 77 251.0 117.1 38 34.4 16.1 98 88.8 41.4 58 143.2 66.8 18 197.6 92.1 78 252.0 117.5 39 35.3 16.5 99 89.7 41.8 59 144.1 67.2 19 198.5 92.6 79 252.9 117.9 40 36.3 16.9 100 90.6 42.3 60 145.0 67.6 20 199.4 93.0 80 253.8 118.3 41 37.2 17.3 101 91.5 42.7 161 145.9 68.0 221 200.3 93.4 281 254.7 118.8 42 38.1 17.7 02 92.4 43.1 62 146.8 68.5 22 201.2 93.8 82 255.6 119.2 43 39.0 18.2 03 93.3 43.5 63 147.7 68.9 23 202.1 94.2 83 256. 5 119.6 44 39.9 18.6 04 94.3 44.0 64 148.6 69.3 24 203.0 94.7 84 257.4 120.0 45 40.8 19.0 05 95.2 44.4 65 149.5 69.7 25 203.9 95.1 85 258.3 120.4 46 41.7 19.4 06 96.1 44.8 66 150.4 70.2 26 204.8 95.5 86 259.2 120.9 47 42.6 19.9 07 97.0 45.2 67 151.4 70.6 27 205.7 95.9 87 260.1 121.3 48 43.5 20.3 08 97.9 45.6 68 152.3 71.0 28 206.6 96.4 88 261.0 121.7 49 44.4 20.7 09 98.8 46.1 69 153.2 71.4 29 207.5 96.8 89 261.9 122.1 50 45.3 21.1 10 99.7 46.5 70 154.1 155.0 71.8 30 208.5 97.2 90 262.8 122.6 51 46.2 21.6 111 100.6 46.9 171 72.3 231 209.4 97.6 291 263.7 123.0 52 47.1 22.0 12 101.5 47.3 72 155.9 72.7 32 210.3 98.0 92 264.6 123.4 53 48.0 22.4 13 102.4 47.8 73 156.8 73.1 33 211.2 98.5 93 265.5 123.8 54 48.9 22.8 14 103.3 48.2 74 157.7 73.5 34 212.1 98.9 94 266.5 124.2 55 49.8 23.2 15 104.2 48.6 75 158.6 74.0 35 213.0 99.3 95 267.4 124.7 56 50.8 2.3.7 16 105.1 49.0 76 159.5 74.4 36 213.9 99.7 96 268.3 125.1 57 51.7 24.1 17 106.0 49.4 77 160.4 74.8 37 214.8 100.2 97 269.2 125.5 58 52.6 24.5 18 106.9 49.9 78 161.3 75.2 38 215.7 100.6 98 270.1 125.9 59 53.5 24.9 19 107.9 50.3 79 162.2 75.6 39 216.6 101.0 99 271.0 126.4 60 54.4 25.4 20 108.8 50.7 80 163.1 76.1 40 217.5 101.4 300 271.9 126.8 DiBt. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. D«p. Lat. Dist. Dep. Lat. 35° (1 15°, 245°, 295° )• TABLE 2. [Page 681 Difference of Latitude and Departure for 25° (155°, 205°, 335° )• Dist. Lat. 1 Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 272.8 127.2 361 327.1 152.5 421 381.5 177.9 481 435.9 203.3 541 490.3 228.6 02 273.7 127.6 62 328.0 153.0 22 382.4 178.3 82 436.8 203.7 42 491.2 229.0 03 274.6 128.0 63 329.0 153.4 23 383.3 178.7 83 437.7 204.1 43 492.1 229.4 04 275.5 128.4 64 329.9 153.8 24 384.2 179.2 84 438.6 204.6 44 493.0 229.9 05 276.4 128.9 65 330.8 154.2 25 385.1 179.6 86 439.6 204.9 45 493.9 230.3 06 277.3 129.3 66 331.7 154.6 26 386.0 180.0 86 440.4 206.4 46 494.8 •230.7 07 278.2 129.7 67 332.6 155. 1 27 387.0 180.4 87 441.3 205.8 47 495.7 231.1 08 279.1 130.1 68 333.5 155.5 28 387.9 180.9 88 442.2 206.2 48 496.6 231.6 09 280.0 130.6 69 334.4 155.9 29 388.8 181.3 89 443.1 206.6 49 497. 5 232.0 10 280.9 131.0 70 335.3 156.3 30 389.7 181.7 90 444.0 207.1 60 498.4 232.4 311 281.8 131.4 371 336.2 156.8 431 390.6 182.1 491 444.9 207.6 651 499. 3 232.8 12 282.7 131.8 72 337. 1 157.2 32 391.5 182.5 92 445.9 207.9 62 500.2 2.33. 2 13 283.6 132.2 73 338.0 157.6 33 392.4 183.0 93 446.8 208. 3 53 501.1 233.7 14 284.5 132.7 74 338.9 158.0 34 393.3 183.4 94 447.7 208.7 54 502.0 234.1 15 285.4 133.1 75 339.8 158.5 35 394.2 183.8 95 448.6 209.1 66 503.0 234.5 16 286.4 133.5 76 340.7 158.9 36 395.1 184.2 96 449.6 209.6 66 503.9 235.0 17 287.3 133.9 77 341.6 159.3 37 396.0 184.7 97 450.4 210.0 57 604.8 236.4 18 288.2 134.4 78 342.5 159.7 38 396.9 185.1 98 451.3 210.4 58 505.7 236.8 19 289.1 134.8 79 343.5 160.1 39 397.8 185.5 99 462.2 210.9 59 506.6 236.2 20 290.0 135.2 80 344.4 160.6 40 398.7 185.9 500 453.1 211.3 60 607.5 236.6 321 290.9 135.6 381 345.3 161.0 441 399.6 186.3 501 454.0 211.7 561 508.4 237.1 22 291.8 136.1 82 346.2 161.4 42 400.6 186.8 02 464.9 212.1 62 609.3 237. 6 23 292.7 136.5 83 347.1 161.8 43 401.5 187.2 03 456.8 212.5 63 510.2 237.9 24 293.6 136.9 84 348.0 162.3 44 402.4 187.6 04 456.7 213.0 64 511.1 238.3 25 294.5 137.3 85 348.9 162.7 45 403.3 188.0 05 467.7 213.4 66 512.0 238.7 26 295.4 137.7 86 349.8 163.1 46 404.2 188.5 06 468.6 213.8 66 512.9 239.2 27 296.3 138.2 87 350.7 163.5 47 405.1 188.9 07 459.5 214.2 67 613.8 239.6 28 297.2 138.6 88 351.6 163.9 48 406.0 189.3 08 460.4 214.7 68 514.8 240.1 29 298.1 139.0 89 352.5 164.4 49 406.9 189.7 09 461.3 215.1 69 515.7 240.6 30 331 299.0 139.4 90 363.4 164.8 50 407.8 190.1 10 462.2 215.5 70 616.6 240.9 300.0 139.9 391 354.3 165.2 451 408.7 190.6 511 463.1 215.9 571 517.5 241. J 32 300.9 140.3 92 355.2 165.6 52 409.6 191.0 12 464.0 216.4 72 518.4 241.7 33 301.8 140.7 93 356.1 166.1 53 410.5 191.4 13 464.9 216.8 73 519.3 242.1 34 302.7 141.1 94 357.0 166.5 54 411.4 191.8 14 466.8 217.2 74 520.2 242.6 35 303.6 141.5 95 358.0 166.9 55 412.3 192.3 15 466.7 217.7 75 521.1 243.0 36 304.5 142.0 96 358.9 167.3 56 413. 2 192.7 16 467.6 218. 1 76 522.0 243.4 37 305.4 142.4 97 359.8 167.7 57 414.1 193.1 17 468.5 218.5 77 622.9 243.8 38 306.3 142.8 98 360.7 168.2 58 415.1 193.5 18 469.4 218.9 78 523.8 244.3 39 307.2 143.2 99 361.6 168.6 59 416.0 194.0 19 470.3 219.3 79 524.7 244.7 40 308.1 143.7 400 362.5 169.0 60 416.9 194.4 20 471.2 219.8 80 525.6 245.1 341 309.0 144.1 401 363.4 169.4 461 417.8 194.8 521 472.2 220.2 581 526.5 245.5 42 309.9 144.5 02 364.3 169.9 62 418.7 195.2 22 473.1 220.6 82 527. 4 246.0 43 310.8 144.9 03 365.2 170.3 63 419.6 195.6 23 474.0 221.0 83 528. 3 246.4 44 311.7 145.4 04 366.1 170.7 64 420.5 196.1 24 474.9 221.4 84 529.3 246.8 45 312.6 145.8 05 367.0 171.1 66 421.4 196.5 26 475.8 221.9 85 530.2 247.2 46 313.5 146.2 06 367.9 171.6 66 422.3 196.9 26 476.7 222.3 86 531.1 247.7 47 314.5 146.6 07 368.8 172.0 67 423.2 197.3 27 477.6 222.7 87 532.0 248.1 48 315.4 147.0 08 369.7 172.4 68 424.1 197.8 28 478.5 223.2 88 532.9 248.5 49 316.3 147.5 09 370.6 172.8 69 425.0 198.2 29 479.4 223.6 89 533. 8 248.9 50 317.2 147.9 10 371.5 173.2 70 425.9 426.8 198.6 30 480.3 481.2 224.0 224. 4 90 591 534.7 635.6 249.4 249.8 351 318.1 148.3 411 372.5 173.7 471 199.0 631 52 319.0 148.7 12 373.4 174.1 72 427.7 199.4 32 482.1 224.8 92 636.5 250.2 53 319.9 149.2 13 374.3 174.5 73 428.6 199.9 33 483.0 225.3 93 537.4 260.6 54 320.8 149.6 14 375.2 174.9 74 429.6 200.3 34 483.9 226.7 94 538.3 261.1 55 321.7 150.0 15 376.1 175.4 75 430.5 200.7 36 484.8 226.1 96 539.2 251.5 56 322.6 150.4 16 377.0 175.8 76 431.4 201.1 36 485.7 226.5 96 540.1 251.9 57 323.5 150.8 17 377.9 176.2 77 432.3 201.6 37 486.7 226.9 97 541.0 262.3 58 324.4 151.3 18 378.8 176.6 78 433.2 202.0 38 487.6 227.4 98 541.9 262.7 59 325.3 151.7 19 379.7 177.0 79 434.1 202.4 39 488.6 227.8 99 542.8 263.1 60 326.2 152.1 20 380.6 177.5 80 435.0 202.8 40 489.4 228.2 600 543.8 253.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. .. ( 55° (1 16°, 245 °, 295° )• Page 682] TABLE 2. Difference of Latitude and Departure for 26° (154°, 206°, 334= )• Dist. Lat. Dep. Dist. Lat. Dep. Disl. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.4 61 54.8 26.7 121 108.8 53.0 181 162.7 79.3 241 216.6 105.6 2 1.8 0.9 62 55.7 27.2 22 109.7 53.5 82 163.6 79.8 42 217.5 106.1 3 2.7 1.3 63 56.6 27.6 23 110.6 53.9 83 164.5 80.2 43 218.4 106.5 4 3.6 1.8 64 57.5 28.1 24 111.5 54.4 84 165.4 80.7 44 219.3 107.0 5 4.5 2.2 65 58.4 28.5 25 112.3 54.8 85 166.3 81.1 45 220.2 107.4 6 f 5.4 2.6 66 59.3 28.9 26 113.2 55.2 86 167.2 81.5 46 221.1 107.8 7 6.3 3.1 67 60.2 29.4 27 114.1 55.7 87 168.1 82.0 47 222.0 108. 3 8 7.2 3.5 68 61.1 29.8 28 115.0 56.1 88 169.0 82.4 48 222.9 108.7 9 8.1 3.9 69 62.0 30.2 29 115.9 56.5 89 169.9 82.9 49 223.8 109.2 10 11 9.0 9.9 4.4 70 62.9 30.7 30 116.8 57.0 90 191 170.8 83.3 50 224.7 109.6 4.8 71 63.8 31.1 131 117.7 57.4 171.7 83.7 251 225.6 110.0 12 10.8 5.3 72 64.7 31.6 32 118.6 57.9 92 172.6 84.2 52 226.5 110.5 13 11.7 5.7 73 65.6 32.0 33 119.5 58.3 93 173.5 84.6 53 227.4 110.9 14 12.6 6.1 74 66.5 32.4 34 120.4 58.7 94 174.4 85.0 54 228.3 111.3 15 13.5 6.6 75 67.4 32.9 35 121.3 59.2 95 175.3 85.5 55 229.2 111.8 16 14.4 7.0 76 68.3 33.3 36 122.2 59.6 96 176.2 85.9 56 230.1 112.2 17 15.3 7.5 77 69.2 33.8 37 123.1 60.1 97 177.1 86.4 57 231. 112.7 18 16.2 7.9 78 70.1 34.2 38 124.0 60.5 98 178.0 86.8 58 231.9 113.1 19 17.1 8.3 79 71.0 34.6 39 124.9 60.9 99 178.9 87.2 59 232.8 113.5 20 18.0 8.8 80 71.9 35.1 40 125.8 61.4 200 179.8 87.7 60 233.7 114.0 21 18.9 9.2 81 72.8 35.5 141 126.7 61.8 201 180.7 88.1 261 234.6 114.4 22 19.8 9.6 82 73.7 35.9 42 127.6 62.2 02 181.6 88.6 62 235.5 114.9 23 20.7 10.1 83 74.6 36.4 43 128.5 62.7 03 182.5 89.0 63 236.4 115.3 24 21.6 10.5 84 75.5 36.8 44 129.4 63.1 04 183.4 89.4 64 237.3 115.7 25 22.5 11.0 85 76.4 37.3 45 130.3 63.6 05 184.3 89.9 65 238.2 116.2 26 23.4 11.4 86 77.3 37.7 46 131.2 64.0 06 185.2 90.3 66 239.1 116.6 27 24.3 11.8 87 78.2 38.1 47 132.1 64.4 07 186.1 90.7 67 240.0 117.0 28 25.2 12.3 88 79.1 38.6 48 133.0 64.9 08 186.9 91.2 68 240.9 117.5 29 26.1 12.7 89 80.0 39.0 49 133.9 65.3 09 187. 8 91.6 69 241.8 117.9 30 27.0 13.2 90 80.9 39.5 50 134.8 65.8 10 188.7 92.1 92.5 70 271 242.7 118.4 31 27.9 13.6 91 81.8 39.9 151 135.7 66.2 211 189.6 243.6 118.8 32 28.8 14.0 92 82.7 40.3 52 136.6 66.6 12 190.5 92.9 72 244.5 119.2 33 29.7 14.5 93 83.6 40.8 53 137.5 67.1 13 191.4 93.4 73 245.4 119.7 34 30.6 14.9 94 84.5 41.2 54 138.4 67.5 14 192.3 93.8 74 246.3 120.1 35 31.5 15.3 95 85.4 41.6 55 139.3 67.9 15 193.2 94.2 75 247.2 120.6 36 32.4 15.8 96 86.3 42.1 56 140.2 68.4 16 194. 1. 94.7 76 248.1 121.0 37 33.3 16.2 97 87.2 42.5 57 141.1 68.8 17 195.0 95.1 77 249.0 121.4 38 34.2 16.7 98 88.1 43.0 58 142.0 69.3 18 195.9 95.6 78 249.9 121.9 39 35.1 17.1 99 89.0 43.4 59 142.9 69.7 19 196.8 96.0 79 250.8 122.3 40 36.0 36.9 17.5 100 89.9 43.8 44.3 60 161 143.8 70.1 20 197.7 96.4 80 251.7 122.7 41 18.0 101 90.8 144.7 70.6 221 198.6 96.9 281 252.6 123.2 42 37.7 18.4 02 91.7 44.7 62 145.6 71.0 22 199.5 97.3 82 253.5 123.6 43 38.6 18.8 03 92.6 45.2 63 146.5 71.5 23 200.4 97.8 83 254.4 124.1 44 39.5 19.3 04 93.5 45.6 64 147.4 71.9 24 201.3 98.2 84 255.3 124.5 45 40.4 19.7 05 94.4 46.0 65 148.3 72.3 25 202.2 98.6 85 256.2 124.9 46 41.3 20.2 06 95.3 46.5 66 149.2 72.8 26 203.1 99.1 86 257.1 125.4 47 42.2 20.6 07 96.2 46.9 67 150.1 73.2 27 204.0 99.5 87 258.0 125.8 48 43.1 21.0 08 97.1 47.3 68 151.0 73.6 28 204.9 99.9 88 258.9 126.3 49 44.0 21.5 09 98.0 47.8 69 151.9 74.1 29 205.8 100.4 89 259.8 126.7 50 51 44.9 21.9 22.4 10 98.9 48.2 70 152.8 74.5 30 206.7 100.8 90 260.7 127.1 45.8 111 99.8 48.7 171 153.7 75.0 231 207.6 101.3 291 261.5 127.6 52 46.7 22.8 12 100.7 49.1 72 154.6 75.4 32 208.5 101.7 92 262.4 128.0 53 47.6 23.2 13 101.6 49.5 73 155.5 75.8 33 209.4 102.1 93 263.3 128.4 54 48.5 23.7 14 102.5 50.0 74 156.4 76.3 34 210.3 102.6 94 264.2 128.9 55 49.4 24.1 15 103.4 50.4 75 157.3 76.7 35 211.2 103.0 95 265.1 129.3 56 50.3 24.5 16 104.3 50.9 76 158.2 77.2 36 212.1 103.5 96 266.0 129.8 57 51.2 25.0 17 105.2 51.3 77 159.1 77.6 37 213.0 103.9 97 266.9 130.2 58 52.1 25.4 18 106.1 51.7 78 160.0 78.0 38 213.9 104.3 98 267.8 130.6 59 53.0 25.9 19 107.0 52.2 79 160.9 78.5 39 214.8 104.8 99 268.7 131.1 60 53.9 26.3 20 107.9 52.6 80 161.8 78.9 40 215.7 105.2 300 269.6 131.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. ( 34° (1 16°, 244 °, 296° ). TABLE 2. [Page 683 Difference of Latitude and Departure for 26° (154°, 206°, 334). 1 Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 270.5 132.0 361 324. 5 158. 3 421 378.4 184.6 481 432.3 210.9 541 486.2 237.2 02 271.4 132.4 62 325.4 158.7 22 379.3 185.0 82 433.2 211.3 42 487.1 237.6 03 272.3 132.8 63 326.3 159.1 23 380.2 185.4 83 434.1 211.7 43 488.0 238.0 04 273.2 133.3 64 327.2 159.6 24 381.1 185.9 84 435.0 212.2 44 488.9 238.5 05 274.1 133.7 65 328.1 160.0 25 382.0 186.3 85 435.9 212.6 45 489.8 238.9 06 275.0 134.1 66 329.0 160.4 26 382.9 186.7 86 436.8 213.0 46 490.7 239.3 07 275.9 134.6 67 329.9 160.9 27 383.8 187.2 87 437.7 213.5 47 491.6 239.8 08 276.8 135. 68 330.8 161.3 28 384.7 187.6 88 438.6 213.9 48 492.5 240.2 09 277.7 135. 5 69 331.7 161.8 29 385.6 188.1 89 439.5 214.4 49 493.4 240.7 10 278.6 135. 9 136.3 70 332.6 162. 2 30 431 386.5 387.4 188.5 90 491 440. 4 214. 8 50 494.3 241.1 241.5 311 279.5 371 333. 5 162.6 188.9 441.3 215.2 551 495.2 12 280.4 136.8 72 334.4 163.1 32 388.3 189.4 92 442.2 215.7 52 496.1 242.0 13 281. 3 137.2 73 335.3 163.5 33 389.2 189.8 93 443.1 216.1 53 497.0 242.4 14 282.2 137.7 74 336.2 164.0 34 390.1 190.3 94 444.0 216.6 54 497.9 242.9 15 283.1 138.1 75 337.1 164.4 35 391.0 190.7 95 444.9 217.0 55 498.8 243.3 16 284.0 138.5 76 338.0 164.8 36 391.9 191.1 96 445.8 217.4 56 499.7 243.7 17 284.9 139.0 77 338.9 165.3 37 392.8 191.6 97 446.7 217.9 57 500.6 244.2 18 285.8 139.4 78 339.8 165.7 38 393.7 192.0 98 447.6 218.3 58 501.5 244.6 19 286.7 139.8 79 340.7 166.2 39 394.6 192.4 99 448.5 218.7 59 502.4 245.0 20 287.6 288.5 140.3 80 381 341.5 342.4 166.6 167.0 40 395.5 192.9 500 449.4 219.2 60 561 503.3 504.2 245.5 321 140.7 441 396.4 193.3 501 450.3 219.6 245.9 22 289.4 141.2 82 343.3 167.5 42 397.3 193.8 02 451.2 220.1 62 505.1 246.4 23 290.3 141.6 83 344.2 167.9 43 398.2 194.2 03 452.1 220.5 63 506.0 246.8 24 291.2 142.0 84 345. 1 168.3 44 399.1 194.7 04 453.0 221.0 64 506.9 247.3 25 292.1 142.5 85 346.0 168.8 45 400.0 195.1 05 453.9 221.4 66 507.8 247.7 26 293.0 142.9 86 346.9 169.2 46 400.9 195.5 06 454.8 221.8 66 508.7 248.1 27 293.9 143.4 87 347.8 169.7 47 401.8 196.0 07 455.7 222.3 67 509.6 248.6 28 294.8 143.8 88 348.7 170.1 48 402.7 196.4 08 456.6 222.7 68 510.5 249.0 29 295.7 144.2 89 349.6 170.5 49 403.6 196.8 09 457.5 223.1 69 511.4 249.4 30 296.6 144.7 145.1 90 391 350.5 351.4 171.0 50 404.5 197.3 197. 7 10 458.4 223.6 70 512.3 513.2 249.9 331 297.5 171.4 451 405.4 511 459.3 224.0 571 250.3 32 298.4 145.6 92 352.3 171.8 52 406.3 198.1 12 460.2 224.4 72 514.1 250.8 33 299.3 146.0 93 353.2 172.3 53 407.2 198.6 13 461.1 224.9 73 515.0 251.2 34 300.2 146.4 94 354.1 172.7 54 408.1 199.0 14 462.0 225.3 74 515.9 251.6 35 301.1 146.9 95 355.0 173.2 55 409.0 199.5 15 462.9 225.8 75 516.8 252.1 36 302.0 147.3 96 355.9 173.6 56 409.9 199.9 16 463.8 226.2 76 517.7 252.5 37 302.9 147.7 97 356.8 174.0 57 410.8 200.3 17 464.7 226.6 77 518.6 252.9 38 303.8 148.2 98 357.7 174.5 58 411.7 200.8 18 465.6 227.1 78 519.5 253.4 39 304.7 148.6 99 358.6 174.9 59 412.6 201.2 19 466.5 227.5 79 520.4 253.8 4Q 305.6 149.0 400 359.5 175.4 60 413.5 201.7 20 521 467.4 228.0 80 521.3 254.3 341 306.5 149.5 401 360.4 175.8 461 414.4 202.1 468.3 228.4 581 522.2 254.7 42 307.4 149.9 02 361.3 176.2 62 415.2 202.5 22 469.2 228.8 82 523.1 255.1 43 308.3 150.4 03 362.2 176.7 63 416.1 203.0 23 470.1 229.3 83 524.0 255.6 44 309.2 150.8 04 363.1 177.1 64 417.0 203.4 24 471.0 229.7 84 524.9 256.0 45 310.1 151.2 05 364.0 177.5 65 417.9 203.8 25 471.9 230.1 85 525.8 256.4 46 311.0 151.7 06 364.9 178.0 66 418.8 204.3 26 472.8 230.6 86 526.7 256.9 47 311.9 152.1 07 365.8 178.4 67 419.7 204.7 27 473.7 231.0 87 527.6 257.3 48 312.8 152.6 08 366.7 178.9 68 420.6 205.2 28 474.6 231.5 88 528.5 257.8 49 313.7 153.0 09 367.6 179.3 69 421.5 205.6 29 475.5 231.9 89 529.4 258.2 50 314.6 315. 5 153.4 10 368.5 179.7 70 471 422.4 206.0 30 476.4 232.3 90 530.3 258.6 259.1 351 153.9 411 369.4 180.2 423.3 206.5 531 477.3 232.8 591 531.2 52 316.4 154.3 12 370.3 180.6 72 424.2 206.9 32 478.2 233.2 92 532.1 259.5 53 317.3 154.7 13 371.2 181.1 73 425.1 207.3 33 479.1 233.6 93 533.0 259.9 54 318.2 155.2 14 372.1 181.5 74 426.0 207.8 34 480.0 234.1 94 533.9 260.4 55 319.1 155.6 15 373.0 181.9 75 426.9 208.2 35 480.9 234.5 95 534.8 260.8 56 320.0 156.1 16 373.9 182.4 76 427.8 208.7 36 481.8 235.0 96 535.7 261.3 57 320.9 156.5 17 374.8 182.8 77 428.7 209.1 37 482.7 235.4 97 536.6 261.7 58 321.8 156.9 18 375.7 183.2 78 429.6 209.5 38 483.6 235.8 98 537.5 262.1 59 322.7 157.4 19 376.6 183.7 79 430.5 210.0 39 484.5 236.3 90 538.4 262.6 60 323.6 157.8 20 377.5 184.1 80 431.4 210.4 40 485.3 236.7 600 539.3 263.0 DiBt. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 64° (116°, 244°, 296°). Page 684] TABLE 2. Difference of Latitude and Departure for 27° (153°, 207 °, 333° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 54.4 27.7 121 107.8 54.9 181 161.3 82.2 241 214.7 109.4 2 1.8 0.9 62 55.2 28.1 22 108.7 55.4 82 162.2 82.6 42 215.6 109.9 3 2.7 1.4 63 56.1 28.6 23 109.6 55.8 83 163.1 83.1 43 216.5 110.3 4 3.6 1.8 64 57.0 29.1 24 110.5 56.3 84 163.9 83.5 44 217.4 110.8 5 4.5 2.3 65 57.9 29.5 25 111.4 56.7 85 164.8 84.0 45 218.3 111.2 6 5.3 2.7 66 58.8 30.0 26 112.3 57.2 86 165.7 84.4 46 219.2 111.7 7 6.2 3.2 67 59.7 30.4 27 113.2 57.7 87 166.6 84.9 47 220.1 112.1 8 7.1 3.6 68 60.6 30.9 28 114.0 58.1 88 167.5 85.4 48 221.0 112.6 9 8.0 4.1 69 61.5 31.3 29 114.9 58.6 89 168.4 85.8 49 221.9 113.0 10 8.9 4.5 70 62.4 31.8 30 115.8 116.7 59.0 90 169.3 86.3 50 222.8 113.5 11 9.8 5.0 71 63.3 32.2 131 59.5 191 170.2 86.7 251 223.6 114.0 12 10.7 5.4 72 64.2 32.7 32 117.6 59.9 92 171.1 87.2 52 224.5 114.4 13 11.6 5.9 73 65.0 33.1 33 118.5 60.4 93 172.0 87.6 53 225.4 114.9 14 12.5 6.4 74 65.9 33.6 34 119.4 60.8 94 172.9 88.1 54 226.3 115.3 15 13.4 6.8 75 66.8 34.0 35 120.3 61.3 95 173.7 88.5 55 227.2 115.8 16 14.3 7.3 76 67.7 34.5 36 121.2 61.7 96 174.6 89.0 56 228.1 116.2 17 15.1 7.7 77 68.6 35.0 37 122.1 62.2 97 175.5 89.4 57 229.0 116.7 18 16.0 8.2 78 69.5 35.4 38 123.0 62.7 98 176.4 89.9 58 229.9 117.1 19 16.9 8.6 79 70.4 35.9 39 123.8 63.1 99 177.3 90.3 59 230.8 117.6 20 17.8 9.1 80 71.3 36.3 40 124.7 63.6 200 178.2 90.8 60 231.7 118.0 21 18.7 9.5 81 72.2 36.8 141 125.6 64.0 201 179.1 91.3 261 232.6 118.5 22 19.6 10.0 82 73.1 37.2 42 126.5 64.5 02 180.0 91.7 62 233.4 118.9 23 20.5 10.4 83 74.0 37.7 43 127.4 64.9 03 180.9 92.2 63 234.3 119.4 24 21.4 10.9 84 74.8 38.1 44 128.3 65.4 04 181.8 92.6 64 235.2 119.9 25 22.3 11.3 85 75.7 38.6 45 129.2 65.8 05 182.7 93.1 65 236.1 120.3 26 23.2 11.8 86 76.6 39.0 46 130.1 66.3 06 183.5 93.5 66 237.0 120.8 27 24.1 12.3 87 77.5 39.5 47 131.0 66.7 07 184.4 94.0 67 237.9 121.2 28 24.9 12.7 88 78.4 40.0 48 131.9 67.2 08 185.3 94.4 68 238.8 121.7 29 25.8 13.2 89 79.3 40.4 49 132.8 67.6 09 186.2 94.9 69 239.7 122.1 30 26.7 13.6 90 80.2 40.9 50 133.7 68.1 10 187.1 95.3 70 240.6 122. 6 31 27.6 14.1 91 81.1 41.3 151 134.5 68.6 211 188.0 95.8 271 241.5 123.0 32 28.5 14.5 92 82.0 41.8 52 135.4 69.0 12 188.9 96.2 72 242.4 123.5 33 29.4 15.0 93 82.9 42.2 53 136.3 69.5 13 189.8 96.7 73 243.2 123.9 34 30.3 15.4 94 83.8 42.7 54 137.2 69.9 14 190.7 97.2 74 244.1 124.4 35 31.2 15.9 95 84.6 43.1 55 138.1 70.4 15 191.6 97.6 75 245.0 124.8 36 32.1 1G.3 96 85.5 43.6 56 139.0 70.8 16 192.5 98.1 76 245.9 125.3 37 33.0 16.8 97 86.4 44.0 57 139.9 71.3 17 193.3 98.5 77 246.8 125.8 38 33.9 17.3 98 87.3 44.5 58 140.8 71.7 18 194.2 99.0 78 247.7 126.2 39 34.7 17.7 99 88.2 44.9 59 141.7 72.2 19 195.1 99.4 79 248.6 126.7 40 35.6 18.2 100 89.1 45.4 60 142.6 72.6 20 196.0 99.9 80 249.5 127.1 41 36.5 18.6 101 90.0 45.9 161 143.5 73.1 221 196.9 100.3 281 250.4 127.6 42 37.4 19.1 02 90.9 46.3 62 144.3 73.5 22 197.8 100.8 82 251.3 128.0 43 38.3 19.5 03 91.8 46.8 63 145.2 74.0 23 198.7 101.2 83 252.2 128.5 44 39.2 20.0 04 92.7 47.2 64 146.1 74.5 24 199.6 101.7 84 253.0 128.9 45 40.1 20.4 05 93.6 47.7 65 147.0 74.9 25 200.5 102.1 85 253.9 129.4 46 41.0 20.9 06 94.4 48.1 66 147.9 75.4 26 201.4 102.6 86 254. 8 129.8 47 41.9 21.3 07 95.3 48.6 67 148.8 75.8 27 202.3 103.1 87 255.7 130.3 48 42.8 21.8 08 96.2 49.0 68 149.7 76.3 28 203.1 103.5 88 256.6 130.7 49 43.7 22.2 09 97.1 49.5 69 150.6 76.7 29 204.0 104.0 89 257.5 131.2 50 44.6 22.7 10 98.0 49.9 70 151.5 77.2 30 204.9 104.4 90 258.4 131.7 51 45.4 23.2 111 98.9 50.4 171 152.4 77.6 231 205.8 104.9 291 259.3 132.1 52 46.3 23.6 12 99.8 50.8 72 153.3 78.1 32 206.7 105.3 92 260.2 132.6 53 47.2 24.1 13 100.7 51.3 73 154.1 78.5 33 207.6 105.8 93 261. 1 133.0 54 48.1 24.5 14 101.6 51.8 74 155.0 79.0 34 208.5 106.2 94 262.0 133.5 55 49.0 25.0 15 102.5 52.2 75 155.9 79.4 35 209.4 106.7 95 262.8 133.9 56 49.9 25.4 16 103.4 52.7 76 156.8 79.9 36 210.3 107.1 96 263.7 134.4 57 50.8 25.9 17 104.2 53.1 77 157.7 80.4 37 211.2 107.6 97 264.6 134.8 58 51.7 26.3 18 105.1 53.6 78 158.6 80.8 38 212.1 108.0 98 265.5 135.3 59 52.6 26.8 19 106.0 54.0 79 159.5 81.3 39 213.0 108.5 99 266.4 135. 7 60 53.5 27.2 20 106.9 54.5 80 160.4 81.7 40 213.8 109.0 300 267. 3 136.2 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 63° (117°, 243°, 297° ). TABLE 2. [Page 585 Difference of Latitude and Departure for 27° (153°, 207°, 333° ). Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 268.2 136.7 361 321.7 163.9 421 375.1 191.1 481 428.6 218.3 541 482.0 245.6 02 269.1 137.1 62 322.5 164.4 22 376.0 191.6 82 429.4 218.8 42 482.9 246.1 03 270.0 137.6 63 323.4 164.8 23 376.9 192.0 83 430.3 219.2 43 483.8 246.5 04 270.9 138.0 64 324.3 165.3 24 377.8 192.5 84 431.2 219.7 44 484.7 247.0 05 271.8 138. 5 65 325.2 165.7 25 378.7 193.0 85 432.1 220.1 45 485.6 247.4 06 272.7 138.9 66 326.1 166.2 26 379.6 193.4 86 433.0 220.6 46 486.4 247.9 07 273.5 139.4 67 327.0 166.6 27 380.5 193.9 87 433.9 221.1 47 487.3 248.4 08 274.4 139.8 68 327.9 167.1 28 381.4 194.3 88 434.8 221.5 48 488.2 248.8 09 275.3 140.3 69 328.8 167.5 29 382.2 194.8 89 435.7 222.0 49 489.1 249.2 10 276.2 140.7 70 329.7 168.0 30 383.1 195.2 90 436.6 222.4 50 490.0 249.7 311 277.1 141.2 371 330.6 168.4 431 384.0 195.7 491 437.5 222. 9 551 490.9 250.1 12 278.0 141.7 72 331.5 168.9 32 384.9 196.1 92 438.3 223.3 52 491.8 250.6 13 278.9 142.1 73 332.3 169.3 33 385.8 196.6 93 439.2 223.8 53 492.7 251.0 14 279.8 142.6 74 333. 2 169.8 34 386.7 197.0 94 440.1 224.2 54 493.6 251.5 15 280.7 143.0 75 334.1 170.3 35 387.6 197.5 95 441.0 224.7 55 494.5 252.0 16 281.6 143. 5 76 335.0 170.7 36 388.5 197.9 96 441.9 225.2 56 495.4 252.4 17 282.5 143.9 77 335.9 171.2 37 389.4 198.4 97 442.8 225.6 57 496.3 252.9 18 283. 3 144.4 78 336.8 171.6 38 390.3 198.9 98 443.7 226.1 58 497.2 253. 3 19 284.2 144.8 79 337.7 172.1 39 391.2 199.3 99 444.6 226.5 59 498.1 253.8 20 285.1 145.3 80 338.6 172.5 40 392.0 199.8 500 445.5 227.0 60 499.0 254.2 321 286.0 145.7 381 339.5 173.0 441 392.9 200.2 501 446.4 227.5 561 499.8 254.7 22 286.9 146.2 82 340.4 173.4 42 393.8 200.7 02 447.3 227.9 62 500.7 255.1 23 287.8 146.6 83 341.3 173.9 43 394.7 201.1 03 448.2 228.4 63 501.6 255.6 24 288.7 147.1 84 342.1 174.3 44 395.6 201.6 04 449.0 228.8 64 502.5 256.0 25 289.6 147.6 85 343.0 174.8 45 396.5 202.0 05 449.9 229.3 65 503.4 256.5 26 290.5 148.0 86 343.9 175.2 46 397.4 202.5 06 450.8 229.8 66 504.3 257.0 27 291.4 148.5 87 344.8 175.7 47 398.3 202.9 07 451.7 230.2 67 505.2 257.4 28 292.3 148.9 88 345.7 176.2 48 399.2 203.4 08 452.6 230.6 68 506.1 257.9 29 293.2 149.4 89 346.6 176.6 49 400.1 203.8 09 453.5 231.0 69 507.0 258. 3 30 294.0 294.9 149.8 90 347. 5 177.1 177. 5 50 401.0 204.3 10 454.4 231.5 70 571 507.9 508.7 258. 8 259. 2 331 150. 3 391 348.4 451 401.8 204.7 511 455.3 231.9 32 295.8 150.7 92 349.3 178.0 52 402.7 205.2 12 456.2 232.4 72 509.6 259. 7 33 296.7 151.2 93 350.2 178.4 53 403.6 205.7 13 457.1 232.9 73 510.5 260.1 34 297.6 151.6 94 351.1 178.9 54 404.5 206.1 14 458.0 233.3 74 511.4 260.6 35 298.5 152.1 95 352.0 179.3 55 405.4 206.6 15 458. 8 233.8 75 512.3 261.1 36 299.4 152. 5 96 352.8 179.8 56 406.3 207.0 16 459.7 234.2 76 513.2 261.5 37 300.3 153.0 97 353.7 180.2 57 407.2 207.5 17 460.6 234.7 77 514.1 262.0 38 301.2 153.5 98 354.6 180.7 58 408.1 207.9 18 461.5 235.2 78 515.0 262.4 39 302.1 153.9 99 355.5 181.2 59 409.0 208.4 19 462.4 235.7 79 515.9 262.9 40 302.9 154.4 400 401 356.4 357.3 181.6 60 409.9 208.8 209. 3~ 20 521 463.3 464. 2 236.1 80 516.8 263.4 341 303.8 154.8 182.1 461 410.8 236.6 581 517.7 263.8 42 304.7 155.3 02 358.2 182.5 62 411.6 209.8 22 465.1 237.0 82 518.5 264.3 43 305.6 155.7 03 359.1 183.0 63 412.5 210.2 23 466.0 237.5 83 519.4 264.7 44 306.5 156.2 04 360.0 183.4 64 413.4 210.7 24 466.9 237.9 84 520.3 265.2 45 307.4 156.6 05 360.9 183.9 65 414.3 211.1 25 467.8 238.4 85 521.2 265.6 46 308.3 157.1 06 361.8 184.3 66 415.2 211.6 26 468.7 238.8 86 522. 1 1 266. 1 47 309.2 157.5 07 362.6 184.8 67 416.1 212.0 27 469.5 239.3 87 523.0 266.5 48 310.1 158.0 08 363.5 185.2 68 417.0 212.5 28 470.4 239.7 88 523.9 267.0 49 311.0 158.5 09 364.4 185. 7 69 417.9 212.9 29 471.3 240.2 89 524.8 267.4 50 311.9 158.9 10 365. 3 186.1 70 418.8 213.4 30 472.2 240.6 90 525. 7 267.9 351 312.7 159.4 411 366.2 186.6 471 419.7 213.8 531 473.1 241.1 591 526.6 268.3 52 313.6 159.8 12 367.1 187.1 72 420.6 214.3 32 474.0 241.5 92 527.5 268.8 53 314.5 160.3 13 368.0 187.5 73 421.4 214.7 33 474.9 242.0 93 528.4 269.2 54 315.4 160.7 14 368.9 188.0 74 422.3 215.2 34 475.8 242.4 94 529.3 269.7 55 316.3 161.2 15 369.8 188.4 75 423.2 215.7 35 476.7 242.9 95 530.1 270.1 56 317.2 161.6 16 370.7 188.9 76 424.1 216.1 36 477.6 243.4 96 531.0 270.6 57 318.1 162. '1 17 371.6 189.3 77 425.0 216.6 37 478.4 243.8 97 531.9 271.1 58 319.0 162.5 18 372.4 189.8 78 425.9 217.0 38 479.3 244.3 98 532.8 271.5 59 319.9 163.0 19 373.3 190.2 79 426.8 217.5 39 480.2 244.7 99 533.7 272.0 60 320.8 163.4 20 374.2 190.7 80 427.7 217.9 40 481.1 245,2 600 534.6 272.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 63° (1 17°, 243°, 297° ). 1 Page 586] TABLE 2. Difference of Latitude and Departure for 28° (152°, 208 °, 332° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 53.9 28.6 121 106.8 56.8 181 159.8 85.0 241 212.8 113.1 2 1.8 0.9 62 54.7 29.1 22 107.7 57.3 82 160.7 85.4 42 213.7 113.6 3 2.6 1.4 63 55.6 29.6 23 108.6 57.7 83 161.6 85.9 43 214.6 114.1 . 4 3.5 1.9 64 56.5 30.0 24 109.5 58.2 84 162.5 86.4 44 215.4 114.6 5 4.4 2.3 65 67.4 30.5 25 110.4 58.7 85 163.3 86.9 45 216.3 115.0 6 5.3 2.8 66 58.3 31.0 26 111.3 59.2 86 164.2 87.3 46 217.2 115.5 7 6.2 3.3 67 59.2 31.5 27 112.1 59.6 87 165.1 87.8 47 218.1 116.0 8 7.1 3.8 68 60.0 31.9 28 113.0 60.1 88 166.0 88.3 48 219.0 116.4 9 7.9 4.2 69 60.9 32.4 29 113.9 60.6 89 166.9 88.7 49 219.9 116.9 10 8.8 4.7 70 61.8 32.9 30 114.8 61.0 90 167.8 89.2 50 220.7 117.4 11 9.7 5.2 71 62.7 33.3 131 115.7 61.5 191 168.6 89.7 251 221. 6 117.8 12 10.6 5.6 72 63.6 33.8 32 116.5 62.0 92 169.5 90.1 52 222.5 118.3 13 11.5 6.1 73 64.5 34.3 33 117.4 62.4 93 170.4 90.6 53 223.4 118.8 14 12.4 6.6 74 65.3 34.7 34 118.3 62.9 94 171.3 91.1 54 224.3 119.2 15 13.2 7.0 75 66.2 35.2 35 119.2 63.4 95 172.2 91.5 55 225.2 119.7 16 14.1 7.5 76 67.1 35.7 36 120.1 63.8 96 173.1 92.0 56 226.0 120.2 17 15.0 8.0 77 68.0 36.1 37 121.0 64.3 97 173.9 92.5 57 226.9 120.7 18 15.9 8.5 78 68.9 36.6 38 121.8 64.8 98 174.8 93.0 58 227.8 121.1 19 16.8 8.9 79 69.8 37.1 39 122.7 65.3 99 175.7 93.4 59 228.7 121.6 20 17.7 9.4 80 70.6 37.6 40 123.6 65.7 200 176.6 93.9 60 229.6 122.1 122.5 21 18.5 9.9 81 71.5 38.0 141 124.5 66.2 201 177.5 94.4 261 230.4 22 19.4 10.3 82 72.4 38.5 42 125.4 66.7 02 178.4 94.8 62 231.3 123.0 23 20.3 10.8 83 73.3 39.0 43 126.3 67.1 03 179.2 95.3 63 232.2 123.5 24 21.2 11.3 84 74.2 39.4 44 127.1 67.6 04 180.1 95.8 64 233.1 123.9 25 22.1 11.7 85 75.1 39.9 45 128.0 68.1 05 181.0 96.2 65 234. 124.4 26 23.0 12.2 86 75.9 40.4 46 128.9 68.5 06 181.9 96.7 66 234.9 124.9 27 23.8 12.7 87 76.8 40.8 47 129.8 69.0 07 182.8 97.2 67 235.7 125.3 28 24.7 13.1 88 77.7 41.3 48 130.7 69.5 08 183.7 97.7 68 236.6 125.8 29 25.6 13.6 89 78.6 41.8 49 131.6 70.0 09 184.5 98.1 69 237.5 126.3 30 26.5 14.1 90 79.5 42.3 '42.7 50 132.4 70.4 10 185.4 98.6 70 238.4 239.3 126.8 31 27.4 14.6 91 80.3 151 133.3 70.9 211 186.3 99.1 271 127.2 32 28.3 15.0 92 81.2 43.2 52 134.2 71.4 12 187.2 99.5 72 240.2 127.7 33 29.1 15.5 93 82.1 43.7 53 135.1 71.8 13 188.1 100.0 73 241.0 128.2 34 30.0 16.0 94 83.0 44.1 54 136.0 72.3 14 189.0 100.5 74 241.9 128.6 35 30.9 16.4 95 83.9 44.6 55 136.9 72.8 15 189.8 100.9 75 242.8 129.1 36 31.8 16.9 96 84.8 45.1 56 137.7 73.2 16 190.7 101.4 76 243.7 129.6 37 32.7 17.4 97 85.6 45.5 57 138.6 73.7 17 191.6 101.9 77 244.6 130.0 38 33.6 17.8 98 86.5 46.0 58 139.5 74.2 18 192.5 102.3 78 245.5 130.5 39 34.4 18.3 99 87.4 46.5 59 140.4 74.6 19 193.* 4 102.8 79 246.3 131.0 40 35.3 18.8 100 88.3 46.9 60 141.3 75.1 20 194.2 103.3 "103. 8 80 247.2 248. 1 131.5 41 36.2 19.2 101 89.2 47.4 161 142.2 75.6 221 195.1 281 131.9 42 37.1 19.7 02 90.1 47.9 62 143.0 76.1 22 196.0 104.2 82 249.0 132.4 43 38.0 20.2 03 90.9 48.4 63 143.9 76.5 23 196.9 104.7 83 249.9 132.9 44 38.8 20.7 04 91.8 48.8 64 144.8 77.0 24 197.8 105.2 84 250.8 133.3 45 39.7 21.1 05 92.7 49.3 65 145, 7 77.5 25 198.7 105.6 85 251.6 133.8 46 40.6 21.6 06 93.6 49.8 66 146.6 77.9 26 199.5 106.1 86 252.5 134.3 47 41.5 22.1 07 94.5 50.2 67 147.5 78.4 27 200.4 106.6 87 253.4 134.7 48 42.4 22.5 08 95.4 50.7 68 148.3 78.9 28 201.3 107.0 88 254.3 135.2 49 43.3 23.0 09 96.2 51.2 69 149.2 79.3 29 202.2 107.5 89 255.2 135.7 50 44.1 23.5 10 97.1 51.6 70 150.1 79.8 30 203.1 204.0 108.0 108.4 90 256.1 136.1 51 45.0 23.9 111 98.0 52.1 171 151.0 80.3 231 291 256.9 136.6 52 45.9 24.4 12 98.9 52.6 72 151.9 80.7 32 204.8 108.9 92 257.8 137.1 53 46.8 24.9 13 99.8 53.1 73 152.7 81.2 33 205.7 109.4 93 258.7 137.6 54 47.7 25.4 14 100.7 53.5 74 153.6 81.7 34 206.6 109.9 94 259.6 138.0 55 48.6 25.8 15 101.5 54.0 75 154.5 82.2 35 207.5 110.3 95 260.5 138.5 56 49.4 26.3 16 102.4 54.5 76 155.4 82.6 36 208.4 110.8 96 261.4 139.0 57 50.3 26.8 17 103.3 54.9 77 156.3 83.1 37 209.3 111.3 97 262.2 139.4 58 51.2 27.2 18 104.2 55.4 78 157.2 83.6 38 210.1 111.7 98 263.1 139.9 59 52.1 27.7 19 105.1 55.9 79 158.0 84.0 39 211.0 112.2 99 264.0 140.4 60 53.0 28.2 20 106.0 56.3 80 158.9 84.5 40 211.9 112.7 300 264.9 140.8 Dist. Dcp. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 62° (1 18°, 242 °, 298°). , TABLE 2. [Page 687 Dist. Difference of Latitude and Departure for 28° (152°, 208°, 332' ). Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 265.7 141.3 361 318.7 169.5 421 371.7 197.7 481 424.7 225.8 541 477,7 254.0 02 266.6 141.8 62 319.6 170.0 22 372.6 198.1 82 425.6 226. 3 42 478.6 254.5 03 267.5 142.3 63 320.5 170.4 23 373.5 198.6 83 426.5 226,8 43 479.4 255.0 04 268.4 142.7 64 321.4 170.9 24 374.3 199.1 84 427.4 227.3 44 480.3 255.5 05 269.3 143.2 65 322.2 171.4 25 375.2 199.5 85 428.3 227.7 45 481.1 255.9 06 270.2 143.7 66 323.1 171.8 26 376.1 200.0 86 429.2 228.2 46 482.0 256.4 07 271.0 144.1 67 324.0 172.3 27 377.0 200.5 87 430.1 228,6 47 482.9 256.9 08 271.9 144.6 68 324.9 172.8 28 377.9 200.9 88 430.9 229.1 48 483.8 257. 3 09 272.8 145.1 69 325.8 173.2 29 378.8 201.4 89 431.8 229.6 49 484.7 257.8 10 273.7 274.6 145.5 70 371 326.7 173.7 30 379.6 201.9 90 432.6 230.0 50 485.6 258.2 311 146.0 327.5 174.2 431 380.5 202.3 491 433.5 230.5 551 486.5 258.7 12 275.5 146.5 72 328.4 174.6 32 381.4 202.8 92 434.4 231.0 52 487.4 259.1 13 276.3 146.9 73 329.3 175.1 33 382.3 203.3 93 435.3 231.4 53 488.3 259.6 14 277.2 147.4 74 330.2 175.6 34 383.2 203.8 94 436.2 231.9 54 489.2 260.1 15 278.1 147.9 75 331.1 176.1 35 384.1 204.2 95 437.1 232.4 55 490.1 260.6 16, 279.0 148.4 76 332.0 176.5 36 384.9 204.7 96 437.9 232.9 56 490.9 261.0 17 279.9 148.8 77 332.8 177.0 37 385.8 205.2 97 438.8 233.4 57 491.8 261.5 18 280.7 149.3 78 333.7 177.5 38 386.7 205.6 98 439.7 233.8 58 492.7 262.0 19 281.6 149. 8 79 334.6 177.9 39 387.6 206.1 99 440.6 234.3 59 493.5 262.6 20 282.5 150.2 80 335.5 178.4 40 388.5 206.6 500 441.5 234. 7 235. 2 60 494,4 262.9 321 283.4 150.7 381 336.4 178.9 441 389.4 207.0 501 442.3 561 495,3 263.4 22 284.3 151.2 82 337.3 179.3 42 390.2 207.5 02 443.2 235.6 62 496. 2 ! 263. 8 1 23 285.2 151.6 83 338.1 179.8 43 391.1 208.0 03 444.1 236.1 63 497. 1 ! 264. 3 1 24 286.0 152.1 84 339. 180.3 44 392.0 208.4 04 445.0 236.6 64 498.0 264.7 25 286.9 152.6 85 339.9 180.8 45 392.9 208.9 05 445.9 237.1 65 498.9 265,2 26 287.8 153.1 86 340.8 181.2 46 393.8 209.4 06 446.8 237. 5 66 499.8 265,7 27 288.7 153.5 87 341.7 181.7 47 394.6 209.9 07 447.6 238.0 67 500.7 266.2 28 289.6 154.0 88 342.6 182.2 48 395.5 210.3 08 448.5 238.5 68 501.6 266.6 29 290.5 154. 5 89 343.4 182.6 49 396.4 210.8 09 449.4 239.0 69 502.4 267. 1 30 291.3 292.2 154.9 155.4 90 391 344.3 345.2 183.1 50 397.3 211.3 10 450.3 239.4 70 503.3 504.2 267.6 268.0 331 183.6 451 398.2 211.7 511 451.2 239.9 571 32 293.1 155.9 92 346.1 184.0 52 399.1 212,2 12 452.1 240.4 72 505.1 268.5 33 294.0 156.3 93 347.0 184.5 53 399.9 212.7 13 452.9 240.8 73 505.9 269.0 34 294.9 156.8 94 347.9 185.0 54 400.8 213.1 14 453.8 241,3 74 506.8 269.4 35 295.8 157.3 95 348.7 185.4 55 401.7 213.6 15 454.7 241.8 75 507.7 269.9 36 296.6 157.7 96 349.6 185.9 56 402.6 214.1 16 455.6 242.2 76 508.6 270. 4 37 297.5 158.2 97 350.5 186.4 57 403.5 214.6 17 456.4 242.7 77 509.4 270.9 38 298.4 158.7 98 351.4 186.9 58 404.4 215.0 18 457.3 243.2 78 510.3 271.3 39 299.3 159.2 99 352.3 187.3 59 405.2 215.5 19 458.2 243.7 79 511.2 271.8 40 300.2 159.6 400 353.1 187.8 60 406.1 216.0 20 459.1 244.1 80 512.1 513.0 272.3 341 301.0 160.1 401 354.0 188.3 461 407.0 216.4 521 460.0 244.6 581 272,7 42 301.9 160.6 02 354.9 188.7 62 407.9 216.9 22 460.9 245. 82 513.9 273,2 43 302.8 161.0 03 355.8 189.2 63 408.8 217.4 23 461.8 245.5 83 514.8 273.7 44 303.7 161.5 04 356.7 189.7 64 409.7 217.8 24 462.7 246.0 84 515.7 274.2 45 304.6 162.0 05 357.6 190.1 65 410.5 218.3 25 463.5 246.5 85 516,5 274.7 46 305.5 162.4 06 358.4 190.6 66 411.4 218.8 26 464.4 246.9 86 517.4 275.1 47 306.4 162.9 07 359.3 191.1 67 412.3 219.2 27 465.3 247,4 87 518.3 276.5 48 307.2 163.4 08 360.2 191.5 68 413.2 219.7 28 466.2 247.9 88 519,2 276.0 49 308.1 163.8 09 361.1 192.0 69 414.1 220.2 29 467.1 248.3 89 520.1 276.5 50 309.0 164.3 10 362.0 192.5 70 415.0 220.7 30 468.0 248.8 90 521.0 277.0 361 309.9 164.8 411 362.9 193.0 471 415.8 221.1 531 468.9 249.3 591 521.8 277.4 52 310.8 165.3 12 363.7 193.4 72 416.7 221.6 32 469.8 249.8 92 522.6 277.9 58 311.7 165.7 13 364.6 193.9 73 417.6 222.1 33 470.7 250.2 93 523.6 278.4 54 312.5 166.2 14 365.5 194.4 74 418.5 222.5 34 471.5 250.7 94 524,4 278.8 55 313.4 166.7 15 366.4 194.8 75 419.4 223.0 35 472.4 251.1 95 625.3 279.3 56 314.3 167.1 16 367.3 195.3 76 420.3 223.5 36 473.3 251.6 96 626.2 279.8 57 315.2 167.6 17 368.2 195.8 77 421.1 223,9 37 474.2 252.1 97 527.1 280.3 58 316.1 168.1 18 369.0 196.2 78 422.0 224,4 38 475.1 252.6 98 528.0 280.8 59 316.9 168.5 19 369.9 196.7 79 422.9 224.9 39 476.0 253.1 99 528.9 281.3 60 317.8 169.0 20 370.8 197.2 80 423.8 225,3 40 476.8 253.6 600 529.8 281.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat, Dist, Dep. Lat. Dist. Dep, Lat. ( 32° (1 18°, 242°, 298° ). Page 588] TABLE 2. Difference of Latitude and Departure for 29° ( 151°, 209°, 331 n- Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 53.4 29.6 121 105.8 58.7 181 158.3 87.8 241 210.8 116.8 2 1.7 1.0 62 54.2 30.1 22 106.7 59.1 82 159.2 88.2 42 211.7 117.3 3 2.6 1.5 63 55.1 30.5 23 107.6 59.6 83 160.1 88.7 43 212.5 117.8 4 3.5 1.9 64 56.0 31.0 24 108.5 60.1 84 160.9 89.2 44 213.4 118.3 5 4.4 2.4 65 56.9 31.5 25 109.3 60.6 85 161.8 89.7 45 214.3 118.8 6 5.2 2.9 66 57.7 32.0 26 110.2 61.1 86 162.7 90.2 46 215.2 119.3 7 6.1 3.4 67 58.6 32.5 27 111.1 61.6 87 163.6 90.7 47 216.0 119.7 8 7.0 3.9 68 59.5 33.0 28 112.0 62.1 88 164.4 91.1 48 216.9 120.2 9 7.9 4.4 69 60.3 33.5 29 112.8 62.5 89 165.3 91.6 49 217.8 120.7 10 8.7 4.8 70 61.2 33.9 30 113.7 63.0 90 166.2 92.1 50 218.7 219.5 121.2 11 9.6 5.3 71 62.1 34.4 131 114.6 63.5 191 167.1 92.6 251 121.7 12 10.5 5.8 72 63.0 34.9 32 115.4 64.0 92 167.9 93.1 52 220.4 122.2 13 11.4 6.3 73 63.8 35.4 33 116.3 64.5 93 168.8 93.6 53 221.3 122.7 14 12.2 6.8 74 64.7 35.9 34 117.2 65.0 94 169.7 94.1 54 222.2 123.1 15 13.1 7.3 75 65.6 36.4 35 118.1 65.4 95 170.6 94.5 55 223.0 123.6 16 14.0 7.8 76 66.5 36.8 36 118.9 65.9 96 171.4 95.0 56 223.9 124.1 17 14.9 8.2 77 67.3 37.3 37 119.8 66.4 97 172.3 95.5 67 224.8 124.6 18 15.7 8.7 78 68.2 37.8 38 120.7 66.9 98 173.2 96.0 58 225.7 125.1 19 16.6 9.2 79 69.1 38.3 39 121.6 67.4 99 174.0 96.5 59 226.5 125.6 20 17.5 9.7 80 70.0 38.8 40 122.4 67.9 200 174.9 97.0 60 227.4 126.1 21 18.4 10.2 81 70.8 39.3 141 123.3 68.4 201 175.8 97.4 261 228.3 126.5 22 19.2 10.7 82 71.7 39.8 42 124.2 68.8 02 176.7 97.9 62 229.2 127.0 23 20.1 11.2 83 72.6 40.2 43 125.1 69.3 03 177.5 98.4 63 230.0 127.5 24 21.0 11.6 84 73.5 40.7 44 125.9 69.8 04 178.4 98.9 64 230.9 128.0 25 21.9 12.1 85 74.3 41.2 45 126.8 70.3 05 179.3 99.4 65 231.8 128.5 26 22.7 12.6 86 75.2 41.7 46 127.7 70.8 06 180.2 99.9 66 232.6 129.0 27 23.6 13.1 87 76.1 42.2 47 128.6 71.3 07 181.0 100.4 67 233.5 129.4 28 24.5 13.6 88 77.0 42.7 48 129.4 71.8 08 181.9 100.8 68 234.4 129.9 29 25.4 14.1 89 77.8 43.1 49 130.3 72.2 09 182.8 101.3 69 235.3 130.4 30 26.2 14.5 90 78.7 43.6 50 131.2 72.7 10 183.7 101.8 70 236.1 130.9 31 27.1 15.0 91 79.6 44.1 151 132.1 73.2 211 184.5 102.3 271 237.0 131.4 32 28.0 15.5 92 80.5 44.6 52 132.9 73.7 12 185.4 102.8 72 237.9 131.9 33 28.9 16.0 93 81.3 45.1 53 133. 8 74.2 13 186.3 103.3 73 238.8 132.4 34 29.7 16.5 94 82.2 45.6 54 134.7 74.7 14 187.2 103.7 74 239.6 132.8 35 30.6 17.0 95 83.1 46.1 55 135.6 75.1 15 188.0 104.2 75 240.5 133.3 36 31.5 17.5 96 84.0 46.5 56 136.4 75.6 16 188.9 104.7 76 241.4 133.8 37 32.4 17.9 97 84.8 47.0 57 137.3 76.1 17 189.8 105.2 77 242.3 134.3 38 33.2 18.4 98 85.7 47.5 58 138.2 76.6 18 190.7 105.7 78 243.1 134.8 39 34.1 18.9 99 86.6 48.0 59 139.1 77.1 19 191.5 106.2 79 244.0 135.3 40 35.0 35.9 19.4 100 87. 5 48.5 60 139.9 77.6 20 192.4 106.7 80 244.9 135.7 41 19.9 101 88.3 49.0 161 140.8 78.1 221 193.3 107.1 281 245.8 136.2 42 36.7 20.4 02 89.2 49.5 62 141.7 78.5 22 194.2 107.6 82 246.6 136.7 43 37.6 20.8 03 90.1 49.9 63 142.6 79.0 23 195.0 108.1 83 247.5 137.2 44 38.5 21.3 04 91.0 50.4 64 143.4 79.5 24 195.9 108.6 84 248.4 137.7 45 39.4 21.8 05 91.8 50.9 65 144.3 80.0 25 196.8 109.1 85 249.3 138.2 46 40.2 22.3 06 92.7 51.4 66 145.2 80.5 26 197.7 109. 6 86 250.1 138.7 47 41.1 22.8 07 93.6 51.9 67 146.1 81.0 27 198.5 110. 1 87 251.0 139.1 48 42.0 23.3 08 94.5 52.4 68 146.9 81.4 28 199. 4 110.5 88 251.9 139.6 49 42.9 23.8 09 95.3 52.8 69 147.8 81.9 29 200.3 111.0 89 252.8 140.1 50 43.7 24.2 10 96.2 53.3 70 148.7 82.4 30 201.2 111.5 90 253.6 140.6 51 44.6 24.7 111 97.1 53.8 171 149.6 82.9 231 202.0 112.0 291 254. 5 141.1 52 45.5 25.2 12 98.0 54.3 72 150.4 83.4 32 202.9 112.5 92 255.4 141.6 53 46.4 25.7 13 98.8 54.8 73 151.3 83.9 33 203.8 113.0 93 256.3 142.0 54 47.2 26.2 14 99.7 55.3 74 152.2 84.4 34 204.7 113.4 94 257.1 142.5 55 48.1 26.7 15 100.6 55.8 75 153. 1 84.8 35 205.5 113.9 95 258.0 143.0 56 49.0 27.1 16 101.5 56.2 76 153.9 85.3 36 206.4 114.4 96 258.9 143.5 57 49.9 27.6 17 102.3 56.7 77 154.8 85.8 37 207.3 114.9 97 259.8 144.0 58 50.7 28.1 18 103.2 57.2 78 155.7 86.3 38 208.2 115.4 98 260.6 144.5 59 51.6 28.6 19 104.1 57.7 79 156.6 86.8 39 209.0 115.9 99 261.5 145.0 60 52.5 29.1 20 105.0 58.2 80 157.4 87.3 40 209.9 116.4 300 262.4 145.4 Dist. Dep. Lat Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 61° (1 19°, 241°, 299° )• TABLE 2. [Page 589 Difference of Latitude and Departure for 29° (151°, 209°, 331° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 263.2 145.9 361 315.7 175.0 421 368.2 204.1 481 420.7 233.2 541 473.2 262.3 02 264.1 146.4 62 316.6 175.5 22 369.1 204.6 82 421.5 233.7 42 474.0 262.8 03 265.0 146.9 63 317.5 176.0 23 369.9 205.1 83 422.4 234.2 43 474.9 263.2 04 265.9 147.4 64 318. 3 176.5 24 370.8 205.6 84 423.3 234.6 44 475.8 263.7 05 266.7 147.9 65 319.2 177.0 25 371.7 206.0 85 424.2 235.1 45 476.6 264.2 06 267.6 148.4 66 320.1 177.4 26 372.6 206.5 86 425.0 235.6 46 477.5 264.7 07 268.5 148. 8 67 321.0 177.9 27 373.4 207.0 87 425.9 236.1 47 478.4 265. 2 08 269.4 149.3 68 321.8 178.4 28 374.3 207.5 88 426.8 236.6 48 479.3 265.7 09 270.2 149.8 69 322.7 178.9 29 375.2 208.0 89 427.7 237.1 49 480.1 266.2 10 311 271.1 150.3 70 323.6 179.4 30 376.1 208.5 90 491 428.5 237.6 50 481.0 266.6 272.0 150.8 371 324.5 179.9 431 376.9 209.0 429.4 238.0 551 481.9 267.1 12 272.9 151.3 72 325.3 180.4 32 377.8 209.4 92 430.3 238.5 52 482.8 267.6 13 273.7 151.7 73 326.2 180.8 33 378.7 209.9 93 431.2 239.0 53 483.6 268.1 14 274.6 152.2 74 327.1 181.3 34 379.6 210.4 94 432.0 239.5 54 484.5 268.6 15 275.5 152.7 75 328.0 181.8 35 380.4 210.9 95 432.9 240.0 55 485.4 269.1 16 276.3 153.2 76 328.8 182.3 36 381.3 211.4 96 433. 8 240.5 56 486.3 269.5 17 277.2 153.7 77 329.7 182.8 37 382.2 211.9 97 434.7 240.9 57 487.1 270.0 18 278.1 154.2 78 330.6 183.3 38 383.1 212.3 98 435.5 241.4 58 488.0 270.5 19 279.0 154.7 79 331.4 183.7 39 383.9 212.8 99 436.4 241.9 59 488.9 271.0 20 279.8 155.1 80 332.3 184.2 184.7 40 384.8 213.3 500 437.3 242.4 60 489.8 271.5 321 280.7 155. 6 381 333.2 441 385.7 213.8 501 438.2 242.9 561 490.6 272.0 22 281.6 156.1 82 334.1 185.2 42 386.6 214.3 02 439.0 243. 4 62 491.5 272.5 23 282.5 156.6 83 334. 9 185.7 43 387.4 214.8 03 439.9 243.9 63 492.4 272.9 24 283.3 157.1 84 335.8 186.2 44 388.3 215.3 04 440.8 244.3 64 493.2 273.4 25 284.2 157.6 85 336.7 186.7 45 389.2 215. 7 05 441.6 244.8 65 494.1 273.9 26 285. 1 158.1 86 337.6 187.1 46 390.0 216.2 06 442.5 245.3 66 495.0 274.4 27 i 286.0 158.5 87 338.4 187.6 47 390.9 216.7 07 443.4 245.8 67 495.9 274.9 28 286. 8 159.0 88 339.3 188.1 48 391.8 217.2 08 444.3 246.3 68 496.8 275.4 29 287.7 159.5 89 340.2 188.6 49 392.7 217.7 09 445.2 246.8 69 497.7 275.9 30 288.6 289.5 160.0 90 341.1 189.1 50 393.5 218.2 218.7 10 511 446.1 247.3 70 498.5 276.3 276.8 331 160.5 391 341.9 189.6 451 394.4 447.0 247.8 571 499.4 32 290.3 161.0 92 342.8 190.0 52 395.3 219.1 12 447.8 248.2 72 500.3 277.3 33 291.2 161.4 93 343.7 190.5 53 396.2 219.6 13 448.6 248.7 73 501.1 277.8 34 292.1 161.9 94 344.6 191.0 54 397.0 220.1 14 449.5 249.2 74 502.0 278.3 35 293.0 162.4 95 345.4 191.5 55 397.9 220.6 15 450.4 249.7 75 502.9 278.8 36 293.8 162.9 96 346.3 192.0 56 398.8 221.1 16 451.3 250.2 76 503.7 279.2 37 294.7 163.4 97 347.2 192.5 57 399.7 221.6 17 452.2 250.6 77 504.6 279.7 38 295.6 163.9 98 348.1 193.0 58 400.5 222.0 18 453.1 251.1 78 505.5 280.2 39 296.5 164.4 99 348.9 193.4 59 401.4 222.5 19 463.9 251.6 79 506.4 280.7 40 297.3 298.2 164.8 400 349.8 193.9 60 402.3 223.0 20 454.8 252. 1 80 507.2 281.2 341 165.3 401 350.7 194.4 461 403.2 223.5 521 455.6 252.6 581 508.1 281.7 42 299.1 165.8 02 351.6 194.9 62 404.0 224.0 22 456.5 253.1 82 509.0 282.2 43 300.0 166.3 03 352.4 195.4 63 404.9 224.5 23 457.4 253.6 83 509.9 282.7 44 300.8 166.8 04 353.3 195.9 64 405.8 225.0 24 458.3 254.0 84 510.7 283.2 45 301.7 167.3 05 354.2 196.3 65 406.7 225.4 25 459.1 254.5 85 511.6 283.6 46 302.6 167.7 06 355.1 196.8 66 407.5 225.9 26 460.0 255.0 86 512.5 284.1 47 303.5 168.2 07 355.9 197.3 67 408.4 226.4 27 460.9 255.5 87 513.4 284.6 48 304.3 168.7 08 356.8 197.8 68 409.3 226.9 28 461.8 256.0 88 514. 3 285.0 49 305.2 169.2 09 357.7 198.3 69 410.2 227.4 29 462.6 256.5 89 515.1 285.5 50 306.1 169.7 10 358.6 198.8 70 411.0 227.9 228.3 30 531 463.5 256.9 90 516.0 286.0 351 307.0 170.2 411 359.4 199.3 471 411.9 464.4 257.4 591 516.9 286.5 52 307.8 170.7 12 360.3 199.7 72 412.8 228.8 32 465.3 257.9 92 517.7 287.0 53 308.7 171.1 13 361.2 200.2 73 413.7 229.3 33 466.1 258.4 93 518.6 287.5 54 309.6 171.6 14 362.1 200.7 74 414.5 229.8 34 467.0 258.9 94 519. 5 288.0 55 310.5 172.1 15 362.9 201.2 75 415.4 230. 3 35 467.9 259.4 95 520.4 288.5 56 311.3 172.6 16 363.8 201.7 76 416.3 230.8 36 468.8 259.9 96 521.2 288.9 57 312.2 173.1 17 364.7 202.2 77 417.2 231.3 37 469.6 260.3 97 522.1 289.4 58 313.1 173.6 18 365.6 202.7 78 418.0 231.7 38 470.5 260.8 98 523.0 289.9 59 314.0 174.0 19 366.4 203.1 79 418.9 232.2 39 471.4 261.3 99 523.9 290.4 60 314.8 174.5 20 367.3 203.6 80 419.8 232.7 40 472.3 261.8 600 524. 8 290.9 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 1 6 1° (119°, 241°, 299°] . Page 690] TABLE 2. Difference of Latitude and Departure for . 30° (150°, 210 °, 330° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 52.8 30.5 121 104.8 60.5 181 156.8 90.5 241 208.7 120.6 2 1.7 1.0 62 53.7 31.0 22 105.7 61.0 82 157.6 91.0 42 209.6 121.0 3 2.6 1.5 63 54.6 31.5 23 106.5 61.5 83 158.5 91.5 43 210.4 121.5 4 3.5 2.0 64 55.4 32.0 24 107.4 62.0 84 159.3 92.0 44 211.3 122.0 5 4.3 2.5 65 56.3 32.5 25 108.3 62.5 85 160.2 92.5 45 212.2 122.5 6 5.2 3.0 66 57.2 33.0 26 109.1 63.0 86 161.1 93.0 46 213.0 123.0 7 6.1 3.5 67 58.0 33.5 27 110.0 63.5 87 161.9 93.5 47 213.9 123.5 8 6.9 4.0 68 58.9 34.0 28 110.9 64.0 88 162.8 94.0 48 214.8 124.0 9 7.8 4.5 69 59.8 34.5 29 111.7 64.5 89 163.7 94.5 49 215.6 124.5 10 11 8.7 5.0 70 60.6 35.0 30 112.6 65.0 90 164. 5 95.0 50 216.5 125.0 9.5 5.5 71 61.5 35.5 131 113.4 65.5 191 165.4 95.5 251 217.4 125.5 12 10.4 6.0 72 62.4 36.0 32 114.3 66.0 92 166.3 96.0 52 218.2 126.0 13 11.3 6.5 73 63.2 36.5 33 115.2 66.5 93 167.1 96.5 53 219.1 126.5 14 12.1 7.0 74 64.1 37.0 34 116.0 67.0 94 168.0 97.0 54 220.0 127.0 15 13.0 7.5 75 65.0 37.5 35 116.9 67.5 95 168.9 97.5 55 220.8 127.5 16 13.9 8.0 76 65.8 38.0 36 117.8 68.0 96 169.7 98.0 56 221.7 128.0 17 14.7 8.5 77 66.7 38.5 37 118.6 68.5 97 170.6 98.5 57 222.6 128.5 18 15.6 9.0 78 67.5 39.0 38 119.5 69.0 98 171.5 99.0 58 223. 4 129.0 19 16.5 9.5 79 68.4 39.5 39 120.4 69.5 99 172.3 99.5 59 224.3 129.5 20 17.3 10.0 80 69.3 40.0 40.5 40 141 121.2 70.0 200 173.2 100.0 60 225.2 1.30. 21 18.2 10.5 81 70.1 122.1 70.5 201 174.1 100.5 261 226.0 130.5 22 19.1 11.0 82 71.0 41.0 42 123.0 71.0 02 174.9 101.0 62 226.9 131.0 23 19.9 11.5 83 71.9 41.5 43 123.8 71.5 03 175.8 101.5 63 227.8 131.5 24 20.8 12.0 84 72.7 42.0 44 124.7 72.0 04 176.7 102.0 64 228.6 132.0 25 21.7 12.5 85 73.6 42.5 45 125.6 72.5 05 177.5 102.5 65 229.5 132.5 26 22.5 13.0 86 74.5 43.0 46 126.4 73.0 06 178.4 103.0 66 230. 4 133.0 27 23.4 13.5 • 87 75.3 43.5 47 127.3 73.5 07 179.3 103.5 67 231.2 133.5 28 24.2 14.0 88 76.2 44.0 48 128.2 74.0 08 180.1 104.0 68 232.1 134.0 29 25.1 14.5 89 77.1 44.5 49 129.0 74.5 09 181.0 104.5 69 233.0 134.5 30 26.0 15.0 90 77.9 78.8 45.0 45.5 50 151 129.9 75.0 10 181.9 105. 70 233. 8 135.0 135.5 31 26.8 15.5 91 130.8 75.5 211 182.7 105.5 271 234.7 32 27.7 16.0 92 79.7 46.0 52 131.6 76.0 12 183. 6 106.0 72 23-3. 6 136.0 33 28.6 16.5 93 80.5 46.5 53 132.5 76.5 13 184.5 106.5 73 236.4 136.5 34 29.4 17.0 94 81.4 47.0 54 133.4 77.0 14 185.3 107.0 74 237.3 137.0 35 30.3 17.5 95 82.3 47.5 55 134.2 77.5 15 186.2 107.5 75 238.2 137.5 36 31.2 18.0 96 83.1 48.0 56 135.1 78.0 16 187.1 108.0 76 239.0 138. 37 32.0 18.5 97 84.0 48.5 57 136.0 78.5 17 187.9 108.5 77 239. 9 138.5 38 32.9 19.0 98 84.9 49.0 58 136.8 79.0 18 188.8 109.0 78 240.8 139.0 39 33.8 19.5 99 85.7 49.5 59 137.7 79.5 19 189.7 109.5 79 241.6 139.5 40 34.6 20.0 100 86.6 50.0 60 138.6 80.0 20 190.5 110.0 80 242.5 243.4 140.0 140.5 41 35.5 20.5 101 87.5 50.5 161 139.4 80.5 221 191.4 110.5 281 42 36.4 21.0 02 88.3 51.0 62 140.3 81.0 22 192.3 111.0 82 244.2 141.0 43 37.2 21.5 03 89.2 51.5 63 141.2 81.5 23 193.1 111.5 83 245. 1 141.5 44 38.1 22.0 04 90.1 52.0 64 142.0 82.0 24 194.0 112.0 84 246.0 142.0 45 39.0 22.5 05 90.9 52.5 65 142.9 82.5 25 194.9 112.5 85 246.8 142.5 46 39.8 23.0 06 91.8 ^3.0 66 143.8 83.0 26 195.7 113.0 86 247.7 143.0 47 40.7 23.5 07 92.7 53.5 67 144.6 83.5 27 196.6 113.5 87 248.5 143.5 48 41.6 24.0 08 93.5 54.0 68 145.5 84.0 28 197.5 114.0 88 249.4 144.0 49 42.4 24.5 09 94.4 54.5 69 146.4 84.5 29 198.3 114.5 89 250.3 144.5 50 43.3 25.0 10 95.3 55.0 55.5 70 171 147.2 148.1 85.0 30 199.2 115.0 90 251.1 145.0 51 44.2 25.5 111 96.1 85.5 231 200.1 115.5 291 252. 145.5 52 45.0 26.0 12 97.0 56.0 72 149.0 86.0 32 200.9 116.0 92 252.9 146.0 53 45.9 26.5 13 97.9 56.5 73 149.8 86.5 33 201.8 116.5 93 253.7 146.5 54 46.8 27.0 14 98.7 57.0 74 150.7 87.0 34 202.6 117.0 94 254. 6 147.0 55 47.6 27.5 15 99.6 57.5 75 151.6 87.5 35 203.5 117.5 95 255.5 147.5 56 48.5 28.0 16 100.5 58.0 76 152.4 88.0 36 204.4 118.0 96 256.3 148.0 57 49.4 28.5 17 101.3 58.5 77 153.3 88.5 37 205.2 118.5 97 257.2 148.5 58 50.2 29,0 18 102.2 59.0 78 154.2 89.0 38 206.1 119.0 98 258.1 149.0 59 51.1 29.5 19 103.1 59.5 79 155. 89.5 39 207.0 119.5 99 258.9 149.5 60 52.0 30.0 20 103.9 60.0 80 155.9 90.0 40 207.8 120.0 300 259.8 150.0 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 60° (1 20°, 240°, 300° ). TABLE 2. [Page 691 Difference of Latitude and Departure for 30 ° (150°, 210°, 330°). Dist. [ Lat. Dep. Dist. Lat. Dep. Dist. 1 Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 260.7 150.5 361 312.6 180.5 421 364.6 210.5 481 416.6 240.5 541 468.5 270.5 02 261.5 151.0 62 313.5 181.0 22 365.5 211.0 82 417.4 241.0 42 469.4 271.0 03 262.4 151.5 63 314.4 181.5 23 366. 3 211.5 83 418.3 241.5 43 470.3 271.5 04 263.3 152.0 64 315.2 182.0 24 367.2 212.0 84 419.2 242.0 44 471.1 272.0 05 264.1 152.5 65 316.1 182.5 25 368.1 212.5 85 420.0 242.5 45 472.0 272.5 06 265.0 153.0 66 317.0 183.0 26 368.9 213.0 86 420.9 243.0 46 472.9 273.0 07 265.9 153.5 67 317.8 183.5 27 369. 8 213.5 87 421.8 243.5 47 473.7 273.5 08 266.7 154.0 68 318.7 184.0 28 370.7 214.0 88 422.6 244.0 48 474.6 274.0 09 267.6 154.5 69 319.6 184.5 29 371.5 214.5 89 423.5 244.5 49 475.5 274.5 10 268.5 155.0 70 320.4 185.0 30 372.4 215.0 90 424.4 245.0 50 476.3 275.0 311 269.3 155.5 371 321.3 185.5 431 373.3 215.5 491 425.2 245.5 551 477.2 275.5 12 270.2 156.0 72 322.2 186.0 32 374.1 216.0 92 426.1 246.0 52 478.1 276.0 13 271.1 156.5 73 323.0 186.5 33 375.0 216.5 93 426.9 246.5 53 478.9 276.5 14 271.9 157.0 74 323.9 187.0 34 375.9 217.0 94 427.8 247.0 54 479.8 277.0 15 272.8 157.5 75 324.8 187.5 35 376.7 217.5 95 428.7 247.5 55 480.7 277.5 16 273.7 158.0 76 325.6 188.0 36 377.6 218.0 96 429.6 248.0 56 481.5 278.0 17 274.5 158.5 77 326.5 188.5 37 378.5 218.5 97 430.4 248.5 57 482.4 278.5 18 275.4 159.0 78 327.4 189.0 38 379. 3 219.0 98 431.3 249.0 58 483.3 279.0 19 276.3 159.5 79 328.2 189.5 39 380.2 219.5 99 432.2 249.5 59 484.1 279.5 20 277.1 160.0 80 329. 1 190.0 40 381.1 220.0 500 433. 250.0 60 485.0 280.0 321 278.0 160.5 381 330.0 190.5 441 381.9 220. 5 501 433.9 250. 5 561 485.9 280.5 22 278.9 161.0 82 330.8 191.0 42 382.8 221.0 02 434.8 251.0 62 486.7 281.0 23 279.7 161.5 83 331.7 191.5 43 383.7 221.5 03 435.6 251.5 63 487.6 281.5 24 280.6 162.0 84 332.6 192. 44 384.5 222.0 04 436.5 252.0 64 488.5 282.0 25 281.5 162.5 85 333. 4 192.5 45 385.4 222.5 05 437.4 252.5 65 489.3 282.5 26 282.3 163. 86 334.3 193.0 46 386. 3 223.0 06 438.2 253.0 66 490.2 283.0 27 283.2 163. 5 87 335.2 193.5 47 387.1 223.5 07 439.1 253.5 67 491.1 283.5 28 284.1 164.0 88 336.0 194.0 48 388.0 224.0 08 440.0 254.0 68 491.9 284.0 29 284.9 164.5 89 336.9 194.5 49 388.9 224.5 09 440.8 254.5 69 492.8 284.5 30 331 285.8 165.0 90 337.8 195.0 50 389.7 390.6 225.0 10 441.7 255.0 70 493.6 285. 286.7 165.5 391 338.6 195.5 451 225.5 511 442.6 255.5 571 494.5 285. 5 32 287.5 166.0 92 339. 5 196.0 52 391.5 226.0 12 443.4 256.0 72 495.4 286.0 33 288.4 166.5 93 340.4 196.5 53 392.3 226.5 13 444.3 256.5 73 496.3 286.5 34 289.3 167.0 94 341.2 197.0 54 393.2 227.0 14 445.2 257.0 74 497.1 287.0 35 290.1 167.5 95 342.1 197.5 55 394.0 227.5 15 446.0 257.5 75 497.9 287.5 36 291.0 168.0 96 343.0 198.0 56 394.9 228.0 16 446.9 258.0 76 498.8 288.0 37 291.9 168.5 97 343.8 198. 5 57 395.8 228.5 17 447.8 258.5 77 499.7 288. 5 38 292.7 169.0 98 344.7 199.0 58 396.6 229.0 18 448.6 259. 78 500.5 289.0 39 293.6 169.5 99 345.6 199.5 59 397.5 229.5 19 449.4 259.5 79 501.3 289.5 40 341 294.5 170.0 400 346.4 200.0 60 398.4 230.0 20 450.3 260.0 80 502.2 503.1 290.0 290.5 295.3 170.5 401 347.3 200.5 461 399.2 230.5 521 451.2 260.5 581 42 296.2 171.0 02 348.1 201.0 62 400.1 231.0 22 452.1 261.0 82 504.0 291.0 43 297.1 171.5 03 349.0 201.5 63 401.0 231.5 23 452.9 '261.5 83 504.9 291.5 44 297.9 172.0 04 349.9 202.0 64 401.8 232.0 24 453.8 262.0 84 505.8 292.0 45 298.8 172.5 05 350.7 202.5 65 402.7 232.5 25 454.7 262.5 85 506.6 292.5 46 299.7 173.0 06 351.6 203.0 66 403.6 233.0 26 455.5 263.0 86 507.5 293.0 47 300.5 173.5 07 352. 5 203.5 67 404.4 233.5 27 456.4 263.5 87 508.4 293.5 48 301.4 174.0 08 353.3 204.0 68 405.3 234.0 28 457.3 264.0 88 509.2 294.0 49 302.3 174.5 09 354.2 204.5 69 406.2 234.5 29 458.1 264.5 89 510.1 294.5 50 351 303.1 175.0 10 355.1 355.9 205.0 70 407.0 235.0 30 459.0 265.0 90 511.0 295.0 304.0 175.5 411 205.5 471 407.9 235.5 531 459.9 265.5 591 511.8 295.5 52 304.8 176.0 12 356. 8 206.0 72 408.8 236.0 32 460.7 266.0 92 512.7 296.0 53 305.7 176.5 13 357.7 206.5 73 409.6 236.5 33 461.6 266.5 93 513.6 296.5 54 306.6 177.0 14 358.5 207.0 74 410.5 237.0 34 462.5 267.0 94 514.4 297.0 55 307.4 177.5 15 359.4 207.5 75 411.4 237.5 35 463.3 267.5 95 515.3 297.5 56 308.3 178.0 16 360.3 208.0 76 412.2 238.0 36 464.2 268.0 96 516.2 298.0 57 309.2 178. 5 17 361.1 208.5 77 413.1 238.5 37 465.1 268.5 97 517.0 298.5 58 310.0 179.0 18 362. 209.0 78 414.0 239. 38 465.9 269.0 98 517.9 299.0 59 310.9 179.5 19 362.9 209.5 79 414.8 2.39. 5 39 466.8 269.5 99 518.8 299.5 60 311.8 180.0 20 363.7 210.0 80 415.7 240.0 40 467.7 270.0 600 519.6 300.0 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 60° (120°, 240°, 300° ). 1 Page 592] TABLE 2. Difference of Latitude and Departure for 31° (149°, 211 °, 329° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.9 0.5 61 52.3 31.4 121 103.7 62.3 181 155.1 93.2 241 206.6 124.1 2 1.7 1.0 62 53.1 31.9 22 104.6 62.8 82 156.0 93.7 42 207.4 124.6 3 2.6 1.5 63 54 32.4 23 105.4 63.3 83 156.9 94.3 43 208.3 125.2 4 3.4 2.1 64 54.9 33.0 24 106.3 63.9 84 157.7 94.8 44 209.1 125.7 5 4.8 2.6 65 55.7 33.5 25 107.1 64.4 85 158.6 95.3 45 210.0 126.2 6 5.1 3.1 66 56.6 34.0 26 108.0 64.9 86 159.4 95.8 46 210.9 126.7 7 6.0 3.6 67 57.4 34.5 27 108.9 65.4 87 160.3 96.3 47 211.7 127.2 8 6.9 4.1 68 58.3 35.0 28 109.7 65.9 88 161.1 96.8 48 212.6 127.7 9 7.7 4.6 69 59.1 35.5 29 110.6 66.4 89 162.0 97.3 49 213.4 128.2 10 8.6 5.2 70 60.0 36.1 30 111.4 67,0 90 162.9 97.9 50 214.3 128.8 11 9.4 5.7 71 60.9 36.6 131 112.3 67.5 191 163.7 98.4 251 215.1 129.3 12 10.3 6.2 72 61.7 37.1 32 113.1 68.0 92 164.6 98.9 52 216.0 129.8 13 11.1 6.7 73 62.6 37.6 33 114.0 68.5 93 165.4 99.4 53 216.9 130.3 14 12.0 7.2 74 63.4 38.1 34 114.9 69.0 94 166.3 99.9 54 217.7 130.8 15 12.9 7.7 75 64.3 38.6 35 115.7 69.5 95 167.1 100.4 55 218.6 131.3 16 13.7 8.2 76 65.1 39.1 36 116.6 70.0 96 168.0 100.9 56 219.4 131.8 17 14.6 8.8 77 66,0 39.7 37 117.4 70.6 97 168.9 101.5 57 220.3 132.4 18 15.4 9.3 78 66.9 40.2 38 118.3 71.1 98 169.7 102.0 58 221.1 132.9 19 16.3 9.8 79 67.7 40.7 39 119.1 71.6 99 170.6 102.5 59 222.0 133.4 20 17.1 10.3 80 68.6 41.2 40 120.0 72.1 200 171.4 103.0 60 222.9 133.9 21 18.0 10.8 81 69.4 41.7 141 120.9 72.6 201 172.3 103.5 261 223.7 134.4 22 18.9 11.3 82 70.3 42.2 42 121.7 73.1 02 173.1 104.0 62 224.6 134.9 23 19.7 11.8 83 71.1 42.7 43 122.6 73,7 03 174.0 104.6 63 225.4 135.5 24 20.6 12.4 84 72.0 43.3 44 123.4 74.2 04 174.9 105.1 64 22(5.3 136.0 25 21.4 12.9 85 72.9 43.8 45 124.3 74.7 05 175.7 105.6 65 227.1 136.5 26 22.3 13.4 86 73.7 44.3 46 125.1 75.2 06 176.6 106.1 66 228.0 137.0 27 23.1 13.9 87 74.6 44.8 47 126.0 75.7 07 177.4 106.6 67 228.9 137.5 28 24.0 14.4 88 75.4 45.3 48 126.9 76.2 08 178.3 107.1 68 229.7 138.0 29 24.9 14.9 89 76.3 45.8 49 127.7 76.7 09 179.1 107.6 69 230.6 138.5 30 25.7 15.5 90 77.1 46.4 50 128.6 77.3 10 180.0 180.9 108.2 70 231.4 139.1 31 26.6 16.0 91 78.0 46.9 151 129.4 77.8 211 108.7 271 232.3 139.6 32 27.4 16.5 92 78.9 47.4 52 130.3 78.3 12 181.7 109.2 72 233.1 140.1 33 28.3 17.0 93 79.7 47.9 53 131.1 78.8 13 182.6 109.7 73 234.0 140.6 34 29.1 17.5 94 80.6 48.4 54 132.0 79.3 14 183.4 110.2 74 234.9 141.1 35 30.0 18.0 95 81.4 48.9 55 132.9 79.8 15 184.3 110.7 75 235.7 141.6 36 30.9 18.5 96 82.3 49.4 56 133.7 80.3 16 185.1 111.2 76 236.6 142.2 37 31.7 19.1 97 83.1 50.0 57 134.6 80.9 17 186.0 111.8 77 237.4 142.7 38 32.6 19.6 98 84.0 50.5 58 135.4 81.4 18 186.9 112.3 78 238.3 143.2 39 33.4 20.1 99 84.9 51.0 59 136.3 81.9 19 187.7 112.8 79 239.1 143. 7 40 34.3 20.6 100 85.7 51.5 60 137.1 82.4 20 188.6 189.4 113.3 80 240.0 144.2 41 35.1 21.1 101 86.6 52.0 161 138.0 82.9 221 113.8 281 240.9 144.7 42 36.0 21.6 02 87.4 52.5 62 138.9 83.4 22 190.3 114.3 82 241.7 145.2 43 36.9 22.1 03 88.3 53.0 63 139.7 84.0 23 191.1 114.9 83 242.6 145.8 44 37.7 22.7 04 89.1 53.6 64 140.6 84.5 24 192.0 115.4 84 243.4 146.3 45 38.6 23.2 05 90.0 54.1 65 141.4 85.0 25 192.9 115.9 85 244.3 146.8 46 39.4 23.7 06 90.9 54.6 66 142.3 85.5 26 193.7 116.4 86 245.1 147.3 47 40.3 24.2 07 91.7 55.1 67 143.1 86.0 27 194.6 116.9 87 246.0 147.8 48 41.1 24.7 08 92.6 55.6 68 144.0 86.5 28 195.4 117.4 88 246.9 148.3 49 42.0 25.2 09 93.4 56.1 69 144.9 87.0 29 196.3 117.9 89 247.7 148.8 50 42.9 25.8 10 94.3 56.7 70 145.7 87.6 30 197.1 118.5 90 291 248.6 149.4 51 43.7 26.3 111 95.1 57.2 171 146.6 88.1 231 198.0 119.0 249.4 149.9 52 44.6 26.8 12 96.0 57.7 72 147.4 88.6 32 198.9 119.5 92 250.3 150.4 1 53 45.4 27.3 13 96.9 58.2 73 148.3 89.1 33 199.7 120.0 93 251.2 150.9 1 54 46.3 27.8 14 97.7 58.7 74 149.1 89.6 34 200.6 120.5 94 252.0 151.4 1 56 47.1 28.3 15 98.6 59.2 75 150.0 90.1 35 201.4 121.0 95 252.9 151.9 1 56 48.0 28.8 16 99.4 59.7 76 150.9 90.6 36 202.3 121.5 96 253.7 152.5 1 57 48.9 29.4 17 100.3 60.3 77 151.7 91.2 37 203.1 122.1 97 254.6 153.0 58 49.7 29.9 18 101.1 60.8 78 152.6 91.7 38 204.0 122.6 98 255.4 153.5 59 50.6 30.4 19 102.0 61.3 79 153.4 92.2 39 204.9 123.1 99 256.3 154.0 1 60 51.4 30.9 20 102.9 61.8 80 154.3 92.7 40 205.7 123.6 300 257.1 154.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 59° (1 21°, 239 °, 301° )• 1 TABLE 2. [Page 693 Difference of Latitude and Departure for 31° (149", 211°, 329° ). Dist. Lat. Dep. Dist. Lat Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 258.0 155.0 361 309.4 185.9 421 360.9 216.8 481 412.3 247.7 541 463.7 278.6 02 258.9 155.5 62 310.3 186.4 22 361.7 217.3 82 413.2 248.2 42 464.6 279.1 03 259.7 156.1 63 311.2 187.0 23 362.6 217.9 83 414.0 248.8 43 465.4 279.7 04 260.6 156.6 64 312.0 187.5 24 363.4 218.4 84 414.9 249.3 44 466.3 280.2 05 261.4 157.1 65 312.9 188.0 25 364.3 218.9 85 415.7 249.8 45 467.2 280.7 06 262.3 157.6 66 313.7 188.5 26 365.2 219.4 86 416.6 250.3 46 468.0 281.2 07 263.2 158.1 67 314.6 189.0 27 366.0 219.9 87 417.4 250.8 47 468.9 281.7 08 264.0 158.6 68 315.4 189.5 28 366.9 220.4 88 418.3 251.3 48 469.7 282.3 09 264.9 159.2 69 316.3 190.1 29 367.7 221.0 89 419.2 251.9 49 470.6 282.8 10 265.7 159.7 70 317.2 190.6 30 431 368.6 221.5 90 420.0 252.4 50 551 471.4 472.3 283.3 311 266.6 160.2 371 318.0 191.1 369.4 222.0 491 420.9 '252. 9 283.8 12 267.4 160.7 72 318.9 191.6 32 370.3 222.5 92 421.7 253.4 52 473.2 284.3 13 268.3 161.2 73 319.7 192.1 33 371.2 223.0 93 422.6 253.9 53 474.0 284.8 14 269.2 161.7 74 320.6 192.6 34 372.0 223.5 94 423.4 254.4 54 474.9 285.3 15 270.0 162.2 75 321.4 193.1 35 372.9 224.0 95 424.3 254.9 55 475.7 285.8 16 270.9 162.8 76 322.3 193.7 36 373.7 224.6 96 425.2 255.5 56 476.6 286.4 17 271. 7 163.3 77 323.2 194.2 37 374.6 225.1 97 426.0 256.0 57 477.4 286.9 18 272.6 163.8 78 324.0 194.7 38 375.4 225.6 98 426.9 256.5 58 478.3 287.4 19 273.4 164.3 79 324.9 195.2 39 376.3 226.1 99 427.7 257.0 59 479.2 287.9 20 321 274.3 164.8 80 325.7 195.7 40 377.2 226.6 500 428.6 257.5 60 480.0 288.4 275.2 165.3 381 326.6 196.2 441 378.0 227.1 501 429.4 258.0 561 480.9 288.9 22 276.0 165.8 82 327.4 196.7 42 378.9 227.7 02 430.3 258.6 62 481.7 289.5 23 276.9 166.4 83 328.3 197.3 43 379.7 228.2 03 431.2 259.1 63 482.6 290.0 24 277.7 166.9 84 329.2 197.8 44 380.6 228.7 04 432.0 259.6 64 483.4 290.5 25 278.6 167.4 85 330.0 198.3 45 381.4 229.2 05 432.9 260.1 65 484.3 291.0 26 279.4 167.9 86 330.9 198.8 46 382.3 229.7 06 433.7 260.6 66 485.2 291.5 27 280.3 168.4 87 331.7 199.3 47 383.2 230.2 07 434.6 261.1 67 486.0 292.0 28 281.2 168.9 88 332.6 199.8 48 384.0 230.7 08 435.4 261.6 68 486.9 292.5 29 282.0 169.5 89 333.4 200.4 49 384.9 231.3 09 436.3 262.2 69 487.7 293.1 30 282 9 170.0 90 334.3 200.9 50 385.7 231.8 10 437.2 262.7 70 488.6 293.6 331 283.7 170.5 391 335.2 201.4 451 386.6 232.3 511 438.0 263.2 571 489.4 294.1 32 284.6 171.0 92 336.0 201.9 52 387.4 232.8 12 438.9 263.7 72 490.3 294.6 33 285.4 171.5 93 336.9 202.4 53 388.3 233.3 13 439.7 264.2 73 491.2 295.1 34 286.3 172.0 94 337.7 202.9 54 389.2 233.8 14 440.6 264.7 74 492.0 295.6 35 287.2 172.5 95 338.6 203.4 55 390.0 234.3 15 441.4 265.2 75 492.9 296.1 36 288.0 173.1 96 339.4 204.0 56 390.9 234.9 16 442.3 265.8 76 493.7 296.7 37 288.9 173.6 97 340.3 204.5 57 391.7 235.4 17 443.2 266.3 77 494.6 297.2 38 289.7 174.1 98 341.2 205.0 58 392.6 235.9 18 444.0 266.8 78 495.4 297.7 39 290.6 174.6 99 342.0 205.5 59 393.4 236.4 19 444.9 267.3 79 496.3 298.2 40 291.4 175.1 400 342.9 206.0 60 394.3 236.9 20 445.7 267.8 80 497.2 298.7 341 292.3 175.6 401 343.7 206.5 461 395.2 237.4 521 446.6 268.3 581 498.0 299.2 42 293.2 176.1 02 344.6 207.0 62 396.0 238.0 22 447.4 268.9 82 498.9 299.8 43 294.0 176.7 03 345.4 207.6 63 396.9 238.5 23 448.3 269.4 83 499.7 300.3 44 294.9 177.2 04 346.3 208.1 64 397.7 239.0 24 449.2 269.9 84 500.6 300.8 45 295.7 177.7 05 347.2 208.6 65 398.6 239.5 25 450.0 270.4 85 501.4 301.3 46 296.6 178.2 06 348.0 209.1 66 399.4 240.0 26 450.9 270.9 86 502.3 301.8 47 297.4 178.7 07 348.9 209.6 67 400.3 240.5 27 451.7 271.4 87 503.2 302.3 48 298.3 179.2 08 349.7 210.1 68 401.2 241.0 28 452.6 271.9 88 504.0 302.8 49 299.2 179.8 09 350.6 210.7 69 402.0 241.5 29 453.4 272.4 89 504.9 303.3 50 300.0 180.3 10 351.4 211.2 70 402.9 242.1 30 454.3 273.0 90 505.7 303.9 351 300.9 180.8 411 352.3 211.7 471 403.7 242.6 531 455.2 273.5 591 506.6 304.4 52 301.7 181.3 12 353.2 212.2 72 404.6 243.1 32 456.0 274.0 92 507.4 304.9 53 302.6 181.8 13 354.0 212.7 73 405.4 243.6 33 456.9 274.5 93 508.3 305.4 54 303.4 182.3 14 354.9 213.2 74 406.3 244.1 34 457.7 275.0 94 509.2 305.9 55 304.3 182.8 15 355.7 213.7 75 407.2 244.6 35 458.6 275.5 95 510.0 306.4 56 305.2 183.4 16 356.6 214.3 76 408.0 245.2 36 459.4 276.1 96 510.9 307.0 57 306.0 183.9 17 357.4 214.8 77 408.9 245.7 37 460.3 276.6 97 511.7 307.5 58 306.9 184.4 18 358.3 215.3 78 409.7 246.2 38 461.2 277.1 98 512.6 308.0 59 307.7 184.9 19 359.2 215.8 79 410.6 246.7 39 462.0 277.6 99 513.4 308.5 60 308.6 186.4 20 360.0 216.3 80 411.4 247.2 40 462.9 278.1 600 514.3 309.0 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 59° (1 21°, 239°, 301° ). 1 21594°— 14- -31 Page 694] TABLE 2. Difference of Latitude and Departure for 32° (148°, 212°, 328° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.5 61 51.7 32.3 121 102.6 64.1 181 153.5 95.9 241 204.4 127.7 2 1.7 1.1 62 52.6 32.9 22 103.5 64.7 82 154.3 96.4 42 205.2 128.2 3 2.5 1.6 63 53.4 33.4 23 104.3 65.2 83 155.2 97.0 43 206.1 128.8 4 3.4 2.1 64 54.3 33.9 24 105.2 65.7 84 156.0 97.5 44 206.9 129.3 5 4.2 2.6 65 55.1 34.4 25 106.0 66.2 85 156.9 98.0 45 207.8 129.8 6 5.1 3.2 66 56.0 35.0 26 106.9 66.8 86 157.7 98.6 46 208.6 130.4 7 5.9 3.7 67 56.8 35.5 27 107.7 67.3 87 158.6 99.1 47 209.5 130.9 8 6.8 4.2 68 57.7 36.0 28 108.6 67.8 88 159.4 99.6 48 210.3 131.4 9 7.6 4.8 69 58.5 36.6 29 109.4 68.4 89 160.3 100.2 49 211.2 131.9 10 8.5 5.3 70 59.4 37.1 30 110.2 68.9 90 161.1 100.7 50 212.0 132.5 11 9.3 5.8 71 60.2 37.6 131 111.1 69.4 191 162.0 101.2 251 212.9 133.0 12 10.2 6.4 72 61.1 38.2 32 111.9 69.9 92 162.8 101.7 52 213.7 133.5 13 11.0 6.9 73 61.9 38.7 33 112.8 70.5 93 163.7 102.3 53 214.6 134.1 14 11.9 7.4 74 62.8 39.2 34 113.6 71.0 94 164.5 102.8 54 215.4 134.6 15 12.7 7.9 75 63.6 39.7 35 114.5 71.5 95 165.4 103.3 55 216.3 135.1 16 13.6 8.5 76 64.5 40.3 36 115.3 72.1 96 166.2 103.9 56 217.1 135.7 17 14.4 9.0 77 65.3 40.8 37 116.2 72.6 97 167.1 104.4 57 217.9 136.2 18 15.3 9.5 78 66.1 41.3 38 117.0 73.1 98 167.9 104.9 58 218.8 136.7 19 16.1 10.1 79 67.0 41.9 39 117.9 73.7 99 168.8 105.5 59 219.6 137.2 20 17.0 10.6 80 67.8 42.4 40 118.7 74.2 200 169.6 170.5 106.0 106.5 60 261 220.5 221.3 137.8 21 17.8 11.1 81 68.7 42.9 141 119.6 74.7 201 138.3 22 18.7 11.7 82 69.5 43.5 42 120.4 75.2 02 171. 3 107.0 62 222.2 138.8 23 19.5 12.2 83 70.4 44.0 43 121.3 75.8 03 172.2 107.6 63 223.0 139.4 24 20.4 12.7 84 71.2 44.5 44 122.1 76.3 04 173.0 108.1 64 223.9 139.9 25 21.2 13.2 85 72.1 45.0 45 123.0 76.8 05 173.8 108.6 65 224.7 140.4 26 22.0 13.8 86 72.9 45.6 46 123.8 77.4 06 174.7 109.2 66 225.6 141. 27 22.9 14.3 87 73.8 46.1 47 124.7 77.9 07 175.5 109.7 67 226.4 141.5 28 23.7 14.8 88 74.6 46.6 48 125.5 78.4 08 176.4 110.2 68 227.3 142.0 29 24.6 15.4 89 75.5 47.2 49 126.4 79.0 09 177.2 110.8 69 228.1 142. 5 30 25.4 15.9 90 76.3 47.7 50 127.2 79.5 10 178.1 111.3 70 229.0 143.1 31 26.3 16.4 91 77.2 48.2 151 128.1 80.0 211 178.9 111.8 271 229.8 143.6 32 27.1 17.0 92 78.0 48.8 52 128.9 80.5 12 179.8 112.3 72 230.7 144.1 33 28.0 17.5 93 78.9 49.3 53 129.8 81.1 13 180.6 112.9 73 231.5 144.7 34 28.8 18.0 94 79.7 49.8 54 130.6 81.6 14 181.5 113.4 74 232.4 145.2 35 29.7 18.5 95 80.6 50.3 55 131.4 82.1 15 182. 3 113.9 75 233.2 145.7 36 30.5 19.1 96 81.4 50.9 56 132.3 82.7 16 183.2 114.5 76 234.1 146.3 37 31.4 19.6 97 82.3 51.4 57 133.1 83.2 17 184.0 115.0 77 234.9 146.8 38 32.2 20.1 98 83.1 51.9 58 134.0 83.7 18 184.9 115.5 78 235.8 147.3 39 33.1 20.7 99 84.0 52.5 59 134.8 84.3 19 185.7 116.1 79 236.6 147.8 40 33.9 21.2 100 84.8 53.0 60 135.7 84.8 20 186.6 116.6 80 237.5 238.3 148.4 41 34.8 21.7 101 85.7 53.5 161 136.5 85.3 221 187.4 117.1 281 148.9 42 35.6 22.3 02 86.5 54.1 62 137.4 85.8 22 188.3 117.6 82 239.1 149.4 43 36.5 22.8 03 87.3 54.6 63 138.2 86.4 23 189.1 118.2 83 240.0 150.0 44 37.3 23.3 04 88.2 55.1 64 139.1 86.9 24 190.0 118.7 84 240.8 150.5 45 38.2 23.8 05 89.0 55.6 65 139.9 87.4 25 190.8 119.2 85 241.7 151.0 46 39.0 24.4 06 89.9 56.2 66 140.8 88.0 26 191.7 119.8 86 242.5 151.6 47 39.9 24.9 07 90.7 56.7 67 141.6 88.5 27 192.5 120.3 87 243.4 152.1 48 40.7 25.4 08 91.6 57.2 68 142.5 89.0 28 193.4 120.8 88 244.2 152. 6 49 41.6 26.0 09 92.4 57.8 69 143.3 89.6 29 194.2 121.4 89 245.1 153.1 50 42.4 26.5 10 93.3 58.3 70 144.2 90.1 30 195.1 121.9 90 245.9 153.7 51 43.3 27.0 111 94.1 58.8 171 145.0 90.6 231 195.9 122.4 291 246.8 154.2 52 44.1 27.6 12 95.0 59.4 72 145.9 91.1 32 196.7 122.9 92 247.6 154.7 53 44.9 28.1 13 95.8 59.9 73 146.7 91.7 33 197.6 123.5 93 248.5 155.3 54 45.8 28.6 14 96.7 60.4 74 147.6 92.2 34 198.4 124.0 94 249.3 155.8 55 46.6 29.1 15 97.5 60.9 75 148.4 92.7 35 199. 3 124.5 95 250.2 156.3 56 47.5 29.7 16 98.4 61.5 76 149.3 93.3 36 200.1 125.1 96 251.0 156.9 57 48.3 30.2 17 99.2 62.0 77 150.1 93.8 37 201.0 125.6 97 251.9 157,4 58 49.2 30.7 18 100.1 62.5 78 151.0 94.3 38 201.8 126.1 98 252.7 157.9 59 50.0 31.3 19 100.9 63.1 79 151.8 94.9 39 202.7 126.7 99 253.6 158.4 60 50.9 31.8 20 101.8 63.6 80 152.6 95.4 40 203.5 127.2 300 254.4 159.0 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. { 58° (122°, 238°, 302' ). : TABLE 2. [Page 595 Difference of Latitude and Departure for 32° (148°, 212°, 328* ). [DIst. Lat Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 255.3 159.5 361 306.2 191.3 421 357.0 223.1 481 407.9 254.9 541 458.8 286.7 0*2 256.1 160.0 62 307.0 191.8 22 367.9 223.6 82 408.8 266.4 42 459.6 287.2 03 257.0 160.5 63 307.9 192.3 23 368.7 224.1 83 409.6 255.9 43 460.6 287.7 04 257.8 161.1 64 308.7 192.9 24 359. 6 224.7 84 410.6 256.5 44 461.3 288.3 05 258.7 161.6 65 309.5 193.4 25 360.4 225.2 85 411.3 267.0 45 462.2 288.8 06 259.5 162.1 66 310. 4 193.9 26 361.3 225.7 86 412.2 257.5 46 463.0 289.3 07 260.4 162.7 67 311.2 194.5 27 362.1 226.3 87 413.0 258.1 47 463.9 289.9 08 261.2 163.2 68 312.1 195.0 28 363.0 226.8 88 413.9 258.6 48 464.7 290.4 09 262.1 163.7 69 312.9 195.5 29 363. 8 227.3 89 414.7 259.1 49 466.6 290.9 10 262.9 164.3 164.8 70 371 313.8 196.0 30 364.7 227.8 90 416.6 259.6 50 466.4 291.5 311 263.8 314.6 196.6 431 365.6 228.4 491 416.4 260.2 551 467.3 292.0 12 264.6 165.3 72 315.5 197.1 32 366.4 228.9 92 417.3 260.7 52 468.1 292.5 13 265.4 165.8 73 316.3 197.6 33 367.2 229.4 93 418.1 261.2 53 469.0 293.0 14 266.3 166.4 74 317.2 198.2 34 368. 1 230.0 94 419.0 261.8 54 469.8 293.6 15 267.1 166.9 75 318.0 198.7 35 368.9 230.5 95 419,8 262.3 65 470.7 294.1 16 268.0 167.4 76 318.9 199.2 36 369.8 231.0 96 420.6 262.8 56 471.6 294.6 17 268.8 168.0 77 319.7 199.8 37 370.6 231.6 97 421.5 263.4 57 472.4 295.2 18 269.7 168.5 78 320.6 200.3 38 371.5 232.1 98 422. 3 263,9 58 473.2 295.7 19 270.5 169.0 79 321.4 200,8 39 372.3 232.6 99 423.2 264.4 69 474.1 296.2 20 271.4 169.6 80 322.3 201.3 40 373.2 233.1 500 424.0 265.0 60 474.9 296.7 321 272.2 170.1 381 323.1 201.9 441 374.0 233.7 601 424.9 26.5. 5 561 475.8 297.3 22 273.1 170.6 82 324.0 202.4 42 374.8 234.2 02 425.7 266.0 62 476.6 297.8 23 273.9 171.1 83 324.8 202.9 43 375.7 234.7 03 426.6 266.5 63 477.5 298.3 24 274.8 171.7 84 325.7 203.5 44 376.5 235.3 04 427.4 267.1 64 478.3 298.9 25 275.6 172.2 85 326.5 204.0 45 377.4 235.8 05 428.3 267.6 65 479.2 299.4 26 276.5 172.7 86 327.4 204.5 46 378.2 236.3 06 429.1 268.1 66 480.0 299.9 27 277.3 173.3 87 328.2 205.1 47 379.1 236.9 07 430.0 268.7 67 480.9 300.5 28 278.2 173.8 88 329.1 205.6 48 379.9 237.4 08 430.8 269.2 68 481.7 301.0 29 279.0 174.3 89 329.9 206.1 49 380.8 237.9 09 431.7 269.7 69 482.6 301.5 30 279.9 174.9 90 330.8 206.6 50 381.6 238. 4 10 432.5 270.3 70 483.4 302.1 331 280.7 175.4 391 331. 6 207.2 451 382.5 239.0 511 433.4 270.8 571 484.3 302.6 32 281.6 176.9 92 332.5 207.7 52 383.3 239. 5 12 434.2 271.4 72 486.1 303.2 33 282.4 176.4 93 333.3 208.2 53 384.2 240.0 13 435.1 271.9 73 486.0 303. 7 34 283.3 177.0 94 334.2 208.8 54 385.0 240.6 14 436.9 272.4 74 486.8 304.2 35 284.1 177.5 95 335.0 209.3 55 385.9 241.1 16 436.8 272.9 75 487.7 304.7 36 285.0 178.0 96 335.8 209.8 56 386.7 241.6 16 437.6 273.5 76 488.6 305.3 37 285.8 178.6 97 336.7 210.4 57 387.6 242.2 17 438.5 274.0 77 489.4 305.8 38 286.7 179.1 98 337.5 210.9 58 388.4 242.7 18 439.3 274.5 78 490.2 306.3 39 287.5 179.6 99 338.4 211.4 59 389.3 243.2 19 440.2 275.0 79 491.1 306.8 40 288.3 180.2 400 339.2 211.9 60 390.1 243.8 20 441.0 276.6 80 491.9 307.4 341 289.2 180.7 401 340.1 212.5 461 391.0 244.3 521 441.9 276.1 581 492.8 307.9 42 290.0 181.2 02 340.9 213.0 62 391.8 244.8 22 442.7 276.6 82 493,6 308.4 43 290.9 181.7 03 341.8 213.5 63 392.7 245.4 23 443.6 277.2 83 494.5 309.0 44 291.7 182.3 04 342.6 214.1 64 393.5 246.9 24 444.4 277.7 84 495. 3 309.5 45 292.6 182.8 05 343.5 214.6 66 394.4 246.4 25 445.3 278.2 85 496.2 310.0 46 293.4 183.3 06 344.3 215.1 66 395.2 246.9 26 446.1 278.7 86 497.0 310.6 47 294.3 183.9 07 345.2 215.7 67 396.0 247.5 27 446.9 279.3 87 497.8 311.1 48 295.1 184.4 08 346.0 216.2 68 396.9 248.0 28 447.8 279.8 88 498.7 311.6 49 296.0 184.9 09 346.9 216.7 69 397.7 248.5 29 448.6 280.3 89 499.5 312.1 50 296.8 185.4 10 347.7 217.2 70 398.6 249.0 30 449.5 280,9 90 500.3 312.6 351 297.7 186.0 411 348.6 217.8 471 399.4 249.6 531 450.3 281,4 591 601.2 313.2 52 298.5 186.5 12 349.4 218.3 72 400.3 250.1 32 461.1 281,9 92 502.0 313.7 53 299.4 187.0 13 350.3 218.8 73 401.1 250.6 33 462.0 282.4 93 502.9 314.2 54 300.2 187.6 14 351.1 219.4 74 402.0 251.2 34 452.8 283.0 94 503.7 314.8 55 301.1 188.1 15 352.0 219.9 75 402.8 261.7 35 453.7 283.5 95 504.6 315.3 56 301.9 188.6 16 352.8 220.4 76 403.7 262.2 36 464.6 284.0 96 605.4 315.8 57 302.8 189.2 17 353.6 221.0 77 404.5 252.8 37 465.4 284.6 97 606.2 316.4 58 303.6 189.7 18 354.5 221.5 78 405.4 253.3 38 456.2 285.1 98 607.1 316.9 59 304.5 190.2 19 355.3 222.0 79 406.2 253.8 39 457.1 286.6 •99 508.0 317.4 60 305. 3 190.8 20 356.2 222.5 80 407.1 254.3 40 457.9 286.2 600 508. 8 318. 1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 1 5 8° (122°, 238°, 302° )• 1 Page 596] TABLE 2. Difference of Latitude and Departure for 33° (147°, 213", 327= )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 as 0.5 61 51.2 33.2 121 101.5 65.9 181 151.8 98.6 241 202.1 131.3 2 L7 1.1 62 52.0 33.8 22 102.3 66.4 82 152.6 99.1 42 203.0 131.8 3 2.5 1.6 63 52.8 34.3 23 103.2 67.0 83 153.5 99.7 43 203.8 132.3 4 8.4 2.2 64 53.7 34.9 24 104.0 67.5 84 154.3 100.2 44 204.6 132.9 5 4.2 2.7 65 54.5 35.4 25 104.8 68.1 85 155.2 100.8 45 205.5 133.4 6 5.0 8.3 66 55.4 35.9 26 105. 7 i 68. 6 86 156.0 101.3 46 206.3 134.0 7 5.9 3.8 67 56.2 36.5 27 106.5 69.2 87 156.8 101.8 47 207.2 134.5 8 6.7 4.4 68 57.0 37.0 28 107.3 69.7 88 157.7 102.4 48 208.0 135.1 9 7.5 4.9 69 57.9 37.6 29 108.2 70.3 89 158.5 102.9 49 208.8 135.6 10 8.4 5.4 70 58.7 38.1 30 109.0 70.8 90 159.3 103.5 50 209.7 210.5' 136.2 11 9.2 6.0 71 59.5 38.7 131 109.9 71.3 191 160.2 104.0 251 136.7 12 10.1 6,5 72 60.4 39.2 32 110.7 71.9 92 161.0 104.6 52 211.3 137.2 13 10.9 7.1 73 61.2 39.8 33 111.5 72.4 93 161.9 105.1 53 212.2 137.8 14 11.7 7.6 74 62.1 40.3 34 112.4 73.0 94 162.7 105.7 54 213.0 138.3 15 12.6 8.2 75 62.9 40.8 35 113.2 73.5 95 163.5 106.2 55 213.9 138.9 16 13.4 8.7 76 63.7 41.4 36 114.1 74.1 96 164.4 106.7 56 214.7 139.4 17 14.3 9.3 77 64.6 41.9 37 114.9 74.6 97 165.2 107.3 57 215.5 140.0 18 15.1 9.8 78 65.4 42.5 38 115.7 75.2 98 166.1 107.8 58 216.4 140.5 19 15.9 10.3 79 66.3 43.0 39 116.6 75.7 99 166.9 108.4 59 217.2 141.1 20 16.8 10.9 80 67.1 43.6 40 117.4 76.2 200 167.7 108.9 60 218.1 218.9 141.6 21 17.6 11.4 81 67.9 44.1 141 118.3 76.8 201 168.6 109.5 261 142.2 22 18.5 12.0 82 68.8 44.7 42 119.1 77.3 02 169.4 110.0 62 219.7 142.7 23 19.3 12.5 83 69.6 45.2 43 119.9 77.9 03 170.3 110.6 63 220.6 143.2 24 20.1 13.1 84 70.4 45.7 44 120.8 78.4 04 171.1 111.1 64 221.4 143.8 25 21.0 13.6 85 71.3 46.3 45 121.6 79.0 05 171.9 111.7 65 222.2 144.3 26 21.8 14.2 86 72.1 46.8 46 122.4 79.5 06 172.8 112.2 66 223.1 144.9 27 22.6 14.7 87 73.0 47.4 47 123.3 80.1 07 173.6 112.7 67 223.9 145.4 28 23.5 15.2 88 73.8 47.9 48 124.1 80.6 08 174.4 113.3 68 224.8 146.0 29 , 24.3 15.8 89 74.6 48.5 49 125.0 81.2 09 175.3 113.8 69 225.6 146.5 30 31 25.2 26.0 16.3 90 75.5 49.0 50 125.8 81.7 10 176.1 114.4 70 226.4 147.1 16.9 9il 76.3 49.6 151 126.6 82.2 211 177.0 114.9 271 227.3 147.6 32 26.8 17.4 92 77.2 50.1 52 127.5 82.8 12 177.8 115.5 72 228.1 148.1 33 27.7 18.0 93 78.0 50.7 53 128.3 83.3 13 178.6 116.0 73 229.0 148.7 34 28.5 18.5 94 78.8 51.2 54 129.2 83.9 14 179.5 116.6 74 229.8 149.2 35 29.4 19.1 95 79.7 51.7 55 130.0 84.4 15 180.3 117.1 75 230.6 149.8 36 30.2 19.6 96 80.5 52.3 56 130.8 85.0 16 181.2 117.6 76 231.5 150.3 37 31.0 20.2 97 81.4 52.8 57 131.7 85.5 17 182.0 118.2 77 232.3 150.9 38 31.9 20.7 98 82.2 53.4 58 132.5 86.1 18 182.8 118.7 78 233.2 151.4 39 32.7 21.2 99 83.0 53.9 59 133.3 86.6 19 183.7 119.3 79 234.0 152.0 40 33.5 21.8 100 83.9 54.5 60 134.2 87.1 20 184.5 119.8 80 234.8 152.5 41 34.4 22.3 101 84.7 55.0 161 135.0 87.7 221 185.3 120.4 281 235.7 153.0 42 35.2 22.9 02 85.5 55.6 62 135.9 88.2 22 186.2. 120.9 82 236.5 153.6 43 36.1 23.4 03 86.4 56.1 63 136.7 88.8 23 187.0 121.5 83 237.3 154.1 44 36.9 24.0 04 87.2 56.6 64 137.5 89.3 24 187.9 122.0 84 238.2 154.7 45 37.7 24.5 05 88.1 57.2 65 138.4 89.9 25 188.7 122.5 85 239.0 155.2 46 38.6 25.1 06 88.9 57.7 66 139.2 90.4 26 189.5 123.1 86 239.9 155.8 47 39.4 25.6 07 89.7 58.3 67 140.1 91.0 27 190.4 123.6 87 240.7 156.3 48 40.3 26.1 08 90.6 58.8 68 140.9 91.5 28 191.2 124.2 88 241.5 156.9 49 41.1 26.7 09 91.4 59.4 69 141.7 92.0 29 192.1 124.7 89 242.4 157.4 50 51 41.9 27.2 10 92.3 59.9 70 142.6 92.6 30 192.9 125.3 90 243.2 157.9 42.8 27.8 111 93.1 60.5 171 143.4 93.1 231 193.7 125.8 291 244.1 158.5 52 43.6 28.3 12 93.9 61.0 72 144.3 93.7 32 194.6 126.4 92 244.9 159.0 53 44.4 28.9 13 94.8 61.5 73 145.1 94.2 33 195.4 126.9 93 245.7 159.6 54 45.3 29.4 14 95.6 62.1 74 145.9 94.8 34 196.2 127.4 94 246.6 160.1 55 46.1 30.0 15 96.4 62.6 75 146.8 95.3 35 197.1 128.0 95 247.4 160.7 56 47.0 30.5 16 97.3 63.2 76 147.6 95.9 36 197.9 128.5 96 248.2 161.2 57 47.8 31.0 17 98.1 63.7 77 148.4 96.4 37 198.8 129.1 97 249.1 161.8 58 48.6 31.6 18 99.0 64.3 78 149.3 96.9 38 199.6 129.6 98 249.9 162.3 59 49.5 32.1 19 99.8 64.8 79 150.1 97.5 39 200.4 130.2 99 250.8 162.8 60 50.3 32.7 20 100.6 65.4 80 151.0 98.0 40 201.3 130.7 300 251.6 163.4 Dlst. Dep. Lat. Diat. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 5 7° (15 J3°, 237°, 303°) . TABLE 2. [Page 597 Difference of Latitude and Departure for 33° (147°, 213°, 327' )• Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. :Dist. Lat. Dep. 301 252.4 163.9 361 302.8 196.6 421 353.1 229.3 481 403.4 262.0 541 453.7 294.6 02 253.3 164.4 62 303.6 197.1 22 363.9 229.8 82 404.2 262.5 42 464.6 296.2 03 254.1 165.0 63 304.4 197.7 23 364.7 230.4 83 405.1 263.1 43 455.4 296.7 04 255.0 165.5 64 305.3 198.2 24 356.6 230.9 84 405.9 263.6 44 456.2 296.2 05 255.8 166.1 65 306.1 198.8 26 356.4 231.4 86 406.7 264.1 45 467.1 296.8 06 256.6 166.6 66 307.0 199.3 26 357.3 232.0 86 407.6 264.7 46 467.9 297.3 07 257.5 167.2 67 307.8 199.8 27 358.1 232.5 87 408.4 265.2 47 458.8 297.9 08 258.3 167.7 68 308.6 200.4 28 359.0 233.1 88 409.3 266.8 48 459.6 298.4 09 259.2 168.3 69 309.5 200.9 29 359.8 233.6 89 410.1 266.3 49 460.4 299.0 10 260.0 168.8 70 310.3 201.6 30 360.6 234.2 90 411.0 266.8 60 461.3 299.5 311 260.8 169.3 371 311.2 202.0 431 361.6 234.7 491 411.8 267.4 651 462.1 300.1 12 261.7 169.9 72 312.0 202.6 32 362.3 235.2 92 412.6 267.9 52 463.0 300.6 13 262.5 170.4 73 312.8 203.1 33 363.1 235.8 93 413.6 268.6 63 463.8 301.2 14 263.3 171.0 74 313.7 203.7 34 364.0 236.3 94 414.3 269.0 64 464.6 301.7 15 264.2 171.5 75 314.5 204.2 36 364.8 236.9 95 416.1 269.6 55 465.5 302.3 16 265.0 172.1 76 315.3 204.7 36 366.7 237.4 96 416.0 270.1 56 466.3 302.9 17 265.9 172.6 77 316.2 205.3 37 366.5 238.0 97 416.8 270.7 57 467.2 303.4 18 266.7 173.2 78 317.0 205.8 38 367.3 238.5 98 417.6 271.2 58 468.0 303.9 19 267.5 173.7 79 317.9 206.4 39 368.2 239.1 99 418.5 271.8 69 468.8 304.5 20 268.4 174.2 80 318.7 206.9 40 369.0 239.6 500 419.3 272.3 60 469.7 305.0 321 269.2 174.8 381 319.6 207.6 441 369.9 240.1 601 420.2 272.8 661 470.5 305.5 22 270.1 175.3 82 320.4 208.0 42 370.7 240.7 02 421.0 273.4 62 471.3 306.1 23 270.9 176.9 83 321.2 208.6 43 371.6 241.2 03 421.9 273.9 63 472.2 306.6 24 271.7 176.4 84 322.1 209.1 44 372.4 241.8 04 422.7 274.5 64 473.0 307.2 25 272.6 177.0 85 322.9 209.6 46 373.2 242.3 06 423.5 275.0 65 473.8 307.7 26 273.4 177.5 86 323.7 210.2 46 374.1 242.9 06 424.4 276.6 66 474.7 308.3 27 274.2 178.1 87 324.6 210.7 47 374.9 243.4 07 425.2 276.1 67 475.5 308.8 28 275.1 178.6 88 325.4 211.3 48 375.7 244.0 08 426.0 276.7 68 476.4 309.4 29 275.9 179.1 89 326.2 211.8 49 376.6 244.5 09 426.9 277.2 69 477.2 309.9 30 276.8 179.7 90 327.1 212.4 212. 9 50 377.4 245.1 10 427.7 277.8 70 478.0 310.4 331 277.6 180.2 391 327.9 451 378.2 245.6 511 428.5 278.3 571 478.9 311.0 32 278.4 180.8 92 328.8 213.6 52 379.1 246.1 12 429.4 278.8 72 479.7 311.6 33 279.3 181.3 93 329.6 214.0 53 379.9 246.7 13 430.2 279.4 73 480.6 312.0 34 280.1 181.9 94 330.4 214.6 54 380.8 247.2 14 431.1 279.9 74 481.4 312.6 35 281.0 182.4 95 331.3 215.1 56 381.6 247.8 16 431.9 280.4 75 482.2 313.1 36 281.8 183.0 96 332.1 215.6 56 382.4 248.3 16 432.7 281.0 76 483.1 313.7 37 282.6 183.5 97 333.0 216.2 57 383.3 248.9 17 433.6 281.5 77 483.9 314.2 38 283.5 184.1 98 333.8 216.7 58 384.1 249.4 18 434.4 282.1 78 484.7 314.8 39 284.3 184.6 99 334.6 217.3 69 385.0 260.0 19 436.3 282.6 79 485.6 315.3 40 285.2 185.1 400 335.5 217.8 60 386.8 250.5 20 436.1 283.2 80 486.4 315.9 341 286.0 185.7 401 336.3 218.4 461 386.6 261.0 521 436.9 283.7 581 487.2 316.4 42 286.8 186.2 02 337.1 218.9 62 387. 6 251.6 22 437.8 284.3 82 488.1 317.0 43 287.7 186.8 03 338.0 219.6 63 388.3 252.1 23 438.6 284.8 83 488.9 317.5 44 288.5 187.3 04 338.8 220.0 64 389.1 252.7 24 439.4 286.4 84 489.8 318.1 45 289.3 187.9 05 339.7 220.5 65 390.0 263.2 26 440.3 285.9 86 490.6 318.6 46 290.2 188.4 06 340.5 221.1 66 390.8 263.8 26 441.1 286.5 86 491.5 319.2 47 291.0 189.0 07 341.3 221.6 67 391.7 254.3 27 442.0 287.0 87 492.3 319.7 48 291.9 189.5 08 342.2 222.2 68 392.5 264.9 28 442.8 287.5 88 493.1 320.2 49 292.7 190.0 09 343.0 222.7 69 393.3 265.4 29 443.6 288.1 89 494.0 320.8 50 293.5 190.6 10 343.9 223.3 70 394.2 255.9 30 444.6 288.6 90 494.8 321.3 351 294.4 191.1 411 344.7 223.8 471 395.0 256.6 531 445.3 289.2 591 496.7 321.9 52 295.2 191.7 12 345.5 224.4 72 395.8 267.0 32 446.1 289.7 92 496.6 322.4 53 296.1 192.2 13 346.4 224.9 73 396.7 267.6 33 447.0 290.3 93 497.3 322.9 54 296.9 192.8 14 347.2 225.4 74 397.5 258.1 34 447.8 290.8 94 498.1 323.6 55 297.7 193.3 15 348.1 226.0 75 398.3 258.7 35 448.7 291.4 95 499.0 324.1 56 298.6 193.9 16 348.9 226.5 76 399.2 269.2 36 449.6 291.9 96 499.8 324.6 57 299.4 194.4 17 349.7 227.1 77 400.0 259.8 37 460.3 292.6 97 600.6 325.1 58 300.2 194.9 18 350.6 227.6 78 400.9 260.3 38 451.2 293.0 98 501.5 326.7 59 301.1 195.5 19 361.4 228.2 79 401.7 260.9 39 452.0 293.6 99 502.3 326.2 60 301.9 196.0 20 362.2 228.7 80 Dist. 402.6 261.4 40 452.9 294.1 600 503.2 326.8 Dist. Dep. Lat. Dist. Dep. Lat. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 57° (1 23°, 237°, 303°] . Page 598] TABLE 2. Difference of Latitude and Departure for 34° (146°, 214 °, 326° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 50.6 34.1 121 100.3 67.7 181 150.1 101.2 241 199.8 134.8 2 1.7 1.1 62 51.4 34.7 22 101.1 68.2 82 150.9 101.8 42 200.6 135.3 3 2.5 1.7 63 52.2 35.2 23 102.0 68.8 83 151.7 102.3 43 201.5 135.9 4 3.3 2.2 64 53.1 35.8 24 102.8 69.3 84 152. 5 102.9 44 202.3 136.4 6 4.1 2.8 65 53.9 36.3 25 103.6 69.9 85 153.4 103.5 45 203.1 137.0 6 5.0 3.4 66 54.7 36.9 26 104.5 70.5 86 154.2 104.0 46 203.9 137.6 7 5.8 3.9 67 55.5 37.5 27 105.3 71.0 87 155.0 104.6 47 204.8 138.1 8 6.6 4.5 68 56.4 38.0 28 106.1 71.6 88 155.9 105.1 48 205.6 138.7 9 7.5 5.0 69 57.2 38.6 29 106.9 72.1 89 156.7 105.7 49 206.4 139.2 10 8.3 5.6 70 58.0 58.9 39.1 30 107.8 72.7 90 157.5 106.2 50 207.3 208.1 139.8 11 9.1 6.2 71 39.7 131 108. 6 73.3 191 158.3 106.8 251 140.4 12 9.9 6.7 72 59.7 40.3 32 109.4 73.8 92 159.2 107.4 52 208.9 140.9 13 10.8 7.3 73 60.5 40.8 33 110.3 74.4 93 160.0 107.9 53 209.7 141.5 14 11.6 7.8 74 61.3 41.4 34 111.1 74.9 94 160.8 108.5 54 210.6 142.0 15 12.4 8.4 75 62.2 41.9 35 111.9 75.5 95 161.7 109.0 55 211.4 142.6 16 13.3 8.9 76 63.0 42.5 36 112.7 76.1 96 162.5 109.6 56 212.2 143.2 17 14.1 9.5 77 63.8 43.1 37 113.6 76.6 97 163.3 110.2 57 213.1 143.7 18 14.9 10.1 78 64.7 43.6 38 114.4 77.2 98 164.1 110.7 58 213.9 144.3 19 15.8 10.6 79 65.5 44.2 39 115.2 77.7 99 165.0 111.3 59 214.7 144.8 20 16.6 11.2 80 66.3 44.7 40 116.1 78.3 200 165.8 111.8 60 261 215.5 216.4 145.4 21 17.4 11.7 81 67.2 45.3 141 116.9 78.8 201 166.6 112.4 145.9 22 18.2 12.3 82 68.0 45.9 42 117.7 79.4 02 167.5 113.0 62 217.2 146.5 23 19.1 12.9 83 68.8 46.4 43 118.6 80.0 03 168.3 113.5 63 218.0 147.1 24 19.9 13.4 84 69.6 47.0 44 119.4 80.5 04 169.1 114.1 64 218.9 147.6 25 20.7 14.0 85 70.5 47.5 45 120.2 81.1 05 170.0 114.6 65 219.7 148.2 26 21.6 14.5 86 71.3 48.1 46 121.0 81.6 06 170.8 115.2 66 220.5 148.7 27 22.4 15.1 87 72.1 48.6 47 121.9 82.2 07 171.6 115.8 67 221.4 149.3 28 23.2 15.7 88 7.3.0 49.2 48 122.7 82.8 08 172.4 116.3 68 222.2 149.9 29 24.0 16.2 89 73.8 49.8 49 123.5 83.3 09 173.3 116.9 69 223.0 150.4 30 24.9 16.8 90 74.6 50.3 50 124.4 83.9 10 174.1 117.4 70 223.8 151.0 31 25.7 17.3 91 75.4 50.9 1.51 125.2 84.4 211 174.9 118.0 271 224.7 151.5 32 26.5 17.9 92 76.3 51.4 52 126.0 85.0 12 175.8 118.5 72 225. 5 152.1 33 27.4 18.5 93 77.1 52.0 53 126.8 85.6 13 176.6 119.1 73 226.3 152.7 34 28.2 19.0 94 77.9 52.6 54 127.7 86.1 14 177.4 119.7 74 227.2 153.2 35 29.0 19.6 95 78.8 53.1 55 128.5 86.7 15 178.2 120.2 75 228.0 153.8 36 29.8 20.1 96 79.6 53.7 56 129.3 87.2 16 179.1 120.8 76 228.8 154.3 37 30.7 20.7 97 80.4 54.2 57 130.2 87.8 17 179.9 121.3 77 229.6 154.9 38 31.5 21.2 98 81.2 54.8 58 131.0 88.4 18 180.7 121.9 78 230.5 155.5 39 32.3 21.8 99 82.1 55.4 59 131.8 88.9 19 181.6 122.5 79 231.3 156. 40 33.2 22.4 100 82.9 55.9 60 132.6 89.5 20 182.4 123.0 80 232.1 156.6 41 34.0 22.9 101 83.7 56.5 161 133.5 90.0 221 183.2 123.6 281 233.0 157. 1 42 34.8 23.5 02 84.6 57.0 62 134.3 90.6 22 184.0 124.1 82 233.8 157.7 43 35.6 24.0 03 85.4 57.6 63 135.1 91.1 23 184.9 124.7 83 234. 6 158.3 44 36.5 24.6 04 86.2 58.2 64 136.0 91.7 24 185.7 125.3 84 235.4 158.8 45 37.3 25.2 05 87.0 58.7 65 136.8 92.3 25 186.5 125.8 85 236.3 159.4 46 38.1 25.7 06 87.9 59.3 66 137.6 92.8 26 187.4 126.4 86 237.1 159.9 47 39.0 26.3 07 88.7 59.8 67 138.4 93.4 27 188.2 126.9 87 237.9 160.5 48 39.8 26.8 08 89.5 60.4 68 139.3 93.9 28 189.0 127.5 88 238.8 161.0 49 40.6 27.4 09 90.4 61.0 69 140.1 94.5 29 189.8 128.1 89 239.6 161.6 50 41.5 28.0 10 91.2 61.5 70 140.9 95.1 30 190.7 128.6 90 240.4 241.2 162.2 162.7 51 42.3 28.5 111 92.0 62.1 171 141.8 95.6 231 191.5 129.2 291 52 43.1 29.1 12 92.9 62.6 72 142.6 96.2 32 192.3 129.7 92 242.1 163.3 53 43.9 29.6 13 93.7 63.2 73 143.4 96.7 33 193.2 130.3 93 242.9 163.8 54 44.8 30.2 14 94.5 63.7 74 144.3 97.3 34 194.0 130.9 94 243.7 164.4 55 45.6 30.8 15 95.3 64.3 75 145.1 97.9 35 194.8 131.4 95 244.6 165.0 56 46.4 31.3 16 96.2 64.9 76 145.9 98.4 36 195. 7 132.0 96 245.4 165. 5 57 47.3 31.9 17 97.0 65.4 77 146.7 99.0 37 196.5 132.5 97 246.2 166.1 58 48.1 32.4 18 97.8 66.0 78 147.6 99.5 38 197.3 133.1 98 247.1 166.6 59 48.9 33.0 19 98.7 66.5 79 148.4 100.1 39 198.1 133.6 99 247.9 167.2 60 49.7 33.6 20 99.5 67.1 80 149.2 100.7 40 199.0 134.2 300 248.7 167.8 Diet. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 1 )6° (1 24°, 236 °, 304° ). TABLE 2. [Page 599 | Difference of Latitude and Departure for 34° (146°, 214 », 326° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 249.5 168.3 361 299.3 201.9 421 349.0 235.4 481 398.8 269.0 541 448.5 302.5 02 250.4 168.9 62 300.1 202.4 22 349.9 236.0 82 399.6 269.5 42 449.4 303.1 03 251.2 169.4 63 300.9 203.0 23 350.7 236. 5 83 400.4 270.1 43 450.2 303.6 04 252. 170.0 64 301.8 203.5 24 351.5 237.1 84 401.3 270.6 44 451.0 304.2 05 252. 9 170.6 65 302.6 204.1 25 352.3 237.7 85 402.1 271.2 45 451.8 304.8 06 253.7 171.1 66 303.4 204.7 26 353.2 238.2 86 402.9 271.8 46 452.6 305.3 07 254.5 171.7 67 304.3 205.2 27 354.0 238.8 87 403.8 272.3 47 453.5 305.9 08 255. 3 172.2 68 305.1 205.8 28 354.8 239.3 88 404.6 272.8 48 454.3 306.4 09 256.2 172.8 69 305. 9 206.3 29 355.7 239. 9 89 405.4 273.4 49 455.2 307.0 10 257.0 173.3 70 306.7 206.9 30 356.5 357.3 240.4 90 406.2 274.0 50 456.0 307.5 311 257.8 173.9 371 307.6 207.5 431 241.0 491 407.1 274.6 551 456.8 308.1 12 258.7 !l74.5 72 308.4 208.0 32 358.1 241.6 92 407.9 275.1 52 457.6 308.7 13 259.5 175.0 73 309.2 208.6 33 359.0 242.1 93 408.7 275.7 53 458.4 309.2 14 260.3 175.6 74 310.1 209.1 34 359.8 242.7 94 409.5 276.2 54 459.3 309.8 15 261.2 176.1 75 310.9 209.7 35 360.6 243.2 95 410.4 276.8 55 460.1 310.3 16 262.0 176.7 76 311.7 210.3 36 361.5 243.8 96 411.2 277.4 56 460.9 310.9 17 262.8 177.3 77 312.6 210.8 37 362.3 244.4 97 412.0 277.9 57 461.7 311.5 18 263.7 177.8 78 313.4 211.4 38 363.1 244.9 98 412.8 278.4 58 462.6 312.0 19 264.5 178.4 79 314.2 211.9 39 364.0 245.5 99 413.7 279.0 59 463.4 312.6 20 265.3 178.9 80 315.0 212.5 40 364.8 246.0 500 414.5 279.6 60 464.2 313.1 321 266.1 179.5 381 315.9 213.0 441 365.6 246.6 501 415.3 280.1 561 465.1 313.7 22 267.0 180.1 82 316.7 213.6 42 366.4 247.2 02 416.2 280.7 62 465.9 314.3 23 267.8 180.6 83 317.5 214.2 43 367.3 247.7 03 417.0 281.3 63 466.8 314.8 24 268.6 181.2 84 318.4 214.7 44 368.1 248.3 04 417.8 281.8 64 467.6 315.4 25 269.5 181.7 85 319.2 215.3 45 368.9 248.8 05 418.6 282.4 65 468.4 315.9 26 270.3 182.3 86 320.0 215.8 46 369.8 249.4 06 419.4 282.9 66 469.2 316.5 27 271.1 182.9 87 320.8 216.4 47 370.6 250.0 07 420.3 283.5 67 470.1 317.1 28 271.9 183.4 88 321.7 217.0 48 371.4 250.5 08 421.1 284.1 68 470.9 317.6 29 272.8 184.0 89 322.5 217.5 49 372.2 251.1 09 421.9 284.6 69 471.7 318.2 30 273.6 274.4 184.5 90 323.3 218.1 50 373.1 251.6 10 422.8 285.2 70 472.6 318.7 319.3 331 185.1 391 324.2 218.6 451 373.9 252.2 511 423.6 285.8 571 473.4 32 275.2 185.6 92 325.0 219.2 52 374.7 252.8 12 424.4 286.3 72 474.2 319.9 33 276.1 186.2 93 325.8 219.8 53 375.6 253.3 13 425.3 286.9 73 475.0 320.4 34 276.9 186.8 94 326.6 220.3 54 376.4 253.9 14 426.1 287.4 74 475.9 321.0 35 277.7 187.3 95 327.5 220.9 55 377.2 254.4 15 426.9 288.0 75 476.7 321.5 36 278.6 187.9 96 328.3 221.4 56 378.0 255.0 16 427.8 288.5 76 477.5 322.1 37 279.4 188.4 97 329.1 222.0 57 378.9 255.5 17 428.6 289.1 77 478.3 322.7 38 280.2 189.0 98 330.0 222.6 58 379.7 256.1 18 429.4 289.6 78 479.2 323.2 39 281.0 189.6 99 330.8 223.1 59 380.5 256.7 19 430.3 290.2 79 480.0 323.8 40 281.9 190.1 400 331.6 223.7 60 381.3 257.2 20 431.1 290.8 80 480.8 324.3 341 282. 7 190.7 401 332.4 224. 2 461 382.2 257.8 521 431.9 291.3 581 481.6 324.9 42 283.5 191.2 02 333.3 224.8 62 383.0 258.3 22 432.8 291.9 82 482.5 325.4 43 284.4 191.8 03 334.1 225.4 63 383.8 258.9 23 433.6 292.5 83 483.3 326.0 44 285.2 192.4 04 334.9 225.9 64 384.7 259.5 24 434.4 293.0 84 484.1 326.6 45 286.0 192.9 05 335.8 226.5 65 385.5 260.0 25 435.3 293.6 85 485.0 327.2 46 286.9 193.5 06 336.6 227.0 66 386.3 260.6 26 436.1 294.1 86 485.8 327.7 47 287.7 194.0 07 337.4 227.6 67 387.2 261.1 27 436.9 294.7 87 486.6 328.2 48 288.5 194.6 08 338.3 228.1 68 388.0 261.7 28 437.8 295.3 88 487.5 328.8 49 289.3 195.2 09 339.1 228.7 69 388.8 262.3 29 438.6 295.8 89 488.3 329.4 50 290.2 195.7 10 339.9 229.3 70 389.7 262.8 30 439.4 296.4 90 489.2 329.9 351 291.0 196.3 411 340.7 229.8 471 390.5 263.4 531 440.3 296.9 591 490.0 330.5 52 291.8 196.8 12 341.6 230.4 72 391.3 263.9 32 441.1 297.4 92 490.8 331.0 53 292.7 197.4 13 342.4 230.9 73 392.1 264.5 33 441.9 298.0 93 491.6 331.6 54 293.5 198.0 14 343.2 231.5 74 393.0 265.0 34 442.7 298.6 94 492.5 332.2 55 294.3 198.5 15 344.1 232.1 75 393.8 265.6 35 443.6 299.1 95 493.3 332.7 56 295.1 199.1 16 344.9 232.6 76 394.6 266.2 36 444.4 299.7 96 494.1 333.3 57 296.0 199.6 17 345.7 233.2 77 395.5 266.7 37 445.3 300.2 97 494.9 333.8 58 296.8 200.2 18 346.5 233.7 78 396.3 267.3 38 446.1 300.8 98 495.8 334.4 59 297.6 200.7 19 347.4 234.3 79 397.1 267.9 39 446.9 301.4 99 496.6 334.9 60 298.5 201.3 20 348.2 234.9 80 397.9 268.4 40 447.7 302.0 600 497.4 335.5 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. DUt. Dep. Lat. 56° (124°, 236°, 304°). 1 Page 600] TABLE 2. Difference of Latitude and Departure for 35° (145°, 215°, 325° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 50.0 35.0 121 99.1 69.4 181 148.3 103.8 241 197.4 138.2 2 1.6 1.1 62 50.8 35.6 22 99.9 70.0 82 149.1 104.4 42 198.2 138.8 3 2.5 1.7 63 51.6 36.1 23 100.8 70.5 83 149.9 105.0 43 199.1 139.4 4 3.3 2.3 64 52.4 36.7 24 101.6 71.1 84 150.7 105.5 44 199.9 140.0 5 4.1 2.9 65 53.2 37.3 25 102.4 71.7 85 151.5 106.1 45 200.7 140.5 6 4.9 3.4 66 54.1 37.9 26 103.2 72.3 86 153.4 106.7 46 201.5 141.1 7 5.7 4.0 67 54.9 38.4 27 104.0 72.8 87 153.2 107.3 47 202.3 141.7 8 6.6 4.6 68 55.7 39.0 28 104.9 73.4 88 154.0 107.8 48 203.1 142.2 9 7.4 5.2 69 56.5 39.6 29 105.7 74.0 89 154.8 108.4 49 204.0 142.8 10 8.2 5.7 70 57.3 40.2 30 106.5 107.3 74.6 90 155.6 109.0 50 204.8 143.4 11 9.0 6.3 71 58.2 40.7 131 75.1 191 156.5 109.6 251 205.6 144.0 12 9.8 6.9 72 59.0 41.3 32 108.1 75.7 92 157.3 110.1 52 206.4 144.5 13 10.6 7.5 73 59.8 41.9 33 108.9 76.3 93 158.1 110.7 53 207.2 145.1 14 11.5 8.0 74 60.6 42.4 34 109.8 76.9 94 158.9 111.3 54 208.1 145.7 15 12.3 8.6 75 61.4 43.0 35 110.6 77.4 95 159.7 111.8 55 208.9 146.3 16 13.1 9.2 76 62.3 43.6 36 111.4 78.0 96 160.6 112.4 56 209.7 146.8 17 13.9 9.8 77 63.1 44.2 37 112.2 78.6 97 161.4 113.0 57 210.5 147.4 18 14.7 10.3 78 63.9 44.7 38 113.0 79.2 98 162.2 113.6 58 211.3 148.0 19 15.6 10.9 79 64.7 45.3 39 113.9 79.7 99 163.0 114.1 59 212.2 148.6 20 16.4 11.5 80 65.5 45.9 40 114.7 80.3 200 163.8 114.7 60 213.0 213.8 149.1 21 17.2 12.0 81 66.4 46.5 141 115.5 80.9 201 164.6 115.3 261 149.7 22 18.0 12.6 82 67.2 47.0 42 116.3 81.4 02 165.5 115.9 62 214.6 150.3 23 18.8 13.2 83 68.0 47.6 43 117.1 82.0 03 166.3 116.4 63 215.4 150.9 24 19.7 13.8 84 68.8 48.2 44 118.0 82.6 04 leiV.i 117.0 64 216.3 151.4, 25 20.5 14.3 85 69.6 48.8 45 118.8 83.2 05 167.9 117.6 65 217.1 152.0 26 21.3 14.9 86 70.4 49.3 46 119.6 83.7 06 168.7 118.2 66 217.9 152.6 27 22.1 15.5 87 71.3 49.9 47 120.4 84.3 07 169.6 118.7 67 218.7 153.1 28 22.9 16.1 88 72.1 50.5 48 121.2 84.9 08 170.4 119.3 68 219.5 153.7 29 23.8 16.6 89 72.9 51.0 49 122.1 85.5 09 171.2 119.9 69 220.4 154.3 30 24.6 17.2 90 73.7 51.6 50 122.9 86.0 10 172.0 120.5 70 221.2 154.9 31 26.4 17.8 91 74.5 52.2 151 123.7 86.6 211 172.8 121.0 271 222.0 155.4 32 26.2 18.4 92 75.4 52.8 52 124.5 87.2 12 173.7 121.6 72 222.8 156.0 33 27.0 18.9 93 76.2 53.3 53 125.3 87.8 13 174.5 122.2 73 223.6 156.6 34 27.9 19.5 94 77.0 53.9 54 126.1 88.3 14 175.3 122.7 74 224.4 157.2 35 28.7 20.1 95 77.8 54.5 55 127.0 88.9 15 176.1 123.3 75 225.3 157.7 36 29.5 20.6 96 78.6 55.1 56 127.8 89.5 16 176.9 123.9 76 226.1 158.3 37 30.3 21.2 97 79.5 55.6 57 128.6 90.1 17 177.8 124.5 77 226.9 158.9 38 31.1 21.8 98 80.3 56.2 58 129.4 90.6 18 178.6 125.0 78 227.7 159.5 39 31.9 22.4 99 81.1 56.8 59 130.2 91.2 19 179.4 125.6 79 228.5 160.0 40 32.8 22.9 100 81.9 57.4 60 131.1 91.8 20 180.2 181.0 126.2 80 229.4 160.6 41 33.6 23.5 101 82.7 57.9 161 131.9 92.3 221 126.8 281 230.2 161.2 42 34.4 24.1 02 83.6 58.5 62 132.7 92.9 22 181.9 127.3 82 231.0 161.7 43 35.2 24.7 03 84.4 59.1 63 133.5 93.5 23 182.7 127.9 83 231.8 162.3 44 36.0 25.2 04 85.2 59.7 64 134.3 94.1 24 183.5 128.5 84 232.6 162.9 45 36.9 25.8 05 86.0 60.2 65 135.2 94.6 25 184.3 129.1 85 233.5 163.5 46 37.7 26.4 06 86.8 60.8 66 136.0 95.2 26 185.1 129.6 86 234.3 164.0 47 38.5 27.0 07 87.6 61.4 67 136.8 95.8 27 185.9 130.2 87 235.1 164.6 48 39.3 27.5 08 88.5 61.9 68 137.6 96.4 28 186.8 130.8 88 235.9 165.2 49 40.1 28.1 09 89.3 62.5 69 138.4 96.9 29 187.6 131.3 89 236. 7 165.8 50 41.0 28.7 10 90.1 63.1 70 139.3 97.5 30 188.4 131.9 90 237.6 166.3 51 41.8 29.3 111 90.9 63.7 171 140.1 98.1 231 189.2 132.5 291 238.4 166.9 52 42.6 29.8 12 91.7 64.2 72 140.9 98.7 32 190.0 133.1 92 239.2 167.5 53 43.4 30.4 13 92.6 64.8 73 141.7 99.2 33 190.9 133.6 93 240.0 168.1 54 44.2 31.0 14 93.4 65.4 74 142.5 99.8 34 191.7 134.2 94 . 240. 8 168.6 55 45.1 31.5 15 94.2 66.0 75 143.4 100.4 35 192.5 134.8 95 241.6 169.2 56 45.9 32.1 16 95.0 66.5 76 144.2 100.9 36 193.3 135.4 96 242.5 169.8 57 46.7 32.7 17 95.8 67.1 77 145.0 101.5 37 194.1 135.9 97 243.3 170.4 58 47.5 33.3 18 96.7 67.7 78 145.8 102.1 38 195.0 136.5 98 244.1 170.9 59 48.3 33.8 19 97.5 68.3 79 146.6 102.7 39 195.8 137.1 99 244.9 171.5 60 49.1 34.4 20 98.3 68.8 80 147.4 103.2 40 196.6 137.7 300 245.7 172.1 Diet. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 55° (1 25°, 235 °, 305° ). TABLE 2. [Page 601 Difference of Latitude and Departure for 35° (145°, 215°, 325° )• Dist. Lat Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 246.6 172.6 361 295.7 207.0 421 344.9 241.5 481 394.0 275.9 541 443.2 310.3 02 247.4 173. 2 62 296.5 207.6 22 345.7 242.0 82 394.8 276.4 42 444.0 310.9 03 248.2 173.8 63 297.4 208.2 23 346.5 242.6 83 395.7 277.0 43 444.8 311.4 04 249.0 174.3 64 298.2 208.8 24 347.3 243.2 84 396.5 277.6 44 445.6 312.0 05 249.9 174.9 65 299.0 209.3 25 348.1 243.8 85 397.3 278.2 45 446.4 312.6 06 250.7 175.5 66 299.8 209.9 26 349.0 244.3 86 398.1 278.7 46 447.3 313.2 07 251.5 176.1 67 300.6 210.5 27 349.8 244.9 87 398.9 279.3 47 448.1 313.7 08 232.3 176.6 68 301.5 211.1 28 350.6 245.5 88 399.8 279.9 48 448.9 314.3 09 253.1 177.2 69 302.3 211.6 29 351.4 246.0 89 400.6 280.5 49 449.7 314.9 10 253.9 177.8 70 303.1 212.2 30 352.2 353.1 246.6 90 401.4 281.0 50 450.5 315.4 311 254.8 178.4 371 303.9 212.8 431 247.2 491 402.2 281.6 551 451.4 316.0 12 255.6 178.9 72 304.7 213.4 32 353.9 247.8 92 403.0 282.2 52 452.2 316.6 13 256.4 179.5 73 305.6 213.9 33 354.7 248.3 93 403.9 282.8 53 453.0 317.2 14 257.2 180.1 74 306.4 214.5 34 355.5 248.9 94 404.7 283.3 54 453.8 317.7 15 258.0 180.7 75 307.2 215.1 35 356.3 249.5 95 405.5 283.9 55 454.6 318.3 16 258.9 181.2 76 308.0 215.6 36 357.2 250.1 96 406.3 284.5 56 455.5 318.9 17 259.7 181.8 77 308.8 216.2 37 358.0 250.6 97 407.1 285.1 57 456.3 319.5 18 260.5 182.4 78 309.6 216.8 38 358.8 251.2 98 408.0 285.6 58 457.1 320.0 19 261.3 183.0 79 310.5 217.4 39 359.6 251.8 99 408.8 286.2 59 457.9 320.6 20 321 262.1 183.5 80 311.3 217.9 40 360.4 252.4 500 409.6 286.8 60 458.7 321.2 263.0 184.1 381 312.1 218.5 441 361.3 252.9 501 410.4 287.4 561 459.6 321.8 22 263.8 184.7 82 312.9 219.1 42 362.1 253.5 02 411.2 287.9 62 460.4 322.3 23 264.6 185.2 83 313.7 219.7 43 362.9 254.1 03 412.1 288.5 63 461.2 322.9 24 265.4 185.8 84 314. ff 220.2 44 363.7 254.7 04 412.9 289.1 64 462.0 323.5 25 266.2 186.4 85 315.4 220.8 45 364. 5 255.2 05 413.7 289.7 65 462.8 324.1 26 267.1 187.0 86 316.2 221.4 46 365.4 255.8 06 414.5 290.2 66 463.7 324.6 27 267.9 187.5 87 317.0 222.0 47 366.2 256.4 07 415.3 290.8 67 464.5 325.2 28 268.7 188.1 88 317.8 222.5 48 367.0 256.9 08 416.1 291.4 68 465.3 325.8 29 269.5 188.7 89 318.7 223.1 49 367.8 257.5 09 417.0 291.9 69 466.1 326.4 30 331 270.3 189.3 90 319.5 223.7 50 368.6 258.1 10 417.8 292.5 70 466.9 326.9 327.5 271.1 189.8 391 320.3 224.3 451 369.4 258.7 511 418.6 293.1 571 467.8 32 272.0 190.4 92 321.1 224.8 52 370.3 259.2 12 419.4 293.7 72 468.6 328.1 33 272.8 191.0 93 321.9 225.4 53 371.1 259.8 13 420.2 294.2 73 469.4 328.7 34 273.6 191.6 94 322.8 226.0 54 371.9 260.4 14 421.1 294.8 74 470.2 329.2 35 274.4 192.1 95 323.6 226.5 55 372.7 261.0 15 421.9 295.4 75 471.0 329.8 36 275.2 192.7 96 324.4 227.1 56 373.5 261.5 16 422.7 296.0 76 471.9 330.4 37 276.1 193.3 97 325.2 227.7 57 374.4 262.1 17 423.5 296.5 77 472.7 331.0 38 276.9 193.9 98 326.0 228.3 58 375.2 262.7 18 424.3 297.1 78 473.5 331.5 39 277.7 194.4 99 326.9 228.8 59 376.0 263.3 19 425.2 297.7 79 474.3 332.1 40 278.5 195.0 400 327.7 229.4 60 376.8 263.8 20 426.0 298.3 80 475.1 332.7 333.3 341 279.3 195.6 401 328.5 230.0 461 377.6 264.4 521 426.8 298.8 581 476.0 42 280.2 196.1 02 329.3 230.6 62 378.5 265.0 22 427.6 299.4 82 476.8 333.8 43 281.0 196.7 03 330.1 231. 1 63 379.3 265.5 23 428.4 300.0 83 477.6 334.4 44 281.8 197.3 04 330.9 231.7 64 380.1 266.1 24 429.3 300.5 84 478.4 335.0 45 282.6 197.9 05 331.8 232.3 65 380.9 266.7 25 430.1 301.1 85 479.2 335.6 46 283.4 198.4 06 332.6 232.9 66 381.7 267.3 26 430.9 301.7 86 480.1 336.1 47 284.3 199.0 07 333.4 233.4 67 382.6 267.8 27 431.7 302.3 87 480.9 336.7 48 285.1 199.6 08 334.2 234.0 68 383.4 268.4 28 432.5 302.8 88 481.7 337.3 49 285.9 200.2 09 335.0 234.6 69 384.2 269.0 29 433.4 303.4 89 482.5 337.9 50 286.7 200.7 10 335.9 235.1 70 385.0 269.6 30 434.2 304.0 90 483.3 338.4 351 287.5 201.3 411 336.7 235.7 471 385.8 270.1 531 435.0 304.5 591 484.2 339.0 52 288.3 201.9 12 337.5 236.3 72 386.6 270.7 32 435.8 305.1 92 485.0 339.6 53 289.2 202.5 13 338.3 236.9 73 387.5 271.3 33 436.6 305.7 93 485.8 340.2 54 290.0 203.0 14 339.1 237.4 74 388.3 271.9 34 437.5 306.3 94 486.6 340.7 55 290.8 203.6 15 340.0 238.0 75 389.1 272.4 35 438.3 306.8 95 487.4 341.3 56 291.6 204.2 16 340.8 238.6 76 389.9 273.0 36 439,1 307.4 96 488.3 341.9 57 292.4 204.7 17 341.6 239.2 77 390.7 273.6 37 439.9 308.0 97 489.1 342.5 58 293.3 205.3 18 342.4 239.7 78 391.6 274.2 38 440.7 308.6 98 489.9 343.0 59 294.1 205.9 19 343.2 240.3 79 392.4 274.7 39 441.5 309.1 99 490.7 343.6 60 294.9 206.5 20 344.1 240.9 80 393.2 275.3 40 442.3 309.7 600 491.5 344.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 55° (1 25°, 235°, 305° )• Page 602] TABLE 2. Difference of Latitude and Departure for 36° (144°, 216°, 324° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 49.4 35.9 121 97.9 71.1 181 146.4 106.4 241 195.0 141.7 2 1.6 1.2 62 50.2 36.4 22 98.7 71.7 82 147.2 107.0 42 195.8 142.2 3 2.4 1.8 63 51.0 37.0 23 99.5 72.3 83 148.1 107.6 43 196.6 142.8 4 3.2 2.4 64 51.8 37.6 24 100.3 72.9 84 148.9 108.2 44 197.4 143.4 5 4.0 2.9 65 52.6 38.2 25 101.1 73.5 85 149.7 108.7 45 198.2 144.0 6 4.9 3.5 66 53.4 38.8 26 101.9 74.1 86 150.5 109.3 46 199.0 144.6 7 5.7 4.1 67 54.2 39.4 27 102.7 74.6 87 151.3 109.9 47 199.8 145.2 8 6.5 4.7 68 55.0 40.0 28 103.6 75.2 88 152.1 110.5 48 200. 6. 145.8 9 7.3 5.3 69 55.8 40.6 29 104.4 75.8 89 152.9 111.1 49 201.4 146.4 10 8.1 5.9 70 56.6 41.1 30 105.2 106.0 76.4 90 153.7 111.7 50 202.3 146.9 11 8.9 6.5 71 57.4 41.7 131 77.0 191 154.5 112.3 251 203.1 147.5 12 9.7 7.1 72 58.2 42.3 32 106.8 77.6 92 155.3 112.9 52 203.9 148.1 13 10.5 7.6 73 59.1 42.9 33 107.6 78.2 93 156.1 113.4 53 204.7 148.7 14 11.3 8.2 74 59.9 43.5 34 108.4 78.8 94 156.9 114.0 54 205.5 149.3 15 12.1 8.8 75 60.7 44.1 35 109.2 79.4 95 157.8 114.6 55 206.3 149.9 16 12.9 9.4 76 61.5 44.7 36 110.0 79.9 96 158.6 115.2 56 207.1 150.5 17 13.8 10.0 77 62.3 45.3 37 110.8 80.5 97 159.4 115.8 57 207.9 151.1 18 14.6 10.6 78 63.1 45.8 38 111.6 81.1 98 160.2 116.4 58 208.7 151.6 19 15.4 11.2 79 63.9 46.4 39 112.5 81.7 99 161.0 117.0 59 209.5 152.2 20 21 16.2 17.0 11.8 12.3 80 81 64.7 47.0 40 113.3 82.3 200 161.8 162.6 117.6 60 210.3 152.8 65.5 47.6 141 114.1 82.9 201 118.1 261 211.2 153.4 22 17.8 12.9 82 66.3 48.2 42 114.9 83.5 02 163.4 118.7 62 212.0 154.0 23 18.6 13.5 83 67.1 48.8 43 115.7 84.1 03 164.2 119.3 63 212.8 154.6 24 19.4 14.1 84 68.0 49.4 44 116.5 84.6 04 165.0 119.9 64 213.6 155.2 25 20.2 14.7 85 68.8 50.0 45 117.3 85.2 05 165.8 120.5 65 214.4 155.8 26 21.0 15.3 86 69.6 50.5 46 118.1 85.8 06 166.7 121.1 66 215.2 156.4 27 21.8 15.9 87 70.4 51.1 47 118.9 86.4 07 167.5 121.7 67 216.0 156.9 28 22.7 16.5 88 71.2 51.7 48 119.7 87.0 08 168.3 122.3 68 216.8 157.5 29 23.5 17.0 89 72.0 52.3 49 120.5 87.6 09 169.1 122.8 69 217.6 158.1 30 24.3 25.1 17.6 90 72.8 52.9 50 121.4 88.2 10 169.9 123.4 70 218.4 158.7 31 18.2 91 73.6 53.^ 151 122.2 88.8 211 170.7 124.0 271 219.2 159.3 32 25.9 18.8 92 74.4 54.1 52 123.0 89.3 12 171.5 124.6 72 220.1 159.9 33 26.7 19.4 93 75.2 54.7 53 123.8 89.9 13 172.3 125.2 73 220.9 160.5 34 27.5 20.0 94 76.0 55.3 54 124.6 90.5 14 173. 1 125.8 74 221.7 161.1 35 28.3 20.6 95 76.9 55.8 55 125.4 91.1 15 173.9 126.4 75 222.5 161.6 36 29.1 21.2 96 77.7 56.4 56 126.2 91.7 16 174.7 127.0 76 223.3 162.2 37 29.9 21.7 97 78.5 57.0 57 127.0 92.3 17 175.6 127.5 77 224.1 162.8 38 30.7 22.3 98 79.3 57.6 58 127.8 92.9 18 176.4 128.1 78 224.9 163. 4 39 31.6 22.9 99 80.1 58.2 59 128.6 93.5 19 177.2 128.7 79 225.7 164.0 40 32.4 23.5 100 80.9 58.8 60 129.4 94.0 20 178.0 129.3 80 226.5 164.6 41 33.2 24.1 101 81.7 59.4 161 130.3 94.6 221 178.8 129.9 281 227.3 165. 2 42 34.0 24.7 02 82.5 60.0 62 131.1 95.2 22 179.6 130.5 82 228.1 165.8 43 34.8 25.3 03 83.3 60.5 63 131.9 95.8 23 180.4 131.1 83 229.0 166.3 44 35.6 25.9 04 84.1 61.1 64 132.7 96.4 24 181 2 131.7 84 229.8 166.9 45 36.4 26.5 05 84.9 61.7 65 133.5 97.0 25 182.0 132.3 85 230.6 167.5 46 37.2 27.0 06 85.8 62.3 66 134.3 97.6 26 182.8 132.8 86 231.4 168.1 47 38.0 27.6 07 86.6 62.9 67 135.1 98.2 27 183.6 133.4 87 232.2 168.7 48 38.8 28.2 08 87.4 63.5 68 135.9 98.7 28 184.5 134.0 88 233.0 169.3 49 39.6 28.8 09 88.2 64.1 69 136.7 99.3 29 185.3 134.6 89 233. 8 169.9 50 40.5 29.4 10 89.0 64.7 70 137.5 138.3 99.9 30 186.1 135.2 90 234.6 235.4 170.5 51 41.3 30.0 111 89.8 65.2 171 100.5 231 186.9 135.8 291 171.0 52 42.1 30.6 12 90.6 65.8 72 139.2 101.1 32 187.7 136.4 92 236.2 171.6 53 42.9 31.2 13 91.4 66.4 73 140.0 101.7 33 188.5 137.0 93 237.0 172.2 54 43.7 31.7 14 92.2 67.0 74 140.8 102.3 34 189.3 137.5 94 237.9 172.8 55 44.5 32.3 15 93.0 67.6 75 141.6 102.9 35 190.1 138.1 95 238.7 173.4 56 45.3 32.9 16 93.8 68.2 76 142.4 103.5 36 190.9 138.7 96 239.5 174.0 57 46.1 33.5 17 94.7 68.8 77 143.2 104.0 37 191.7 139.3 97 240.3 174.6 58 46.9 34.1 18 95.5 69.4 78 144.0 104.6 38 192.5 139.9 98 241.1 175.2 59 47.7 34.7 19 96.3 69.9 79 144.8 105.2 39 193.4 140.5 99 241.9 175.7 60 48.6 35.3 20 97.1 70.5 80 145.6 105.8 40 194.2 141.1 300 242.7 176.3 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 54° (1 26°, 234 °, 306° )• TABLE 2. [Page 603 Difference of Latitude and Departure for 36° (144°, 216°, 324° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat Dep. 301 243.5 176.9 361 292.1 212.2 421 340.6 247.5 481 389.1 282.7 541 437.7 318.0 02 244.3 177.5 62 292.9 212.8 22 341.4 248.1 82 390.0 283.3 42 438.5 318.6 03 245.1 178.1 63 293.7 213.4 23 342.2 248.6 83 390.8 283.9 43 439.3 319.1 04 246.0 178.7 64 294.5 214.0 24 343.0 249.2 84 391.6 284.5 44 440.2 319.7 05 246.8 179.3 65 295.3 214.6 25 343.8 249.8 85 392.4 285.1 45 441.0 320.3 06 247.6 179.9 66 296.1 215.1 26 344.7 250.4 86 393.2 285.6 46 441.8 320.9 07 248.4 180.5 67 296.9 215.7 27 345.5 251.0 87 394.0 286.2 47 442.6 321.5 08 249.2 181.1 68 297.7 216.3 28 346.3 251.6 88 394.8 286.8 48 443.4 322.1 09 250. 1 181.6 69 298.5 216.9 29 347.1 252.2 89 395.6 287.4 49 444.2 322.7 10 250.8 182.2 70 299.3 217.5 30 347.9 252.8 90 396.4 288.0 50 445.0 323.3 311 251.6 182.8 371 300.2 218.1 431 348.7 253.3 491 397.3 288.6 551 445.8 323.8 12 252.4 183.4 72 301.0 218.7 32 349.5 253.9 92 398.1 289.2 52 446.6 324.4 13 253.2 184.0 73 301.8 219.3 33 350.3 254.5 93 398.9 289.8 53 447.4 325.0 14 254.0 184.6 74 302.6 219.8 34 351.1 255.1 94 399.7 290.3 54 448.2 325.6 15 254.9 185.2 75 303.4 220.4 35 351.9 255.7 95 400.5 290.9 55 449.0 326.2 16 255.7 185.8 76 304.2 221.0 36 352.7 256.3 96 401.3 291.5 56 449.8 326.8 17 256.5 186.4 77 305.0 221.6 37 353.6 256.9 97 402.1 292.1 57 450.7 327.4 18 257.3 186.9 78 305.8 222.2 38 354.4 257.5 98 402.9 292.7 58 451.5 328.0 19 258.1 187.5 79 306.6 222.8 39 355.2 258.0 99 403.7 293.3 59 452.3 328.5 20 258.9 188.1 80 307.4 223.4 40 356.0 258.6 500 404.5 293. 9 60 453.1 329.1 321 259.7 188.7 381 308.2 224.0 441 356.8 259.2 501 405.3 294.5 561 453.9 329.7 22 260.5 189.3 82 309.1 224.5 42 357.6 259.8 02 406.1 295.0 62 454.7 330.3 23 261.3 189.9 83 309.9 225.1 43 358.4 260.4 03 407.0 295.6 63 455.5 330.9 24 262.1 190.5 84 310.7 225.7 44 359.2 261.0 04 407.8 296.2 64 456.3 331.5 25 262.9 191.0 85 311.5 226.3 45 360.0 261.6 05 408.6 296.8 65 457.1 332.1 26 263.7 191.6 86 312.3 226.9 46 360.8 262.2 06 409.4 297.4 66 457.9 332.7 27 264.6 192.2 87 313.1 227.5 47 361.6 262.8 07 410.2 298.0 67 458.7 333.3 28 265.4 192.8 88 313.9 228.1 48 362.4 263.3 08 411.0 298.6 68 459.5 333.8 29 266.2 193.4 89 314.7 228.7 49 363.3 263.9 09 411.8 299.2 69 460.3 334.4 30 267.0 194.0 90 315.5 229.2 50 364.1 264.5 10 412.6 299.8 70 461.1 335.0 331 267.8 194.6 391 316.3 229.8 451 364.9 265.1 511 413.4 300.3 571 462.0 335.6 32 268.6 195.2 92 317.1 230.4 52 365.7 265.7 12 414.2 300.9 72 462.8 336.2 33 269.4 195.7 93 318.0 231.0 53 366.5 266.3 13 415.1 301.5 73 463.6 336.8 34 270:2 196.3 94 318.8 231.6 54 367.3 266.9 14 415.9 302.1 74 464.4 337.4 36 271.0 196.9 95 319.6 232.2 55 368.1 267.5 15 416.7 302.7 75 465.2 338.0 36 271.8 197.5 96 320.4 232.8 56 368.9 268.0 16 417.5 303.3 76 466.0 338.5 37 272.6 198.1 97 321.2 233.4 57 369.7 268.6 17 418.3 303.9 77 466.8 339.1 38 273.5 198.7 98 322.0 233.9 58 370. 5 269.2 18 419.1 304.4 78 467.6 339.7 39 274.3 199.3 99 322.8 234.5 59 371.3 269.8 19 419.9 305.0 79 468.4 340.3 40 275.1 199.9 400 323.6 235.1 60 372.2 270.4 20 420.7 305.6 80 469.3 340.9 341 275.9 200.4 401 324.4 235.7 461 373.0 271.0 521 421.5 306.2 581 470.1 341.5 42 276.7 201.0 02 325.2 236.3 62 373.8 271.6 22 422.3 306.8 82 470.9 342.1 43 277.5 201.6 03 326.0 236.9 63 374.6 272.2 23 423.1 307.4 83 471.7 342.7 44 278.3 202.2 04 326.9 237.5 64 375.4 272.7 24 423.9 308.0 84 472.5 343.2 45 279.1 202.8 05 327.7 238.1 65 376.2 273.3 25 424.7 308.6 85 473.3 343.8 46 279.9 203.4 06 328.5 238.7 66 377.0 273.9 26 425.5 309.2 86 474.1 344.4 47 280.7 204.0 07 329.3 239.2 67 377.8 274.5 27 426.4 309.7 87 474.9 345.0 48 281.5 204.6 08 330.1 239.8 68 378.6 275.1 28 427.2 310.3 88 475.7 345.6 49 282.4 205.1 09 330.9 240.4 69 379.4 275.7 J9 428.0 310.9 89 476.5 346.2 50 283.2 205.7 10 331.7 241.0 70 380.2 276.3 30 428.8 311.5 90 477.3 346.8 351 284.0 206.3 411 332.5 241.6 471 381.1 276.9 531 429.6 312.1 591 478.2 347.4 52 284.8 206.9 12 333.3 242.2 72 381.9 277.4 32 430.4 312.7 92 479.0 347.9 53 285.6 207.5 13 334.1 242.8 73 382.7 278.0 33 431.2 313.3 93 479.8 348.5 54 286.4 208.1 14 334.9 243.4 74 383.5 278.6 34 432.0 313.9 94 480.6 349.1 55 287.2 208.7 15 335.8 243.9 75 384.3 279.2 35 432.9 314.4 95 481.4 349.7 56 288.0 209.3 16 336.6 244.5 76 385.1 279.8 36 433.7 315.0 96 482.2 350.3 57 288.8 209.8 17 337. 4 245.1 77 385.9 280.4 37 434.5 315.6 97 483.0 350.9 58 289.6 210.4 18 338.2 245.7 78 386.7 281.0 38 435.3 316.2 98 483.8 351.5 59 290.4 211.0 19 339.0 246.3 79 387.5 281.6 39 436.1 316.8 99 484.6 352.1 60 291.3 211.6 20 339.8 246.9 80 388.3 282.1 40 436.9 317.4 600 485.4 352.7 Diat. Dep. Lat. Dist. Dep. Lat. Diat. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 54° (] 26°, 23^ 1°, 306'= ). Page 604] TABLE 2. Difference of Latitude and Departure for 37* (143°, 217", 823* )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 48.7 36.7 121 96.6 72.8 181 144.6 108.9 241 192.5 145.0 2 1.6 1.2 62 49.5 37.3 22 97.4 73.4 82 145.4 109.5 42 193.3 145.6 3 2.4 1.8 63 50.3 37.9 23 98.2 74.0 83 146.2 110.1 43 194.1 146.2 4 3.2 2.4 64 51.1 38.5 24 99.0 74.6 84 146.9 110.7 44 194.9 146.8 5 4.0 3.0 65 51.9 39.1 25 99.8 75.2 85 147.7 111.3 45 195.7 147.4 6 4.8 3.6 66 52.7 39.7 26 100.6 75.8 86 148.5 111.9 46 196.5 148.0 7 5.6 4.2 67 53.5 40.3 27 101.4 76.4 87 149.3 112.5 47 197.3 148.6 8 6.4 4.8 68 54.3 40.9 28 102.2 77.0 88 150.1 113.1 48 198.1 149.3 9 7.2 5.4 69 55.1 41.5 29 103.0 77.6 89 150.9 113.7 49 198.9 149.9 10 8.0 6.0 70 55.9 42.1 30 103.8 78.2 90 151.7 114.3 50 199.7 150.5 11 8.8 6.6 71 56.7 42.7 131 104.6 78.8 191 152.5 114.9 251 200.5 151.1 12 9.6 7.2 72 57.5 43.3 32 105.-4 79.4 92 153.3 115.5 52 201.3 151.7 13 10.4 7.8 73 58.3 43.9 33 106.2 80.0 93 154.1 116.2 53 202.1 152.3 14 11.2 8.4 74 59.1 44.5 34 107.0 80.6 94 154.9 116.8 54 202.9 152.9 15 12.0 9.0 75 59.9 45.1 35 107.8 81.2 95 155.7 117.4 55 203.7 153.5 16 12.8 9.6 76 60.7 45.7 36 108.6 81.8 96 156.5 118.0 56 204.5 154.1 17 13.6 10.2 77 61.5 46.3 37 109.4 82.4 97 157.3 118.6 57 205.2 154.7 18 14.4 10.8 78 62.3 46.9 38 110.2 83.1 98 158.1 119.2 58 206.0 155.3 19 16.2 11.4 79 63.1 47.5 39 111.0 83.7 99 158.9 119.8 59 206.8 155.9 20 16.0 12.0 80 63.9 48.1 40 111.8 112.6 84.3 200 159.7 120.4 60 207.6 208.4 156.5 21 16.8 12.6 81 64.7 48.7 141 84.9 201 160.5 121.0 261 157.1 22 17.6 13.2 82 65.5 49.3 42 113.4 85.5 02 161.3 121.6 62 209.2 157.7 23 18.4 13.8 83 66.3 50.0 43 114.2 86.1 03 162.1 122.2 63 210.0 158.3 24 19.2 14.4 84 67.1 50.6 44 115.0 86.7 04 162.9 122.8 64 210.8 158.9 25 20.0 15.0 85 67.9 51.2 45 115.8 87.3 05 163.7 123.4 65 211.6 159.5 26 20.8 15.6 86 68.7 51.8 46 116.6 87.9 06 164.5 124.0 66 212.4 160.1 27 21.6 16.2 87 69.5 52.4 47 117.4 88.5 07 165.3 124.6 67 213.2 160.7 28 22.4 16.9 88 70.3 53.0 48 118.2 89.1 08 166.1 125.2 68 214.0 161.3 29 23.2 17.5 89 71.1 53.6 49 119.0 89.7 09 166.9 125.8 69 214.8 161.9 30 24.0 18.1 90 71.9 54.2 50 119.8 90.3 10 167.7 126.4 70 215.6 162.5 31 24.8 18.7 91 72.7 54.8 151 120.6 90.9 211 168.5 127.0 271 216.4 163.1 32 25.6 19.3 92 73.5 55.4 52 121.4 91.5 12 169.3 127.6 72 217.2 163.7 33 26.4 19.9 93 74.3 56.0 53 122.2 92.1 13 170.1 128.2 73 218.0 164.3 34 27.2 20.5 94 75.1 56.6 54 123.0 92.7 14 170.9 128.8 74 218.8 164.9 35 28.0 21.1 95 75.9 57.2 55 123.8 93.3 15 171.7 129.4 75 219.6 165.5 36 28.8 21.7 96 76.7 57.8 56 124.6 93.9 16 172.5 130.0 76 220.4 166.1 37 29.5 22.3 97 77.5 58.4 57 125.4 94.5 17 173.3 130.6 77 221.2 166.7 38 30.3 22.9 98 78.3 59.0 58 126.2 95.1 18 174.1 131.2 78 222.0 167.3 39 31.1 23.5 99 79.1 59.6 59 127.0 95.7 19 174.9 131.8 79 222.8 167.9 40 31.9 24.1 100 79.9 60.2 60 127.8 96.3 20 175.7 132.4 80 223.6 168.5 41 32.7 24.7 101 80.7 60.8 161 128.6 96.9 221 176.5 133.0 281 224.4 169.1 42 33.5 25.3 02 81.5 61.4 62 129.4 97.5 22 177.3 133.6 82 225.2 169.7 43 34.3 25.9 03 82.3 62.0 63 130.2 98.1 23 178.1 134.2 83 226.0 170.3 44 35.1 26.5 04 83.1 62.6 64 131.0 98.7 24 178.9 134.8 84 226.8 170.9 45 35.9 27.1 05 83.9 63.2 65 131.8 99.3 25 179.7 135.4 85 227.6 171.5 46 36.7 27.7 06 84.7 63.8 66 132.6 99.9 26 180.5 136.0 86 228.4 172.1 47 37.5 28.3 07 85.5 64.4 67 133.4 100.5 27 181.3 136.6 87 229.2 172.7 48 38.3 28.9 08 86.3 65.0 68 134.2 101.1 28 182.1 137.2 88 230.0 173.3 49 39.1 29.5 09 87.1 65.6 69 135.0 101.7 29 182.9 137.8 89 230.8 173.9 50 39.9 30.1 10 87.8 66.2 70 135.8 102.3 30 183.7 138.4 90 231.6 174.5 51 40.7 30.7 111 88.6 66.8 171 136.6 102.9 231 184.5 139.0 291 232.4 175.1 52 41.5 31.3 12 89.4 67.4 72 137.4 103.5 32 185.3 139.6 92 233.2 175.7 53 42.3 31.9 13 90.2 68.0 73 138.2 104.1 33 186.1 140.2 93 234.0 176.3 54 43.1 32.5 14 91.0 68.6 74 139.0 104.7 34 186.9 140.8 94 234.8 176.9 55 43.9 33.1 15 91.8 69.2 75 139.8 105.3 35 187.7 141.4 95 235.6 177.5 56 44.7 33.7 16 92.6 69.8 76 140.6 105.9 36 188.5 142.0 96 236.4 178.1 57 45.5 34.3 17 93.4 70.4 77 141.4 106.5 37 189.3 142.6 97 237.2 178.7 58 46.3 34.9 18 94.2 71.0 78 142.2 107.1 38 190.1 143.2 98 238.0 179.3 59 47.1 35.5 19 95.0 71.6 79 143.0 107.7 39 190.9 143.8 99 238.8 179.9 60 Dist. 47.9 36.1 20 95.8 72.2 80 143.8 108.3 40 191.7 144.4 300 239.6 180.5 Dep. Lat. DiBt. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 53° (127°, 233 °, 307° )• TABLE 2. [Page 605 I Difference of Latitude and Departure for 37° (143°, 217°, 323°). 1 Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 240.4 181.1 361 288.3 217.3 421 336.2 253.4 481 384.1 289.5 541 432.0 325.6 02 241.2 181.7 62 289.1 217.9 22 337.0 254.0 82 384.9 290.0 42 432.8 326.2 03 242.0 182.4 63 289.9 218.5 23 337.8 254.6 83 385.7 290.6 43 433.6 326.8 04 242.7 183.0 64 290.7 219.1 24 338.6 255.2 84 386.5 291.2 44 434.4 327.3 05 243.5 183.6 65 291.5 219.7 25 339.4 255.8 85 387.3 291.8 45 435.2 327.9 06 244.3 184.2 66 292.3 220.3 26 340.2 256.4 86 388.1 292.4 46 436.0 328.5 07 245.1 184.8 67 293.1 220.9 27 341.0 257.0 87 388.9 293.0 47 436.8 329.1 08 245.9 185.4 68 293.9 221.5 28 341.8 257.6 88 389.7 293.6 48 437.6 329.7 09 246.7 186.0 69 294.7 222.1 29 342.6 258.2 89 390.5 294.2 49 438.4 330.3 10 247.5 186.6 70 295.5 222.7 30 343.4 258.8 90 391.3 294.8 50 439.2 330.9 311 248.3 187.2 371 296.3 223.3 431 344.2 259.4 491 392.1 295.4 551 440.0 331.5 12 249.1 187.8 72 297.1 223.9 32 345.0 260.0 92 392.9 296.0 52 440.8 332.1 13 249.9 188.4 73 297.9 224.5 33 345.8 260.6 93 393.7 296.6 53 441.6 332.7 14 250.7 189.0 74 298.7 225.1 34 346.6 261.2 94 394.5 297.2 54 442.4 333. 3 15 251.5 189.6 75 299.5 225. 7 35 347.4 261.8 95 395.3 297.8 55 443.2 333.9 16 252.3 190.2 76 300.3 226.3 36 348.2 262.4 96 396.1 298.5 56 444.0 334.6 17 253.1 190.8 77 301.1 226.9 37 349.0 263.0 97 396.9 299.1 57 444.8 235.2 18 253.9 191.4 78 301.8 227.5 38 349.8 263.6 98 397.7 399.7 58 445.6 335.8 19 254.7 192.0 79 302.6 228.1 39 350. 6 264.2 99 398.5 300.3 59 446.4 336.4 20 255.5 256.3 192.6 80 303.4 228.7 40 351.4 264.8 500 399.3 300.9 60 447.2 337.0 321 193.2 381 304.2 229.3 441 352.2 265.4 501 400.1 301.5 561 448.0 337.6 22 257.1 193.8 82 305.0 229.9 42 353.0 266.0 02 400.9 302.1 62 448.8 338.2 23 257.9 194.4 83 305.8 230.5 43 353.8 266.6 03 401.7 302.7 63 449.6 338.8 24 258.7 195.0 84 306.6 231.1 44 354.6 267.2 04 402.5 303.3 64 450.4 339.4 25 259.5 195. 6 85 307.4 231.7 45 355.4 267.8 05 403.3 303.9 65 451.2 340.0 26 260.3 196.2 86 308.2 232.3 46 356.2 268.4 06 404.1 304.5 66 452.0 340.6 27 261.1 196.8 87 309.0 232.9 47 357.0 269.0 07 404.9 305.1 67 452.8 341.2 28 261.9 197.4 88 309.8 233.5 48 357.8 269.6 08 405.7 305.7 68 453.6 341.8 29 262.7 198.0 89 310.6 234.1 49 358.6 270.2 09 406.5 306.3 69 454.4 342.4 30 263.5 264.3 198.6 90 311.4 234.7 50 359.4 270.8 10 407.3 306.9 70 455.2 343.0 331 199.2 391 312.2 235.3 451 360.1 271.4 511 408.1 307.5 571 456.0 343.6 32 265.1 199.8 92 313.0 235.9 52 360.9 272.0 12 408.9 308.2 72 456.8 344.3 33 265.9 200.4 93 313.8 236. 5 53 361.7 272.6 13 409.7 308.8 73 457.6 344.9 34 266.7 201.0 94 314.6 237.1 54 362.5 273.2 14 410.5 309.4 74 458.4 345.5 35 267.5 201.6 95 315.4 237.7 55 363.3 273.8 15 411.3 310.0 75 459.2 346.1 36 268.3 202.2 96 316.2 238.3 56 364.1 274.4 16 412.1 310.6 76 460.0 346.7 37 269.1 202.8 97 317.0 238.9 57 364.9 275.0 17 412.9 311.2 77 460.8 347.3 38 269.9 203.4 98 317.8 239. 5 58 365.7 275.6 18 413.7 311.8 78 461.6 347.9 39 270.7 204.0 99 318.6 240.1 59 366.5 276.2 19 414.5 312.4 79 462.4 348.5 40 271.5 204.6 400 319.4 240.7 60 367.3 276.8 20 415.3 313.0 80 463.2 349.1 341 272.3 205.2 401 320.2 241.3 461 368.1 277.4 521 416.1 313.6 581 464.0 349.7 42 273.1 205.8 02 321.0 241.9 62 368.9 278.0 22 416.9 314.2 82 464.8 350.3 43 273.9 206.4 03 321.8 242.5 63 369.7 278.6 23 417.7 314.8 83 465.6 350.9 44 274.7 207.0 (^4 322.6 243.1 64 370.5 279.2 24 418.5 315.4 84 466.4 351.5 45 275.5 207.6 05 323.4 243.7 65 371.3 279.8 25 419.3 316.0 85 467.2 352.1 46 276.3 208.2 06 324.2 244.3 66 372.1 280.4 26 420.1 316.6 86 468.0 352.7 47 277.1 208.8 07 325.0 244.9 67 372.9 281.0 27 420.9 317.2 87 468.8 353.3 48 277.9 209.4 08 325.8 245.5 68 373.7 281.6 28 421.7 317.8 88 469.6 353.9 49 278.7 210.0 09 326.6 246.1 69 374.5 282.3 29 422.5 318.4 89 470.4 354.5 50 279.5 210.6 10 327.4 246.7 70 375.3 282.9 30 423.3 319.0 90 471.2 355.1 351 280.3 211.2 411 328.2 247.3 471 376.1 283.5 531 424.1 319.6 591 472.0 355.7 52 281.1 211.8 12 329.0 247.9 72 376.9 284.1 32 424.9 320.2 92 472.8 356.3 53 281.9 212.4 13 329.8 248.5 73 377.7 284.7 33 425.7 320.8 93 473.6 356.9 54 282.7 213.0 14 330.6 249.2 74 378.5 285.3 34 426.5 321.4 94 474.4 357.5 55 283.5 213.6 15 331.4 249.8 75 379.3 285.9 35 427.3 322.0 95 475.2 358.1 56 284.3 214.2 16 332.2 250.4 76 380.1 286.5 36 428.1 322.6 96 476.0 358.7 57 285.1 214.8 17 333.0 251.0 77 380.9 287.1 37 428.9 323.2 97 476.8 359.3 58 285.9 215.4 18 333.8 251.6 78 381.7 287.7 38 429.7 323.8 98 477.6 359.9 59 286.7 216.1 19 334.6 252.2 79 382.5 288.3 39 430.5 324.4 99 478.4 360.5 60 287.5 216.7 20 335.4 252.8 80 383.3 288.9 40 431.3 325.0 600 479.2 361.1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. 1 e )3° (127°, 233°, 307° ). 1 Page 606] TABLE 2. Difference of Latitude and Departure for 38° (142°, 218°, 322' ')• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 48.1 37.6 121 95.3 74.5 181 142.6 111.4 241 189.9 148.4 2 1.6 1.2 62 48.9 38.2 22 96.1 75.1 82 143.4 112.1 42. 190.7 149.0 3 2.4 1.8 63 49.6 38.8 23 96.9 75.7 83 144.2 112.7 43 191.5 149.6 4 3.2 2.5 64 50.4 39.4 24 97.7 76.3 84 145.0 113.3 44 192.3 150.2 5 3.9 3.1 65 51.2 40.0 25 98.5 77.0 85 145.8 113.9 45 193.1 150.8 6 4.7 3.7 66 52.0 40.6 26 99.3 77.6 86 146.6 114.5 46 193.9 151.5 7 5.5 4.3 67 52.8 41.2 27 100.1 78.2 87 147.4 115.1 47 194.6 152.1 8 6.3 4.9 68 53.6 41.9 28 100.9 78.8 88 148.1 115.7 48 195.4 152.7 9 7.1 5.5 69 54.4 42.5 29 101.7 79.4 89 148.9 116.4 49 196.2 153.3 10 7.9 6.2 70 55.2 43.1 30 102.4 80.0 90 149.7 117.0 50 197.0 153.9 11 8.7 6,8 71 55.9 43.7 131 103.2 80.7 191 150.5 117.6 251 197.8 154.5 12 9.5 7.4 72 56.7 44.3 32 104.0 81.3 92 151.3 118.2 52 198.6 155.1 13 10.2 8.0 73 57.5 44.9 33 104.8 81.9 93 152.1 118.8 53 199.4 155.8 14 11.0 8.6 74 58.3 45.6 34 105.6 82.5 94 152.9 119.4 54 200.2 156.4 15 11.8 9.2 75 59.1 46.2 35 106.4 83.1 95 153.7 120.1 55 200.9 157.0 16 12.6 9.9 76 59.9 46.8 36 107.2 83.7 96 154.5 120.7 56 201.7 157.6 17 13.4 10.5 77 60.7 47.4 37 108.0 84.3 97 155.2 121.3 57 202.5 158.2 18 14.2 11.1 78 61.5 48.0 38 108.7 85.0 98 156.0 121.9 58 203.3 158.8 19 15.0 11.7 79 62.3 48.6 39 109.5 85.6 99 156.8 122.5 59 204.1 159.6 20 15.8 12.3 12. 9 80 63.0 49.3 40 110.3 86.2 200 157.6 123.1 60 204.9 160.1 21 16.5 81 63.8 49.9 141 111.1 86.8 201 158.4 123.7 261 205. 7 160.7 22 17.3 13.5 82 64.6 50.5 42 111.9 87.4 02 159.2 124.4 62 206.5 161.3 23 18.1 14.2 83 65.4 51.1 43 112.7 •88.0 03 160.0 125.0 63 207.2 161.9 24 18.9 14.8 84 66.2 51.7 44 113.5 88.7 04 160.8 125.6 64 208.0 162.6 25 19.7 15.4 85 67.0 52.3 45 114.3 89.3 05 161.5 126.2 65 208.8 163. 2 26 20.5 16.0 86 67.8 52.9 46 115.0 89.9 06 162.3 126.8 66 209.6 163.8 27 21.3 16.6 87 68.6 53.6 47 115.8 90.5 07 163.1 127.4 67 210.4 164.4 28 22.1 17.2 88 69.3 54.2 48 116.6 91.1 08 163.9 128.1 68 211.2 165.0 29 22.9 17.9 89 70.1 54.8 49 117.4 91.7 09 164.7 128.7 69 212.0 165.6 30 23.6 18.5 19.1 90 70.9 55.4 50 118.2 119.0 92.3 10 165.5 129.3 70 212.8 166.2 31 24.4 91 71.7 56.0 151 93.0 211 166.3 129.9 271 213.6 166.8 32 25.2 19.7 92 72.5 56.6 52 119.8 93.6 12 167.1 130.5 72 214.3 167.5 33 26.0 20.3 93 73.3 57.3 53 120.6 94.2 13 167.8 131.1 73 215. 1 168.1 34 26.8 20.9 94 74.1 57.9 54 121.4 94.8 14 168.6 131.8 74 215.9 168.7 35 27.6 21.5 95 74.9 58.5 55 122.1 95.4 15 169.4 132.4 75 216.7 169.3 36 28.4 22.2 96 75.6 59.1 56 122.9 96.0 16 170.2 133.0 76 217.5 169.9 37 29.2 22.8 97 76.4 59.7 57 123.7 96.7 17 171.0 133.6 77 218.3 170.5 38 29.9 23.4 98 77.2 60.3 58 124.5 97.3 18 171.8 134.2 78 219.1 171.2 39 30.7 24.0 99 78.0 61.0 59 125.3 97.9 19 172.6 134.8 79 219.9 171.8 40 31.5 24.6 100 78.8 61.6 60 126.1 98.5 20 173.4 135.4 80 220.6 172.4 41 32.3 25.2 101 79.6 62.2 161 126.9 99.1 221 174.2 136.1 281 221.4 173.0 42 33.1 25.9 02 80.4 62.8 62 127.7 99.7 22 174.9 136.7 82 222.2 173.6 43 33.9 26.5 03 81.2 63.4 63 128.4 100.4 23 175.7 137.3 83 223.0 174.2 44 34.7 27.1 04 82.0 64.0 64 129.2 101.0 24 176. 5 137.9 84 223.8 174.8 45 35.5 27.7 05 82.7 64.6 65 130.0 101.6 25 177.3 138.5 85 224.6 175.5 46 36.2 28.3 06 83.5 65.3 66 130.8 102.2 26 178.1 139.1 86 225.4 176.1 47 37.0 28.9 07 84.3 65.9 67 131.6 102.8 27 178.9 139.8 87 226.2 176.7 48 37.8 29.6 08 85.1 66.5 68 132.4 103.4 28 179.7 140.4 88 226.9 177.3 49 38.6 30.2 09 85.9 67.1 69 133.2 104.0 29 180. 5 141.0 89 227.7 177.9 50 39.4 30.8 10 86.7 67.7 70 134.0 104.7 30 181.2 182.0 141.6 142.2 90 228.5 178.5 51 40.2 31.4 111 87.5 68.3 171 134.7 105.3 231 291 229.3 179.2 52 41.0 32.0 12 88.3 69.0 72 135.5 105.9 32 182.8 142.8 92 230.1 179.8 53 41.8 32.6 13 89.0 69.6 73 136. 3 106.5 33 183.6 143.4 93 230.9 180.4 54 42.6 33.2 14 89.8 70.2 74 137.1 107.1 34 184.4 144.1 94 231.7 181.0 55 43.3 33.9 15 90.6 70.8 75 137.9 107.7 35 185.2 144,7 95 232.5 181.6 56 44.1 34.5 16 91.4 71.4 76 138.7 108.4 36 186.0 145.3 96 233.3 182.2 57 44.9 35.1 17 92.2 72.0 77 139.5 109.0 37 186.8 145.9 97 234.0 182.9 58 45.7 35.7 18 93.0 72.6 78 140.3 109.6 38 187.5 146.5 98 234.8 183.6 59 46.5 36.3 19 93.8 73.3 79 141.1 110.2 39 188.3 147.1 99 235.6 184.1 60 47.3 36.9 20 94.6 73.9 80 141.8 110.8 40 189.1 147.8 300 236.4 184.7 Dist. Dep. Lat. Dl8t. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 52' ' (128°, 232°, 308°). . TABLE 2. [Page 607 Difference of Latitude and Departure for 38° (142°, 218°, 322° )• Dist. Lat. Dep. 1 DlBt. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. j Dep. 301 237.2 186.3 361 284.5 222.3 421 331.8 259.2 481 379.0 296.2 541 i 426. 3 333. 1 02 238.0 185.9 62 285.3 222.9 22 332.5 259.8 82 379.8 296.8 42 427.1 ' 333.7 03 238.8 186.6 63 286.0 223.5 23 333.3 260.4 83 380.6 297.4 43 427. 9 1 334. 3 04 239.6 187.2 64 286.8 224.1 24 334.1 261.0 84 381.4 298.0 44 428.7 1 335.0 05 240.3 187.8 65 287.6 224.7 25 334.9 261.7 85 382.2 298.6 45 429. 5 335. 6 06 241.1 188.4 66 288.4 225.3 26 335.7 262.3 86 383.0 299.2 46 430.3 336.2 07 241.9 189.0 67 289.2 226.0 27 336.5 262.9 87 383.8 299.8 47 431.0 336.8 08 242.7 189.6 68 290.0 226.6 28 337.3 263.5 88 384.5 300.4 48 431.8 337.4 09 243.5 190.2 69 290.8 227.2 29 338.1 264.1 89 385.3 301.1 49 432.6 338.0 10 244.3 190.9 70 291.6 227.8 30 338.8 264.7 90 386.1 301.7 50 433.4 338.6 311 245.1 191.5 371 292.4 228.4 431 339.6 265.4 491 386.9 302.3 551 434.2 339.3 12 245.9 192.1 72 293.1 229.0 32 340.4 266.0 92 387.7 302.9 52 435.0 339.9 13 246.6 192.7 73 293.9 229.6 33 341.2 266.6 93 388.5 303.5 53 435.8 340.6 14 247.4 193.3 74 294.7 230.3 34 342.0 267.2 94 389.3 304.2 54 436.6 341. 1 15 248.2 193.9 75 295.5 230.9 35 342.8 267.8 95 390.1 304.8 55 437.4 341.7 16 249.0 194.6 76 296.3 231.5 36 343.6 268.4 96 390.9 305.4 56 438.1 342.3 17 249.8 195.2 77 297.1 232.1 37 344.4 269.1 97 391.6 306.0 57 438.9 348.0 18 250.6 195.8 78 297.9 232.7 38 345.2 269.7 98 392.4 306.6 58 439.7 343.6 19 251.4 196.4 79 298.7 233.3 39 345.9 270.3 99 393.2 307.2 69 440.5 344.2 20 321 252.2 197.0 80 299.4 234.0 40 346.7 270.9 500 394.0 307.8 60 441.3 344.8 253.0 197.6 381 300.2 234.6 441 347.5 271.5 501 394.8 308.4 561 442.1 345.4 22 253.7 198.2 82 301.0 235.2 42 348.3 272.1 02 395.6 309.1 62 442.9 346.0 23 254.6 198.9 83 301.8 235.8 43 349.1 272.7 03 396.4 309.7 63 443. 7 346. 6 1 24 255.3 199.5 84 302.6 236.4 44 349.9 273.4 04 397.2 310.3 64 444.4 347.2 25 256.1 200.1 85 303.4 237.0 45 350.7 274.0 05 397.9 310.9 65 445.2 347. 8 26 256.9 200.7 86 304.2 237.7 46 351.5 274.6 06 398.7 311.6 66 446.0 348.6 27 257.7 201.3 87 305.0 238.3 47 352.2 275.2 07 399.5 312.2 67 446.8 349.1 28 258.5 201.9 88 305.7 238.9 48 353.0 275.8 08 400.3 312.8 68 447.6 349.7 29 259.3 202.6 89 306.5 239.5 49 353.8 276.4 09 401.1 313.4 69 448. 4 350. 3 30 260.0 203.2 90 307.3 240.1 50 354.6 277.1 10 401.9 314.0 70 449.2 350.9 331 260.8 203.8 391 308.1 240.7 451 355.4 277.7 511 402.7 314.6 671 460. 361. 6 32 261.6 204.4 92 308.9 241.3 52 356.2 278.3 12 403.6 316.2 72 460. 7 352. 2 33 262.4 205.0 93 309.7 242.0 53 357.0 278.9 13 404.2 316.8 73 461.5 ! 352.8 34 263.2 205.6 94 310.5 242.6 54 357.8 279.5 14 405.0 316.4 74 452.3 ; 353.4 35 264.0 206.3 95 311.3 243.2 55 358.5 280.1 15 405.8 317.1 76 463.1 1 354.0 36 264.8 206.9 96 312.1 243.8 56 359.3 280.7 16 406.6 317.7 76 453.9 ! :i54.6 37 265.6 207.5 97 312.8 244.4 57 360.1 281.4 17 407. 4 318.3 77 464. 7 ' 365. 2 38 266.3 208.1 98 313.6 245.0 58 360.9 282.0 18 408.2 318.9 78 455. 5 :355. 8 39 267.1 208.7 99 314.4 245.7 59 361.7 282.6 19 409.0 319.5 79 456. 3 356. 4 40 267.9 209.3 400 315.2 246.3 60 362.5 283.2 20 409.8 320.2 80 467. 1 357. 1 341 268.7 209.9 401 316.0 246.9 461 363.3 283.8 521 410.6 320.8 581 457. 8 357. 7 42 269.5 210.6 02 316.8 247.5 62 364.1 284.4 22 411.3 321.4 82 458. 6 358. 3 43 270.3 211.2 03 317.6 248.1 63 364.9 285.1 23 412.1 322.0 83 459. 4 358. 9 44 271.1 211.8 04 318.4 248.7 64 365.6 285.7 24 412.9 322.6 84 460. 2 359. 6 45 271.9 212.4 05 319.1 249.3 65 366.4 286.3 25 413.7 323.2 85 461. 360. 2 46 272.7 213.0 06 319.9 250.0 66 367.2 286.9 26 414.5 323.8 86 461. 8 360. 8 47 273.4 213.6 07 320.7 250.6 67 368.0 287.5 27 415.3 324.5 87 462. 6 361. 4 48 274.2 214.3 08 321.5 251.2 68 368.8 288.1 28 416.1 325.1 88 463.3 362.0 49 275.0 214.9 09 322.3 251.8 69 369.6 288.7 29 416.9 325.7 89 464.1 362. 6 50 275.8 215.5 10 323.1 252.4 70 370.4 289.3 30 417.6 326.3 90 464.9 363.2 351 276.6 216.1 411 323.9 253.0 471 371.2 290.0 531 418.4 326.9 591 466.7 363.8 52 277.4 216.7 12 324.7 253.7 72 371.9 290.6 32 419.2 327.5 92 466.6 364.4 53 278.2 217.3 13 325.5 254.3 73 372.7 291.2 33 420.0 328.2 93 467.3 365.1 M 279.0 218.0 14 326.2 254.9 74 373.5 291.8 34 420.8 328.8 94 468.1 365.7 55 279.7 218.6 15 327.0 255.5 75 374.3 292.4 35 421.6 329.4 95 468.9 366.3 56 280.5 219.2 16 327.8 256.1 76 375.1 293.1 36 422.4 330.0 96 469.7 366.9 57 281.3 219.8 17 328.6 256.7 77 375.9 293.7 37 423.2 330.6 97 470.6 367.5 58 282.1 220.4 18 329.4 257.4 78 376.7 294.3 38 424.0 331.2 98 471.2 368.1 59 282.9 221.0 19 330.2 258.0 79 377. 5 294.9 39 424.7 331.8 99 472.0 368.7 60 283.7 221.6 20 331.0 258.6 80 378.2 295.5 40 425.5 332.5 600 472.8 369.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist Dep. Lat. Dist. Dep. Lat. 52° (128°, 235 2°, 308°). 1 Page 608] TABLE 2. Difference of Latitude and Departure for 39° (141°, 219°, 321° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0,8 0.6 61 47.4 38.4 121 94.0 76.1 181 140.7 113.9 241 187.3 151.7 2 1.6 1.3 62 48.2 39.0 22 94.8 76.8 82 141.4 114.5 42 188.1 152.3 3 2.3 1.9 63 49.0 39.6 23 95.6 77.4 83 142.2 115. 2 43 188.8 152.9 4 3.1 2.5 64 49.7 40.3 24 96.4 78.0 84 143.0 115.8 44 189.6 153.6 5 3.9 3.1 65 50.5 40.9 25 97.1 78.7 85 143.8 116.4 45 190.4 154.2 6 4.7 3.8 66 51.3 41.5 26 97.9 79.3 86 144.5 117.1 46 191.2 154.8 7 5.4 4.4 67 52.1 42.2 27 98.7 79.9 87 145.3 117.7 47 192.0 155.4 8 6.2 5.0 68 52.8 42.8 28 99.5 80.6 88 146.1 118.3 48 192.7 156.1 9 7.0 5.7 69 53.6 43.4 29 100.3 81.2 89 146.9 118.9 49 193.5 156.7 10 7.8 6.3 70 54.4 44.1 80 101.0 81.8 90 147.7 119.6 50 194.3 157.3 11 8.5 6.9 71 55.2 44.7 131 101.8 82.4 191 148.4 120.2 251 195.1 158.0 12 9.3 7.6 72 56.0 45.3 32 102.6 83.1 92 149.2 120.8 52 195.8 158.6 13 10.1 8.2 73 56.7 45.9 33 103.4 83.7 93 150.0 121.5 53 196.6 159.2 14 10.9 8.8 74 57.5 46.6 34 104.1 84.3 94 150.8 122.1 54 197.4 159.8 15 11.7 9.4 75 58.3 47.2 35 104.9 85.0 95 151.5 122.7 55 198.2 160.5 16 12.4 10.1 76 59.1 47.8 36 105.7 85.6 96 152.3 123.3 56 198.9 161.1 17 13.2 10.7 77 59.8 48.5 37 106.5 86.2 97 153.1 124.0 57 199.7 161.7 18 14.0 11.3 78 60.6 49.1 38 107.2 86.8 98 153.9 124.6 58 200.5 162.4 19 14.8 12.0 79 61.4 49.7 39 108.0 87.5 99 154.7 125.2 59 201.3 163.0 20 15.5 12.6 80 62.2 50.3 40 108.8 88.1 200 155.4 125.9 60 202.1 163.6 21 16.3 13.2 81 62.9 51.0 141 109.6 88.7 201 156.2 126.5 261 202.8 164.3 22 17.1 13.8 82 63.7 51.6 42 110.4 89.4 02 157.0 127.1 62 203.6 164.9 23 17.9 14.5 83 64.5 52.2 43 111.1 90.0 03 157.8 127.8 63 204.4 165.5 24 18.7 15.1 84 65.3 52.9 44 111.9 90.6 04 158.5 128.4 64 205.2 166.1 25 19.4 15.7 85 66.1 53.5 45 112.7 91.3 05 159.3 129.0 65 205.9 166.8 26 20.2 16.4 86 66.8 54.1 46 113.5 91.9 06 160.1 129.6 66 206.7 167.4 27 21.0 17.0 87 67.6 54.8 47 114.2 92.5 07 160.9 130.3 67 207.5 168.0 28 21.8 17.6 88 68.4 55.4 48 115.0 93.1 08 161.6 130.9 68 208.3 168.7 29 22.5 18.3 89 69.2 56.0 49 115.8 93.8 09 162.4 131.5 69 209.1 169.3 30 23.3 18.9 90 69.9 56.6 50 116.6 94.4 10 163.2 132.2 70 209.8 169.9 31 24.1 19.5 91 70.7 57.3 151 117.3 95.0 211 164.0 132.8 271 210.6 170.5 32 24.9 20.1 92 71.5 57.9 52 118.1 95.7 12 164.8 133.4 72 211.4 171.2 33 25.6 20.8 93 72.3 58.5 53 118.9 96.3 13 165.5 134.0 73 212.2 171.8 34 26.4 21.4 94 73.1 59.2 54 119.7 96.9 14 166.3 134.7 74 212.9 172.4 35 27.2 22.0 95 73.8 59.8 55 120.5 97.5 15 167.1 135.3 75 213.7 173.1 36 28.0 22.7 96 74.6 60.4 56 121.2 98.2 16 167.9 135.9 76 214.5 173.7 37 28.8 23.3 97 75.4 61.0 57 122.0 98.8 17 168.6 136.6 77 215.3 174.3 38 29.5 23.9 98 76.2 61.7 58 122.8 99.4 18 169.4 137.2 78 216.0 175.0 39 30.3 24.5 99 76.9 62.3 59 123.6 100.1 19 170.2 137.8 79 216.8 175.6 40 31.1 25.2 100 77.7 62.9 60 124.3 100.7 20 171.0 138.5 80 217.6 218.4 176.2 41 31.9 25.8 101 78.5 63.6 161 125.1 101.3 221 171.7 139.1 281 176.8 42 32.6 26.4 02 79.3 64.2 62 125.9 101.9 22 172.5 139.7 82 219.2 177.5 43 33.4 27.1 03 80.0 64.8 63 126.7 102.6 23 173.3 140.3 83 219.9 178.1 44 34.2 27.7 04 80.8 65.4 64 127.5 103.2 24 174.1 141.0 84 220.7 178.7 45 35.0 28.3 05 81.6 66.1 65 128.2 103.8 25 174.9 141.6 85 221.5 179.4 46 35.7 28.9 06 82.4 66.7 66 129.0 104.5 26 175.6 142.2 86 222.3 180.0 47 36.5 29.6 07 83.2 67.3 67 129.8 105.1 27 176.4 142.9 87 223.0 180.6 48 37.3 30.2 ,08 83.9 68.0 68 130.6 105.7 28 177.2 143.5 88 223.8 181.2 49 38.1 30.8 09 84.7 68.6 69 131.3 106.4 29 178.0 144.1 89 224.6 181.9 50 38.9 31.5 10 85.5 69.2 70 132.1 107.0 30 178.7 144.7 90 225.4 182.5 51 39.6 32.1 111 86.3 69.9 171 132.9 107.6 231 179.5 145.4 291 226.1 183.1 52 40.4 32.7 12 87.0 70.5 72 133.7 108.2 32 180.3 146.0 92 226.9 183.8 53 41.2 33.4 13 87.8 71.1 73 134.4 108.9 33 181.1 146.6 93 227.7 184.4 54 42.0 34.0 14 88.6 71.7 74 135.2 109.5 34 181.9 147.3 94 228.5 185.0 55 42.7 34.6 15 89.4 72.4 75 136.0 110.1 35 182.6 147.9 95 229.3 185.6 56 43.5 35.2 16 90.1 73.0 76 136.8 110.8 36 183.4 148.5 96 230.0 186.3 57 44.3 35.9 17 90.9 73.6 77 137.6 111.4 37 184.2 149.1 97 230.8 186.9 58 45.1 36.5 18 91.7 74.3 78 138.3 112.0 38 185.0 149.8 98 231.6 187.5 59 45.9 37.1 19 92.5 74.9 79 139.1 112.6 39 185.7 150.4 99 232.4 188.2 60 46.6 37.8 20 93.3 75.5 80 139.9 113.3 40 186.5 151.0 300 233.1 188.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 51° (129°, 231°, 309°). TABLE 2. [Page 609 Difference of Latitude and Departure for 39° (141", 219°, 321° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 233.9 189.4 361 280.6 227.1 421 327.2 264.9 481 373.8 302.6 541 420.4 340.4 02 234.7 190.0 62 281.3 227.8 22 328.0 265.5 82 374.6 303.3 42 421.2 341.0 03 235.5 190.6 63 282.1 228.4 23 328.7 266.2 83 375.4 303.9 43 422.0 341.7 04 236.3 191.3 64 282.9 229.0 24 329.5 266.8 84 376.1 304.5 44 422.7 342.3 05 237.0 1191.9 65 283.7 229.7 25 330.3 267.4 85 376.9 305.2 45 423.5 342.9 06 237.8 192.5 66 284.4 230.3 26 331.1 268.0 86 377.7 305.8 46 424.3 343.6 07 238.6 193.2 67 285.2 230.9 27 331.9 268.7 87 378.5 306.4 47 425.1 344.2 08 239.4 193.8 68 286.0 231.5 28 332.6 269.3 88 379.3 307.1 48 425.9 344.8 09 240.1 194.4 69 286.8 232.2 29 333.4 269.9 89 380.0 307.7 49 426.6 345.5 10 311 240.9 195.0 70 287.6 232.8 30 334.2 270.6 '271.'2 90 380.8 308.3 308.9 50 427.4 346.1 241.7 195.7 371 288.3 233.4 431 335.0 491 381.6 551 428.2 346.7 12 242.5 196.3 72 289.1 234.1 32 335.7 271.8 92 382.4 309.6 52 429.0 347.4 13 243.3 196.9 73 289.9 234.7 33 336.5 272.5 93 383.1 310.2 53 429.7 348.0 14 244.0 197.6 74 290.7 235.3 34 337.3 273.1 94 383.9 310.8 54 430.5 348.6 15 244.8 198.2 75 291.4 236.0 35 338.1 273.7 95 384.7 311.5 55 431.3 349.2 16 245.6 198.8 76 292.2 236.6 36 338.8 274.3 96 386.5 312.1 56 432.1 349.9 17 246.4 199.5 77 293.0 237.2 37 339.6 275.0 97 386.2 312.7 57 432.8 350.6 18 247.1 200.1 78 293.8 237.8 38 340.4 275.6 98 387.0 313.3 58 433.6 361.1 19 247.9 200.7 79 294.5 238.5 39 341.2 276.2 99 387.8 314.0 59 434.4 351.7 20 248.7 201.3 80 295.3 239.1 40 342.0 276.9 500 388.6 314.7 60 436.2 352,4 321 249.5 202.0 381 296.1 239.7 441 342.7 277.5 501 389.4 315.3 561 436.9 353.0 22 250.3 202.6 82 296.9 240.4 42 343.5 278.1 02 390.1 315.9 62 436.7 363.6 23 251.0 203.2 83 297.7 241.0 43 344.3 278.7 03 390.9 316.5 63 437.5 364.3 24 251.8 203.9 84 298.4 241.6 44 345.1 279.4 04 391.7 317.1 64 438.3 364.9 25 252.6 204.5 85 299.2 242.2 45 345.8 280.0 05 392.5 317.8 65 439.1 355.5 26 253.4 205.1 86 300.0 242.9 46 346.6 280.6 06 393.2 318.4 66 439.8 366.2 27 254.1 205.7 87 300.8 243.5 47 347.4 281.3 07 394.0 319.0 67 440.6 366.8 28 254.9 206.4 88 301.5 244.1 48 348.2 281.9 08 394.8 319.6 68 441.4 357.4 29 255.7 207.0 89 302.3 244.8 49 349.0 282.5 09 395.6 320.3 69 442.2 358.1 30 256.5 207.6 90 303.1 245.4 50 349.7 283.2 10 396.3 320.9 70 443.0 443.7 358.7 331 257.2 208.3 391 303.9 246.0 451 350.5 283.8 511 397.1 321.6 571 369.3 32 258.0 208.9 92 304.7 246.7 52 351.3 284.4 12 397.9 322.2 72 444.5 359.9 33 258.8 209.5 93 305.4 247.3 53 352.1 285.0 13 398.7 322.8 73 445.3 360.6 34 259.6 210.2 94 306.2 247.9 54 352.8 285.7 14 399.4 323.4 74 446.1 361.2 35 260.4 210.8 95 307.0 248.5 55 353.6 286.3 15 400.2 324.1 76 446.9 361.8 36 261.1 211.4 96 307.8 249.2 56 354.4 286.9 16 401.0 324.7 76 447.6 362.4 37 261.9 212.0 97 308.5 249.8 57 355.2 287.6 17 401.8 325.3 77 448.4 363.1 38 262.7 212.7 98 309.3 250.4 58 355.9 288.2 18 402.5 325.9 78 449.2 363.7 39 263.5 213.3 99 310.1 251.1 59 356.7 288.8 19 403.3 326.6 79 450.0 364.3 40 264.2 213.9 400 310.9 251.7 60 357.5 289.4 20 404.1 327.2 80 450.7 365.0 341 265.0 214.6 401 311.6 252.3 461 358.3 290.1 521 404.9 327.8 581 451.5 366.6 42 265.8 215.2 02 312.4 252.9 62 359.1 290.7 22 405.7 328.5 82 452.3 366.2 43 266.6 215.8 03 313.2 253.6 63 359.8 291.3 23 406.4 329.1 83 453.1 366.9 44 267.3 216.4 04 314.0 254.2 64 360.6 292.0 24 407.2 329.7 84 453.9 367.6 45 268.1 217.1 05 314.8 254.8 65 361.4 292.6 25 408.0 330.4 85 464.6 368.1 46 268.9 217.7 06 315.5 255.5 66 362.2 293.2 26 408.8 331.0 86 455.4 368.8 47 269.7 218.3 07 316.3 256.1 67 362.9 293.8 27 409.5 331.6 87 456.2 369.4 48 270.5 219.0 08 317.1 256.7 68 363.7 294.5 28 410.3 332.3 88 467.0 370.0 49 271.2 219.6 09 317.9 257.3 69 364.5 295.1 29 411.1 332.9 89 457.8 370.6 50 272.0 220.2 10 411 318.6 258.0 70 365.3 295.7 30 411.9 333.5 90 458.5 371.3 351 272.8 220.8 319.4 258.6 471 366.0 296.4 531 412.6 334.1 591 459.3 371.9 52 273.6 221.5 12 320.2 259.2 72 366.8 297.0 32 413.4 334.8 92 460.1 372.6 53 274.3 222.1 13 321.0 259.9 73 367.6 297.6 33 414.2 335.4 93 460.9 373.2 54 275.1 222.7 14 321.8 260.5 74 368.4 298.3 34 415.0 336.1 94 461.6 373.8 55 275.9 223.4 15 322.5 261.1 75 369.2 298.9 35 415.8 336.7 96 462.4 374.4 56 276.7 224.0 16 323.3 261.8 76 369.9 299. 5 36 416.5 337.3 96 463.2 375.1 57 277.5 224.6 17 324.1 262.4 77 370.7 300.1 37 417.3 337.9 97 464.0 375.7 58 278.2 225.3 18 324.9 263.0 78 371.5 300.8 38 418.1 338.5 98 464.8 376.3 59 279.0 225.9 19 325.6 263.6 79 372.3 301.4 39 418.9 339.1 99 465.6 376.9 60 279.8 226.5 20 326.4 264.3 80 373.0 302.0 40 419.6 339.8 600 466.3 377.6 Diflt. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. | Dist Dep. Lat. 1 )1° (1 29°, 231°, 309° ). 1 21594°— 14- -32 Page 610] TABLE 2. Difference of Latitude and Departure for 40° (140°, 220°, 320° )• Di8t. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.6 61 46.7 39.2 121 92.7 77.8 181 138.7 116.3 241 184.6 164.9 2 1.5 1.3 62 47.5 39.9 22 93.5 78.4 82 139.4 117.0 42 185.4 155.6 3 2.3 1.9 63 48.3 40.5 23 94.2 79.1 83 140.2 117.6 43 186.1 156.2 4 3.1 2.6 64 49.0 41.1 24 95.0 79.7 84 141.0 118.3 44 186.9 166.8 5 3.8 3.2 65 49.8 41.8 25 95.8 80.3 85 141.7 118.9 45 187.7 167.5 6 4.6 3.9 66 50.6 42.4 26 96.5 81.0 86 142.5 119.6 46 188.4 158.1 7 5.4 4.5 67 51.3 43.1 27 97.3 81.6 87 143.3 120.2 47 189.2 158.8 159.4 8 6.1 5.1 68 52.1 43.7 28 98.1 82.3 88 144.0 120.8 48 190.0 9 6.9 5.8 69 52.9 44.4 29 98.8 82.9 89 144.8 121.5 49 190.7 160.1 10 7.7 6.4 70 53.6 45.0 30 99.6 83.6 90 145.5 122.1 60 191.5 160.7 11 8.4 7.1 71 54.4 45.6 131 100.4 84.2 191 146.3 122.8 251 192.3 161.3 12 9.2 7.7 72 55.2 46.3 32 101.1 84.8 92 147.1 123.4 52 193.0 162.0 13 10.0 8.4 73 55.9 46.9 33 101.9 85.5 93 147.8 124.1 53 193.8 162.6 14 10.7 9.0 74 56.7 47.6 34 102.6 86.1 94 148.6 124.7 64 194.6 163.3 15 11.5 9.6 75 57.5 48.2 35 103.4 86.8 95 149.4 125.3 55 195.3 163.9 16 12,3 10.3 76 58.2 48.9 36 104.2 87.4 96 150.1 126.0 56 196.1 164.6 17 13.0 10.9 77 59.0 49.5 37 104.9 88.1 97 150.9 126.6 57 196.9 165.2 18 13.8 11.6 78 59.8 50.1 38 105.7 88.7 98 151.7 127.3 58 197.6 165,8 19 14.6 12.2 79 60.5 50.8 39 106.5 89.3 99 152.4 127.9 59 198.4 166.5 20 15.3 12.9 80 61.3 51.4 40 107.2 90.0 90.6 200 153.2 128.6 60 199.2 167.1 21 16.1 13.5 81 62.0 52.1 141 108.0 201 154.0 129.2 261 199.9 167.8 22 16.9 14.1 82 62.8 52.7 42 108.8 91,3 02 154.7 129.8 62 200.7 168.4 23 17.6 14.8 83 63.6 53.4 43 109.5 91.9 03 155.5 130.5 63 201.5 169.1 24 18.4 15.4 84 64.3 54.0 44 110.3 92.6 04 156.3 131.1 64 202.2 169.7 25 19.2 16.1 85 65.1 54.6 45 111.1 93.2 05 157.0 131.8 65 203,0 170.3 26 19.9 16.7 86 65.9 55.3 46 111.8 93.8 06 157.8 132.4 66 203.8 171.0 27 20.7 17.4 87 66.6 55.9 47 112.6 94.5 07 158.6 133,1 67 204.5 171.6 28 21.4 18.0 88 67.4 56.6 48 113.4 95.1 08 159.3 133.7 68 205,3 172.3 29 22.2 18.6 89 68.2 57.2 49 114.1 95.8 09 160.1 134,3 69 206,1 172.9 30 23.0 19.3 90 68.9 57.9 50 114.9 96.4 10 160.9 135.0 70 206,8 173.6 31 23.7 19.9 91 69.7 58.5 151 115.7 97.1 211 161.6 135.6 271 207.6 174.2 32 24.5 20.6 92 70.5 59.1 52 116.4 97.7 12 162.4 136.3 72 208.4 174.8 33 25.3 21.2 93 71.2 59.8 53 117.2 98.3 13 163.2 136.9 73 209.1 175.5 34 26.0 21.9 94 72.0 60.4 54 118.0 99.0 14 163.9 137,6 74 209.9 176.1 35 26.8 22.5 95 72.8 61.1 55 118.7 99.6 15 164.7 138,2 75 210,7 176.8 36 27.6 23.1 96 73.5 61.7 56 119.5 100.3 16 165.5 138.8 76 211,4 177,4 37 28.3 23.8 97 74.3 62.4 57 120.3 100.9 17 166.2 139.5 77 212,2 178,1 38 29.1 24.4 98 75.1 63.0 58 121.0 101.6 18 167.0 140.1 78 213.0 178.7 39 29.9 25.1 99 75.8 63.6 59 121.8 102.2 19 167.8 140.8 79 213.7 179.3 40 30.6 25.7 100 76.6 64.3 60 122.6 102.8 20 168.5 141.4 80 214,5 180,0 41 31.4 26.4 101 77.4 64.9 161 123.3 103.5 221 169.3 142.1 281 215,3 180,6 42 32.2 27.0 02 78.1 65.6 62 124.1 104.1 22 170.1 142.7 82 216.0 181,3 43 32.9 27.6 03 78.9 66.2 63 124.9 104,8 23 170,8 143,3 83 216.8 181.9 44 33.7 28.3 04 79.7 66.8 64 125.6 105.4 24 171.6 144.0 84 217.6 182.6 46 34.5 28.9 05 80.4 67.5 65 126.4 106.1 25 172.4 144.6 85 218,3 183.2 46 35.2 29.6 06 81.2 68.1 66 127.2 106.7 26 173.1 145.3 86 219.1 183.8 47 36,0 30.2 07 82.0 68.8 67 127.9 107.3 27 173.9 145.9 87 219.9 184.5 48 36.8 30.9 08 82.7 69.4 68 128.7 108.0 28 174.7 146.6 88 220.6 186.1 49 37.5 31.5 09 83.5 70.1 69 129.5 108.6 29 175.4 147.2 89 221.4 186.8 50 38.3 32.1 10 84.3 70.7 70 130.2 109.3 30 176.2 147.8 90 222.2 186.4 51 39.1 32.8 111 85.0 71.3 171 131.0 109.9 231 177.0 148.5 291 222.9 187.1 52 39.8 33.4 12 85.8 72.0 72 131.8 110.6 32 177,7 149.1 92 223.7 187.7 53 40.6 34.1 13 86.6 72.6 73 132.5 111.2 33 178.5 149.8 93 224.5 188.3 54 41.4 34.7 14 87.3 73,3 74 133.3 111.8 34 179.3 150.4 94 225.2 189.0 55 42.1 35.4 15 88.1 73.9 75 134.1 112.5 35 180.0 151.1 95 226.0 189.6 56 42.9 36.0 16 88.9 74.6 76 134.8 113.1 36 180.8 151.7 96 226.7 190.3 57 43.7 36.6 17 89.6 75.2 77 135.6 113.8 37 181.6 152.3 97 227.5 190.9 58 44.4 37.3 18 90.4 75.8 78 136.4 114,4 38 182.3 153.0 98 228.3 191.6 59 45.2 37.9 19 91.2 76.5 79 137.1 115.1 39 183.1 153.6 99 229.0 192,2 60 46.0 38.6 20 91.9 77.1 80 137.9 115.7 40 183.9 154,3 300 229.8 192.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist, Dep. Lat. 50° (130°, 230°, 310°). TABLE 2. [Page 611 1 DifiEerence of Latitude and Departure for 40° (140°, 220°, 320° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 Dist. Lat. Dep. Dist. Lat. Dep. 301 230.6 193.5 361 276,5 232.1 421 322.5 270.6 481 368.5 309.2 541 414.4 347.7 02 231.3 194.1 62 277.3 232.7 22 323.3 271.3 82 369.2 309.8 42 415.2 348.4 03 232.1 194.8 63 278.1 233.3 23 324.0 271.9 83 370.0 310.5 43 416.0 349.0 04 232.9 195.4 64 278.8 234.0 24 324.8 272.6 84 370.8 311.1 44 416.7 349.7 05 233.6 196.1 65 279.6 234.6 25 325.6 273.2 85 371.5 311.7 45 417.5 350.3 06 234.4 196.7 66 280.4 235.3 26 326.3 273.8 86 372.3 312.4 46 418.3 361.0 07 235.2 197.3 67 281.1 235.9 27 327.1 274.5 87 373.1 313.0 47 419.0 351.6 08 235.9 198.0 68 281.9 236.6 28 327.9 275.1 88 373.8 313.6 48 419.8 352.2 09 236.7 198.6 69 282.7 237. 2 29 328.6 275.8 89 374,6 314.3 49 420.6 352.9 10 237.5 199.3 70 283.4 237.8 30 329.4 276.4 90 375,4 314.9 50 551 421.3 363.5 311 238.2 199.9 371 284.2 238.5 431 330.2 277.1 491 376,1 315.6 422.1 354.2 12 239.0 200.6 72 285.0 239.1 32 330.9 277.7 92 376.9 316.2 52 422.9 354.8 13 239.8 201.2 73 285.7 239.7 33 331.7 278.3 93 377.7 316.9 53 423.6 355.5 14 240.5 201.8 74 286.5 240.4 34 332.5 279.0 94 378.4 317.5 54 424.4 356.1 15 241.3 202.5 75 287.3 241.0 35 333.2 279.6 95 379.2 318.2 55 425.2 356.8 16 242.1 203.1 76 288.0 241,7 36 334.0 280.3 96 380.0 318.8 56 425.9 357.4 17 242.8 203.8 77 288.8 242.3 37 334.8 280.9 97 380.7 319.5 57 426.7 358.0 18 243.6 204.4 78 289.6 243.0 38 335.5 281.6 98 381.5 320.1 58 427.5 358.7 19 244.4 205.1 79 290.3 243.6 39 336.3 282.2 99 382.3 320.8 59 428.2 359.3 20 245.1 205.7 80 291.1 244.3 40 337.1 282.8 500 383.0 321.4 60 429.0 360.0 321 245.9 206.3 381 291.9 244.9 441 337.8 283.5 501 383.8 322.0 561 429.8 360.6 22 246.7 207.0 82 292.6 245.6 42 338.6 284.1 02 384.6 322.7 62 430.5 361.2 23 247.4 207.6 83 293.4 246.2 43 339.4 284.8 03 385.3 323.3 63 431.3 361.9 24 248.2 208.3 84 294.2 246.8 44 340.1 285.4 04 386.1 324.0 64 432.1 362.5 25 249.0 208.9 85 294.9 247.5 45 340.9 286.0 05 386.8 324.6 65 432.8 363.2 26 249.7 209.6 86 295.7 248.1 46 341.7 286.7 06 387,6 325.2 66 433.6 363.8 27 250.5 210.2 87 296.5 248.8 47 342.4 287.3 07 388,4 325.9 67 434.3 364.5 28 251.3 210.8 88 297.2 249.4 48 343.2 288.0 08 389.2 326,5 68 435.1 366.1 29 252.0 211.5 89 298.0 250.1 49 344.0 288.6 09 389.9 327.1 69 435.9 366,8 30 252.8 212.1 90 298.8 250.7 50 344.7 289.3 10 390.7 327.8 70 436.6 366,4 331 253.6 212.8 391 299.5 251.3 451 345.5 289,9 511 391.5 328.4 571 437.4 367,0 32 254.3 213.4 92 300.3 252.0 52 346.3 290,5 12 392.2 329.1 72 438.2 367.7 33 255.1 214.1 93 301.1 252.6 53 347.0 291.2 13 393.0 329.7 73 438.9 368.3 34 255.9 214.7 94 301.8 253.3 54 347.8 291.8 14 393.8 330.4 74 439.7 369.0 35 256.6 215.3 95 302.6 253.9 55 348.6 292.5 15 394.5 331.0 75 440.5 369.6 36 257.4 216.0 96 303.4 254.6 56 349.3 293.1 16 395.3 331.6 76 441.2 370.2 37 258.2 216.6 97 304.1 255.2 57 350.1 293.8 17 396.1 332.3 77 442.0 370.9 38 258.9 217.3 98 304.9 255.8 58 350.8 294.4 18 396.8 332.9 78 442.8 371.6 39 259.7 217.9 99 305.7 256.5 59 351.6 295.0 19 397.6 333.6 79 443.5 372.2 40 260.5 218.6 400 306.4 257.1 60 352.4 295.7 20 398.3 334.2 80 444.3 372.8 341 261.2 219.2 401 307.2 257.8 461 353.1 296.3 521 399.1 334.9 581 445.1 373.6 42 262.0 219.8 02 308.0 258.4 62 353.9 297.0 22 399.9 335.5 82 445,8 374.1 43 262.8 220.5 03 308.7 259.1 63 354.7 297,6 23 400,6 336.1 83 446.6 374.8 44 263.5 221.1 04 309.5 259.7 64 355.4 298.3 24 401.4 336.8 84 447.4 375.4 45 264.3 221.8 05 310.2 260.3 65 356.2 298.9 25 402.2 337.4 85 448.1 376,0 46 265.1 222.4 06 311.0 261.0 66 357.0 299.5 26 402.9 338.1 86 448.9 376.7 47 265.8 223.1 07 311.8 261.6 67 367.7 300.2 27 403.7 338.7 87 449.7 377.3 48 266.6 223.7 08 312.5 262.3 68 358.5 300.8 28 404.5 339.4 88 450.4 378.0 49 267.4 224.3 09 313.3 262.9 69 359.3 301.5 29 405.2 340.0 89 451.2 378.6 50 268.1 225.0 10 314.1 263.6 70 360.0 302.1 30 406.0 340.6 341.3 90 452.0 379.2 351 268.9 225.6 411 314.8 264.2 471 360.8 302.8 531 406. 8 591 452.7 379.9 52 269.6 226.3 12 315.6 264.8 72 361.6 303.4 32 407.5 341.9 92 453.5 380.5 53 270.4 226.9 13 316.4 265.5 73 362.3 304.0 33 408.3 342.6 93 454.3 381.2 54 271.2 227.6 14 317.1 266.1 74 363.1 304.7 34 409.1 343.2 94 455.0 381.8 55 271.9 228.2 15 317.9 266.8 75 363.9 305.3 35 409.8 343.9 95 455.8 382.4 56 272.7 228.8 16 318.7 267.4 76 364.6 306.0 36 410.6 344.5 96 456.6 383.1 57 273.5 229.5 17 319.4 268.1 77 365.4 306.6 37 411.4 345.2 97 457.3 383.7 58 274.2 230.1 18 320.2 268.7 78 366.2 307.3 38 412.1 345.8 98 458.1 384.4 59 275.0 230.8 19 321.0 269.3 79 366.9 307.9 39 412,9 346.4 99 458.9 386.0 60 275.8 231.4 20 321.7 270.0 80 367,7 308.5 40 413,7 347.1 600 459.6 385,7 Dist. Dep. Lat. Dist. Dep. Lat. Diflt. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat, 50° (130°, 230°, 310° )• Page 612] TABLE 2. Difference of Latitude and Departure for 41° (139°, 221°, 319° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.8 0.7 61 46.0 40.0 121 91.3 79.4 181 136.6 118.7 241 181.9 158.1 2 1.5 1.3 62 46.8 40.7 22 92.1 80.0 82 137.4 119.4 42 182.6 158.8 3 2.3 2.0 63 47.5 41.3 23 92.8 80.7 83 138.1 120.1 43 183.4 159.4 4 3.0 2.6 64 48.3 42.0 24 93.6 81.4 84 138.9 120.7 44 184.1 160.1 5 3.8 3.3 65 49.1 42.6 25 94.3 82.0 85 139.6 121.4 45 184.9 160.7 6 4.6 3.9 66 49.8 43.3 26 95.1 82.7 86 140.4 122.0 46 185.7 161.4 7 5.3 4.6 67 50.6 44.0 27 95.8 83.3 87 141.1 122.7 47 186.4 162.0 8 6.0 5.2 68 51.3 44.6 28 96.6 84.0 88 141.9 123.3 48 187.2 162.7 9 6.8 5.9 69 52.1 45.3 29 97.4 84.6 89 142.6 124.0 49 187.9 163.4 10 7.5 6.6 70 52.8 45.9 30 98.1 85.3 90 143.4 124.7 50 188.7 164.0 11 8.3 7.2 71 53.6 46.6 131 98.9 85.9 191 144.1 125.3 251 189.4 164.7 12 9.1 7.9 72 54.3 47.2 32 99.6 86.6 92 144.9 126.0 52 190.2 165.3 13 9.8 8.5 73 55.1 47.9 33 100.4 87.3 93 145.7 126.6 53 190.9 166.0 14 10.6 9.2 74 55.8 48.5 34 101.1 87.9 94 146.4 127.3 54 191.7 166.6 15 11.3 9.8 75 56.6 49.2 35 101.9 88.6 95 147.2 127.9 55 192.5 167.3 16 12.1 10.5 76 57.4 49.9 36 102.6 89.2 96 147.9 128.6 56 193.2 168.0 17 12.8 11.2 77 58.1 50.5 37 103.4 89.9 97 148.7 129.2 57 194.0 168.6 18 13.6 11.8 78 58.9 51.2 38 104.1 90.5 98 149.4 129.9 58 194.7 169.3 19 14.3 12.5 79 59.6 51.8 39 104.9 91.2 99 150.2 130.6 59 195.5 169.9 20 15.1 13.1 80 60.4 52.5 40 105.7 91.8 200 150.9 131.2 60 196.2 170.6 21 15.8 13.8 81 61.1 53.1 141 106.4 92.5 201 151.7 131.9 261 197.0 171.2 22 16.6 14.4 82 61.9 53.8 42 107.2 93.2 02 152.5 132.5 62 197.7 171.9 23 17.4 15.1 83 62.6 54.5 43 107.9 93.8 03 153.2 133.2 63 198.5 172.5 24 18.1 15.7 84 63.4 55.1 44 108.7 94.5 04 154.0 133.8 64 199.2 173.2 25 18.9 16.4 85 64.2 55.8 45 109.4 95.1 05 154.7 134.5 65 200.0 173.9 26 19.6 17.1 86 64.9 56.4 46 110.2 95.8 06 155.5 135.1 66 200.8 174.5 27 20.4 17.7 87 65.7 57.1 47 110.9 96.4 07 156.2 135.8 67 201.5 175.2 28 21.1 18.4 88 66.4 57.7 48 111.7 97.1 08 157.0 136.5 68 202.3 175.8 29 21.9 19.0 89 67.2 58.4 49 112.5 97.8 09 157.7 137.1 69 203.0 176.5 30 22.6 19.7 90 67.9 59.0 50 113.2 98.4 10 158.5 137.8 70 203.8 177.1 177.8 31 23.4 20.3 91 68.7 59.7 151 114.0 99.1 211 159.2 138.4 271 204.5 32 24.2 21.0 92 69.4 60.4 52 114.7 99.7 12 160.0 139.1 72 205.3 178.4 33 24.9 21.6 93 70.2 61.0 53 115.5 100.4 13 160.8 139.7 73 206.0 179.1 34 25.7 22.3 94 70.9 61.7 54 116.2 101.0 14 161.5 140.4 74 206.8 179.8 35 26.4 23.0 95 71.7 62.3 55 117.0 101.7 15 162.3 141.1 75 207.5 180.4 36 27.2 23.6 96 72.5 63.0 56 117.7 102.3 16 163.0 141.7 76 208.3 181.1 37 27.9 24.3 97 73.2 63.6 57 118.5 103.0 17 163.8 142.4 77 209.1 181.7 38 28.7 24.9 98 74.0 64.3 58 119.2 103.7 18 164.5 143.0 78 209.8 182.4 39 29.4 25.6 99 74.7 64.9 59 120.0 104.3 19 165.3 143.7 79 210.6 183.0 40 30.2 26.2 100 75.5 65.6 60 120.8 105.0 20 166.0 144.3 80 211.3 183.7 41 30.9 26.9 101 76.2 66.3 161 121.5 105.6 221 166.8 145.0 281 212.1 184.4 42 31.7 27.6 02 77.0 66.9 62 122.3 106.3 22 167.5 145.6 82 212.8 185.0 43 32.5 28.2 03 77.7 67.6 63 123.0 106.9 23 168.3 146.3 83 213.6 185.7 44 33.2 28.9 04 78.5 68.2 64 123.8 107.6 24 169.1 147.0 84 214.3 186.3 45 34.0 29.5 05 79.2 68.9 65 124.5 108.2 25 169.8 147.6 85 215.1 187.0 46 34.7 30.2 06 80.0 69.5 66 125.3 108.9 26 170.6 148.3 86 215.8 187.6 47 35.5 30.8 07 80.8 70.2 67 126.0 109.6 27 171.3 148.9 87 216.6 188.3 48 36.2 31.5 08 81.5 70.9 68 126.8 110.2 28 172.1 149.6 88 217.4 188.9 49 37.0 32.1 09 82.3 71.5 69 127.5 110.9 29 172.8 150.2 89 218.1 189.6 50 37.7 32.8 10 83.0 72.2 70 128.3 111.5 30 173.6 150.9 90 218.9 190.3 51 38.5 33.5 111 83.8 72.8 171 129.1 112.2 231 174.3 151.5 291 219.6 190.9 52 39.2 34.1 12 84.5 73.5 72 129.8 112.8 32 175.1 152.2 92 220.4 191.6 53 40.0 34.8 13 85.3 74.1 73 130.6 113.5 33 175.8 152.9 93 221.1 192.2 54 40.8 35.4 14 86.0 74.8 74 131.3 114.2 34 176.6 153.5 94 221.9 192.9 55 41.5 36.1 15 86.8 75.4 75 132.1 114.8 35 177.4 154.2 95 222.6 193.5 56 42.3 36.7 16 87.5 76.1 76 132.8 115.5 36 178.1 154.8 96 223.4 194.2 57 43.0 37.4 17 88.3 76.8 77 133.6 116.1 37 178.9 155.5 97 224.1 194.8 58 43.8 38.1 18 89.1 77.4 78 134.3 116.8 38 179.6 156.1 98 224.9 195.5 59 44.5 38.7 19 89.8 78.1 79 135.1 117.4 39 180.4 156.8 99 225.7 196.2 60 45.3 39.4 20 90.6 78.7 80 135.8 118.1 40 181.1 157.5 300 226.4 196.8 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Diat. Dep. Lat. 49° (131°, 229°, 311° ). 1 TABLE 2. [Page 613 Difference of Latitude and Departure for 41° (139°, 221°, 319° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 227.2 197.5 361 272.5 236.9 421 317.7 276.2 481 363.0 315.6 641 408.3 354.9 02 227.9 198.1 62 273.2 237.5 22 318.5 276.9 82 363.8 316.2 42 409.0 355.6 03 228.7 198.8 63 274.0 238.2 23 319.2 277.5 83 364.5 316.9 43 409.8 356.2 04 229.4 199.4 64 274.7 238.8 24 320.0 278.2 84 365.3 317.5 44 410.6 356.9 05 230.2 200.1 65 275.5 239.5 25 320.8 278.8 85 366.0 318.2 46 411.3 367.5 06 230.9 200.8 66 276.2 240.1 26 321.5 279.5 86 366.8 318.8 46 412.1 358.2 07 231.7 201.4 67 277.0 240.8 27 322.3 280.1 87 367.5 319.5 47 412.8 358.8 08 232.5 202.1 68 277.7 241.4 28 323.0 280.8 88 368.3 320.1 48 413.6 359.5 09 233.2 202.7 69 278.5 242.1 29 323.8 281.5 89 369.0 320.8 49 414.3 360.2 10 234.0 203.4 70 279.2 242.7 30 324.5 282.1 90 369.8 321.5 50 415.1 360.8 311 234.7 204.0 371 280.0 243.4 431 325.3 282.8 491 370.6 322.1 551 415.8 361.5 12 235.5 204.7 72 280.8 244.1 32 326.0 283.4 92 371.3 322.8 52 416.6 362.1 13 236.2 205.4 73 281.5 244.7 33 326.8 284.1 93 372.1 323.4 63 417.3 362.8 14 237.0 206.0 74 282.3 245.4 34 327.5 284.7 94 372.8 324.1 54 418.1 363.4 15 237.7 206.7 75 283.0 246.0 36 328.3 285.4 95 373.6 324.7 55 418.9 364.1 16 238.5 207.3 76 283.8 246.7 36 329.1 286.0 96 374.3 325.4 56 419.6 364.8 17 239.2 208.0 77 284.5 247.3 37 329.8 286.7 97 375.1 326.0 57 420.4 365.4 18 240.0 208.6 78 285.3 248.0 38 330.6 287.4 98 375.8 326.7 58 421.1 366.1 19 240.8 209.3 79 286.0 248.7 39 331.3 288.0 99 376.6 327.4 59 421.9 366.7 20 241.5 209.9 80 286.8 249.3 40 332.1 288.7 500 377.3 328.0 60 422.6 367.4 321 242.3 210.6 381 287.5 250.0 441 332.8 289.3 501 378.1 328.7 661 423.4 368.0 22 243.0 211.3 82 288.3 250.6 42 333.6 290.0 02 378.9 329.3 62 424.1 368.7 23 243.8 211.9 83 289.1 251.3 43 334.3 290.6 03 379.6 330.0 63 424.9 369.4 24 244.5 212.6 84 289.8 251.9 44 335.1 291.3 04 380.4 330.6 64 425.7 370.0 25 245.3 213.2 85 290.6 252.6 45 335.8 292.0 05 381.1 331.3 66 426.4 370.7 26 246.0 213.9 86 291.3 253.2 46 336.6 292.6 06 381.9 332.0 66 427.2 371.3 27 246.8 214.5 87 292.1 253.9 47 337.4 293.3 07 382.6 332.6 67 427.9 372.0 28 247.5 215.2 88 292.8 254.6 48 338.1 293.9 08 383.4 333.3 68 428.7 372.6 29 248.3 215.9 89 293.6 255.2 49 338.9 294.6 09 384.1 333.9 69 429.4 373.3 30 249.1 216.5 90 294.3 255.9 50 339.6 295.2 10 384.9 334.6 70 430.2 374.0 331 249.8 217.2 391 295.1 256.5 451 340.4 295.9 511 385.7 335.2 571 430.9 374.6 32 250.6 217.8 92 295.8 257.2 52 341.1 296.5 12 386.4 335.9 72 431.7 375.3 33 251.3 218.5 93 296.6 257.8 53 341.9 297.2 13 387.2 336.5 73 432.4 375.9 34 252.1 219.1 94 297.4 258.5 54 342.6 297.9 14 387.9 337.2 74 433.2 376.6 35 252.8 219.8 95 298.1 259.2 55 343.4 298.5 15 388.7 337.9 75 434.0 377.2 36 253.6 220.4 96 298.9 259.8 56 344.1 299.2 16 389.4 338.5 76 434.7 377.9 37 254.3 221.1 97 299.6 260.5 57 344.9 299.8 17 390.2 339.2 77 435.6 378.5 38 255.1 221.8 98 300.4 261.1 58 345.7 300.5 18 390.9 339.8 78 436.2 379.2 39 255.8 222.4 99 301.1 261.8 59 346.4 301.1 19 391.7 340.5 79 437.0 379.8 40 256.6 223.1 400 301.9 262.4 60 347.2 301.8 20 392.4 341.1 80 437.7 380.5 341 257.4 223.7 401 302.6 263.1 461 347.9 302.6 521 393.2 341.8 581 438.5 381.2 42 258.1 224.4 02 303.4 263.7 62 348.7 303.1 22 394.0 342.6 82 439.2 381.8 43 258.9 225.0 03 304.2 264.4 63 349.4 303.8 23 394.7 343.1 83 440.0 382.6 44 259.6 225.7 04 304.9 265.1 64 350.2 304.4 24 395.5 343.8 84 440.7 383.2 45 260.4 226.3 05 305.7 265.7 65 350.9 305.1 25 396.2 344.4 85 441.5 383.8 46 261.1 227.0 06 306.4 266.4 66 351.7 305.7 26 397.0 346.1 86 442.3 384.5 47 261.9 227.7 07 307. 2 267.0 67 352.5 306.4 27 397.7 346.7 87 443.0 385.1 48 262.6 228.3 08 307.9 267.7 68 353. 2 307.0 28 398.5 346.4 88 443.8 386.8 49 263.4 229.0 09 308.7 268.3 69 354.0 307.7 29 399.2 347.0 89 444.6 386.4 50 851 264.2 229.6 10 309.4 269.0 70 354.7 308.4 30 400.0 347.7 90 445.3 387.1 264.9 230.3 411 310.2 269.6 471 355.5 309.0 531 400.7 348.4 591 446.0 387.7 52 265.7 230.9 12 310. 9 270.3 72 356.2 309.7 32 401.6 349.0 92 446.8 388.4 53 266.4 231.6 13 311.7 271.0 73 357.0 310.3 33 402.2 349.7 93 447.5 389.1 54 267.2 232.3 14 312.5 271.6 74 357.7 311.0 34 403.0 360.3 94 448.3 389.7 55 267.9 232.9 15 313.2 272.3 75 358.5 311.6 36 403.8 351.0 96 449.1 390.4 56 268.7 233.6 16 314.0 272.9 76 359.2 312.3 36 404.5 351.6 96 449.8 391.0 57 269.4 234.2 17 314.7 273.6 77 360.0 312.9 37 406.3 352.3 97 450.6 391.7 58 270.2 234.9 18 315.5 274.2 78 360.8 313.6 38 406.0 362.9 98 451.3 392.3 59 270.9 235.5 19 316.2 274.9 79 361.5 314.3 39 406.8 353.6 99 452.1 393.0 60 271.7 236.2 20 317.0 275.6 80 362.3 314.9 40 407.5 364.3 600 452.8 393.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. i9° (1 31°, 229°, 311° )• Page 614] TABLE 2. Difference of Latitude and Departure for 42° (138°, 222°, 318° ). Dlst. Lai. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.7 0.7 61 45.3 40.8 121 89.9 81.0 181 134.5 121.1 241 179.1 161.3 2 1.5 1.3 62 46.1 41.5 22 90.7 81.6 82 135.3 121.8 42 179.8 161.9 3 2.2 2.0 63 46.8 42.2 23 91.4 82.3 83 136.0 122.5 43 180.6 162.6 4 3.0 2.7 64 47.6 42.8 24 92.1 83.0 84 136.7 123.1 44 181.3 163.3 5 3.7 3.3 65 48.3 43.5 25 92.9 83.6 85 137.5 123.8 45 182.1 163.9 6 4.5 4.0 66 49.0 44.2 26 93.6 84.3 86 138.2 124.5 46 182.8 164.6 7 5.2 4.7 67 49.8 44.8 27 94.4 85.0 87 139.0 125.1 47 183. 6 165.3 8 5.9 5.4 68 50.5 45.5 28 95.1 85.6 88 139.7 125.8 48 184.3 165.9 9 6.7 6.0 69 51.3 46.2 29 95.9 86.3 89 140.5 126.5 49 185.0 166.6 10 7.4 6.7 70 52.0 46.8 30 96.6 87.0 90 141.2 127.1 50 185.8 167.3 11 8.2 7.4 71 52.8 47.5 131 97.4 87.7 191 141.9 127.8 251 186.5 168.0 12 8.9 8.0 72 53.5 48.2 32 98.1 88.3 92 142.7 128.5 52 187.3 168.6 13 9.7 8.7 73 54.2 48.8 33 98.8 89.0 93 143.4 129.1 53 188.0 169.3 14 10.4 9.4 74 55.0 49.5 34 99.6 89.7 94 144.2 129.8 54 188.8 170.0 15 11.1 10.0 75 55.7 50.2 35 100.3 90.3 95 144.9 130.5 55 189.5 170.6 16 11.9 10.7 76 56.5 50.9 36 101.1 91.0 96 145.7 131.1 56 190.2 171.3 17 12.6 11.4 77 57.2 51.5 37 101.8 91.7 97 146.4 131.8 57 191.0 172.0 18 13.4 12.0 78 58.0 52.2 38 102.6 92.3 98 147.1 132.5 58 191.7 172.6 19 14.1 12.7 79 58.7 52.9 39 103.3 93.0 99 147.9 133.2 59 192.5 173.3 20 14.9 13.4 80 59.5 53.5 40 104.0 93.7 200 148.6 133.8 60 193.2 174.0 21 15.6 14.1 81 60.2 54.2 141 104.8 94.3 201 149.4 134.5 261 194.0 174.6 22 16.3 14.7 82 60.9 54.9 42 105.5 95.0 02 150.1 135.2 62 194.7 175. 3 23 17.1 15.4 83 61.7 55.5 43 106.3 95.7 03 150.9 135.8 63 195.4 176.0 24 17.8 16.1 84 62.4 56.2 44 107.0 96.4 04 151.6 136.5 64 196.2 17(5. 7 25 18.6 16.7 85 63.2 56.9 45 107.8 97.0 05 152.3 137.2 65 196.9 177.3 26 19.3 17.4 86 63.9 57.5 46 108.5 97.7 06 153.1 137.8 66 197.7 178.0 27 20.1 18.1 87 64.7 58.2 47 109.2 98.4 07 153.8 138.5 67 198.4 178.7 28 20.8 18.7 88 65.4 58.9 48 110.0 99.0 08 154.6 139.2 68 199.2 179.3 29 21.6 19.4 89 66.1 59.6 49 110.7 99.7 09 155.3 139.8 69 199.9 180.0 30 22.3 20.1 90 66.9 60.2 50 111.5 100.4 10 156.1 140.5 70 200.6 180.7 31 23.0 20.7 91 67.6 60.9 151 112.2 101.0 211 156.8 141.2 271 201.4 181.3 32 23.8 21.4 92 68.4 61.6 52 113.0 101.7 12 157.5 141.9 72 202.1 182.0 33 24.5 22.1 93 69.1 62.2 53 113.7 102.4 13 158.3 142.5 73 202.9 182.7 34 25.3 22.8 94 69.9 62.9 54 114.4 103.0 14 159.0 143.2 74 203.6 183.3 35 26.0 23.4 95 70.6 63.6 55 115.2 103.7 15 159.8 143.9 75 204.4 184.0 36 26.8 24.1 96 71.3 64.2 56 115.9 104.4 16 160.5 144. 5 76 205. 1 184.7 37 27.5 24.8 97 72.1 64.9 57 116.7 105.1 17 161.3 145.2 77 205.9 185.3 38 28.2 25.4 98 72.8 65.6 58 117.4 105.7 18 162.0 145.9 78 206.6 186.0 39 29.0 26.1 99 73.6 66.2 59 118.2 106.4 19 162.7 146.5 79 207.3 186.7 40 29.7 26.8 100 101 74.3 75.1 66.9 60 118.9 107.1 20 163.5 147.2 80 208.1 208.8 187.4 188.0 41 30.5 27.4 67.6 161 119.6 107.7 221 164.2 147.9 281 42 31.2 28.1 02 75.8 68.3 62 120.4 108.4 22 165.0 148.5 82 209.6 188.7 43 32.0 28.8 03 76.5 68.9 63 121.1 109.1 23 165.7 149.2 83 210.3 189.4 44 32.7 29.4 04 77.3 69.6 64 121.9 109.7 24 166.5 149.9 84 211.1 190.0 45 33.4 30.1 05 78.0 70.3 65 122.6 110.4 25 167.2 150.6 85 211.8 190.7 46 34.2 30.8 06 78.8 70.9 66 123.4 111.1 26 168.0 151.2 86 212. 5 191.4 47 34.9 31.4 07 79.5 71.6 67 124.1 111.7 27 168.7 151.9 87 213.3 192.0 48 35.7 32.1 08 80.3 72.3 68 124.8 112.4 28 169.4 152.6 88 214. 192.7 49 36.4 32.8 09 81.0 72.9 69 125.6 113.1 29 170.2 153.2 89 214.8 193.4 50 37.2 33.5 10 81.7 73.6 70 126.3 113.8 30 170.9 153.9 90 215.5 194.0 51 37.9 34.1 111 82.5 74.3 171 127.1 114.4 231 171.7 154.6 291 216.3 194.7 52 38.6 34.8 12 83.2 74.9 72 127.8 115.1 32 172.4 155.2 92 217.0 195. 4 53 39.4 35.5 13 84.0 75.6 73 128.6 115.8 33 173.2 155.9 93 217.7 196.1 54 40.1 36.1 14 84.7 76.3 74 129.3 116.4 34 173.9 156.6 94 218.5 196.7 55 40.9 36.8 15 85.5 77.0 75 130.1 117.1 35 174.6 157.2 95 219.2 197.4 56 41.6 37.5 16 86.2 77.6 76 130.8 117.8 36 175.4 157.9 96 220.0 198. 1 57 42.4 38.1 17 86.9 78.3 77 131.5 118.4 37 176.1 158.6 97 220.7 198.7 58 43.1 38.8 18 87.7 79.0 78 132.3 119.1 38 176.9 159.3 98 221.5 199.4 59 43.8 39.5 19 88.4 79.6 79 133.0 119.8 39 177.6 159.9 99 222.2 200.1 60 44.6 40.1 20 89.2 80.3 80 133.8 120.4 40 178.4 160.6 300 222.9 200.7 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 4 18° (i: J2°, 228° ,312). TABLE 2. [Page 615 Difference of latitude and Departure for 42° (138°, 222°, 318° )• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. 1 Dep. 301 223.7 201.4 361 268.3 241.6 421 312.9 281.7 481 357.5 321.9 541 402.1 362.0 02 224.4 202.1 62 269.0 242.2 22 313.6 282.4 82 358.2 322.5 42 402.8 362.7 03 225.2 202.8 63 269.8 242.9 23 314.4 283.0 83 358.9 323.2 43 403.5 363.3 04 225.9 203.4 64 270.5 243.6 24 315.1 283.7 84 359.7 323.9 44 404.3 364.0 05 226.6 204.1 65 271.2 244.2 25 315.8 284.4 85 360.4 324.6 45 405.0 364.7 06 227.4 204.8 66 272.0 244.9 26 316.6 285.1 86 361.2 325.2 46 405.8 365.4 07 228.1 205.4 67 272.7 245.6 27 317.3 285.7 87 361.9 325.9 47 406.5 366.0 08 228.9 206.1 68 273.5 246.2 28 318.1 286.4 88 362.7 326.6 48 407.2 366.7 09 229.6 206.8 69 274.2 246.9 29 318.8 287.1 89 363.4 327.2 49 408.0 367.4 10 311 230.4 231.1 207.4 70 275.0 247.6 30 319.6 287.7 90 364. 1 327.9 50 408.7 368.0 208.1 371 275.7 248.3 431 320.3 288.4 491 364.9 328.6 551 409.5 368.7 12 231.9 208.8 72 276.5 248.9 32 321.0 289.1 92 365.6 329.2 52 410.2 369.4 13 232.6 209.4 73 277.2 249.6 33 321.8 289.7 93 366. 4 329.9 53 411.0 370.0 14 233.3 210.1 74 277.9 250.3 34 322.5 290.4 94 367.1 330,6 54 411.7 370.7 15 234.1 210.8 75 278.7 250.9 35 323.3 291.1 95 367.9 331.3 55 412.4 371.4 16 234.8 211.5 76 279.4 251.6 36 324.0 291.7 96 368.6 331.9 56 413.2 372.0 17 235.6 212.1 77 280.2 252.3 37 324.8 292.4 97 369.3 332.6 57 413.9 372.7 18 236.3 212.8 78 280.9 252.9 38 325.5 293. 1 98 370.1 333. 3 58 414.7 373.4 19 237.1 213.5 79 281.7 253. 6 39 326.2 293.8 99 370.8 333.9 59 415.4 374.1 20 237.8 214.1 80 282.4 254.3 40 327.0 294.4 500 371.6 334.6 60 416.2 374.7 321 238.6 214.8 381 283.1 254.9 441 327. 7 295.1 501 372.3 335.3 561 416.9 375.4 22 239.3 215.5 82 283.9 255.6 42 328. 5 295.8 02 373.1 335.9 62 417.6 376.1 23 240.0 216.1 83 284.6 256.3 43 329.2 296.4 03 373.8 336.6 63 418.4 376.7 24 240.8 216.8 84 285.4 257.0 44 330.0 297.1 04 374.5 337.2 64 419.1 377.4 25 241.5 217.5 85 286.1 257.6 45 330.7 297.8 05 375.3 337.9 65 419.9 378.1 26 242.3 218.1 86 286.9 258.3 46 331.4 298.4 06 376.0 338.6 66 420.6 378.7 27 243.0 218.8 87 287.6 259.0 47 332.2 299.1 07 376.8 339.3 67 421,4 379.4 28 243.8 219.5 88 288.3 259.6 48 332.9 299.8 08 377.5 339.9 68 422.1 380.1 29 244.5 220.1 89 289.1 260.3 49 333. 7 300.4 09 378.3 340.6 69 422.8 380.7 30 245.2 220.8 90 289.8 261.0 50 334.4 335.2 301.1 10 379.0 341.3 70 423.6 381.4 331 246.0 221.5 391 290.6 261.6 451 301.8 511 379.7 341.9 571 424.3 382.1 32 246.7 222.2 92 291.3 262.3 52 335.9 302.5 12 380.5 342.6 72 425.1 382.8 33 247.5 222.8 93 292.1 263.0 53 336.6 303.1 13 381.2 343.3 73 425.8 383.4 34 248.2 223.5 94 292.8 263.6 54 337.4 303.8 14 382.0 343.9 74 426.6 384.1 35 249.0 224.2 95 293.5 264.3 55 338.1 304.5 15 382.7 344.6 75 427.3 384.8 36 249.7 224.8 96 294.3 265.0 56 338.9 305.1 16 383.5 345.3 76 428.0 385.4 37 250.4 225.5 97 295.0 265.7 57 339.6 305.8 17 384.2 346.0 77 428.8 386.1 38 251.2 226.2 98 295.8 266.3 58 340.4 306.5 18 384.9 346.6 78 429.5 386.8 39 251.9 226.8 99 296.5 267.0 59 341.1 307.1 19 385.7 347.3 79 430.3 387.4 40 252.7 227.5 400 297.3 267.7 60 341.8 307.8 20 386.4 348.0 80 431.0 388.1 341 253.4 228.2 401 298.0 268.3 461 342.6 308.5 521 387.2 348.6 581 431.8 388.8 42 254.2 228.8 02 298.7 269.0 62 343.3 309.1 22 387.9 349.3 82 432.5 389.4 43 254.9 229.5 03 299.5 269.7 63 344.1 309.8 23 388.7 350.0 83 433.2 390.1 44 255.6 230.2 04 300.2 270.3 64 344.8 310.5 24 389.4 350.6 84 434.0 390.8 45 256.4 230.9 05 301.0 271.0 65 345.6 311.2 25 390.1 351.3 85 434.7 391.4 46 257.1 231.5 06 301.7 271.7 66 346.3 311.8 26 390.9 352.0 86 435.5 392.1 47 257.9 232.2 07 302.5 272.3 67 347.0 312.5 27 391.6 352.6 87 436.2 392.8 48 258.6 232.9 08 303.2 273.0 68 347.8 313.2 28 392.4 353.3 88 437.0 393.4 49 259.4 233.5 09 303.9 273.7 69 348.5 313.8 29 393.1 354.0 89 437.7 394.1 50 260.1 234.2 10 304.7 274.3 70 349.3 350.0 314.5 30 393.9 354.6 90 438.4 394.8 351 260.8 234.9 411 305.4 275.0 471 315.2 531 394.6 355.3 591 439.2 395.4 52 261.6 235.5 12 306.2 275.7 72 350.8 315.8 32 395.3 356.0 92 440.0 396.1 53 262.3 236.2 13 306.9 276.4 73 351.5 316.5 33 396.1 356.6 93 440.7 396.8 54 263.1 236.9 14 307.7 277.0 74 352.3 317.2 34 396.8 357.3 94 441.4 397.5 55 263.8 237.5 15 308.4 277.7 75 353.0 317.8 35 397.6 358.0 95 442.2 398.1 56 264.6 238.2 16 309.1 278.4 76 353.7 318.5 36 398.3 358.6 96 442.9 398.8 67 265.3 238.9 17 309.9 279.0 77 354.5 319.2 37 399.1 359.3 97 443.7 399.5 58 266.0 239.6 18 310.6 279.7 78 355.2 319.9 38 399.8 360.0 98 444.4 400.1 59 266.8 240.2 19 311.4 280.4 79 356.0 320.5 39 400.6 360.6 99 445.2 400.8 60 267.5 240.9 20 312.1 281.0 80 356.7 321.2 40 401.3 361.3 600 445.9 401.5 Dist. Dep. Lat. Dist. Dep. Lat. DiBt. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 48° (132°, 228°, 312°). Page 616] TABLE 2. Difference of Latitude and Departure for 43° (137°, 22S °, 317° )• Dlst. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0,7 0.7 61 44.6 41.6 121 88.5 82.5 181 132.4 123.4 241 176.3 164.4 2 1.5 1.4 62 45.3 42.3 22 89.2 83.2 82 133.1 124.1 42 177.0 165.0 3 2.2 2.0 63 46.1 43.0 23 90.0 83.9 83 133.8 124.8 43 177.7 165.7 4 2.9 2.7 64 46.8 43.6 24 90.7 84.6 84 134.6 125.5 44 178.6 166.4 5 3.7 3.4 65 47.5 44.3 25 91.4 85.2 85 135.3 126.2 46 179.2 167.1 6 4.4 4.1 66 48.3 45.0 26 92.2 85.9 86 136.0 126.9 46 179.9 167.8 7 5.1 4.8 67 49.0 45.7 27 92.9 86.6 87 136.8 127.6 47 180.6 168.5 8 5.9 5.6 68 49.7 46.4 28 93.6 87.3 88 137.5 128.2 48 181.4 169.1 9 6.6 6.1 69 50.5 47.1 29 94.3 88.0 89 138.2 128.9 49 182.1 169.8 10 7.3 6.8 70 51.2 47.7 30 96.1 88.7 90 139.0 129.6 60 182.8 170.5 11 8.0 7.5 71 51.9 48.4 131 95.8 89.3 191 139.7 130.3 251 183.6 171.2 12 8.8 8.2 72 52.7 49.1 32 96.5 90.0 92 140.4 130.9 52 184.3 171.9 13 9.5 8.9 73 53.4 49.8 33 97.3 90.7 93 141.2 131.6 53 185.0 172.5 14 10.2 9.5 74 54.1 50.5 34 98.0 91.4 94 141.9 132.3 54 185.8 173.2 15 11.0 10.2 75 54.9 61.1 35 98.7 92.1 96 142.6 133.0 55 186.5 173.9 16 11.7 10.9 76 55.6 51.8 36 99.6 92.8 96 143.3 133.7 56 187.2 174.6 17 12.4 11.6 77 56.3 52.5 37 100.2 93.4 97 144.1 134.4 57 188.0 175.3 18 13.2 12.3 78 57.0 53.2 38 100.9 94.1 98 144.8 136.0 58 188.7 176.0 19 13.9 13.0 79 57.8 53.9 39 101.7 94.8 99 145.6 136.7 59 189.4 176.6 20 14.6 13.6 80 58.5 54.6 40 102.4 103.1 95.6 200 146.3 136.4 60 190.2 177.3 21 15.4 14.3 81 59.2 55.2 141 96.2 201 147.0 137.1 261 190.9 178.0 22 16.1 15.0 82 60.0 55.9 42 103.9 96.8 02 147.7 137.8 62 191.6 178.7 23 16.8 15.7 83 60.7 56.6 43 104.6 97.6 03 148.5 138.4 63 192.3 179.4 24 17.6 16.4 84 61.4 57.3 44 105.3 98.2 04 149.2 139.1 64 193.1 180.0 25 18.3 17.0 85 62.2 58.0 46 106.0 98.9 06 149.9 139.8 65 193.8 180.7 26 19.0 17.7 86 62.9 58.7 46 106.8 99.6 06 150.7 140.6 66 194.5 181.4 27 19.7 18.4 87 63.6 59.3 47 107.6 100. 3. 07 151.4 141.2 67 195.3 182.1 28 20.5 19.1 88 64.4 60.0 48 108.2 100.9 08 152.1 141.9 68 196.0 182.8 29 21.2 19.8 89 65.1 60.7 49 109.0 101.6 09 162.9 142.6 69 196.7 183.5 30 21.9 20.5 90 65.8 61.4 50 109.7 102.3 10 163.6 143.2 70 197.6 184.1 31 22.7 21.1 91 66.6 62.1 151 110.4 103. 211 164.3 143.9 271 198.2 184.8 32 23.4 21.8 92 67.3 62.7 52 111.2 103.7 12 156.0 144.6 72 198.9 185.6 33 24.1 22.5 93 68.0 63.4 53 111.9 104.3 13 155.8 146.3 73 199.7 186.2 34 24.9 23.2 94 68.7 64.1 54 112.6 106.0 14 156.6 145.9 74 200.4 186.9 35 25.6 23.9 95 69.5 64.8 55 113.4 106.7 16 157.2 146.6 76 201.1 187.5 36 26.3 24.6 96 70.2 65.5 66 114.1 106.4 16 168.0 147.3 76 201.9 188.2 37 27.1 25.2 97 70.9 66.2 67 114.8 107.1 17 168.7 148.0 77 202.6 188.9 38 27.8 25.9 98 71.7 66.8 68 115.6 107.8 18 159.4 148.7 78 203.3 189.6 39 28.5 26.6 99 72.4 67.5 69 116.3 108.4 19 160.2 149.4 79 204.0 190.3 40 29.3 27.3 100 73.1 68.2 60 117.0 109.1 20 160.9 160.0 80 281 204.8 205.5" 191.0 41 30.0 28.0 101 73.9 68.9 161 117.7 109.8 221 161.6 150.7 191.6 42 30.7 28.6 02 74.6 69.6 62 118.5 110.6 22 162.4 151.4 82 206.2 192.3 43 31.4 29.3 03 75.3 70.2 63 119.2 111.2 23 163.1 162.1 83 207.0 193.0 44 32.2 30.0 04 76.1 70.9 64 119.9 111.8 24 163.8 152.8 84 207.7 193.7 45 32.9 30.7 05 76.8 71.6 65 120.7 112.6 26 164.6 163.4 85 208.4 194.4 46 33.6 31.4 06 77.5 72.3 66 121.4 113.2 26 165.3 164.1 86 209.2 195.1 47 34.4 32.1 07 78.3 73.0 67 122.1 113.9 27 166.0 154.8 87 209.9 195.7 48 35.1 32.7 08 79.0 73.7 68 122.9 114.6 28 166.7 155.5 88 210.6 196.4 49 35.8 33.4 09 79.7 74.3 69 123.6 115.3 29 167.5 156.2 89 211.4 197.1 50 36.6 34.1 10 80.4 75.0 75.7 70 124.3 116.9 30 168.2 156.9 157.5 90 212.1 197.8 51 37.3 34.8 111 81.2 171 125.1 116.6 231 168.9 291 212.8 198.5 52 38.0 35.5 12 81.9 76.4 72 126.8 117.3 32 169.7 158.2 92 213.6 199.1 53 38.8 36.1 13 82.6 77.1 73 126.6 118.0 33 170.4 158.9 93 214.3 199.8 54 39.5 36.8 14 83.4 77.7 74 127.3 118.7 34 171.1 169.6 94 215.0 200.6 55 40.2 37.5 15 84.1 78.4 75 128.0 119.3 35 171.9 160.3 96 215.7 201.2 56 41.0 38.2 16 84.8 79.1 76 128.7 120.0 36 172.6 161.0 96 216.5 201.9 57 41.7 38.9 17 85.6 79.8 77 129.4 120.7 37 173.3 161.6 97 217.2 202.6 58 42.4 39.6 18 86.3 80.5 78 130.2 121.4 38 174.1 162.3 98 217.9 203.2 59 43.1 40.2 19 87.0 81.2 79 130.9 122.1 39 174.8 163.0 99 218.7 203.9 60 43.9 40.9 20 87.8 81.8 80 131.6 122.8 40 175.5 163.7 300 219.4 204.6 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dlst Dep. Lat. Dist. Dep. Lat. 17° (1 33°, 227°, 313° )• TABLE 2. [Page 617 Difference of Latitude and Departure for 43" (137°, 223°, 317° ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 220.1 205.3 361 264.0 246.2 421 307.9 287.1 481 351.8 328.1 541 396.7 369.0 02 220.9 206.0 62 264.8 246.9 22 308.6 287.8 82 352.5 328.7 42 396.4 369.7 03 221.6 206.7 63 265.5 247.6 23 309.4 288.5 83 353.2 329.4 43 397.1 370.3 04 222.3 207.3 64 266.2 248.3 24 310.1 289.2 84 354.0 330.1 44 397.9 371.0 05 223.1 208.0 65 267.0 248.9 25 310.8 289.9 85 354.7 330.8 45 398.6 371.7 06 223.8 208.7 66 267.7 249.6 26 311.6 290.5 86 355.4 331.4 46 399.3 372.4 07 224.5 209.4 67 268.4 250.3 27 312.3 291.2 87 356.2 332.1 47 400.1 373.1 08 225.3 210.1 68 269.1 251.0 28 313.0 291.9 88 356.9 332.8 48 400.8 373.7 09 226.0 210.7 69 269.9 251.7 29 313.8 292.6 89 357.7 333.5 49 401.5 374.4 10 226.7 211.4 70 270.6 252. 3 30 314.5 293.3 90 358.4 334.2 50 402.2 403.0 375.1 311 227.5 212.1 371 271.3 253.0 431 315.2 293.9 491 359.1 334.9 561 375.8 12 228.2 212.8 72 272.1 253.7 32 316.0 294.6 92 359.8 335.5 52 403.7 376.5 13 228.9 213.5 73 272.8 254.4 33 316.7 295.3 93 360.6 336.2 53 404.4 377.1 14 229.7 214.2 74 273.5 255.1 34 317.4 296.0 94 361.3 336.9 54 405.2 377.8 15 230.4 214.8 75 274.3 255.8 35 318.1 296.7 95 362.0 337.6 •55 405.9 378.5 16 231.1 215.5 76 275.0 256.4 36 318.9 297.4 96 362.8 338.3 56 406.6 379.2 17 231.8 216.2 77 275.7 257.1 37 319.6 298.0 97 363.5 338.9 67 407.4 379.9 18 232.6 216.9 78 276.5 257.8 38 320.3 298.7 98 364.2 339.6 58 408.1 380.6 19 233.3 217.6 79 277.2 258.5 39 321.1 299.4 99 364.9 340.3 59 408.8 381.2 20 321 234.0 218.2 80 277.9 259.2 40 321.8 300.1 500 365.7 366.4 341.0 60 409.6 381.9 234.8 218.9 381 278.7 259.8 441 322.5 300.8 501 341.7 561 410.3 382.6 22 235.5 219.6 82 279.4 260.5 42 323.3 301.4 02 367.1 342.4 62 411.0 383.3 23 236.2 220.3 83 280.1 261.2 43 324.0 302.1 03 367.8 343.0 63 411.8 384.0 24 237.0 221.0 84 280.8 261.9 44 324.7 302.8 04 368.6 343.7 64 412.5 384.6 25 237.7 221.7 85 281.6 262.6 45 325.5 303.5 05 369.3 344.4 65 413.2 385.3 26 238.4 222.3 86 282.3 263.3 46 326.2 304.2 06 370.0 345.1 66 414.0 386.0 27 239.2 223.0 87 283.0 263.9 47 326.9 304.9 07 370.8 345.8 67 414.7 386.7 28 239.9 223.7 88 283.7 264.6 48 327.7 305.5 08 371.5 346.5 68 415.4 387.4 29 240.6 224.4 89 284.5 265.3 49 328.4 306.2 09 372.3 347,1 69 416.2 388.1 30 241.4 225.1 90 285.2 266.0 50 329.1 306.9 10 373.0 347.8 70 416.9 388. 7 389.4 331 242.1 225.7 391 286.0 266.7 451 329.9 307.6 511 373.8 348.5 571 417.6 32 242.8 226.4 92 286.7 267.3 52 330.6 308.3 12 374.5 349.2 72 418.3 390.1 33 243.5 227.1 93 287.4 268.0 53 331.3 309.0 13 375.2 349.9 73 419.1 390.8 34 244.3 227.8 94 288.2 268.7 54 332.1 309.6 14 376.0 350.5 74 419.8 391.5 35 245.0 228.5 95 288.9 269.4 55 332.8 310.3 15 376.6 351.2 75 420.5 392.2 36 245.7 229.2 96 289.6 270.1 56 333.5 311.0 16 377.4 361.9 76 421.3 392.8 37 246.5 229.8 97 290.4 270.8 57 334.3 311.7 17 378.2 362.6 77 422.0 393.5 38 247.2 230. 5 98 291.1 271.4 58 335.0 312.4 18 378.9 353.3 78 422.7 394.2 39 247.9 231.2 99 291.8 272.1 59 335.7 313.0 19 379.6 354.0 79 423. 5 394.9 40 248.7 231.9 400 292.6 272.8 60 336.5 313.7 20 380.3 354.6 80 424.2 395.6 341 249.4 232.6 401 293.3 273.5 461 337.2 314.4 521 381.1 365. 3 681 424.9 396.2 42 250.1 233.2 02 294.0 274.2 62 337.9 315.1 22 381.8 356.0 82 426.7 396.9 43 250.9 233.9 03 294.7 274.9 63 338.7 315.8 23 382.6 366.7 83 426.4 397.6 44 251.6 234.6 04 295.5 275.5 64 339.4 316.5 24 383.3 357.4 84 427.1 398.3 45 252.3 235.3 05 296.2 276.2 65 340.1 317.1 25 384.0 358.1 85 427.9 399.0 46 253.1 236.0 06 296.9 276.9 66 340.8 317.8 26 384.7 368.7 86 428.6 399.6 47 253.8 236.7 07 297.7 277.6 67 341.6 318.5 27 385.5 359.4 87 429.3 400.3 48 254.5 237.3 08 298.4 278.3 68 342.3 319.2 28 386.2 360.1 88 430.1 401.0 49 255.3 238.0 09 299.1 278.9 69 343.0 319.9 29 386.9 360.8 89 430.8 401.7 50 256.0 238.7 10 299.9 279.6 70 343.7 344.5 320.5 321.2 30 387.6 388.4 361.5 90 431.5 402.4 351 256.7 239.4 411 300.6 280.3 471 531 362.1 591 432.3 403.1 52 257.4 240.1 12 301.3 281.0 72 345.2 321.9 32 389.1 362.8 92 433.0 403.7 53 258.2 240.8 13 302.1 281.7 73 345.9 322.6 33 389.9 363.5 93 433.7 404.4 54 258.9 241.4 14 302.8 282.4 74 346.7 323.3 34 390.6 364.2 94 434.5 405.1 55 259.6 242.1 15 303.5 283.0 75 347.4 324.0 35 391.3 364.9 95 436.2 405.8 56 260.4 242.8 16 304.3 283.7 76 348.1 324.6 36 392.0 366.5 96 436.9 406.5 57 261.1 243.5 17 305.0 284.4 77 348.9 325.3 37 392.8 366.2 97 436.7 407.2 58 261.8 244.2 18 305.7 286.1 78 349.6 326.0 38 393.5 366.9 98 437.4 407.8 59 262.6 244.8 19 306.4 285.8 79 350.3 326.7 39 394.2 367.6 99 438.1 408.6 60 263.3 245.5 20 307.2 286.4 80 351.1 327.4 40 394.9 368.3 600 438.8 409.2 Dist. I)ep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 4 17° (1 33°, 227 °, 313° )• Page 618] TABLE 2. Difference of Latitude and Departure for 44° (136°, 224°, 316« '). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.7 0.7 61 43.9 42.4 121 87.0 84.1 181 130.2 125.7 241 173.4 167.4 2 1.4 1.4 62 44.6 43.1 22 87.8 84.7 82 130.9 126.4 42 174.1 168.1 3 2.2 2.1 63 45.3 43.8 23 88.5 85.4 83 131.6 127.1 43 174.8 168.8 4 2.9 2.8 64 46.0 44.5 24 89.2 86.1 84 132.4 127.8 44 175.5 169.5 5 3.6 3.5 65 46.8 45.2 25 89.9 86.8 85 133.1 128.5 45 176.2 170.2 6 4.3 4.2 66 47.5 45.8 26 90.6 87.5 86 133.8 129.2 46 177.0 170.9 7 5.0 4.9 67 48.2 46.5 27 91.4 88.2 87 134.5 129.9 47 177.7 171.6 8 5.8 5.6 68 48.9 47.2 28 92.1 88.9 88 135.2 130.6 48 178.4 172.3 9 6.5 6.3 69 49.6 47.9 29 92.8 89.6 89 136.0 131.3 49 179.1 173.0 10 7.2 6.9 70 50.4 48.6 30 93.5 90.3 90 136.7 132.0 50 179.8 173.7 11 7.9 7.6 71 51.1 49.3 131 94.2 . 91.0 191 137.4 132.7 251 180.6 174.4 12 8.6 8.3 72 51.8 50.0 32 95.0 91.7 92 138.1 133.4 52 181.3 175.1 13 9.4 9.0 73 52.5 50.7 33 95.7 92.4 93 138.8 134.1 53 182.0 175.7 14 10.1 9.7 74 53.2 51.4 34 96.4 93.1 94 139.6 134.8 54 182.7 176.4 15 10.8 10.4 75 54.0 52.1 35 97.1 93.8 96 140.3 135.5 55 183.4 177.1 16 11.5 11.1 76 54.7 52.8 36 97.8 94.5 96 141.0 136.2 56 184.2 177.8 17 12.2 11.8 77 55.4 53.5 37 98.5 95.2 97 141.7 136.8 57 184.9 178.5 18 12.9 12.5 78 56.1 54.2 38 99.3 95.9 98 142.4 137.5 58 185.6 179.2 19 13.7 13.2 79 56.8 54.9 39 100.0 96.6 99 143.1 138.2 59 186.3 179.9 20 14.4 13.9 80 81 57.5 55.6 40 100.7 97.3 200 143.9 138.9 60 187.0 180.6 21 15.1 14.6 58.3 56.3 141 101.4 97.9 201 144.6 139.6 261 187.7 181.3 22 15.8 15.3 82 59.0 57.0 42 102.1 98.6 02 145.3 140.3 62 188.5 182.0 23 16.5 16.0 83 59.7 57.7 43 102.9 99.3 03 146.0 141.0 63 189.2 182.7 24 17.3 16.7 84 60.4 58.4 44 103.6 100.0 04 146.7 141.7 64 189.9 183. 4 25 18.0 17.4 85 61.1 59.0 45 104.3 100.7 05 147.5 142.4 65 190.6 184.1 26 18.7 18.1 86 61.9 59.7 46 105.0 101.4 06 148.2 143.1 66 191.3 184.8 27 19.4 18.8 87 62.6 60.4 47 105.7 102.1 07 148.9 143.8 67 192.1 185.5 28 20.1 19.5 88 63.3 61.1 48 106.5 102.8 08 149.6 144.5 68 192.8 186.2 29 20.9 20.1 89 64.0 61.8 49 107.2 103.5 09 150.3 145.2 69 193.5 186.9 30 31 21.6 20.8 90 64.7 62.5 50 107.9 104.2 10 151.1 145. 9 70 194.2 187.6 22.3 21.5 91 65.5 63.2 151 108.6 104.9 211 151.8 146.6 271 194.9 188.3 32 23.0 22.2 92 66.2 63.9 52 109.3 105.6 12 152.5 147.3 72 195.7 188.9 33 23.7 22.9 93 66.9 64.6 53 110.1 106.3 13 153.2 148.0 73 196.4 189.6 34 24.5 23.6 94 67.6 65.3 54 110.8 107.0 14 153.9 148.7 74 197.1 190.3 35 25.2 24.3 95 68.3 66.0 55 111.5 107.7 15 154.7 149.4 75 197.8 191.0 36 25.9 25.0 96 69.1 66.7 56 112.2 108.4 16 155.4 150.0 76 198.5 191.7 37 26.6 25.7 97 69.8 67.4 57 112.9 109.1 17 156.1 il50.7 77 199. 3 192.4 38 27.3 26.4 98 70.5 68.1 58 113.7 109.8 18 156.8 151.4 78 200.0 193.1 39 28.1 27.1 99 71.2 68.8 59 114.4 110.5 19 157. 5 i 152. 1 79 200.7 193.8 40 28.8 27.8 100 71.9 69.5 60 115.1 111.1 20 158.3 152.8 80 201.4 194.5 41 29.5 28.5 101 72.7 70.2 161 115.8 111.8 221 159.0 153.5 281 202. 1 195.2 42 30.2 29.2 02 73.4 70.9 62 116.5 112.5 22 159.7 154.2 82 202.9 195.9 43 30.9 29.9 03 74.1 71.5 63 117.3 113.2 23 160.4 154.9 83 203.6 196.6 44 31.7 30.6 04 74.8 72.2 64 118.0 113.9 24 161.1 155.6 84 204.3 197.3 45 32.4 31.3 05 75.5 72.9 65 118.7 114.6 25 161.9 156.3 85 205.0 198.0 46 33.1 32.0 06 76.3 73.6 66 119.4 115.3 26 162.6 157.0 86 205.7 198.7 47 33.8 32.6 07 77.0 74.3 67 120.1 116.0 27 163.3 157.7 87 206.5 199.4 48 34.5 33.3 08 77.7 75.0 68 120.8 116.7 28 164.0 158.4 88 207.2 200.1 49 35.2 34.0 09 78.4 75.7 69 121.6 117.4 29 164.7 159.1 89 207.9 200.8 50 36.0 34.7 10 79.1 76.4 70 122.3 118.1 30 165.4 166.2 159.8 90 208.6 201.5 51 36.7 35.4 111 79.8 77.1 171 123.0 118.8 231 160.5 291 209.3 202.1 52 37.4 36.1 12 80.6 77.8 72 123.7 119.5 32 166.9 161.2 92 210.0 202.8 53 38.1 36.8 13 81.3 78.5 73 124.4 120.2 33 167.6 161.9 93 210.8 203.5 54 38.8 37.5 14 82.0 79.2 74 125.2 120.9 34 168.3 162.6 94 211.5 204.2 55 39.6 38.2 15 82.7 79.9 75 125.9 121.6 35 169.0 163.2 95 212.2 204.9 56 40.3 38.9 16 83.4 80.6 76 126.6 122.3 36 169.8 163.9 96 212.9 205.6 57 41.0 39.6 17 84.2 81.3 77 127.3 123.0 37 170.5 164.6 97 213.6 206.3 58 41.7 40.3 18 84.9 82.0 78 128.0 123.6 38 171.2 165.3 98 214.4 207.0 59 42.4 41.0 19 85.6 82.7 79 128.8 124.3 39 171.9 166.0 99 215.1 207.7 60 43.2 41.7 20 86.3 83.4 80 129.5 125.0 40 172.6 166.7 300 215.8 208.4 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. i 16° (1 J4°, 226°, 314° ). TABLE 2. [Page 619 ] Mfference of Latitude and Depart are for 44° (136°, 224°, 316 '). Dist. Lat Dep. Dist. Lat. Dep. Diet. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 216.5 209.1 361 259.7 250.8 421 302.8 292.5 481 346.0 334.1 541 389.2 375.8 02 217.2 209.8 62 260.4 251.5 22 303.6 293.2 82 346.7 334.8 42 389.9 376.5 03 218.0 210.5 63 261.1 252.2 23 304.3 293.8 83 347.4 335.5 43 390.6 377.2 04 218.7 211.2 64 261.8 252.9 24 305.0 294.5 84 348.2 336.2 44 391.3 377.9 05 219.4 211.9 65 262.6 253.6 25 305.7 295.2 85 348.9 336. 9 45 392.0 378.6 06 220.1 212.6 66 263.3 254.3 26 306.4 295.9 86 349.6 337.6 46 392.8 379. 3 07 220.8 213.3 67 264.0 254.9 27 307.2 296.6 87 350.3 338.3 47 393.5 380.0 08 221.6 214.0 68 264.7 255.6 28 307.9 297.3 88 351.0 339.0 48 394.2 380.7 09 222.3 214.7 69 265.4 256.3 29 308.6 298.0 89 351.7 339.7 49 394.9 381.4 10 223.0 215.4 70 266.2 257.0 30 309.3 310.0 298.7 90 352.5 340.4 50 396.6 382.1 311 223.7 216.0 371 266.9 257.7 431 299.4 491 353.2 341.1 551 396.4 382.7 12 224.4 216.7 72 267.6 258.4 32 310.8 300.1 92 353.9 341.8 52 397.1 383.4 13 225.2 217.4 73 268.3 259.1 33 311.5 300.8 93 354.6 342.5 53 397.8 384.1 14 225.9 218.1 74 269.0 259.8 34 312.2 301.5 94 355.3 343.2 54 398.5 384.8 15 226.6 218.8 75 269.8 260.5 35 312. 9 302. 2 95 356.1 343.9 55 399.2 386.5 16 227.3 219.5 76 270.5 261.2 36 313. 6 302. 9 96 356.8 344.6 56 400.0 386.2 17 228.0 220.2 77 271.2 261.9 37 314.4 303.6 97 357.5 346.2 57 400.7 386.9 18 228.8 220.9 78 271.9 262.6 38 315.1 304.3 98 358.2 345.9 58 401.4 387.6 19 229.5 221.6 79 272.6 263.3 39 315.8 305. 99 358.9 346. 6 59 402.1 388.3 20 230.2 222.3 80 273.4 264.0 40 316.5 305.7 500 359.7 347.3 60 402.8 389.0 321 230.9 223.0 381 274.1 264.7 441 317.2 306.4 501 360.4 348.0 561 403.6 389.7 22 231.6 223.7 82 274.8 265.4 42 318.0 307.0 02 361.1 348.7 62 404.3 390.4 23 232.3 224.4 83 275.5 266.1 43 318.7 307.7 03 361.8 349.4 63 406.0 391.1 24 233.1 225.1 84 276.2 266.8 44 319.4 308.4 04 362.5 350.1 64 406.7 391.8 25 233.8 225.8 85 276.9 267.5 45 320. 1 309.1 05 363.3 350.8 65 406.4 392.6 26 234.5 226.5 86 277.7 268.1 46 320.8 309.8 06 364.0 351.5 66 407.2 393.2 27 235.2 227.2 87 278.4 268.8 47 321.5 310.5 07 364.7 352.2 67 407.9 393.9 28 235.9 227.9 88 279.1 269.5 48 322.3 311.2 08 365.4 352.9 68 408.6 394.6 29 236.7 228.6 89 279.8 270.2 49 323.0 311.9 09 366.1 353.6 69 409.3 396.3 30 237.4 229.2 90 280.5 270.9 50 323.7 312.6 10 366.9 354.3 70 410.0 396.0 331 238.1 229.9 391 281.3 271.6 451 324.4 313.3 511 367.6 355.0 571 410.7 396.7 32 238.8 230.6 92 282.0 272.3 52 325.2 314.0 12 368.3 355.7 72 411.5 397.3 33 239.5 231.3 93 282.7 273.0 53 325.9 314.7 13 369.0 356.4 73 412.2 398.0 34 240.3 232.0 94 283.4 273.7 54 326.6 315.4 14 369.7 357.1 74 412.9 398.7 35 241.0 232.7 95 284.1 274.4 55 327.3 316.1 15 . 370. 5 357.8 75 413.6 399.4 36 241.7 233.4 96 284.9 275.1 56 328.0 316.8 16 371.2 358.4 76 414.3 400.1 37 242.4 234.1 97 285.6 275.8 57 328.7 317.5 17 371.9 359.1 77 415.1 400.8 38 243.1 234.8 98 286.3 276.5 58 329.5 318.2 18 372.6 359.8 78 416.8 401.5 39 243.9 235.5 99 287.0 277.2 59 330.2 318.9 19 373.3 360.5 79 416.5 402.2 40 244.6 236. 2 400 287.7 277.9 60 330.9 319.6 20 374.1 361.2 80 581 417.2 402.9 403.6 341 245.3 236.9 401 288.5 278.6 461 331.6 320.2 521 374.8 361.9 417.9 42 246.0 237.6 02 289.2 279.3 62 332.3 320.9 22 375. 5 362.6 82 418.7 404.3 43 246.7 238.3 03 289.9 280.0 63 333.1 321.6 23 376.2 363.3 83 419.4 405.0 44 247.5 239.0 04 290.6 280.7 64 333.8 322.3 24 376.9 364.0 84 420.1 405.7 45 248.2 239.7 05 291.3 281.3 65 334.5 323.0 25 377.7 364.7 86 420.8 406.4 46 248.9 240.4 06 292.1 282.0 66 335.2 323.7 26 378.4 365.4 86 421.5 407.1 47 249.6 241.1 07 292.8 282.7 67 335.9 324.4 27 379.1 366.1 87 422.3 407.8 48 250.3 241.7 08 293.5 283.4 68 336.7 325.1 28 379.8 366.8 88 423.0 408.5 49 251.1 242.4 09 294.2 284.1 69 337.4 325.8 29 380.5 367.5 89 423.7 409.1 50 251.8 243.1 10 294.9 284.8 70 338.1 326. 5 30 381.2 368.2 90 424.4 409.9 351 252.5 243.8 411 295.7 285.5 471 338.8 327. 2 531 382.0 368.9 591 426.1 410.5 52 253.2 244.5 12 296.4 286.2 72 339.5 327.9 32 382.7 369.6 92 426.9 411.2 53 253.9 245.2 13 297.1 286.9 73 340.3 328.6 33 383.4 370.3 93 426.6 411.9 54 254.6 245.9 14 297.8 287.6 74 341.0 329.3 34 384.1 371.0 94 427.3 412.6 55 255.4 246.6 15 298.5 288.3 75 341.7 330.0 35 384.8 371.7 96 428.0 413.3 56 256.1 247.3 16 299.2 289.0 76 342.4 330.7 36 385.6 372.4 96 428.7 414.0 57 256.8 248.0 17 300.0 289.7 77 343.1 331.4 37 386.3 373.1 97 429.5 414.7 58 257.5 248.7 18 300.7 290.4 78 343.8 332.1 38 387.0 373.7 98 430.2 415.4 59 258.2 249.4 19 301.4 291.1 79 344.6 332.7 39 387.7 374.4 99 430.9 416.1 60 259.0 250.1 20 302.1 291.8 80 345.3 333.4 40 388.4 375.1 600 431.6 416.8 Dist. Dep. Lat Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 46° (134°, 226' , 314°). 1 Page 620] TABLE 2. Difference of Latitude and Departure for 45° (135°, 225°, 315' ). Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 1 0.7 0.7 61 43.1 43.1 121 85.6 85,6 181 128.0 128.0 241 170.4 170.4 2 1.4 1.4 62 43.8 43.8 22 86.3 86,3 82 128.7 128.7 42 171.1 171.1 3 2.1 2.1 63 44.5 44.5 23 87.0 87.0 83 129.4 129.4 43 171.8 171.8 4 2.8 2.8 64 45.3 45.3 24 87.7 87.7 84 130.1 130.1 44 172.5 172.5 5 3.5 3.5 65 46.0 46.0 25 88.4 88.4 85 130.8 130.8 45 173.2 173.2 6 4.2 4.2 66 46.7 46.7 26 89.1 89.1 86 131.5 131.5 46 173.9 173.9 7 4.9 4.9 67 47.4 47.4 27 89.8 89.8 87 132.2 132.2 47 174.7 174.7 8 5.7 5.7 68 48.1 48.1 28 90.5 90,5 88 132.9 132.9 48 175.4 175.4 9 6.4 6.4 69 48.8 48.8 29 91.2 91,2 89 133.6 133.6 49 176.1 176.1 10 7.1 7.1 70 49.5 49.5 30 91.9 91.9 90 134.4 134.4 50 176.8 176.8 11 7.8 7.8 71 50.2 50.2 131 92.6 92.6 191 135.1 135.1 251 177.5 177.5 12 8.5 8.5 72 50.9 50.9 32 93.3 93.3 92 135.8 135,8 52 178.2 178.2 13 9.2 9.2 73 51.6 51.6 33 94.0 94.0 93 136,5 136,5 53 178.9 178.9 14 9.9 9.9 74 52.3 52.3 34 94,8 94.8 94 137.2 137,2 54 179.6 179.6 15 10.6 10.6 75 53.0 53.0 35 95.5 95.5 95 137.9 137,9 55 180.3 180.3 16 11.3 11.3 76 53.7 53.7 36 96.2 96.2 96 138.6 138.6 56 181.0 181.0 17 12,0 12.0 77 54.4 54.4 37 96.9 96.9 97 139.3 139.3 57 181.7 181.7 18 12.7 12.7 78 55.2 55.2 38 97,6 97.6 98 140.0 140.0 58 182.4 182.4 19 13.4 13.4 79 55.9 55.9 39 98,3 98.3 99 140.7 140.7 59 183.1 183.1 20 14.1 14.1 80 56.6 56.6 40 99.0 99.0 200 141.4 141,4 60 183.8 183.8 21 14.8 14.8 81 57.3 57.3 141 99,7 99.7 201 142.1 142,1 261 184.6 184.6 22 15.6 15.6 82 58.0 58.0 42 100.4 100.4 02 142.8 142.8 62 185.3 185.3 23 16.3 16.3 83 58.7 58.7 43 101.1 101.1 03 143.5 143.5 63 186.0 186,0 24 17.0 17.0 84 59.4 59.4 44 101.8 101.8 04 144.2 144.2 64 186.7 186,7 25 17.7 17.7 85 60.1 60.1 45 102.5 102.5 05 145.0 145.0 65 187.4 187,4 26 18.4 18.4 86 60.8 60.8 46 103.2 103.2 06 145.7 145.7 66 188.1 188.1 27 19.1 19.1 87 61.5 61.5 47 103.9 103.9 07 146.4 146.4 67 188.8 188.8 28 19.8 19.8 88 62.2 62.2 48 104.7 104.7 08 147.1 147.1 68 189.5 189.5 29 20.5 20.5 89 62.9 62.9 49 105.4 105.4 09 147.8 147.8 69 190.2 190.2 30 21.2 21.2 90 63.6 63.6 50 106.1 106.1 10 148.5 148.5 70 190.9 190.9 31 21.9 21.9 91 64.3 64.3 151 106.8 106.8 211 149.2 149.2 271 191.6 191.6 32 22.6 22.6 92 65.1 65.1 52 107.5 107.5 12 149.9 149.9 72 192.3 192.3 33 23.3 23.3 93 65.8 65.8 53 108.2 108.2 13 150.6 150.6 73 193.0 193.0 34 24.0 24.0 94 66.5 66.5 54 108.9 108.9 14 151.3 151.3 74 193.7 193.7 35 24.7 24.7 95 67.2 67.2 55 109,6 109.6 15 152.0 152.0 75 194.5 194.5 36 25.5 25.5 96 67.9 67.9 56 110,3 110.3 16 152.7 152.7 76 195.2 195.2 37 26.2 26.2 97 68.6 68.6 57 111.0 111.0 17 153.4 153.4 77 195.9 195.9 38 26.9 26.9 98 69.3 69.3 58 111.7 111.7 18 154.1 154.1 78 196.6 196.6 39 27.6 27.6 99 70.0 70.0 59 112.4 112.4 19 154.9 154.9 79 197.3 197.3 40 28.3 28.3 100 70.7 70.7 60 113.1 113.1 20 155.6 155.6 80 198.0 198.0 41 29.0 29.0 101 71.4 71.4 161 113.8 113.8 221 156.3 156.3 281 198.7 198.7 42 29.7 29.7 02 72.1 72.1 62 114.6 114.6 22 157.0 157.0 82 199.4 199.4 43 30.4 30.4 03 72.8 72.8 63 115.3 115.3 23 157.7 157.7 83 200.1 200.1 44 31.1 31.1 04 73.5 73.5 64 116.0 116.0 24 158.4 158.4 84 200.8 200.8 45 31.8 31.8 05 74.2 74.2 65 116.7 116.7 25 159.1 159.1 85 201.5 201.5 46 32.5 32.5 06 75.0 75.0 66 117.4 117.4 26 159.8 159.8 86 202.2 202.2 47 33.2 33.2 07 75.7 75.7 67 118.1 118.1 27 160.5 160.5 87 202.9 202.9 48 33.9 33.9 08 76.4 76.4 68 118.8 118.8 28 161.2 161.2 88 203.6 203.6 49 34.6 34.6 09 77.1 77.1 69 119.5 119.5 29 161.9 161.9 89 204.4 204.4 50 35.4 35.4 10 77.8 77,8 70 120.2 120,2 30 162.6 162,6 90 205.1 205.1 51 36.1 36.1 111 78.5 78.5 171 120.9 120,9 231 163.3 163.3 291 205.8 205.8 52 36.8 36.8 12 79.2 79.2 72 121.6 121,6 32 164.0 164,0 92 206.5 206.5 53 37.5 37.5 13 79.9 79.9 73 122.3 122,3 33 164.8 164.8 93 207.2 207. 2 54 38.2 38.2 14 80.6 80.6 74 123.0 123,0 34 165.5 165.5 94 207.9 207.9 55 38.9 38.9 15 81.3 81.3 75 123.7 123.7 35 166.2 166.2 95 208.6 208.6 56 39.6 39.6 16 82.0 82.0 76 124.5 124.5 36 166.9 166.9 96 209.3 209.3 57 40.3 40.3 17 82.7 82.7 77 125.2 125.2 37 167.6 167.6 97 210.0 210.0 58 41.0 41.0 18 83.4 83.4 78 125. 9 125.9 38 168.3 168.3 98 210.7 210.7 59 41.7 41.7 19 84.1 84.1 79 126.6 126.6 39 169.0 169.0 99 211.4 211,4 60 42.4 42.4 20 84.9 84.9 80 127.3 127.3 40 169.7 169.7 300 212.1 212. 1 Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 4 S°(K J5°, 225°, 815° ). 1 TABLE 2. [Page 620a | Difference of Latitude and Departure for 45° (135°, 225°, 315 ')• Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. Dist. Lat. Dep. 301 212.8 212.8 361 255.3 255.3 421 297.7 297.7 481 340.1 340.1 541 382.6 382.5 02 213.5 213.5 62 256.0 256.0 22 298.4 298.4 82 340.8 340.8 42 383.2 383.2 03 214.3 214.3 63 256.7 256.7 23 299.1 299.1 83 341.6 341.5 43 383.9 383.9 04 215.0 215.0 64 257.4 257.4 24 299.8 299.8 84 342.2 342.2 44 384.7 384.7 05 215.7 215.7 65 258.1 258.1 25 300.5 300.5 85 342.9 342.9 45 385.4 386.4 06 216.4 216.4 66 258.8 258.8 26 301.2 301.2 86 343.6 343.6 46 386.1 386.1 07 217.1 217.1 67 259.5 259.5 27 301.9 301.9 87 344.3 344.3 47 386.8 386.8 08 217.8 217.8 68 260.2 260.2 28 302.6 302.6 88 346.1 345.1 48 387.5 387.6 09 218.5 218.5 69 260.9 260.9 29 303.4 303.4 89 345.8 345.8 49 388.2 388.2 10 219.2 219.2 70 261.6 261.6 30 304.1 304.1 90 346.5 346.5 50 388.9 388.9 311 219.9 219.9 371 262,3 262.3 431 304.8 304.8 491 347.2 347.2 561 389.6 389.6 12 220.6 220.6 72 263.0 263.0 32 306. 5 305.6 92 347.9 347.9 62 390.3 390.3 13 221.3 221.3 73 263.8 263.8 33 306.2 306.2 93 348.6 348.6 53 391,0 391.0 14 222.0 222.0 74 264.5 264.5 34 306.9 306.9 94 349.3 349.3 54 391.7 391.7 15 222.7 222.7 75 266.2 265.2 35 307.6 307.6 95 350.0 360.0 55 392.4 392.4 16 223.4 223.4 76 265.9 266.9 36 308.3 308.3 96 350.7 350.7 56 393.1 393.1 17 224.2 224.2 77 266.6 266.6 37 309.0 309.0 97 361.4 351.4 57 393.9 393.9 18 224.9 224.9 78 267.3 267.3 38 309.7 309.7 98 352.1 352.1 58 394.6 394.6 19 225.6 225.6 79 268.0 268.0 39 310.4 310.4 99 352.8 352.8 69 396.3 396.3 20 226.3 226.3 80 268.7 268.7 40 311.1 311.1 500 353.5 353.6 60 396.0 396.0 321 227.0 227.0 381 269.4 269.4 441 311.8 311.8 501 354.3 354.3 661 396,7 396.7 22 227.7 227.7 82 270.1 270.1 42 312.5 312.6 02 365.0 355.0 62 397.4 397.4 23 228.4 228.4 83 270.8 270.8 43 313.3 313.3 03 355.7 366.7 63 398.1 398.1 24 229.1 229.1 84 271.5 271.5 44 314.0 314.0 04 356.4 366.4 64 398.8 398.8 25 229.8 229.8 85 272.2 272.2 45 314.7 314.7 05 357.1 357.1 65 399.6 399.6 26 230.5 230.5 86 272.9 272.9 46 315.4 315.4 06 367.8 367.8 66 400.2 400.2 27 231.2 231.2 87 273.7 273.7 47 316.1 316.1 07 358.6 358.5 67 400.9 400.9 28 231.9 231.9 88 274.4 274.4 48 316.8 316.8 08 359.2 369.2 68 401.6 401.6 29 232.6 232.6 89 275.1 275.1 49 317.5 317.5 09 359.9 369.9 69 402.3 402.3 30 233.3 233.3 90 275.8 275.8 50 318.2 318.2 10 360.6 360.6 70 403,0 403.0 331 234.1 234.1 391 276.5 276.5 451 318.9 318.9 511 361.3 361.3 571 403.8 403,8 32 234.8 234.8 92 277.2 277.2 52 319.6 319.6 12 362.0 362.0 72 404.5 404,5 33 235.5 235.5 93 277.9 277.9 63 320.3 320.3 13 362.7 362.7 73 405.2 405.2 34 236.2 236.2 94 278.6 278.6 54 321.0 321.0 14 363.5 363.5 74 406.9 406.9 35 236.9 236.9 95 279.3 279.3 55 321.7 321.7 15 364.2 364.2 75 406.6 406.6 36 237.6 237.6 96 280.0 280.0 56 322.4 322.4 16 364.9 364.9 76 407.3 407.3 37 238.3 238.3 97 280.7 280.7 57 323.2 323.2 17 365.6 365.6 77 408.0 408.0 38 239.0 239.0 98 281.4 281.4 58 323.9 323.9 18 366.3 366.3 78 408.7 408.7 39 239.7 239.7 99 282.1 282.1 59 324.6 324.6 19 367.0 367.0 79 409.4 409,4 40 240.4 240.4 400 282.8 282.8 60 326.3 326.0 325.3 20 367.7 367.7 80 410.1 410,1 341 241.1 241.1 401 283.6 283.6 461 326.0 521 368.4 368.4 581 410.8 410.8 42 241.8 241.8 02 284.3 284.3 62 326.7 326.7 22 369.1 369.1 82 411.6 411.6 43 242.5 242.5 03 285.0 286.0 63 327.4 327.4 23 369.8 369.8 83 412.2 412.2 44 243.2 243.2 04 285.7 285.7 64 328.1 328.1 24 370.5 370.6 84 412.9 412.9 45 244.0 244.0 05 286.4 286.4 66 328.8 328.8 25 371.2 371.2 85 413.7 413.7 46 244.7 244.7 06 287.1 287.1 66 329.5 329.5 26 371.9 371.9 86 414.4 414.4 47 245.4 245.4 07 287.8 287.8 67 330.2 330.2 27 372.6 372.6 87 415.1 416.1 48 246.1 246.1 08 288.5 288.5 68 330.9 330.9 28 373.4 373.4 88 415.8 415.8 49 246.8 246.8 09 289.2 289.2 69 331.6 331.6 29 374.1 374.1 89 416.5 416.6 50 247.5 247.5 10 289.9 289.9 70 332.3 332.3 30 374.8 374.8 90 417.2 417.2 351 248.2 248.2 411 290.6 290.6 471 333.1 333.1 631 375.5 375.6 691 417.9 417.9 52 248.9 248.9 12 291.3 291.3 72 333.8 333.8 32 376.2 376.2 92 418.6 418.6 53 249.6 249.6 13 292.0 292.0 73 334.5 334.5 33 376.9 376.9 93 419.3 419.3 54 260.3 250.3 14 292.7 292.7 74 336.2 335.2 34 377.6 377.6 94 420.0 420.0 55 251.0 251.0 15 293.5 293.5 75 335.9 335.9 35 378.3 378.3 96 420.7 420,7 56 251.7 251.7 16 294.2 294.2 76 336.6 336.6 36 379.0 379.0 96 421.4 421,4 57 252.4 252.4 17 294.9 294.9 77 337.3 337.3 37 379.7 379.7 97 422,1 422,1 58 253.1 253.1 18 295.6 296.6 78 338.0 338.0 38 380.4 380.4 98 422,8 422,8 59 253.9 253.9 19 296.3 296.3 79 338.7 338.7 39 381.1 381.1 99 423,6 423.6 60 254.6 254.6 20 297.0 297.0 80 339.4 339.4 40 381.8 381.8 600 424.3 424.3 DIflt. Dep. Lat. Diat. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. Dist. Dep. Lat. 45° (135°, 225°, 315°). 1 TABLE 3. [Page 621 Meridional Parts, or Increased Latitadee. Comp 1 • 293.465 M. 0° 1° go 8° 4° 6° 6° 70 8° 90 M. 0.0 69.6 119.2 178.9 238.6 298.3 368.2 418.2 478.3 538.6 1 1.0 60.6 20.2 79.9 39.6 99.3 69.2 19.2 79.3 39.6 1 2 2.0 61.6 21.2 80.8 40.6 300.3 60.2 20.2 80.3 40.6 2 3 3.0 62.6 22.2 81.8 41.6 01.3 61.2 21.2 81.3 41.6 3 4 4.0 63.6 23.2 82.8 42.5 02.3 62.2 22.2 82.3 42.6 4 5 5.0 64.6 124.2 183.8 243.5 303.3 363.2 423.2 483.3 543.6 6 6 6.0 66.6 25.2 84.8 44.5 04.3 64.2 24.2 84.3 44.6 6 7 7.0 66.5 26.2 86.8 46.6 . 06.3 65.2 25.2 85.3 46.6 7 8 7.9 67.5 27.2 86.8 46.5 06.3 66.2 26.2 86.3 46.6 8 9 8.9 68.5 28.2 87.8 47.5 07.3 67.2 27.2 87.3 47.6 548.6 9 10 9.9 69.6 129.1 188.8 248.6 308.3 368.2 428.2 488.3 10 11 10.9 70.6 30.1 89.8 49.5 09.3 69.2 29.2 89.3 49.6 11 12 11.9 71.5 31.1 90.8 50.5 10.3 70.2 30.2 90.4 50.6 12 13 12.9 72.5 32.1 91.8 51.6 11.3 71.2 31.2 91.4 61.7 13 14 13.9 73.5 33.1 92.8 52.6 12.3 T2.2 32.2 92.4 52.7 14 15 14.9 74.5 134.1 193.8 253.5 313.3 373.2 433.2 493.4 553.7 15 16 15.9 75.5 35.1 94.8 54.5 14.3 74.2 34.2 94.4 54.7 16 17 16.9 76.5 36.1 95.8 55.6 16.3 76.2 35.2 95.4 55.7 17 18 17.9 77.5 37.1 96.8 56.5 16.3 76.2 36.2 96.4 66.7 18 19 18.9 78.5 38.1 97.8 57.6 17.3 77.2 37.2 97.4 67.7 19 20 19.9 79.6 139.1 198.8 258.5 318.3 378.2 438.2 498.4 658.7 20 21 20.9 80.5 40.1 99.7 59.5 19.3 79.2 39.2 99.4 59.7 21 22 21.9 81.5 41.1 200.7 60.5 20.3 80.2 40.2 500.4 60.7 22 23 22.8 82.4 42.1 01.7 61.5 21.3 81.2 41.2 01.4 61.7 23 24 23.8 83.4 43.1 02.7 62.5 22.3 82.2 42.2 02.4 62.7 24 25 24.8 84.4 144.1 203.7 263.6 323.3 383.2 443.2 503.4 563.7 25 26 25.8 85.4 45.1 04.7 64.5 24.3 84.2 44.2 04.4 64.7 26 27 26.8 86.4 46.0 06.7 65.5 25.3 85.2 45.2 05.4 65.7 27 28 27.8 87.4 47.0 06.7 66.6 26.3 86.2 46.2 06.4 66.8 28 29 28.8 88.4 48.0 07.7 67.4 27.3 87.2 47.2 07.4 67.8 29 30 29.8 89.4 149.0 208.7 268.4 328.3 388.2 448.2 508.4 568.8 30 31 30.8 90.4 50.0 09.7 69.4 29.3 89.2 49.2 09.4 69.8 31 32 31.8 91.4 61.0 10.7 70.4 30.3 90.2 50.2 10.4 70.8 32 33 32.8 92.4 62.0 11.7 71.4 31.3 91.2 61.2 11.4 71.8 33 34 33.8 93.4 53.0 12.7 72.4 32.3 92.2 52.2 12.4 72.8 34 35 34.8 94.4 164.0 213.7 273.4 333.3 393.2 453.2 513.4 673.8 36 36 35.8 96.4 66.0 14.7 74.4 34.3 94.2 54.3 14.6 74.8 36 37 36.7 96.4 56.0 16.7 76.4 36.3 95.2 55.3 15.6 75.8 37 38 37.7 97.3 57.0 16.7 76.4 36.2 96.2 66.3 16.6 76.8 38 39 38.7 98.3 58.0 17.7 77.4 37.2 97.2 57.3 17.5 77.8 39 40 39.7 99.3 159.0 218.7 278.4 338.2 398.2 458.3 518.5 578.8 40 41 40.7 100.3 60.0 19.7 79.4 39.2 99.2 59.3 19.5 79.9 41 42 41.7 01.3 61.0 20.6 80.4 40.2 400.2 60.3 20.6 80.9 42 43 42.7 02.3 62.0 21.6 81.4 41.2 01.2 61.3 21.5 81.9 43 44 45 43.7 03.3 63.0 22.6 82.4 42.2 02.2 62.3 22.5 82.9 44 44.7 104.3 164.0 223.6 283.4 343.2 403.2 463.3 523.5 583.9 46 46 46.7 05.3 65.0 24.6 84.4 44.2 04.2 64.3 24.5 84.9 46 47 46.7 06.3 66.0 25.6 85.4 45.2 05.2 65.3 25.5 85.9 47 48 47.7 07.3 67.0 26.6 86.4 46.2 06.2 66.3 26.5 86.9 48 49 48.7 08.3 68.0 27.6 87.4 47.2 07.2 67.3 27.5 87.9 49 50 49.7 109.3 168.9 228.6 288.4 348.2 408.2 468.3 628.6 688.9 60 51 50.7 10.3 69.9 29.6 89.4 49.2 09.2 69.3 29.5 89.9 51 52 51.6 11.3 70.9 30.6 90.4 50.2 10.2 70.3 30.5 90.9 52 53 52.6 12.3 71.9 31.6 91.4 51.2 11.2 71.3 31.5 91.9 63 54 53.6 13.2 72.9 32.6 92.4 52.2 12.2 72.3 32.5 93.0 54 56 54.6 114.2 173.9 233.6 293.4 363.2 413.2 473.3 533.5 594.0 55 56 55.6 16.2 74.9 34.6 94.4 54.2 14.2 74.3 34.6 95.0 66 57 56.6 16.2 75.9 36.6 95.4 65.2 16.2 75.3 36.6 96.0 67 58 67.6 17.2 76.9 36.6 96.3 66.2 16.2 76.3 36.6 97.0 58 59 58.6 18.2 77.9 37.6 97.3 67.2 17.2 77.3 37.6 98.0 59 M. 0° 1° go 8° 4° 6° 6° 7° 8° »o M. Page 622] TABLE 3. Meridional Parts, or Increased Latitudes. Comp 1 2^3.466 M. 10° 11° 12° 13° 14° 15° 16° 17° 18° 19° M. 599.0 659.6 720.5 781.5 842.8 904.4 966.3 1028. 5 1091. 1153. 9 1 600.0 60.6 21.5 82.5 43.9 05.4 67.3 29.5 92.0 54.9 1 2 01.0 61.7 22.5 83.6 44.9 06.5 68.3 30.5 93.1 56.0 2 3 02.0 62.7 23.5 84.6 45.9 07.5 69.4 31.6 94.1 57.0 3 4 03.0 63.7 24.5 85.6 46.9 08.5 70.4 32.6 95.2 58.1 4 5 604.1 664.7 725.5 786.6 847.9 909.6 971.4 1033. 7 1096. 2 1159. 1 5 6 05.1 65.7 26.6 87.6 49.0 10.6 72.5 34.7 97.3 60.2 6 7 06.1 66.7 27.6 88.7 50.0 11.6 73.5 35.7 98.3 61.2 7 8 07.1 67.7 28.6 89.7 51.0 12.6 74.6 36.8 99.4 62.3 8 9 08.1 68.7 29.6 90.7 52.0 13.7 75.6 37.8 1100. 4 63.3 9 10 609.1 669.8 730.6 791.7 853.1 914.7 976.6 1038. 9 1101. 4 1164. 4 10 11 10.1 70.8 31.6 92.7 54.1 15.7 77.7 39.9 02.5 65.4 11 12 11.1 71.8 32.7 93.8 55.1 16.8 78.7 40.9 03.5 66.5 12 13 12.1 72.8 33.7 94.8 56.1 17.8 79.7 42.0 04.6 67.5 13 14 15 13.1 73.8 34.7 95.8 57.2 18.8 80.8 43.0 05.6 68.6 14 614.1 674.8 735.7 796.8 858.2 919.8 981.8 1044.1 1106. 7 1169. 7 15 16 15.2 75.8 36.7 97.8 59.2 20.9 82.8 45.1 07.7 70.7 16 17 16.2 76.8 37.7 98.9 60.2 21.9 83.9 46.1 08.8 71.8 17 18 17.2 77.9 38.8 99.9 .61.3 22.9 84.9 47.2 09.8 72.8 18 19 18.2 78.9 39.8 800.9 62.3 24.0 85.9 48.2 10.9 73.9 19 20 619.2 679.9 740.8 801.9 863.3 925.0 987.0 1049. 3 1111.9 1174. 9 20 21 20.2 80.9 41.8 02.9 64.3 26.0 88.0 50.3 13.0 76.0 21 22 21.2 81.9 42.8 04.0 65.4 27.1 89.0 51.3 14.0 77.0 22 23 22.2 82.9 43.8 05.0 66.4 28.1 90.1 52.4 15.0 78.1 23 24 23.2 83.9 44.9 06.0 67.4 29.1 91.1 53.4 16.1 79.1 24 25 624.2 684.9 745.9 807.0 868.5 930.1 992.1 1054. 5 1117. 1 1180. 2 25 26 25.3 86.0 46.9 08.1 69.5 31.2 93.2 55.5 18.2 81.2 26 27 26.3 87.0 47.9 09.1 70.5 32.2 94.2 56.6 19.2 82.3 27 28 27.3 88.0 48.9 10.1 71.5 33.2 95.3 57.6 20.3 83.3 28 29 28.3 89.0 49.9 11.1 72.6 34.3 96.3 58.6 21.3 84.4 29 30 629.3 690.0 751.0 812.1 873.6 935.3 997.3 1059. 7 1122. 4 1185.5 30 31 30.3 91.0 52.0 13.2 74.6 36.3 98.4 60.7 23.4 86.5 31 32 31.3 92.0 53.0 14.2 75.6 37.4 99.4 61.8 24.5 87.6 32 33 32.3 93.1 54.0 15.2 76.7 38.4 1000.4 62.8 25.5 88.6 33 34 33.3 94.1 55.0 16.2 77.7 39.4 01.5 63.9 26.6 89.7 34 36 634,3 695.1 756.0 817.3 878.7 940.5 1002.5 1064. 9 1127. 6 1190.7 35 36 35.4 96.1 57.1 18.3 79.7 41.5 03.6 65.9 28.7 91.8 36 37 36.4 97.1 58.1 19.3 80.8 42.5 04.6 67.0 29.7 92.8 37 38 37.4 98.1 59.1 20.3 81.8 43.6 05.6 68.0 30.8 93.9 38 39 38.4 99.1 60.1 21.3 82.8 44.6 06.7 69.1 31.8 95.0 39 40 639.4 700.2 761.1 822.4 883.8 945.6 1007. 7 1070. 1 1132. 9 1196. 40 41 40.4 01.2 62.2 23.4 84.9 46.7 08.7 71.2 33.9 97.1 41 42 41.4 02.2 63.2 24.4 85.9 47.7 09.8 72.2 35.0 98.1 42 43 42.4 03.2 64.2 25.4 86.9 48.7 10.8 73.2 36.0 99.2 43 44 43.4 04.2 65.2 26.5 88.0 49.7 11.8 74.3 37.1 1200.2 44 45 644.5 705.2 766.2 827.5 889.0 950.8 1012. 9 1075. 3 1138. 1 1201. 3 45 46 45.5 06.2 67.3 28.5 90.0 51.8 13.9 76.4 39.2 02.3 46 47 46.5 07.3 68.3 29.5 91.0 52.8 15.0 77.4 40.2 03.4 47 48 47.5 08.3 69.3 30.5 92.1 53.9 16.0 78.5 41.3 04.5 48 49 48.5 09.3 70.3 31.6 93.1 54.9 17.0 79.5 42.3 05.5 49 50 649.5 710.3 771.3 832.6 894.1 955.9 1018. 1 1080. 5 1143. 4 1206.6 50 51 50.5 11.3 72.3 33.6 95.2 57.0 19.1 81.6 44.4 07.6 51 52 51.5 12.3 73.4 34.6 96.2 58.0 20.2 82.6 45.5 08.7 52 53 52.5 13.4 74.4 35.7 97.2 59.0 21.2 83.7 46.5 09.7 53 54 53.6 14.4 75.4 36.7 98.2 60.1 22.2 84.7 47.6 10.8 54 55 664.6 715.4 776.4 837.7 899.3 961.1 1023. 3 1085. 8 1148. 6 1211. 8 55 56 55.6 16.4 77.4 38.7 900.3 62.1 24.3 86.8 49.7 12.9 56 57 56.6 17.4 78.5 39.8 01.3 63.2 25.3 87.9 50.7 14.0 57 58 57.6 18.4 79.5 40.8 02.3 64.2 26.4 88.9 51.8 15.0 58 59 58.6 19.4 80.5 41.8 03.4 65.2 27.4 89.9 52.8 16.1 59 M. 100 11° 12° 18° 14° 16° 16° 17° 18° 19° M. TABLE 3. [Page 623 Meridional Parts, or Increased Latitudes. Comp 1 293.465 M. 20° 210 ago 2»o 24° 25° 26° 27° 28° 29° M. 1217. 1 1280.8 1344.9 1409.5 1474. 5 1540.1 1606.2 1672. 9 1740.2 1808.1 1 18.2 81.9 46.0 10.6 75.6 41.2 07.3 74.0 41.3 09.2 1 2 19.3 82.9 47.1 11.6 76.7 42.3 08.4 75.1 42.4 10.4 2 3 20.3 84.0 48.1 12.7 77.8 43.4 09.5 76.2 43.6 11.5 3 4 21.4 85.1 49.2 13.8 78.9 44.5 10.6 77.4 44.7 12.6 4 5 1222. 4 1286. 1 1350.3 1414. 9 1480.0 1545. 6 1611. 7 1678. 5 1745.8 1813. 8 5 6 23.5 87.2 51.4 16.0 81.1 46.7 12.9 79.6 46.9 14.9 6 7 24.5 88.3 52.4 17.1 82.2 47.8 14.0 80.7 48,1 16.1 7 8 25.6 89.3 53.5 18.1 83.3 48.9 15.1 81.8 49.2 17.2 8 9 26.7 90.4 54.6 19.2 84.3 50.0 16.2 82.9 50.3 18.3 9 10 1227. 7 1291.5 1355.7 1420.3 1485.4 1551. 1 1617. 3 1684.1 1751.5 1819. 5 10 11 28.8 92.5 56.7 21.4 86.5 52.2 18.4 85.2 52.6 20.6 11 12 29.8 93.6 57.8 22.5 87.6 53.3 19.5 86.3 53.7 21.8 12 13 30.9 94.7 58.9 23.5 88.7 54.4 20.6 87.4 54.8 22.9 13 14 32.0 95.7 59.9 24.6 89.8 55.5 21.7 88.5 56.0 24.0 14 15 1233. 1296.8 1361.0 1425. 7 1490.9 1556.6 1622. 8 1689.7 1757. 1 1825.2 15 16 34.1 97.9 62.1 26.8 92.0 57.7 23.9 90.8 58.2 26.3 16 17 35.1 98.9 63.2 27.9 93.1 58.8 25.0 91.9 59.4 27.5 17 18 36.2 1300.0 64.2 29.0 94.2 59.9 26.2 93.0 60,5 28.6 18 19 37.3 01.1 65.3 30.0 95.2 61.0 27.3 1628, 4 94.1 61.6 29.7 19 20 1238. 3 1302.1 1366.4 1431. 1 1496. 3 1562.1 1695. 3 1762. 7 1830.9 20 21 39.4 03.2 67.5 32.2 97.4 63.2 29.5 96.4 63.9 32.0 21 22 40.4 04.3 68.5 33.3 98.5 64.3 30.6 97.5 65.0 33.2 22 23 41.5 05.3 69.6 34.4 99.6 65.4 31,7 98.6 66.1 34.3 23 24 42.6 06.4 70.7 35.4 1500.7 66.5 32.8 99.7 67.3 35.4 24 25 1243. 6 1307. 5 1371. 8 1436. 5 1501.8 1567.6 1633.9 1700.9 1768.4 1836.6 25 26 44.7 08.5 72.8 37.6 02.9 68.7 35.0 02.0 69.5 37,7 26 27 45.7 09.6 73.9 38.7 04.0 69.8 36.1 03.1 70.7 38,9 27 28 46.8 10.7 75.0 39.8 05.1 70.9 37.3 04.2 71.8 40.0 28 29 47.9 11.7 76.1 40.9 06.2 72.0 38.4 05.3 72.9 41.2 29 30 1248. 9 1312. 8 1377. 1 1442.0 1507. 3 1573. 1 1639,5 1706.5 1774, 1 1842.3 30 81 50.0 13.9 78.2 43.0 08.4 74.2 40,6 07.6 75,2 43.4 31 32 51.0 14.9 79.3 44.1 09.4 75.3 41.7 08.7 76.3 44.6 32 33 52.1 16.0 80.4 45.2 10.5 76.4 42.8 09.8 77.4 45.7 33 34 53.2 17.1 81.5 46.3 11.6 77.5 43.9 10.9 78.6 46.9 34 35 1254. 2 1318. 2 1382. 5 1447.4 1512. 7 1578, 6 1645.0 1712. 1 1779, 7 1848. 36 36 55.3 19.2 83.6 48.5 13.8 79.7 46.2 1.3.2 80.8 49.2 36 37 56.4 20.3 84.7 49.5 14,9 80.8 47.3 14.3 82,0 ' 50.3 37 38 57.4 21.4 85.8 50.6 16.0 81.9 48,4 15.4 83,1 51.4 38 39 58.5 22.4 86.8 51.7 17.1 83.0 49.5 16.6 84.2 52.6 39 40 1259. 5 1323. 5 1387. 9 1452.8 1518. 2 1584.1 1650.6 1717. 7 1785.4 1853.7 40 41 60.6 24.6 89.0 53.9 19.3 86.2 51.7 18,8 86.5 54.9 41 42 61.7 25.6 90.1 55.0 20.4 86.3 52.8 19.9 87.6 56.0 42 43 62.7 26.7 91.1 56.1 21.5 87.4 53.9 21.1 88.8 57.2 43 44 63.8 27.8 92.2 57.1 22.6 88.5 55.1 22.2 89.9 58.3 44 45 1264.9 1328. 9 1393. 3 1458.2 1523. 7 1589. 6 1656.2 1723. 3 1791. 1 1859.5 45 46 65.9 29.9 94.4 59.3 24.8 90.7 57.3 24.4 92.2 60.6 46 47 67.0 31.0 95.5 60.4 25.9 91.8 58.4 25.5 93.3 61.8 47 48 68.0 32.1 96.5 61.5 27.0 92.9 59.5 26.7 94.5 62.9 48 49 69.1 33.1 97.6 62.6 28.0 94.1 60.6 27.8 95.6 64.0 49 50 1270. 2 1334. 2 1398. 7 1463.7 1529.1 1595. 2 1661.7 1728. 9 1796. 7 1865.2 50 51 71.2 35.3 99.8 64.8 30.2 96.3 62.9 30.0 97.9 66.3 51 52 72.3 36.3 1400.9 65.8 31.3 97.4 64.0 31.2 99.0 67.5 52 53 73.4 37.4 01.9 66.9 32.4 98.5 65.1 32.3 1800.1 68.6 53 54 74.4 38.5 03.0 68.0 33.5 99.6 66.2 33.4 01.3 69.8 1870. 9 54 55 1275. 5 1339.6 1404.1 1469. 1 1534. 6 1600.7 1667. 3 1734.5 1802. 4 55 56 76.6 40.6 05.2 70.2 35.7 01.8 68.4 35.7 03.5 72.1 56 57 77.6 41.7 06.2 71.3 36.8 02.9 69.5 36.8 04.7 73.2 57 58 78.7 42.8 07.3 72.4 37.9 04.0 70.7 37.9 05.8 74.4 58 59 79.7 43.8 08.4 73.5 39.0 05.1 71.8 39.1 07.0 75,5 59 M. 20° 210 220 28° 24° 25° 26° 27° 28° 29° M. 21594°— 14- -33 Page 624] TABLE 3. Meridional Parts, or Increased Latitudes. Comp. 1 293.465 M. 80° 81° 82° 88° 84° 36° 86° 87° 88° 89° M. 1876. 7 1946. 2016. 2086. 8 2158. 4 2230. 9 2304.2 2378. 5 2453. 8 2530. 2 1 77.8 47.1 17.2 88.0 59.6 32.1 05.5 79.8 55.1 31.5 1 2 79.0 48.3 18.3 89.2 60.8 33.3 06.7 81.0 56.4 32.8 2 3 80.1 49.4 19.5 90.3 62.0 34.5 07.9 82.3 57.6 34.0 3 4 81.3 50.6 20.7 91.5 63.2 35.7 09.2 83.5 58.9 35.3 4 5 1882. 4 1951. 8 2021. 9 2092.7 2164.4 2236. 9 2310. 4 2384. 8 2460. 2 2536. 6 5 6 83.6 52.9 23.0 93.9 65.6 38.2 11.6 86.0 61.4 37.9 6 7 84.7 54.1 24.2 95.1 66.8 39.4 12.9 87.3 62.7 39.2 7 8 85.9 55.3 25.4 96.3 68.0 40.6 14.1 88.5 64.0 40.5 8 9 87.0 56.4 26.6 97.5 69.2 41.8 15.3 89.8 65.2 41.7 9 10 1888. 2 1957. 6 2027. 7 2098. 7 2170. 4 2243. 2316. 5 2391. 2466. 5 2543. 10 11 89.3 58.7 28.9 99.8 71.6 44.2 17.8 92.3 67.8 44.3 11 12 90.5 59.9 30.1 2101. 72.8 45.5 19.0 93.5 69.0 45.6 12 13 91.6 61.1 31.3 02.2 74.0 46.7 20.3 94.8 70.3 46.9 13 14 92.8 62.2 32.4 03.4 75.2 47.9 21.5 96.0 71.6 48.2 14 15 1893. 9 1963. 4 2033. 6 2104. 6 2176. 4 2249. 1 2322. 7 2397. 3 2472. 8 2549. 5 15 16 95.1 64.6 34.8 05.8 77.6 50.3 24.0 98.5 74.1 50.7 16 17 96.2 65.7 36.0 07.0 78.8 51.6 25.2 99.8 75.4 52.0 17 18 97.4 66.9 37.1 08.2 80.0 52.8 26.4 2401. 76.6 53.3 18 19 98.5 68.1 38.3 09.4 81.2 54.0 27.7 02.3 77.9 54.6 19 20 1899. 7 1969. 2 2039. 5 2110. 6 2182. 5 2255. 2 2328. 9 2403. 5 2479. 2 2555. 9 20 21 1900.8 70.4 40.7 11.8 83.7 56.4 30.1 04.8 80.4 57.2 21 22 02.0 71.5 41.8 12.9 84.9 57.7 31.4 06.0 81.7 58.5 22 23 03.1 72.7 43.0 14.1 86.1 58.9 32.6 07.3 83.0 59.8 23 24 04.3 73.9 44.2 15.3 87.3 60.1 33.8 08.5 84.3 61.0 24 25 1905.5 1975. 2045. 4 2116. 5 2188. 5 2261. 3 2335. 1 2409. 8 2485. 5 2562. 3 25 26 06.6 76.2 46.6 17.7 89.7 62.5 36.3 11.1 86.8 63.6 26 27 07.8 77.4 47.7 18.9 90.9 63.8 37.6 12.3 88.1 64.9 27 28 08.9 78.5 48.9 20.1 92.1 65.0 38.8 13.6 89.3 66.2 28 29 10.1 79.7 50.1 21.3 93.3 66.2 40.0 14.8 90.6 67.5 29 30 1911.2 1980. 9 2051. 3 2122. 5 2194. 5 2267. 4 2341. 3 2416. 1 2491. 9 2568. 8 30 31 12.4 82.0 52.5 23.7 95.7 68.7 42.5 17.3 93.2 70.1 31 32 13.5 83.2 53.6 24.9 96.9 69.9 43.7 18.6 94.4 71.4 32 33 14.7 84.4 54.8 26.1 98.1 71.1 45.0 19.8 95.7 72.7 33 34 15.8 85.5 56.0 27.3 99.4 72.3 46.2 21.1 97.0 73.9 34 35 1917. 1986. 7 2057.2 2128. 5 2200.6 2273. 5 2347. 5 2422. 3 2498. 3 2575. 2 35 36 18.2 87.9 58.4 29.6 01.8 74.8 48.7 23.6 99.5 76.5 36 37 19.3 89.1 59.5 30.8 03.0 76.0 49.9 24.9 2500.8 77.8 37 38 20.5 90.2 60.7 32.0 04.2 77.2 51.2 26.1 02.1 79.1 38 39 21.6 91.4 61.9 33.2 05.4 78.4 52.4 27.4 03.4 80.4 39 40 1922. 8 1992.6 2063. 1 2134. 4 2206. 6 2279. 7 2353. 7 2428. 6 2504.6 2581. 7 40 41 23.9 93.7 64.3 35.6 07.8 80.9 54.9 29.9 05.9 83.0 41 42 26.1 94.9 65.5 36.8 09.0 82.1 56.1 31.2 07.2 84.3 42 43 26.3 96.1 66.6 38.0 10.2 83.3 57.4 32.4 08.5 85.6 43 44 27.4 97.2 67.8 39.2 11.5 84.6 58.6 33.7 09.7 86.9 44 45 1928. 6 1998. 4 2069. 2140. 4 ^2212. 7 2285. 8 2359. 9 2434. 9 2511. 2588. 2 45 46 29.7 99.6 70.2 41.6 13.9 87.0 61.1 36.2 12.3 89.5 46 47 30.9 2000. 7 71.4 42.8 15.1 88.3 62.4 37.4 13.6 90.8 47 48 32.0 01.9 72.6 44.0 16.3 89.5 63.6 38.7 14.8 92.1 48 49 33.2 03.1 73.7 45.2 17.5 90.7 64.8 40.0 16.1 93.4 49 50 1984. 4 2004.3 2074. 9 2146. 4 2218. 7 2291. 9 2366. 1 2441.2 2517. 4 2594. 7 50 51 35.5 05.4 76.1 47.6 19.9 93.2 67.3 42.5 18.7 96.0 51 52 36.7 06.6 77.3 48.8 21.1 94.4 68.6 43.7 20.0 97.3 52 53 37.8 07.8 78.5 50.0 22.4 95.6 69.8 45.0 21.2 98.5 53 54 39.0 08.9 79.7 51.2 23.6 96.9 71.1 46.3 22.5 99.8 54 55 1940. 2 2010. 1 2080. 8 2152. 4 2224. 8 2298. 1 2372. 3 2447. 5 2523. 8 2601. 1 55 56 41.3 11.3 82.0 53.6 26.0 99.3 73.6 48.8 25.1 02.4 56 57 42.5 12.5 83.2 54.8 27.2 2300. 5 74.8 50.1 26.4 03.7 57 58 43.6 13.6 84.4 56.0 28.4 01.8 76.1 51.3 27.6 05.0 58 59 44.8 14.8 85.6 57.2 29.6 03.0 77.3 £2.3 28.9 06.3 59 M. 80° 81° 82° 88° 84° 86° 86° 87° 88° 89° M. ' • TABLE 3. [Page 625 { Meridional Parte, or Increased Latitades. Comp 1 293.465 M. 40° 41° 48° 48° 44° 46° 46° 47° 48° 49° M. 2607. 6 2686.2 2766.0 2847.1 2929.5 3013.4 3098.7 3185.6 3274. 1 3364.4 1 08.9 87.6 67.4 48.5 30.9 14.8 3100.1 87.1 75.6 65.9 1 2 10.2 88.9 68.7 49.9 32.3 16.2 01.6 88.5 77.1 67.4 2 3 11.5 90.2 70.1 51.2 33.7 17.6 03.0 90.0 78.6 69.0 3 4 12.8 91.5 71.4 52.6 35.1 2936.5 19.0 04.4 91.4 3192. 9 80.1 3281. 6 70.5 3372.0 4 5 5 2614. 1 2692. 8 2772. 8 2853.9 3020. 4 3105. 9 6 15.4 94.2 74.1 55.3 37.9 21.8 07.3 94.4 83.1 73.5 6 7 16.8 95.5 75.4 56.7 39.3 23.3 08.8 95.8 84.6 75.1 7 8 18.1 96.8 76.8 58.0 40.6 24.7 10.2 97.3 86.1 76.6 8 9 19.4 98.1 78.1 59.4 42.0 26.1 11.6 1 98.8 87.6 78.1 9 10 2620. 7 2699. 6 2779. 5 2860.8 2943.4 3027. 5 3113. 1 3200.2 3289. 3379.6 10 11 22.0 2700.8 80.8 62.1 44.8 28.9 14.5 01.7 90.5 81.2 11 12 23.3 02.1 82.2 63.5 46.2 30.3 16.0 03.2 92.0 82.7 12 13 24.6 03.4 83.5 64.9 47.6 31.7 17.4 04.6 93.5 84.2 13 14 25.9 04.8 84.8 66.2 49.0 33.2 18.8 06.1 95.0 85.7 14 15 16 2627. 2 28.5 2706.1 07.4 2786.2 87.5 2867. 6 69.0 2950.4 51.8 3034.6 36.0 3120.3 21.7 3207.6 09.0 3296.5 98.0 3387. 3 88.8 15 16 17 29.8 08.7 88.9 70.3 53.2 37.4 23.2 10.5 99.5 90.3 17 18 31.1 10.1 90.2 71.7 54.5 38.8 24.6 12.0 3301.0 91.8 18 19 ■ 20 32.4 11.4 91.6 73.1 55.9 40.2 26.0 13.4 02.5 93.4 19 2633. 7 2712. 7 2792.9 2874. 4 2967.3 3041.7 3127. 5 3214. 9 3304.0 3394.9 20 21 35.0 14.0 94.3 75.8 58.7 43.1 28.9 16.4 05.5 96.4 21 22 36.3 15.4 95.6 77.2 60.1 44.5 30.4 17.9 07.0 98.0 22 23 37.6 16.7 97.0 78.6 61.5 45.9 31.8 19.3 08.5 99.5 23 24 25 38.9 18.0 98.3 79.9 62.9 47.3 33.3 20.8 10.0 3401.0 24 2640.2 2719. 3 2799.7 2881.3 2964.3 3048.7 3134. 7 3222. 3 3311.5 3402.6 26 26 41.6 20.7 2801. 82.7 65.7 50.2 36.2 23.7 13.0 04.1 26 27 42.9 22.0 02.4 84.0 67.1 51.6 37.6 25.2 14.5 06.6 27 28 44.2 23.3 03.7 85.4 68.5 53.0 39.0 26.7 16.0 07.2 28 29 45.5 24.7 05.1 86.8 69.9 54.4 40.5 28.2 17.5 08.7 29 30 2646.8 2726. 2806.4 2888.2 2971.3 3055.9 3141. 9 3229.6 3319.0 3410.2 30 31 48.1 27.3 07.8 89.5 72.7 57.3 43.4 31.1 20.5 11.8 31 32 49.4 28.6 09.1 90.9 74.1 58.7 44.8 32.6 22.1 13.3 32 33 50.7 30.0 10.5 92.3 75.5 60.1 46.3 34.1 23.6 14.8 33 34 35 52.0 ~2653. 3 31.3 11.8 93.7 76.9 61.5 47.7 35.6 25.1 16.4 34 2732. 6 2813. 2 2895. 2978.3 3063.0 3149. 2 3237. 3326. 6 3417. 9 35 36 54.7 34.0 14.5 96.4 79.7 64.4 50.6 38.5 28.1 19.5 36 37 56.0 35.3 15.9 97.8 81.1 65.8 52.1 40.0 29.6 21.0 37 38 57.3 36.6 17.2 99.2 82.5 67.2 53.5 41.5 31.1 22.5 38 39 40 58.6 38.0 18.6 2900.5 83.9 68.7 55.0 42.9 32.6 24.1 39 2659.9 2739. 3 2820.0 2901.9 2985.3 3070. 1 3156. 4 3244.4 3334.1 3425.6 40 41 61.2 40.6 21.3 03.3 86.7 71.5 57.9 45.9 35.6 27.2 41 42 62.5 42.0 22.7 04.7 88.1 72.9 59.4 47.4 37.1 28.7 42 43 63.9 43.3 24.0 06.1 89.5 74.4 60.8 48.9 38.6 30.2 43 44 65.2 44.6 25.4 07.4 90.9 75.8 62.3 50.3 40.2 31.8 44 45 2666. 5 2746. 2826. 7 2908.8 2992.3 3077. 2 3163.7 3251.8 3341. 7 3433.3 46 46 67.8 47.3 28.1 10.2 93.7 78.7 65.2 53.3 43.2 34.9 46 47 69.1 48.6 29.4 11.6 95.1 80.1 66.6 54.8 44.7 36.4 47 48 70.4 50.0 30.8 13.0 96.5 81.5 68.1 56.3 46.2 38.0 48 49 71.7 51.3 32.2 14.3 97.9 82.9 69.5 57.8 47.7 39.5 49 50 2673. 1 2752. 7 2833. 5 2915. 7 2999. 3 3084. 4 3171.0 3259. 3 3349. 2 3441.0 50 51 74.4 54.0 34.9 17.1 3000.7 85.8 72.5 60.7 50.8 42.6 51 52 75.7 55.3 36.2 18.5 02.1 87.2 73.9 62.2 52.3 44.1 52 53 77.0 56.7 37.6 19.9 03.5 88.7 75.4 63.7 53.8 45.7 53 54 78.3 58.0 39.0 21.2 04.9 90.1 76.8 65.2 55.3 47.2 64 55 2679. 6 2759. 3 2840.3 2922. 6 3006.3 3091.5 3178. 3 3266.7 3356. 8 3448. 8 55 56 81.0 60.7 41.7 24.0 07.7 93.0 79.7 68.2 58.3 50.3 56 57 82.3 62.0 43.0 25.4 09.2 94.4 81.2 69.7 59.9 51.9 57 58 83.6 63.4 44.4 26.8 10.6 95.8 82.7 71.1 61.4 53.4 58 59 84.9 64.7 45.8 28.2 12.0 97.3 84.1 72.6 62.9 55.0 59 M. 40° 41° 42° 48° 44° 46° 46° 47° 48° 49° M. Page 626] TABLE 3. Meridional Parts, or Increased Latitudes. Comp. 1 293.465 M. 50* 51° 62° 68° 54° 55° 58° 67° 68° 69° H. 3456. 5 3550.6 3646. 7 3745.1 3845.7 3948. 8 4054. 5 4163. 4274. 4 4389. 1 1 58.1 52.2 48.4 46.7 47.4 50.5 56.3 64.8 76.3 91.0 1 2 59.6 53.8 50.0 48.4 49.1 52.3 58.1 66.6 1 78.2 92.9 2 3 61.2 55.4 51.6 50.0 50.8 54.0 59.8 68.5 80.1 94.9 3 4 62.7 56.9 53.2 3654.8 51.7 52.5 55.7 61.6 70.3 82.0 96.8 4 5 3464. 3 3558. 5 3753. 4 3854. 2 3957. 5 4063. 4 4172. 1 4283. 9 4398. 8 5 6 65.9 60.1 56.5 55.0 55.9 59.2 65.2 74.0 85.7 4400.7 6 7 67.4 61.7 58.1 56.7 57.6 61.0 67.0 75.8 87.6 02.6 7 8 69.0 63.3 59.7 58.3 59.3 62.7 68.8 77.7 89.5 04.6 8 9 70.5 64.9 61.3 60.0 61.0 64.5 70.6 79.5 91.4 06.5 9 10 3472. 1 3566.5 3663.0 3761. 7 3862. 7 3966. 2 4072. 4 4181. 3 4293.3 4408. 5 10 11 73.6 68.1 64.6 63.3 64.4 68.0 74.2 83.2 95.2 10.4 11 12 75.2 69.7 66.2 65.0 66.1 69.7 76.0 85.0 97.1 12.4 12 13 76.7 71.3 67.9 66.7 67.8 71.5 77.7 86.9 99.0 14.3 13 14 78.3 72.8 69.5 68.3 69.5 73.2 79.5 88.7 4300.9 16.3 14 15 3479. 9 3574. 4 3671. 1 3770. 3871. 2 3975. 4081. 3 4190.6 4302. 8 4418.2 15 16 81.4 76.0 72.7 71.7 72.9 76.7 83.1 92.4 04.7 20.2 16 17 83.0 77.6 74.4 73.8 74.6 78.5 84.9 94.2 06.6 22.1 17 18 84.5 79.2 76.0 75.0 76.3 80.2 86.7 96.1 08.5 24.1 18 19 86.1 80.8 77.6 76.7 78.1 82.0 88.5 97.9 10.4 26.1 19 20 3487. 7 3582. 4 3679. 3 3778. 3 3879. 8 3983. 7 4090. 3 4199. 8 4312. 3 4428. 20 21 89.2 84.0 80.9 80.0 81.5 85.5 92.1 4201. 6 14.2 30.0 21 22 90.8 85.6 82.5 81.7 83.2 87.2 93.9 03.5 16.1 31.9 22 23 92.4 87.2 84.2 83.3 84.9 89.0 95.7 05.3 18.0 33.9 23 24 93.9 88.8 85.8 85.0 86.6 90.7 97.5 07.2 19.9 35.8 24 25 3495. 5 3590.4 3687. 4 3786. 7 3888. 3 3992. 5 4099.3 4209. 4321. 8 4437. 8 25 26 97.1 92.0 89.1 88.4 90.0 94.3 4101. 1 10.9 23.7 39.8 26 27 98.6 93.6 90.7 90.0 91.8 96.0 02.9 12.8 25.6 41.7 27 28 3500. 2 95.2 92.3 91.7 93.5 97.8 04.8 14.6 27.5 43.7 28 29 01.8 96.8 94.0 93.4 95.2 99.5 06.6 16.5 29.4 45.7 29 30 3503. 3 3598. 4 3695.6 3795. 1 3896. 9 4001.3 4108. 4 4218. 3 4331. 3 4447.6 30 31 04.9 3600. 97.3 96.8 98.6 03.1 10.2 20.2 33.2 49.6 31 32 06.5 01.6 98.9 98.4 3900.4 04.8 12.0 22.0 35.2 51.6 32 33 08.0 03.2 3700.5 3800.1 02.1 06.6 13.8 23.9 37.1 53.5 33 34 09.6 04.8 02.2 01.8 03.8 08.3 15.6 25.8 39.0 55.5 34 35 3511. 2 3606.4 3703. 8 3803. 5 3905. 5 4010. 1 4117. 4 4227. 6 4340. 9 4457. 5 35 36 12.7 08.0 05.5 05.1 07.2 11.9 19.2 29.5 42.8 59.4 36 37 14.3 09.6 07.1 06.8 09.0 13.6 21.0 31.3 44.7 61.4 37 38 15.9 11.2 08.7 08.5 10.7 15.4 22.9 33.2 46.6 63.4 38 39 17.5 12.8 10.4 10.2 12.4 17.2 24.7 35.1 48.6 65.4 39 40 3519. 3614. 5 3712. 3811. 9 3914. 1 4018.9 4126. 5 4236. 9 4350. 5 4467. 3 40 41 20.6 16.1 13.7 13.6 15.9 20.7 28.3 38.8 52.4 69.3 41 42 22.2 17.7 15.3 15.2 17.6 22.5 30.1 40.7 54.3 71.3 42 43 23.7 19.3 17.0 17.0 19.3 24.3 31.9 42.5 56.2 73.3 43 44 25.3 20.9 18.6 18.6 21.0 26.0 33.8 44.4 58.2 75.3 44 45 3526. 9 3622. 5 3720. 3 3820. 3 3922. 8 4027. 8 4135.6 4246. 3 4360. 1 4477.2 45 46 28.5 24.1 21.9 22.0 24.5 29.6 37.4 48.1 62.0 79.2 46 47 30.1 25.7 23.6 23.7 26.2 31.4 39.2 50.0 63.9 81.2 47 48 31.6 27.3 25.2 25.4 28.0 33.1 41.0 51.9 65.9 83.2 48 49 33.2 29.0 26.9 27.1 29.7 34.9 42.9 53.8 67.8 85.2 49 50 3534. 8 3630. 6 3728. 5 3828. 7 3931. 4 4036. 7 4144. 7 4255. 6 4369. 7 4487.2 50 51 36.4 32.2 30.2 30.4 33.2 38.5 46.5 57.5 71.7 89.1 51 52 37.9 33.8 31.8 32.1 34.9 40.2 48.3 59.4 73.6 91.1 52 53 39.5 35.4 33.5 33.8 36.6 42.0 50.2 61.3 75.5 93.1 53 54 41.1 37.0 35.1 35.5 38.4 43.8 52.0 63.1 77.4 95.1 54 55 3542. 7 3638. 6 3736. 8 3837. 2 3940. 1 4045.6 4153. 8 4265.0 4379. 4 4497. 1 55 56 44.3 40.3 38.4 38.9 41.8 47.4 55.7 66.9 81.3 99.1 56 57 45.9 41.9 40.1 40.6 43.6 49.1 57.5 68.8 83.2 4501. 1 57 58 47.4 43.5 41.7 42.3 45.3 50.9 59.3 70.7 85.2 03.1 58 59 49.0 45.1 43.4 45.0 47.0 52.7 61.1 72.5 87.1 05.1 59 M. 50° 61° 62° 58° 54° 66° 66° 67° 58° 69° M. TABLE 3. [Page 627 Meridional Parte, or Increased Latitudes. Comp 1 ■ 293.466 M. 60° 61° 62° 68° 64° 66° 66° 67° 68° 69° M. 4507.1 4628. 7 4754.3 4884.1 5018. 4 5157. 6 5302. 1 5452. 4 5609.1 6772. 7 1 09.1 30.8 56.4 86.3 20.6 59.9 04.6 55.0 11.8 75.5 1 2 11.1 32.9 58.6 88.5 22.9 62.3 07.0 57.6 14.4 78.3 2 3 13.1 34.9 60.7 90.7 25.2 64.7 09.5 60.1 17.1 81.1 3 4 15.1 37.0 62.8 92.9 27.5 67.0. 11.9 62.7 19.8 83.8 4 6 4517. 1 4639. 4764.9 4895. 1 5029.8 5169. 4 5314. 4 5465.2 5622. 4 5786. 6 5 6 19.1 41.1 67.1 97.3 32.1 71.8 16.9 67.8 25.1 89.4 6 7 21.1 43.2 69.2 99.5 34.3 74.2 19.3 70.4 27.8 92.2 7 8 23.1 45.2 71.3 4901. 7 36.6 76.5 21.8 72.9 30.5 95.1 8 9 25.1 47.3 73.5 03.9 38.9 78.9 24.3 75.5 33.2 97.9 9 10 4527. 1 4649.4 4775. 6 4906.1 5041.2 5181.3 5326. 7 5477.1 5636.9 5800.7 10 11 29.1 51.5 77.8 08.3 43.5 83.7 29.2 80.7 38.5 03.5 11 12 31.1 53.5 79.9 10.5 45.8 86.0 31.7 83.2 41.2 06.3 12 13 33.1 55.6 82.0 12.8 48.1 88.4 34.2 85.8 43.9 09.1 13 14 35.1 57.7 84.2 15.0 50.4 90.8 36.6 88.4 46.6 11.9 14 15 4537. 1 4659.7 4786. 3 4917. 2 5052.7 5193. 2 5339. 1 5491.0 5649.3 5814. 7 16 16 39.2 61.8 88.5 19.4 55.0 95.6 41.6 93.6 52.0 17.6 16 17 41.2 63.9 90.6 21.6 57.3 98.0 44.1 96.2 54.7 20.4 17 18 43.2 66.0 92.8 23.9 59.6 5200.4 46.6 98.7 57.4 23.2 18 19 20 45.2 68.1 94.9 26.1 61.9 02.7 49.1 5501.3 60.1 26.0 19 20 4547.2 4670. 1 4797. 1 4928. 3 5064.2 5205.1 5351.5 5503. 9 5662. 8 5828. 9 21 49.2 72.2 99.2 30.5 66.5 07.5 54.0 06.5 65.5 31.7 21 22 51.3 74.3 4801. 4 32.8 68.8 09.9 56.5 09.1 68.2 34.5 22 23 53.3 76.4 03.5 35.0 71.1 12.3 59.0 11.7 70.9 37.4 23 24 55.3 78.5 05.7 37.2 73.4 14.7 61.5 14.3 73.7 5676. 4 40.2 24 25 4557.3 4680. 6 4807. 8 4939. 4 5075.7 5217. 1 5364.0 5516.9 5843. 25 26 59.3 82.6 10.0 41.7 78.1 19.5 66.5 19.5 79.1 46.9 26 27 61.4 84.7 12.1 43.9 80.4 21.9 69.0 22.1 81.8 48.7 27 28 63.4 86.8 14.3 46.1 82.7 24.3 71.5 24.7 84.5 51.6 28 29 65.4 88.9 16.5 48.4 85.0 26.7 74.0 27.3 87.3 54.4 29 30 4567. 4 4691. 4818. 6 4950.6 5087. 3 5229.1 5376. 5 5529. 9 5690.0 5857.3 30 31 69.5 93.1 20.8 52.9 89.6 -31.6 79.0 32.5 92.7 60.1 31 32 71.5 95.2 23.0 55.1 92.0 34.0 81.5 36.2 95.4 63.0 32 33 73.5 97.3 25.1 57.3 94.3 36.4 84.0 37.8 98.2 65.9 33 34 75.6 99.4 27.3 59.6 96.6 38.8 86.5 40.4 5700.9 5703. 6 68.7 34 35 4577.6 4701. 5 4829.5 4961.8 5098.9 5241. 2 5389. 1 5543. 6871. 6 36 36 79.6 03.6 31.6 64.1 5101.3 43.6 91.6 45.6 06.4 74.4 36 37 81.7 05.7 33.8 66.3 03.6 46.0 94.1 48.3 09.1 77.3 37 38 83.7 07.8 36.0 68.6 05.9 48.5 96.6 50.9 11.9 80.2 38 39 85.7 09.9 38.1 70.8 08.3 50.9 99.1 53.5 14.6 83.1 39 40 4587. 8 4712. 4840.3 4973. 1 5110. 6 5253. 3 5401. 6 5556.1 5717. 3 6885.9 40 41 89.8 14.1 42.5 75.3 12.9 55.7 04.2 58.8 20.1 88.8 41 42 91.8 16.2 44.7 77.6 15.3 58.2 06.7 61.4 22.8 91.7 42 43 93.9 18.3 46.8 79.8 17.6 60.6 09.2 64.0 25.6 94.6 43 44 95.9 20.4 49.0 82.1 19.9 63.0 11.8 66.7 28.3 97.4 44 45 4598. 4722. 5 4851.2 4984.3 5122. 3 5265.4 5414.3 5569. 3 5731. 1 5900.3 45 46 4600.0 24.6 53.4 86.6 24.6 67.9 16.8 71.9 33.9 03.2 46 47 02.1 26.7 55.6 88.9 27.0 70.3 19.3 74.6 36.6 06.1 47 48 04.1 28.9 57.8 91.1 29.3 72.8 21.9 77.2 39.4 09.0 48 49 06.1 31.0 59.9 4862. 1 93.4 31.7 75.2 5277. 6 24.4 79.9 42.1 11.9 49 50 4608. 2 4733. 1 4995. 6 5134. 5427.0 5582. 5 5744.9 5914. 8 60 51 10.2 35.2 64.3 97.9 36.4 80.1 29.5 85.2 47.7 17.7 61 52 12.3 37.3 66.5 5000.2 38.7 82.5 32.0 87.8 50.4 20.6 62 53 14.3 39.4 68.7 02.4 41.1 85.0 34.6 90.5 53.2 23.5 63 54 16.4 41.6 70.9 04.7 43.4 87.4 37.1 93.1 56.0 26.4 54 55 4618. 5 4743. 7 4873. 1 5007.0 5145. 8 5289. 8 5439. 7 5595. 8 5758. 8 5929. 3 56 56 20.5 45.8 75.3 09.3 48.1 92.3 42.2 98.4 61.5 32,2 66 57 22.6 47.9 77.5 11.5 50.5 94.7 44.8 5601. 1 64.3 36.1 67 58 24.6 50.0 79.7 13.8 52.8 97.2 47.3 03.8 67.1 38.1 58 59 26.7 52.2 81.9 16.1 55.2 99.7 49.9 06.4 69.9 41.0 59 M. 60° 61° 62° 68» 64° 65° 66° 67° 68° 69° M. Page 628] TABLE 3. Meridional Parts, or Increased Latitudes. Comp. 1 293.465 M. 70° 71" 72° 78° 74° 75° 78° 77° 78° 7»° M. 5943. 9 6123. 5 6312.5 6512.0 6723. 2 6947. 7 7187. 3 7444.4 7721. 6 8022. 7 1 46.8 26.6 15.8 15.4 26.8 51.6 91.5 48.8 26.4 27.9 1 2 49.7 29.7 19.0 18.9 30.5 55.4 95.6 53.3 31.3 33.2 2 3 52.7 32.8 22.3 22.3 34.1 59.3 99.7 57.7 36.1 38.5 3 4 55.6 35.8 25.5 25.7 37.7 63.2 7203. 9 62.2 40.9 43.7 4 5 5958. 5 6138. 9 6328. 8 6529.1 6741. 4 6967. 1 7208. 7466. 7 7745.8 8049.0 5 6 61.5 42.0 32.0 32.6 45.0 70.9 12.2 71.1 50.6 54.3 6 7 64.4 45.1 35.3 36.0 48.7 74.8 16.4 75.6 55.5 59.6 7 8 67.3 48.2 38.5 39.5 52.3 78.7 20.5 80.1 60.3 64.9 8 9 70.3 51.3 41.8 42.9 56.0 82.6 24.7 84.6 65.2 70.2 9 10 10 5973. 2 6154. 4 6345.0 6546.4 6759. 7 6986.5 7228. 9 7489. 1 7770. 1 8075. 5 11 76.2 57.5 48.3 49.8 63.3 90.4 33.1 93.6 74.9 80.8 11 12 79.1 60.6 51.6 53.3 67.0 94.3 37.3 98.1 79.8 86.1 12 13 82.1 63.7 54.8 56.7 70.7 98.3 41.5 7502.6 84.7 91.5 13 14 85.0 66.8 58.1 60.2 74.3 7002.2 45.7 07.1 89.6 96.8 14 15 5988. 6169. 9 6361. 4 6563.7 6778. 7006. 1 7249. 9 7511. 7 7794. 5 8102. 2 15 16 90.9 73.0 64.7 67.1 81.7 10.0 54.1 16.2 99.4 07.5 16 17 93.9 76.1 67.9 70.6 85.4 14.0 58.3 20.7 7804. 3 12.9 17 18 96.9 79.2 71.2 74.1 89.1 17.9 62.5 25.3 09.3 18.3 18 19 99.8 82.3 74.5 77.6 92.8 21.8 66.7 29.8 14.2 23.7 19 20 6002.8 6185. 5 6377. 8 6581. 6796. 5 7025. 8 7270. 9 7534. 4 7819. 1 8129.1 20 21 05.8 88.6 81.1 84.5 6800.2 29.7 75.2 38.9 24.1 34.5 21 22 08.7 91.7 84.4 88.0 03.9 33.7 79.4 43.5 29.0 39.9 22 23 11.7 94.8 87.7 91.5 07.6 37.7 83.7 48.1 34.0 45.3 23 24 14.7 98.0 91.0 95.0 11.3 41.6 87.9 52.7 39.0 50.8 24 25 6017.7 6201.1 6394. 3 6598.5 6815. 7045.6 7292.2 7557. 3 7844. 8156. 2 25 26 20.7 04.2 97.6 6602. 18.8 49.6 96.4 61.8 48.9 61.6 26 27 23.6 07.4 6400.9 05.5 22.5 53.5 7300.7 66.4 53.9 67.1 27 28 26.6 10.5 04.3 09.0 26.2 57.5 05.0 71.0 58.9 72.6 28 29 29.6 13.7 07.6 12.5 30.0 61.5 09.2 75.7 63.9 78.0 29 30 80 6032. 6 6216. 8 6410.9 6616.1 6833. 7 7065.5 7313. 5 7580. 3 7868. 9 8183. 5 31 35.6 20.0 14.2 19.6 37.4 69.5 17.8 84.9 74.0 89.0 31 32 38.6 23.1 17.6 23.1 41.2 73.5 22.1 89.5 79.0 94.5 32 33 41.6 26.3 20.9 26.6 44.9 77.5 26.4 94.2 84.0 8200.0 33 34 35 44.6 29.4 24.2 30.2 48.7 81.5 30.7 98.8 89.1 05.5 34 6047.6 6232. 6 6427.6 6633. 7 6852.4 7085. 5 7335.0 7603. 4 7894. 1 8211. 1 35 36 50.6 35.8 30.9 37.2 56.2 89.5 39.3 08.1 99.2 16.6 36 37 53.6 38.9 34.2 40.8 60.0 93.5 43.6 12.8 7904.2 22.1 37 38 56.6 42.1 37.6 44.3 63.7 97.6 47.9 17.4 09.3 27.7 38 39 59.7 45.3 40.9 47.9 67.5 7101.6 52.3 22.1 14.4 33.3 39 40 6062.7 6248. 4 6444.3 6651.4 6871. 3 7105. 6 7356. 6 7626. 8 7919. 4 8238. 8 40 41 65.7 51.6 47.6 55.0 75.1 09.7 60.9 31.4 24.5 44.4 41 42 68.7 54.8 51.0 58.5 78.9 13.7 65.3 36.1 29.6 50.0 42 43 71.7 58.0 54.4 62.1 82.6 17.8 69.6 40.8 34.7 55.6 43 44 74.8 61.2 57.7 65.7 86.4 21.8 74.0 45.5 39.9 61.2 44 45 6077. 8 6264. 4 6461.1 6669.2 6890. 2 7125. 9 7378. 3 7650. 2 7945. 8266. 8 45 46 80.8 67.6 64.5 72.8 94.0 29.9 82.7 55.0 50.1 72.4 46 47 83.9 70.8 67.8 76.4 97.8 34.0 87.1 59.7 55.2 78.1 47 48 86.9 74.0 71.2 80.0 6901.7 38.1 91.4 64.4 60.4 83.7 48 49 89.9 77.2 74.6 83.5 05.5 42.2 95.8 69.1 65.5 89.3 49 50 6093.0 6280.4 6478.0 6687. 1 6909. 3 7146. 2 7400. 2 7673. 9 7970. 7 8295.0 50 51 96.0 83.6 81.4 90.7 13.1 50.3 04.6 78.6 75.9 8300.7 51 52 99.1 86.8 84.8 94.3 16.9 54.4 09.0 83.4 81.0 06.4 52 53 6102. 1 90.0 88.2 97.9 20.8 58.5 13.4 88.1 86.2 12.0 53 54 05.2 93.2 91.6 6701. 5 24.6 62.6 17.8 92.9 91.4 17.7 8323. 4 54 55 6108. 2 6296. 4 6495.0 6705. 1 6928. 4 7166. 7 7422. 2 7697. 7 7996. 6 55 56 11.3 99.6 98.4 08.7 32.3 70.8 26.6 7702. 5 8001. 8 29.2 56 57 14.3 6302. 9 6501.8 12.4 36.1 75.0 31.1 07.2 07.0 34.9 57 58 17.4 06.1 05.2 16.0 40.0 79.1 35.5 12.0 12.2 40.6 58 59 20.5 09.3 08.6 19.6 43.8 83.2 39.9 16.8 17.5 46.4 59 H. 70° 71° 72° 73° 74° 76° 76° 77° 78° 79° M. TABLE 4. [Page 629 | Lenji^h of a Degree in Latitude and Longitude. Degree of Long. Degree of Lat. Lat Lat. Naut. miles. statute miles. Meters. Naut. miles. statute miles. Meters. O 60.068 69. 172 Ill 321 59.661 68.704 110 567 o 1 0.059 9.162 1 304 .661 .704 568 1 2 0.031 9.130 1 253 .662 .705 669 2 3 59. 986 9.078 1 169 .663 .706 670 3 4 9.922 9.005 1 061 .664 .708 573 4 5 59.840 68.911 110 900 59.666 68.710 110 576 6 6 9.741 8.795 715 .668 .712 580 6 7 9.622 8.660 497 .670 .715 584 7 8 9.487 8.504 245 .673 .718 589 8 9 9.333 8.326 109 959 .676 .721 596 9 10 59. 161 68.129 109 641 59.680 68.726 110 601 10 11 8.971 7.910 9 289 .684 .730 608 11 12 8.764 7.670 8 904 .687 .734 616 12 13 8.538 7.410 8 486 .692 .739 624 13 14 8.295 7.131 8 036 .697 .744 633 14 15 58.034 66.830 107 563 59. 702 68.761 110 643 16 16 7.756 6.510 7 036 .707 .757 663 16 17 7.459 6.169 6 487 .713 .764 663 17 18 7.146 5.808 5 906 .719 .771 675 18 19 6.816 5.427 5 294 .726 .778 686 19 20 56.468 65.026 104 649 59. 732 68.786 110 699 20 21 6.102 4.606 3 972 .739 .794 712 21 22 5.720 4.166 3 264 .746 .802 726 22 23 5.321 3.706 2 624 .754 .811 739 23 24 4.905 3.228 1 754 .761 .820 68.829 763 24 25 54.473 62.729 100 952 59. 769 110 768 25 26 4.024 2. 212 119 .777 .839 783 26 27 3.558 1.676 99 257 .786 .848 799 27 28 3.076 1.122 8 364 .795 .858 816 28 29 2.578 0.548 7 441 .804 .869 832 29 30 52.064 59. 956 96 488 59. 813 68.879 110 849 30 31 1.534 9.346 5 506 .822 .890 866 31 32 0.989 8.716 4 495 .831 .901 883 32 33 0.428 8.071 3 455 .841 .912 901 33 34 49.851 7.407 2 387 .851 .923 919 34 36 49. 259 56.725 91 290 59. 861 68.936 110 938 35 36 8.653 6.027 166 .871 .946 956 36 37 8.031 5.311 89 014 .881 .958 975 37 38 7.395 4.579 7 835 .891 .969 994 38 39 6.744 3.829 6 629 .902 .981 111 013 39 40 46.079 53. 063 86 396 59. 912 68.993 111 033 40 41 5.399 2.281 4 137 .923 69.006 052 41 42 4.706 1.483 2 853 .933 .018 072 42 43 4.000 0.669 1 543 .944 .030 091 43 44 3.280 49.840 208 .954 .042 111 44 ^^^^ 45 2.546 8.995 78 849 .965 .054 131 46 Page 630] TABLE 4. 1 Length of a Degree in Latitude and Longitude. Lat. Degree of Long. Degree of Lat. Lat. Naut. miles. statute miles. Meters. Naut. miles. Statute miles. Meters. o 45 42.546 48. 995 78 849 59.965 69. 054 Ill 131 o 45 46 1.801 8.136 7 466 .976 .066 151 46 47 1.041 7.261 6 058 .987 .079 170 47 48 0.268 6.372 4 628 .997 .091 190 48 49 39.484 5.469 3 174 60. 008 .103 210 49 50 88. 688 44. 552 71 698 60. 019 69. 115 111 229 50 51 7.880 3.621 200 .029 .127 249 51 52 7.060 2.676 68 680 .039 .139 268 52 53 6.229 1.719 7 140 .050 .151 287 53 54 5.386 0.749 5 578 .060 .163 306 54 55 34. 532 39. 766 63 996 60. 070 69. 175 111 325 55 56 3.668 8.771 2 395 .080 .086 343 56 57 2.794 7.764 774 .090 .197 362 57 58 1.909 6.745 59 135 .100 .209 380 58 59 1.015 5.716 7 478 .109 .220 397 59 60 30. 110 34. 674 55 802 60. 118 69. 230 111 415 60 61 29. 197 3.623 4 110 .128 .241 432 61 62 8.275 2.560 2 400 .137 .251 448 62 63 7.344 1.488 675 .145 .261 464 63 64 6.404 0.406 48 934 .154 .271 480 64 65 25. 456 29. 315 47 177 60.162 69. 281 111 496 65 66 4.501 8.215 5 407 .170 .290 511 66 67 3.538 7.106 3 622 .178 .299 525 67 68 2.567 5.988 1 823 .186 .308 539 68 69 1.590 4.862 012 .193 .316 553 69 70 20. 606 23. 729 38 188 60.200 69. 324 111 566 70 71 19. 616 2.589 6 353 .207 .332 578 71 72 8.619 1.441 4 506 .213 .340 590 72 73 7.617 0.287 2 648 .220 .347 602 73 74 6.609 19. 127 781 .225 .354 613 74 75 15. 596 17. 960 28 903 60. 231 69. 360 111 623 75 76 4.578 6.788 7 017 .236 .366 633 76 77 3.556 5.611 5 123 .241 .372 642 77 78 2.529 4.428 3 220 .246 .377 650 78 79 1.499 3.242 1 311 .250 .382 658 79 80 10.465 12. 051 19 394 60. 254 69. 386 111 665 80 81 9.428 10.857 7 472 .257 .390 671 81 82 8.388 9.659 5 545 .260 .394 677 82 83 7.345 8.458 3 612 .263 .397 682 83 84 6.300 7.255 1 675 .265 .400 687 84 85 5.253 6.049 9 735 60.268 69. 402 111 691 85 86 4.205 4.842 7 792 .269 .404 694 86 87 3.154 3.632 5 846 .270 .405 696 87 88 2.103 2.422 3 898 .271 .407 698 88 89 1.052 1.211 1 949 .272 .407 699 89 90 .272 .407 699 90 TABLE 6A. [Page 631 | Distance of an Object by Two Bearings. Difference between the course Difference between the course and first bearing, in pointa and second bearing, in points. 2/ 2li 2M iy* I 8« 8H 1 3 1.96 1.09 3i 1.57 0.94 2.19 1.31 3i 1.32 0.84 1.76 1.12 2.42 1.53 3f 1.14 0.76 1.47 0.99 1.94 1.30 2.64 1.77 4 1.00< .0. 71. 1.27 0.90 1.62 1.15 2.12 1.50 2.85 2.01 4i 0.90 0.66 1.12 0.83 1.40 1.04 1.77 1.31 2.29 1.69 3.05 2.26 ^ 0.81 0.63 1.00 0.77 1.23 0.95 1.53 1.18 1.91 1.48 2.45 1.90 3.25 2.51 4f 0.74 0.60 0.91 0.73 1.10 0.89 1.34 1.08 1.65 1.32 2.05 1.65 2.61 2.10 5 0.69 0.57 0.83 0.69 1.00 0.83 1.20 1.00 1.45 1.21 1.77 1.47 2.19 1.82 5J 0.64 0.55 0.77 0.66 0.92 0.79 1.09 0.94 1.30 1.11 1.56 1.34 1.88 1.62 5i 0.60 0.53 0.72 0.63 0.85 0.75 1.00 0.88 1.18 1.04 1.39 1.23 1.66 1.46 5f 0.57 0.52 0.68 0.61 0.79 0.72 0.93 0.84 1.08 0.98 1.26 1.14 1.48 1.34 6 0.54 0.50 0.64 0.59 0.74 0.69 0.86 0.80 1.00 0.92 1.16 1.07 1.35 1.24 6i 0.52 0.49 0.60 0.57 0,70 0.66 0.81 0.76 0.93 0.88 1.07 1.01 1.23 1.16 6J 0.50 0.47 0.58 0.55 0.67 0.64 0.77 0.73 0.88 0.84 1.00 0.96 1.14 1.09 6| 0.48 0.46 0.55 0.54 0.64 0.62 0.73 0.71 0.83 0.80 0.94 0.91 1.06 1.03 7 0.46 0.45 0.53 0.52 0.61 0.60 0.69 0.68 0.79 0.77 0.89 0.87 1.00 0.98 7i 0.45 0.44 0.51 0.51 0.59 0.58 0.67 0.66 0.75 0.74 0.84 0.83 0.94 0.93 7i 0.43 0.43 0.50 0.50 0.57 0.56 0.64 0.64 0.72 0.72 0.80 0.80 0.90 0.89 7f 0.42 0.42 0.48 0.48 0.55 0.55 0.62 0.62 0.69 0.69 0.77 0.77 0.86 0.86 8 0.41 0.41 0.47 0.47 0.53 0.53 0.60 0.60 0.67 0.67 0.74 0.74 0.82 0.82 8i 0.41 0.41 0.46 0.46 0.52 0.52 0.58 0.58 0.65 0.65 0.72 0.72 0.79 0.79 8J 0.40 0.40 0.45 0.45 0.51 0.51 0.57 0.57 0.63 0.63 0.69 0.69 0.76 0.76 81 0.39 0.39 0.45 0.44 0.50 0.50 0.56 0.55 0.61 0.61 0.68 0.67 0.74 0.73 9 0.39 0.38 0.44 0.43 0.49 0.48 0.55 0.54 0.60 0.59 0.66 0.65 0.72 0.71 9i 0.39 0.38 0.44 0.42 0.49 0.47 0.54 0.52 0.59 0.57 0.64 0.63 0.70 0.68 9i 0.38 0.37 0.43 0.41 0.48 0.46 0.53 0.51 0.58 0.56 0.63 0.61 0.69 0.66 9i 0.38 0.36 0.43 0.40 0.48 0.45 0.52 0.49 0.57 0.54 0.62 0.59 0.67 0.63 10 0.38 0.35 0.43 0.40 0.47 0.44 0.52 0.48 0.57 0.52 0.61 0.57 0.66 0.61 lOi 0.38 0.35 0.43 0.39 0.47 0.43 0.52 0.47 0.56 0.51 0.61 0.55 0.65 0.59 lOJ 0.38 0.34 0.43 0.38 0.47 0.42 0.51 0.45 0.56 0.49 0.60 0.53 0.65 0.57 lOf 0.39 0.33 0.43 0.37 0.47 0.40 0.51 0.44 0.56 0.48 0.60 0.51 0.64 0.55 11 0.39 0.32 0.43 0.36 0.47 0.39 0.61 0.43 0.56 0.46 0-60 0.50 0.64 0.53 lU 0.39 0.31 0.44 0.35 0.48 0.38 0.52 0.41 0.56 0.45 0.60 0.48 0.64 0.51 Hi 0.40 0.31 0.44 0.34 0.48 0.37 0.52 0.40 0.56 0.43 0.60 0.46 0.63 0.49 111 0.41 0.30 0.45 0.33 0.49 0.36 0.52 0.39 0.56 0.42 0.60 0.44 0.64 0.47 12 0.41 0.29 0.45 0.32 0.49 0.35 0.53 0.37 0.57 0.40 0.60 0.43 0.64 0.45 m 0.42 0.28 0.46 0.31 0.50 0.34 0.54 0.36 0.57 0.38 0.61 0.41 0.64 0.42 m 0.43 0.28 0.47 0.30 0.51 0.32 0.55 0.35 0.58 0.37 0.61 0.39 0.65 0.41 12f 0.45 0.27 0.48 0.29 0.52 0.31 0.56 0.33 0.59 0.35 0.62 0.37 0.65 0.39 13 0.46 0.26 0.50 0.28 0.53 0.30 0.57 0.32 0.60 0.33 0.63 0.35 0.66 0.37 13i 0.48 0.24 0.51 0.26 0.55 0.28 0.58 0.30 0.61 0.32 0.64 0.33 0.67 0.35 13J 0.50 0.23 0.53 0.25 0.57 0.27 0.60 0.28 0.63 0.30 0.66 0.31 0.69 0.32 131 0.52 0.22 0.55 0.24 0.59 0.25 0.62 0.26 0.65 0.28 0.68 0.29 0.70 0.30 14 0.54 0.21 0.58 0.22 0.61 0.23 0.64 0.24 0.67 0.26 0.69 0.27 0.72 0.28 / f 4-^^ p^> L ii h ,/.. Page 632] TABLE 5A. Distance of an Object by Two Bearinga. Difference between the course Difference between the course and first bearing, in points. and second bearing, in points. m 4 4K *H iK i ^v. 1 4| 3.44 2.76 5 2.76 2.30 3.62 3.01 H 2.31 1.98 2.91 2.50 3.80 3.26 5i 1.99 1.76 2.44 2.15 3.05 2.69 3.96 3.49 51 1.75 1.59 2.10 1.90 2.55 2.31 3.18 2.88 4.12 3.72 6 1.57 1.45 1.85 1.71 2.20 2.03 2.66 2.46 3.31 3.05 4.26 3.94 6i 1.42 1.34 1.65 1.56 1.94 1.82 2.29 2.16 2.77 2.61 3.42 3.22 4.40 4.14 6i 1.31 1.25 1.50 1.44 1.73 1.66 2.02 1.93 2.38 2.28 2.86 2.74 3.53 3.38 61 1.21 1.17 1.38 1.33 1.57 1.52 1.81 1.75 2.10 2.04 2.47 2.39 2.95 2.87 7 1.13 1.11 1.27 1.25 1.44 1.41 1.64 1.61 1.88 1.84 2.17 2.13 2.55 2.50 7i 1.06 1.05 1.19 1.17 1.33 1.32 1.50 1.49 1.70 1.69 1.94 1.92 2.24 2.22 7i 1.00 1.00 1.11 1.11 1.24 1.24 1.39 1.38 1.56 1.55 1.76 1.76 2.01 2.00 71 0.95 0.95 1.05 1.05 1.17 1.17 1.30 1.30 1.45 1.44 1.62 1.62 1.82 1.82 8 0.91 0.91 1.00 1.00 1.10 1.10 1.22 1.22 1.35 1.35 1.50 1.50 1.67 1.67 8J 0.87 0.87 0.95 0.95 1.05 1.05 1.15 1.15 1.27 1.26 1.40 1.39 1.54 1.54 8^ 0.84 0.83 0.91 0.91 1.00 1.00 1.09 1.09 1.20 1.19 1.31 1.30 1.44 1.43 81 0.81 0.80 0.88 0.87 0.96 0.95 1.04 1.03 1.14 1.12 1.24 1.22 1.35 1.34 9 0.78 0.77 0.85 0.83 0.92 0.90 1.00 0.98 1.08 1.06 1.18 1.15 1.28 1.25 9i 0.76 0.74 0.82 0.80 0.89 0.86 0.96 0.93 1.04 1.01 1.12 1.09 1.21 1.18 9i 0.74 0.71 0.80 0.77 0.86 0.83 0.93 0.89 1.00 0.96 1.08 1.03 1.16 1.11 91 0.73 0.68 0.78 0.74 0.84 0.79 0.90 0.85 0.97 0.91 1.04 0.97 1.11 1.04 10 0.71 0.66 0.77 0.71 0.82 0.76 0.88 0.81 0.94 0.87 1.00 0.92 1.07 0.99 lOi 0.70 0.63 0.75 0.68 0.80 0.72 0.86 0.77 0.91 0.82 0.97 0.88 1.03 0.93 10} 0.69 0.61 0.74 0.65 0.79 0.69 0.84 0.74 0.89 0.78 0.94 0.83 1.00 0.88 101 0.68 0.59 0.73 0.63 0.77 0.66 0.82 0.70 0.87 0.75 0.92 0.79 0.97 0.83 11 0.68 0.56 0.72 0.60 0.76 0.64 0.81 0.67 0.85 0.71 0.90 0.75 0.95 0.79 Hi 0.67 0.54 0.71 0.57 0.76 0.61 0.80 0.64 0.84 0.67 0.88 0.71 0.93 0.75 Hi 0.67 0.52 0.71 0.55 0.75 0.58 0.79 0.61 0.83 0.64 0.87 0.67 0.91 0.70 llf 0.67 0.50 0.71 0.52 0.74 0.55 0.78 0.58 0.82 0.61 0.86 0.64 0.90 0.66 12 0.67 0.48 0.71 0.50 0.74 0.52 0.78 0.55 0.81 0.57 0.85 0.60 0.88 0.63 12i 0.67 0.45 0.71 0.48 0.74 0.50 0.77 0.52 0.81 0.54 0.84 0.56 0.87 0.59 12} 0.68 0.43 0.71 0.45 0.74 0.47 0.77 0.49 0.80 0.51 0.84 0.53 0.87 0.55 12f 0.68 0.41 0.71 0.43 0.74 0.44 0.77 0.46 0.80 0.48 0.83 0.50 0.86 0.51 13 0.69 0.38 0.72 0.40 0.75 0.42 0.78 0.43 0.80 0.45 0.83 0.46 0.86 0.48 13i 0.70 0.36 0.73 0.37 0.76 0.39 0.78 0.40 0.81 0.41 0.83 0.43 0.86 0.44 13} 0.71 0.34 0.74 0.35 0.76 0.36 0.79 0.37 0.81 0.38 0.84 0.39 0.86 0.41 131 0.73 0.31 0.75 0.32 0.77 0.33 0.80 0.34 0.82 0.35 0.84 0.36 0.86 0.37 14 0.74 0.28 0.77 0.29 0.79 0.30 0.81 0.31 0.83 0.32 0.85 0.32 0.87 0.33 &y2 6K 6 eK 6J^ 6% ' 1 6} 4.52 4.33 6| 3.63 3.52 4.63 4.49 7 3.04 2.98 3.72 3.65 4.74 4.64 7i 2.62 2.59 3.11 3.08 3.80 3.76 4.83 4.77 7} 2.30 2.29 2.68 2.67 3.18 3.17 3.87 3.86 4.91 4.88 7f 2.06 2.06 2.36 2.36 2.74 2.74 3.24 3.24 3.94 3.93 4.97 4.97 8 1.87 1.87 2.11 2.11 2.41 2.41 2.79 2.79 3.30 3.30 3.99 3.99 5.03 5.03 8* 1.72 1.71 1.92 1.92 2.16 2.16 2.46 2.46 2.84 2.84 3.34 3.34 4.04 4.03 8} 1.59 1.58 1.76 1.75 1.96 1.95 2.20 2.19 2.50 2.49 2.88 2.87 3.38 3.36 81 1.48 1.46 1.63 1.61 1.80 1.78 2.00 1.98 2.24 2.21 2.53 2.51 2.91 2.88 9 1.39 1.36 1.52 1.49 1.66 1.63 1.83 1.80 2.03 1.99 2.27 2.23 2.56 2.51 9J 1.31 1.27 1.42 1.38 1.55 1.50 1.69 1.64 1.86 1.81 2.06 2.00 2.29 2.23 9} 1.25 1.19 1.35 1.29 1.46 1.39 1.58 1.51 1.72 1.65 1.89 1.81 2.08 1.99 91 1.19 1.12 1.28 1.20 1.38 1.30 1.48 1.40 1.61 1.51 1.75 1.64 1.91 1.80 10 1.14 1.05 1.22 1.13 1.31 1.21 1.40 1.30 1.51 1.39 1.62 1.50 1.77 1.63 lOi 1.10 0.99 1.17 1.06 1.25 1.13 1.33 1.20 1.42 1.29 1.53 1.38 1.65 1.49 10} 1.06 0.94 1.13 0.99 1.20 1.05 1.27 1.12 1.35 1.19 1.44 1.27 1.55 1.36 lOf 1.03 0.88 1.09 0.93 1.15 0.99 1.22 1.04 1.29 1.11 1.37 1.18 1.46 1.25 11 1.00 0.83 1.05 0.88 1.11 0.92 1.17 0.97 1.24 1.03 1.31 1.09 1.39 1.15 lU 0.98 0.78 1.03 0.82 1.08 0.87 1.13 0.91 1.19 0.96 1.25 1.01 1.32 1.06 11} 0.95 0.73 1.00 0.77 1.05 0.81 1.10 0.85 1.15 0.89 1.21 0.93 1.27 0.98 111 0.94 0.69 0.98 0.72 1.02 0.76 1.07 0.79 1.12 0.83 1.17 0.86 1.22 0.90 12 0.92 0.65 0.96 0.68 1.00 0.71 1.04 0.73 1.09 0.77 1.13 0.80 1.18 0.83 12i 0.91 0.61 0.94 0.63 0.98 0.66 1.02 0.68 1.06 0.71 1.10 0.74 1.14 0.77 12} 0.90 0.57 0.93 0.59 0.97 0.61 1.00 0.63 1.04 0.66 1.07 0.68 1.11 0.71 12| 0.89 0.53 0.92 0.55 0.95 0.57 0.98 0.59 1.02 0.61 1.05 0.63 1.08 0.65 13 0.89 0.49 0.91 0.51 0.94 0.52 0.97 0.54 1.00 0.56 1.03 0.57 1.06 0.59 13J 0.88 0.45 0.91 0.47 0.93 0.48 0.96 0.49 0.99 0.51 1.01 0.52 1.04 0.54 13} 0.88 0.42 0.91 0.43 0.93 0.44 0.95 0.45 0.98 0.46 1.00 0.47 1.02 0.48 13i 0.88 0.38 0.90 0.39 0.92 0.40 0.95 0.41 0.97 0.41 0.99 0.42 1.01 0.43 14 0.89 0.34 0.91 0.35 0.92 0.35 0.94 0.36 0.90 0.37 0.98 0.38 1.00 0.38 TABLE 5A. [Page 633 Distance of an Object by Tyro Bearings. Difference between Difference between the course and first bearing, in points. the course and second bearing, in points. 75i 7H m 8 8K 8J4 8K 9 Si 5.07 5.06 H 4.07 4.05 5.10 5.08 8| 3.41 3.37 4.10 4.06 5.12 5.06 9 2.94 2.88 3.43 3.36 4.11 4.03 5.13 5.03 9k 2.58 2.51 2.95 2.87 3.44 3.34 4.12 3.39 5.12 4.97 9J 2.31 2.21 2.60 2.49 2.96 2.84 3.44 3.30 4.11 3.93 5.10 4.88 9J 2.10 1.98 2.33 2.19 2.61 2.46 2.97 2.79 3.44 3.24 4.10 3.86 5.07 4.77 10 1.92 1.78 2.11 1.95 2.34 2.16 2.61 2.41 2.96 2.74 3.43 3.17 4.07 3.76 5.03 4.64 lOJ 1.78 1.61 1.93 1.75 2.12 1.92 2.34 2.11 2.61 2.36 2.95 2.67 3.41 3.08 4.04 3.65 lOJ 1.66 1.46 1.79 1.58 1,94 1.71 2.12 1.87 2.34 2.06 2.60 2.29 2.94 2.59 3.38 2.98 lOJ 1.56 1.34 1.67 1.43 1.80 1.54 1.95 1.67 2.12 1.82 2.33 2.00 2.58 2.22 2.91 2.50 11 1.47 1.22 1.57 1.30 1.68 1.39 1.80 1.50 1.94 1.62 2.11 1.76 2.31 1.92 2.56 2.13 lli 1.40 1.12 1.48 1.19 1.57 1.26 1.68 1.35 1.80 1.44 1.93 1.55 2.10 1.69 2.29 1.84 Hi 1.34 1.03 1.41 1.09 1.49 1.15 1.58 1.22 1.68 1.30 1.79 1.38 1.92 1.49 2.08 1.61 iif 1.28 0.95 1.34 1.00 1.41 1.05 1.49 1.10 1.57 1.17 1.67 1.24 1.78 1.32 1.91 1.41 12 1.23 0.87 1.29 0.91 1.35 0.95 1.41 1.00 1.49 1.05 1.57 1.11 1.66 1.17 1.77 1.25 12i 1.19 0.80 1.24 0.83 1.29 0.87 1.35 0.91 1.41 0.95 1.48 1.00 1.56 1.05 1.65 1.11 12} 1.15 0.73 1.20 0.76 1.24 0.79 1.29 0.82 1.35 0.86 1.41 0.89 1.47 0.93 1.55 0.98 12f 1.12 0.67 1.16 0.69 1.20 0.72 1.25 0.74 1.29 0.77 1.34 0.80 1.40 0.83 1.46 0.87 13 1.09 0.61 1.13 0.63 1.16 0.65 1.20 0.67 1.24 0.69 1.29 0.72 1.34 0.74 1.39 0.77 13i 1.07 0.55 1.10 0.57 1.13 0.58 1.17 0.60 1.20 0.62 1.24 0.64 1.28 0.66 1.32 0.68 13i 1.05 0.50 1.08 0.51 1.10 0.52 1.13 0.53 1.16 0.55 1.20 0.56 1.23 0.58 1.27 0.60 13i 1.03 0.44 1.06 0.45 1.08 0.46 1.11 0.47 1.13 0.48 1.16 0.50 1.19 0.51 1.22 0.52 14 1.02 0.39 1.04 0.40 1.06 0.41 1.08 0.41 1.10 0.42 1.13 0.43 1.15 0.44 1.18 0.45 9y* »J^ »K 10 105i lOM lOK " 1 10} 4.97 4.50 lOi 3.99 3.52 4.91 4.33 lOJ 3.34 2.87 3.94 3.38 4.83 4.14 11 2.88 2.39 3.30 2.74 3.87 3.22 4.74 3.94 lU 2.53 2.04 2.84 2.28 3.24 2.61 3.80 3.05 4.63 3.72 in 2.27 1.75 2.50 1.93 2.79 2.16 3.18 2.46 3.72 2.88 4.52 3.49 111 2.06 1.52 2.24 1.66 2.46 1.82 2.74 2.03 3.11 2.31 3.63 2.69 4.40 3.20 12 1.89 1.33 2.03 1.44 2.20 1.56 2.41 1.71 2.68 1.90 3.04 2.15 3.53 2.50 4.26 3.01 m 1.75 1.18 1.86 1.25 2.00 1.34 2.16 1.45 2.36 1.59 2.62 1.76 2.95 1.98 3.42 2.30 12i 1.62 1.03 1.72 1.09 1.83 1.16 1.96 1.24 2.11 1.34 2.30 1.46 2.55 1.62 2.86 1.82 12f 1.53 0.91 1.61 0.96 1.69 1.01 1.80 1.07 1.92 1.14 2.06 1.23 2.24 1.34 2.47 1.47 13 1.44 0.80 1.51 0.84 1.58 0.88 1.66 0.92 1.76 0.98 1.87 1.04 2.01 1.11 2.17 1.21 13} 1.37 0.71 1.42 0.73 1.48 0.76 1.55 0.80 1.63 0.84 1.72 0.88 1.82 0.94 1.94 1.00 13J 1.31 0.62 1.35 0.64 1.40 0.66 1.46 0.69 1.52 0.72 1.59 0.75 1.67 0.79 1.76 0.83 131 1.25 0.54 1.29 0.55 1.33 0.57 1.38 0.59 1.42 0.61 1.48 0.63 1.54 0.66 1.62 0.69 14 1.21 0.46 1.24 0.47 1.27 0.49 1.31 0.50 1.35 0.52 1.39 0.53 1.44 0.55 1.50 0.57 llJi n^A nK 1 " 1 125< 1 12J^ 1 12)i 1 n 1 12} 4.12 2.77 12i 3.31 2.10 3.96 2.51 12| 2.77 1.65 3.18 1.90 3.80 2.26 13 2.38 1.32 2.66 1.48 3.05 1.69 3.62 2.01 13} 2.10 1.08 2.29 1.18 2.55 1.31 2.91 1.50 3.44 1.77 13J 1.88 0.89 2.02 0.95 2.20 1.04 2.44 1.15 2.76 1.30 3.25 1.53 13| 1.70 0.73 1.81 0.77 1.94 0.83 2.10 0.90 2.31 0.99 2.61 1.12 3.05 1.31 14 1.56 0.60 1.64 0.63 1.73 0.66 1.85 0.71 1.99 0.76 2.19 0.84 2.45 0.94 2.85 1.09 Page 634] TABLE 5B. Distance of an Object by Two Bearings. Difference between the course and second bearing. Difierence between the course and first bearing. 20° 22° 24° 26° 28° 30° 82° 1 30° 1.97 0.98 32 1.64 0.87 2.16 1.14 34 1.41 0.79 1.80 1.01 2.34 1.31 36 1.24 0.73 1.55 0.91 1.96 1.15 2.52 1.48 38 1.11 0.68 1.36 0.84 1.68 1.04 2.11 1.30 2.70 1.66 40 1.00 0.64 1.21 0.78 1.48 0.95 1.81 1.16 2.26 1.45 2.88 1.85 42 0.91 0.61 1.10 0.73 1.32 0.88 1.59 1.06 1.94 1.30 2.40 1.61 3.05 2.04 44 0.84 0.58 1.00 0.69 1.19 0.83 1.42 0.98 1.70 1.18 2.07 1.44 2.55 1.77 46 0.78 0.56 0.92 0.66 1.09 0.78 1.28 0.92 1.52 1.09 1.81 1.30 2.19 1.58 48 0.73 0.54 0.85 0.64 1.00 0.74 1.17 0.87 1.37 1.02 1.62 1.20 1.92 1.43 50 0.68 0.52 0.80 0.61 0.93 0.71 1.08 0.83 1.25 0.96 1.46 1.12 1.71 1.31 52 0.65 0.51 0.75 0.59 0.87 0.68 1.00 0.79 1.15 0.91 1.33 1.05 1.55 1.22 54 0.61 0.49 0.71 0.57 0.81 0.66 0.93 0.76 1.07 0.87 1.23 0.99 1.41 1.14 56 0.58 0.48 0.67 0.56 0.77 0.64 0.88 0.73 1.00 0.83 1.14 0.95 1.30 1.08 58 0.56 0.47 0.64 0.54 0.73 0.62 0.83 0.70 0.94 0.80 1.07 0.90 1.21 1.03 60 0.53 0.46 0.61 0.53 0.69 0.60 0.78 0.68 0.89 0.77 1.00 0.87 1.13 0.98 62 0.51 0.45 0.58 0.51 0.66 0.58 0.75 0.66 0.84 0.74 0.94 0.83 1.06 0.94 64 0.49 0.44 0.56 0.50 0.63 C.57 0.71 0.64 0.80 0.72 0.89 0.80 1.00 0.90 66 0.48 0.43 0.54 0.49 0.61 0.56 0.68 0.62 0.76 0.70 0.85 0.78 0.95 0.87 68 0.46 0.43 0.52 0.48 0.59 0.54 0.66 0.61 0.73 0.68 0.81 0.75 0.90 0.84 70 0.45 0.42 0.50 0.47 0.57 0.53 0.63 0.59 0.70 0.66 0.78 0.73 0.86 0.81 72 0.43 0.41 0.49 0.47 0.55 0.52 0.61 0.58 0.68 0.64 0.75 0.71 0.82 0.78 . 74 0.42 0.41 0.48 0.46 0.53 0.51 0.59 0.57 0.65 0.63 0.72 0.69 0.79 0.76 76 0.41 0.40 0.46 0.45 0.52 0.50 0.57 0.56 0.63 0.61 0.70 0.67 0.76 0.74 78 0.40 0.39 0.45 0.44 0.50 0.49 0.56 0.54 0.61 0.00 0.67 0.66 0.74 0,72 80 0.39 0.39 0.44 0.44 0.49 0.48 0.54 0.53 0.60 0.59 0.65 0.64 0.71 0.70 82 0.39 0.38 0.43 0.43 0.48 0.47 0.53 0.52 0.58 0.57 0.63 0.63 0.69 0.69 84 0.38 0.38 0.42 0.42 0.47 0.47 0.52 0.51 0.57 0.56 0.62 0.61 0.67 0.67 86 0.37 0.37 0.42 0.42 0.46 0.46 0.51 0.51 0.55 0.55 0.60 0.60 0.66 0.65 88 0.37 0.37 0.41 0.41 0.45 0.45 0.50 0.50 0.54 0.54 0.59 0.59 0.64 0.64 90 0.36 0.36 0.40 0.40 0.45 0.45 0.49 0.49 0.53 0.53 0.58 0.58 0.62 0.62 92 0.36 0.36 0.40 0.40 0.44 0.44 0.48 0.48 0.52 0.52 0.57 0.57 0.61 0.61 94 0.36 0.35 0.39 0.39 0.43 0.43 0.47 0.47 0.51 0.51 0.56 0.55 0.60 0.60 96 0.35 0.35 0.39 0.39 0.43 0.43 0.47 0.46 0.51 0.50 0.55 0.54 0.59 0.59 98 0.35 0.35 0.39 0.38 0.42 0.42 0.46 0.46 0.50 0.50 0.54 0.53 0.58 0.57 100 0.35 0.34 0.38 0.38 0.42 0.41 0.46 0.45 0.49 0.49 0.53 0.52 0.57 0.56 102 0.35 0.34 0.38 0.37 0.42 0.41 0.45 0.44 0.49 0.48 0.53 0.51 0.56 0.55 104 0.34 0.33 0.38 0.37 0.41 0.40 0.45 0.43 0.48 0.47 0.52 0.50 0.56 0.54 106 0.34 0.33 0.38 0.36 0.41 0.39 0.45 0.43 0.48 0.46 0.52 0.50 0.55 0.53 108 0.34 0.32 0.38 0.36 0.41 0.39 0.44 0.42 0.48 0.45 0.51 0.49 0.55 0.52 110 0.34 0.32 0.37 0.35 0.41 0.38 0.44 0.41 0.47 0.44 0.51 0.48 0.54 0.51 112 0.34 0.32 0.37 0.35 0.41 0.38 0.44 0.41 0.47 0.44 0.50 0.47 0.54 0.50 114 0.34 0.31 0.37 0.34 0.41 0.37 0.44 0.40 0.47 0.43 0.50 0.46 0.54 0.49 116 0.34 0.31 0.38 0.34 0.41 0.37 0.44 0.39 0.47 0.42 0.50 0.45 0.53 0.48 118 0.35 0.31 0.38 0.33 0.41 0.36 0.44 0.39 0.47 0.41 0.50 0.44 0.53 0.47 120 0.35 0.30 0.38 0.33 0.41 0.36 0.44 0.38 0.47 0.41 0.50 0.43 0.53 0,46 122 0.35 0.30 0.38 0.32 0.41 0.35 0.44 0.37 0.47 0.40 0.50 0.42 0.53 0.45 124 0.35 0.29 0.38 0.32 0.41 0.34 0.44 0.37 0.47 0.39 0.50 0.42 0.53 0.44 126 0.36 0.29 0.39 0.31 0.42 0.34 0.45 0.36 0.47 0.38 0.50 0.41 0.53 0.43 128 0.36 0.28 0.39 0.31 0.42 0.33 0.45 0.35 0.48 0.38 0.50 0.40 0.53 0.42 130 0.36 0.28 0.39 0.30 0.42 0.32 0.45 0.35 0.48 0.37 0.51 0.39 0.54 0.41 132 0.37 0.27 0.40 0.30 0.43 0.32 0.46 0.34 0.48 0.36 0.51 0.38 0,54 0.40 134 0.37 0.27 0.40 0.29 0.43 0.31 0.46 0.33 0.49 0.35 0.52 0.37 0.54 0.39 136 0.38 0.26 0.41 0.28 0.44 0.30 0.47 0.32 0.49 0.34 0.52 0.36 0.55 0.38 138 0.39 0.26 0.42 0.28 0.45 0.30 0.47 0.32 0.50 0.33 0.53 0.36 0.55 0,37 140 0.39 0.25 0.42 0.27 0.45 0.29 0.48 0.31 0.51 0.33 0.53 0.34 0.56 0,36 142 0.40 0.25 0.43 0.27 0.46 0.28 0.49 0.30 0.51 0.32 0.54 0.33 0.56 0,35 144 0.41 0.24 0.44 0.26 0.47 0.28 0.50 0.29 0.52 0.31 0.55 0.32 0.57 0,34 146 0.42 0.24 0.45 0.25 0.48 0.27 0.51 0.28 0.53 0.30 0.56 0.31 0.58 0,32 148 0.43 23 0.46 0.25 0.49 0.26 0.52 0.27 0.54 0.29 0.57 0.30 0.59 0.31 150 0.45 0.22 0.48 0.24 0.50 0.25 0.53 0.26 0.55 0.28 0.58 0.29 0.60 0.30 152 0.46 0.22 0.49 0.23 0.52 0.24 0.54 0.25 0.57 0.27 0.59 0.28 0.61 0.29 154 0.48 0.21 0.50 0.22 0.53 0.23 0.56 0.24 0.58 0.25 0.60 26 0.62 0.27 156 0.49 0.20 0.52 0.21 0.55 0.22 0.57 0.23 0.60 0.24 0.62 25 0.64 0.26 158 0.51 0.19 0.54 0.20 0.57 0.21 0.59 0.22 0.61 0.23 0.63 0.24 0.66 0.25 160 0.53 0.18 0.56 0.19 0.59 0.20 0.61 0.21 0.63 0.22 0,65 0.22 0.67 0.23 TABLE 5B. [Page 635 Difference Distance of an Object by Two Bearings. Difference between the course and first bearing. between the course 1 1 md second bearing. 84° 36° 88° 40° 48° 1 44° 46° 1 44° 3.22 2.24 46 2.69 1.93 3.39 2.43 48 2.31 1.72 2.83 2.10 3.55 2.63 50 2.03 1.55 2.43 1.86 2.96 2.27 3.70 2.84 52 1.81 1.43 2.13 1.68 2.54 2.01 3.09 2.44 3.85 3.04 54 1.63 1.32 1.90 1.54 2.23 1.81 2.66 2.15 3.22 2.60 4.00 3.24 56 1.49 1.24 1.72 1.42 1.99 1.65 2.33 1.93 2.77 2.29 3.34 2.77 4.14 3.43 58 1.37 1.17 1.57 1.33 1.80 1.53 2.08 1.76 2.43 2.06 2.87 2.44 3.46 2.93 60 1.28 1.10 1.45 1.25 1.64 1.42 1.88 1.63 2.17 1.88 2.52 2.18 2.97 2.57 62 1.19 1.05 1.34 1.18 1.51 1.34 1.72 1.52 1.96 1.73 2.25 1.98 2.61 2.30 64 1.12 1.01 1.25 1.13 1.40 1.26 1.58 1.42 1.79 1.61 2.03 1.83 2.33 2.09 66 1.06 0.96 1.18 1.07 1.31 1.20 1.47 1.34 1.65 1.51 1.85 1.69 2.10 1.92 68 1.00 0.93 1.11 1.03 1.23 1.14 1.37 1.27 1.53 1.42 1.71 1.58 1.92 1.78 70 0.95 0.89 1.05 0.99 1.16 1.09 1.29 1.21 1.43 1..34 1.58 1.49 1.77 1.66 72 0.91 0.86 1.00 0.95 1.10 1.05 1.21 1.15 1.34 1.27 1.48 1.41 1.64 1.56 74 0.87 0.84 0.95 0.92 1.05 1.01 1.15 1.10 1.26 1.21 1.39 1.34 1.53 1.47 76 0.84 0.81 0.91 0.89 1.00 0.97 1.09 1.06 1.20 1.16 1.31 1.27 1.44 1.40 78 0.80 0.79 0.88 0.86 0.96 0.94 1.04 1.02 1.14 1.11 1.24 1.22 1.36 1.33 80 0.78 0.77 0.85 0.83 0.92 0.91 1.00 0.98 1.09 1.07 1.18 1.16 1.28 1.27 82 0.75 0.75 0.82 0.81 0.89 0.88 0.96 0.95 1.04 1.03 1.13 1.12 1.22 1.21 84 0.73 0.73 0.79 0.79 0.86 0.85 0.93 0.92 1.00 0.99 1.08 1.07 1.17 1.16 86 0.71 0.71 0.77 0.77 0.83 0.83 0.89 0.89 0.96 0.96 1.04 1.04 1.12 1.12 88 0.69 0.69 0.75 0.75 0.80 0.80 0.86 0.86 0.93 0.93 1.00 1.00 1.08 1.07 90 0.67 0.67 0.73 0.73 0.78 0.78 0.84 0.84 0.90 0.90 0.97 0.97 1.04 1.04 92 0.66 0.66 0.71 0.71 0.76 0.76 0.82 0.82 0.67 0.87 0.93 0.93 1.00 1.00 94 0.65 0.64 0.69 0.69 0.74 0.74 0.79 0.79 0.85 0.85 0.91 0.90 0.97 0.97 96 0.63 0.63 0.68 0.67 0.73 0.72 0.78 0.77 0.83 0.82 0.88 0.88 0.94 0.93 98 0.62 0.62 0.67 0.66 0.71 0.70 0.76 0.75 0.81 0.80 0.86 0.85 0.91 0.90 100 0.61 0.60 0.65 0.64 0.70 0.69 0.74 0.73 0.79 0.78 0.84 0.83 0.89 0.88 102 0.60 0.59 0.64 0.63 0.68 0.67 0.73 0.71 0.77 0.76 0.82 0.80 0.87 0.85 104 0.60 0.58 0.63 0.61 0.67 0.65 0.72 0.69 0.76 0.74 0.80 0.78 0.85 0.82 106 0.59 0.57 0.63 0.60 0.66 0.64 0.70 0.68 0.74 0.72 0.79 0.76 0.83 0.80 108 0.58 0.55 0.62 0.59 0.66 0.62 0.69 0.66 0.73 0.70 0.77 0.74 0.81 0.77 110 0.58 0.54 0.61 0.57 0.65 0.61 0.68 0.64 0.72 0.68 0.76 0.71 0.80 0.75 112 0.57 0.53 0.61 0.56 0.64 0.59 0.68 0.63 0.71 0.66 0.75 0.69 0.79 0.73 114 0.57 0.52 0.60 0.55 0.63 0.58 0.67 0.61 0.70 0.64 0.74 0.68 0.78 0.71 116 0.56 0.51 0.60 0.54 0.63 0.57 0.66 0.60 0.70 0.63 0.73 0.66 0.77 0.69 118 0.56 0.50 0.59 0.52 0.63 0.55 0.66 0.58 0.69 0.61 0.72 0.64 0.76 0.67 120 0.56 0.49 0.59 0.51 0.62 0.54 0.65 0.57 0.68 0.59 0.72 0.62 0.75 0.65 122 0.56 0.47 0.59 0.50 0.62 0.53 0.65 0.55 0.68 0.58 0.71 0.60 0.74 0.63 124 0.56 0.46 0.59 0.49 0.62 0.51 0.65 0.54 0.68 0.56 0.71 0.58 0.74 0.61 126 0.56 0.45 0.59 0.48 0.62 0.50 0.64 0.52 0.67 0.54 0.70 0.57 0.73 0.59 128 0.56 0.44 0.59 0.46 0.62 0.49 0.64 0.51 0.67 0.53 0.70 0.55 0.73 0.57 130 0.56 0.43 0.59 0.45 0.62 0.47 0.64 0.49 0.67 0.51 0.70 0.53 0.72 0.55 132 0.56 0.42 0.59 0.44 0.62 0.46 0.64 0.48 0.67 0.50 0.70 0.52 0.72 0.54 134 0.57 0.41 0.59 0.43 0.62 0.45 0.64 0.46 0.67 0.48 0.69 0.50 0.72 0.52 136 0.57 0.40 0.60 0.41 0.62 0.43 0.65 0.45 0.67 0.47 0.70 0.48 0.72 0.50 138 0.58 0.39 0.60 0.40 0.63 0.42 0.65 0.43 0.67 0.45 0.70 0.47 0.72 0.48 140 0.58 0.37 0.61 0.39 0.63 0.40 0.65 0.42 0.68 0.43 0.70 0.45 0.72 0.46 142 0.59 0.36 0.61 0.38 0.63 0.39 0.66 0.41 0.68 0.42 0.70 0.43 0.72 0.45 144 0.60 0.35 0.62 0.36 0.64 0.38 0.66 0.39 0.68 0.40 0.71 0.41 0.73 0.43 146 0.60 0.34 0.63 0.35 0.65 0.36 0.67 0.37 0.69 0.39 0.71 0.40 0.73 0.41 148 0.61 0.32 0.63 0.34 0.66 0.35 0.68 0.36 0.70 0.37 0.72 0.38 0.74 0.39 150 0.62 0.31 0.64 0.32 0.66 0.33 0.68 0.34 0.70 0.35 0.72 0.36 0.74 0.37 152 0.63 0.30 0.65 0.31 0.67 0.32 0.69 0.33 0.71 0.33 0.73 0.34 0.75 0.35 154 0.65 0.28 0.67 0.29 0.68 0.30 0.70 0.31 0.72 0.32 0.74 0.32 0.76 0.33 156 0.66 0.27 0.68 0.28 0.70 0.28 0.72 0.29 0.73 0.30 0.75 0.30 0.77 0.31 158 0.67 0.25 0.69 0.26 0.71 0.27 0.73 0. 27 0. 74 0.28 0.76 0.28 0.78 0.29 160 0.69 0.24 0.71 0.24 0.73 0.25 0.74 0. 25 0. 76 0.26 0.77 0.26 0.79 0.27 Page 636] TABLE 6B. Distance of an Object by Two Bearings. Difference between Difference between the course and first bearing. the course I and second bearing. 48° 50« 52° 64° 56° 68° 60° 68° 4.28 3.63 • 60 3.57 3.10 4.41 3.82 62 3.07 2.71 3.68 3.26 4.64 4.01 64 2.70 2.42 3.17 2.86 3.79 3.41 4.66 4.19 66 2.40 2.20 2.78 2.54 3.26 2.98 3.89 3.55 4.77 4.36 68 2.17 2.01 2.48 2.30 2.86 2.66 3.34 3.10 3.99 3.71 4.88 4.53 70 1.98 1.86 2.24 2.10 2.55 2.39 2.94 2.76 3.43 3.22 4.08 3.83 4.99 4.69 72 1.83 1.74 2.04 1.94 2.30 2.19 2.62 2.49 3.01 2.86 3.51 3.33 4.17 3.96 74 1.70 1.63 1.88 1.81 2.10 2.02 2.37 2.27 2.68 2.58 3.08 2.96 3.68 3.44 76 1.58 1.54 1.75 1.70 1.94 1.88 2.16 2.10 2.42 2.36 2.74 2.66 3.14 3.05 78 1.49 1.45 1.63 1.60 1.80 1.76 1.99 1.95 2.21 2.16 2.48 2.43 2.80 2.74 80 1.40 1.38 1.53 1.51 1.68 1.66 1.86 1.82 2.04 2.01 2.26 2.23 2.63 2.49 82 1.33 1.32 1.45 1.43 1.58 1.56 1.72 1.71 1.89 1.87 2.08 2.06 2.31 2.29 84 1.26 1.26 1.37 1.36 1.49 1.48 1.62 1.61 1.77 1.76 1.93 1.92 2.13 2.12 86 1.21 1.20 1.30 1.30 1.41 1.41 1.53 1.62 1.66 1.65 1.81 1.80 1.98 1.97 88 1.16 1.16 1.24 1.24 1.34 1.34 1.46 1.45 1.56 1.56 1.70 1.70 1.84 1.84 90 1.11 1.11 1.19 1.19 1.28 1.28 1.38 1.38 1.48 1.48 1.60 1.60 1.73 1.73 92 1.07 1.07 1.14 1.14 1.23 1.23 1.31 1.31 1.41 1.41 1.62 1.62 1.63 1.63 94 1.03 1.03 1.10 1.10 1.18 1.17 1.26 1.26 1.36 1.34 1.44 1.44 1.55 1.54 96 1.00 0.99 1.06 1.06 1.13 1.13 1.21 1.20 1.29 1.28 1.38 1.37 1.47 1.47 98 0.97 0.96 1.03 1.02 1.10 1.08 1.16 1.15 1.24 1.23 1.32 1.31 1.41 1.39 100 0.94 0.93 1.00 0.98 1.06 1.04 1.12 1.11 1.19 1.18 1.27 1.25 1.35 1.33 102 0.92 0.90 0.97 0.95 1.03 1.01 1.09 1.06 1.15 1.13 1.22 1.19 1.29 1.27 104 0.90 0.87 0.95 0.92 1.00 0.97 1.06 1.02 1.12 1.08 1.18 1.14 1.25 1.21 106 0.88 0.84 0.92 0.89 0.97 0.94 1.03 0.99 1.09 1.04 1.14 1.10 1.20 1.16 108 0.86 0.82 0.90 0.86 0.95 0.90 1.00 0.96 1.05 1.00 1.11 1.05 1.17 1.11 110 0.84 0.79 0.88 0.83 0.93 0.87 0.98 0.92 1.02 0.96 1.08 1.01 1.13 1.06 112 0.83 0.77 0.87 0.80 0.91 0.84 0.95 0.88 1.00 0.93 1.05 0.97 1.10 1.02 114 0.81 0.74 0.86 0.78 0.89 0.82 0.93 0.86 0.98 0.89 1.02 0.93 1.07 0.98 116 0.80 0.72 0.84 0.76 0.88 0.79 0.92 0.82 0.96 0.86 1.00 0.90 1.04 0.94 118 0.79 0.70 0.83 0.73 0.86 0.76 0.90 0.79 0.94 0.83 0.98 0.86 1.02 0.90 120 0.78 0.68 0.82 0.71 0.86 0.74 0.89 0.77 0.91 0.80 0.96 0.83 1.00 0.87 122 0.77 0.66 0.81 0.68 0.84 0.71 0.87 0.74 0.90 0.77 0.96 0.80 0.98 0.83 124 0.77 0.63 0.80 0.66 0.83 0.69 0.86 0.71 0.90 0.74 0.93 0.77 0.96 0.80 126 0.76 0.61 0.79 0.64 0.82 0.66 0.85 0.69 0.88 0.71 0.91 0.74 0.96 0.77 128 0.75 0.59 0.78 0.62 0.81 0.64 0.84 0.66 0.87 0.69 0.90 0.71 0.93 0.74 130 0.75 0.57 0.78 0.60 0.81 0.62 0.83 0.64 0.86 0.66 0.89 0.68 0.92 0.71 132 0.75 0.56 0.77 0.57 0.80 0.59 0.83 0.61 0.86 0.64 0.88 0.66 0.91 0.68 134 0.74 0.54 0.77 0.56 0.80 0.57 0.82 0.59 0.86 0.61 0.87 0.63 0.90 0.65 136 0.74 0.52 0.77 0.53 0.80 0.55 0.82 0.57 0.84 0.58 0.87 0.60 0.89 0.62 138 0.74 0.50 0.77 0.51 0.79 0.53 0.81 0.54 0.84 0.56 0.86 0.58 0.89 0.59 140 0.74 0.48 0.77 0.49 0.79 0.51 0.81 0.62 0.83 0.54 0.86 0.56 0.88 0.57 142 0.74 0.46 0.77 0.47 0.79 0.49 0.81 0.50 0.83 0.61 0.85 0.62 0.87 0.54 144 0.75 0.44 0.77 0.45 0.79 0.46 0.81 0.48 0.83 0.49 0.86 0.50 0.87 0.51 146 0.75 0.42 0.77 0.43 0.79 0.44 0.81 0.46 0.83 0.46 0.86 0.47 0.87 0.49 148 0.76 0.40 0.77 0.41 0.79 0.42 0.81 0.43 0.83 0.44 0.85 0.45 0.87 0.46 150 0.76 0.38 0.78 0.39 0.80 0.40 0.81 0.41 0.83 0.42 0.85 0.42 0.87 0.43 152 0.77 0.36 0.78 0.37 0.80 0.38 0.82 0.38 0.83 0.39 0.85 0.40 0.87 0.41 154 0.77 0.34 0.79 0.36 0.81 0.35 0.82 0.36 0.84 0.37 0.85 0.37 0.87 0.38 156 0.78 0.32 0.80 0.32 0.81 0.33 0.83 0.34 0.84 0..34 0.86 0.35 0.87 0.35 158 0.79 0.30 0.81 0.30 0.82 0.31 0.83 0.31 0.85 0.32 0.86 0.32 0.87 0.33 160 0.80 0.27 0.82 0.28 0.83 0.28 0.84 0.29 0.85 0.29 0.86 0.30 0.88 0.30 TABLE 5B. [Page 637 Distance of an Object by Two Bearings. Difference Difference between the course and first bearing. between the course I md second bearing. 62° 64° 66° 68° 70° 72° 740 76° 1 72° 6.08 4.84 74 4.25 4.08 5.18 4.98 76 3.&5 3.54 4.32 4.19 5.26 5.10 78 3.20 3.13 3.72 3.63 4.39 4.30 5.34 5.22 80 2.86 2.81 3.26 3.21 3.78 3.72 4.46 4.39 5.41 5.33 82 2.58 2.56 2.91 2.88 3.31 3.28 3.83 3.80 4.52 4.48 5.48 5.42 84 2.36 2.34 2.63 2.61 2.96 2.94 3.36 3.35 3.88 3.86 4.57 4.55 5.54 5.51 86 2.17 2.17 2.40 2.39 2.67 2.66 3.00 2.99 3.41 3.40 3.93 3.92 4.62 4.61 5.59 5.57 88 2.01 2.01 2.21 2.21 2.44 2.44 2.71 2.71 3.04 3.04 3.45 3.45 3.97 3.97 4.67 4.66 90 1.88 1.88 2.05 2.05 2.25 2.25 2.48 2.48 2.75 2.75 3.08 3.08 3.49 3.49 4.01 4.01 92 1.77 1.76 1.91 1.91 2.08 2.08 2.28 2.28 2.51 2.51 2.78 2.78 3.11 3.11 3.52 3.52 94 1.67 1.66 1.80 1.79 1.95 1.94 2.12 2.11 2.31 2.30 2.54 2.53 2.81 2.80 3.14 3.13 96 1.58 1.57 1.70 1.69 1.83 1.82 1.97 1.96 2.14 2.13 2.34 2.33 2.57 2.55 2.84 2.82 98 1.50 1.49 1.61 1.59 1.72 1.71 1.85 1.84 2.00 1.98 2.17 2.15 2.36 2.34 2.59 2.56 100 1.43 1.41 1.53 1.51 1.63 1.61 1.75 1.72 1.88 1.85 2.03 2.00 2.19 2.16 2.39 2.35 102 1.37 1.34 1.46 1.43 1.55 1.52 1.66 1.62 1.77 1.73 1.90 1.86 2.05 2.00 2.21 2.16 104 1.32 1.28 1.40 1.36 1.48 1.44 1.58 1.53 1.68 1,63 1.79 1.74 1.92 1.87 2.07 2.01 106 1.27 1.22 1.34 1.29 1.42 1.37 1.51 1.45 1.60 1.54 1.70 1.63 1.81 1.74 1.94 1.87 108 1.23 1.17 1.29 1.23 1.37 1.30 1.44 1.37 1.53 1.45 1.62 1.54 1.72 1.63 1.83 1.74 110 1.19 1.12 1.25 1.17 1.32 1.24 1.39 1.30 1.46 1.37 1.54 1.45 1.64 1.54 1.74 1.63 112 1.15 1.07 1.21 1.12 1.27 1.18 1.33 1.24 1.40 1.30 1.48 1.37 1.56 1.45 1.65 1.53 114 1.12 1.02 1.17 1.07 1.23 1.12 1.29 1.18 1.35 1.24 1.42 1.30 1.50 1.37 1.58 1.44 116 1.09 0.98 1.14 1.03 1.19 1.07 1.25 1.12 1.31 1.17 1.37 1.23 1.44 1.29 1.51 1.36 118 1.07 0.94 1.11 0.98 1.16 1.02 1.21 1.07 1.26 1.12 1.32 1.17 1.38 1.22 1.45 1.28 120 1.04 0.90 1.08 0.94 1.13 0.98 1.18 1.02 1.23 1.06 1.28 1.11 1.34 1.16 1.40 1.21 122 1.02 0.86 1.06 0.90 1.10 0.93 1.15 0.97 1.19 1.01 1.24 1.05 1.29 1.10 1.35 1.14 124 1.00 0.83 1.04 0.86 1.08 0.89 1.12 0.93 1.16 0.96 1.21 1.00 1.25 1.04 1.31 1.08 126 0.98 0.79 1.02 0.82 1.05 0.85 1.09 0.88 1.13 0.92 1.18 0.95 1.22 0.99 1.27 1.02 128 0.97 0.76 1.00 0.79 1.03 0.82 1.07 0.84 1.11 0.87 1.15 0.90 1.19 0.94 1.23 0.97 130 0.95 0.73 0.98 0.75 1.02 0.78 1.05 0.80 1.09 0.83 1.12 0.86 1.16 0.89 1.20 0.92 132 0.94 0.70 0.97 0.72 1.00 0.74 1.03 0.77 1.06 0.79 1.10 0.82 1.13 0.84 1.17 0.87 134 0.93 0.67 0.96 0.69 0.99 0.71 1.01 0.73 1.04 0.75 1.08 0.77 1.11 0.80 1.14 0.82 136 0.92 0.64 0.95 0.66 0.97 0.68 1.00 0.69 1.03 0.71 1.06 0.74 1.09 0.76 1.12 0.78 138 0.91 0.61 0.94 0.63 0.96 0.64 0.99 0.66 1.01 0.68 1.04 0.70 1.07 0.72 1.10 0.74 140 0.90 0.58 0.93 0.60 0.95 0.61 0.97 0.63 1.00 0.64 1.03 0.66 1.05 0.68 1.08 0.70 142 0.90 0.55 0.92 0.57 0.94 0.58 0.96 0.59 0.99 0.61 1.01 0.62 1.04 0.64 1.06 0.65 144 0.89 0.52 0.91 0.54 0.93 0.55 0.96 0.56 0.98 0.57 1.00 0.59 1.02 0.60 1.05 0.62 146 0.89 0.50 0.91 0.51 0.93 0.52 0.95 0.53 0.97 0.54 0.99 0.55 1.01 0.57 1.03 0.58 148 0.89 0.47 0.90 0.48 0.92 0.49 0.94 0.50 0.96 0.51 0.98 0.52 1.00 0.53 1.02 0.54 150 0.88 0.44 0.90 0.45 0.92 0.46 0.94 0.47 0.95 0.48 0.97 0.49 0.99 0.50 1.01 0.50 152 0.88 0.41 0.90 0.42 0.92 0.43 0.93 0.44 0.95 0.45 0.97 0.45 0.98 0.46 1.00 0.47 154 0.88 0.39 0.90 0.39 0.91 0.40 0.93 0.41 0.94 0.41 0.96 0.42 0.98 0.43 0.99 0.43 156 0.89 0.36 0.90 0.37 0.91 0.37 0.93 0.38 0.94 0.38 0.96 0.39 0.97 0.39 0.99 0.40 158 0.89 0.33 0.90 0.34 0.91 0.34 0.93 0.35 0.94 0.35 0.95 0.36 0.97 0.36 0.98 0.37 160 0.89 0.30 0.90 0.31 0.91 0.31 0.93 0.32 0.94 0.32 0.95 0.33 0.96 0.33 0.98 0.33 Page 638] TABLE 5B. Distance of an Object by Two Bearings. Difference between the course and second bearing. Difference between the course and first bearing. 78° 80° 82° 84° 86° 88° 90° 92° 1 88° 5.63 5.63 90 4.70 4.70 5.67 5.67 92 4.04 4.04 4.74 4.73 5.70 5.70 94 3.55 3.54 4.07 4.06 4.76 4.75 5.73 5.71 96 3.17 3.15 3.57 3.55 4.09 4.07 4.78 4.76 5.74 5.71 98 2.86 2.83 3.19 3.16 3.59 3.56 4.11 4.07 4.80 4.75 5.76 5.70 100 2.61 2.57 2.88 2.84 3.20 3.16 3.61 3.55 4.12 4.06 4.81 4.73 5.76 5.67 102 2.40 2.35 2.63 2.57 2.90 2.83 3.22 3.15 3.62 3.54 4.13 4.04 4.81 4.70 5.76 5.63 104 2.23 2.16 2.42 2.35 2.64 2.56 2.91 2.82 3.23 3.13 3.63 3.52 4.13 4.01 4.81 4.66 106 2.08 2.00 2.25 2.16 2.43 2.34 2.65 2.55 2.92 2.80 3.23 3.11 3.63 3.49 4.13 3.97 108 1.96 1.86 2.10 2.00 2.26 2.15 2.45 2.33 2.66 2.53 2.92 2.78 3.24 3.08 3.63 3.45 110 1.85 1.73 1.97 1.85 2.11 1.98 2.27 2.13 2.45 2.31 2.67 2.51 2.92 2.75 3.23 3.04 112 1.75 1.62 1.86 1.72 1.98 1.83 2.12 1.96 2.28 2.11 2.46 2.28 2.67 2.48 2.92 2.71 114 1.66 1.52 1.76 1.61 1.87 1.71 1.99 1.82 2.12 1.94 2.28 2.08 2.46 2.25 2.67 2.44 116 1.59 1.43 1.68 1.51 1.77 1.59 1.88 1.69 2.00 1.79 2.13 1.91 2.28 2.05 2.46 2.21 118 1.52 1.34 1.60 1.41 1.68 1.49 1.78 1.57 1.88 1.66 2.00 1.76 2.13 1.88 2.28 2.01 120 1.46 1.27 1.53 1.33 1.61 1.39 1.69 1.47 1.78 1.54 1.89 1.63 2.00 1.73 2.13 1.84 122 1.41 1.19 1.47 1.25 1.54 1.31 1.62 1.37 1.70 1.44 1.79 1.52 1.89 1.60 2.00 1.70 124 1.36 1.13 1.42 1.18 1.48 1.23 1.55 1.28 1.62 1.34 1.70 1.41 1.79 1.48 1.89 1.56 126 1.32 1.06 1..S7 1.11 1.43 1.15 1.48 1.20 1.55 1.26 1.62 1.31 1.70 1.38 1.79 1.45 128 1.28 1.01 1.33 1.04 1.38 1.08 1.43 1.13 1.49 1.17 1.55 1.23 1.62 1.28 1.70 1.34 130 1.24 0.95 1.29 0.98 1..33 1.02 1.38 1.06 1.44 1.10 1.49 1.14 1.56 1.19 1.62 1.24 132 1.21 0.90 1.25 0.93 1.29 0.96 1.34 0.99 1.39 1.03 1.44 1.07 1.49 1.11 1.55 1.16 134 1.18 0.85 1.22 0.88 1.26 0.90 1.30 0.93 1.34 0.97 1.39 1.00 1.44 1.04 1.49 1.07 136 1.15 0.80 1.19 0.83 1.22 0.85 1.26 0.88 1.30 0.90 1.34 0.93 1.39 0.97 1.44 1.00 138 1.13 0.76 1.16 0.78 1.19 0.80 1.23 0.82 1.27 0.85 1.30 0.87 1.35 0.90 1.39 0.93 140 1.11 0.71 1.14 0.73 1.17 0.75 1.20 0.77 1.23 0.79 1.27 0.82 1.31 0.84 1.34 0.86 142 1.09 0.67 1.12 0.69 1.14 0.70 1.17 0.72 1.20 0.74 1.24 0.76 1.27 0.78 1.30 0.80 144 1.07 0.63 1.10 0.64 1.12 0.66 1.15 0.67 1.18 0.69 1.21 0.71 1.24 0.73 1.27 0.75 146 1.05 0.59 1.08 0.60 1.10 0.62 1.13 0.63 1.15 0.64 1.18 0.66 1.21 0.67 1.24 0.69 148 1.04 0.55 1.06 0.56 1.08 0.57 1.11 0.59 1.13 0.60 1.15 0.61 1.18 0.62 1.21 0.64 150 1.03 0.51 1.05 0.52 1.07 0.53 1.09 0.54 1.11 0.55 1.13 0.57 1.15 0.58 1.18 0.59 152 1.02 0.48 1.04 0.49 1.05 0.49 1.07 0.50 1.09 0.51 1.11 0.52 1.13 0.53 1.15 0.54 154 1.01 0.44 1.02 0.45 1.04 0.46 1.06 0.46 1.08 0.47 1.09 0.48 1.11 0.49 1.13 0.50 156 1.00 0.41 1.01 0.41 1.03 0.42 1.05 0.43 1.06 0.43 1.08 0.44 1.09 0.45 1.11 0.45 158 0.99 0.37 1.01 0.38 1.02 0.38 1.03 0.39 1.05 0.39 1.06 0.40 1.08 0.40 1.09 0.41 160 0.99 0.34 1.00 0.34 1.01 0.35 1.02 0.35 1.04 0.35 1.05 0.36 1.06 0.36 1.08 0.37 94° 96° 98° 100° 102° 104° 106° 108° 1 104° 5.74 5.57 106 4.80 4.61 5.78 5.51 108 4.12 3.92 4.78 4.55 5.70 5.42 110 3.62 3.40 4.11 3.86 4.76 4.48 5.67 5.33 112 3.23 2.99 3.61 3.35 4.09 3.80 4.74 4.40 5.63 5.22 114 2.92 2.66 3.22 2.94 3.59 3.28 4.07 3.72 4.70 4.30 5.59 5.10 116 2.66 2.39 2.91 2.61 3.20 2.88 3.57 3.21 4.04 3.63 4.67 4.19 5.54 4.98 118 2.45 2.17 2.65 2.34 2.90 2.56 3.19 2.81 3.55 3.13 4.01 3.54 4.62 4.08 5.48 4.84 120 2.28 1.97 2.45 2.12 2.64 2.29 2.88 2.49 3.17 2.74 3.52 3.05 3.97 3.44 4.57 3.96 122 2,12 1.80 2.27 1.92 2.43 2.06 2.63 2.23 2.86 2.43 3.14 2.66 3.49 2.96 3.93 3.33 124 2.00 1.65 2.12 1.76 2.26 1.87 2.42 2.01 2.61 2.16 2.84 2.35 3.11 2.58 3.45 2.86 126 1.88 1.52 1.99 1.61 2.11 1.71 2.25 1.82 2.40 1.95 2.59 2.10 2.81 2.27 3.08 2.49 128 1.78 1.41 1.88 1.48 1.98 1.56 2.10 1.65 2.23 1.76 2.39 1.88 2.57 2.02 2.78 2.19 130 1.70 1.30 1.78 1.36 1.87 1.43 1.97 1.51 2.08 1.60 2.21 1.70 2.36 1.81 2.54 1.94 132 1.62 1.20 1.69 1.26 1.77 1.32 1.86 1.38 1.96 1.45 2.07 1.54 2.19 1.63 2.34 1.74 134 1.55 1.12 1.62 1.16 1.68 1.21 1.76 1.27 1.85 1.33 1.94 1.40 2.05 1.47 2.17 1.56 136 1.49 1.04 1.55 1.07 1.61 1.12 1.68 1.16 1.75 1.22 1.83 1.27 1.92 1.34 2.03 1.41 138 1.44 0.96 1.49 0.99 1.54 1.03 1.60 1.07 1.66 1.11 1.74 1.16 1.81 1.21 1.90 1.27 140 1.39 0.89 1.43 0.92 1.48 0.95 1.53 0.98 1.59 1.02 1.65 1.06 1.72 1.10 1.79 1.15 142 1.34 0.83 1.38 0.85 1.43 0.88 1.47 0.91 1.52 0.94 1.58 0.97 1.64 1.01 1.70 1.05 144 1.30 0.77 1.34 0.79 1.38 0.81 1.42 0.83 1.46 0.86 1.51 0.89 1.56 0.92 1.62 0.95 146 1.27 0.71 1.30 0.73 1.33 0.75 1.37 0.77 1.41 0.79 1.45 0.81 1.50 0.84 1.54 0.86 148 1.2* 0.65 1.26 0.67 1.29 0.69 1.33 0.70 1.36 0.72 1.40 0.74 1.44 0.76 1.48 0.78 150 1.20 0.60 1.23 0.61 1.26 0.63 1.29 0.64 1.32 0.66 1.35 0.67 1.38 0.69 1.42 0.71 152 1.18 0.55 1.20 0.56 1.22 0.57 1.25 0.59 1.28 0.60 1.31 0.61 1.34 0.63 1.37 0.64 154 1.15 0.50 1.17 0.51 1.19 0.52 1.22 0.53 1.24 0.54 1.27 0.56 1.29 0.57 1.32 0.58 156 1.13 0.46 1.15 0.47 1.17 0.47 1.19 0.48 1.21 0.49 1.23 0.50 1.25 0.51 1.28 0.52 158 1.11 0.42 1.13 0.42 1.14 0.43 1.16 0.44 1.18 0.44 1.20 0.45 1.22 0.46 1.24 0.47 160 1.09 0.37 1.11 0.38 1.12 0.38 1.14 0.39 1.15 0.39 1.17 0.40 1.19 0.41 1.21 0.41 TABLE 5B. [Page 639 Distance of an Object by Two Bearings. Difference between the course and second bearing. Difference between the course and first bearin«r. 110° 112° 114° 116° 118° 120° 122° 120° 5.41 4.69 122 4.52 3.83 5.34 4.53 124 3.88 3.22 4.46 3.70 5.26 4.36 126 3.41 2.76 3.83 3.10 4.39 3.55 5.18 4.19 128 3.04 2.40 3.36 2.65 3.78 2.98 4.32 3.41 5.08 4.01 130 2.75 2.10 3.00 2.30 3.31 2.54 3.72 2.85 4.25 3.25 4.99 3.82 132 2.51 1.86 2.71 2.01 2.96 2.20 3.26 2.42 3.65 2.71 4.17 3.10 4.88 3.63 134 2.31 1.66 2.48 1.78 2.67 1.92 2.91 2.09 3.20 2.30 3.58 2.57 4.08 2.93 136 2.14 1.49 2.28 1.58 2.44 1.69 2.63 1.83 2.86 1.98 3.14 2.18 3.51 2.44 138 2.00 1.34 2.12 1.42 2.25 1.50 2.40 1.61 2.58 1.73 2.80 1.88 3.08 2.06 140 1.88 1.21 1.97 1.27 2.08 1.34 2.21 1.42 2.36 1.52 2.53 1.63 2.74 1.76 142 1.77 1.09 1.85 1.14 1.95 1.20 2.05 1.26 2.17 1.34 2.31 1.42 2.48 1.53 144 1.68 0.99 1.75 1.03 1.83 1.07 1.91 1.13 2.01 1.18 2.13 1.25 2.26 1.33 146 1.60 0.89 1.66 0.93 1.72 0.96 1.80 1.01 1.88 1.05 1.98 1.10 2.08 1.17 148 1.53 0.81 1.58 0.84 1.63 0.87 1.70 0.90 1.77 0.94 1.84 0.98 1.93 1.03 150 1.46 0.73 1.51 0.75 1.55 0.78 1.61 0.80 1.67 0.83 1.73 0.87 1.81 0.90 152 1.40 0.66 1.44 0.68 1.48 0.70 1.53 0.72 1.58 0.74 1.63 0.77 1.70 0.80 154 1.35 0.59 1.39 0.61 1.42 0.62 1.46 0.64 1.50 0.66 1.55 0.68 1.60 0.70 156 1.31 0.53 1.33 0.54 1.37 0.56 1.40 0.57 1.43 0.58 1.47 0.60 1.52 0.62 158 1.26 0.47 1.29 0.48 1.32 0.49 1.34 0.50 1.37 0.51 1. 41 0. 53 1.44 0.54 160 1.23 0.42 1.25 0.43 1.27 0.43 1.29 0.44 1.32 0.45 1. 35 0. 46 1.38 0.47 124° 126° 128° 180° 182° 184° 186° 1 134° 4.77 3.43 136 3.99 2.77 4.66 3.23 138 3.43 2.29 3.89 2.60 4.54 3.04 140 3.01 1.93 3.34 2.15 3.79 2.44 4.41 2.84 142 2.68 1.65 2.94 1.81 3.26 2.01 3.63 2.27 4.28 2.63 144 2.42 1.42 2.62 1.54 2.86 1.68 3.17 1.86 3.57 2.10 4.14 2.43 146 2.21 1.24 2.37 1.32 2.55 1.43 2.78 1.55 3.07 1.72 3.46 1.93 4.00 2.24 148 2.04 1.08 2.16 1.14 2.30 1.22 2.48 1.31 2.70 1.43 2.97 1.58 3.34 1.77 150 1.89 0.95 1.99 0.99 2.10 1.05 2.24 1.12 2.40 1.20 2.61 1.30 2.87 1.44 152 1.77 0.83 1.85 0.87 1.94 0.91 2.04 0.96 2.17 1.02 2.33 1.09 2.52 1.18 154 1.66 0.73 1.72 0.76 1.80 0.79 1.88 0.83 1.98 0.87 2.10 0.92 2.25 0.99 156 1.56 0.64 1.62 0.66 1.68 0.68 1.75 0.71 1.83 0.74 1.92 0.78 2.03 0.83 158 1.48 0.56 1.53 0.57 1.58 0.59 1.63 0.61 1.70 0.64 1.77 0.66 1.85 0.69 160 1.41 0.48 1.45 0.49 1.49 0..51 1.53 0.52 1.58 0.54 1.64 0.56 1.71 0.58 138° 140° 142° 1 1*4° 1 146° 1 148° 160° 1 148° 3.85 2.04 150 3.22 1.61 3.70 1.85 152 2.77 1.30 3.09 1.45 3.55 1.66 154 2.43 1.06 2.66 1.16 2.96 1.30 3.38 1.48 156 2.17 0.88 2.33 0.95 2.54 1.04 2.83 1.15 3.22 1.31 158 1.96 0.73 2.08 0.78 2.23 0.84 2.43 0.91 2.69 1.01 3.05 1.14 160 1.79 0.61 1.88 0.64 1.99 0.68 2.13 0.73 2.31 0.79 2.55 0.87 2.88 0.98 21594°— 14- -34 Page 640] TABLE 6. 1 ■Distance of Visibility of Objects at Sea. Height. Nautical statute Height, Nautical Statute Height, Nautical Statute feet. miles. miles. feet. miles. miles. feet. miles. miles. 1 1.1 1.3 100 11.5 13.2 760 31.6 36.4 2 1.7 1.9 105 11.7 13.5 780 32.0 36.9 3 2.0 2.3 110 12.0 13.8 800 32.4 37.3 4 2.3 2.6 115 12.3 14.1 820 32.8 37.8 5 2.5 2.9 120 12.6 14.5 840 33.2 38.3 6 2.8 3.2 125 12.9 14.8 860 33.6 38.7 7 2.9 3.5 130 13.1 15.1 880 34.0 39.2 8 3.1 3.7 135 13.3 15.3 900 34.4 39.6 9 3.5 4.0 140 13.6 15.6 920 34.7 40.0 10 3.6 4.2 145 13.8 15.9 940 35.2 40.5 11 3.8 4.4 150 14.1 16.2 960 35.5 40.9 12 4.0 4.6 160 14.5 16.7 980 35.9 41.3 13 4.2 4.8 170 14.9 17.2 1,000 36.2 41.7 14 4.3 4.9 180 15.4 17.7 1,100 38.0 43.8 15 4.4 5.1 190 15.8 18.2 1,200 39.6 45.6 16 4.6 6.3 200 16.2 18.7 1,300 41.3 47.6 17 4.7 6.4 210 16.6 19.1 1,400 42.9 49.4 18 4.9 6.6 220 17.0 19.6 1,500 44.4 51.1 19 5.0 5.8 230 17.4 20.0 1,600 45.8 52.8 20 6.1 6.9 240 17.7 20.4 1,700 47.2 54.4 21 5.3 6.1 250 18.2 20.9 1,800 48.6 56.0 22 5.4 6.2 260 18.5 21.3 1,900 49.9 57.5 23 5.5 6.3 270 18.9 21.7 2,000 51.2 59.0 24 5.6 6.5 280 19.2 22.1 2,100 52.5 60.6 25 6.7 6.6 290 19.6 22.5 2,200 63.8 61.9 26 5.8 6.7 300 19.9 22.9 2,300 55.0 63.3 27 6.0 6.9 310 20.1 23.2 2,400 56.2 64,7 28 6.1 7.0 320 20.5 23.6 2,500 57.3 66.0 29 6.2 7.1 330 20.8 24.0 2,600 58.5 67.3 30 6.3 7.2 340 21.1 24.3 2,700 59.6 68.6 31 6.4 7.3 350 21.5 24.7 2,800 60.6 69.8 32 6.5 7.5 360 21.7 25.0 2,900 61.8 71.1 33 6.6 7.6 370 22.1 25.4 3,000 62.8 72.3 34 6.7 7.7 380 22.3 25.7 3,100 63.8 73.6 35 6.8 7.8 390 22.7 26.1 3,200 64.9 74.7 36 6.9 7.9 400 22.9 26.4 3,300 65.9 75.9 37 6.9 8.0 410 23.2 26.7 3,400 66.9 77.0 38 7.0 8.1 420 23.5 27.1 3,500 67.8 78.1 39 7.1 8.2 430 23.8 27.4 3,600 68.8 79.2 40 7.2 8.3 440 24.1 27.7 3,700 69.7 80.3 41 7.3 8.4 450 24.3 28.0 3,800 70.7 81.4 42 7.4 8.5 460 24.6 28.3 3,900 71.6 82.4 43 7.5 8.7 470 24.8 28.6 4,000 72.5 83.5 44 7.6 8.8 480 25.1 28.9 4,100 73.4 84.6 45 7.7 8.9 490 25.4 29.2 4,200 74.3 85.6 46 7.8 9.0 500 25.6 29.5 4,300 75.2 86.6 47 7.9 9.0 520 26.1 30.1 4,400 76.1 87.6 48 7.9 9.1 540 26.7 30.7 4, 500 76.9 88.5 49 8.0 9.2 560 27.1 31.2 4,600 77.7 89.6 50 8.1 9.3 580 27.6 31.8 4,700 78.6 90.6 55 8.5 9.8 600 28.0 32.3 4,800 79.4 91.4 60 8.9 10.2 620 28.6 32.9 4,900 80.2 92.4 65 9.2 10.6 640 29.0 33.4 5,000 81.0 93.3 70 9.6 11.0 660 29.4 33.9 6,000 88.8 102.2 75 9.9 11.4 680 29.9 34.4 7,000 96.0 110.6 80 10.3 11.8 700 30.3 34.9 8,000 102.6 118.1 85 10.6 12.2 720 30.7 35.4 9,000 108.7 125.2 90 10.9 12.5 740 31.1 35.9 10,000 114.6 132.0 95 11.2 12.9 TABLE 7 . [Page 641 | For converting Arc into Time and the reverse. o H. M. o H. M. o H. M. o H. M. o H. M. o H. M. / M. S. / M. 8. 1 M. S. ' M. s. ' M. S. / M. S. H 8. A // R A II 8. A II 8. A // 8. A " s. A 1 4 61 4 4 121 8 4 181 12 4 241 16 4 301 20 4 2 8 62 4 8 122 8 8 182 12 8 242 16 8 302 20 8 3 12 63 4 12 123 8 12 183 12 12 243 16 12 303 20 12 4 16 64 4 16 124 8 16 184 12 16 244 16 16 304 20 16 5 20 65 4 20 125 8 20 185 12 20 245 16 20 305 20 20 6 24 66 4 24 126 8 24 186 12 24 246 16 24 306 20 24 7 28 67 4 28 127 8 28 187 12 28 247 16 28 307 20 28 8 32 68 4 32 128 8 32 188 12 32 248 16 32 308 20 32 9 36 69 4 36 129 8 36 189 12 36 249 16 36 309 20 36 10 40 70 4 40 130 8 40 190 12 40 250 16 40 310 20 40 11 44 71 4 44 131 8 44 191 12 44 261 16 44 311 20 44 12 48 72 4 48 132 8 48 192 12 48 252 16 48 312 20 48 13 52 73 4 52 133 8 52 193 12 52 253 16 52 313 20 52 14 56 74 4 66 134 8 56 194 12 56 254 16 66 314 20 56 15 1 75 5 135 9 195 13 265 17 315 21 16 1 4 76 5 4 136 9 4 196 13 4 256 17 4 316 21 4 17 1 8 77 5 8 137 9 8 197 13 8 257 17 8 317 21 8 18 1 12 78 5 12 138 9 12 198 13 12 268 17 12 318 21 12 19 1 16 79 5 16 139 9 16 199 13 16 259 17 16 319 21 16 20 1 20 80 5 20 140 9 20 200 13 20 260 17 20 320 21 20 21 1 24 81 5 24 141 9 24 201 13 24 261 17 24 321 21 24 22 1 28 82 5 28 142 9 28 202 13 28 262 17 28 322 21 28 23 1 32 83 5 32 143 9 32 203 13 32 263 17 32 323 21 32 24 1 36 84 5 36 144 9 36 204 13 36 264 17 36 324 21 36 25 1 40 85 5 40 145 9 40 205 13 40 265 17 40 326 21 40 26 1 44 86 5 44 . 146 9 44 206 13 44 266 17 44 326 21 44 27 1 48 87 5 48 147 9 48 207 13 48 267 17 48 327 21 48 28 1 52 88 5 52 148 9 52 208 13 52 268 17 52 328 21 52 29 1 56 89 5 56 149 9 56 209 13 56 269 17 56 329 21 56 30 2 90 6 150 10 210 14 270 18 330 331 22 31 2 4 91 6 4 151 10 4 211 14 4 271 18 4 22 4 32 2 8 92 6 8 152 10 8 212 14 8 272 18 8 332 22 8 33 2 12 93 6 12 153 10 12 213 14 12 273 18 12 333 22 12 34 2 16 94 6 16 154 10 16 214 14 16 274 18 16 334 22 16 35 2 20 95 6 20 155 10 20 215 14 20 275 18 20 335 22 20 36 2 24 96 6 24 156 10 24 216 14 24 276 18 24 336 22 24 37 2 28 97 6 28 157 10 28 217 14 28 277 18 28 337 22 28 38 2 32 98 6 32 158 10 32 218 14 32 278 18 32 338 22 32 39 2 36 99 6 36 159 10 36 219 14 36 279 18 36 339 22 36 40 2 40 100 6 40 160 10 40 220 14 40 280 18 40 340 22 40 41 2 44 101 6 44 161 10 44 221 14 44 281 18 44 341 22 44 42 2 48 102 6 48 162 10 48 222 14 48 282 18 48 342 22 48 43 2 52 103 6 52 163 10 52 223 14 52 283 18 52 343 22 52 44 2 56 104 6 56 164 10 56 224 14 56 284 18 56 344 22 56 45 3 105 7 165 11 225 15 285 19 345 23 46 3 4 106 7 4 166 11 4 226 15 4 286 19 4 346 23 4 47 3 8 107 7 8 167 11 8 227 15 8 287 19 8 347 23 8 48 3 12 108 7 12 168 11 12 228 15 12 288 19 12 348 23 12 49 3 16 109 7 16 169 11 16 229 15 16 289 19 16 349 23 16 50 51 3 20 110 7 20 170 11 20 230 15 20 290 19 20 350 23 20 3 24 111 7 24 171 11 24 231 15 24 291 19 24 361 23 24 52 3 28 112 7 28 172 11 28 232 15 28 292 19 28 352 23 28 53 3 32 113 7 32 173 11 32 233 15 32 293 19 32 353 23 32 54 3 36 114 7 36 174 11 36 234 15 36 294 19 36 354 23 36 55 3 40 115 7 40 175 11 40 235 15 40 295 19 40 355 23 40 56 3 44 116 7 44 176 11 44 236 15 44 296 19 44 366 23 44 57 3 48 117 7 48 177 11 48 237 15 48 297 19 48 367 23 48 58 3 52 118 7 52 178 11 52 238 15 52 298 19 62 358 23 62 59 3 56 119 7 56 179 11 56 239 15 56 299 19 66 359 23 56 60 4 120 8 180 12 240 16 300 20 360 24 MoTK.— When turning seconds of arc into time, and vice versa, it should be remembered that the fractions are slxtiethar thus, the value in time ol 42" is not 2*.48, but S^U-a^.S. Page 642] TABLE 8. Sidereal into Mean Solar Time. 73 To be subtracted from a sidereal time interral. Ofc 1" 21. 3t 4h Sh Ok 7h For seconds. TO. 1 2 3 4 m. «. 0.000 0.164 0. 328 0. 491 0. 655 m. s. 9.830 9.993 10. 157 10. 321 10. 485 TO. 8. 19. 659 19. 823 19.987 20. 151 20. 314 TO. «. 29. 489 29. 653 29. 816 29. 980 30. 144 TO. S. 39. 318 39.482 39. 646 39. 810 39. 974 m. s. 49. 148 49. 312 49. 475 49. 639 49. 803 m. s. 58. 977 59. 141 59. 305 59. 469 59. 633 TO. 8.807 8.971 9.135 9.298 9.462 s. 1 2 3 4 s. 0.003 .005 .008 .011 5 6 7 8 9 0. 819 0. 983 1. 147 1.311 1.474 10.649 10.813 10.976 11. 140 11. 304 20. 478 20. 642 20. 806 20. 970 21. 134 30. 308 30. 472 30. 635 30. 799 30. 963 40. 137 40. 301 40. 465 40. 629 40. 793 40. 956 41. 120 41. 284 41. 448 41.612 49. 967 50. 131 50. 295 50. 458 50. 622 59. 796 59. 960 1 0.124 1 0.288 1 0.452 9.626 9.790 9.954 10. 118 10. 281 5 6 7 8 9 .014 .016 .019 .022 .025 10 11 12 13 14 1. 638 1. 802 1.966 2. 130 2. 294 11. 468 11. 632 11. 795 11. 959 12. 123 21. 297 21. 461 21. 625 21. 789 21. 953 31. 127 31. 291 31. 455 31. 618 31. 782 50. 786 50. 950 51.114 51. 278 51. 441 1 0.616 1 0.779 1 0.943 1 1. 107 1 1.271 10.445 10. 609 10. 773 10. 937 11. 100 10 11 12 13 14 .027 .030 .033 .035 .038 15 16 17 18 19 2. 457 2. 621 2. 785 2. 949 3. 113 12. 287 12. 451 12. 615 12. 778 12. 942 22. 117 22. 280 22. 444 22. 608 22. 772 31. 946 32. 110 32. 274 32. 438 32. 601 41. 776 41. 939 42. 103 42. 267 42. 431 51.605 51. 769 51. 933 52. 097 52. 260 1 1. 435 1 1. 599 1 1.762 1 1.926 1 2. 090 11. 264 11. 428 11. 592 11. 756 11.920 15 16 17 18 19 .041 .044 .046 .049 .052 .055 .057 .060 .063 .066 20 21 22 23 24 3. 277 3.440 3. 604 3. 768 3. 932 13. 106 13.270 13. 434 13.598 13. 761 22. 936 23. 099 23. 263 23. 427 23. 591 32. 765 32. 929 33. 093 33. 257 33.420 42. 595 42. 759 42. 922 43. 086 43. 250 52. 424 52. 588 52. 752 52. 916 53. 080 1 2.254 1 2.418 1 2. 582 1 2. 745 1 2. 909 12. 083 12. 247 12.411 12. 575 12. 739 20 21 22 23 24 25 26 27 28 29 4.096 4. 259 4. 423 4. 587 4. 751 13.925 14.089 14. 253 14.417 14. 581 23. 755 23. 919 24. 082 24. 246 24. 410 33. 584 33. 748 33. 912 34. 076 34. 240 43. 414 43. 578 43. 742 43. 905 44. 069 53. 243 53. 407 53. 571 53. 735 53. 899 1 3.073 1 3.237 1 3. 401 1 3.564 1 3.728 12. 903 13.066 13. 230 13. 394 13. 558 25 26 27 28 29 .068 .071 .074 .076 .079 30 31 32 33 34 4. 915 5. 079 5. 242 5. 406 5. 570 14. 744 14.908 15.072 15. 236 15. 400 24. 574 24. 738 24. 902 25.065 25. 229 34. 403 34. 567 34. 731 34. 895 35. 059 44. 233 44. 397 44. 561 44. 724 44. 888 54. 063 54. 226 54. 390 54. 554 54. 718 1 3.892 1 4.056 1 4. 220 1 4.384 1 4.547 13. 722 13. 886 14. 049 14.213 14. 377 30 31 32 33 34 .082 .085 .087 .090 .093 35 36 37 38 39 5. 734 5. 898 6. 062 6. 225 6. 389 15.563 15. 727 15. 891 16. 055 16. 219 25. 393 25. 557 25. 721 25. 885 26. 048 35. 223 35. 386 35. 550 35. 714 35. 878 45. 052 45. 216 45. 380 45. 544 45. 707 54. 882 55. 046 55. 209 55. 373 55. 537 1 4.711 1 4. 875 1 5.039 1 5.203 1 5.367 14. 541 14. 705 14. 868 15. 032 15. 196 35 36 37 38 39 .096 .098 .101 .104 .106 40 41 42 43 44 6. 553 6. 717 6. 881 7.045 7. 208 16.383 16.546 16. 710 16.874 17. 038 26. 212 26. 376 26. 540 26. 704 26. 867 36. 042 36. 206 36. 369 36. 533 36. 697 45. 871 46.035 46. 199 46. 363 46. 527 55. 701 55. 865 56. 028 56. 192 56. 356 1 5.530 1 5.694 1 5.858 1 6. 022 i 6. 186 15. 360 15. 524 15. 688 15. 851 16. 015 40 41 42 43 44 .109 .112 .115 .117 .120 45 46 47 48 49 50 51 52 53 54 7.372 7.536 7. 700 7.864 8. 027 17.202 17.366 17.529 17.693 17. 857 27. 031 27. 195 27. 359 27. 523 27. 687 36. 861 37. 025 37. 188 37. 352 37. 516 46. 690 46. 854 47.018 47. 182 47. 346 56. 520 56. 684 56. 848 57. Oil 57. 175 1 6.350 1 6. 513 1 6.677 1 6.841 1 7.005 -J- 16. 179 16. 343 16. 507 16. 671 16. 834 45 46 47 48 49 .123 .126 .128 .131 .134 8. 191 8. 355 8.519 8. 683 8. 847 18.021 18. 186 18. 349 18. 512 18.676 27. 850 28.014 28. 178 28. 342 28. 506 37. 680 37. 844 38. 008 38. 171 38. 335 47. 510 47. 673 47. 837 48. 001 48. 165 57. 339 57. 503 57. 667 57. 831 57. 994 1 7. 169 1 7. 332 1 7. 496 1 7.660 1 7.824 16. 998 17. 162 17. 326 17. 490 17. 654 50 51 52 53 54 .137 .139 .142 .145 .147 55 56 57 58 59 9. 010 9. 174 9. 338 9. 502 9. 666 18.840 19.004 19. 168 19. 331 19. 495 28. 670 28. 833 28. 997 29. 161 29. 325 38. 499 38. 663 38. 827 38. 991 39. 154 48. 329 48. 492 48. 656 48. 820 48. 984 58. 158 58. 322 58. 486 58. 650 58. 814 1 . 1 7. 988 1 8.152 1 8. 315 1 8. 479 1 8.643 17.817 17. 981 18. 145 18. 309 18. 473 55 56 57 58 59 .150 .153 .156 .158 0.161 TABLE 8. [Page 643 Sidereal into Mean Solar Time. To be subtracted from a sidereal time interval. , 1 SO 9* 10k llfc 121. Igi- u^ 15fc For seconds.! m. 1 2 3 4 m. «. 1 18.636 1 18.800 1 18.964 ' 1 19.128 1 19.292 m. «. 1 28.466 1 28.630 1 28. 794 1 28.958 1 29. 121 m. «. 1 38. 296 1 38.459 1 38.623 1 38.787 1 38.951 ■m. 8. 1 48.125 1 48.289 1 48.453 1 48.617 1 48. 780 m. s. 1 57.965 1 58. 119 1 58.282 1 68.446 1 58.610 2 7.784 2 7.948 2 8.112- 2 8.276 2 8.440 in. t. 2 17.614 2 17. 778 2 17.941 2 18. 105 2 18. 269 m. 8. 2 27.443 2 27. 607 2 27. 771 2 27. 935 2 28. 099 8. 1 2 3 4 0.003 .005 .008 .011 5; 1 19.456 6 1 19.619 7 1 19.783 8 1 19.947 9 1 20. Ill 10 1 20.275 11 1 1 20. 439 12 1 1 20. 602 13 ; 1 20. 766 141 1 20.930 1 29.285 1 29.449 1 29.613 1 29. 777 1 29.940 1 30. 104 1 30. 268 1 30.432 1 30.696 1 30. 760 1 39.115 1 39.279 1 39.442 1 39.606 1 39. 770 1 48.944 1 49. 108 1 49.272 1 49.436 1 49.600 1 68. 774 1 58.938 1 69. 101 1 69. 265 1 59.429 2 8.603 2 8.767 2 8.931 2 9.095 2 9.259 2 18. 433 2 28. 263 2 18. 597 2 28. 426 2 18. 761 2 28. 590 2 18. 924 2 28. 764 2 19. 088 2 28. 918 5 6 7 8 9 .014 .016 .019 .022 .025 1 39.934 1 40.098 1 40. 261 1 40.425 1 40.589 1 49. 763 1 49.927 1 60.091 1 50.256 1 60.419 1 69.593 1 59. 757 1 59.921 2 0.084 2 0.248 2 9.423 2 9.586 2 9.760 2 9.914 2 10.078 2 10.242 2 10.405 2 10.669 2 10. 733 2 10.897 2 19.252 2 19.416 2 19.580 2 19. 744 2 19.907 2 29. 082 2 29. 245 2 29.409 2 29. 673 2 29. 737 10 11 12 13 14 .027 .030 .033 .036 .038 15 16 17 18 19 1 21.094 i 21.258 i 21.422 i 21.585 1 21.749 1 30.923 1 31.087 1 31.261 1 31.415 1 31.579 1 40. 753 1 40.917 1 41.081 1 41.244 1 41.408 1 50.583 1 50. 746 1 50.910 1 51.074 1 51.238 2 0.412 2 0.576 2 0.740 2 0.904 2 1.067 2 20. 071 2 20.235 2 20. 399 2 20.563 2 20. 727 2 29.901 2 30. 065 2 30. 228 2 30. 392 2 30. 566 16 16 17 18 19 .041 .044 .046 .049 .052 .055 .057 .060 .063 .066 20 21 22 23 24 1 21.913 1 22.077 1 22.241 1 22.404 1 22.568 1 31.743 1 31.906 1 32.070 1 32.234 1 32.398 1 41.672 1 41. 736 1 41.900 1 42.064 1 42. 227 1 61.402 1 51.665 1 51.729 1 51.893 1 62.057 2 1.231 2 1.395 2 1.569 2 1.723 2 1.887 2 11.061 2 11. 225 2 11.388 2 11.562 2 11. 716 2 20. 890 2 21.064 2 21.218 2 21. 382 2 21.646 2 30. 720 2 30. 884 2 31. 048 2 31.211 2 31. 376 20 21 22 23 24 26 26 27 28 29 1 22. 732 1 22.896 1 23.060 1 23.224 1 23,387 1 32.562 1 32. 726 1 32.889 1 33.053 1 33.217 1 42.391 1 42. 665 1 42. 719 1 42.883 1 43.047 1 52.221 1 62.385 1 52.548 1 52. 712 1 52.876 2 2.050 2 2.214 2 2.378 2 2.642 2 2.706 2 11.880 2 12.044 2 12.208 2 12.371 2 12.535 2 21. 709 2 21.873 2 22.037 2 22.201 2 22.365 2 31. 539 2 31. 703 2 31. 867 2 32. 031 2 32. 194 26 26 27 28 29 30 31 32 33 34 .068 .071 .074 .076 .079 .082 .085 .087 .090 .093 30 31 32 33 34 1 23.551 1 23. 715 1 23. 879 1 24.043 1 24.207 1 33.381 1 33.545 1 33.708 1 33.872 1 34.036 1 43.210 1 43.374 1 43.638 1 43. 702 1 43.866 1 53.040 1 63.204 1 63. 368 1 53.531 1 53.695 2 2.869 2 3.033 2 3.197 2 3.361 2 3.525 2 12.699 2 12.863 2 13. 027 2 13.191 2 13.354 2 22. 629 2 22. 692 2 22. 856 2 23. 020 2 23. 184 2 32. 358 2 32. 622 2 32. 686 2 32. 860 2 33.013 35 36 37 38 39 1 24.370 1 24.534 1 24.698 1 24.862 1 25.026 1 34.200 1 34.364 1 34.528 1 34.691 1 34.855 1 44.029 1 44. 193 1 44.357 1 44.621 1 44.686 1 53. 859 1 54.023 1 54. 187 1 54.351 1 54.514 2 3.689 2 3.852 2 4.016 2 4.180 2 4.344 2 13.518 2 13.682 2 13. 846 2 14.010 2 14.173 2 23. 348 2 23.512 2 23. 675 2 23. 839 2 24.003 2 33. 177 2 33. 341 2 33. 506 2 33. 669 2 33. 833 35 36 37 38 39 .096 .098 .101 .104 .106 40 41 42 43 44 1 25.190 1 26.353 1 25.617 1 25.681 1 25.846 1 35.019 1 36. 183 1 36.347 1 35.511 1 35.674 1 44.849 1 46. 012 1 45. 176 1 46.340 1 45. 604 1 54.678 1 54.842 1 55.006 1 55. 170 1 55.333 2 4.608 2 4.672 2 4.835 2 4.999 2 6.163 2 14.337 2 14.501 2 14. 665 2 14.829 2 14.993 2 24. 167 2 24. 331 2 24. 495 2 24. 668 2 24. 822 2 33. 996 2 34. 160 2 34. 324 2 .34. 488 2 34.652 40 41 42 43 44 .109 .112 .115 .117 .120 45 46 47 48 49 1 26.009 1 26.172 1 26.336 1 26.500 1 26.664 1 35.838 1 36.002 1 36.166 1 36.330 1 36.493 1 45.668 1 45. 832 1 46.995 1 46. 169 1 46.323 1 65.497 1 65.661 1 55.825 1 65. 989 1 66. 163 2 5.327 2 5.491 2 5.655 2 5.818 2 5.982 2 15. 156 2 15. 320 2 15.484 2 15.648 2 15.812 2 24. 986 2 25. 150 2 25. 314 2 25.477 2 26.641 2 34.816 2 34. 979 2 35. 143 2 35. 307 2 35.471 2 35. 635 2 35. 798 2 36. 962 2 36. 126 2 36. 290 2 36. 454 2 36. 618 2 36. 781 2 36. 945 2 37. 109 45 46 47 48 49 .123 .126 .128 .131 .134 50 51 52 53 54 1 26.828 1 26.992 1 27.156 1 27.319 1 27.483 1 36. 657 1 36.821 1 36.985 1 37.149 1 37.313 1 46.487 1 46.651 1 46.816 1 46.978 1 47.142 1 56. 316 1 66.480 1 66.644 1 66.808 1 66.972 2 6.146 2 6.310 2 6.474 2 6.637 2 6.801 2 16.976 2 16. 139 2 16. 303 2 16.467 2 16.631 2 25. 805 2 26.969 2 26. 133 2 26. 297 2 26. 460 50 51 62 63 54 .137 .139 .142 .145 .147 55 56 57 58 59 1 27.647 1 27.811 1 27.975 1 28. 138 1 28.302 1 37.476 1 37. 640 1 37. 804 1 37.968 1 38.132 1 47.306 1 47.470 1 47.634 1 47. 797 1 47.961 1 57. 136 1 57. 299 1 57.463 1 57.627 1 57. 791 2 6.965 2 7.129 2 7.293 2 7.467 2 7.620 2 16. 795 2 16.969 2 17. 122 2 17.286 2 17.460 2 26. 624 2 26. 788 2 26. 962 2 27. 116 2 27. 280 55 56 57 68 59 .150 .153 .156 .168 0.161 Page 644] TABLE 8. Sidereal into Mean Solar Time. To be subtracted from a sidereal time interval. 50 51 52 53 54 55 56 57 58 69 16k 2 37.273 2 37. 437 2 37. 601 2 37. 764 2 37. 928 38.092 38. 256 38. 420 38. 584 38. 747 2 38. 911 2 39.075 2 39. 239 2 39.403 2 39. 566 2 39. 730 2 39. 894 2 40. 058 2 40. 222 2 40. 386 2 40. 549 2 40. 713 2 40. 877 2 41.041 2 41. 205 2 41.369 2 41. 532 2 41. 696 2 41. 860 2 42. 024 2 42. 188 2 42. 352 2 42. 515 2 42. 679 2 42. 843 43.007 43. 171 43. 334 43. 498 43. 662 43. 826 43. 990 44.154 44. 317 44. 481 44.645 44.809 44. 973 45. 137 45. 300 45.464 45. 628 45. 792 45. 956 46. 120 46. 283 46. 447 46.611 46. 755 46.939 170 47. 102 47.266 47. 430 47. 594 47. 758 2 47. 922 2 48. 085 2 48. 249 2 48.413 2 48. 577 2 48. 741 2 48. 905 2 49. 068 2 49. 232 2 49. 396 2 49. 560 2 49. 724 2 49. 888 2 50.051 2 50. 215 2 50. 379 2 50. 543 2 50. 707 2 50. 870 2 51. 034 2 51. 198 2 51. 362 2 51.526 2 51. 690 2 51. 853 2 52. 017 2 52. 181 2 52. 345 2 52. 509 2 52. 673 2 52. 836 2 53.000 2 53. 164 2 53. 328 2 53. 492 2 53. 656 2 53. 819 2 53.983 2 54. 147 2 54. 311 2 54. 475 2 54. 638 2 54. 802 2 54. 966 2 55. 130 55.294 55.458 55. 621 55.785 55. 949 2 56. 113 2 56. 277 2 56. 441 2 56. 604 2 56. 768 ISO 2 56. 932 2 57. 096 2 57. 260 2 57.424 2 57. 587 57. 751 57. 915 58. 079 58. 243 58. 406 2 58. 570 2 58. 734 2 58. 898 2 59. 062 2 59. 226 2 59. 389 2 59. 553 2 59. 717 2 59. 881 3 0.045 0.209 0.372 0. 536 0.700 0.864 1.028 1.192 1.355 1.519 1.683 1.847 2.011 2.174 2.338 2.502 2.666 2.830 2.994 3.157 3.321 3.485 3.649 3.813 3.977 4.140 4.304 4.468 4.632 4.796 4.960 5.123 5.287 5.451 5.615 5.779 5.942 6.106 6.270 6.434 6.598 ISfc 6.762 6.925 7.089 7.253 7.417 7.581 7.745 7.908 8.072 8.236 8.400 8.564 8.728 8.891 9.055 9.219 9.383 9.547 9.710 9.874 10. 038 10. 202 10. 366 10. 530 10. 693 3 10.857 3 11.021 3 11. 185 3 11.349 3 11.513 3 11.676 3 11.840 3 12.004 3 12.168 3 12. 332 12. 496 12.659 12. 823 12. 987 13. 151 13. 315 13. 478 13.642 13.806 13. 970 14. 134 14.298 14. 461 14. 625 14. 789 14. 953 15. 117 15. 281 15.444 15.608 3 15. 772 3 15. 936 3 16. 100 3 16.264 3 16.427 20» 3 16.591 3 16. 755 3 16.919 3 17.083 3 17.246 3 17.410 3 17.574 3 17. 738 3 17.902 3 18.066 3 18.229 3 18. .393 3 18.557 3 18. 721 3 18. 885 3 19.049 3 19.212 3 19.376 3 19.540 3 19. 704 19. 868 20. 032 20. 195 20. 359 20. 523 3 20. 687 3 20.851 3 21.014 3 21. 178 3 21. 342 3 21. 506 3 21.670 3 21. 834 3 21.997 3 22. 161 3 22. 325 3 22. 489 3 22. 653 3 22. 817 3 22. 980 23. 144 23. 308 23. 472 23. 636 23. 800 3 23. 963 3 24. 127 3 24. 291 3 24. 455 3 24. 619 3 24. 782 3 24.946 3 25. 110 3 25. 274 3 25. 438 3 25.602 3 25. 765 3 25.929 3 26. 093 3 26.257 aih 3 26.421 3 26. 585 3 26. 748 3 26. 912 3 27.076 3 27. 240 3 27. 404 3 27. 568 3 27. 731 3 27. 895 3 28. 059 3 28. 223 3 28. 387 3 28.550 3 28. 714 28. 878 29.042 29.206 29. 370 29. 533 3 29. 697 3 29. 861 3 30. 025 3 30. 189 3 30. 353 3 30. 516 3 30. 680 3 30.844 3 31. 008 3 31. 172 3 31.336 3 31. 499 3 31. 663 3 31. 827 3 31.991 3 32. 155 3 32. 318 3 32. 482 3 32. 646 3 32. 810 3 32.974 3 33. 138 3 33. 301 3 33.465 3 33. 629 3 33. 793 3 33.957 3 34. 121 3 34.284 3 34. 448 3 34. 612 3 34. 776 3 34.940 3 35.104 3 35. 267 3 35. 431 3 35. 595 3 35. 759 3 35. 923 3 36.086 22i> 36. 250 36. 414 36. 578 36. 742 36. 906 3 37.069 3 37. 233 3 37. 397 3 37. 561 3 37. 725 3 37. 889 3 38. 052 3 38. 216 3 38. 380 3 38. 544 3 38. 708 3 38. 871 3 39.035 3 39. 199 3 39. 363 3 39.527 3 39. 691 3 39. 854 3 40. 018 3 40. 182 3 40. 346 3 40. 510 3 40.674 3 40. 837 3 41. 001 3 41. 165 3 41. 329 3 41. 493 3 41. 657 3 41. 820 3 41. 984 3 42. 148 3 42. 312 3 42. 476 3 42. 639 3 42. 803 3 42. 967 3 43. 131 3 43. 295 3 43. 459 3 43.622 3 43. 786 3 43. 950 3 44. 114 3 44. 278 3 44.442 3 44.605 3 44. 769 3 44. 933 3 45. 097 3 45. 261 3 45.425 3 45. 588 3 45. 752 3 45. 916 28'' 46. 080 46. 244 46. 407 46. 571 46. 735 3 46. 899 3 47. 063 3 47. 227 3 47. 390 3 47. 554 3 47. 718 3 47. 882 3 48. 046 3 48.210 3 48. 373 48. 537 48. 701 48.865 49. 029 49. 193 3 49. 356 3 49. 520 3 49. 684 3 49. 848 3 50. 012 3 50. 175 3 50. 339 3 50. 503 3 50. 667 3 50. 831 50. 995 51. 158 51. 322 51. 486 51.650 3 51. 814 3 51. 978 3 52. 141 3 52. 305 3 52. 469 3 52. 633 3 52. 797 3 52. 961 3 53. 124 3 53. 288 3 53. 452 3 53. 616 3 53. 780 3 53. 943 3 54. 107 3 54. 271 3 54. 435 3 54. 599 3 54. 763 3 54. 926 3 55. 090 3 55. 254 3 55. 418 3 55. 582 3 55, 746 For seconds. TABLE 9. [Page 646 | Mean Solar into Sidereal Time. s To be added to a mean time interval. 1 Oh 1 lb Sh 3>> 4h oh 6h 7h For secondsJ m. 1 2 3 4 m. 0.000 0.164 0.329 0.493 0.657 m. t. 9.856 10.021 10. 185 10. 349 10. 514 m. s. 19. 713 19. 877 20. 041 20. 206 20. 370 20. 534 20. 699 20. 863 21. 027 21. 191 m. s. 29. 569 29. 734 29. 898 30. 062 30. 227 m. 8. 39.426 39. 590 39. 754 39. 919 40. 083 m. «. 49. 282 49. 447 49.611 49. 775 49. 939 m. 1. 59. 139 59. 303 59. 467 59. 632 59. 796 m. s. 1 8.995 1 9.160 1 9.324 1 9.488 1 9.652 «. 1 2 3 4 s. 0.003 .005 .008 .011 5 6 7 8 9 0.821 0.986 1.150 1.314 1.478 10.678 10. 842 11.006 11.171 11.335 30.391 30. 555 30. 719 30. 884 31. 048 40. 247 40. 412 40. 576 40. 740 40.904 50. 104 50. 268 50.432 50. 597 50. 761 59. 960 1 0.124 1 0.289 1 0. 453 1 0.617 1 9.817 1 9.981 1 10.145 1 10.310 1 10.474 5 6 7 8 9 .014 .016 .019 .022 .025 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1.643 1.807 1.971 2.136 2.300 11. 499 11.663 11. 828 11.992 12. 156 21. 356 21. 520 21. 684 21.8i9 22. 013 31. 212 31. 376 31. 541 31. 705 31. 869 41.069 41. 233 41. 397 41.561 41. 726 50. 925 51. 089 51. 254 51.418 51. 582 0.782 0.946 1.110 1.274 1.439 1 10.638 1 10.802 1 10.967 1 11.131 1 11.295 10 11 12 13 14 .027 .030 .033 .036 .038 2.464 2.628 2.793 2.957 3.121 12.321 12. 485 12.649 12. 813 12.978 22. 177 22. 341 22.506 22.670 22. 834 32. 034 32. 198 32. 362 32.526 32. 691 41.890 42.054 42. 219 42. 383 42. 547 51. 746 51.911 52. 075 52. 239 52. 404 1.603 1.767 1.932 2.096 2.260 1 11.459 1 11.624 1 11.788 1 11.952 1 12.117 15 16 17 18 19 .041 .044 .047 .049 .052 3.285 3.450 3.614 3.778 3.943 13. 142 13. 306 13. 471 13. 636 13.799 22. 998 23. 163 23. 327 23. 491 23.656 32. 855 33. 019 33.183 33. 348 33. 512 42.711 42. 876 43. 040 43.204 43.368 52. 568 52. 732 52. 896 53. 061 53. 225 2.424 2.589 2.753 2.917 3.081 1 12.281 1 12.445 1 12.609 1 12. 774 1 12.938 20 21 22 23 24 25 26 27 28 29 .055 .067 .060 .063 .066 .068 .071 .074 .077 .079 25 26 27 28 29 4.107 4.271 4.435 4.600 4.764 13.963 14. 128 14. 292 14.456 14.620 23. 820 23.984 24. 148 24. 313 24. 477 33. 676 33. 841 34. 005 34. 169 34. 333 43. 533 43. 697 43. 861 44. 026 44.190 53. 389 53. 554 53. 718 53. 882 54.046 3.246 3.410 3.574 3.739 3.903 1 13.102 1 13.266 1 13.431 1 13.595 1 13.759 30 31 32 33 34 35 36 37 38 39 4.928 5.093 5.257 5.421 5.585 14. 785 14.949 15. 113 15. 278 15. 442 24, 641 24. 805 24. 970 25. 134 25. 298 34. 498 34.662 34. 826 34.990 35. 155 44. 354 44. 518 44. 683 44. 847 45. Oil 54. 211 54. 375 54. 539 54. 703 54. 868 4.067 4.231 4.396 4.560 4.724 1 13.924 1 14.088 1 14.252 1 14.416 1 14.581 30 31 32 33 34 36 36 37 38 39 .082 .085 .088 .090 .093 .096 .099 .101 .104 .107 5.750 5.914 6.078 6.242 6.407 15.606 15.770 15.935 16.099 16. 263 25. 463 25. 627 25. 791 25. 955 26. 120 35. 319 35.483 35.648 35. 812 35. 976 45. 176 45.340 45. 504 45.668 45.833 55. 032 55.196 55. 361 55. 525 55. 689 4.888 5.053 5.217 5.381 5.546 1 14.745 1 14.909 1 15.073 1 15.238 1 15.402 40 41 42 43 44 6.571 6.735 6.900 7.064 7.228 16. 427 16.592 16. 756 16.920 17.085 26. 284 26. 448 26. 612 26. 777 26. 941 36. 140 36. 305 36. 469 36.633 36. 798 45.997 46. 161 46. 325 46.490 46. 654 55. 853 56. 018 56. 182 56.346 56. 510 5.710 5.874 6.038 6.203 6.367 1 15.566 1 15. 731 1 15.895 1 16.059 1 16.223 40 41 42 43 44 .110 .112 .115 .118 .120 45 46 47 48 49 50 51 52 53 54 7.392 7.557 7.721 7.885 8.049 17.249 17. 413 17. 577 17. 742 17.906 27. 105 27. 270 27. 434 27. 598 27. 762 36. 962 37. 126 37.290 37.455 37. 619 46. 818 46. 983 47. 147 47. 311 47. 475 56. 675 56. 839 57. 003 57. 168 57. 332 T 6.531 6.695 6.860 7.024 7.188 7.353 7.517 7.681 7.845 8.010 1 16.388 1 16.552 1 16.716 1 16.881 1 17.045 45 46 47 48 49 .123 .126 .129 .131 .134 8.214 8.378 8.542 8.707 8.871 18.070 18.234 18. 399 18.563 18. 727 27. 927 28. 091 28. 255 28.420 28. 584 37. 783 37. 947 38. 112 38. 276 38. 440 47.640 47. 804 47. 968 48. 132 48. 297 57. 496 57.660 57. 825 57. 989 58. 153 1 17.209 1 17.373 1 17.538 1 17.702 1 17.866 50 51 52 53 64 .137 .140 .142 .145 .148 55 56 57 58 59 9.035 9.199 9.364 9.528 9.692 18.892 19.056 19. 220 19.384 19.549 28. 748 28. 912 29. 077 29. 241 29. 405 38. 605 38. 769 38. 933 39. 097 39. 262 48. 461 48. 625 48. 790 48. 954 49. 118 58. 317 58. 482 58. 646 58. 810 58. 975 8.174 8.338 8.502 8.667 8.831 1 18.030 1 18.195 1 18.359 1 18.523 1 18.688 55 56 57 58 59 .151 .153 .156 .159 0.162 1 Page 646] TABLE 9. Mean Solar into Sidereal Time. a To be added to a mean time interval. 1 S*- 91" 10" Ilk 121. Igi" 14» IS" For secondsJ TO. 1 2 3 4 m. s. 1 18.852 1 19.016 1 19.180 1 19.345 1 19.609 m. s. 1 28.708 1 28.873 1 29.037 1 29.201 1 29.365 m. s. 1 38.565 1 38. 729 1 38.893 1 39.058 1 39.222 TO. S. 1 48.421 1 48.585 1 48. 750 1 48.914 1 49.078 m. s. 1 58.278 1 58. 442 1 58.606 1 58.771 1 58.935 TO. S. 2 8.134 2 8.298 2 8.463 2 8.627 2 8.791 m. s. 2 17. 991 2 18. 166 2 18.319 2 18.483 2 18.648 TO. S. 2 27. 847 2 28.011 2 28. 176 2 28. 340 2 28. 604 8. 1 2 3 4 5 6 7 8 9 s. 0.003 .005 .008 .011 .014 .016 .019 .022 .025 5 6 7 8 9 1 19.673 1 19.837 1 20. 002 1 20. 166 1 20. 330 1 29.530 1 29.694 1 29.858 1 30.022 1 30.187 1 39.386 1 39.550 1 39. 715 1 39.879 1 40. 043 1 49.243 1 49.407 1 49.571 1 49. 735 1 49.900 1 69.099 1 59. 263 1 59.428 1 59.592 1 59. 756 2 8.956 2 9.120 2 9.284 2 9.448 2 9.613 2 18. 812 2 18.976 2 19. 141 2 19.306 2 19.469 2 28.668 2 28. 833 2 28. 997 2 29. 161 2 29. 326 10 11 12 13 14 1 20.495 1 20.659 1 20.823 1 20.987 1 21.152 1 30.351 1 30.515 1 30.680 1 30.844 1 31.008 1 40. 207 1 40. 372 1 40. 536 1 40. 700 1 40. 865 1 50.064 1 50.228 1 50. 393 1 50. 557 1 50. 721 1 59.920 2 0.085 2 0.249 2 0.413 2 0.578 2 9.777 2 9.941 2 10. 105 2 10. 270 2 10.434 2 19.633 2 19. 798 2 19.962 2 20. 126 2 20. 290 2 29.490 2 29. 664 2 29. 818 2 29. 983 2 30. 147 10 11 12 13 14 15 16 17 18 19 .027 .030 .033 .036 .038 15 16 17 18 19 1 21.316 1 21.480 1 21.644 1 21.809 1 21.973 1 31.172 1 31.337 1 31.501 1 31.665 1 31.829 1 41.029 1 41.193 1 41. 357 1 41.522 1 41.686 1 50. 885 1 51.050 1 51.214 1 51. 378 1 51. 542 2 0.742 2 0.906 2 1.070 2 1.235 2 1. 399 2 10.698 2 10.763 2 10.927 2 11.091 2 11.255 2 20. 455 2 20. 619 2 20. 783 2 20. 948 2 21. 112 2 30. 311 2 30. 476 2 30. 640 2 30. 804 2 30. 968 .041 .044 .047 .049 .052 20 21 22 23 24 1 22.137 1 22.302 1 22,466 1 22.630 1 22. 794 1 31.994 1 32.158 1 32.322 1 32.487 1 32. 651 1 41.850 1 42.015 1 42.179 1 42. 343 1 42. 507 1 51. 707 1 51.871 1 52.035 1 52.200 1 52.364 2 1. 563 2 1. 727 2 1.892 2 2.056 2 2.220 2 11. 420 2 11.584 2 11. 748 2 11. 912 2 12.077 2 21. 276 2 21.440 2 21. 605 2 21. 769 2 21. 933 2 31. 133 2 31. 297 2 31.461 2 31.626 2 31. 790 20 21 22 23 24 25 26 27 28 29 .066 .067 .060 .063 .066 25 26 27 28 29 1 22.959 1 23. 123 1 23.287 1 23. 45] 1 23. 616 1 32. 815 1 32.979 1 33. 144 1 33. 308 1 33.472 1 42.672 1 42. 836 1 43.000 1 43. 164 1 43.329 1 52. 528 1 52. 692 1 52. 857 1 53.021 1 53. 185 2 2.385 2 2.549 2 2.713 2 2.877 2 3.042 2 12.241 2 12.405 2 12.570 2 12. 734 2 12. 898 2 22. 098 2 22. 262 2 22. 426 2 22. 590 2 22. 766 2 31. 964 2 32. 118 2 32. 283 2 32. 447 2 32. 611 .068 .071 .074 .077 .079 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 1 23. 780 1 23.944 1 24.109 1 24.273 1 24.437 1 33.637 1 33. 801 1 33.965 1 34. 129 1 34. 294 1 43. 493 1 43. 657 1 43. 822 1 43.986 1 44. 150 1 53. 349 1 53.514 1 53.678 1 53. 842 1 54.007 2 3.206 2 3.370 2 3.534 2 3.699 2 3.863 2 13.062 2 13.227 2 13.391 2 13. 555 2 13. 720 2 22.919 2 23. 083 2 23. 247 2 23.412 2 23. 676 2 32. 776 2 32. 940 2 33. 104 2 33. 268 2 33. 432 30 31 32 33 34 .082 .085 .088 .090 .093 1 24.601 1 24.766 1 24.930 1 25.094 1 25.259 1 34. 458 1 34.622 1 34. 786 1 34. 951 1 35.115 1 44. 314 1 44.479 1 44.643 1 44.807 1 44.971 1 54. 171 1 54. 335 1 54.499 1 54. 664 1 54.828 2 4.027 2 4.192 2 4.356 2 4.520 2 4.684. 2 13.884 2 14. 048 2 14. 212 2 14. 377 2 14.541 2 23. 740 2 23.906 2 24. 069 2 24. 233 2 24. 397 2 33. 697 2 33. 761 2 33. 925 2 34. 090 2 34. 254 35 36 37 38 39 .096 .099 .101 .104 .107 1 25.423 1 25. 587 1 25.751 1 25.916 1 26.080 1 35.279 1 35.444 1 35.608 1 35. 772 1 35.936 1 45. 136 1 45.300 1 45. 464 1 45. 629 1 45. 793 1 54. 992 1 55. 156 1 55.321 1 55.485 1 55. 649 2 4.849 2 5.013 2 6.177 2 6.342 2 5.606 2 14. 705 2 14. 869 2 16.034 2 15. 198 2 15. 362 2 24. 562 2 24. 726 2 24. 890 2 25. 054 2 25. 219 2 34.418 2 34. 582 2 34. 747 2 34.911 2 35. 075 2 35. 239 2 35. 404 2 35. 668 2 35. 732 2 35. 897 40 41 42 43 44 .110 .112 .115 .118 .120 45 46 47 48 49 50 51 52 53 54 1 26. 244 1 26.408 1 26.573 1 26.737 1 26. 901 1 27.066 1 27.230 1 27.394 1 27.558 1 27. 723 1 36. 101 1 36.265 1 36.429 1 36.593 1 36.758 1 36.922 1 37.086 1 37.251 1 37. 415 1 37.579 1 45. 957 1 46. 121 1 46. 286 1 46.450 1 46.614 1 55. 814 1 55. 978 1 56. 142 1 56. 306 1 56.471 2 5.670 2 6.834 2 5.999 2 6.163 2 6.327 2 16.627 2 15. 691 2 15. 855 2 16. 019 2 16. 184 2 26. 383 2 26. 647 2 25. 712 2 25. 876 2 26. 040 46 46 47 48 49 50 51 52 53 54 .123 .126 .129 .131 .134 1 46. 778 1 46. 943 1 47. 107 1 47. 271 1 47.436 1 56.635 1 56. 799 1 56.964 1 57. 128 1 57.292 2 6.491 2 6.656 2 6.820 2 6.984 2 7.149 2 16. 348 2 16.512 2 16. 676 2 16. 841 2 17.005 2 26. 204 2 26. 369 2 26. 633 2 26. 697 2 26. 861 2 36. 061 2 36. 225 2 36. 389 2 36. 554 2 36. 718 .137 .140 .142 .145 .148 55 56 57 58 59 1 27.887 1 28.051 1 28. 215 1 28.380 1 28.544 1 37. 743 1 37.908 1 38.072 1 38.236 1 38.400 1 47. 600 1 47. 764 1 47.928 1 48.093 1 48.257 1 57.456 1 57. 621 1 57. 785 1 57.949 1 58. 113 2 7.313 2 7.477 2 7.641 2 7.806 2 7.970 2 17. 169 2 17.334 2 17. 498 2 17.662 2 17. 826 2 27. 026 2 27. 190 2 27.354 2 27. 5] 9 2 27.683 2 36. 882 2 37. 047 2 37. 211 2 37. 375 2 37. 539 65 66 67 68 59 .151 .153 .156 .159 0.162 TABLE 9. [Page 647 Mean Solar into Sidereal time. i To be added to a mean time interval. 16i> iJfc ISk 19'' 20'' ai* 22b 281' For seconds. m. 1 2 3 4 m. £. 2 37. 704 2 37. 868 2 38. 032 2 38. 196 2 38. 361 OT. «. 2 47. 560 2 47. 724 2 47. 889 2 48. 053 2 48. 217 m. «. 2 57.417 2 57.581 2 57. 745 2 57. 909 2 68. 074 »« 3 3 3 3 3 7.273 7.437 7.602 7.766 7.930 m. «. 3 17.129 3 17.294 3 17.458 3 17.622 3 17. 787 m. «. 3 26. 986 3 27. 160 3 27. 315 3 27. 479 3 27. 643 m. 8. 3 36. 842 3 37. 007 3 37.171 3 37. 335 3 37.500 m. d. 3 46. 699 3 46. 863 3 47.027 3 47. 192 3 47. 356 s. 1 2 3 4 s. 0.003 .005 .008 .011 5 6 7 8 9 2 38.525 2 38. 689 2 38. 854 2 39. 018 2 39. 182 2 48. 381 2 48. 546 2 48. 710 2 48. 874 2 49. 039 2 58. 238 2 58. 402 2 58. 566 2 58. 731 2 58. 895 3 3 3 3 3 8.094 8.269 8.423 8.587 8.751 3 17.951 3 18. 116 3 18.279 3 18.444 3 18.608 3 27. 807 3 27. 972 3 28. 136 3 28. 300 3 28.464 3 37. 664 3 37. 828 3 37.992 3 38. 157 3 38. 321 3 47.520 3 47. 685 3 47. 849 3 48. 013 3 48. 177 5 6 7 8 9 .014 .016 .019 .022 .026 10 11 12 13 14 2 39. 346 2 39. 511 2 39. 675 2 39. 839 2 40. 003 2 49. 203 2 49. 367 2 49. 531 2 49. 696 2 49. 860 2 59. 059 2 59. 224 2 59. 388 2 59. 552 2 59. 716 3 3 3 3 3 8.916 9.080 9.244 9.409 9.573 3 18.772 3 18.937 3 19.101 3 19.265 3 19.429 3 28. 629 3 28. 793 3 28.967 3 29. 122 3 29. 286 3 38. 485 3 38.649 3 38. 814 3 38. 978 3 39. 142 3 39.307 3 39. 471 3 39.636 3 39. 799 3 39. 964 3 48. 342 3 48.606 3 48. 670 3 48. 834 3 48. 999 3 49. 163 3 49. 327 3 49. 492 3 49. 666 3 49. 820 10 11 12 13 14 15 16 17 18 19 .027 .030 .033 .036 .038 15 16 17 18 19 2 40. 168 2 40. 332 2 40. 496 2 40. 661 2 40. 825 2 50. 024 2 50. 188 2 50. 353 2 50. 517 2 50. 681 2 59. 881 3 0.045 3 0.209 3 0.373 3 0.638 3 3 3 3 3 9.737 9.901 10. 066 10. 230 10. 394 3 19.594 3 19. 758 3 19.922 3 20. 086 3 20. 251 3 29. 450 3 29. 614 3 29. 779 3 29.943 3 30. 107 .041 .044 .047 .049 .052 20 21 22 23 24 2 40. 989 2 41. 153 2 41.318 2 41. 482 2 41. 646 2 50. 846 2 51.010 2 51. 174 2 51. 338 2 51. 503 3 3 3 3 3 0.702 0.866 1.031 1.195 1.369 3 3 3 3 3 10. 569 10. 723 10. 887 11. 061 11. 216 3 20.415 3 20. 579 3 20. 744 3 20.908 3 21.072 3 30. 271 3 30.436 3 30. 600 3 30. 764 3 30.929 3 40. 128 3 40.292 3 40. 456 3 40. 621 3 40. 785 3 49. 984 3 60. 149 3 60. 313 3 50. 477 3 50. 642 20 21 22 23 24 .056 .057 .060 .063 .066 25 26 27 28 29 2 41. 810 2 41.975 2 42. 139 2 42. 303 2 42. 468 2 51. 667 2 51. 831 2 51. 995 2 52. 160 2 52. 324 3 3 3 3 3 1.523 1.688 1.862 2.016 2.181 3 11. 380 3 11.644 3 11. 708 3 11.873 3 12.037 3 21. 236 3 21.401 3 21.566 3 21. 729 3 21. 893 3 31.093 3 31. 257 3 31.421 3 31.586 3 31. 750 3 40. 949 3 41. 114 3 41.278 3 41.442 3 41.606 3 50. 806 3 50. 970 3 61. 134 3 51. 299 3 51.463 25 26 27 28 29 .068 .071 .074 .077 .079 30 31 32 33 34 2 42. 632 2 42. 796 2 42. 960 2 43. 125 2 43. 289 2 52. 488 2 52. 653 2 52. 817 2 52.981 2 53. 145 3 3 3 3 3 2.345 2.509 2.673 2.838 3.002 3 3 3 3 3 12. 201 12. 366 12. 530 12. 694 12.858 3 22. 058 3 22. 222 3 22.386 3 22.561 3 22. 715 3 31.914 3 32. 078 3 32. 243 3 32. 407 3 32.571 3 41.771 3 41.936 3 42.099 3 42. 264 3 42. 428 3 51.627 3 51. 791 3 51. 966 3 52. 120 3 62. 284 30 31 32 33 34 .082 .086 .088 .090 .093 35 36 37 38 39 2 43. 453 2 43. 617 2 43. 782 2 43.946 2 44. 110 2 53. 310 2 53. 474 2 53. 638 2 53. 803 2 53.967 3 3 3 3 3 3.166 3.330 3.495 3.659 3.823 3 3 3 3 3 13. 023 13. 187 13.351 13. 616 13.680 3 22. 879 3 23.043 3 23.208 3 23. 372 3 23. 536 3 32. 736 3 32.900. 3 33. 064 3 33. 228 3 33.393 3 42. 592 3 42. 756 3 42. 921 3 43. 085 3 43. 249 3 52. 449 3 62. 613 3 52. 777 3 62. 941 3 53. 106 35 36 37 38 39 .096 .099 .101 .104 .107 40 41 42 43 44 2 44. 275 2 44. 439 2 44.603 2 44. 767 2 44. 932 2 54. 131 2 54. 295 2 54. 460 2 54. 624 2 54. 788 3 3 3 3 3 3.988 4.162 4.316 4.480 4.645 3 3 3 3 3 13.844 14.008 14. 173 14. 337 14.501 3 23. 700 3 23. 865 3 24.029 3 24. 193 3 24. 368 3 33.567 3 33. 721 3 33. 886 3 34. 050 3 34. 214 3 43. 413 3 43.578 3 43. 742 3 43. 906 3 44. 071 3 53. 270 3 53. 434 3 63.598 3 53. 763 3 53. 927 40 41 42 43 44 .110 .112 .116 .118 .120 45 46 47 48 49 2 45. 096 2 45. 260 2 45. 425 2 45.589 2 45. 753 2 54. 952 2 55.117 2 55. 281 2 55. 445 2 55. 610 3 3 3 3 3 4.809 4.973 5.137 5.302 5.466 3 14.666 3 14.830 3 14.994 3 16. 158 3 15.322 3 15. 487 3 15. 661 3 16. 815 3 16.980 3 16. 144 3 24. 622 3 24.686 3 24. 850 3 25.015 3 25. 179 3 34. 378 3 34. 543 3 34. 707 3 34. 871 3 35. 036 3 44. 236 3 44. 399 3 44. 563 3 44. 728 3 44. 892 3 64. 091 3 64. 256 3 64.420 3 54. 584 3 54. 748 45 46 47 48 49 .123 .126 .129 .131 .134 50 51 52 53 54 55 56 57 58 59 2 45. 917 2 46. 082 2 46. 246 2 46. 410 2 46. 574 2 55. 774 2 55. 938 2 56. 102 2 56. 267 2 56. 431 3 3 3 3 3 5.630 6.795 5.969 6.123 6.287 3 25. 343 3 25.508 3 25. 672 3 25. 836 3 26. 000 3 35. 200 3 36.364 3 .35. 528 3 35. 693 3 35. 857 3 45. 056 3 45. 220 3 46. 386 3 46.549 3 46. 713 3 64. 913 3 55. 077 3 55. 241 3 55. 405 3 55. 570 60 51 52 53 54 .137 .140 .142 .145 .148 2 46. 739 2 46. 903 2 47. 067 2 47. 232 2 47. 396 2 56. 595 2 56. 759 2 56. 924 2 57. 088 2 57. 252 3 3 3 3 6.452 6.616 6.780 6.944 7.109 3 16.308 3 16.472 3 16.637 3 16.801 3 16.966 3 26. 165 3 26.329 3 26.493 3 26. 657 3 26.822 3 36.021 3 36. 185 3 36. 350 3 36. 514 3 36. 678 3 45. 878 3 46. 042 3 46. 206 3 46. 370 3 46. 535 3 65. 734 3 55. 898 3 66. 063 3 56. 227 3 56. 391 55 66 57 58 59 .151 .153 .156 .169 0.162 Page 648] TABLE 10. Mean Time of Sun's Visible Rising and Setting. -^ a 1 S -S "*^ on 2 i o a 3 ,.OOa COaiiOi-4 00COrHiCO4t iO00'»**OC^C^OCC0i»0 (MOiCOQO»CKOi«Ot-'^a>COO.-lr-l O rH C^ « GOOtOC^li^'*CO':Or-tX) I— OOOO'^r-tOOCCi-tva COrHCOi-HCOrHCOC^COC^ COi-ICO»-(CCtHCCC^COC^ COrHCOi-iCOrHCOrHC055 CO.-(COr--OQ00V0100O OiOOiOOiOOlOtH codc^coi-'Tt*ai»j:?ooo iOiH!£JC^iOCO^Tt*«iO Tf«a> c^ M T-4 -^ rH ^r-OXlCiOlOOOt^rH tJ*i-H00i-tCOC^CO0»0 r-( -rj* ,-4 CO ^ kOCO^^OCDOOiC^ r-lrHQlNaiC^aCCOCO"^ SiOOi^OiOOiOOiOO locc^oo-^aicoi^c^o (NrHr-tr-irHC^OCOaiCO i3o»00i00i00u30 c-OOOOCOOOOOiOOOiOO ?:OOOOOOiCOiOO £»QOOOOOOCOOQlOOi 5:000000 oooo 0000000000 '£2?<=^S^O a> 0000 00 rH OOiOOiCi— (lOrHiOf-t i-lOtHOOOOOOi-H OrHOrHOiHOrHOiH CO CO CO CO CO CO CO CO CO CO -NOi-tOr-IOrHOrHr-t OrHOi-HOr-lOiHOi-H cOcococococococococo C0i-tC^r-tC^THC^r-4O»i-l Oi-lOi- iCOiCCOiOCOiOCO 5 tOiOcOu SiOCOiCCOOOiOCO JCOiOCO OQlCit-^'tO'lOCOCOt^ lAcOLf^COiACOiOcO ^ 55 i-t -^ r-t -^ i-H '^ir-t 5iOcoiccoic:oinco CO CO (N Tt< coudcOiOco )i—tiOr-(iArHiOi-HiCT-t >CO>OCOtCCOiOCOiCCO OrHC 50<0(Ntoc<5'Ocoiraeoio-*iO'9< >coioeouDeotO:OLCcokOto 3c^oo«ooeooocot~-cot^co SrHOiHL" ■" ■" jtomtoi: lOtOiO O ^ CO to to > to to CO gss CO to to rH lOrHlCr-t coiOtOOcO <0i-l0rH0r-10t-c jcocococotocococo ) iH CO 1-1 CO r-l >i-IOrHOi-l > COCO CO CO CO TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 649 5 a I 1 1 a a at 0) s 5^^ xojdav "iz; ■xojdav ^^ S ?J e^ cj CJ a^OitafilKPitDOicO Mc»04aQO4GdO4aQ(4cD CI c< c-« s g ssssssssss ^ 3 P^oitf tnBSoQOiaitfod tfcoMoQP^ccPJcQpjcd OiOf-llOr-l'^i-l'J'i-l SS§S2§2;gS5S^S§8SISgSSSS|Sg3SSSSS5S ^\£i to *o 'O *a 3» t>- r; 5; g» f-H c^ o> »o ^ 00 lO tOu3*0 iraiA lO O ^O ^ O ^ O f r^ 00 r^ COrH tacoo--AO^ocooto \iQto*o*oto^*oto-^oS> kQC^COeOC4kOOr«9DCQ tOCOiOQOO ^lOCOiOCOtOCOiO^tOcO tOcOtOeOOCOtOcOOco ^tCtOtOCOOCOtOCOiOCO «c^iO(Mioe^cOi-(eOi-it» ■ - ■ - •— lOi-oOi-l to CO to CO S is f^ to iH to i-l ^ to CO lO CO to CO St^OQOO>ooo%o>aoo> i-ltOrH^i-OJIrH^r-l tOcfttOcOtOcOtOcOtOcO .c£to CO to cotO'O WtOOJCO to CO lO CO tOrHtO ,c*tOcOtO CO to CO gSS2 lO CO to CO g O* CO OS .cfiOcOtO CO to CO 0>CO QOCC to CO to CO 'HPJi-ICJrtMi-COJi-He^ ^co coco tHOi-l CO CO CO OrHOrH CO CO CO CO SoSo ^cococo CO CO CO Oi-lOr-l CO CO CO CO tfccQJGQaSaiojGQQjcn i-oor-oicoo'iopiO'-i tOCOtOCOtOCOtOCOtOCO Scoiyjcoc^t— «t^iHt^ i-HiOi-'tOt-HtOrHtOf-H tOcOtOcOtOcOtOcOiCco CO tO to to to rH tO t^H to CO to CO in to to CO '«i CO tO cOtO CO tO CO tOOtOCOtOOiOtOtOCO 5'?35 ^ t^ ■^ to CO to <0 to CO t^iOa>tocotoOcocoeo tOCOtOCOtOCOtOCOtOCO J^COt-IOOOCO i O rH O 1-* O »H > CO CO CO CO CO CO CO CO O CO CO CO CO CO CO CO MrHM>-l«r-lM<-(m-l ^cocococococococo Oi'^fiaiOicnBi'nX'Ji rHiO CO CO to eoo»eo!NcoeS CO to CO to CO SS3 to CO to CO lo CO [3 1^ -jr t~ CO tO CO to CO lO CO ^ 0> T)« OtO c > CO CO CO CO CO CO CO S C; SS S S CO OO CO CO ^^ Page 650] TABLE 10. Mean Time of Sun's Visible Rising and Setting. o v »H '^ 3 v "m . T! > H 00 OS a S ••1 JS o X PI o » a <«» •a^Bp •xojddv •9JBP •xojady S lO p^0QP^0Qp:icop<'aQpdcQ|Q[^cupia5p:jaipijcoda3b4QQ0^cQtf^ gC^CCC^-^tM^JfrH-^T-dCIOlCOOiCOlOOiCrH .■^c~-*i>'*c--^t>-'*t^-^t-TicooDccoo JO^or^Oicoc^ocotoo "i-tCCIC^eOCOINKlT-HTr.t^iCOOiOO-Vr-lKKN ccooccoo»sooMQOcooo:ecoccccsc^o>e^o>iMO> lOeoooi'^iOoQi-i.-ioo O^OOCOQOCOOOCOOOCCX) kl-lOOOmO> !i-l-*OlOlOOTI- ^ l>» TJ* t"« ^ t* ^t^cot-*Ci^iOosr-tMsor».Hc^tot^i-(cc»oooo5'^(Ni-<»^Oir^t ■"^ t^ -^ I^ -rtt t^ -.J* t^ »i>a5cce<5oomoc;ccoo TCXCOCOCCMCCOOeCOO :CCrt«lr-ICO< ^Hi-Hco-n'iot^C4i-too-.*' ect^'X>o« -U-OCCrHCOi-KNlNINCO COODCOQOCOQOCCOOCOOO lOOOi-llMt^tOOQOOira rHCOi-l'^O'^OiOiOlO COO«iCC^10tO-^0« iCO'*0-*i-iKii-l«liN CC0CMO0C<5 0O«0OMO0 M.-ieOrtccc^(Nc^Mc'i T l^ -»• l^ f I~ ^ I^ "tH^- oc^i'-or^QC^i'^coaico OiOiOiCiSO"9.cOf-i SiC-^QOSi^-^OoOiC ■.^lOiCiCiOiOO-^O § U3 iO lO iClS O pfii ^ to ■.** CO "ij* t^ C^C00siCl^r^iCOC4C00»iO«O00 mi-iQ'^t^t^'VfHO'^ toooe'ic^t~t^e3C- : 53 M © Ifi 00 t^ CO :oidOio>OLOiO ;i0C0i050-.«»< > O -^ O -^ .H -.Ji r-t 1 1^ ■* t^ Tf r~ -.»' t^ OJlftcOOOCOrHQlCt^QO coi-ie<3iHeo?-o't>-9n> lOC^COCCiHOOil^ I^OiiOi-HWCOi-t fkOCOiOCOiCCOiC iCiCiOOiOCSiOO'^O ■.JlCO-Wt^-^t^Tjlt^Tft^ corHeomocoi-~o>-*?) ."Jir-ITJirHTrrHCOrHCCC^ ii-lt>"a>ODQpOCOr-t^CO ri-H'.j^O-^oiooiOOvO *tACDlCCOlOCOinCOLOCO eoiCHi^o>o>cOf-4'^co OiCOlCiCiOiOOlOO iC-^iOtO-^CO'^t^'«Joo>S>ao>Ao>co :iOcoioco'^t»'*r~i't^ .■■Vt^cOOOOJOi-liHOC^ fiOCOiOCOi/^COiCCOiCCO l»T)4-C<301r-( SloiNoO'^coco^iooe^o iC&iAOiCOiCO lOCOiOCOiOCOlOCOiCCOl^OCOiOCO^COiOCDiOt^lrft*'.*' 00 Oi IC CC.H CO 00 I CO 0> 0> CD Ci5 W CO < 1-1 CC r-l CO 0> CO IM " t^ •* c^ ■.*< t^ -^ t^ C^t^OiOt^CCTjlcOTHOO o>2J'~'*'Ot^i^o> SIN »oQ-***i^iccocoior*-^Oi :CHCcc*iccc^coc^»coc^cc AiCCOiCcOiOCOLOCOiOCO lOCOiOCOvCCOlCCOUDCO lOt^^OiMr-IOC^OO'J" i-^ to ic r* ic c* *t< i> »c^rHc^c^.-(coO'*j*coicr-'X)tC'r-i/5Ci^oci'-"VHCooi'-OStoaiiOO'^iMCC'CS :coc4coc4cocococccocc ^iCtOkCtOiCtOiCtOiCtO C^CCi-(Tf?DO'**'-'C»3CMOi-iOi-l— ^i-*^ lOf-tiOCMiCC^iOCMiOCM iCtOiOtOiCCOtCtOiCtO .*qo 1,0 00 :iOiHio » lO to iO iC C51 lO 00 <0 t;; to |l> to t^ tO t^ to lO to HiOi-tlO 3 iC to iC to |iCi— tiOrHiOrHiOi—tiOrH iiCtOiOtOiOOiCtOiOtO ^^i '^^ J^CMC^CMCMCMCMCOCMCO ^cototototocototototo CMCOCMCOCMCOi-iCOtHCO ~ ■* O rH O tH O r-t O r-( to to to to ^ 'OtOi-HvOCOCO'toooiccoioooicoi uii— (»Oi— (iOr-tl£if-liOi— t iCtOiCtOiOtOiOtOU^tO Oi-^OcOOOQi-<0 p lO CO CO CO CO CO CO CO tfQQP^OSP^cdPJQQOHCa iOiOlO iCiOiCiCCO TABLE 10. Mean Time of Sun'a Visible Rising and Setting. [Page 651 B S S^ •xojdd dV •xoidd V .12; ii!z5 O IH M SHcnQicQftSaitfGOP^ad QjrnOiaQOiacOdsiO^gg O i-( ?i w OncntfcoPji/jOjcnMcn e»9kt^O)t^O>t^0>t^9>t^ 0>t^9kt^9>t^0kr«9)aQ iCTkGO9>QQOkOO0)OO9^OO OJcnMcotfcDC^cfiS^cdQJai COOOSOCCaOCOOQOQaOCOCOGQ .-i.^.-irt^?is^3co ocoo>s90>coo>3"o>5' aoa>ooiet~ior-iOt^.o ■OtOiOtO>OtO>00<0>OtOiOa<0>0<0>0<0 SS8£8SgSSSS3SSS3SgS32|gSS?25S?253 icoicoiooooi25p^ S 2 SSSSSSSS2S3 ■»c -^ lO --o lO to tOfiftecf^coiSc^Oi-it- SCO — -^50»OC^*O — r* ;'.s><:coicAco ■aeo-r-^cctoc^t^i-ioQpsi SSS82SS3S2B2 vH lO ^H lO r^ U3 1^ U^ 1-^ S3>o>poo^r^w«'^ SSS82S5S2SB2 .^not9 p82S2SE:g2SS Udr-(OrHS<-llO.-'lOrt ■£^)S -OiOtO i/l "^o O :0 rf C5 -"T C^ •* IN ■«J' M ■* «M ic o lO to lO 'O ic ^ i^ eo £j a> CO 00 lO to '^ "I f^ ^CC'fCOCOCOCOCQCCCOCOCO intO^tOOtOkCtOlOtOiAtO Sg2SS82SSS2 [g2s; SSS2 >tO>A to ^tom tooto i/^ t^iO to ac-»t--totor-Tjtoio 1-1 lO c^ to in to 0> Jl 00 -^ 1 -r -N ■TC^ j xO tOiO O I >inmt~OTooiNoocj ^tOiCtOiCtO^tOiOtO intOtittOiCtOiOtOiCtOlOtO SSSS « to to to ^ GO C^ t^ -^ lO to r^ lO rH IC f-» »C r-l to otoo too to 0>Q'-1 MiSlN tO>A to lO tOiO to •OtOCOt^dOJOi-JOOIN iOtOUOtOir3tOiCtOU3tO tO'sf'^tOCCOOrHOiOSrHt^CO eococoeoMMcococ^'VC^M' lOtOiOtOiAtOiOtOiOtOiOtO OOOOCTH^i-liOMWJ" : 5ou5 '' to to o oinSSS to »r5 to »c t I too StOiC 00 OJ to>oo Or-liBrt rr rt lO to to to .t>iOtor~'T'OOCMOi-iO) Jin OiO "lOtom OtOOiOr toio to in t MooKcQMcnOHOQQicn . into t~ ) to lO to in to u-:) to Minr-lt-350Dt^OlOIN inointcintoioointo 3 0» to iH ■>»< CO MCOCOCOCCC'SOlCOlM'^C^-T intointointoiotoiotoioto ??3 CXI Tf to to -^ 00 N o cocjcoc^coc^eoco intointointointointo KmeiiaifixiOixiaiwlcii'xiOitxiciaiKait^ai -s^^s-" c- 00 oa -^sr-^ QCJoQ'fl'totOTjiooiNOOej 55co?Sco?Jcce pj OQ pj «} P4 OQ CO CO CO ^ p^OQe^COpf^OOP^tnplSaQ PJCCpSCOp^iAQSOQpljCIQ p^ccp^xipi^izip^inci^cQ g'aOi©CO«0005000«000<0 05 CO oa 00 Oi 00 0> lO -.Jf lO Tj< iC -^ »o -0-*0-*0-5'0 tciC «o lO to la -Ol^Ot^Q«0QtC>Q^CH0C> t^lM50C)«5C0-*o^OT»ic5 lOCOlCCOiCCOiOCOlCCO t~cor»cot^eoooc^oo mooc^CTi-hoithooo 1 CO lO CO iC CO vO CO 90-^oo'»j'o>3;oJcog;coO(Noc-j.-ii-i.-i.Hc^oooeoo5coCTi'o c^coco cOkO CO C^COM-*ii-liOOiOOto — • — — ,J1 rt .^ ._, IQ to U2 to lC CO iC CO kC to ii ostoost^opoot^Qor^cs COt^COi— (COr^CO.HCOi-1 lOCOiOCOiCCOlCCOvOCO ^■rfeO'^tjicofcoincjco S-^rH— ■— •— ■— ■ .cjkOCOkC StOiOtClO tOU5 to tomtoio 00 .-to tOiOtO -.Jl rH CO S^ CO (N iC to iA to kO to g' CO Oi c^ to tC to vC c S-tflN-* ooo> ■^ rH -.f tH -.Ji r-t lO to 1^5 to kC to CO .H CO 1-1 iC COlCCO CCOt-OCO.-ICOlMtQCO COI<1CONCOCJCOC^COC^ tCCOl/SCOiCCCk^cOkOCO l-»Nt~CO CO 6) COIN lOtOift to c5eoc^coc<> tc to kC to kC to CO r^ -^ to iO ic to COC^COM iCtOiOtO JtOt^t^t^OOtOOOtOOi rlCO iC CO tC i-( CO --* CO 1-1 CO r-i CO kO CO iC CO kO CO tooujT-iTjiiHcoc^eoc coc^co lOtOiiS C^ CO iM CO C>4 CO CJ to IC CO iC CO IC CO <-OO0>-^00(N CO0 CD IC to lO to _ lOtotoic t^ eO(NooMcoM iO tOkCtoiC to 300 CO OS t/5 tOiO to CT O T-J .^ CM —- ?5 00 ■* COCOCOCOCOCO-MCOC^CO kCCOlOtOmcOiCtCiAtO t^iototxinoocooic^o C^eONCOlMCOMCOlM'* iCtOkCcOiOcOiCcOiOtO esi-^CSO-^OiiCOOtOt^t^ S-^cS-^M CONCOCT coc^ <*iCtOiCtOiOtOintOiCtO to 00 lO g> -cc o SSieowcoco lC to tC to iC to CO CO CO CO 10 to tA CO cocococo?icoc^coc^eo lOCOiCCOiOCOkOCOiCCO 10 05-* INCOCl llOCOiO ■* e< -.J" c-» -ic CM •.»' CO ift CO iC CO lO CO S'gcco>t^ocoot-o>coo "Ji^COCMMINCOfjeOCO .C^if^cOiCCOiCtOiOtOtOCO S"oaQoooaawoco.-t»cco coiNcoficococoeococo rfjiftCOiOCOiOCOkCCOiCCD iftr^'^CMCOCOi-f^QlCast^OCQQCOaii/SO'^'ClCMCOrH CO CO CO CO CO CO lO to iC to lO CO coco iO to ire CO T^cocMe<5cMcocM'*N-*f<| iCCOiOCOiACOiCCOiACO; iC O CD 00 00 t^ OS to lO CO 10 to ifl to ■.((^•coiOi-itDOgoosos CO CO CO CO CO CO CO Co CM CO 'iretOiCtOiCtOiOCOiCtO p-oco.-i-.j'coeo-.jifico CM-*Cq'.eOQOCMOQr-IOSCO :cococoeoco'*cO'«j'(M'j< aOtOiCtOiCtOiAtOiCtO CMCOi-IOOOsOSOQ'-l COCOCOCOJNCOCM-^ lOtOiOtOiretDi^tO CM-<}< lOco iCCO-fliiOeMCO-^OCOSO! 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SS iS S5 9S iS S2 ?3 2 CQeOCO€OC*COC«'<«'C4'^ SOQlOe^MtOaOiHCOtQ ro'*e<<»"M'<>'r-(iOr-liO S5S2S52S2SSS SSSSBSSSSS ,^oo^ooi»Goeooooooo ir^oOrHCIt^toc^OqOiO ^OOCCOOCCQOCOOOCOOO !iOt^c»cceoo>t^tOQec c4aocOQOoooocooocooo C4 ^ CO CO CQ CO CO t^ ^ t- ■«»< t~ ■* t^ i-li-IOQiC'S"OOr-INt»tO eo->>'e!i-*c^-.»i5to©i-(>otooM'.t'r~ r-nr5iHlOi-lOjO©Oi-l3T-lCC<-«l>(M ■.>it^'*t-'»»'aO'*aO'^cocooocoooeoec ■. •<)< t^ .-i<3>t^cocoocaoc4co30r»eo-H i-iiOOOOO * — " "J" r- ^ 00 ■»' CO cococoxcooocoooeoco :coco?» oiiccOfHt^-r^t-tcOkCOOs-^coQooinco CO 0 t» T(< r» -.!< t- T»< t~ 800 lA CO 0>Om Tf 00 ■* 00 CO 00 ;r»tO'*ooeotoi>-c^^;aoin- iC^COCl-^M^i-l-^.-liO 000( > as ^ lO 05 Q -^ )co xcooocooo •ajBp •xojdd V ^2 I PAosp^cfiPJOQtfcoC^aQMaQBiHcnCiHaoMcoPjco •^jz; ■.J" »X^! SOO'O'COOOOJCOOiOC^ ■-i^ciwfjcoeoc^-"}' cOQCcoooeoooeoooco» ^?J:iC>'^ootoi0^eo cocoeO'^c^^iHusoo cooocooocococooocoo) o>e^NO>"»'t^iou5r-co f»T»iH>nooiOi-i coooeoooeo»eoo»c^o> oOOi »-tt^Cc40> ■^rosoioco.-ttor-O'^ ■^i-Hcoc^cocorJWi-i^ CO00COXCO30CO00CO00 MooPJaQp^GoMcnKod p^cdPJaQpjcaPEiaoPjcQ C^C^'«1 .Q0iG0O':0(NTf-^C>) i-iC0rHCOr-t?S(NW5sC^IC>lC^ r-i6*rHC^rHOC0OC0O0QO00OC0]O(NOC^r-S o c^ o cs o 6i i-f 2s »-i ci gQ00r-t?pCSiOCO3*TjO>0Qr-(r- OCOiCCOiCCQiOCOiOCO OCSOMOCSOCSOC^OCM iO O ^ lC ^ ^ ilO U^ O ^ iC lO cD^ tC lO eO^ '^lO too !OC4t*'-tcoO!:7>o>or* ,-H(OCSiOC0'^>0«t$CS i/SCOOCOiCCOiOCOiOCO Sr^-40!Mu5'^'^oco!oiNt>'fHGoa»o>aOf-Hr*^to COiOCOiCCOOCOOCOliCCOiOMUjiMOC^OCSOC^ ^ ^ ^ ^ '^ ^ ^ ^ ^ CO gOOOi-HI>.-IOe^lCCO-^N*'COiO^COr-*^QOO^ SQ00r-(r-.CSt^»0!OT*«iC US-^iOCO^OC^b-rHMO ^lOO U5 lOiO vf^ lO O lO lO irt iCiddC lO O O »0 tO gr-ta>(MC0!Nt^C0t>'^«liOiO>C-^«O?5t-C0a0CS lOCOOC^OC'lCXNOCMOC^ ijCOOCOiCCOiOCOiOOO iccococsr*QQOo>a>Q0Qr-» iOLOiOiOiCiOiOOidO''-0 a>aiOoQr-.cstocoic ■^'a> ■^•WiOCOiCCOiOOOiOCO lOCOOCOtOCOiOCOiOCCiOCS O lO tfti lO O iO O O tCO lOO »Oia lO lO lO O »C lO >C O ■'!?«'«*rHa>CSQ0C0G0C0l^'^^*^O^OlCC0^t^'<1•00C0'a0C^C>rHO^-H^HOfH01,!^^0lC0QQCC^-■^C0lOl0C0»£5 ^lOOiOiOOifliOiOiCiO ,iOiO*C»rtiOiCiOift»OiO gC^OccaiccaoTj*oO'^t-!iCi^iCtocoict^»oaO'^ r*c^ocoo>-^a>Tfcooool' ■^^-Ttr^a>F-oor^oo lO iCiOOiOiCiOiOiOiO ooaoooi>aii'*aiOOO ^ lO ^ Ij - - - - - - If) iC O L " 40 "^ lO 'OOOiOiCiOlOO r-l'(J<.-('-ot>-o OOOlCOOOOlGO^opOit^tD irt lO lO OtOQtO'-'tOi-tiO t^c^r^cst^r-f^-T- 'oorH'oO'HoooaiOa>o>oi(j>'o •«# lO T}< iO ■^ "O ■^ lO -^ lO —* — ■*—' ■^—' ----—' ■" ■< tO -^ iO lO lO iC 00 O CO i-H 00 r-* CO ■^ lO ■^^ lO ^ «0 "^ iOO»C»CnOiOiOiO i> CO r^ CO t^ CI t CCMOOCSOOtMCOi— 'Ol'-fO'r-tClOajQ Tf tO -mo - iCiCiOO»0»OiO»COiC a>oo>oooQO ^ lO "^ V5 10*0^10 lOiOiOiOiO'dOO 'xojdd V ^z • GOiCOOiOOOiCCOOOOiO r^-^t^-^GO-^coTPGO-q* gOOiOCOiOOOiOoOiC • idOOiOtOLAiCLC OS to OltOCOtOCOtOOOtOOOtO 40i/5lOOiO*0»C*OiOiO fi^copisQQQ^cdp^cdp^ai OO'^OOCOCOCOO'. COOCClCTi'MOHNOS'MOfNOiOaxN TptO^iOTT^iO'^iO'TT'iC'^* ' ————— — .—— — OOiCCOiCCOOOO'^OO-^ OO'^OO-^OO'^CO'^OO-^WTf uCiCtCu3iAiCO>OtO>OOLO ootoootoootoaotoontolooo'ao SOOtpOOtOQOtOOOtO pJGQpi^c»P^ciiQ^O3P^xQOCOOCOtC a « "-1 00 o g eo 1-1 1-- N X5 eo'soococo^oogog ^ CO kO CO tC CO kO CO in CO to CO lO CO *0 CO iO CO lO CO tO ai005aS!Nr^Og>0>Ot~-UJCOCOin-»COCO5»Ot;?J«M5riON .^cOiOCOiOcOiOcOiOcoOCOiOcOOcOiAcOiOcOtO cOiCCOtOCOiOCOiOcOiO •*2'C021QQOQO>ejt^ s^ocNofSoeoioSsiO co>aco>oco>ncoTfco'4i co^co^co^co^co^ cO>ACSiOCOtOCO>OcO^ goocjco'tl'ONOQO ra>Am>Aeoiacoon>o eO'«<«OT)ooo!Sm2 IcOiOcOTfcO'J'CO'VCO'^ g«iOj('*g?»t-<-cgo»jgooor-eaMi0 coiocomcO'Oco^co^ ^CO>OCOiOCO>CCOiACO>0 r^OQpo>a>«f-it^?^*oi'*'^»owcOF-iaooo4gp O !?» O i-H C> 1-1 .1 i-H r-l rH r-1 f-1 r1 rt rH i-H 1-1 f-C 1-1 C5 CO iC CO lO CO lO CO O CO to CO tO CO 10 CO lO CO lO CO lO gSS8SS8SS22 21594°— 14- -SJco -35 S^SSS'-^oQS'f^tSco iO«5?)gpi-ilm©oo>.-Qoo»rHor) SSeoaMioSoc^oc^ .^iOiOiOtOtOOCOtOcOtO ^aoeoc-'fl'coiOxiO'.i' cOiOcOiOCOiOCOOCOiC ocoiac4>oco>oeooeo tCfOtOiOiCLOiCkOiOCOiO Scococoioi^irat— ^ooeo SiOop»cr*coi^cocot>.»o S?3S?!SS2SS2 S22gSSa8SS COtOCOiOCOiOcOtOCOiO •o-»coeOQQp C0iOC0iC«0iOC0>OC0>0 nt^cocO'^2)0QC<5t-5't- SOC^OMOC^O'N C0i0c0i0c0t0c0«0c0t0 Scocpiot^^gpcoacJ (N O IN O -^ O CO O N OOiOCOOOOOOO lO t/d tO CO tO r^ r- r^ tN. CO CO o J CO lO CO 40 CO lO CO cOiAO 00 lO I^ »0 CO CO irt lO CO tO CO kO CO 5;S?3SSJ2Sa8 COtOcOtOOOtOCOtO cOlO ocoo COlOCO ^^ CO o 000* ^ 00 lACOiACOlO coo S558 0*0 CO 3; r-( 05 i-l CO CJ C^ CO O CO O CO O CO lOCOiOcOO coo 3'^O'fl'O'ViO'^iO^ 30IOOICOOOOO ooco OtOO •rocoiccot o 000 Ou 000 r* o» tr o» CO o CO COiOOTOCOOCO 00 00 icco 8g ^"5 iOiMirae9'<>>cO'<»ie5co iOiOiOiOiO>0*CiOiC iOiOiO IN ■5; N 10 00 o» rji u5 iji lO CO i25 eo 'i-jt^i-ir-Nr-iNcoNcomcomiOeoiO'j'io i lO rji ic *«!« lO Til ^iniCiOiCtotOiCiOio to tO lO u JiJiO "lO^ JiOiO lOiOiO •ci'io OOOSfHOSi— tOSt-100 ^lOTTiO'^iO'^iO'V tOiOiCtOiOtOiOtOiO -c;o tOOtOOOOOOO SQOCOOOCOOOCOQOCpOOCD *^0^iC^0'^O'^0 iiCiOiCOiOOOOvCO rHO0*-4O0C^C»C^QO ^ 0> '^ 04 ^ OOOiOiOOOOiOO CO O CO tft CO o cs ^o ^ o ^ o ^ lO OiOO O tCO iO-» COOCOOCOOCOiOCOtO 8S8K8 CO kO CO to CO inomSS! 10 CO 10 CO 10 S 1-1 5205" MOCO© COlO CO 10 CO 88S8gS lO COlO COlO SlOrH-fllN eo©MO CO lO CO 10 CO o coo coo -_ -3 04Q0 04 O coo CO o 00000 l^Ot>-Ocp coocooco OCOOCOO flCOfHCp O '*»"0^0 00000 ■^o-^o^ 00000 00000 o '^ o 00 t3« O "^ O ^ 00000 C^OC^OC^OiC^OiNO* O 'VO 00000 ^O '^ij 00000 ^ O Tj< o ■^ o 000000 Oi CO O CO -*j»ooo 0000 C30cooot>-oot^oor-oof- '«i'0'(NC4COiMC<5CN 25QDCaT)<«00>-ltOiOr-l eoi-oj'.-i^iHiooioo OCOOTO.-INi-IC^>-liOeOOeOOCOOC^O(NrHO»THr-ti-li-llNi-l S©r-l(NO»-*«5C~C»50i-teOOO«3>O^IM(NOOtO>0 CTJl40CO>OM>OCOOCOOC40!NOC^rHT-liHi-l gOM t^ 1-1 0> 00 IN «P IC CO t» o CO »0 CO --^ TJ< -^ Tj* Tp '^ TJH -IS* -^ -^ CO iC CO »C CO UD CO t^C^QCSCOtOtOCOOO iOCOOo ko 5tOiOiH^tO«>0(N-* SiOOkOTH-^rH-VC^CO oocooocococooocoooco lO^iOiOO'^OCOr-ICO t>-eor~cooocoooeoooeo OjcQpijccp^oop^aopi^aQ Cat^tOO-^COC^iOr^tO IM»5 OOCOOOCOOOCOOOCOOOIM Wt-r^COC^OOt^COtNt^COr-t-^iOrHOOCOi-ltOCO ■* lO •>Ji lO lO ■* lO ■* O CO O CO 1-1 C^ (N 1-1 C^ i-l CO o t» eo t~ CO t~ CO t^ CO 00 CO oo eo oo co oo co oo co oo eo •<»|c^oot^cocooooococo COOCOiO'*1CCOO»-*'^<3> (NOCOOCOU5COiCI'«I''<*i t~Tjlt»TlM>IN iOCOOeOlH(Ni-liHlMr-l t^cococooocooocoooeo a>T» -.ji t» T»< t~ CO r~ eo t~ CO t~ CO t~ eo csi to ■* eo t^ 1-1 o 00 CO lO to (N o> 00 eo lO to 1-1 p 00 l0C0l0C0>ac0O?>O(N 0coiOQOOeoiO lMOiM>OCOiOeOiO'3<'03t»eo StNiCi^COtOr-ICOOiOl^ comeoiocoioco-*'*-* <;tO''i^t^-JOCOO> ^jtOiOtOiO o^c»-^t^eotoiCTft*(N ojioeoiocoiocoiccoio tO"#tO"^tO'^tO'iM(— C^OlNOINOCOiOCOiO tO^tO^tOiOtO'^tO^ INOlCOt^iOtOtO'^OQCO toio toio toiO to oMOc lO tOiO t 05rHiHOC000>0t0t^^ ^C^i-IO^COt^tOiCaOC<» (NOeOOCOiOCOiOCOiO co lO ■**< -^ -^ ■'J* -^ -i^* i^ -^ tOiO tOiO to 1* to^ tO^ to "^ tO'^ to ^ to ^ to ^ OOrJiOl tOiOtO C^Or-l lOtOiO toio toio ■^OOiO iHr-lr-l tOiOtO t^toto lOtOiO OOiOcnrJ" 1-(1-t1-*1-) tOiOtOiO »tOt^t^t^00tOO>iOC>'^ SO(NO(N rfjtoiOtOtO 0(N0(M01N to>ato>atou3 S-iJ<(M^»HiOOtOOtOO> ocoocooeoocoOfN ^tOOtOOtOiOtOiCtO^ SrHtOiHiOdiQlN-^eOt' oeooeoocoocoooi ^COiOtOiOtOiOtOiCtOiC I*00O00CJ>0at3iOCiO100 Ro-Tjiioeoocoiocoiooo - lO t#l to -^ to Tj< t «iOU3kOiO^U3tO Seo^cooacoooeoooeooo e'2«2<5'^'5«^=>cOQeo •(•iCLOiCiOiCiOiCiOiOiO Sr^t^i-*t^t^t^t^QOt^oo .^^ Pi OQ Ph CO plH cc P4 cc CtH oi 0SO iH -^ asooosr^otD ;OiOCOiCCOiOOiCCOtO .. 5 -^ lO "^ "^ >0 '/3 LOO^^iOLOLO^tOL/3 pHGQpC^OQP^GQp^CQpjcO Q^COp^CQP^cdp^OQpC^CO plHCOpHCOPE^O^P^ODpi^CQ SiOt/3 kCioSlOCO TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 667 I ^ I ^ s (-1 s ^ a a r^ S 3 1 II to 1 o g 3 -2 (^ O ." "^ 10 .•5 =1 !^ DO I I 5^ g •xojddv •ajBp •xojddy .■SS; Or-tOCO'* io«or~oo 0» OrHNOT'* ico pjoipjcoOi^ino^aDpijaiMaiPdaid^aQPi^aQe^od^P^aQedcnP^cdoi^ S^ CO ^^ CO r-( CO 1^ CO r^ i-HOr-tOrHOr-tOrH CO'HCO^HCO^^CO^HCOt^ CO^^COi-HCO^COrHCO^COFH OiHO^Or-(C5rtOi-t 0rH0»H0i-H0i-10i-l0lH CO cO CO CO CO CO CO CO CO CO CO CO CO CO ^ CO CO CO CO CO sasasssasa CO cO CO <0 CO O CO CO CO CO P< en 04 CO tf* CC p^ QQ P^ CO P^ CQ rHOr-*OrHOiHOiHO?H CO CO CO CO CO CO CO CO CO CO CO CO sasassssss CO CO CO CO CO CO CO CO CO CO r^eoweor^dt^wtrCi r*crH^*o^*o^ot«o OfHOi-tOrHOfHOiHOr^ COCOCOCOCOCOCOCOCOtOCOCO S" to '^ t^ ^ t^ ^ r^ so r^ CO OrHOiHOrHOr-tOr-t ^ CO O CO CO CO CO cO CO CO CO «^cDcococococococococo jjoocOOOuoCgiCCJ-^Cft'^ t^cOcococOco^cOcOCOcO ^oococ^co2*''50»coM* ^ '"O CO O CO cO CO CO CO CO CO g^t^-OCOOiCrHlCr-t^ f^cocOcOcOCOcDCOCOCOcO QOCOQOCOOOC^OOMgM COCOCOCOCOCOCOCOCOCO Sc^g>r-*o»Ho»-^oo»-tOi-HOi-^wi-t2ic*^c^2> cococDco^cococococo 'co cocococOcococococo^co >^0»C0OC0OC0OM— *Wi-*W^r^C<.-(WOCOOCOOC02aC0 24'*2>'^C COcOCOCOcOcDcOcOcOCOcOCOCOCOCOCOCOcOcOcCcOcOCOCOCOCOCOCOCOCOCOCO o-^oco^eoiHcoi-tcsc^c^Ni-tcoi-ieoO'^o CO CO CO CO CO CO CO CO CO CO |cO CO CO CO CO CO CO CO CO CO t-t'^^COCSCO(NC^COC4!COi-('^TH'»<0»OOiO IcO 1-1 -^ tH 'J^ c CO CO CO CO CD CO CO COcOCO COCOCOcOcOcDCOcO CO CO CO CO CO ^ CO CO CO CO CO CO CO CO COCOCOCDCOCOCOCOCOCOCOCO 3SSSSSJ C<-^MCOCOCOCOC<^i-H|iOi-HiOOCDOcOgt^g|r-gOOgO>^OigOgOg cocococococococococo !co coco^cocococococDcocococococococococococo ggt*OcO»-tco»-tiOWiO *<£cOCOCOCOcOcOcOcOcOco ^oao»-»r^^coc« iH i-t tH r^ i-H i-H fH CO CO CO CO CO CO CO >oaoc» i CO CO CO r>- CO CO -^ iC kO -^ tH 1-H i-( r-t rH iH ^H CO CO CO CO CO CO CO ;oooi-f * CO CO CO CO C^ iC CO M* '<** CO f-4 1-1 i-H r-trH rH fH CO CO CO CO CO CO CO ;cotO<0 to w lO CO eo ■* c» CO CO CO CO CO CO CO CO CO CO CO CO ^ CO CO CO CO CO'^'^'J'lOCOlOe^COrH CO CO CO CO CO CO CO CO CO CO i-H iH rH r-l iH rt .H .H rH r-l lH rH rl O rH S S O N © CO O CO CO CO CO CO CO CO CO COCOCOCOCOCOCOCOCOCO CO CO CO CO CO CO CO CO CO CO CO COCOCOCOCOCOCOCOCO CO CO COCOCOCOCOCDCOCOCOCO iC^lOCOcOCJt^rHXO CO CO CO CO CO CO CO CO CO CO iC^COeOt^C*OOr-40>0 CO CO CO CO CO CO CO CO CO CO OCOCOC^t^rHCOOOiC cOcocOcocOcocO'-OcOcO 2SSS?5B?38?5S COCOcOcOcOcOcOcOCOCO S8SSS?J8?5gSS COCOcOcOcOcOcOCOcOcO IcO COCOCDCO'-OCOCOCOCO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO CO ^ CO CO CO CD CO CO CO cocococococococococococo ■«^lQMC0CJt^.H0QO0»0> C©»-(gp rHr^r-*THr-)t-Hi-(OC^O COCO^COCOCOCOCOCOCD ?5Sg58S5SS§8 COCOCOCOCOCOCOCOCOCO cOcocoCOCOiOCOiOcOiOco^ coc^r>-i-Hco^<3igor-4r* cDi-Ht*oooopa>t*tHco cocococococococococo cocococococococococo CO kC CO iC CO ^ CO lO CO lO CO U3 tococococococococoic ;OrHrH £ CO CO CO lO iH -^t* cococococococo isas » CO CO CO or^ooot^ocp T-tOOOOrH© CO CO CO CO CO CO CO >O00i-l :ooo » CO CO CO ggggggg CO CO CO CO CO CO CO lOOlcOcOcOr^OicpQ'^ COCOCOCOCOCOCOCOCOCO 0«C0C0rHlftOC0 000Qt* cocococOcocOcoiOcOtC '■^Qocor-*r^*oa>"^oc^ rHOr-(Oi-c^i^-^cDco'^r*c^ cOtOcOiOCOiOcOiOcOiC 6iioco25o31r5coSwicco55 COtCCOiCCOU^^OiACOiO'-O^ SScoScoiocoicSTfco^ COU^COlOcOlCcOtCCOiCCOUd isSjcoiocoSco^co-^cc"^ COiCcOiCcOiCCOi/iCOiCCOiC aa^-IQO>CSt^'^C0cO-^t>-(M c- »-H cp CO us ^ UO iC CO lO §SS28S§5S!J COiOCOiCcoUDCOtOcOiO dcodaapiaaoiisfiaa ^^^ '^ir- IC «3 t^ 00 04 CO lO CO O CO lO CO lO to lO CO lO CD lO CO us CO iO CO iC CO lO COiOCOiOcOiOcOiOcOiC COLOcOkOCOiOCOiOcOiOcO^ (4 CO 0^ CO p4 cc p^ oD p4 00 O —I IN CO C< 00 p$ OQ P4 00 P4 CO P4 00 P4 OQ 1/5 CO oS"^S~^^"^ Page 658] TABLE 10. Mean Time of Sun's Visible Rising and Setting. B a a s ^ I 3 o .=^^ •xoiddv q"* •aj'Bp •xojddv -(Nr-cot^coocooN?M rHOiHOfHO»-HOr-(Ot-tOf-HOi-HOtHOrHO oooooooooo oooooooooo g'OQOifttSOiOt^OI^OO r-10rHOT-lOi-HOr-tO ^oooooooooo t^OI>iOt>iOQOiOGO-<^ i-tO.-HOr-lOrHOr-(0 oooooooooo SI>l>t^O00O00i00i»0 r-iOi-lOi-HOt-tOi-tO ^OOOOOOOOOO ji a>oo>iO ovoo -^ 1-H CO (M co c^ '^0-^OCOrHCOf-l»OC^O ^ oooooooooo SiOC^O(Nr^rHI>OOOOl 0JOcNO(NOCmOCS»0 p^OOOOOOOOOjO OOOOOOOvOOiO oor^o>oooio>aooii:^ OOOiOOiCOtCO^ Oi'JiOGOrHt^'NOC^t cr>a»o>a>'3>oO(^GOOooocoot-*ot^ot^oi>' OOOOOOOOrHOi-HOi-lOr-lOr-lOrHO oooooooooo 'oooooooooo ^i-(iMi-tciocoocoa» OOOOOOOOOiO C^ (N C^ f-( CO rH CO O "^ O Tj< C> >C 00 O CO O !>- t^ O oooooooooo O vO O lO O lO O lO O lO >iOi3>oo>ocoi>-t^iQOt^a>oaiioO'^r-ico >-i-H00QO>O^Ot^ i-iOOJiOcO-^vOCOOrH OOlOCOlOCOiOCO'^'^Tr -<^^Tf<-«J4-^'ie}*^TtTf<-^ O »0 O »0 O »0 O lO OiO O lO OiO O lO OiC OiO Sa>ooo>i-Hcc-coo CSOCOtOCO*OCOiOCOiO ^OOOtOOiOOiOOiO CO»OCO»OCOtOCOiOOOiO OOiO^-^-^Tj^TjfTjtTt*^ OiOOiOOiOOiOOiO O»00v00v0 0i00i0 io-^oc^t^i-*a>ooao *OODi-HXNOCOiO»i , ,_ iiQ-^ocor^c^oOt-i^OQco - CO lO CO iC CO O CO lO CO lO CO lO CO O COiO CO »o ^ -^ ^ O lO O ^ O iCi O iC O tO O »C O »C O O O iC O lO OiOOtOOiOOiOO»OOiOO»OOiOOvOOiO StNt-COtO-f^iOCOt^C^ CO»OCOiOCO»OCOiOCOiO ^Olooioo^o^ou:^ SCOtOTf^OCOt^rHajQ COUttCOOCOiCCOiOCOiO ^OiOOiOOiOOiOOO ;iftCOOC^OOf-tOiC3>»-HCO ;COlOCOiOCOiC00Tj-QooirHr*coo COiOCOOTfTf'^Jf-^T**'^ OiOOUDOiOOiCOiO Tt<'*iOCOI>C^opQQ(3ii-H>COO-^-*fOCOt^f-< ■^■^-^■^■^-^^■^iScOUCiCCiOCOiOCOiOCOiOCO o»oo»ootoo»oo»o iOicoioovoo*noio 00>r-iOOC^O-*»THGOOOO OiOOiOOiCOiOOiO St>.a>'-HO(N-^Tf«co COT}«CO'^^Tjf'*3^T}*'^'^ ^OtrtOiCOiCOiOOiC »O»-lt-*O000QQOC^»O ^■^^■^•/iOvOOiOOiO S*cr>cor-4c^(NOTjcorHi-*cooiiOt^ i>.iooico»-4«-*coa>inr* i^ioococ^oicoot^io COTi00i00i£500 Oi00i01>i0t*»0t*»0 t>->Ct^iCr^iOt^»Ot^iO H-^focor^i-iaiaiwoo TJir^-^CbiOCOiOCO OCOiOCOOCOiOC^OC^ OiCOiOO»OOiOOiC OiCOiO O iC o»oc*»o 35 0> «-< CO <>) O ■" CO t-^f-tOiOSi-HCOCOOiC-^ Tt* CO »o CO »rt CO S CO S CO tocoib(NO oi otNOC^ o ic o lO o lO o lO o o o iC o o t^icr»ior*io T-tOOOidOCOO<-*OOOi OoQ^lO^'^fOC^aOO lOCQiOCOiCCOiOCOiOCJ 0?iOC^OCJOC^O(N Oic o o o lO o vo o lO r* ic r^ lO t^ tc t-* ic D» lO C0C0intHr*0*0l00rHOC0-^iD(Nt^OCll^i-t^01iOi-HM'COCJ »0!NOC^iCC^OC^OC^ OiOOiOOiCt*vOI>»0 iooi^r^giiCcot^"«tOi-HiococoiOi— ii^o> oat^r-tiococoiCi-Hr^o* CO CO Tji CO -^ 00 "* CO TJ< CM Tj* C^ lO 04 O CM lO CM tO iH ^ O lO OiO O lO O tO O lO O lOO lO OiC O »CO iC ^r^comioco St-.-ia>05t-H, ... COCOCOCM-^CM-^CMTfCM pcfOtOOiOOiAOiOOiO SCMTjf-^CMOOOOCOOO COCMCOCMCOCMCOrH-^r-i ^OOOtOOiOOiOOiO P^COtfc^P^CfiP^COPiHCG -, rH CM CO Tf« O CM CM CM CM 'T O O I-* -^ ^ CM OO 00 t^ rH lO CO CM O O Oi C^ f-H -^ lO PH O rH O rH O •-< O O iH O i-( O r-l O «— I O CM lO o tO t*io t* o r»vc i> ic r» »o t^o t> lO t> TT t> ^ _ 00 i-l O CO "^ lO CM QOOOr^COiCiCC^GOO TJ< CM TJ1 T-) lO *-l lO i-H lO rH lOrHOOOOOOOO oo o»c o ic o ic o »o o >o t* lO r* lO t^ lO r- »o CM'^iCCMt^OOit^i-HiQ OiOOOOkOOOOiO '''«3*l>'^ S^COCtJodP^CGt^COP^GQ fO r* oQ o> ^5^ CM CM CM CM CO OI>C0iCOCMe7>ClCM<0 ^Q^t^CM-^iOr-tOOQO ^oiP^coPtHxPtHCA'P^co PehgoP^qqPhgqPhcqP^od TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 659 S -s -a ' CD t> Q II .1^ ■xojddv •»)BP xojddv .-I e-j cc pHodMcnC^copiHaiPiiaD EOi-lOi-lOrtOrHOrH Or-«0.-10r-IOlHOlH rf* CC to to to to to to to to to ^ ?0 CO <0 to <0 <0 <0 to CO CO giOgio^ce^coMcom tti to CO CO CO CO CO CO CO to CO t^cototococototototoco ^tOtCco^tOiOCOiAtOiO OdoQP^OQpHCCP^CAf^QQ P^QdpEJcCp^QQP^odpciQd SccMcoMcoi-Hcoi-teo rlOi-lOi-lOi-lOi-l CO totocotocotoco^to tfoQMoipjaQPgadpiiod rH 00 f^ CO tH CO 1— t ^ ^^ Tf* Oi-iOf-iOi-iOf-OtO>OtOU3tOiOtO>0 ^lAtOiOtOiOtOiO^kO M'tOQt^O>CQaOO>t~QtQ rfftOiOtOlCtOtOtOiCtOlA tototototototovtoto totototototototototo t-iOi-iorH©«55e5io totototototototototo c^iisco?5S tOiOtOtOtOtOtOOtOiO 'Mto>oto>o>QtoiQt^^^-cQaQC4a>c40iH.-io tOiOtOlCtOiOtOiCtOlCtOiOtOtCtOtOtOiCtOiC occc4>ocoiAco'«< tOiOtOkOtOiOtOtOtOlO !SS!8G:C;2SS!222 tOiOtotCtOiOtOiOtOiC i-Heoc^cjOT^^otoo ^ ^ ^ ^ ^ ^ ^ ''t' ^ CO cOiOtOtOtOiOtoiOtOiO ^^^^^*^.T^^^ ■"^ c5 ^ rt ^ CO *o CO lO CO to lO to to to iC to IC to lA to kO to iC to lO to lO to lO gS5;5J^g!g5555! .CftOlOtOiOtOiOtOiOtOiO iC'ar^QOOOJOJt^rHtD ^^''It'T^CO^COlOCQ tOtOtOtOtOiOtOiOtOtO B'^tytOCQtOftcOOOaO ■^^^^^^^.^■ItcO .citoiotoiotoiotoiotoia ioco>ccoioco>am£c^ tOtOtOiOtotOtOiOtOiO St^Ntocosi'^wtOi-i CQiOCOiOCCiOCOiOCO tOtOtOkOtO^tOtOtOiO sStocSotNOc^oSI toioto>ot«iat^ior«io ^■"Ttrcoioeoiomioco ^toiotototoiotoioto^ >OCOtOiHqOQC»OQ'^tOCOlQ>CeOt^l-IOO>f-ltO ;><5cOiOCO>Oe^OC4 0C40C^OM0r-li-lrH to>oto>otoiotoior>io t«>or>ior»iot^>ot^io S'e^tieoioio^'tDMooiH tOCOtOCQUScQiOOOlOCO ^tOiOtOiOtOlOtOiOtOiO toiOt~>ot«iOt«ior>io SSeoioeoiOOToSSM tCJtOlOtOlOtOiOt-lOC^iO gO.HooeoiOioeo«> — r-ioc*iot^»oi^iot*io SS8?3SS222i:; SS22S2SSSS t^iOt~iOt>.iOt»iOt~iO t»iOt~iOt~iO»^iOt^iO S"»O>^0QS0tO3'.9<^C^ iOC^oSlOot~iot^iot^>ot~io gpO00NtDiC'*t~r-l J5rt.-,rtr-l.-liHi-li-> t*iOt^lOl^lOt^»Ot*iO g'eotoiO'>»;i--fio>Qr-ioo .Cjt^iOt^iOt^iOC^iOt^iO cotoi0^t^.-cpg>ri^ t^iOt^lOt^iOt^iOt^iO oNo?5o?»ocoi?5 t~iOt~iOt^iOt~iOt^'W Sic5SSoco2eoiocou5 t^iOt^iOt»^t~^t»"«< ONONrlrHrHrHr-trH ■Tj*tO C^4CC^USC^(OCO*^CO^ COiOCOtOCOiO^^T))'^ 5J*TfOt^iOt~iOt^Vt^'>»' tDC^<3>ooco>ototH<3aQi'«<^aQa>eOiOoOQeoio «ioco->»a0!N>O>OCM0QO> NOCiiraeoiocoiOco->»' r»iot^'»'r-'9't~Ti. ^ t** .^ r* ^ t» ^ t* ^ tocoo>o^i-icoc>c>?< "COiO«lOeOiONON l^^C^^t*^t*^O0^ ■.j'ost^toocj'^OJaoira CO^CO^^^'^CO^CO COtJitCCOtTCO^C S;^*-J^.ooo»Ococ^r^oi OiC-^csooooim eiNiOIN-ooeo-*QOO gooust^totot^iOCR'* co^co^co^co^co^ toioto>oto>oto>oto>o SlS2£20£22!2S2SS cOiOCOtOtOtCtOiCtOkC r-t^OaCOQ^CICO'^r-* ^CO^CCiOCOiCCOiCCO COiOCOtOcOkCtOiOtOiO Sc^coor^oQoitOfH^ toiototototOtOiOr^kO t^iOt^tOt^kOt^kOt^iO I>pOOOMtO'<«-'*t^* iSSSS -iOt^-«"r--*r»--^r»'»'t»'^oo^oo'* ^^tOiO^^OtOtOrHf-ttO OCJOMi-lrt-trHNO oot>«oo'<«'oO'*aO'>«< r> -9 1^ ^ 00 ■vcoyr t* ^ 00 ^ 00 'tf' 00 OiOg •«i4'« 3 0iOi-l-^i-(^CSCO cocooocooocooocoooco PjcOCtfCTpScOQ^ico'OScO to r^ 00 oi '-^r t;'~C'5 Oi-iiH.-iiHoeeOiOt»tHC»0QiO r^Oi-ic5e5ioeoio«S^ oo-otco^oocoaocoooco ootoTfc^r-oi-ite^ cjioeMioeo-^co-w^co oocooocooocooocoooco tOOSNCOOtOtOOi-^rH I"CO'^COCO'*(NiOC< ooeoooeoooeocccoooco ot»t^e5TfcoNiOi-i» COCOCOCO-^C^iOi-lOO oocooocooccooocooco o>r»toO'*eoN>Oi-ito flC<«(N'*i-HiOOOu5 ooeooocooocooocoosiN CsScoo^oDOjocDSoopjco QicoftScdoScoftSoopjai Page 660] TABLE 10. Mean Time of Sun's Visible Rising and Setting. J i •xo jdd V fE^ 02 P3 CO p:5 ad o4aQp3«i cs^oQptJoQPi^aQrtcQpdaQ oizcpi^pia^^a^pi^^ Cc!Mip:5«ip:HCBPc3aic^cQaHa!i -JOiCOi-^i-tCOCO^'^aiUot^QOCOO-'t'T-HfMCOO s£iocot^c3qoooa;»Ht>. SOiCusTf-ErtNOQQgco -ji^-,^-:,^^-,^-,^ .^ iC CO tO ?D iC ^ CO lO O lO CO tO to lO CO iC iX> vO <0 lO cO lO CD lO CO lO cO iC CO lO c^t>Tto rtfOcOOOOOcOO-^C^OaTt^O COiCCOOcOiOcOiOcOiOCOtO tHGOCOCOiO-^COIMOOOQOO !M00(MCOCNCOtMC0(NC0CO(M fO»CCOiOCOiOcOiOcOiOCO»0 S'-^c^iTiOt^aicor^Qco ^lOcOiOCOiOiOiCiOcOiO S'COi-*'^OCDGOt^cOCs»C ^SjiCcOiOOiOiCiOiCvCtO afNQ-^OSiCt^t^COQOiC iiCcOi-OiCiOOiCiOiOiO g'c^O'g«asicoococoGO»o (M"*C0C^i0rHCD0lQDI>O«0i-HTt00I^OC0(N'^00CMiOOt^Q0 cOiOCOiOCOiOCOiOcOiCCOiOCOiOCOiOCOiCCDi^CDiOCOiOtOiCCOiOCOiOeOin WC^^COQiCOitOt* ODCOai-^i-HCOCOi-H-Tt^OJ CO iC CO la CO »0 CO lO CO vO CO lO CD O CO iC CO O CO lO lOiCcOtOCDiCtOl^CDvO r*CDOO-^OOOr-li-HCOO OlCO QliooocDcDoo»cgicoiHOJ rfiiOcOiOiCiCiCiOiOtO»0 lOiOcOiCJCOiCCOiOCDiOCOvCCDiOcOtOcOiCOi^ S*C^JO*^'J>'Oopcpr^t^cD lOO'OiOiCiOiOiOlOiO ^iCCD»OiOiOvCO>OiOiC -JWrH-g^CaiLOCOCOt-t^CD QOiOQ'^i-ICOMCNCOQ $: ic o »o ut" lO ic i5 lO lO lo iCiOOiOOiooiooio ,^ iO CO UO lO lO lO lO vO >0 lO lO lO CO vO CO lO CO iC CO lO GO'^OCOi-t(M(NfHCOai!'»*l:^CDQO^OCO iCOcOiOCDiOCDiOCDiOCOtOCO^CCDiOCOiOcOiC ■«fOii«oo^r-*QOcocj»ic S"COt-i'«tQiOOs^00l>t^ ,^iCCDiOcO»dCiOtOiOiLO 2cOOiOrH'^C^COCOl^t^COCD aiCDO-^(N00C«0C^Tt OiCcOiOcOiO^OiOCDiO COiOCDiCcO»C«0»CcOiC '^lOCOiOCOiOCOiOcOiOCOiO ^-^(NiCi-tCOQt^OiQOGO ^i/^CDOcOiCtOiOiCiOiC a>t^ocpi-4ioc^'^coco vOiCO»OOiOOiOOiO lOvCCOUDCDiCCDiOcDiO S'-^oJliCi-icoot^oaoai 10000100*0001^ ^lOCOiOCOiOCOiOCOiOiO crscOOt^i-HCOtNiOCO-^ - ^OiOOiOOiOOiO iOiOcOiOOOtOOiOOiCiO ,^iOCDiOCD»OCOiOCOiCvO _ O O CO i-H t* (N CO CC lO lOiCOtOOiCOiOOiO lOiOCOiOcOiOCDOCDiO •xoiddv ft*^ giOOiCOiOOOOiOO ^lOcOiOCOiOCDiOCDiOcD ; CO ^ I- CO i> c^ c giOOiOOibOuSOiOO ^cjiOCOiOcOiOCOiOCDiOcD r-;i>iOGO*OOlTfO'^ OeOiHCOTH(NC^^l(Ni-» ;i00>0 OiOO »00 OO OOOOOOOOOO itOCDiOcOiCOiOCDCOCO COCOCOCDCOCOCOCDCOCO :ooococoo-*ti-(coco.-i-«* rHCOi-tCOCN|COCNCOC^CO(N(N CDiOcOiOCOiOcOiOCOiOcOiO -*COcot^COiC04COi-HM(NO r-ICOr-iCOrHCOi-(CO(MCO(N0O cOiOCOiOcOOcOiOcOiOcOtO COOliOOOCOCOOOiOOlCOi-HiN ■C0i-ICCrHCOr-tC0rHCO(NCO COiOCOiOCD»OCDiOCDiOcO>0 'Nt-HCOCliOOOCOcOOOvOaiCO rHTf i-t'^rH'^rH-^.-HTr'rHCOr-tOO CDiOcOOCOiOCOiOCOlOtOiO ^CMiOrHCOQt^^OOOp Ol t- O CO .H g< C _, _J^t>-OCOrHiOC^'rHCOCO 0'^0'aiOiOCOi-Ht*00i0000i00i00i00»00i0 lO lO CO »0 CO iC CO »0 CD »0 CO iC CO lO CO lO ^ lO CD »0 t'-CN QO tH O^C )01r-1QOrH t- a>OQQr-ia>r-IGO(NI> lOOOOOiOOiOOiO lOcOCOCOCOiOCOiOCOtO Mt'-'^'CD^OiO'^CO'^ O»00t00»00i00i0 COiOCOOcOiOcOiCCDiO g,-H^r-t^OCJQCa(5 00000000»0 '^COCOCDCDCDCDCOCOiO OOOOOOOOOO ^DcococDcocococococo ioOt^GSCOO^O'OOiO $iiOOiOOOOOOOO rf*iOCOiOCDCOCOCDCOCDCD OOOOOOOOOO OOOOOOOOOO CDCOCDCDCOCOCOCOCDCD COCOCOCDCOCDCDCOCOCO ^OOOOt^Ot^i-tcpi— ICO goooooooooo ^ CO COCDCOCDCOCOCOCDCD i-ICOiMCOiNOC^iOCCiO OOOOOOOOOO COcOcOCOCDCOOCDCDCO ^OX-i-^OOi-HOOi-Ht^fHt^ ?=oooooooooo ^ CDCDCOcDCDCOCDcOCOCD 'Mr»-C?t~-^CDCNOCOCO OOOOOOOOOO COCDCOCDCOCOCOCDCOCO goooooooooo ^COCOCOOCOCDCOCDCOCC SOOC^QpCOOOCOCOCOCO ooooooooo i:OCOCDCDCDCOCDCDCDCO g*C:JOMo>^ai(Ng?(N05 OiHOOOOOOOO ^CDCOCDCOCDCDCOCOCOCO g'eOrHCOOCOOCOOCOO 0f-t0r-10r-t0rH0i-« fC^CDCOCDCDCOCDCOCDCDCD ^COCOCOCO^OCOCDCOCOCO p;;xp^cQQ^cfip^cQp:jai Soc cOiOCDiOCDLO^iOcOiCCOiO 5'*J*00"^l>tOcpcDCD SoooiooSoio CDiCcOiCcOiCCO»OCDiO cooi'^(3>*^oo\noo»oi> OiOOtOOiOOiOOiO CDiOCOiOCOiOCOiOCOlO COt^COCOt>CDCO»n00'^OS-^ O.iO O»00i00t00i00i0 CD»OcDiOCOiOCOiOCDiOCOiO ,. .HCOO^O-^aiiOOi OOOOOOOiOOiO COCOCDCDCDCOCD»OCO»0 lOCO-^^Tl^-tJ^COiOOO OOOOOOOOO COCOCOCOCOCOCDCOCDCD C0cOC0»O"^iOxJ*'«:J<^-^ OOOOOOOOOO COCOCOCDCOCOCOCDCOCO .)COt--^t^-TtcooicoCT>coo> OOOOOOOOOO COCOCOCDCOCOCDCOsOCO COOfiOOCOOCOOCOO Oi-lO»-tOrHOi-tOrH CO CO cOCOCDCOcOCD^CO -, .-tCOrHCOi-tCOfHCOi-i Oi-tOl-lOrHOfHOrH COCDCOCOCO^OOCDCO OCJGQQJCOp^OlpljCQpl^GQ lO CO l> oooicoooeooo-^oo^QO OOOOOOOOOO CDCOCOCOCDCOCOCOCOCO St^C^QOC^a>tHOQOO> OiOOiOOiOi-tiOi-H'i* COiOCOiOCOiiacDiOCDLOCOLO »Ot-'^CO-^OOCO^(NO(N lOOiOOiOOiOOiOi— ttO CD»OCD»OCDiOOCD»0 iO0DCOC0cOC0l>t*t^CO00Cp OiOOOOiCOiOOiOOtO CDiOCOtOCOiOCDOcOUDcDiO COiHCOi-(COi-'»0 i-C^r-C^rHCOi-tOOrHCOr-fCO CD lO CO iC CO lO CO lO CD lO CO lO I ioo=oocDOcooi^-ait>-co OOOOOOOiOOiOOiO COcOCOcOCDCOCOUSCDtOCD'O l0(N»O(NCp0 ^ »0 CO tO iC lO lO lO >o OOOOOOOOOOOO 5DCOCOCOCOCOCDCDCDCDCOO OOOOOOOOOOOO CDCOCOcOCOcOCDCOCDCDCOCO coocoocoo'^0"<*-vo-^o-^Q>^ OrHOrHOiHO—lOi-* Oi-HOr-tOrHOOOOOO CDCOCDCDCDCOCOCOCOCO CDCOOCOcOCDCOCDCOCOCDCD Sr-tCOrHCOi-HCOrHCOiHCOrH r-IOt-HOr-fOrHOf-)OrH COCDCDCDCDCOCOCDCDCOCO^ ^a^^mp^mf^aip^oip^m TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 661 2 I ^ 3 .2 » cojddy •a;Bp xojdd V "Jz; 5J!2i o Si gj SJ S 3 OjCOpJQQpjCQMaQQjaS (NC^OOINCOlMOTNeOr-l S'tOC-OOtOO'O'r-ICiCOO S'T-IOJC).-C>»iO00t^5O ■-(•0««0 O lO O O O O O O lO O S to O CO tO ^ lO CO lO CO lO CO to t^ lO C« O r* -^ t* ^ (NC0>O'^t-IN0»Oi-l00 ■"iJlrHTHi-l^— tTjOHiOO coiocoiocoocoiacoio (3> r- r-ltO « M «0 » C0u3c0t0c0i0c0>0c0>0 lOOOt^COOi^^NMO eoiHOOi-ieor-iTiii-i'^i-i COOCOlOCOOCOUdCOtO C^OgCtOiO COiOCOiOtOiOCOiCCOtO Nc0 CO lO CO O CO tO CO lA CO tO CO to CO lO CO o COiOCOiOCOtOCOtOCOiO COiOCOtOcOtOcOtOCOtO OTCI0OC>100OI0OC4COrH cOtOcOtOcOtOCOiOCOtO r-i'*5)eococM'»ocoo> Oime<)eoc:coc4mc40i cOiOcOiOcOtOcOiOCOiO COtOcOkOcOkOcOtOcOiO 00 gj o» 00 p r- 1-1 CO fj lO eo -"i! -i< eg co e< t^ 'H oo o> CO lO CO lO CO lO O lO CO lO CO lO CO lO CO tO CO lO CO lO COO*0QC^0Qi-fCQ-H0OrH cOOCOiOcOtOcOtOCOiO pjcotfoQOJcQp^aQpjaQ OtooiooSo-qOr-lNS"Qcpt>' lOUSiOiOOiOOiOO^ CO'Oi-ICOOOOg>»t-rHCO COiOcOiOtO^COtOCOiO COCJt~i-iOOOO>0>000 cOtOCOiOCOtOCOtOcOtO 6'.-(QO(Nooeot~»coTfio r-(TjiH^rHVrH'*i-IT(< •cicoiocoiocoiocoiocoio iHiOr-li25i-i-l^ .c;coiOco^O>OcOiOcOiO SOeOOC^rHlNi^HrHI^Q fHiOrHlOi-ttOfHlOrHlO .C^COtOCOiOcOtOCOiOCOkO gSSS3232SSS ^COiO^tOCOOCOiOtOiO ^COiOCOiOCOiOCOiOcOtO gssssssssss <*cocococo-i OrHOr-IOrHOr-IOrt ^COCOCOCOCOCOCOCOCOCO pcioitfcopjaipiicoojco o "S""^'^ S "§" tOiOCO'^r^MOOCjjQOr-t COiOCOiOcOiOCOtOcOiO :OiC00 <iCOQCOOQr>-r« eOtOCOiOoaoi-( SS2 tOCOiO o^ggggg CD O CO <0 O CO CO g§g CO CO CO >cococo^LOr*iot^iO oooooo CO CO CO CO CO CO CO Soo CO CO CO T*40>iOQ>iOO>iOC OOOOOOOC CO CO CO CO CO CO CO c «C4eooJco(MeoNeoc>» O i-t O 11 O rH O CO CO CO CO CO CO CO r-iOr-l CO CO CO c^ciSiMrt ooeoScooi co<3coaa(^O>t>0000t« i-(lO»-t^f-(^rH^fH^ COiOcOiOCOiOCOtOCOiO ■^rresiocoiOocoN lOdiOf— tiOrHiOr-ciO COiOcOiOco^cOiOCOO i-it^pjt-.c^t^eOOSO-*0-*rHTf< ■.?^ait^^occccosr*cO;0(N-.j*cftoQicc^. TPCTitO-^IOl-fO^i-liOODOOiCrHjq 0-OOiOOiCiOiCiO 833 t-i lo o go to o M m O ■* O ■* i-l TT ^ t>. ^ t^ ^ t>. Tj* lMf5.-t ooeocccooocoooMooco t^tocCi-HaiTt*eDooc*Di-t oocooocooocooocoooco t^coaocoooccoocoooco ^Ht-H(£Jto»-<^Ht^?OCOOS t>.-.jii>ccooccoomooco t-.TJH>TI't-COt^OT00CO t^tOi-KMiOr-QNiOt^ S<00>0Ct^O>OtO»C &COCO-.1*«— 0 O lO to-oit--* 0-*rH-*i-ITl-i-*i-i'.)< aO5I>f-HtDC<5*»#".J'(NCOrH00OiQt^C^iO'.f*CCtprH ScDiO<£)iO«DiCtOiCeC>iO CO lO to L xioS :OOT-lt~!NlO >COCO-^J<-^(OCOt— T-IOiO :COIMCO'*«oiCin ;C0COMMCC!NCOCSICOlN »«0»CC0iOCDi0CD»OC0iO BCO»OCDiO?DiOCDiOtOiC CO iCCO rHT)-vi>T("THccicoaiiO t~oo^in-*^oooo(NT)< TH>0'.J<(Nt-01.-ICOT>'(M lOiOOOOiOOiO.H'^ cO'*r--*t~-*t-T»t^!NO>Oi-IOO!cO C001C064CO(MtICOOCTHlO^H".t* :rt ■ci-cOCOopiOO^CO»-tM cOiCCOtCcOiOcOiCCO^ -^MC^MCOrHTfOCOOD coMWMeocoeibcccoiN COiACO^CO^COiOCOiO (MC0CCC*5-^C^'.t<»-*iOO CDOat^0000t^OiCO.HlC CDiOCOincOiOco^cOiC (MMCNMMmiNOTCOm COiCCO^COiCCOiCCOiO Sc lOOOiOOiO COiOCOiOCO»Ct^'^t*'-( cootie cocomco CO iC CO iC cc coccus coiocotrs cOrHt^i-it^ocooocoilojooaioooi^^t^rH CO c^iOM-^-^ com cocoes jcDiOCO )coic co»o COOCOiOCOiCcOvCCCiO COiCCOiCcOiCCOiOcOiO •xojddv P^ lO CO 'X) C*3 to CS t- (M ^- r-l 'cOiOtDiCcDiO«OiC?OU3 s CO to (O SrH Oi T-H Oi -N Ol f— t lO r-i iO i—t lO (O «0 lO <0 iC O lO C^QOMoOOOOOMI^OOtO Sgo^co^oocoooccgoco :oooooooooo S(OcOtOtO«OOcOcOCOcO iCOOiCQOOCOiOQOiOOO :000 ;'0co<0 ooooooo CO O CO CO O '^ CO iCoOiAQOiOGOiCaOiCOO oooooooooo cOcOCOcOCOCOcOCOcOCO CO CO CO CO CO *0 CO CO CO CO • CO CO CO •N C^l 04 (M CC Ol CO T-* O Tl O i-t O r-1 CO CO CO CO CO CO CO PC? CO Cc; 03 PCh cc tf a5 pc; cri g§s§sss§s§ CO CO CO CO CO CO CO CO CO CO oOOCiOOsOiOCarHOO COifScOiCcOiOcOiCcOiO -fHQOOOlOiOCC'-HCO CM"<*C^CO cDiO cOiC coco CO iC CO lO i-it^c^t^cocO'^ 2§2g2g2S::!o COCOcOCOcO^cOcOCOCO Icooocpoocpoocpcocpoo lOOOOOOOOOO co^t-'^r-cooocooiC^ T-HiOf-iiCt— •lOi-HiO'— -Qt>-QCOQcp ^^0Q'-(QOi-ir^i-'r>--Ht^ 1— (r*c^t^c^t>-ococ^cD c^coc^cococooptoeotococp 'iO^^OUOiCiOLn^iC lOiOiCOtOOuCiCidO lCiClOiOiC^iOLOiQIOlO^ lO lC iC tO iC iOiO ^ ^ lO lC iC lC^US ^ ^O iC iC lC iCiO lA >0 iC O iC iC iO iO ^ S"i-i04MCic>oac^aiC^co *N GO doocooo coco coco coaoc5r^'«3*r^'^co-^coHl'(D»ocOiCcOintoiOiCiO*0 ^iC^iAiCtC^LO^iA^ kCi/SidQiOiOiOidCiC iC^^^tC^iCiOkOiO iCiOiOiCtA^iOiAiCiOiOiO ^c^ocoQcoococacocs h^OJ'TOi'^op'^apiooo iOcOiQt>»or^:p«ocpto Kocot^cot^iOt^iOcOiOooift ^lOcOiCCO^COiCtOiOiC uOiCiCtCiCiOLOiC^iC LOtdO)>OLOiCidOtOiO OlnU^lQtCiOkClOLdOlO^ f^CCi-''T''--'T*'-^*^Q-^Ql>COu0Cic0CiO04c0C5k0 00t^t>-00l^a0(0C0C0 fciooiooiooiOoioOjU5oo»oiCkCiCiOiOioioicioiOioiOii5ira»i5»o ^iO:OiOOiOtO»ft«0»CcoJu^COiOiOiOiOiOi0^iOi»OiCiCiOiO»OiOiCiO»0 ^lOcOiCCOUOCOi^COiOCO iOeO^iO^OU^^iakO -alCC0U5M«OC^Cpr-(t^.-l r*oooooooo»ososQO ^iC<0^<0kAC0tO(0i<^c0>Ac0iOC0iOiOiOtOiOiO SSoiftOicoiooSoLcooSSooiooS ^iCCOiOCOiCOkOCOiOCO 'iACO>OCDCOCOtOtCCOtO ^lOCOtAcOtOtO^COtCCO •OCO"iOGO'3'©^oicoQco •-'N<-ti-i^ocoo^04 '^oo»ftr^-tot*»e 5»oo25ofeoioooc5 oooooooooo oiooiooiooicoS5 ^lOCO^ COiCCO tOCOtOCO CO CO CO CO CD CO CO CO CO lO CO iO CO lO CO lO CO to CO ta GOcOOacOOiiCOs'OQiOO'^ iCiciCt/^kC40kOioOu50ira kOlCOUOU^tOlOiACOiCCOLO 00 CO CO t^ 0» »-• 0» CO O CD OiC'-iuj^-^^'^CI^WCO iCtO lO lO iO O iO ^O O O ^ OiC O^C O iC Oo OtC iC iO lO lO kO ^ to lO CO iC CO tO 1^ tC CO tO CO to CO lO CO lO ScoQt>--^i--iHcDMOOOOOOOOtO OiOOiOOiCOiOOtO iitOr-ltOi-tiO^iOrHiOrHtO ^tOCOtOCOCOCOCOCOCOCO CDCOCOCOCOCOCOCOCOkO C04OC0t0C0tOc0i0^tO COtOCOtOCOiOCOtOcOiOcOiO iOOOOOOOOOOiOOOOOC.OOOinOiOO>COiOi-li(5.H>Oi-liA.--liO.-iiOi-llOi-liOfH^ Sooooooooo ooooooooo>c o>ni-ia.-nnrHi5r-iiA ^COCOtOOCOCO-i r^ (N CO CO lO 'j"^ lO ro CO e^ 00 1-1 o> o o o> -^ 00 CO lO CO lO CO lO CO iC CO iC CO lO CO iC CO iC CO iC CO IC CO IC Soooooooooo ^COCOCOCOCOCOCOCO^CO ^COCOCOCOCOCOCOCOCOCO -ic^ocooo-^r^iocptoio •^cococDcococococococo -oeot>-cjoo»- OOOOOOOOriiO COCO^COCOOOCDCOtO '^■n'tOrtCOC^t^r^OCOOOi ^HiOf^iOr-*iOrHtOf-HtO'-*^ OiOcOiOcOtOcOiOcOtOcOiO i-tooc^r*cocoiO»ocD'^r^«oowo>Qoa>5^cco2r* COtCcOtOcOtOcOtCCOtO .COiOCOtOcOtOCOiOCOtOCOtO t^«OpMOii-HOOWCacCOO"*r*tOcOcO'-*'t>-COC^C^prH.-i^MQQ'fl'tr»OcD 000000*HOrHtO^»OrHiOi-iiOf-HiOrHtOf-Hi0^tOW^C4^CS^6l'V COCOCOCOtOCOCOCOCOtO OiCcDtOCDiOcOtOtOtO {COtOCOtOcOiOCOtO-cOiOOO-^OacO i-HiOrHOi— «iO»-HiOi— tiO CDtOcOiOcOtOCOtOCOiO — ■■♦5iQW<^'^<^co COkOcOtOcOtOCOtOcOtOCOtO xoaddv q"^ j*S30'j'S?coooScooom eor-toooooooo ^cococococococococDco OrHOrHOi-cOrnS COcOCOcOCOCOCOCOCOtO cor~t^mc»-^oc^?)i-H r-HlOi-llOr-(U5CliClMlO COlACOiCCOlCCOiOCOtO ^^MO'^ouDi^r^cpoO'^ S0.-1000000 00 ^cocococococococococo: HO'-IOi-COCOCDCOCOCOlCCOlC COiCCOiC .H—IMO COiOCOO eQO»icoococoooc5.HCi COiOCOlCCOiCCOiCCOiCCOlO Tj'opcor-oQiooco-Heic^o iCOlCCOiACOiOCOt^cOiACOLO S'cjOMooiet^ccmoo^' OrHOOOOOOOO ^cDcococococococococO iN-H.-(iNcn ■^OOiCCO T-( lO rH 40 coiacotc S'r-r-l.-IO(M00 >OrHO.-IU5 >COCOCOCOiO rtiOiHiO CO to CO iC > cOCOlOCOtC i-tiOi-tO COiOcoiO .iCOOOOOIN cotOcoiO cOiCcOU^ mt-COiOOOMO(MC^OMOO COiCCOiOCOiCCOiCCOtCcOiC -coaiciOQ(Noo-i'coco>nr-eooi.-ii-io ji-doniot SCO icco»o t co>nr-eooi.-ii-iOMQO''Jco COiOCOtCCOiOCOlCCO^CCOO CO rH oooaooo COkOCOiO CDlOCOlO !t>.OOCOO-*. >iCO>OiHlOr >ioco>aco>oc pjOQP^QQMCQOiUitf QQ ^ QQ pj UQ p^ oo.Ht^ccioicco o)'j'ce<5OTo5co cOiOCOiOCOif^cOiOCOtACO^ ■.»iocooooccoQtl^£J22 C^ -^ C^ CO C^ CO CO CO CO CO COOT COlOCOiacOtACOiOcOiCcOiA O^COp^COpiJOQOjCCpjCfipJGQ Page 664] TABLE 10. Mean Time of Sun's Visible Rising and Setting. a< 3 o S o t« •* H o (/) p o o 9 tH XI P (N ■p -<1 (U -§ •■;3 ^ ^ r-( fj 00 ■* lO 50 t- e^ M e5 (N IN (N (N •xoidd V (A^fAcapiixPiwA^ l^xfii^pitBP6aic:^m ^tOiCiOtOiOtOiOtOtOiO 'xoiadv S' 1-t CO 1-i to T-l CD i-H CO i-H (O ft CD rH Cp i-l to »H CO «-H CO ^ kOiO ^ tO^iCO lO kO iC lO ^ in u:^ O iO tO lO in ^ »0 »0 O lO lO »0 lO *0 »0 i^ iC lO lO lO »0 lO idO iO lO s O i-< C^l CO '^ CO CO CO CO OOcOOOt^Qpt^OOt^COt P^a^p^c6;^c^^a2p^t:n PhoqPhoqPhqqpc^cgPhcq 00 r- oo t^ 00 1> 00 c- CO r- oo •^lO'Tj^iO'^iOTriO^iO ■^iO-^iGriiiOTf^O'^iO rj*inT}. _iCOrHCOrHiCt-iiOrHO LOiOtOiOiOiOiCkOtCiO ; CO "C CO iC CO »0 CO ■«}'^ t^"«**t^'^t"*COt-COI:^CO00C0COCO00C400C^Oi(M lO iO lO lO lO lO lO lO lO »0 lO lO iO lO lO lO »0 lO lO lO lO O lO lO iO lO uO lO »o o eOO'^OO'^Oa'^OiOOOCO S^iOiOOiOiOiOiOOOiO ,^iOi/5iOiOiOOiOif^tOiO gi-Cflr-tCOfNCOMC^C^C^ OiOOiOOiOOiOOO ^COiCcOiCcOvOCOiOCO^ QCOOC^O'Mi-t'Mi-KM Oi0 0u3 0»0 0u3 0i0 COiCCOiOCOiOcOOCOiO COC^COrH00r-(^iH-^Q OtOOiOOOOiOOtO '-.OiOCOiOCOiOCOkOtOiA OOOiO ^ (NocMoeoo CO lO to lO CO lO CO lO CO tO CO to CO lO to lO CO kO to lO »OQiOo>toa»coooi>oo tOiOCOiCCOiOtOOCOiO Scocoeod'^iM'^r-iiOfH >ootootoo>r^Oii:^QOoooooot^a>t^aicooto ^COvOcOiO"OincDiOtOiO tOiOtOiOCDiOCOiOtOiC COiOtOiOtOiCCOiCtOiC girtC^tOfMCOt-T^i-IOOO ^COiCtOiCtOiOCOiCeOiC si 00 i-< Ci >-< O O O O i-H Cl 1-1 00 Ol 00 *< ^tOiOOiOCOiOtOuOCOiO tOiOCOtOtOiOCOiOCOiO OOOiOOOiOOOOOOt^h-HtOCNCDtNtftCOiO-^"^ OiOCOiOtOiCCOtOtOiO tOiOCOiftCOiCCOiCtOiO Si-ti-Hi-HQ'Mai coo coco i-HOi- 00 00 r-- a> to o m rH '^ c^ co co (N Tt^ r-i lo o to o> ^tOiOcOiOCOiOtOiCCOtO 'OkOCOtOCOtOtOkOtOO -^t^iOt^iCtOtOiOt^iC tOiOCOiCtOtOcOiOtOiO OtOt-i/SOO^JOCOOCO COiOtOiOtOiOtOiOtOO O^lCO-^i-HCO-MfNCOrH :OiCtOiacOiOtOiOtO>C So 00 rH t* C^l CO CO -T** 'Tj* CO lO 1 -^ -c^ ^tOtCtOOtOtCtOLCtOiC g'^-rtfcpvOiOtOCOOOfMOiO ^tOtOOLOCOiOtOiOtOiC OOrHO>OOai»HI>-COtp C^-*(Nt(t-(oocor-"^iotO"'^t* :Cs|Tj*CO'^0Q't*iOI>-t--tO CO'^CO'^COCOCOCOCOCO ^COiOtOiCCOlOtOiOtOlO S(NQTt*a>iOt^t^toa>Tp co-vcocococococococo ^tOtCtOiOtOiOCOtOtOO S'^aotot^t*ioaiTtiOCOtCtOOcOLOtOLO rtcdrtcotfcoPtSodrtoQ PiicopJHcnrtcwtf oqPhqq tOOOCOiOOCOCOTHiOOS TrrH-^i-HiOi-tiOi-liOO COiOCOtOtOkQCOiOtOiO c^?i?3mS e»oc>iO'-'»-r^OitO ^•QOoor-otoi-fiQtNeo MCOC^COCOCOCOCOCOOO tOiOCOiOCOiOCOtOCOiO rHCOC^lOCO'tOkCtOLO T-tiOC^iOC^vOOiOdiO LOtCiOiQiOiCtOiOiOiQ iOiCOiOOiOiOidO»0 vCCOtOCOtOeOCOCOCDCO lOi^iOiOtCOiOiOiOiO 0>iMOi-hOt-(0'-<00 lOiOOidOuOOiCoiC lOiOCOiOtOiOCOiOCOtO coo-^o>'^o>'^coinoo ^-pO-^O'^O'^J^OTjt r*t^ooi>coto©cOQ>to 0'^0'^0'«J<0"^0-^ COiOtOiCtOiOtOtCtOiO OlCrHTr(MT^COCOOO-COOit:^ COCOCOOOCOCOCOC^COOl tOiOtOiOtOtOtOiOCOiO t^OO>OiOt-(MtOOO'«»t CO0O0OC^OOtHOO»-IOQCOtO lOiOtOCOOOcNOOrHOO CO 00 CO CO T>< CO Tt* CS '^ (N ^C^^^C^yrOi^OiiOyH to to to tjO CO iO CO lO CO lO ;o ^ CO tO to tc to tc CO lO OO(N0>C0t>-i0C0t-'^ ^CO'^t0l>00»CQC0C^O'3'C0 ■^(N-^u^t^iOt»iO oico?-iiHeoo4iQooi>coa>"^t-ti-Hcoo>^r-.co^ Tj< C^ U5 C* iC iH lO rH lO rl lO rH O r-( O O O O O O to lO to iC to »0 CO iO to lO CO to t> lO l> O l> lO C^ lO CSO'^OOtOtOQO-^OC^ iOC^»Oi-n5iHiO.-HOi-l tOOcOiOtOiOCOiOt^iO ^t^to»oa>coiHi-*cooi lOrHtOrHiOrHOrHOO tOkOOtOCOiOt^tOt^iO t^TfOiC^i-tOiCOt^-t gOOt^COtOtOC^OOO .-HOOOOOOOO cDiOt^iOt^tOt^iOt^iO tpO-^CMrHiOO>t--tp OOOOOOiOOiO tOiCt>-iOt>-iOt^'«*-iot^iOi>iOt*iO iOoco-tocp OOOOi-iOrllOi-liO t^iOt-lOt^iOt--T)'t-Tf 00C-)rHOC0t^t0-^0>-HOrtlOrH-3'i-l-»lhcqMcoP4c»Ce;qq TABLE 10. Mean Time of Sun' a Visible Rieing and Setting. [Page 665 M ■2> 00>00>0 r-(COr-*COrHCOr-*0QiH00 Ri-HeOr-cMe^WINOTINM 6i>-'>l'0QC5a>«i-n-i(MO e^eoe5MfjMooeoco« c<«c5oO(M03ClcoNeo 0QS4a><-IQQr-IOQe^C- o>c^i-ioeoo>Tj"t»to>(5 «Or-i>op%aocoi>-o>a aQOOQtOt-l->»"«INiQO ^f-*»i3fHlOiHii5rHiOt— 1 a«OCJtO^OOO>OOOr-(tO ■^i-HlOrHlOr-IOr-liOi-l ^coiacotocoto^tocoiA S28S§88SSS S09tOtO'*t-(NO>Oi-lOO lOrHiOr-ltCrHiQt-tOO OOOOSOfllOrHlO t^ ^ t^ ^ t* ^ t* ^ t^ ^ i-lOi-IOi-(iOtHi4(NiO S&5 •^OJ ■ Tj< t"» ^ 1^ ^ t* ^ SOO « -^ rl Tf 00 CO0QC0i-(O _. . . _ 3;o ■'T CO "^ CO CO ■oo(Orte^iQg>oo«o go>coc>ScOcoeoco6icoiM lOt^r-too-^r-ie^coo Ti-l'o»h-tS'S s s Qjcritfcnc^aiaiaQpicn gO*00>00»OTO'-'*oOinootot^t~to rlcOrlSSrlCOiHeOrH-O Srtcl§5?Jeo?3«8« M f< ?1 (M fl C^ CO C<«3 C5 SNM?Jeoortr-c«eOt— iriOCOOOOOrH OOCOOrHOm^C-COlO -^f-ttOr-llCO>OOtOO iQgot^«00>eo£ji-(5"oo SSSSBSSSSS OOOOOiOr-iOr-liO StOW^lCr-«eC00i-llO '^'-'S?SCOlOCOr-lo99 O0»N«0lO-^00><8 ^■^INr-li/JOOOQlQi-IM rtidcausiNfM-^co-* T}"o>r-tOOooeooit^«o c^-^ra-^co'^oicocoOT ■^ ?i ^ 00 OT o5 OT ^ t^ ^ t^ ^ t^ "f S^eO' ■CCC0C4Q ■>»nMr-l -SC SCO 0>T|<(NrHiqt^0>'*C0O oi-^cO'S'cococoeo^co >c^-*oo t^^r^-^oo-^ oO'«)!< 00 -}■ OO •* 00 CO 00 CO 30 If 00 CO CO CO OI--C0O ^ -^ CO ^ 00 CO 00 CO COQQt^iQOrHTJ'OOQO'* eoMcoeo-^co-^fS-^c^ CiOioc CO CO ■>}• Ol ■'l' « ■> t~ ■<»• t- ^ r- ■^ t ?co5jooc:cOiMcoooco '00 CO 00 CO >OOOr J^OOtJIC 1-1 g 5< <3> 00 — (N ^ 64 ■»< ■-( t^ ^ t^ ^ t^ "^ iar-liO.H t>- ■»)< t^ ■)<00 CO 00 CO pTjltOOO cS-'j'c^co 00 CO 00 CO t^ oS~ 0» O rH C^ CO "J" iS"^ cOlOC^QoocOlO^^'T^O i-iioc<«OMT)"eo oocoooeooocoooooooco ' r- o r-( r- f iTf^TfCOCO 00 CO 00 CO 00 CO •* iH O ■* t^ to in 00 1 CO -O" 04 ■* 1-1 00 CO 00 CO 00 CO Sot OOCOOlM ediMCiicDpiaifiiaafiiad to r^ a6 o» C? lO tO u3 lO ^ Page 666] TABLE 10. Mean Time of Sun's Visible Rising and Setting. •xoiddy a s g "S 0) CD Ol »£) i-H CO CO T 3COlOQI>-r^OiiCO'^(N(N'^ lOiCiC^OiOtOiO^iCCO lOXiiOtOvCiCOiCCOiCCD g't^IOi-HC^OCOCOiOcOcOliCoOCOOiWrHOfNai-^ '"^ lO "^ lO '^ ic CO lO CO lO co»o coiocoocoocao ^ iC lO lO Ut> »0 lOiCiCiC iC tO lO iCiO »0 to iC to iC CO g -^ Tj* ^ lO CO lO CO lO CO iC COiOCOiCCCiOOOOC^O g*O000iOQ0»-(I^C^iCC0l'^iCC0c0<— it^OascOQ t^i-HCOCOiO-^COiitiC^r^ •<^TfC0iOC0iOC0iCc0iC|C0t0C0iOC0iCC0iOC4O C^OC^OOIOC^OC^O ^iOiC»OiOiOiCiO>dU5iC ;iCiO»OiddCiOidOtO iftl«OiC«OiCCOiCcOiCtO o»oosr»i>-Oiioococ^c^-^ CNrH,-l,-(i-ti-(i-)(Mr-*C^*i~iCl lOcDiOtOiOtOiCtDiOOiCtD t^iOtCt^iCCOCOOi-HTH iCCOiCCDxOCOiCCOiOtO OCOOa-<*«l:^CDiCOOCOC>C^i-H i-HiC(N ^Tt^-^COiCi-HCOOOCCiOi Tj«Tj(co-^coiccoiocoiO|coiocoiocou:5coiocsiC ■t010:.0^*C'i~IOC^iC-f C^OC^O(NOC>)OC^O CSOCSIOrHOi-frHi-Hrlf^rH lOtOiCcOiCCOiCcOiCCO lOtOiCCCiCcOiCcOiCOiOcO g^T^COTfCOiCCOiCCOlO COiCCOlCCOiCCQiCC^OjC^iOC^OC-JOC^OC^OC^OCSOC^OrHOi-Hi^T-ir-l iCiCiOiOiO>OiCiOiO*CiOiCiC«OiCtOiCcOiOCO iCCOiCcOLCCOiOcOiCcOiCCO g'OODOldODOr^^tO'M '^Tt*cOT}«coiC»iCcou:2 uticO'^^c^ii^i-Hcoot^asccoooir^Qcoc^iOco-Tf^'^^^'-Hcoor^OiOiooc) COiOCOiOCOiCCOiCCOiO CS iCi WvO C^ 25 CS t) (N O (MOCMOcNOC^Or-iOr-irH iOiCiOiC»CiOiOiCiCiCiC»OiCiOiCcDiCCDiCCOiOCOiOcOiOCOiOCOiCcOiOCO g'OOOOiCsGCQt-^i-icDOJ iCC0*f^-^C0iCC1cOi-4r^ Tt< Tj« CO "«*< CO lO CO lO CO lO CO lO CO lO CO iC CC lO CO »c f^* iC 1^ lO iC lO vC O iC lO iC tC lO iC iC iC »dC lO »C vC CCiO!MiOC^Oi>JO(NO iCiOidCiOtOiOcOiOCO 'OOO-Tt^TfMiOi— *COOi>CiOO fMC-1<«0 COtOC^t^daOi-iOOO ■* •<** -^ Tj< -^ to CO lO CO iC CO iC CO iC CO to CO lO CO lO CO lO CO iC CO io CO lO CO o rfjiOiCiC»CiC»dOiCiOiC iCvCiCiOu^iC>OiO»0>0 iCiCiOiCiOiCuOiiliOCO '^io-^iOTt*iocoicccicco»ocoic;coi?5coiccoiocoiccoio rfrjiCiCUSiOiCiCiOiCiOioKciCCOiCi^iCiOiOiCiCOiOiCiCiCiOiOiCiCiO ^^^'^'Z^'^nt^'^ ^^ "^ T-HCOOCOO-^Ci-^OsiC & Th iC •<* lO '<^ lO -^ iC TT lO Tj< lO -* lO "^ t6 CO iC CO iO ^ lO iC iC lO lO lO lO iCi lO iO iO iC lO »0 »C »C iC ift »0 lO tDI>CDt^t~^COr^COC0 lOCOiOCOiOCOiOCOO iCiCiOiCiOiOiOOiOiC ja;T^C^Tt<C i-HCCrHtOOcOOt^Ot^ '^ lO Tt< lO Tj* lo "Tj* lO -^ ic '^ lo '«rt lO "*:j< ic Tf< lO -^ ic lOidOiOiCiCiOiOiCiC iCiOiCiOiOiCiCiOiCUti •xojddv ™;iCCOiOCOxCCOiCTt.COr^Tf< COOcOOC^OC^OCnIOC^O iCCOiCCDiOCOiCtOiCtOiOCD ■«^0iC00i(NO'Mi-(r-(r-(r-(O COiCCOiCCOOCOOCOOCOO iCiO^OiOiCCOiOtOiCtOvCcO lOOOiCOS-rfCl-^OCCOCOi-i COkCCOiOCOiOCOOCOOCOO iOiCidC»CiOiCCOiCCDiCCD r^oot^Oicocscoocoooo COUtiCOiC'COiOCOiCCOOCOO lOiCiCiOiCiOiCiOiCtCiOCC C0iCc0iOC0iCC0iOC0Li*C0»O iOiCiCidCiCiO>0»CiC»CiO 'cc^co-fcococococolcor^cor-'Mt^Mr-.c^oO'Mc^ . - .. - ^ _ .. I*, P^J^^ ^ J^ ^ ^ _ ^ ^lOiCiCiCiCiOidCiCiO iCiCiC»CiOiCidO^>OliC>C>CiCiCiOtOidCiCiO»OiC»OiOuOu:)»OtO»OiOiit> ^OiOiOuS»OiCiCiOiOiOOiOiOiCiC»OiCiCiCOuOiCUtiiOiCif3vCiC»OiCiCiO»OiCiCiCi^ rf*iOidC»OidOiCidCiCUCidOiC»dOidCiCUD iO»OiCiCiCiCidOidO oscoQpcpoocpcotoooco iCiCiOiOiCiCiOidOiC goocooccp -^ lO "^iC •sOCOCOcOcOOCOCOCDcoOCO iCiOiCiCiC»CiOvCiCiCi.OiC ooooOcooocooccooococcto ■^iO'^iOTt«iOTto i5r"'co t- ""oT*" OS O rH C^l CO pHdQfl^Gdpl^I^PC^CCpiH'cCCCH^ TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 667 o tX II T o S cQ a • xo J ad V ■xoiddy OHGQpHodOHCCPJadPJcd P^aQP^odCdooPJcoPJud 9-'^t^'^t^'^t^1'C^ coi-(Mi-ieor-ic^T-oc^.-lOc3'^'"'rn <0 >0 CO ^io;o>o«o>na0'fl'>0'» t^ -T lO !0 CS 00 Q -J Op CO (Q >0 CC OO lO ^tO CO ^ ^^ ^ ^ O ^ CO ^ ^ ^ CO *i* CO ^ CO ^ CO ^ CO ^ CO ^ co^ to SiQcjc-ooQQOQt^eQ:i;?5cor-igooiQtcjlig-g!eocg>- lOcOtOCOiOCO^COuOCO ^iaco>Aco>aco>aco>aco ^'lacotocovacoiocoioco ^tCcOiOcOiAcO^CO^CO :coocoocco^omo :ocoocoLocoiOcoiOco ^iflCOiO -H •«< 2» eo c^ CO CO oeoocoocoo :D lA CO iC CO Ud CO coe«>«eO'fl<'*eococ.Heooit»eoco^iOiO ioco>acoioco>ncoiaco rt©000>i-ICOCo>t— r-iiftcoeoiq c*3eoi5eo>AeOi«o5 lOWfeo-*'*-*-*'-*^ lO CO ^ CO "^l* CO '^ CO "^ CO ^ CO "^ CO 'oQr-ococ3 oiNo?<< ^CO^CO^CO^CO^^'CO iOn!noooni<3ASco ■"J'cO-iI'cOtI'cO'^CO'J'CO t © CO i-l lO CO CO ■* 2! CO o t^ o> o> t~ r-< >Q c^ ■v -^ incotoco'ocoiocoioco >ocO'«co^co'4O.Hg»Mt^COCO'-liH.-lr-(i-li-(i-liHr.|fH lOCOtOcOtCCOtOCOiOCO tocoiacotAOtocoiAco COOi«r^-9'rHCOC>)COCO C4i-l(NiHCSiH6ii-tMi-l (OCOtftcOtCCOiOcO^CO Sr^cooooDOii^ost^o tOCOO^>OCOiOcOtOCO SOOiOCS oa>o<»ooOi-i OCOOCO OCOO O lO CO O CO lO CO i-Hr^rHr»c^coricpc^'cocoiOco«i5^'^ CO o CO o CO o CO lO CO ^ coo CO lO as :0 lO o iOCO»0'^"f'^ - — coocoocOoooocoo ^COlOCOOCOiOCOiOO grHOOi-t^i-HaarHaiC ^ TJ* lO -^ O O lO iC lO O lO Q Oi O Q Oi O OS lO lO ^ ^ tC oo ^ it5 iC lO STj< OO -^ GO CO op Tf »3 -1< lO Tt* l3 lO lO lO lO iC iCiO COGOCOOliMOiriOiC^OS »:Or^^r*cot>-':ot^Ot^ lO '^ lO ^ lO "^ lO 40 iO»0 O O »OiO ^ tC >0 lO too iC^O lO lO P^cnP!HOQp!5cdP£5adrtaQ r-l C^ CO Sa>*H lai^HQQrHOOC^t^Cflt^CO cooicoocoooSocooooo cOlOcOiOcoiO<:oiOcOiAcO*AO COiOCOtOiMCO^t^r^r- coocoocoocooooo lOOLOCOtCcOiOOiOcO t^COeOCOCO'3«u5r-iOift COOCOOCQOCOOCOO lOOiOcOiCCOiOCOiOCO tOOvOcOiOCOiOCOiOCO i -^ iC "«J* »o -^ t lOoO'^oO'^aO'^co-^oo *>»• iO '^ lO Tf »o -^ lO lO >CiO lO tO iC >r>-aor^coi> oot*-oor*oot^c30r>.ooi>' iCiOiC -rfno'^iO-^iO-^^'^ia i> 00 a> Q pEHodP^cntfodP^aQpc^cn tHT-*Oi-HOtNOi^a>^ Tj*o^o-vocoocoo lOOiOOtCeOiOCOiCcO oot— cor*t>-r*t^r*r^t^ P^qoP^oqP^cqPhcqP^cq Page 668] TABLE 10. Mean Time of Sun's Visible Rising and Setting. Xi Jr Q P © o P 0) n 4^ 53 ^ ^ fl z 1 S &, eg I o s ^ .1 •8JBp •xojddv •aiBp •xoaddy g QHtnpHcdpiHaipHasp^os s OiiacA(B(iimpiuifii< t> •* t~ ■^ ■^MOOOCIN Di-KNi-Crl ,c* ^ t^ ^ t*» ^ gt~ (Q ■f aa r^ ,ei ■* t^ Tji t^ •* t> -Jt t^ T)« t^ go QOOCOvO COO(MOC3 rfi ■<*> r~ ■^ t^ Tf tOOlOCOIN 06lOi-lr-l C~ TJI t>. Tjl t>. jgCOlCrHOOOOOlOCOC^C : CO U5 CO li^ C^i .!)< to Tjl to lO ^ U3 lC !8 POi*'i0-*OC0OC0i-l(NrH»oo-«<>-ieoiM CO00CO0OINO> OOOSOtOt-'lOC^^fHlO ocoo-«'iCiri-<»c>)0> !COO->J"iO-*iOT)<'ii5'*ir5COOeOO(Nr-i(NC0'<»'>0>Cl'Vi/3 • coc-coc- cot»cooocooocoooeooo COOOCO<»IMOOIN'* OfNOCOOCOlOCOiO-^ tf*i->r-'0 CO tt> Tt* -^ •>!< CO lO tc t~ Tji t- -i* f. Tji t- • CO t>- CO r~ CO t^ oa ^ to (N CO »o o OS r^ (N CO to a>oiOTf "if t^ tc t^ Uji t~ CO t~ CO t^ CO r~ CO j> co t~ co t~ co i> co oo co oo r*iCr-(CM''!foor^icoco C^Oe^rHrHi-IOINOCO cocoeooocooocooocooo TtM COiScNOINOrHrlOM cot-eooocoooeOQOcooo ^OOtOCOOOi-^-^CCf-f ■>l<-*r-ltO00OiiCCO(NtO00O>iOC0r-it^t~. coocoiraoooc-iiot^r C^tSNOi-HOrH^^i-llSi-iONOOjfecOuSSTfTf'^TjiTOiOcOiOCSO ■T)'^t~'^t-'>ft~-t)cot~cot^cot^cot~eot^cot~eoao o>ij>tOrHcO'*ot~r-o CmO(N000010i-l>H T(to^eoinooot^'-iTf<'*or~r».-icoioooc»'S< to -J< to 1* t- •* t~ 'f t» ■* r~ •* t» rf t^ Tj( t- "Jl t^ CO t~ CO t"- CO 1> CO c~ g oocitOi-H ^e ^ -"J" to -S" to -J' t '00CJ>tOdCO'<}'-JI>O0O> iCO-^COiOCOiOCOiOlMiO ■*tOtJ'tO"«"tOT)CMiCQt^O>0>t^»-liOCOCO>OT-lt^C>05tOC<)TfM* ?= lO CO »0 CO 'jin"*coioiNt^ ?:»ocoiccoiO"* rfi ■* to "f to t(< coic coioco to ^ to ^ to -q^^jf-^^CO-^COlOCOiC "»**tO-^tO"^tO"^tO'^tO tOMCOvCOCCr^THCO"*' rJOCMO(NOrHi-ti-Hi-t JtOCftOltOiMCOiOOQp 'tOT)ttO-^t^T(lt~Tj«< 6joc^o rfjiCtOiO to lO 3t~ (N to iC to lO to coa>f-ioo(Noo-*;oin " (NOcoocomcoioco lOtOiOtOiOtO-^tOrftO acoonA to oo»ctotoiooocoa>CMi-t 0coo Si-ti-lf-tiHi-HiHi-0 to lO lOOtO COt^ to vO to iC to StoTHio>-imcM-<»0>OO00t-( COOCOO(NOlNi-l(NrH .ejictoictoiotoictoicto T^tO'^tOTfto-^tO^tO pf* tO"ft0^tO"^tO^tO GOCOto-1*'CMt^''S<»e3iOirerHcc<».-i COiC.HlNO o d r- -^ lO t~ lO CO lO CO lO Tf -^ Tf Tf -^ -^ Tf -^ -^ Tf lO CO ift CO o ^ to ■^ to ^ to -^ to ^ to Tj* to ■'f to "^ to "^ to "*• to SCM(T>-<»-cooa COiOCOiOCOlOCOlOCO i^tOTftC^tO'^tO^tO - --(Oscot^iriicoocoQ tftO'^tOTt*tO'^tO"!ftO to 00 ^ 05 CO i-H .H N O ■r' 00 to to t^ -^ CJa CM i-l Q CO oc5oc^ocoocooco lo CO iS CO lO CO lO ■>»< S T»i IC to »0 to »0 to lO to lO to ■'f to -^ to -^ to -^ to -3< to r-OOtOOSlOO-^r-^COC^ 0»tOCOI^t-OS lOO'^fC^CMCOOincCt^ 1-H i-l rl rH 1-1. CM iH C-) iH e^ rHCMt-((N0040CMOCM OCOOCOOCOOCOiOCO iCtOiCtOvOtOlOtOiCtO lOtOl/StOiOasiOtOiOtO lOtOiOtOiCtOiOtO'^tO cM-.j<.-iio.Htoor-o>oo ooo»i>oiOi-i-*CMcoeo ■Hi-Ii-HCMiHCMt-ICMi-ICM lOtOLCtOlOtOlCtOiOtO t~-Ht^e^tOOlOCO>n'* TflOCOtOCMt^rHOOOOO CMiOi-ltOO>t"-OOCJ5tOO iHCMi-ICMOCMOOOCO liStOiOtOiOtOiCtOiOtO OOOO— CO TfO^O'^O-^O'^O ■*0-*0"»<0-«'OCOO tf3 to to to lO to »0 to lO to ITD to lO to iC to iC to »c to tD'*"n>o-*tocor~c^oo CMr-ICMi-OtO COmCMOWOOr-igcM eOOeOTHCOr-(Mi-ICOF-l lOtOtCtOtCtOLOtOOtO cn^o0'2'ooicr»ict~o coocoocoocooeoo iOtO»CtOiCtOiOtOiOtO St^r"-r>-i>-t*t^t>-oot^op QOt~00t-00t^COtO00 u5-'itiO'^iO-»fiO"tt»tc iCtCiCiOiOiCiCiOiCtC McOP^OSDhCOPIhCCP^CO aizaaixoixA-Mt:iociinaaiO inoi>OCiinoaiOOiOO ■^O'^iO'VO'^rOT)!© inuoioiAtciOiCtoiOto a^ccC^QOtfasMccOHCO IC kO tO to to Q O rH rH rH rH iH « P^odP^cdp^osoicdtfadpico §.-ieoi-i«Oi-(coi-ieOi-i eOtH05r-ieO'-icoi-i«.-t~t>.QcpQ MiONiOC5i06liO«iSc5 COcotCcOtOcOOcoiACOiCCO ScnSSoSSSSS CO CO CO CO CO CO CO CO CO CO 0>gpC0O>t~-QC0i-liQ'-l>oe} kOcOiCcOtOcOiCco^cOiOcO 5jJ5i-icOi-it^oaQo>o> cocOCOcOcOCOcocOiOCO S"O00OC3>0?Qe0^t^oc5ioeo COcocOcOiOCCiOcOiOco iocoiOo5iCcoi/5eo>Scoiom cCCOiOcOiCCOiOCOOcOkCCO t^>-icoc^u5e5'fl<'o e<5 >4 05 55 55 iCCOOCOiCCOiOCO NcOi-i t^ Id CO to CO iOc*5-^-^coiOCJcot-(t--Qccoac>ooor^i-icoc* '•OCOCOCOCOCOCOCOCOCO (CO COiOCOiOCOtCCOiOCO ujeC'^'^cocoiMt^ lOcoioeoicniaoo iOCOiCCOlOCOiOCO •HOOOO lOCOiOcO t^ CO CO CO CO CO CO CO CO CO 80»0>O00r-tC0C^^?C0 NioeoiBeoiOcoiOeo cOcoOcoiCCOk/^cOiOco 'j'-feoirtoit^t-ioo >oco>acooco>om lOCOiCCOiOCOiOCO ^ CO ^ ^ lOcOlOCO S-^C^HQCJCOi-tt-OCS CO CO CO CO CO CO CO CO CO CO o> !5 00 1-" i» d CO is 6q >o CO is m CO lO CO lO CO lO CO COiOPJt^CDOQOOJ lOeoioeoiOM^OT iQCOiOCOiCCOtACO OOrHCOM lacoiaco gS2S2SSSS§?5 •^totototototococotoco SS§S3S8S5gg3 CO CO CO CO CO CO CO CO lO CO SnS niSmiSnSn CO U3 CO lO CO IC CO S"®t^C»COt~OCOr-('J<5J Oi-IOr-IOtHOMOM tC^COCOCOCOCOCOcOcOCOCO CO'*CJinOCOOQt^Ol oco CO la CO >o CO CO iC CO kC CO lO CO Scoio to CO CO C< (N CO Q -Ji 0> CO CO >o CO iS CO ^ CO CO to CO to CO lO CO c-i o 1-1 e< o» CO CO ^* CO ^ CO ^ CO CO to CO to CO to CO go a> rH t^ O CO ■* lOcoio - - - _ - 3! CO CO ^ CO ^ CO *g* CO CO to CO tO CO tO CO lOOOtOCQ^OO^'^ iOCOiOCOtOcOtOCO to CO lO CO o>r»coo>cooiQi-i ^co^oo^^^^ tOCOtOcOiOcOiOCO lOtOiOtO t^t^tOO-^i-HC^WrH-^OiiO ^ CO ^ CO ^ ^ ^ ^ ^ ^ 00 ^ iOtOiOtO»OtOiOCOiOtOiOtO ioooeoa>f-ii-HOcoQO'^t;tp ^ CO M* CO ^ ^ TT ^ CO Tl* CO ^ iOcOiOtOiOtOiOtOiOtOiOtO c^r-i-iOiOSf-ir*Mu5^^cQ ^ CO ^ CO CO ^ CO Tj* CO ^ CO ^ lOtOtCtOiCtOOtO^cOiCcO tOO'^t-HCSCOOiOOSI-* lOtOiOtOLOtDOCOiOtO lO tOUD CO lO to iC CO iO to COCOCOCOCO'^CO^OO'^CO'^ LOtOiOtOiOtOOtOiOcO^tO g8gS ^cOcOtO gt^l-l lOi-l COiOCO lOrHiOi-l .O CO to CO CNCOOt^OQOJCOrHlOCO iOi-liOi-l^i-tTj ■flilM-* lOCOiO C-0>0Qt~Ot0dC0'^IMC0O000Q0JC0rH-«e0 Coc»t~ «>i-lCO to CO to IM CO ei CO CQ OJ (N CD lO CO lO CO to CO CE^OQpjCCB^OQajaO^OO '-3-'- -"iT'^r' I^OiiO»-lCOCOi-nOO»t^t^O» e^e^NcoMcoocor-icOi-ieo tOcOtOcOlOCOtOCOtOCOiOCO PE^OQPljQQp^aQPI^CCP^aQp^OQ -sr-z^- -^sr-^ Page 670] TABLE 10. Mean Time of Sun's Visible Rising and Setting. -2 a I i 2 •xojddv WW •xoiddy i^tn PdQQSJCOQjcxipI^OQPlHCIS pjoQP^cdP^'cdP^cdtfai g'C2rHCOi-l«lrHOTi-ICO.H OiHOi-IOrHOr-IOi-l Oi-IOiHOr-IOrHOrM OrHOi-HOi-IO— 'Oi-H ^0000000000 0000000000 M r-tOrHO.-lOrHO»-H P^copHcdP^cdPtHcdP^cn O^oqPh'^P^oqP^cqCehcq OiHOr-(Ot-HO'-^ OrH C5 .-( O rH O r-t O iH O i-H (^^ O CO ^ O '.O 'O O -^ O C O 'O O CO 'O O -o o -o S* 21 CO ^J '-0 -M O C^ CO i-KD ^-^cocococococococo^o OrlO^Or-IOiHOrH Or-t'SC^iOC^idMiO'N ^ CO CO CO CO CO O CO CO ?0 CO CO CO CO CO iC CO lO CO lO CO i-lcOTHt>Qr^Qt^Q00 O.-HOi-HO^Or-)0rH COCOOCOCOCOCOCOCOCO JOOSOOOOirH O^iOrHlCi— llOf-HiCi-HLCt-HiOrHCOQcOQcOQcO COCOCOOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCOCO >aooiaoo5oOdo0050i cocoio?OiOcoiCcou:^co OcOiOcOvCcOiOCOiOCO ^COCOCOCOCO^COCOlCCo'ocOiOCOiOCOiOCOlOCD S"Ocoococooi'^aO'^botOt>»cr^cocpcocpi:^ fCJcOCOCOCOiOcOiOcOOcokocOiOCOi/iCOiOtOiCCO S'aiioooi^GOcot^cor^r" ^lOcOiCcOiOcOOCOUTiCO ^iCCOiOCOiOcOiOcOiOcO lOCOiOCDii^cOvOcOiOCD iQCOtOCOiOCOiCCOiOcO t^'^cp-^cpiCiOiOiOco lOcOiOCOiCcOiOCOiOCO lAcOiOcO^COiOCOiOco lOcOOcOiCCOU^cOiOCO t-COcOCOcOrffiO-^iOiA »OCOiOcOiCCOiOtOiOcO iOCOiOCO»OcOiOCOiOCO lOCOiOcOiCCOiCCOiOcO lOcOiOcOiCCOiOcOiOCO lOcOiOCOiOcOiCCOiCco S*cOascOOtOOiOi-*"**'N COC^I-NCOrHTfOiOQ'-O lA 'M >0 CO lO 00 iO CO »0 CO lO CO lO CO uO CO lO CO »0 CO ,^iOCO»CCOiCcOiOCOirtcO iOCOiOCO>OCOiCCOiOCO iflCOiO'OiOCOiOcOiOCO lOCOiOCOtOCOiOcOiOCO '^0O^COtPCO'^CO^'<»< OCO»OCO>OcO»OcoiOcO S*u^»M-*'c^-<#cococooj'^K-iinQcoait^oqcoQoa> lOCOiOCOiOCOiOCOiOCOiCCOiOCO'^CO^CO'^CO ^OcOiOCO»OCOiOCOiOcO»OCOiOCOur5COU3cOiOcO I^OCOfHirtCq^JCOCO'^ lOcOiOcOiOcotOcoi^co iCt-t^C^00C00>cpOI>T-lcp(NU0c0 5cO-^"*Ti<^^Tfas0SO00rHI>'^3iOC0Nj*^C0iO'NI>O000>05 00r-4I>!NiOC0'*»0C^C0 lOcOOCOtOCOiOCOiOCO gOOOC^i-tCDCOiO^COiO rf-OcOiCcOiOCOiCCOiOcO S* r* Ci CO CO Tf ■<}* CO CO iH *^ OOpOOt^ rH COCO'* "^ '^'^^'^-^■^Tj'^Tji-^ '(J^'^COiOCOiOCOiOCOiO .iS^ lO CO O CO lO CO lO CO O CO iC CO lO CO tO CO lO CO O CO r^ t-^ OS o 1-1 tx Tji CO ■'J' CO ■* CO m CO lO comcoiC?»iocot^.^ >C^O(MOi-(rHi-(r-( lO c^ lO t~-iO OQOOOOt~f5COCO>n iooioi>iot^iot*ot-* >>-lOi-l 1-liOCOCOiO t^iH vOCOCO lO t^ lO t^ lO Si-ioa>c t>iflt-U5t >lO!NCO -lOl-iO ■»»'^ogao c0 COTfcO-^COi^COiOiMiO ^lOOiOOiOOiOOiftO S'^^SS^oQ^^ocoT^in nt^oosoOr-ioco-.j0'.»li-llMC02imt^00>OOIN(N OOiO ic t lOoDNOoeor^iCOoQ Oi-IOC^OINiitHNiO?) (NiOin(Nt^ r^Niocc^oooo iO(NOC^iOC^-*CO S'9S2S^"*'^J1'*oo » CO o o ■"}< o M ■* M ic e^ uo 6< 10 ^J iS i-iOrHOrHOrt 000 ^looicoiooiooioo ioo»ot*ior*ot*ot* ggooooooooiNTft-* (Noosoor-Oiococ^in ^ C^ "^ (N -^ iH iC 1-1 lO rH »0 iHirZl 0»000 O 000 i^iiCOiOOiiSOu^OiCO iOOiOOiCt*iOt>"OI:- r-( (M Tjl OS O t~ a> rH O iH U3 r-l 10 i-l t~ m t^ T)" t^ ->f t~ T«*rHC^-.**Osb-OOCOCO 10 (N-* C^T) T)< r~ -.ji t» Tji t fi ai pita pi in piMoicni .-I C^ CO Tf lA N f) . Tt< C- -* t~ QjcopiHOSP^ccQjoQOjcn I TABLE 10. Mean Time of Sun's Visible Rising and Setting. [Page 671 O ^ a a O OS •xojddy rH N eo 5 pjoQpjaOC^CQOJCQMoQ Or-lOrHOr-lOi-l&i-c giOiO^iA'Vtocococor- ^ CO ^ CQ ■^ CO '•1' ^ ^ 1< S"eOIMC^Ni-lCOO-«>c3>^ S? lO iO lO u^ >c (licDticofd'npi^oiai oixfico^itafitDtiaa f4aQdaQajcnp:ia5p4cd c3co5ico-i'*i.-ir)"0'<«<0'*ou50io Oi-lOrHOr-iOrHOrH OrHOi-(OrHOi-cOrH|Oi-lOrtOi-lOr-aOOQQOGQO>QOO> ■I lO rt lo t-1 lo 5i ic (N eo^e9ioeMioe<a»ooo>ooQ >Oe4ia(NiA04>OC4lOC40C^SC4'MOOi-CQOQO>OOlO>00>rJOOe»t-e^tOCO ^S 31 '^5995^^^® 0«-H0> lA to lO CO lO to to CO lO CO kO CO lO CO lO CO lO CO lO CO ior~"»'ooe03>c30e^'-i't~iOcgco'i2oO'i(N©.HCig»co '^C0^0Q^C0'"#^^^^^^^C0^'C0^C0^C0^»0?^C0lOC0»OC^iO >ocoiocoioco>ocoiocoiacoiocsiocoioco>oco,iaco>aco>acoocooco <-iooo5e>TCooior~co •o«>iQO>eooc^^i--T(iej>f«.-i 'J' ■>)< ^ ■»(" CO -^ CO ■* CO -V OT-^CO-fCOScOiOeOiO lCJiOMOiMiOO>OC40 tCCOiOCOtO'^tOCOtOcO iCCOiOcOkOCOiOCOiCCokccoOCOiC«OiACOiOr* )t^i>.ooio3>focoe^i-i-»»'i-iijeop>ooot>-og» S^co'^cOT(ocoiOcoiocMi3e<>3iN>oeMOcr~oooot^a>iOQ ■«)'0>iooc02jr}^0'S ocigpcoO'*(Ni-i'*mco ^TenTTeo-vmrrcoia eoiocoiocO"OcoiflSiO|c^iOC• lO r* lO t* »0 1^ lO t^ lO t^ »c c* S't-oco-HSic^coco^jira Qcog>oot~o»ift-jTiieooi3'©coQ050coo-<'C^ c<-*ot^t^a>iON£j"* eo*M'OcOioeoiocoiC e0i5f- S'eo-fiMio— Q0 t^OiOC'ICO-^^^0040ahP»-«CO^^Ht^QQOiOC^ MOC^OIMOINOr-IO i-CrHi-li-li-lr-Ci-li-iOr-c 0(NOC^OC4i?5cO'<5eO lO t~ lO t^ lO t~ K5 1^ lO t~ lO t~ lO r~ lO t~ lO t» lO t» iOf-ior-i/3t~^t~'^t^ iOt^iOt*tct^icr*iOt^itOt^iOt*iOt^iOt^tot^ a)OoiM'*'*e>r~o»oi gOiOI^C^t^^COCO-^OO ^U5t*»Ot^iOt^»Ot^tCt^ g»CCOCO>Or-*OO^OCpS^I oc4 0?3oc5oe^>o§ ?5ioeo>ocoioco^^ t^tHio-^c^coOiOir^M OMOMOd'OfJ'OCO i5cou5eoiSOT'»*-*^'v lOCOlOOT^-^'^'^'^-^ i^?JeoiOQO>coooc^t~ TT^^^^fcoioeoiO oocoe^c^c -a" t~- ^ r- Tj- 1» ^00^00 STTCjr-OQCOMCOiQ e^oc4ioeoi5coioM »o CO ^ ^ •* T)" — I 00 t^ -^ TJ. •»!•■»»■ ■"fCOlO ^ t^ ^ t^ ^ t^ eocooiO'^S COi0 040!' 00 .-lOr-ll-t •^oo-ctioo !q>»t~c i-l.-IOf-IONO(NOCJ iOfllOCOi600iOC0^'VlTlo t~ lO r- -^ r» ^ t^ tj" t~ "* t~ ^ t^ I >}< t~ -^ r, SSc3S?3S8ioSSot OC^OiMiOf»iOCO>OCO •<# t» -* t^ •* t- •* 3; r-l CO 00 C» iOCOiOOTtCCO •* t- •<»' t~ •* t~ ■*r»-Jit~ coioiNodo •* r- >«' 00 •>»' 00 o5 ^ ^ ^ "^ ^ t^ ^ t* ^ t^ 0005iQ.7fcoi3>gior) 1 1^ ^ 00 •* 00 T(" 00 ^t~>i»1"*5tCCO eocjcooi ^ ^ CO ^ CO 00 CO 00 lO CO 21594°— 14- -36 Page 672] TABLE 11. For reducing the Time of the Moon's passage over the Meridian of Greenwich to the Time of its pass- age over any other Meridian. The numbers taken from this Table are to be added to the Time at Greenwich in West Longitude, subtracted in Kast Longitude. Longi- tude. Daily variation of the moon's passing the meridian. Longi- tude. 40" 42m 44m 46m 48" 60" 52" 54" 66" 68" 60" 62" 64" 66" O 5 10 15 20 25 30 m. 1 1 2 2 3 3 m. 1 1 2 2 3 3 m. 1 1 2 2 3 4 TO.' 1 1 3 2 3 4 m. 1 1 2 3 3 4 m. 1 1 2 3 3 4 m. 1 1 2 3 4 4 m. 1 1 2 3 4 4 m. 1 2 2 3 4 5 TO. 1 2 2 3 4 5 TO. 1 2 2 3 4 5 TO. 1 2 3 3 4 5 m. 1 2 3 4 4 5 TO. 1 2 3 4 5 5 o 5 10 15 20 25 30 35 40 45 50 55 4 4 5 6 6 4 5 I 6 4 5 5 6 7 4 5 6 6 7 5 5 6 7 7 8 9 9 10 11 5 6 6 7 8 5 6 6 7 8 5 6 7 7 8 5 6 7 8 9 6 6 7 8 9 6 7 7 8 9 6 7 8 9 9 6 7 8 9 10 6 7 8 9 10 35 40 45 50 55 60 65 70 75 80 7 7 8 8 9 7 8 8 9 9 7 8 9 9 10 8 8 9 10 10 8 9 10 10 11 12 12 13 14 15 9 9 10 11 12 9 10 10 11 12 9 10 11 12 12 10 10 11 12 13 10 11 12 12 13 10 11 12 13 14 11 12 12 13 14 11 12 13 14 15 60 65 70 75 80 85 90 95 100 105 9 10 11 11 12 10 10 11 12 12 10 11 12 12 13 11 11 12 13 13 11 12 13 13 14 12 13 14 14 15 13 13 14 15 16 13 14 15 16 16 14 14 15 16 17 14 15 16 17 17 15 15 16 17 18 15 16 17 18 19 16 16 17 18 19 85 90 95 100 105 110 115 120 125 130 12 13 13 14 14 13 13 14 15 15 13 14 15 15 16 14 15 15 16 17 15 15 16 17 17 15 16 17 17 18 16 17 17 18 19 16 17 18 19 19 17 18 19 19 20 18 19 19 20 21 18 19 20 21 22 19 20 21 22 22 20 20 21 22 23 20 21 22 23 24 110 115 120 125 130 135 140 145 150 155 15 16 16 17 17 16 16 17 17 18 16 17 18 18 19 17 18 19 19 20 18 19 19 20 21 19 19 20 21 22 19 20 21 22 22 20 21 22 22 23 21 22 23 23 24 22 23 23 24 25 22 23 24 25 26 23 24 25 26 27 24 25 26 27 28 25 26 27 27 28 135 140 145 150 155 160 165 170 175 180 18 18 19 19 20 19 19 20 20 21 20 20 21 21 22 20 21 22 22 23 21 22 23 23 24 22 23 24 24 25 23 24 25 25 26 24 25 25 26 27 25 26 26 27 28 26 27 27 28 29 27 27 28 29 30 28 28 29 30 31 28 29 30 31 32 29 30 31 32 33 160 165 170 175 180 40" 42" 44m 46" 48m 50" 52" 64" 56m 68" 60" 62" 64" 66" TABLE 12. [Page 673 For finding the Variation of the Sun'B Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. M. 1" 2" 8" 4" 6" 6" 7" 8" 9" 10" 11" 12" 18" 14" 15" 16" 17" 18" 19" 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 6 J 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 1 2 3 4 5 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 3 2 2 2 2 3 2 2 2 3 3 2 2 2 3 3 2 2 3 3 3 6 7 8 9 10 1 1 -^ •*■ 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 2 2 2 3 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 7 7 2 3 3 3 3 3 4 4 4 4 3 3 3 3 4 4 4 4 4 5 3 3 3 4 4 4 4 5 5 6 3 3 3 4 4 3 3 4 4 4 3 4 4 4 5 3 4 4 4 5 11 12 13 14 15 16 17 18 19 20 4 5 5 5 5 5 5 5 5 6 5 5 5 6 6 5 5 6 6 6 16 17 18 19 20 21 22 23 24 26 5 6 5 5 5 6 6 6 6 7 7 7 7 7 8 t 5 6 6 6 6 7 7 7 7 7 8 8 8 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 6 6 6 6 7 7 7 7 8 8 8 9 9 9 9 6 6 7 7 7 6 7 7 7 8 7 7 7 8 8 21 22 23 24 25 26 27 28 29 30 —J- 2 2 2 2 2 2 7 8 8 8 9 8 8 8 9 9 8 9 9 9 10 26 27 28 29 30 31 32 33 34 35 9 9 9 10 10 9 10 10 10 11 10 10 10 11 11 31 32 33 34 35 36 37 38 39 40 ■l 2 2 2 1 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 5 5 5 6 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 9 8 9 9 9 9 9 9 10 10 10 10 10 10 10 11 10 10 11 11 11 11 11 11 12 12 11 12 12 12 13 36 37 38 39 40 41 42 43 44 45 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 4 4. 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 5 5 5 6 5 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 5 6 6 6 6 6 6 6 8 8 8 8 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 9 9 9 9 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 10 10 10 10 8 8 8 8 8 8 9 9 9 9 9 10 10 10 10 10 10 11 11 11 8 8 9 9 9 9 9 10 10 10 10 10 11 11 11 11 11 12 12 12 9 9 9 10 10 10 10 10 11 11 11 11 11 12 12 12 12 13 13 13 10 10 10 10 11 11 11 11 11 12 12 12 12 13 13 13 13 14 14 14 10 11 11 11 11 11 11 11 12 12 12 12 12 12 13 12 13 13 13 14 13 13 14 14 14 41 42 43 44 45 46 47 48 49 50 12 12 12 12 13 12 13 13 13 13 13 13 14 14 14 14 14 14 15 15 15 15 15 16 16 46 47 48 49 50 51 52 53 54 55 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 13 13 13 14 14 14 14 14 14 15 14 15 15 15 16 15 16 16 16 17 16 16 17 17 17 51 52 53 54 55 56 57 58 59 60 14 14 15 15 15 15 15 15 16 16 16 16 16 17 17 17 17 17 18 18 18 18 18 19 19 56 57 58 59 60 Page 674] TABLE 12. For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. M. 20" 21" 22" 23" 1 1 2 2 2 3 3 3 4 24" 25" 26" 27" 28" 29" 80" 31" 32" 33" 84" 86" 36" 1 2 3 4 5 1 1 1 2 1 1 1 2 1 1 1 2 2 3 3 3 4 1 1 2 2 2 3 3 4 4 1 1 2 2 3 3 3 4 4 1 1 2 2 3 3 3 4 4 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 3 1 1 2 2 3 1 1 2 2 3 1 1 2 2 3 1 1 2 2 3 1 1 2 2 3 1 1 2 2 3 1 2 3 4 5 6 7 8 9 10 2 2 3 3 3 2 2 3 3 4 3 3 4 4 5 3 3 4 4 5 3 3 4 4 5 3 4 4 5 5 3 4 4 5 5 3 4 4 5 5 3 4 4 5 6 3 4 5 5 6 4 4 5 5 6 4 4 5 5 6 6 7 8 9 10 11 12 13 14 15 4 4 4 5 5 5 6 6 6 7 4 4 5 5 5 6 6 6 7 7 4 4 5 5 6 6 6 7 7 7 4 5 5 5 6 4 5 5 6 6 5 5 5 6 6 5 5 6 6 7 5 5 6 6 7 5 6 6 7 7 5 6 6 7 7 6 6 7 7 8 6 6 7 7 8 6 6 7 7 8 6 7 7 8 8 6 7 If i 8 9 6 7 8 8 9 7 7 8 8 9 11 12 13 14 15 16 17 18 19 20 6 7 7 7 8 6 7 7 8 8 7 7 8 8 8 7 1 8 8 9 7 8 8 9 9 7 8 8 9 9 8 8 9 9 10 8 9 9 10 10 8 9 9 10 10 9 9 10 10 11 9 9 10 10 11 9 10 10 11 11 9 10 11 11 12 10 10 11 11 12 16 17 18 19 20 21 22 23 24 25 7 7 8 8 8 7 8 8 8 9 8 8 8 9 9 8 8 9 9 10 8 9 9 10 10 9 9 10 10 10 9 10 10 10 11 9 10 10 11 11 10 10 11 11 12 10 11 11 12 12 11 11 12 12 13 11 11 12 12 13 11 12 12 13 13 12 12 13 13 14 12 12 13 14 14 12 13 13 14 15 13 13 14 14 15 21 22 23 24 25 26 27 28 29 30 9 9 9 10 10 9 9 10 10 11 10 10 10 11 11 10 10 11 11 12 12 12 13 13 13 14 14 15 15 15 16 16 16 17 17 18 18 18 19 19 20 20 20 21 21 21 22 22 23 23 10 11 11 12 12 12 13 13 14 14 14 15 15 16 16 16 17 17 18 18 18 19 19 20 20 20 21 21 22 22 11 11 12 12 13 11 12 12 13 13 12 12 13 13 14 12 13 13 14 14 13 13 14 14 15 13 14 14 15 15 13 14 14 15 16 14 14 15 15 16 14 15 15 16 17 15 15 16 16 17 15 16 16 17 18 16 16 17 17 18 26 27 28 29 30 31 32 33 34 35 10 11 11 11 12 11 11 12 12 12 13 13 13 14 14 11 12 12 12 13 13 14 14 14 15 15 15 16 16 17 17 17 18 18 18 19 19 19 20 20 21 21 21 22 22 13 13 14 14 15 15 15 16 16 17 17 18 18 18 19 13 14 14 15 15 16 16 16 17 17 14 14 15 15 16 14 15 15 16 16 15 15 16 16 17 17 18 18 19 19 16 16 17 17 18 16 17 17 18 18 17 17 18 18 19 17 18 18 19 19 18 18 19 19 20 18 19 19 20 20 19 19 20 20 21 31 32 33 34 35 36 37 38 39 40 12 12 13 13 13 16 17 17 18 18 17 17 18 18 19 18 19 19 20 20 19 19 20 20 21 19 20 20 21 21 20 20 21 21 22 20 21 22 22 23 21 22 22 23 23 22 22 23 23 24 36 37 38 39 40 41 42 43 44 45 14 14 14 15 15 14 15 15 15 16 16 16 17 17 18 18 18 19 19 20 18 19 19 20 20 19 20 20 21 21 20 20 21 21 22 21 21 22 22 23 21 22 22 23 23 22 22 23 23 24 23 23 24 24 25 25 26 26 27 28 23 24 24 25 26 24 25 25 26 26 25 25 26 26 27 41 42 43 44 45 46 47 48 49 50 15 16 16 16 17 19 20 20 20 21 21 22 22 23 23 20 20 21 21 22 22 23 23 23 24 21 21 22 22 23 21 22 22 23 23 22 23 23 24 24 23 24 24 25 25 24 24 25 25 26 25 25 26 26 27 26 27 27 28 28 27 27 28 29 29 28 28 29 29 30 46 47 48 49 50 51 52 53 54 55 17 17 18 18 18 18 18 19 19 19 20 20 20 21 21 23 23 24 24 25 24 24 25 25 26 25 25 26 26 27 26 26 27 27 28 26 27 27 28 28 27 28 28 29 29 28 29 29 30 30 29 29 30 31 31 30 30 81 32 32 31 31 32 32 33 51 52 53 54 55 56 57 58 59 60 19 19 19 20 20 22 23 23 24 24 23 24 24 25 25 24 25 25 26 26 25 26 26 27 27 26 27 27 28 28 27 28 28 29 29 28 29 29 30 30 29 29 30 30 31 30 30 31 31 32 31 31 32 32 33 32 32 33 33 34 33 33 34 34 35 34 34 35 35 36 56 57 58 59 60 TABLE 12. [Page 676 For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. M. 87" 88" 89" 40" 41" 42" 48" 44" 45" 46" 47" 48" 49" 50" 51" 62" 68" 1 2 3 4 5 1 1 2 2 3 1 1 2 3 3 1 1 2 3 3 1 1 2 3 3 1 1 2 3 3 1 1 2 3 4 1 1 2 3 4 1 1 2 3 4 1 2 2 3 4 1 2 2 3 4 1 2 2 3 4 1 2 2 3 4 1 2 2 3 4 1 2 3 3 4 1 2 3 3 4 1 2 3 3 4 1 2 3 4 4 1 2 3 4 5 6 7 8 9 10 4 4 5 6 6 7 7 8 9 9 4 4 5 6 6 7 8 8 9 10 4 5 5 6 7 7 8 8 9 10 10 11 12 12 13 14 14 15 16 16 17 18 18 19 20 20 21 21 22 23 23 24 25 25 26 27 27 28 29 29 30 31 31 32 33 33 34 34 35 36 36 37 38 38 39 4 5 5 6 7 7 8 9 9 10 11 11 12 13 13 14 15 15 16 17 17 18 19 19 20 21 21 22 23 23 4 5 5 6 7 8 8 9 10 10 11 IS 12 13 14 4 5 6 6 7 8 8 9 10 11 4 5 6 6 7 4 5 6 7 7 5 5 6 7 8 5 6 6 7 8 5 5 6 7 8 5 6 6 7 8 5 6 7 7 8 5 6 7 8 8 5 6 7 8 9 5 6 7 8 9 5 6 7 8 9 6 7 8 9 10 11 12 13 14 15 8 9 9 10 11 8 9 10 10 11 8 9 10 11 11 8 9 10 11 12 9 9 10 11 12 9 10 10 11 12 9 10 11 11 12 9 10 11 12 13 9 10 11 12 13 10 10 11 12 13 10 11 11 12 13 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 10 10 11 12 12 13 14 14 15 15 16 17 17 18 19 19 20 20 21 22 10 11 11 12 13 13 14 15 15 16 "16 17 18 18 19 20 20 21 22 22 23 23 24 25 25 26 27 27 28 29 29 30 30 31 32 32 33 34 34 35 35 36 37 37 38 11 12 13 13 14 11 12 13 14 14 15 16 16 17 18 19 19 20 21 22 12 12 13 14 15 15 16 17 18 18 12 13 14 14 15 12 13 14 15 15 13 13 14 15 16 13 14 14 15 16 13 14 15 16 16 13 14 15 16 17 14 14 15 16 17 14 15 16 16 17 14 15 16 17 18 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 14 15 16 16 17 15 15 16 17 18 16 17 17 18 19 16 17 18 18 19 16 17 18 19 20 17 18 18 19 20 17 18 19 20 20 18 18 19 20 21 18 19 20 20 21 18 19 20 21 22 19 19 20 21 22 21 22 23 24 25 18 18 19 20 21 18 19 20 20 21 19 20 21 21 22 20 20 21 22 23 20 21 21 22 ■23 20 21 22 23 24 21 22 22 23 24 21 22 23 24 25 22 23 23 24 25 22 23 24 25 26 23 23 24 25 26 23 24 25 26 27 26 27 28 29 30 21 22 23 23 24 22 22 23 24 25 22 23 24 24 25 23 23 24 25 26 23 24 25 26 26 24 25 25 26 27 24 25 26 27 27 25 26 26 27 28 25 26 27 28 29 26 27 28 28 29 26 27 28 29 30 27 28 29 29 30 27 28 29 30 31 31 32 33 34 35 36 37 38 39 40 22 23 23 24 25 25 26 27 27 28 28 29 30 30 31 31 32 33 33 34 24 25 25 26 27 27 28 29 29 30 31 31 32 33 33 34 35 35 36 37 37 38 39 39 40 25 25 26 27 27 25 26 27 27 28 26 27 27 28 29 26 27 28 29 29 27 28 29 29 30 28 28 29 30 31 28 29 30 31 31 29 30 30 31 32 29 30 31 32 33 30 31 32 33 33 31 31 32 33 34 31 32 33 34 35 32 33 34 34 35 36 37 38 39 40 41 42 43 44 45 28 29 29 30 31 31 32 33 33 34 29 29 30 31 32 29 30 31 32 32 30 31 32 32 33 31 32 32 33 34 31 32 33 34 35 32 33 34 34 35 33 34 34 35 36 33 34 35 36 37 34 35 36 37 38 35 36 37 37 38 36 36 37 38 39 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 32 33 34 34 35 33 34 34 35 36 34 34 35 36 37 35 35 36 37 38 35 36 37 38 38 36 37 38 38 39 37 38 38 39 40 38 38 39 40 41 38 39 40 41 42 39 40 41 42 43 40 41 42 42 43 41 42 42 43 44 45 46 47 48 49 46 47 48 49 50 51 52 53 54 55 35 36 36 37 38 36 36 37 38 39 37 37 38 39 39 37 38 39 40 40 38 39 40 41 41 39 40 41 41 42 40 41 42 42 43 41 42 42 43 44 42 42 43 44 45 43 43 44 45 46 43 44 45 46 47 44 45 46 47 48 51 52 53 54 55 56 57 58 59 60 35 35 36 36 37 38 39 40 40 41 39 40 41 41 42 40 41 42 42 43 41 42 43 43 44 42 43 44 44 45 43 44 44 45 46 44 45 45 46 47 45 46 46 47 48 46 47 47 48 49 47 48 48 49 50 48 48 49 50 51 49 49 50 51 52 49 50 51 52 53 56 57 58 59 60 Page 676] TABLE 12. For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Eight Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. 1 M. 54" 56" 56" 57" 68" 59" 1 2 3 4 5 60" 1 2 3 4 5 61" 1 2 3 4 5 62" 63" 64" 65" 66" 67" 68" 69" 70" 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 6 7 7 8 9 10 11 12 13 14 15 16 17 18 19 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 6 1 2 3 4 6 1 2 3 5 6 1 2 3 5 6 1 2 4 5 6 1 2 3 4 5 6 7 8 ■ 9 10 5 6 7 8 9 6 6 7 8 9 10 11 12 13 14 6 7 8 9 10 10 11 12 13 14 15 16 17 18 19 6 7 8 9 10 11 12 13 14 15 6 7 8 9 10 6 7 8 9 10 6 7 8 9 10 6 7 8 9 10 6 7 8 9 11 6 7 9 10 11 7 8 9 10 11 7 8 9 10 11 7 8 9 10 11 7 8 9 10 11 7 8 9 10 12 7 8 9 11 12 6 7 8 9 10 11 12 13 14 15 10 11 12 13 14 11 12 13 14 15 11 12 13 14 15 11 12 13 14 15 11 12 13 14 16 12 13 14 15 16 12 13 14 15 16 12 13 14 15 16 12 13 14 15 17 12 13 15 16 17 12 14 15 16 17 13 14 15 16 17 13 14 15 16 18 11 12 13 14 15 16 17 18 19 20 16 17 18 19 20 14 15 16 17 18 15 16 17 17 18 15 16 17 18 19 16 17 18 19 20 16 17 18 19 20 16 17 18 19 20 17 18 19 20 21 17 18 19 20 21 17 18 19 20 21 17 18 20 21 22 18 19 20 21 22 18 19 20 21 22 18 19 20 22 23 18 20 21 22 23 19 20 21 22 23 21 22 23 24 25 19 20 21 22 23 19 20 21 22 23 20 21 21 22 23 20 21 22 23 24 20 21 22 23 24 21 22 23 24 25 21 22 23 24 25 21 22 23 24 25 26 27 28 29 31 22 23 24 25 26 22 23 24 25 26 22 23 25 26 27 23 24 25 26 27 23 24 25 26 28 23 25 26 27 28 24 25 26 27 28 24 25 26 28 29 25 26 27 28 29 21 22 23 24 25 26 27 28 29 30 26 27 28 29 30 23 24 25 26 27 24 25 26 27 28 28 29 30 31 32 33 34 35 36 37 38 39 39 40 41 42 43 44 45 46 24 25 26 27 28 29 30 31 32 33 34 35 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 49 50 51 52 53 54 55 56 25 26 27 28 29 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 48 49 50 51 52 53 54 55 56 57 25 26 27 28 29 26 27 28 29 30 26 27 28 29 30 27 28 29 30 31 27 28 29 30 32 28 29 30 31 32 28 29 30 31 33 29 30 31 32 33 29 30 31 32 34 29 31 32 33 34 30 31 32 33 35 30 32 33 34 35 31 32 33 34 35 28 29 30 31 32 30 31 32 33 34 35 36 37 38 39 30 31 32 33 34 31 32 33 34 35 32 33 34 35 36 32 33 34 35 36 33 34 35 36 37 33 34 35 36 37 34 35 36 37 38 34 35 36 37 39 35 36 37 38 39 35 36 37 39 40 36 37 38 39 40 36 37 39 40 41 31 32 33 34 35 36 37 38 39 40 32 33 34 35 36 35 36 37 38 39 36 37 38 39 40 37 38 39 40 41 37 38 39 40 41 38 39 40 41 42 43 44 45 46 47 38 39 41 42 43 39 40 41 42 43 40 41 42 43 44 40 41 42 44 45 41 42 43 44 45 41 43 44 45 46 42 43 44 46 47 48 49 50 51 53 36 37 38 39 40 41 42 43 44 45 37 38 39 40 41 40 41 42 43 44 40 41 42 43 44 41 42 43 44 45 42 43 44 45 46 42 43 44 45 47 44 45 46 47 48 44 46 47 48 49 45 46 47 48 50 46 47 48 49 50 46 48 49 50 51 47 48 49 51 52 41 42 43 44 45 46 47 48 49 50 41 42 43 44 45 44 45 46 47 48 45 46 47 48 49 46 47 48 49 50 51 52 53 54 55 47 48 49 50 51 48 49 50 51 52 48 49 50 51 53 49 50 51 52 53 50 51 52 53 54 51 52 53 54 55 51 52 54 55 56 52 53 54 56 57 53 54 55 56 58 54 55 56 57 58 60 61 62 63 64 65 67 68 69 70 46 47 48 49 50 51 52 53 54 55 46 47 48 49 50 50 51 52 53 54 47 48 49 50 50 51 52 53 54 55 49 50 51 52 53 54 55 56 57 58 50 51 52 53 54 55 56 57 58 59 52 53 54 55 56 53 54 55 56 57 54 55 56 57 58 54 55 57 58 59 55 56 57 59 60 56 57 58 59 61 57 58 59 60 61 63 64 65 66 67 58 59 60 61 62 59 60 61 62 63 51 52 53 54 55 56 57 58 59 60 56 57 58 59 60 67 58 59 60 61 58 59 60 61 62 59 60 61 62 63 60 61 62 63 64 61 62 63 64 65 62 63 64 65 66 63 65 66 67 68 64 66 67 68 69 56 57 58 59 60 TABLE 12. [Page 677 For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. M. 71" 72" 78" 74" 76" 76" 77" 78" 79" 80" 81" 82" 88" 84" 86" 86» 87" 1 2 3 4 5 6 7 8 9 10 1 2 4 5 6 7 8 9 11 12 1 2 4 5 6 7 8 10 11 12 1 2 4 5 6 7 9 10 11 12 13 15 16 17 18 19 21 22 23 24 26 27 28 29 30 32 33 34 36 37 38 39 40 41 43 44 45 46 47 49 50 51 52 54 55 56 57 58 60 61 62 63 64 66 67 68 69 71 72 73 1 2 4 5 6 7 9 10 11 12 14 15 16 17 19 20 21 22 23 25 1 3 4 5 6 8 9 10 11 13 14 15 16 18 19 20 21 23 24 25 1 3 4 5 6 8 9 10 11 13 14 15 16 18 19 1 3 4 5 6 8 9 10 12 13 1 3 4 5 7 1 3 4 5 7 1 3 4 5 7 1 3 4 5 7 1 3 4 6 7 1 3 4 6 7 1 3 4 6 7 1 3 4 6 7 1 3 4 6 7 1 3 4 6 7 1 2 3 4 6 8 9 10 12 13 8 9 11 12 13 8 9 11 12 13 8 9 11 12 14 8 10 11 12 14 15 16 18 19 21 8 10 11 12 14 8 10 11 13 14 9 10 11 13 14 9 10 11 13 14 9 10 12 13 15 6 7 8 9 10 11 12 13 14 15 13 14 15 17 18 13 14 16 17 18 14 15 17 18 19 14 16 17 18 20 14 16 17 18 20 15 16 17 19 20 15 16 18 19 20 15 17 18 19 21 15 17 18 20 21 16 17 18 20 21 16 17 19 20 22 16 17 19 20 22 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 19 20 21 22 24 25 26 27 28 30 19 20 22 23 24 25 26 28 29 30 31 32 34 35 36 37 38 40 41 42 43 44 46 47 48 49 50 52 53 54 55 56 58 59 60 61 62 64 65 66 67 68 70 71 72 20 22 23 24 25 21 22 23 24 26 21 22 23 25 26 21 22 24 25 26 21 23 24 25 27 22 23 24 26 27 22 23 25 26 27 22 24 26 26 28 22 24 25 27 28 23 24 26 27 28 23 24 26 27 29 23 25 26 28 29 16 17 18 19 20 26 27 28 30 31 32 33 35 36 37 38 39 41 42 43 44 46 47 48 49 51 52 53 54 56 57 58 59 60 62 63 64 65 67 68 69 70 72 73 74 26 28 29 30 31 27 28 29 30 32 27 28 30 31 32 27 29 30 31 33 28 29 30 32 33 28 29 31 32 33 28 30 31 32 34 29 30 31 33 34 29 30 32 33 35 29 31 32 34 36 30 31 33 34 35 30 32 33 34 36 30 32 33 34 36 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 33 34 35 36 38 33 34 35 37 38 33 35 36 37 39 34 35 36 38 39 34 36 37 38 40 35 36 37 39 40 35 36 38 39 41 36 37 38 40 41 36 37 39 40 42 36 38 39 41 42 37 38 40 41 43 37 39 40 42 43 38 39 41 42 44 26 27 28 29 30 31 32 33 34 35 37 38 39 40 41 39 40 41 43 44 45 46 48 49 50 51 53 54 55 56 58 59 60 61 63 64 65 66 68 69 70 71 73 74 75 39 41 42 43 44 46 47 48 49 51 52 53 54 56 57 40 41 42 44 45 40 42 43 44 46 41 42 43 45 46 41 43 44 45 47 42 43 45 46 47 42 44 45 46 48 43 44 46 47 48 43 46 46 48 49 44 45 47 48 50 44 46 47 49 60 45 46 48 49 61 31 32 33 34 35 36 37 38 39 40 43 44 45 46 47 49 50 51 52 53 54 56 57 58 59 46 47 49 50 51 47 48 49 51 52 47 49 50 51 53 48 49 51 52 53 49 50 51 53 54 49 51 52 53 55 56 57 69 60 62 50 51 53 54 55 60 52 63 66 56 51 52 64 55 57 52 53 54 56 67 62 54 55 57 58 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 53 54 55 56 58 53 55 56 57 59 54 55 57 58 59 55 56 57 59 60 55 57 58 59 61 57 58 59 61 62 67 59 60 62 63 58 60 61 62 64 59 60 62 63 65 59 61 62 64 65 41 42 43 44 45 58 60 61 62 63 65 66 67 68 70 59 60 62 63 64 60 61 62 64 65 61 62 63 65 66 61 63 64 65 67 62 63 65 66 68 63 64 66 67 68 64 65 66 68 69 64 66 67 69 70 66 67 68 69 71 66 67 69 70 72 67 68 70 71 73 46 47 48 49 60 51 52 53 54 55 51 52 53 54 55 56 57 58 59 60 60 62 63 64 65 "66 67 69 70 71 65 67 68 69 71 66 68 69 70 72 67 68 70 71 72 74 75 76 78 79 68 69 71 72 73 69 70 72 73 74 70 71 72 74 75 71 72 73 75 76 71 73 74 76 77 72 74 75 77 78 73 75 76 77 79 74 75 77 78 80 71 72 73 75 76 72 73 74 76 77 73 74 75 77 78 75 76 77 79 80 76 77 78 80 81 77 78 79 81 82 77 79 80 82 83 78 80 81 83 84 79 81 82 84 86 80 82 83 85 86 81 83 84 86 87 66 67 58 59 60 Page 678] TABLE 12. For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension, in seconds of time, the motion in one minute being given at the top and the numbers in the side column being taken for seconds. M. Horary motion. M. 88" 89" 90" 91" 92" 93" 94" 96" 96" 97" 98" 99" 100" 101" 102" 103" 104" 1 2. 3 4 5 1 3 4 6 7 1 3 4 6 7 2 3 5 6 8 9 11 12 14 15 2 3 5 6 8 9 11 12 14 15 2 3 5 6 '8 9 11 12 14 15 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 6 8 2 3 5 7 8 2 3 5 7 8 2 3 5 7 8 2 3 5 7 8 2 3 5 7 9 2 3 5 7 9 2 3 5 7 9 1 2 3 4 5 6 7 8 9 10 9 10 12 13 15 9 10 12 13 15 9 11 12 14 16 9 11 13 14 16 10 11 13 14 16 10 11 13 14 16 10 11 13 15 16 10 11 13 15 16 10 12 13 15 17 10 12 13 15 17 10 12 13 15 17 10 12 14 15 17 10 12 14 15 17 10 12 14 16 17 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 16 18 19 21 22 23 25 26 28 29 31 32 34 35 37 16 18 19 21 22 24 25 27 28 30 31 33 34 36 37 39 40 42 43 45 17 18 20 21 23 24 26 27 29 30 32 33 35 36 38 39 41 42 44 45 17 18 20 21 23 24 26 27 29 30 17 18 20 21 23 25 26 28 29 31 17 19 20 22 23 25 26 28 29 3] 17 19 20 22 24 25 27 28 30 31 17 19 21 22 24 18 19 21 22 24 18 19 21 23 24 18 20 21 23 25 18 20 21 23 25 18 20 22 23 25 19 20 22 24 25 19 20 22 24 26 19 21 22 24 26 19 21 23 24 26 11 12 13 14 15 25 27 29 30 32 26 27 29 30 32 26 27 29 31 32 26 28 29 31 33 26 28 30 31 33 27 28 30 32 33 27 29 30 32 34 27 29 31 32 34 27 29 31 33 34 28 29 31 33 35 16 17 18 19 20 32 33 35 36 38 39 41 42 44 46 32 34 35 37 38 33 34 36 37 39 33 34 36 38 39 33 35 36 38 40 34 35 37 38 40 34 36 37 39 40 34 36 38 39 41 35 36 38 40 41 35 37 38 40 42 35 37 39 40 42 36 37 39 41 43 36 38 39 41 43 36 38 40 42 43 21 22 23 24 25 26 27 28 29 30 26 27 28 29 30 38 40 41 43 44 40 41 43 44 46 40 42 43 45 47 41 42 44 45 47 41 43 44 46 48 42 43 45 46 48 42 44 45 47 49 42 44 46 47 49 43 45 46 48 50 43 45 47 48 50 44 45 47 49 51 44 46 48 49 51 45 46 48 50 52 45 47 49 50 52 31 32 33 34 35 36 37 38 39 40 45 47 48 50 51 53 54 56 57 59 46 47 49 50 52 53 55 56 58 59 47 48 50 51 53 54 56 57 59 60 62 63 65 66 68 69 71 72 74 75 47 49 50 62 53 55 56 58 59 61 62 64 65 67 68 70 71 73 74 76 48 49 51 52 54 48 50 51 53 54 49 50 52 53 55 49 51 52 54 55 50 51 53 54 56 50 52 53 55 57 51 52 54 56 57 51 53 54 56 58 52 53 55 57 58 52 54 56 57 59 53 54 56 58 60 53 55 57 58 60 54 55 57 59 61 31 32 33 34 35 55 57 58 60 61 63 64 66 67 69 71 72 74 75 77 56 57 59 60 62 56 58 60 61 63 57 59 60 62 63 58 59 61 62 64 58 60 61 63 65 59 60 62 64 65 59 61 63 64 66 60 62 63 65 67 61 62 64 66 67 61 63 65 66 68 62 64 65 67 69 62 64 66 68 69 36 37 38 39 40 41 42 43 44 45 60 62 63 65 66 67 69 70 72 73 61 62 64 65 67 68 70 71 73 74 64 65 67 68 70 64 66 67 69 71 65 67 68 70 71 66 67 69 70 72 66 68 70 71 73 67 •69 70 72 74 68 69 71 73 74 68 70 72 73 75 69 71 72 74 76 70 71 73 75 77 70 72 74 76 77 71 73 75 76 78 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 71 73 74 76 78 72 74 75 77 78 73 74 76 78 79 74 75 77 78 80 74 76 78 79 81 75 77 78 80 82 76 78 79 81 83 77 78 80 82 83 77 79 81 82 84 78 80 82 83 85 79 81 82 84 86 80 81 83 85 87 46 47 48 49 50 75 76 78 79 81 76 77 79 80 82 77 78 80 81 83 77 79 80 82 83 78 80 81 83 84 79 81 82 84 85 80 81 83 85 86 81 82 84 86 87 82 83 85 86 88 82 84 86 87 89 83 85 87 88 90 84 86 87 89 91 85 87 88 90 92 86 88 89 91 93 87 88 90 92 94 88 89 91 93 94 88 90 92 94 95 51 52 53 54 55 56 57 58 59 60 82 84 85 87 88 83 85 86 88 89 84 86 87 89 90 85 86 88 90 91 86 87 89 90 92 87 88 90 91 93 88 89 91 92 94 89 90 92 93 95 90 91 93 94 96 91 92 94 95 97 91 93 95 96 98 92 94 96 97 99 93 95 97 98 100 94 96 98 99 101 95 97 99 100 102 96 98 100 101 103 97 99 101 102 104 56 57 58 59 60 TABLE 12. [Page 679 For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variatior of the Moon's Declination or Right Ascension, in seconds of time, the motion in one minute being given at the top and the numbers in the side column being taken for seconds. M. Horary motion. M. 106" 106" 107" 108" 109" 110" 111" 112" 118" 114" 116" 116" 117" 118" 1 2 3 4 5 2 4 5 7 9 2 4 5 7 9 2 4 5 7 9 2 4 5 7 9 2 4 5 7 9 2 4 6 7 9 2 4 6 7 9 2 4 6 7 9 2 4 6 8 9 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 1 2 3 4 5 6 7 8 9 10 11 12 14 16 18 11 12 14 16 18 11 12 14 16 18 11 13 14 16 18 11 13 15 16 18 11 13 15 17 18 11 13 15 17 19 11 13 15 17 19 11 13 15 17 19 11 13 15 17 19 12 13 15 17 19 12 14 15 17 19 12 14 16 18 20 12 14 16 18 20 6 7 8 9 10 11 12 13 14 15 19 21 23 25 26 19 21 23 25 27 20 21 23 25 27 20 22 23 25 27 20 22 24 25 27 20 22 24 26 28 20 22 24 26 28 21 22 24 26 28 21 23 24 26 28 21 23 25 27 29 21 23 25 27 29 21 23 25 27 29 21 23 25 27 29 22 24 26 28 30 11 12 13 14 15 16 17 18 19 20 28 30 32 33 35 28 30 32 34 35 29 30 32 34 36 29 31 32 34 36 29 31 33 35 36 29 31 33 35 37 30 31 33 35 37 30 32 34 35 37 30 32 34 36 38 30 32 34 36 38 .31 33 35 36 38 31 33 35 37 39 31 33 35 37 39 31 33 35 37 39 16 17 18 19 20 21 22 23 24 25 37 39 40 42 37 39 41 42 44 37 39 41 43 45 38 40 41 43 45 38 40 42 44 45 39 40 42 44 46 39 41 43 44 46 39 41 43 45 47 40 41 43 45 47 40 42 44 46 48 40 42 44 46 48 41 43 44 46 48 41 43 45 47 49 41 43 45 47 49 21 22 23 24 25 26 27 28 29 30 46 47 49 51 53 46 48 49 51 53 46 48 50 52 54 47 49 50 52 54 47 49 51 53 55 48 50 61 53 55 48 50 52 54 56 49 50 52 54 56 49 51 53 55 57 49 51 63 55 57 50 52 54 66 68 50 52 54 56 58 51 53 55 57 59 51 53 55 57 59 26 27 28 29 30 31 32 33 34 35 54 56 58 60 61 55 57 58 60 62 55 57 59 61 62 56 58 59 61 63 56 58 60 62 64 57 59 61 62 64 57 59 61 63 66 58 60 62 63 65 58 60 62 64 66 59 61 63 65 67 69 61 63 65 67 60 62 64 66 68 60 62 64 66 68 61 63 65 67 69 31 32 33 34 35 36 37 38 39 40 63 65 67 68 70 64 65 67 69 71 64 66 68 70 71 65 67 68 70 72 65 67 69 71 73 66 68 70 72 73 67 68 70 72 74 67 69 71 73 75 68 70 72 73 75 68 70 72 74 76 69 71 73 75 77 70 72 73 75 77 70 72 74 76 78 71 73 75 77 79 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 72 74 75 77 79 81 82 84 86 88 72 74 76 78 80 73 75 77 78 80 74 76 77 79 81 74 . 76 78 80 82 75 77 79 81 83 76 78 80 81 83 77 78 80 82 84 77 79 81 83 85 78 80 82 84 86 79 81 82 84 86 79 81 83 85 87 80 82 84 86 88 81 83 85 87 89 41 42 43 44 45 81 83 85 87 88 82 84 86 87 89 83 85 86 88 90 84 85 87 89 91 84 86 88 90 92 85 87 89 91 93 86 88 90 91 93 87 89 90 92 94 87 89 91 93 95 88 90 92 94 96 89 91 93 95 97 90 92 94 96 98 90 92 94 96 98 46 47 48 49 50 51 52 53 54 55 89 91 93 95 96 90 92 94 95 97 91 93 95 96 98 92 94 95 97 99 93 94 96 98 100 94 95 97 99 101 94 96 98 100 102 95 97 99 101 103 96 98 100 102 104 97 99 101 103 105 98 100 102 104 105 99 101 102 104 106 99 101 103 105 107 100 102 104 106 108 51 52 53 54 55 56 57 58 59 1 60 98 100 102 103 105 99 101 102 104 106 100 102 103 105 107 101 103 104 106 108 102 104 105 107 109 103 105 106 108 110 104 105 107 109 111 105 106 108 110 112 105 107 109 111 113 106 108 110 112 114 107 109 111 113 115 108 110 112 114 116 109 111 113 115 117 110 112 114 116 118 56 57 58 59 60 Page 680] TABLE 12. For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. M. 119" 120" 121" 122" 123" 124" 126" 126" 127" 128" 129" 130" 131" 132" 1 2 3 4 5 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 10 2 4 6 8 11 2 4 6 8 11 2 4 6 9 11 2 4 11 2 4 7 9 11 2 4 7 9 11 2 4 7 9 11 1 2 3 4 5 6 7 8 9 10 6 7 8 9 10 12 14 16 18 20 12 14 16 18 20 12 14 16 18 20 12 14 16 18 20 12 14 16 18 21 12 14 17 19 21 13 15 17 19 21 13 15 17 19 21 13 15 17 19 21 13 15 17 19 21 13 15 17 19 22 13 15 17 20 22 13 15 17 20 22 13 15 18 20 22 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 22 24 26 28 30 22 24 26 28 30 22 24 26 28 30 22 24 26 28 31 23 25 27 29 31 23 25 27 29 31 23 25 27 29 31 23 25 27 29 32 23 25 28 30 32 23 26 28 30 32 24 26 28 30 32 24 26 28 30 33 24 26 28 31 33 24 26 29 31 33 11 12 13 14 15 32 34 36 38 40 42 44 46 48 50 32 34 36 38 40 32 34 36 38 40 33 35 37 39 41 33 35 37 39 41 33 35 37 39 41 33 35 38 40 42 34 36 38 40 42 34 36 38 40 42 34 36 38 41 43 34 37 39 41 43 35 37 39 41 43 35 37 39 41 44 35 37 40 42 44 16 17 18 19 20 42 44 46 48 50 42 44 46 48 50 43 45 47 49 51 43 45 47 49 51 43 45 48 50 52 44 46 48 50 52 44 46 48 50 53 44 47 49 51 53 45 47 49 51 53 45 47 49 52 54 46 48 50 52 54 46 48 50 52 55 46 48 51 53 55 21 22 23 24 25 26 27 28 29 30 52 54 56 58 60 52 54 56 58 60 52 54 56 58 61 53 55 57 59 61 53 55 57 59 62 54 56 58 60 62 54 56 58 60 63 55 57 59 61 63 55 57 59 61 64 55 58 60 62 64 56 58 60 62 65 56 59 61 63 65 57 59 61 63 66 57 59 62 64 66 26 27 28 29 30 31 32 33 34 35 61 63 65 67 69 62 64 66 68 70 63 65 67 69 71 63 65 67 69 71 64 66 68 70 72 64 66 68 70 72 65 67 69 71 73 65 67 69 71 74 66 68 70 72 74 66 68 70 73 75 67 69 71 73 75 67 69 72 74 76 68 70 72 74 76 68 70 73 75 77 31 32 33 34 35 36 37 38 39 40 71 73 75 77 79 72 74 76 78 80 73 75 77 79 81 73 75 77 79 81 74 76 78 80 82 74 76 79 81 83 75 77 79 81 83 76 78 80 82 84 76 78 80 83 85 77 79 81 83 85 77 80 82 84 86 78 80 82 85 87 89 91 93 95 98 79 81 83 85 87 79 81 84 86 88 36 37 38 39 40 41 42 43 44 45 81 83 85 87 89 82 84 86 88 90 83 85 87 89 91 83 85 87 89 92 84 86 88 90 92 85 87 89 91 93 85 88 90 92 94 86 88 90 92 95 87 89 91 93 95 87 90 92 94 96 88 90 92 95 97 90 92 94 96 98 90 92 95 97 99 41 42 43 44 45 46 47 48 49 50 91 93 95 97 99 92 94 96 98 100 93 95 97 99 101 94 96 98 100 102 94 96 98 100 103 95 97 99 101 103 96 98 100 102 104 97 99 101 103 105 97 99 102 104 106 98 100 102 105 107 99 101 103 105 108 100 102 104 106 108 100 103 105 107 109 101 103 106 108 110 46 47 48 49 50 51 52 53 54 55 101 103 105 107 109 102 104 106 108 110 103 105 107 109 111 104 106 108 110 112 105 107 109 111 113 105 107 110 112 114 106 108 110 113 115 107 109 111 113 116 108 110 112 114 116 109 111 113 115 117 110 112 114 116 118 111 113 115 117 119 111 114 116 118 120 112 114 117 119 121 51 52 53 54 55 56 57 58 59 60 111 113 115 117 119 112 114 116 118 120 113 115 117 119 121 114 116 118 120 122 115 117 119 121 123 116 118 120 122 124 117 119 121 123 125 118 120 122 124 126 119 121 123 125 127 119 122 124 126 128 120 123 125 127 129 121 124 126 128 130 122 124 127 129 131 123 125 128 130 132 56 57 58 59 60 TABLE 12. [Page 681 For finding the Variation of the Sun's Right Ascension or Declination, or of the Equation of Time, in any number of minutes of time, the Horary Motion being given %t the top of the page in seconds, and the number of minutes of time in the side column. Also for findmg the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. M. 138" 184" 185" 186" 137" 188" 139" 140" 141" 142" 148" 144" 145" 146" 1 2 3 4 5 6 7 8 9 10 2 4 7 9 11 2 4 7 9 11 2 5 7 9 11 2 5 7 9 11 2 5 7 9 11 2 5 7 9 12 2 5 7 9 12 2 5 7 9 12 2 5 7 9 12 2 5 7 9 12 2 5 7 10 12 2 5 7 10 12 2 5 7 10 12 2 5 7 10 12 1 2 3 4 5 13 16 18 20 22 13 16 18 20 22 14 16 1* 20 23 14 16 18 20 23 14 16 18 21 23 14 16 18 21 23 14 16 19 21 23 14 16 19 21 23 14 16 19 21 24 14 17 19 21 24 14 17 19 21 24 26 29 31 33 36 14 17 19 22 24 15 17 19 22 24 15 17 19 22 24 6 7 8 9 10 11 12 13 14 15 11 12 13 14 15 24 27 29 31 33 25 27 29 31 34 ' 25 27 29 32 34 25 27 29 32 34 25 27 30 32 34 25 28 30 32 35 25 28 30 32 36 26 28 30 33 35 26 28 31 33 35 26 28 31 33 36 26 29 31 34 36 27 29 31 34 36 27 29 32 34 37 16 17 18 19 20 35 38 40 42 44 36 38 40 42 45 36 38 41 43 45 36 39 41 43 45 37 39 41 43 46 37 39 41 44 46 37 39 42 44 46 37 40 42 44 47 38 40 42 45 47 38 40 43 45 47 38 41 43 45 48 38 41 43 46 48 39 41 44 46 48 39 41 44 46 49 16 17 18 19 20 21 22 23 24 25 47 49 51 53 55 47 49 51 54 56 47 50 52 54 56 48 50 52 54 57 48 50 53 55 57 48 51 53 55 58 49 51 53 56 58 49 51 54 56 58 49 52 54 56 59 50 52 54 57 59 50 52 55 57 60 60 53 55 58 60 61 53 56 68 60 61 54 56 58 61 21 22 23 24 25 26 27 28 29 30 58 60 62 64 67 58 60 63 65 67 59 61 63 65 68 59 61 63 66 68 59 62 64 66 69 60 62 64 67 69 60 63 65 67 70 61 63 65 68 70 61 63 66 68 71 62 64 66 69 71 62 64 67 69 72 62 65 67 70 72 63 65 68 70 73 63 66 68 71 73 26 27 28 29 30 31 32 33 34 35 69 71 73 75 78 69 71 74 76 78 70 72 74 77 79 70 73 75 77 79 71 73 75 78 80 71 74 76 78 81 72 74 76 79 81 72 75 77 79 82 73 75 78 80 82 73 76 78 80 83 74 76 79 81 83 74 77 79 82 84 75 77 80 82 85 76 78 80 83 85 31 32 33 34 35 36 37 38 39 40 80 82 84 86 89 80 83 85 87 89 81 83 86 88 90 92 95 97 99 101 82 84 86 88 91 82 84 87 89 91 83 85 87 90 92 83 86 88 90 93 84 86 89 91 93 85 87 89 92 94 85 88 90 92 95 86 88 91 93 95 86 89 91 94 96 87 89 92 94 97 88 90 92 95 97 36 37 38 39 40 41 42 43 44 45 91 93 95 98 100 92 94 96 98 101 93 95 97 100 102 94 96 98 100 103 94 97 99 101 104 95 ' 97 100 102 104 96 98 100 103 105 96 99 101 103 106 97 99 102 104 107 98 100 102 105 107 98 101 103 106 108 99 102 104 106 109 100 102 105 107 110 41 42 43 44 45 46 47 48 49 50 102 104 106 109 111 103 105 107 109 112 104 106 108 110 113 104 107 109 111 113 105 107 110 112 114 106 108 110 113 115 107 109 111 114 116 107 110 112 114 117 108 110 113 115 118 109 111 114 116 118 110 112 114 117 119 110 113 115 118 120 111 114 116 118 121 112 114 117 119 122 46 47 48 49 50 51 52 53 54 55 113 115 117 120 122 114 116 118 121 123 115 117 119 122 124 116 118 120 122 125 116 119 121 123 126 117 120 122 124 127 118 120 123 125 127 119 121 124 126 128 120 122 125 127 129 121 123 125 128 130 122 124 126 129 131 122 125 127 130 132 123 126 128 131 133 124 127 129 131 134 51 52 53 54 55 56 57 58 59 60 124 126 129 131 133 125 127 130 132 134 126 128 131 133 135 127 129 131 134 136 128 130 132 135 137 129 131 133 136 138 130 132 134 137 139 131 133 135 138 140 132 134 136 139 141 133 135 137 140 142 133 136 138 141 143 134 137 139 142 144 135 138 140 143 146 136 139 141 144 146 56 57 58 59 60 Page 682] TABLE 12. For finding the Variation of the Sun's Eight Ascension, or Dechnation, or of the Equation of Time in any number of minutes of time, the Horary Motion being given at the top of the page in seconds, and the number of minutes of time in the side column. Also for finding the Variation of the Moon's Declination or Right Ascension in seconds of time, the motion in one minute being given at the top, and the numbers in the side column being taken for seconds. M. Horary motion. M. 147" 148" 149" 160" 161" 152" 163" 164" 165" 166" 157" 168" 169" 160" 1 2 3 4 5 2 5 7 10 12 2 5 7 10 12 2 5 7 10 12 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 10 13 3 5 8 11 13 3 5 8 11 13 3 5 8 11 13 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 15 17 20 22 25 15 17 20 22 25 15 17 20 22 25 15 18 20 23 25 15 18 20 23 25 15 18 20 23 25 15 18 20 23 26 15 18 21 23 26 16 18 21 23 26 16 18 21 23 26 16 18 21 24 26 16 18 21 24 26 16 19 21 24 27 16 19 21 24 27 6 7 8 9 10 27 29 32 34 37 27 30 32 35 37 39 42 44 47 49 27 30 32 35 37 28 30 33 35 38 28 30 33 35 38 28 30 33 35 38 28 31 33 36 38 28 31 33 36 39 28 31 34 36 39 29 31 34 36 39 29 31 34 37 39 29 32 34 37 40 29 32 34 37 40 29 32 35 37 40 11 12 13 14 15 16 17 18 19 20 39 42 44 47 49 40 42 45 47 50 40 43 45 48 50 40 43 45 48 50 41 43 46 48 51 41 43 46 48 51 41 44 46 49 51 41 44 47 49 52 42 44 47 49 52 42 44 47 50 52 42 45 47 50 53 42 45 48 50 53 43 45 48 51 53 16 17 18 19 20 21 22 23 24 25 51 54 56 59 61 52 54 57 59 62 52 55 57 60 62 53 55 58 60 63 53 55 58 60 63 53 56 58 61 63 54 56 59 61 64 54 56 59 62 64 54 57 59 62 65 55 57 60 62 65 55 58 60 63 65 55 58 61 63 66 56 68 61 64 66 56 59 61 64 67 21 22 23 24 25 26 27 28 29 30 64 66 69 71 74 64 67 69 72 74 65 67 70 72 75 65 68 70 73 75 65 68 70 73 76 66 68 71 73 76 66 69 71 74 77 67 69 72 74 77 67 70 72 76 78 68 70 73 75 78 68 71 73 76 79 68 71 74 76 79 69 ■ 72 74 77 80 69 72 75 77 80 26 27 28 29 30 31 32 33 34 35 76 78 81 83 86 76 79 81 84 86 77 79 82 84 87 78 80 83 85 88 78 81 83 86 88 79 81 84 86 89 79 82 84 87 89 80 82 85 87 90 80 83 85 88 90 81 83 86 88 91 81 84 86 89 92 82 84 87 90 92 82 85 87 90 93 83 85 88 91 93 31 32 33 34 35 36 37 38 39 40 88 91 93 96 98 89 91 94 96 99 89 92 94 97 99 90 93 95 98 100 103 105 108 110 113 91 93 96 98 101 103 106 108 111 113 91 94 96 99 101 92 94 97 99 102 92 95 98 100 103 93 96 98 101 103 94 96 99 101 104 94 97 99 102 105 . 95 97 100 103 105 95 98 101 103 106 96 99 101 104 107 36 37 38 39 40 41 42 43 44 45 100 103 105 108 110 101 104 106 109 111 102 104 107 109 112 104 106 109 111 114 105 107 110 112 115 105 108 110 113 116 106 109 111 114 116 107 109 112 114 117 107 110 113 115 118 108 111 113 116 119 109 111 114 117 119 109 112 115 117 120 41 42 43 44 45 46 47 48 49 50 113 115 118 120 123 113 116 118 121 123 114 117 119 122 124 115 118 120 123 125 116 118 121 123 126 117 119 122 124 127- 117 120 122 125 128 118 121 123 126 128 119 121 124 127 129 120 122 125 127 130 120 123 126 128 131 121 124 126 129 132 122 125 127 130 133 123 125 128 131 133 46 47 48 49 50 51 52 53 54 55 125 127 130 132 135 126 128 131 133 136 127 129 132 .134 137 128 130 133 135 138 128 131 133 136 138 129 132 134 137 139 130 133 135 138 140 131 133 136 139 141 132 134 137 140 142 133 135 138 140 143 133 136 139 141 144 134 137 140 142 145 135 138 140 143 146 136 139 141 144 147 61 62 63 54 65 56 57 58 59 60 137 140 142 145 147 138 141 143 146 148 139 142 144 147 149 140 143 145 148 150 141 343 146 148 151 142 144 147 149 152 143 145 148 150 153 144 146 149 151 154 146 '147 150 152 155 146 148 151 153 156 147 149 162 154 157 147 150 153 155 158 148 151 154 166 159 149 162 155 157 160 56 57 58 59 60 TABLE 13. [Page 683 1 For finding the Sun's change of Right Ascension for any given number of hours. 1 Hourly Number of hours. Hourly varia- tion. tion. 1 2 s 4 5 6 7 8 9 10 11 IS $. 8. «. 8. s. s. 8. 8. 8. 3. 8. 8. 8. 8. 8.50 8.5 17.0 25.5 34.0 42.5 51.0 59.5 68.0 76.5 85.0 93.5 102.0 8.50 8.55 8.6 17.1 25.7 34.2 42.8 51.3 59.9 68.4 77.0 85.5 94.1 102.6 8.55 8.60 8.6 17.2 25.8 34.4 43.0 51.6 60.2 68.8 77.4 86.0 94.6 103.2 8.60 8.65 8.7 17.3 26.0 34.6 43.3 51.9 60.6 69.2 77.9 86.5 95.2 103.8 8.65 8.70 8.7 17.4 17.5 26.1 26.3 34.8 35.0 43.5 43.8 52.2 60.9 69.6 78.3 87.0 95.7 104.4 105.0 8.70 8.75 8.8 52.5 61.3 70.0 78.8 87.5 96.3 8.75 8.80 8.8 17.6 26.4 35.2 44.0 52.8 61.6 70.4 79.2 88.0 96.8 105.6 8.80 8.85 8.9 17.7 26.6 35.4 44.3 53.1 62.0 70.8 79.7 88.5 97.4 106.2 8.85 8.90 8.9 17.8 26.7 35.6 44.5 53.4 62.3 71.2 80.1 89.0 97.9 106.8 8.90 8.95 9.0 17.9 18.0 26.9 27.0 35.8 36.0 44.8 53.7 62.7 71.6 80.6 81.0 89.5 98.5 107.4 8.95 9.00 9.0 45.0 54.0 63.0 72.0 90.0 99.0 108.0 9.00 9.05 9.1 18.1 27.2 36.2 45.3 54.3 63.4 72.4 81.5 90.5 99.6 108.6 9.05 9.10 9.1 18.2 27.3 36.4 45.5 54.6 63.7 72.8 81.9 91.0 100.1 109.2 9.10 9.15 9.2 18.3 27.5 36.6 45.8 54.9 64.1 73.2 82.4 91.5 100.7 109.8 9.15 9.20 9.2 18.4 27.6 27.8 36.8 46.0 55.2 64.4 64.8 73.6 82.8 92.0 101.2 110.4 9.20 9.25 9.25 9.3 18.5 37.0 46.3 55.5 74.0 83.3 92.5 101.8 111.0 9.30 9.3 18.6 27.9 37.2 46.5 55.8 65.1 74.4 83.7 93.0 102.3 111.6 9.30 9.35 9.4 18.7 28.1 37.4 46.8 56.1 65.5 74.8 84.2 93.5 102.9 112.2 9.35 9.40 9.4 18.8 28.2 37.6 47.0 56.4 65.8 75.2 84.6 94.0 103.4 112.8 9.40 9.45 9.5 18.9 28.4 37.8 38.0 47.3 47.5 56.7 66.2 66.5 75.6 85.1 94.5 104.0 104.5 113.4 9.45 9.50 9.5 19.0 28.5 57.0 76.0 85.5 95.0 114.0 9.50 9.55 9.6 19.1 28.7 38.2 47.8 57.3 66.9 76.4 86.0 95.5 105.1 114.6 9.55 9.60 9.6 19.2 28.8 38.4 48.0 57.6 67.2 76.8 86.4 96.0 105.6 115.2 9.60 9.65 9.7 19.3 29.0 38.6 48.3 57.9 67.6 77.2 86.9 96.5 106.2 115.8 9.65 9.70 9.7 9.8 19.4 19.5 29.1 38.8 48.5 58.2 58.5 67.9 77.6 87.3 97.0 106.7 116.4 9.70 9.75 29.3 39.0 48.8 68.3 78.0 87.8 97.5 107.3 117.0 9.75 9.80 9.8 19.6 29.4 39.2 49.0 58.8 68.6 78.4 88.2 98.0 107.8 117.6 9.80 9.85 9.9 19.7 29.6 39.4 49.3 59.1 69.0 78.8 88.7 98.5 108.4 118.2 9.85 9.90 9.9 19.8 29.7 39.6 49.5 59.4 69.3 79.2 89.1 99.0 108.9 118.8 9.90 9.95 10.0 19.9 20.0 29.9 39.8 49.8 59.7 69.7 79.6 80.0 89.6 90.0 99.5 100.0 109.5 119.4 9.95 10.00 10.0 30.0 40.0 50.0 60.0 70.0 110.0 120.0 10.00 10.05 10.1 20.1 30.2 40.2 50.3 60.3 70.4 80.4 90.5 100.5 110.6 120.6 10.05 10.10 10.1 20.2 30.3 40.4 50.5 60.6 70.7 80.8 90.9 101.0 111.1 121.2 10.10 10.15 10.2 20.3 30.5 40.6 50.8 60.9 71.1 81.2 91.4 101.5 111.7 121.8 10.15 10.20 10.2 10.3 20.4 30.6 40.8 51.0 61.2 71.4 71.8 81.6 91.8 92.3 102.0 112.2 122.4 10.20 10.25 20.5 30.8 41.0 51.3 61.5 82.0 102.5 112.8 123.0 10.25 10.30 10.3 20.6 30.9 41.2 51.5 61.8 72.1 82.4 92.7 103.0 113.3 123.6 10.30 10.35 10.4 20.7 31.1 41.4 51.8 62.1 72.5 82.8 93.2 103.5 113.9 124.2 10.35 10.40 10.4 20.8 31.2 41.6 52.0 62.4 72.8 83.2 93.6 104.0 114.4 124.8 10.40 10.45 10.5 20.9 31.4 41.8 52.3 62.7 73.2 83.6 94.1 94.5 104.5 105.0 115.0 125.4 10.45 10.50 10.5 21.0 31.5 42.0 52.5 63.0 73.5 84.0 115.5 126.0 10.50 10.55 10.6 21.1 31.7 42.2 52.8 63.3 73.9 84.4 95.0 105.5 116.1 126.6 10.55 10.60 10.6 21.2 31.8 42.4 53.0 63.6 74.2 84.8 95.4 106.0 116.6 127.2 10.60 10.65 10.7 21.3 32.0 42.6 53.3 63.9 74.6 85.2 95.9 106.5 117.2 127.8 10.65 10.70 10.7 21.4 32.1 42.8 53.5 64.2 74.9 85.6 86.0 96.3 107.0 117.7 128.4 10.70 10.75 10.8 21.5 32.3 43.0 53.8 64.5 75.3 96.8 107.5 118.3 129.0 10.75 10.80 10.8 21.6 32.4 43.2 54.0 64.8 75.6 86.4 97.2 108.0 118.8 129.6 10.80 10.85 10.9 21.7 32.6 43.4 54.3 65.1 76.0 86.8 97.7 108.5 119.4 130.2 10.85 10.90 10.9 21.8 32.7 43.6 54.5 65.4 76.3 87.2 98.1 109.0 119.9 130.8 10.90 10.95 11.0 21.9 32.9 33.0 43.8 44.0 54.8 65.7 66.0 76.7 77.0 87.6 98.6 109.5 120.5 131.4 132.0 10.95 11.00 11.0 22.0 55.0 88.0 99.0 110.0 121.0 11.00 11.05 11.1 22.1 33.2 44.2 55.3 66.3 77.4 88.4 99.5 110.5 121.6 132.6 11.05 11.10 11.1 22.2 33.3 44.4 55.5 66.6 77.7 88.8 99.9 111.0 122.1 133.2 11.10 11.15 11.2 22.3 33.5 44.6 55.8 66.9 78.1 89.2 100.4 111.5 122.7 133.8 11.15 11.20 11.2 11.3 22.4 33.6 33.8 44.8 56.0 67.2 78.4 89.6 100.8 112.0 123.2 134.4 11.20 11.25 22.5 45.0 56.3 67.5 78.8 90.0 101.3 112.5 123.8 135.0 11.25 11.30 11.3 22.6 33.9 45.2 56.5 67.8 79.1 90.4 101.7 113.0 124.3 135.6 11.30 11.35 11.4 22.7 34.1 45.4 56.8 68.1 79.5 90.8 102.2 113.5 124.9 136.2 11.35 11.40 11.4 22.8 34.2 45.6 57.0 68.4 79.8 91.2 102.6 114.0 125.4 136.8 11.40 11.45 11.5 22.9 34.4 45.8 57.3 68.7 80.2 91.6 103. 1 114.5 126.0 137.4 11.45 Page 684] TABLE 13. . 1 For finding the Sun's change of Right Ascension for any given number of hours. | Hoxurly Number of hours. Hourly tion. 18 14 15 161 17 18 19 20 21 22 28 24 tion. «. «. «. s. fi. s. s. «. «. 8. g. «. s. «. 8.50 110.5 119.0 127.5 136.0 144.5 153.0 161.5 170.0 178.5 187.0 195.5 204.0 8.50 8.55 111.2 119.7 128.3 136.8 145.4 153.9 162.5 171.0 179.6 188.1 196.7 205.2 8.55 8.60 111.8 120.4 129.0 137.6 146.2 154.8 163.4 172.0 180.6 189.2 197.8 206.4 8.60 8.65 112.5 121.1 129.8 138.4 147.1 155.7 164.4 173.0 181.7 190.3 199.0 207.6 8.65 8.70 113.1 121.8 122.5 130.5 139.2 147.9 156.6 165.3 174.0 182.7 191.4 200.1 208.8 8.70 8.75 113.8 131.3 140.0 148.8 157.5 166.3 175.0 183.8 192.5 201.3 210.0 8.75 8.80 114.4 123.2 132.0 140.8 149.6 158.4 167.2 176.0 184.8 193.6 202.4 211.2 8.80 8.85 115.1 123.9 132.8 141.6 150.5 159.3 168.2 177.0 185.9 194.7 203.6 212.4 8.85 8.90 115.7 124.6 133.5 142.4 151.3 160.2 169.1 178.0 186.9 195.8 204.7 213.6 8.90 8.95 116.4 117. 125.3 134.3 143.2 152.2 153.0 161.1 162.0 170.1 179.0 180.0 188.0 196.9 198.0 205.9 214.8 8.95 9.00 126.0 135. 144.0 171.0 189.0 207.0 •216. 9.00 9.05 117.7 126.7 135.8 144.8 153.9 162.9 172.0 181.0 190.1 199.1 208.2 217.2 9.05 9.10 118.3 127.4 136.5 145.6 154.7 163.8 172.9 182.0 191.1 200.2 209.3 218.4 9.10 9.15 119.0 128.1 137.3 146.4 155.6 164.7 173.9 183.0 192.2 201.3 210.5 219.6 9.15 9.20 119.6 120.3 128.8 138.0 147.2 156.4 165.6 174.8 184.0 193.2 202.4 211.6 220.8 222.0 9.20 9.25 129.5 138.8 148.0 157.3 166.5 175.8 185.0 194.3 203.5 212.8 9.25 9.30 120.9 130.2 139.5 148.8 158.1 167.4 176.7 186.0 195.3 204.6 213.9 223.2 9.30 9.35 121.6 130.9 140.3 149.6 159.0 168.3 177.7 187.0 196.4 205.7 215.1 224.4 9.35 9.40 122.2 131.6 141.0 150.4 159.8 169.2 178.6 188.0 197.4 206.8 216.2 225.6 9.40 9.45 122.9 132.3 141.8 151.2 160.7 170.1 179.6 189.0 198.5 207.9 217.4 226.8 9.45 9.50 9.50 123.5 133.0 142.5 152.0 161.5 171.0 180.5 190.0 199.5 209.0 218.5 228.0 9.55 124.2 133.7 143.3 152.8 162.4 171.9 181.5 191.0 200.6 210.1 219.7 229.2 9.55 9.60 124.8 134.4 144.0 153.6 163.2 172.8 182.4 192.0 201.6 211.2 220.8 230.4 9.60 9.65 125.5 135.1 144.8 154.4 164.1 173.7 183.4 193.0 202.7 212.3 222.0 231.6 9.65 9.70 126.1 135.8 136.5 145.5 155.2 156.0 164.9 165.8 174.6 175.5 184.3 194.0 203.7 213.4 223.1 232.8 9.70 9.75 126.8 146.3 185.3 195.0 204.8 214.5 224.3 234.0 9.75 9.80 127.4 137.2 147.0 156.8 166.6 176.4 186.2 196.0 205.8 215.6 225.4 235.2 9.80 9.85 128.1 137.9 147.8 157.6 167.5 177.3 187.2 197.0 206.9 216.7 226.6 236.4 9.85 9.90 128.7 138.6 148.5 158.4 168.3 178.2 188.1 198.0 207.9 217.8 227.7 237.6 9.90 9.95 129.4 130.0 139.3 140.0 149.3 159.2 169.2 179.1 189.1 199.0 209.0 210.0 218.9 228.9 230.0 238.8 240.0 9.95 10.00 150.0 160.0 170.0 180.0 190.0 200.0 220.0 10.00 10.05 130.7 140.7 150.8 160.8 170.9 180.9 191.0 201.0 211.1 221.1 231.2 241.2 10.05 10.10 131.3 141.4 151.5 161.6 171.7 181.8 191.9 202.0 212.1 222.2 232.3 242.4 10.10 10.15 132.0 142.1 152.3 162.4 172.6 182.7 192.9 203. 213.2 223.3 233.5 243.6 10.15 10.20 132.6 142.8 143.5 153.0 163.2 173.4 174.3 183.6 184.5 193.8 204.0 205.0 214.2 215.3 224.4 234.6 244.8 10.20 10.25 133.3 153.8 164.0 194.8 225.5 235.8 246.0 10.25 10.30 133.9 144.2 154.5 164.8 175.1 185.4 195.7 206.0 216.3 226.6 236.9 247.2 10.30 10.35 134.6 144.9 155.3 165.6 176.0 186.3 196.7 207. 217.4 227.7 238.1 248.4 10.35 10.40 135.2 145.6 156.0 166.4 176.8 187.2 197.6 208.0 218.4 228.8 239.2 249.6 10.40 10.45 135.9 146.3 156.8 167.2 177.7 188.1 198.6 199.5 209.0 219.5 229.9 240.4 250.8 10.45 10.50 136.5 147.0 157.5 168.0 178.6 189.0 210.0 220.5 231.0 241.5 252.0 10.50 10.55 137.2 147.7 158.3 168.8 179.4 189.9 200.5 211.0 221.6 232.1 242.7 253.2 10.55 10.60 137.8 148.4 159.0 169.6 180.2 190.8 201.4 212.0 222.6 233.2 243.8 254.4 10.60 10.65 138.5 149.1 ]59.8 170.4 181.1 191.7 202.4 213.0 223.7 234.3 245.0 255.6 10.66 10.70 139.1 149.8 160.5 171.2 181.9 182.8 192.6 203.3 204.3 214.0 215.0 224.7 225.8 235.4 246.1 256.8 10.70 10.75 139.8 150.5 161.3 172.0 193.5 236.5 247.3 258.0 10.75 10.80 140.4 151.2 162.0 172.8 183.6 194.4 •205. 2 216.0 226.8 237.6 248.4 259.2 10.80 10.85 141.1 151.9 162.8 173.6 184.5 195.3 206.2 217.0 227.9 238.7 249.6 260.4 10.85 10.90 141.7 152.6 163.5 174.4 185.3 196.2 207.1 218.0 228.9 239.8 250.7 261.6 10.90 10.95 142.4 153.3 164.3 175.2 186.2 197.1 208.1 219.0 220.0 230.0 240.9 242.0 251.9 262.8 10.95 11.00 143.0 154.0 165.0 176.0 187.0 198.0 209.0 231.0 253.0 264.0 11.00 11.05 143.7 154.7 165.8 176.8 187.9 198.9 210.0 221.0 232.1 243.1 254.2 265.2 11.05 11.10 144.3 155.4 166.5 177.6 188.7 199.8 210.9 222.0 233.1 244.2 255.3 266.4 11.10 11.15 145.0 156.1 167.3 178.4 189.6 200.7 211.9 223.0 234.2 245.3 256.5 267.6 11.15 11.20 145.6 156.8 168.0 179.2 190.4 201.6 212.8 213.8 224.0 225.0 235.2 246.4 247.5 257.6 258.8 268.8 11.20 11.25 146.3 157.5 168.8 180.0 191.3 202.5 236.3 270.0 11.25 11.30 146.9 158.2 169.5 180.8 192.1 203.4 214.7 226.0 237.3 248.6 259.9 271.2 11.30 11.35 147.6 158.9 170. 3 181.6 193.0 204.3 215.7 227.0 238.4 249.7 261.1 272.4 11.35 11.40 148.2 159.6 171.0 182.4 193.8 205.2 216.6 228.0 239.4 250.8 262.2 273.6 11.40 11. 45 1 148. 9 160.3 171.8 183.2 194.7 206.1 217.6 229.0 240.5 251.9 263.4 274.8 11.45 TABLES 14, 15, 16. [Page 686 TABLE 14. TABLE 15. Dip of the Sea Horizon. Dip of the Sea at different Distances from the Observer. Dist. of Height of the Eye above the Sea in Feet. Height of Dip of the the Eye. Horizon. Land in Sea Miles. 5 10 16 20 25 30 85 40 Feet. / II / / 1 / / / / / 1 59 i 11 23 34 45 57 68 79 91 2 1 23 i 6 12 17 23 28 34 40 45 3 1 42 f 4 8 12 15 19 23 27 30 4 5 6 7 8 9 10 1 58 2 11 2 24 2 36 2 46 2 56 3 06 1 3 6 9 12 15 17 20 23 2 3 3 2 5 4 4 7 6 5 10 8 7 12 10 8 14 12 9 16 14 11 19 16 12 2J 2 3 4 6 7 8 9 10 3 2 3 4 5 6 7 8 9 11 3 15 3i 2 3 4 5 6 6 7 8 12 13 14 3 24 3 32 3 40 4 6 2 2 3 4 4 5 4 5 5 6 6 7 6 7 7 S 6 2 3 4 4 5 5 6 6 15 16 17 18 19 20 3 48 3 55 4 02 4 09 4 16 4 23 Note to Table 15. — The numbers of this Table below the black lines are the same as are given in Table 14, the visible horizon corres to those heights not being so far distant as the land. ponding 21 4 29 22 4 36 23 4 42 24 4 48 25 4 54 26 5 00 27 5 06 28 5 11 29 5 17 30 31 5 22 5 27 32 5 33 TABLE 16. 33 5 38 The Sun's Parallax 34 5 43 in Altitude. 36 5 48 36 37 5 53 5 58 Altitude. Parallax. 38 6 02 o II 39 6 07 9 40 6 12 10 9 45 6 36 20 8 50 6 56 30 8 55 7 16 40 7 60 7 35 50 6 65 7 54 55 5 70 8 12 60 4 75 8 29 65 4 80 8 46 70 3 85 9 02 75 2 90 9 18 80 2 95 9 33 85 1 • 100 9 48 90 Page 686] TABLE 17. Parallax in Altitude of a Planet. •aprnFHV i OsOiOOCOCDiO-^COCMC^i— lO0500t>.«0C0»Oka'^C0e0(MrH,-(O aooot-coiO'^j'eocoiM.-HOOOioot^coeOiO'ti'^sccoiMr-ii-HO t^r^COiC-^CO(N(Mi-(OOa500t^I:^COiOiCTt<'*iCOiMiCiOTt.l:^tdCiCrtcocC500t^t^=OCO»C'«*<"*'tlO:)CO(MOiCOOOt^t^OCOiOW>*Tti«oa3C<»(MC<)i-li-lOO rHi-ioocioooooot^i-^cooioicti-^coeoeotNiNcMi-ir-ioo ooa:oooot-t^i--co!f.t^CD:0i;0iClO-^'^'*C0CC(MC^M(Mr-(i-(i-(OO OOOOGOt^t^«OiX>COVOiCU3-^-^rtieOMlMCOCOiCiOiO'*Tj<-.^-^tieCC0eOMlM(M(N(Mi ioio»«rt<- 1 15 69 00 19 50 6 32 50 4 1 40 2 18 20 1 15 70 00 18 55 6 28 55 4 50 2 17 40 1 14 71 00 17 8 00 6 24 13 00 3 58 22 00 2 15 36 00 1 13 72 00 16 05 6 21 05 3 57 10 2 14 20 1 12 73 00 16 10 6 17 10 3 55 20 2 13 40 1 11 74 00 15 15 6 13 15 3 54 30 2 12 37 00 1 10 75 00 14 20 6 10 20 3 52 40 2 11 20 1 9 76 00 13 25 6 6 25 3 51 50 2 10 40 1 8 77 00 12 8 30 6 3 13 30 3 49 23 00 2 8 38 00 1 8 78 00 10 35 6 35 3 48 10 2 7 20 1 7 79 00 9 40 5 56 40 3 46 20 2 6 40 1 6 80 00 8 45 5 53 45 3 45 30 2 5 39 00 1 5 81 00 7 50 5 50 50 3 43 40 2 4 20 1 4 82 00 6 55 5 47 55 3 42 50 2 3 40 1 3 83 00 6 9 00 5 44 14 00 3 41 24 00 2 2 40 00 1 2 84 00 5 05 5 41 10 3 38 10 2 1 20 1 2 85 00 4 10 5 38 20 3 35 20 2 40 1 1 86 00 3 15 5 35 30 3 33 30 1 59 41 00 1 87 00 2 20 5 32 40 3 30 40 1 58 20 59 88 00 2 25 5 29 50 3 28 50 1 57 40 58 89 00 1 9 30 5 26 15 00 3 25 25 00 1 56 42 00 58 90 00 Page 690] TABLE 21. 1 Correction of the Mean Refraction for the Height of the Barometer. Barom. Subtract. Mean refraction. Barom. 0' 1' 2' 8' 4' 6' «' V 8' 9' 1 10' 0" 30" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" II ,, „ II II „ „ // II „ /' // „ II /' II II II // II // 27.50 2 5 7 10 12 15 17 20 23 25 28 30 33 35 38 40 43 45 48 51 27.55 2 5 7 10 12 15 17 20 22 25 27 30 32 35 37 40 42 45 47 50 27.60 2 5 7 10 12 14 17 19 22 24 27 29 31 34 36 39 41 44 46 49 27.65 2 5 7 9 12 14 16 19 21 24 26 28 31 33 36 38 40 43 45 48 27.70 2 2 5 4 7 7 9 9 11 11 14 13 16 16 18 18 21 20 23 23 25 26 28 27 30 29 32 32 35 34 37 36 39 39 42 41 44 43 47 27.75 46 27.80 2 4 7 9 11 13 15 18 20 22 24 27 29 31 33 35 38 40 42 45 27.85 2 4 6 9 11 13 15 17 19 22 24 26 28 30 32 35 37 39 41 44 27.90 2 4 6 8 10 13 15 17 19 21 23 25 27 30 32 34 36 38 40 43 27.95 28.00 2 2 4 4 6 6 8 8 10 10 12 12 14 14 16 16 18 18 21 20 23 22 25 24 27 26 29 28 31 30 33 32 35 34 37 36 39 42 38 41 28.05 2 4 6 8 10 12 14 16 18 20 22 24 25 27 29 31 33 35 37 89 28.10 2 4 6 8 9 11 13 15 17 19 21 23 25 27 29 31 33 34 36 38 . 28.15 2 4 6 7 9 11 13 15 17 19 20 22 24 26 28 30 32 34 36 37 28.20 2 2 4 3 5 5 7 7 9 9 11 10 13 12 14 14 16 16 18 18 20 19 22 21 24 23 25 25 27 26 29 28 31 30 33 32 35 34 36 35 28.25 28.30 2 3 5 7 8 10 12 14 15 17 19 21 22 24 26 27 29 31 33 34 28.35 2 3 5 7 8 10 12 13 15 17 18 20 22 23 25 27 28 30 32 33 28.40 2 3 5 6 8 10 11 13 14 16 18 19 21 23 24 26 27 29 31 32 28.45 2 3 3 5 4 6 6 8 7 9 9 11 10 12 12 14 14 16 15 17 17 19 18 20 20 22 2f 23 23 25 24 27 26 28 30 31 28.50 27 29 30 31.50 28.55 3 4 6 7 9 10 12 13 15 16 17 19 20 22 23 25 26 28 29 31. 45 28.60 3 4 6 7 8 10 11 13 14 15 17 18 20 21 23 24 25 27 28 31. 40 28.65 3 4 5 7 8 9 11 12 14 15 16 18 19 20 22 23 25 26 27 31.35 28.70 3 2 4 4 5 5 6 6 8 7 9 9 10 10 12 11 13 13 14 14 16 15 17 16 18 18 20 19 21 20 22 21 24 25 26 31.30 28.75 23 24 25 31.25 28.80 2 4 5 6 7 8 10 11 12 13. 14 16 17 18 19 21 22 23 24 31.20 28.85 2 3 5 6 7 8 9 10 12 13 14 15 16 17 19 20 21 22 23 31.15 28.90 2 3 4 5 7 8 9 10 11 12 13 14 16 17 18 19 20 21 22 31.10 28.95 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 20 21 31.05 29.00 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 31.00 29.05 2 3 4 5 6 7 8 9 10 11 11 12 13 14 15 16 17 18 19 30.95 29.10 2 3 4 4 5 6 7 8 9 10 11 12 13 14 15 15 16 17 18 30.90 29.15 2 3 3 4 5 6 7 8 9 9 10 11 12 13 14 15 15 16 17 30.85 29.20 2 2 3 4 5 6 6 7 8 9 10 10 11 12 13 14 15 15 16 30.80 30. % 29.25 2 3 4 4 5 6 7 8 8 9 10 11 11 12 13 14 14 15 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 2 3 3 4 3 4 4 5 5 6 5 6 7 7 8 8 9 9 10 11 11 30. 55 29.50 2 6 6 7 7 8 8 9 9 10 10 30.50 29.55 2 2 3 3 4 4 5 5 5 6 6 7 7 8 8 9 9 30. 45 29.60 2 2 2 3 3 4 4 4 5 5 6 6 6 7 7 8 8 30.40 29.65 2 2 2 3 3 4 4 4 5 5 5 6 6 6 7 7 30.35 29.70 ~0" -j- 1 1 2 2 2 2 2 3 2 3 3 4 4 4 5 5 5 5 6 6 30. 30 29.75 3 3 3 3 4 4 4 4 5 5 5 30. 25 29.80 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 30.20 29.85 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 30.15 29.90 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 30.10 29.95 1 1 1 1 1 1 1 1 1 1 1 30.05 30.00 30.00 Subtract. Barom. 0" 30" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 1 80" 0" 80" 0" 80" 0" Add. Barom. 0' V 2' 3' i \ i' 6' 1 6' V %' 9' 10' Mean refraction. TABLE 22. [Page 691 Correction of the Mean Refraction for the Height of the Thermometer. Mean refraction. Ther. Ther. Add. 0' 1' a' 8' V o' 6' V 8' 9' 10' Add. 0" 30" 0" // 80" II 0" ;/ 80" II 0" // 30" // 0" 80" II 0" // 30" II 0' II 80" II 0" II 80" II 0" II 80" II 0" 30" 0" o // II II II II o —10 4 8 12 16 20 24 28 33 37 41 46 50 55 60 65 70 75 80 85 90 —10 — 8 4 8 12 15 19 23 27 31 36 40 44 48 53 58 62 67 72 77 82 87 — 8 — 6 4 7 11 15 19 22 26 30 34 38 42 47 51 55 60 64 69 74 79 84 - 6 — 4 4 7 11 14 18 22 25 29 33 37 41 45 49 53 57 62 66 71 76 80 — 4 — 2 3 7 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 3 6 9 12 16 19 22 25 29 32 36 39 43 47 50 54 58 62 66 70 2 4 3 6 9 12 15 18 21 24 28 31 34 37 41 44 48 52 55 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 10 3 3 5 5 8 8 11 10 14 13 16 15 19 18 22 21 25 24 28 26 31 29 34 32 37 35 40 38 43 41 47 44 50 48 54 51 57 54 61 58 8 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 15 2 2 5 4 7 7 9 9 11 11 14 13 16 16 19 18 21 20 24 23 26 25 29 28 31 30 34 33 37 36 40 38 42 41 45 44 48 47 51 50 14 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 11 14 13 16 15 18 17 20 "19 22 22 24 24 27 26 29 28 31 30 34 33 36 35 39 37 41 40 44 42 19 20 2 4 6 8 9 20 21 2 4 6 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 13 15 14 17 16 18 18 20 19 22 21 24 23 26 25 28 27 30 29 32 31 34 33 36 35 24 25 2 3 5 6 8 9 11 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 28 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 30 3 2 4 •4 5 5 6 6 8 7 9 9 11 10 12 11 13 13 15 14 16 15 18 17 19 18 21 20 22 21 24 23 26 24 27 29 29 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 82 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 4 5 5 6 6 7 6 8 7 9 8 10 9 11 10 12 11 13 13 14 14 16 15 17 16 18 17 19 18 21 19 22 34 35 2 3 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 8 8 9 10 10 11 12 13 13 40 41 2 2 3 3 4 4 5 6 6 7 7 8 9 () 10 11 11 12 41 42 2 2 3 3 4 4 5 5 6 7 7 8 8 9 S 10 11 42 43 2 2 3 3 3 4 4 5 5 6 6 7 7 8 8 9 9 43 44 1 2 2 3 3 3 4 4 4 5 5 6 6 7 7 8 8 44 45 1 1 2 2 2 3 3 3 4 4 4 5 5 6 6 6 7 45 46 1 1 1 2 2 2 2 2 3 3 4 4 4 4 5 5 5 46 47 1 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 47 48 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 48 49 1 1 1 1 1 1 1 1 1 1 1 1 49 50 50 0" 30" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" SO" 0" 80" 0" 80" 0" 80" 0" Add. Add. 0' 1' V V 4' 6' 6' V 8' 1 9' 10' Ther Ther. Mean refraction. Page 692] TABLE 22. Correction of the Mean Refraction for the Height of the Thermometer. Ther. Subt. Mean refraction. Ther. Subt. 0' V 2' 8' 4' 6' 6' V 8' 9' 10' 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" o 50 51 52 53 54 II II tt II II 1 1 II 1 1 1 II 1 1 1 n 1 1 2 n 1 1 2 II 1 1 2 2 // 1 1 2 2 II 1 1 2 3 1 1 2 3 II 1 2 2 3 // 1 2 2 3 II 1 2 3 4 II 1 2 3 4 II 1 2 3 4 5 6 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 38 39 40 41 42 43 44 45 46 47 48 49 50 II 1 2 3 5 6 7 8 9 10 11 12 14 15 16 17 18 19 20 21 22 23 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 II 1 2 4 5 6 7 8 10 11 12 13 15 16 17 18 19 20 22 23 24 25 26 27 28 29 31 32 33 34 35 36 37 38 39 40 42 43 44 45 46 47 48 49 50 51 52 53 54 55 II 1 3 4 5 o 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 2 2 2 2 2 2 2 1 1 2 2 2 2 3 3 3 3 1 2 2 2 3 3 3 3 4 4 2 2 2 3 3 3 4 4 5 5 2 2 3 3 4 4 4 5 5 6 2 3 3 4 4 5 5 6 6 7 7 7 8 8 9 9 10 10 11 11 11 12 12 13 13 14 14 14 15 15 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 3 4 4 5 5 6 7 7 8 8 9 9 10 11 11 12 12 13 13 14 14 15 16 16 17 17 18 18 19 19 3 4 5 5 6 7 7 8 8 9 10 10 11 11 12 12 13 14 14 15 16 16 17 18 18 19 20 20 21 21 4 4 5 6 6 7 8 9 9 10 11 11 12 13 13 14 15 16 16 17 18 18 19 20 20 21 21 22 23 23 24 25 25 26 27 27 28 29 29 30 30 31 32 32 33 34 4 5 6 6 7 8 9 9 10 11 12 12 13 14 15 16 16 17 18 18 19 20 21 21 22 23 24 24 25 26 26 27 28 28 29 30 31 31 32 33 33 34 35 35 36 37 4 5 6 7 8 9 9 10 11 12 13 14 14 15 16 17 18 18 19 20 21 22 22 23 24 25 26 26 27 28 29 29 30 31 32 32 33 34 35 35 36 37 38 38 39 40 5 6 6 7 8 9 10 11 12 13 14 15 16 16 17 18 19 20 21 22 22 23 24 25 26 27 28 28 29 30 31 32 32 33 34 35 36 37 37 38 39 40 41 41 42 43 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 20 21 22 23 24 25 26 27 28 29 30 31 31 32 33 34 35 36 37 38 39 39 40 41 42 43 44 44 45 46 6 8 9 10 12 13 14 15 17 18 19 20 22 23 24 25 27 28 29 30 31 32 34 35 36 37 38 40 41 42 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 2 2 2 2 2 3 3 3 o 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 7 6 6 7 7 8 65 66 67 68 69 70 71 72 73 74 2 2 2 3 3 3 3 3 3 3 3 3 4 4 4 3 4 4 4 4 4 4 5 5 5 5 5 5 5 6 5 6 5 5 5 6 6 6 6 6 7 7 7 7 8 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 7 7 8 8 8 8 9 9 9 10 10 10 11 11 11 8 8 9 9 10 10 10 11 11 11 12 12 13 13 13 70 71 72 73 74 75 76 77 78 79 2 2 2 2 2 2 2 75 76 77 78 79 80 81 82 83 84 80 81 82 83 84 86 86 87 88 89 2 2 2 2 2 4 4 4 4 4 6 6 6 6 6 8 8 8 8 9 10 10 10 10 11 12 1 14 12; 14 12! 14 13 1 15 13; 15 16 16 17 17 17 18 18 19 19 20 20 20 21 21 22 22 23 23 24 24 43 44 45 46 48 49 50 51 52 53 54 55 56 58 59 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 2 2 2 2 2 2 2 3 3 3 4 4 5 5 5 6 5 5 5 5 5 7 7 7 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 10 11 11 11 11 11 12 12 12 12 13 13 13 13 13 14 14 14 14 15" 15 15 16 16 16 16 16 17 17 17 18 18 18 19 18 18 19 19 19 20 20 21 21 21 22 20 21 21 22 22 22 23 23 24 24 25 23 23 24 24 25 25 26 26 27 27 28 25 25 26 27 27 28 28 29 29 30 31 90 91 92 93 94 95 96 97 98 99 . 100 3 16 19 53 56 60 100 Subt. Ther. 0" 80" 0" 80" 0" 80" 0" 1 80" 0" 80" 0" 80" 0" 80" 0" 80" 0" 80» 0" 80" 0" Subt. Ther. 0' 1' 2' 8' 4' 6' 6' V j 8' 9' 10' Mean refraction. TABLES 23, 24. [Page 693 TABLE 23. 1 Correction of the Moon's Altitude for parallax and re- fraction corresponding to a mean value of the hori- zontal parallax, 57' SO'-'. Moon's alt. Corr. Moon's alt. Corr. Moon's alt. C!orr. Moon's alt. Corr. o , o 1 o , o / 10 51 31 48 51 35 71 18 11 52 32 47 52 35 72 17 12 52 33 47 53 34 73 17 13 52 34 46 54 33 74 16 14 52 35 46 55 32 75 15 15 52 36 45 56 32 76 14 16 52 37 45 57 31 77 13 17 52 38 44 58 30 78 12 18 52 39 44 59 29 79 11 19 52 40 43 60 28 80 10 20 51 21 51 41 42 61 27 81 9 22 51 42 42 62 26 82 8 23 51 43 41 63 26 83 7 24 50 44 40 64 25 84 6 25 50 45 40 65 24 85 5 26 50 46 39 66 23 86 4 27 49 47 38 67 22 87 3 28 49 48 38 68 21 88 2 29 49 49 37 69 20 89 1 30 48 50 36 70 19 90 1 i TABLE 24. Correction of tl 18 Moon's Apparent Altitude for Parallax and Refraction. [Barometer, 30 Inches.— Fahrenheit's Thermometer, 50°.] H orizontal parallax. Correction for seconds of parallax.— Add. Corr. for Moon's minutes of alt. app. alt. 54' &6' 66' 67' 58' 69' 60' 61' oB 1- 0" 8" 4" V 8" O 1 / // / II / // 1 II ' II 1 II / // / // II // n It n n 5 43 56 44 56 45 56 46 56 47 56 48 55 49 55 50 55 2 4 6 8 10 44 11 45 11 46 11 47 11 48 11 49 10 50 10 5110 10 10 12 14 16 18 20 25 25 25 25 25 24 24 24 20 20 22 24 26 28 30 39 39 38 38 38 38 37 37 30 30 32 34 36 38 40 52 51 51 51 51 51 5^ 51 40 40 42 44 46 48 50 45 4 46 3 47 3 48 3 49 3 50 3 51 6 52 3 50 50 52 2 54 4 56 58 6 45 15 46 15 47 14 48 14 49 14 50 13 51 13 52 13 6 8 10 26 26 25 25 25 25 25 25 10 10 12 14 16 18 20 36 36 36 35 35 34 34 34 20 20 22 24 26 28 30 46 46 45 45 45 44 44 44 30 30 32 34 36 38 40 55 55 55 54 54 54 53 53 40 40 42 44 46 48 50 46 4 47 3 48 3 49 3 50 3 51 2 52 1 53 1 50 50 52 2 54 4 56 6 58 8 7 46 12 47 12 48 12 49 12 50 12 51 11 52 11 53 10 10 21 20 20 20 19 18 18 18 10 10 12 14 16 18 20 29 28 28 27 27 26 25 25 20 20 22 24 26 28 30 36 36 35 35 34 34 34 33 30 30 32 34 36 38 40 43 42 42 41 41 40 40 40 40 40 42 44 46 48 50 50 49 48 48 48 47 46 46 50 50 52 2 54 4 56 6 58 8 Add. 8 46 56 47 56 48 55 49 54 50 54 51 54 52 53 53 53 10 47 2 48 2 49 1 50 51 59 59 58 10 10 12 14 16 18 2 1 20 8 7 7 6 6 52 5 53 4 54 4 20 20 22 24 26 28 3 2 30 13 13 12 11 11 10 10 9 30 30 32 34 36 38 4 2 40 19 18 17 17 16 16 15 14 40 40 42 44 46 48 5 3 50 24 23 22 22 21 20 19 19 50 50 52 54 4 56 6 58 8 6 4 7 4 9 47 28 48 27 49 26 50 26 51 25 52 24 53 24 54 23 2 10 33 32 31 30 30 29 28 27 10 10 12 14 16 18 8 5 20 37 36 35 34 34 33 32 32 20 20 22 24 26 28 9 5 30 41 41 40 39 38 37 37 36 30 30 32 34 36 38 40 45 44 43 43 42 41 40 39 40 40 42 44 46 48 50 49 48 47 46 46 45 44 44 50 49 51 53 55 57 Page 604] TABLE 24. • Correction of the Moon's Apparent Altitude for Parallax and Refraction. [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] Moon'8 Horizontal parallax. 1^" Correction for seconds of parallax. — Add. Corr. for app. alt minutes of alt. 64' 56' 66' 67' 1 58' 59' 60' 61' 0" 2" 4" 6" 8" O / ' // ' // / // ' // / // ' II ' II / II II // II II II „ Add 10 47 63 48 52 49 51 50 50 51 50 52 48 63 48 64 47 2 4 6 8 V ^' 10 56 55 54 53 62 51 60 60 10 10 12 14 16 18 2 1 20 59 58 57 56 65 56 54 63 20 20 22 24 26 28 8 1 30 48 2 49 1 50 59 1 58 57 66 55 30 29 31 33 36 37 4 1 40 5 4 2 51 2 ; 52 1 53 59 58 40 39 41 43 46 47 6 2 50 7 6 5 4 1 4 2 54 1 54 4 55 50 49 61 2 63 4 55 6 67 8 .6 7 2 2 11 48 10 49 9 50 8 51 7 { 62 7 53 5 56 3 10 12 11 10 9 1 9 7 6 6 10 10 12 14 16 18 8 2 20 15 14 12 12 i 11 9 8 7 20 20 22 24 26 28 9 8 30 17 16 14 13 13 11 10 9 30 29 31 33 35 87 40 19 18 17 15 15 13 12 11 40 39 41 43 45 47 50 21 20 18 17 17 15 14 13 50 49 51 2 53 4 55 6 67 8 12 48 22 49 21 50 19 51 18 52 17 53 17 54 16 66 14 10 24 23 21 20 19 18 16 15 10 10 12 14 16 18 20 26 25 23 22 21 20 18 17 20 20 22 24 26 27 30 27 26 24 23 22 20 19 18 30 29 31 33 35 37 40 28 27 25 24 23 21 20 19 40 39 41 43 46 47 50 29 28 26 25 24 62 25 22 53 23 21 20 60 49 51 2 53 4 55 6 57 8 1 13 48 30 49 29 50 27 51 26 64 22 55 20 10 31 30 28 27 26 24 22 21 10 10 12 14 16 18 2 20 32 31 29 27 26 24 23 21 20 19 21 23 25 27 8 30 33 32 30 28 27 25 23 22 30 29 31 33 35 37 4 40 34 32 30 29 28 26 24 22 40 39 41 43 46 47 6 50 35 33 31 30 28 26 25 23 60 49 51 2 53 4 55 6 57 8 6 7 14 48 35 49 33 50 31 51 30 52 28 53 26 54 25 56 23 10 35 34 32 30 28 26 25 23 10 10 12 14 16 18 8 20 36 34 32 30 29 27 26 24 20 19 21 23 25 27 9 30 36 34 32 30 29 27 25 23 30 29 31 33 35 37 40 36 34 32 30 29 27 25 23 40 39 41 43 46 47 50 36 34 32 30 29 27 53 27 25 23 60 49 61 2 53 4 55 6 57 8 15 48 36 49 35 50 33 51 31 52 29 64 25 55 23 10 36 35 32 30 28 26 24 22 10 10 12 14 16 18 20 36 35 32 30 28 26 24 22 20 19 21 23 25 27 30 36 34 31 29 28 25 23 21 30 29 31 33 35 87 40 36 34 31 29 27 25 23 21 40 39 41 43 45 47 50 35 48 35 33 30 28 26 24 21 54 20 19 50 49 61 2 53 4 66 6 57 8 16 49 32 50 29 51 27 52 26 53 23 55 18 10 34 32 29 27 25 23 20 18 10 10 12 13 15 17 20 34 32 29 27 25 22 20 17 20 19 21 23 26 27 30 33 31 28 26 24 21 19 16 30 29 31 33 36 86 40 33 31 28 25 23 21 18 16 40 38 40 42 44 46 50 32 30 27 24 51 23 22 20 17 15 50 48 50 2 62 4 64 6 56 8 Sub. 17 48 31 49 29 50 26 52 21 63 18 54 16 56 13 10 30 28 25 22 20 17 14 12 10 10 12 13 15 17 2 20 28 26 23 20 18 16 12 10 20 19 21 23 25 27 3 30 27 25 22 19 17 14 11 9 30 29 31 33 34 36 4 40 26 24 21 18 16 13 10 7 40 38 40 42 44 46 5 50 26 23 20 17 15 12 9 6 50 48 60 2 62 4 53 6 55 8 6 7 18 48 24 49 21 50 18 61 15 52 13 63 10 54 7 55 4 10 23 20 17 14 12 9 6 3 10 10 11 13 15 17 8 20 22 19 16 13 11 8 5 2 20 19 21 23 25 27 9 30 21 18 15 12 10 6 3 30 29 30 32 34 36 40 20 17 14 10 8 4 1 54 58 40 38 40 42 44 46 50 18 15 12 9 6 2 53 59 53 57 66 50 48 60 2 51 4 53 6 66 8 19 48 16 49 13 50 10 51 7 52 4 63 54 55 10 15 12 8 5 2 52 59 65 53 10 10 11 13 15 17 20 13 10 6 3 67 63 51 20 19 21 23 25 27 30 12 8 5 2 61 58 65 51 49 30 29 30 32 34 36 40 10 6 3 56 53 49 47 40 38 40 42 44 46 50 9 5 2 60 68 55 51 48 45 60 48 60 61 53 55 TABLE 2L [Page 696 ] Correction of the Moon's Apparent Altitude for Parallax and Refraction. [Barometer 30 inches. — Fahrenheit's Thermometer 50°.] Moon's Horizontal parallax. Ox" Correction for seconds of parallax.— Add. Corr. for app. alt. minutes of alt. 64' 66' 66' 57' 58' 69' 60' 61' 0" 2" 4" 6" 8" o / / // ' // ' n / // ' n ' // > II ' II II II II II II „ Snh. 20 48 6 49 3 49 69 50 56 51 52 52 49 53 45 54 42 2 4 6 8 V (y 10 5 2 58 55 51 47 43 40 10 9 11 13 15 17 2 20 3 56 52 49 45 41 37 20 19 21 23 24 26 3 30 1 48 58 53 50 46 42 38 35 30 28 30 32 34 36 4 40 59 56 52 48 44 40 36 33 40 38 39 41 43 4o 5 50 57 54 50 46 42 51 39 38 34 53 31 30 50 47 49 2 51 4 53 6 54 7 6 7 21 47 55 48 51 49 47 50 43 52 35 54 28 10 53 49 45 41 37 33 29 26 10 9 11 13 15 17 8 20 51 47 43 39 35 31 27 23 20 19 21 22 24 26 9 2 30 48 44 40 36 32 28 24 20 30 28 30 32 34 35 40 46 42 38 33 29 25 21 17 40 37 39 41 43 45 50 43 39 35 31 27 22 18 53 16 14 50 47 0' 49 2 50 4 52 6 54 7 22 47 42 48 37 49 33 50 29 51 25 52 20 54 11 10 40 35 30 26 22 17 13 8 10 9 11 13 15 17 20 37 32 27 23 19 14 10 5 20 19 20 22 24 26 30 34 30 25 20 16 11 7 3 30 28 30 31 33 35 40 32 27 22 18 13 9 4 40 37 39 41 43 45 50 29 47 27 25 20 15 11 6 1 52 58 53 57 50 46 48 2 50 4 52 6 54 7 23 48 22 49 17 50 13 51 8 52 3 53 54 10 25 20 15 10 5 55 51 10 9 11 13 15 17 20 22 17 12 7 2 51 57 52 48 20 18 20 22 24 26 30 19 14 9 4 54 49 45 30 28 29 31 33 35 40 16 11 6 1 50 57 51 46 42 40 37 39 40 42 44 50 13 8 3 49 58 49 55 54 50 50 48 43 38 50 46 48 2 50 4 51 5 53 7 1 24 47 10 48 5 49 51 45 52 40 53 35 10 8 3 48 57 52 47 42 37 32 .10 9 11 13 15 16 2 1 20 5 54 49 44 39 33 28 20 18 20 22 24 26 3 1 30 2 47 57 51 46 41 35 30 24 30 27 29 30 32 34 4 1 40 46 59 54 48 43 38 32 27 21 40 36 38 40 42 44 5 2 50 25 56 46 53 51 47 48 45 40 35 29 23 52 20 18 50 46 47 2 49 4 51 5 53 7 6 7 2 2 48 42 49 37 50 31 51 26 53 14 10 50 45 39 33 28 22 16 10 10 9 11 13 14 16 8 2 20 46 41 35 29 24 18 12 6 20 18 20 22 24 25 9 3 30 43 38 32 26 20 14 8 3 30 27 29 31 33 34 40 40 34 28 23 17 11 5 52 59 40 36 38 40 42 43 50 26 37 31 25 19 14 50 10 7 1 56 50 45 47 2 49 4 51 5 52 7 46 34 47 28 48 22 49 16 51 4 51 58 52 52 0- 10 31 25 19 13 7 1 54 48 10 9 11 13 14 16 20 27 21 15 9 3 50 57 50 44 20 18 20 22 23 25 30 24 18 12 6 49 59 53 46 40 30 27 29 31 32 34 40 20 14 8 2 55 49 42 36 40 36 38 39 41 43 50 17 46 14 11 4 48 58 51 45 38 32 "52 28 50 45 47 2 48 4 50 5 52 7 1 27 47 7 48 1 48 54 49 48 50 41 51 35 10 11 4 47 58 51 44 37 31 24 10 9 11 12 14 16 2 1 20 7 1 54 47 40 33 27 20 20 18 20 21 23 25 3 1 30 3 46 57 50 43 36 29 23 16 30 27 28 30 32 34 4 1 40 45 59 53 46 39 32 25 19 12 40 36 37 39 41 43 5 o 50 56 45 53 49 46 46 42 47 38 35 28 49 24 21 15 8 50 44 46 2 48 4 50 5 52 7 6 7 2 3 28 48 31 50 17 51 11 52 4 10 49 42 34 27 20 13 6 5159 10 9 11 12 14 16 8 3 20 45 38 30 23 16 9 2 55 20 18 19 21 23 ,25 9 3 30 41 34 26 19 12 5 50 57 50 30 26 28 30 :32 33 40 37 30 23 15 8 1 54 46 40 35 37 39 41 42 50 34 45 30 26 19 47 15 11 4 49 57 49 42 50 44 46 2 48 4 49 5 51 7 29 46 22 48 7 49 49 53 50 45 5138 10 26 18 11 3 48 56 49 40 34 10 9 10 12 14 16 20 22 14 7 47 59 52 44 36 29 20 17 19 21 23 24 30 18 10 2 55 47 39 31 24 30 26 28 30 31 33 40 14 6 46 58 51 43 35 27 20 40 35 ; 37 38 40 42 50 11 3 55 47 39 31 23 15 50 44 45 47 49 51 Page 696] TABLE 24. Correction of the Moon's Apparent Altitude for Parallax and Refraction. | [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] 1 Moon's Horizontal parallax. ^5 Correction for seconds of parallax.— Add. Corr. for app. alt. minutes of alt. 54' 66' 56' 67' 58' 59' ec 61' 0" 2" 4" II 6" II 8" O / / // / // / // / It / // / II 1 II / II II II // II Sub. 30 45 6 45 57 46 50 47 42 48 34 49 26 50 18 61 10 2 3 6 7 V Q" 10 2 64 46 38 30 22 13 6 10 9 10 12 14 16 2 1 20 44 58 50 42 34 26 18 9 1 20 17 19 21 23 24 3 1 30 54 46 37 29 21 13 4 50 56 30 26 28 29 31 33 4 2 40 50 42 33 25 17 8 52 40 35 36 38 40 42 6 2 50 45 38 29 21 12 4 49 65 49 50 47 50 42 50 43 45 2 47 3 49 5 50 7 6 3 7 3 31 44 41 45 33 46 24 47 16 48 7 48 59 10 37 29 20 12 2 54 45 37 10 9 10 12 14 15 8 4 20 33 24 15 7 47 58 49 40 32 20 17 19 21 22 24 9 4 30 28 20 11 2 54 46 36 27 30 26 27 29 31 32 40 24 16 7 46 58 49 40 31 22 40 34 36 38 39 41 50 20 11 2 53 44 35 26 17 50 43 44 2 46 3 48 5 50 7 32 44 15 45 7 45 58 46 49 47 40 48 31 49 22 50 13 10 11 3 53 44 35 26 17 8 10 8 10 12 14 15 20 7 44 58 48 39 30 21 11 2 20 17 19 20 22 24 30 3 53 44 34 25 16 6 49 57 30 26 27 29 30 32 40 43 58 48 39 29 20 11 1 52 40 34 35 37 39 41 50 54 44 34 24 15 6 48 56 47 50 42 44 2 46 3 47 5 49 7 1 33 43 48 44 39 45 29 46 19 47 10 48 48 50 49 41 10 44 34 26 15 5 47 55 45 36 10 8 10 12 13 15 2 1 20 40 30 20 10 50 40 31 20 17 18 20 22 23 3 1 30 35 25 15 5 46 55 45 35 25 30 25 27 28 30 32 4 2 40 30 20 10 60 40 30 20 40 33 35 37 38 40 5 2 50 25 15 6 45 55 45 46 40 36 24 14 50 42 43 2 45 3 47 5 48 7 6 3 7 3 34 43 21 44 11 45 45 50 47 30 48 19 49 9 10 16 6 44 55 45 34 24 14 3 10 8 10 12 13 15 8 4 20 11 1 50 40 29 19 9 48 58 20 17 18 20 21 23 9 4 30 6 43 66 45 35 24 13 3 52 30 25 26 28 30 31 40 1 61 40 30 19 8 47 58 47 40 33 35 36 38 40 50 42 56 46 35 24 14 3 52 42 50 41 43 44 3 46 5 48 7 35 42 52 43 41 44 30 45 19 46 9 46 58 47 47 48 36 2 10 47 36 25 14 3 52 41 30 10 8 10 11 13 15 20 42 31 20 9 45 58 47 36 25 20 16 18 20 21 23 30 37 26 15 3 52 41 30 19 30 24 26 28 29 31 40 32 21 10 44 58 47 36 26 14 40 33 34 36 38 39 50 27 16 4 53 42 30 19 8 50 41 42 2 44 3 46 5 47 6 36 42 22 43 11 43 69 44 48 45 37 46 25 47 14 48 2 10 17 5 54 42 31 19 8 47 56 10 8 10 11 13 14 1 1 20 12 48 37 25 14 2 50 20 16 18 19 21 23 2 1 30 7 42 55 43 31 20 8 46 56 44 30 24 26 27 29 31 3 2 40 1 50 38 26 14 2 50 39 40 32 34 35 37 39 4 2 50 41 56 44 32 20 8 45 56 44 33 60 40 42 2 43 3 45 6 47 6 5 3 6 3 37 41 51 42 39 43 27 44 15 45 3 45 51 46 39 47 27 10 46 34 21 9 44 67 46 33 21 10 8 10 11 13 14 7 4 20 41 29 16 4 52 40 27 15 20 16 17 19 21 22 8 4 30 35 23 11 43 58 46 34 21 9 30 24 25 27 29 30 9 5 40 30 18 5 53 40 28 16 3 40 32 33 35 37 38 50 25 12 42 59 47 34 44 29 22 9 46 3 46 57 50 40 41 2 43 3 46 5 46 6 38 41 19 42 7 42 54 43 41 46 16 46 51 10 14 2 49 36 23 10 45 57 45 10 8 9 11 13 14 20 . 8 41 56 43 30 17 4 51 38 20 16 17 19 20 22 30 3 ■ 51 38 24 12 44 58 46 32 30 23 25 27 28 30 40 40 58 45 32 18 6 52 39 26 40 31 33 35 36 38 50 52 39 26 13 43 7 46 33 20 50 39 41 2 42 3 44 5 46 6 39 40 47 41 33 42 20 43 54 44 40 45 27 46 13 10 42 28 15 1 48 34 21 7 10 8 9 11 12 14 1 1 20 36 23 9 42 55 42 28 15 1 20 16 17 19 20 22 2 1 30 30 17 3 49 36 22 8 45 54 80 23 25 26 28 29 3 2 40 26 11 41 57 43 30 16 2 48 40 31 32 34 36 37 4 2 50 19 5 51 37 23 9 44 56 42 50 39 40 42 43 45 5 3 I TABLE 24. [Page 697 1 Correction of the Moon's Apparent Altitude for Parallax and Refraction. | [Barometer 30 inches.— Fahrenheit's Thermometer 60°.] Horizontal parallax. B OS Correction for seconds of parallax. — Add. Corr. Moon's app. alt. Si for minutes 64' 56' 66' 57' 58' 69' ec 61' 9. ss 0" •ill 4" 6" 8" of alt. o / 1 II / II / // / II / II / II 1 n ' II II n II II II II Sub. 40 40 14 41 41 46 42 32 43 18 44 4 44 50 45 36 2 3 5 6 & Z" 10 8 40 54 39 25 11 43 57 43 29 10 8 9 11 12 14 7 4 20 2 48 33 19 5 50 36 22 20 15 17 18 20 21 8 5 30 39 56 42 28 13 42 59 44 30 16 30 23 24 26 27 29 9 5 40 50 36 22 7 53 38 24 9 40 30 32 34 36 37 50 45 30 16 1 47. 32 18 3 44 56 50 38 40 2 41 3 43 5 44 6 41 39 39 40 24 41 10 41 55 42 41 43 26 44 11 10 33 18 4 49 34 19 4 49 10 8 9 11 12 14 20 27 12 40 58 43 28 13 43 58 43 20 15 17 18 20 21 30 21 6 51 36 22 7 51 37 30 23 24 26 27 29 40 16 45 30 16 45 30 40 30 32 33 35 36 50 10 39 54 39 48 39 24 9 42 2 42 53 38 23 50 38 39 1 41 3 42 4 44 6 42 39 4 40 33 41 17 42 47 43 31 44 16 10 38 58 42 27 11 41 56 41 25 10 10 7 9 10 12 13 1 1 20 52 36 21 5 50 34 18 3 20 15 16 18 19 21 2 1 30 46 30 14 40 68 43 27 11 43 56 30 22 24 25 27 28 3 2 40 40 24 8 52 36 21 5 49 40 30 31 33 34 36 4 2 50 34 18 2 46 30 14 42 58 42 50 37 38 1 40 3 41 4 43 6 6 3 6 4 43 38 28 39 12 39 56 40 40 41 24 42 8 42 52 43 36 10 22 6 50 34 18 1 46 29 10 7 9 10 12 13 7 4 20 16 38 59 43 27 11 41 54 38 22 20 15 16 18 19 20 8 5 30 10 53 37 20 5 48 31 15 30 22 23 25 26 28 9 5 40 4 47 30 14 40 58 41 24 8 40 29 31 32 34 36 50 37 57 41 24 7 51 34 17 1 50 37 38 1 39 3 41 4 42 6 44 37 51 38 35 39 18 40 1 40 44 41 27 42 10 42 54 10 45 28 11 39 54 37 20 3 46 10 7 9 10 11 13 20 38 21 4 47 30 13 41 56 39 20 14 16 17 19 20 30 32 15 38 58 41 24 7 49 32 30 21 23 24 26 27 40 26 9 51 34 17 42 26 40 29 30 31 33 34 50 20 2 44 27 10 40 3 40 53 35 18 50 36 37 1 39 3 40 4 41 6 1 1 45 37 14 37 56 38 38 39 21 40 46 41 28 42 11 10 7 49 31 14 39 56 39 21 3 10 7 8 10 11 13 2 1 20 43 25 7 49 32 14 41 56 20 14 15 17 18 20 3 2 30 36 54 37 18 1 43 25 7 49 30 21 23 24 25 27 4 3 40 48 30 1 11 38 54 36 18 42 40 28 30 31 32 34 5 3 50 41 23 4 47 29 11 40 52 34 50 35 37 1 38 3 39 4 41 6 6 4 7 5 46 36 35 37 17 37 58 38 40 39 22 40 4 40 46 41 27 10 29 10 51 33 15 39 57 38 20 10 7 8 10 11 12 8 6 20 22 3 44 26 8 49 31 12 20 14 15 17 18 19 9 6 30 16 36 57 38 20 1 42 24 5 30 21 22 23 25 26 40 9 50 32 13 38 54 35 17 40 58 40 28 29 30 32 33 50 2 43 1 25 6 47 28 9 50 50 35 36 1 37 3 39 4 40 6 47 35 56 36 37 37 18 37 59 38 40 39 21 40 2 40 43 10 49 30 11 52 34 14 39 55 36 10 7 8 10 11 12 20 42 23 4 45 26 6 47 28 20 14 15 16 18 19 30 36 17 36 57 38 19 38 59 40 21 30 20 22 23 24 26 40 30 10 50 31 12 52 32 13 40 27 29 30 31 33 50 23 3 43 24 5 45 25 5 50 34 35 1 37 3 38 4 39 5 1 1 48 35 16 35 56 36 36 37 17 37 57 38 37 39 17 39 58 10 10 50 30 10 50 30 10 50 10 7 8 9 11 12 2 1 20 3 43 23 2 43 22 2 42 20 13 15 16 17 19 3 2 30 34 56 36 16 36 55 35 15 38 55 34 30 20 21 23 24 25 4 3 40 49 29 9 48 28 8 48 27 40 27 28 29 31 32 5 3 50 42 22 35 15 1 41 21 40 19 50 33 36 1 36 3 37 4 39 5 6 4 7 6 49 34 35 35 54 36 34 37 13 37 53 38 32 39 11 10 29 8 47 27 6 46 25 4 10 7 8 9 10 12 8 5 20 22 1 40 20 36 59 38 17 38 56 20 13 14 16 17 18 9 6 30 15 34 54 33 12 51 30 9 48 30 20 21 22 23 25 40 8 47 26 5 44 23 2 41 40 26 27 29 30 31 50 1 40 19 35 58 36 15 37 54 33 50 33 34 35 36 38 Page 698] TABLE 24. Correction of the Moon's Apparent Altitude for Parallax and Refraction. | [Baremeter 30 inches.— Fahrenheit's Thermometer 50°.] Moon's app. alt. Horizontal parallax. Correction for seconds of parallax.— Add. Corr. for minutes 64' 66' 66' 67' 58' 59' 60' 61' 0" 2" 4" 6" 8" of alt. O ' ' // » II > II ' II 1 II » II ' II ' II II // II II II II 50 33 54 34 33 35 11 35 50 36 29 37 8 37 46 38 25 1 3 4 5 10 47 26 4 43 21 38 17 10 6 8 9 10 12 20 40 19 84 57 36 14 36 53 31 9 20 13 14 15 17 18 30 33 11 49 28 6 45 23 1 30 19 20 22 23 24 40 26 4 42 20 35 58 37 15 37 53 40 26 27 28 29 31 50 19 33 57 35 34 28 13 35 6 51 29 7 45 50 32 33 35 36 4 37 5 Sub. 51 33 12 33 50 35 44 36 22 36 59 37 37 1 3 10 5 43 21 34 58 36 14 51 29 10 6 8 9 10 11 2 1 20 32 58 36 13 50 28 6 43 21 20 13 14 15 16 18 3 2 30 51 29 6 43 21 35 58 36 13 30 19 20 21 23 24 4 3 40 44 22 33 59 36 14 50 28 5 40 25 26 28 29 30 6 4 50 37 14 33 7 51 28 6 42 20 36 57 50 31 33 1 34 2 35 4 36 5 6 4 7 5 52 32 50 33 44 34 21 34 58 36 35 36 12 36 49 10 23 36 13 50 27 4 41 10 6 7 9 10 11 8 6 20 15 32 52 29 6 43 19 35 56 33 20 12 13 15 16 17 9 6 30 8 45 21 33 58 35 11 48 24 30 18 20 21 22 23 40 1 38 14 50 27 3 40 16 40 24 26 27 28 29 50 31 54 31 7 43 33 35 19 34 11 34 55 32 8 36 50 31 32 1 33 2 34 4 35 5 53 31 47 32 23 32 59 34 47 35 24 10 39 15 51 27 3 39 15 35 51 10 6 7- 8 10 11 20 32 8 44 20 33 56 31 7 43 20 12 13 14 16 17 30 25 36 12 48 23 34 59 35 30 18 19 20 22 23 40 17 31 53 28 4 40 15 51 27 40 24 25 26 28 29 50 10 46 21 32 57 32 33 24 7 43 34 35 19 50 30 31 32 2 34 4 35 6 54 31 3 31 38 32 13 32 49 33 59 35 10 1 10 30 55 30 5 41 16 51 26 1 10 6 7 8 9 11 20 48 22 31 57 33 8 43 18 34 53 20 12 13 14 15 16 30 40 15 49 25 35 10 45 30 18 19 20 21 22 40 33 8 42 17 32 52 27 1 37 40 23 25 26 27 28 50 26 35 9 44 19 33 53 28 50 29 30 1 32 2 33 3 34 5 55 30 18 30 52 31 27 32 1 32 36 33 10 33 45 34 19 10 10 45 19 31 53 28 2 36 11 10 6 7 8 9 10 20 3 38 12 46 20 32 54 28 3 20 11 13 14 15 16 30 29 55 30 4 38 12 46 20 33 54 30 17 18 19 20 22 40 48 22 30 56 30 4 37 11 45 40 23 24 25 26 27 50 66 40 14 48 22 31 55 29 3 37 50 28 30 1 31 2 32 3 33 4 29 33 30 7 30 40 31 14 31 47 32 21 32 55 33 28 10 25 29 59 32 6 39 13 46 20 10 6 7 8 9 10 20 18 51 24 30 58 31 4 37 11 20 11 12 13 14 16 30 10 43 16 60 23 31 56 29 2 30 17 18 19 20 21 1 1 40 3 36 9 42 16 48 21 32 64 40 22 23 24 25 27 2 2 50 28 55 28 1 34 7 40 12 32 3 46 50 28 29 1 30 2 31 3 32 4 3 2 4 3 57 28 47 29 20 29 53 30 25 30 58 31 31 32 36 10 39 12 45 17 50 22 31 55 27 10 6 6 7 9 10 5 4 20 32 5 37 9 42 14 47 19 20 11 12 13 14 16 6 6 30 24 28 57 29 1 33 6 38 10 30 16 17 18 19 21 7 5 40 17 49 21 29 53 25 30 67 29 1 40 22 23 24 25 26 8 6 50 9 41 13 45 17 49 21 3162 50 27 28 1 29 2 30 3 31 4 9 7 58 28 1 28 33 29 5 29 37 30 9 30 41 31 12 3144 10 27 53 25 28 57 28 32 4 35 10 5 6 7 8 9 20 45 17 49 20 29 52 23 30 55 26 20 10 12 13 14 16 30 38 9 41 12 44 15 46 17 30 16 17 18 19 20 40 30 1 33 4 1 35 6 38 9 40 21 22 23 24 26 50 .22 27 14 27 53 24 28 55 27 29 58 29 30 20 30 61 60 26 27 1 28 2 29 3 30 4 59 27 45 28 16 28 47 29 18 29 49 10 6 37 7 38 9 40 11 42 10 5 6 7 8 9 20 26 58 29 27 59 30 1 31 2 33 20 1 10 11 12 13 14 30 51 21 51 22 28 53 23 29 54 24 30 15 16 17 18 19 40 43 13 43 14 44 14 45 16 40 20 21 22 23 24 50 35 5 35 5 36 6 36 6| 50 25 26 27 29 30 TABLE 24. [Page 699 Correction of the Moon's Apparent Altitude for Parallax and Refraction, [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] Moon's spp. alt. Horizontal parallax. §2 Correction for seconds of parallax. — Add. Corr. for minutes 54' 65' 56' 57' 58' 59' 60' 61' 1^ 0" 2" II 4" II 6" II 8" n of alt. / ' n / // t II ' // 1 II 1 II ' II r II II 60 26 26 26 57 27 27 27 57 28 27 28 57 29 27 29 57 1 2 3 4 10 19 49 19 49 19 49 18 48 10 5 6 7 8 9 20 11 41 11 40 10 40 9 39 20 10 11 12 13 14 30 3 32 2 31 1 31 30 30 15 16 17 18 19 40 25 55 24 26 53 23 27 53 22 28 51 21 40 20 21 22 23 24 50 47 16 45 14 44 13 42 12 50 25 26 1 27 2 28 3 29 4 61 25 39 26 8 26 37 27 6 27 36 28 5 28 34 29 3 10 31 29 26 58 27 27 56 25 28 54 10 5 6 7 8 9 20 23 25 52 20 49 18 47 16 45 20 10 11 12 12 13 30 15 43 12 40 10 38 7 35 30 14 15 16 17 18 40 7 35 4 32 1 29 27 58 26 40 19 20 21 22 23 50 24 59 27 25 55 24 26 52 20 49 17 28 8 50 24 25 1 26 2 27 3 28 4 62 24 50 25 19 25 47 26 15 26 43 27 11 27 40 10 42 10 38 6 34 2 30 27 58 10 5 6 6 7 8 20 34 2 29 25 57 25 26 53 21 49 20 9 10 11 12 12 30 26 24 54 21 49 17 45 12 40 30 14 15 16 17 18 40 18 46 13 41 8 36 3 31 40 19 19 20 21 22 50 10 37 4 32 25 59 27 26 54 21 50 23 24 1 25 2 26 3 27 4 63 24 2 24 29 24 56 25 23 25 51 26 18 26 45 27 12 10 23 54 21 48 15 42 9 36 3 10 4 5 6 7 8 20 46 13 39 6 33 27 26 54 20 9 10 11 12 13 30 37 4 31 24 58 24 25 51 18 45 30 13 14 15 16 17 40 29 23 55 22 49 15 42 8 35 40 18 19 20 21 22 50 20 47 13 40 6 33 25 59 26 50 22 23 1 24 2 25 26 64 23 12 23 39 24 5 24 32 24 58 25 24 25 50 26 17 3 3 10 4 31 23 57 23 49 15 41 8 10 4 5 6 7 8 20 22 56 22 48 14 40 6 32 25 58 20 9 10 10 11 12 30 47 13 39 5 31 24 57 22 48 30 13 14 15 16 16 40 39 5 30 23 56 22 48 13 39 40 17 18 19 20 21 50 31 22 57 22 48 13 24 4 39 4 30 50 22 23 1 23 2 24 2 25 3 Sub. 65 22 23 22 48 23 13 23 39 24 30 24 55 25 21 10 14 40 5 30 23 55 20 46 11 10 4 5 6 7 7 V V 20 6 31 22 56 21 46 11 36 1 20 8 9 10 11 12 2 2 30 21 58 23 48 13 37 2 27 24 52 30 13 13 14 15 16 3 3 40 49 14 39 4 28 23 53 18 43 40 17 18 18 19 20 4 4 50 66 41 6 30 22 55 19 23 10 44 8 33 50 21 22 23 2 23 2 24 3 5 5 6 5 21 32 21 57 22 21 22 46 23 35 23 59 24 23 1 10 24 48 12 37 1 25 49 14 10 4 5 6 7 7 7 6 20 15 39 3 28 22 52 15 40 4 20 8 9 10 11 11 8 7 30 7 31 21 55 19 43 6 31 23 55 30 12 13 14 15 16 9 8 40 20 59 22 46 10 34 22 57 21 45 40 16 17 18 19 20 50 50 14 37 1 25 48 12 36 50 20 21 1 22 2 23 2 24 3 67 20 41 21 5 21 28 21 52 22 15 22 39 23 2 23 26 10 33 20 56 19 43 6 29 22 52 16 10 4 5 5 6 7 20 25 48 11 34 21 57 20 43 7 20 8 8 9 10 11 30 16 39 2 25 48 11 34 22 57 30 12 12 13 14 15 40 8 30 20 53 16 39 2 24 47 40 15 16 17 18 18 50 19 59 21 44 7 30 21 52 15 37 50 19 20 1 21 1 22 2 22 3 68 19 50 20 13 20 35 20 58 21 21 21 43 22 5 22 28 10 42 4 27 49 12 34 21 56 19 10 4 4 5 6 7 20 33 19 56 18 40 2 24 47 9 20 7 8 9 9 10 30 25 47 9 31 20 53 15 37 21 59 30 11 12 13 13 14 40 16 38 22 44 5 27 49 40 15 16 16 17 18 50 7 29 19 51 13 34 20 56 17 21 8 39 50 18 19 1 20 1 21 2 21 3 69 18 59 19 21 19 42 20 4 20 25 20 47 21 30 10 50 12 33 19 55 16 37 20 59 20 10 4 4 5 6 6 r 20 42 3 24 45 7 28 49 10 20 7 8 8 9 10 30 33 18 54 15 36 19 57 18 39 30 11 11 12 13 13 40 24 45 6 27 48 9 29 20 50 40 14 15 15 16 17 50 16 37 18 57 18 39 20 41 50 18 18 19 20 20 Page 700] TABLE 24. Correction of the Moon's Apparent Altitude for Parallax and Kefraction. [Barometer 30 inches. — Fahrenheit's Thermometer 50°.] Moon's Horizontal parallax. Correction for seconds of parallax.— Add. Corr. for app. alt. minutes of alt. 64' 65' 66' 67' 68' 59' 60' 61' 0" 2" 4" 6" 8" o / / // / II ' II ' II / // / // ' II II // II II II II 70 18 7 18 28 18 48 19 9 19 30 19 60 20 11 20 31 1 1 2 3 10 17 58 19 39 20 41 1 21 10 3 4 5 5 6 20 50 10 30 18 50 11 31 19 61 11 20 7 7 8 9 9 30 41 1 21 41 1 21 41 1 30 10 11 11 12 13 40 32 17 53 12 32 18 52 12 32 19 52 40 13 14 15 15 16 50 24 44 17 35 3 23 43 3 18 53 22 19 12 42 50 17 17 1 18 1 19 2 19 3 71 17 15 17 54 18 14 18 34 19 32 10 6 26 45 5 24 43 3 22 10 3 4 4 5 6 20 16 57 17 36 17 55 14 33 18 53 12 20 6 7 8 8 9 30 48 8 27 46 5 24 43 2 30 10 10 11 12 12 40 40 16 59 18 37 17 56 15 34 18 52 40 13 13 14 16 16 50 31 50 9 28 47 5 24 42 50 16 17 17 18 19 72 16 22 16 41 17 17 18 17 37 17 55 18 14 18 32 1 1 2 2 10 13 32 16 50 9 27 46 4 22 10 3 4 4 6 6 . 20 5 23 41 16 59 18 36 17 54 12 20 6 7 7 8 8 30 15 57 14 32 50 9 27 46 3 30 9 10 10 11 n 40 48 5 23 41 16 59 17 35 17 63 40 12 13 13 14 14 50 39 15 56 14 32 50 16 40 7 25 43 50 16 16 1 16 1 17 2 18 2 73 15 30 15 47 16 5 16 22 16 58 17 16 17 33 10 21 38 15 56 13 30 48 6 23 10 3 3 4 6 5 20 12 29 47 4 21 39 16 66 13 20 6 6 7 7 8 30 3 20 37 15 55 12 29 46 3 30 9 9 10 10 11 40 14 54 11 28 45 2 19 36 16 63 40 11 12 13 13 14 50 45 2 19 35 15 52 9 26 16 16 42 50 14 15 15 16 2 17 2 Sub. 74 14 36 14 53 15 9 15 26 15 42 15 59 16 32 1 1 10 28 44 17 33 49 6 22 10 3 3 4 4 5 V V 20 19 35 14 51 8 24 40 16 66 12 20 6 6 6 7 8 2 2 30 10 26 42 14 58 14 30 46 2 30 8 9 9 10 11 3 3 40 1 17 33 49 5 20 36 15 62 40 11 11 12 12 13 4 4 50 13 52 8 23 39 14 65 10 26 42 50 13 14 1 14 1 15 2 16 2 5 6 6 6 75 13 43 13 59 14 14 14 29 14 45 16 1 15 ]6 15 32 10 34 50 5 20 36 14 52 7 22 10 3 3 4 4 5 7 7 20 25 41 13 56 11 27 42 14 57 12 20 6 6 6 7 7 8 8 30 16 32 46 1 17 32 47 2 30 8 8 9 9 10 9 9 40 7 22 37 13 52 7 22 37 14 51 40 10 11 11 12 12 50 12 58 13 28 42 13 67 12 27 41 50 13 13 14 1 14 1 16 2 76 12 49 13 4 13 18 13 33 13 47 14 2 14 17 14 31 10 41 12 55 9 24 38 13 53 7 21 10 2 3 3 4 4 20 32 46 14 28 43 13 57 11 20 6 6 6 6 7 30 23 37 12 51 5 19 33 47 1 30 7 8 8 8 9 40 14 27 41 12 55 9 23 36 13 50 40 9 10 10 n 11 50 5 18 32 45 12 69 13 26 40 60 12 12 13 1 13 1 14 2 77 11 56 12 9 12 22 12 36 12 49 13 3 13 16 13 30 10 47 13 27 40 12 63 7 20 10 2 3 3 4 4 20 38 11 51 4 17 30 43 12 57 10 20 4 5 6 6 6 30 29 42 11 55 8 21 33 47 30 7 7 7 8 8 40 19 32 45 11 58 11 23 36 12 49 40 9 9 9 10 10 50 10 23 35 48 1 13 26 12 16 39 50 11 11 12 12 13 2 78 11 1 11 14 11 26 11 39 11 52 12 4 12 29 1 1 10 10 52 5 17 30 42 11 54 6 19 10 2 2 3 3 4 20 43 10 65 8 20 32 44 11 66 8 20 4 4 5 5 6 30 34 46 10 58 10 22 34 46 11 58 30 6 6 7 7 8 40 25 37 48 12 24 36 48 40 8 8 9 9 10 50 16 28 39 10 51 3 15 26 38 50 10 10 11 11 12 79 10 7 10 19 10 30 10 42 10 63 11 5 11 16 11 28 1 1 1 10 9 58 9 21 32 43 10 66 6 17 10 2 2 3 3 3 20 49 11 22 33 44 10 56 7 20 4 4 4 5 5 30 40 9 50 1 12 23 34 45 10 66 30 6 6 6 7 7 40 31 41 9 52 3 13 24 35 46 40 7 8 8 8 9 50 22 32 43 9 54 4 15 25 36 50 9 10 10 10 11 TABLE 24. [Page 701 1 Correction of the Moon's Apparent Altitude for Parallax and Refraction. [Barometer 30 inches.— Fahrenheit's Thermometer 50°.] Moon's app. alt. Horizontal parallax. Is 11 Correction for seconds of parallax. — Add. Corr. for minutes 54' 65' 56' 57' 58' 6^ ec 61' 0" 2" 4" 6" 8" of alt. O / ' n / // / n / // t II / // / II ' II II II II u II II 80 9 13 9 23 9 34 9 44 9 55 10 5 10 15 10 26 1 1 1 10 3 14 24 34 45 9 55 5 15 10 2 2 2 3 3 20 8 54 4 14 24 35 45 9 65 5 20 3 4 4 4 5 30 45 8 55 5 15 25 35 45 9 54 30 5 6 6 6 6 40 36 46 8 55 5 15 25 35 44 40 7 7 7 8 8 50 27 37 46 8 56 6 15 26 34 50 8 9 9 1 9 1 10 1 81 8 18 8 27 8 37 8 46 8 56 9 5 9 14 9 24 10 9 18 27 36 46 8 55 4 13 10 1 2 2 2 3 20 7 59 8 17 26 36 45 8 54 3 20 3 3 4 4 4 30 50 7 59 8 17 26 35 44 8 52 30 4 6 5 6 6 40 41 50 7 59 8 17 25 34 42 40 6 6 6 7 7 50 32 41 7 31 49 7 58 7 15 24 32 50 7 8 8 1 8 1 9 1 82 7 23 7 40 7 48 7 57 8 5 8 13 8 22 10 14 22 30 38 47 7 55 3 11 10 1 2 2 2 2 20 4 12 20 28 37 46 7 62 20 3 3 3 3 4 30 6 55 3 11 19 27 36 42 7 60 30 4 4 6 5 6 40 46 6 54 2 10 17 25 32 40 40 6 6 6 6 6 50 37 45 6 52 7 15 22 30 60 7 7 7 7 1 8 1 Sub. 83 6 28 6 35 6 43 6 50 6 57 7 6 7 12 7 20 10 19 26 33 40 47 6 64 2 9 10 1 1 2 2 2 V V' 20 9 16 23 30 37 44 6 61 6 68 20 2 3 3 3 3 2 2 30 7 13 20 27 34 41 48 30 3 4 4 4 4 3 3 40 5 51 5 58 4 11 18 24 31 38 40 5 6 5 5 6 4 4 50 42 49 5 55 1 8 14 21 27 60 6 6 6 6 1 7 1 5 5 6 6 84 5 33 5 39 5 45 5 52 5 58 6 4 6 10 6 17 10 23 30 36 42 48 5 54 6 10 1 1 1 2 2 7 7 20 14 20 26 32 38 44 5 60 6 55 20 2 2 2 3 3 8 8 30 5 10 16 22 28 34 39 45 30 3 3 3 3 4 9 9 40 4 56 1 7 13 18 24 29 35 40 4 4 4 4 5 50 47 4 52 4 58 3 8 14 19 26 60 5 6 6 5 6 85 4 37 4 43 4 48 4 53 4 58 5 4 5 9 6 14 1 10 28 33 38 43 48 4 53 4 68 3 10 1 1 1 1 1 20 18 24 28 33 38 43 48 4 53 20 2 2 2 2 2 30 9 14 19 23 28 33 38 43 30 2 3 3 3 3 40 5 10 14 19 23 28 33 40 3 3 4 4 4 50 3 51 3 56 5 9 13 18 22 50 4 4 4 6 5 1 86 3 42 3 46 3 50 3 55 3 59 4 3 4 7 4 11 10 33 37 41 45 49 3 53 3 67 1 10 1 1 1 1 1 20 23 27 31 35 39 43 46 3 60 20 1 1 2 2 2 30 14 18 21 25 29 33 36 40 30 2 2 2 2 2 40 5 9 12 16 19 23 26 30 40 3 3 3 3 3 50 2 56 2 59 3 6 9 13 16 19 50 3 3 3 4 4 87 2 47 2 50 2 53 2 56 2 59 3 2 3 5 3 9 10 37 40 43 46 49 2 52 2 55 2 58 10 1 1 1 1 20 28 31 33 36 39 42 45 47 20 1 1 1 1 1 30 19 21 24 26 29 32 34 37 30 1 1 2 2 2 40 10 12 15 17 19 22 24 27 40 2 2 2 2 2 50 1 3 5 7 9 12 14 16 50 2 2 2 3 3 88 1 51 1 53 1 55 1 67 1 59 2 2 2 4 2 6 10 42 43 45 47 49 1 61 1 63 1 55 10 20 32 34 36 38 39 41 43 44 20 1 1 1 1 1 30 23 25 26 28 29 31 32 34 30 1 1 1 1 1 40 14 15 16 19 20 21 22 24 40 1 1 1 1 1 50 5 6 7 9 10 11 12 13 60 1 1 1 2 2 89 56 57 58 59 1 1 1 1 2 1 3 10 46 47 48 49 50 51 51 52 10 20 37 37 38 39 40 40 41 42 20 30 28 28 28 29 30 30 31 31 30 40 19 19 19 19 20 20 21 21 40 50 9 10 10 10 10 10 10 10 60 1 1 1 1 1 Page 702] TABLE 25. Table showing the variation of the altitude of an object arising from a change of 100 seconds in the declination. Unmarked quantities in the Table are positive. If the change move the body toward the elevated pole, apply the correction to the altitude with the signs m the Table; otherwise, change the Signs. a o 'S .g 1 o 3 < Latitude of same name as declination. Latitude of different name from declination. % < d o .g 1 70° 60° 50° 40° 30° 20° 10° 0° 10° 20° 80° 40° 50° 60° 70° o „ // II „ II „ II II „ „ „ II II II „ o 94 87 76 64 50 34 17 17 34 50 64 76 87 94 10 95 88 78 65 51 35 18 18 35 51 65 78 88 95 10 20 100 92 82 68 53 36 18 18 36 53 68 82 92 100 20 30 100 88 74 57 39 20 20 39 57 74 88 100 30 40 100 84 65 45 22 22 45 65 84 100 40 50 100 78 53 27 27 53 78 100 50 60 100 68 35 35 68 100 60 70 100 51 51 100 70 94 87 77 64 50 34 17 17 34 50 64 77 87 94 10 95 87 77 65 50 34 17 - 1 18 35 51 66 78 88 96 10 20 99 91 81 67 52 35 17 - 1 19 37 54 69 83 93 101 20 30 107 98 87 73 56 38 18 - 2 22 41 59 76 90 102 30 2 40 111 98 82 63 42 20 - 2 25 47 68 86 102 40 2 50 116 97 74 50 24 - 3 30 57 81 103 50 60 124 95 64 30 - 5 40 73 103 60 70 139 92 34 43 17 - 8 59 108 70 94 87 77 64 50 17 34 50 64 77 87 94 10 94 87 77 64 50 34 16 — 1 19 36 52 67 79 89 97 10 20 98 90 79 66 51 34 16 - 3 21 39 56 71 84 95 103 20 30 105 96 85 70 54 36 16 - 4 24 44 62 78 93 104 • 30 4 40 107 94 78 59 39 17 - 6 29 51 71 90 106 40 4 50 111 92 70 45 19 - 8 35 62 86 109 50 1 60 117 88 56 23 -12 47 81 112 60 70 127 81 32 -19 70 17 119 65 70 94 87 77 65 50 34 17 34 50 77 87 94 10 94 87 76 64 49 33 16 - 2 20 37 53 67 80 90 98 10 20 97 89 78 65 50 33 15 - 4 22 40 57 73 86 96 104 20 30 103 94 83 69 52 34 14 - 6 26 46 64 81 95 107 30 6 40 105 92 76 57 36 14 - 9 32 54 74 93 109 40 6 50 107 88 66 41 15 -13 40 66 91 113 50 60 111 82 51 17 -18 53 87 119 60 70 118 72 22 -29 80 129 70 95 87 77 65 50 35 18 18 35 50 65 77 87 95 10 94 86 76 63 49 33 15 - 3 20 38 54 68 81 91 99 10 20 96 88 77 64 49 32 14 - 5 24 40 59 74 87 98 106 20 30 101 93 81 67 50 32 12 - 8 28 48 66 83 97 109 30 8 40 102 89 73 54 33 11 -12 35 57 78 97 113 40 8 50 104 84 62 37 11 -17 44 70 95 118 50 60 105 77 45 11 -24 59 93 125 60 70 109 62 13 -39 90 140 70 95 88 78 65 51 35 18 18 35 51 65 78 88 '95 10 94 86 75 63 48 32 15 - 3 21 38 55 69 82 92 100 10 20 95 87 76 63 48 31 12 - 6 25 43 60 76 89 100 20 30 100 91 80 65 49 30 10 -10 30 50 69 86 100 30 10 40 100 87 70 51 31 8 -15 38 60 81 100 40 10 50 . 100 81 58 33 6 -21 48 75 100 50 60 100 71 39 5 -31 66 100 60 70 66 100 51 53 35 3 18 -48 100 18 35 51 96 70 96 89 78 66 78 89 10 94 86 76 63 48 32 14 — 4 22 39 56 70 83 94 101 10 20 94 86 76 62 47 29 11 - 8 27 45 62 78 91 102 20 30 99 90 78 64 47 28 8 -12 33 53 71 88 103 30 12 40 108 98 84 68 49 28 5 -18 41 63 85 104 40 12 50 112 97 77 54 29 2 -25 53 80 105 50 60 120 95 65 33 —1 -37 72 107 60 70 134 91 44 -6 -58 110 70 j 0) 3 3 70° 60° 50° 40= 80° 20° 10° 0° 10° 20° 80° 40° 50° 60° 70° 3 o 1 I latitude of same nam e as c ecllnal ion. Latitude of differen t name from < leclina tion. < < o TABLE 25. [Page 703 1 Table showing the variation of the altitude of an object arising from a change of 100 seconds in the declination. Unmarked quantities in the Table are positive. If the change move the body toward the elevated pole, apply the correction to the altitude with the signs in the Table; otherwise, c bange the signs. 1 § Latitude of same name as declination. Latitude of different name from declination. a o 1 ft •0 1 i a < 70° 60° 60° 40° 80° 20° 10° 0° 10° 20° 80° 40° 50° 60° 70° ^ ft o o H II II II II II II II II II II II II II II o o 97 89 79 66 52 35 18 18 36 62 66 79 89 97 10 94 86 76 63 48 31 14 - 4 23 40 57 72 85 95 103 10 20 94 86 75 61 46 27 10 - 9 28 45 64 80 93 104 20 30 97 89 77 62 45 26 6 - 14 35 55 74 91 106 30 14 40 106 96 82 66 46 25 2 - 21 44 67 88 107 40 14 50 109 93 73 50 25 - 2 - 30 58 85 110 50 60 115 89 60 27 - 7 - 43 79 114 60 70 125 82 35 -16 - 69 121 18 36 70 98 90 80 67 52 36 18 52 67 80 90 98 10 94 86 76 63 48 31 13 - 5 23 41 68 73 86 97 104 10 20 94 85 74 61 45 27 9 - 10 30 48 66 82 96 106 20 80 96 87 75 61 44 25 4 - 17 37 58 77 94 109 30 16 40 104 94 80 63 44 22 - 24 48 70 92 111 40 16 50 106 90 70 47 21 - 6 - 34 62 90 115 50 60 110 84 54 21 -14 - 50 86 121 60 70 117 73 25 -26 - 79 132 18 36 70 99 91 81 68 53 36 18 53 68 81 91 99 10 95 87 76 63 48 31 13 - 6 24 42 59 74 88 98 106 10 20 93 85 74 60 44 26 8 - 12 31 50 68 84 98 109 20 30 95 86 74 59 42 23 2 - 19 40 60 79 97 112 30 18 40 102 92 78 61 41 20 - 3 - 27 51 74 96 116 40 18 50 103 87 66 43 17 -10 - 39 67 96 121 50 60 106 79 49 16 -20 - 56 93 128 60 70 100 108 64 16 -36 - 89 143 70 92 82 68 53 36 18 18 36 53 68 82 92 100 10 95 87 76 63 48 31 12 - 6 25 43 60 76 89 100 10 20 93 85 74 60 43 25 6 - 13 33 52 70 86 100 20 30 94 85 73 58 40 21 - 21 42 63 82 100 30 20 40 100 90 76 59 39 17 - 6 - 31 55 78 100 40 20 50 100 83 63 39 13 -15 - 43 72 100 50 60 100 74 43 10 -26 - 63 100 60 70 100 56 6 -46 -100 69 70 93 83 69 54 37 19 19 37 64 83 93 101 10 96 88 77 63 48 30 12 - 7 26 45 62 78 91 102 10 20 93 85 73 59 43 25 5 - 15 35 54 72 88 103 20 30 94 85 72 57 39 19 - 2 - 23 46 66 86 103 30 22 40 98 88 74 57 36 14 - 9 - 34 58 82 104 40 22 50 110 97 80 60 36 9 -19 - 48 77 106 bO 60 117 95 68 38 4 -33 - 70 107 60 1 70 131 92 47 - 3 -56 -111 70 95 84 70 55 37 19 19 37 56 70 84 96 103 10 97 88 77 64 48 30 11 - 8 27 46 63 79 93 104 10 20 93 85 73 59 42 24 4 - 16 36 56 74 91 106 20 30 93 84 71 56 38 18 - 4 - 26 48 69 89 107 30 24 40 97 86 72 54 34 12 -12 - 37 62 86 109 40 24 50 107 93 77 56 32 5 -23 - 53 83 111 50 60 112 91 64 32 - 2 -39 - 77 115 60 70 123 83 38 -13 -67 -122 vo 96 85 72 56 38 19 19 38 66 72 85 96 105 10 98 89 78 64 48 30 11 - 9 28 47 66 81 96 106 10 20 95 85 73 59 41 23 3 - 18 38 68 77 94 108 20 30 93 83 70 54 36 16 - 6 - 28 50 72 92 111 30 26 40 96 85 70 52 32 9 -16 - 41 66 91 114 40 26 50 105 92 74 53 28 1 -28 - 58 88 117 bO 60 108 86 58 27 - 8 -46 - 84 123 60 70 115 75 29 -23 -78 -134 VO 1 B "3 § a 1 70° 60° 50° 40° 80° 20° 10° 0° 10° 20° 30° 40° 60° 60° 70° •3 declinatioa. Latitude of dififerent name from declination. ft < < ft 21594°— 14- -38 Page 704] TABLE 26. Variation of Altitude in one minute from meridian passage Lati- tude. Declination of the same name as the latitude; upper transit; reduction additlre. Lati- tude. 0° 1° 2° 8° 4° 6° 6° JO 8° 9° \W> 11° o II ;/ II II II II II // n // II II o 28.1 22.4 18.7 16.0 14.0 12.4 11.1 10.1 1 28.0 22.4 18.6 16.0 13.9 12.4 11.1 1 2 28.0 22.3 18.6 15.9 13.9 12.3 2 3 27.9 22.3 18.6 15.8 13.8 3 4 28.1 27.8 22.2 18.5 15.8 4 5 22.4 28.0 27.7 22.1 18.4 5 6 18.7 22.4 28.0 27.6 22.0 6 7 16.0 18.6 22.3 27.9 27.4 7 8 14.0 16.0 18.6 22.3 27.8 8 9 12.4 13.9 15.9 18.5 22.2 27.7 9 10 11.1 12.4 13.9 15.8 18.6 22.1 27.6 10 11 10.1 11.1 12.3 13.8 16.8 18.4 22.0 27.4 11 12 9.2 10.1 11.1 12.3 13.8 16.7 18.3 21.9 27.3 12 13 8.5 9.2 10.0 11.0 12.2 13.7 15.6 18.2 21.7 27.1 13 14 7.9 8.6 9.2 10.0 10.9 12.1 13.6 15.6 18.0 21.6 26.9 21.4 14 15 7.3 7.8 8.4 9.1 9.9 10.9 12.1 13.6 16.4 17.9 26.7 15 16 6.8 7.3 7.8 8.4 9.1 9.8 10.8 12.0 13.4 16.3 17.8 21.3 16 17 6.4 6.8 7.2 7.8 8.3 9.0 9.8 10.7 11.9 13.3 15.2 17.6 17 18 6.0 6.4 6.8 7.2 7.7 8.3 8.9 9.7 10.6 11.8 13.2 16.0 18 19 5.7 6.0 6.3 6.7 7.2 7.6 8.2 8.9 9.6 10.6 11.7 13.1 19 20 6.4 6.7 6.0 6.3 6.7 7.1 7.6 8.1 8.8 9.5 10.5 11.6 20 21 6.1 5.4 6.6 6.9 6.3 6.6 7.0 7.6 8.1 8.7 9.5 10.4 21 22 4.9 5.1 5.3 6.6 6.9 6.2 6.6 7.0 7.5 8.0 8.6 9.4 22 23 4.6 4.8 6.0 5.3 6.5 6.8 6.1 6.5 6.9 7.4 7.9 8.6 23 24 4.4 4.6 4.8 5.0 5.2 6.5 5.8 6.1 6.4 6.8 7.3 7.8 24 25 4.2 4.4 4.6 4.7 6.0 5.2 5.4 6.7 6.0 6.4 6.8 7.2 26 26 4.0 4.2 4.3 4.5 4.7 4.9 6.1 6.4 5.7 6.0 6.3 6.7 26 27 3.9 4.0 4.1 4.3 4.6 4.7 4.9 5.1 5.3 5.6 5.9 6.2 27 28 3.7 3.8 4.0 4.1 4.3 4.4 4.6 4.8 6.0 5.3 6.5 5.8 28 29 3.5 3.7 3.8 3.9 4.1 4.2 4.4 4.2 4.6 4.7 5.0 5.2 5.5 29 30 3.4 3.5 3.6 3.7 3.9 4.0 4.3 4.6 4.7 4.9 5.1 30 31 3.3 3.4 3.5 3.6 3.7 3.8 4.0 4.1 4.3 4.4 4.6 4.8 31 32 3.1 3.2 3.3 3.4 3.5 3.7 3.8 3.9 4.1 4.2 4.4 4.6 32 33 3.0 3.1 3.2 3.3 .3.4 3.5 3.6 3.7 3.9 4.0 4.2 4.3 33 34 2.9 3.0 3.1 3.2 3.2 3.3 3.4 3.6 3.7 3.8 3.9 4.1 3.9 34 35 35 2.8 2.9 3.0 3.0 3.1 3.2 3.3 3.4 3.6 3.6 3.7 36 2.7 2.8 2.8 2,9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 36 37 2.6 2.7 2.7 2.8 2.9 2.9 3.0 3.1 3.2 3.3 3.4 3.5 37 38 2.6 2.6 2.6 2.7 2.8 2.8 2.9 3.0 3.0 3.2 3.2 3.3 38 39 2.4 2.5 2.5 2.6 2.7 2.7 2.8 2.9 2.9 3.0 3.1 3.2 39 40 2.3 2.4 2.4 2.5 2.6 2.6 2.7 2.7 2.8 2.9 3.0 3.0 40 41 2.3 2.3 2.4 2.4 2.5 2.5 2.6 2.6 2.7 2.8 2.8 2.9 41 42 2.2 2.2 2.3 2.3 2.4 2.4 2.6 2.5 2.6 2.6 2.7 2.8 42 43 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5 2.6 2.7 43 44 2.0 2.1 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.5 44 45 2.0 2.0 2.0 2.1 2.1 2.2 2.2 2.2 2.3 2.3 2.4 2.4 46 46 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.2 2.2 2.2 2.3 2.3 46 47 1.8 1.9 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.1 2.2 2.2 47 48 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.1 48 49 1.7 1.7 1.8 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.1 49 50 1.6 1.7 1.7 1.7 1.8 1.8 1.8 1.8 1.9 1.9 1.9 2.0 60 51 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 51 62 1.5 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.8 52 53 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 53 54 1.4 1.4 1.6 1.5 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.7 54 55 1.4 1.4 1.4 1.4 1.5 1.6 1.5 1.5 1.5 1.6 1.6 1.6 65 56 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.6 1.6 1.6 1.5 56 57 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.4 1.5 67 58 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.4 1.4 1.4 68 59 1.2 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 69 60 1.1 1.1 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.3 1.3 60 0° 1° 2° 8° 4° 5° 6° 7° 8° 9° 10° 11° De clinatioi 1 of the same nan le as the latitude; upper tra asit; redu ction add Itlre. TABLE 26. (Page 706 Variation of Altitude in one minute from meridian passage. Lati- tade. Declination of the same name aa the latitude; upper transit ; reduction additive. Lati- tude. 12° 18° 14° 16° 16° 17° 18° 19° 20° 21° 22° 28° 24° o // H „ // // II II // // // II It „ o 9.2 8.5 7.9 7.3 6.8 6.4 6.0 5.7 5.4 5.1 4.9 4.6 4.4 1 10.1 9.2 8.5 7.8 7.3 6.8 6.4 6.0 5.7 5.4 5.1 4.8 4.6 1 2 11.1 10.0 9.2 8.4 7.8 7.2 6.8 6.3 6.0 5.6 5.3 5.0 4.8 2 3 12.3 11.0 10.0 9.1 8.4 7.8 7.2 6.7 6.3 5.9 5.6 5.3 5.0 3 4 13.8 12.2 10.9 9.9 9.1 8.3 7.7 7.2 6.7 6.3 5.9 5.5 5.2 4 5 15.7 13.7 12.1 10.9 9.8 9.0 8.3 7.6 7.1 6.6 6.2 5.8 5.5 5 6 18.3 15.6 13.6 12.1 10.8 9.8 8.9 8.2 7.6 7.0 6.6 6.1 5.8 6 7 21.9 18.2 15.5 13.5 12.0 10.7 9.7 8.9 8.1 7.5 7.0 6.5 6.1 7 8 27.3 21.7 18.0 15.4 13.4 11.9 10.6 9.6 8.8 8.1 7.5 6.9 6.4 8 9 27.1 21.6 17.9 15.3 13.3 11.8 10.6 11.7 9.5 8.7 8.0 7.4 6.8 9 10 10 26.9 21.4 17.8 15.2 13.2 10.5 9.5 8.6 7.9 7.3 11 26.7 21.3 17.6 15.0 13.1 11.6 10.4 9.4 8.5 7.8 11 12 26.5 21.1 17.5 14.9 13.0 11.5 10.3 9.3 8.4 12 13 26.2 20.9 17.3 14.8 12.8 11.3 10.1 9.2 13 14 26.0 20.7 17.1 14.6 12.7 11.2 10.0 14 15 25.7 20.4 16.9 14.4 12.5 11.1 15 16 26.5 25.4 20.2 16.7 14.3 12.4 16 17 21.1 26.2 25.1 20.0 16.5 14.1 17 18 17.5 20.9 26.0 24.8 19.7 16.3 18 19 14.9 17.3 20.7 25.7 24.5 19.5 19 20 13.0 14.8 17.1 20.4 25.4 24.2 20 21 11.5 12.8 14.6 16.9 20.2 25.1 21 22 10.3 11.3 12.7 14.4 16.7 20.0 24.8 22 23 9.3 10.1 11.2 12.5 14.3 16.5 19.7 24.5 23 24 8.4 9.2 10.0 11.1 12.4 14.1 16.3 19.5 24.2 24 25 7.7 8.3 9.0 9.9 10.9 12.2 13.9 16.1 19.2 23.8 25 26 7.1 7.6 8.2 8.9 9.8 10.8 12.1 13.7 15.9 18.9 23.5 26 27 6.6 7.0 7.5 8.1 8.8 9.6 10.6 11.9 13.5 15.6 18.6 23.1 27 28 6.2 6.5 7.0 7.4 8.0 8.7 9.5 10.5 11.7 13.3 15.4 18.3 22.7 28 29 5.7 6.1 6.4 6.9 7.3 7.9 8.6 9.4 10.3 11.5 13.1 15.1 18.0 29 30 5.4 5.7 6.0 6.4 6.8 7.2 7.8 8.4 9.2 10.1 11.3 12.8 14.9 30 31 5.1 5.3 5.6 5.9 6.3 6.7 7.1 7.7 8.3 9.0 10.0 11.1 12.6 31 32 4.8 5.0 5.2 5.5 5.8 6.2 6.5 7.0 7.5 8.1 8.9 9.8 10.9 32 33 4.5 4.7 4.9 5.1 5.4 5.7 6.1 6.4 6.9 7.4 8.0 8.7 9.6 33 34 4.3 4.4 4.6 4.8 5.1 5.3 5.6 5.9 6.3 6.8 7.3 7.8 8.6 34 35 4.0 4.2 4.4 4.5 4.7 5.0 5.2 5.5 5.8 6.2 6.6 7.1 7.7 35 36 3.8 4.0 4.1 4.3 4.5 4.7 4.9 5.1 5.4 5.7 6.1 6.5 7.0 36 37 3.6 3.8 3.9 4.0 4.2 4.4 4.6 4.8 5.0 5.3 5.6 6.0 6.4 37 38 3.4 3.6 3.7 3.8 4.0 4.1 4.3 4.5 4.7 4.9 5.2 5.5 5.8 38 39 3.3 3.4 3.5 3.6 3.8 3.9 4.0 4.2 4.4 4.6 4.8 5.1 5.4 39 40 3.1 3.2 3.3 3.4 3.6 3.7 3.8 4.0 4.1 4.3 4.5 4.7 5.0 40 41 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.9 4.0 4.2 4.4 4.6 41 42 2.9 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.7 3.8 4.0 4.1 4.3 42 43 2.7 2.8 2.9 3.0 3.0 3.1 3.2 3.3 3.5 3.6 3.7 3.9 4.0 43 44 2.6 2.7 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.8 44 45 2.5 2.6 2.6 2.7 2.8 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 45 46 2.4 2.4 2.5 2.6 2.6 2.7 2.8 2.8 2.9 3.0 3.1 3.2 3.3 46 47 2.3 2.3 2.4 2.4 2.5 2.6 2.6 2.7 2.8 2.9 2.9 3.0 3.1 47 48 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.6 2.7 2.8 2.9 3.0 48 49 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.6 2.7 2.8 49 50 2.0 2.0 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 2.6 2.6 50 51 1.9 2.0 2.0 2.0 2.1 2.1 2.2 2.2 2.3 2.3 2.4 2.4 2.5 51 52 1.8 1.9 1.9 1.9 2.0 2.0 2.1 2.1 2.1 2.2 2.2 2.3 2.4 52 53 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.0 2.1 2.1 2.2 2.2 53 54 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 2.1 2.1 54 55 55 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 1.9 2.0 2.0 56 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 1.8 1.9 1.9 56 57 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.8 1.8 67 58 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 1.6 1.7 1.7 58 59 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 1.5 1.6 1.6 1.6 59 60 1.3 1.3 1.3 1.3 1.4 1.4 1.4 1.4 1.4 1.5 1.5 1.5 1.5 60 12° 18° 14° 15° 16° 17° 18° 19° 20° 21° 22° 28° 24° De< 3UnatioE t of the f une nai neasth i latitude; appei transit- reducti on addit iTC. 1 Page 706] TABLE 26. Variation of Altitude in one minute from meridian passage. Lati- tude. Declination of the same name as the latitude; npper transit; reduction addltlre. . Lati- tude. 26° 26° 27° 28° 29° 80° 31° 32° 88° 34° 36° 86° 87° 1 2 3 4 // 4.2 4.4 4.6 4.7 5.0 n 4.0 4.2 4.3 4.5 4.7 It 3.9 4.0 4.1 4.3 4.5 » 3.7 3.8 4.0 4.1 4.3 3.5 3.7 3.8 3,9 4.1 II 3.4 3.5 3.6 3.7 3.9 II 3.3 3.4 3.5 3.6 3.7 II 3.1 3.2 3.3 3.4 3.5 II 3.0 3.1 3.2 3.3 3.4 II 2.9 3.0 3.1 3.2 3.3 II 2.8 2.9 3.0 3.0 3.1 2.7 2.8 2.8 2.9 3.0 2.6 2.7 2.7 2.8 2.9 o 1 2 3 4 5 6 7 8 9 5.2 5.4 5.7 6.0 6.4 4.9 5.1 5.4 5.7 6.0 4.7 4.9 5.1 5.3 5.6 4.4 4.6 4.8 5.0 5.3 4.2 4.4 4.6 4.8 5.0 4.0 4.2 4.3 4.5 4.7 3.8 4.0 4.1 4.3 4.4 3.7 3.8 3.9 4.1 4.2 3.5 3.6 3.7 3.9 4.0 3.3 3.5 3.6 3.7 3.8 3.2 3.3 3.4 3.5 3.6 3.1 3.2 3.3 3.4 3.5 3.0 3.0 3.1 3.2 3.3 5 6 7 8 9 10 11 12 13 14 6.8 7.2 7.7 8.3 9.1 6.3 6.7 7.1 7.6 8.2 5.9 6.2 6.6 7.1 7.6 5.5 5.8 6.2 6.5 7.0 5.2 5.5 5.8 6.1 6.4 4.9 5.1 5.4 5.7 6.0 4.6 4.8 5.1 5.3 5.6 4.4 4.6 4.8 5.0 5.2 4.2 4.3 4.5 4.7 4.9 3.9 4.1 4.3 4.4 4.6 3.8 3.9 4.0 4.2 4.4 3.6 3.7 3.8 4.0 4.1 3.4 3.5 3.6 3.8 3.9 10 11 12 13 14 15 16 17 18 19 9.9 10.9 12.2 13.9 16.1 8.9 9.8 10.8 12.1 13.7 8.1 8.8 9.6 10.6 11.9 7.4 8.0 8.7 9.5 10.5 6.9 7.3 7.9 8.6 9.4 6.4 6.8 7.2 7.8 8.4 5.9 6.3 6.7 7.1 7.7 5.5 5.8 6.2 6.6 7.0 5.2 5.4 5.7 6.1 6.4 4.8 5.1 5.3 5.6 6.0 4.5 4.8 5.0 5.2 5.5 4.3 4.5 4.7 4.9 5.1 4.0 4.2 4.4 4.6 4.8 15 16 17 18 19 20 21 22 23 24 19.2 23.8 15.9 18.9 23.5 13.5 15.6 18.6 23.1 11.7 13.3 15.4 18.3 22.7 10.3 11.5 13.1 15.1 18.0 9.2 10.2 11.3 12.8 14.9 8.3 9.1 10.0 11.1 12.6 7.5 8.2 8.9 9.8 10.9 6.9 7.4 8.0 8.7 9.6 6.3 6.8 7.3 7.9 8.6 5.8 6.2 6.6 7.1 7.7 5.4 5.7 6.1 6.5 7.0 5.0 5.3 5.6 6.0 6.4 20 21 22 23 24 25 26 27 28 29 22.3 22.3 17.7 21.9 14.6 17.4 21.5 12.4 14.3 17.0 21.1 10.7 12.1 14.0 16.7 20.6 9.4 10.5 11.9 13.8 16.3 8.4 9.2 10.3 11.7 13.5 7.5 8.2 9.1 10.1 11.4 6.8 7.4 8.1 8.9 9.9 25 26 27 28 29 30 31 32 33 34 17.7 14.6 12.4 10.7 9.4 21.9 17.4 14.3 12.1 10.5 21.5 17.0 14.0 11.9 21.1 16.7 13.8 20.6 16.3 20.2 20.2 16.0 19.8 13.2 15.6 19.3 y.i 12.9 15.3 18.9 30 31 32 33 34 35 36 37 38 39 8.4 7.5 6.8 6.2 5.7 9.2 8.2 7.4 6.7 6.1 10.3 9.1 8.1 7.2 6.5 11.7 10.1 8.9 7.9 7.1 13.5 11.4 9.9 8.7 7.7 16.0 13.2 11.1 9.6 8.5 19.8 15.6 12.9 10.9 9.4 19.3 15.3 12.6 10.6 18.9 14.9 12.2 18.4 14.5 17.9 35 36 37 38 39 40 41 42 43 44 5.3 4.9 4.5 4.2 3.9 5.6 5.2 4.8 4.4 4.1 6.0 5.5 5.0 4.6 4.3 6.4 5.8 5.3 4.9 4.5 6.9 6.2 5.7 5.2 4.8 7.5 6.7 6.1 5.5 5.1 8.2 7.3 6.6 5.9 5.4 9.2 8.0 7.1 6.4 5.8 10.4 8.9 7.8 6.9 6.2 11.9 10.1 8.7 7.6 6.7 14.1 11.6 9.8 8.5 7.4 17.4 13.8 11.3 9.5 8.2 17.0 13.4 11.0 9.3 40 41 42 43 44 45 46 47 48 49 3.7 3.5 3.3 3.1 2.9 3.8 3.6 3.4 3.2 3.0 4.0 3.7 3.5 3.3 3.1 4.2 3.9 3.6 3.4 3.2 4.4 4.1 3.8 3.5 3.3 4.7 4.3 4.0 3.7 3.4 4.9 4.5 4.2 3.9 3.6 5.2 4.8 4.4 4.0 3.7 5.6 5.1 4.6 4.3 3.9 6.0 5.4 4.9 4.5 4.1 6.6 5.9 5.3 4.8 4.4 7.2 6.4 5.7 5.1 4.6 8.0 7.0 6.2 5.5 5.0 45 46 47 48 49 50 51 52 53 54 2.7 2.6 2.4 2.3 2.2 2.8 2.6 2.5 2.3 2.2 2.9 2.7 2.6 2.4 2.3 3.0 2.8 2.6 2.5 2.3 3.1 2.9 2.7 2.5 2.4 3.2 3.0 2.8 2.6 2.5 3.3 3.1 2.9 2.7 2.5 3.5 3.2 3.0 2.8 2.6 3.6 3.4 3.1 2.9 2.7 3.8 3.5 3.2 3.0 2.8 2.6 2.4 2.3 2.1 2.0 1.9 4.0 3.7 3.4 3.1 2.9 2.7 2.5 2.3 2.2 2.0 1.9 4.2 3.9 3.6 3.3 3.0 4.5 4.1 3.7 3.4 3.2 50 51 52 53 54 55 56 57 58 59 60 2.0 1.9 1.8 1.7 1.6 1.6 2.1 2.0 1.9 1.8 1.7 1.6 2.1 2.0 1.9 1.8 1.7 1.6 2.2 2.1 2.0 1.8 1.7 1.6 2.3 2.1 2.0 1.9 1.8 1.7 2.3 2.2 2.0 1.9 1.8 . 1.7 2.4 2.2 2.1 2.0 1.9 1.7 2.4 2.3 2.2 2.0 1.9 1.8 2.5 2.4 2.2 2.1 1.9 1.8 2.8 2.6 2.4 2.3 2.1 2.0 2.9 2.7 2.5 2.3 2.2 2.0 55 56 57 58 59 60 '26° 26° 27° 28° 29° 80° 81° 32° 38° 84° 85°i 36° 37° Declination of the same name as the latitude; upper transit; reduction addltlre. TABLE 26. [Page 707 Vajiation of Altitude in one minute from meridian passage. Lati- tude. Declination of the same name as the latitude; upper transit reduction addltlre. Lati- tude. 38° 89° 40° 41° 42° 43° 44° 45° 46° 47° 48° 49° 60° o 2.5 2.4 2.3 II 2.3 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 1.7 o 1 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.9 1.8 1.7 1.7 1 2 2.6 2.5 2.4 2.4 2.3 2.2 2.1 2.0 2.0 1.9 1.8 1.8 1.7 2 3 2.7 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.9 1.8 1.7 3 4 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 2.0 1.9 1.8 1.8 4 5 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.9 1.8 5 6 2.9 2.8 2.7 2.6 2.6 2.4 2.3 2.2 2.1 2.0 2.0 1.9 1.8 6 7 3.0 2.9 2.7 2.6 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 1.8 7 8 3.1 2.9 2.8 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 1.9 8 9 3.2 3.0 2.9 2.8 2.8 2.7 2.5 2.4 2.3 2.2 2.2 2.1 2.0 1.9 9 10 3.3 3.1 3.0 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 1.9 10 11 3.4 3.2 3.1 2.9 2.8 2.7 2.6 2.4 2.3 2.2 2.1 2.1 2.0 11 12 3.5 3.3 3.1 3.0 2.9 2.7 2.6 2.5 2.4 2.3 2.2 2.1 2.0 12 13 3.6 3.4 3.2 3.1 2.9 2.8 2.7 2.6 2.4 2.3 2.2 2.1 2.0 13 14 3.7 3.5 3.3 3.2 3.0 2.9 2.7 2.6 2.5 2.4 2.3 2.2 2.1 14 15 3.8 3.6 3.4 3.3 3.1 3.0 2.8 2.7 2.6 2.4 2.3 2.2 2.1 15 16 4.0 3.8 3.6 3.4 3.2 3.0 2.9 2.8 2.6 2.5 2.4 2.3 2.2 16 17 4.1 3.9 3.7 3.5 3.3 3.1 3.0 2.8 2.7 2.6 2.4 2.3 2.2 17 18 4.3 4.1 3.8 3.6 3.4 3.2 3.1 2.9 2.8 2.6 2.6 2.4 2.3 18 19 4.5 4.2 4.0 3.7 3.5 3.3 3.2 3.0 2.8 2.7 2.6 2.4 2.3 19 20 20 4.7 4.4 4.1 3.9 3.7 3.5 3.3 3.1 2.9 2.8 2.6 2.6 2.4 21 4.9 4.6 4.3 4.0 3.8 3.6 3.4 3.2 3.0 2.9 2.7 2.6 2.4 21 22 5.2 4.8 4.5 4.2 4.0 3.7 3.6 3.3 3.1 2.9 2.8 2.6 2.5 22 23 5.5 5.1 4.7 4.4 4.1 3.9 3.6 3.4 3.2 3.0 2.9 2.7 2.6 23 24 5.8 5.4 5.0 4.6 4.3 4.0 3.8 3.5 3.3 3.1 3.0 2.8 2.6 24 25 6.2 5.7 5.3 4.9 4.5 4.2 3.9 3.7 3.5 3.3 3.1 2.9 2.7 26 26 6.7 6.1 5.6 5.2 4.8 4.4 4.1 3.8 3.6 3.4 3.2 3.0 2.8 26 27 7.2 6.5 6.0 5.5 5.0 4.6 4.3 4.0 3.7 3.5 3.3 3.1 2.9 27 28 7.9 7.1 6.4 5.8 5.3 4.9 4.5 4.2 3.9 3.6 3.4 3.2 3.0 28 29 8.7 7.7 6.9 6.2 5.7 5.2 4.8 4.4 4.1 3.8 3.6 3.3 3.1 29 30 9.6 8.5 7.5 6.7 6.1 5.5 5.1 4.7 4.3 4.0 3.7 3.4 3.2 30 31 10.9 9.4 8.2 7.3 6.6 5.9 5.4 4.9 4.6 4.2 3.9 3.6 3.3 31 32 12.6 10.6 9.2 8.0 7.1 6.4 5.8 5.2 4.8 4.4 4.0 3.7 3.5 32 33 14.9 12.2 10.4 8.9 7.8 6.9 6.2 5.6 5.1 4.6 4.3 3.9 3.6 33 34 18.4 14.5 11,9 10.1 8.7 7.6 6. 7 6. 5.4 4.9 4.5 4.1 3.8 34 35 17.9 14.1 11.6 9.8 8.5 7. 4 6. 6 5.9 5.3 4.8 4.4 4.0 35 36 17.4 13.8 11.3 9.5 8.2 7.2 6.4 5.7 5.1 4.6 4.2 36 37 17.0 13.4 11.0 9.3 8.0 7.0 6.2 6.6 5.0 4.6 37 38 16.5 13.0 10.7 9.0 7.7 6.8 6.0 6.3 4.8 38 39 16.0 12.6 10.3 8.7 7.6 6.5 5.8 6.1 39 40 15.6 12.2 10.0 8.4 7.2 6.3 5.6 40 41 15.0 11.8 9.7 8.1 7.0 6.1 41 42 16.5 14.5 11.4 9.3 7.9 6.7 42 43 13.0 16.0 14.0 11.0 9.0 7.6 43 44 10.7 12.6 15.5 13.6 10.6 8.7 44 45 9.0 10.3 12.2 15.0 13.1 10.2 45 46 7.7 *8.7 10.0 11.8 14.5 12.6 46 47 6.8 7.5 8.4 9.7 11.4 14.0 47 48 6.0 6.5 7.2 8.1 9.3 11.0 13.6 48 49 5.3 5.8 6.3 7.0 7.9 9.0 10.6 13.1 49 50 50 4.8 5.1 5.6 6.1 6.7 7.6 8.7 10.2 12.6 51 4.3 4.6 5.0 5.4 5.9 6.6 7.3 8.4 9.9 12.1 1 51 52 3.9 4.2 4.5 4.8 5.2 5.7 6.3 7.0 8.0 9.5 11.6 52 53 3.6 3.8 4.0 4.3 4.6 5.0 5.4 6.0 6.7 7.7 9.1 11.1 63 54 3.3 3.5 3.7 3.9 4.1 4.4 4.8 5.2 5.8 6.6 7.4 8.7 10.6 54 55 3.0 3.2 3.3 3.5 3.7 4.0 4.3 4.6 5.0 5.5 6.2 7.1 8.3 55 56 2.8 2.9 3.1 3.2 3.4 3.6 3.8 4.1 4.4 4.8 5.3 5.9 6.8 56 57 2.6 2.7 2.8 2.9 3.1 3.2 3.4 3.6 3.9 4.2 4.6 6.0 5.6 57 58 2.4 2.5 2.6 2.7 2.8 2.9 3.1 3.3 3.5 3.7 4.0 4.4 4.8 58 59 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.0 3.1 3.3 3.6 3.8 4.2 59 60 2.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 3.0 3.2 3.4 3.6 60 38° 39° 40° 41° 42° 43° 44° 45° 46° 47° 48° 49° 60° De clinatioi 1 of the same na me as the latitude; uppei r transit reducti on addil iTe, Page 708] TABLE 26. Variation of Altitude in one minute from meridian passage. Declination of the f same name as the latitude: nppei transit reduction addltlre. Lati- tude. Lati- tude. 51° 52° 68° 64° 55° 56° 57° 68° 59° 60° 61° 62° 68° II // II 11 u II II 11 II 1/ . II II o 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 1 1.6 1.6 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.1 1.1 1.0 1 2 1.6 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.0 2 3 1.7 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.0 3 4 1.7 1.6 1.6 1.5 1.5 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.0 4 5 1.7 1.7 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.1 1.1 1.1 5 6 1.7 1.7 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 6 7 1.8 1.7 1.6 1.6 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 7 8 1.8 1.7 1.7 1.6 1.5 1.5 1.4 1.4 1.3 1.2 1.2 1.1 1.1 8 9 1.8 1.8 1.7 1.6 1.6 1.5 1.4 1.4 1.3 1.3 1.2 1.1 1.1 9 10 1.9 1.8 1.7 1.6 1.6 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 10 11 1.9 1.8 1.7 1.7 1.6 1.5 1.5 1.4 1.3 1.3 1.2 1.2 1.1 11 12 1.9 1.8 1.8 1.7 1.6 1.6 1.5 1.4 1.4 1.3 1.2 1.2 1.1 12 13 2.0 1.9 1.8 1.7 1.6 1.6 1.5 1.4 1.4 1.3 1.3 1.2 1.1 13 14 2.0 2.0 1.9 1.8 1.7 1.7 1.6 1.5 1.5 1.4 1.3 1.3 1.2 1.2 14 15 1.9 1.9 1.8 1.7 1.6 1.5 1.5 1.4 1.3 1.3 1.2 1.2 15 16 2.1 2.0 1.9 1.8 1.7 1.6 1.6 1.5 1.4 1.4 1.3 1.2 1.2 16 17 2.1 2.0 1.9 1.8 1.8 1.7 1.6 1.5 1.5 1.4 1.3 1.3 1.2 17 18 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.5 1.4 1.3 1.3 1.2 18 19 20 2.2 2.3 2.1 2.0 1.9 1.8 1.7 1.6 1.6 1.5 1.4 1.4 1.3 1.2 19 2.1 2.0 1.9 1.9 1.8 1.7 1.6 1.5 1.4 1.4 1.3 1.2 20 21 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.5 1.4 1.3 1.2 21 22 2.4 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.6 1.5 1.4 1.3 1.3 22 23 2.4 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.4 1.3 23 24 2.5 2.4 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.5 1.4 1.3 24 25 2.6 2.4 2.3 2.2 2.0 1.9 1.8 1.7 1.6 1.6 1.5 1.4 1.3 25 26 2.6 2.5 2.3 2.2 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 26 27 2.7 2.6 2.4 2.3 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.4 27 28 2.8 2.6 2.5 2.3 2.2 2.1 2.0 1.8 1.7 1.6 1.5 1.5 1.4 28 29 2.9 2.7 2.5 2.4 2.3 2.1 2.0 1.9 1.8 1.7 1.6 1.5 1.4 29 80 3.0 2.8 2.6 2.5 2.3 2.2 2.0 1.9 1.8 1.7 1.6 1.5 1.4 30 31 3.1 2.9 2.7 2.5 2.4 2.2 2.1 2.0 1.9 1.7 1.6 1.5 1.4 31 32 3.2 3.0 ?.8 2.6 2.4 2.3 2.2 2.0 1.9 1.8 1.7 1.6 1.5 32 33 3.4 3.1 2.9 2.7 2.5 2.4 2.2 2.1 1.9 1.8 1.7 1.6 1.5 33 34 3.5 3.2 3.0 2.8 2.6 2.4 2.3 2.1 2.0 1.9 1.7 1.6 1.5 34 35 3.7 3.4 3.1 2.9 2.7 2.5 2.3 2.2 2.0 1.9 1.8 1.7 1.6 35 36 3.9 3.6 3.3 3.0 2.8 2.6 2.4 2.3 2.1 2.0 1.8 1.7 1.6 36 37 4.1 3.7 3.4 3.2 2.9 2.7 2.5 2.3 2.2 2.0 1.9 1.7 1.6 37 38 4.3 3.9 3.6 3.3 3.0 2.8 2.6 2.4 2.2 2.1 1.9 1.8 1.7 38 39 4.6 4.2 3.8 3.5 3.2 2.9 2.7 2.5 2.3 2.1 2.0 1.8 1.7 39 40 5.0 4.5 4.0 3.7 3.3 3.1 2.8 2.6 2.4 2.2 2.0 1.9 1.8 40 41 5.4 4.8 4.3 3.9 3.5 3.2 2.9 2.7 2.5 2.3 2.1 1.9 1.8 41 42 5.9 5.2 •1.6 4.1 3.7 3.4 3.1 2.8 2.6 2.4 2.2 2.0 1.9 42 43 6.5 5.7 5.0 4.4 4.0 3.6 3.2 2.9 2.7 2.5 2.3 2.1 1.9 43 44 7.3 6.3 5.4 4.8 4.3 3.8 3.4 3.1 2.8 2.6 2.3 2.2 2.0 44 45 8.4 7.0 6.0 5.2 4.6 4.1 3.6 3.3 3.0 2.7 2.4 2.2 2.0 45 46 9.9 8.0 6.7 5.8 5.0 4.4 3.9 3.5 3.1 2.8 2.6 2.3 2.1 46 47 12.1 9.5 7.7 6.5 5.5 4.8 4.2 3.7 3.3 3.0 2.7 2.4 2.2 47 48 11.6 9.1 7.4 6.2 5.3 4.6 4.0 3.6 3.2 2.8 2.6 2.3 48 49 11.1 8.7 7.1 5.9 5.0 4.4 3.8 3.4 3.0 2.7 2.4 49 50 10.6 8.3 6.8 5.6 4.8 4.2 3.6 3.2 2.9 2.6 50 51 10.2 7.9 6.4 5.4 4.6 4.0 3.5 3.0 2.7 51 52 9.7 7.6 6.1 5.1 4.3 3.8 3.3 2.9 52 53 9.2 7.2 5.9 4.9 4.1 3.6 3.1 53 54 8.8 6.8 5.5 4.6 3.9 3.4 54 55 10.2 8.3 6.5 5.3 4.3 3.7 55 56 7.9 9.7 7.9 6.1 5.0 4.1 56 57 6.4 7.6 9.2 7.4 5.8 4.7 57 58 5.4 6.1 7.2 8.8 7.0 5.4 58 59 4.6 5.1 5.9 6.8 8.3 6.6 59 60 4.0 4.3 4.9 5.5 6.5 7.9 60 51° 520 580 54° 55° 56° 57° 68° 59° 60° 61° 62° 68° De clinatio Q of the same na me as th e latitude; uppe r transit ; reduct ion addl tire. TABLE 26. [Page 709 Variation of Altitude in one minute from meridian passage • Declination of a different name from the latitude ; apper transit: reduction addltlre. Lati- tnde. Lati- tude. 0° 1° 2° 3° 4" 6° 6° 7° 8° »° 10° 11° O H » « u H n H » K II n II o 28.1 22.4 18.7 16.0 14.0 12.4 11.1 10.1 1 28.1 22.4 18.7 16.0 14.0 12.4 11.2 10.1 9.3 1 2 28.1 22.4 18.7 16.0 14.0 12.5 11.2 10.2 9.3 8.6 2 3 28.1 22.4 18.7 16.0 14.0 12.5 11.2 10.2 9.3 8.6 8.0 3 4 28.1 22.4 18.7 16.0 14.0 12.5 11.2 10.2 9.3 8.6 8.0 7.4 4 5 22,4 18.7 16.0 14.0 12.5 11.2 10.2 9.3 8.6 8.0 7.4 7.0 6 6 18.7 16.0 14.0 12.5 11.2 10.2 9.3 8.6 8.0 7.6 7.0 6.6 6 7 16.0 14.0 12.4 11.2 10.2 9.3 8.6 8.0 7.5 7.0 6.6 6.2 7 8 14.0 12.4 11.2 10.2 9.3 8.6 8.0 7.5 7.0 6.6 6.2 5.9 8 9 12.4 11.2 10.2 9.3 8.6 8.0 7.5 7.0 6.6 6.2 6.2 5.9 5.6 9 10 11.1 10.1 9.3 8.6 8.0 7.4 7.0 6.6 5.9 5.6 6.3 10 11 10.1 9.3 8.6 8.0 7.4 7.0 6.6 6.2 6.9 5.6 5.3 5.1 11 12 9.2 8.5 7.9 7.4 7.0 6.5 6.2 5.9 6.6 5.3 6.0 4.8 12 13 8.5 7.9 7.4 6.9 6.5 6.2 5.8 5.6 5.3 5.0 4.8 4.6 13 14 7.9 7.4 6.9 6.5 6.2 5.8 5.5 5.3 6.0 4.8 4.6 4.4 14 15 7.3 6.9 6.5 6.1 5.8 5.5 5.3 5.0 4.8 4.6 4.4 4.2 15 16 6.8 6.5 6.1 5.8 5.5 5.2 5.0 4.8 4.6 4.4 4.2 4.1 16 17 6.4 6.1 5.8 5.5 5.2 5.0 4.8 4.6 4.4 4.2 4.1 3.9 17 18 6.0 5.7 5.5 5.2 5.0 4.8 4.6 4.4 4.2 4.1 3.9 3.8 18 19 5.7 5.4 5.2 4.9 4.7 4.5 4.4 4.2 4.0 3.9 3.8 3.6 19 20 5.4 5.1 4.9 4.7 4.5 4.3 4.2 4.0 3.9 3.8 3.6 3.5 20 21 5.1 4.9 4.7 4.5 4.3 4.2 4.0 3.9 3.7 3.6 3.5 3.4 21 22 4.9 4.7 4.6 4.3 4.1 4.0 3.9 3.7 3.6 3.6 3.4 3.3 22 23 4.6 4.4 4.3 4.1 4.0 3.8 3.7 3.6 3.6 3.4 3.3 3.2 23 24 4.4 4.2 4.1 3.9 3.8 3.7 3.6 3.5 3.3 3.4 3.3 3.2 3.1 24 25 4.2 4.1 3.9 3.8 3.7 3.5 3.4 3.2 3.1 3.1 3.0 25 26 4.0 3.9 3.8 3.6 3.5 3.4 3.3 3.2 3.1 3.0 3.0 2.9 26 27 3.9 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.9 2.8 27 28 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.8 2.7 28 29 3.5 3.4 3.3 3.2 3.1 3.1 3.0 2.9 2.8 2.8 2.7 2.6 29 30 3.4 3.3 3.2 3.1 3.0 3.0 2.9 2.8 2.7 2.7 2.6 2.5 30 31 3.3 3.2 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.6 2.5 2.5 31 32 3.2 3.1 3.0 2.9 2.8 2.8 2.7 2.6 2.6 2.6 2.5 2.4 32 33 3.0 2.9 2.9 2.8 2.7 2.7 2.6 2.5 2.6 2.4 2.4 2.3 33 34 2.9 2.8 2.8 2.7 2.6 2.6 2.5 2.5 2.4 2.4 2.3 2.3 34 35 2.8 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 35 36 2.7 2.6 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 36 37 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.2 2.1 2.1 37 38 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.1 2.0 38 39 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.1 2.0 2.0 2.0 39 40 2.3 2.3 2.2 2.2 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 40 41 2.3 2.2 2.2 2.1 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 41 42 2.2 2.1 2.1 2.1 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.8 42 43 2.1 2.1 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.8 1.7 43 44 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.7 44 45 2.0 1.9 1.9' 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.6 45 46 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.6 1.6 1.6 46 47 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 47 48 1.8 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.5 1.6 48 49 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.6 49 50 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 50 51 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 51 52 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 52 53 1.5 1.5 1.4 1.4 1.4 \A 1.4 1.4 1.3 1.3 1.3 1.3 53 54 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 54 55 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 55 56 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 56 57 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 57 58 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 58 59 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 59 60 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1 1.0 1.0 60 0° 1° 2° 8° 4° 5° 6° 7° 8° 9° 10° 11° Declii lation o a differ ent name from th e latitude ; upper ti ansit; rec luction a( Idltire. Page 710] TABLE 26. Variation of Altitude in one minute from meridian passage. Lati- tude. Declination of a different name from the latitude; upper transit; reduction additive. Lati- tude. 12° 18° 14° 16° 16° 17° 18° 19° 20° 21° 22° 23° 24° o // II II II II II II II II II II II II o 9.2 8.5 7.9 7.3 6.8 6.4 6.0 5.7 5.4 5.1 4.9 4.6 4.4 1 8.5 7.9 7.4 6.9 6.5 6.1 5.7 5.4 5.1 4.9 4.7 4.4 4.2 1 2 7.9 7.4 6.9 6.5 6.1 5.8 5.5 5.2 4.9 4.7 4.5 4.3 4.1 2 3 7.4 6.9 6.5 6.1 5.8 5.5 5.2 4.9 4.7 4.5 4.3 4.1 3.9 3 4 7.0 6.5 6.2 5.8 5.5 5.2 5.0 4.7 4.5 4.3 4.1 4.0 3.8 4 5 6.5 6.2 5.8 5.5 5.2 5.0 4.8 4.5 4.3 4.2 4.0 3.8 3.7 6 6 6.2 5.8 5.5 5.3 5.0 4.8 4.6 4.4 4.2 4.0 3.9 3.7 3.6 6 7 5.9 5.6 5.3 5.0 4.8 4.6 4.4 4.2 4.0 3.9 3.7 3.6 3.5 7 8 5.6 5.3 5.0 4.8 4.6 4.4 4.2 4.0 3.9 3.7 3.6 3.5 3.4 8 9 10 5.3 6.0 4.8 4.6 4.4 4.2 4.1 3.9 3.8 3.6 3.5 3.4 3.3 9 5.0 4.8 4.6 4.4 4.2 4.1 3.9 3.8 3.6 3.5 3.4 3.3 3.2 10 11 4.8 4.6 4.4 4.2 4.1 3.9 3.8 3.6 3.5 3.4 3.3 3.2 3.1 11 12 4.6 4.4 4.3 4.1 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 12 13 4.4 4.3 4.1 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 13 14 4.2 4.1 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 14 15 4.1 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.8 15 16 3.9 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.8 2.7 16 17 3.8 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.8 2.7 2.6 17 18 3.7 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.5 18 19 3.5 3.4 3.3 3.2 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.6 2.5 19 20 3.4 3.3 3.2 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.6 2.5 2.4 20 21 3.3 3.2 3.1 3.0 2.9 2.8 2.8 2.7 2.6 2.6 2.5 2.4 2.4 21 22 3.2 3.1 3.0 2.9 2.8 2.8 2.7 2.6 2.6 2.5 2.4 2.4 2.3 22 23 3.1 3.0 2.9 2.8 2.8 2.7 2.6 2.6 2.5 2.4 2.4 2.3 2.3 23 24 3.0 2.9 2.8 2.8 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 24 25 2.9 2.8 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.2 25 26 2.8 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.3 2.2 2.1 2.1 26 27 2.7 2.7 2.6 2.5 2.5 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.1 27 28 2.6 2.6 2.5 2.5 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.1 2.0 28 29 2.6 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 2.0 29 30 2.5 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 2.0 1.9 30 31 2.4 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 31 32 2.3 2.3 2.2 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 32 33 2.3 2.2 2.2 2.1 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 1.8 33 34 2.2 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.8 34 35 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 1.8 1.8 1.8 1.7 1.7 35 36 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.7 36 37 2.0 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.6 37 38 2.0 1.9 1.9 1.9 1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 38 39 40 1.9 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.6 39 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 40 41 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.6 41 42 1.8 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.6 42 43 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 43 44 1.7 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 ,1.4 1.4 1.4 44 45 45 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 46 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 46 47 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 47 48 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 48 49 50 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 49 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 60 51 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 61 52 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.1 1.1 52 53 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 53 54 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 54 55 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 66 56 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 66 57 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 57 58 1.1 1.1 1.1 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 58 59 1.1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 59 60 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 0.9 0.9 60 12° 18° 14° 15° 16° 17° 18° 19° 20° 21° 22° 23° 24° Decl ination 3f a diffe rent nai ne from the latit ude; up per trans it; redu ction ad dltlve. TABLE 26. [Page 711 Variation of Altitude in one minute from meridian passage. Declination of a different name from the latitude; upper transit; reduction additire. tude. Lati- tude. 26° 26° 27° 28° 29° 30° 81° 82° 83° 84° 86° 36° 87° II // n II u II n II II II II II // 4.2 4.0 3.9 3.7 3.5 3.4 3.3 3.1 3.0 2.9 2.8 2.7 2.6 1 4.1 3.9 3.7 3.6 3.4 3.3 3.2 3.1 2.9 2.8 2.7 2.6 2.6 1 2 3.9 3.8 3.6 3.5 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2 3 3.8 3.6 3,5 3.4 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 3 4 3.7 3.5 3.4 3.3 3.2 3.0 2.9 2.8 2.7 2.6 2.6 2.5 2.4 4 5 3.6 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.3 5 6 3.4 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.4 2.4 2.3 6 7 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.5 2.4 2.3 2.2 7 8 3.2 3.1 3.0 2.9 2.8 2.7 2.7 2.6 2.5 2.4 2.3 2.3 2.2 8 9 3.1 3.0 2.9 2.9 2.8 2.7 2.6 2.5 2.4 2.4 2.3 2.2 2.2 9 10 10 3.1 3.0 2.9 2.8 2.7 2.6 2.5 2.5 2.4 2.3 2.2 2.2 2.1 11 3.0 2.9 2.8 2.7 2.6 2.5 2.5 2.4 2.3 2.3 2.2 2.1 2.1 11 12 2.9 2.8 2.7 2.6 2.6 2.5 2.4 2.3 2.3 2.2 2.2 2.1 2.0 12 13 2.8 2.7 2.7 2.6 2.5 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.0 13 14 2.7 2.7 2.6 2.5 2.4 2.4 2.3 2.3 2.2 2.1 2.1 2,0 2.0 14 15 2.7 2.6 2.5 2.5 2.4 2.3 2.3 2.2 2.1 2.1 2.0 2.0 1.9 15 16 2.6 2.5 2.6 2.4 2.3 2.3 2.2 2.2 2.1 2.0 2.0 1.9 1.9 16 17 2.5 2.5 2.4 2.3 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 17 18 2.5 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 18 19 2.4 2.4 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 19 20 2.4 2.3 2.3 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.9 1.8 1.8 20 21 2.3 2.3 2.2 2.1 2.1 2.0 2.0 2.0 1.9 1.9 1.8 1.8 1.7 21 22 2.3 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.7 1.7 22 23 2.2 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.8 1.7 1.7 23 24 2.2 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.8 1.7 1.7 1.6 24 25 2.1 2.1 2.0 2.0 1.9 1.9 1.8 1.8 1.8 1,7 1.7 1.6 1.6 25 26 2.1 2.0 2.0 1.9 • 1.9 1.9 1.8 1.8 1.7 1.7 1.7 1.6 1.6 26 27 2.0 2.0 1.9 1.9 1.9 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 27 28 2.0 1.9 1.9 1.9 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 28 29 1.9 1.9 1.9 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 29 30 1.9 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 30 31 1.8 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 31 32 1.8 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1,4 32 33 1.8 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1,4 33 34 1.7 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1,4 34 35 1.7 1.7 1.6 1.6 1.6 1.5 1.5 1.5 1.4 1.4 1.4 1,4 35 36 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1,3 36 37 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 37 38 1.6 1.5 1.5 1.5 1.5- 1.5 1.4 1.4 1.4 1.4 1.3 1.3 1.3 38 39 1.5 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 39 40 1.5 1.5 1.5 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 40 41 1.5 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 41 42 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 42 43 1.4 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 43 44 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1,2 44 45 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 45 46 1.3 1.3 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 46 47 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 47 48 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 48 49 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 49 50 1.2 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 50 51 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.0 51 52 1.1 1.1 1.1 1.1 1.1 1.1 1.0 1.0 52 53 1.1 1.1 1.1 1.1 1.0 1.0 1.0 53 54 1.1 1.0 1.0 1.0 1.0 1.0 54 55 1.0 1.0 1.0 1.0 1.0 55 56 1.0 1.0 1.0 1.0 56 57 1.0 1.0 1.0 57 58 59 60 1.0 0.9 0.9 58 59 60 6.8 0.8 0.^ 26° 26° 27° 28° 29° S0° Sl° 82° 88° 84° 86° 36° 87° Dec] ination of the 8 tmenan le as the latitud* 3; lower transit; reductic )n snbtr Mtire. Page 712] TABLE 26. Variation of Altitude in one minute from meridian passage. Lati- tude. Declination of a different name from tlie latitude; upper transit; reduction addltire. 1 Lati- tude. 88° 89° 40° 41° 42° 48° 44° 45° 46° 47° 48° 49° 50° o 1 2 3 4 // 2.5 2.5 2.4 2.4 2.3 2.4 2.4 2.3 2.3 2.2 II 2.3 2.3 2.3 2.2 2.2 II 2.3 2.2 2.2 2.1 2.1 n 2.2 2.1 2.1 2.1 2.0 II 2.1 2.1 2.0 2.0 2.0 // 2.0 2.0 2.0 1.9 1.9 II 2.0 1.9 1.9 1.9 1.8 II 1.9 1.9 1.8 1.8 1.8 II 1.8 1.8 1.8 1.8 1.7 II 1,8 1.7 1.7 1.7 1.7 II 1.7 1.7 1.7 1.6 1.6 II 1.7 1.6 1.6 1.6 1.6 o 1 2 3 4 5 6 7 8 9 2.3 2.2 2.2 2.1 2.1 2.2 2.2 2.1 2.1 2.0 2.1 2.1 2.0 2.0 2.0 2.1 2.0 2.0 1.9 1.9 2.0 2.0 1.9 1.9 1.9 1.9 1.9 1.9 1.8 1.8 1.9 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.7 1.7 1.8 1.7 1.7 1.7 1.6 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 5 6 7 8 9 10 11 12 13 14 2.1 2.0 2.0 1.9 1.9 2.0 2.0 1.9 1.9 1.9 1.9 1.9 1.9 1.8 1.8 1.9 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.7 1.7 1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.6 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 10 11 12 13 14 15 16 17 18 19 1.9 1.8 1.8 1.8 1.7 1.8 1.8 1.8 1.7 1.7 1.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.6 1.6 1.7 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.6 1.6 1.5 1.5 1.5 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.4 1.3 1.3 1.3 1.3 15 16 17 18 19 20 21 22 23 24 1.7 1.7 1.7 1.6 1.6 1.7 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.6 1.5 1.6 1.6 1.5 1.5 1.5 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.4 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.3 1.3 1.2 1.2 1.2 20 21 22 23 24 25 26 27 28 29 1.6 1.6 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.4 1.5 1.5 1.5 1.4 1.4 1.5 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.3 1.4 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3^ 1.3 1.3 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 25 26 27 28 29 30 31 32 33 34 1.5 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.3 1.4 1.4 1.3 1.3 1.3 1.4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.1 1.2 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 30 31 32 33 34 35 36 37 38 39 1.3 1.3 1.3 1.3 1.2 1.3 1.3 1.3 1.2 1.2 1.3 1.3 1.2 1.2 1.2 1.3 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.1 1.2 1.2 . 1.2 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 35 36 37 38 39 40 41 42 43 44 1.2 1.2 1.2 1.2 1.1 1.2 1.2 1.2 1.1 1.1 1.2 1.2 1.1 1.1 1.1 1.2 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 40 41 42 43 44 45 46 47 48 49 1.1 1.1 1.1 45 46 47 48 49 0.9 0.9 0.9 0.8 0.9 0.9 0.9 0.9 0.9 0.9 50 51 52 53 54 0.9 0.9 0.9 0.8 0.8 0.9 0.9 0.8 0.8 0.8 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 50 51 52 53 54 0.9 0.9 0.8 0.8 0.9 0.9 0.8 0.9 0.9 0.9 55 56 57 58 59 60 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.8 0.8 0.8 0.8 0.8 0.7 0.8 0.8 0.8 0.8 0.7 0.7 0.8 0.8 0.8 0.8 0.7 0.7 0.8 0.8 0.8 0.7 0.7 0.7 0.8 0.8 0.7 0.7 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 55 56 57 58 59 60 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 88° 89° 40° 41° 42° 48° 44° 43° 46° 47° 48° 49° 50° Declination of the same name as the latitude; lower transit; reduction snbtractlre. TABLE 26. [Page 713 Variation of Altitude in one minute from meridian passj^e. Lati- tude. Declination of a different name from the latitude; upper transit; reduction addltlre. 1 Lati- tude. 51° 520 58° 54° 55° 56° 57° 68° 59° 60° 61° 62° 68° o „ „ II II „ „ II „ „ „ II II II o 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 1 1.6 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 1 2 1.5 1.5 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 2 3 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 3 4 1.5 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 4 5 1.5 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.0 1.0 1.0 5 6 1.5 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.1 'l.l 1.0 1.0 1.0 6 7 1.4 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 0.9 7 8 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 0.9 8 9 1.4 1.4 1.3 1.3 1.2 1.2 1.2 1.1 1.1 1.0 1.0 1.0 0.9 9 10 1.4 1.4 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 10 11 1.4 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 11 12 1.4 1.3 1.3 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 0.9 0.9 12 13 1.3 1.3 1.3 1.2 1.2 1.2 1.1 1.1 1.0 1.0 1.0 0.9 0.9 13 14 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 14 15 1.3 1.3 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 15 16 1.3 1.3 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 0.9 16 17 1.3 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 0.9 17 18 1.3 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 0.9 18 19 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 1.0 0.9 0.9 0.9 19 20 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 0.9 0.8 20 21 1.2 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 0.9 0.8 21 22 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 1.0 0.9 0.9 0.9 22 23 1.2 1.2 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 0.9 23 24 1.2 1.1 1.1 1.1 1.1 1.0 1.0 1.0 0.9 0.9 24 25 1.2 1.1 1.1 1.1 1.0 1.0 1.0 1.0 0.9 25 26 1.1 1.1 1.1 1.1 1.0 1.0 1.0 0.9 26 27 1.1 1.1 1.1 1.0 1.0 1.0 1.0 27 28 1.1 1.1 1.1 1.0 1.0 1.0 28 29 1.1 1.1 1.0 1.0 1.0 29 30 1.1 1.1 1.0 1.0 30 31 1.1 1.0 1.0 31 32 33 34 1.1 1.1 1.0 32 33 34 6.8 0.7 6.6 35 36 37 38 39 6.^ 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 35 36 37 38 39 40 41 42 43 44 6.8 0.8 0.8 0.8 6.^ 0.8 0.8 0.8 0.8 6.^ 40 41 42 43 44 6.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0,8 0.7 0.7 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.9 0.8 0.8 0.8 0.9 0.9 0.8 0.9 0.9 0.9 45 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 45 46 0.9 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 46 47 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.6 47 48 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.6 48 49 0.8 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 49 50 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 50 51 0.8 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 51 52 0.8 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 52 53 0.8 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 53 54 0.8 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 54 55 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 55 56 0.7 0.7 •0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 56 57 0.7 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 57 58 0.7 0.7 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 58 59 0.7 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 59 60 0.7 0.7 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.5 60 51° 52° 53° 54° 55° 56° 57° 68° 69° 60° 61° 62° 68° D eclinati( )n of the same nt ime as t tie latitu de; lone r transit ; reduct ion Bttbt ractire. Page 714] TABLE 27. Reduction to be applied to Altitudes near the Meridian. Var. Time from meridian passage. 1 Var. 1 min. (Table (Table m. s. m. s. TO. 8. 7». S. m. s. TO. S. TO. 8. TO. 8. TO. «. TO. 8. TO. «. TO. «. TO. i. 26.) 80 1 1 30 2 2 30 S 3 80 4 4 80 5 5 30 6 6 30 26.) // / n 1 II / // 1 n I II ' n 1 II / II / // 1 II / // / // ' // II 0.1 00 1 1 1 2 2 2 3 4 4 0.1 0.2 00 1 1 2 3 3 4 5 6 7 8 0.2 0.3 1 1 2 3 4 5 6 7 9 11 13 0.3 0.4 1 2 2 4 5 6 8 10 12 14 17 0.4 0.5 1 2 3 4 6 8 10 12 15 18 21 0.5 0.6 1 1 2 4 5 7 10 12 15 18 22 25 0.6 0.7 1 2 3 4 6 9 11 14 17 21 25 30 0.7 0.8 1 2 3 5 7 10 13 16 20 24 29 34 0.8 0.9 1 2 4 6 8 11 14 18 22 27 32 38 0.9 1.0 1 2 4 6 9 12 16 20 25 30 36 42 1.0 2.0 00 2 4 8 12 18 24 32 41 50 1 1 12 1 24 2.0 3.0 1 3 7 12 19 27 37 48 1 1 1 15 1 31 1 48 2 6 3.0 4.0 1 4 9 16 25 36 49 1 4 1 21 1 40 2 1 2 24 2 49 4.0 5.0 1 5 11 20 31 45 1 1 1 20 1 41 2 5 2 31 3 3 31 5.0 6.0 1 6 13 24 37 54 1 13 1 36 2 1 2 30 3 1 3 36 4 13 6.0 7.0 2 7 16 28 44 1 3 1 26 1 52 2 22 2 55 3 32 4 12 4 56 7.0 8.0 2 8 18 32 50 1 12 1 38 2 8 2 42 3 20 4 2 4 48 5 38 8.0 9.0 2 9 20 36 56 1 21 1 50 2 24 3 2 3 45 4 32 5 24 6 20 9.0 10.0 2 10 22 40 1 2 1 30 2 3 2 40 3 23 4 10 5 2 6 7 2 10.0 11.0 3 11 25 44 1 9 1 39 2 15 2 56 3 43 4 35 5 32 6 36 7 45 11.0 12.0 3 12 27 48 1 15 1 48 2 27 3 12 4 3 5 6 3 7 12 8 27 12.0 13.0 3 13 29 52 1 21 1 57 2 39 3 28 4 23 5 25 6 33 7 48 9 9 13.0 14.0 3 14 31 56 1 27 2 6 2 51 3 44 4 43 5 50 7 4 8 24 9 51 14.0 15.0 4 15 34 1 1 34 2 15 3 4 4 5 3 6 15 7 34 9 10 34 11 16 15.0 16.0 4 16 36 1 4 1 40 2 24 3 16 4 16 5 24 6 40 8 4 9 36 16.0 17.0 4 17 38 1 8 1 46 2 33 3 28 4 32 5 44 7 5 8 34 10 12 11 58 17.0 18.0 4 18 40 1 12 1 52 2 42 3 40 4 48 6 4 7 30 9 4 10 48 12 40 18.0 19.0 5 19 43 1 16 1 59 2 51 3 53 5 4 6 25 7 55 9 35 11 24 13 23 19.0 20.0 5 20 45 1 20 2 5 3 4 5 5 20 6 45 8 20 10 5 12 14 5 20.0 21.0 5 21 47 1 24 2 11 3 9 4 17 5 36 7 5 8 45 10 35 12 36 14 47 21.0 22.0 5 22 49 1 28 2 17 3 18 4 30 5 52 7 25 9 10 11 5 13 12 15 29 22.0 23.0 6 23 52 1 32 2 24 3 27 4 42 6 8 7 46 9 35 11 36 13 48 16 12 23.0 24.0 6 24 54 1 36 2 30 3 36 4 54 6 24 8 6 10 12 6 14 24 16 54 24.0 25.0 6 25 56 1 40 2 36 3 45 5 6 6 40 8 26 10 25 12 36 15 25.0 26.0 6 26 58 1 44 2 42 3 54 5 18 6 56 8 46 10 50 13 6 26.0 27.0 7 27 1 1 1 48 2 49 4 3 5 30 7 12 9 7 11 15 27.0 28.0 7 28 1 3 1 52 2 55 4 12 5 43 7 28 9 27 11 40 28.0 TABLE 2T. [Page 715 | Reduction to be applied to Altitudes near the Meridian. Var. Time from meridian passage. Var. (Table m. s. m. 8. m. s. m. s. m. s. m. 8. m. 8. m. 8. m. 8. m. s. m. 8. m. 8. m. 8. (Table 26.) 7 7 SO 80 8 30 9 9 80 10 10 80 11 11 80 12 12 80 18 26.) „ ' n / // e n t It / // / // f tr / // / // t II » II / II 1 II II 0.1 5 6 6 7 8 9 10 11 12 13 14 16 17 0.1 0.2 10 11 13 14 16 18 20 22 24 26 29 31 34 0.2 0.3 15 17 19 22 24 27 30 33 36 40 43 47 51 0.3 0.4 0.5 20 23 26 29 32 36 40 44 48 53 58 1 2 1 8 0.4 24 28 32 36 40 45 50 55 1 1 6 1 12 1 18 1 24 0.5 0.6 29 34 38 43 49 54 1 1 6 1 13 1 19 1 26 1 34 1 41 0.6 0.7 34 39 45 51 57 1 3 1 10 1 17 1 25 1 33 1 41 1 49 1 58 0.7 0.8 39 45 51 58 1 5 1 12 1 20 1 28 1 37 1 46 1 55 2 5 2 15 0.8 0.9 44 51 57 1 5 1 13 1 21 1 30 1 39 1 49 1 59 2 10 2 21 2 32 0.9 1.0 49 56 1 4 1 12 1 21 1 30 1 40 1 50 2 1 2 12 2 24 2 36 2 49 1.0 2.0 1 38 1 52 2 8 2 24 2 42 3 3 20 3 40 4 2 4 24 4 48 5 12 5 38 2.0 3.0 2 27 2 49 3 12 3 37 4 3 4 30 5 5 31 6 3 6 37 7 12 7 49 8 27 3.0 4.0 3 16 3 45 4 16 4 49 5 24 6 1 6 40 7 21 8 4 8 49 9 36 10 25 11 16 4.0 5.0 4 5 4 41 5 20 6 1 6 45 7 31 8 20 9 11 10 5 11 1 12 13 1 14 5 5.0 6.0 4 54 5 37 6 24 7 14 8 6 9 1 10 11 1 12 6 13 13 14 24 15 37 16 54 6.0 7.0 5 43 6 34 7 28 8 26 9 27 10 32 11 40 12 52 14 7 15 26 16 48 18 14 19 43 7.0 8.0 6 32 7 30 8 32 9 38 10 48 12 2 13 20 14 42 16 8 17 38 19 12 20 50 22 32 8.0 9.0 7 21 8 26 9 36 10 50 12 9 13 32 15 16 32 18 9 19 50 21 36 23 26 25 21 9.0 10.0 8 10 9 22 10 40 12 2 13 30 15 2 16 33 16 40 18 20 18 22 20 13 20 10 22 11 22 2 24 26 2 28 10 10.0 11.0 11.0 8 59 10 19 11 44 13 15 14 51 24 15 26 24 28 39 12.0 9 48 11 15 12 48 14 27 16 12 18 3 20 22 3 24 12 26 27 28 48 12.0 13.0 10 37 12 11 13 52 15 39 17 33 19 33 21 40 23 53 26 13 28 39 13.0 14.0 11 26 13 7 14 56 16 51 18 54 21 3 23 20 25 43 28 14 14.0 15.0 12 15 14 4 16 18 14 20 15 22 34 25 27 34 15.0 16.0 13 4 15 17 4 19 16 21 36 24 4 26 40 16.0 17.0 13 53 15 56 18 8 20 28 22 57 25 34 17.0 18.0 14 42 16 52 19 12 21 40 24 18 18.0 19.0 15 31 17 49 20 16 19.0 20.0 16 20 18 45 20.0 21.0 17 9 21.0 Page 716 TABLE 27. Reduction to be applied to Altitudes near the Meridian Var. Imin. (Table 26.) Time from meridian passage. Var. 1 min. (Table 26.) m. t. 18 80 m. 8. 14 wi. a. 14 80 m. 8. 15 TO. 8. 15 80 TO. 8. 16 TO. «. 16 80 TO. 8. 17 TO. 8. 17 80 TO. 8. 18 TO. 8. 18 80 TO. 8. 19 TO. 8. 19 80 // 0,1 0.2 0.3 0.4 ' // 018 36 55 113 / // 20 39 59 118 1 II 21 42 1 3 124 1 II 22 45 1 7 130 1 II 24 48 112 136 / II 26 51 117 142 / II 27 54 122 149 / II 29 58 127 166 1 II 31 1 1 132 2 2 / // 32 1 5 137 210 / // 34 1 8 143 2 17 / // 36 112 148 2 24 1 II 38 116 154 2 32 II 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 131 149 2 8 2 26 244 138 158 2 17 2 37 2 56 145 2 6 2 27 2 48 3 9 152 2 15 2 37 3 3 22 2 2 24 2 48 312 3 36 2 8 2 34 2 59 3 25- 3 50 2 16 2 43 3 11 3 38 4 5 2 24 2 53 3 22 3 61 4 20 2 33 3 4 3 34 4 5 4 36 2 42 314 3 47 419 4 62 2 51 3 25 4 4 34 5 8 3 1 3 37 413 4 49 6 26 3 10 3 48 4 26 6 4 5 42 0.5 0.6 0.7 0.8 0.9 ' 1.0 2.0 3.0 4.0 5.0 3 2 6 4 9 7 12 9 15 11 3 16 6 32 9 48 1314 16 20 3 30 7 10 30 14 1 17 31 3 45 7 30 1115 15 18 45 4 8 12 1 16 1 20 1 416 8 32 12 48 17 4 2120 4 32 9 4 13 38 18 9 22 41 4 49 9 38 14 27 19 16 24 5 5 6 1012 1519 20 25 25 31 5 24 10 48 1612 2136 27 5 42 1124 17 7 22 49 28 31 6 1 12 2 18 3 24 4 6 20 12 40 19 1 25 21 1.0 2.0 3.0 4.0 5.0 ; 6.0 7.0 8.0 9.0 Var. Imin. (Table 26.) 18 13 21 16 2418 27 20 19 36 22 52 26 8 21 2 24 32 28 2 22 30 26 15 24 1 28 1 25 36 27 13 6.0 7.0 8.0 9.0 ; T ime from meridi an passage. Var. Imin. (Table 26.) m. 8. 20 m. s. 20 30 m. s. 21 TO. «. 21 80 m. 8. 22 m. 8. 22 30 TO. ». 23 TO. 8. 23 30 TO. 8. 24 TO. 8. 24 80 TO. 8. 25 TO. 8. 25 80 m. 8. 26 // 0.1 0.2 0.3 0.4 0.6 0.6 0.7 0.8 0.9 t u 40 120 2 2 40 42 124 2 6 2 48 ' II 044 128 212 2 56 1 II 46 132 2 19 3 5 48 137 2 25 3 14 / II 51 141 2 32 3 22 / II 53 146 2 39 3 32 / // 65 150 2 46 3 41 / // 58 155 2 53 3 50 / II 1 2 3 4 1 II 1 2 2 5 3 7 4 10 1 II 1 6 2 10 3 15 4 20 ' // 1 8 215 3 23 4 30 II 0.1 0.2 0.3 0.4 < 3 20 4 440 5 20 6 3 30 4 12 454 5 36 618 3 41 4 25 5 9 5 53 6 37 3 51 4 37 5 24 6 10 6 56 4 2 4 50 5 39 6 27 716 4 13 5 4 554 6 45 7 36 4 24 517 610 7 3 7 66 4 36 5 31 6 27 7 22 8 17 4 48 5 46 6 43 7 41 8 38 5 6 7 8 9 5 12 615 7 17 8 20 9 22 5 25 6 30 7 35 8 40 9 45 5 38 6 46 7 53 9 1 10 8 0.5 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 6 40 13 20 20 26 40 7 14 21 28 1 7 21 14 42 22 3 29 24 7 42 15 24 23 7 8 4 16 8 2412 8 26 16 52 2519 8 49 17 38 26 27 912 18 24 27 37 9 36 1912 28 48 10 20 30 10 25 20 50 10 50 2140 1116 22 32 1.0 2.0 3.0 4.0 ' Note. — Tlie pages formerly occupied with Tables 28A, %8B, 28C, and /S8D liave been dropped, and consecutive page numbering iK tliereby broken. TABLE 29. [Page 725 I Conversion Tables for Nautical and Statute Miles. Nautical miles into statute miles. statute miles into nautical miles. 1 nautical mile or knot= 6,080.20 feet. 1 statute mile = 5,280 feet 1 statute mUe -=5,280 feet. 1 nautical mile or knot= 6,080.20 feet. Nautical Statute Nautical Statute Statute Nautical Statute Nautical miles. miles. miles. miles. miles. miles. miles. miles. 1 1.15 51 58. 729 1 0.87 61 44.288 2 2.30 52 59. 881 2 1.74 52 45. 156 3 3.45 53 61. 032 3 2.61 53 46. 025 4 4.61 54 62. 184 4 3.47 54 46. 893 5 5.76 55 63. 335 5 4.34 55 47. 762 6 6.91 56 64.487 6 5.21 56 48. 630 7 8.06 57 65. 639 7 6.08 57 49. 498 8 9.21 58 66. 790 8 6.95 58 50. 367 9 10.36 59 67. 942 9 7.82 59 51. 235 10 11.52 60 69. 093 10 8.68 60 52. 104 11 12. 667 61 70. 245 11 9.552 61 52. 972 12 13. 819 62 71.396 12 10. 421 62 53. 840 13 14. 970 63 72.548 13 11.289 63 54. 709 14 16. 122 64 73. 699 14 12. 158 64 55. 577 15 17. 273 65 74. 851 15 13. 026 65 56. 445 16 18. 425 66 76.003 16 13. 894 66 57. 314 17 19. 576 67 77. 154 17 14. 763 67 58. 182 18 20. 728 68 78. 306 18 15. 631 68 59. 051 19 21. 880 69 79.457 19 16.499 69 59. 919 20 23. 031 70 80. 609 20 17. 368 70 60. 787 21 24.183 71 81. 760 21 18. 236 71 61. 656 22 25. 334 72 82. 912 22 19. 105 72 62. 524 23 26. 486 73 84.063 23 19. 973 73 63. 393 24 27. 637 74 85. 215 24 20. 841 74 64. 261 25 28. 789 75 86. 366 25 21. 710 75 65. 129 26 29. 940 76 87. 518 26 22. 578 76 65. 998 27 31. 092 77 88. 670 27 23. 447 77 66. 866 28 32. 243 78 89. 821 28 24. 315 78 67. 735 29 33. 395 79 90. 973 29 25. 183 79 68. 603 30 34. 547 80 92. 124 30 26. 052 80 69. 471 31 35. 698 81 93. 276 31 26. 920 81 70. 340 32 36. 850 82 94. 427 32 27. 789 82 71. 208 33 38.001 83 95. 579 33 28. 657 83 72. 077 34 39.153 i 84 96. 730 34 29. 525 84 72. 945 35 40. 304 85 97. 882 35 30. 394 85 73. 813 36 41.456 86 99. 034 36 31. 262 86 74. 682 37 42. 607 87 100. 185 37 32. 131 87 75. 550 38 43. 759 88 101. 337 38 32. 999 88 76.419 39 44. 911 1 89 102. 488 39 33. 867 89 77. 287 40 46.062 i 90 103. 640 40 34.736 90 78. 155 41 47.214 91 104. 791 41 35. 604 91 79. 024 42 48. 365 92 105. 942 42 36. 473 92 79. 892 43 49. 517 93 107. 094 43 37. 341 93 80. 760 44 50.668 94 108. 246 44 38. 209 94 81. 629 45 51. 820 95 109. 397 45 39. 078 95 82. 497 46 52. 971 96 110. 549 46 39. 946 96 83. 366 47 54.123 97 111. 701 47 40. 814 97 84.234 48 55. 275 98 112. 852 48 41. 683 98 85. 102 49 56. 426 99 114.004 49 42. 551 99 85. 971 50 57. 578 100 115. 155 50 43. 420 100 86. 839 I Page 726] TABLE 30. Conversion Tables for Metric and English Linear Measure. Metric to English. Meters. Feet. Yards. Statute miles. Nautical miles. 1 2 3 4 3.280 833 3 6.561 666 7 9.842 500 13.123 333 3 1.093 611 1 2.187 222 2 3.280 833 3 4.374 444 4 0.000 621 369 .001 242 738 . 001 864 106 .002 485 475 0.000 539 593 .001 079 185 .001 618 778 .002 158 .370 5 6 7 8 9 16.404 166 7 19.685 000 22.965 833 3 26.246 666 7 29.527 500 5.468 055 6 6.561 666 7 7.655 277 8 8.748 888 9 9.842 500 .003 106 844 .003 728 213 .004 349 582 .004 970 950 .005 592 319 .002 697 963 .003 237 556 .003 777 148 .004 316 741 .004 856 333 English to metric. No. Feet to meters. Yards to meters. Statute miles to meters. Nautical miles to meters. 1 2 3 4 0.304 800 6 0.609 601 2 0.914 401 8 1.219' 202 4 0.914 401 8 1.828 803 7 2.743 205 5 3.657 607 3 1, 609. 35 8, 218. 70 4, 828. 05 6, 437. 40 1, 853. 25 3, 706. 50 5, 559. 75 7,413.00 5 6 7 8 9 1.524 003 1.828 803 7 2.133 604 3 2.438 404 9 2.743 205 5 4.572 009 1 5.486 411 6.400 812 8 7.315 214 6 8.229 616 5 8, 046. 75 9, 656. 10 11, 265. 45 12, 874. 80 14, 484. 15 9, 266. 25 11, 119. 50 12, 972. 75 14, 826. 00 16, 679. 25 TABLE 31. (Page 727 1 Conversion Tables for Thermometer Scales. [po^ Fahrenheit temperature; C°=Centlgrade temperature; R«>=R6aumur temperature.] Equivalent temj>erature»—Fahr., CetU., Riau RO=J c°=J (F°- Co={RO=j(FO- -32°). -32°). F°. C°. R°. F°. C°. R°. 1 -17.2 -13.8 51 +10.6 + 8.4 2 16.7 13.3 52 11.1 8.9 EquivcUetU temperatures — Centigrade and FhhrenheiL 3 4 5 16.1 15.6 15.0 12.9 12.4 12.0 53 54 55 11.7 12.2 12.8 9.3 9.8 10.2 F°=|C°+32°. C°. F°. c°. F°. c°. F°. c°. F°. C°. F°. 6 7 g 14.4 13.9 13.3 11.6 11.1 10.7 56 57 58 13.3 13.9 14.4 10.7 11.1 11.6 -10 14.0 32.0 10 50.0 20 68.0 30 86.0 9 12.8 10.2 59 15.0 12.0 - 9 15.8 1 33.8 11 51.8 21 69.8 31 87.8 10 12.2 9.8 60 15.6 12.4 - 8 17.6 2 35.6 12 53.6 22 71.6 32 89.6 11 11.7 9.3 61 16.1 12.9 - 7 19.4 3 37.4 13 55.4 23 73.4 33 91.4 12 ll!l 8.9 62 16.7 13.3 - 6 21.2 4 39.2 14 57.2 24 75.2 34 93.2 13 10.6 8.4 63 17.2 13.8 - 5 23.0 5 41.0 15 59.0 25 77.0 35 95.0 14 10.0 8.0 64 17.8 14.2 - 4 24.8 6 42.8 16 60.8 26 78.8 36 96.8 15 9.4 7.6 65 18.3 14.7 - 3 26.6 7 44.6 17 62.6 27 80.6 37 98.6 16 8 9 7.1 66 18.9 15.1 - 2 28.4 8 46.4 18 64.4 28 82.4 38 100.4 17 8.3 6.7 67 19.4 15.6 - 1 30.2 9 48.2 19 66.2 29 84.2 39 102.2 18 19 7.8 7.2 6.2 5.8 68 69 20.0 20.6 16.0 16.4 1 20 6.7 5.3 70 21.1 16.9 21 6.1 4.9 71 21.7 17.3 22 5.6 4.4 72 22.2 17.8 23 5.0 4.0 73 22.8 18.2 24 4.4 3.6 74 23.3 18.7 25 3.9 3.1 75 23.9 19.1 26 3.3 2.7 76 24.4 19.6 27 2.8 2.2 77 25.0 20.0 Equivalent temperatures— JUaumur and Fahrenheit 28 2.2 1.8 78 25.6 20.4 F°=| R°+32°. 29 30 1.7 1.1 1.3 0.9 79 80 26.1 26.7 20.9 21.3 E°. F°. R°. F°. Ro. F<>. R°. F". 31 — 0.6 — 04 81 27.2 21.8 32 33 34 35 36 37 38 39 40 41 42 o!o + 0.6 1.1 1.7 2.2 2.8 3.3 3.9 4.4 5.0 5.6 olo + 0.4 0.9 1.3 1.8 2.2 2.7 3.1 3.6 4.0 4.4 82 83 84 85 86 87 88 89 90 91 92 27.8 28.3 28.9 29.4 30.0 30.6 31.1 31.7 32.2 32.8 33.3 22.2 22.7 23.1 23.6 24.0 24.4 24.9 25.3 25.8 26.2 26.7 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 9.5 11.8 14.0 16.2 18.5 20.8 23.0 25.2 27.5 29.8 1 2 3 4 5 6 7 8 9 32.0 34.2 36.5 38.8 41.0 43.2 45.5 47.8 50.0 52.2 10 11 12 13 14 15 16 17 18 19 54.5 56.8 59.0 61.2 63.5 65.8 68.0 70.2 72.5 74.8 20 21 22 23 24 25 26 27 28 29 77.0 79.2 81.5 83.8 86.0 88.2 90.5 92.8 95.0 97.2 43 6. 1 4 9 93 33.9 27. 1 44 a? 5.3 94 34! 4 27.6 45 7.2 5.8 95 35.0 28.0 46 7.8 6.2 96 35.6 28.4 47 8.3 6.7 97 36.1 28.9 48 8.9 7.1 98 36.7 29.3 49 9.4 7.6 99 37.2 29.8 50 +10.0 + 8.0 100 +37.8 + 30.2 21594°— 14 39 Page 728] TABLE 32. To obtain the True Force and Direction of the Wind from its Apparent Force and Direction on a Moving Vessel. 1 "§ 1 1 ■s g < •8JB0B ^jojnBag 'aojoj arux Neisioe>5-*io->}(ictoio«2j>tot-eo t^OOQOaOOC09CCa>0030rHOrHrH rHrH01(N(NCs>CJe*«OCD»/5vCiOtC iOLOiCiOiOi^lO»OtO»C>OiOiO»Ci^ iClO«0»OiOiOiOlOLO ;Jl •ajBos jjojnBag 'aojtoj arux e«ooioeo««00roO0»OOOrHrH rH rH rHrHrHrH rHrHNC^(N(NNCJ(N •M.oq 9X1% jjo sjuiod 'uotjoaitp anjx i/5JI'0-t»OOJ>OCO>00090>05000rHr- rHrHJI-*-* ■0<-<><-«<-*-*-*Tfl-*.OlTI.-«'-*00-*-<}< CC-<»'-*CO-*TjlCO«>-<* •aiBos jjojnBag 'aojoj anjx Neo-^eo'^ic-'fiintoiotoixor-i^ t*l~-0DI>00000005O0SOOOOrH rHrHIN(NN(NntO'j'io->*i-*-<((co-*-* cc^-jeoTO^TOcoeoMCOTOcoeoTO COCOCCtNTOTOC^TOCC •aiBos ^ojnBag 'aojoj anjx INM-^MTfliC-fliiOtDiCOtOiCtOt^ ^Ct^OCt^OOODODOOOSOsOSOOOO rHrHrHrH(N(No>cnoooo rHrHrHrHCioiOTC-*K5eoc<5-*iN«j«)e^c->ro MC4MrH(MC»'in-<(ooooooosO!Oioo OrHrHrHrHlNeMC^IN •Aioq amsosjniod'uopoajtp amx lOiOiOM-*-rl<(NKl-<)<(NC^eCi-H(NeQ rHCJNrHrHNOrHrHOrHrHOOrH OOrHOOOOOC 00 •aXBOs wojnBag 'aojoj anjx t^l>t^OOeOOOC»OlCVOV OOOrHrHrH«(M!N 1 •Aioq aqj 50 ejoiod 'aopoaiip amx lC»ClOCC'*T}<(NCCCCrHC^ICOOT-tC^ OrHt^t-r»l>WOOOOO>0»Oo|oOOrHr-lr-IC^(NCl 1 •Aioqaq^ go ffjuiod 'uonoajip anjx lOiOlOCO-a<-«.-llN«iO.-l(NOrH(N OSOrHO>OOCeOaOOOOS(»000»0> QOOOOlQOOOOiOOOOOC « •axB08 ^jojnBag 'aojoj anJX r-1 THr-ir-(!Hr-(r-^ 1 •Moq aqj go Rioiod 'uotjoajip amx iOiomet"*<0(Neoo5r-i(NOsOTW aoosooooioi>oc>cii^ocoat>oooc t> I:~ « C~ t^ 00 l> t^ t> 1 >s •aiBOS jjojnBag 'aoioj anJX i-iiN-.t-i~-cooooocnaiO>c>ooCN-ooot^ooo:^l>oocot^oototoi> 5 ■* •aiBOs iiojnBag 'aojoj anjx •Aioq aqj go ffjntod 'uoi^oajip anJX iOmiOM«lCOO(NI>000 rH r-1 i-H rH l-H rH rH rH rH rH rH COt*O55Ot^00iOt£>l>iC^^^»OeO lOiOOiCiOiO-^lOiC 1 09 •aiBOs iiojnBag 'aojoj amx rHCq ■* rH C^ CO rH rH Ca t^.rH C^ N (N M |tOTOeOT("HJleCHOlCl-fl'r^tOl>|oiOOaOOOO>rHrHrH 1 •Moq aqj jgosjuiod 'uotjoajip anjx miotoc^-*ici».*iotD-*-Tij<-*io rJ<-rj'*jitoos eoiot~eo->}(irieoTO.9> rH rH O rH rHrHrH •Moqaq^ go s^uiod 'nopoajip amx -lrH01rHrH(NrHrH!M DiOOOiOOOiOO -HrHoct^-i.-iO oooooo 00 r^-^e^iN S§g8S OOOOO OOOOO OOOOO OOOOO t* t^ JDiC'VTOTO N.-1-^OOO OOOOO OOOOO oooooo s t-TOMlH gssss l-lTHt-lOO OOOOO OOOOO OOOOO 00 1~ t~ «eH r-l tH r-( OOOOO eocoddiH OOOOO o o to ^ O »C -v » O iCOi-HrH oio-*toS rHOOOO OOOOO IM.T-lrtrHr-l OOOOO ;OiOtJ1t)r*OlO rH iO ^ "^ TO TO OOOOO OOOOO OiCCt^^Oift Tjt -^t* CO Ci M t-c.-(000 o o OOOOO OOOOO OOOOO -^Ni-trH S^cSSS sssss t^tClO-0» o OOOOO OOOOO OOOOO OOOOO OOOOO o >* TOr-lrHO OOOOO CO *HO>t^ to 10-*TOCON 1-H^OOO o o> Oft 00 00 OOOOO 00 o OOOOO OOOOO OOOOO 5ai i-IC^eO'* iO«Ot^00Oi OiHMTO-* lotot^aaoi Or-KMCO-* •OtOt^oOO) oe<'*c»eoo eoOMr;r-i ^-((^^■-(eoc^ 8S ooe o oooeo O OOIN3> ■<1<0r-l>0 r-i«?ii-ci-( e^eoiocjS toioeoc^r-i ■ O^ 00 - JOOOl-* o>o>oooot^ Tlaot»t»«o lOC^Ncor- iHioeoiHirj tOCOrHOOl V5 o e< o 53 iM-^oeoo aor»t~to«D iCift ^ ■* ^ ■"S" f) CO C< rH tfllNOOlOO T)OOC- sssss I-* 0> 00 t^ o 00(NO2j 0->S lO in -*■*■* OOOiMINCO (M -sjl Tjl o .-( a> i> 'o in lO 0>n r» >o lO Tllc^rHOlO ■* ^ ^ ^ CO fHOm-S'eO ^ ^ CO CO CO i-iioeoi-<>o (O tO vo »n ■* Tjn ■*■*■* COlNiHOlO * ■* * ^ CO «0t^05 C 01-*rHO.-l — -^ 'j'^coiN CO CO ^ t*" tH iO-*cOC^0 O CO ''J* o» COiOCOrHlO CO'NCJOJrt COI^ClC^rH 5JSS22 COCie< • OOQCOC- ^eoeoc>»r-i OOC^t-'-l'O COCOMINrH ■>)lcONC^ 0 (^^l^^o^atac~aoo> CO(MIMC^r-( - -5 neoiHO>oo * ■* ^ CO 00 OOOOO ** ^ ■* ^ CO CO eoi^(NOoo C^O>0-<)< C^ ^ r-( e^ CO OiO-<) i-H ■»!< i> >-i :0 ■* ■* CO " rH 00 lNlMiHrHi-(0 ) 1-1 1- coo <>-lOOO - lA in ■* ■* T* OOOOOO OOinCOrHO COCOCOCOCO OOOOO tOTfc^OOO CO CO CO CO CN OOOOO eocococ>Sc^ OOOOO COCOfSMlN OOOOO OOOOO OIN-^fOOO (oooinio (r-liH-HOO ^ ^ CO CO CO CO OOOOOO 00 t- CO lO Tjl CO OOOOOO t- to-*co^ 3* 4* 6* 2* 2* 2* 2* 2* 3* 2* 2* 1* 1* 1* .2* .1* .1* .0 .1 .2 .1* .1* .0 .1 .3 .6 .1* .0 .1 .3 .5 1.2 .1* .1 .2 .5 .9 75 20 30 40 50 60 70 20 30 40 50 60 70 70 .4* .4* .5* .6* .9* 1 4* 4* 4* 5* 6* 2* 3* 3* 3* 3* 4* 6* 3* 3* 3* 2* 3* 3* .3* .2* .2* .2* .1* .1* .3* .2* .1* .0 .1 .2 .2* .1* .0 .1 .2 .6 .2* .1* .1 .3 .5 L2 .2* 3.1 70 20 30 40 50 60 70 i' P GO P OQ 0° 6° 10° 16° 20° 26° 80° 86° 40° 46° 60° 66° •0° 66° 70° 76° ^s Latitude. Page 740] TABLE 39. Amplitudes. Declination. Lati- tude. Lati- tude. o°.o 0°.6 1°.0 10.5 2<^.0 2°. 6 s°.o 8°. 6 4°.0 4°. 5 6°.0 5°. 6 6°.0 o o o o o o o o o o 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 10 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.1 4.6 5.1 5.6 6.1 10 15 0.0 0.5 1.0 1.5 2.1 2.6 3.1 3.6 4.2 4.7 5.2 5.7 6.2 15 20 0.0 0.5 1.1 1.6 2.1 2.7 3.2 3.7 4.3 4.8 5.3 5.8 6.4 20 25 0.0 0.5 1.1 1.6 2.2 2.8 3.3 3.8 4.4 5.0 5.5 6.0 6.6 25 30 0.0 0.6 1.2 1.7 2.3 2.9 3.4 4.0 4.6 5.2 5.8 6.3 6.9 30 32 0.0 0.6 1.2 1.8 2.4 2.9 3.5 4.1 4.7 5.3 5.9 6.5 7.0 32 34 0.0 0.6 1.2 1.8 2.4 3.0 3.6 4.2 4.8 5.4 6.0 6.6 7.2 34 36 0.0 0.6 1.2 1.8 2.5 3.1 3.7 4.3 4.9 5.6 6.1 6.8 7.4 36 38 0.0 0.6 1.3 1.9 2.5 3.2 3.8 4.4 5.1 5.7 6.3 7.0 7.6 38 40 0.0 0.7 1.3 2.0 2.6 3.3 3.9 4.6 5.2 5.9 6.5 7.2 7.8 40 42 0.0 0.7 1.3 2.0 2.7 3.4 4.0 4.7 5.4 6.1 6.7 7.4 8.0 42 44 0.0 0.7 1.4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 6.9 7.6 8.3. 44 46 0.0 0.7 1.4 2.2 2.9 3.6 4.3 5.0 5.8 6.5 7.2 7.9 8.6 46 48 0.0 0.7 1.5 2.2 3.0 3.7 4.5 5.2 6.0 6.7 7.5 8.2 9.0 48 50 0.0 0.8 1.5 2.3 3.1 3.9 4.7 5.4 6.2 7.0 7.8 8.6 9.3 50 51 0.0 0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0 8.8 9.5 51 52 0.0 0.8 1.6 2.4 3.3 4.1 4.9 5.7 6.5 7.3 8.1 9.0 9.7 52 53 0.0 0.8 1.6 2.5 3.3 4.2 5.0 5.8 6.7 7.5 8.3 9.2 10.0 53 54 0.0 0.9 1.7 2.5 3.4 4.3 5.1 6.0 6.8 7.7 8.5 9.4 0.2 54 55 0.0 0.9 1.7 2.6 3.5 4.4 5.2 6.1 7.0 7.9 8.7 9.6 10.5 55 56 0.0 0.9 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 9.0 9.9 0.8 56 57 0.0 0.9 1.8 2.7 3.7 4.6 5.5 6.4 7.4 8.3 9.2 10.1 1.1 57 58 0.0 0.9 1.9 2.8 3.8 4.7 5.7 6.6 7.6 8.5 9.5 0.4 1.4 58 59 0.0 1.0 1.9 2.9 3.9 4.9 5.8 6.8 7.8 8.8 9.7 0.7 1.7 59 60 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.1 60 61 0.0 1.0 2.1 3.1 4.1 5.2 6.2 7.2 8.3 9.3 0.3 1.4 2.5 61 62 0.0 1.1 2.1 3.2 4.3 5.3 6.4 7.5 8.5 9.6 0.7 1.8 2.9 62 63 0.0 1.1 2.2 3.3 4.5 5.5 6.6 7.7 8.8 9.9 1.1 2.2 3.4 63 64 0.0 1.1 2.3 3.4 4.6 5.7 6.9 8.0 9.2 10.3 1.5 2.6 3.9 64 65.0 0.0 1.2 2.4 3.5 4.8 5.9 7.1 8.3 9.5 10.7 11.9 13.1 14.4 65.0 5.5 0.0 1.2 2.4 3.6 4.8 6.0 7.2 8.5 9.7 0.9 2.1 3.4 4.6 5.5 6.0 0.0 1.2 2.5 3.7 4.9 6.1 7.4 8.6 9.9 1.1 2.4 3.6 4.9 6.0 6.5 0.0 1.2 2.5 3.8 5.0 6.3 7.5 8.8 10.1 1.3 2.6 3.9 5.2 6.5 7.0 0.0 1.3 2.6 3.8 5.1 6.4 7.7 9.0 0.3 1.6 2.9 4.2 5.5 7.0 67.5 0.0 1.3 2.6 3.9 5.2 6.5 7.9 9.2 10.5 11.8 13.2 14.5 15.9 67.5 8.0 0.0 1.3 2.7 4.0 5.3 6.7 8.0 9.4 0.7 2.1 3.5 4.8 6.2 8.0 8.5 0.0 1.4 2.7 4.1 5.4 6.8 8.2 9.6 1.0 2.4 3.8 5.2 6.6 8.5 9.0 0.0 1.4 2.8 4.2 5.5 7.0 8.4 9.8 1.2 2.6 4.1 5.5 7.0 9.0 9.5 0.0 1.4 2.9 4.3 5.7 7.2 8.6 10.0 1.5 2.9 4.4 5.9 7.4 9.5 70.0 0.0 1.5 2.9 4.4 5.8 7.3 8.8 10.3 11.8 13.3 14.8 16.3 17.8 70.0 0.5 0.0 1.5 3.0 4.5 6.0 7.5 9.0 0.5 2.1 3.6 5.1 6.7 8.2 0.5 1.0 0.0 1.5 3.1 4.6 6.2 7.7 9.3 0.8 2.4 3.9 5.5 7.1 8.7 1.0 1.5 0.0 1.6 3.2 4.7 6.3 7.9 9.5 1.1 2.7 4.3 5.9 7.8 9.2 1.5 2.0 0.0 1.6 3.2 4.9 6.5 8.1 9.8 1.4 3.0 4.7 6.4 8.1 9.8 2.0 72.5 0.0 1.7 3.3 5.0 6.7 8.3 10.0 11.7 13.4 15.1 16.9 18.6 20.3 72.5 3.0 0.0 1.7 3.4 5.1 6.9 8.6 0.3 2.0 3.8 5.5 7.4 9.1 0.9 3.0 3.5 0.0 1.8 3.5 5.2 7.1 8.8 0.6 2.4 4.2 6.0 7.9 9.7 1.6 3.5 4.0 0.0 1.8 3.6 5.4 7.3 9.1 0.9 2.8 4.6 6.5 8.4 20.3 2.3 4.0 4.5 0.0 1.9 3.7 5.6 7.5 9.4 1.3 3.2 5.1 7.1 9.0 1.0 3.0 4.5 75.0 0.0 1.9 3.8 5.8 7.7 9.7 11.7 13.6 15.6 17.7 19.7 21.7 23.8 75.0 5.5 0.0 2.0 3.9 6.0 8.0 10.0 2.1 4.1 6.2 8.3 20.4 2.5 4.7 5.5 6.0 0.0 2.1 4.0 6.2 8.3 0.4 2.5 4.6 6.8 8.9 1.1 3.3 5.6 6.0 6.5 0.0 2.1 4.2 6.4 8.6 0.8 3.0 5.2 7.4 9.6 1.9 4.2 6.6 6.5 7.0 0.0 2.2 4.4 6.6 8.9 1.2 3.5 5.8 8.1 20.4 2.8 5.2 7.7 7.0 TABLE 39. [Page 741 Amplitudes. Lati- tude. Decimation. 1 Lati- tude. 6°.0 «°.5 ;°.o 7°. 5 8°.0 8°. 5 9°.0 1 9°. 5 10°.0 10°. 5 11°.0 11°.6 li°.0 o o o o o o o o o o o o o 6.0 6.5 7.0 7.5 8.0 8.5 9.0 1 9.5 10.0 10.5 11.0 11.5 12.0 10 6.1 6.6 7.1 7.6 8.1 8.6 9.1 1 9.7 0.1 0.7 1.2 1.7 2.2 10 15 6.2 6.7 7.2 7.8 8.3 8.8 9.3 9.8 0.4 0.9 1.4 1.9 2.5 15 20 6.4 6.9 7.4 8.0 8.5 9.1 9.6 10,1 0.7 1.2 1.7 2.3 2.8 20 25 30 6.6 7.1 7.7 8.3 8.8 9.4 9.9 0.5 1.1 1.6 2.2 2.8 3.3 25 6.9 7.5 8.1 8.7 9.3 9.8 10.4 1 11.0 11.5 12.1 12.7 13.3 13.9 30 32 7.0 7.7 8.3 8.8 9.5 10.0 0.6 i 1.2 1.8 2.4 3.0 3.6 4.2 32 34 7.2 7.8 8.5 9.0 9.7 0.3 0.8 1 1.5 2.1 2.7 3.3 8.9 4.5 34 36 7.4 8.0 8.7 9.3 9.9 0.5 1.1 ! 1.8 2.4 3.0 3.6 4.3 4.9 36 38 7.6 8.2 8.9 9.5 10.2 0.8 1.4 ! 2.1 2.7 3.4 4.0 4.7 5.3 38 40 7.8 8.5 9.1 9.8 10.5 11.1 11.7 12.4 13.1 13.8 14.4 15.1 15.7 40 42 8.0 8.8 9.4 10.1 0.8 1.5 2.1 2.8 3.5 4.2 4.8 5.6 6.2 42 44 8.3 9.1 9.7 0.5 1.1 1.9 2.5 3.3 4.0 4.7 5.3 6.1 6.8 44 46 8.6 9.4 10.1 0.8 1.5 2.3 3.0 3.8 4.5 5.2 5.9 6.7 7.4 46 48 9.0 9.7 0.5 1.2 2.0 2.8 3.5 4.3 5.0 5.8 6.6 7.3 8.1 48 50 9.3 10.1 10.9 11.7 12.5 13.3 14.1 14.9 15.7 16.5 17.3 18.1 18.9 50 51 9.5 0.4 1.2 2.0 2.8 3.6 4.4 5.2 6.0 6.8 7.7 8.5 9.3 51 52 9.7 0.6 1.4 2.2 3.1 3.9 4. 7 5. 6 6.4 7.2 8.1 8.9 9.7 52 53 10.0 0.8 1.7 2.5 3.4 4.2 5.1 5.9 6.8 7.6 8.5 9.4 20.2 53 54 0.2 1.1 2.0 2.8 3.7 4.6 5.4 6.3 7.2 8.1 8.9 9.8 0.7 54 55 10.5 11.4 12.3 13.1 14.0 14.9 15.8 16.7 17.6 18.5 19.4 20.3 21.2 55 56 0.8 1.7 2.6 3.5 4.4 5.3 6.2 7.2 8.1 9.0 9.9 0.9 1.8 56 57 1.1 2.0 2.9 3.9 4.8 5.8 6.7 7.7 8.6 9.6 20.5 1.5 2.4 57 58 1.4 2.3 3.3 4.3 5.2 6.2 7.2 8.2 9.1 20.1 1.1 2.1 3.1 58 59 1.7 2.7 3.7 4.7 5.7 6.7 7.7 8.7 9.7 0.7 1.7 2.8 3.8 59 60 12.1 13.1 14.1 15.1 16.2 17.2 18.2 19.3 20.3 21.4 22.4 23.5 24.6 60 61 2.5 3.5 4.6 5.6 6.7 7.8 8.8 9.9 1.0 2.1 3.1 4.3 5.4 61 62 2.9 3.9 5.1 6.1 7.3 8.4 9.4 20.6 1.7 2.9 3.9 5.2 6.3 62 63 3.4 4.4 5.6 6.7 7.9 9.0 20.1 1.3 2.5 3.7 4.8 6.1 7.2 63 64 3.9 5.0 6.2 7.3 8.5 9.7 0.9 2.1 3.3 4.6 5.7 7.1 8.3 64 65.0 14.4 15.5 16.8 18.0 19.3 20.5 21.7 23.0 24.2 25.6 26.8 28. 2 29. 5 65.0 5.5 4.6 5.8 7.1 8.3 9.6 0.9 2.2 3.5 4.7 6.1 7.4 8. 7 30. 1 5.5 6.0 4.9 6.2 7.4 8.7 20.0 1.3 2.6 3.9 5.3 6.6 8.0 9. 3 0. 7 6.0 6.5 5.2 6.5 7.8 9.1 0.4 1.8 3.1 4.4 5.8 7.2 8.6 30.0 1.4 6.5 7.0 5.5 6.8 8.2 9.5 0.9 2.2 3.6 5.0 6.4 7.8 9.2 0. 7 2. 1 7.0 67.5 15.9 17.2 18.6 19.9 21.3 22.7 24.1 25.5 27.0 28.4 29.9 31. 4 1 32. 9 67.5 8.0 6.2 7.6 9.0 20.4 1.8 3.2 4.7 6.1 7.6 9.1 30.6 2. 2 1 3. 7 8.0 8.5 6.6 8.0 9.4 0.9 2.3 3.8 5.3 6.8 8.3 9.8 1.4 3.0 4.6 8.5 9.0 7.0 8.4 9.9 1.4 2.8 4.4 5.9 7.4 9.0 30.6 2.2 3.8 5.5 9.0 9.5 7.4 8.9 20.4 1.9 3.4 5.0 6.5 8.1 9.7 1.4 3.0 4.7 6.4 9.5 70.0 17.8 19.3 20.9 22.4 24.0 25.6 27.2 28.8 30.5 32.2 33.9 35.7 37.4 70.0 0.5 8.2 9.8 1.4 3.0 4.6 6.3 7.9 9.6 1.3 3.1 4.9 6.7 8.5 0.5 1.0 8.7 20.3 2.0 3.6 5.3 7.0 8.7 30.5 2.2 4.0 5.9 7.8 9.7 1.0 1.5 9.2 0.9 2.6 4.3 6.0 7.8 9.5 1.4 3.2 5.0 7.0 8.9 40.9 1.5 2.0 9.8 1.5 3.2 5.0 6.8 8.6 30.4 2.3 4.2 6.1 8.1 40.2 2.3 2.0 72.5 20.3 22.1 23.9 25.7 27.6 29.5 31.4 33.3 35.3 37.3 39.4 41.5 43.7 72.5 3.0 0.9 2.8 4.6 6.5 8.4 30.4 2.4 4.4 6.5 8.6 40.8 3.0 5.3 3.0 3.5 1.6 3.5 5.4 7.4 9.3 1.4 3.4 5.5 7.7 9.9 2.2 4.6 7.0 3.5 4.0 2.3 4.3 6.2 8.3 30.3 2.5 4.6 6.8 9.1 41.4 3.8 6.3 8.9 4.0 4.5 3.0 5.1 7.1 9.3 1.4 3.6 5.8 8.2 40.5 3.0 5.6 8.2 51.1 4.5 75.0 23.8 26.0 28.1 30.3 32.5 34.8 37.2 39.6 42.1 44.8 47.5 50.4 53.5 75.0 5.5 4.7 6.9 9.1 1.4 3.8 6.2 8.7 41.2 3.9 6.7 9.6 2.8 6.2 5.5 6.0 5.6 7.9 30.2 2.6 5.1 7.7 40.3 3.0 5.9 8.9 52.1 5.5 9.3 6.0 6.5 6.6 9.0 1.4 4.0 6.6 9.3 2.1 5.0 8.1 51.3 4.8 8.7 63.0 6.5 7.0 7. 7 30.2 2.8 5.5 8.2 41.1 4.1 7.2 50.5 4.1 8.0 62.4 7.6 7.0 Page 742; TABLE 39. Amplitudes. Lati- tude. Declination. Lati- tude. 12°.0 12°. 5 13°.0 18°. 6 14°. 14°. 5 16°.0 16°. 5 16°. 16°. 5 17°.0 17°. 5 18°.o o c o o o o o o o o o o o 12.0 12.5 13.0 13.6 14.0 14.5 15.0 15.6 16.0 16.5 17.0 17.5 18.0 10 2.2 2.7 3.2 3.7 4.2 4.7 5.3 6.8 6.3 6.8 7.3 7.9 8.3 10 15 2.5 2.9 3.6 4.0 4.5 6.0 5.6 6.1 6.6 7.1 7.7 8.2 8.7 15 20 2.8 3.3 3.8 4.4 4.9 6.6 6.0 6.5 7.1 7.6 8.1 8.7 9.2 20 25 3.3 3.8 4.4 4.9 5.6 6.1 6.6 7.1 7.7 8.3 8.8 9.4 9.9 25 30 13.9 14.6 16.0 15.6 16.2 16.8 17.4 18.0 18.6 19.2 19.7 20.3 20.9 30 32 4.2 4,8 6.3 6.0 6.6 7.2 7.8 8.4 9.0 9.6 20.2 0.8 1.4 32 34 4.5 5.1 5.7 6.4 7.0 7.6 8.2 8.8 9.5 20.0 0.7 1.3 1.9 34 36 4.9 5.6 6.1 6.8 7.4 8.0 8.7 9.3 20.0 0.6 1.2 1.8 2.5 36 38 5.3 6.0 6.6 7.2 7.9 8.6 9.2 9.8 0.6 1.1 1.8 2,4 3.1 38 40 15.7 16.4 17.1 17.8 18.4 19.1 19.7 20.4 21.1 21.8 22.4 23.1 23.8 40 41 6.0 6.7 7.3 8.0 8.7 9.4 20.0 0.8 1.4 2.1 2.8 3.5 4.2 41 42 6.2 6.9 7.6 8.3 9.0 9.7 0.4 1.1 1.8 2.5 3.2 3.9 4.6 42 43 6.5 7.2 7.9 8.6 9.3 20.0 0.7 1.4 2.2 2.9 3.6 4.3 6.0 43 44 6.8 7.6 8.2 8.9 9.6 0.4 1.1 1.8 2.6 3.3 4.0 4.7 6.4 44 45 17.1 17.8 18.5 19.3 20.0 20.7 21.6 22.2 23.0 23.7 24.4 26.2 26.9 45 46 7.4 8.2 8.9 9.6 0.4 1.1 1.9 2.6 3.4 4.1 4.9 6.7 6.4 46 47 7.7 8.5 9.3 20.0 0.8 1.5 2.3 3.1 3.8 4.6 5.4 6.2 6.9 47 48 8.1 8.9 9.7 0.4 1.2 2.0 2.8 3.6 4.3 6.1 5.9 6.7 7.5 48 49 8.5 9.3 20.1 0.8 1.6 2.4 3.2 4.1 4.9 6.7 6.6 7.3 8.1 49 50 18.9 19.7 20.6 21.3 22.1 22.9 23.7 24.6 26.4 26.2 27.0 27.9 28.7 50 51 9.3 20.1 0.9 1.8 2.6 3.5 4.3 5.1 6.0 6.8 7.6 8.5 9.4 61 52 9.7 0.6 1.4 2.3 3.1 4.0 4.9 5.7 6.6 7.6 8.3 9.2 30.1 62 53 20.2 1.1 1.9 2.8 3.7 4.6 5.6 6.4 7.3 8.2 9.0 30.0 0.9 63 54 0.7 1.6 2.5 3.4 4.3 5.2 6.1 7.1 8.0 8.9 9.8 0.8 1.7 54 55 21.2 22.2 23.1 24.0 24.9 25.9 26.8 27.8 28.7 29.7 30.6 31.6 32.6 55 56 1.8 2.8 3.7 4.7 5.6 6.6 7.6 8.6 9.5 30.6 1.6 2.5 3.6 56 57 2.4 3.4 4.4 6.4 6.4 7.4 8.4 9.4 30.4 1.4 2.5 3.5 4.6 57 58 3.1 4.1 6.1 6.1 7.2 8.2 9.2 30.3 1.3 2.4 3.5 4.6 6.7 58 59 3.8 4.8 6.9 6.9 8.0 9.1 30.2 1.3 2.3 3.5 4.6 6.7 6.9 59 60 24.6 25.6 26.7 27.8 28.9 30.1 31.2 32.3 33.4 34.6 36.8 36.9 38.2 60 61 5.4 6.6 7.6 8.8 9.9 1.1 2.2 3.5 4.6 5.8 7.1 8.3 9.6 61 62 6.3 7.6 8.6 9.8 31.0 2.2 3.4 4.7 5.9 7.2 8.5 9.8 41.2 62 63 7.2 8.5 9.7 31.0 2.2 3.6 4.7 6.1 7.4 8.7 40.1 41.5 2.9 63 64 8.3 9.6 30.9 2.2 3.6 4.8 6.2 7.6 9.0 40.4 1.8 3.3 4.8 64 65.0 29.5 30.8 32.2 33.6 34.9 36.3 37.8 39.2 40.7 42.2 43,8 46.4 47.0 65.0 5.5 30.1 1.6 2.9 4.3 5.7 7.1 8.6 40.1 1.6 3.2 4.8 6.6 8.2 5.5 6.0 0.7 2.2 3.6 5.0 6.6 8.0 9.6 1.1 2.7 4.3 6.9 7.7 9.4 6.0 6.5 1.4 2.9 4.3 5.8 7.3 8.9 40.6 2.1 3.8 5.4 7.1 8.9 60.8 6.5 7.0 2.1 3.6 5.1 6.7 8.2 9.8 1.6 3.2 4.9 6.6 8.4 50.3 2.3 7.0 67.5 32.9 34.4 36.0 37.6 39.2 40.8 42.6 44.3 46.1 47.9 49.8 61.8 53.9 67.5 8.0 3.7 6.3 6.9 8.6 40.2 1.9 3.7 6.6 7.4 9.3 51.3 3.4 6.6 8.0 8.5 4.6 6.2 7.9 9.6 1.3 3.1 4.9 6.8 8.8 60.8 2.9 5.1 7.5 8.5 9.0 5.6 7.2 8.9 40.7 2.5 4.3 6.2 8.2 50.3 2.4 4.6 7.0 9.6 9.0 9.5 6.4 8.2 40.0 1.8 3.7 5.6 7.6 9.7 1.9 4.2 6.5 9.1 61.9 9.5 70.0 37.4 39.3 41.1 43.0 45.0 47.0 49.2 61.4 53.7 66.1 68.7 61.5 64.6 70.0 0.5 8.5 40.4 2.4 4.4 6.4 8.6 50.8 3.2 5.7 8.3 61.1 4.3 7.8 0.5 1.0 9.7 1.7 3.7 5.8 8.0 60.3 2.6 5.2 7.9 60.7 3.9 7.5 71.7 1.0 1.5 40.9 3.0 5.1 7.4 9.7 2.1 4.6 7.4 60.3 3.6 7.1 71.4 6.9 1.5 2.0 2.3 4.4 6.7 9.1 51.5 4.1 6.9 9.9 3.1 6.8 71.1 6.7 90.0 2.0 72.5 43.7 46.0 48.4 50.9 53.6 56.4 59.4 62.7 66.4 70.9 76.5 90.0 72.5 3.0 6.3 7.7 50.3 3.0 6.9 8.9 62.2 6.1 70.6 6.3 90.0 3.0 3.5 7.0 9.6 2.3 6.3 8.4 61.8 6.6 70.3 6.1 90.0 3.5 4.0 8.9 51.7 4.7 7.9 61.4 5.3 9.8 75.9 90.0 4.0 4.5 51.1 4.1 7.3 60.9 1 4.9 1 9.6 76.5 90.0 4.5 TABLE 39. [Page 743 | Amplitudes. Declination. Lati- tude. Lati- tude. 18°.0 18°. 6 19°.0 19°. 5 20°.0 20°. 6 21°.0 21°. 6 22°.0 22°. 6 28°. 28°. 6 24°.0 o o o o o o o o o o o 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0 10 8.3 8.8 9.3 9.8 0.3 0.8 1.3 1.8 2.3 2.9 3.4 3.9 4.4 10 15 8.7 9.2 9.7 20.2 0.7 1.3 1.8 2.3 2.8 3.3 3.9 4.4 4.9 15 20 9.2 9.7 20.3 0.8 1.4 1.9 2.4 3.0 3.5 4.0 4.6 5.1 5.7 20 25 9.9 20.5 1.1 1.6 2.2 2.7 3.3 3.9 4.4 5.0 5.5 6.1 6.7 25 30 20.9 21.5 22.1 22.7 23.3 23.8 24.4 25.0 25.6 26.2 26.8 27.4 28.0 30 32 1.4 2.0 2.6 3.2 3.8 4.4 5.0 5.6 6.2 6.8 7.4 8.0 8.7 32 34 1.9 2.5 3.1 3.8 4.4 5.0 5.6 6.2 6.9 7.5 8.1 8.7 9.4 34 36 2.5 3.1 3.7 4.4 5.0 5.7 6.3 6.9 7.6 8.2 8.9 9.5 30.2 36 38 40 3.1 3.8 4.4 5.1 5.7 6.4 7.0 7.7 8.4 9.1 9.7 30.4 1.1 38 23.9 24.4 25.1 25.8 26.5 27.2 27.9 28.6 29.3 30.0 30.7 31.3 32.1 40 41 4.2 4.8 5.5 6.2 6.9 7.7 8.3 9.1 9.8 0.5 1.2 1.8 2.6 41 42 4.6 5.3 6.0 6.7 7.4 8.1 8.8 9.6 30.3 1.0 1.7 2.4 3.2 42 43 5.0 5.7 6.4 7.2 7.9 8.6 9.3 30.1 0.8 1.6 2.3 3.0 3.8 43 44 5.4 6.2 6.9 7.7 8.4 9.1 9.8 0.6 1.4 2.2 2.9 3.6 4.4 44 45 25.9 26.7 27.4 28.2 28.9 29.7 30.4 31.2 32.0 32.8 33.5 34.3 36.1 45 46 6.4 7.2 7.9 8.7 9.6 30.3 1.0 1.8 2.6 3.4 4.2 5.0 5.8 46 47 6.9 7.7 8.5 9.3 30.1 0.9 1.7 2.5 3.3 4.1 4.9 5.7 6.6 47 48 7.5 8.3 9.1 9.9 0.7 1.6 2.4 3.2 4.0 4.9 5.7 6.5 7.4 48 49 8.1 8.9 9.7 30.6 1.4 2.3 3.1 4.0 4.8 5.7 6.5 7.4 8.3 49 50 28.7 29.6 30.4 31.3 32,1 33.0 33.9 34.8 35.6 36.5 37.4 38.3 39.2 50 51 9.4 30.3 1.1 2.0 2.9 3.8 4.7 5.6 6.5 7.4 8.4 9.3 40.2 51 52 30.1 1.0 1.9 2.8 3.7 4.7 5.6 6.5 7.5 8.4 9.4 40.3 1.3 62 53 0.9 1.8 2.7 3.7 4.6 5.6 6.6 7.5 8.5 9.5 40.5 1.4 2.5 53 54 1.7 2.7 3.6 4.6 5.6 6.6 7.6 8.6 9.6 40.6 1.7 2.6 3.8 64 55 32.6 33.6 34.6 35.6 36.6 37.6 38.7 39.7 40.8 41.9 42.9 44.0 45.2 56 56 3.6 4.6 5.6 6.7 7.7 8.8 9.8 41.0 2.1 3.2 4.3 5.4 6.7 56 57 4.6 5.6 6.7 7.8 8.9 40.0 41.1 2.3 3.5 4.6 5.8 7.0 8.3 57 58 5.7 6.8 7.9 9.1 40.2 1.4 2.5 3.8 5.0 6.2 7.5 8.8 50.1 58 59 6.9 8.0 9.2 40.4 1.6 2.8 4.1 5.4 6.7 8.0 9.3 50.7 2.2 59 60.0 38.2 39.4 40.6 41.9 43.2 44.5 45.8 47.2 48.6 49.9 51.4 52.9 54.4 60.0 0.5 8.9 40.1 1.4 2.7 4.0 5.4 6.7 8.1 9.6 51.0 2.5 4.1 5.7 0.5 1.0 9.6 0.9 2.2 3.5 4.9 6.3 7.7 9.1 50.6 2.1 3.7 5.3 7.0 1.0 1.5 40.4 1.7 3.0 4.4 5.8 7.3 8.7 50.2 1.7 3.3 5.0 6.7 8.5 1.5 2.0 1.2 2.5 3.9 5.3 6.8 8.3 9.8 1.3 2.9 4.6 6.3 8.1 60.0 2.0 62.5 42.0 43.4 44.9 46.3 47.8 49.4 51.0 52.6 54.2 56.0 57.8 59.7 61.7 62.5 3.0 2.9 4.3 5.9 7.4 8.9 50.5 2.2 3.9 5.6 7.5 9.4 61.4 3.6 3.0 3.5 3.8 5.3 6.9 8.5 50.1 1.7 3.5 5.3 7.1 9.1 61.1 3.4 5.7 3.5 4.0 4.8 6.4 8.0 9.7 1.3 3.0 4.9 6.7 8.7 60.7 3.0 5.5 8.1 4.0 4.5 5.9 7.5 9.2 50.9 2.6 4.5 6.4 8.4 60.5 2.8 5.2 7.8 70.9 4.5 65.0 47.0 48.7 50.4 52.2 54.0 56.0 58.0 60.2 62.5 64.9 67.6 70.6 74.4 65.0 5.5 8.2 50.0 1.8 3.6 5.6 7.6 9.8 2.2 4.7 7.3 70.4 4.1 8.9 5.5 6.0 9.4 1.3 3.2 5.1 7.3 9.4 61.8 4.4 7.1 70.2 3.8 8.6 90.0 6.0 6.5 50.8 2.7 4.7 6.8 9.1 61.4 4.0 6.8 70.0 3.7 8.4 90.0 6.5 7.0 2.3 4.3 6.4 8.7 61.1 3.7 6.5 9.8 3.5 8.3 90.0 7.0 67.5 53.9 56.0 58.3 60.7 63.4 66.2 69.5 73.3 78.2 90.0 67.5 8.0 5.6 7.9 60.3 3.0 5.9 9.2 73.0 8.1 90.0 8.0 8.5 7.5 60.0 2.6 5.6 8.9 72.8 7.9 90.0 8.5 9.0 9.6 2.3 5.3 8.7 72.7 7.7 90.0 9.0 9.5 61.9 5.0 8.4 72.4 7.6 90.0 ■ 9.5 70.0 64.6 69.1 72.2 77.4 90.0 70.0 0.5 7.8 71.9 7.2 90.0 0.5 1.0 71.7 7.1 90.0 1.0 1.5 6.9 90.0 1.6 2.0 90.0 2.0 Page 744] TABLE 39. Amplitudes. Declination. Lati- tude. Lati- tude. 24°.0 24°. 6 25°.0 25°. 6 26°. 26°. 5 27°.0 27°.5 28°.0 28°. 5 29°. 29°.6 80°. o o o o o o o o o o o o o o 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 4 4.1 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1 8.6 9.1 9.6 0.1 4 8 4.3 4.8 5.3 5.8 6.3 6.8 7.3 7.8 8.3 8.8 9.3 9.8 0.3 8 12 4.6 5.1 5.6 6.1 6.6 7.1 7.6 8.1 8.7 9.2 9.7 30.2 0.7 12 16 5.0 5.6 6.1 6.6 7.1 7.6 8.2 8.7 9.2 9.8 30.3 0.8 1.3 16 20 25.7 26.2 26.7 27.3 27.8 28.3 28.9 29.4 30.0 30.5 31.1 31.6 32.1 20 22 6.0 6.6 7.1 7.7 8.2 8.8 9.3 9.9 0.4 1.0 1.5 2.1 2.6 22 24 6.4 7.0 7.6 8.1 8.7 9.2 9.8 30.4 0.9 1.5 2.0 2.6 3.2 24 26 6.9 7.5 8.1 8.6 9.2 9.7 30.3 0.9 1.5 2.1 2.6 3.2 3.8 26 28 30 7.4 8.0 8.6 9.2 9.8 30.3 0.9 1.5 2.1 2.7 3.3 3.9 4.5 28 28.0 28.6 29.2 29.8 30.4 31.0 31.6 32.2 32.8 33.4 34.0 34.7 35.3 30 31 8.3 8.9 9.5 30.1 0.8 1.4 2.0 2.6 3.2 3.8 4.5 5.1 5.7 31 32 8.7 9.3 9.9 0.5 1.1 1.7 2.4 3.0 3.6 4.2 4.9 5.5 6.1 32 33 9.0 9.6 30.2 0.9 1.5 2.1 2.8 3.4 4.0 4.7 5.3 6.0 6.6 33 34 9.4 30.0 0.6 31.3 1.9 2.6 3.2 3.8 4.5 5.1 5.8 6.4 7.1 34 35 29.8 30.4 31.1 31.7 32.3 33.0 33.6 34.3 35.0 35.6 36.3 36.9 37.6 35 36 30.2 0.8 1.5 2.1 2.8 3.5 4.1 4.8 5.5 6.1 6.8 7.5 8.2 36 37 0.6 1.3 1.9 2.6 3.3 4.0 4.6 5.3 6.0 6.7 7.4 8.1 8.8 37 38 1.1 1.7 2.4 3.1 3.8 4.5 5.2 5.9 6.6 7.3 8.0 8.7 9.4 38 39 1.6 2.2 2.9 3.6 4.3 5.0 5.7 6.5 7.2 7.9 8.6 9.3 40.0 39 40 32.1 32.8 33.5 34.2 34.9 35.6 36.3 37.1 37.8 38.5 39.3 40.0 40.7 40 41 2.6 3.3 4.1 4.8 5.5 6.2 7.0 7.7 8.5 9.2 40.0 0.7 1.5 41 42 3.2 3.9 4.7 5.4 6.1 6.9 7.7 8.4 9.2 9.9 0.7 1.5 2.3 42 43 3.8 4.5 5.3 6.1 6.8 7.6 8.4 9.2 9.9 40.7 1.5 2.3 3.1 43 44 4.4 5.2 6.0 6.8 7.5 8.3 9.1 40.0 40.7 41.6 1.6 2.4 3.2 4.0 44 45 35.1 35.9 36.7 37.5 38.3 39.1 39.9 40.8 42.5 43.3 44.1 45.0 45 46 5.8 6.6 7.5 8.3 9.1 40.0 40.8 1.7 2.5 3.4 4.3 5.1 6.0 46 47 6.6 7.4 8.3 9.1 40.0 0.9 1.7 2.6 3.5 4.4 5.3 6.2 7.1 47 48 7.4 8.3 9.2 40.0 0.9 1.8 2.7 3.6 4.6 5.5 6.4 7.4 8.3 48 49 8.3 9.2 40.1 1.0 1.9 2.8 3.8 4.7 5.7 6.7 7.6 8.6 9.6 49 50 39.2 40.2 41.1 42.0 43.0 43.9 44.9 45.9 46.9 47.9 48.9 50.0 51.1 50 51 40.2 1.2 2.2 3.2 4.1 5.1 6.2 7.2 8.2 9.3 50.4 1.5 2.6 51 52 1.3 2.3 3.3 4.4 5.4 6.4 7.5 8.6 9.7 50.8 2.0 3.1 4.3 52 53 2.5 3.5 4.6 5.7 6.7 7.8 9.0 50.1 51.3 2.5 3.7 4.9 6.2 53 54 3.8 4.9 6.0 7.1 8.2 9.4 50.6 1.8 3.0 4.3 5.6 6.9 8.3 54 55.0 45.2 46.3 47.5 48.6 49.8 51.1 52.3 53.6 54.9 56.3 57.7 59.1 60.7 55.0 5.5 5.9 7.1 8.3 9.5 50.7 2.0 3.3 4.6 6.0 7.4 8.9 60.4 2.0 5.5 6.0 6.7 7.9 9.1 50.4 1.6 2.9 4.3 5.7 7.1 8.6 60.1 1.7 3.4 6.0 6.5 7.5 8.8 50.0 1.3 2.6 3.9 5.4 6.8 8.3 9.9 1.5 3.2 5.0 6.5 7.0 8.3 9.6 0.9 2.2 3.6 5.0 6.5 8.0 9.5 61.2 2.9 4.7 6.6 7.0 57.5 49.2 50.5 51.9 53.2 54.7 56.2 57.7 59.3 60.9 62.6 64.5 66.4 68.5 57.5 8.0 50.1 1.5 2.9 4.3 5.8 7.4 8.9 60.6 2.4 4.2 6.2 8.3 70.7 8.0 8.5 1.1 2.5 4.0 5.5 7.0 8.6 60.3 2.1 3.9 6.0 8.1 70.4 3.1 8.5 9.0 2.2 3.6 5.1 6.7 8.3 60.0 1.8 3.7 5.7 7.9 70.3 3.0 6.2 9.0 9.5 3.3 4.8 6.4 8.0 9.7 1.5 3.4 5.5 7.7 70.1 2.8 5.9 80.1 9.5 60.0 54.4 56.0 67.7 59.4 61.2 63.2 65.2 67.4 69.9 72.6 75.8 80.0 90.0 60.0 0.5 5.7 7.4 9.1 61.0 2.9 5.0 7.2 9.6 72.4 5.8 9.9 90.0 0.5 1.0 7.0 8.8 60.7 2.6 4.7 7.0 9.5 72.3 5.5 9.8 90.0 1.0 1.5 8.5 60.3 2.3 4.4 6.7 9.2 72.0 5.4 9.7 90.0 1.5 2.0 60.0 2.0 4.2 6.5 9.0 71.9 5.2 9.6 90.0 2.0 62.5 61.7 63.9 66.2 68.8 71.7 75.1 9.5 90.0 62.5 3.0 3.6 6.0 8.6 71.5 4.9 9.4 90.0 3.0 3.5 5.7 8.3 71.3 4.8 9.3 90.0 3.5 4.0 8.1 71.1 4.6 9.2 90.0 4.0 4.5 70.9 4.4 9.0 90.0 4.5 TABLE 40. [Page 746 j Correction of the Amplitude as observed on the Apparent Horizon, Declination. Lati- tude. o Lati- tude. 0° 5° 10° 12° 14° 1«° 18° 20° 22° 24° 2«° 28° 80° o o o o o o o o o o . o 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 5 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 5 10 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 10 15 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 .2 15 20 .2 .2 _ 2 .2 .2 .2 .3 .3 .3 .3 .3 .3 .3 0.4 20 24 24 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.4 28 .3 .4 .4 .4 .4 .4 .4 .4 .4 .4 .4 .4 .4 28 32 .4 .4 .4 .4 .4 .4 .4 .5 .5 .5 .5 .5 .5 32 36 .5 .5 .5 .5 .5 .5 .5 .5 .6 .6 .6 .6 .6 36 38 .5 .5 .5 .5 .6 .6 .6 .6 .6 .6 .6 .7 .7 38 40 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.7 0.7 0.7 0.7 40 42 .6 .6 .6 .6 .6 .7 .7 .7 .7 .7 .8 .8 .8 42 44 .6 .6 .7 .7 .7 .7 .7 .7 .8 .8 .8 .9 .9 44 46 .7. .7 .7 .7 .7 .8 .8 .8 .8 .9 .9 .9 1.0 46 48 .7 .8 .8 .8 .8 .8 .8 .9 .9 1.0 1.0 1.0 .1 48 50 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9 1.0 1.1 1.1 1.1 1.3 50 52 .8 .9 .9 .9 .9 1.0 1.0 1.0 .1 .2 .2 .3 .5 52 54 .9 .9 1.0 1.0 1.0 .1 .1 .1 .2 .3 .4 .5 .8 54 56 1.0 1.0 .1 .1 .1 .2 .2 .2 .3 .5 .6 .8 2.2 56 68 .1 .1 .2 .2 .2 .3 .3 .4 .5 .7 .9 2.3 3.2 58 60 1.2 1.2 1.3 1.3 1.3 1.4 1.5 1.6 1.7 2.0 2.4 3.4 60 62 .3 .3 .4 .4 .4 .6 .7 .8 2.1 .5 3.5 62 64 .4 .4 .5 .5 .6 .8 .9 2.2 .6 3.7 64 66 .5 .5 .7 .7 .9 2.0 2.3 .8 3.8 66 68 .6 .7 .9 2.0 2.2 .4 .9 4.0 68 70 1.8 1.9 2.1 2.3 2.6 3.1 4.3 70 72 2.0 2.1 .5 .8 3.3 4.6 72 74 .2 .5 3.0 3.5 4.8 74 76 .6 3.0 .8 5.2 76 78 3.1 .6 5.7 78 80 3.8 4.4 80 I Page 746] TABLE 41. Natural Sines and Cosines. Prop. OO 1 D 2° S° 4 o Prop. parts 29 parts 2 M. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine N. COS. 00000 100000 01745 99985 03490 99939 05234 99863 06976 99756 60 2 1 00029 100000 01774 99984 03519 99938 05263 99861 07005 99754 59 2 1 2 00058 100000 01803 99984 03548 99937 05292 99860 07034 99752 58 2 1 3 00087 100000 01832 99983 03577 99936 05321 99858 07063 99750 57 2 2 4 00116 100000 01862 99983 03606 99935 05350 99857 07092 99748 56 2 2 5 00145 100000 01891 99982 03635 99934 05379 99855 07121 99746 55 2 3 6 00175 100000 01920 99982 03664 99933 05408 99854 07150 99744 54 2 3 7 00204 100000 01949 99981 03693 99932 05437 99852 07179 99742 53 2 4 8 00233 100000 01978 99980 03723 99931 05466 99851 07208 99740 52 2 4 9 00262 100000 02007 99980 03752 99930 05495 99849 07237 99738 51 2 5 10 00291 100000 02036 99979 03781 99929 05524 99847 07266 99736 50 2 5 11 00320 99999 02065 99979 03810 99927 05553 99846 07295 99734 49 2 6 12 00349 99999 02094 99978 03839 99926 05582 99844 07324 99731 48 2 6 13 00378 99999 02123 99977 03868 99925 05611 99842 07353 99729 47 2 7 14 00407 99999 02152 99977 03897 99924 05640 99841 07382 99727 46 2 7 15 00436 99999 02181 99976 03926 99923 05669 99839 07411 99725 45 2 8 16 00465 99999 02211 99976 03955 99922 05698 99838 07440 99723 44 8 17 00495 99999 02240 99975 03984 99921 05727 99836 07469 99721 43 9 18 00524 99999 02269 99974 04013 04042 99919 05756 99834 99833 07498 99719 42 9 19 00553 99998 02298 99974 99918 05785 07527 99716 41 10 20 00582 99998 02327 99973 04071 99917 05814 99831 07556 99714 40 10 21 00611 99998 02356 99972 04100 99916 05844 99829 07585 99712 39 11 22 00640 99998 02385 99972 04129 99915 05873 99827 07614 99710 38 11 23 00669 99998 02414 99971 04159 99913 05902 99826 07643 99708 37 12 24 00698 99998 02443 99970 99969 04188 99912 05931 05960 99824 07672 99705 36 12 25 00727 99997 02472 04217 99911 99822 07701 99703 35 13 26 00756 99997 02501 99969 04246 99910 05989 99821 07730 99701 34 13 27 00785 99997 02530 99968 04275 99909 06018 99819 07769 99699 33 14 28 00814 99997 02560 99967 04304 99907 06047 99817 07788 99696 32 14 29 00844 99996 02589 99966 04333 99906 06076 99815 07817 99694 31 15 30 00873 99996 02618 99966 04362 04391 99905 06105 99813 07846 99692 30 15 31 00902 99996 02647 99965 99904 06134 99812 07875 99689 29 15 32 00931 99996 02676 99964 04420 99902 06163 99810 07904 99687 28 16 33 00960 99995 02705 99963 04449 99901 06192 99808 07933 99685 27 16 34 00989 99995 02734 99963 04478 99900 06221 99806 07962 99683 26 17 35 01018 99995 02763 99962 04507 99898 06250 99804 07991 99680 25 17 36 01047 99995 02792 99961 04536 99897 06279 99803 08020 99678 99676 24 23 18 37 01076 99994 02821 99960 04565 99896 06308 99801 08049 18 38 01105 99994 02850 99959 04594 99894 06337 99799 08078 99673 22 19 39 01134 99994 02879 99959 04623 99893 06366 99797 08107 99671 21 19 40 01164 99993 02908 99958 04653 99892 06395 99795 08136 99668 20 20 41 01193 99993 02938 99957 04682 99890 06424 99793 08165 99666 19 20 42 01222 99993 02967 99956 99955 04711 99889 06453 99792 08194 99664 18 21 43 01251 99992 02996 04740 99888 06482 99790 08223 99661 17 21 44 01280 99992 03025 99954 04769 99886 06511 99788 08252 99659 16 22 45 01309 99991 03054 99953 04798 99885 06540 99786 08281 99657 15 22 46 01338 99991 03083 99952 04827 99883 06569 99784 08310 99654 14 23 47 01367 99991 03112 99952 04856 99882 06598 99782 08339 99652 13 23 48 01396 99990 03141 99951 04885 99881 06627 99780 08368 99649 99647 12 11 24 49 01425 99990 03170 99950 04914 99879 06656 99778 08397 24 50 01454 99989 03199 99949 04943 99878 06685 99776 08426 99644 10 25 51 01483 99989 03228 99948 04972 99876 06714 99774 08455 99642 9 25 52 01513 99989 03257 99947 05001 99875 06743 99772 08484 99639 8 26 53 01542 99988 03286 99946 05030 99873 06773 99770 08513 99637 7 26 54 01571 99988 03316 99945 05059 99872 06802 99768 08542 99635 6 27 55 01600 99987 03345 99944 05088 99870 06831 99766 08571 99632 5 27 56 01629 99987 03374 99943 05117 99869 06860 99764 08600 99630 4 28 57 01658 99986 03403 99942 05146 99867 06889 99762 08629 99627 3 28 58 01687 99986 03432 99941 05175 99866 06918 99760 08658 99625 2 29 59 01716 99985 03461 99940 05205 99864 06947 99758 08687 99622 1 29 60 01745 99985 03490 99939 05234 99863 06976 99756 08716 99619 N. COB. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. M. __ 89° 88° 87° 8 8° 86° TABLE 41. [Page 747 Natural Sines and Coeinea. Prop, parts 29 6 o 6< > 7° - - Prop, parts 4 M. N.sina N.cos. N.sine. N.cos. N. sine. N.cos. N. sine. N. cos. N. sine. N. coa. 08716 99619 10453 99452 12187 99255 13917 99027 15643 98769 60 4 1 08745 99617 10482 99449 12216 99251 13946 99023 15672 98764 59 4 1 2 08774 99614 10511 99446 12245 99248 13975 99019 15701 98760 58 4 1 3 08803 99612 10540 99443 12274 99244 14004 99015 15730 98755 57 4 2 4 08831 99609 10569 99440 12302 99240 14033 99011 15758 98751 56 4 2 5 08860 99607 10597 99437 12331 99237 14061 99006 15787 98746 55 4 3 6 08889 99604 10626 99434 12360 99233 99230 14090 99002 15816 98741 54 4 3 7 08918 99602 10655 99431 12389 14119 98998 15845 98737 53 4 4 8 08947 99599 10684 99428 12418 99226 14148 98994 15873 98732 52 3 4 9 08976 99596 10713 99424 12447 99222 14177 98990 15902 98728 51 3 5 10 09005 99594 10742 99421 12476 99219 14205 98986 15931 98723 50 3 6 11 09034 99591 10771 99418 12504 99215 14234 98982 15959 98718 49 3 6 12 09063 99588 99586 10800 99415 99412 12533 99211 14263 98978 15988 98714 48 3 6 13 09092 10829 12562 99208 14292 98973 16017 98709 47 3 7 14 09121 99583 10858 99409 12591 99204 14320 98969 16046 98704 46 3 7 15 09150 99580 10887 99406 12620 99200 14349 98965 16074 98700 45 3 8 16 09179 99578 10916 99402 12649 99197 14378 98961 16103 98695 44 3 8 17 09208 99575 10945 99399 12678 99193 14407 98957 16132 98690 43 3 9 18 09237 99572 10973 99396 12706 99189 14436 98953 16160 98686 42 3 9 19 09266 99570 11002 99393 12735 99186 14464 98948 16189 98681 41 3 10 20 09295 99567 11031 99390 12764 99182 14493 98944 16218 98676 40 3 10 21 09324 995M 11060 99386 12793 99178 14522 98940 16246 98671 39 3 11 22 09353 99562 11089 99383 12822 99175 14551 98936 16275 98667 38 3 11 23 09382 99559 11118 99380 12851 99171 14580 98931 16304 98662 37 2 12 12 24 09411 99556 11147 99377 12880 99167 14608 98927 16333 98657 36 2 25 09440 99553 11176 99374 12908 99163 14637 98923 16361 98652 35 2 13 26 09469 99551 11205 99370 12937 99160 14666 98919 16390 98648 34 2 13 27 09498 99548 11234 99367 12966 99156 14695 98914 16419 98643 33 2 14 28 09527 99545 11263 99364 12995 99152 14723 98910 16447 98638 32 2 14 29 09556 99542 11291 99360 13024 99148 14752 98906 16476 98633 31 2 15 30 09585 99540 11320 99357 13053 99144 14781 98902 16505 16533 98629 30 2 15 31 09614 99537 11349 99354 13081 99141 14810 98897 98624 29 2 15 32 09642 99534 11378 99351 13110 99137 14838 98893 16562 98619 28 2 16 33 09671 99531 11407 99347 13139 99133 14867 98889 16591 98614 27 2 16 34 09700 99528 11436 99344 13168 99129 14896 98884 16620 98609 26 2 17 35 09729 99526 11465 99341 13197 99125 14925 98880 16648 98604 25 2 17 36 37 09758 09787 99523 11494 99337 13226 99122 14954 14982 98876 16677 98600 24 2 18 99520 11523 99334 13254 99118 98871 16706 98595 23 2 18 38 09816 99517 11552 99331 13283 99114 15011 98867 16734 98590 22 19 39 09845 99514 11580 99327 13312 99110 15040 98863 16763 98585 21 19 40 09874 99511 11609 99324 13341 99106 15069 98858 16792 98580 20 20 41 09903 99508 11638 99320 13370 99102 15097 98854 16820 98575 19 20 21 42 09932 99506 11667 99317 13399 99098 15126 98849 16849 98570 18 43 09961 99503 11696 99314 13427 99094 15155 98845 16878 98565 17 21 44 09990 99500 11725 99310 13456 99091 15184 98841 16906 98561 16 22 45 10019 99497 11754 99307 13485 99087 15212 98836 16935 98556 15 22 46 10048 99494 11783 99303 13514 99083 15241 98832 16964 98551 14 23 47 10077 99491 11812 99300 13543 99079 15270 98827 16992 98546 13 23 48 10106 99488 11840 99297 13572 99075 15299 98823 17021 98541 12 24 49 10135 99485 11869 99293 13600 99071 15327 98818 17050 98536 11 24 50 10164 99482 11898 99290 13629 99067 15356 98814 17078 98531 10 25 51 10192 99479 11927 99286 13658 99063 15385 98809 17107 98526 9 25 52 10221 99476 11956 99283 13687 99059 15414 98805 17136 98521 8 26 53 10250 99473 11985 99279 13716 99055 15442 98800 17164 98516 7 26 54 10279 99470 12014 99276 13744 99051 15471 98796 17193 98511 6 27 55 10308 99467 12043 99272 13773 99047 15500 98791 17222 98506 5 27 56 10337 99464 12071 99269 13802 99043 15529 98787 17250 98501 4 28 57 10366 99461 12100 99265 13831 99039 15557 98782 17279 98496 3 28 58 10395 99458 12129 99262 13860 99035 15586 98778 17308 98491 2 29 59 10424 99455 12158 99258 13889 99031 15615 98773 17336 98486 1 29 60 10453 99452 12187 99255 13917 99027 15643 98769 17365 98481 N.cos. N. sine. N. COS. N. sine. N. COS. N. sine. N. cos. N. Bine. N. coa. N. sine. M. 84° 83 o 82° 8 lo 80° 21594°— 14- -40 Page 748] TABLE 41. Natural Sines and Cosinee, Prop. parte 28 lOO 1 11 o 12° 1 18° 1 14° 1 Prop. parte 6 M. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. 17365 98481 19081 98163 20791 97815 22495 97437 24192 97030 60 6 1 17393 9M76 19109 98157 20820 97809 22623 97430 24220 97023 69 6 1 2 17422 98471 19138 98162 20848 97803 22562 97424 24249 97015 68 6 1 3 17451 98466 19167 98146 20877 97797 22580 97417 24277 97008 57 6 2 4 17479 98461 19195 98140 20905 97791 22608 97411 24305 97001 66 6 2 5 17508 98456 19224 98136 20933 97784 22637 97404 24333 96994 65 6 3 6 17537 98450 19252 98129 20962 97778 22665 97398 24362 96987 54 5 3 7 17565 98445 19281 98124 20990 97772 22693 97391 24390 96980 63 5 4 8 17594 98440 19309 98118 21019 97766 22722 97384 24418 96973 62 5 4 9 17623 98435 19338 98112 21047 97760 22750 97378 24446 96966 51 5 5 10 17661 98430 19366 98107 21076 97764 22778 97371 24474 96959 50 5 5 11 17680 98426 19396 98101 21104 97748 22807 97365 24503 96952 49 5 6 6 12 13 17708 98420 19423 98096 21132 97742 22835 97358 24531 96945 48 5 17737 98414 19462 98090 21161 97735 22863 97351 24559 96937 47 5 7 14 17766 98409 19481 98084 21189 97729 22892 97346 24587 96930 46 5 7 15 17794 98404 19509 98079 21218 97723 22920 97338 24616 96923 45 5 7 16 17823 98399 19638 98073 21246 97717 22948 97331 24644 96916 44 4 8 17 17852 98394 19666 98067 21275 97711 22977 97325 24672 96909 43 4 8 18 17880 98389 19596 98061 21303 97705 23006 97318 24700 96902 42 41 4 9 19 17909 98383 19623 98056 21331 97698 23033 97311 24728 96894 4 9 20 17937 98378 19662 98050 21360 97692 23062 97304 24766 96887 40 4 10 21 17966 98373 19680 98044 21388 97686 23090 97298 24784 96880 39 4 10 22 17995 98368 19709 98039 21417 97680 23118 97291 24813 96873 38 4 11 23 18023 98362 19737 98033 21445 97673 23146 97284 24841 96866 37 4 11 12 24 25 18052 98367 19766 98027 21474 97667 23175 97278 24869 96868 36 4 18081 98352 19794 98021 21502 97661 23203 97271 24897 96861 35 4 12 26 18109 98347 19823 98016 21530 97655 23231 97264 24926 96844 34 3 13 27 18138 98341 19861 98010 21659 97648 23260 97257 24964 96837 33 3 13 28 18166 98336 19880 98004 21587 97642 23288 97261 24982 96829 32 3 14 29 18195 98331 19908 97998 21616 97636 23316 97244 26010 96822 31 3 14 30 18224 98325 19937 97992 21644 97630 97623 23345 97237 26038 96816 30 3 14 31 18252 98320 19966 97987 21672 23373 97230 25066 96807 29 3 15 32 18281 98315 19994 97981 21701 97617 23401 97223 25094 96800 28 3 15 33 18309 98310 20022 97975 21729 97611 23429 97217 25122 96793 27 3 16 34 18338 98304 20051 97969 21758 97604 23458 97210 25151 96786 26 3 16 35 18367 98299 20079 97963 21786 97598 23486 97203 26179 96778 26 3 17 36 18396 98294 20108 97958 21814 97692 23614 97196 26207 96771 24 2 17 37 18424 98288 20136 97952 21843 97585 23542 97189 26235 96764 23 2 18 38 18452 98283 20165 97946 21871 97679 23571 97182 25263 96756 22 2 18 39 18481 98277 20193 97940 21899 97573 23599 97176 25291 96749 21 2 19 40 18509 98272 20222 97934 21928 97566 23627 97169 26320 96742 20 2 19 41 18538 98267 20250 97928 21966 97560 23656 97162 26348 96734 19 2 20 42 18567 98261 20279 97922 21986 97663 23684 97155 25376 96727 18 2 20 43 18596 98256 20307 97916 22013 97547 23712 97148 25404 96719 17 2 21 44 18624 98260 20336 97910 22041 97641 23740 97141 25432 96712 16 2 21 45 18652 98246 20364 97906 22070 97634 23769 97134 25460 96705 16 2 21 46 18681 18710 98240 20393 97899 22098 97528 23797 97127 25488 96697 14 22 47 98234 20421 97893 22126 97521 23825 97120 25516 96690 13 22 23 48 49 18738 98229 20460 97887 22165 97516 23863 97113 26646 96682 12 18767 98223 20478 97881 22183 97508 23882 97106 25573 96676 11 23 50 18795 98218 20507 97876 22212 97502 23910 97100 26601 96667 10 24 51 18824 98212 20535 97869 22240 97496 23938 97093 26629 96660 9 24 52 18862 98207 20563 97863 22268 97489 23966 97086 26667 96653 8 1 25 53 18881 98201 20592 97867 22297 97483 23995 97079 25686 96645 7 25 54 18910 98196 20620 97851 22325 97476 24023 97072 25713 96638 6 26 55 18938 98190 20649 97845 22353 97470 24051 97066 26741 96630 6 26 56 18967 98186 20677 97839 22382 97463 24079 97068 25769 96623 4 27 57 18995 98179 20706 97833 22410 97467 24108 97051 25798 96615 3 27 58 19024 98174 20734 97827 22438 97460 24136 97044 25826 96608 2 28 59 19052 98168 20763 97821 22467 97444 24164 97037 26864 96600 1 28 60 19081 98163 20791 97815 22496 97437 24192 97030 26882 96593 N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. M. 79° 78° 77° 76° 75° TABLE 41. [Page 749 Natural Sines and Cosines. Prop, parts 27 16° 16° 17° 18° 1V> Prop. parts 9 M. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N.coe. N.Bine. N.cos. 1 1 2 2 3 3 4 4 5 5 5 1 2 3 4 5 6 7 8 9 10 11 12 25882 25910 25938 25966 25994 26022 26050 26079 26107 26135 26163 26191 26219 96593 96585 96578 96570 96562 96555 96647 27564 27592 27620 27648 27676 27704 27731 96126 96118 96110 96102 96094 96086 96078 29237 29265 29293 29321 29348 29376 29404 29432 29460 29487 29515 29543 29571 95630 95622 95613 95605 95596 95588 95579 30902 30929 30957 30985 31012 31040 31068 95106 95097 95088 95079 95070 95061 95052 32557 32584 32612 32639 32667 32694 32722 94552 94542 94533 94523 94514 94504 94495 94485 94476 94466 94457 94447 94438 60 59 58 57 56 55 54 9 9 9 9 8 8 8 96540 96532 96524 96517 96509 96502 96494 96486 96479 96471 96463 96456 27759 27787 27815 27843 27871 27899 27927' 27955 27983 28011 28039 28067 96070 96062 96054 96046 96037 96029 95571 95562 95554 95545 95536 95528 31095 31123 31151 31178 31206 31233 95043 95033 95024 95015 95006 94997 94988 94979 94970 94961 94952 94943 94933 94924 94915 94906 94897 94888 32749 32777 32804 32832 32859 32887 32914 32942 32969 32997 33024 33051 33079 33106 33134 33161 33189 33216 33244 33271 33298 33326 33353 33381 33408 33436 33463 33490 33518 33545 33573 33600 33627 33655 33682 33710 53 52 51 50 49 48 8 8 8 8 6 6 7 7 8 8 9 9 9 10 10 11 11 12 12 13 13 14 14 14 15 15 16 16 17 17 18 18 18 19 19 20 20 21 21 22 22 23 23 23 24 24 25 25 26 26 27 27 13 14 15 16 17 18 19 20 21 22 23 24 26247 26275 26303 26331 26359 26387 96021 96013 96005 95997 95989 95981 29599 29626 29654 29682 29710 29737 95519 95511 95502 95493 95485 95476 31261 31289 31316 31344 31372 31399 31427 31454 31482 31510 31537 31565 94428 94418 94409 94399 94390 94380 94370 94361 94351 94342 94332 94322 94313 94303 94293 94284 94274 94264 47 46 45 44 43 42 41 40 39 38 37 36 6 6 26415 26443 26471 26500 26528 26556 96448 96440 96433 96425 96417 96410 28095 28123 28150 28178 28206 28234 95972 95964 95956 95948 95940 95931 95923 95915 95907 95898 95890 95882 29765 29793 29821 29849 29876 29904 29932 29960 29987 30015 30043 30071 95467 95459 95450 95441 95433 95424 6 6 6 6 6 5 25 26 27 28 29 30 26584 26612 26640 26668 26696 26724 96402 96394 96386 96379 96371 96363 28262 28290 28318 28346 28374 28402 95415 95407 95398 95389 95380 95372 31593 31620 31648 31675 31703 31730 94878 94869 94860 94851 94842 94832 36 34 33 32 31 30 6 5 5 5 5 5 31 32 33 34 35 36 37 38 39 40 41 42 26752 26780 26808 26836 26864 26892 96355 96347 96340 96332 96324 96316 28429 28457 28485 28513 28541 28569 95874 95865 95857 95849 95841 95832 95824 95816 95807 95799 95791 95782 95774 95766 95757 95749 95740 95732 95724 95715 95707 95698 95690 95681 30098 30126 30154 30182 30209 30237 95363 95354 95345 95337 95328 95319 31758 31786 31813 31841 31868 31896 94823 94814 94805 94795 94786 94777 94254 94245 94235 94225 94215 94206 29 28 27 26 25 24 4 4 4 4 4 4 26920 26948 26976 27004 27032 27060 96308 96301 96293 96285 96277 96269 28597 28625 28652 28680 28708 28736 30265 30292 30320 30348 30376 30403 30431 30459 30486 30514 30542 30570 95310 95301 95293 95284 95275 95266 95257 95248 95240 95231 95222 95213 31923 31951 31979 32006 32034 32061 94768 94758 94749 94740 94730 94721 94196 94186 94176 94167 94157 94147 23 22 21 20 19 18 3 3 3 3 3 3 3 2 2 2 2 2 43 44 45 46 47 48 27088 27116 27144 27172 27200 27228 96261 96253 96246 96238 96230 96222 28764 28792 28820 28847 28875 28903 32089 32116 32144 32171 32199 32227 94712 94702 94693 94684 94674 94665 33737 33764 33792 33819 33846 33874 94137 94127 94118 94108 94098 94088 17 16 15 14 13 12 49 50 51 52 53 54 55 56 57 58 59 60 27256 27284 27312 27340 27368 27396 96214 96206 96198 96190 96182 96174 28931 28959 28987 29015 29042 29070 30597 30625 30653 30680 30708 30736 95204 95195 95186 95177 95168 95159 95150 95142 95133 95124 95115 95106 32254 32282 32309 32337 32364 32392 94656 94646 94637 94627 94618 94609 33901 33929 33956 33983 34011 34038 94078 94068 94058 94049 94039 94029 11 10 9 8 7 6 2 27424 27452 27480 27508 27536 27564 96166 96158 96150 96142 96134 96126 29098 29126 29154 29182 29209 29237 95673 95664 95656 95647 95639 95630 30763 30791 30819 30846 30874 30902 32419 32447 32474 32502 32529 32557 94599 94590 94580 94571 94561 94552 34065 34093 34120 34147 34175 34202 94019 94009 93999 93989 93979 93969 5 4 3 2 1 N. COS. N. sine. N. COS. N. sine. N. COS. N.sine. N. COS. N. sine. N. COS. N.sine. M. 740 J 3° 72° 71° 70° Page 760] TABLE 41. Natural Sines and Coeines, Prop. parts 27 M. 20' 21° 22° 23° 24° Prop. parts 11 N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. 1 1 2 2 3 1 2 3 4 5 6 34202 34229 34257 34284 34311 34339 34366 93969 93959 93949 93939 93929 93919 93909 35837 35864 35891 35918 36945 35973 36000 93368 93348 93337 93327 93316 93306 93295 37461 37488 37516 37542 37669 37695 37622 92718 92707 92697 92686 92675 92664 92653 39073 39100 39127 39163 39180 39207 39234 92060 92039 92028 92016 92005 91994 91982 40674 40700 40727 40763 40780 40806 40833 91366 91343 91331 91319 91307 91295 91283 60 59 58 57 56 55 54 11 11 11 10 10 10 10 3 4 4 5 5 5 7 • 8 9 10 11 12 34393 34421 34448 34475 34503 34530 93899 93889 93879 93869 93859 93849 36027 36054 36081 36108 36135 36162 93285 93274 93264 93263 93243 93232 37649 37676 37703 37730 37767 37784 92642 92631 92620 92609 92598 92687 39260 39287 39314 39341 39367 39394 91971 91959 91948 91936 91925 91914 40860 40886 40913 40939 40966 40992 91272 91260 91248 91236 91224 91212 53 52 51 50 49 48 10 10 9 9 9 9 6 6 7 7 8 8 13 14 15 16 17 18 34557 34584 34612 34639 34666 34694 93839 93829 93819 93809 93799 93789 36190 36217 36244 36271 36298 36326 93222 93211 93201 93190 93180 93169 37811 37838 37865 37892 37919 37946 92676 92665 92664 92643 92532 92521 39421 39448 39474 39501 39528 39555 91902 91891 91879 91868 91856 91845 41019 41046 41072 41098 41125 41151 91200 91188 91176 91164 91152 91140 47 46 45 44 43 42 41 40 39 38 37 36 9 8 8 8 8 8 9 9 9 10 10 11 19 20 21 22 23 24 34721 34748 34775 34803 34830 34867 93779 93769 93759 93748 93738 93728 36362 36379 36106 36434 36461 36488 93169 93148 93137 93127 93116 93106 37973 37999 38026 38063 38080 38107 92610 92499 92488 92477 92466 92455 39681 39608 39636 39661 39688 39715 91833 91822 91810 91799 91787 91775 91764 91752 91741 91729 91718 91706 41178 41204 41231 41257 41284 41310 91128 91116 91104 91092 91080 91068 8 7 7 7 7 7 11 12 12 13 13 14 14 14 15 15 16 16 25 26 27 28 29 30 31 32 33 34 35 36 34884 34912 34939 34966 34993 35021 93718 93708 93698 93688 93677 93667 36515 36542 36569 36596 36623 36660 93096 93084 93074 93063 93062 93042 38134 38161 38188 38215 38241 38268 92444 92432 92421 92410 92399 92388 39741 39768 39796 39822 39848 39875 41337 41363 41390 41416 41443 41469 91056 91044 91032 91020 91008 90996 36 34 33 32 31 30 6 6 6 6 6 6 35048 35075 35102 35130 36157 35184 93657 93647 93637 93626 93616 93606 36677 36704 36731 36768 36785 36812 93031 93020 93010 92999 92988 92978 38295 38322 38349 38376 38403 38430 92377 92366 92356 92343 92332 92321 39902 39928 39956 39982 40008 40035 91694 91683 91671 91660 91648 91636 41496 41522 41649 41575 41602 41628 90984 90972 90960 90948 90936 90924 29 28 27 26 25 24 5 5 5 5 5 4 17 17 18 18 18 19, 19 20 20 21 21 22 22 23 23 23 24 24 25 25 26 26 27 27 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 35211 35239 35266 36293 35320 35347 93696 93585 93676 93665 93655 93544 36839 36867 36894 36921 36948 36976 92967 92956 92946 92935 92924 92913 92902 92892 92881 92870 92859 92849 38456 38483 38610 38537 38564 38691 92310 92299 92287 92276 92265 92254 40062 40088 40116 40141 40168 40196 91625 91613 91601 91590 91578 91666 41655 41681 41707 41734 41760 41787 90911 90899 90887 90876 90863 90851 23 22 21 20 19 18 17 16 15 14 13 12 4 4 4 4 3 3 36376 35402 35429 35456 35484 35511 93634 93524 93614 93503 93493 93483 37002 37029 37066 37083 37110 37137 38617 38644 38671 38698 38725 38752 92243 92231 92220 92209 92198 92186 40221 40248 40276 40301 40328 40365 91666 91543 91531 91619 91508 91496 41813 41840 41866 41892 41919 41945 90839 90826 90814 90802 90790 90778 3 3 3 3 i 35638 35665 35592 35619 35647 36674 93472 93462 93462 93441 93431 93420 37164 37191 37218 37245 37272 37299 92838 92827 92816 92806 92794 92784 38778 38805 38832 38869 38886 38912 92176 92164 92162 92141 92130 92119 40381 40408 40434 40461 40488 40514 91484 91472 91461 91449 91437 91425 41972 41998 42024 42051 42077 42104 90766 90753 90741 90729 90717 90704 11 10 9 8 7 6 2 2 2 36701 35728 36755 35782 35810 35837 93410 93400 93389 93379 93368 93368 37326 37353 37380 37407 37434 37461 92773 92762 92761 92740 92729 92718 38939 38966 38993 39020 39046 39073 92107 92096 92085 92073 92062 92050 40541 40567 40594 40621 40647 40674 91414 91402 91390 91378 91366 91355 42130 42156 42183 42209 42235 42262 90692 90680 90668 90655 90643 90631 5 4 3 2 1 N. COS. N, sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N.slne. M. i 69° 68" 1 67° 1 .66° 1 6»° 1 J TABLE 41. [Page 761 Natural Sines and Cosinee. Prop. part* 26 «6° 1 2«o 27° 1 28° 29° 1 Prop. parts 14 M. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N.cos. N. sine. N.cos. 1 1 2 2 3 3 3 4 4 5 5 1 2 3 4 5 6 42262 42288 42315 42341 42367 42394 42420 90631 90618 90606 90594 90582 90569 90557 43837 43863 43889 43916 43942 43968 43994 89879 89867 89864 89841 89828 89816 89803 45399 46425 45461 46477 45603 45529 46554 89101 89087 89074 89061 89048 89036 89021 46947 46973 46999 47024 47050 47076 47101 88295 88281 88267 88254 88240 88226 88213 48481 48606 48532 48567 48683 48608 48634 48659' 48684 48710 48736 48761 48786 87462 87448 87434 87420 87406 87391 87377 60 69 58 57 56 56 54 14 14 14 13 13 13 13 7 8 9 10 11 12 42446 42473 42499 42525 42552 42578 90545 90532 90520 90607 90496 90483 44020 44046 44072 44098 44124 44151 89790 89777 89764 89762 89739 89726 46580 45606 46632 46658 45684 45710 89008 88996 88981 88968 88955 88942 47127 47153 47178 47204 47229 47255 88199 88185 88172 88158 88144 88130 87363 87349 87335 87321 87306 87292 87278 87264 87250 87235 87221 87207 87193 87178 87164 87150 87136 87121 53 62 51 50 49 48 12 12 12 12 11 11 6 6 7 7 7 8 13 14 15 16 17 18 42604 42631 42657 42683 42709 42736 90470 90468 90446 90433 90421 90408 44177 44203 44229 44266 44281 44307 89713 89700 89687 89674 89662 89649 46736 45762 45787 45813 45839 46865 88928 88915 88902 88888 88875 88862 88848 88835 88822 88808 88795 88782 47281 47306 47332 47368 47383 47409 47434 47460 47486 47611 47537 47562 88117 88103 88089 88076 88062 88048 48811 48837 48862 48888 48913 48938 47 46 45 44 43 42 41 40 39 38 37 36 11 11 11 10 10 10 8 9 9 10 10 10 19 20 21 22 23 24 42762 42788 42815 42841 42867 42894 90396 90383 90371 90368 90346 90334 44333 44369 44385 44411 44437 44464 89636 89623 89610 89597 89584 89671 45891 45917 46942 45968 45994 46020 88034 88020 88006 87993 87979 87965 48964 48989 49014 49040 49065 49090 10 9 9 9 8 11 11 12 12 13 13 25 26 27 28 29 30 42920 42946 42972 42999 43025 43051 90321 90309 90296 90284 90271 90259 44490 44516 44542 44568 44594 44620 89668 89546 89532 89519 89506 89493 46046 46072 46097 46123 46149 46175 88768 88756 88741 88728 88716 88701 47588 47614 47639 47666 47690 47716 47741 47767 47793 47818 47844 47869 87951 87937 87923 87909 87896 87882 87868 87854 87840 87826 87812 87798 49116 49141 49166 49192 49217 49242 49268 49293 49318 49344 49369 49394 87107 87093 87079 87064 87050 87036 87021 87007 86993 86978 86964 86949 35 34 33 32 31 30 29 28 27 26 25 24 8 8 8 7 7 7 13 14 14 15 15 16 31 32 33 34 36 36 43077 43104 43130 43156 43182 43209 90246 90233 90221 90208 90196 90183 44646 44672 44698 44724 44750 44776 89480 89467 89454 89441 89428 89415 46201 46226 46252 46278 46.304 46330 46:^56 46381 46407 46433 46458 46484 46510 46536 46561 46587 46613 46639 88688 88674 88661 88647 88634 88620 7 7 6 6 6 6 16 16 17 17 18 18 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 43235 43261 43287 43313 43340 43366 90171 90158 90146 90133 90120 90108 44802 44828 44854 44880 44906 44932 89402 89389 89376 89363 89350 89337 89324 89311 89298 89286 89272 89259 88607 88693 88580 88566 88553 88539 88526 88512 88499 88485 88472 88468 47895 47920 47946 47971 47997 48022 48048 48073 48099 48124 48150 48176 87784 87770 87766 87743 87729 87715 49419 49445 49470 49495 49621 49546 49571 49596 49622 49647 49672 49697 86935 86921 86906 86892 86878 86863 23 22 21 20 19 18 5 5 6 5 4 4 19 19 20 20 20 21 21 22 22 23 23 23 43392 43418 43445 43471 43497 43523 90095 90082 90070 90067 90045 90032 44958 44984 45010 45036 46062 45088 87701 87687 87673 87659 87645 87631 86849 86834 86820 86806 86791 86777 17 16 15 14 13 12 4 4 4 3 3 3 43549 43575 43602 43628 43664 43680 90019 90007 89994 89981 89968 89966 45114 45140 4516G 46192 45218 45243 89245 89232 89219 89206 89193 89180 46664 46690 46716 46742 46767 46793 88445 88431 88417 88404 8S390 88377 48201 48226 48252 48277 48303 48328 87617 87603 87689 87575 87561 87.546 87532 87618 87604 87490 87476 87462 49723 49748 49773 49798 49824 49849 49874 49899 49924 49950 49975 60000 86762 86748 86733 86719 86704 86690 86676 86661 86646 86632 86617 86603 11 10 9 8 7 6 3 2 2 2 2 1 24 24 25 25 26 26 43706 43733 43759 43785 43811 43837 89943 89930 89918 89905 89892 89879 45269 45296 45321 45347 45373 45399 89167 89153 89140 89127 89114 89101 46819 46844 46870 46896 46921 46947 88363 88349 88336 88322 88308 88295 48354 48379 48405 48430 48456 48481 5 4 3 2 1 1 1 1 N. COB. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. M. ., 64° 68° 62° 61° 60° 1 Page 752] TABLE 41. Natural Sines and Cosines. Prop, parts. 35 80° 81° 32° S3° 34° Prop. parts, 16 M. N. sine. N. cos. N. sine. N. COS, N, sine. N. COS. N. sine. N. COS. N, sine. N. COS. 1 1 2 2 3 1 2 3 4 6 6 50000 50025 50050 50076 50101 50126 50151 86603 86588 86573 86559 86544 86530 86515 51504 51529 51554 51579 51604 51628 51653 85717 85702 85687 85672 85657 85642 85627 52992 53017 63041 53066 63091 63115 53140 84805 84789 84774 84759 84743 84728 84712 54464 64488 64513 54637 54561 54586 54610 83867 83861 83835 83819 83804 83788 83772 65919 55943 66968 65992 56016 56040 56064 82904 82887 82871 82855 82839 82822 82806 60 69 58 57 56 55 54 16 16 16 15 15 15 14 3 3 4 4 5 5 7 8 9 10 11 12 50176 50201 50227 50252 50277 50302 86501 86486 86471 86457 86442 86427 51678 51703 51728 51753 51778 51803 85612 85597 85582 85567 85551 85536 53164 53189 53214 53238 53263 53288 84697 84681 84666 84650 84635 84619 84604 84688 84573 84557 84542 84526 64635 54659 54683 54708 54732 54766 83766 83740 83724 83708 83692 83676 66088 56112 56136 56160 56184 66208 82790 82773 82767 82741 82724 82708 53 52 51 50 49 48 14 14 14 13 13 13 5 6 6 7 7 8 13 14 15 16 17 18 19 20 21 22 23 24 50327 50352 50377 50403 50428 50453 86413 86398 86384 86369 86354 86340 51828 51852 51877 51902 51927 51952 85521 85506 85491 85476 85461 85446 53312 63337 53361 53386 53411 53436 54781 64806 54829 64864 54878 64902 83660 83645 83629 83613 83597 83581 66232 56266 56280 56306 56329 66353 82692 82675 82669 82643 82626 82610 47 46 46 44 43 42 13 12 12 12 11 11 8 8 9 9 10 10 50478 50503 50528 50553 60578 50603 86325 86310 86295 86281 86266 86251 86237 86222 86207 86192 86178 86163 51977 52002 52026 52051 52076 52101 85431 85416 85401 85385 85370 85355 85340 85325 85310 85294 85279 85264 63460 53484 63509 63634 53558 63683 84611 84495 84480 84464 84448 84433 64927 64951 54975 64999 56024 55048 83565 83549 83533 83617 83601 83485 66377 56401 66426 66449 56473 56497 82693 82677 82561 82544 82528 82511 41 40 39 38 37 36 11 11 10 10 10 10 10 11 11 12 12 13 25 26 27 28 29 30 50628 50654 50679 50704 50729 50754 52126 52151 52175 52200 52225 52250 63607 53632 63656 53681 63705 53730 84417 84402 84386 84370 84356 84339 55072 66097 55121 55145 66169 55194 83469 83453 83437 83421 83405 83389 66621 56545 66669 56593 56617 56641 82495 82478 82462 82446 82429 82413 35 34 33 32 31 30 9 9 9 9 8 8 13 13 14 14 15 15 15 16 16 17 17 18 31 32 33 34 35 36 37 38 39 40 41 42 50779 50804 50829 50854 50879 50904 86148 86133 86119 86104 86089 86074 52275 52299 52324 52349 52374 52399 85249 85234 85218 85203 85188 85173 53764 53779 63804 63828 63863 53877 84324 84308 84292 84277 84261 84245 84230 84214 84198 84182 84167 84161 65218 65242 55266 66291 55316 56339 65363 55388 55412 55436 56460 65484 83373 83356 83340 83324 83308 83292 56665 66689 66713 66736 56760 56784 82396 82380 82363 82347 82330 82314 29 28 27 26 25 24 23 22 21 20 19 18 8 7 7 7 7 6 50929 50954 50979 51004 51029 51054 86059 86045 86030 86015 86000 85985 52423 52448 52473 52498 52522 52547 85157 85142 85127 85112 85096 85081 53902 63926 63951 63976 54000 64024 83276 83260 83244 83228 83212 83195 56808 56832 56856 66880 56904 56928 82297 82281 82264 82248 82231 82214 6 6 6 5 5 5 18 18 19 19 20 20 43 44 45 46 47 48 51079 51104 51129 51154 51179 51204 85970 85956 85941 85926 85911 85896 52572 52597 52621 52646 52671 52696 85066 85051 85035 85020 85005 84989 64049 54073 54097 54122 64146 54171 84136 84120 84104 84088 84072 84067 84041 84025 84009 83994 83978 83962 56609 55633 66657 55681 55605 55630 83179 83163 83147 83131 83115 83098 56952 66976 67000 57024 67047 57071 57096 67119 57143 57167 57191 57215 82198 82181 82165 82148 82132 82115 17 16 15 14 13 12 5 4 4 4 3 3 20 21 21 22 22 23 49 50 51 52 53 54 51229 51254 51279 51304 51329 51354 85881 85866 85851 85836 85821 85806 52720 52745 52770 52794 52819 52844 84974 84959 84943 84928 84913 84897 54195 54220 64244 54269 54293 54317 56654 56678 55702 55726 56750 66775 83082 83066 83050 83034 83017 83001 82098 82082 82065 82048 82032 82015 11 10 9 8 7 6 5 4 3 2 1 3 3 2 2 2 2 23 23 24 24 25 25 55 56 57 58 59 60 51379 51404 51429 51454 51479 51504 85792 85777 85762 85747 85732 85717 52869 52893 52918 52943 52967 52992 84882 84866 84851 84836 84820 84805 54342 54366 64391 54415 54440 54464 83946 83930 83915 83899 83883 83867 55799 55823 55847 65871 55895 55919 82985 82969 82953 82936 82920 82904 67238 57262 57286 67310 67334 57358 81999 81982 81965 81949 81932 81915 1 1 1 1 N. COS. N. sine. N. COS. N. Bine. N. cos. N. sine. N. COS. N. sine. N. COS. N.sine. M. 69° 68° 57° 66° 66° • TABLE 41. [Page 763 Natural Sines and Cosines. Prop, parts S3 85° 1 86° 37° 38° 1 89° 1 Prop, parts 18 M. N. sine. N. COS. N. sine. N. cos. N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. 1 1 2 2 2 1 2 o 4 5 6 57358 57381 57405 57429 57453 57477 57501 81915 81899 81882 81865 81848 81832 81815 58779 58802 58826 58849 58873 58896 58920 80902 80885 80867 80850 80833 80816 80799 60182 60205 60228 60251 60274 60298 60321 79864 79846 79829 79811 79793 79776 79758 61566. 61589 61612 61635 61658 61681 61704 78801 78783 78765 78747 78729 78711 78694 62932 62955 62977 63000 63022 63045 63068 77715 77696 77678 77660 77641 77623 77605 60 59 58 57 56 55 54 18 18 17 17 17 17 16 3 3 3 4 4 5 7 8 9 10 11 12 57524 57548 57572 57596 57619 57643 81798 81782 81765 81748 81731 81714 58943 58967 58990 59014 59037 59061 80782 80765 80748 80730 80713 80696 60344 60367 60390 60414 60437 60460 79741 79723 79706 79688 79671 79653 61726 61749 61772 61795 61818 61841 78676 78658 78640 78622 78604 78586 63090 63113 63135 63158 63180 63203 77586 77568 77550 77531 77513 77494 53 52 51 50 49 48 47 46 45 44 43 42 16 16 15 15 15 14 5 5 6 6 7 7 13 14 15 16 17 18 57667 57691 57715 57738 57762 57786 81698 81681 81664 81647 81631 81614 59084 59108 59131 59154 59178 59201 80679 80662 80644 80627 80610 80593 60483 60506 60529 60553 60576 60599 79635 79618 79600 79583 79565 79547 61864 61887 61909 61932 61955 61978 78568 78550 78632 78514 78496 78478 63225 63248 63271 63293 63316 63338 77476 77458 77439 77421 77402 77384 14 14 14 13 13 13 7 • 8 8 8 9 9 19 20 21 22 23 24 57810 57833 57857 57881 57904 57928 81597 81580 81563 81546 81530 81513 59225 59248 59272 59295 59318 59342 59365 59389 59412 59436 59459 59482 80576 80558 80541 80524 80507 80489 80472 80455 80438 80420 80403 80386 60622 60645 60668 60691 60714 60738 79530 79512 79494 79477 79459 79441 62001 62024 62046 62069 62092 62115 62138 62160 62183 62206 62229 62251 62274 62297 62320 62342 62365 62388 78460 78442 78424 78405 78387 78369 78351 78333 78315 78297 78279 78261 78243 78225 78206 78188 78170 78152 63361 63383 63406 63428 63451 63473 77366 77347 77329 77310 77292 77273 41 40 39 38 37 36 12 12 12 11 11 11 10 10 10 11 11 12 25 26 27 28 29 30 57952 57976 57999 58023 58047 58070 81496 81479 81462 81445 81428 81412 60761 60784 60807 60830 60853 60876 60899 60922 60945 60968 60991 61015 79424 79406 79388 79371 79353 79335 79318 79300 79282 79264 79247 79229 63496 63518 63540 63563 63585 63608 63630 63653 63675 63698 63720 63742 77255 77236 77218 77199 77181 77162 35 34 33 32 31 30 11 10 10 10 9 9 12 12 13 13 13 14 31 32 33 34 35 36 58094 58118 58141 58165 58189 58212 81395 81378 81361 81344 81327 81310 59506 59529 59552 59576 59599 59622 80368 80351 80334 80316 80299 80282 77144 77125 77107 77088 77070 77051 29 28 27 26 25 24 9 8 8 8 8 7 14 15 15 15 16 16 37 38 39 40 41 42 58236 58260 58283 58307 58330 58354 81293 81276 81259 81242 81225 81208 59646 59669 59693 59716 59739 59763 80264 80247 80230 80212 80195 80178 61038 61061 61084 61107 61130 61153 79211 79193 79176 79158 79140 79122 79105 79087 79069 79051 79033 79016 62411 62433 62456 62479 62502 62524 62547 62570 62592 62615 62638 62660 78134 78116 78098 78079 78061 78043 78025 78007 77988 77970 77952 77934 63765 63787 63810 63832 63854 63877 63899 63922 63944 63966 63989 64011 77033 77014 76996 76977 76959 76940 76921 76903 76884 76866 76847 76828 23 22 21 20 19 18 17 16 15 14 13 12 7 7 6 6 6 5 16 17 17 18 18 18 43 44 45 46 47 48 58378 58401 58425 58449 58472 58496 81191 81174 81157 81140 81123 81106 59786 59809 59832 59856 59879 59902 80160 80143 80125 80108 80091 80073 61176 61199 61222 61245 61268 61291 5 5 5 4 4 4 19 19 20 20 20 21 49 50 51 52 53 54 55 56 57 58 59 60 58519 58543 58567 58590 58614 58637 81089 81072 81055 81038 81021 81004 59926 59949 59972 59995 60019 60042 80056 80038 80021 80003 79986 79968 61314 61337 61360 61383 61406 61429 78998 78980 78962 78944 78926 78908 62683 62706 62728 62751 62774 62796 62819 62842 62864 62887 62909 62932 77916 77897 77879 77861 77843 77824 77806 77788 77769 77751 77733 77715 64033 64056 64078 64100 64123 64145 76810 76791 76772 76754 76735 76717 11 10 9 8 7 6 3 3 3 2 2 2 2 1 1 1 21 21 22 22 23 23 58661 58684 58708 58731 58755 58779 80987 80970 80953 80936 80919 80902 60065 60089 60112 60135 60158 60182 79951 79934 79916 79899 79881 79864 61451 61474 61497 61520 61543 61566 78891 78873 78855 78837 78819 78801 64167 64190 64212 64234 64256 64279 76698 76679 76661 76642 76623 76604 5 4 3 2 1 N.C08. N. sine. K.C08. 1 N. sine. N. COS. N. sine. N. COS. N. sine. N. COS. N. sine. M. 64° 68° 58° '1 61° 50° Page 764j TABLE 41. • Natural Sines and Cosines. Prop. parte 82 M. 40° 41° 42° 48° 44° Prop. parte 19 N.Bine. N. COS. N. Bine. N.coa N.sine. N. COS. N.sine. N. COS. N. sine. N. cos. 1 1 1 2 2 1 2 3 4 5 6 64279 64301 64323 64346 64368 64390 64412 76604 76586 76567 76548 76530 76511 76492 65606 65628 65650 65672 65694 65716 65738 75471 75452 75433 75414 75395 75375 75356 66913 66936 66956 66978 66999 67021 67043 74314 74296 74276 74266 74237 74217 74198 68200 68221 68242 68264 68285 68306 68327 73135 73116 73096 73076 73056 73036 73016 69466 69487 69608 69629 69649 69570 69591 71934 71914 71894 71873 71853 71833 71813 71792 71772 71762 71732 71711 71691 60 59 58 57 56 55 54 19 19 18 18 18 17 17 3 3 3 4 4 4 7 8 9 10 11 12 64435 64457 64479 64501 64524 64546 76473 76455 76436 76417 76398 76380 65759 65781 65803 65825 65847 65869 75337 75318 76299 76280 76261 75241 67064 67086 67107 67129 67151 67172 74178 74159 74139 74120 74100 74080 68349 68370 68391 68412 68434 68455 72996 72976 72957 72937 72917 72897 69612 69633 69654 69676 69696 69717 53 52 51 50 49 48 17 16 16 16 16 15 6 5 6 6 6 7 13 14 15 16 17 18 64568 64590 64612 64635 64657 64679 76361 76342 76323 76304 76286 76267 65891 65913 65935 65956 65978 66000 75222 75203 75184 75165 75146 75126 67194 67215 67237 67258 67280 67301 74061 74041 74022 74002 73983 73963 68476 68497 68618 68639 68561 68582 72877 72867 72837 72817 72797 72777 69737 69758 69779 69800 69821 69842 71671 71650 71630 71610 71590 71669 47 46 45 44 43 42 15 16 14 14 14 13 13 13 12 12 12 11 7 7 8 8 8 9 19 20 21 22 23 24 64701 64723 64746 64768 64790 64812 76248 76229 76210 76192 76173 76154 66022 66044 66066 66088 66109 66131 75107 75088 75069 75050 75030 75011 67323 67344 67366 67387 67409 67430 73944 73924 73904 73885 73866 73846 68603 68624 68645 68666 68688 68709 72757 72737 72717 72697 72677 72657 69862 69883 69904 69926 69946 69966 71649 71629 71608 71488 71468 71447 41 40 39 38 37 36 9 10 10 10 11 11 25 26 27 28 29 30 64834 64856 64878 64901 64923 64945 76135 76116 76097 76078 76059 76041 66153 66175 66197 66218 66240 66262 74992 74973 74953 74934 74915 74896 67452 67473 67495 67616 67538 67659 73826 73806 73787 73767 73747 73728 68730 68751 68772 68793 68814 68835 72637 72617 72697 72577 72557 72537 72517 72497 72477 72457 72437 72417 69987 70008 70029 70049 70070 70091 71427 71407 71386 71366 71.S45 71325 35 34 33 32 31 30 29 28 27 26 25 24 11 11 10 10 10 10 11 12 12 12 13 13 31 32 33 34 35 36 64967 64989 65011 65033 65055 65077 76022 76003 75984 75965 75946 75927 66284 66306 66327 66349 66371 66393 74876 74867 74838 74818 74799 74780 67580 67602 67623 67645 67666 67688 73708 73688 73669 73649 73629 73610 68867 68878 68899 68920 68941 68962 70112 70132 70153 70174 70195 70215 71305 71284 71264 71243 71223 71203 9 9 9 8 8 8 14 14 14 15 15 15 37 38 39 40 41 42 65100 65122 65144 65166 65188 65210 75908 75889 75870 75851 75832 75813 66414 66436 66458 66480 66501 66523 74760 74741 74722 74703 74683 74664 67709 67730 67752 67773 67795 67816 73690 73670 73551 73531 73511 73491 68983 69004 69026 69046 69067 69088 72397 72377 72367 72337 72317 72297 70236 70267 70277 70298 70319 70339 71182 71162 71141 71121 71100 71080 23 22 21 20 19 18 7 7 7 6 6 6 16 16 17 17 17 18 43 44 45 46 47 48 65232 65254 65276 65298 66320 65342 75794 75775 75756 75738 75719 75700 66545 66566 66688 66610 66632 66653 74644 74625 74606 74586 74567 74548 67837 67859 67880 67901 67923 67944 73472 73462 73432 73413 73393 73373 69109 69130 69161 69172 69193 69214 72277 72267 72236 72216 72196 72176 70360 70381 70401 70422 70443 70463 71059 71039 71019 70998 70978 70967 17 16 15 14 13 12 6 5 5 4 4 4 18 18 19 19 19 20 49 50 51 52 53 54 65364 65386 65408 65430 65452 65474 75680 75661 75642 75623 75604 75585 66675 66697 66718 66740 66762 66783 74628 74509 74489 74470 74451 74431 67966 67987 68008 68029 68061 68072 73353 73333 73314 73294 73274 73254 69235 69266 69277 69298 69319 69340 72156 72136 72116 72095 72075 72055 70484 70505 70526 70546 70567 70587 70937 70916 70896 70876 70855 70834 11 10 9 8 7 6 3 3 3 3 2 2 20 21 21 21 22 22 55 56 57 58 59 60 65496 65518 65540 65562 65584 65606 75566 75547 75528 75509 75490 75471 66805 66827 66848 66870 66891 66913 74412 74392 74373 74363 74334 74314 68093 68116 68136 68157 68179 68200 73234 73215 73195 73175 73155 73135 69361 69382 69403 69424 69445 69466 72035 72016 71996 71974 71964 71934 70608 70628 70649 70670 70690 70711 70813 70793 70772 70752 70731 70711 5 4 3 2 1 2 1 1 1 N.C08. N.slne. N.cos. N. sine. N. COS. N. sine. N. COS. N.sine. N.cos. N. sine. M. 49° 48° 47° 46° 46° TABLE 42. [Page 766 Ix^arithms of Numbers. No. 1 100. Log. 0.00000 ^2.00000. | No. Log. No. Log. No. Log. No. Log. No. Log. 1 0.00000 21 1. 32222 41 1. 61278 61 1.78533 81 1.90849 2 0. 30103 22 1.34242 42 1. 62325 62 1. 79239 82 1. 91381 3 0.47712 23 1. 36173 43 1. 63347 63 1. 79934 83 1. 91908 4 0.60206 24 1.38021 44 1.64345 64 1. 80618 84 1. 92428 5 0. 69897 25 1.39794 45 1. 65321 65 1. 81291 86 1.92942 6 0. 77815 26 1. 41497 46 1. 66276 66 1. 81954 86 1.93450 7 0. 84510 27 1. 43136 47 1. 67210 67 1. 82607 87 1. 93952 8 0. 90309 28 1. 44716 48 1.68124 68 1. 83251 88 1.94448 9 0. 95424 29 1.46240 49 1. 69020 69 1. 83885 89 1.94939 10 1.00000 30 1. 47712 50 1. 69897 70 1. 84510 90 1.95424 11 1.04139 31 1. 49136 51 1. 70757 71 1. 85126 91 1.95904 12 1. 07918 32 1. 50515 52 1.71600 72 1.86733 92 1. 96379 13 1. 11394 33 1.51851 53 1. 72428 73 1.86332 98 1.96848 14 1. 14613 34 1. 53148 54 1. 73239 74 1. 86923 94 1. 97313 15 1. 17609 35 1.54407 65 1.74036 75 1. 87606 95 1. 97772 16 1. 20412 36 1. 55630 56 1. 74819 76 1. 88081 96 1. 98227 17 1. 23045 37 1.56820 57 1. 75587 77 1. 88649 97 1. 98677 18 1. 25527 38 1. 57978 58 1. 76343 78 1. 89209 98 1. 99123 19 1. 27875 39 1. 59106 59 1. 77085 79 1. 89763 99 1.99664 20 1. 30103 1 40 1.60206 60 1. 77815 80 1.90309 100 2.00000 Page 766] TABLE 42. Logarithms of Numbers. No. 100 1600. Log. 00000 20412. No. 1 1 8 3 4 5 6 7 8 9 100 101 102 103 104 00000 00043 00432 1 00475 00860 00903 01284 01326 01703 01745 00087 00518 00945 01368 01787 00130 00561 00988 01410 01828 00173 00604 01030 01452 01870 00217 00647 01072 01494 01912 00260 00689 01115 01536 01953 00303 00732 01157 01578 01995 00346 00775 01199 01620 02036 00389 00817 01242 01662 02078 02490 02898 03302 03703 04100 43 43 1 2 3 4 5 6 7 8 9 4 9 13 17 22 26 30 34 39 4 8 13 17 21 25 29 34 38 105 106 107 108 109 02119 02531 02938 03342 03743 02160 02572 02979 03383 03782 02202 02612 03019 03423 03822 02243 02653 03060 03463 03862 02284 02694 03100 03503 03902 04297 04689 05077 05461 05843 02325 02735 03141 03543 03941 02366 02776 03181 03583 03981 02407 02816 03222 03623 04021 02449 02857 03262 03663 04060 110 111 112 113 114 04139 04532 04922 05308 05690 04179 04571 04961 05346 05729 04218 04610 04999 05385 05767 04258 04650 05038 05423 05805 04336 04727 05115 05500 05881 06258 06633 07004 07372 07737 08099 08458 08814 09167 09517 04376 04766 05154 05538 05918 04415 04805 05192 05576 05956 04454 04844 05231 05614 05994 04493 04883 05269 05652 06032 41 40 1 2 3 4 5 6 7 8 9 4 8 12 16 21 25 29 33 37 4 8 12 16 20 24 28 32 36 115 116 117 118 119 06070 06446 06819 07188 07555 06108 06483 06856 07225 07591 07954 08314 08672 09026 09377 06145 06521 06893 07262 07628 06183 06558 06930 07298 07664 06221 06595 06967 07335 07700 06296 06670 07041 07408 07773 06333 06707 07078 07445 07809 06371 06744 07115 07482 07846 06408 06781 07151 07518 07882 120 121 122 123 124 07918 08279 08636 08991 09342 07990 08350 08707 09061 09412 08027 08386 08743 09096 09447 08063 08422 08778 09132 09482 08135 08493 08849 09202 09552 09899 10243 10585 10924 11261 08171 08529 08884 09237 09587 08207 08565 08920 09272 09621 08243 08600 08955 09307 09656 39 88 1 2 3 4 5 6 7 8 9 4 8 12 16 20 23 27 31 35 4 8 11 15 19 23 27 30 34 125 126 127 128 129 09691 10037 10380 10721 11059 09726 10072 10415 10755 11093 09760 10106 10449 10789 11126 09795 10140 10483 10823 11160 09830 10175 10517 10857 11193 09864 10209 10551 10890 11227 09934 10278 10619 10958 11294 09968 10312 10653 10992 11327 10003 10346 10687 11025 11361 130 131 132 133 134 11394 11727 12057 12385 12710 11428 11760 12090 12418 12743 11461 11793 12123 12450 12775 11494 11826 12156 12483 12808 11528 11860 12189 12516 12840 11561 11893 12222 12548 12872 11594 11926 12254 12581 12905 11628 11959 12287 12613 12937 11661 11992 12320 12646 12969 11694 12024 12352 12678 13001 37 36 1 2 3 4 5 6 7 8 9 4 7 11 15 19 22 26 30 33 4 7 11 14 18 22 25 29 32 135 136 137 138 139 13033 13354 13672 13988 14301 13066 13386 13704 14019 14333 13098 13418 13735 14051 14364 13130 13450 13767 14082 14395 13162 13481 13799 14114 14426 13194 13513 13830 14145 14457 13226 13545 13862 14176 14489 13258 13577 13893 14208 14520 13290 13609 13925 14239 14551 13322 13640 13956 14270 14582 140 141 142 143 144 14613 14922 15229 15534 15836 14644 14953 15259 15564 15866 14675 14983 15290 15594 15897 14706 15014 15320 15625 15927 14737 15045 15351 15655 15957 14768 15076 15381 15685 15987 14799 15106 15412 15715 16017 14829 15137 15442 15746 16047 16346 16643 16938 17231 17522 14860 15168 15473 15776 16077 14891 15198 15503 15806 16107 35 34 1 2 3 4 5 ? 8 9 4 7 11 14 18 21 25 28 32 3 7 10 14 17 20 24 27 31 145 146 147 148 149 16137 16435 16732 17026 17319 16167 16465 16761 17056 17348 16197 16495 16791 17085 17377 16227 16524 16820 17114 17406 16256 16554 16850 17143 17435 16286 16584 16879 17173 17464 16316 16613 16909 17202 17493 16376 16673 16967 17260 17551 16406 16702 16997 17289 17580 150 151 152 153 154 17609 17898 18184 18469 18752 17638 17926 18213 18498 18780 17667 17955 18241 18526 18808 17696 17984 18270 18554 18837 17725 18013 18298 18583 18865 17754 18041 18327 18611 18893 17782 18070 18355 18639 18921 17811 18099 18384 18667 18949 17840 18127 18412 18696 18977 17869 18156 18441 18724 19005 33 82 1 2 3 4 5 6 7 8 9 3 7 10 13 17 20 23 26 30 3 6 10 13 16 19 22 26 29 155 156 157 158 159 19033 19312 19590 19866 20140 19061 19340 19618 19893 20167 19089 19368 19645 19921 20194 19117 19396 19673 19948 20222 19145 19424 19700 19976 20249 19173 19451 19728 20003 20276 19201 19479 19756 20030 20303 19229 19507 19783 20058 20330 19257 19535 19811 20085 20358 19285 19562 19838 20112 20385 No. 1 a 8 4 6 e 7 8 9 TABLE 42. [Page 767 Logarithms of Numbers. No. 1600 2200. Log. 20412 34242. No. 1 2 8 4 6 6 7 8 9 160 161 162 163 164 20412 20683 20952 21219 21484 20439 20710 20978 21245 21511 20466 20737 21005 21272 21537 20493 20763 21032 21299 21564 20520 20790 21059 21325 21590 20548 20817 21085 21352 21617 20575 20844 21112 21378 21643 21906 22167 22427 22686 22943 20602 20871 21139 21405 21669 20629 20898 21165 21431 21696 20656 20925 21192 21458 21722 31 80 1 2 3 4 5 6 7 8 28 28 8< 42 42 1 4' 56 56 1 6' 69 70 1 6i 83 84 1 TABLE 44. [Page 779 Log. Sines, Tangents, and Secants. 7" A A B B C C 178° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 11 4 56 9. 08589 10.91411 9. 08914 10. 91086 10. 00325 9. 99675 1 3 52 56 8 08692 2 91308 09019 2 90981 00326 1 99674 59 2 3 44 56 16 08795 3 91205 09123 3 90877 00328 ! 99672 58 3 3 36 56 24 08897 5 91103 09227 5 90773 00330 1 99670 57 4 3 28 56 32 08999 6 91001 09330 9.09434 1 8 90670 10. 90566 00331 99669 9. 99667 56 55 5 11 3 20 56 40 9. 09101 8 10. 90899 10. 00333 6 3 12 56 48 09202 10 90798 09537 10 90463 00334 99666 54 7 3 4 56 56 09304 11 90696 09640 11 90360 00336 99664 53 8 2 56 57 4 09405 13 90595 09742 13 90258 00337 99663 52 9 2 48 57 12 09506 14 16 90494 10. 90394 09845 9. 09947 15 16 90155 10. 90053 00339 99661 51 10 11 2 40 57 20 9. 09606 10. 00341 9. 99659 50 11 2 32 57 28 09707 18 90293 10049 18 89951 00342 99658 49 12 2 24 57 36 09807 19 90193 10150 20 89850 00344 99656 48 13 2 16 57 44 09907 21 1 90093 10252 21 89748 00346 99655 47 14 2 8 57 52 10006 22 89994 10353 9. 10454 23 89647 00347 99653 46 45 15 11 2 58 9. 10106 24 10. 89894 24 10. 89546 10. 00349 9. 99651 16 1 52 58 8 10205 26 89795 10555 26 89445 00350 1 99650 44 17 1 44 58 16 10304 27 89696 10656 28 89344 00352 99648 43 18 1 36 58 24 10402 29 89598 10756 29 89244 00353 99647 42 19 1 28 58 32 10501 9. 10599 30 89499 10856 31 89144 00355 99645 41 20 11 1 20 58 40 32 10. 89401 9.10956 33 10.89044 10. 00357 9. 99643 40 21 1 12 58 48 10697 34 89303 11056 34 88944 00358 99642 39 22 1 4 58 56 10795 35 i 89205 11155 36 88845 00360 1 1 99640 38 23 56 59 4 10893 37 ! 89107 11254 37 88746 00362 1 , 99638 37 24 48 59 12 10990 38 89010 11353 39 88647 00363 10.00365 1 1 99637 36 35 25 11 40 59 20 9. 11087 40 10. 88913 9. 11452 41 10. 88548 9. 99635 26 32 59 28 11184 42 88816 11551 42 88449 00367 99633 34 27 24 59 36 11281 43 i 88719 11649 44 88351 00368 99632 33 28 16 59 44 11377 45 : 88623 11747 46 88253 00370 99630 32 29 8 59 52 11474 46 88526 11845 47 88155 00371 J- 99629 9. 99627 31 30 30 11 10 9. 11570 48 10,88430 9. 11943 49 10. 88057 10. 00373 31 10 59 52 8 11666 50 88334 12040 51 87960 00375 1 : 99625 29 32 59 44 16 11761 51 88239 12138 52 87862 00376 99624 28 33 59 36 24 11857 53 88143 12235 54 877a5 00378 99622 27 34 59 28 32 11952 54 88048 12332 55 57 87668 10. 87572 00380 10.00382 99620 26 35 10 59 20 1 40 9. 12047 56 10. 87953 9. 12428 9. 99618 25 36 59 12 48 12142 58 87858 12525 59 87475 00383 99617 24 37 59 4 56 12236 59 87764 12621 60 ! 87379 00385 99615 23 38 58 56 1 4 12331 61 87669 12717 62 1 87283 00387 99613 22 39 58 48 1 12 12425 62 87575 12813 64 87187 00388 —Y 99612 9.99610 21 20 40 10 58 40 1 1 20 9. 12519 64 10. 87481 9.12909 65 10. 87091 10. 00390 41 58 32 1 28 12612 66 87388 13004 67 86996 00392 1 99608 19 42 58 24 1 36 12706 67 87294 13099 68 86901 00393 99607 18 43 58 16 1 44 12799 69 87201 13194 70 86806 00395 99605 17 44 58 8 1 52 12892 70 87108 13289 72 86711 00397 ■'■ 99603 16 45 10 58 12 9. 12985 72 10. 87015 9. 13384 73 10. 86616 10. 00399 1 9. 99601 15 46 57 52 2 8 13078 74 86922 13478 75 86522 00400 99600 14 47 57 44 2 16 13171 75 86829 13573 77 86427 00402 99598 13 48 57 36 2 24 13263 77 86737 13667 78 86333 00404 99596 12 49 57 28 2 32 13355 78 86645 13761 80 86239 00405 99595 11 50 10 57 20 1 2 40 9.13447 80 10. 86553 9.13854 81 10. 86146 10.00407 9. 99593 10 51 57 12 2 48 13539 82 86461 13948 83 86052 00409 99591 9 52 57 4 2 56 13630 83 86370 14041 85 85959 00411 99589 8 53 56 56 3 4 13722 85 86278 14134 86 85866 00412 99588 7 54 56 48 3 12 13813 87 86187 14227 88 90 85773 00414 2 99586 9. 99584 6 5 55 10 56 40 1 3 20 9.13904 88 10. 86096 9. 14320 10. 85680 10. 00416 2 56 56 32 3 28 13994 90 86006 14412 91 85588 00418 2 99582 4 57 56 24 3 36 14085 91 85915 14504 93 85496 00419 2 99581 3 58 56 16 3 44 14175 93 85825 14597 95 85403 00421 2 99579 2 59 56 8 3 52 14266 95 85734 14688 96 85312 00423 2 99577 1 60 56 4 14356 96 85644 14780 98 85220 00425 2 99575 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Difl. Tangent. Cosecant. Difl. Sine. M. 97J A A B B C C 82° 1 Seconds of time !■ 2' 8" 4" 6- 1 6- 7« 1 Prop, parts of cols. ■{ B 12 12 24 24 36 48 37 49 1 1 60 61 1 72 84 73 1 86 1 I 1 21594°— 14- -42 Page 780] TABLE 44. Log. Sines, Tangents, and Secante. 8° A A B B C C 171= M. Hour A, M. Hour p. M. Sine. Diff. Cosecant. Tangent. Difl. Cotangent. Secant. DiflE. Cosine. M. 10 56 14 9. 14356 10. 85644 9. 14780 10. 85220 10. 00425 9. 99575 60 1 55 52 4 8 14445 1 85555 14872 1 85128 00426 99574 59 2 55 44 4 16 14535 3 85465 14963 3 85037 00428 99572 58 3 55 36 4 24 14624 4 85376 15054 4 84946 00430 99570 57 4 55 28 4 32 14714 6 85286 15145 6 84855 00432 99568 56 5 10 55 20 1 4 40 9. 14803 7 10. 85197 9. 15236 7 10. 84764 10. 00434 9. 99566 55 6 55 12 4 48 14891 8 85109 15327 9 84673 00435 99565 54 7 55 4 4 56 14980 10 85020 15417 10 84583 00437 99563 53 8 54 56 5 4 15069 11 84931 15508 12 84492 00439 99561 52 9 54 48 5 12 15157 13 84843 15598 13 84402 00441 99559 51 10 10 54 40 1 5 20 9. 15245 14 10. 84755 9. 15688 14 10. 84312 10. 00443 9. 99557 50 11 54 32 5 28 15333 16 84667 15777 16 84223 00444 99556 49 12 54 24 5 36 15421 17 84579 15867 17 84133 00446 99554 48 13 54 16 5 44 15508 18 84492 15956 19 84044 00448 99552 47 14 54 8 5 52 15596 20 84404 16046 20 83954 00450 99550 46 15 10 54 1 6 9. 15683 21 10. 84317 9. 16135 22 10. 83865 10. 00452 9. 99548 45 16 53 52 6 8 15770 23 84230 16224 23 83776 00454 99546 44 17 53 44 6 16 15857 24 84143 16312 25 83688 00455 99545 43 18 53 36 6 24 15944 25 84056 16401 26 83599 00457 99543 42 19 53 28 6 32 16030 27 83970 16489 27 83511 00459 99541 41 40 20 10 53 20 1 6 40 9. 16116 28 10. 83884 9. 16577 29 10. 83423 10. 00461 9. 99539 21 53 12 6 48 16203 30 83797 16665 30 83335 00463 99537 39 22 53 4 6 56 16289 31 83711 16753 32 83247 00465 99535 38 23 52 56 7 4 16374 32 83626 16841 33 83159 00467 99533 37 24 52 48 7 12 16460 34 83540 16928 35 83072 00468 99532 36 25 10 52 40 1 7 20 9. 16545 35 10. 83455 9. 17016 36 10. 82984 10. 00470 9. 99530 35 26 52 32 7 28 16631 37 83369 17103 37 82897 00472 99528 34 27 52 24 7 36 16716 38 83284 17190 39 82810 00474 99526 33 28 52 16 7 44 16801 39 83199 17277 40 82723 00476 99524 32 29 30 52 8 7 52 16886 41 83114 17363 42 82637 00478 99522 31 10 52 1 8 9. 16970 42 10. 83030 9. 17450 43 10. 82550 10. 00480 9. 99520 30 31 51 52 8 8 17055 44 82945 17536 45 82464 00482 99518 29 32 51 44 8 16 17139 45 82861 17622 46 82378 00483 99517 28 33 51 36 8 24 17223 47 82777 17708 48 82292 00485 99515 27 34 51 28 8 32 17307 48 82693 17794 49 82206 00487 99513 26 35 10 51 20 1 8 40 9. 17391 49 10. 82G09 9. 17880 50 10. 82120 10. 00489 9. 99511 25 36 51 12 8 48 17474 51 82526 17965 52 82035 00491 99509 24 37 51 4 8 56 17558 52 82442 18051 53 81949 00493 99507 23 38 50 56 9 4 17641 54 82359 18136 55 81864 00495 99505 22 39 50 48 9 12 17724 9. 17807 55 82276 18221 56 81779 00497 99503 21 40 10 50 40 1 9 20 56 10. 82193 9. 18306 58 10. 81694 10. 00499 9. 99501 20 41 50 32 9 28 17890 58 82110 18391 59 81609 00501 99499 19 42 50 24 9 36 17973 59 82027 18475 61 81525 00503 99497 18 43 50 16 9 44 18055 61 81945 18560 62 81440 00505 99495 17 44 50 8 9 52 18137 62 81863 18644 63 81356 00506 99494 16 45 10 50 1 10 9. 18220 63 10. 81780 9. 18728 65 10. 81272 10. 00508 9. 99492 15 46 49 52 10 8 18302 65 81698 18812 66 81188 00510 99490 14 47 49 44 10 16 18383 66 81617 18896 68 81104 00512 99488 13 48 49 36 10 24 18465 68 81535 18979 69 81021 00514 2 99486 12 49 49 28 10 32 18547 69 81453 19063 71 80937 10. 80854 00516 2 99484 9. 99482 11 10 50 10 49 20 1 10 40 9. 18628 71 10. 81372 9. 19146 72 10. 00518 2 51 49 12 10 48 18709 72 81291 19229 74 80771 00520 2 99480 9 52 49 4 10 56 18790 73 81210 19312 75 80688 00522 2 99478 8 53 48 56 11 4 18871 75 81129 19395 76 80605 00524 2 99476 7 54 55 48 48 10 48 40 11 12 1 11 20 18952 76 81048 19478 78 79 80522 00526 2 2 99474 6 5 9. 19033 78 10. 80967 9. 19561 10. 80439 10. 00528 9. 99472 56 48 32 11 28 19113 79 80887 19643 81 80357 00530 2 99470 4 57 48 24 11 36 19193 80 80807 19725 82 80275 00532 2 99468 3 58 48 16 11 44 19273 82 80727 19807 84 80193 00534 2 99466 2 59 48 8 11 52 19353 83 80647 19889 85 80111 00536 2 99464 1 60 48 12 19433 85 80567 19971 87 80029 00538 2 99462 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. u. 98° A A B B C C 81° 1 Seconds of time ! !■ 1 2- 3- 4' 5< 6< 7- Prop, parts of cols. iB 11 11 21 22 32 32 42 43 1 53 54 1 63 65 1 74 76 2 Log. TABLE 44. Sines, Tangents, and Secants. [Page 781 9° A A B B C C 170° M. Hour A. M. Hour p. M. Sine. Dift. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 10 48 1 12 9. 19433 10. 80567 9. 19971 10. 80029 10. 00538 9. 99462 60 1 47 52 12 8 19513 1 80487 20053 1 79947 00540 99460 59 2 47 44 12 16 19592 3 80408 20134 3 79865 00542 99458 58 3 47 36 12 24 19672 4 80328 20216 4 79784 00544 99456 57 4 47 28 12 32 19751 5 80249 20297 5 6 79703 10. 79622' 00546 10. 00548 99454 9. 99452 56 55 5 10 47 20 1 12 40 9. 19830 6 10. 80170 9. 20378 6 47 12 12 48 19909 8 80091 20459 8 79541 00550 99450 54 7 47 4 12 56 19988 9 80012 20540 9 79460 00552 99448 53 8 46 56 13 4 20067 10 79933 20621 10 79379 00554 99446 52 9 10 46 48 13 12 20145 9. 20223 11 13 79855 10. 79777 20701 9. 20782 12 79299 00556 99444 51 10 46 40 1 13 20 13 10. 79218 10. 00558 9. 99442 50 11 46 32 13 28 20302 14 79698 20862 14 79138 00560 99440 49 12 46 24 13 36 20380 15 79620 20942 16 79058 00562 99438 48 13 46 16 13 44 20458 16 79542 21022 17 78978 00564 99436 47 14 46 8 13 52 20535 18 79465 21102 18 19 78898 10.78818 00566 99434 46 45 15 10 46 1 14 9. 20613 19 10. 79387 9. 21182 10. 00568 1 9. 99432 16 45 52 14 8 20691 20 79309 21261 21 78739 00571 99429 44 17 45 44 14 16 20768 21 79232 21341 22 78659 00573 99427 43 18 45 36 14 24 20845 23 79155 21420 23 78580 00575 99425 42 19 20 45 28 14 32 20922 24 79078 21499 25 78501 00577 99423 41 10 45 20 1 14 40 9.20999 25 10. 79001 9. 21578 26 10. 78422 10. 00579 9. 99421 40 21 45 12 14 48 21076 26 78924 21657 27 78343 00581 99419 39 22 45 4 14 56 21153 28 78847 21736 28 78264 00583 99417 38 23 44 56 15 4 21229 29 78771 21814 30 78186 00585 99415 37 24 44 48 16 12 21306 9. 21382 30 31 78694 10. 78618 21893 9. 21971 31 32 78107 00587 io:o6589 99413 36 25 10 44 40 1 15 20 10. 78029 9. 99411 35 26 44 32 15 28 21458 33 78542 22049 34 77951 00591 99409 34 27 44 24 15 36 21534 34 78466 22127 35 77873 00593 99407 33 28 44 16 15 44 21610 35 78390 22205 36 77795 00596 99404 32 29 44 8 15 52 21685 37 78315 22283 38 39 77717 00598 99402 31 30 10 44 1 16 9.21761 38 10. 78239 9. 22361 10. 77639 10.00600 9.99400 30 31 43 52 16 8 21836 39 78164 22438 40 77562 00602 99398 29 32 43 44 16 16 21912 40 78088 22516 41 77484 00604 99396 28 33 43 36 16 24 21987 42 78013 22593 43 77407 00606 99394 27 34 43 28 16 32 22062 43 44 77938 10. 77863 22670 44 77330 00608 99392 26 35 10 43 20 1 16 40 9. 22137 9. 22747 45 10. 77253 10. 00610 9. 99390 25 36 43 12 16 48 22211 45 77789 22824 47 77176 00612 99388 24 37 43 4 16 56 22286 47 77714 22901 48 77099 00615 99385 23 38 42 56 17 4 22361 48 77639 22977 49 77023 00617 99383 22 39 40 42 48 17 12 1 17 20 22435 49 77565 23054 50 76946 00619 99381 21 10 42 40 9. 22509 50 10. 77491 9. 23130 52 10. 76870 10. 00621 9. 99379 20 41 42 32 17 28 22583 52 77417 23206 53 76794 00623 99377 19 42 42 24 17 36 22657 53 77343 23283 54 76717 00625 99375 18 43 42 16 17 44 22731 54 77269 23359 56 76641 00628 2 99372 17 44 42 8 17 52 1 18 22805 55 77195 23435 57 76565 00630 2 99370 16 45 10 42 9. 22878 57 10. 77122 9. 23510 58 10. 76490 10. 00632 2 9. 99368 15 46 41 52 18 8 22952 58 77048 23586 60 76414 00634 2 99366 14 47 41 44 18 16 23025 59 76975 23661 61 76339 00636 2 99364 13 48 41 36 18 24 23098 60 76902 23737 62 76263 00638 2 99362 12 49 41 28 18 32 23171 62 76829 23812 63 76188 00641 2 99359 11 50 10 41 20 1 18 40 9. 23244 63 10. 76756 9. 23887 65 10. 76113 10. 00643 2 9. 99357 10 51 41 12 18 48 23317 64 76683 23962 66 76038 00645 2 99355 9 52 41 4 18 56 23390 65 76610 24037 67 75963 00647 2 99353 8 53 40 56 19 4 23462 67 76538 24112 69 75888 00649 2 99351 7 54 55 40 48 19 12 23535 68 76465 24186 70 75814 00652 2 99348 6 10 40 40 1 19 20 9. 23607 69 10. 76393 9. 24261 71 10. 75739 10.00654 2 9. 99346 5 56 40 32 19 28 23679 71 76321 24335 73 75665 00656 2 99344 4 57 40 24 19 36 23752 72 76248 24410 74 75590 00658 2 99342 3 58 40 16 19 44 23823 73 76177 24484 75 75516 00660 2 99340 2 59 40 8 19 52 23895 74 76105 24558 76 75442 00663 2 99337 1 60 40 20 23967 76 76033 24632 78 75368 00665 2 99335 M. Hour P. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Difl. Tangent. Cosecant. Diff. Sine. M. 99° A A B B C C 80° 1 Seconds of time !• 2- 3' 4> 6" 6- 7.i A Prop, parts of eols.^B Ic 9 10 19 19 1 28 29 1 38 39 1 47 49 1 57 58 2 66 68 2 Page 782 TABLE 44. Log. Sines. Tangents, and Secants. 10° A A B B C C 169° M. Hour A. M. Hour p. M. Sine. DifiE. Cosecant. Tangent. Diff. ; Cotangent. Secant. Diff. Cosine. M. 10 40 1 20 9. 23967 10. 76033 9. 24632 10. 75368 10. 00665 9. 99335 60 1 39 62 20 8 24039 1 75961 24706 1 75294 00667 99333 59 2 39 44 20 16 24110 2 75890 24779 2 75221 00669 99331 58 3 39 36 20 24 24181 3 75819 24853 4 75147 00672 99328 57 4 39 28 20 32 24253 5 75747 24926 5 75074 00674 99326 56 55 5 10 39 20 1 20 40 9. 24324 6 10. 75676 9. 25000 6 10. 75000 10. 00676 9. 99324 6 39 12 20 48 24395 7 75605 25073 7 74927 00678 99322 54 7 39 4 20 56 24466 8 75534 25146 8 74854 00681 99319 53 8 38 56 21 4 24536 9 75464 25219 9 74781 00683 99317 52 9 38 48 21 12 24607 10 75393 25292 11 12 74708 00685 99315 51 10 10 38 40 1 21 20 9. 24677 11 10. 75323 9. 25365 10. 74635 10. 00687 9. 99313 50 11 38 32 21 28 24748 13 75252 25437 13 74563 00690 99310 49 12 38 24 21 36 24818 14 75182 25510 14 74490 00692 99308 48 13 38 16 21 44 24888 15 75112 25582 15 74418 00694 99306 47 14 15 38 8 21 52 24958 16 75042 25655 16 18 74345 00696 99304 46 45 10 38 1 22 9. 25028 17 10. 74972 9. 25727 10. 74273 10. 00699 9. 99301 16 37 52 22 8 25098 18 74902 25799 19 74201 00701 99299 44 17 37 44 22 16 25168 19 74832 25871 20 74129 00703 99297 43 18 37 36 22 24 25237 20 74763 25943 21 74057 00706 99294 42 19 20 37 28 22 32 25307 9. 25376 22 23 74693 10. 74624 26015 22 73985 00708 99292 41 10 37 20 1 22 40 9. 26086 24 10. 73914 10. 00710 9. 99290 40 21 37 12 22 48 25445 24 74555 26158 25 73842 00712 99288 39 22 37 4 22 56 25514 25 74486 26229 26 73771 00715 99285 38 23 36 56 23 4 25583 26 74417 26301 27 73699 00717 99283 37 24 36 48 23 12 25652 27 28 74348 10. 74279 26372 28 29 73628 00719 99281 36 35 25 10 36 40 1 23 20 9. 25721 9. 26443 10. 73557 10. 00722 9. 99278 26 36 32 23 28 25790 30 74210 26514 31 73486 00724 99276 34 27 36 24 23 36 25858 31 74142 26585 32 73415 00726 99274 33 28 36 16 23 44 25927 32 74073 26655 33 73345 00729 99271 32 29 30 36 8 23 52 25995 33 74005 26726 34 35 73274 00731 99269 31 30 10 36 1 24 9. 26063 34 10. 73937 9. 26797 10. 73203 10. 00733 9. 99267 31 35 52 24 8 26131 35 73869 26867 36 73133 00736 99264 29 32 35 44 24 16 26199 36 73801 26937 38 73063 00738 99262 28 33 35 36 24 24 26267 38 73733 27008 39 72992 00740 99260 27 34 35 28 24 32 26335 39 40 73665 27078 40 41 72922 00743 99257 9. 99255 26 35 10 35 20 1 24 40 9. 26403 10. 73597 9. 27148 10. 72852 10. 00745 36 35 12 24 48 26470 41 73530 27218 42 72782 00748 99252 24 37 35 4 24 56 26538 42 73462 27288 44 72712 00750 99250 23 38 34 56 25 4 26605 43 73395 27357 45 72643 00752 99248 22 39 40 34 48 25 12 26672 44 73328 27427 46 47 72573 00755 10.00757' 2 2 99245 9. 99243 21 20 10 34 40 1 25 20 9. 26739 45 10. 73261 9. 27496 10. 72504 41 34 32 25 28 26806 47 73194 27566 48 72434 00759 2 99241 19 42 34 24 25 36 26873 48 73127 27635 49 72365 00762 2 99238 18 43 34 16 25 44 26940 49 73060 27704 51 72296 00764 2 99236 17 44 34 8 25 52 27007 50 72993 27773 52 72227 00767 2 99233 16 15 45 10 34 1 26 9. 27073 51 10. 72927 9. 27842 53 10. 72158 10. 00769 2 9. 99231 46 33 52 26 8 27140 52 72860 27911 54 72089 00771 2 99229 14 47 33 44 26 16 27206 53 72794 27980 55 72020 00774 2 99226 13 48 33 36 26 24 27273 55 72727 28049 56 71951 00776 2 99224 12 49 33 28 26 32 27339 56 72661 28117 58 71883 00779 2 99221 11 10 50 10 33 20 1 26 40 9. 27405 57 10. 72595 9. 28186 59 10. 71814 10. 00781 2 9. 99219 51 33 12 26 48 27471 58 72529 28254 60 71746 00783 2 99217 9 52 33 4 26 56 27537 59 72463 28323 61 71677 00786 2 99214 8 53 32 56 27 4 27602 60 72396 28391 62 71609 00788 2 99212 7 54 55 32 48 27 12 27668 61 72332 28459 9. 28527 63 65 71541 00791 2 99209 9. 99207 6 5 10 32 40 1 27 20 9. 27734 63 10. 72266 10. 71473 10. 00793 2 56 32 32 27 28 27799 64 72201 28595 66 71405 00796 2 99204 4 57 32 24 27 36 27864 65 72136 28662 67 71338 00798 2 99202 3 58 32 16 27 44 27930 66 72070 28730 68 71270 00800 2 99200 2 59 32 8 27 52 27995 67 72005 28798 69 71202 00803 2 99197 1 60 32 28 28060 68 71940 28865 71 71135 00805 2 99195 M. Hour P.M. Hour A. H. Cosine. Dili. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 100° A A B B C C 79° Seconds of time 1> 2- S« 4* 5« G" 7» Prop, parts of cols, i B Ic 9 9 17 26 18 26 34 36 1 43 44 1 51 53 2 60 62 TABLE 44. [Page 783 Log. Sines, Tangents, and Secants. 11° A A B B C C 168° M. Hour A. M. Hotir p. M. Sine. Difl. Cosecant. TanKent. Diff. Cotangent. Secant. Diff. Cosine. M. 10 32 1 28 9.28060 10. 71940 9. 28865 ' 10. 71135 10. 00805 9. 99195 60 1 31 52 28 8 28125 1 71875 28933 1 71067 00808 99192 59 2 31 44 28 16 28190 2 71810 29000 2 71000 00810 99190 58 3 31 36 28 24 28254 3 71746 29067 3 70933 00813 99187 57 4 31 28 28 32 28319 4 71681 29134 4 70866 00816 99185 56 55 5 10 31 20 1 28 40 9. 28384 5 10. 71616 9. 29201 5 10. 70799 10. 00818 9. 99182 6 31 12 28 48 28448 6 71552 29268 6 70732 00820 99180 64 7 31 4 28 56 28512 7 71488 29335 8 ! 70665 00823 99177 53 8 30 56 29 4 28577 8 71423 29402 9 70598 00826 99175 52 9 30 48 29 12 28641 9 71359 29468 10 70532 00828 99172 51 10 10 30 40 1 29 20 9. 28705 10 10. 71295 9.29535 11 10. 70466 10. 00830 9. 99170 60 n 30 32 29 28 28769 11 71231 29601 12 70399 008.33 99167 49 12 30 24 29 36 28833 12 71167 29668 13 70332 00835 99165 48 13 30 16 29 44 28896 13 , 71104 29734 14 70266 00838 99162 47 14 30 8 29 52 28960 14 ! 71040 29800 15 70200 00840 99160 46 45 15 10 30 1 30 9. 29024 16 jlO. 70976 9.29866 16 10. 70134 10. 00843 9. 99157 16 29 52 30 8 29087 17 1 70913 29932 1 17 70068 00846 99156 44 17 29 44 30 16 29150 18 70850 29998 18 70002 00848 99162 43 18 29 36 30 24 29214 19 70786 30064 19 69936 00850 99150 42 19 29 28 30 32 29277 20 ! 70723 30130 20 69870 00853 99147 41 40 20 10 29 20 1 30 40 9. 29340 21 10.70660 9. 30195 22 10. 69806 10.00866 9. 99145 21 29 12 30 48 29403 22 1 70597 30261 23 69739 00868 99142 39 22 29 4 30 56 29466 23 1 70534 30326 24 69674 00860 99140 38 23 28 56 31 4 29529 24 70471 30391 25 69609 00863 99137 37 24 28 48 31 12 29591 25 ' 70409 30457 26 69543 00865 99135 36 35 25 10 28 40 1 31 20 9. 29654 26 10.70346 9. 30522 27 10.69478 10. 00868 9. 99132 26 28 32 31 28 29716 27 i 70284 .30587 28 69413 00870 99130 34 27 28 24 31 36 29779 28 1 70221 30652 29 69348 00873 99127 33 28 28 16 31 44 29841 29 j 70159 30717 30 69283 00876 99124 32 29 28 8 31 52 29903 30 70097 30782 31 69218 00878 99122 31 30 10 28 1 32 9. 29966 31 10. 70034 9.30846 32 10. 69164 10. 00881 9.99119 30 31 27 52 32 8 30028 32 69972 30911 33 69089 00883 99117 29 32 27 44 32 16 30090 33 69910 30975 35 69026 00886 99114 28 33 27 36 32 24 .30151 34 69849 31040 36 68960 00888 99112 27 34 35 27 28 32 32 30213 35 69787 31104 37 68896 00891 2 99109 26 10 27 20 1 32 40 9. 30275 36 10. 69725 9. .31168 38 10. 68882 10. 00894 9. 99106 25 36 27 12 32 48 30336 37 69664 31233 39 68767 00896 2 99104 24 37 27 4 32 56 30398 38 69602 31297 40 68703 00899 2 99101 23 38 26 56 33 4 30459 39 1 69.^^41 31361 41 68639 00901 2 99099 22 39 26 48 33 12 30521 40 1 69479 31425 42 68575 00904 2 99096 21 20 40 10 26 40 1 33 20 9. 30582 41 10.69418 9. 31489 43 10. 68511 10. 00907 2 9. 99093 41 26 32 33 28 30643 42 69357 31562 44 68448 00909 2 99091 19 42 26 24 33 36 30704 43 1 69296 31616 45 68384 00912 2 99088 18 43 26 16 33 44 30765 45 : 69236 31679 46 68321 00914 2 99086 17 44 26 8 33 52 30826 46 1 69174 31743 47 68257 00917 2 99083 16 45 10 26 1 34 9. 30887 47 10.69113 9. 31806 49 10. 68194 10. 00920 2 9. 99080 15 46 25 52 34 8 30947 48 69053 31870 50 68130 00922 2 99078 14 47 25 44 34 16 31008 49 ! 68992 31933 51 68067 00925 2 99075 13 48 25 36 34 24 31068 50 1 68932 31996 52 68004 00928 2 99072 12 49 50 25 28 34 32 31129 51 68871 32059 53 67941 00930 2 99070 11 10 25 20 1 34 40 9. 31189 52 10. 68811 9. 32122 54 10. 67878 10. 00933 2 9. 99067 10 51 25 12 34 48 31250 53 68750 32185 56 67815 00936 2 99064 9 52 25 4 34 56 31310 54 68690 32248 56 67752 00938 2 99062 8 53 24 56 35 4 31370 55 68630 32311 57 67689 00941 2 99059 7 54 24 48 35 12 31430 56 68570 32373 58 67627 00944 2 99056 6 55 10 24 40 1 35 20 9. 31490 57 10. 68510 9. 32436 59 10. 67564 10. 00946 2 9. 99054 5 56 24 32 35 28 31549 58 68451 32498 60 67502 00949 2 99051 4 57 24 24 35 36 31609 59 68391 32661 61 67439 00962 2 99048 3 58 24 16 35 44 31669 60 68331 32623 63 67377 00954 2 99046 2 59 24 8 35 52 31728 61 68272 32685 64 67315 00957 3 99043 1 60 24 36 31788 62 68212 32747 65 67253 00960 3 99040 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Difl. Sine. M. 101° A A B B C C 78° 1 Seconds of time 1" 2- 8» 4' o> 6. 7" Prop, parts of cols. {B ic 8 8 16 16 1 23 24 1 31 32 1 39 40 2 47 49 2 54 67 2 Page 784] TABLE 44. I/^. Sines, Tangents, and Secants. l«o A A B B C C 167° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. DiS. Cotangent. Secant. Diff. Cosine. M. 10 24 1 36 9. 31788 10. 68212 9. 32747 10. 67253 10. 00960 9.99040 60 1 23 52 36 8 31847 1 68153 32810 1 67190 00962 99038 59 2 23 44 36 16 31907 2 68093 32872 2 67128 00965 99035 58 3 23 36 36 24 31966 3 68034 32933 3 67067 00968 99032 57 4 23 28 36 32 32025 4 67975 32995 4 67005 00970 99030 56 55 5 10 23 20 1 36 40 9. 32084 5 10. 67916 9. 33057 5 10. 66943 10. 00973 9. 99027 6 23 12 36 48 32143 6 67857 33119 6 66881 00976 99024 54 7 23 4 36 56 32202 7 67798 33180 7 66820 00978 99022 53 8 22 56 37 4 32261 8 67739 33242 8 66758 00981 99019 52 9 22 48 37 12 32319 9 67681 33303 9 66697 00984 99016 51 10 10 22 40 1 37 20 9. 32378 10 10. 67622 9. 33365 10 10. 66635 10. 00987 9. 99013 50 11 22 32 37 28 32437 10 67563 33426 11 66574 00989 99011 49 12 22 24 37 36 32495 11 67505 33487 12 66513 00992 99008 48 13 22 16 37 44 32553 12 67447 33548 13 66452 00995 99005 47 14 22 8 37 52 32612 13 67388 33609 14 66391 10. 66330 00998 99002 46 45 15 10 22 1 38 9. 32670 14 10. 67330 9. 33670 15 10. 01000 9. 99000 16 21 52 38 8 32728 15 67272 33731 16 66269 01003 98997 44 17 21 44 38 16 32786 16 67214 33792 17 66208 01006 98994 43 18 21 36 38 24 32844 17 67156 33853 18 66147 01009 1 98991 42 19 20 21 28 38 32 32902 18 67098 33913 19 66087 01011 98989 41 10 21 20 1 38 40 9. 32960 19 10. 67040 9. 33974 20 10. 66026 10. 01014 9. 98986 40 21 21 12 38 48 33018 20 66982 34034 21 65966 01017 98983 39 22 21 4 38 56 33075 21 66925 34095 22 65905 01020 98980 38 23 20 56 39 4 33133 22 66867 34155 23 65845 01022 98978 37 24 20 48 39 12 33190 23 66810 34215 24 65785 01025 98975 36 26 10 20 40 1 39 20 9. 33248 24 10. 66752 9. 34276 25 10. 65724 10. 01028 9. 98972 35 26 20 32 39 28 33305 25 66695 34336 26 65664 01031 98969 34 27 20 24 39 36 33362 26 66638 34396 27 65604 01033 98967 33 28 20 16 39 44 33420 27 66580 :M456 28 65544 01036 98964 32 29 20 8 39 52 33477 28 66523 34516 29 65484 01039 98961 31 30 10 20 1 40 9.33534 29 10. 66466 9. 34576 30 10. 65424 10. 01042 9. 98958 30 31 19 52 40 8 33591 29 66409 34635 31 65365 01045 98955 29 32 19 44 40 16 33647 30 66353 34695 32 65305 01047 98953 28 33 19 36 40 24 33704 31 66296 34755 33 65245 01050 2 98950 27 34 19 28 40 32 33761 32 66239 34814 34 65186 01053 2 98947 26 35 10 19 20 1 40 40 9. 33818 33 10. 66182 9. 34874 35 10. 65126 10. 01056 2 9. 98944 25 36 19 12 40 48 33874 34 66126 34933 36 65067 01059 2 98941 24 37 19 4 40 56 33931 35 66069 34992 37 65008 01062 2 98938 23 38 18 56 41 4 33987 36 66013 35051 38 64949 01064 2 98936 22 39 18 48 41 12 34043 37 65957 35111 39 64889 01067 2 ! 98933 21 40 10 18 40 1 41 20 9.34100 38 10. 65900 9. .35170 40 10. 64830 10. 01070 2 19.98930 20 41 18 32 41 28 34156 39 65844 35229 41 64771 01073 2 1 98927 19 42 18 24 41 36 34212 40 65788 35288 42 64712 01076 2 1 98924 18 43 18 16 41 44 34268 41 65732 35347 43 64653 01079 2 98921 17 44 18 8 41 52 34324 42 65676 35405 44 64595 01081 2 98919 16 45 10 18 1 42 9. 34380 43 10. 65620 9.35464 45 10. 64536 10. 01084 2 9. 98916 15 46 17 52 42 8 34436 44 65564 35523 46 64477 01087 2 98913 14 47 17 44 42 16 34491 45 65509 35581 47 64419 01090 2 98910 13 48 17 36 42 24 34547 46 65453 35640 48 64360 01093 2 98907 12 49 17 28 42 32 34602 47 65398 35698 49 64302 01096 2 98904 11 50 10 17 20 1 42 40 9. 34658 48 10. 65342 9. 35757 50 10. 64243 10. 01099 2 9. 98901 10 51 17 12 42 48 34713 48 65287 35815 51 64185 01102 2 98898 9 52 17 4 42 56 34769 49 65231 35873 52 64127 01104 2 98896 8 53 16 56 43 4 34824 50 65176 35931 53 64069 01107 2 98893 7 54 16 48 43 12 34879 51 65121 35989 54 64011 OHIO 3 98890 6 5 55 10 16 40 1 43 20 9.34934 52 10. 65066 9. 36047 55 10. 63953 10. 01113 3 9. 98887 56 16 32 43 28 34989 53 65011 36105 56 63895 01116 3 98884 4 57 16 24 43 36 35044 54 64956 36163 57 63837 01119 3 98881 3 58 16 16 43 44 35099 55 64901 36221 58 63779 01122 3 98878 2 59 16 8 43 52 35154 56 64846 36279 59 63721 01125 3 98875 1 60 16 44 35209 57 64791 36336 60 63664 01128 3 98872 M. Hour p. u. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 102° A A B B C C 77° 1 Seconds of time !• 2" 8- 4« 6' 6- 7" fA Prop, parts of cols. B 7 7 14 15 1 21 22 1 29 30 1 36 37 2 43 45 2 50 62 2 TABLE 44. [Page 785 liOg. Sines, Tangents, and Secants. 18° A A B B C C 166° M. Hour A, M. Hour p. M. Sine. Dlfl. Cosecant. Tangent. Difl. Cotangent. Secant Difl. Cosine. M. 10 16 1 44 9. 36209 10. 64791 9. 36336 10, 63664 10. 01128 9. 98872 60 1 15 52 44 8 35263 1 64737 36394 1 63606 01131 98869 59 2 15 44 44 16 35318 2 64682 36452 2 63648 01133 98867 58 3 15 36 44 24 35373 3 64627 36509 3 63491 01136 98864 67 4 15 28 44 32 35427 4 64573 36566 4 63434 01139 98861 56 55 5 10 15 20 1 44 40 9. 36481 4 10. 64519 9.36624 5 10. 63376 10. 01142 9. 98858 6 15 12 44 48 36636 5 64464 36681 6 63319 01145 98856 54 7 15 4 44 56 35690 6 64410 36738 6 63262 01148 98852 53 8 14 56 45 4 35644 7 64356 36795 7 63205 01151 98849 52 9 14 48 45 12 35698 9. 36762 8 9 64302 36852 8 63148 01154 98846 9.98843 51 60 10 10 14 40 1 45 20 10. 64248 9. 36909 9 10. 63091 10. 01157 n 14 32 45 28 36806 10 64194 36966 10 63034 01160 98840 49 12 14 24 45 36 36860 11 64140 37023 11 62977 01163 98837 48 13 14 16 45 44 36914 11 64086 37080 12 62920 01166 98834 47 14 14 8 45 52 36968 12 64032 37137 13 62863 01169 98831 46 15 10 14 1 46 9. 36022 13 10. 63978 9. 37193 14 10. 62807 10.01172 9. 98828 45 16 13 52 46 8 36075 14 63925 37260 15 62750 01175 98825 44 17 13 44 46 16 36129 15 63871 37306 16 62694 01178 98822 43 18 13 36 46 24 36182 16 63818 37363 17 62637 01181 98819 42 19 13 28 46 32 36236 17 63764 37419 18 62581 01184 98816 41 40 20 10 13 20 1 46 40 9. 36289 18 10. 63711 9. 37476 19 10. 62524 10.01187 9. 98813 21 13 12 46 48 36342 18 63658 37532 19 62468 01190 98810 39 22 13 4 46 56 36395 19 63605 37688 20 62412 01193 98807 38 23 12 56 47 4 36449 20 63551 37644 21 62356 01196 98804 37 24 25 12 48 47 12 36502 21 63498 37700 22 62300 01199 98801 36 35 10 12 40 1 47 20 9. 36566 22 10. 63445 9. 37756 23 10. 62244 10. 01202 9. 98798 26 12 32 47 28 36608 23 63392 37812 24 62188 01205 98795 34 27 12 24 47 36 36660 24 63340 37868 25 62132 01208 98792 33 28 12 16 47 44 36713 25 63287 37924 26 62076 01211 98789 32 29 12 8 47 52 36766 25 63234 37980 27 62020 01214 98786 31 30 10 12 1 48 9. 36819 26 10. 63181 9. 38035 28 10. 61965 10.01217 2 9. 98783 30 31 11 52 48 8 36871 27 63129 38091 29 61909 01220 2 98780 29 32 11 44 48 16 36924 28 63076 38147 30 61853 01223 2 98777 28 33 11 36 48 24 36976 29 63024 38202 31 61798 01226 2 98774 27 34 11 28 48 32 37028 30 62972 38257 32 61743 01229 2 98771 26 25 35 10 11 20 1 48 40 9. 37081 31 10. 62919 9. 38313 32 10. 61687 10.01232 2 9. 98768 36 11 12 48 48 37133 32 62867 38368 33 61632 01235 2 98765 24 37 11 4 48 56 37185 32 62815 38423 34 61577 01238 2 98762 23 38 10 56 49 4 37237 33 62763 38479 35 61521 01241 2 98759 22 39 10 48 49 12 37289 34 62711 38534 36 61466 01244 2 98756 21 40 10 10 40 1 49 20 9. 37341 35 10. 62659 9. 38589 37 10.61411 10.01247 2 9. 98753 20 41 10 32 49 28 37393 36 62607 38644 38 61356 01250 2 98760 19 42 10 24 49 36 37445 37 62555 38699 39 61301 01254 2 98746 18 43 10 16 49 44 37497 38 62503 38754 40 61246 01267 2 98743 17 44 45 10 8 49 52 37549 39 62451 38808 41 61192 01260 2 98740 16 10 10 1 50 9.3760vy 39 10. 62400 9. 38863 42 10. 61137 10.01263 2 9. 98737 15 46 9 52 50 8 37652 40 62348 38918 43 61082 01266 2 98734 14 47 9 44 50 16 37703 41 62297 38972 44 61028 01269 2 98731 13 48 9 36 50 24 37765 42 62245 39027 45 60973 01272 2 98728 12 49 50 9 28 50 32 37806 43 62194 39082 45 60918 01275 2 98725 11 10 9 20 1 50 40 9. 37868 44 10. 62142 9. 39136 46 10. G0864 10. 01278 3 9. 98722 10 51 9 12 50 48 37909 45 62091 39190 47 60810 01281 3 98719 9 52 9 4 50 56 37960 46 62040 39245 48 60755 01285 3 98715 8 53 8 56 51 4 38011 47 61989 39299 49 60701 01288 3 98712 7 54 55 8 48 51 12 38062 47 61938 39353 50 60647 01291 3 98709 6 10 8 40 1 51 20 9.38113 48 10. 61887 9. 39407 51 10. 60593 10. 01294 \ 3 9. 98706 5 56 8 32 51 28 38164 49 61836 39461 62 60539 01297 / 3 98703 4 57 8 24 51 36 38215 50 61785 39615 63 60485 01300 3 98700 3 58 8 16 51 44 38266 61 61734 39669 54 60431 01303 3 98697 2 59 8 8 51 52 38317 52 61683 39623 55 60377 01306 3 98694 1 60 8 52 38368 53 61632 39677 56 60323 01310 3 98690 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Difl. Tangent. Cosecant. Diff. Sine. M. 103° A A B B C C 76° 1 Seconds of time 1« 2» 8> *• 5" 6* ?• fA Prop, parts of cols. B 7 7 13 14 1 20 21 1 26 28 2 33 35 2 39 42 2 46 49 3 Page 786] TABLE 44. Log. Sines, Tangents, and Secants. 14° A A B B C C 1«6° M. Hour A. H. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant Diff. Cosine. M. 10 8 1 52 9. 38368 10. 61632 9. 39677 10. 60323 10. 01310 9. 98690 60 1 7 52 52 8 38418 1 61582 39731 1 60269 01313 98687 59 2 7 44 52 16 38469 2 61531 39785 2 60215 01316 98684 58 3 7 36 52 24 38519 2 61481 39838 3 60162 01319 98681 57 4 7 28 52 32 38570 3 61430 39892 3 60108 01322 98678 56 55 5 10 7 20 1 52 40 9. 38620 4 10. 61380 9. 39945 4 10. 60055 10. 01325 9. 98675 6 7 12 52 48 38670 5 61330 39999 5 60001 01329 98671 54 7 7 4 52 56 38721 6 61279 40052 6 599-»8 01332 98668 53 8 6 56 53 4 38771 7 61229 40106 7 59894 01335 98665 52 9 6 48 53 12 38821 7 61179 40159 8 59841 01338 98662 51 50 10 10 6 40 1 53 20 9. 38871 8 10. 61129 9. 40212 9 10. 69788 10. 01341 9. 98659 11 6 32 53 28 38921 9 61079 40266 10 59734 01344 98656 49 12 6 24 53 36 38971 10 61029 40319 10 59681 01348 98652 48 13 6 16 53 44 39021 11 60979 40372 11 59628 01351 98649 47 14 6 8 53 52 39071 11 60929 40425 12 59575 01354 98646 46 45 15 10 6 1 54 9. 39121 12 10. 60879 9. 40478 13 10. 59522 10. 01357 9. 98643 16 5 62 54 8 39170 13 60830 40531 14 59469 01360 98640 44 17 5 44 54 16 39220 14 60780 40584 15 59416 01364 98636 43 18 5 36 54 24 39270 15 60730 40636 16 59364 01367 98633 42 19 5 28 54 32 39319 15 60681 40689 17 59311 01370 98630 41 40^ 20 10 5 20 1 54 40 9. 39369 16 10.60631. 9. 40742 17 10. 59258 10. 01373 9. 98627 21 5 12 54 48 39418 17 60582 40795 18 59205 01377 98623 39 22 5 4 54 56 39467 18 60533 40847 19 59153 01380 98620 38 23 4 56 55 4 39517 19 60483 40900 20 59100 01383 98617 37 24 4 48 55 12 39566 20 60434 40952 21 59048 01386 98614 36 25 10 4 40 1 55 20 9. 39615 20 10. 60385 9. 41005 22 10. 58995 10. 01390 9. 98610 35 26 4 32 55 28 39664 21 60336 41057 23 58943 01393 98607 34 27 4 24 55 36 39713 22 60287 41109 23 58891 01396 98604 33 28 4 16 55 44 39762 23 60238 41161 24 58839 01399 2 98601 32 29 30 4 8 55 52 39811 9. 39860 24 60189 41214 25 58786 01403 2 98597 31 30 10 4 1 56 24 10. 60140 9. 41266 26 10. 58734 10. 01406 2 9. 98594 31 3 52 56 8 39909 25 60091 41318 27 58682 01409 2 98591 29 32 3 44 56 16 39958 26 60042 41370 28 58630 01412 2 98588 28 33 3 36 56 24 40006 27 59994 41422 29 58578 01416 2 98584 27 34 3 28 56 32 40055 28 59945 41474 30 58526 01419 2 98581 26 36 10 3 20 1 56 40 9. 40103 29 10. 59897 9. 41526 30 10. 58474 01422 2 9. 98578 25 36 3 12 56 48 40152 29 59848 41578 31 58422 01426 2 98574 24 37 3 4 56 56 40200 30 59800 41629 32 58371 01429 2 98571 23 38 2 56 57 4 40249 31 59751 41681 33 58319 01432 2 98568 22 39 2 48 57 12 40297 32 59703 41733 34 58267 01435 2 98565 21 40 10 2 40 1 57 20 9. 40346 33 10. 59654 9. 41784 35 10. 58216 10. 01439 2 9. 98561 20 41 2 32 57 28 40394 33 59606 41S36 36 58164 01442 2 98558 19 42 2 24 57 36 40442 34 59558 41887 36 58113 01445 2 98556 18 43 2 16 57 44 40490 35 59510 41939 37 58061 01449 2 98551 17 44 2 8 57 52 40538 36 59462 41990 38 58010 01452 2 985*8 16 45 10 2 1 58 9. 40586 37 10. 59414 9. 42041 39 10. 57959 10. 01455 2 9. 98545 16 46 1 52 58 8 40634 37 59366 42093 40 57907 01459 3 98541 14 47 1 44 58 16 40682 38 59318 42144 41 57856 01462 3 98538 13 48 1 36 58 24 40730 39 59270 42195 42 57805 01465 3 98535 12 49 1 28 58 32 40778 40 59222 42246 43 57754 01469 3 98531 11 50 10 1 20 1 58 40 9. 40825 41 10. 59175 9. 42297 43 10. 57703 10. 01472 3 9. 98528 10 51 1 12 58 48 40873 42 59127 42348 44 57652 01475 3 98525 9 62 1 4 58 56 40921 42 59079 42399 45 57601 01479 3 98521 8 53 56 59 4 40968 43 59032 42450 46 57550 01482 3 98518 7 54 48 59 12 41016 44 58984 42501 47 67499 01485 3 98515 6 55 10 40 1 59 20 9.41063 45 10. 58937 9. 42552 48 10. 57448 10. 01489 3 9. 98511 6 56 32 59 28 41111 46 58889 42603 49 57397 01492 3 98508 4 57 24 59 36 41158 46 58842 42653 50 57347 01495 3 98505 3 58 16 59 44 41205 47 58795 42704 50 57296 01499 3 98501 2 59 8 59 52 41252 48 58748 42755 51 67246 01602 3 98498 1 60 2 41300 49 58700 42805 52 57196 01506 3 98494 M. Hour p. M. Hour A. M. Cosine. Difif. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 104'= A A B B C C 76° j Seconds of time 1' » S* 4* 6- 6» 7" Prop, parts of cols.'tB Ic 6 7 12 13 1 18 20 1 24 26 2 31 38 2 87 S9 2 43 46 3 TABLE 44. Log. Sines, Tangents, and Secants. [Page 787 16° A A B B C C 164° M. Hour A.M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 10 2 9. 41300 10. 58700 9. 42805 10. 57195 10. 01606 9. 98494 60 1 9 59 52 8 41347 1 58653 42856 1 57144 01609 98491 69 2 59 44 16 41394 2 58606 42906 2 67094 01512 98488 58 3 59 36 24 41441 2 58559 42957 2 57043 01616 98484 67 4 59 28 32 41488 3 58512 43007 3 56993 01619 98481 56 ft 9 59 20 2 40 9. 41535 4 10. 58465 9. 43057 4 10. 66943 10. 01623 9. 98477 55 6 59 12 48 41582 5 58418 43108 6 56892 01626 98474 54 7 59 4 56 41628 5 58372 43158 6 56842 01529 98471 58 8 58 56 1 4 41675 6 58325 43208 7 56792 01633 98467 52 9 58 48 1 12 41722 7 58278 43258 7 66742 01536 98464 61 10 9 58 40 2 1 20 9.41768 8 10. 58232 9. 43308 8 10. 66692 10. 01540 9.98460 50 11 58 32 1 28 41815 8 58185 43358 9 56642 01543 98467 49 12 58 24 1 36 41861 9 58139 43408 10 56592 01647 98453 48 13 58 16 1 44 41908 10 58092 43458 11 56542 01550 98450 47 14 1ft 58 8 1 52 41954 11 58046 43508 11 56492 01553 1 98447 46 9 58 2 2 9. 42001 11 10. 57999 9. 43558 12 10. 56442 10. 01557 1 [9.98443 45 16 57 52 2 8 42047 12 57953 43607 13 56393 01560 1 98440 44 17 57 44 2 16 42093 13 57907 43657 14 56343 01664 1 98436 43 18 57 36 2 24 42140 14 57860 43707 15 66293 01567 1 98433 42 19 20 57 28 2 32 42186 14 57814 43756 16 16 66244 01571 98429 41 40 9 57 20 2 2 40 9. 42232 15 10. 57768 9. 43806 10. 66194 10. 01574 9. 98426 21 57 12 2 48 42278 16 57722 43855 17 66145 01578 98422 39 22 57 4 2 56 42324 17 57676 43905 18 56095 01581 1 98419 38 23 56 56 3 4 42370 17 57630 43954 19 56046 01585 1 98415 37 24 56 48 3 12 42416 18 57584 44004 20 65996 01588 1 1 98412 36 2ft 9 56 40 2 3 20 9. 42461 19 10. 57539 9. 44053 20 10.55947 10. 01591 1 •*• 9.98409 35 26 56 32 3 28 42507 20 57493 44102 21 66898 01596 2 98405 34 27 56 24 3 36 42553 21 57447 44151 22 56849 01598 2 98402 33 28 56 16 3 44 42599 21 57401 44201 23 55799 01602 2 98398 32 29 30 56 8 3 52 42644 22 23 57356 44250 24 65750 01605 2 98395 31 9 56 2 4 9. 42690 10. 57310 9.44299 25 10. 55701 10. 01609 2 9. 98391 30 31 55 52 4 8 42735 24 57265 44348 25 55652 01612 2 98388 29 32 55 44 4 16 42781 24 57219 44397 26 56603 01616 2 98384 28 33 55 36 4 24 42826 25 57174 44446 27 65554 01619 2 98381 27 34 55 28 4 32 42872 26 57128 44495 28 66605 01623 2 ; 98377 26 25 3ft 9 55 20 2 4 40 9. 42917 27 10. 57083 9.44644 29 10. 66456 10. 01627 2 i 9. 98373 36 55 12 4 48 42962 27 57038 44692 29 66408 01630 2 1 98370 24 37 55 4 4 56 43008 28 56992 44641 30 55359 01634 2 98366 23 38 54 56 5 4 43053 29 56947 44690 .31 66310 01637 2 98363 22 39 40 54 48 5 12 43098 30 56902 44738 32 55262 01641 2 98369 21 20 9 54 40 2 5 20 9. 43143 30 10. 56867 9. 44787 33 10.55213 10. 01644 2 9.98366 41 54 32 5 28 43188 31 56812 44836 34 65164 01648 2 98362 19 42 54 24 5 36 43233 32 56767 44884 34 66116 01651 2 98349 18 43 54 16 5 44 43278 33 56722 44933 36 55067 01655 3 98345 17 44 4ft 54 8 5 52 43323 33 56677 44981 36 37 55019 01658 3 98342 16 9 54 2 6 9. 43367 34 10. 56633 9. 45029 10. 54971 10. 01662 3 9. 98338 15 46 53 52 6 8 43412 35 56588 45078 38 54922 01666 3 98334 14 47 53 44 6 16 43457 36 56543 45126 38 54874 01669 3 98331 13 48 53 36 6 24 43502 36 56498 46174 39 64826 01673 3 98327 12 49 ftO 53 28 6 32 43546 37 56454 46222 40 64778 01676 3 98324 11 10 9 53 20 2 6 40 9. 43591 38 10. 56409 9. 45271 41 10. 54729 10. 01680 3 9. 98320 ft! 53 12 6 48 43635 39 56365 46319 42 54681 01683 3 98317 9 ft2 53 4 6 56 43680 39 56320 45367 43 54633 01687 3 98313 8 ft3 52 56 7 4 43724 40 56276 45415 43 54585 01691 3 98309 7 54 ft5 52 48 7 12 2 7 20 43769 41 56231 46463 9.45511 44 45 54537 01694 3 3 98306 6 9 52 40 9. 43813 42 10. 56187 10. 54489 10. 01698 9. 98302 6 56 52 32 7 28 43857 43 56143 46559 46 54441 01701 3 98299 4 57 52 24 7 36 43901 43 56099 45606 •47 54394 01705 3 98295 3 58 52 16 7 44 43946 44 56054 45654 47 54346 01709 3 98291 2 59 52 8 7 52 43990 45 56010 45702 48 54298 01712 3 98288 1 60 52 8 44034 46 55966 46750 49 54250 01716 4 98284 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Di£f. Sine. M. 106 3 A A B B C C 74° 1 Seconds of time , Prop, parts of cols, i Page 788 ] ^ TABLE 44. Log. Sines, Tangents, and Secants. 16° A A B B C C 168° M. Hour A. M. Hour p. M. Sine. Diflf. Cosecant. Tangent. Diff. Cotangent. Secant. DiS. Cosine. M. 9 52 2 8 9. 44034 10. 55966 9. 45750 10. 54250 10.01716 9. 98284 60 1 51 52 8 8 44078 1 55922 45797 1 54203 01719 98281 59 2 51 44 8 16 44122 1 55878 45845 2 54155 01723 98277 58 3 51 36 8 24 44166 2 55834 45892 2 54108 01727 98273 57 4 51 28 8 32 44210 3 55790 45940 3 54060 01730 98270 9. 98266 56 55 5 9 51 20 2 8 40 9. 44253 4 10. 55747 9. 45987 4 10. 54013 10. 01734 6 51 12 8 48 44297 4 55703 46035 5 53965 01738 98262 54 7 51 4 8 56 44341 5 55659 46082 5 53918 01741 98259 53 8 50 56 9 4 44385 6 55615 46130 6 53870 01745 98255 52 9 10 50 48 9 12 44428 6 55572 46177 7 8 53823 01749 -Y 98251 51 50 9 50 40 2 9 20 9. 44472 7 10. 55528 9. 46224 10. 53776 10. 01752 9. 98248 11 50 32 9 28 44516 8 55484 46271 9 53729 01756 98244 49 12 50 24 9 36 44559 9 55441 46319 9 53681 01760 98240 48 13 50 16 9 44 44602 9 55398 46366 10 53634 01763 98237 47 14 50 8 9 52 44646 10 55354 46413 11 53587 01767 98233 46 15 9 50 2 10 9.44689 11 10. 55311 9. 46460 12 10. 53540 10. 01771 9. 98229 45 16 49 52 10 8 44733 11 55267 46507 12 53493 01774 98226 44 17 49 44 10 16 44776 12 55224 46554 13 53446 01778 98222 43 18 49 36 10 24 44819 13 55181 46601 14 53399 01782 98218 42 19 20 49 28 10 32 44862 14 55138 46648 9. 46694 15 15 53352 01785 1 98215 41 40 9 49 20 2 10 40 9. 44905 14 10. 55095 10. 53306 10. 01789 9. 98211 21 49 12 10 48 44948 15 55052 46741 16 53259 01793 98207 39 22 49 4 10 56 44992 16 55008 46788 17 53212 01796 98204 38 23 48 56 11 4 45035 16 54965 46835 18 53165 01800 98200 37 24 48 48 11 12 45077 17 18 54923 10.54880 46881 19 53119 01804 98196 9. 98192 36 35 25 9 48 40 2 11 20 9. 45120 9. 46928 19 10. 53072 10. 01808 2 26 48 32 11 28 45163 18 54837 46975 20 53025 01811 2 98189 34 27 48 24 11 36 45206 19 54794 47021 21 52979 01815 2 98185 33 28 48 16 11 44 45249 20 54751 47068 22 52932 01819 2 98181 32 29 48 8 11 52 45292 21 21 54708 47114 22 52886 01823 2 98177 31 30 30 9 48 2 12 9. 45334 10. 54666 9. 47160 23 10. 52840 10. 01826 2 9. 98174 31 47 52 12 8 45377 22 54623 47207 24 52793 01830 2 98170 29 32 47 44 12 16 45419 23 54581 47253 25 52747 01834 2 98166 28 33 47 36 12 24 45462 23 54538 47299 26 52701 01838 2 98162 27 34 47 28 12 32 45504 24 54496 47346 26 52654 01841 2 98159 9. 98155 26 25 35 9 47 20 2 12 40 9.45547 25 10. 54453 9. 47392 27 10. 52608 10. 01845 2 36 47 12 12 48 45589 26 54411 47438 28 52562 01849 2 98151 24 37 47 4 12 56 45632 26 54368 47484 29 52516 01853 2 98147 23 38 46 56 13 4 45674 27 54326 47530 29 52470 01856 2 98144 22 39 46 48 13 12 45716 28 54284 47576 30 52424 01860 2 98140 21 40 9 46 40 2 13 20 9. 45758 28 10. 54242 9. 47622 31 10. 52378 10. 01864 2 9. 98136 20 41 46 32 13 28 45801 29 54199 47668 32 52332 01868 3 98132 19 42 46 24 13 36 45843 30 54157 47714 32 52286 01871 3 98129 18 43 46 16 13 44 45885 31 54115 47760 33 52240 01875 3 98125 17 44 46 8 13 52 45927 31 54073 47806 34 52194 01879 3 98121 16 15 45 9 46 2 14 9. 45969 32 10. 54031 9. 47852 35 10. 52148 10. 01883 3 9. 98117 46 45 52 14 8 46011 33 53989 47897 36 52103 01887 3 98113 14 47 45 44 14 16 46053 33 53947 47943 36 52057 01890 3 98110 13 48 45 36 14 24 46095 34 53905 47989 37 52011 01894 3 98106 12 49 60 45 28 14 32 46136 35 53864 48035 38 51965 01898 3 98102 11 10 9 45 20 2 14 40 9. 46178 36 10. 53822 9.48080 39 10. 51920 10. 01902 3 9.98098 51 45 12 14 48 46220 36 53780 48126 39 51874 01906 3 98094 9 52 45 4 14 56 46262 37 53738 48171 40 51829 01910 3 98090 8 53 44 56 15 4 46303 38 53697 48217 41 51783 01913 3 98087 7 54 55 44 48 15 12 46345 38 53655 48262 42 51738 01917 3 98083 6 5 9 44 40 2 15 20 9. 46386 39 10. 53614 9. 48307 43 10. 51693 10. 01921 3 9. 98079 56 44 32 15 28 46428 40 53572 48353 43 51647 01925 3 98075 4 57 44 24 15 36 46469 41 ,53531 48398 44 51602 01929 4 98071 3 58 44 16 15 44 46511 41 53489 48443 45 51557 01933 4 98067 2 59 44 8 15 52 46552 42 53448 48489 46 51511 01937 4 98063 1 60 44 16 46594 43 53406 48534 46 51466 01940 4 98060 M. M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent Diff. Tangent. Cosecant. Diff. Sine. 106° A ' A B B C C 78° 1 Seconds of time 1« 2' 3« 4* 6* 6« 7« Prop, parts of cols, -i B 5 6 11 12 1 16 17 I 21 23 2 27 29 2 32 S5 3 37 41 3 . TABLE 44. [Page 789 Log. Sines, Tangents, and Secants. JJO A A B B C C 168° M. Hour A. M. Hour P. u. Sine. DIff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 9 44 2 16 9. 46594 10. 53406 9.48534 10. 51466 10. 01940 9. 98060 60 1 43 62 16 8 46635 1 53365 48679 1 51421 01944 98066 69 2 43 44 \ 16 16 i6676 1 53324 48624 1 51376 01948 98062 58 3 43 36 16 24 46717 2 53283 48669 2 51331 01962 98048 57 4 43 28 16 32 46758 3 53242 48714 3 51286 01966 ■ 98044 56 55 5 9 43 20 2 16 40 9. 46800 3 10. 53200 9. 48759 4 10. 51241 10. 01960 9. 98040 6 43 12 16 48 46841 4 53159 48804 4 51196 01964 98036 54 7 43 4 16 56 46882 5 53118 48849 5 51161 01968 98032 63 8 42 56 17 4 46923 5 53077 48894 6 61106 01971 98029 62 9 10 42 48 17 12 46904 6 7' 53036 48939 7 51061 01975 98025 51 50 9 42 40 2 17 20 9. 47005 10. 52995 9. 48984 7 10. 51016 10. 01979 9. 98021 11 42 32 17 28 47045 7 52955 49029 8 60971 01983 98017 49 12 42 24 17 36 47086 8 52914 49073 9 60927 01987 98013 48 13 42 16 17 44 47127 9 52873 49118 10 50882 01991 98009 47 14 42 8 17 52 47168 9 10 52832 49163 10 11 50837 01995 98005 9.98001 46 45 15 9 42 2 18 9. 47209 10. 52791 9. 49207 10. 50793 10. 01999 16 41 52 18 8 47249 11 52751 49262 12 60748 02003 97997 44 17 41 44 18 16 47290 11 52710 49296 12 60704 02007 97993 43 18 41 36 18 24 47330 12 52670 49341 13 50659 02011 97989 42 19 41 28 18 32 47371 13 52629 49386 14 50616 02014 97986 41 40 20 9 41 20 2 18 40 9. 47411 13 10. 52589 9. 49430 16 10. 60570 10. 02018 9. 97982 21 41 12 18 48 47452 14 52548 49474 16 50526 02022 97978 39 22 41 4 18 56 47492 15 52608 49619 16 60481 02026 97974 38 23 40 56 19 4 47533 15 52467 49563 17 50437 02030 2 97970 37 24 40 48 19 12 47573 16 52427 49607 18 50393 02034 2 97966 36 35 25 9 40 40 2 19 20 9. 47613 17 10. 52387 9.49652 18 10. 50348 10. 02038 2 9. 97962 26 40 32 19 28 47654 17 52346 49696 19 50304 02042 2 97968 34 27 40 24 19 36 47694 18 52306 49740 20 50260 02046 2 97964 33 28 40 16 19 44 47734 19 52266 49784 21 50216 02060 2 97950 32 29 40 8 19 52 47774 19 52226 49828 21 50172 02054 2 97946 31 30 30 9 40 2 20 9. 47814 20 10. 52186 9. 49872 22 10. 50128 10. 02068 2 9. 97942 31 39 52 20 8 47854 21 52146 49916 23 50084 02062 2 97938 29 32 39 44 20 16 47894 21 52106 49960 24 60040 02066 2 97934 28 33 39 36 20 24 47934 22 52066 50004 24 49996 02070 2 97930 27 34 39 28 20 32 47974 23 52026 50048 25 49952 02074 2 97926 26 26 35 9 39 20 2 20 40 9. 48014 23 10. 51986 9.50092 26 10. 49908 10. 02078 2 9. 97922 36 39 12 20 48 48054 24 51946 50136 26 49864 02082 2 97918 24 37 39 4 20 56 48094 25 61906 60180 27 49820 02086 2 97914 23 38 38 56 21 4 48133 25 51867 60223 28 49777 02090 3 97910 22 39 38 48 21 12 48173 26 51827 50267 29 49733 02094 3 97906 21 40 9 38 40 2 21 20 9.48213 27 10. 51787 9. 50311 29 10.49689 10. 02098 3 9. 97902 20 41 38 32 21 28 48252 27 51748 50366 30 49645 02102 3 97898 19 42 , 38 24 21 36 48292 28 51708 60398 31 49602 02106 3 97894 18 43 38 16 21 44 48332 29 51668 50442 32 49568 02110 3 97890 17 44 38 8 21 52 48371 29 30 51629 10. 51589 60486 9. 50529 32 33 49515 02114 3 97886 16 15 45 9 38 2 22 9. 48411 10. 49471 10.02118 3 9. 97882 46 37 52 22 8 48450 31 51550 50572 34 49428 02122 3 97878 14 47 37 44 22 16 48490 31 61510 50616 35 49384 02126 3 97874 13 48 37 36 22 24 48529 32 51471 60659 35 49341. 02130 3 97870 12 49 37 28 22 32 48568 33 33 51432 10. 51393 60703 36 49297 02134 3 97866 11 10 60 9 37 20 2 22 40 9.48607 9. 50746 37 10. 49264 10. 02139 3 9. 97861 51 37 12 22 48 48647 34 51363 50789 37 49211 02143 3 97867 9 52 37 4 22 56 48686 35 51314 50833 38 49167 02147 3 97863 8 53 36 56 23 4 48725 35 51276 60876 39 49124 02151 4 97849 7 54 36 48 23 12 48764 36 51236 60919 40 49081 02166 4 4 97846 6 5 55 9 36 40 2 23 20 9. 48803 37 10. 51197 9. 60962 40 10. 49038 10. 02159 9. 97841 56 36 32 23 28 48842 37 51158 51005 41 48995 02163 4 97837 4 67 36 24 23 36 48881 38 51119 51048 42 48952 02167 4 97833 3 58 36 16 23 44 48920 39 51080 51092 43 48908 02171 4 97829 2 59 36 8 23 52 48959 39 51041 61135 43 48865 02176 4 97826 1 60 36 24 48998 40 51002 51178 44 48822 02179 4 97821 M. Hour p. M. Hour A.M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 103° A A B B C C 78»I Seconds of time 1" 2" 3" 4* 6. 6» 7- Prop, parts of cols. ^B ic 6 6 10 11 1 15 17 1 20 22 2 25 9.8 2 30 33 ,3 35 39 3 Page 790] TABLE 44. Log. Sines, Tangents, and Secanta. 18° A A B B C C 1610 M. Hour A. M. Hour p. M. Sine. DiGE. Cosecant. Tangent. Difl. Cotangent. Secant. DiS. Cosine. M. 9 36 2 24 9. 48998 10. 51002 9.51178 10. 48822 10. 02179 9. 97821 60 I 35 52 24 8 49037 1 50963 51221 1 48779 02183 97817 59 2 35 44 24 16 49076 1 50924 51264 1 48736 02188 97812 58 3 35 36 24 24 49115 2 50885 51306 2 48694 02192 97808 57 4 35 28 24 32 49153 3 50847 51349 3 48651 02196 97804 56 55 5 9 35 20 2 24 40 9. 49192 3 10. 50808 9. 51392 3 10. 48608 10. 02200 9. 97800 6 35 12 24 48 49231 4 50769 51435 4 48565 02204 97796 54 7 35 4 24 56 49269 4 50731 51478 5 48522 02208 97792 53 8 34 56 25 4 49308 5 50692 51520 6 48480 02212 97788 52 9 10 34 48 25 12 49347 6 50653 51563 6 7 48437 02216 97784 51 50 9 34 40 2 25 20 9. 49385 6 10. 50615 9. 51606 10. 48394 10. 02221 9. 97779 11 34 32 25 28 49424 7 50576 51648 8 48352 02225 97775 49 12 34 24 25 36 49462 8 50538 51691 8 48309 02229 97771 48 13 34 16 25 44 49500 8 50500 51734 9 48266 02233 97767 47 14 34 8 25 52 49539 9 50461 51776 10 48224 02237 97763 46 15 9 34 2 26 9. 49577 9 10. 50423 9. 51819 10 10. 48181 10. 02241 9. 97759 45 16 33 52 26 8 49615 10 50385 51861 11 48139 02246 97754 44 17 33 44 26 16 49654 11 50346 51903 12 48097 02250 97750 43 18 33 36 26 24 49692 11 50308 51946 13 48054 02254 97746 42 19 20 33 28 26 32 49730 12 50270 51988 13 48012 02258 97742 41 40 9 33 20 2 26 40 9. 49768 13 10. 50232 9. 52031 14 10. 47969 10. 02262 9. 97738 21 33 12 26 48 49806 13 50194 52073 15 47927 02266 97734 39 22 33 4 26 56 49844 14 50156 52115 15 47885 02271 2 97729 38 23 32 56 27 4 49882 14 50118 52157 16 47843 02275 2 97725 37 24 32 48 27 12 49920 15 50080 52200 17 17 47800 02279 2 97721 36 35 25 9 32 40 2 27 20 9. 49958 16 10. 50042 9. 52242 10. 47758 10. 02283 2 9. 97717 26 32 32 27 28 49996 16 50004 52284 18 47716 02287 2 97713 34 27 32 24 27 36 50034 17 49966 52326 19 47674 02292 2 97708 33 28 32 16 27 44 50072 18 49928 52368 20 47632 02296 2 97704 32 29 32 8 27 52 50110 18 49890 52410 20 47590 02300 2 97700 31 30 9 32 2 28 9. 50148 19 10. 49852 9. 52452 21 10. 47548 10. 02304 2 9. 97696 30 31 31 52 28 8 50185 20 49815 52494 22 47506 02309 2 97691 29 32 31 44 28 16 50223 20 49777 52536 22 47464 02313 2 97687 28 33 31 36 28 24 50261 21 49739 52578 23 47422 02317 2 97683 27 34 31 28 28 32 50298 21 49702 52620 24 47380 02321 2 97679 26 25 35 9 31 20 2 28 40 9. 50336 22 10. 49664 9. 52661 24 10. 47339 10. 02326 2 9. 97674 36 31 12 28 48 50374 23 49626 52703 25 47297 02330 3 97670 24 37 31 4 28 56 50411 23 49589 52745 26 47255 02334 3 97666 23 38 30 56 29 4 50449 24 49551 52787 27 47213 02338 3 97662 22 39 30 48 29 12 50486 25 49514 52829 27 47171 02343 3 97657 21 20 40 9 30 40 2 29 20 9. 50523 25 10. 49477 9. 52870 28 10. 47130 10. 02347 3 9. 97653 41 30 32 29 28 50561 26 49439 52912 29 47088 02351 3 97649 19 42 30 24 29 36 50598 26 49402 52953 29 47047 02355 3 976^ 18 43 30 16 29 44 50635 27 49365 52995 30 47005 02360 3 97640 17 44 45 30 8 29 52 50673 28 49327 53037 31 46963 02364 3 97636 9. 97632 16 15 9 30 2 30 9. 50710 28 10.49290 9. 53078 31 10. 46922 10. 02368 3 46 29 52 30 8 50747 29 49253 53120 32 46880 02372 3 97628 14 47 29 44 30 16 50784 30 49216 53161 33 46839 02377 3 97623 13 48 29 36 30 24 50821 30 49179 53202 34 46798 02381 3 97619 12 49 50 29 28 30 32 50858 31 49142 53244 34 46756 02385 3 97615 11 10 9 29 20 2 30 40 9. 50896 31 10. 49104 9. 53285 35 10.46715 10. 02390 4 9. 97610 51 29 12 30 48 50933 32 49067 53327 36 46673 02394 4 97606 9 52 29 4 30 56 50970 33 49030 53368 36 46632 02398 4 97602 8 53 28 56 31 4 ri007 33 48993 53409 37 46591 02403 4 97597 7 54 28 48 31 12 51043 34 48957 53450 38 46550 02407 4 97593 6 55 9 28 40 2 31 20 9. 51080 35 10. 48920 9. 53492 38 10. 46508 10.02411 4 9. 97589 5 56 28 32 31 28 51117 35 48883 53533 39 46467 02416 4 97584 4 57 28 24 31 36 51154 36 48846 53574 40 46426 02420 4 97580 3 58 28 16 31 44 51191 37 48809 53615 41 46385 02424 4 97576 2 59 28 8 31 52 51227 37 48773 53656 41 46344 02429 4 97571 1 60 28 32 51264 38 48736 53697 42 46303 02433 4 97567 M. M. Hour p. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Diff. Tangent. Cosecant. Difl. Sine. 108' A A B B C C 71«>l Seconds of time !• 2* 8- 4« 6> 6- 7' IK Prop, parts of cols. • B 5 5 1 9 10 1 14 16 2 19 21 2 24 26 3 28 31 3 33 37 4 TABLE 44. [Page 791 Log. Sines, Tangents, and Secants. 19° A A B B C c 160O M. Hour A. M. Hour p. M. Sine. Diflf. Cosecant. Tangent. Diff. Cotanger.t. Secant. Dlfl. Cosine. M. 9 28 2 32 9. 51264 10. 48736 9. 53697 10. 46303 10. 02433 9.97567 60 1 27 52 32 8 51301 1 48699 53738 1 46262 02437 97563 59 2 27 44 32 16 51338 1 48662 53779 1 46221 02442 97558 58 3 27 36 32 24 51374 2 48626 53820 2 46180 02446 97554 57 4 27 28 32 32 51411 2 48589 53861 3 46139 02450 97550 56 5 9 27 20 2 32 40 9. 51447 3 10. 48553 9. 53902 3 10. 46098 10. 02455 9. 97545 55 6 27 12 32 48 51484 4 48516 53943 4 46057 02459 97541 54 7 27 4 32 56 51520 4 48480 53984 5 46016 02464 97536 53 8 26 56 33 4 51557 5 48443 54025 5 ] 45975 02468 97532 52 9 10 26 48 33 12 2 33 20 51593 5 48407 54065 6 45935 02472 97528 51 50 9 26 40 9. 51629 6 10. 48371 9. 54106 7 10. 45894 10. 02477 9. 97523 11 26 32 33 28 51666 7 48334 54147 7 45853 02481 1 97519 49 12 26 24 33 36 51702 7 48298 54187 8 45813 02485 1 97515 48 18 26 16 33 44 51738 8 48262 54228 9 45772 02490 97510 47 14 26 8 33 52 51774 8 48226 54269 9 45731 02494 97506 46 45 15 9 26 2 34 9. 51811 9 10. 48189 9. 54309 10 10. 45691 10. 02499 9. 97501 16 25 52 34 8 51847 10 48153 54350 11 45650 02503 97497 44 17 25 44 34 16 51883 10 48117 54390 11 45610 02508 97492 43 18 25 36 34 24 51919 11 48081 54431 12 45569 02512 97488 42 19 25 28 34 32 51955 11 48045 54471 13 45529 02516 97484 9. 97479 41 40 20 9 25 20 2 34 40 9. 51991 12 10. 48009 9. 54512 13 10. 45488 10. 02521 21 25 12 34 48 52027 12 47973 54552 14 45448 02525 2 97475 39 22 25 4 34 56 52063 13 47937 54593 15 45407 02530 2 97470 38 23 24 56 35 4 52099 14 47901 54633 15 45367 02534 2 97466 37 24 25 24 48 9 24 40 35 12 52135 14 47865 54673 16 45327 02539 2 97461 36 35 2 35 20 9. 52171 15 10. 47829 9. 54714 17 10. 45286 10. 02543 2 9. 97457 26 24 32 35 28 52207 15 47793 54754 17 45246 02547 2 97453 34 27 24 24 36 36 52242 16 47758 54794 18 45206 02.552 2 97448 33 28 24 16 35 44 52278 17 47722 54835 19 45165 02556 2 97444 32 29 24 8 35 52 52314 17 47686 54875 19 45125 02561 2 97439 9. 97435 31 30 30 9 24 2 36 9. 52350 18 10. 47650 9. 54915 20 10. 45085 10. 02565 2 31 23 52 36 8 52385 18 47615 54955 21 45045 02570 2 97430 29 32 23 44 36 16 52421 19 47579 54995 21 45005 02574 2 97426 28 33 23 36 36 24 52456 20 47544 55035 22 44965 02579 2 97421 27 34 23 28 36 32 52492 20 47508 55075 23 44925 02583 3 3 97417 26 35 9 23 20 2 36 40 9. 52527 21 10. 47473 9.55115 23 10. 44885 10. 02588 9. 97412 25 36 23 12 36 48 52563 21 47437 55155 24 44845 02592 3 97408 24 37 23 4 36 56 52598 22 47402 55195 25 44805 02597 3 97403 23 38 22 56 37 4 52634 23 47366 55235 25 44765 02601 3 97399 22 39 22 48 37 12 52669 23 47331 55275 26 44725 02606 3 3 97394 21 40 9 22 40 2 37 20 9. 52705 24 10. 47295 9.55315 i 27 10. 44685 10.02610 9. 97390 20 41 22 32 37 28 52740 24 47260 55355 27 44645 02615 3 97385 19 42 • 22 24 37 36 52775 25 47225 55395 28 44605 02619 3 97381 18 43 22 16 37 44 52811 26 47189 55434 29 44566 02624 3 97376 17 44 45 22 8 9 22 37 52 2 38 52846 26 47154 55474 29 44526 02628 3 97372 16 15 9. 52881 27 10. 47119 9. 55514 30 10. 44486 10. 026^3 3 9. 97367 46 21 52 38 8 52916 27 47084 55554 31 44446 02637 3 97363 14 47 21 44 38 16 52951 28 47049 55593 31 44407 02642 3 97358 13 48 21 36 38 24 52986 29 47014 55633 32 44367 02647 4 97353 12 49 50 21 28 9 21 20 38 32 2 38 40 53021 9. 53056 29 46979 55673 33 44327 02651 4 97349 11 30 10. 46944 9. 55712 33 10. 44288 10. 02656 4 9. 97344 10 51 21 12 38 48 53092 30 46908 55752 34 44248 02660 4 97340 9 52 21 4 38 56 53126 31 46874 55791 35 44209 02665 4 97335 8 53 20 56 39 4 53161 32 46839 55831 35 44169 02669 4 97331 7 54 55 20 48 39 12 2 39 20 53196 32 46804 55870 36 44130 02674 4 97326 6 5 9 20 40 9. 53231 33 10. 46769 9. 55910 37 10. 44090 10. 02678 4 9.97322 56 20 32 39 28 53266 33 46734 55949 37 44051 02683 4 97317 4 57 20 24 39 36 53301 34 46699 55989 38 44011 02688 4 97312 3 58 20 16 39 44 53336 34 46664 56028 39 4.3972 02692 4 97308 2 59 20 8 39 52 53370 35 46630 56067 39 43933 02697 4 97303 1 60 20 40 53405 36 46595 56107 40 43893 02701 4 97299 M. Hour p. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 109'= A A B B c C 70° 1 Seconds of time 1' 2' 3» 4> o' 6' 7. Prop, parts of cols. 8" 4" 6> e- 7' (A Prop, parts of cols.^B Ic 4 4 1 8 9 1 11 13 2 16 18 3 19 22 3 23 27 4 27 31 5 TABLE 44. Log. Sines, Tangents, and Secants. [Page 795 «3° A A B B C C 166° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 8 56 3 4 9. 59188 10. 40812 9. 62785 10. 37215 10. 03597 9.96403 60 1 55 52 4 8 59218 40782 62820 1 37180 03603 96397 59 ? 55 44 4 16 59247 1 40753 62855 1 37145 03608 96392 58 3 55 36 4 24 59277 1 40Z23 62890 2 37110 03613 96387 57 4 55 28 4 32 59307 2 40693 62926 2 37074 03619 96381 9.96376 56 55 5 8 55 20 3 4 40 9. 59336 2 10. 40664 9. 62961 3 10. 37039 10. 03624 fi 55 12 4 48 59366 3 40634 62996 3 37004 03630 96370 54 7 55 4 4 56 59396 3 40604 63031 4 36969 03635 96365 53 8 54 56 5 4 59425 4 40575 63066 5 36934 03640 96360 52 9 54 48 5 12 59455 4 40545 63101 5 36899 03646 96354 51 50 10 8 54 40 3 5 20 9. 59484 5 10. 40516 9. 63135 6 10. 36865 10. 03651 9.96349 11 54 32 5 28 59514 5 40486 63170 6 36830 03667 96343 49 12 54 24 5 36 59543 6 40457 63205 7 36795 03662 96338 48 13 54 16 5 44 59573 6 40427 63240 7 36760 03667 96333 47 14 15 54 8 5 52 59602 7 40398 63275 8 36725 03673 96327 46 8 54 3 6 9. 59632 7 10. 40368 9. 63310 9 10. 36690 10. 03678 9. 96322 45 16 53 52 6 8 59661 8 40339 63345 9 36655 03684 96316 44 17 53 44 6 16 59690 8 40310 63379 10 36621 03689 2 96311 43 18 53 36 6 24 59720 9 40280 63414 10 36586 03695 2 96305 42 19 53 28 6 32 59749 9 40251 63449 11 36551 03700 2 96300 41 20 8 53 20 3 6 40 9. 59778 10 10. 40222 9.63484 12 10. 36516 10. 03706 2 9. 96294 40 21 53 12 6 48 59808 10 40192 63519 12 36481 03711 2 96289 39 22 53 4 6 56 59837 11 40163 63553 13 36447 03716 2 96284 38 2r, 52 56 7 4 59866 11 40134 63588 13 36412 03722 2 96278 37 24 25 52 48 8 52 40 7 12 59895 12 40105 63623 14 36377 03727 2 96273 36 36 3 7 20 9. 59924 12 10. 40076 9. 63657 14 10. 36343 10. 03733 2 9. 96267 26 52 32 7 28 59954 13 40046 63692 15 36308 03738 2 96262 34 27 52 24 7 36 59983 13 40017 63726 16 36274 03744 2 96256 33 28 52 16 7 44 60012 14 39988 63761 16 36239 03749 3 96251 32 29 52 8 7 52 60041 14 39959 63796 17 36204 03755 3 96245 31 30 30 8 52 3 8 9. 60070 15 10. 39930 9. 63830 17 10. 36170 10. 03760 3 9. 96240 31 51 52 8 8 60099 15 39901 63865 18 36135 03766 3 96234 29 32 51 44 8 16 60128 15 39872 63899 18 36101 03771 3 96229 28 33 51 36 8 24 60157 16 39843 63934 19 36066 03777 3 96223 27 34 51 28 8 32 60186 16 39814 63968 20 36032 03782 3 96218 26 35 8 51 20 3 8 40 9. 60215 17 10. 39785 9.64003 20 10. 35997 10. 03788 3 9. 96212 25 36 51 12 8 48 60244 17 39756 64037 21 35963 03793 3 96207 24 37 51 4 8 56 60273 18 39727 64072 21 35928 03799 3 96201 23 38 50 56 9 4 60302 18 39698 64106 22 35894 03804 3 96196 22 39 50 48 9 12 60331 19 39669 64140 22 35860 03810 4 96190 21 40 8 50 40 3 9 20 9. 60359 19 10. 39641 9. 64175 23 10. 35825 10. 03815 4 9. 96185 20 41 50 32 9 28 60388 20 39612 64209 24 35791 03821 4 96179 19 42 50 24 9 36 G0417 20 39583 64243 24 35757 03826 4 96174 18 43 50 16 9 44 60446 21 39554 64278 25 35722 03832 4 96168 17 44 50 8 9 52 60474 21 39526 64312 25 35688 03838 4 96162 16 45 8 50 3 10 9. 60503 22 10. 39497 9.64346 26 10. 35654 10. 03843 4 9. 96157 15 46 49 52 10 8 60532 22 39468 64381 26 35619 03849 4 96151 14 47 49 44 10 16 60561 23 39439 64415 27 35585 03854 4 96146 13 48 49 36 10 24 60589 23 39411 64449 28 35551 03860 4 96140 12 49 49 28 10 32 60618 24 39382 64483 28 35517 03865 4 96135 11 10 50 8 49 20 3 10 40 9. 60646 24 10. 39354 9. 64517 29 10. 35483 10. 03871 5 9. 96129 51 49 12 10 48 60675 25 39325 64552 29 35448 03877 5 96123 9 52 49 4 10 56 60704 25 39296 64586 30 35414 03882 5 96118 8 53 48 56 11 4 60732 26 39268 64620 31 35380 03888 5 96112 7 54 48 48 11 12 60761 26 27 39239 64654 31 35346 03893 5 96107 6 55 8 48 40 3 11 20 9. 60789 10. 39211 9. 64688 32 10. 35312 10. 03899 5 9. 96101 5 56 48 32 11 28 60818 27 39182 64722 32 35278 03905 5 96095 4 57 48 24 11 36 60846 28 39154 64756 33 35244 03910 5 96090 3 58 48 16 11 44 60875 28 39125 64790 33 35210 03916 5 96084 2 59 48 8 11 52 60903 29 39097 64824 34 35176 03921 5 96079 1 60 48 12 60931 29 39069 64858 35 35142 03927 6 96073 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. ICosecant. DIfl. Sine. M. 118° A A B B C C 66° Seconds of time 1> 2» 8- 4* 6" 6» 7» Prop, parts of cols. -< B 4 4 1 7 9 1 11 13 2 15 17 3 18 22 3 22 26 4 25 31 5 21594°— 14 43 Page 796] TABLE 44. Log. Sines, Tangents, and Secants. 24° A • A B B C C 155° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 60 8 48 3 12 9. 60931 10. 39069 9. 64858 10. 35142 10. 03927 9. 96073 1 47 52 12 8 60960 39040 64892 1 35108 03933 96067 59 2 47 44 12 16 60988 1 39012 64926 1 35074 03938 96062 58 3 47 36 12 24 61016 1 38984 64960 2 35040 03944 96056 57 4 47 28 12 32 61045 2 38955 64994 2 35006 03950 96050 9. 96045 56 55 5 8 47 20 3 12 40 9. 61073 2 10. 38927 9. 65028 3 10. 34972 10. 03955 6 47 12 12 48 61101 3 38899 65062 3 34938 03961 96039 54 7 47 4 12 56 61129 3 38871 65096 4 34904 03966 96034 53 8 46 56 13 4 61158 4 38842 65130 4 34870 03972 96028 52 9 46 48 13 12 61186 4 38814 65164 5 34836 03978 96022 51 10 8 46 40 3 13 20 9. 61214 5 10. 38786 9. 65197 6 10. 34803 10. 03983 9. 96017 50 11 46 32 13 28 61242 5 38758 65231 6 34769 03989 96011 49 12 46 24 13 36 61270 6 38730 65265 7 34735 03995 96005 48 13 46 16 13 44 61298 6 38702 65299 7 34701 04000 96000 47 14 46 8 13 52 61326 6 38674 65333 8 34667 04006 95994 46 45 15 8 46 3 14 9. 61354 7 10. 38646 9. 65366 8 10. 34634 10. 04012 9. 95988 16 45 52 14 8 61382 7 38618 65400 9 34600 04018 2 95982 44 17 45 44 14 16 61411 8 38589 65434 9 34566 04023 2 95977 43 18 45 36 14 24 61438 8 38562 65467 10 34533 04029 2 95971 42 19 45 28 14 32 61466 9 38534 65501 11 34499 04035 2 95965 41 20 8 45 20 3 14 40 9. 61494 9 10. 38506 9. 65535 11 10. 34465 10. 04040 2 9. 95960 40 21 45 12 14 48 61522 10 38478 65568 12 34432 04046 2 95954 39 22 45 4 14 56 61550 10 38450 65602 12 34398 04052 2 95948 38 23 44 56 15 4 61578 11 38422 65636 13 34364 04058 2 95942 37 24 44 48 15 12 61606 11 38394 65669 13 34331 04063 2 95937 36 26 8 44 40 3 15 20 9. 61634 12 10. 38366 9. 65703 14 10. 34297 10. 04069 2 9. 95931 35 26 44 32 15 28 61662 12 38338 65736 15 34264 04075 2 95925 34 27 44 24 15 36 61689 12 38311 65770 15 34230 04080 3 95920 33 28 44 16 15 44 61717 13 38283 65803 16 34197 04086 3 95914 32 29 44 8 15 52 61745 13 38255 65837 16 34163 04092 3 95908 31 30 8 44 3 16 9.61773 14 10. 38227 9. 65870 17 10. 34130 10. 04098 3 9. 95902 30 31 43 52 16 8 61800 14 38200 65904 17 34096 04103 3 95897 29 32 43 44 16 16 61828 15 38172 65937 18 34063 04109 3 95891 28 33 43 36 16 24 61856 15 38144 65971 18 34029 04115 3 95885 27 34 43 28 16 32 61883 16 38117 66004 19 33996 04121 3 95879 26 35 8 43 20 3 16 40 9.61911 16 10. 38089 9. 66038 20 10. 33962 10. 04127 3 9. 95873 25 36 43 12 16 48 61939 17 38061 66071 20 33929 04132 3 95868 24 37 43 4 16 56 61966 17 38034 66104 21 33896 04138 4 95862 23 38 42 56 17 4 61994 18 38006 66138 21 33862 04144 4 95856 22 39 42 48 17 12 62021 18 37979 66171 22 33829 04150 4 95850 21 40 8 42 40 3 17 20 9. 62049 18 10. 37951 9. 66204 22 10. 33796 10. 04156 4 9. 95844 20 41 42 32 17 28 62076 19 37924 66238 23 33762 04161 4 95839 19 42 42 24 17 36 62104 19 37896 66271 23 33729 04167 4 95833 18 43 42 16 17 44 62131 20 37869 66304 24 33696 04173 4 95827 17 44 42 8 17 52 62159 20 37841 66337 25 33663 04179 4 95821 16 15 45 8 42 3 18 9. 62186 21 10. 37814 9. 66371 25 10. 33629 10. 04185 4 9. 95815 46 41 52 18 8 62214 21 37786 66404 26 33596 04190 4 95810 14 47 41 44 18 16 62241 22 37759 66437 26 33563 04196 5 95804 13 48 41 36 18 24 62268 22 37732 66470 27 33530 04202 5 95798 12 49 41 28 18 32 62296 23 37704 66503 27 33497 04208 5 95792 11 bO 8 41 20 3 18 40 9. 62323 23 10. 37677 9. 66537 28 10. 33463 10. 04214 5 9. 95786 10 51 41 12 18 48 62350 24 37650 66570 28 33430 04220 5 95780 9 52 41 4 18 56 62377 24 37623 66603 29 33397 04225 5 95775 8 53 40 56 19 4 62405 24 37595 66636 30 33364 04231 5 95769 7 54 40 48 19 12 62432 25 37568 66669 30 33331 04237 5 95763 6 5 55 8 40 40 3 19 20 9. 62459 25 10. 37541 9. 66702 31 10. 33298 10. 04243 5 9. 95757 56 40 32 19 28 62486 26 37514 66735 31 33265 04249 5 95751 4 67 40 24 19 36 62513 26 37487 66768 32 33232 04255 5 95745 3 68 40 16 19 44 62541 27 37459 66801 32 33199 04261 6 95739 2 59 40 8 19 52 62568 27 37432 66834 33 33166 04267 6 95733 1 60 40 20 62595 28 37405 66867 33 33133 04272 6 95728 M. M. Hour p. H. Hour A. M Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 114° A A B B C C 65° 1 Seconds of time 1» 2" 8* *• 6* 6< 7" Prop, parts of col8.'(B Ic 3 4 1 7 8 1 10 13 2 14 17 3 17 21 4 21 26 4 24 29 6 TABLE 44. [Page 797 Log. Sines, Tangents, and Secanta. 26° A A B B C C 16*0 M. Hour A. M. Hour p. M. Sine. Difif. Cosecant. Tangent. Diff. Cotangent. Secant. Dilf. Cosine. M. 60 8 40 3 20 9. 62595 10. 37405 9. 66867 10. 33133 10. 04372 9. 95728 1 39 52 20 8 62622 37378 66900 1 3310© 04278 95722 59 2 39 44 20 16 62649 1 37351 66933 1 33067 04284 95716 58 3 39 36 20 24 62676 1 37324 66966 2 33034 04290 95710 57 4 39 28 20 32 62703 2 37297 66999 2 33001 04296 95704 56 55 5 8 39 20 3 20 40 9. 62730 2 10. 37270 9. 67032 3 10. 32968 10.04302 9. 95698 6 39 12 20 48 62757 3 37243 67065 3 32935 04308 95692 54 7 39 4 20 56 62784 3 37216 67098 4 32902 04314 95686 53 8 38 56 21 4 62811 4 37189 67131 4 32869 04320 95680 52 9 10 38 48 21 12 62838 4 37162 67163 5 32837 04326 95674 51 8 38 40 3 21 20 9. 62865 4 10. 37135 9. 67196 5 10. 32804 10. 04332 9. 95668 50 11 38 32 21 28 62892 5 37108 67229 6 32771 04337 95663 49 12 38 24 21 36 62918 5 37082 67262 7 32738 04343 95657 48 13 38 16 21 44 62945 6 37055 67295 7 32705 04349 95651 47 14 38 8 21 52 62972 6 37028 67327 8 32673 04355 95645 46 15 8 38 3 22 9. 62999 7 10. 37001 9. 67360 8 10. 32640 10.04361 2 9. 95639 45 16 37 52 22 8 63026 7 36974 67393 9 32607 04367 2 95633 44 17 37 44 22 16 63052 8 36948 67426 9 32574 04373 2 95627 43 18 37 36 22 24 63079 8 36921 67458 10 32542 04379 2 95621 42 19 20 37 28 22 32 63106 8 36894 67491 10 32509 04385 2 95615 41 40 8 37 20 3 22 40 9.63133 9 10. 36867 9. 67524 11 10. 32476 10. 04391 2 9.95609 21 37 12 22 48 63159 9 36841 67556 11 32444 04397 2 95603 39 22 37 4 22 56 63186 10 36814 67589 12 32411 04403 2 95597 38 23 36 56 23 4 63213 10 36787 67622 12 32378 04409 2 95591 37 24 25 36 48 23 12 63239 11 36761 67654 13 32346 04415 2 3 95585 36 35 8 36 40 3 23 20 9. 63266 11 10. 36734 9. 67687 14 10. 32313 10. 04421 9.95579 26 36 32 23 28 63292 11 36708 67719 14 32281 04427 3 95573 34 27 36 24 23 36 63319 12 36681 67752 15 32248 04433 3 95567 33 28 36 16 23 44 63345 12 36655 67785 15 32215 04439 3 95561 32 29 36 8 23 52 63372 13 36628 67817 16 32183 04445 3 95555 31 m 30 8 36 3 24 9. 63398 13 10. 36602 9.67850 16 10. 32150 10. 04451 3 9. 95549 31 35 52 24 8 63425 14 36575 67882 17 32118 04457 3 95543 29 32 35 44 24 16 63451 14 36549 67915 17 32085 04463 3 95537 28 33 35 36 24 24 63478 15 36522 67947 18 32053 04469 3 95531 27 34 35 28 24 32 63504 15 36496 67980 18 32020 04475 3 95525 26 25 35 8 35 20 3 24 40 9. 63531 15 10. 36469 9. 68012 19 10. 31988 10. 04481 4 9. 95519 36 35 12 24 48 63557 16 36443 68044 20 31956 04487 4 95513 24 37 35 4 24 56 63583 16 36417 68077 20 31923 04493 4 95507 23 38 34 56 25 4 63610 17 36390 68109 21 31891 04500 4 95500 22 39 40 34 48 25 12 63636 17 36364 68142 21 31858 04506 4 95494 21 8 34 40 3 25 20 9. 63662 18 10. 36338 9. 68174 22 10. 31826 10. 04512 4 9. 95488 20 41 34 32 25 28 63689 18 36311 68206 22 31794 04518 4 95482 19 42 34 24 25 36 63715 19 36285 68239 23 31761 04524 4 95476 18 43 34 16 25 44 63741 19 36259 68271 23 31729 04530 4 95470 17 44 34 8 25 52 63767 19 36233 68303 24 31697 04536 4 95464 16 45 8 34 3 26 9. 63794 20 10. 36206 9. 68336 24 10. 31664 10. 04542 5 9. 95458 15 46 33 52 26 8 63820 20 36180 68368 25 31632 04548 5 95452 14 47 33 44 26 16 63846 21 36154 68400 25 31600 04554 5 95446 13 48 33 36 26 24 63872 21 36128 68432 26 31568 04560 5 95440 12 49 33 28 26 32 63898 22 36102 68465 27 31535 04566 5 95434 11 10 50 8 33 20 3 26 40 9. 63924 22 10. 36076 9. 68497 27 10. 31503 10. 04573 5 9. 95427 51 33 12 26 48 63950 23 36050 68529 28 31471 04579 5 95421 9 52 33 4 26 56 63976 23 36024 68561 28 31439 04585 5 95415 8 53 32 56 27 4 64002 23 35998 68593 29 31407 04591 5 95409 7 54 55 32 48 27 12 64028 24 35972 68626 29 31374 04597 5 95403 6 5 8 32 40 3 27 20 9. 64054 24 10. 35946 9. 68658 30 10. 31342 10. 04603 6 9. 95397 56 32 32 27 28 64080 25 35920 68690 30 31310 04609 6 95391 4 57 32 24 27 36 64106 25 35894 68722 31 31278 04616 6 95384 3 58 32 16 27 44 64132 26 35868 68754 31 31246 04622 6 95378 2 59 32 8 27 52 64158 26 35842 68786 32 31214 04628 6 95372 1 60 32 28 64184 26 35816 68818 33 31182 04634 6 95366 M. Hour p. u. Hour A. K. Cosine. Diff. Secant. Cotangent. Diflf. Tangent. Cosecant. Diff. Sine. M. 116° A A B B C C 64° j Seconds of time . Prop, parts of cols. •< 1» 10 12 2 Page 798] TABLE 44. Log. Sines, Tangents, and Secants. 26° A A B B C C 1680 M. Hoar A. H. riour p. M. Sine. Dift. Cosecant. Tangent. Difl. Cotangent. Secant. Difl. Cosine. M. 8 32 3 28 9.64184 10. 35816 9. 68818 10. 31182 10. 04634 9. 96366 60 1 31 52 28 8 64210 35790 68860 1 31150 04640 96360 59 2 31 44 28 16 64236 1 35764 68882 1 31118 04646 96354 58 3 31 36 28 24 64262 1 35738 68914 2 31086 04652 96348 57 4 31 28 28 32 64288 2 35712 68946 2 31064 04659 96341 56 55 5 8 31 20 3 28 40 9. 64313 2 10. 35687 9. 68978 3 10. 31022 10. 04665 9. 96335 6 31 12 28 48 64339 3 35661 69010 3 30990 04671 95329 64 7 31 4 28 56 64365 3 35635 69042 4 30968 04677 95323 63 8 30 56 29 4 64391 3 35609 69074 4 30926 04683 95317 52 9 30 48 29 12 64417 4 35583 69106 5 30894 04690 95310 51 60 10 8 30 40 3 29 20 9. 64442 4 10. 35558 9. 69138 5 10. 30862 10. 04696 9. 95304 11 30 32 29 28 64468 5 35532 69170 6 30830 04702 96298 49 12 30 24 29 36 64494 5 35506 69202 6 30798 04708 96292 48 13 30 16 29 44 64519 5 35481 69234 7 30766 04714 96286 47 14 30 8 29 52 64545 6 35455 69266 7 30734 04721 95279 46 45 15 8 30 3 30 9. 64571 6 10. 35429 9. 69298 8 10. 30702 10. 04727 2 9. 96273 16 29 52 30 8 64596 7 35404 69329 8 30671 04733 2 95267 44 17 29 44 30 16 64622 7 35378 69361 9 30639 04739 2 95261 43 18 29 36 30 24 64647 8 35353 69393 9 30607 04746 2 95264 42 19 29 28 30 32 64673 8 35327 69425 10 30575 04752 2 95248 41 20 8 29 20 3 30 40 9. 64698 8 10. 35302 9. 69457 11 10. 30543 10. 04758 2 9. 96242 40 21 29 12 30 48 64724 9 35276 69488 11 30512 04764 2 96236 39 22 29 4 30 56 64749 9 35251 69520 12 30480 04771 2 95229 38 23 28 56 31 4 64775 10 35225 69562 12 30448 04777 2 95223 37 24 28 48 31 12 64800 10 35200 69584 13 30416 04783 3 96217 36 35 25 8 28 40 3 31 20 9. 64826 11 10. 35174 9. 69616 13 10. 30386 10. 04789 3 9.95211 26 28 32 31 28 64851 11 35149 69647 14 30353 04796 3 95204 34 27 28 24 31 36 64877 11 35123 69679 14 30321 04802 3 96198 33 28 28 16 31 44 64902 12 35098 69710 16 30290 04808 3 95192 32 29 28 8 31 52 64927 12 35073 69742 16 30268 04815 3 96186 31 30 30 8 28 3 32 9. 64953 13 10. 35047 9. 69774 16 10. 30226 10. 04821 3 9. 95179 31 27 52 32 8 64978 13 35022 69805 16 30195 04827 3 95173 29 32 27 44 32 16 65003 14 34997 69837 17 30163 04833 3 95167 28 33 27 36 32 24 65029 14 34971 69868 17 30132 04840 3 95160 27 34 35 27 28 32 32 65054 14 34946 69900 18 30100 04846 4 96154 26 25 8 27 20 3 32 40 9. 65079 15 10. 34921 9. 69932 18 10. 30068 10. 04862 4 9. 96148 36 27 12 32 48 65104 15 34896 69963 19 30037 04859 4 95141 24 37 27 4 32 56 65130 16 34870 69996 20 30006 04866 4 95136 23 38 26 56 33 4 65155 16 34845 70026 20 29974 04871 4 96129 22 39 26 48 33 12 65180 16 34820 70068 21 29942 04878 4 95122 21 40 8 26 40 3 33 20 9. 65205 17 10. 34795 9. 70089 21 10.29911 10. 04884 4 9. 96116 20 41 26 32 33 28 65230 17 34770 70121 22 29879 04890 4 95110 19 42 26 24 33 36 65255 18 34745 70162 22 29848 04897 4 95103 18 43 26 16 33 44 65281 18 34719 70184 23 29816 04903 5 95097 17 44 26 8 33 52 65306 19 34694 70215 23 29785 04910 5 95090 16 45 8 26 3 34 9. 65331 19 10. 34669 9. 70247 24 10. 29763 10. 04916 5 9. 95084 15 46 25 52 34 8 65356 19 34644 70278 24 29722 04922 5 95078 14 47 25 44 34 16 65381 20 34619 70309 26 29691 04929 5 96071 13 48 25 36 34 24 65406 20 34594 70341 25 29669 04936 6 96066 12 49 25 28 34 32 65431 21 34569 70372 26 29628 04941 5 96069 11 10 60 8 25 20 3 34 40 9. 65456 21 10. 34544 9.70404 26 10. 29596 10. 04948 5 9. 95052 51 25 12 34 48 65481 22 34519 70435 27 29566 04954 5 95046 9 52 25 4 34 56 65506 22 34494 70466 27 29634 04961 6 96039 8 53 24 56 35 4 65531 22 34469 70498 28 29602 04967 6 96033 7 54 24 48 35 12 65556 23 34444 70529 28 29471 04973 6 96027 6 55 8 24 40 3 35 20 9. 65580 23 10. 34420 9. 70560 29 10. 29440 10. 04980 6 9. 95020 5 •56 24 32 35 21 65605 24 34395 70592 30 29408 04986 6 95014 4 57 24 24 35 36 65630 24 34370 70623 30 29377 04993 6 95007 3 58 24 16 35 44 65655 25 34345 70654 31 29346 04999 6 95001 2 59 24 8 35 52 65680 25 34320 70685 31 29315 05006 6 94995 1 60 24 36 65705 25 34295 70717 32 29283 05012 6 94988 M. Hour p. M. Hour A. M. Cosine. Di£f. Secant. Cotangent. Difl. Tangent. Cosecant. Difl. Sine. M. 116° A A B B C C 63° 1 Seconds of time 1« 2" 8» 4« 6» I C» 7> Prop, parts of cols. < B 3 4 1 6 8 2 10 12 2 13 16 3 16 20 4 19 24 5 22 28 6 TABLE 44. [Page 799 Log. Sines, Tangents, and Secants. 27° A A B B C C 162° M. Hour A. M. Hour p. M, Sine. DIff. Cosecant. Tangent. Difl. Cotangent. Secant. Difl. Cosine. M. 60 n 8 24 3 36 9. 65705 10. 34295 9. 70717 10. 29283 10. 05012 9. 94988 1 23 52 36 8 65729 34271 70748 1 29252 05018 94982 59 9 23 44 36 16 65754 1 34246 70779 1 29221 05025 94975 58 3 23 36 36 24 65779 1 34221 70810 2 29190 05031 94969 57 4 5 23 28 36 32 65804 2 34196 70841 2 29159 05038 94962 56 8 23 20 3 36 40 9. 65828 2 10. 34172 9. 70873 3 10. 29127 10.05044 9. 94956 55 6 23 12 36 48 65853 2 34147 70904 3 29096 05051 1 94949 54 7 23 4 36 56 65878 3 34122 70935 4 29065 05057 94943 53 S 22 56 37 4 65902 3 34098 70966 4 29034 05064 94936 52 9 22 48 37 12 65927 4 34073 70997 5 29003 05070 94930 51 50 10 8 22 40 3 37 20 9. 65952 4 10. 34048 9. 71028 5 10. 28972 10. 05077 9. 94923 11 22 32 37 28 65976 4 34024 71059 6 28941 05083 94917 49 1? 22 24 37 36 66001 5 33999 71090 6 28910 05089 94911 48 18 22 16 37 44 66025 5 33975 71121 7 28879 05096 94904 47 14 15 22 8 37 52 66050 6 33950 71153 7 28847 05102 2 94898 46 8 22 3 38 9. 66075 6 10. 33925 9. 71184 8 10. 28816 10. 05109 2 9. 94891 45 16 21 52 38 8 66099 6 33901 71215 8 28785 05115 2 94885 44 17 21 44 38 16 66124 7 33876 71246 9 28754 05122 2 94878 43 18 21 36 38 24 66148 7 33852 71277 9 28723 05129 2 94871 42 19 21 28 38 32 66173 8 33827 71308 10 28692 05135 2 2 94865 41 40 ^0 8 21 20 3 38 40 9. 66197 8 10. 33803 9. 71339 10 10.28661 10. 05142 9. 94858 ?1 21 12 38 48 66221 8 33779 71370 11 - 286.30 05148 2 94852 39 ?? 21 4 38 56 66246 9 83754 71401 11 28599 05155 2 94845 38 ?8 20 56 39 4 66270 9 33730 71431 12 28569 05161 3 94839 37 24 20 48 39 12 66295 10 33705 71462 12 28538 05168 3 94832 36 ?5 8 20 40 3 39 20 9. 66319 10 10. 33681 9. 71493 13 10. 28507 10. 05174 3 9. 94826 35 ^6 20 32 39 28 66343 11 33657 71524 13 28476 05181 3 94819 34 ?7 20 24 39 36 66368 11 33632 71555 14. 28445 05187 3 94813 33 7.f>, 20 16 39 44 66392 11 33608 71586 14 28414 05194 3 94806 32 29 20 8 39 52 66416 12 33584 71617 15 28383 05201 3 94799 31 80 8 20 3 40 9.66441 12 10. 33559 9. 71648 15 10. 28352 10. 05207 3 9. 94793 30 81 19 52 40 8 66465 13 33635 71679 16 28321 05214 3 94786 29 8? 19 44 40 16 66489 13 33511 71709 16 28291 05220 4 94780 28 88 19 36 40 24 66513 13 33487 71740 17 28260 05227 4 94773 27 34 19 28 40 32 66537 14 33463 71771 17 28229 05233 10. 05240 4 94767 26 25 85 8 19 20 3 40 40 9. 66562 14 10. 33438 9. 71802 18 10. 28198 4 9. 94760 86 19 12 40 48 66586 15 33414 71833 19 28167 05247 4 94753 24 87 19 4 40 56 66610 15 33390 71863 19 28137 05253 4 94747 23 88 18 56 41 4 66634 15 33366 71894 20 28106 05260 4 94740 22 39 18 48 41 12 66658 16 33342 71925 20 28075 05266 4 4 94734 21 40 8 18 40 3 41 20 9. 66682 16 10. 33318 9. 71955 21 10. 28045 10. 05273 9. 94727 20 41 18 32 41 28 66706 17 33294 71986 21 28014 05280 4 94720 19 42 18 24 41 36 66731 17 33269 72017 22 27983 05286 5 94714 18 48 18 16 41 44 66755 17 33245 72048 22 27952 05293 5 94707 17 44 45 18 8 41 52 66779 18 33221 72078 23 27922 05300 5 94700 9. 94694 16 15 8 18 3 42 9. 66803 18 10. 33197 9. 72109 23 10. 27891 10. 05306 5 46 17 52 42 8 66827 19 33173 72140 24 27860 05313 5 94687 14 47 17 44 42 16 66851 19 33149 72170 24 27830 05320 5 94680 13 48 17 36 42 24 66875 19 33125 72201 25 27799 05326 5 94674 12 49 50 17 28 8 17 20 42 32 66899 20 33101 72231 25 27769 05333 5 94667 11 3 42 40 9. 66922 20 10. 33078 9. 72262 26 10. 27738 10. 05340 5 9. 94660 10 51 17 12 42 48 66946 21 33054 72293 26 27707 05346 6 94654 9 52 17 4 42 56 66970 21 33030 72323 27 27677 05353 6 94647 8 53 16 56 43 4 66994 21 33006 72354 27 27646 05360 6 94640 7 54 16 48 43 12 67018 22 32982 72384 28 27616 05366 6 94634 6 55 8 16 40 3 43 20 9. 67042 22 10. 32958 9. 72415 28 10. 27585 10. 05373 6 9. 94627 5 56 16 32 43 28 67066 23 32934 72445 29 27555 05380 6 94620 4 57 16 24 43 36 67090 23 32910 72476 29 27524 05386 6 94614 3 58 16 16 43 44 67113 23 32887 72506 30 27494 05393 6 94607 2 59 16 8 43 52 67137 24 32863 72537 30 27463 05400 6 94600 1 60 16 44 67161 24 32839 72567 31 27433 05407 7 94593 M. Hour p. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Dlff. Tangent. Cosecant. Difl. Sine. M. 117° A A B B C C 62° j Seconds of time 1« «• 8« 4> &> 6« 7« fA Prop, parts of cols. {B Ic 3 4 1 6 8 2 9 12 2 12 16 3 15 19 4 18 23 6 21 27 6 Page 800] TABLE 44. Log. Sines, Tangents, and Secants. 88° A A B B C C 161° M. Hour A. M. Hour p. M. Sine. Diflf. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 8 16 3 44 9. 67161 10. 32839 9. 72567 10. 27433 10. 05407 9. 94593 60 1 15 52 44 8 67185 32815 72598 1 27402 05413 94587 59 2 15 44 44 16 67208 1 32792 72628 1 27372 05420 94580 58 3 15 36 44 24 67232 1 32768 72659 2 27341 05427 94573 57 4 15 28 44 32 67256 2 32744 72689 2 27311 05433 94567 56 55 5 8 15 20 3 44 40 9. 67280 2 10. 32720 9. 72720 3 10. 27280 10. 05440 9. 94560 6 15 12 44 48 67303 2 32697 72750 3 27250 05447 94553 54 7 15 4 44 56 67327 3 32673 72780 4 27220 05454 94546 53 8 14 56 45 4 67350 3 32650 72811 4 27189 05460 94540 52 9 10 14 48 45 12 67374 3 32626 72841 5 27159 05467 94533 51 8 14 40 3 45 20 9. 67398 4 10. 32602 9. 72872 5 10. 27128 10. 05474 9. 94526 50 11 14 32 45 28 67421 4 32579 72902 6 27098 05481 94519 49 12 14 24 45 36 67445 5 32555 72932 6 27068 05487 94513 48 13 14 16 45 44 67468 5 32532 72963 7 27037 05494 94506 47 14 14 8 45 52 67492 9. 67515 5 32508 72993 7 27007 05501 2 94499 46 45 15 8 14 3 46 6 10. 32485 9. 73023 8 10. 26977 10. 05508 2 9. 94492 16 13 52 46 8 67539 6 32461 73054 8 26946 05515 2 94485 44 17 13 44 46 16 67562 7 32438 73084 9 26916 05521 2 94479 43 18 13 36 46 24 67586 7 32414 73114 9 26886 05528 2 94472 42 19 13 28 46 32 67609 7 32391 73144 10 26856 05535 2 94465 41 40 20 8 13 20 3 46 40 9. 67633 8 10. 32367 9. 73175 10 10. 26825 10. 05542 2 9. 94458 21 13 12 46 48 67656 8 32344 73205 11 26795 05549 2 94451 39 22 13 4 46 56 67680 9 32320 73235 11 26765 05555 3 94445 38 23 12 56 47 4 67703 9 32297 73265 12 26735 05562 3 94438 37 24 12 48 47 12 67726 9 32274 73295 12 26705 05569 3 3 94431 9. 94424 36 35 25 8 12 40 3 47 20 9. 67750 10 10. 32250 9. 73326 13 10. 26674 10. 05576 26 12 32 47 28 67773 10 32227 73356 13 26644 05583 3 94417 34 27 12 24 47 36 67796 10 32204 73386 14 26614 05590 3 94410 33 28 12 16 47 44 67820 11 32180 73416 14 26584 05596 3 94404 32 29 12 8 47 52 67843 11 32157 73446 15 26554 05603 3 94397 31 30 8 12 3 48 9. 67866 12 10. 32134 9. 73476 15 10. 26524 10. 05610 3 9. 94390 30 31 11 52 48 8 67890 12 32110 73507 16 26493 05617 4 94383 29 32 11 44 48 16 67913 12 32087 73537 16 26463 05624 4 94376 28 33 11 36 48 24 67936 13 32064 73567 17 26433 05631 4 94369 27 34 11 28 48 32 67959 13 14 32041 73597 17 26403 05638 10. 05645 4 4 94362 9. 94355 26 25 35 8 11 20 3 48 40 9. 67982 10. 32018 9. 73627 18 10. 26373 36 11 12 48 48 68006 14 31994 73657 18 26343 05651 4 94349 24 37 11 4 48 56 68029 14 31971 73687 19 26313 05658 4 94342 23 38 10 56 49 4 68052 15 31948 73717 19 26283 05665 4 94335 22 39 40 10 48 8 10 40 49 12 68075 9. 68098 15 31925 73747 20 26253 05672 4 94328 21 20 3 49 20 16 10. 31902 9. 73777 20 10. 26223 10. 05679 5 9. 94321 41 10 32 49 28 68121 16 31879 73807 21 26193 05686 5 94314 19 42 10 24 49 36 68144 16 31856 73837 21 26163 05693 5 94307 18 43 10 16 49 44 68167 17 31833 73867 22 26133 05700 5 94300 17 44 45 10 8 49 52 68190 17 31810 73897 22 26103 10. 26073 05707 5 5 94293 16 15 8 10 3 50 9. 68213 17 10. 31787 9. 73927 23 10. 05714 9. 94286 46 9 52 50 8 68237 18 31763 73957 23 26043 05721 5 94279 14 47 9 44 50 16 68260 18 31740 73987 24 26013 05727 5 94273 13 48 9 36 50 24 68283 19 31717 74017 24 25983 05734 5 94266 12 49 50 9 28 50 32 68305 19 31695 74047 25 25953 05741 6 6 94259 9. 94252 11 10 8 9 20 3 50 40 9. 68328 19 10.31672 9. 74077 25 10. 25923 10. 05748 51 9 12 50 48 68351 20 31649 74107 26 25893 05755 6 94245 9 52 9 4 50 56 68374 20 31626 74137 26 25863 05762 6 94238 8 53 8 56 51 4 68397 21 31603 74166 27 25834 05769 6 94231 7 54 8 48 51 12 68420 21 31580 74196 27 25804 05776 6 94224 6 55 8 8 40 3 51 20 9. 68443 21 10. 31557 9. 74226 28 10. 25774 10. 05783 6 9. 94217 5 56 8 32 51 28 68466 22 31534 74256 28 25744 05790 6 94210 4 57 8 24 51 36 68489 22 31511 74286 29 25714 05797 7 94203 3 58 8 16 51 44 68512 22 31486 74316 29 25684 05804 7 94196 2 59 8 8 51 52 68534 23 31466 74345 30 25655 05811 7 94189 1 60 8 52 68557 23 31443 74375 30 25625 05818 7 94182 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M 118° A A B B C C 61° 1 Seconds of time 1« 2" 8- 4* 6* 6* 7« Prop, parts of cols. < B 3 4 1 6 8 2 9 11 3 3 15 19 4 17 23 6 20 26 6 TABLE 44. [Page 801 Log. Sines, Tangents, and Secants. w> A A B B G C 160° M. Hoar A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diff. Cotangent Secant. Diff. Cosine. M. 8 8 3 52 9.68557 10. 31443 9. 74375 10. 25625 10. 05818 9. 94182 60 1 7 52 52 8 68580 31420 74405 25595 05825 94175 59 2 7 44 52 16 68603 1 31397 74435 1 25565 05832 94168 58 3 7 36 52 24 68625 1 31375 74465 1 25535 05839 94161 57 4 7 28 52 32 68648 1 31352 74494 2 25506 05846 94154 56 55 5 8 7 20 3 52 40 9. 68671 2 10. 31329 9. 74524 2 10. 25476 10. 05853 9. 94147 6 7 12 52 48 68694 2 31306 74554 3 25446 05860 94140 54 T 7 4 52 56 68716 3 31284 74583 3 25417 05867 94133 53 8 6 56 53 4 68739 3 31261 74613 4 25387 05874 94126 52 9 6 48 53 12 68762 3 31238 74643 4 25357 05881 94119 51 50 10 8 6 40 3 53 20 9. 68784 4 10. 31216 9. 74673 5 10. 25327 10. 05888 9.94112 11 6 32 53 28 68807 4 31193 74702 5 25298 05895 94105 49 12 6 24 53 36 68829 4 31171 74732 6 25268 05902 94098 48 13 6 16 53 44 68852 5 31148 74762 6 25238 05910 2 94090 47 14 15 6 8 53 52 68875 5 31125 74791 7 25209 05917 2 94083 46 8 6 3 54 9. 68897 6 10.31103 9. 74821 7 10. 25179 10. 05924 2 9. 94076 45 16 5 52 54 8 68920 6 31080 74^51 8 25149 05931 2 94069 44 17 5 44 54 16 68942 6 31058 74880 8 25120 05938 2 94062 43 18 5 36 54 24 68965 7 31035 74910 9 25090 05945 2 94055 42 19 20 5 28 54 32 68987 7 31013 74939 9 25061 05952 2 94048 41 8 5 20 3 54 40 9. 69010 7 10.30990 9. 74969 10 10. 25031 10. 05959 2 9. 94041 40 21 5 12 54 48 69032 8 30968 74998 10 25002 05966 3 94034 39 22 5 4 54 56 69055 8 30945 75028 11 24972 05973 3 94027 38 23 4 56 55 4 69077 9 30923 75058 11 24942 05980 3 94020 37 24 25 4 48 55 12 69100 9 30900 75087 12 24913 10. 24883 05988 3 94012 36 36 8 4 40 3 55 20 9. 69122 9 10. 30878 9. 75117 12 10. 05995 3 9.94005 26 4 32 55 28 69144 10 30856 75146 13 24854 06002 3 93998 34 27 4 24 55 36 69167 10 30833 75176 13 24824 06009 3 93991 33 28 4 16 55 44 69189 10 30811 75205 14 24795 06016 3 93984 32 29 4 8 55 52 69212 11 30788 75235 14 24765 06023 3 93977 31 30 8 4 3 56 9. 69234 11 10. 30766 9. 75264 15 10. 24736 10. 06030 4 9. 93970 30 31 3 52 56 8 69256 12 30744 75294 15 24706 06037 4 93963 29 32 3 44 56 16 69279 12 30721 75323 16 24677 06045 4 93955 28 33 3 36 56 24 69301 12 30699 75353 16 24647 06052 4 93948 27 34 3 28 56 32 69323 13 30677 75382 17 24618 06059 4 93941 26 35 8 3 20 3 56 40 9. 69345 13 10. 30655 9.75411 17 10. 24589 10.06066 4 9. 93934 25 36 3 12 56 48 69368 13 30632 75441 18 24559 06073 4 93927 24 37 3 4 56 56 69390 14 30610 75470 18 24530 06080 4 93920 23 38 2 56 57 4 69412 14 30588 75500 19 24500 06088 5 93912 22 39 2 48 57 12 69434 15 30566 75529 19 24471 06095 5 93905 21 20 40 8 2 40 3 57 20 9. 69456 15 10. 30544 9. 75558 20 10.24442 10. 06102 5 9. 93898 41 2 32 57 28 69479 15 30521 75588 20 24412 06109 5 93891 19 42 2 24 57 36 69501 16 30499 75617 21 24383 06116 5 93884 18 43 2 16 57 44 69523 16 30477 75647 21 24353 06124 5 93876 17 44 45 2 8 57 52 69545 16 17 30455 75676 22 24324 06131 5 93869 16 8 2 3 58 9. 69567 10. 30433 9. 75705 22 10. 24295 10. 06138 5 9. 93862 15 46 1 52 58 8 69589 17 30411 75735 23 24265 06145 5 93855 14 47 1 44 58 16 69611 17 30389 75764 23 24236 06153 6 93847 13 48 1 36 58 24 69633 18 30367 75793 24 24207 06160 6 93840 12 49 50 1 28 58 32 69655 18 30345 75822 24 24178 06167 6 93833 11 10 8 1 20 3 58 40 9. 69677 19 10. 30323 9. 75852 25 10. 24148 10. 06174 6 9. 93826 51 1 12 58 48 69699 19 30301 75881 25 24119 06181 6 93819 9 52 1 4 58 56 69721 19 30279 75910 26 24090 06189 6 93811 8 53 56 59 4 69743 20 30257 75939 26 24061 06196 6 93804 7 54 48 59 12 69765 20 30235 75969 27 24031 06203 6 93797 6 5 55 8 40 3 59 20 9. 69787 20 10. 30213 9. 75998 27 10. 24002 10. 06211 7 9. 93789 56 32 59 28 69809 21 30191 76027 28 23973 06218 7 93782 4 57 24 59 36 69831 21 30169 76056 28 23944 06225 7 93775 3 58 16 59 44 69853 22 30147 76086 29 23914 06232 7 93768 2 59 8 59 52 69875 22 30125 76115 29 23885 06240 7 93760 1 60 4 69897 22 30103 76144 29 23856 06247 7 93753 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 11»° A A B B C C 60° 1 Seconds of time Prop, parts of cols.^B 6* 17 22 5 Page 802] TABLE U. Log. Sines, Tangents, and Secants. 800 ▲ A B B C C 149° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Difl. Cotangent. Secant. Difl. Cosine. M. 8 4 9. 69897 10. 30103 9. 76144 10. 23856 10. 06247 9. 93753 60 1 7 59 52 8 69919 30081 76173 23827 06254 93746 59 2 59 44 16 69941 1 30059 76202 1 23798 06262 93738 58 3 59 36 24 69963 1 30037 76231 1 23769 06269 93731 57 4 59 28 32 69984 1 30016 76261 2 23739 06276 93724 56 fi 7 59 20 4 40 9. 70006 2 10. 29994 9. 76290 2 10. 23710 10. 06283 9. 93717 55 6 59 12 48 70028 2 29972 76319 3 23681 06291 93709 54 7 59 4 56 70050 3 29950 76348 3 23652 06298 93702 53 8 58 56 1 4 70072 3 29928 76377 4 23623 06305 93695 52 9 58 48 1 12 70093 3 29907 76406 4 23594 06313 93687 51 10 7 58 40 4 1 20 9. 70115 4 10. 29885 9. 76435 5 10. 23565 10. 06320 9. 93680 50 n 58 32 1 28 70137 4 29863 76464 5 23536 06327 93673 49 12 58 24 1 36 70159 4 29841 76493 6 23507 06335 93665 48 13 58 16 1 44 70180 5 29820 76522 6 23478 06342 2 93658 47 14 58 8 1 52 70202 5 29798 76551 7 23449 06350 2 93650 46 45 15 7 58 4 2 9. 70224 5 10. 29776 9. 76580 7 10. 23420 10. 06357 2 9. 93643 16 57 52 2 8 70245 6 29755 76609 8 23391 06364 2 93636 44 17 57 44 2 16 70267 6 29733 76639 8 23361 06372 2 93628 43 18 57 36 2 24 70288 6 29712 76668 9 23332 06379 2 93621 42 19 57 28 2 32 70310 7 29690 76697 9 23303 06386 2 2 93614 41 40 20 7 57 20 4 2 40 9. 70332 7 10. 29668 9. 76725 10 10. 23275 10. 06394 9. 93606 21 57 12 2 48 70353 8 29647 76754 10 23246 06401 3 93599 39 22 57 4 2 56 70375 8 29625 76783 11 23217 06409 3 93591 38 23 56 56 3 4 70396 8 29604 76812 11 23188 06416 3 93584 37 24 56 48 3 12 70418 9 29582 76841 12 23159 06423 3 93577 36 25 7 56 40 4 3 20 9. 70439 9 10. 29561 9. 76870 12 10. 23130 10. 06431 3 9. 93569 35 26 56 32 3 28 70461 9 29539 76899 13 23101 06438 3 93562 34 27 56 24 3 36 70482 10 29518 76928 13 23072 06446 3 93554 33 28 56 16 3 44 70504 10 29496 76957 13 23043 06453 3 93547 32 29 56 8 3 52 70525 10 29475 76986 14 23014 06461 4 4 93539 31 30 7 56 4 4 9. 70547 11 10. 29453 9. 77015 14 10. 22985 10. 06468 9. 93532 30 31 55 52 4 8 70568 11 29432 77044 15 22956 06475 4 93525 29 32 55 44 4 16 70590 11 29410 77073 15 22927 06483 4 93517 28 33 55 36 4 24 70611 12 29389 77101 16 22899 06490 4 93510 27 34 55 28 4 32 70633 12 29367 77130 16 22870 06498 4 93502 26 35 7 55 20 4 4 40 9. 70654 13 10. 29346 9. 77159 17 10. 22841 10. 06505 4 9. 93495 25 36 55 12 4 48 70675 13 29325 77188 17 22812 06513 4 93487 24 37 55 4 4 56 70697 13 29303 77217 18 22783 06520 5 93480 23 38 54 56 5 4 70718 14 29282 77246 18 22754 06528 5 93472 22 39 40 54 48 5 12 • 70739 14 29261 77274 19 22726 06535 5 93465 21 7 54 40 4 5 20 9. 70761 14 10. 29239 9. 77303 19 10. 22697 10. 06543 5 9. 93457 20 41 54 32 5 28 70782 15 29218 77332 20 22668 06550 5 93450 19 42 54 24 5 36 70803 15 29197 77361 20 22639 06558 5 93442 18 43 54 16 5 44 70824 15 29176 77390 21 22610 06565 5 93435 17 44 54 8 5 52 70846 16 29154 77418 21 22 22582 10. 22553 06573 5 93427 16 15 45 7 54 4 6 9. 70867 16 10. 29133 9. 77447 10. 06580 6 9. 93420 46 53 52 6 8 70888 16 29112 77476 22 22524 06588 6 93412 14 47 53 44 6 16 70909 17 29091 77505 23 22495 06595 6 93405 13 48 53 36 6 24 70931 17 29069 77533 23 22467 06603 6 93397 12 49 53 28 6 32 70952 18 29048 77562 24 22438 06610 6 93390 11 10 50 7 53 20 4 6 40 9. 70973 18 10. 29027 9. 77591 24 10. 22409 10. 06618 6 9. 93382 51 53 12 6 48 70994 18 29006 77619 25 22381 06625 6 93375 9 52 53 4 6 56 71015 19 28985 77648 25 22352 06633 6 93367 8 53 52 56 7 4 71036 19 28964 77677 26 22323 06640 7 93360 7 54 52 48 7 12 71058 19 28942 77706 26 22294 06648 7 93352 6 5 55 7 52 40 4 7 20 9. 71079 20 10. 28921 9. 77734 26 10. 22266 10. 06656 7 9. 93344 56 52 32 7 28 71100 20 28900 77763 27 22237 06663 7 93337 4 57 52 24 7 36 71121 20 28879 77791 27 22209 06671 7 93329 3 58 52 16 7 44 71142 21 28858 77820 28 22180 06678 7 93322 2 59 52 8 7 52 71163 21 28837 77849 28 22151 06686 7 93314 1 60 52 8 71184 21 28816 77877 29 22123 06693 7 93307 M. Hour p. M. Hour A. H. Cosine. Difl. Secant. Cotangent. Difl. Tangent. Cosecant. Difl. Sine. M. 120^ > A A B B C C 69°l Seconds of time !■ 2« 8« 4- &> 6- ?• A Prop, parts of cols. B Ic 3 4 1 5 7 2 8 U 8 11 14 4 13 18 5 16 22 6 19 25 7 TABLE 44. [Page 803 Log. Sines, Tangents, and Secants. 81° A A B B C C 148° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Difif. Cotangent. Secant. Diff. Cosine. M. 7 52 4 8 9. 71184 10. 28816 9. 77877 10. 22123 10. 06693 9. 93307 60 1 51 52 8 8 71205 28795 77906 22094 06701 93299 59 '?, 51 44 8 16 71226 1 28774 77935 1 22065 06709 93291 58 3 51 36 8 24 71247 1 28753 77963 1 22037 06716 93284 57 4 5 51 28 8 32 71268 1 2 28732 10. 28711 77992 2 22008 06724 93276 56 55 7 51 20 4 8 40 9. 71289 9. 78020 2 10. 21980 10. 06731 9. 93269 6 51 12 8 48 71310 2 28690 78049 3 21951 06739 93261 54 7 51 4 8 56 71331 2 28669 78077 3 21923 06747 93253 53 « 50 56 9 4 71352 3 28648 78106 4 21894 06754 93246 52 9 50 48 9 12 71373 3 28627 78135 4 21865 06762 93238 51 10 7 50 40 4 9 20 9. 71393 3 10. 28607 9. 78163 5 10. 21837 10. 06770 9. 93230 50 11 50 32 9 28 71414 4 28586 78192 5 21808 06777 93223 49 12 50 24 9 36 71435 4 28565 78220 6 21780 06785 2 93215 48 13 50 16 9 44 71456 4 28544 78249 6 21751 06793 2 93207 47 14 50 8 9 52 71477 5 28523 78277 7 21723 06800 2 93200 9. 93192 46 45 1ft 7 50 4 10 9. 71498 5 10. 28502 9. 78306 7 10. 21694 10. 06808 2 16 49 52 10 8 71519 5 28481 78334 8 21666 06816 2 93184 44 17 49 44 10 16 71539 6 28461 78363 8 21637 06823 2 93177 43 18 49 36 10 24 71560 6 28440 78391 9 21609 06831 2 93169 42 19 20 49 28 10 32 71581 7 28419 78419 9 21581 06839 2 93161 41 40 7 49 20 4 10 40 9. 71602 7 10. 28398 9.78448 9 10. 21552 10. 06846 3 9. 93154 21 49 12 10 48 71622 7 28378 78476 10 21524 06854 3 93146 39 22 49 4 10 56 71643 8 28357 78505 10 21495 06862 3 93138 38 23 48 56 11 4 71664 8 28336 78533 11 21467 06869 3 93131 37 24 48 48 11 12 71685 8 28315 78562 11 21438 06877 3 93123 36 3ft 2ft 7 48 40 4 11 20 9. 71705 9 10. 28295 9. 78590 12 10. 21410 10. 06885 3 9.93115 26 48 32 11 28 71726 9 28274 78618 12 21382 06892 3 93108 34 27 48 24 11 36 71747 9 28253 78647 13 21353 06900 3 93100 33 28 48 16 11 44 71767 10 28233 78675 13 21325 06908 4 93092 32 29 48 8 11 52 71788 10 28212 78704 14 21296 06916 4 93084 31 30 30 7 48 4 12 9. 71809 10 10. 28191 9. 78732 14 10. 21268 10. 06923 4 9. 93077 31 47 52 12 8 71829 11 28171 78760 15 21240 06931 4 93069 29 32 47 44 12 16 71850 11 28150 78789 15 21211 06939 4 93061 28 33 47 36 12 24 71870 11 28130 78817 16 21183 06947 4 93053 27 34 47 28 12 32 71891 12 28109 78845 16 21155 06954 4 93046 26 3ft 7 47 20 4 12 40 9. 71911 12 10. 28089 9. 78874 17 10. 21126 10. 06962 5 9. 93038 •25 36 47 12 12 48 71932 12 28068 78902 17 21098 06970 5 93030 24 37 47 4 12 56 71952 13 28048 78930 17 21070 06978 5 93022 23 38 46 56 13 4 71973 13 28027 78959 18 21041 06986 5 93014 22 39 46 48 13 12 71994 13 14 28006 78987 18 21013 06993 5 93007 21 40 7 46 40 4 13 20 9. 72014 10. 27986 9. 79015 19 10. 20985 10. 07001 5 19.92999 20 41 46 32 13 28 72034 14 27966 79043 19 20957 07009 5 92991 19 42 46 24 13 36 72055 14 27945 79072 20 20928 07017 5 92983 18 43 46 16 13 44 72075 15 27925 79100 20 20900 07024 6 92976 17 44 46 8 13 52 72096 15 27904 79128 21 20872 07032 6 92968 16 4ft 7 46 4 14 9. 72116 15 10. 27884 9. 79156 21 10. 20844 10. 07040 6 9. 92960 15 46 45 52 14 8 72137 16 27863 79185 22 20815 07048 6 92952 14 47 45 44 14 16 72157 16 27843 79213 22 20787 07056 6 92944 13 48 45 36 14 24 72177 16 27823 79241 23 20759 07064 6 92936 12 49 45 28 14 32 72198 17 27802 79269 23 20731 07071 6 92929 11 ftO 7 45 20 4 14 40 9. 72218 17 10. 27782 9. 79297 24 10. 20703 10. 07079 6 9. 92921 10 ftl 45 12 14 48 72238 18 27762 79326 24 20674 07087 7 92913 9 ft2 45 4 14 56 72259 18 27741 79354 25 20646 07095 7 92905 8 ft3 44 56 15 4 72279 18 27721 79382 25 20618 07103 7 92897 7 54 44 48 15 12 72299 19 27701 79410 26 20590 07111 7 92889 6 ftft 7 44 40 4 15 20 9. 72320 19 10. 27680 9. 79438 26 10. 20562 10. 07119 7 9. 92881 5 ft6 44 32 15 28 72340 19 27660 79466 26 20534 07126 7 92874 4 ft7 44 24 15 36 72360 20 27640 79495 27 20505 07134 7 92866 3 ft8 44 16 15 44 72381 20 27619 79523 27 20477 07142 7 92858 2 ft9 44 8 15 52 72401 20 27599 79551 28 20449 07150 8 92850 1 60 44 16 72421 21 27579 79579 28 20421 07158 8 92842 M. Hour p. M. Hour A.M. Cosine. Di«f. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 121° A A B B C C 68° 1 Seconds of time !■ 2« 8> 4« 6> 6« 7« Prop, parts of cols.^ B |c 3 4 1 5 7 2 8 11 3 10 14 4 13 18 5 15 21 6 18 26 7 Page 804] TABLE 44. Log. Sines, Tangents, and Secants. 82° A A B B C C 147° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 7 44 4 16 9. 72421 10. 27579 9. 79579 10. 20421 10. 07158 9. 92842 60 1 43 52 16 8 72441 27559 79607 20393 07166 92834 59 2 43 44 16 16 72461 1 27539 79635 1 20365 07174 92826 58 3 43 36 16 24 72482 1 27518 79663 1 20337 07182 92818 57 4 43 28 16 32 72502 1 27498 79691 2 20309 07190 92810 56 5 7 43 20 4 16 40 9. 72522 2 10. 27478 9. 79719 2 10. 20281 10. 07197 9. 92803 55 6 43 12 16 48 72542 2 27458 79747 3 20253 07205 92795 54 7 43 4 16 56 72562 2 27438 79776 3 20224 07213 92787 53 8 42 56 17 4 72582 3 27418 79804 4 20196 07221 92779 52 9 42 48 17 12 72602 3 27398 79832 4 20168 07229 92771 51 50 10 7 42 40 4 17 20 9. 72622 3 10. 27378 9. 79860 5 10. 20140 10. 07237 9. 92763 11 42 32 17 28 72643 4 27357 79888 5 20112 07245 92755 49 12 42 24 17 36 72663 4 27337 79916 6 20084 07253 2 92747 48 13 42 16 17 44 72683 4 27317 79944 6 20056 07261 2 92739 47 14 15 42 8 17 52 72703 5 27297 79972 7 20028 07269 2 92731 46 45 7 42 4 18 9. 72723 5 10. 27277 9. 80000 7 10. 20000 10. 07277 2 9. 92723 16 41 52 18 8 72743 5 27257 80028 7 19972 07285 2 92715 44 17 41 44 18 16 72763 6 27237 80056 8 19944 07293 2 92707 43 18 41 36 18 24 72783 6 27217 80084 8 19916 07301 2 92699 42 19 20 41 28 18 32 72803 6 27197 80112 9 19888 07309 3 92691 41 40 7 41 20 4 18 40 9. 72823 7 10. 27177 9. 80140 9 10. 19860 10. 07317 3 9. 92683 21 41 12 18 48 72843 7 27157 80168 10 19832 07325 3 92675 39 22 41 4 18 56 72863 7 27137 80195 10 19805 07333 3 92667 38 23 40 56 19 4 72883 8 27117 80223 11 19777 07341 3 92659 37 24 40 48 19 12 72902 8 27098 80251 11 19749 07349 3 92651 36 25 7 40 40 4 19 20 9. 72922 8 10. 27078 9. 80279 12 10. 19721 10. 07357 3 9. 92643 35 26 40 32 19 28 72942 9 27058 80307 12 19693 07365 3 92635 34 27 40 24 19 36 72962 9 27038 80335 13 19665 07373 4 92627 33 28 40 16 19 44 72982 9 27018 80363 13 19637 07381 4 92619 32 29 40 8 19 52 73002 10 26998 80391 13 19609 07389 4 92611 31 30 7 40 4 20 9. 73022 10 10. 26978 9. 80419 14 10. 19581 10. 07397 4 9. 92603 30 31 39 52 20 8 73041 10 26959 80447 14 19553 07405 4 92595 29 32 39 44 20 16 73061 11 26939 80474 15 19526 07413 4 92587 28 33 39 36 20 24 73081 11 26919 80502 15 19498 07421 4 92579 27 34 35 39 28 20 32 73101 11 26899 80530 16 19470 07429 5 92571 26 7 39 20 4 20 40 9. 73121 12 10. 26879 9. 80558 16 10. 19442 10. 07437 5 9. 92563 25 36 39 12 20 48 73140 12 26860 80586 17 19414 07445 5 92555 24 37 39 4 20 56 73160 12 26840 80614 17 19386 07454 5 92546 23 38 38 56 21 4 73180 13 26820 80642 18 19358 07462 5 92538 22 39 38 48 21 12 73200 13 26800 80669 18 19331 07470 5 92530 21 20 40 7 38 40 4 21 20 9. 73219 13 10. 26781 9. 80697 19 10. 19303 10. 07478 5 9. 92522 41 38 32 21 28 73239 14 26761 80725 19 19275 07486 6 92514 19 42 38 24 21 36 73259 14 26741 80753 20 19247 07494 6 92506 18 43 38 16 21 44 73278 14 26722 80781 20 19219 07502 6 92498 17 44 38 8 21 52 73298 15 26702 80808 20 19192 07510 6 92490 16 15 45 7 38 4 22 9. 73318 15 10. 26682 9. 80836 21 10. 19164 10. 07518 6 9. 92482 46 37 52 22 8 73337 15 26663 80864 21 19136 07527 6 92473 14 47 37 44 22 16 73357 16 26643 80892 22 19108 07535 6 92465 13 48 37 36 22 24 73377 16 26623 80919 22 19081 07543 6 92457 12 49 37 28 22 32 73396 16 26604 80947 23 19053 07551 7 92449 11 10 50 7 37 20 4 22 40 9. 73416 17 10. 26584 9. 80975 23 10. 19025 10. 07559 7 9. 92441 51 37 12 22 48 73435 17 26565 81003 24 18997 07567 7 92433 9 52 37 4 22 56 73455 17 26545 81030 24 18970 07575 7 92425 8 53 36 56 23 4 73474 18 26526 81058 25 18942 07584 7 92416 7 54 36 48 23 12 73494 18 26506 81086 25 18914 07592 7 92408 6 55 7 36 40 4 23 20 9. 73513 18 10. 26487 9.81113 26 10. 18887 10. 07600 7 9. 92400 5 56 36 32 23 28 73533 19 26467 81141 26 18859 07608 8 92392 4 57 36 24 23 36 73552 19 26448 81169 26 18831 07616 8 92384 3 58 36 16 23 44 73572 19 26428 81196 27 18804 07624 8 92376 2 59 36 8 23 52 73591 20 26409 81224 27 18776 07633 8 92367 1 60 M. 36 24 73611 20 26389 81252 28 18748 07641 8 92359 Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 122° A A B B C C 67° 1 Seconds of time 1" 2' 8« 4' 5> 6- T Prop, parts of cols. ■{B Ic 2 3 1 6 7 2 7 10 3 10 14 4 12 17 6 15 21 6 17 24 7 TABLE 44. [Page 806 Log. Sines, Tangents, and Secants. 88« M. A A B B C C 1460 Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. DiflE. Cotangent. Secant. Diff. Cosine. M. 7 36 4 24 9. 73611 10. 26389 9. 81252 10. 18748 10. 07641 9. 92359 60 1 35 52 24 8 73630 26370 81279 18721 07649 92351 59 2 35 44 24 16 73660 1 26350 81307 1 18693 07657 92343 58 3 35 36 24 24 73669 1 26331 81335 1 18665 07665 92335 57 4 35 28 24 32 73689 1 26311 81362 2 18638 07674 92326 56 55 5 7 35 20 4 24 40 9. 73708 2 10. 26292 9. 81390 2 10. 18610 10. 07682 9. 92318 6 35 12 24 48 73727 2 26273 81418 3 18682 07690 92310 54 7 35 4 24 56 73747 2 26253 81445 3 18656 07698 92302 53 8 34 56 25 4 73766 3 26234 81473 4 18627 07707 92293 52 9 34 48 25 12 73785 3 26215 81500 4 18600 07715 92285 51 10 7 34 40 4 25 20 9. 73805 3 10. 26195 9. 81628 5 10. 18472 10. 07723 9. 92277 50 11 34 32 25 28 73824 3 26176 81556 5 18444 07731 2 92269 49 12 34 24 26 36 73843 4 26157 81583 5 18417 07740 2 92260 48 13 34 16 25 44 73863 4 26137 81611 6 18389 07748 2 92262 47 14 15 34 8 25 52 73882 4 26118 81638 6 18362 07756 2 92244 46 46 7 34 4 26 9. 73901 5 10. 26099 9. 81666 7 10. 18334 10. 07765 2 9. 92236 16 33 52 26 8 73921 6 26079 81693 7 18307 07773 2 92227 44 17 33 44 26 16 73940 6 26060 81721 8 18279 07781 2 92219 43 18 33 36 26 24 73959 6 26041 81748 8 18252 07789 3 92211 42 19 33 28 26 32 73978 6 26022 81776 9 9 18224 10. 18197 07798 3 92202 41 20 7 33 20 4 26 40 9. 73997 6 10. 26003 9. 81803 10. 07806 3 9.92194 40 21 33 12 26 48 74017 7 25983 81831 10 18169 07814 3 92186 39 22 33 4 26 56 74036 7 25964 81858 10 18142 07823 3 92177 38 23 32 56 27 4 74055 7 25946 81886 11 18114 07831 3 92169 37 24 32 48 27 12 74074 8 25926 81913 11 18087 07839 3 92161 36 25 7 32 40 4 27 20 9.74093 8 10. 25907 9. 81941 11 10. 18069 10. 07848 3 9. 92162 35 26 32 32 27 28 74113 8 26887 81968 12 18032 07856 4 92144 34 27 32 24 27 36 74132 9 25868 81996 12 18004 07864 4 92136 33 28 32 16 27 44 74151 9 25849 82023 13 17977 07873 4 92127 32 29 32 8 27 52 74170 9 25830 82051 13 17949 07881 4 92119 31 30 7 32 4 28 9. 74189 10 10.25811 9. 82078 14 10. 17922 10. 07889 4 9. 92111 30 31 31 52 28 8 74208 10 25792 82106 14 17894 07898 4 92102 29 32 31 44 28 16 74227 10 25773 82133 15 17867 07906 4 92094 28 33 31 36 28 24 74246 10 25764 82161 15 17839 07914 5 92086 27 34 31 28 28 32 74265 11 25735 82188 16 17812 07923 5 92077 26 35 7 31 20 4 28 40 9. 74284 11 10. 25716 9. 82215 16 10. 17786 10. 07931 5 9. 92069 26 36 31 12 28 48 74303 11 25697 82243 16 17757 07940 6 92060 24 37 31 4 28 56 74322 12 25678 82270 17. 17730 07948 5 92062 23 38 30 56 29 4 74341 12 25659 82298 17 17702 07966 5 92044 22 39 30 48 29 12 74360 12 25640 82325 18 17675 07965 5 92035 21 20 40 7 30 40 4 29 20 9. 74379 13 10. 25621 9. 82362 18 10. 17648 10. 07973 6 9. 92027 41 30 32 29 28 74398 13 25602 82380 19 17620 07982 6 92018 19 42 30 24 29 36 74417 13 25583 82407 19 17593 07990 6 92010 18 43 30 16 29 44 74436 14 25564 82436 20 17565 07998 6 92002 17 44 30 8 29 52 74455 14 25546 82462 20 17538 08007 6 91993 16 45 7 30 4 30 9. 74474 14 10. 26526 9. 82489 21 10.17511 10. 08016 6 9.91986 16 46 29 52 30 8 74493 15 26507 82617 21 17483 08024 6 91976 14 47 29 44 30 16 74512 15 25488 82644 22 17466 08032 7 91968 13 48 29 36 30 24 74531 15 25469 82671 22 17429 08041 7 91969 12 49 29 28 30 32 74549 16 25461 82599 22 17401 08049 7 91951 11 50 7 29 20 4 30 40 9. 74568 16 10. 25432 9. 82626 23 10. 17374 10. 08058 7 9. 91942 10 61 29 12 30 48 74587 16 25413 82653 23 17347 08066 7 91934 9 52 29 4 30 56 74606 17 26394 82681 24 17319 08075 7 91925 8 53 28 56 31 4 74625 17 25375 82708 24 17292 08083 7 91917 7 54 28 48 31 12 74644 17 25356 82735 25 17266 08092 8 91908 6 55 7 28 40 4 31 20 9. 74662 17 10. 25338 9. 82762 25 10.17238 10. 08100 8 9. 91900 5 56 28 32 31 28 74681 18 25319 82790 26 17210 08109 8 91891 4 57 28 24 31 36 74700 18 25300 82817 26 17183 08117 8 91883 3 58 28 16 31 44 74719 18 25281 82844 27 17166 08126 8 91874 2 59 28 8 31 52 74737 19 25263 82871 27 17129 08134 8 91866 1 60 28 32 74756 19 25244 82899 27 17101 08143 8 91867 M. Hour p. M. Hour A. M. Cosine. Difif. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 128= A A B B C C 66° 1 Seconds of time 1» 2» S< 4» S* 6' 7- Prop, parte of cols. ^B 2 3 1 5 7 2 7 10 3 10 14 4 12 17 6 14 21 6 17 24 7 Page 806] TABLE 44. Log. Sines, Tangents, and Secants. 840 A A B B C C 145° M. Hour A.M. Hoiir p. M. Sine. Difl. Cosecant Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 7 28 4 32 9. 74766 10. 25244 9. 82899 10. 17101 10. 08143 9. 91857 60 1 27 62 32 8 74775 25226 82926 17074 08161 91849 59 2 27 44 32 16 74794 1 26206 82953 1 17047 08160 91840 58 3 27 36 32 24 74812 1 26188 82980 1 17020 08168 91832 67 4 27 28 32 32 74831 1 26169 83008 2 16992 08177 91823 56 5 7 27 20 4 32 40 9. 74850 2 10. 26150 9. 83036 2 10. 16965 10. 08186 9. 91816 65 6 27 12 32 48 74868 2 25132 83062 3 16938 08194 91806 64 7 27 4 32 56 74887 2 26113 83089 3 16911 08202 91798 53 8 26 56 33 4 74906 2 26094 83117 4 16883 08211 91789 52 9 26 48 33 12 74924 3 25076 83144 4 16856 08219 91781 51 50 10 7 26 40 4 33 20 9. 74943 3 10. 25067 9. 83171 6 10. 16829 10. 08228 9. 91772 11 26 32 33 28 74961 3 25039 83198 6 16802 08237 2 91763 49 12 26 24 33 36 74980 4 25020 83225 5 16775 08246 2 91755 48 13 26 16 33 44 74999 4 25001 83262 6 16748 08264 2 91746 47 14 26 8 33 62 76017 4 24983 83280 6 16720 08262 2 91738 46 15 7 26 4 34 9. 75036 5 10. 24964 9. 83307 7 10. 16693 10. 08271 2 9. 91729 45 16 25 52 34 8 75054 5 24946 83334 7 16666 08280 2 91720 44 17 25 44 34 16 76073 6 24927 83361 8 16639 08288 2 91712 43 18 25 36 34 24 76091 6 24909 83388 8 16612 08297 3 91703 42 19 25 28 34 32 75110 6 24890 83416 9 16585 08306 3 91695 41 20 7 25 20 4 34 40 9. 75128 6 10. 24872 9. 83442 9 10. 16668 10. 08314 3 9. 91686 40 21 25 12 34 48 76147 6 24853 83470 9 16530 08323 3 91677 39 22 25 4 34 66 75166 7 24835 83497 10 16503 08331 3 91669 38 23 24 66 35 4 75184 7 24816 83524 10 16476 08340 3 91660 37 24 24 48 35 12 75202 7 24798 83661 11 16449 08349 3 91651 36 25 7 24 40 4 35 20 9. 75221 8 10. 24779 9. 83678 11 10. 16422 10. 08367 4 9. 91643 36 26 24 32 35 28 75239 8 24761 83606 12 16395 08366 4 91634 34 27 24 24 35 36 76268 8 24742 83632 12 16368 08376 4 91626 33 28 24 16 35 44 75276 9 24724 83659 13 16341 08383 4 91617 32 29 24 8 35 52 75294 9 24706 83686 13 16314 08392 4 91608 31 30 7 24 4 36 9. 76313 9 10. 24687 9. 83713 14 10. 16287 10. 08401 4 9. 91599 30 31 23 52 36 8 76331 9 24669 83740 14 16260 08409 4 91591 29 32 23 44 36 16 76350 10 24650 83768 14 16232 08418 5 91582 28 33 23 36 36 24 75368 10 24632 83795 15 16205 08427 6 91673 27 34 23 28 36 32 75386 10 24614 83822 15 16178 08436 5 91565 26 26 35 7 23 20 4 36 40 9. 75405 11 10. 24596 9. 83849 16 10. 16151 10. 08444 5 9. 91566 36 23 12 36 48 76423 11 24577 83876 16 16124 08453 6 91647 24 37 23 4 36 56 76441 11 24559 83903 17 16097 08462 5 91538 23 38 22 66 37 4 76459 12 24541 83930 17 16070 08470 5 91630 22 39 22 48 37 12 76478 12 24622 83967 18 16043 08479 6 91621 21 20 40 7 22 40 4 37 20 9. 76496 12 10. 24504 9. 83984 18 10. 16016 10. 08488 6 9. 91612 41 22 32 37 28 75514 13 24486 84011 18 15989 08496 6 91504 19 42 22 24 37 36 75533 13 24467 84038 19 16962 08505 6 91495 18 43 22 16 37 44 76661 13 24449 84065 19 15936 08514 6 91486 17 44 22 8 37 52 76669 13 24431 84092 20 15908 08523 6 91477 16 45 7 22 4 38 9. 75587 14 10. 24413 9. 84119 20 10. 15881 10. 08531 7 9. 91469 15 46 21 62 38 8 75605 14 24395 84146 21 15854 08540 7 91460 14 47 21 44 38 16 75624 14 24376 84173 21 15827 08549 7 91451 13 48 21 36 38 24 75642 15 24358 84200 22 16800 08558 7 91442 12 49 50 21 28 38 32 75660 15 16 24340 84227 22 16773 08567 7 91433 11 10 7 21 20 4 38 40 9. 75678 10. 24322 9. 84254 23 10. 16746 10. 08575 7 9. 91425 51 21 12 38 48 75696 16 24304 84280 23 15720 08584 7 91416 9 52 21 4 38 56 75714 16 24286 84307 23 15693 08693 8 91407 8 53 20 56 39 4 75733 16 24267 84334 24 15666 08602 8 91398 7 54 20 48 39 12 76751 17 24249 84361 24 16639 08611 8 91389 6 65 7 20 40 4 39 20 9. 76769 17 10. 24231 9. 84388 25 10. 16612 10. 08619 8 9. 91381 5 56 20 32 39 28 75787 17 24213 84415 25 16686 08628 8 91372 4 57 20 24 39 36 75806 17 24195 84442 26 15668 08637 8 91363 3 58 20 16 39 44 75823 18 24177 84469 26 15531 08646 8 91354 2 59 20 8 39 52 76841 18 24159 84496 27 15504 08655 9 91345 1 60 20 40 75859 18 24141 84523 27 15477 08664 9 91336 M. M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Difl. Tangent. Cosecant. Difl. Sine. ia4< t A A B B C C 66 1 Seconds of time !• «• S> 4^ 6' e* T fA Prop, parts of cols. B Ic 2 3 1 5 7 2 7 10 3 9 14 4 11 17 6 14 20 7 16 24 8 TABLE 4A. [Page 807 Log. Sines, Tangents, and Secants. 86<» ▲ A B B C C 144° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Diff. Cotangent. Secant. Dlfif. Cosine. M. 7 20 4 40 9. 75859 10. 24141 9. 84623 10. 15477 10. 08664 9. 91336 60 1 19 52 40 8 75877 24123 84660 15450 08672 91328 69 2 19 44 40 16 75895 1 24105 84576 1 15424 08681 91319 68 3 19 36 40 24 75913 1 24087 84603 1 16397 08690 91310 57 4 19 28 40 32 75931 1 24069 84630 2 16370 08699 91301 56 5 7 19 20 4 40 40 9. 75949 1 10. 24051 9.84657 2 10. 16343 10. 08708 9. 91292 55 6 19 12 40 48 75967 2 24033 84684 3 16316 08717 91283 54 7 19 4 40 56 75985 2 24015 84711 3 15289 08726 91274 53 8 18 56 41 4 76003 2 23997 84738 4 16262 08734 91266 52 9 18 48 41 12 76021 3 23979 84764 4 15236 08743 91257 51 10 7 18 40 4 41 20 9. 76039 3 10. 23961 9. 84791 4 10. 15209 10. 08752 2 9.91248 60 11 18 32 41 28 76067 3 23943 84818 5 15182 08761 2 91239 49 12 18 24 41 36 76075 4 23925 84845 5 15165 08770 2 91230 48 13 18 16 41 44 76093 4 23907 84872 6 15128 08779 2 91221 47 14 18 8 41 52 76111 4 23889 84899 6 15101 08788 2 2 91212 46 45 15 7 18 4 42 9. 76129 4 10. 23871 9.84925 7 10. 15075 10. 08797 9. 91203 16 17 52 42 8 76146 5 23854 84952 7 15048 08806 2 91194 44 17 17 44 42 16 76164 5 23836 84979 8 16021 08815 3 91186 43 18 17 36 42 24 76182 5 23818 85006 8 14994 08824 3 91176 42 19 20 17 28 42 32 76200 6 23800 85033 8 14967 10. 14941 08833 3 91167 9.91158 41 40 7 17 20 4 42 40 9. 76218 6 10. 23782 9. 85059 9 10.08842 3 21 17 12 42 48 76236 6 23764 86086 9 14914 08851 3 91149 39 22 17 4 42 56 76253 6 23747 86113 10 14887 08869 3 91141 38 23 16 56 43 4 76271 7 23729 85140 10 14860 08868 3 91132 37 24 25 16 48 43 12 76289 7 23711 85166 11 14834 08877 4 91123 36 7 16 40 4 43 20 9. 76307 7 10. 23693 9. 86193 11 10. 14807 10. 08886 4 9.91114 35 26 16 32 43 28 76324 8 23676 85220 12 14780 08896 4 91105 34 27 16 24 43 36 76342 8 23658 85247 12 14753 08904 4 91096 33 28 16 16 43 44 76360 8 23640 85273 12 14727 08913 4 91087 32 29 30 16 8 43 62 76378 9 23622 85300 13 14700 08922 4 91078 31 7 16 4 44 9. 76395 9 10. 23605 9. 85327 13 10. 14673 10. 08931 5 9. 91069 30 31 15 52 44 8 76413 9 23587 86364 14 14646 08940 5 91060 29 32 15 44 44 16 76431 9 23569 86380 14 14620 08949 5 91061 28 33 15 36 44 24 76448 10 23552 85407 16 14693 08968 5 91042 27 34 35 15 28 44 32 76466 10 23534 85434 15 14666 08967 5 91033 26 7 15 20 4 44 40 9. 76484 10 10. 23516 9.85460 16 10. 14640 10. 08977 5 9. 91023 25 36 15 12 44 48 76501 11 23499 85487 16 14513 08986 6 91014 24 37 15 4 44 56 76519 11 23481 85614 16 14486 08996 6 91006 23 38 14 66 45 4 76537 11 23463 86640 17 14460 09004 6 90996 22 39 14 48 45 12 76554 12 23446 85567 17 14433 09013 6 90987 9. 90978 21 20 40 7 14 40 4 45 20 9. 76572 12 10. 23428 9.85594 18 10. 14406 10. 09022 6 41 14 32 . 45 28 76590 12 23410 85620 18 14380 09031 6 90969 19 42 14 24 45 36 76607 12 23393 85647 19 14353 09040 6 90960 18 43 14 16 45 44 76625 13 23375 85674 19 14326 09049 6 90951 17 44 14 8 45 52 76642 13 23358 85700 20 14300 09058 7 90942 16 45 7 14 4 46 9.76660 13 10. 23340 9. 86727 20 10. 14273 10. 09067 7 9. 90933 15 46 13 52 46 8 76677 14 23323 86764 20 14246 09076 7 90924 14 47 13 44 46 16 76695 14 23305 85780 21 14220 09086 7 90915 13 48 13 36 46 24 76712 14 23288 85807 21 14193 09094 7 90906 12 49 13 28 46 32 76730 14 23270 85834 22 14166 09104 7 90896 11 50 7 13 20 4 46 40 9. 76747 15 10. 23253 9. 85860 22 10. 14140 10.09113 8 9. 90887 10 51 13 12 46 48 76765 15 23235 86887 23 14113 09122 8 90878 9 52 13 4 46 56 76782 15 23218 85913 23 14087 09131 8 90869 8 53 12 56 47 4 76800 16 23200 85940 24 14060 09140 8 90860 7 54 12 48 47 12 76817 16 23183 85967 24 14033 09149 8 8 90861 6 55 7 12 40 4 47 20 9. 76835 16 10. 23165 9. 85993 24 10. 14007 10. 09168 9. 90842 5 56 12 32 47 28 76852 17 23148 86020 25 13980 09168 8 90832 4 57 12 24 47 36 76870 17 23130 86046 26 13954 09177 9 90823 3 58 12 16 47 44 76887 17 23113 86073 26 13927 09186 9 90814 2 59 12 8 47 52 76904 17 23096 86100 26 13900 09195 9 90805 1 60 12 48 76922 18 23078 86126 27 13874 09204 9 90796 M. Hour p. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Diff. Tangent. Cosecant. Difl. Sine. M. 125° A A B B C C 64° 1 Seconds of time 1" 2» S* 4« 5- 6» 7» fA Prop, parts of cols.^JB 2 3 1 4 7 2 7 10 3 9 13 5 11 17 6 13 20 7 16 23 8 Page 808] TABLE 44. Log. Sines, Tan gents, and Secants. 86° A A B B C C 14S° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Difl. Cotangent. Secant. DifiE. Cosine. M. 7 12 4 48 9. 76922 10. 23078 9. 86126 10. 13874 10. 09204 9. 90796 60 1 11 52 48 8 76939 23061 86153 13847 09213 90787 59 2 11 44 48 16 76957 1 23043 86179 1 13821 09223 90777 58 3 11 36 48 24 76974 1 23026 86206 1 13794 09232 90768 57 4 11 28 48 32 76991 1 23009 86232 2 13768 09241 90759 56 55 5 7 11 20 4 48 40 9. 77009 1 10. 22991 9. 86259 2 10. 13741 10. 09250 9. 90750 6 11 12 48 48 77026 2 22974 86285 3 13715 09259 90741 54 7 11 4 48 56 77043 2 22957 86312 3 13688 09269 90731 53 8 10 56 49 4 77061 2 22939 86338 4 13662 09278 90722 52 9 10 10 48 49 12 77078 3 22922 10.22905 86365 4 13635 09287 90713 51 50 7 10 40 4 49 20 9. 77095 3 9. 66392 4 10. 13608 10. 09296 2 9. 90704 11 10 32 49 28 77112 3 22888 86418 5 13582 09306 2 90694 49 12 10 24 49 36 77130 3 22870 86445 5 13555 09316 2 90686 48 13 10 16 49 44 77147 4 22853 86471 6 13529 09324 2 90676 47 14 15 10 8 49 52 77164 4 22836 86498 6 13502 09333 2 90667 46 45 7 10 4 50 9. 77181 4 10. 22819 9. 86524 7 10. 13476 10. 09343 2 9. 90657 16 9 52 50 8 77199 5 22801 86551 7 13449 09352 2 90648 44 17 9 44 50 16 77216 5 22784 86577 7 13423 09361 3 90639 43 18 9 36 50 24 77233 5 22767 86603 8 13397 09370 3 90630 42 19 9 28 50 32 77250 5 22750 86630 8 13370 09380 3 90620 41 20 7 9 20 4 50 40 9. 77268 6 10. 22732 9. 86656 9 10. 13344 10. 09389 3 9. 90611 40 21 9 12 50 48 77285 6 22715 86683 9 13317 09398 3 90602 39 22 9 4 50 56 77302 6 22698 86709 10 13291 09408 3 90592 38 23 8 56 51 4 77319 7 22681 86736 10 13264 09417 4 90583 37 24 25 8 48 51 12 77336 7 22664 86762 11 13238 09426 4 90574 36 36 7 8 40 4 61 20 9. 77353 7 10. 22647 9. 86789 11 10. 13211 10. 09435 4 9. 90665 26 8 32 51 28 77370 7 22630 86815 11 13185 09446 4 90566 34 27 8 24 51 36 77387 8 22613 86842 12 13158 09454 4 90546 33 28 8 16 51 44 77405 8 22595 86868 12 13132 09463 4 90537 32 29 8 8 51 52 77422 8 9 22578 86894 13 13106 09473 6 90527 31 30 30 7 8 4 52 9. 77439 10. 22561 9. 86921 13 10. 13079 10. 09482 5 9. 90518 31 7 52 52 8 77456 9 22544 86947 14 13053 09491 6 90509 29 32 7 44 52 16 77473 9 22527 86974 14 13026 09601 6 90499 28 33 7 36 52 24 77490 9 22510 87000 16 13000 09510 5 90490 27 34 7 28 52 32 77507 10 22493 87027 16 12973 09520 5 90480 26 35 7 7 20 4 52 40 9. 77524 10 10. 22476 9. 87053 16 10. 12947 10. 09529 5 9. 90471 26 36 7 12 52 48 77541 10 22459 87079 16 12921 09538 6 90462 24 37 7 4 52 56 77558 11 22442 87106 16 12894 09548 6 90452 23 38 6 56 53 4 77575 11 22425 87132 17 12868 09567 6 90443 22 39 6 48 53 12 77592 11 22408 87158 17 12842 09566 6 90434 21 20 40 7 6 40 4 53 20 9. 77609 11 10. 22391 9. 87185 18 10. 12815 10. 09576 6 9. 90424 41 6 32 53 28 77626 12 22374 87211 18 12789 09685 6. 90416 19 42 6 24 53 36 77643 12 22357 87238 18 12762 09595 7 90405 18 43 6 16 53 44 77660 12 22340 87264 19 12736 09604 7 90396 17 44 6 8 63 52 77677 13 22323 87290 19 12710 09614 7 90386 16 45 7 6 4 54 9. 77694 13 10. 22306 9. 87317 20 10. 12683 10. 09623 7 9. 90377 15 46 5 52 54 8 77711 13 22289 87343 20 12667 09632 7 90368 14 47 5 44 54 16 77728 13 22272 87369 21 12631 09642 7 90358 13 48 5 36 54 24 77744 14 22256 87396 21 12604 09651 7 90349 12 49 5 28 54 32 77761 14 22239 87422 22 12678 09661 8 90339 11 10 50 7 5 20 4 54 40 9. 77778 14 10. 22222 9. 87448 22 10. 12552 10. 09670 8 9. 90330 51 5 12 54 48 77796 15 22205 87476 22 12625 09680 8 90320 9 52 5 4 54 56 77812 16 22188 87501 23 12499 09689 8 90311 8 53 4 56 55 4 77829 16 22171 87527 23 12473 09699 8 90301 7 54 4 48 55 12 77846 16 22154 87554 24 12446 09708 8 90292 9. 90282 6 5 55 7 440 4 55 20 9. 77862 16 10. 22138 9. 87580 24 10. 12420 10. 09718 9 56 4 32 55 28 77879 16 22121 87606 25 12394 09727 9 90273 4 57 4 24 55 36 77896 16 22104 87633 25 12367 09737 9 90263 3 58 4 16 55 44 77913 16 22087 87659 26 12341 09746 9 90264 2 59 4 8 55 52 77930 17 22070 87686 26 12316 09766 9 90244 1 60 4 56 77946 17 22054 87711 26 12289 09766 9 90235 M. Hour p. K. Hour A. M. Cosine. Difif. Secant. Cotangent. DiflF. Tangent. Cosecant. Difl. Sine. M. 126« A A B B C C 58° 1 Seconds of time 1» 2« 8' 4" &• 6> 7« Prop, parts of cols. ■{B Ic 2 3 1 4 7 2 6 10 4 9 13 6 11 17 6 13 20 7 16 28 8 -" TABLE 44. [Page 809 Log. Sines, Tangents, and Secants. 87° A A B B C C 142° M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 7 4 4 56 9. 77946 10. 22054 9. 87711 10. 12289 10. 09765 9. 90235 60 1 3 52 56 8 77963 22037 87738 12262 09775 90225 59 2 3 44 56 16 77980 1 22020 87764 1 12236 09784 90216 58 3 3 36 56 24 77997 1 22003 87790 1 12210 09794 90206 57 4 3 28 56 32 78013 1 21987 87817 2 12183 09803 90197 56 6 7 3 20 4 56 40 9. 78030 1 10. 21970 9. 87843 2 10. 12157 10. 09813 9. 90187 55 6 3 12 56 48 78047 2 21953 87869 3 12131 09822 90178 54 7 3 4 56 56 78063 2 21937 87895 3 12105 09832 90168 53 8 2 56 57 4 78080 2 21920 87922 3 12078 09841 90159 52 9 2 48 67 12 78097 2 21903 87948 4 12052 09851 90149 51 50 10 7 2 40 4 57 20 9. 78113 3 10. 21887 9. 87974 4 10. 12026 10. 09861 2 9. 90139 11 2 32 57 28 78130 3 21870 88000 5 12000 09870 2 90130 49 12 2 24 57 36 78147 3 21853 88027 5 11973 09880 2 90120 48 13 2 16 57 44 78163 4 21837 88053 6 11947 09889 2 90111 47 14 2 8 57 52 78180 4 21820 88079 9. 88105 6 7 11921 09899 2 90101 46 15 7 2 4 58 9. 78197 4 10. 21803 10. 11895 10. 09909 2 9.90091 45 16 1 52 58 8 78213 4 21787 88131 7 11869 09918 3 90082 44 17 1 44 58 16 78230 5 21770 88158 7 11842 09928 3 90072 43 18 1 36 58 24 78246 5 21754 88184 8 11816 09937 3 90063 42 19 1 28 58 32 78263 5 21737 88210 8 11790 09947 3 90053 41 40 20 7 1 20 4 58 40 9. 78280 5 10. 21720 9. 88236 9 10. 11764 10. 09957 3 9.90043 21 1 12 58 48 78296 6 21704 88262 9 11738 09966 3 90034 39 22 1 4 58 56 78313 6 21687 88289 10 11711 09976 4 90024 38 23 56 59 4 78329 6 21671 88315 10 11685 09986 4 90014 37 24 48 59 12 78346 7 21654 88341 10 11659 09995 4 90005 36 35 25 7 40 4 59 20 9. 78362 7 10. 21638 9. 88367 11 10. 11633 10. 10005 4 9. 89995 26 32 59 28 78379 7 21621 88393 11 11607 10015 4 89985 34 27 24 59 36 78395 7 21605 88420 12 11580 10024 4 89976 33 28 16 59 44 78412 8 21588 88446 12 11554 10034 5 89966 32 29 8 59 52 78428 8 21572 88472 13 11528 10044 5 89956 31 30 80 7 5 9.78445 8 10. 21555 9. 88498 13 10. 11502 10. 10053 5 9. 89947 31 6 59 52 8 78461 ^ 21539 88524 14 11476 10063 5 89937 29 32 59 44 16 78478 9 21522 88550 14 11450 10073 5 89927 28 33 59 36 24 78494 9 21506 88577 14 11423 10082 5 89918 27 34 59 28 32 78510 9 21490 88603 15 11397 10092 5 89908 26 25 35 6 59 20 5 40 9. 78527 10 10. 21473 9. 88629 15 10. 11371 10. 10102 6 9. 89898 36 59 12 48 78543 10 21457 88655 16 11345 10112 6 89888 24 37 59 4 56 78560 10 21440 88681 16 11319 10121 6 89879 23 38 58 56 1 4 78576 10 21424 88707 17 11293 10131 6 89869 22 39 40 58 48 1 12 78592 11 21408 88733 17 11267 10141 6 89859 21 6 58 40 5 1 20 9. 78609 11 10. 21391 9. 88759 17 10. 11241 10. 10151 6 9. 89849 20 41 58 32 1 28 78625 11 21375 88786 18 11214 10160 7 89840 19 42 58 24 1 36 78642 12 21358 88812 18 11188 10170 7 89830 18 43 58 16 1 44 78658 12 21342 88838 19 11162 10180 7 89820 17 44 45 58 8 1 52 78674 12 21326 88864 19 11136 10190 7 89810 9. 89801 16 15 6 58 5 2 9. 78691 12 10. 21309 9. 88890 20 10. 11110 10. 101y9 7 46 57 52 2 8 78707 13 21293 88916 20 11084 10209 7 89791 14 47 57 44 2 16 78723 13 21277 88942 20 11058 10219 8 89781 13 48 57 36 2 24 78739 13 21261 88968 21 11032 10229 8 89771 12 49 57 28 2 32 78756 13 21244 88994 21 11006 10239 8 89761 11 50 6 57 20 5 2 40 9. 78772 14 10. 21228 9. 89020 22 10. 10980 10. 10248 8 9. 89752 10 51 57 12 2 48 78788 14 21212 89046 22 10954 10258 8 89742 9 52 57 4 2 56 78805 14 21195 89073 23 10927 10268 8 89732 8 53 56 56 3 4 78821 15 21179 89099 23 10901 10278 9 89722 7 54 56 48 3 12 78837 15 21163 89125 24 10875 10288 9 89712 6 5 55 6 56 40 5 3 20 9. 78853 15 10. 21147 9. 89151 24 10. 10849 10. 10298 9 9. 89702 56 56 32 3 28 78869 15 21131 89177 24 10823 10307 9 89693 4 57 56 24 3 36 78886 16 21114 89203 25 10797 10317 9 89683 3 58 56 16 3 44 78902 16 21098 89229 25 10771 10327 9 89673 2 59 56 8 3 52 78918 16 21082 89255 26 10745 10337 10 89663 1 60 M. 56 4 78934 16 21066 89281 26 10719 10347 10 89653 M. Hour p. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. 127° A A B B C C 52° 1 Seconds of time !• 2- S- 4" 6' 6" 7» (A Prop, parts of cols.^B Ic 2 3 1 4 7 t 6 10 4 8 13 6 10 16 6 12 20 7 14 23 8 Page 810] TABLE 44. Log, Sines, Tangents, and Secants. 88° A A B B C C 141° M. Hour A.M. Hour P.M. Sine. DifE. Cosecant. Tangent. Diff. Cotangent. Secant. Difl. Cosine. M. 6 66 5 4 9. 78934 10. 21066 9. 89281 10. 10719 10. 10347 9. 89653 60 1 55 52 4 8 78950 21050 89307 10693 10357 89643 59 2 55 44 4 16 78967 1 21033 89333 1 10667 10367 89633 58 3 55 36 4 24 78983 1 21017 89359 1 10641 10376 89624 57 4 55 28 4 32 78999 1 1 21001 89385 2 10615 10386 89614 56 55 5 6 55 20 5 4 40 9. 79015 10. 20985 9. 89411 2 10. 10589 10. 10396 9. 89604 6 55 12 4 48 79031 2 20969 89437 3 10563 10406 89594 54 7 55 4 4 56 79047 2 20953 89463 3 10537 10416 89584 53 8 54 56 5 4 79063 2 20937 89489 3 10511 10426 89574 52 9 54 48 5 12 79079 2 20921 89515 4 10485 10436 2 89564 51 50 10 6 54 40 5 5 20 9. 79095 3 10. 20905 9. 89541 4 10. 10459 10. 10446 2 9. 89554 11 54 32 5 28 79111 3 20889 89567 5 10433 10456 2 89544 49 12 54 24 5 36 79128 3 20872 89593 5 10407 10466 2 89534 48 13 54 16 5 44 79144 3 20856 89619 6 10381 10476 2 89524 47 14 54 8 5 52 79160 4 20840 89645 6 10355 10486 2 89514 46 45 15 6 54 5 6 9. 79176 4 10. 20824 9. 89671 6 10. 10329 10. 10496 3 9. 89504 16 53 52 6 8 79192 4 20808 89697 7 10303 10505 3 89495 44 17 53 44 6 16 79208 5 20792 89723 7 10277 10515 3 89485 43 18 53 36 6 24 79224 5 20776 89749 8 10251 10525 3 89475 42 19 53 28 6 32 79240 5 20760 89775 8 10225 10535 3 89465 41 20 6 53 20 5 6 40 9. 79256 5 10. 20744 9. 89801 9 10. 10199 10. 10545 3 9. 89455 40 21 53 12 6 48 79272 6 20728 89827 9 10173 10555 4 89445 39 22 53 4 6 56 79288 6 20712 89853 10 10147 10565 4 89435 38 23 52 56 7 4 79304 6 20696 89879 10 10121 10575 4 89425 37 24 52 48 7 12 79319 6 7 20681 10. 20665 89905 10 10095 10585 4 89415 36 25 6 52 40 5 7 20 9. 79335 9. 89931 11 10. 10069 10. 10595 4 9. 89405 35 26 52 32 7 28 79351 7 20649 89957 11 10043 10605 4 89395 34 27 52 24 7 36 79367 7 20633 89983 12 10017 10615 5 89385 33 28 52 16 7 44 79383 7 20617 90009 12 09991 10625 5 89375 32 29 52 8 7 52 79399 8 20601 90035 13 09965 10636 5 89364 31 30 6 52 5 8 9. 79415 8 10. 20585 9. 90061 13 10. 09939 10. 10646 5 9. 89354 30 31 51 52 8 8 79431 8 20569 90086 13 . 09914 10656 5 89344 29 32 51 44 8 16 79447 8 20553 90112 14 09888 10666 5 89334 28 33 51 36 8 24 79463 9 20537 90138 14 09862 10676 6 89324 27 34 51 28 8 32 79478 9 20522 90164 15 09836 10686 6 89314 26 35 6 51 20 5 8 40 9. 79494 9 10. 20506 9. 90190 15 10. 09810 10. 10696 6 9. 89304 25 36 51 12 8 48 79510 10 . 20490 90216 16 09784 10706 6 89294 24 37 51 4 8 56 79526 10 20474 90242 16 09758 10716 6 89284 23 38 50 56 9 4 79542 10 20458 90268 16 09732 10726 6 89274 22 39 50 48 9 12 79558 10 20442 90294 17 09706 10736 7 89264 21 40 6 50 40 5 9 20 9. 79573 11 10. 20427 9. 90320 17 10. 09680 10. 10746 7 9. 89254 20 41 50 32 9 28 79589 11 20411 90346 18 09654 10756 7 89244 19 42 50 24 9 36 79605 11 20395 90371 18 09629 10767 7 89233 18 43 50 16 9 44 79621 11 20379 90397 19 09603 10777 7 89223 17 44 50 8 9 52 79636 12 20364 90423 .19 09577 10787 7 89213 16 15 45 6 50 6 10 9. 79652 12 10. 20348 9. 90449 19 10. 09551 10. 10797 8 9. 89203 46 49 52 10 8 79668 12 20332 90475 20 09525 10807 8 89193 14 47 49 44 10 16 79684 12 20316 90501 20 09499 10817 8 89183 13 48 49 36 10 24 79699 13 20301 90527 21 09473 10827 8 89173 12 49 49 28 10 32 79715 13 20285 90553 21 09447 10838 8 89162 11 50 6 49 20 5 10 40 9. 79731 13 10. 20269 9. 90578 22 10. 09422 10. 10848 8 9. 89152 10 51 49 12 10 48 79746 14 20254 90604 22 09396 10858 9 89142 9 52 49 4 10 56 79762 14 20238 90630 22 09370 10868 9 89132 8 53 48 56 11 4 79778 14 20222 90656 23 09344 10878 9 89122 7 54 48 48 11 12 79793 14 20207 90682 23 09318 10888 9 89112 6 5 55 6 48 40 5 11 20 9. 79809 15 10. 20191 9. 90708 24 10. 09292 10. 10899 9 9. 89101 56 48 32. 11 28 79825 15 20175 90734 24 09266 10909 9 89091 4 57 48 24 11 36 79840 15 20160 90759 25 09241 10919 10 89081 3 58 48 16 11 44 79856 15 20144 90785 25 09215 10929 10 89071 2 59 48 8 11 52 79872 16 20128 90811 26 09189 10940 10 89060 1 60 48 12 79887 16 20113 90837 26 09163 10950 10 89050 M. 1 Hour P.M. Hour A. M. Cosine. Biff. Secant. Cotangent. Die. Tangent. Cosecant. Diff. Sine. M. 128° A A B B C C 61° 1 Seconds of time !■ 2* 8> 4- 6* 6* 7« A Prop, parts of cols.'jB 2 3 1 4 6 3 6 10 4 8 13 6 10 16 6 12 19 8 14 23 9 r TABLE 44. [Page 811 Log. Sines, Tangents, and Secants. 80° JL A B B C C 140° M. Hour X. H. Hour p. M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 6 48 5 12 9. 79887 10. 20113 9. 90837 10. 09163 10. 10950 9.89050 60 1 47 52 12 8 79903 20097 90863 09137 10960 89040 59 2 47 44 12 16 79918 1 20082 90889 1 09111 10970 89030 58 3 47 36 12 24 79934 1 20066 90914 1 09086 10980 89020 57 4 5 47 28 6 47 20 12 32 5 12 40 79950 1 20050 10. 20035 90940 "9. 90966 2 09060 10991 89009 56 9. 79965 1 2 10. 09034 10. 11001 9. 88999 55 6 47 12 12 48 79981 2 20019 90992 3 09008 11011 88989 54 7 47 4 12 56 79996 2 20004 91018 3 08982 11022 88978 53 8 46 56 13 4 80012 2 19988 91043 3 08957 11032 88968 52 9 46 48 13 12 80027 2 19973 91069 4 08931 11042 2 88958 51 50 10 6 46 40 5 13 20 9. 80043 3 10. 19957 9. 91095 4 10. 08905 10. 11052 2 9. 88948 11 46 32 13 28 80058 3 19942 91121 5 08879 11063 2 88937 49 12 46 24 13 36 80074 3 19926 91147 5 08853 11073 2 88927 48 13 46 16 13 44 80089 3 19911 91172 6 08828 11083 2 88917 47 14 46 8 13 52 5 14 80105 4 19895 91198 6 08802 11094 2 88906 46 45 15 6 46 9. 80120 4 10. 19880 9. 91224 6 10. 08776 10. 11104 3 9. 88896 16 45 52 14 8 80136 4 19864 91250 7 08750 11114 3 88886 44 17 45 44 14 16 80151 4 19849 91276 7 08724 11125 3 88875 43 18 45 36 14 24 80166 5 19834 91301 8 08699 11135 3 88865 42 19 45 28 14 32 80182 9. 80197 5 19818 91327 8 08673 11145 3 88855 41 20 6 45 20 5 14 40 5 10. 19803 9. 91353 9 10. 08647 10. 11156 3 9.88844 40 21 45 12 14 48 80213 5 19787 91379 9 08621 11166 4 88834 39 22 45 4 14 56 80228 6 19772 91404 9 08596 11176 4 88824 38 23 44 56 15 4 80244 6 19756 91430 10 08570 11187 4 88813 37 24 25 44 48 15 12 80259 6 19741 91456 10 08544 11197 4 4 88803 9. 88793 36 35 6 44 40 5 15 20 9. 80274 6 10. 19726 9. 91482 11 10. 08518 10. 11207 26 44 32 15 28 80290 7 19710 91507 11 08493 11218 5 88782 34 27 44 24 15 36 80305 7 19695 91533 12 08467 11228 5 88772 33 28 44 16 15 44 80320 7 19680 91559 12 08441 11239 6 88761 32 29 44 8 15 52 80336 7 19664 91585 12 13 08415 11249 5 88751 31 30 6 44 5 16 9. 80351 8 10. 19649 9. 91610 10. 08390 10. 11259 5 9. 88741 30 31 43 52 16 8 80366 8 19634 91636 13 08364 11270 6 88730 29 32 43 44 16 16 80382 8 19618 91662 14 08338 11280 6 88720 28 33 43 36 16 24 80397 8 19603 91688 14 08312 11291 6 88709 27 34 43 28 16 32 80412 9.80428 9 19588 91713 15 08287 11301 6 88699 26 25 35 6 43 20 5 16 40 9 10. 19572 9. 91739 15 10. 08261 10. 11312 6 9. 88688 36 43 12 16 48 80443 9 19557 91765 15 08235 11322 6 88678 24 37 43 4 16 56 80458 9 19542 91791 16 08209 11332 6 88668 23 38 42 56 17 4 80473 10 19527 91816 16 08184 11343 7 88657 22 39 40 42 48 17 12 80489 10 10 19511 91842 9. 91868 17 08158 11353 7 88647 21 6 42 40 5 17 20 9. 80504 10. 19496 17 10. 08132 10. 11364 7 9. 88636 20 41 42 32 17 28 80519 10 19481 91893 18 08107 11374 7 88626 19 42 42 24 17 36 80534 11 . 19466 91919 18 08081 11385 7 88615 18 43 42 16 17 44 80550 11 19450 91945 18 08055 11395 7 88605 17 44 45 42 8 17 52 80565 9.80580 11 12 19435 91971 19 08029 11406 8 88594 16 15 6 42 5 18 10. 19420 9. 91996 19 10. 08004 10. 11416 8 9. 88584 46 41 52 18 8 80595 12 19405 92022 20 07978 11427 8 88573 14 47 41 44 18 16 80610 12 19390 92048 20 07952 11437 8 88563 13 48 41 36 18 24 80625 12 19375 92073 21 07927 11448 8 88552 12 49 50 41 28 18 32 5 18 40 80641 13 19359 92099 21 07901 11458 9 88542 11 10 6 41 20 9. 80656 13 10. 19344 9. 92125 21 10. 07875 10. 11469 9 9. 88531 51 41 12 18 48 80671 13 19329 92150 22 07850 11479 9 88521 9 52 41 4 18 56 80686 13 19314 92176 22 07824 11490 9 88510 8 53 40 56 19 4 80701 14 19299 92202 23 07798 11501 9 88499 7 54 40 48 19 12 80716 14 19284 92227 23 07773 11511 9 88489 6 5 55 6 40 40 5 19 20 9. 80731 14 10. 19269 9. 92253 24 10. 07747 10. 11522 10 9. 88478 56 40 32 19 28 80746 14 19254 92279 24 07721 11532 10 88468 4 57 40 24 19 36 80762 15 19238 92304 24 07696 11543 10 88457 3 58 40 16 19 44 80777 15 19223 92330 25 07670 11553 10 88447 2 59 40 8 19 52 80792 15 19208 92356 25 07644 11564 10 88436 1 60 40 20 80807 15 19193 92381 26 07619 11675 10 88425 M. Hour p. M. Hour A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 129° A A B B C C 50° 1 Seconds of time 1» 2" &' 4> 6> 6- 7- fA Prop, parts of cols.'jB Ic 2 3 1 4 6 3 6 10 4 8 13 6 10 16 7 12 19 8 13 23 9 21594°— 14- -44 Page 812] TABLE 44. Log. Sines, Tangents, and Secants. 40° A . A B B C C 189° M. Honr A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. DiflE. Cotangent. Secant. Diff. Cosine. M. 6 40 6 20 9. 80807 10. 19193 9. 92381 10. 07619 10. 11575 9. 88425 60 1 39 52 20 8 80822 19178 92407 07593 11585 88415 59 2 39 44 20 16 80837 19163 92433 1 07567 11596 88404 58 3 39 36 20 24 80852 1 19148 92458 1 07542 11606 88394 57 4 39 28 20 32 80867 1 19133 92484 2 07516 11617 88383 56 5 6 39 20 5 20 40 9. 80882 1 10. 19118 9. 92510 2 10. 07490 10. 11628 9. 88372 55 6 39 12 20 48 80897 1 19103 92535 3 07465 11638 88362 54 7 39 4 20 56 80912 2 19088 92561 3 07439 11649 88351 53 8 38 56 21 4 80927 2 19073 92587 3 07413 11660 88340 52 9 38 48 21 12 80942 2 19058 92612 4 07388 11670 2 88330 51 10 6 38 40 5 21 20 9. 80957 2 10. 19043 9. 92638 4 10. 07362 10. 11681 2 9. 88319 50 11 38 32 21 28 80972 3 19028 92663 5 07337 11692 2 88308 49 12 38 24 21 36 80987 3 19013 92689 5 07311 11702 2 88298 48 13 38 16 21 44 81002 3 18998 92715 6 07285 11713 2 88287 47 14 38 8 21 62 81017 3 18983 92740 6 07260 11724 3 88276 46 15 6 38 5 22 9. 81032 4 10. 18968 9. 92766 6 10. 07234 10. 11734 3 9. 88266 45 16 37 52 22 8 81047 4 18953 92792 7 07208 11745 3 88255 44 17 37 44 22 16 81061 4 18939 92817 7 07183 11756 3 88244 43 18 37 36 22 24 81076 4 18924 92843 8 07157 11766 3 88234 42 19 37 28 22 32 81091 5 18909 92868 8 07132 11777 3 88223 41 20 6 37 20 5 22 40 9. 81106 5 10. 18894 9. 92894 9 10. 07106 10. 11788 4 9. 88212 40 21 37 12 22 48 81121 5 18879 92920 9 07080 11799 4 88201 39 22 37 4 22 56 81136 6 18864 92945 9 07055 11809 4 88191 38 23 36 56 23 4 81151 6 18849 92971 10 07029 11820 4 88180 37 24 36 48 23 12 81166 6 18834 92996 10 07004 11831 4 88169 36 25 6 36 40 5 23 20 9. 81180 6 10. 18820 9. 93022 11 10. 06978 10. 11842 4 9. 88158 35 26 36 32 23 28 81195 6 18805 93048 11 06952 11852 5 88148 34 27 36 24 23 36 81210 7 18790 93073 12 06927 11863 5 88137 33 28 36 16 23 44 81225 7 18775 93099 12 06901 11874 5 88126 32 29 36 8 23 52 81240 7 18760 93124 12 06876 11885 5 88115 31 30 6 36 5 24 9. 81254 7 10. 18746 9. 93150 13 10. 06850 10. 11895 5 9. 88105 30 31 35 52 24 8 81269 8 18731 93175 13 06825 11906 6 88094 29 32 35 44 24 16 81284 8 18716 93201 14 06799 11917 6 88083 28 33 35 36 24 24 81299 8 18701 93227 14 06773 11928 6 88072 27 34 35 28 24 32 81314 8 18686 93252 14 06748 11939 6 88061 26 25 35 6 35 20 5 24 40 9. 81328 9 10. 18672 9. 93278 15 10. 06722 10. 11949 6 9.88051 36 35 12 24 48 81343 9 18657 93303 15 06697 11960 6 88040 24 37 35 4 24 56 81358 9 18642 93329 16 06671 11971 7 88029 23 38 34 56 25 4 81372 9 18628 93354 16 06646 11982 7 88018 22 39 40 34 48 25 12 81387 10 18613 93380 17 06620 11993 7 88007 21 6 34 40 5 25 20 9. 81402 10 10. 18598 9. 93406 17 10. 06594 10. 12004 7 9. 87996 20 41 34 32 25 28 81417 10 18583 93431 17 06569 12015 7 87985 19 42 34 24 25 36 81431 10 18569 93457 18 06543 12025 8 87975 18 43 34 16 25 44 81446 11 18554 93482 18 06518 12036 8 87964 17 44 34 8 25 52 81461 11 18539 93508 19 06492 12047 8 87953 16 45 6 34 5 26 9. 81475 11 10. 18525 9. 93533 19 10. 06467 10. 12058 8 9. 87942 15 46 33 52 26 8 81490 11 18510 93559 20 06441 12069 8 87931 14 47 33 44 26 16 81505 12 18495 93584 20 06416 12080 8 87920 13 48 33 36 26 24 81519 12 18481 93610 20 06390 12091 9 87909 12 49 33 28 26 32 81534 12 18466 93636 21 06364 12102 9 87898 9. 87887 11 10 50 6 33 20 5 26 40 9. 81549 12 10. 18451 9. 93661 21 10. 06339 10. 12113 9 51 33 12 26 48 81563 13 18437 93687 22 06313 12123 9 87877 9 52 33 4 26 56 81578 13 18422 93712 22 06288 12134 9 87866 8 53 32 56 27 4 81592 13 18408 93738 23 06262 12145 10 87855 7 54 32 48 27 12 81607 13 18393 93763 23 06237 12156 10 87844 6 55 6 32 40 5 27 20 9. 81622 14 10. 18378 9. 93789 23 10. 06211 10. 12167 10 9. 87833 5 56 32 32 27 28 81636 14 18364 93814 24 06186 12178 10 87822 4 57 32 24 27 36 81651 14 18349 93840 24 06160 12189 10 87811 3 58 32 16 27 44 81665 14 18335 93865 25 06135 12200 10 87800 2 59 32 8 27 52 81680 15 18320 93891 25 06109 12211 11 87789 1 60 32 28 81694 15 18306 93916 26 06084 12222 11 87778 M. Hour p. M. Hour A. M. Cosine. DiflE. Secant. Cotangent. Diff. Tangent. Cosecant. DiS. Sine. M. 180^ A A B B C C 49° 1 Seconds of time 1« 2« 8* 4< 6* 1 6> 1 1 ' A Prop, parts of cols. B C 2 8 1 4 6 3 6 7 10 13 4 6 9 16 7 11 19 8 13 22 9 TABLE 44. [Page 813 Log. Sines, Tangents, and Secants. il° A A B B C C 1880 M. Hour A. M. Hour p. M. Sine. Diff. Cosecant. Tangent. Difl. Cotangent. Secant. Difl. Cosine. M. 6 32 5 28 9. 81694 10. 18306 9. 93916 10.06084 10. 12222 9. 87778 ,60 1 31 52 28 8 81709 18291 93942 06058 12233 87767 69 2 31 44 28 16 81723 18277 93967 1 06033 12244 87756 58 3 31 36 28 24 81738 1 18262 93993 1 06007 12256 87746 57 4 31 28 28 32 81752 1 18248 94018 2 05982 12266 87734 56 55 5 6 31 20 5 28 40 9. 81767 1 10. 18233 9.94044 2 10. 05956 10. 12277 9. 87723 6 31 12 28 48 81781 1 18219 94069 3 05931 12288 87712 54 7 31 4 28 56 81796 2 18204 94095 3 05905 12299 87701 53 8 30 56 29 4 81810 2 18190 94120 3 05880 12310 87690 52 9 10 30 48 29 12 81825 2 18175 94146 4 05854 12321 2 87679 51 6 30 40 5 29 20 9. 81839 2 lO: 18161 9.94171 4 10. 05829 10. 12332 2 9. 87668 50 11 30 32 29 28 81854 3 18146 94197 5 05803 12343 2 87657 49 12 30 24 29 36 81868 3 18132 94222 5 06778 12364 2 87646 48 13 30 16 29 44 81882 3 18118 94248 6 05762 12366 2 87636 47 14 15 30 8 29 52 81897 3 18103 94273 6 05727 12376 3 87624 46 45 6 30 5 30 9. 81911 4 10. 18089 9. 94299 6 10. 05701 10. 12387 3 9. 87613 16 29 52 30 8 81926 4 18074 94324 7 05676 12399 3 87601 44 17 29 44 30 16 81940 4 18060 94350 7 05650 12410 3 87590 43 18 19 20 29 36 30 24 81955 4 18045 94375 8 05625 12421 3 87679 42 29 28 30 32 81969 5 18031 94401 8 06599 12432 87568 41 40 6 29 20 5 30 40 9. 81983 5 10. 18017 9.94426 8 10. 05574 10. 12443 9. 87557 21 29 12 30 48 81998 5 18002 94452 9 06548 12464 87546 39 22 29 4 30 56 82012 5 17988 94477 9 05523 12466 87536 38 23 28 56 31 4 82026 6 17974 94503 10 06497 12476 87524 37 24 28 48 31 12 82041 6 17959 94528 10 05472 12487 87613 36 35 25 6 28 40 6 31 20 9. 82055 6 10. 17945 9.94554 11 10.06446 10. 12499 5 9. 87501 26 28 32 31 28 82069 6 17931 94679 11 06421 12510 5 87490 34 27 28 24 31 36 82084 6 17916 94604 11 05396 12521 5 87479 33 28 28 16 31 44 82098 7 17902 94630 12 05370 12532 5 87468 32 29 28 8 31 52 82112 7 17888 94655 12 05346 12543 5 87457 31 30 30 6 28 5 32 9. 82126 7 10. 17874 9. 94681 13 10. 05319 10. 12554 6 9. 87446 31 27 52 32 8 82141 7 17859 94706 13 05294 12566 6 87434 29 32 27 44 32 16 82155 8 17845 94732 14 05268 12577 6 87423 28 33 27 36 32 24 82169 8 17831 94757 14 05243 12588 6 87412 27 34 35 27 28 32 32 82184 8 17816 94783 14 05217 12699 6 87401 26 6 27 20 5 32 40 9. 82198 8 10. 17802 9. 94808 15 10. 05192 10. 12610 7 9. 87390 25 36 27 12 32 48 82212 9 17788 94834 15 06166 12622 7 87378 24 37 27 4 32 56 82226 9 17774 94859 16 05141 12633 7 87367 23 38 26 56 33 4 82240 9 17760 94884 16 05116 12644 7 87356 22 39 40 26 48 33 12 82255 9 17745 94910 17 05090 12655 7 87345 21 20 6 26 40 6 33 20 9. 82269 10 10. 17731 9. 94936 17 10. 05066 10. 12666 7 9. 87334 41 26 32 33 28 82283 10 17717 94961 17 05039 12678 8 87322 19 42 26 24 33 36 82297 10 17703 94986 18 05014 12689 8 87311 18 43 26 16 33 44 82312 10 17689 95012 18 04988 12700 8 87300 17 44 45 26 8 33 52 82326 10 17674 95037 19 04963 12712 8 87288 16 15 6 26 5 34 9. 82340 11 10. 17660 9. 95062 19 10. 04938 10. 12723 8 9. 87277 46 25 52 34 8 82354 11 17646 95088 20 04912 12734 9 87266 14 47 25 44 34 16 82368 11 17632 95113 20 04887 12745 9 87255 13 48 25 36 34 24 82382 11 17618 95139 20 04861 12757 9 87243 12 49 25 28 34 32 82396 12 17604 95164 21 04836 12768 9 87232 11 10 50 6 25 20 5 34 40 9. 82410 12 10. 17590 9. 95190 21 10. 04810 10. 12779 9 9. 87221 51 25 12 34 48 82424 12 17576 95215 22 04785 12791 10 87209 9 52 25 4 34 56 82439 12 17561 95240 22 04760 12802 10 87198 8 53 24 56 35 4 82453 13 17547 95266 22 04734 12813 10 87187 7 54 24 48 35 12 82467 13 17533 95291 23 04709 12825 10 87175 6 55 6 24 40 5 35 20 9. 82481 13 10. 17519 9. 95317 23 10. 04683 10. 12836 10 9. 87164 5 56 24 32 35 28 82495 13 17505 95342 24 04658 12847 10 87153 4 57 24 24 35 36 82509 14 17491 95368 24 04632 12859 11 87141 3 58 24 16 35 44 82523 14 17477 95393 25 04607 12870 11 87130 2 59 24 8 35 52 82537 14 17463 95418 25 04582 12881 11 87119 1 60 M. 24 36 82551 14 17449 95444 25 04556 12893 11 87107 Hour p. M. Hour A. M. Cosine. Difl. Secant. Cotangent. Difl. Tangent. Cosecant. Difl. Sine. M. 181° A A B B C C 48*1 Seconds of time 1" 2" 3- 4' &• 6> 7« A Prop, parts of cols. B 2 3 2 4 6 8 6 10 4 7 13 6 9 16 7 11 19 8 12 22 10 Page 814] TABLE 44. Log. Bines, Tangents, and Secants. j 42° A A B B C C 187° 1 M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. DifE. Cotangent. Secant. Diff. Cosine. M. 6 24 5 36 9. 82551 10. 17449 9. 95444 10. 04566 10. 12893 9. 87107 60 1 23 52 36 8 82566 17435 95469 04531 12904 87096 59 2 23 44 36 16 82579 17421 95496 1 04505 12915 87085 58 3 23 36 36 24 82593 1 17407 95520 1 04480 12927 87073 57 4 5 23 28 36 32 82607 1 17393 95545 2 04455 12938 87062 9. 87050 56 55 6 23 20 5 36 40 9. 82621 1 10. 17379 9. 95671 2 10. 04429 10. 12960 6 23 12 36 48 82635 1 17366 95696 3 04404 12961 87039 54 7 23 4 36 56 82649 2 17351 96622 3 04378 12972 87028 53 8 22 56 37 4 82663 2 17337 96647 3 04353 12984 2 87016 52 9 22 48 37 12 82677 2 17323 96672 4 04328 12995 2 87005 51 60 10 6 22 40 5 37 20 9. 82691 2 10. 17309 9. 95698 4 10. 04302 10. 13007 2 9. 86993 11 22 32 37 28 82705 3 17295 95723 5 04277 13018 2 86982 49 12 22 24 37 36 82719 3 17281 95748 6 04252 13030 2 86970 48 13 22 16 37 44 82733 3 17267 96774 5 04226 13041 3 86959 47 14 22 8 37 52 82747 3 17263 95799 6 04201 13053 3 3 86947 46 45 15 6 22 5 38 9. 82761 3 10. 17239 9. 95825 6 10. 04175 10. 13064 9. 86936 16 21 52 38 8 82775 4 17226 95850 7 04160 13076 3 86924 44 17 21 44 38 16 82788 4 17212 95876 7 04125 13087 3 86913 43 18 21 36 38 24 82802 4 17198 95901 8 04099 13098 3 86902 42 19 20 21 28 38 32 82816 4 17184 95926 8 04074 13110 4 86890 41 6 21 20 6 38 40 9. 82830 5 10. 17170 9. 95952 8 10. 04048 10. 13121 4 9. 86879 40 21 21 12 38 48 82844 5 17166 95977 9 04023 13133 4 86867 39 22 21 4 38 56 82858 5 17142 96002 9 03998 13145 4 86855 38 23 20 56 39 4 82872 5 17128 96028 10 03972 13156 4 86844 37 24 20 48 39 12 82885 6 17115 96063 10 03947 13168 6 86832 36 35 25 6 20 40 5 39 20 9. 82899 6 10. 17101 9. 96078 11 10. 03922 10. 13179 6 9. 86821 26 20 32 39 28 82913 6 17087 96104 11 03896 13191 5 86809 34 27 20 24 39 36 82927 6 17073 96129 11 03871 13202 6 86798 33 28 20 16 39 44 82941 6 17069 96155 12 03845 13214 6 86786 32 29 30 20 8 39 52 82955 7 17046 10. 17032 96180 12 03820 13225 6 86776 31 30 6 20 5 40 9. 82968 7 9. 96205 13 10. 03795 10. 13237 6 9. 86763 31 19 52 40 8 82982 7 17018 96231 13 03769 13248 6 86762 29 32 19 44 40 16 82996 7 17004 96266 14 03744 13260 6 86740 28 33 19 36 40 24 83010 8 16990 96281 14 03719 13272 6 86728 27 34 19 28 40 32 83023 8 16977 96307 14 03693 13283 7 86717 26 36 6 19 20 5 40 40 9. 83037 8 10. 16963 9. 96332 15 10. 03668 10. 13296 7 9. 86706 25 36 19 12 40 48 83051 8 16949 96357 15 03643 13306 7 86694* 24 37 19 4 40 56 83065 8 16936 96383 16 03617 13318 7 86682 23 38 18 56 41 4 83078 9 16922 96408 16 03592 13330 7 86670 22 39 18 48 41 12 83092 9 16908 96433 16 03567 13341 8 86659 21 40 6 18 40 6 41 20 9. 83106 9 10. 16894 9.96459 17 10. 03541 10. 13353 8 9. 86647 20 41 18 32 41 28 83120 9 16880 96484 17 03616 13366 8 86635 19 42 18 24 41 36 83133 10 16867 96610 18 03490 13376 8 86624 18 43 18 16 41 44 83147 10 16853 96635 18 03466 13388 8 86612 17 44 45 18 8 41 52 83161 10 16839 96560 19 03440 13400 8 86600 16 15 6 18 5 42 9.83174 10 10. 16826 9. 96686 19 10. 03414 10. 13411 9 9. 86589 46 17 52 42 8 83188 11 16812 96611 19 03389 13423 9 86677 14 47 17 44 42 16 83202 11 16798 96636 20 03364 13436 9 86665 13 48 17 36 42 24 83215 11 16786 96662 20 03338 13446 9 86654 12 49 17 28 42 32 83229 11 16771 96687 21 21 03313 13458 9 10 86542 11 10 50 6 17 20 5 42 40 9. 83242 11 10. 16758 9. 96712 10. 03288 10. 13470 9. 86530 51 17 12 42 48 83266 12 16744 96738 22 03262 13482 10 86618 9 52 17 4 42 56 83270 12 16730 96763 22 03237 13493 10 86507 8 53 16 56 43 4 83283 12 16717 96788 22 03212 13606 10 86495 7 54 16 48 43 12 83297 12 16703 96814 23 03186 13617 10 86483 6 55 6 16 40 5 43 20 9. 83310 13 10. 16690 9. 96839 23 10.03161 10. 13528 11 9. 86472 5 66 16 32 43 28 83324 13 16676 96864 24 03136 13540 11 86460 4 57 16 24 43 36 83338 13 16662 96890 24 03110 13552 11 86448 3 58 16 16 43 44 83361 13 16649 96915 26 03086 13564 11 86436 2 59 16 8 43 52 83365 14 16636 96940 25 03060 13575 11 86425 1 60 16 44 83378 14 16622 96966 25 03034 13587 12 86413 M. Hour P.M. Hour A. M. Cosine. DifE. Secant. Cotangent. Did. Tangent. Cosecant. Diff. Sine. M. | 132 A A B B C C 4701 Seconds of time 1' 2« 3« 4« 6' 9 16 7 6" 7» Prop, parts of cols. < B ic 2 3 1 3 6 3 6 10 4 7 13 6 10 19 9 12 22 10 TABLE 44. [Page 816 Log. Sines, Tangents, and Secants. 4«o A A B B C C 186° M. Hour A. M. Hour P.M. Sine. Diff. Cosecant. Tangent. Diff. Cotangent. Secant. Diff. Cosine. M. 6 16 5 44 9. 83378 10. 16622 9. 96966 10. 03034 10. 13587 9. 86413 60 1 15 52 44 8 83392 16608 96991 03009 13599 86401 59 2 15 44 44 16 83405 16595 97016 1 02984 13611 86389 58 3 15 36 44 24 83419 1 16581 97042 1 02958 13623 86377 57 4 15 28 44 32 83432 1 16568 97067 2 02933 13634 86366 9. 86.354 56 55 5 6 15 20 5 44 40 9. 83446 1 10. 16554 9. 97092 2 10. 02908 10. 13646 6 15 12 44 48 83459 1 16541 97118 3 02882 13658 86342 54 7 15 4 44 56 83473 2 16527 97143 3 02857 13670 86330 53 8 14 56 45 4 83486 2 16514 97168 3 02832 13682 2 86318 52 9 14 48 45 12 83500 2 16500 97193 4 02807 13694 2 86306 51 50 10 6 14 40 5 45 20 9. 83513 2 10. 16487 9. 97219 4 10. 02781 10. 13705 2 9. 86295 11 14 32 45 28 83527 2 16473 97244 5 02756 13717 2 86283 49 12 14 24 45 36 83540 3 16460 97269 5 02731 13729 2 86271 48 13 14 16 45 44 83554 3 16446 97295 o 02705 13741 3 86259 47 14 14 8 45 52 83567 3 16433 97320 6 02680 13753 3 86247 46 15 6 14 6 46 9. 83581 3 10. 16419 9. 97345 6 10. 02655 10. 13765 3 9.86235 45 16 13 52 46 8 83594 4 16406 97371 7 02629 13777 3 86223 44 17 13 44 46 16 83608 4 16392 97396 7 02604 13789 3 86211 43 18 13 36 46 24 83621 4 16379 97421 8 02579 13800 4 86200 42 19 13 28 46 32 83634 4 16366 97447 8 02553 13812 4 86188 41 40 20 6 13 20 5 46 40 9, 83648 4 10. 16352 9. 97472 8 10. 02528 10. 13824 4 9. 86176 21 13 12 46 48 83661 5 16339 97497 9 02503 13836 4 86164 39 22 13 4 46 56 83674 5 16.326 97523 9 02477 . 13848 4 86152 38 23 12 56 47 4 83688 5 16312 97548 10 02452 13860 5 86140 37 24 12 48 47 12 83701 5 16299 97573 10 02427 13872 5 86128 36 25 6 12 40 5 47 20 9. 83715 6 10. 16285 9. 97598 11 10. 02402 10. 13884 5 9. 86116 35 26 12 32 47 28 83728 6 16272 97624 11 02376 13896 5 86104 34 27 12 24 47 36 83741 6 16259 97649 11 02351 13908 5 86092 33 28 12 16 47 44 83755 6 16245 97674 12 02326 13920 6 86080 32 29 12 8 47 52 83768 6 16232 97700 12 02300 13932 6 86068 31 30 30 6 12 5 48 9. 83781 7 10. 16219 9. 97725 13 10. 02275 10. 13944 6 9. 86056 31 11 52 48 8 83795 7 16205 97750 13 02250 13956 6 86044 29 32 11 44 48 16 83808 7 16192 97776 13 02224 13968 6 86032 28 33 11 36 48 24 83821 7 16179 97801 14 02199 13980 7 86020 27 34 11 28 48 32 83834 8 16166 97826 14 02174 13992 7 86008 26 35 6 11 20 5 48 40 9. 83848 8 10. 16152 9. 97851 15 10. 02149 10.14004 7 9. 85996 25 36 11 12 48 48 83861 8 16139 97877 15 02123 14016 7 85984 24 37 11 4 48 56 83874 8 16126 97902 16 02098 14028 7 85972 23 38 10 56 49 4 83887 8 16113 97927 16 02073 14040 8 85960 22 39 10 48 49 12 83901 9 16099 97953 16 02047 14052 8 85948 21 40 6 10 40 5 49 20 9. 83914 9 10. 16086 9. 97978 17 10. 02022 10. 14064 8 9. 85936 20 41 10 32 49 28 83927 9 16073 98003 17 01997 14076 8 85924 19 42 10 24 49 36 83940 9 16060 98029 18 01971 14088 8 8.5912 18 43 10 16 49 44 83954 10 . 16046 98054 18 01946 14100 9 85900 17 44 45 10 8 49 52 83967 10 16033 98079 19 01921 14112 9 85888 16 6 10 5 50 9. 83980 10 10. 16020 9. 98104 19 10. 01896 10. 14124 9 9. 85876 15 46 9 52 50 8 83993 10 16007 98130 19 01870 14136 9 85864 14 47 9 44 50 16 84006 10 15994 98155 20 01845 14149 9 85851 13 48 9 36 50 24 84020 11 15980 98180 20 01820 14161 10 85839 12 49 9 28 50 32 84033 11 15967 98206 21 01794 14173 10 85827 11 10 50 6 9 20 5 50 40 9. 84046 11 10. 15954 9. 98231 21 10. 01769 10. 14185 10 9. 85815 51 9 12 50 48 84059 11 15941 98256 22 01744 14197 10 85803 9 52 9 4 50 56 84072 12 15928 98281 22 01719 14209 10 85791 8 53 8 56 51 4 84085 12 15915 98307 22 01693 14221 11 85779 7 54 8 48 51 12 84098 12 15902 98332 23 01668 14234 11 85766 6 55 6 8 40 5 51 20 9.84112 12 10. 15888 9. 98357 23 10. 01643 10. 14246 11 9. 85754 5 56 8 32 51 28 84125 12 15875 98383 24 01617 14258 11 85742 4 57 8 24 51 36 84138 13 15862 98408 24 01592 14270 11 85730 3 58 8 16 51 44 84151 13 15849 98433 24 01567 14282 12 85718 2 59 8 8 51 52 84164 13 15836 98458 25 01542 14294 12 85706 1 60 8 52 84177 13 15823 98484 25 01516 14307 12 85693 M. Hour p. M. Hgur A. M. Cosine. Diff. Secant. Cotangent. Diff. Tangent. Cosecant. Diff. Sine. M. 188° A A B B C C 46° 1 Seconds of time 1> 2" 3' 4' fj» 6» 7' A Prop, parts of cols. B [0 2 3 2 3 5 7 6 9 13 3 i 6 6 8 16 8 10 19 9 12 22 11 Page 816] Log. TABLE 44. Sines, Tangents, and Secanta 440 A A B B C C 185° M. Hour A. M. Hour p. M. Sine. Difl. Cosecant. Tangent. Difl. Cotangent. Secant. Difl. Cosine. M. 60 6 8 5 52 9. 84177 10. 15823 9. 98484 10. 01516 10. 14307 9. 85693 1 7 52 52 8 84190 15810 98509 01491 14319 85681 59 2 7 44 52 16 84203 15797 98534 1 01466 14331 85669 58 3 7 36 52 24 84216 1 15784 98560 1 01440 14343 85657 57 4 7 28 52 32 84229 9. 84242 1 15771 98585 2 01415 14355 85645 56 5 6 7 20 5 52 40 1 10. 15758 9. 98610 2 10. 01390 10. 14368 9. 85632 55 6 7 12 52 48 84255 1 15745 98635 3 01365 14380 85620 54 7 7 4 52 56 84269 2 15731 98661 3 01339 14392 85608 53 8 6 56 53 4 84282 2 15718 98686 3 01314 14404 2 85596 52 9 6 48 53 12 84295 2 15705 98711 4 01289 14417 2 85583 51 10 6 6 40 5 53 20 9. 84308 2 10. 15692 9. 98737 4 10. 01263 10. 14429 2 9. 85571 50 11 6 32 53 28 84321 2 15679 98762 5 01238 14441 2 85559 49 12 6 24 53 36 84334 3 15666 98787 5 01213 14453 2 85547 48 13 6 16 53 44 84347 3 15653 98812 5 01188 14466 3 85534 47 14 6 8 53 52 84360 3 15640 98838 6 01162 14478 3 85522 46 15 6 6 5 54 9. 84373 3 10. 15627 9. 98863 6 10. 01137 10. 14490 3 9. 85510 45 16 5 52 54 8 84385 3 15615 98888 7 01112 14503 3 85497 44 17 5 44 54 16 84398 4 15602 98913 7 01087 14515 4 85485 43 18 5 36 54 24 84411 4 15589 98939 8 01061 14527 4 85473 42 19 5 28 54 32 84424 4 15576 98964 8 01036 14540 4 85460 41 40 20 6 5 20 5 54 40 9.84437 4 10. 15563 9. 98989 8 10. 01011 10. 14552 4 9. 85448 21 5 12 54 48 84450 5 15550 99015 9 00985 14564 4 85436 39 22 5 4 54 56 84463 5 15537 99040 9 00960 14577 5 85423 38 23 4 56 55 4 84476 5 15524 99065 10 00935 14589 5 85411 37 24 4 48 55 12 84489 5 15511 99090 10 00910 14601 5 85399 36 25 6 4 40 5 55 20 9. 84502 5 10. 15498 9.99116 11 10. 00884 10. 14614 5 9. 85386 35 26 4 32 55 28 84515 6 15485 99141 11 00859 14626 5 85374 34 27 4 24 55 36 84528 6 15472 99166 11 00834 14639 6 85361 33 28 4 16 55 44 84540 6 15460 99191 12 00809 14651 6 85349 32 29 4 8 55 52 84553 6 15447 99217 12 00783 14663 6 85337 31 30 30 6 4 5 56 9. 84566 6 10. 15434 9. 99242 13 10. 00758 10. 14676 6 9. 85324 31 3 52 56 8 84579 7 15421 99267 13 00733 14688 6 85312 29 32 3 44 56 16 84592 7 15408 99293 13 00707 14701 7 85299 28 33 3 36 56 24 84605 7 15395 99318 14 00682 14713 7 85287 27 34 3 28 56 32 84618 7 15382 99343 14 00657 14726 7 85274 26 25 35 6 3 20 5 56 40 9. 84630 8 10. 15370 9. 99368 15 10. 00632 10. 14738 7 9. 85262 36 3 12 56 48 84643 8 15357 99394 15 00606 14750 7 85250 24 37 3 4 56 56 84656 8 15344 99419 16 00581 14763 8 85237 23 38 2 56 57 4 84669 8 15331 99444 16 00556 14775 8 85225 22 39 2 48 57 12 84682 8 15318 99469 16 00531 14788 8 85212 21 20 40 6 2 40 5 57 20 9. 84694 9 10. 15306 9. 99495 17 10. 00505 10. 14800 8 9. 85200 41 2 32 57 28 84707 9 15293 99520 17 00480 14813 8 85187 19 42 2 24 57 36 84720 9 15280 99545 18 00455 14825 9 85175 18 43 2 16 57 44 84733 9 15267 99570 18 00430 14838 9 85162 17 44 2 8 57 52 84745 9 15255 99596 19 00404 14850 9 85150 16 15 45 6 2 5 58 9. 84758 10 10. 15242 9. 99621 19 10. 00379 10. 14863 9 9. 85137 46 1 52 58 8 84771 10 15229 99646 19 00354 14875 10 85125 14 47 1 44 58 16 84784 10 15216 99672 20 00328 14888 10 85112 13 48 1 36 58 24 84796 10 15204 99697 20 00303 14900 10 85100 12 49 1 28 58 32 84809 11 15191 99722 21 21 00278 10. 00253 14913 10 85087 11 10 50 6 1 20 5 58 40 9. 84822 11 10. 15178 9. 99747 10. 14926 10 9. 85074 51 1 12 58 48 84835 11 15165 99773 21 00227 14938 11 85062 9 52 1 4 58 56 84847 11 15153 99798 22 00202 14951 11 85049 8 53 56 59 4 84860 11 15140 99823 22 00177 14963 11 85037 7 54 48 59 12 84873 12 15127 99848 23 00152 14976 11 85024 6 5 55 6 40 5 59 20 9. 84885 12 10. 15115 9. 99874 23 10. 00126 10. 14988 11 9. 85012 56 32 59 28 84898 12 15102 99899 24 00101 15001 12 84999 4 57 24 59 36 84911 12 15089 99924 24 00076 15014 12 84986 3 58 16 59 44 84923 12 15077 99949 24 00051 15026 12 84974 2 59 8 69 52 84936 13 15064 99975 25 00025 15039 12 84961 1 60 6 84949 13 15051 10.00000 25 00000 15051 12 84949 M. Hour p. M. Hour A. H. Cosine. Difl. Secant. Cotangent. Difl. Tangent. Cosecant. Difl. Sine. M. 184° A A B B C C 46° 1 Seconds of time 1" 2' 8< 4- 5" 6" 7» fA Prop, parts of coIs.^B 2 3 2 3 6 3 5 5 6 13 6 8 16 8 10 19 9 11 22 11 TABLE 45. [Page 817 Haversines. 8 ' Oh 0»» 0° O' Oh 2m 0° 3(K Oh 4m 1° (K Oh em 1° 30^ 0h8m2°9^ s Log. Hav. Nat. Hav. Log. Hav. Nat Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat Hav. -00 0.00000 5.27963 0.00002 5.88168 0.00008 6.23385 0.00017 6.48371 0.00030 60 2 1.72333 .00000 .29399 .00002 .88889 .00008 .23866 .00017 .48732 .00031 58 4-\- 1 2.32539 .00000 .30811 .00002 .89604 .00008 .24345 .00018 .49092 .00031 56 6 2.67757 .00000 .32201 .00002 .90313 .00008 .24821 .00018 .49450 .00031 54 8+ 2 2.92745 0.00000 5.33569 0.00002 5.91016 0.00008 6.25294 0.00018 6.49807 0.00031 52 10 3.12127 .00000 .34916 .00002 .91714 .00008 .25765 .00018 .50162 .00032 50 12+ 3 3.27963 .00000 .36242 .00002 .92406 .00008 .26233 .00018 .50516 .00032 48 U 3.41353 .00000 .37548 .00002 .93093 .00009 .26699 .00018 .50868 .00032 46 16+ 4 3.52951 0.00000 5.38835 0.00002 5.93774 0.00009 6.27162 0.00019 6.51219 0.00033 44 18 3.63182 .00000 .40103 .00003 .94450 .00009 .27623 .00019 .51568 .00033 42 20+ 5 3.72333 .00000 .41352 .00003 .95121 .00009 .28081 .00019 .51916 .00033 40 22 3.80612 .00000 .42585 .00003 .95786 .00009 .28537 .00019 0.00019 .52263 .00033 38 24+ 6 3.88169 0.00000 5.43799 0.00003 5.96447 0.00009 6.28991 6.52608 0.00034 S6 26 3.95122 .00000 .44997 .00003 .97102 .00009 29442 .00020 .52952 .00034 S4 28+ 7 4.01559 .00000 .46179 .00003 .97753 .00010 .29891 .00020 .53295 .00034 32 SO 4.07551 .00000 .47345 .00003 .98399 .00010 .30337 .00020 .53636 .00034 SO 32+ 8 4.13157 0.00000 5.48496 0.00003 5.99040 0.00010 6.30781 0.00020 6.53976 0.00035 28 54 .18423 .00000 .49631 .00003 5.99676 .00010 .31223 .00021 .54315 .00035 26 56+ 9 .23388 .00000 .50752 .00003 6.00308 .00010 .31663 .00021 .54652 .00035 24 S8 .28084 .00000 .51858 .00003 .00935 .00010 .32101 .00021 0.00021 .54988 .00035 0.00036 22 20 40+10 4.32539 0.00000 5.52951 0.00003 6.01557 0.00010 6.32536 6.55323 42 .36777 .00000 .54030 .00003 .02176 .00011 .32969 .00021 .55656 .00036 18 44+n .40818 .00000 .55095 .00004 .02789 .00011 .33400 .00022 .55988 .00036 16 46 .44679 .00000 .56148 .00004 .03399 .00011 .33829 .00022 .56319 .00037 14 48+n 4.48375 0.00000 5.57189 0.00004 6.04004 0.00011 6.34256 0.00022 6.56649 0.00037 12 50 .51921 .00000 .58216 .00004 .04605 .00011 .34681 .00022 .56977 .00037 10 52+13 .55328 .00000 .59232 .00004 .05202 .00011 .35103 .00022 .57304 .00037 8 54 .58606 .00000 .60236 .00004 0.00004 .05795 .00011 0.00012 .35524 6.35943" .00023 .57630 '6.57955 .00038 6 66+U 4.61765 0.00000 5.61229 6.06384 0.00023 0.00038 4 58 4.64813 0.00000 5.62211 0.00004 6.06969 0.00012 6.36359 0.00023 6.58278 0.00038 2 2Sh 59m 2Sh 57m 2Sh 65m 23h 53m 2Sh 5im 8 ' 0+15 Oh im 0° (/ Oh Sm 0° 30^ Oh 5m 1° r Oh 7m 1° 30/ Oh gm 2° O' s 60 4.67757 0.00000 5.63181 0.00004 6.07550 0.00012 6.36774 0.00023 6.58600 0.00039 2 .70605 .00000 .64141 .00004 .08127 .00012 .37186 .00024 .58921 .00039 58 4+16 .73363 .00001 .65090 .00004 .08700 .00012 .37597 .00024 .59241 .00039 56 6 .76036 .00001 .66029 .00005 .09270 .00012 .38006 .00024 .59560 .00039 54 52 8+n 4.78629 0.00001 5.66958 0.00005 6.09836 0.00013 6.38412 0.00024 6.59878 0.00040 10 .81147 .00001 .67877 .00005 .10398 .00013 .38817 .00024 .60194 .00040 50 12+l'i .83594 .00001 .68787 .00005 .10956 .00013 .39220 .00025 .60509 .00040 48 14 .85973 .00001 .69687 .00005 .11511 .00013 .39622 .00025 .60823 .00041 46 16+19 4.88290 0.00001 5.70578 0.00005 6.12063 0.00013 6.40021 0.00025 6.61136 0.00041 U 18 .90546 .00001 .71460 .00005 .12611 .00013 .40418 .00025 .61448 .00041 42 20+%^ .92745 .00001 .72332 .00005 .13155 .00014 .40814 .00026 .61759 .00041 40 22 .94890 .00001 .73197 .00005 .13696 .OOOUj .41208 .00026 .62068 .00042 S8 36 24+21 4.96983 0.00001 5.74052 0.00006 6.14234 0.00014 6.41600 0.00026 6.62377 0.00042 26 4.99027 .00001 .74900 .00006 .14769 .00014 .41990 .00026 .62684 .00042 S4 28+22 5.01024 .00001 .75739 .00006 .15300 .00014 .42379 .00027 .62991 .00043 32 SO .02976 .00001 .76570 .00006 .15828 .00014 .42766 .00027 .63296 .00043 30 S2+23 5.04885 0.00001 5.77394 0.00006 6.16353 0.00015 6.43151 0.00027 6.63600 0.00043 28 S4 .06753 .00001 .78209 .00006 .16874 .00015 .43534 .00027 .63903 .00044 26 56+24 .08581 .00001 .79017 .00006 .17393 .00015 .43916 .00027 .64205 .00044 24 S8 .10372 .00001 .79818 .00006 .17908 .00015 .44296 .00028 .64504 .00044 22 40+25 5.12127 0.00001 5.80611 0.00006 6.18421 0.00015 6.44675 0.00028 6.64806 0.00044 20 42 .13847 .00001 .81397 .00007 .18930 .00015 .45052 .00028 .65105 .00045 18 44+26 .15534 .00001 .82176 .00007 .19437 .00016 .45427 .00028 .65403 .00045 16 46 .17188 .00001 .82948 .00007 .19940 .00016 .45800 .00029 .65700 .00045 14 48+21 5.18812 0.00002 5.83713 0.00007 6.20441 0.00016 6.46172 0.00029 6.65996 0.00046 12 50 .20406 .00002 .84472 .00007 .20938 .00016 .46543 .00029 .66291 .00046 10 62+2S .21971 .00002 .85224 .00007 .21433 .00016 .46911 .00029 .66585 .00046 8 54 .23508 .00002 .85969 .00007 .21925 .00017 .47279 6.47644 .00030 0.00030 .66878 .00047 6 4 66+29 5.25019 0.00002 5.86709 0.00007 6.22415 0.00017 6.67170 0.00047 68 .26503 .00002 .87442 .00008 .22901 .00017 .48008 .00030 .67461 .00047 2 60+30 5.27963 0.00002 5.88168 0.00008 6.23385 0.00017 6.48371 0.00030 6.67751 0.00048 2Sh 58m 23h 56m 2Sh 5pn 23h 52m 2Sh 50m Page 818] TABLE 45. Haversines. s OA lOm 2° 30' Oh 12m. 30 (y Oh 14m 3° 30^ Oh 16m 4° 0' Oh 18m 4° 30' s Log. Hav. Xat. Ilav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 6.67751 0.00048 6.83584 0.00069 6.96970 0.00093 7.08564 0.00122 7.18790 0.00154 60 2 .68040 .00048 .83825 .00069 .97176 .00094 .08745 .00122 .18950 .00155 58 4+ 1 .68328 .00048 .84065 .00069 .97382 .00094 .08925 .00123 .19111 .00155 56 6 .68615 .00049 .84304 .00070 .97588 .00095 .09105 .00123 .19271 .00156 54 8+ % 6.68901 0.00049 6.84543 0.00070 6.97793 0.00095 7.09284 0.00124 7.19430 0.00156 52 10 .69186 .00049 .84782 .00070 .97997 .00095 .09464 .00124 .19590 .00157 50 12+ 3 .69470 .00050 .85019 .00071 .98201 .00096 .09642 .00125 .19749 .00158 48 14 .69754 .00050 .85256 .00071 .98405 .00096 .09821 .00125 .19908 .00158 46 16+ i 6.70036 0.00050 6.85492 0.00072 6.98608 0.00097 7.09999 0.00126 7.20060 0.00159 44 18 .70318 .00050 .85728 .00072 .98811 .00097 .10177 .00126 .20225 .00159 42 20+ 5 .70598 .00051 .85963 .00072 .99013 .00098 .10354 .00127 .20383 .00160 40 22 .70878 .00051 .86197 .00073 .99214 .00098 .10531 .00127 .20540 .00160 38 24+ 6 6.71157 0.00051 6.86431 0.00073 6.99416 0.00099 7.10708 0.00128 7.20098 0.00161 36 26 .71435 .00052 .86664 .00074 6.99616 .00099 .10884 .00128 .20855 .00162 34 28+ 7 .71712 .00052 .86897 .00074 6.99817 .00100 .11060 .00129 .21012 .00163 32 SO .71988 .00052 .87129 .00074 7.00017 .00100 .11236 .00130 .21168 .00163 30 S2+ 8 6.72263 0.00053 6.87360 0.00075 7.00216 0.00101 7.11411 0.00130 7.21325 0.00163 28 S4 .72537 .00053 .87591 .00075 .00415 .00101 .11586 .00131 .21481 .00164 26 S6+ 9 .72811 .00053 .87821 .00076 .00613 .00101 .11760 .00131 .21636 .00165 24 S8 .73084 .00054 .88050 .00076 .00811 7.01009 .00102 .11934 .00132 .21792 .00165 22 20 40+10 6.73355 0.00054 6.88279 0.00076 0.00102 7.12108 0.00132 7.21947 0.00166 42 .73626 .00054 .88507 .00077 .01206 .00103 .12282 .00133 .22102 .00166 18 u+ti .73896 .00055 .88735 .00077 .01403 .00103 .12455 .00133 .22256 .00167 16 46 .74166 .00055 .88962 .00078 .01599 .00104 .12627 .00134 .22411 .00168 14 48+12 6.74434 0.00056 6.89188 0.00078 7.01795 0.00104 7.12800 0.00134 7.22565 0.00168 12 50 .74702 .00056 .89414 .00078 .01990 .00105 .12972 .00135 .22718 .00169 10 62+lS .74969 .00056 .89639 .00079 .02185 .00105 .13144 .00135 .22872 .00169 8 54 .75235 .00057 .89864 .00079 0.00080 .02379 .00106 .13315 .00136 .23025 7.23178 .00170 6 4 56 +U 6.75500 0.00057 6.90088 7.02573 0.00106 7.13486 0.00136 0.00171 58 6.75764 0.00057 6.90312 0.00080 7.02767 0.00107 7.13657 0.00137 7.23331 0.00171 2 23 k 59m 23 h 47m 23h 45m 23h 43m 23h 41m a ' 0+15 Oh 11m 3° 30^ Oh ism 3° 0' Oft 15m 3° 30' Oh 17m 4° 0' Oh 19m 4° 30' s 60 6.76028 0.00058 6.90535 0.00080 7.02960 0.00107 7.13827 0.00137 7.23483 0.00172 2 .76290 .00058 .90757 .00081 .03153 .00108 .13997 .00138 .23035 .00173 58 •4+16 .76552 .00058 .90979 .00081 .03345 .00108 .14167 .00139 .23787 .00173 56 6 .76814 .00059 .91200 .00082 .03537 00108 .14337 7.14500 .00139 .23939 .00174 54 8+Vi 6.77074 0.00059 6.91421 0.00082 7.03729 0.00109 0.00140 7.24090 0.00174 52 10 .77334 .00059 .91641 .00082 .03920 .00109 .14674 .00140 .24241 .00175 50 12+\& .77592 .00060 .91860 .00083 .04110 .00110 .14843 .00141 .24392 .00175 48 14 .77851 .00060 .92079 .00083 .04300 .00110 .15011 .00141 .24543 .00176 46 16+n 6.78108 0.00060 6.92298 0.00084 7.04490 0.00111 7.15179 0.00142 7.24093 0.00177 44 18 .78364 .00061 .92516 .00084 .04680 .00111 .15346 .00142 .24843 .00177 42 fO+20 .78620 .00061 .92733 .00085 .04809 .00112 .15513 .00143 .24993 .00178 40 22 .78875 .00061 .92950 6.93166 .00085 .05057 .00112 0.00113 .15680 .00143 .25143 .00178 38 24+21 6.79129 0.00062 0.00085 7.05245 7.15846 0.00144 7.25292 0.00179 36 26 .79383 .00062 .93382 .00086 .05433 .00113 .16013 .00145 .25441 .00180 34 28+22 .79630 .00063 .93597 .00086 .05620 .00114 .16178 .00145 .25590 .00180 32 30 .79888 .00063 .93812 .00087 .05807 .00114 .16344 .00146 .25738 .00181 30 32+2S 6.80139 0.00063 6.94026 0.00087 7.05994 0.00115 7.16509 0.00146 7.25886 0.00181 28 S4 .80390 .00064 .94239 .00088 .06180 .00115 .16674 .00147 .26034 .00182 26 S6+U .80640 .00064 .94453 .00088 .06366 .00116 .16839 .00147 .26182 .00183 24 38 .80889 .00064 .94665 .00088 .06551 .00116 .17003 .00148 .26330 .00183 22 20 40+25 6.81137 0.00065 6.94877 0.00089 7.06736 0.00117 7.17167 0.00148 7.26477 0.00184 42 .81385 .00065 .95089 .00089 .06920 .00117 .17331 .00149 .26624 .00185 18 44+26 .81632 .00066 .95300 .00090 .07105 .00118 .17494 .00150 .26771 .00185 16 46 .81879 .00060 .95510 .00090 .07288 .00118 .17657 .00150 .20917 .00186 14 48+21 6.82124 0.00066 6.95720 0.00091 7.07472 0.00119 7.17820 0.00151 7.27004 0.00186 12 50 .82369 .00067 .95930 .00091 .07655 .00119 .17982 .00151 .27210 .00187 10 52+2S .82614 .00067 .96139 .00091 .07837 .00120 .18144 .00152 .27355 .00188 8 54 .82857 .00067 .90347 .00092 0.00092 .08019 7.08201 .00120 .18306 .00152 0.00153 .27501 .00188 6 56+29 6.83100 0.00068 6.90555 0.00121 7.18468 7.27046 0.00189 4 58 .83342 .00068 .60763 .00093 .08383 .00121 .18029 .00154 .27791 .00190 2 60+30 6.83584 0.00069 6.96970 0.00093 7.08504 0.00122 7.18790 0.00154 7.27936 0.00190 23^48^ 23)^ 46 '« 23h 44m 2Sh 42m 23h40m TABLE 45. [Page 819 Haversines. s ' OA :20'» 5° 0' Oh 22^n 5° 30^ Oh 24"' 6° 0' Oh 26m 6° 30' Oh 28m 7° (K s Log. Ilav. Nat. Hav. Log. Ilav. Nat. Ilav. Log. Ilav. Nat. Ilav. Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. 2 4+ 1 6 7.27936 .28080 .28225 .28369 0.00190 .00191 .00192 .00192 0.00193 .00193 .00194 .00195 0.00195 .00196 .00197 .00197 0.00198 .00199 .00199 .00200 0.00201 .00201 .00202 .00203 7.36209 .36340 .36471 .36602 7.36733 .36864 .36994 .37124 7.37254 .37384 .37514 .37643 7.37773 .37902 .38030 .38159 7.38288 .38416 .38544 .38672 7.38800 .38927 .39054 .39182 7.39309 .39435 .39562 .39688 0.00230 .00231 .00233 .00333 0.00233 .00334 .00334 .00335 0.00336 .00237 .00337 .00338 0.00339 .00239 .00240 .00341 0.00341 .00343 .00343 .00244 0.00244 .00245 .00246 .00247 0.00247 .00248 .00249 .00249 0.00250 0.00251 7.43760 .43880 .44001 .44121 0.00274 .00275 .00275 .00276 7.50706 .50817 .50928 .51039 0.00321 .00322 .00323 .00324 7.57135 .57238 .57341 .57444 0.00373 .00374 .00374 .00375 60 58 56 54 52 50 48 46 U 42 40 38 8+ 2 10 12+ 3 14 16+ 4 18 20+ 5 22 7.28513 .28656 .28800 .28943 7.29086 .29228 .29371 .29513 7.44241 .44361 .44480 .44600 7.44719 .44838 .44957 .45076 0.00277 .00278 .00278 .00279 0.00280 .00281 .00282 .00282 0.00283 .00284 .00385 .00385 0.00386 .00287 .00288 .00289 0.00289 .00290 .00291 .00292 0.00392 .00293 .00294 .00295 7.51149 .51260 .51370 .51481 7.51591 .51701 .51811 .51921 7.52030 .52140 .52249 .52358 7.52467 .52576 .52685 .52794 7.52902 .53011 .35119 .53227 7.53335 .53443 .53550 .53658 0.00325 .00326 .00326 .00327 0.00328 .00329 .00330 .00331 0.00331 .00332 .00333 .00334 0.00335 .00336 .00336 .00337 0.00338 .00339 .00340 .00341 0.00341 .00342 .00343 .00344 0.00345 0.00346 7.57547 .75650 .57752 .57855 7.57957 .58060 .58162 .58264 7.58366 .58467 .58569 .58670 7.58772 .58873 .58974 .59075 0.00376 .00377 .00378 .00379 0.00380 .00381 .00383 .00383 24+ 6 26 28+ 7 30 32+ 8 34 36+ 9 38 7.29655 .29797 .29938 .30079 7.30220 .30361 .30502 .30642 7.45194 .45313 .45431 .45549 7.45667 .45785 .45903 .46020 7.46138 .46255 .46372 .46489 7.46605 .46722 .46838 .46955 0.00383 .00384 .00385 .00386 0.00387 .00388 .00389 .00390 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 40+10 42 44+11 46 4S+12 50 52+lZ 54 7.30782 .30922 .31062 .31201 7.31340 .31479 .31618 .31757 0.00203 .00204 .00204 .00205 0.00206 .00206 .00207 .00208 7.59176 .59277 .59378 .59478 7.59579 .59679 .59779 .59879 0.00391 .00392 .00392 .00393 0.00394 .00395 .00396 .00397 56+14 58 7.31895 7.32033 0.00208 0.00209 7.39815 7.39941 7.47071 7.47187 0.00396 0.00296 7.53766 7.53873 7.59979 7.60079 0.00398 0.00399 4 2 23^ 39"* 23 1^ 37 ri 23 h .?5"' 23 h 33 m 23h31m 8 ' 0+15 2 4+16 6 ^+17 io 12+lS 14 16+19 18 20+20 22 0Afi'»5°0" Oh 23^ 5° W Oh 25m 6° 0' Oh 27m 6° 30^ Oh 29m 7° 0" s 60 58 56 54 7.32171 .32309 .32446 ,32583 0.00210 .00210 .00211 .00212 7.40067 .40192 .40318 .40443 0.00252 .00252 .00353 .00254 0.00255 .00255 .00256 .00257 0.00257 .00258 .00259 .00260 7.47302 .47418 .47533 .47649 0.00297 .00298 .00299 .00300 7.53980 .54087 .54194 .54301 7.54407 .54514 .54620 .54727 7.54833 .54939 .55045 .55150 7.55256" .55361 .55467 .55572 7.55677 .55782 .55887 .55992 0.00347 .00347 .00348 .00349 0.00350 .00351 .00352 .00353 0.00353 .00354 .00355 .00356 0.00357 .00358 .00359 .00360 0.00360 .00361 .00362 .00363 0.00364 .00385 .00366 .00367 0.00367 .00368 .00369 .00370 7.60179 .60279 .60378 .60478 0.00400 .00401 .00403 .00403 0.00403 .00404 .00405 .00406 0.00407 .00408 .00409 .00410 7.32720 .32857 .32994 .33130 7.332G6 .33402 .33538 .33673 7.33809 .33944 .34079 .34213 7.34348 .34482 .34616 .34750 7.34884 .35017 .35150 .35283 7.35416 .35549 .35681 .35813 0.00212 .00213 .00214 .00214 0.00215 .00216 .00216 .00217 7.40568 .40693 .40818 .40943 7.41067 .41191 .41315 .41439 7.47764 .47879 .47994 .48109 7.48223 .48337 .48452 .48566 0.00300 .00301 .00302 .00303 0.00304 .00304 .00305 .00306 0.00307 .00308 .00308 .00309 0.00310 .00311 .00312 .00312 7.60577 .60676 .60775 .60874 7.60973 .61072 .61170 .61269 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 24+21 26 28+22 30 32+2Z 34 .S6+24 38 40+25 42 44+26 46 48+21 50 52+2S 54 0.00218 .00218 .00219 .00220 0.00221 .00231 .00222 .00223 7.41563 .41686 .41810 .41933 7.42056 .42179 .42301 .42424 0.00260 .00261 .00362 .00263 0.00263 .00264 .00265 .00266 7.48680 .48794 .48907 .49021 7.49134 .49247 .49360 .49473 7.49586 .49699 .49811 .49923 7.50036 .50148 .50259 .50371 7.61367 .61466 .61564 .61662 7.61760 .61858 .61955 .62053 0.00411 .00413 .00413 .00414 0.00415 .00416 .00416 .00417 0.00223 .00224 .00225 .00225 0.00226 .00227 .00227 .00228 7.42546 .42668 .42790 .42912 7.43034 .43155 .43277 .43398 0.00266 .00267 .00268 .00269 0.00369 .00370 .00371 .00272 0.00313 .00314 .00315 .00316 0.00316 .00317 .00318 .00319 7.56096 .56201 .56305 .56409 7.56513 .56617 .56721 .56825 7.62151 .62248 .62345 .62442 7.62540 .62636 .62733 .62830 0.00418 .00419 .00430 .00431 0.00433 .00423 .00424 .00435 20 18 16 14 12 10 8 6 56+29 58 60+30 7.35945 .36077 7.36209 0.00229 .00229 0.00230 7.43519 .43639 7.43760 0.00272 .00273 0.00274 7.50483 .50594 7.50706 0.00330 .00331 0.00331 7.56928 .57032 7.57135 0.00371 .00372 0.00373 7.62927 .63023 7,63120 0.00426 .00427 0.00428 4 2 23h 38^ 23h 36m 23 h 34m 23h 32m 23h 30m Page 820] TABLE 45. | Haversines. 1 s OMO^T'^SO' 1 0» 5;?™ 8° C Oh 34^ 8° 30^ 1 Oh 36m 9° (K 1 01^ 38m 9° W 1 3 Log. Hav. Nat. Hav. Ivog. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 7.63120 0.0042S 7.68717 0.00487 7.73974 0.00549 7.78929 0.00616 7.83615 0.00686 60 2 .63216 .00429 .68807 .00488 .74059 .00550 .79009 .00617 .83691 .00687 58 4+ 1 .63312 .00430 .68897 .00489 .74143 .00551 .79089 .00618 .83767 .00688 56 6 .63408 .00431 0.00432 .68987 .00490 .74228 .00552 .79169 .00619 .83842 .00689 54 8-\- 3 7.63504 7.69077 0.00491 7.74313 0.00554 7.79249 0.00620 7.83918 0.00691 52 10 .63600 .00433 .69167 .00492 .74398 .00555 .79329 .00621 .83994 .00692 50 12+ 3 .63696 .00433 .69257 .00493 .74482 .00556 .79409 .00622 .84070 .00693 48 U .63792 .00434 .69347 .00494 .74567 .00557 .79489 .00624 .84145 .00694 46 16+ 4 7.63887 0.00435 7.69437 0.00495 7.74651 0.00558 7.79568 0.00625 7.84221 0.00695 U 18 .63983 .00436 .69526 .00496 74735 .00559 .79648 .00626 .84296 .00697 42 20+ 5 .64078 .00437 .69616 .00497 .74819 .00560 .79728 .00627 .84372 .00698 40 22 .64173 .00438 .69705 .00498 .74904 .00561 .79807 .00628 .84447 .00699 38 24+ 6 7.64269 0.00439 7.69794 0.00499 7.74988 0.00562 7.79886 0.00629 7.84522 0.00700 36 26 .64364 .00440 .69883 .00500 .75072 .00563 .79966 .00630 .84597 .00701 34 28+ 7 .64458 .00441 .69972 .00501 .75155 .00564 .80045 .00632 .84672 .00703 32 50 .64553 .00442 .70061 .00502 .75239 .00565 .80124 .00633 .84747 .00704 SO 32+ 8 7.64648 0.00443 7.70150 0.00503 7.75323 0.00567 7.80203 0.00634 7.84822 0.00705 28 54 .64743 .00444 .70239 .00504 .75407 .00568 .80282 .00635 .84897 .00706 26 56+ 9 .64837 .00445 .70328 .00505 .75490 .00569 .80361 .00636 .84972 .00707 24 S8 .64932 .00446 .70416 .00506 .75574 .00570 .80440 .00637 0.00639 .85047 .00709 22 40+10 7.65026 0.00447 7.70505 0.00507 7.75657 0.00571 7.80519 7.85122 0.00710 20 42 .65120 .00448 .70593 .00508 .75740 .00572 .80598 .00640 .85196 .00711 18 44+11 .65214 .00449 .70682 .00509 .75824 .00573 .80677 .00641 .85271 .00712 16 46 .65308 .00450 .70770 .00510 .75907 .00574 .80755 .00642 .85346 .00714 14 48+n 7.65402 0.00451 7.70858 0.00511 7.75990 0.00575 7.80834 0.00643 7.85420 0.00715 12 50 .65496 .00452 .70946 .00512 .76073 .00576 .80912 .00644 .85494 .00716 10 52+lZ .65590 .00453 .71034 .00513 .76156 .00578 .80991 .00646 .85569 .00717 8 54 .65683 .00454 .71122 .00514 .76239 .00579 .81069 7.81147 .00647 .85643 .00719 6 56+14 7.65777 0.00455 7.71210 0.00515 7.76321 0.00580 0.00648 7.85717 0.00720 4 58 7.65870 0.00456 7.71298 0.00516 7.76404 0.00581 7.81225 0.00649 7.85791 0.00721 2 23h 29^ 2Sh 27'^ 23 h 25m 2Sh 23m 23h 21m 8 ' 0+15 Oh Sim 7° 30' Oh ssm 8° O' OA S5m 8° 30" Oh 37m 9° 0' Oh 39m 9° 30' s 60 7.65964 0.00457 7.71385 0.00517 7.76487 0.00582 7.81303 0.00650 7.85866 0.00722 f .66057 .00458 .71473 .00518 .76669 .00583 .81382 .00651 .85940 .00723 58 4+16 .66150 .00459 .71560 .00520 .76652 .00584 .81459 .00653 .86014 .00725 56 6 .66243 .00460 .71648 .00521 .76734 .00585 .81537 7.81615 .00654 .86087 .00726 0.00727 54 52 5+17 7.66336 0.00461 7.71735 0.00522 7.76816 0.00586 0.00655 7.86161 io .66429 .00462 .71822 .00523 .76898 .00587 .81693 .00656 .86235 .00728 50 1^+18 .66521 .00463 .71909 .00524 .76981 .00589 .81771 .00657 .86309 .00730 48 14 .66614 .00464 .71996 .00525 .77063 .00590 .81848 .00658 .86382 .00731 46 16+19 7.66706 0.00465 7.72083 0.00526 7.77145 0.00591 7.81926 0.00860 7.86456 0.00732 44 18 .66799 .00466 .72170 .00527 .77227 .00592 .82003 .00661 .86530 .00733 42 20+20 .66891 .00467 .72257 .00528 .77308 .00593 .82081 .00662 .86603 .00735 40 22 .66983 .00468 .72343 .00529 .77390 .00594 0.00595 .82158 7.82235 .00663 .86676 .00736 0.00737 38 36 24+n 7.67075 0.00469 7.72430 0.00530 7.77472 0.00664 7.86750 26 .67167 .00470 .72516 .00531 .77553 .00596 .82313 .00665 .86823 .00738 34 28+22 .67259 .00471 .72603 .00532 .77635 .00598 .82390 .00667 .86896 .00740 32 SO .67351 .00472 .72689 .00533 .77716 .00599 .82467 .00668 .86969 .00741 SO S2+23 7.67443 0.00473 7.72775 0.00534 7.77798 0.00600 7.82544 0.00669 7.87042 0.00742 28 84 .67535 .00474 .72861 .00535 .77879 .00601 .82621 .00670 .87115 .00743 26 56+34 .67626 .00475 .72948 .00536 .77960 .00602 .82698 .00671 .87188 .00745 24 88 .67718 .00476 .73034 .00537 .78041 .00603 .82774 .00673 .87261 .00746 22 40+26 7.67809 0.00477 7.73119 0.00539 7.78122 0.00604 7.82851 0.00674 7.87334 0.00747 20 42 .67900 .00478 .73205 .00540 .78203 .00605 .82928 .00675 .87407 .00748 18 44+20 .67991 .00479 .73291 .00541 .78284 .00607 .83004 .00676 .87480 .00750 16 46 .68082 .00480 .73377 .00542 .78365 .00608 .83081 .00677 .87552 .00751 14 48+21 7.68173 0.00481 7.73462 0.00543 7.78446 0.00609 7.83157 0.00679 7.87625 0.00752 12 50 .68264 .00482 .73548 .00544 .78526 .00610 .83234 .00680 .87697 .00753 10 52+29, .68355 .00483 .73633 .00545 .78607 .00611 .83310 .00681 .87770 .00755 8 54 .68445 .00484 .73718 .00546 .78688 .00612 .83386 .00682 .87842 .00756 6 56+29 7.68536 0.00485 7.73803 0.00547 7.78768 0.00613 7.83463 0.00683 7.87915 0.00757 4 58 .68627 .00486 .73889 .00548 .78848 .00614 .83539 .00685 .87987 .00758 2 60+30 7.68717 0.00487 7.73974 0.00549 7.78929 0.00616 7.83615 0.00686 7.88059 0.00760 23h 28r^ 2Sh 26m 23 h 24^ 23h 22m 23 h 20m TABLE 45. [Page 821 Haversines. s ' Qh 40in 10° 0" Oh 42m 10° 30^ Oh 44m u° 0" Ok .^e™ 11° SO' 1 Oh 4smia°o' 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 2 4+ 1 6 7.88059 .88131 .88203 .88276 0.00760 .00761 .00762 .00763 7.92286 .92354 .92423 .92492 0.00837 .00839 .00840 .00841 0.00843 .00844 .00845 .00847 0.00848 .00849 .00851 .00852 7.96315 .96380 .96446 .96511 0.00919 .00920 .00921 .00923 0.00924 .00926 .00927 .00928 0.00930 .00931 .00933 .00934 0.00935 .00937 .00938 .00940 0.00941 .00942 .00944 .00945 8.00163 .00226 .00289 .00351 0.01004 .01005 .01007 .01008 0.01010 .01011 .01012 .01014 0.01015 .01017 .01018 .01020 0.01021 .01023 .01024 .01026 0.01027 .01029 .01030 .01032 8.03847 .03907 .03967 .04027 8.04087 .04147 .04207 .04267 8.04326 .04386 .04446 .04506 0.01093 .01094 .01096 .01097 0.01099 .01100 .01102 .01103 0.01105 .01106 .01108 .01109 60 58 56 54 52 50 48 46 44 42 40 38 8+ 2 10 12+ 3 14 16+ 4 18 20+ 6 22 7.88348 .88419 .88491 .88563 7.88635 .88707 88778 .88850 0.00765 .00766 .00767 .0076S 0.00770 .00771 .00772 .00774 0.00775 .00776 .00777 .00779 0.00780 .00781 .00783 .00784 0.00785 .00786 .00788 .00789 0.00790 .00792 .00793 .00794 7.92560 .92629 .92697 .92766 7.92834 .92902 .92970 .93039 7.93107 .93175 .93243 .93311 7.93379 .93447 .93514 .93582 7.96577 .96642 .96707 .96773 7.96838 .96903 .96968 .97033 8.00414 .00476 .00539 .00601 8.00664 .00726 .00788 .00851 8.00913" .00975 .01037 .01099 8.01161 .01223 .01285 .01347 8:01469 .01471 .01532 .01594 8.01656 .01717 .01779 .01840 8.01902 8.01963 24+ 6 26 28+ 7 SO 32+ 8 34 36+ 9 38 7.88921 .88993 .89064 .89135 7.89207 .89278 .89349 .89420 0.00853 .00855 .00856 .60857 0.00859 .00860 .00861 .00863 7.97098 .97163 .97228 .97293 7.97358 .97423 .97478 .97552 8.04565 .04625 .04684 .04744 8.04803 .04863 .04922 .04981 0.01111 .01112 .01114 .01115 0.01117 .01118 .01120 .01122 0.01123 .01125 .01126 .01128 0.01129 .01131 .01132 .01134 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 40+19 42 U+11 46 48+12 50 52+lZ 54 7.89491 .89562 .89633 .89704 7.89775 .89846 .89916 .89987 7.93650 .93717 .93785 .93852 7.93920 .93987 .94055 .94122 0.00864 .00865 .00867 .00888 0.00869 .00871 .00872 .00873 0.00875 0.00876 7.97617 .97681 .97746 .97810 7.97875 .97939 .98003 .98068 0.00947 .00948 .00949 .00951 0.00952 .00954 .00955 .00956 0.01033 .01034 .01036 .01037 0.01039 .01040 .01042 .01043 0.01045 0.01046 8.05041 .05100 .05159 .05218 8.05277 .05336 .05395 .05454 56+U 58 7.90057 7.90128 0.00795 0.00797 7.94189 7.94257 7.98132 7.98196 0.00958 0.00959 8.05513 8.05572 0.01135 0.01137 4 2 231^ 19m 23h nm 23h 15m 2Sh ISm 2Sh 11m 6 ' 0+15 2 4+10 6 Oft 4-?™ 10° O' OA 43^ 10° 30' Oh 45m 11° 0' Oh 47m 11° 30' Oh 49m 12° O' s 60 58 56 54 52 50 48 46 44 42 40 38 7.90198 .90269 .90339 .90409 0.00798 .00799 .00801 .00802 7.94324 .94391 .94458 .94525 0.00877 .00879 .00880 .00882 7.98260 .98325 .98389 .98453 0.00961 .00962 .00964 .00965 8.02025 .02086 .02148 .02209 8.02270 .02331 .02392 .02453 8.02515 .02576 .02637 .02697 0.01048 .01049 .01051 .01052 8.05631 .05690 .05749 .05808 0.01138 .01140 .01142 .01143 0.01145 .01146 .01148 .01149 0.01151 .01152 .01154 .01155 8+n 10 12+18 14 16+19 18 20+20 22 7.90480 .90550 .90620 .90690 7.90760 .90830 .90900 .90970 0.00803 .00804 .00806 .00807 0.00808 .00810 .00811 .00812 7.94592 .94659 .94726 .94792 7.94859 .94926 .94992 .95059 0.00883 .00884 .00886 .00887 0.00888 .00890 .00891 .00892 7.98517 .98581 .98644 .98708 7.98772 .98836 .98899 .98963 0.00966 .00968 .00969 .00971 0.00972 .00974 .00975 .00976 0.01054 .01055 .01057 .01058 0.01060 .01061 .01063 .01664 8.05866 .05925 .05984 .06042 8.06101 .06159 .06218 .06276 24+21 26 28+22 SO S2+2Z 34 36+24 38 7.91039 .91109 .91179 .91248 7.91318 .91387 .91457 .91526 0.00814 .00815 .00816 .00817 0.00819 .00820 .00821 .00823 7.95126 .95192 .95259 .95325 7.95391 .95458 .95524 .95590 0.00894 .00895 .00897 .00898 0.00899 .00901 .00902 .00903 7.99027 99090 .99154 .99217 7.99281 .99344 .99407 .99470 0.00978 .00979 .00981 .00982 0.00984 .06985 .00886 .00888 8.02758 .02819 .02880 .02941 8.03001 .03062 .03123 .03183 0.01066 .01087 .01089 .01070 0.01072 .01073 .01075 .01076 8.06335 .06393 .06451 .06510 8.06568 .06626 .06684 .06742 0.01157 .01159 .01160 .01162 0.01163 .01165 .01166 .01168 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 40+25 42 44+20 46 48+21 50 52+28 54 7.91596 .91665 .91734 .91803 7.91872 .91941 .92010 .92079 0.00824 .00825 .00827 .00828 0.00829 .00831 .00832 .00833 7.95656 .95722 .95788 .95854 7.95920 .95986 .96052 .96118 0.00905 .00906 .00908 .00909 0.00910 .00912 .00913 .00914 7.99534 .99597 .99660 .99723 7.99786 .99849 .99912 7.99975 0.00989 .00991 .00992 .00994 0.00995 .00997 .00898 .00999 8.03244 .03304 .03365 .03425 8.03486 .03546 .03606 .03666 0.01078 .01079 .01081 .01082 0.01084 .01085 .01087 .01088 8.06800 .06859 .06917 .06975 8.07032 .07090 .07148 .07206 0.01170 .01171 .01173 .01174 0.01176 .01177 .01179 .01180 0.01182 .01184 0.01185 56+219 58 60+30 7.92148 .92217 7.92286 0.00835 .00836 0.00837 7.96183 .96249 7.96315 0.00916 .00917 0.00919 8.00038 .00100 8.00163 0.01001 .01002 0.01004 8.03727 .03787 8.03847 0.01090 .01091 0.01093 8.07264 .07322 8.07379 4 2 2Sh 18'n 23h 16^ 23h 14m 2S>^ 12m 2St^ lOrn Page 822] TABLE 45. | Haversines. 1 s Oft 60r» 12° 3(K Oh 52m 13° 0' Oh 54^ 13° 30^ Oh 56m 14° 0' Oh 68r<^ 14° 30^ s Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 8.07379 0.01185 8.10772 0.01282 8.14035 0.01382 8.17179 0.01485 8.20211 0.01593 60 2 .07437 .01187 .10827 .01283 .14089 .01383 .17230 .01487 .20261 .01594 58 4+ 1 .07494 .01188 .10883 .01285 .14142 .01385 .17282 .01489 .20310 .01596 56 6 .07552 .01190 .10938 .01286 0.01288 .14195 .01387 .17333 8.17384 .01491 .20360 8.20410 .01598 0.01600 54 52 8+ 2 8.07610 0.01193 8.10993 8.14248 0.01388 0.01492 10 .07667 .01193 .11049 .01290 .14302 .01390 .17436 .01494 .20459 .01603 50 12+ 3 .07725 .01195 .11104 .01291 .14355 .01392 .17487 .01496 .20509 .01604 4S 14 .07782 .01196 .11159 .01393 .14408 .01393 .17538 .01498 .20558 .01605 46 16+ 4 8.07839 0.01198 8.11214 0.01395 8.14461 0.01395 8.17590 0.01499 8.20608 0.01607 44 18 .07897 .01199 .11269 .01396 .14514 .01397 .17641 .01501 .20657 .01609 42 20+ 5 .07954 .01301 .11324 .01398 .14567 .01399 .17692 .01503 .20706 .01011 40 22 .08011 .01303 .11379 .01300 .14620 .01400 .17743 .01505 .20756 .01613 38 24+ 6 8.08069 0.01304 8.11435 0.01301 8.14673 0.01402 8.17794 0.01506 8.20805 0.01615 36 26 .08126 .01306 .11490 .01303 .14726 .01404 .17845 .01508 .20854 .01616 34 28+ 7 .08183 .01307 .11544 .01305 .14779 .01405 .17896 .01510 .20904 .01618 32 ^0 .08240 .01309 .11599 .01306 .14832 .01407 .17947 .01512 .20953 .01630 30 32+ 8 8.08297 0.01311 8.11654 0.01308 8.14885 0.01409 8.17998 0.01513 8.21002 0.01633 28 ^4 .08354 .01312 .11709 .01309 .14938 .01411 .18049 .01515 .21051 .01624 26 56+ 9 .08411 .01214 .11764 .01311 .14991 .01413 .18100 .01517 .21100 .01626 24 S8 .08468 .01315 .11819 8.11873 .01313 .15043 .01414 .18151 .01519 0.01521 .21149 .01637 22 20 40+10 8.08525 0.01317 0.01314 8.15096 0.01416 8.18202 8.21199 0.01629 42 .08582 .01318 .11928 .01316 ..15149 .01417 .18253 .01522 .21248 .01631 18 44+n .08639 .01330 .11983 .01317 .15201 .01419 .18303 .01524 .21297 .01633 16 46 .08696 .01232 .12038 .01319 .15254 .01431 .18354 .01526 .21346 .01635 14 48+12 8.08752 0.01233 8.12092 0.01331 8.15307 0.01433 8.18405 0.01528 8.21395 0.01637 12 SO .08809 .01335 .12147 .01323 .15359 .01434 .18455 .01530 .21444 .01638 10 62+13 .08866 .01226 .12201 .01334 .15412 .01436 .18506 .01531 .21493 .01640 8 54 .08922 .01228 .12256 .01326 .15464 8.15517 .01438 0.01429 .18557 .01533 .21541 .01643 0.01644 6 4 56 +U 8.08979 0.01330 8.12310 0.01328 8.18607 0.01535 8.21590 58 8.09036 0.01331 8.12365 0.01329 8.15569 0.01431 8.18658 0.01537 8.21639 0.01646 2 23h9rn 23h 7'« 23h 5™ 23 h 3 "I 2Sh Im B ' 0+15 Oh 51^ 13° W Oh 53m 13° 0' Oh 55r^ TABLE 45. [Page 823 Haversines. s nomi5°(^ 1 iW»15°15' 1 JA:^''15°30' 1 iA5™15°45' 1 iA4'»16°0' 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.23140 .23164 .23188 .23212 .01704 .01705 .01706 .01707 8.24567 .24591 .24614 .24638 .01761 .01762 .01763 .01764 8.25971 .25994 .26017 .26040 .01818 .01819 .01820 .01821 8.27352 .27375 .27398 .27420 .01877 .01878 .01879 .01880 8.28711 .28734 .28756 .28779 .01937 .01938 .01939 .01940 60 59 58 67 + r 5 6 7 8.23235 .23259 .23283 .23307 .01707 .01708 .01709 .01710 8.24661 .24685 .24708 .24732 .01764 .01765 .01766 .01767 8.26064 .26087 .26110 .26133 .01822 .01823 .01824 .01835 8.27443 .27466 .27489 .27512 .01881 .01883 .01883 .01884 .01885 .01886 .01887 .01888 8.28801 .28823 .28846 .28868 .01941 .01943 .01943 .01944 .01945 .01946 .01947 .01948 56 55 54 53 52 51 50 49 + 2' 9 10 11 8.23331 .23355 .23379 .23403 .01711 .01713 .01713 .01714 8.24755 .24779 .24803 .24826 .01768 .01769 .01770 .01771 8.26156 .26179 .26203 .26226 .01836 .01827 .01828 .01829 8.27534 .27557 .27580 .27603 8.28891 .28913 .28936 .28958 8.28980 .29003 .29025 .29048 + 3' 13 14 15 8.23427 .23451 .23475 .23499 .01715 .01716 .01717 .01718 8.24850 .24873 .24897 .24920 .01773 .01773 .01774 .01775 8.26249 .26272 .26295 .26318 .01830 .01831 .01832 .01833 8.27626 .27648 .27671 .27694 .01889 .01890 .01891 .01893 .01949 .01950 .01951 .01952 48 47 46 45 + 4^ 17 18 19 8.23523 .23546 .23570 .23594 .01719 .01730 .01731 .01733 8.24944 .24967 .24991 .25014 .01776 .01777 .01778 .01779 8.26341 .26364 .26388 .26411 .01834 .01835 .01836 .01837 8.27717 .27739 .27762 .27785 .01893 .01894 .01895 .01896 8.29070 .29092 .29115 .29137 .01953 .01954 .01955 .01956 44 43 42 41 + 5' 21 22 23 8.23618 .23642 .23666 .23690 .01723 .01734 .01734 .01735 8.25037 .25061 .25084 .25108 .01780 .01781 .01783 .01783 8.26434 .26457 .26480 .26503 .01838 .01839 .01840 .01841 8.27807 .27830 .27853 .27876 .01897 .01898 .01899 .01900 8.29159 .29182 .29204 .29226 .01957 .01958 .01959 .01960 40 39 38 37 + 6' 25 26 27 8.23713 .23737 .23761 .23785 .01736 .01727 .01738 .01729 8.25131 .25155 .25178 .25202 8.25225 .25248 .25272 .25295 .01784 .01785 .01786 .01787 .01788 .01789 .01789 .01790 8.26526 .26549 .26572 .26595 8.26618 .26641 .26664 .26687 .01843 .01843 .01844 .01845 8.27898 .27921 .27944 .27966 .01901 .01903 .01903 .01904 8.29249 .29271 .29293 .29316 .01961 .01962 .01963 .01964 36 35 34 33 32 31 30 29 + r 29 30 31 8.23809 .23832 .23856 .23880 .01730 .01731 .01732 .01733 .01846 .01847 .01848 .01849 8.27989 .28012 .28034 .28057 .01905 .01906 .01907 .01908 8.29338 .29360 .29383 .29405 .01965 .01966 .01967 .01968 + 8' 33 34 35 8.23904 .23928 .23951 .23975 .01734 .01735 .01736 .01737 8.25319 .25342 .25365 .25389 .01791 .01793 .01793 .01794 8.26710 .26733 .26756 .26779 .01850 .01851 .01852 .01853 8.28080 .28102 .28125 .28147 .01909 .01910 .01911 .01913 8.29427 .29449 .29472 .29494 .01969 .01970 .01971 .01973 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 IS + 9^ 37 38 39 8.23999 .24022 .24046 .24070 .01738 .01739 .01740 .01741 8.25412 .25435 .25459 .25482 .01795 .01796 .01797 .01798 8.26802 .26825 .26848 .26871 .01854 .01855 .01856 .01857 8.28170 .28193 .28215 .28238 .01913 .01914 .01915 .01916 8.29516 .29539 .29561 .29583 .01973 .01974 .01975 .01976 .01977 .01978 .01979 .01980 41 42 43 8.24094 .24118 .24141 .24165 .01742 .01743 .01743 .01744 8.25505 .25529 .25552 .25575 .01799 .01800 .01801 .01803 8.26894 .26917 .26940 .26963 .01858 .01859 .01860 .01861 8.28260 .28283 .28306 .28328 .01917 .01918 .01919 .01930 8.29605 .29628 .29650 .29672 + ir 45 46 47 8.24189 .24212 .24236 .24260 .01745 .01746 .01747 .01748 8.25599 .25622 .25645 .25669 .01803 .01804 .01805 .01806 8.26986 .27009 .27032 .27055 .01861 .01862 .01863 .01864 8.28351 .28373 .28396 .28418 .01931 .01933 .01933 .01924 8.29694 .29716 .29739 .29761 .01981 .01982 .01983 .01984 + 13' 49 60 51 8.24283 .24307 .24331 .24354 .01749 .01750 .01751 .01753 8.25692 .25715 .25738 .25762 .01807 .01808 .01809 .01810 .01811 .01813 .01813 .01814 8.27078 .27100 .27123 .27146 .01865 .01866 .01867 .01868 8.28441 .28464 .28486 .28509 .01935 .01936 .01937 .01938 .01939 .01930 .01931 .01933 8.29783 .29805 .29827 .29850 8.29872 .29894 .29916 .29938 .01985 .01986 .01987 .01988 12 11 10 9 + 13' 53 64 65 8.24378 .24402 .24425 .24449 .01753 .01754 .01755 .01756 8.25785 .25808 .25831 .25855 8.27169 .27192 .27215 .27238 .01869 .01870 .01871 .01873 8.28531 .28554 .28576 .28599 .01989 .01990 .01991 .01992 8 7 6 5 + U' 67 68 69 8.24473 .24496 .24520 .24543 .01757 .01758 .01759 .01760 8.25878 .25901 .25924 .25948 .01815 .01816 .01817 .01818 8.27261 .27283 .27306 .27329 .01873 .01874 .01875 .01876 8.28621 .28644 .28666 .28689 .01933 .01934 .01935 .01936 8.29960 .29982 .30005 .30027 .01993 .01994 .01995 .01997 4 s 2 1 + 15' 8.24567 .01761 8.25971 .01818 8.27352 .01877 8.28711 1 .01937 8.30049 .01998 22 h 59m 22" 58^ 1 22k 57m f^ft 5(5 "» 22 h 55m Page 824] TABLE 45. Haversines. s J* 5m 16° 15' ift 6m 16° 30' lA 7m 16° 45' lA5ml7°0' Ih 9m 17° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.30049 .30071 .30093 .30115 .01998 .01999 .03000 .03001 8.31366 .3138. .31410 .31431 .02059 .02060 .02061 .02062 8.32663 .32684 .32706 .32727 .02121 .02122 .02124 .02125 8.33940 .33962 .33983 .34004 .02185 .02186 .02187 .02188 8.35199 .35220 .35241 .35261 .02249 .02250 .02251 .02252 60 59 58 67 + 1' 6 6 7 8.30137 .30159 .30182 .30204 .03002 .02003 .02004 .02005 8.31453 .31475 .31497 .31518 .02063 .02064 .02065 .02066 8.32749 .32770 .32792 .32813 .02126 .02127 .02128 .02129 8.34025 .34046 .34067 .34088 .02189 .02190 .02191 .02192 8.35282 .35303 .35324 .35345 .02253 .02254 .02255 .02257 56 55 54 53 + 2' 9 10 11 8.30226 .30248 .30270 .30292 .02006 .02007 .02008 .02009 8.31540 .31562 .31584 .31605 .02067 .02068 .02069 .02070 8.32834 .32856 .32877 .32899 .02130 .02131 .02132 .02133 8.34109 .34130 .34152 .34173 .02193 .02194 .02195 .02196 8.35365 .35386 .35407 .35428 .02258 .02259 .02260 .02261 52 51 50 49 48' 47 46 45 + 3' 13 14 15 8.30314 .30336 .30358 .30380 .02010 .02011 .02012 .02013 8.31627 .31649 .31670 .31692 .02071 .02072 .02074 .02075 8.32920 .32941 .32963 .32984 .02134 .02135 .02136 .02137 8.34194 .34215 .34236 .34257 .02198 .02199 .02200 .02201 8.35449 .35469 .35490 .35511 .02262 .02263 .02264 .02265 + 4' 17 19 8.30402 .30424 .30446 .30468 .02014 .02015 .02016 .02017 8.31714 .31735 .31757 .31779 .02076 .02077 .02078 .02079 8.33006 .33027 .33048 .33070 .02138 .02139 .02140 .02141 8.34278 .34299 .34320 .34341 .02202 .02203 .02204 .02205 8.35532 .35552 .35573 .35594 .02266 .02267 .02268 .02270 44 43 42 41 + 6' ;?1 «5 8.30490 .30512 .30534 .30556 .02018 .02019 .02020 .02021 8.31800 .31822 .31844 .31865 .02080 .02081 .02082 .02083 8.33091 .33112 .33134 .33155 .02142 .02143 .02145 .02146 8.34362 .34383 .34404 .34425 .02206 .02207 .02208 .02209 8.35614 .35635 .35656 .35677 .02271 .02272 .02273 .02274 40 S9 38 37 36 35 34 33 32 31 30 29 ^7 8.30578 .30600 .30622 .30644 .02022 .02023 .02024 .02025 8.31887 .31909 .31930 .31952 .02084 .02085 .02086 .02087 8.33176 .33198 .33219 .33240 .02147 .02148 .02149 .02150 8.34446 .34467 .34488 .34509 .02210 .02211 .02212 .02214 8.35697 .35718 .35739 .35759 .02275 .02276 .02277 .02278 + r 29 30 31 8.30666 .30688 .30710 .30732 .02026 .02027 .02028 .02029 8.31974 .31995 .32017 .32039 .02088 .02089 .02090 .02091 8.33262 .33283 .33304 .33325 .02151 .02152 .02153 .02154 8.34530 .34551 .34572 .34593 .02215 .02216 .02217 .02218 8.35780 .35801 .35821 .35842 .02279 .02280 .02281 .02283 + 8' 33 34 35 8.30754 .30776 .30798 .30820 .02030 .02031 .02032 .02033 8.32060 .32082 .32103 .32125 .02092 .02093 .02094 .02095 8.33347 .33368 .33389 .33411 .02155 .02156 .02157 .02158 8.34614 .34635 .34656 .34677 .02219 .02220 .02221 .02222 8.35863 .35883 .35904 .35925 .02284 .02285 .02286 .02287 28 27 26 25 24 23 22 21 + 9^ 37 38 39 8.30842 .30863 .30885 .30907 .02034 .02035 .02036 .02037 8.32147 .32168 .32190 .32211 .02096 .02097 .02098 .02099 8.33432 .33453 .33474 .33496 .02159 .02160 .02161 .02162 8.34698 .34719 .34740 .34761 .02223 .02224 .02225 .02226 8.35945 .35966 .35987 .36007 .02288 .02289 .02290 .02291 + W 41 42 43 8.30929 .30951 .30973 .30995 .02038 .02039 .02040 .02042 8.32233 .32254 .32276 .32297 .02101 .02102 .02103 .02104 8.33517 .33538 .33559 .33580 .02164 .02165 .02166 .02167 8.34782 .34803 .34823 .34844 .02227 .02229 .02230 .02231 8.36028 .36048 .36069 .36090 .02292 .02293 .02295 .02296 20 19 18 17 16 15 14 13 + 11' 45 46 47 8.31017 .31039 .31060' .31082 .02043 .02044 .02045 .02046 8.32319 .32341 .32362 .32384 .02105 .02106 .02107 .02108 8.33602 .33623 .33644 .33665 .02168 .02169 .02170 .02171 8.34865 .34886 .34907 .34928 .02232 .02233 .02234 .02235 8.36110 .36131 .36151 .36172 .02297 .02298 .02299 .02300 + 12' 49 50 51 8.31104 .31126 .31148 .31170 .02047 .02048 .02049 .02050 8.32405 .32427 .32448 .32470 .02109 .02110 .02111 .02112 8.33686 .33708 .33729 .33750 .02172 .02173 .02174 .02175 8.34949 .34970 .34991 .35011 .02236 .02237 .02238 .02239 8.36193 .36213 .36234 .36254 .02301 .02302 .02303 .02304 12 11 10 9 8 7 6 5 + 13' 53 54 55 8.31192 .31213 .31235 .31257 .02051 .02052 .02053 .02054 8.32491 .32513 .32534 .32556 .02113 .02114 .02115 .02116 8.33771 .33792 .33814 .33835 .02176 .02177 .02178 .02179 8.35032 .35053 .35074 .35095 .02240 .02241 .02243 .02244 8.36275 .36295 .36316 .36337 .02305 .02307 .02308 .02309 + 14' 57 55 59 8.31279 .31301 .31322 .31344 .02055 .02056 .02057 .02058 8.32577 .32599 .32620 .32642 .02117 .02118 .02119 .02120 8.33856 .33877 .33898 .33919 .02181 .02182 .02183 .02184 8.35116 .35137 .35157 .35178 .02245 .02246 .02247 .02248 .02249 8.36357 .36378 .36398 .36419 .02310 .02311 .02312 .03313 4 3 2 1 + 15' 8.31366 .02059 8.32663 .02121 8.33940 .02185 8.35199 8.36439 .02314 22^ 54^ 22h 5Sm 22h 52m 22h 51r^ 22h 50m TABLE 45. [Page 825 Haversines. s nior^nw niimn° i5' Ih 12ml%°(i' nis^WW 1*^4" 18° SO' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.36439 .36460 .36480 .36501 .02314 .02315 .02316 .02317 8.37662 .37682 .37702 .37722 .02380 .02381 .02382 .02384 8.38867 .38886 .38906 .38926 .02447 .02448 .02449 .02451 8.40055 .40074 .40094 .40114 .02515 .02516 .02517 .02518 8.41226 .41246 .41265 .41284 .02584 .02585 .02586 .02587 60 59 58 57 + r 6 6 7 8.36521 .36542 .36562 .36583 .02319 .02320 .02321 .02322 8.37742 .37763 .37783 .37803 .02385 .02386 .02387 .02388 8.38946 .38966 .38986 .39006 .02452 .02453 .02454 .02455 8.40133 .40153 .40172 .40192 .02520 .02521 .02522 .02523 8.41304 .41323 .41343 .41362 .02588 .02590 .02591 .02592 56 55 54 53 + 2^ 9 10 11 8.36603 .36624 .36644 .36665 .02323 .02324 .02325 .02326 8.37823 .37843 .37864 .37884 .02389 .02390 .02391 .02392 8.39026 .39046 .39066 .39086 8.39105 .39125 .39145 .39165 .02456 .02457 .02458 .02460 8.40212 .40231 .40251 .40271 .02524 .02525 .02526 .02528 8.41381 .41401 .41420 .41439 .02593 .02594 .02595 .02597 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 + 3' 13 14 16 8.36685 .36706 .36726 .36746 .02327 .02328 .02329 .02331 8.37904 .37924 .37944 .37964 .02394 .02395 .02396 .02397 .02461 .02462 .02463 .02464 8.40290 .40310 .40329 .40349 .02529 .02530 .02531 .02532 8.41459 .41478 .41497 .41517 .02598 .02599 .02600 .02601 + 4' 17 18 19 8.36767 .36787 .36808 .36828 .02332 .02333 .02334 .02335 8.37985 .38005 .38025 .38045 .02398 .02399 .02400 .02401 .02402 .02404 .02405 .02406 8.39185 .39205 .39225 .39245 .02465 .02466 .02467 .02469 8.40369 .40388 .40408 .40427 .02533 .02534 .02536 .02537 8.41536 .41555 .41575 .41594 8.41613 .41632 .41652 .41671 .02602 .02603 .02605 .02606 .02607 .02608 .02609 .02610 + y 21 22 23 8.36849 .36869 .36889 .36910 .02336 .02337 .02338 .02339 8.38065 .38085 .38105 .38126 8.39264 .39284 .39304 .39324 .02470 .02471 .02472 .02473 8.40447 .40467 .40486 .40506 .02538 .02539 .02540 .02541 + 6' 25 26 27 8.36930 .36951 .36971 .36991 .02340 .02342 .02343 .02344 8.38146 .38166 .38186 .38206 .02407 .02408 .02409 .02410 8.39344 .39364 .39384 .39403 .02474 .02475 .02476 .02478 8.40525 .40545 .40564 .40584 .02542 .02544 .02545 .02546 8.41690 .41710 .41729 .41748 .02612 .02613 .02614 .02615 36 85 34 33 + r 29 SO 31 8.37012 .37032 .37053 .37073 .02345 .02346 .02347 .02348 8.38226 .38246 .38266 .38286 .02411 .02412 .02414 .02415 8.39423 .39443 .39463 .39482 .02479 .02480 .02481 .02482 8.40603 .40623 .40642 .40662 .02547 .02548 .02549 .02550 8.41767 .41787 .41806 .41825 .02616 .02617 .02619 .02620 32 31 30 29 28 27 26 25 + 8' 33 34 35 8.37093 .37114 .37134 .37154 .02349 .02350 .02351 .02353 8.38306 .38326 .38346 .38367 .02416 .02417 .02418 .02419 8.39502 .39522 .39542 .39562 .02483 .02484 .02486 .02487 8.40681 .40701 .40721 .40740 .02552 .02553 .02554 .02555 8.41845 .41864 .41883 .41902 .02621 .02622 .02623 .02624 + 9^ 37 38 39 8.37175 .37195 .37215 .37236 .02354 .02355 .02356 .02357 8.38387 .38407 .38427 .38447 .02420 .02421 .02423 .02424 8.39581 .39601 .39621 .39641 .02488 .02489 .02490 .02491 8.40760 .40779 .40799 .40818 .02556 .02557 .02559 .02560 8.41921 .41941 .41960 .41979 .02626 .02627 .02628 .02629 24 23 22 21 + W 41 42 43 8.37256 .37276 .37297 .37317 .02358 .02359 .02360 .02361 8.38467 .38487 .38507 .38527 .02425 .02426 .02427 .02428 8.39660 .39680 .39700 .39720 .02492 .02493 .02495 .02496 8.40837 .40857 .40876 .40896 .02561 .02562 .02563 .02564 8.41998 .42018 .42037 .42056 .02630 .02631 .02633 .02634 20 19 18 17 16 15 14 13 + 11' 45 46 47 8.37337 .37358 .37378 .37398 .02363 .02364 .02365 .02366 8.38547 .38567 .38587 .38607 .02429 .02430 .02431 .02433 8.39739 .39759 .39779 .39799 .02497 .02498 .02499 .02500 8.40915 .40935 .40954 .40974 .02565 .02567 .02568 .02569 8.42075 .42095 .42114 .42133 .026351 .02636 .02637 .02638 + lit' 49 50 61 8.37419 .37439 .37459 .37479 .02367 .02368 .02369 .02370 8.38627 .38647 .38667 .38687 .02434 .02435 .02436 .02437 8.39818 .39838 .39858 .39877 .02501 .02503 .02504 .02505 8.40993 .41013 .41032 .41052 .02570 .02571 .02572 .02573 8.42152 .42171 .42190 ,42210 .02639 .02641 .02642 .02643 12 11 10 9 + 13^ 53 54 55 8.37500 .37520 .37540 .37560 .02371 .02372 .02374 .02375 8.38707 .38727 .38747 .38767 .02438 .02439 .02440 .02442 8.39897 .39917 .39937 .39956 .02506 .02507 .02508 .02509 8.41071 .41090 .41110 .41129 .02575 .02576 .02577 .02578 8.42229 .42248 .42267 .42286 .02644 .02645 .02646 .02648 8 7 6 6 + W 67 68 59 8.37581 .37601 .37621 .37641 .02376 .02377 .02378 .02379 .02380 8.38787 .38807 .38827 .38847 .02443 .02444 .02445 .02446 8.39976 .39996 .40015 .40035 .02510 .02512 .02513 .02514 8.41149 .41168 .41187 .41207 .02579 .02580 .02582 .02583 8.42305 .42324 .42344 .42363 .02649 .02650 .02651 .02652 4 3 2 1 + 15' 8.37662 8.38867 .02447 8.40055 .02515 8.41226 .02584 8.42382 .02653 221^ 49"" 22^48^'* 22^ 47 ■^ 22^46-«^ 22^46^ Page 826] TABLE 45. Haversines. s Ih 15m 18° 45' Ih 16m 19° 0' Ih 17m 19° 15/ lM8m 19° 30' Ih 19m 19° 45' s 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.42382 .42401 .42420 .42439 .03053 .03655 .03656 .02657 8.43522 .43541 .43560 .43578 .03734 .03735 .03736 .03738 8.44647 .44665 .44684 .44703 .03796 .03797 .03798 .03799 8.45757 .45775 .45794 .45812 .03868 .03869 .03870 .03871 8.46852 .46871 .46889 .46907 .03941 .03943 .03944 .03945 + r 5 6 7 8.42458 .42477 .42497 .42516 .0365S .02659 .03661 .03663 8.43597 .43616 .43635 .43654 .03739 .03730 .03731 .03733 8.44721 .44740 .44758 .44777 8:44796 .44814 .44833 .44851 .03800 .02803 .03803 .03804 .03805 .03806 .03808 .03809 8.45830 .45849 .45867 .45885 8.45904 .45922 .45940 .45959 .03873 .03874 .03875 .03376 8.46925 .46943 .46961 .46979 .03946 .03947 .03949 .03950 56 55 54 53 + 2^ 9 10 11 8.42535 .42554 .42573 .42592 .03663 .02664 .03665 .03666 8.43673 .43692 .43710 .43729 .03734 .03735 .03736 .03737 .03878 .03879 .03880 .03881 8.46998 .47016 .47034 .47052 .03951 .03953 .03954 .03955 .03956 .03957 .03958 .03960 52 51 50 49 48 47 46 45 44 43 42 41 + 3' 13 14 15 8.42611 .42630 .42649 .42668 .03668 .03669 .03670 .03671 8.43748 .43767 .43786 .43805 .03738 .03739 .03741 .03743 8.44870 .44889 .44907 .44926 .03810 .03811 .03813 .03814 8.45977 .45995 .46014 .46032 .03883 .03884 .03885 .03886 8.47070 .47088 .47106 .47124 + 4' 17 18 19 8.42687 .42706 .42725 .42745 .03673 .03673 .02675 .03676 8.43823 .43842 .43861 .43880 .03743 .03744 .03745 .03747 8.44944 .44963 .44981 .45000 .03815 .03816 .03817 .03818 8.46050 .46069 .46087 .46105 .03887 .03889 .03890 .03891 8.47142 .47160 .47178 .47197 .03961 .03963 .03963 .03965 + 5^ 21 22 23 8.42764 .42783 .42802 .42821 .03677 .02678 .03679 .036S0 8.43899 .43917 .43936 .43955 8.43974 .43992 .44011 .44030 .03748 .03749 .03750 .03751 8.45018 .45037 .45055 .45074 .03830 .03831 .03833 .03833 8.46124 .46142 .46160 .46179 .03893 .03893 .03895 .03896 8.47215 .47233 .47251 .47269 .03966 .03967 .03968 .03970 40 39 38 37 + 6^ 25 26 27 8.42840 .42859 .42878 .42897 .03683 .03683 .03684 .03685 .03753 .03754 .03755 .03756 8.45093 .45111 .45130 .45148 .03834 .03836 .03837 .03838 8.46197 .46215 .46233 .46252 .03897 .03898 .03900 .03901 8.47287 .47305 .47323 .47341 .03971 .03973 .03973 .02974 36 35 34 33 + r 29 30 31 8.42916 .42935 .42954 .42973 .03686 .03688 .03689 .03890 8.44049 .44067 .44086 .44105 .03757 .03759 .03760 .03761 8.45167 .45185 .45204 .45222 .03839 .03830 .03832 .03833 .03834 .03835 .03836 .03838 .03839 .03840 .03841 .03843 8.46270 .46288 .46306 .46325 .03903 .03903 .03904 .03906 8.47359 .47377 .47395 .47413 .03976 .03977 .03978 .03979 32 31 30 29 + 8' 33 34 35 8.42992 .43011 .43030 .43049 .03691 .03693 .03693 .03695 8.44124 .44142 .44161 .44180 .03763 .03763 .02764 .03766 8.45241 .45259 .45278 .45296 8.46343 .46361 46379 .46398 .03907 .03908 .03909 .03911 8.47431 .47449 .47467 .47485 .03981 .03983 .03983 .02984 28 27 26 25 + r 37 38 39 8.43068 .43087 .43106 .43125 .03696 .03697 .03698 .03699 8.44199 .44217 .44236 .44255 .03767 .03768 .03769 .03771 8.45315 .45333 .45352 .45370 8.46416 .46434 .46452 .46471 .03913 .03913 .03914 V03915 8.47503 .47521 .47539 .47557 .03986 .03987 .03988 .03989 24 23 22 21 + 10' 41 42 43 8.43144 .43163 .43181 .43200 .03700 .03703 .03703 .03704 8.44273 .44292 .44311 .44330 .03773 .03773 .03774 .03775 8.45388 .45407 .45425 .45444 .02844 .03845 .03846 .03847 8.46489 .46507 .46525 .46544 .03917 .03918 .03919 .03930 8.47575 .47593 .47611 .47629 .03991 .03993 .03993 .03994 20 19 18 17 + 11' 45 46 47 8.43219 .43238 .43257 .43276 .03705 .03706 .03708 .03709 8.44348 .44367 .44386 .44404 .03776 .03778 .03779 .03780 8.45462 .45481 .45499 .45518 .03849 .03850 .03851 .03853 8.46562 .46580 .46598 .46616 .03933 .03933 .03934 .03935 8.47647 .47665 .47683 .47701 .03996 .03997 .03998 .03999 16 15 14 IS + n' 49 50 51 8.43295 .43314 .43333 .43352 .03710 .03711 .03713 .03713 8.44423 .44442 .44460 .44479 .03781 .03783 .03784 .03785 8.45536 .45554 .45573 .45591 .03853 .03855 .03856 .03857 8.46634 .46653 .46671 .46689 .03936 .03938 .03939 .03930 8.47719 .47737 .47755 .47773 .03000 .03003 .03003 .03004 12 11 10 9 + 13' 53 54 55 8.43371 .43390 .43409 .43427 .03715 .03716 .03717 .03718 8.44498 .44516 .44535 .44554 .03786 .03787 .03788 .03790 8.45610 .45628 .45646 .45665 .03858 .02859 .02861 .02863 8.46707 .46725 .46744 .46762 .03931 .03933 .03934 .03935 8.47791 .47809 .47827 .47844 .03005 .03007 .03008 .03009 8 7 6 5 4 S 2 1 + W 57 58 59 8.43446 .43465 .43484 .43503 8.43522 .03719 .03731 .03733 .02733 8.44572 .44591 .44610 .44628 .03791 .03793 .03793 .03794 8.45683 .45702 .45720 .45738 .03863 .02864 .02868 .02867 8.46780 .46798 .46816 .46834 .03936 .03938 .03939 .03940 8.47862 .47880 .47898 .47916 .03010 .03013 .03013 .03014 + 15' .03734 8.44647 .03796 8.45757 .03868 8.46852 .03941 8.47934 .03015 22 h 44m 22 "■ 43^ 22 >^ 42 m 22!^ 4im 22h 40n TABLE 45. [Page 827 Haversines. s lh20mW°fy Ih 2irn. 20° 15' lh22:rn, 20° 30' Ih 23m 20° ^5' Ih 24m 21° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 8 8.47934 .47952 .47970 .47988 .03015 .03017 .03018 .03019 8.49002 .49020 .49037 .49055 .03090 .03092 .03093 .03094 8.50056 .50074 .50091 .50109 .03166 .03168 .03169 .03170 8.51098 .51115 .51132 .51150 .03243 .03245 .03246 .03247 8.52127 .52144 .52161 .52178 .03321 .03322 .03324 .03325 60 59 58 57 66 55 54 53 52 51 50 49 48 47 46 45 + 1^ 5 6 7 8.48006 .48024 .48041 .48059 .03020 .03022 .03023 .03024 8.49073 .49090 .49108 .49126 .03095 .03097 .03098 .03099 8.50126 .50144 .50161 .50179 .03171 .03173 .03174 .03175 8.51167 .51184 .51201 .51219 .03248 .03250 .03251 .03252 8.52195 .52212 .52229 .52246 .03326 .03328 .03329 .03330 + V 9 10 11 8.48077 .48095 .48113 .48131 .03025 .03027 .03028 .03029 8.49143 .49161 .49179 .49196 .03101 .03102 .03103 .03104 8.50196 .50214 .50231 .50248 .03177 .03178 .03179 .03180 8.51236 .51253 .51270 .51287 .03254 .03255 .03256 .03257 8.52263 .52280 .52297 .52314 .03331 .03333 .03334 .03335 + 3' IS 14 15 8.48149 .48167 .48184 .48202 .03030 .03032 .03033 .03034 8.49214 .49232 .49249 .49267 .03106 .03107 .03108 .03109 8.50266 .50283 .50301 .50318 .03182 .03183 .03184 .03186 8.51305 .51322 .51339 .51356 .03259 .03260 .03261 .03263 8.52331 .52348 .52365 .52382 .03337 .03338 .03339 .03341 + 4^ 17 18 19 8.48220 .48238 .48256 .48274 .03035 .03037 .03038 .03039 8.49284 .49302 .49320 .49337 .03111 .03112 .03113 .03114 8.50335 .50353 .50370 .50388 8.50405 .50422 .50440 .50457 .03187 .03188 .03189 .03191 8.51374 .51391 .51408 .51425 .03264 .03265 .03266 .03268 8.52399 .52416 .52433 .52450 .03342 .03343 .03344 .03346 U 43 42 41 40 39 38 37 36 35 34 33 21 22 2S 8.48292 .48309 .48327 .48345 .03040 .03042 .03043 .03044 8.49355 .49373 .49390 .49408 .03116 .03117 .03118 .03119 .03192 .03193 .03194 .03196 8.51442 .51459 .51477 .51494 .03269 .03270 .03272 .03273 8.52467 .52484 .52501 .52518 .03347 .03348 .03350 .03351 •+ 6' 25 26 27 8.48363 .48381 .48399 .48416 .03045 .03047 .03048 .03049 8.49425 .49443 .49461 .49478 .03121 .03122 .03123 .03125 8.50475 .50492 .50509 .50527 .03197 .03198 .03200 .03201 8.51511 .51528 .51545 .51562 .03274 .03275 .03277 .03278 8.52535 .52552 .52569 .52585 .03352 .03354 .03355 .03356 + r 29 SO SI 8.48434 .48452 .48470 .48488 .03050 .03052 .03053 .03054 8.49496 .49513 .49531 .49548 .03126 .03127 .03128 .03130 8.50544 .50561 .50579 .50596 .03202 .03204 .03205 .03206 8.51580 .51597 .51614 .51631 .03279 .03281 .03282 .03283 8.52602 .52619 .52636 .52653 .03358 .03359 .03360 .03361 32 31 SO 29 28 27 26 25 + 8' ss S4 S5 8.48505 .48523 .48541 .48559 .03055 .03057 .03058 .03059 8.49566 .49584 .49601 .49619 .03131 .03132 .03133 .03135 8.50614 .50631 .50648 .50666 .03207 .03209 .03210 .03211 8.51648 .51665 .51682 .51700 .03285 .03286 .03287 .03288 8.52670 .52687 .52704 .52721 .03363 .03364 .03365 .03367 + 9^ S7 S8 S9 8.48576 .48594 .48612 .48630 .03060 .03062 .03063 .03064 8.49636 .49654 .49671 .49689 .03136 .03137 .03138 .03140 8.50683 .50700 .50718 .50735 .03212 .03214 .03215 .03216 8.51717 .51734 .51751 .51768 .03290 .03291 .03292 .03294 8.52738 .52755 .52772 .52789 .03368 .03369 .03371 .03372 24 23 22 21 + 10' 41 42 4S 8.48648 .48665 .48683 .48701 .03065 .03067 .03068 .03069 8.49706 .49724 .49742 .49759 .03141 .03142 .03144 .03145 8.50752 .50770 .50787 .50804 .03218 .03219 .03220 .03221 8.51785 .51802 .51819 .51836 .03295 .03296 .03298 .03299 8.52806 .52822 .52839 .52856 .03373 .03375 .03376 .03377 20 19 18 17 + 11^ 45 46 47 8.48719 .48736 .48754 .48772 .03070 .03073 .03073 .03074 8.49777 .49794 .49812 .49829 .03146 .03147 .03149 .03150 8.50821 .50839 .50856 .50873 .03223 .03224 .03225 .03227 8.51854 .51871 .51888 .51905 .03300 .03301 .03303 .03304 8.52873 .52890 .52907 .52924 .03379 .03380 .03381 .03382 16 15 14 13 + 12' 49 50 51 8.48789 .48807 .48825 .48843 .03075 .03077 .03078 .03079 8.49847 .49864 .49882 .49899 .03151 .03152 .03154 .03155 8.50891 .50908 .50925 .50943 .03228 .03229 .03230 .03232 8.51922 .51939 .51956 .51973 .03305 .03307 .03308 .03309 8.52941 .52958 .52974 .52991 .03384 .03385 .03386 .03388 12 11 10 9 4- 13' 53 54 55 8.48860 .48878 .48896 .48914 .03080 .03082 .03083 .03084 8.49917 .49934 .49952 .49969 .03156 .03157 .03159 .03160 8.50960 .50977 .50994 .51012 .03233 .03234 .03236 .03237 8.51990 .52007 .52024 .52041 .03311 .03312 .03313 .03314 8.53008 .53025 .53042 .53059 .03389 .03390 .03392 .03393 8 7 6 5 4- U' 57 58 59 8.48931 .48949 .48967 .48984 .03085 .03087 .03088 .03089 8.49987 .50004 .50022 .50039 .03161 .03163 .03164 .03165 8.51029 .51046 .51063 .51081 .03238 .03239 .03241 .03242 8.52058 .52076 .52093 .52110 .03316 .03317 .03318 .03320 8.53076 .53092 .53109 .53126 .03394 .03396 .03397 .03398 4 3 2 1 f 15' 8.49002 .03090 8.50056 .03166 8.51098 .03243 8.52127 .03321 8.53143 .03400 22^ 39'"^ 22^ SS^ 22^ 37^ 22h 36m 22^ 35m 21594°— 14- -45 Page 828] TABLE 45. Haversines. s Ih 25m 21° 15^ ift 26m 21° 30^ Ih 27m 21° 45' jh 28m 23° 0' J ft 29m 22° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.53143 .53160 .53177 .53193 .03400 .03401 .03403 .03404 8.54147 .54164 .54180 .54197 .03479 .03480 .03483 .03483 8.55139 .55156 55172 .55189 .03560 .03561 .03563 .03564 8.56120 .56136 .56152 .56169 .03641 .03643 .03644 .03645 8.57089 .57105 .57121 .57137 .03733 .03734 .03736 .03737 60 59 58 57 + 1' 5 6 7 8.53210 .53227 .53244 .53261 .03405 .03406 .03408 .03409 8.54214 .54230 .54247 .54263 .03484 .03486 .03487 .03488 8.55205 .55221 55238 .55254 .03565 .03566 .03568 .03569 8.56185 .56201 .56217 .56233 .03646 .03648 .03649 .03650 8.57153 .57169 .57185 .57201 .03738 .03730 .03731 .03733 56 55 54 53 + 2' 9 10 11 8.53277 .53294 .53311 .53328 .03410 .03411 .03413 .03414 8.54280 .54297 .54313 .54330 .03490 .03491 .03493 .03494 8.55271 .55287 .55303 .55320 .03570 .03573 .03573 .03574 8.56250 .56266 .56282 .56298 .03653 .03053 .03654 .03656 8.57217 .57233 .57230 .57266 .03734 .03735 .03737 .03738 52 51 50 49 + 3' 13 14 15 8.53345 .53361 .53378 .53395 .03415 .03417 .03418 .03419 8.54346 .54363 .54380 .54396 .03495 .03496 .03498 .03499 8.55336 .55353 .55369 .55385 .03576 .03577 .03578 .03580 8.56315 .56331 .56347 .56363 .03657 .03659 .03660 .03661 8.57282 .57298 .57314 .57330 .03740 .03741 .03743 .03744 48 47 46 45 + 4' 17 18 19 8.53412 .53429 .53445 .53462 .03431 .03433 .03433 .03435 8.54413 .54429 .54446 .54462 .03500 .03503 .03503 .03504 8.55402 .55418 .55435 .55451 .03581 .03583 .03584 .03585 8.56379 .56396 .56412 .56428 .03663 .03664 .03665 .03667 8.57346 .57362 .57378 .57394 .03745 .03746 .03748 .03749 44 43 42 41 + 5^ 21 22 23 8.53479 .53496 .53512 .53529 .03436 .03437 .03439 .03430 8.54479 .54496 .54512 .54529 .03506 .03507 .03509 .03510 8.55467 .55484 .55500 .55516 .03587 .03588 .03589 .03591 8.56444 .56460 .56477 .56493 .03668 .03669 .03671 .03673 8.57410 .57426 .57442 .57458 .03751 .03753 .03753 .03755 40 39 38 37 + 6^ 25 26 27 8.53546 .53563 .53580 .53596 .03431 .03433 .03434 .03435 8.54545 .54562 .54578 .54595 .03511 .03513 .03514 .03515 8.55533 .55549 .55566 .55582 .03593 .03593 .03595 .03596 8.56509 .56525 .56541 .56557 .03674 .03675 .03676 .03678 8.57474 .57490 .57506 .57522 .03756 .03757 .03759 .03760 36 35 34 33 + r 29 30 31 8.53613 .53630 .53646 .53663 .03437 .03438 .03439 .03441 8.54612 .54628 .54645 .54661 .03517 .03518 .03519 .03531 8.55598 .55615 .55631 .55647 .03597 .03599 .03600 .03601 8.56574 .56590 .56606 .56622 .03679 .03680 .03683 .03683 8.57538 .57554 .57570 .57585 .03763 .03763 .03764 .03766 32 31 30 29 + 8' 33 34 35 8.53680 .53697 .53713 .53730 .03443 .03443 .03445 .03446 8.54678 .54694 .54711 .54727 .03533 .03533 .03535 .03536 8.55664 .55680 .55696 .55713 .03603 .03604 .03605 .03607 8.56638 .56654 .56670 .56687 .03685 .03686 .03687 .03689 8.57601 .57617 .57633 .57649 .03767 .03769 .03770 .03771 28 27 26 25 + 9" 37 38 39 8.53747 .53764 .53780 .53797 .03447 .03449 .03450 .03451 8.54744 .54760 .54777 .54793 .03537 .03539 .03530 .03531 8.55729 .55745 .55762 .55778 .03608 .03610 .03611 .03613 8.56703 .56719 .56735 .56751 .03690 .03691 .03693 .03694 8.57665 .57681 .57697 .57713 .03773 .03774 .03775 .03777 24 23 22 21 + W 41 42 43 8.53814 .53830 .53847 .53864 .03453 .03454 .03455 .03457 8.54810 .54826 .54843 .54859 .03533 .03534 .03535 .03537 8.55794 .55811 .55827 .55843 .03614 .03615 .03616 .03618 8.56767 .56783 .56799 .56816 .03695 .03697 .03698 .03700 8.57729 .57745 .W761 .57777 .03778 .03780 .03781 .03783 20 19 18 17 16 15 14 13 + ir 45 46 47 8.53880 .53897 .53914 .53930 .03448 .03459 .03460 .03463 8.54876 .54892 .54909 .54925 .03538 .03539 .03541 .03543 8.55859 .55876 .55892 .55908 .03619 .03630 .03633 .03633 8.56832 .56848 .56864 .56880 .03701 .03703 .03704 .03705 8.57793 .57809 .57825 .57841 .03784 .03785 .03787 .03788 + ir 49 50 51 8.53947 .53964 .53980 .53997 .03463 .03464 .03466 .03467 8.54942 .54958 .54975 .54991 .03543 .03545 .03546 .03547 8.55925 55941 .55957 .55973 .03634 .03636 .03637 .03639 8.56896 .56912 56928 .56944 .03706 .03708 .03709 .03711 8.57856 .57872 .57888 .57904 .03789 .03791 .03793 .03794 12 11 10 9 + 13^ 53 54 55 8.54014 .54030 .54047 .45064 .03468 .03470 .03471 .03473 8.55008 .55024 .55041 .55057 .03549 .03550 .03551 .03553 8.55990 56006 .56022 .56039 .03630 .03631 .03633 .03634 8.56960 56977 .56993 .57009 .03713 .03713 .03715 .03716 8.57920 .57936 57952 .57968 .03795 .03796 .03798 .03799 8 7 6 5 + W 57 58 59 8.54080 .54097 .54114 .54130 .03474 .03475 .03476 .03478 8.55073 .55090 .55106 .55123 .03554 .03555 .03557 .03558 8.56055 .56071 .56087 .56104 .03635 .03637 .03638 .03639 8.57025 .57041 .57057 .57073 .03717 .03719 .03730 .03733 8.57984 .58000 .58015 .58031 .03800 .03803 .03803 .03805 4 3 2 1 + 16' 8.54147 .03479 8.55139 .03560 8.56120 .03641 8.57089 .03733 8.58047 .03806 22^ 34"^ ff ft 33m 22^ 32m 1 22^ 3lm 22^ 30m TABLE 45. [Page 829 Havereines. s insOrn 22° 30' lhSim^°i5' lhS2mZ3°0' in ssm 23° 15' 1A54"»23°30' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 s s 8.58047 .58063 .58079 .58095 .03806 .03807 .03809 .03810 8.58994 .59010 .59026 .59042 .03890 .03891 .03893 .03894 8.59931 .59947 .59962 .59978 .03975 .03976 .03978 .03979 8.60857 .60873 .60888 .60903 .04060 .04062 .04063 .04065 8.61773 61789 .61804 .61819 .04147 .04148 .04150 .04151 60 59 58 57 + r 5 6 7 8.58111 .58127 .58142 .58158 .03812 .03813 .03814 .03816 8.59057 .59073 .59089 .59104 .03896 .03897 .03898 .03900 8.59993 .60009 .60024 .60040 .03980 .03982 .03983 .03985 8.60919 .60934 .60949 .60965 .04066 .04068 .04069 .04070 8.61834 .61849 .61864 .61880 .04153 .04154 .04156 .04157 56 55 54 53 52 51 50 49 4S 47 46 45 U 43 42 41 40 39 38 37 36 35 34 33 + r 9 10 11 8.58174 .58190 .58206 .58222 .03817 .03819 .03820 .03821 8.59120 .59136 .59151 .59167 .03901 .03903 .03904 .03905 8.60055 .60071 ,60086 .60102 .03986 .03988 .03989 .03990 8.60980 .60995 .61011 .61026 8.61041 .61057 .61072 .61087 .04072 .04073 .04075 .04076 8.61895 .61910 .61925 .61940 .04159 .04160 .04162 .04163 + 3' IS 14 15 8.58238 .58253 .58269 .58285 .03823 .03824 .03826 .03827 8.59183 .59198 .59214 .59230 .03907 .03908 .03910 .03911 8.60117 .60133 .60148 .60164 .03992 .03993 .03995 .03996 .04078 .04079 .04081 .04082 8.61955 .61971 .61986 .62001 .04164 .04166 .04167 .04169 17 18 19 8.58301 .58317 .58333 .58348 .03828 .03830 .03831 .03833 8.59245 .59261 .59277 .59292 .03912 .03914 .03915 .03917 8.60179 .60195 .60210 .60226 .03998 .03999 .04000 .04002 8.61103 .61118 .61133 .61149 .04083 .04085 .04086 .04088 8.62016 .62031 .62046 .62061 .04170 .04172 04173 .04175 + 5' 21 22 2S 8.58364 .58380 .58396 .58412 .03834 .03835 .03837 .03838 8.59308 .59323 .59339 .59355 8.59370 .59386 .59402 .59417 .03918 .03920 .03921 .03922 8.60241 .60256 .60272 .60287 .04003 .04005 .04006 .04007 8.61164 .61179 .61194 .61210 .04089 .04091 .04092 .04094 8.62077 .62092 .62107 .62122 .04176 .04177 .04179 .04180 + 6' 25 26 27 8.58427 .58443 .58459 .58475 .03839 .03841 .03842 .03844 .03924 .03925 .03927 .03928 8.60303 .60318 .60334 .60349 .04009 .04010 .04012 .04013 8.61225 .61240 .61256 .61271 .04095 .04096 .04098 .04099 8.62137 .62152 .62167 .62182 .04182 .04183 .04185 .04186 + r 29 SO SI 8.58491 .58506 .58522 .58538 .03845 .03846 .03848 .03849 8.59433 .59448 .59464 .59480 .03929 .03931 .03932 .03934 8.60365 .60380 .60396 .60411 .04015 .04016 .04017 .04019 8.61286 .61301 .61317 .61332 .04101 .04102 .04104 .04105 8.62197 .62213 .62228 .62243 .04188 .04189 .04191 .04192 32 31 30 29 + 8' SS 34 S5 8.58554 .58570 .58585 .58601 .03851 .03852 .03853 .03855 8.59495 .59511 .59527 .59542 .03935 .03936 .03938 .03939 8.60426 .60442 .60457 .60473 .04020 .04022 .04023 .04025 8.61347 .61362 .61378 .61393 .04106 .04108 .04109 .04111 8.62258 .62273 .62288 .62303 .04194 .04195 .04196 .04198 28 27 26 25 + 9' S7 S8 S9 8.58617 .58633 .58648 .58664 .03856 .03858 .03859 .03860 8.59558 .59573 .59589 .59604 .03941 .03942 .03944 .03945 8.60488 .60504 .60519 .60534 .04026 .04027 .04029 .04030 8.61408 .61423 .61439 .61454 .04112 .04114 .04115 .04117 8.62318 .62333 .62348 .62363 .04199 .04201 .04202 .04204 24 23 22 21 + W 41 42 4S 8.58680 .58696 .58711 .58727 .03862 .03863 .03865 .03866 8.59620 .59636 .59651 .59667 .03946 .03948 .03949 .03951 8.60550 .60565 .60581 .60596 .04032 .04033 .04035 .04036 8.61469 .61484 .61500 .61515 .04118 .04119 .04121 .04122 8.62379 .62394 .62409 .62424 .04205 .04207 .04208 .04210 20 19 18 17 + 11' 45 46 47 8.58743 .58759 .58774 .58790 .03867 .03869 .03870 .03872 8.59682 .59698 .59714 .59729 .03952 .03953 .03955 .03956 8.60611 .60627 .60642 .60658 .04038 .04039 .04040 .04042 8.61530 .61545 .61561 .61576 .04124 .04125 .04127 .04128 8.62439 .62454 .62469 .62484 .04211 .04212 .04214 .04215 16 15 14 13 + 13' 49 50 51 8.58806 .58822 .58837 .58853 .03873 .03875 .03876 .03877 8.59745 .59760 .59776 .59791 .03958 .03959 .03961 .03962 8.60673 .60688 .60704 .60719 .04043 .04045 .04046 .04048 8.61591 .61606 .61621 .61637 .04130 .04131 .04133 .04134 8.62499 .62514 .62529 .62544 .04217 .04218 .04220 .04221 12 11 10 9 + 13' 5S 54 55 8.58869 .58885 .58900 .58916 .03879 .03880 .03882 .03883 8.59807 .59822 .59838 .59853 .03963 .03965 .03966 .03968 8.60734 .60750 .60765 .60781 .04049 .04050 .04052 .04053 8.61652 .61667 .61682 .61697 .04135 .04137 .04138 .04140 8.62559 .62574 .62589 .62604 .04223 .04224 .04226 .04227 8 7 6 5 + 14' 57 55 59 8.58932 .58947 .58963 .58979 .03884 .03886 .03887 .03889 5.59869 .59885 .59900 .59916 .03969 .03971 .03972 .03973 8.60796 .60811 .60827 .60842 .04055 .04056 .04058 .04059 8.61713 .61728 .61743 .61758 .04141 .04143 .04144 .04146 8.62619 .62634 .62649 .62664 .04229 .04230 .04232 .04233 4 3 2 1 + . 16' 8.58994 .03890 8.59931 .03975 8.60857 .04060 8.61773 .04147 8.62680 .04234 _ 22'h' 29in 22^ 28^ 22h 2Tm 22^26^ 22^ 25m 1 Page 830] TABLE 45. Haversines. 3 Ih35m^3°i5' lhS6m24k°0' Ih37m2i°15' lhS8m2i°W lh§9mzi°^5' s 60 69 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.62680 .62695 .62710 .62725 .04234 .04236 .04237 .04239 8.63576 .63591 .63606 .63620 .04333 .04334 .04336 .04337 8.64463 .64477 .64492 .64507 .04413 .04413 .04415 .04416 8.65340 .65355 .65369 .65384 .04503 .04503 .04505 .04506 8.66208 .66223 .66237 .66251 .04593 .04594 .04596 .04597 + r 6 6 7 8.62740 .62755 .62770 .62785 .04340 .04242 o04243 .04345 8.63635 .63650 .63665 .63680 .04329 .04330 .04333 .04333 8.64521 .64536 .64551 .64565 .04418 .04419 .04431 .04433 8.65398 .65413 .65427 .65442 .04508 .04509 .04511 .04513 8.66266 .66280 .66295 .66309 .04599 .04600 .04602 .04604 66 65 64 63 + 3' 9 10 11 8.62800 .62815 .62830 .62845 .04246 .04248 .04249 .04351 8.63695 .63709 .63724 .63739 .04335 .04336 .04338 .04339 8.64580 .64595 .64609 .64624 .04434 .04435 .04437 .04428 8.65456 .65471 .65485 .65500 .04514 .04516 .04517 .04519 8.66323 .66338 .66352 .66366 .04605 .04607 .04608 .04610 62 61 60 49 + 3' IS 14 15 8.62860 .62875 .62890 .62904 8.62919 .62934 .62949 .62964 .04352 .04353 .04355 .04256 8.63754 .63769 .63784 .63798 .04340 .04343 .04343 .04345 8.64639 .64653 .64668 .64683 .04430 .04431 .04433 .04434 8.65514 .65529 .65543 .65558 .04530 .04533 .04533 .04525 8.66381 .66395 .66409 .66424 .04611 .04613 .04614 .04616 48 47 46 46 + i' 17 18 19 .04258 .04259 .04361 .04363 8.63813 .63828 .63843 .63858 .04346 .04348 .04349 .04351 8.64697 .64712 .64727 .64741 .04436 .04437 .04439 .04440 8.65572 .65587 .65601 .65616 .04526 .04538 .04539 .04531 8.66438 .66453 .66467 .66481 .04617 .04619 .04620 .04622 44 43 42 41 + 5' 21 22 23 8.62979 .62994 .63009 .63024 8.63039 .63054 .63069 .63084 .04364 .04365 .04367 .04268 8.63872 .63887 .63902 .63917 .04353 .04354 .04355 .04357 8.64756 .64771 .64785 .64800 .04442 .04443 .04445 .04446 8.65630 .65645 .65659 .65674 .04532 .04534 .04535 .04537 8.66496 .66510 .66524 .66539 .04623 .04625 .04636 .04638 40 39 38 37 36 36 34 33 + 6' 25 26 27 .04270 .04271 .04373 .04374 8.63932 .63946 .63961 .63976 .04358 .04360 .04361 .04363 8.64815 .64829 .64844 .64859 .04448 .04449 .04451 .04452 8.65688 .65703 .65717 .65732 .04538 .04540 .04541 .04543 8.66553 .66567 .66582 .66596 .04639 .04631 .04633 .04634 + r 29 SO 31 8.63099 .63114 .63129 .63144 .04376 .04377 .04378 .04280 8.63991 .64006 .64020 .64035 .04364 .04366 .04367 .04369 8.64873 .64888 .64902 .64917 .04454 .04455 .04457 .04458 8.65746 .65761 .65775 .65790 .04544 .04546 .04547 .04549 8.66610 .66625 .66639 .66653 .04636 .04637 .04639 .04640 32 31 30 29 { + S' S3 34 35 8.63159 .63174 .63189 .63204 .04281 .04283 .04284 .04286 8.64050 .64065 .64079 .64094 .04370 .04372 .04373 .04375 8.64932 .64946 .64961 .64976 .04460 .04461 .04463 .04464 8.65804 .65819 .65833 .65848 .04550 .04553 .04553 .04555 8.66668 .66682 .66696 .66710 .04643 .04643 .04645 .04646 28 27 26 25 + 9^ 37 38 39 8.63218 .63233 .63248 .63263 .04287 .04289 .04290 .04292 8.64109 .64124 .64139 .64153 .04376 .04378 .04379 .04381 8.64990 .65005 .65019 .65034 .04466 .04467 .04469 .04470 8.65862 .65876 .65891 .65905 .04556 .04558 .04559 .04561 8.66725 .66739 .66753 .66768 .04648 .04649 .04651 .04653 24 23 22 21 + 10' 41 42 43 8.63278 .63293 .63308 .63323 .04293 .04295 .04396 .04398 8.64168 .64183 .64198 .64212 .04383 .04384 .04385 .04387 8.65049 .65063 .65078 .65092 .04472 .04473 .04475 .04476 8.65920 .65934 .65949 .65963 .04563 .04564 .04565 .04567 8.66782 .66796 .66811 .66825 .04654 .04655 .04657 .04659 20 19 18 17 + 11' 45 46 47 8.63338 .63353 .63368 .63382 .04399 .04301 .04303 .04304 8.64227 .64242 .64257 .64271 .04388 .04390 .04391 .04393 8.65107 .65122 .65136 .65151 .04478 .04479 .04481 .04482 8.65978 .65992 .66006 .66021 .04569 .04570 .04573 .04573 8.66839 .66853 .66868 .66882 .04660 .04663 .04663 .04665 16 15 14 13 + 13' 49 50 51 8.63397 .63412 .63427 .63442 .04305 .04306 .04308 .04309 8.64286 .64301 .64315 .64330 .04394 .04395 .04397 .04398 8.65165 .65180 .65194 .65209 .04484 .04485 .04487 .04488 8.66035 .66050 .66064 .66079 .04575 .04576 .04578 .04579 8.66896 .66911 .66925 .66939 .04666 .04668 .04669 .04671 12 11 10 9 1 + 13' 53 54 55 8.63457 .63472 .63487 .63502 .04311 .04313 .04314 .04315 8.64345 .64360 .64374 .64389 .04400 .04401 .04403 .04404 8.65224 .65238 .65253 .65267 .04490 .04491 .04493 .04494 8.66093 .66107 .66122 .66136 .04581 .04582 .04584 .04585 .04587 .04588 .04590 .04591 8.66953 .66968 .66982 .66996 .04673 .04674 .04675 .04677 8 7 6 5 + 14' 57 58 59 8.63516 .63531 .63546 .63561 .04317 .04318 .04330 .04331 8.64404 .64418 .64433 .64448 .04405 .04407 .04409 .04410 8.65282 .65296 .65311 .65325 .04496 .04497 .04499 .04500 8.66151 .66165 .66179 .66194 8.67010 .67025 .67039 .67053 .04678 .04680 .04682 .04683 4 3 2 1 + 15' 8.63576 .04333 8.64463 .04413 8.65340 .04502 8.66208 .04593 8.67067 .04685 22fi' 24'"'' ^:gft 23->n 22^ 22^ 22 Jt 21'"* 22Ji20m 1 1 TABLE 45. [Page 831 Havereines. s Ih 40m 25° (K | Ih 4im 25° 15^ in 42m 25° W 1 lh43mU°i5' 1 lhum2&°0' 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.67067 .67082 .67096 .67110 .04685 .04686 .04688 .04689 8.67918 .67932 .67946 .67960 .04777 .04779 .04780 .04782 8.68760 .68773 .68787 .68801 .04871 .04872 .04874 .04875 8.69593 .69607 .69620 .69634 .04965 .04967 .04968 .04970 8.70418 .70431 .70445 .70459 .05060 .05062 .05063 .05085 60 59 58 57 + 1^ 5 6 7 8.67124 .67139 .67153 .67167 .04691 .04692 .04694 .04695 8.67974 .67988 .68002 .68016 .04783 .04785 .04787 .04788 8.68815 .68829 .68843 .68857 .04877 .04879 .04880 .04882 8.69648 .69662 .69676 .69690 .04971 .04973 .04975 .04976 8.70472 .70486 .70500 .70513 .05067 .05068 .05070 .05071 56 55 54 53 + 2^ 9 10 11 8.67181 .67196 .67210 .67224 .04697 .04698 .04700 .04702 8.68030 .68045 .68059 .68073 .04790 .04791 .04793 .04794 8.68871 .68885 .68899 .68913 .04883 .04885 .04886 .04888 8.69703 .69717 .69731 .69745 .04978 .04979 .04981 .04982 8.70527 .70541 .70554 .70568 .05073 .05075 .05076 .05078 52 51 50 49 48 47 46 45 44 4S 42 41 40 39 38 37 + 3^ IS 14 15 8.67238 .67252 .67267 .67281 .04703 .04705 .04706 .04708 8.68087 .68101 .68115 .68129 .04796 .04797 .04799 .04801 8.68927 .68941 .68955 .68969 .04890 .04891 .04893 .04894 8.69758 .69772 .69786 .69800 .04984 .04986 .04987 .04989 8.70582 .70595 .70609 .70623 .05079 .05081 .05083 .05084 + 4^ 17 18 19 8.67295 .67309 .67323 .67338 .04709 .04711 .04712 .04714 8.68143 .68157 .68171 .68185 .04802 .04804 .04805 .04807 8.68983 .68996 .69010 .69024 .04896 .04897 .04899 .04901 8.69814 .69827 .69841 .69855 .04990 .04992 .04994 .04995 8.70636 .70650 .70664 .70677 .05086 .05087 .05089 .05091 + ^ 21 22 23 8.67352 .67366 .67380 .67394 .04715 .04717 .04718 .04720 8.68199 .68213 .68227 .68241 .04808 .04810 .04811 .04813 8.69038 .69052 .69066 .69080 .04902 .04904 .04905 .04907 8.69869 .69882 .69896 .69910 .04997 .04998 .05000 .05001 8.70691 .70704 .70718 .70732 .05092 .05094 .05095 .05097 + 6^ 25 26 27 8.67409 .67423 .67437 .67451 .04722 .04723 .04725 .04726 8.68256 .68270 .68284 .68298 .04815 .04816 .04818 .04819 8.69094 .69108 .69122 .69136 .04908 .04910 .04912 .04913 8.69924 .69937 .69951 .69965 .05003 .05005 .05006 .05008 8.70745 .70759 .70773 .70786 .05099 .05100 .05102 .05104 36 35 34 33 + r 29 SO SI 8.67465 .67480 .67494 .67508 .04728 .04729 .04731 .04732 8.68312 .68326 .68340 .68354 .04821 .04822 .04824 .04825 8.69149 .69163 .69177 .69191 .04915 .04916 .04918 .04919 8.69979 .69992 .70006 .70020 .05009 .05011 .05013 .05014 8.70800 .70813 .70827 .70841 .05105 .05107 .05108 .05110 32 31 30 29 28 27 26 25 24 23 22 21 + 8^ SS S4 35 8.67522 .67536 .67550 .67565 .04734 .04735 .04737 .04739 8.68368 .68382 .68396 .68410 .04827 .04829 .04830 .04832 8.69205 .69219 .69233 .69247 .04921 .04923 .04924 .04926 8.70034 .70047 .70061 .70075 .05016 .05017 .05019 .05021 8.70854 .70868 .70881 .70895 .05111 .05113 .05115 .05116 + 9^ S7 38 39 8.67579 .67593 .67607 .67621 .04740 .04742 .04743 .04745 8.68424 .68438 .68452 .68466 .04833 .04835 .04836 .04838 8.69260 .69274 .69288 .69302 .04927 .04929 .04930 .04932 8.70089 .70102 .70116 .70130 .05022 .05024 .05025 .05027 8.70909 .70922 .70936 .70949 .05118 .05119 .05121 .05123 + W 41 42 AS 8.67635 .67649 .67664 .67678 .04746 .04748 .04749 .04751 8.68480 .68494 .68508 .68522 .04839 .04841 .04843 .04844 8.69316 .69330 .69344 .69358 .04934 .04935 .04937 .04938 8.70144 .70157 .70171 .70185 .05028 .05030 .05032 .05033 8.70963 .70977 .70990 .71004 .05124 .05126 1 .05127 .05129 20 19 18 17 + 11^ 45 46 47 8.67692 .67706 .67720 .67734 .04752 .04754 .04756 .04757 8.68536 .68550 .68564 .68578 .04846 .04847 .04849 .04850 8.69371 .69385 .69399 .69413 .04940 .04941 .04943 .04945 8.70198 .70212 .70226 .70240 .05035 .05036 .05038 .05040 8.71017 .71031 .71045 .71058 .05131 .05132 .05134 .05135 16 15 U IS 12 11 10 9 + ir 5i 8.67748 .67763 .67777 .67791 .04759 .04760 .04762 .04763 8.68592 .68606 .68620 .68634 .04852 .04854 .04855 .04857 8.69427 .69441 .69454 .69468 .04946 .04948 .04949 .04951 8.70253 .70267 .70281 .70294 .05041 .05043 .05044 .05046 8.71072 .71085 .71099 .71112 .05137 .05139 .05140 .05142 + 13^ 53 54 55 8.67805 .67819 .67833 .67847 .04765 .04766 .04768 .04769 8.68648 .68662 .68676 .68690 .04858 .04860 .04861 .04863 8.69482 .69496 .69510 .69524 .04952 .04954 .04956 .04957 8.70308 .70322 .70336 .70349 .05048 .05049 .05051 .05052 8.71126 .71140 .71153 .71167 .05144 .05145 .05147 .05148 8 7 6 5 + 14^ 57 55 59 8.67861 .67875 .67890 .67904 .04771 .M773 .•4V74 .04776 8.68704 .68718 .68732 .68746 .04864 .04866 .04868 .04869 8.69537 .69551 .69565 .69579 .04959 .04960 .04962 .04964 8.70363 .70377 .70390 .70404 .05054 .05055 .05057 .05059 8.71180 .71194 .71207 .71221 .05150 .05152 .05153 .05155 4 3 2 1 + W 8.67918 .•1777 8.68760 .04871 8.69593 .04965 8.70418 .05060 8.71234 .05156 22^ 19^ 22n igm 22h nm 22^ 16m 22h 15m Page 832] TABLE 45. Haversines. s ift ^"« 26° 15' Ih 46m 36° 30' Ih 47m 26° 45' Ih 48m 27° 0' Ih 49m 27° 15' s Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.71234 .71248 .71261 .71275 .05156 .05158 .05160 .05161 8.72043 .72057 .72070 .72083 .05253 .05255 .05257 .05258 8.72844 .72857 .72871 .72884 .05351 .05353 .05354 .05356 8.73637 .73650 .73663 .73677 .05450 .05451 .05453 .05455 8.74423 .74436 .74449 .74462 .05549 .05551 .05552 .05554 60 59 58 57 66 65 54 53 + r 5 6 7 8.71289 .71302 .71316 .71329 .05163 .05164 .05166 .05168 8.72097 .72110 .72124 .72137 .05260 .05261 .05263 .05265 8.72897 .72910 .72924 .72937 .05358 .05359 .05361 .05363 8.73690 .73703 .73716 .73729 .05456 .05458 .05460 .05461 8.74475 .74488 .74501 .74514 .05556 .05557 .05559 .05561 + 2' 9 10 11 8.71343 .71356 .71370 .71383 .05169 .05171 .05172 .05174 8.72150 .72164 .72177 .72191 .05266 .05268 .05270 .05271 8.72950 .72963 .72977 .72990 .05364 .05366 .05367 .05369 8.73742 .73755 .73769 .73782 .05463 .05464 .05466 .05468 8.74527 .74540 .74553 .74566 .05562 .05564 .05566 .05567 52 51 60 49 + 3' IS 14 15 8.71397 .71410 .71424 .71437 .05176 .05177 .05179 .05181 8.72204 .72217 .72231 .72244 .05273 .05274 .05276 .05278 8.73003 .73016 .73030 .73043 .05371 .05372 .05374 .05376 8.73795 .73808 .73821 .73834 .05470 .05471 .05473 .05474 8.74579 .74592 .74605 .74618 .05569 .05571 .05572 .05574 48 47 46 46 + 4' 17 18 19 8.71451 .71464 .71478 .71491 .05182 .05184 .05185 .05187 8.72257 .72271 .72284 .72298 .05279 .05281 .05283 .05284 8.73056 .73069 .73083 .73096 .05377 .05379 .05381 .05382 8.73847 .73860 .73874 .73887 .05476 .05478 .05479 .05481 8.74631 .74644 .74657 .74670 .05576 .05577 .05579 .05581 44 43 42 41 + ^ 21 22 23 8.71505 .71518 .71532 .71545 .05189 .05190 .05192 .05193 8.72311 .72324 .72338 .72351 .05286 .05287 .05289 .05291 8.73109 .73122 .73136 .73149 .05384 .05385 .05387 .05389 8.73900 .73913 .73926 .73939 .05483 .05484 .05486 .05488 8.74683 .74696 .74709 .74722 .05582 .05584 .05586 .05587 40 39 38 37 36 36 34 33 + 6' 25 26 27 8.71559 .71572 .71586 .71599 .05195 .05197 .05198 .05200 8.72364 .72378 .72391 .72404 .05292 .05294 .05296 .05297 8.73162 .73175 .73189 .73202 .05390 .05392 .05394 .05395 8.73952 .73965 .73978 .73992 .05489 .05491 .05493 .05994 8.74735 .74748 .74761 .74774 .05589 .05591 .05593 .05594 + r 29 SO SI 8.71613 .71626 .71640 .71653 .05201 .05203 .05205 .05206 8.72418 .72431 .72445 .72458 .05299 .05300 .05302 .05304 8.73215 .73228 .73241 .73255 .05397 .05399 .05400 .05402 8.74005 .74018 .74031 .74044 .05496 .05498 .05499 .05501 8.74787 .74800 .74813 .74826 .05596 .05597 .05599 .05601 32 31 30 29 + 8' 33 34 35 8.71667 .71680 .71694 .71707 .05208 .05210 .05211 .05213 8.72471 .72485 .72498 .72511 .05305 .05307 .05309 .05310 8.73268 .73281 .73294 .73308 .05404 .05405 .05407 .05408 8.74057 .74070 .74083 .74096 .05503 .05504 .05506 .05508 8.74839 .74852 .74864 .74877 .05603 .05604 .05606 .05607 28 27 26 25 37 38 39 8.71721 .71734 .71748 .71761 .05214 .05216 .05218 .05219 8.72525 .72538 .72551 .72565 .05312 .05314 .05315 .05317 8.73321 .73334 .73347 .73360 .05410 .05412 .05413 .05415 8.74109 .74122 .74135 .74149 .05509 .05511 .05513 .05514 8.74890 .74903 .74916 .74929 .05609 .05611 .05613 .05614 24 23 22 21 + lO' 41 42 43 8.71774 .71788 .71801 .71815 .05221 .05222 .05224 .05226 8.72578 .72591 .72605 .72618 .05318 .05320 .05322 .05323 8.73374 .73387 .73400 .73413 .05417 .05418 .05420 .05422 8.74162 .74175 .74188 .74201 .05516 .05518 .05519 .05521 8.74942 .74955 .74968 .74981 .05616 .05618 .05619 .05621 20 19 18 17 + 11' 45 46 47 8.71828 .71842 .71855 .71869 .05227 .05229 .05231 .05232 8.72631 .72644 .72658 .72671 .05325 .05326 .05328 .05330 8.73426 .73440 .73453 .73466 .05423 .05425 .05427 .05428 8.74214 .74227 .74240 .74253 .05523 .05524 .05526 .05528 8.74994 .75007 .75020 .75033 .05623 .05624 .05626 .05628 16 16 14 13 + 12' 50 5/ 8.71882 .71895 .71909 .71922 .05234 .05235 .05237 .05239 8.72684 .72698 .72711 .72724 .05331 .05333 .05335 .05336 8.73479 .73492 .73505 .73519 .05430 .05431 .05433 .05435 8.74266 .74279 .74292 .74305 .05529 .05531 .05533 .05534 8.75046 .75059 .75072 .75084 .05629 .05631 .05633 .05634 12 11 10 9 + 13' 53 54 55 8.71936 .71949 .71963 .71976 .05240 .05242 .05244 .05245 8.72738 .72751 .72764 .72778 .05338 .05340 .05341 .05343 8.73532 .73545 .73558 .73571 .05436 .05438 .05440 .05441 8.74318 .74331 .74344 .74357 .05536 .05537 .05539 .05541 8.75097 .75110 .75123 .75136 .05636 .05638 .05639 .05641 8 7 6 5 + 14' 55 59 8.71989 .72003 .72016 .72030 .05247 .05248 .05250 .05252 8.72791 .72804 .72817 .72831 .05345 .05346 .05348 .05349 8.73584 .73598 .73611 .73624 .05443 .05445 .05446 .05448 8.74371 .74384 .74397 .74410 .05542 .05544 .05546 .05547 8.75149 .75162 .75175 .75188 .05643 .05644 .05646 .05648 4 3 2 1 + 15' 8.72043 .05253 8.72844 .05351 8.73637 .05450 8.74423 .05549 8.75201 .05649 : 22^ 14™- 1 SSfi 13m 1 ■ 22h 12m 22^ llm 22^ IQm TABLE 45. [Page 833 Haversines. s iA5om27o30' 1 lh5iTO27°45' 1 Ih 52m 28° O' Ih 53m 28° 15' Ih 54-^ 28° 3^ 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.75201 .75214 .75227 .75239 .05649 .05651 .05653 .05655 8.75972 .75984 .75997 .76010 .05751 .05752 .05754 .05756 8.76735 .76748 .76760 .76773 .05853 .05854 .05856 .05858 8.77492 .77504 .77517 .77529 .05955 .05957 .05959 .05961 8.78241 .78254 .78266 .78278 .06059 .06061 .06063 .06064 60 59 58 57 + r 5 6 7 8.75252 .75265 .75278 .75291 .05656 .05658 .05660 .05661 8.76023 .76035 .76048 .76061 .05757 .05759 .05761 .05762 8.76786 .76798 76811 .76824 .05859 .05861 .05863 .05865 8.77542 .77554 .77567 .77579 .05962 .05964 .05966 .05968 8.78291 .78303 .78316 .78328 .06066 .06068 .06070 .06071 66 55 54 53 + 2' 9 10 11 8.75304 .75317 .75330 .75343 .05663 .05665 .05666 .05668 .05670 .05671 .05673 .05675 8.76074 .76086 .76099 .76112 .05764 .05766 .05768 .05769 8.76836 .76849 .76862 .76874 .05866 .05868 .05870 .05871 8.77592 .77604 .77617 .77630 .05969 .05971 .05973 .05974 8.78341 .78353 .78365 .78378 .06073 .06075 .06077 .06078 62 51 50 49 + 3' IS 14 15 8.75355 .75368 .75381 .75394 8.76125 .76138 .76150 .76163 .05771 .05773 .05774 .05776 8.76887 .76900 .76912 .76925 .05873 .05875 .05877 .05878 8.7.7642 .77655 .77667 .77680 .05976 .05978 .05980 .05981 .05983 .05985 .05986 .05988 8.78390 .78403 .78415 .78428 8.78440 .78452 .78465 .78477 .06080 .06082 .06083 .06085 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 S3 + 4' 17 18 19 8.75407 .75420 .75433 .75446 .05676 .05678 .05680 .05681 .05683 .05685 .05686 .05688 8.76176 .76189 .76201 .76214 .05778 .05779 .05781 .05783 .05785 .05786 .05788 .05790 8.76938 .76950 .76963 .76975 8.76988 .77001 .77013 .77026 8.77039 .77051 .77064 .77076 .05880 .05882 .05883 .05885 .05887 .05888 .05890 .05892 8.77692 .77705 .77717 .77730 .06087 .06089 .06090 .96092 + 5' 21 22 23 8.75458 .75471 .75484 .75497 8.76227 .76240 .76252 .76265 8.77742 .77755 .77767 .77780 .05990 .05992 .05993 .05995 .05997 .05999 .06000 .06002 8.78490 .78502 .78514 .78527 .06094 .06096 .06097 .06099 + 6' 25 26 27 8.75510 .75523 .75536 .75548 .05690 .05691 .05693 .05695 .05697 .05698 .05700 .05702 8.76278 .76291 .76303 .76316 .05791 .05793 .05795 .05796 .05894 .05895 .05897 .05899 8.77792 .77805 .77817 .77830 8.78539 .78551 .78564 .78576 .06101 .06103 .06104 .06106 + r 29 SO 31 8.75561 .75574 .75587 .75600 8.76329 .76341 .76354 .76367 .05798 .05800 .05802 .05803 8.77089 .77102 .77114 .77127 .05901 .05902 .05904 .05906 8.77842 .77855 .77867 .77880 .06004 .06005 .06007 .06009 8.78589 .78601 .78613 .78626 .06108 .06110 .06111 .06113 32 31 SO 29 + S' 33 34 35 8.75613 .75626 .75638 .75651 .05703 .05705 .05707 .05708 8.76380 .76392 .76405 .76418 .05805 .05807 .05808 .05810 8.77139 .77152 .77165 .77177 .05907 .05909 .05911 .05913 8.77892 .77905 .77917 .77930 .06011 .06012 .06014 .06016 8.78638 .78651 .78663 .78675 .06115 .06117 .06118 .06120 28 27 26 25 + r 37 38 39 8.75664 .75677 .75690 .75703 .05710 .05712 .05713 .05715 8.76431 .76443 .76456 .76469 .05812 .05813 .05815 .05817 8.77190 .77202 .77215 .77228 .05914 .05916 .05918 .05919 8.77942 .77955 .77967 .77980 .06018 .06019 .06021 .06023 8.78688 .78700 .78712 .78725 .06122 .06124 .06125 .06127 24 23 22 21 + W 41 42 43 8.75715 .75728 .75741 .75754 .05717 .05718 .05720 .05722 8.76481 .76494 .76507 .76519 .05819 .05820 .05822 .05824 8.77240 .77253 .77265 .77278 .05921 .05923 .05925 .05926 8.77992 .78005 .78017 .78029 .06024 .06026 .06028 .06030 8.78737 .78749 .78762 .78774 .06129 .06130 .06132 .06134 20 19 18 17 + 11' 45 46 47 8.75767 .75779 .75792 .75805 .05724 .05725 .05727 .05729 8.76532 .76545 .76558 .76570 .05825 .05827 .05829 .05830 8.77291 .77303 .77316 .77328 .05928 .05930 .05931 .05933 8.78042 .78054 .78067 .78079 .06031 .06033 .06035 .06037 8.78787 .78799 .78811 .78824 .06136 .06137 .06139 .06141 16 15 14 13 + ir 49 50 51 8.75818 .75831 .75844 .75856 .05730 .05732 .05734 .05735 8.76583 .76596 .76608 .76621 .05832 .05834 .05836 .05837 8.77341 .77353 .77366 .77379 .05935 .05936 .05938 .05940 8.78092 .78104 .78117 .78129 .06038 .06040 .06042 .06044 8.78836 .78848 .78861 .78873 .06143 .06144 .06146 .06148 12 11 10 9 + 13' 53 54 55 8.75869 .75882 .75895 .75908 .05737 .05739 .05740 .05742 8.76634 .76646 .76659 .76672 .05839 .05841 .05842 .05844 8.77391 .77404 .77416 .77429 .05942 .05943 .05945 .05947 8.78142 .78154 .78167 .78179 .06045 .06047 .06049 .06050 .06052 .06054 .06056 .06057 8.78885 .78898 .78910 .78922 .06150 .06151 .06153 .06155 8 7 6 5 + ir 57 58 59 8.75920 .75933 .75946 .75959 .05744 .05745 .05747 .05749 8.76684 .76697 .76710 .76722 8.76735 .05846 .05847 .05849 .05851 .05853 8.77441 .77454 .77466 .77479 .05949 .05950 .05952 .05954 8.78191 .78204 .78216 .78229 8.78935 .78947 .78959 .78972 .06157 .06158 .06160 .06162 4 S 2 1 + 15' 8.75972 .05751 8.77492 1 .05955 8.78241 .06059 8.78984 .06164 22h9m, 22^ Sm 22^ 7m 22^ 6m 22^ 5m Page 834] TABLE 45. Haversines. s J A 55"» 38° 45' ^'t 56"* 29° 0' Ih 57m 29° 15' 1^ 58mZ9° 30' Ifi59m29° W s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.78984 .78996 .79009 .79021 .06164 .06165 .06167 .06169 8.79720 .79732 .79744 .79757 .06369 .06371 .06373 .06374 8.80449 .80462 .80474 .80486 .06375 .06377 .06379 .06381 8.81172 .81184 .81196 .81208 .06482 .08484 .06486 .06488 8.81889 .81901 .81913 .81925 .06590 .06593 .06594 .06595 60 59 58 57 + r 5 6 7 8.79033 .79046 .79058 .79070 .06171 .06172 .06174 .06176 8.79769 .79781 .79793 .79805 .06376 .06378 .06380 .06281 8.80498 .80510 .80522 .80534 .06382 .06384 .06386 .06388 8.81220 .81232 .81244 .81256 .06489 .06491 .06493 .06495 8.81937 .81948 .81960 .81972 .06597 .06599 .06601 .06603 56 55 54 53 + 2^ 9 10 11 8.79082 .79095 .79107 .79119 .06178 .06179 .06181 .06183 8.79818 .79830 .79842 .79854 .06383 .06385 .06387 .06388 8.80546 .80558. .80570 .80582 .06389 .06391 .06393 .06395 8.81268 .81280 .81292 .81304 .06497 .06498 .06500 .06502 8.81984 .81996 .82008 .82020 .06605 .06606 .06608 .06610 52 51 50 49 + 3' 13 14 15 8.79132 .79144 .79156 .79169 .06185 .06186 .06188 .06190 8.79866 .79879 .79891 .79903 .06390 .06392 .06294 .06295 8.80595 .80607 .80619 .80631 .06397 .06398 '.06400 .06402 8.81316 .81328 .81340 .81352 .06504 .06505 .06507 .06509 8.82032 .82043 .82055 .82067 .08613 .06614 .06615 .06617 48 47 46 45 44 43 42 41 + 4^ 17 18 19 8.79181 .79193 .79205 .79218 .06192 .06193 .06195 .06197 8.79915 .79927 .79940 .79952 .06397 .06399 .06301 .06303 8.80643 .80655 .80667 .80679 /^. 06404 .06405 .06407 .06409 8.81364 -♦.81376 .81388 .81400 .06511 .06513 .06514 .06516 8.82079 .82091 .82103 .82115 .06619 .06621 .06633 .08634 + r 21 22 23 8.79230 .79242 .79255 .79267 .06199 .06300 .06202 .06204 8.79964 .79976 .79988 .80000 .06304 .06306 .06308 .06310 8.80691 .80703 .80715 .80727 .06411 .06413 .06414 .06416 8.81412 .81424 .81436 .81448 .06518 .06520 .06522 .06523 8.82126 .82138 .82150 .82162 .06836 .06638 .06630 .06633 40 39 38' 37 + 6^ 25 26 27 8.79279 .79291 .79304 .79316 .06206 .06207 .06209 .06211 8.80013 .80025 .80037 .80049 .06311 .06313 .06315 .06317 8.80739 .80751 .80764 .80776 .06418 .06420 .06431 .06433 8.81460 .81472 .81484 .81496 .06525 .06527 .06529 .06531 8.82174 .82186 .82198 .82209 .06633 .06635 .06637 .06639 36 35 34 33 + r 29 SO 31 8.79328 .79341 .79353 .79365 .06213 .06214 .06216 .06218 8.80061 .80073 .80086 .80098 .06318 .06330 .06323 .06324 8.80788 .80800 .80812 .80824 .06435 .06437 .06439 .06430 8.81508 .81520 .81531 .81543 .06533 .06534 .06536 .06538 8.82221 .82233 .82245 .82257 .06641 .06643 .06644 .06646 32 SI SO 29 28 27 26 25 + 8' 33 34 35 8.79377 .79390 .79402 .79414 .06220 .06221 .06233 .06325 8.80110 .80122 .80134 .80146 .06326 .06327 .06329 .06331. 8.80836 .80848 .80860 .80872 .06433 .06434 .06436 .06438 8.81555 .81567 .81579 .81591 .06540 .06541 .06543 .06545 8.82269 .82280 .82292 .82304 .06648 .06650 .06652 .06853 + 9' 59 8.79426 .79439 .79451 .79463 .06237 .06229 .06230 .06233 8.80158 .80171 .80183 .80195 .06333 .06334 .06336 .06338 8.808;54 .80896 .80908 .80920 .06439 .06441 .06443 .06445 8.81603 .81615 .81627 .81639 .06547 .06549 .06550 .06552 8.82316 .82328 .82340 .82351 .06855 .06657 .06659 .06661 24 23 22 21 + 10' 41 42 43 8.79475 .79488 .79500 .79512 .06234 .06236 .06337 .06339 8.80207 .80219 .80231 .80243 .06340 .06341 .06343 .06345 8.80932 .80944 .80956 .80968 .06446 .06448 .06450 .06452 8.81651 .81663 .81675 .81687 .06554 .06556 .06558 .06559 8.82363 .82375 .82387 .82399 .08882 .06684 .06868 .06668 20 19 18 17 + ir •^7 8.79524 .79537 .79549 .79561 .06241 .06343 .06344 .06346 8.80256 .80268 .80280 .80292 .06347 .06349 .06350 .06352 8.80980 .80992 .81004 .81016 .06454 .06455 .06457 .06459 8.81699 .81710 .81722 .81734 .06561 .06563 .06565 .06567 8.82410 .82422 .82434 .82446 .06670 .06871 .06673 .06675 16 15 14 IS + ir 49 50 51 8.79573 .79586 .79598 .79610 .06348 ,06350 .06351 .06353 8.80304 .80316 .80328 .80340 .06354 .06356 ,.06357 .06359 8.81028 .81040 .81052 .81064 .06461 .06463 .06464 .06466 8.81746 .81758 .81770 .81782 .06568 •.06570 .06572 .06574 8.82458 .82470 .82481 .82493 , .06877 \ .06679 \08881 .06683 12 11 10 9 8 7 6 5 + 13' 53 54 55 8.79622 .79634 .79647 .79659 .06355 .06357 .06358 .06360 8.80353 .80365 .80377 .80389 .06361 .06363 .06365 .66366 8.81076 .81088 .81100 .81112 .06468 .06470 .06471 .06473 8.81794 .81806 .81818 .81830 .06576 .06577 .06579 .06581 8.82505 .82517 .82529 .82540 .06684 .06886 .06688 .08690 + 14' 57 55 59 8.79671 .79683 .79696 .79708 .06363 .06264 .06265 .06367 8.80401 .80413 .80425 .80437 .06368 .06370 .06373 .06373 8.81124 .81136 .81148 .81160 .06475 .06477 .06479 .06480 8.81841 .81853 .81865 .81877 .06583 .06585 .06586 .06588 8.82552 .82564 .82576 .82588 .06691 .08693 .08695 .08697 4 3 2 1 + 15' 8.79720 .06369 8.80449 .06375 8.81172 .06482 8.81889 .06590 8.82599 .08899 22h4m 22h3'm 22h 2m 22^ im o^h Qm TABLE 45. [Page 836 Havereines. s 2h Om 30° (K 1 2h im 30° 15' | 2h 2m 30° 30' 2h 3m 30° 45' 5 .gft 4^ 31° C s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav.' Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.82599 .82611 .82623 .82635 .06699 .06701 .06702 .06704 8.83303 .83315 .83327 .83338 .06808 .06810 .06812 .06814 8.84002 .84013 .84025 .84036 .06919 .06920 .06923 .06924 8.84694 .84705 .84717 .84728 .07030 1 .07032 .07033 .07035 8.85380 .85391 .85403 .85414 .07142 .07144 .07145 .07147 60 59 58 57 + r 5 6 7 8.82646 .82658 .82670 .82682 .06706 .06708 .06710 .06711 8.83350 .83362 .83374 .83385 .06816 .06817 .06819 .06821 8.84048 .84059 .84071 .84083 8.84094 .84106 .84117 .84129 .06926 .06928 .06930 .06931 8.84740 .84751 .84762 .84774 .07037 .07039 .07041 .07043 8.85425 .85437 .85448 .85459 8^85471 .85482 .85494 .85505 .07149 .07151 .07153 .07155 56 55 54 53 + 3^ 9 10 11 8.82694 .82705 .82717 .82729 .06713 .06715 .06717 .06719 8.83397 .83409 .83420 .83432 .06823 .06825 .06826 .06828 .06933 .06935 .06937 .06939 8.84785 .84797 .84808 .84820 .07045 .07046 .07048 .07050 .07157 .07158 .07160 .07162 52 51 50 49 + 3' 13 14 15 8.82741 .82752 .82764 .82776 .06721 .07722 .06724 .06726 8.834^ .83455 .83467 .83479 .06830 .06832 .06834 .06836 8.84140 .84152 .84164 .84175 .06941 .06943 .06944 .06946 8.84831 .84843 .84854 .84866 .07052 .07054 .07056 .07058 8.85516 .85528 .85539 .85550 .07164 .07166 .07168 .07170 48 47 46 45 + *' 17 18 19 8.82788 .82799 .82811 .82823 .06728 .06730 .06731 .06733 8.83490 .83502 .83513 .83525 .06838 .06839 .06841 .06843 8.84187 .84198 .84210 .84221 .06948 .06950 .06952 .06954 8.84877 .84889 .84900 .84912 .07059 .07061 .07063 .07065 8.85562 .85573 .85585 .85596 8.85607 .85619 .85630 .85641 8.85653 .85664 .85675 .85687 .07172 .07173 .07175 .07177 44 43 42 41 + 5' 21 22 23 8.82835 .82846 .82858 .82870 8.82882 .82893 .82905 .82917 .06735 .06737 .06730 .06741 .06742 .06744 .06746 .06748 8.83537 .83548 .83560 .83572 8.83583 .83595 .83607 .83618 .06845 .06847 .06849 .06850 8.84233 .84244 .84356 .84268 8:84279 .84291 .84302 .84314 .06956 .06957 .06959 .06961 .06963 .06965 .06967 .06968 8.84923 .84934 .84946 .84957 8.84969 .84980 .84992 .85003 .07067 .07069 .07071 .07073 .07179 .07181 .07183 .07185 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 23 22 21 20 19 18 17 16 15 14 13 + 6' 25 26 27 .06852 .06854 .06856 .06858 .07074 .07076 .07078 .07080 .07187 .07189 .07190 .07192 + r 29 30 31 8.82929 .82940 .82952 .82964 .06750 .06752 .06753 .06755 8.83630 .83642 .83653 .83665 .06860 .06861 .06863 .06865 8.84325 .84337 .84348 .84360 8.84371 .84383 .84394 .84406 8.84417 .84429 .84441 .84452 .06970 .06972 .06974 .06976 .06978 .06980 .06981 .06983 .06985 .06987 .06989 .06991 8.85015 .85026 .85037 .85049 .07082 .07084 .07086 .07087 .07089 .07091 .07093 .07095 .07097 .07099 .07100 .07102 .07104 .07106 .07108 .07110 8.85698 .85709 .85721 .85732 .07194 .07196 .07198 .07200 + 8' 33 24 35 8.82976 .82987 .82999 .83011 .06757 .06759 .06761 .06763 8.83676 .83688 .83700 .83711 .06867 .06869 .06871 .06872 8.85060 .85072 .85083 .85095 8.85106 .85117 .85129 .85140 8.85152 .85163 .85175 .85186 8.85743 .85755 .85766 .85777 8.85789 .85800 .85811 .85823 8.85834 .85845 .85857 .85868 .07203 .07304 .07205 .07207 .07209 .07311 .07213 .07215 .07217 .07219 .07330 .07333 + 9" 37 38 39 8.83023 .83034 .83046 .83058 .06764 .06766 .06788 .06770 8.83723 .83735 .83746 .83758 .06874 .06876 .06878 .06880 + 1(K 41 42 43 8.83069 .83081 .83093 .83105 .06772 .06773 .06775 .06777 8.83769 .83781 .83793 .83804 .06882 .06884 .06885 .06887 8.84464 .84475 .84487 .84498 .06993 .06994 .06996 .06998 + ir 45 46 47 8.83116 .83128 .83140 .83151 .06779 .06781 .06783 .06784 8.83816 .83828 .83839 .83851 .06889 .06891 .06893 .06895 8.84510 .84521 .84533 .84544 8.84556 .84567 .84579 .84590 .07000 .07003 .07004 .07006 8.85197 .85209 .85220 .85232 .07112 .07114 .07115 .07117 8.85879 .85891 .85902 .85913 .07324 .07236 .07238 .07330 + 12' 49 50 51 8.83163 .83175 .83187 .83198 .06786 .06788 .06790 .06792 8.83862 .83874 .83886 .83897 .06896 .06898 .06900 .06902 .07007 .07009 .07011 .07013 8.85243 .85254 .85266 .85277 .07119 .07121 .07123 .07125 8.85925 .85936 .85947 .85959 .07333 .07334 .07236 .07337 12 11 10 9 + 13' 53 54 55 8.83210 .83222 .83233 .83245 .06794 .06795 .06797 .06799 8.83909 .83920 .83932 .83944 .06904 .06906 .06907 .06909 8.84602 .84613 .84625 .84636 .07015 .07017 .07019 .07030 8.85289 .85300 .85311 .85323 .07127 .07129 .07130 .07132 8.85970 .85981 .85992 .86004 .07339 .07341 .07343 .07345 .07347 .07249 .07251 .07253 .07254 8 7 6 5 4 3 2 1 + 14' 57 58 59 8.83257 .83268 .83280 .83292 .06801 .06803 .06805 .06806 8.83955 .83967 .83978 .83990 .06911 .06913 .06915 .06917 8.84648 .84659 .84671 .84682 .07022 .07024 .07026 .07028 8.85334 .85346 .85357 .85368 .07134 .07136 .07138 .07140 8.86015 .86026 .86038 .86049 + 15' 8.83303 .06808 8.84002 ! .06919 8.84694 .07030 8.85380 .07142 8.86060 21^59^ 21^ 58^ 21h 57m 21''' 56m 21h 55m Page 836] TABLE 45. Haversineg. s 2h 5m 31° 15' 2h 6m 31° 30' 2h Tm 31° 45/ 2li 8m 33° C 2h gm 33° 15/ s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.86060 .86072 .86085 .86094 .07354 .07256 .07258 .07260 8.86735 .86746 .86757 .86769 .07368 .07370 .07373 .07374 8.87404 .87415 .87426 .87437 .07483 .07484 .07486 .07488 8.88068 .88079 .88090 .88101 .07598 .07600 .07601 .07603 8.88726 .88737 .88748 .88759 .07714 .07716 .07717 .07719 60 59 58 57 + r 5 6 7 8.86105 .86117 .86128 .86139 .07263 .07264 .07266 .07268 8.86780 .86791 .86802 .86813 .07376 .07377 .07379 .07381 8.87448 .87460 .87471 .87482 .07490 .07493 .07494 .07496 8.88112 .88123 .88134 .88145 .07605 .07607 .07609 .07611 8.88769 .88780 .88791 .88802 .07721 .07723 .07725 .07727 56 55 54 53 + 2^ 9 10 11 8.86151 .86162 .86173 .86184 .07270 .07271 .07273 .07275 8.86825 .86836 .86847 .86858 .07383 .07385 .07387 .07389 8.87493 .87504 .87515 .87526 .07498 .07500 .07503 .07503 8.88156 .88167 .88178 .88189 .07613 .07615 .07617 .07619 8.88813 .88824 .88835 .88846 .07729 .07731 .07733 .07735 52 51 50 49 + 3' 13 14 15 8.86196 .86207 .86218 .86229 .07277 .07279 .07281 .07283 8.86869 .86880 .86892 .86903 .07391 .07393 .07395 .07397 8.87537 .87548 .87559 .87570 .07505 .07507 .07509 .07511 8.88200 .88211 .88222 .88233 .07631 .07633 .07635 .07637 8.88857 .88868 .88879 .88890 .07737 .07739 .07741 .07743 48 47 46 45 + *^ 17 18 19 8.86241 .86252 .86263 .86275 .07285 .07287 .07288 .07290 8.86914 .86925 .86936 .86947 .07398 .07400 .07403 .07404 8.87582 .87593 .87604 .87615 .07513 .07515 .07517 .07519 8.88244 .88255 .88266 .88277 .07638 .07630 .07633 .07634 8.88900 .88911 .88922 .88933 .07745 .07747 .07749 .07751 44 43 42 41 + 5^ 21 22 23 8.86286 .86297 .86308 .86320 .07292 .07294 .07296 .07298 8.86959 .86970 .86981 .86992 .07406 .07408 .07410 .07413 8.87626 .87637 .87648 .87659 .07531 .07533 .07535 .07527 8.88288 .88299 .88310 .88321 .07636 .07638 .07640 .07643 8.88944 .88955 .88966 .88977 .07753 .07754 .07756 .07758 40 39 38 37 + 6' 25 26 27 8.86331 .86342 .86353 .86365 .07300 .07302 .07304 .07305 8.87003 .87014 .87026 .87037 .07414 .07416 .07417 .07419 8.87670 .87681 .87692 .87703 .07528 .07530 .07533 .07534 8.88332 .88343 .88354 .88364 .07644 .07646 .07648 .07650 8.88988 .88998 .89009 .89020 .07760 .07762 .07764 .07766 36 35 34 33 + r 29 30 31 8.86376 .86387 .86398 .86410 .07307 .07309 .07311 .07323 8.87048 .87059 .87070 .87081 .07431 .07433 .07435 .07437 8.87714 .87725 .87737 .87748 .07536 .07538 .07540 .07543 8.88375 .88386 .88397 .88408 8.88419 .88430 .88441 .88452 .07652 .07654 .07656 .07657 8.89031 .89042 .89053 .89064 .07768 .07770 .07772 .07774 32 31 SO 29 + 8' 33 34 35 8.86421 .86432 .86443 .86455 .07315 .07317 .07319 .07321 8.87093 .87104 .87115 .87126 .07439 .07431 .07433 .07435 8.87759 .87770 .87781 .87792 .07544 .07546 .07548 .07549 .07659 .07661 .07663 .07665 8.89075 .89086 .89096 .89107 .07776 .07778 .07780 .07782 28 27 26 25 + 9^ 37 38 39 8.86466 .86477 .86488 .86499 .07323 .07324 .07326 .07328 8.87137 .87148 .87159 .87171 .07437 .07438 .07440 .07443 8.87803 .87814 .87825 .87836 .07551 .07553 .07555 .07557 8.88463 .88474 .88485 .88496 .07667 .07669 .07671 .07673 8.89118 .89129 .89140 .89151 .07784 .07786 .07788 .07789 24 23 22 21 20 19 18 17 16 15 14 IS + W 41 42 43 8.86511 .86522 .86533 .86544 .07330 .07332 .07334 .07336 8.87182 .87193 .87204 .87215 .07444 .07446 .07448 .07450 8.87847 .87858 .87869 .87880 .07559 .07561 .07563 .07565 8.88507 .88518 .88529 .88540 .07675 .07677 .07679 .07681 8.89162 .89172 .89183 .89194 .07791 .07793 .07795 .07797 + n' 45 46 47 8.86556 .86667 .86578 .86589 .07338 .07340 .07341 .07343 8.87226 .87237 .87248 .87260 .07453 .07454 .07456 .07458 8.87891 .87902 .87913 .87924 .07567 .07569 .07571 .07573 8.88551 .88562 .88573 .88584 .07683 .07685 .07686 .07688 8.89205 .89216 .89227 .89238 .07799 .07801 .07803 .07805 + ir 49 50 51 8.86600 .86611 .86623 .86634 .07345 .07347 .07349 .07351 8.87271 .87282 .87293 .87304 .07459 .07461 .07463 .07465 8.87935 .87946 .87957 .87968 .07574 .07576 .07578 .07580 8.88595 .88606 .88616 .88627 .07690 .07692 .07694 .07696 8.89248 .89259 .89270 .89281 .07807 .07809 .07811 .07813 12 11 10 9 + 13' 5S 54 55 8.86645 .86657 .86668 .86679 .07353 .07355 .07357 .07359 8.87315 .87326 .87337 .87349 .07467 .07469 .07471 .07473 8.87980 .87991 .88002 .88013 .07582 .07584 .07586 .07588 8.88638 .88649 .88660 .88671 .07698 .07700 .07702 .07704 8.89292 .89303 .89314 .89324 .07815 .07817 .07819 .07821 8 7 6 5 + 14' 57 58 59 8.86690 .86701 .86713 .86724 .07360 .07362 .07364 .07366 8.87360 .87371 .87382 ■ .87393 .07475 .07477 .07479 .07480 8.88024 .88035 .88046 .88057 .07590 .07592 .07694 .07590 8.88682 .88693 .88704 .88715 .07706 .07708 .07710 .07712 8.89335 .89346 .89357 .89368 .07823 .07825 .07827 .07829 4 3 2 1 + 15' 8.86735 .07368 8.87404 .07483 8.88068 .07598 8.88726 .07714 8.89379 .07830 21^ 54^ 21 h 53m 21h 52m 1 21h Sim 21h50m 1 TABLE 45. [Page 837 Havereinea. s 2^iam^°w 1 2hlim^°^^ 1 2h ipn 33° o' 1 2^ 13m 33/ U' 2hl4m^°S(/ 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.89379 .89389 .89400 .89411 .07830 .07832 .07834 .07836 8.90026 .90037 .90048 .90058 .07948 .07950 .07952 .07954 8.90668 .90679 .90690 .90700 8.90711 .90722 .90732 .90743 .08066 .08068 .08070 .08072 8.91306 .91316 .91327 .91337 .08186 .08188 .08190 .08192 8.91938 .91948 .91959 .91969 .08306 .08308 .08310 .08312 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 U 43 42 41 40 39 38 37 36 35 34 33 + r 5 6 7 8.89422 .89433 .89444 .89454 .07838 .07840 .07843 .07844 8.90069 .90080 .90091 .90101 8.90112 .90123 .90134 .90144 .07956 .07958 .07960 .07962 .07964 .07966 .07968 .07970 .08074 .08076 .08078 .08080 8.91348 .91358 .91369 .91380 .08194 .08196 .08198 .08200 8.91980 .91990 .92001 .92011 .08314 .08316 .08318 .08320 + 2' 9 10 11 8.89465 .89476 .89487 .89498 .07846 .07848 .07850 .07853 8.90754 .90764 .90775 .90786 .08082 .08084 .08086 .08088 8.91390 .91401 .91411 .91422 .08202 .08204 .08206 .08208 8.92022 .92032 .92043 .92053 .08322 .08324 .08326 .08328 + 3' 13 14 15 8.89509 .89519 .89530 .89541 .07854 .07856 .07858 .07860 8.90155 .90166 .90176 .90187 .07972 .07974 .07976 .07978 8.90796 .90807 .90818 .90828 8.90839 .90849 .90860 .90871 .08090 .08092 .08094 .08096 .08098 .08100 .08102 .08104 8.91432 .91443 .91454 .91464 .08210 .08212 .08214 .08216 8.92064 .92074 .92084 .92095 .08330 .08332 .08334 .08336 + *' 17 18 19 8.89552 .89563 .89573 .89584 .07862 .07864 .07866 .07868 8.90198 .90209 .90219 .90230 8.90241 .90252 .90262 .90273 .07980 .07982 .07983 .07985 .07987 .07989 .07991 .07993 8.91475 .91485 .91496 .91506 .08218 .08220 .08222 .08224 8.92105 .92116 .92126 .92137 8.92147 .92158 .92168 .92179 8.92189 .92200 .92210 .92221 .08338 .08340 .08342 .08344 .08346 .08348 .08350 .08352 + 5^ 21 22 23 8.89595 .89606 .89617 .89627 .07870 .07872 .07873 .07875 .07877 .07879 .07881 .07883 8.90881 .90892 .90903 .90913 8.90924 .90935 .90945 .90956 .08106 .08108 .08110 .08112 8.91517 .91527 .91538 .91549 .08226 .08228 .08230 .08232 .08234 .08236 .08238 .08240 + 6' 25 26 27 8.89638 .89649 .89660 .89671 8.90284 .90294 .90305 .90316 .07995 .07997 .07999 .08001 .08114 .08116 .08118 .08120 8.91559 .91570 .91580 .91591 .08354 .08356 .08358 .08360 + r 29 30 31 8.89681 .89692 .89703 .89714 .07885 .07887 .07889 .07891 8.90326 .90337 .90348 .90359 .08003 .08005 .08007 .08009 8.90966 .90977 .90988 .90998 .08122 .08124 .08126 .08128 8.91601 .91612 .91622 .91633 .08242 .08244 .08246 .08248 8.92231 .92241 .92252 .92262 8.92273 .92283 .92294 .92304 .08362 .08364 .08366 .08368 .08370 .08372 .08374 .08376 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 + S" 33 34 35 8.89725 .89735 .89746 .89757 .07893 .07895 .07897 .07899 8.90369 .90380 .90391 .90401 .08011 .08013 .08015 .08017 8.91009 .91019 .91030 .91041 .08130 .08132 .08134 .08136 8.91643 .91654 .91664 .91675 .08250 .08252 .08254 .08256 + IK 37 38 39 8.89768 .89779 .89789 .89800 .07901 .07903 .07905 .07907 8.90412 .90423 .90433 .90444 .08019 .08021 .08023 .08025 8.91051 .91062 .91073 .91083 .08138 .08140 .08142 .08144 8.91685 .91696 .91707 .91717 .08258 .08260 .08262 .08264 8.92315 .92325 .92335 .92346 .08378 .08380 .08382 .08384 + W 41 42 43 8.89811 .89822 .89832 .89343 .07909 .07911 .07913 .07915 8.90455 .90466 .90476 .90487 .08027 .08029 .08031 .08033 8.91094 .91104 .91115 .91126 .08146 .08148 .08150 .08152 8.91728 .91738 .91749 .91759 .08266 .08268 .08270 .08272 8.92356 .92367 .92377 .92388 .08386 .08388 .08390 .08392 + 11' 45 46 47 8.89854 .89865 .89875 .89886 .07917 .07919 .07921 .07923 8.90498 .90508 .90519 .90530 .08035 .08037 .08039 .08041 8.91136 .91147 .91157 .91168 .08154 .08156 .08158 .08160 8.91770 .91780 .91791 .91801 .08274 .08276 .08278 .08280 8.92398 .92409 .92419 .92429 .08394 .08396 .08398 .08400 16 15 14 13 12 11 10 9 + IV 49 50 51 8.89897 .89908 .89919 .89929 .07924 .07926 .07928 .07930 8.90540 .90551 .90562 .90572 .08043 .08045 .08047 .08049 8.91179 .91189 .91200 .91210 .08162 .08164 .08166 .08168 8.91812 .91822 .91833 .91843 .08282 .08284 .08286 .08288 8.92440 .92450 .92461 .92471 .08402 .08404 .08406 .08408 + 13^ 53 54 55 8.89940 .89951 .89962 .89972 .07932 .07934 .07936 .07938 8.90583 .90594 .90604 .90615 .08051 .08053 .08055 .08057 8.91221 .91232 .91242 .91253 .08170 .08172 .08174 .08176 8.91854 .91864 .91875 .91885 .08290 .08292 .08294 .08296 8.92482 .92492 .92502 .92513 .08410 .08412 .08414 .08416 8 7 6 5 + W 57 58 59 8.89983 .89994 .90005 .90015 .07940 .07942 .07944 .07946 8.90626 .90636 .90647 .90658 .08059 .08061 .08063 .08065 8.91263 .91274 .91284 .91295 .08178 .08180 .08182 .08184 8.91896 .91906 .91917 .91927 .08298 .08300 .08302 .08304 .08306 8.92523 .92534 .92544 .92554 .08418 .08420 .08422 .08425 4 3 2 1 + 15' 8.90026 .07948 8.90668 .08066 8.91306 .08186 8.91938 8.92566 .08427 2lTi49m 21h48m 1 21^47'm 21^46^ 21h45m k Page 838] TABLE 45. Haversines. s 2Ji 15m 33° 45^ 2li l&n 340 (K 2h 17m 34° 15' 2h igm 34° 3r 2h 19m 34° 45' s Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav. Nat. Hav Log. Hav Nat. Hav 1 2 3 8.92565 .92575 .92586 .92596 .08437 .08439 .08431 .08433 8.93187 .93197 .93208 .93218 .08548 .08550 .08553 .08554 8.93805 .93815 .93825 .93835 .08671 .08673 .08675 .08677 8.94417 .94427 .94438 .94448 .08794 .08796 .08798 .08800 8.95025 .95035 .95045 .95055 .08918 .08930 .08933 .08934 60 59 58 57 + r 5 6 7 8.92607 .92617 .92627 .92638 .08435 .08437 .08439 .08441 8.93228 .93239 .93249 .93259 .08556 .08558 .08560 .08563 8.93846 .93856 .93866 .93876 .08679 .08681 .08683 .08685 8.94458 .94468 .94478 .94488 .08803 .08804 .08806 .08808 8.95065 .95076 .95086 .95096 .08936 .08938 .08930 .08933 56 55 54 53 + r 9 10 11 8.92648 .32659 .92669 .92679 .08443 .08445 .08447 .08449 8.93270 .93280 .93290 .93301 .08564 .08566 .08568 .08571 8.93886 .93897 .93907 .93917 .08687 .08689 .08691 .08693 8.94498 .94509 .94519 .94529 .08810 .08813 .08814 .08816 8.95106 .95116 .95126 .95136 .08934 .08936 .08938 .08940 52 51 50 49 48 47 46 45 + y IS u 15 8.92690 .92700 .92710 .92721 .08451 .08453 .08455 .08457 8.93311 .93321 .93332 .93342 .08573 .08575 .08577 .08579 8.93927 .93938 .93948 .93958 .08695 .08697 .08699 .08701 8.94539 .94549 .94559 .94570 .08818 .08830 .08833 .08835 8.95146 .95156 .95166 .95176 .08943 .08945 .08947 .08949 + i' 17 18 19 8.92731 .92742 .92752 .92762 .08459 .08461 .08463 .08465 8.93352 .93363 .93373 .93383 .08581 .08583 .08585 .08587 8.93968 .93979 .93989 .93999 .08703 .08705 .08707 .08709 8.94580 .94590 .94600 .94610 .08837 .08839 .08831 .08833 8.95186 .95197 .95207 .95217 .08951 .08953 .08955 .08957 44 43 42 41 + 5^ 21 22 23 8.92773 .92783 .92794 .92804 .08467 .08469 .08471 .08473 8.93393 .93404 .93414 .93424 .08589 .08591 .08593 .08595 8.94009 .94019 .94030 .94040 .08711 .08714 .08716 .08718 8.94620 .94630 .94641 .94651 .08835 .08837 .08839 .08841 8.95227 .95237 .95247 .95257 .08959 .08961 .08963 .08965 40 39 38 37 + 6' 25 26 27 8.92814 .92825 .92835 .92845 .08475 .08477 .08479 .08481 8.93435 .93445 .93455 .93466 .08597 .08599 .08601 .08603 8.94050 .94060 .94071 .94081 .08730 .08733 .08734 .08736 8.94661 .94671 .94681 .94691 .08843 .08845 .08847 .08849 8.95267 .95277 .95287 .95297 .08967 .08970 .08973 .08974 36 35 34 S3 + r 29 SO 31 8.92856 .92866 .92877 .92887 .08483 .08485 .08487 .08489 8.93476 .93486 .93496 .93507 .08605 .08607 .08609 .08611 8.94091 .94101 .94111 .94122 .08738 .08730 .08733 .08734 8.94701 .94712 .94722 .94732 .08851 .08853 .08856 .08858 8.95307 .95317 .95327 .95337 .08976 .08978 .08980 .08983 32 SI SO 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 IS + 8^ 33 34 35 8.92897 .92908 .92918 .92928 .08491 .08493 .08495 .08497 8.93517 .93527 .93538 .93548 .08613 .08615 .08617 .08619 .08631 .08634 .08636 .08638 8.94132 .94142 .94152 .94162 .08736 .08738 .08740 .08743 8.94742 .94752 .94762 .94772 .08860 .08863 .08864 .08866 8.95347 .95357 .95368 .95378 .08984 .08986 .08988 .08990 + r 37 38 39 8.92939 .92949 .92960 .92970 .08499 .08501 .08503 .08505 8.93558 .93568 .93579 .93589 8.94173 .94183 .94193 .94203 .08744 .08746 .08748 .08750 8.94782 .94793 .94803 .94813 .08868 .08870 .08873 .08874 8.95388 .95398 .95408 .95418 .08993 .08994 .08997 .08999 + 10^ 41 42 43 8.92980 .92991 .93001 .93011 .08508 .08510 .08513 .08514 8.93599 .93610 .93620 .93630 .08630 .08633 .08634 .08636 8.94213 .94224 .94234 .94244 .08753 .08755 .08757 .08759 8.94823 .94833 .94843 .94853 .08876 .08878 .08880 .08883 8.95428 .95438 .95448 .95458 .09001 .09003 .09005 .09007 + 11' 45 46 47 8.93022 .93032 .93042 .93053 .08516 .08518 .08530 .08533 8.93640 .93651 .93661 .93671 .08638 .08640 .08643 .08644 8.94254 .94264 .94275 .94285 .08761 .08763 .08765 .08767 8.94863 .94874 .94884 .94894 .08885 .08887 .08889 .08891 8.95468 .95478 .95488 .95498 .09009 .09011 .09013 .09015 + 12' 49 50 51 8.93063 .93073 .93084 .93094 .08534 .08536 .08538 .08530 8.93681 .93692 .93702 .93712 .08646 .08648 .08650 .08653 8.94295 .94305 .94315 .94326 .08769 .08771 .08773 .08775 8.94904 .94914 .94924 .94934 .08893 .08895 .08897 .08899 8.95508 .95518 .95528 .95538 .09017 .09019 .09033 .09034^ 12 11 10 9 8 7 6 5 + 13' 53 54 55 8.93104 .93115 .93125 .93135 .08533 .08534 .08536 .08538 8.93722 .93733 .93743 .93753 .08654 .08656 .08658 .08660 8.94336 .94346 .94356 .94366 .08777 .08779 .08781 .08783 8.94944 .94954 .94965 .94975 .08901 .08903 .08905 .08907 8.95548 .95558 .95568 .95578 8.95588 .95598 .95608 .95618 .09036 .09038 .09030 .09033 + 14' 57 58 59 8.93146 .93156 .93166 .93177 .08540 .08543 .08544 .08546 8.93764 .93774 .93784 .93794 .08663 .08664 .08666 .08668 8.94376 .94387 .94397 .94407 .08785 .08788 .08790 .08793 8.94985 .94995 .95005 .95015 .08909 .08911 .08914 .08916 .09034 .09036 .09038 .09040 4 3 2 1 + 15' 8.93187 .08548 8.93805 .08071 8.94417 j .08794 8.95025 .08918 8.95628 .09043 21^ 44"^ 1 21h4Sm I 21h 42m 2lh 41m 1 21h40m TABLE 45. [Page 839 Haversinea. s 2^2(ym^°(y 2h 2m 35° 15' 2h22rnS5°W | 2h2Sm35°i5' | 2h 24^ 36° 0' 1 s 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.95628 .95638 .95648 .95658 .09043 .09044 .09047 .09049 8.96227 .96237 .96247 .96257 .09168 .09170 .09173 .09174 8.96821 .96831 .96841 .96851 .09294 .09296 .09298 .09301 8.97411 .97421 .97431 .97441 .09421 .09423 .09436 .09438 8.97997 .98006 .98016 .98026 .09549 .09551 .09553 .09556 + r 5 6 7 8.95668 .95678 .95688 .95698 .09051 .09053 .09055 .09057 8.96267 .96277 .96287 .96297 .09176 .09178 .09181 .09183 8.96861 .96871 .96881 .96890 .09303 .09305 .09307 .09309 8.97450 .97460 .97470 .97480 .09430 .09432 .09434 .09436 8.98035 .98045 .98055 .98065 .09558 .09560 .09563 .09564 56 55 54 53 52 51 50 49 48 47 46 45 + 2^ 9 10 11 8.95709 .95719 .95729 .95739 .09059 .09061 .09063 .09065 8.96307 .96317 .96326 .96336 .09185 .09187 .09189 .09191 8.96900 .96910 .96920 .96930 .09311 .09313 .09315 .09317 8.97489 .97499 .97509 .97519 .09438 .09440 .09443 .09445 8.98074 .98084 .98094 .98103 .09566 .09568 .09571 .09573 + 3' IS 14 15 8.95749 .95759 .95769 .95779 .09067 .09070 .09072 .09074 8.96346 .96356 .96366 .96376 .09193 .09195 .09197 .09199 8.96940 .96950 .96959 .96969 .09320 .09322 .09324 .09326 8.97529 .97538 .97548 .97558 .09447 .09449 .09451 .09453 8.98113 .98123 .98132 .98142 .09575 .09577 .09579 .09581 + 4^ 17 18 19 8.95789 .95799 .95809 .95819 .09076 .09078 .03080 .09083 8.96386 .96396 .96406 .96416 .09303 .09204 .09306 .09308 8.96979 .96989 .96999 .97009 .09338 .09330 .09333 .09334 8.97568 .97577 .97587 .97597 .09455 .09457 .09460 .09463 8.98152 .98162 .98171 .98181 .09583 .09586 .09588 .09590 44 43 42 41 + 5' 21 29 23 8.95828 .95838 .95848 .95858 .09084 .09086 .09088 .09090 8.96426 .96436 .96446 .96455 .09210 .09212 .09314 .09316 8.97018 .97028 .97038 .97048 .09337 .09339 .09341 .09343 8.97607 .97617 .97626 .97636 .09464 .09466 .09468 .09470 8.98191 .98200 .98210 .98220 .09593 .09594 .09596 .09598 40 39 38 37 + 6' 25 26 27 8.95868 .95878 .95888 .95898 .09093 .09095 .09097 .09099 8.96465 .96475 .96485 .96495 .09318 .09330 .09223 .09225 8.97058 .97068 .97077 .97087 .09345 .09347 .09349 .09351 8.97646 .97656 .97665 .97675 .09473 .09474 .09477 .09479 8.98229 .98239 .98249 .98259 .09601 .09603 .09605 .09607 36 35 34 33 + r 29 SO 31 8.95908 .95918 .95928 .95938 .09101 .09103 .09105 .09107 8.96505 .96515 .96525 .96535 .09227 .09229 .09231 .09333 8.97097 .97107 .97117 .97127 .09353 .09356 .09358 .09360 8.97685 .97695 .97704 .97714 .09481 .09483 .09485 .09487 8.98268 .98278 .98288 .98297 .09609 .09611 .09613 .09616 32 31 30 29 + 8' SS 34 35 8.95948 .95958 .95968 .95978 .09109 .09111 .09113 .09116 8.96545 .96555 .96564 .96574 .09235 .09237 .09239 .09242 8.97136 .97146 .97156 .97166 .09362 .09364 .09366 .09368 8.97724 .97734 .97743 .97753 .09489 .09493 .09494 .09496 8.98307 .98317 .98326 .98336 .09618 .09630 .09622 .09624 28 27 26 25 + 9^ 37 38 39 8.95988 .95998 .96008 .96018 .09118 .09120 .09122 .09124 8.96584 .96594 .96604 .96614 .09244 .09246 .092*8 .09250 8.97176 .97186 .97195 .97205 .09370 .09372 .09375 .09377 8.97763 .97773 .97782 .97792 .09498 .09500 .09503 .09504 8.98346 .98355 .98365 .98375 .09626 .09638 .09631 .09633 24 23 22 21 + W 41 42 43 8.96028 .96038 .96048 .96058 .09126 .09128 .09130 .09132 8.96624 .96634 .96644 .96653 .09252 .09254 .09256 .09258 8.97215 .97225 .97235 .97244 .09379 .09381 .09383 .09385 8.97802 .97812 .97821 .97831 .09506 .09509 .09511 .09513 8.98384 .98394 .98404 .98413 .09635 .09837 .09639 .09641 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 47 8.96068 .96078 .96088 .96098 .09134 .09136 .09139 .09141 8.96663 .96673 .96683 .96693 .09260 .09263 .09265 .09267 8.97254 .97264 .97274 .97284 .09387 .09389 .09392 .09394 8.97841 .97851 .97860 .97870 .09515 .09517 .09519 .09531 8.98423 .98433 .98442 .98452 .09643 .09646 .09648 .09650 + 13' 5i 8.96108 .96118 .96128 .96138 .09143 .09145 .09147 .09149 8.96703 .96713 .96723 .96733 .09269 .09271 .09273 .09275 8.97294 .97303 .97313 .97323 .09396 .09398 .09400 .09403 8.97880 .97890 .97899 .93909 .09534 .09536 .09538 .09530 8.98462 .98471 .98481 .98491 .09652 .09654 .09656 .09658 + 13' 53 54 55 8.96148 .96158 .96167 .96177 .09151 .09153 .09155 .09157 8.96742 .96752 .96762 .96772 .09277 .09280 .09282 .09284 8.97333 .97343 .97352 .97362 .09404 .09406 .09409 .09411 8.97919 .97928 .97938 .9y948 .09533 .09534 .09536 .09538 8.98500 .98510 .98520 .98529 .09661 .09663 .09665 .09667 + 14' 57 58 59 8.96187 .96197 .96207 .96217 .09160 .09162 .09164 .09166 8.96782 .96792 .96802 .96812 .09286 .09288 .09290 .09292 8.97372 .97382 .97392 .97401 .09413 .09115 .09417 .09419 8.97958 .97967 .97977 .97987 .09541 .09543 .09545 .09547 8.98539 .98549 .98558 .98568 .09669 .09671 .09673 .09676 4 3 2 1 + 15' 8.96227 .09168 8.96821 .09294 8.97411 .09431 8.97997 .09549 8.98578 .09678 21h S9m 21hS8^ 21h 37m 21h S6m 21h 35m Page 840] TABLE 45. Haversines. s 2h 25m 36° 15' 2^ 26m 36° 30'' 2h 27^ 36° 45' 2h 28m 37° Q/ 2h 29m 37° 15/ s Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.98578 .98587 .98597 .98606 .09678 .09680 .09683 .09684 8.99154 .99164 .99173 .99183 .09807 .09809 .09811 .09814 8.99727 .99736 .99746 .99755 .09937 .09939 .09952 .09944 9.00295 .00305 .00314 .00324 .10068 .10070 .10073 .10075 9.00860 .00869 .00878 .00888 .10200 .10202 .10204 .10206 60 59 58 57 + 1" 5 6 7 8.98616 .98626 .98635 .98645 .09686 .09689 .09691 .09693 8.99193 .99202 .99212 .99221 .09816 .09818 .09820 .09822 8.99765 .99774 .99784 .99793 .09946 .09948 .09950 .09953 9.00333 .00342 .00352 .00361 .10077 .10079 .10081 .10C34 9.00897 .00906 .00916 .00925 .10209 .10211 .10213 .10215 56 55 54 53 + V 9 10 11 8.98655 .98664 .98674 .98684 .09695 .09697 .09699 .09701 8.99231 .99240 .99250 .99260 .09824 .09827 .09829 .09831 8.99803 .99812 .99822 .99831 .09955 .09957 .09959 .09961 9.00371 .00380 .00390 .00399 .10086 .10688 .10090 .10092 9.00935 .00944 .00953 .00963 .10218 .10220 .10222 .10224 52 51 50 49 + 3' IS 14 15 8.98693 .98703 .98712 .98722 .09704 .09706 .09708 .09710 8.99269 .99279 .99288 .99298 .09833 .09835 .09837 .09840 8.99841 .99850 .99860 .99869 8.99879 .99888 .99898 .99907 .09963 .09966 .09968 .09970 9.00408 .00418 .00427 .00437 .10095 .10097 .10099 .10101 9.00972 .00981 .00991 .01000 .10226 .10228 .10231 .10233 48 47 46 45 + 4' 17 18 19 8.98732 .98741 .98751 .98761 .09712 .09714 .09717 .09719 8.99307 .99317 .99327 .99336 .09842 .09844 .09846 .09848 .09972 .09974 .09977 .09979 9.00446 .00456 .00465 .00474 .10103 .10105 .10108 .10110 9.01009 .01019 .01028 .01037 .10235 .10237 .10240 .10242 U 43 42 41 + 5' ^^ + 6' 25 26 27 8.98770 .98780 .98790 .98799 .09721 .09723 .09725 .09727 8.99346 .99355 .99365 .99374 .09850 .09853 .09855 .09857 8.99917 .99926 .99936 .99945 .09981 .09983 .09985 .09987 9.00484 .00493 .00503 .00512 .10112 .10114 .10116 .10119 9.01047 .01056 .01065 .01075 .10244 .10246 .10248 .10251 40 39 38 37 8.98809 .98818 .98828 .98838 .09729 .09732 .09734 .09736 8.99384 .99393 .99403 .99412 .09859 .09861 .09863 .09866 8.99955 .99964 .99974 .99983 .09990 .09992 .09994 .09996 9.00522 .00531 .00540 .00550 .10121 .10123 .10125 .10127 9.01084 .01094 .01103 01112 .10253 .10255 .10257 .10259 36 35 34 33 + r 29 30 31 8.98847 .98857 .98866 .98876 .09738 .09740 .09742 .09745 8.99422 .99432 .99441 .99451 .09868 .09870 .09872 .09874 8.99993 9.00002 .00012 .00021 .09998 .10000 .10003 .10005 9.00559 .00569 .00578 .00587 .10130 .10132 .10134 .10136 9.01122 .01131 .01140 .01150 .10262 .10264 .10266 .10268 32 31 30 29 + 8' 33 34 35 8.98886 .98895 .98905 .98915 .09747 .09749 .09751 .09753 8.99460 .99470 .99479 .99489 .09876 .09879 .09881 .09883 9.00031 .00040 .00049 .00059 .10007 .10009 .10011 .10014 9.00597 .00606 .00616 .00625 .10138 .10141 .10143 .10145 9.01159 .01168 .01178 .01187 .10270 .10273 .10275 .10277 28 27 26 25 + r 59 8.98924 .98934 .98943 .98953 .09755 .09757 .09760 .09762 8.99498 .99508 .99517 .99527 .09885 .09887 .09890 .09892 9.00068 .00078 .00087 .00097 .10016 .10018 .10020 .10022 9.00634 .00644 .00653 .00663 .10147 .10149 .10152 .10154 9.01196 .01206 .01215 .01224 .10279 .10281 .10284 .10286 24 23 22 21 + W 41 42 43 8.98963 .98972 .98982 .98991 .09764 .09766 .09768 .09770 8.99536 .99546 .99556 .99565 .09894 .09896 .09898 .09900 9.00106 .00116 .00125 .00135 .10025 .10027 .10029 .10031 9.00672 .00681 .00691 .00700 .10156 .10158 .10160 .10163 9.01234 .01243 .01252 .01262 .10288 .10290 .10293 .10295 20 19 18 17 + ir 45 46 47 8.99001 .99011 .99020 .99030 .09773 .09775 .09777 .09779 8.99575 .99584 .99594 .99603 .09903 .09905 .09907 .09909 9.00144 .00154 .00163 .00172 .10033 .10035 .10038 .10040 .10042 .10044 .10046 .10049 9.00710 .00719 .00728 .00738 .10165 .10167 .10169 .10171 .10174 .10176 .10178 .10180 9.01271 .01280 .01289 .01299 9.01308 .01317 .01327 .01336 .10297 .10299 .10301 .10304 16 15 14 13 + W 49 50 51 8.99039 .99049 .99058 .99068 .09781 .09783 .09786 .09788 8.99613 .99622 .99632 .99641 .09911 .09913 .09916 .09918 .09920 .09922 .09924 .09926 9.00182 .00191 .00201 .00210 9.00747 .00756 .00766 .00775 .10306 .10308 .10310 .10312 12 11 10 9 + 13' 53 54 55 8.99078 .99087 .99097 .99106 .09790 .09792 .09794 .09796 8.99651 .99660 .99670 .99679 9.00220 .00229 .00239 .00248 .10051 .10053 .10055 .10057 9.00785 .00794 .00803 .00813 .10182 .10184 .10187 .10189 9.01345 .01355 .01364 .01373 .10315 .10317 .10319 .10321 8 7 6 5 + W 57 58 59 8.99116 .99126 .99135 .99145 .09799 .09801 .09803 .09805 8.99689 .99698 .99708 .99717 .09929 .09931 .09933 .09935 9.00258 .00267 .00276 .00286 9.00295 .10059 .10C62 .10064 .10066 9.00822 .00831 .00841 .00850 .10191 .10193 .10196 .10198 9.01383 .01392 .01401 .01411 .10323 .10326 .10328 .10330 4 S 2 1 + 15' 8.99154 .09807 8.99727 .09937 .10068 9.00860 .10200 9.01420 1 .10332 21h spn, £lh S3m 21h 32m 21h Sim 21h30m TABLE 45. [Page 841 Haversines. s 2^ SOm 37° W 2h 31^ 37° 45' 2^ 32m 38° 0' 2^ 33m 38° 15' 2hS4^3S°W s 60 59 58 51 56 55 54 53 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.01420 .01429 .01438 .01448 .10333 .10335 .10337 .10339 9.01976 .01985 .01995 .02004 .10466 .10468 .10470 .10473 9.02528 .02538 .02547 .02556 .10599 .10603 .10604 .10606 9.03077 .03086 .03095 .03104 .10734 .10736 .10739 .10741 9.03621 .03630 .03639 .03648 .10870 .10873 .10874 .10876 + r 5 6 1 9.01457 .01466 .01476 .01485 .10341 .10343 .10346 .10348 9.02013 .02022 .02031 .02041 .10474 .10477 .10479 .10481 9.02565 .02574 .02583 .02593 .10608 .10611 .10613 .10615 9.03113 .03122 .03131 .03141 .10743 .10745 .10748 .10750 9.03657 .03667 .03676 .03685 .10879 .10881 .10883 .10885 + 2' 9 10 11 9.01494 .01504 .01513 .01522 .10350 .10353 .10354 .10357 9.02050 .02059 .02068 .02078 .10483 .10486 .10488 .10490 9.02602 .02611 .02620 .02629 .10017 .10630 .10633 .10634 9.03150 .03159 .03168 .03177 .10753 .10754 .10757 .10759 9.03094 .03703 .03712 .03721 .10888 .10890 .10893 .10895 62 51 50 49 48 41 46 45 + 3^ 13 14 15 9.01531 .01541 .01550 .01559 .10359 .10361 .10363 .10366 9.02087 .02096 .02105 .02115 .10493 .10494 .10497 .10199 9.02638 .02648 .02657 .02666 .10636 .10639 .10631 .10633 9.03186 .03195 .03204 .03213 .10761 .10763 .10766 .10768 9.03730 .03739 .03748 .03757 .10897 .10899 .10901 .10904 + 4' 11 18 19 9.01569 .01578 .01587 .01596 .10368 .10370 .10373 .10374 9.02124 .02133 .02142 .02151 .10501 .10503 .10506 .10508 9.02675 .02684 .02693 .02702 .10635 .10638 .10640 .10643 9.03222 .03231 .03241 .03250 .10770 .10773 .10775 .10777 9.03766 .03775 .03784 .03793 .10906 .10908 .10910 .10913 U 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 21 26 25 24 23 22 21 + 5' 21 22 23 9.01606 .01615 .01624 .01634 .10377 .10379 .10381 .10383 9.02161 .02170 .02179 .02188 .10510 .10513 .10515 .10517 9.02712 .02721 .02730 .02739 .10644 .10647 .10649 .10651 9.03259 .03268 .03277 .03286 .10779 .10781 .10784 .10786 9.03802 .03811 .03820 .03829 .10915 .10917 .10919 .10923 + 6^ 25 26 21 9.01643 .01652 .01661 .01671 .10386 .10388 .10390 .10393 9.02197 .02207 .02216 .02225 .10519 .10531 .10533 .10536 9.02748 .02757 .02767 .02776 .10653 .10655 .10658 .10660 9.03295 .03304 .03313 .03322 .10788 .10796 .10793 .10795 9.03838 .03847 .03856 .03865 .10934 .10926 .10939 .10931 + r 29 30 31 9.01680 .01689 .01698 .01708 .10394 .10397 .10399 .10401 9.02234 .02244 .02253 .02262 .10538 .10530 .10533 .10535 9.02785 .02794 .02803 .02812 .10663 .10664 .10667 .10669 9.03331 .03340 .03350 .03359 .10797 .10799 .10802 .10804 9.03874 .03883 .03892 .03901 .10933 .10935 .10938 .10940 + 8' S3 34 35 9.01717 .01726 .01736 .01745 .10403 .10405 .10408 .10410 9.02271 .02280 .02290 .02299 .10537 .10539 .10541 .10544 .10546 .10548 .10550 .10553 9.02821 .02830 .02840 .02849 .10671 .10673 .10676 .10678 9.03368 .03377 .03386 .03395 .10806 .10809 .10811 .10813 9.03910 .03919 .03928 .03937 .10943 .10944 .10947 .10949 + r 31 38 39 9.01754 .01763 .01773 .01782 .10413 .10414 .10417 .10419 9.02308 .02317 .02326 .02336 9.02858 .02867 .02876 .02885 .10680 .10683 .10685 .10687 9.03404 .03413 .03422 .03431 .10815 .10818 .10830 .10833 9.03946 .03955 .03964 .03973 .10951 .10953 .10956 .10958 + W 41 42 43 9.01791 .01800 .01810 .01819 .10431 .10433 .10435 .10438 9.02345 .02354 .02363 .02372 .10555 .10557 .10559 .10561 9.02894 .02904 .02913 .02922 .10689 .10691 .10694 .10696 9.03440 .03449 .03458 .03467 .10834 .10837 .10839 .10831 9.03982 .03991 .04000 .04009 .10960 .10963 .10965 .10967 20 19 18 11 16 15 14 13 + 11' 45 46 47 9.01828 .01837 .01847 .01856 .10430 .10433 .10434 .10436 9.02381 .02391 .02400 .02409 .10564 .10566 .10568 .10570 9.02931 .02940 .02949 .02958 .10698 .10700 .10703 .10705 9.03476 03486 .03495 .03504 .10833 .10836 .10838 .10840 9.04018 .04027 .04036 .04045 .10969 .10973 .10974 .10976 + 13' 49 50 51 9.01865 .01874 .01884 .01893 .10439 .10441 .10443 .10445 9.02418 .02427 .02437 .02446 .10573 .10575 .10577 .10579 9.02967 .02977 .02986 .02995 .10707 .10709 .10713 .10714 9.03513 .03522 .03531 .03540 .10843 .10845 .10847 .10849 9.04054 .04063 .04072 .04081 .10978 .10981 .10983 .10985 12 11 10 9 + 13^ 53 54 55 9.01902 .01911 .01921 .01930 .10448 .10450 .10453 .10454 9.02455 .02464 .02473 .02483 .10583 .10584 .10586 .10588 9.03004 .03013 .03022 .03031 .10716 .10718 .10731 .10723 9.03549 .03558 .03567 .03576 .10851 .10854 .10856 .10858 9.04090 .04099 .04108 .04117 .10988 .10990 .10992 .10994 8 1 6 5 + 14^ 51 58 59 9.01939 01948 .01958 .01967 .10457 .10459 .10461 .10463 9.02492 .10591 .02501 .10593 .02510 .10595 .02519 .10597 9.03040 .03050 .03059 .03068 .10725 .10727 .10730 .10733 9.03585 .03594 .03603 .03612 .10861 .10863 .10865 .10867 9.04126 .04135 .04144 .04153 .10997 .10999 .11001 .11004 4 3 2 1 + 15^ 9.01976 .10466 9.02528 1 .10599 9.03077 .10734 9.03621 .10870 9.04162 .11006 21h 29m 21h 28^ 2in 27m 2in 26m 21h £5m Page 842] TABLE 45. Haversines. + r 5 6 7 + V 9 10 11 + 3^ 13 14 15 + 4' 17 18 19 + 5^ 21 + 6^ 25 26 27 + r 29 30 31 2^ 35m 38° 45^ 2h 36m 39° (/ 2^ ST"i 39° 15^ jgft 55m 39° 3©/ Log. Hav. Nat. Ilav 9.04162 .04171 .04180 .04189 9.04198 .04207 .04216 .04225 9.04234 .04243 .04252 .04261 9.04270 .04279 .04288 .04297 9.04306 .04315 .04324 .04333 9.04341 .04350 .04359 .04368 9.04377 .04386 .04395 .04404 .llOOG .11008 .11010 .11013 .11015 .11017 .11019 .11032 .11034 .11036 .11039 .11031 .11033 .11033 .11038 .11040 .11043 .11044 .11047 .11049 + 8^ + 9^ 37 + W 41 + 11^ 45 46 47 + 1%' 49 50 51 + ir 53 54 55 + w 57 58 59 + W 9.04413 .04422 .04431 .04440 9.04449 .04458 .04467 .04476 9.04485 .04494 .04503 .04512 9.04520 .04529 .04538 .04547 9.04556 .04565 .04574 .04583 .04592 .04601 .04610 .04619 .04628 .04637 .04646 .04654 9.04663 .04672 .04681 .04690 .11051 .11054 .11056 .11058 .11063 .11065 .11067 Log. Hav. Nat. Hav 9.04699 .04708 .04717 .04726 9.04735 .04744 .04753 .04761 9.04770 .04779 .04788 .04797 9.04806 .04815 .04824 .04833 9.04842 .04851 .04859 .04868 9.04877 .04886 .04895 .04904 .11143 .11145 .11147 .11150 .11153 .11154 .11156 .11159 .11161 .11163 .11166 .11168 .11170 .11173 .11175 .11177 .11179 .11183 .11184 11186 .11060 9.04913 .11070 .11073 .11074 .11076 .11079 .11081 .11083 .11086 .11088 .11090 .11093 .11095 .11097 .11099 .11103 .11104 .11106 .11108 .11111 .11113 .11115 .11117 .11130 .11133 .11134 .11137 .11139 .11131 9.04699 .11134 .11136 .11138 .11140 .11143 .04922 .04931 .04939 9.04948 .04957 .04966 .04975 9.04984 .04993 .05002 .05011 9.05019 .05028 .05037 .05046 9.05055 .05064 .05073 .05082 9.05090 .05099 .05108 .05117 9.05126 .05135 .05144 .05153 9.05161 .05170 .05179 .05188 9.05197 .05206 .05215 .05223 .11189 .11191 .11193 .11195 .11198 .11300 .11303 .11305 Log. Hav. Nat. Hav 9.05232 .05241 .05250 .05259 9.05268 .05277 .05285 .05294 9.05303 .05312 .05321 .05330 9.05339 .05347 .05356 .05365 9.05374 .05383 .05392 .05400 9.05409 .05418 .05427 .05436 .11380 .11383 .11385 .11387 .11390 .11393 .11394 .11396 .11399 .11301 .11303 .11306 .11308 .11310 .11313 .11315 .11317 .11330 .11333 .11334 .11307 .11309 .11311 .11314 .11316 .11318 .11331 .11333 .11335 .11338 .11330 .11333 .11334 .11337 .11339 .11341 .11344 .11346 .11348 .11351 .11353 .11355 .11357 .11260 .11363 .11364 .11367 .11269 21h 24m 9.05232 .11371 .11374 .11376 .11378 .11380 21^ 23^ 9.05445 .05453 .05462 .05471 9.05480 .05489 .05498 .05506 9.05515 .05524 .05533 .05542 9.05551 .05559 .05568 .05577 9.05586 .05595 .05603 .05612 9.05621 .05630 .05639 .05648 9.05656 .05665 .05674 .05683 9.05692 .05700 .05709 .05718 .11336 .11339 .11331 .11333 .11336 .11338 .11340 .11343 .11345 .11347 .11349 .11353 .11354 .11356 .11359 .11361 .11363 .11366 .11368 .11370 .11373 .11375 .11377 .11379 .11383 .11384 .11386 .11389 Log. Hav. Nat. Hav 9.05762 .05771 .05780 .05788 9.05797 .05806 .05815 .05823 9.05832 .05841 .05850 .05859 9.05867 .05876 .05885 .05894 9.05903 .05911 .05920 .05929 .11419 .11431 .11433 .11436 .11438 .11430 .11433 .11435 .11437 .11440 .11443 .11444 .11447 .11449 .11451 .11453 9.05938 .05946 .05955 .05964 9.05973 .05982 .05990 .05999 9.06008 .06017 .06025 .06034 9.06043 .06052 .06060 .06069 9.06078 .06087 .06095 .06104 9.06113 .06122 .06131 .06139 .11391 .11393 .11396 .11398 9.05727 .05736 .05744 .05753 9.05762 .11400 .11403 .11405 .11407 .11410 .11413 .11414 .11416 .11419 21h 22in 9.06148 .06157 .06166 .06174 9.06183 .06192 .06201 .06209 .11456 .11458 .11460 .11463 .11465 .11467 .11470 .11473 :il474 .11477 .11479 .11481 .11484 .11486 .11488 .11491 .11493 .11495 .11498 .11500 .11503 .11504 .11507 .11509 2h 39m 39° 45^ Log. Hav. Nat. Hav 9.06288 .06297 .06305 .06314 9.06323 .06332 .06340 .06349 9.06358 .06367 .06375 .06384 9.06393 .06401 .06410 .06419 9.06428 .06436 .06445 .06454 9.06462 .06471 .06480 .06489 9.06497 .06506 .06515 .06523 9.06532 .06541 .06550 .06558 9.06567 .06576 .06584 .06593 .11511 .11514 .11516 .11518 .11531 .11523 .11535 ^11538 .11530 .11533 .11535 .11537 9.06218 .06227 .06235 .06244 9.06253 .06262 .06270 .06279 9.06288 .11539 .11542 .11544 .11546 .11549 .11551 .11553 .11556 .11558 21h 21m 9.06602 .06611 .06619 .06628 9.06637 .06645 .06654 .06663 .11558 .11560 .11563 .11565 .11567 .11569 .11572 .11574 .11577 .11579 .11581 .11584 .11586 .11588 .11590 .11593 .11595 .11597 .11600 .11602 .11604 .11607 .11609 .11611 .11614 .11616 .11618 .11621 .11623 .11625 .11638 .11630 .11632 .11635 .11637 .11639 9.06671 .06680 .06689 .06697 9.06706 .06715 .06724 .06732 9.06741 .06750 .06758 .06767 9.06776 .06784 .06793 .06802 9.06810 .11642 .11644 .11646 ^11649 .11651 .11653 .11656 .11658 .11660 .11663 .11665 .11667 .11670 .11672 .11674 .11677 .11679 .11681 .11684 .11686 .11688 .11691 .11693 .11695 .11698 21h 20m TABLE 45. [Page 843 Haveraines. s 2h40mM°0' 1 2h4imiO° 15^ 1 2h 42m 40° 30' 2h43mM°i5' | 2hUm^V^ 1 s Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.06810 .06819 .06828 .06836 .11698 .11700 .11703 .11705 9.07329 .07338 .07346 .07355 .11838 .11841 .11843 .11845 9.07845 .07853 .07862 .07870 9.07879 .07887 .07896 .07905 .11980 .11982 .11984 .11987 .11989 .11992 .11994 .11996 9.08357 .08365 .08374 .08382 .12122 .13134 .13137 .13129 9.08865 .08874 .08882 .08890 .13365 .13367 .13369 .13373 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 + r 5 6 7 9.06845 .06854 .06862 .06871 .11707 .11709 .11713 .11714 .11710 .11719 .11721 .11724 9.07364 .07372 .07381 .07390 .11848 .11850 .11852 .11855 9.08391 .08399 .08408 .08416 9.08425" .08433 .08442 .08450 .12131 .12134 .12136 .12138 9.08899 .08907 .08916 .08924 .13374 .13376 .13379 .12281 .12284 .12286 .12288 .12291 + r 9 10 11 9.06880 .06888 .06897 .06906 9.07398 .07407 .07415 .07424 .11857 .11860 .11862 .11864 9.07913 .07922 .07930 .07939 .11999 .12001 .12003 .12006 .12141 .12143 .12146 .12148 9.08933 .08941 .08949 .08958 + 3' 13 14 15 + i' 17 18 19 9.06914 .06923 .06932 .06940 '9.06949 .06958 .06966 .06975 9.06984 .06992 .07001 .07010 .11736 .11738 .11731 .11733 .11735 .11738 .11740 .11743 .11745 .11747 .11749 .11752 9.07433 .07441 .07450 .07458 .11867 .11869 .11871 .11874 9.07947 .07956 .07964 .07973 9.07981 .07990 .07999 .08007 .12008 .12010 .13013 .13015 .13018 .12020 .12022 .12025 .12027 .12029 .12032 .12034 9.08459 .08467 .08475 .08484 .12150 .12153 .12155 .12157 9.08966 .08975 .08983 .08992 .12293 .13396 .13398 .13300 .13303 .13305 .13307 .13310 .13313 .13315 .13317 .13319 .13333 .13334 .13337 .12329 .12331 .13334 .13336 .12339 .13341 .12343 .13346 .13348 9.07467 .07476 .07484 .07493 9.07501 .07510 .07519 .07527 .11876 .11878 .11881 .11883 9.08492 .08501 .08509 .08518 9.08526 .08535 .08543 .08552 .12160 .12162 .12165 .12167 .12169 .13172 .13174 .13176 9.09000 .09009 .09017 .09025 9.09034 .09042 .09051 .09059 9.09068 .09076 .09084 .09093 9.09101 .09110 .09118 .09126 9.09135 .09143 .09152 .09160 9.09169 .09177 .09185 .09194 9.09202 .09211 .09219 .09227 + 5' 21 22 23 .11885 .11888 .11890 .11892 9.08016 .08024 .08033 .08041 + 6' 25 26 27 9.07018 .07027 .07036 .07044 9^07053' .07062 .07070 .07079 .11754 .11756 .11759 .11761 .11763 .11766 .11768 .11770 .11773 .11775 .11777 .11780 9.07536 .07544 .07553 .07562 9.07570 .07579 .07587 .07596 9.07605 .07613 .07622 .07630 .11895 .11897 .11900 .11902 .11904 .11907 .11909 .11911 9.08050 .08058 .08067 .08075 9.08084 .08092 .08101 .08110 .12036 .12039 .12041 .12044 .12046 .12048 .12051 .12053 9.08560 .08569 .08577 .08586 .12179 .12181 .12184 .12186 .12188 .12191 .12193 .12195 .13198 .13300 .13203 .13305 .13307 .13310 .13313 .13314 .13317 .12219 .12233 .13324 + r 29 SO 31 9.08594 .08603 .08611 .08620 9.08628 .08637 .08645 .08654 + 8' 33 34 35 9.07088 .07096 .07105 .07113 9.07122 .07131 .07139 .07148 .11914 .11916 .11918 .11921 9.08118 .08127 .08135 .08144 .12055 .12058 .12060 .12062 + 9' 37 38 39 .11782 .11784 .11787 .11789 9.07639 .07647 .07656 .07665 .11923 .11925 .11928 .11930 9.08152 .08161 .08169 .08178 .12065 .12067 .12070 .12073 9.08662 .08671 .08679 .08687 .12351 .12353 .12355 .12358 24 23 22 21 + 10' 41 42 43 9.07157 .07165 .07174 .07183 .11791 .11794 .11796 .11798 9.07673 .07682 .07690 .07699 9.07708 .07716 .07725 .07733 .11933 .11935 .11937 .11940 .11942 .11944 .11947 .11949 9.08186 .08195 .08203 .08212 .12074 .12077 .12079 .12081 9.08696 .08704 .08713 .08721 .12360 .12363 .12365 .12367 20 19 18 17 + 11^ 45 46 47 9.07191 .07200 .07208 .07217 .11801 .11803 .11806 .11808 9.08220 .08229 .08237 .08246 .12084 .12086 .12089 .12091 9.08730 .08738 .08747 .08755 .12226 .12229 .12231- .12233 9.09236 .09244 .09253 .09261 .12370 .12372 .12374 .12377 .12379 .13383 .13384 .12386 16 15 14 13 12 11 10 9 8 7 6 5 + 12' 49 60 51 9.07226 .07234 .07243 .07252 9.07260 .07269 .07277 .07286 .11810 .11813 .11815 .11817 .11830 .11833 .11834 .11837 9.07742 .07750 .07759 .07768 9.07776" .07785 .07793 .07802 .11951 .11954 .11956 .11958 9.08254 .08263 .08271 .08280 .12093 .12096 .12098 .13100 9.08764 .08772 .08781 .08789 .12236 .12238 .12241 .12243 9.09269 .09278 .09286 .09295 + 13' 53 54 55 + 14' 57 '58 59 .11961 .11963 .11966 .11968 9.08288 .08297 .08306 .08314 .13103 .12105 .12108 .12110 9.08797 .08806 .08814 .08823 .12245 .12248 .12250 .12253 9.09303 .09311 .09320 .09328 .12389 .12391 .12394 .12396 9.07295 .07303 .07312 .07321 .11839 .11831 .11834 .11836 .11838 9.07810 .07819 .07827 .07836 .11970 .11973 .11975 .11977 9.08323 .08331 .08340 .08348 .12112 .13115 .13117 .13119 9.08831 .08840 .08848 .08857 .13355 .13257 .12260 .12262 9.09337 .09345 .09353 .09362 .13398 .12401 .12403 .12406 4 S 2 1 + 15' 9.07329 9.07845 .11980 9.08357 .12122 9.08865 .12365 9.09370 1 .13408 £2h 19m 21h ism 21h nm 21h 16m 21h 15m 21594°— 14- -46 Page 844] TABLE 45. Haversines. s 2h45m 41° W 2h46m 41° 30^ 2^47^ 41° 45^ 2h48m 42° 0^ 2h 49m 43° 15/ s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.09370 .09379 .09387 .09395 .12408 .12410 .12413 .12416 9.09872 .09880 .09889 .09897 .12552 .12555 .12557 .12559 9.10371 .10379 .10387 .10395 .12697 .12700 .12702 .12704 9.10866 .10874 .10882 .10891 .12843 .12845 .12848 .12850 9.11358 .11366 .11374 .11382 .12989 .12992 .12994 .12996 60 59 58 57 + r 5 6 7 9.09404 .09412 .09421 .09429 .12418 .12420 .12422 .12425 9.09905 .09914 .09922 .09930 .12562 .12564 .12567 .12569 9.10404 .10412 .10420 .10429 .12707 .12709 .12712 .12714 9.10899 .10907 .10915 .10923 .12852 .12855 .12857 .12860 9.11391 .11399 .11407 .11415 .12999 .13001 .13004 .13006 56 55 54 53 + 2^ 9 10 11 9.09437 .09446 .09454 .09462 .12427 .12430 .12432 .12434 9.09939 .09947 .09955 .09964 .12572 .12574 .12576 .12579 9.10437 .10445 .10453 .10462 .12717 .12719 .12721 .12724 9.10932 .10940 .10948 .10956 .12862 .12865 .12867 .12870 9.11423 .11431 .11440 .11448 .13009 .13011 .13014 .13016 52 51 50 49 + 3^ 13 14 15 9.09471 .09479 .09488 .09496 .12437 .12439 .12442 .12444 9.09972 .09980 .09989 .09997 .13581 .12584 .12586 .12588 9.10470 .10478 .10486 .10495 .12726 .12729 .12731 .12733 9.10965 .10973 .10981 .10989 .12872 .12874 .12877 .12879 9.11456 .11464 .11472 .11480 .13018 .13021 .13023 .13026 48 47 46 45 + *^ 17 18 19 9.09504 .09513 .09521 .09529 .12446 .12449 .12451 .12454 9.10005 .10014 .10022 .10030 .12591 .12593 .12596 .12598 9.10503 .10511 .10519 .10528 .12736 .12738 .12741 .12743 9.10997 .11006 .11014 .11022 .12882 .12884 .12887 .12889 9.11489 .11497 .11505 .11513 .13028 .13031 .13033 .13036 44 43 42 41 + 5' 21 22 23 9.09538 .09546 .09555 .09563 .12456 .12458 .12461 .12463 9.10039 .10047 .10055 .10064 .12600 .12603 .12605 .12608 9.10536 .10544 .10553 .10561 .12746 .12748 .12750 .12753 9.11030 .11038 .11047 .11055 .12891 .12894 .12896 .12899 9.11521 .11529 .11538 .11546 .13038 .13041 .13043 .13045 40 39 38 37 + 6^ 25 26 27 9.09571 .09580 .09588 .09596 .12466 .12468 .12470 .12473 9.10072 .10080 .10088 .10097 .12610 .12613 .12615 .12617 9.10569 .10577 .10586 .10594 .12755 .12758 .12760 .12763 9.11063 .11071 .11079 .11088 .12901 .12904 .12906 .12909 9.11554 .11562 .11570 .11578 .13048 .13050 .13053 .13055 36 35 34 33 32 31 30 29 + r 29 30 31 9.09605 .09613 .09622 .09630 .12475 .12478 .12480 .12482 9.10105 .10113 .10122 .10130 .12620 .12622 .12625 .12627 9.10602 .10610 .10619 .10627 .12765 .12767 .12770 .12772 9.11096 .11104 .11112 .11120 .12911 .12913 .12916 .12918 9.11586 .11595 .11603 .11611 .13058 .13060 .13063 .13065 + 8^ S3 34 35 9.09638 .09647 .09655 .09663 .12485 .12487 .12490 .12492 9.10138 .10147 .10155 .10163 .12629 .12632 .12634 .12637 9.10635 .10643 .10652 .10660 .12775 .12777 .12780 .12782 9.11129 .11137 .11145 .11153 .12921 .12923 .12926 .12928 9.11619 .11627 .11635 .11643 .13067 .13070 .13072 .13075 28 27 26 25 + 0^ 37 38 39 9.09672 .09680 .09688 .09697 .12494 .12497 .12499 .12502 9.10172 .10180 .10188 .10196 .12639 .12641 .12644 .12646 9.10668 .10676 .10685 .10693 .12784 .12787 .12789 .12792 9.11161 .11170 .11178 .11186 .12930 .12933 .12935 .12938 9.11652 .11660 .11668 .11676 .13077 .13080 .13082 .13085 24 23 22 21 + 10^ 41 42 43 9.09705 .09713 .09722 .09730 .12504 .12506 .12509 .12511 9.10205 .10213 .10221 .10230 .12649 .12651 .12654 .12656 9.10701 .10709 .10718 .10726 .12794 .12797 .12799 .12801 9.11194 .11202 .11211 .11219 .12940 .12943 .12945 .12948 9.11684 .11692 .11700 .11709 .13087 .13090 .13092 .13095 20 19 18 17 + 11^ 45 46 47 9.09739 .09747 .09755 .09764 .12514 .12516 .12519 .12521 9.10238 .10246 .10255 .10263 .12658 .12661 .12663 .12666 9.10734 .10742 .10751 .10759 .12804 .12806 .12809 .12811 9.11227 .11235 .11243 .11252 .12950 .12952 .12955 .12957 9.11717 .11725 .11733 .11741 .13097 .13099 .13102 .13104 16 15 14 IS + 12^ 49 50 51 9.09772 .09780 .09789 .09797 .12523 .12526 .12528 .12531 9.10271 .10279 .10288 .10296 .12668 .12671 .12673 .12675 9.10767 .10775 .10784 .10792 .12814 .12816 .12818 .12821 9.11260 .11268 .11276 .11284 .12960 .12962 .12965 .12967 9.11749 .11757 .11766 .11774 .13107 .13109 .13112 .13114 12 11 10 9 8 7 6 5 + 13^ 54 55 9.09805 .09814 .09822 .09830 .12533 .12536 .12538 .12540 9.10304 .10313 .10321 .10329 .12678 .12680 .12683 .12685 9.10800 .10808 .10816 .10825 .12823 .12826 .12828 .12831 9.11292 .11301 .11309 .11317 .12970 .12972 .12974 .12977 9.11782 .11790 .11798 .11806 .13116 .13119 .13121 .13124 + 14^ 57 58 59 9.09839 .09847 .09856 .09864 .12543 .12545 .12547 .12550 9.10337 .10346 .10354 .10362 .12687 .12690 .12692 .12695 9.10833 .10841 .10849 .10858 .12833 .12836 .12838 .12840 9.11325 .11333 .11342 .11350 .12979 .12982 .12984 .12987 9.11814 .11822 .11831 .11839 .13126 .13129 .13131 .13134 4 3 2 1 + W 9.09872 .12552 9.10371 .12697 9.10866 .12843 9.11358 .12989 9.11847 .13136 21^ 14m 21h 13m 21h 12m 21f>' lim 21h lOm TABLE 45. [Page 846 Haversines. s £h 50^ 42° SCK 2h Sim 43° 45/ 2h 52m. 43° 0" 2h 53m 43° 15' 2h 54m 43° 30^ s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.11847 .11855 .11863 .11871 .13136 .13139 .13141 .13143 9.12332 .12341 .12349 .12357 .13284 .13286 .13289 .13291 9.12815 .12823 .12831 .12839 .13432 .13435 .13437 .13440 9.13295 .13303 .13311 .13319 .13581 .13584 .13586 .13589 9.13771 .13779 .13787 .13795 .13731 .13734 .13736 .13739 60 59 58 57 + r 5 6 7 9.11879 .11887 .11895 .11904 .13146 .13148 .13151 .13153 9.12365 .12373 .12381 .12389 .13294 .13296 .13299 .13301 9.12847 .12855 .12863 .12871 .13442 .13445 .13447 .13450 9.13326 .13334 .13342 .13350 9.13358 .13366 .13374 .13382 .13591 .13594 .13596 .13599 9.13803 .13811 .13819 .13827 .13741 .13744 .13746 .13749 56 55 54 53 + r 9 10 11 9.11912 .11920 .11928 .11936 .13156 .13158 .13161 .13163 9.12397 .12405 .12413 .12421 .13304 .13306 .13309 .13311 9.12879 .12887 .12895 .12903 .13452 .13455 .13457 .13460 .13601 .13604 .13607 .13609 9.13834 .13842 .13850 .13858 .13751 .13754 .13756 .13759 52 51 50 49 + 3' 13 14 15 9.11944 .11952 .11960 .11968 .13166 .13168 .13171 .13173 9.12429 .12437 .12445 .12453 .13314 .13316 .13318 .13321 9.12911 .12919 .12927 .12935 .13462 .13465 .13467 .13470 9.13390 .13398 .13406 .13414 .13611 .13614 .13616 .13619 9.13866 .13874 .13882 .13890 .13761 .13764 .13766 .13769 48 47 46 45 17 18 19 9.11977 .11985 .11993 .12001 .13175 .13178 .13180 .13183 9.12461 .12470 .12478 .12486 .13323 .13326 .13328 .13331 9.12943 .12951 .12959 .12967 .13472 .13474 .13477 .13479 9.13422 .13430 .13438 .13446 .13621 .13624 .13626 .13629 9.13898 .13906 .13913 .13921 9.13929 .13937 .13945 .13953 .13771 .13774 .13776 .13779 44 43 42 41 40 39 38 37 + 5^ 21 22 23 9.12009 .12017 .12025 .12033 .13185 .13188 .13190 .13193 9.12494 .12502 .12510 .12518 .13333 .13336 .13338 .13341 9.12975 .12983 .12991 .12999 .13482 .13484 .13487 .13489 9.13454 .13462 .13470 .13478 .13631 .13634 .13636 .13639 .13781 .13784 .13786 .13789 + 6' 25 26 27 9.12041 .12050 .12058 .12066 .13195 .13198 .13200 .13203 9.12526 .12534 .12542 .12550 .13343 .13346 .13348 .13351 9.13007 .13015 .13023 .13031 .13492 .13494 .13497 .13499 9.13486 .13494 .13501 .13509 .13641 .13644 .13646 .13649 9.13961 .13969 .13977 .13985 .13791 .13794 .13796 .13799 36 35 34 33 + r 29 30 31 9.12074 .12082 .12090 .12098 .13205 .13207 .13210 .13212 9.12558 .12566 .12574 .12582 .13353 .13356 .13358 .13360 9.13039 .13047 .13055 .13063 .13502 .13504 .13507 .13509 9.13517 .13525 .13533 .13541 .13651 .13654 .13656 .13659 9.13992 .14000 .14008 .14016 .13801 .13804 .13806 .13809 32 31 30 29 + 8' 33 34 35 9.12106 .12114 .12122 .12130 .13215 .13217 .13220 .13222 .13225 .13227 .13230 .13232 9.12590 .12598 .12606 .12614 9.12622 .12630 .12638 .12647 .13363 .13365 .13368 .13370 .13373 .13375 .13378 .13380 9.13071 .13079 .13087 .13095 9.13103 .13111 .13119 .13127 .13512 .13514 .13517 .13519 .13522 .13524 .13527 .13529 9.13549 .13557 .13565 .13573 .13661 .13664 .13666 .13669 9.14024 .14032 .14040 .14048 .13811 .13814 .13816 .13819 28 27 26 25 24 23 22 21 20 19 18 17 + r 37 38 39 9.12139 .12147 .12155 .12163 9.13581 .13589 .13597 .13605 .13671 .13674 .13676 .13679 9.14056 .14063 .14071 .14079 .13822 .13824 .13827 .13829 + W 41 42 43 9.12171 .12179 .12187 .12195 .13235 .13237 .13239 .13242 9.12655 .12663 .12671 .12679 .13383 .13385 .13388 .13390 9.13135 .13143 .13151 .13159 .13532 .13534 .13537 .13539 9.13613 .13621 .13628 .13636 .13681 .13684 .13686 .13689 9.14087 .14095 .14103 .14111 .13832 .13834 .13837 .13839 + ir 45 46 47 9.12203 .12211 .12219 .12228 .13244 .13247 .13249 .13252 9.12687 .12695 .12703 .12711 .13393 .13395 .13398 .13400 9.13167 .13175 .13183 .13191 .13542 .13544 .13547 .13549 9.13644 .13652 .13660 .13668 .13691 .13694 .13696 .13699 9.14119 .14127 .14134 .14142 .13842 .13844 .13847 .13849 16 15 14 IS + 12' 49 50 51 + 13' 53 54 55 + 14' 57 58 59 9.12236 .12244 .12252 .12260 .13254 .13257 .13259 .13262 9.12719 .12727 .12735 .12743 .13403 .13405 .13408 .13410 9.13199 .13207 .13215 .13223 913231 .13239 .13247 .13255 .13552 .13554 .13557 .13559 9.13676 .13684 .13692 .13700 .13701 .13704 .13706 .13709 9.14150 .14158 .14166 .14174 .13852 .13854 .13857 .13859 12 11 10 9 9.12268 .12276 .12284 .12292 .13264 .13267 .13269 .13272 9.12751 .12759 .12767 .12775 .13412 .13415 .13417 .13420 .13562 .13564 .13567 .13569 9.13708 .13716 .13724 .13732 .13711 .13714 .13716 .13719 9.14182 .14190 .14197 .14205 .13862 .13864 .13867 .13869 8 7 6 5 4 S 2 1 9.12300 .12308 .12316 .12324 .13274 .13276 .13279 .13281 .13284 9.12783 .12791 .12799 .12807 9.12815 .13422 .13425 .13427 .13430 .13432 9.13263 .13271 .13279 .13287 .13571 .13574 .13576 .13579 9.13739 .13747 .]3755 .13763 .13721 .13724 .13726 .13729 9.14213 .14221 .14229 .14237 .13872 .13874 .13877 .13879 + 15' 9.12332 9.13295 .13581 9.13771 .13731 9.14245 .13882 21h9m glhSm 2lh 7m 21fi6m 21h5m 1 h Page 846] TABLE 45. Haveraines. s ^ft 55-m 43° 45' 2h 56m 44° 0' 2h 57m 44° 15' 2h 58m 44° W 2h 59m 44° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.14245 .14252 .14260 .14268 .13883 .13884 .13887 .13889 9.14715 .14723 .14731 .14739 .14033 .14035 .14038 .14041 9.15183 .15190 .15198 .15206 .14185 .14187 .14190 .14192 9.15647 .15655 .15663 .15670 .14337 .14340 .14343 .14345 9.16109 .16117 .16124 .16132 .14491 .14493 .14496 .14498 60 59 58 57 + r 5 6 7 9.14276 .14284 .14292 .14300 .13892 .13894 .13897 .13899 9.14746 .14754 .14762 .14770 .14043 .14046 .14048 .14051 9.15214 .15221 .15229 .15237 .14195 .14198 .14200 .14203 9.15678 .15686 .15694 .15701 .14348 .14350 .14353 .14355 9.16140 .16147 .16155 .16163 .14501 .14504 .14506 .14509 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 + 2^ 9 10 11 9.14307 .14315 .14323 .14331 .13903 .13904 .13907 .13909 9.14778 .14785 .14793 .14801 .14053 .14056 .14058 .14061 9.15245 .15253 .15260 .15268 .14305 .14208 .14210 .14213 9.15709 .15717 .15724 .15732 .14358 .14360 .14363 .14366 .14368 .14371 .14373 .14376 9.16170 .16178 .16186 .16193 .14511 .14514 .14516 .14519 + 3^ 13 14 15 9.14339 .14347 .14355 .14362 .13913 .13914 .13917 .13930 9.14809 .14817 .14824 .14832 .14063 .14066 .14068 .14071 9.15276 .15284 .15291 .15299 .14215 .14218 .14220 .14223 .14236 .14328 .14331 .14333 9.15740 .15748 .15755 .15763 9.16201 .16209 .16216 .16224 .14521 .14524 .14537 .14539 + 4' 17 18 19 9.14370 .14378 .14386 .14394 .13933 .13935 .13937 .13930 9.14840 .14848 .14856 .14863 .14073 .14076 .14079 .14081 9.15307 .15315 .15322 .15330 9.15771 .15778 .15786 .15794 .14378 .14381 .14383 .14386 9.16232 .16239 .16247 .16255 .14533 .14534 .14537 .14539 + 5^ 22 23 9.14402 .14410 .14417 .14425 .13933 .13935 .13937 .13940 9.14871 .14879 .14887 .14895 .14084 .14086 .14089 .14091 9.15338 .15346 .15353 .15361 .14336 .14238 .14241 .14243 9.15802 .15809 .15817 .15825 .14388 .14391 .14394 .14396 9.16262 .16270 .16278 .16285 .14543 .14545 .14547 .14550 + 6^ 26 27 9.14433 .14441 .14449 .14457 .13943 .13945 .13947 .13950 9.14902 .14910 .14918 .14926 .14094 .14096 .14099 .14101 9.15369 .15377 .15384 .15392 .14246 .14248 .14251 .14253 9.15832 .15840 .15848 .15855 .14399 .14401 .14404 .14406 9.16293 .16301 .16308 .16316 .14553 .14555 .14557 .14560 36 35 34 33 + r 30 31 9.14465 .14472 .14480 .14488 .13953 .13955 .13957 .13960 9.14934 .14941 .14949 .14957 .14104 .14106 .14109 .14111 9.15400 .15408 .15415 .15423 .14256 .14259 .14261 .14264 9.15863 .15871 .15879 .15886 .14409 .14411 .14414 .14417 9.16324 .16331 .16339 .16346 .14563 .14565 .14568 .14570 32 31 30 29 + 8^ 34 35 9.14496 .14504 .14512 .14519 .13963 .13965 .13967 .13970 9.14965 .14973 .14980 .14988 .14114 .14116 .14119 .14133 9.15431 .15439 .15446 .15454 .14266 .14269 .14271 .14274 9.15894 .15902 .15909 .15917 .14419 .14433 .14434 .14427 9.16354 .16362 .16369 .16377 .14573 .14575 .14578 .14580 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 + 9^ 38 39 9.14527 .14535 .14543 .14551 .13973 .13975 .13977 .13980 9.14996 .15004 .15012 .15019 .14134 .14137 .14139 .14133 9.15462 .15470 .15477 .15485 .14276 .14279 .14281 .14284 9.15925 .15932 .15940 .15948 .14429 .14432 .14434 .14437 9.16385 .16392 .16400 .16408 .14583 .14586 .14588 .14591 + ir 42 43 9.14559 .14566 .14574 .14582 .13983 .13985 .13988 .13990 9.15027 .15035 .15043 .15050 .14134 .14137 .14139 .14143 9.15493 .15500 .15508 .15516 .14287 .14289 .14292 .14294 9.15955 .15963 .15971 .15978 .14440 .14442 .14445 .14447 9.16415 .16423 .16431 .16438 .14593 .14596 .14598 .14601 + 11^ 46 47 9.14590 .14598 .14606 .14613 .13993 .13995 .13998 .14000 9.15058 .15066 .15074 .15082 .14144 .14147 .14149 .14153 .14154 .14157 .14160 .14163 9.15524 .15531 .15539 .15547 .14297 .14299 .14303 .14304 9.15986 .15994 .16002 .16009 .14450 .14452 .14455 .14457 9.16446 .16453 .16461 .16469 .14604 .14606 .14609 .14611 + 12^ 49 50 51 9.14621 .14629 .14637 .14645 .14003 .14005 .14008 .14010 9.15089 .15097 .15105 .15113 9.15555 .15562 .15570 .15578 .14307 .14309 .14313 .14315 9.16017 .16025 .16032 .16040 .14460 .14463 .14465 .14468 9.16476 .16484 .16492 .16499 .14614 .14616 .14619 .14633 12 11 10 9 + 13^ 5^ 54 55 9.14653 .14660 .14668 .14676 .14013 .14015 .14018 .14030 9.15120 .15128 .15136 .15144 .14165 .14167 .14170 .14172 9.15585 .15593 .15601 .15609 .14317 .14330 .14333 .14335 9.16048 .16055 .16063 .16071 .14470 .14473 .14475 .14478 9.16507 .16515 .16522 .16530 .14634 .14637 .14639 .14633 8 7 6 5 + 14' 57 58 59 9.14684 .14692 .14699 .14707 .14033 .14035 .14038 .14030 9.15152 .15159 .15167 .15175 .14175 .14177 .14180 .14183 9.15616 .15624 .15632 .15640 .14327 .14330 .14332 .14335 9.16078 .16086 .16094 .16101 .14480 .14483 .14486 .14488 9.16537 .16545 .16553 .16560 .14634 .14637 .14639 .14643 4 3 2 1 + 15' 9.14715 .14033 9.15183 .14185 9.15647 .14337 9.16109 .14491 9.16568 .14645 21^ ^m 21hsm 21^ 2m 21^ im 21^ Om TABLE 45. Haveraines. [Page 847 s 3h am 45° 0^ Sh im 45° 15' Sh 2m 45° 3^ Sh .5"» 45° W Shpn 46° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.16568 .16576 .16583 .16591 .11645 .14647 .14650 .14653 9.17024 .17032 .17039 .17047 .14799 .14803 .14804 .14807 9.17477 .17485 .17492 .17500 .14955 .14957 .14960 .14963 9.17928 .17935 .17943 .17950 .15110 .15113 .15116 .15118 9.18376 .18383 .18390 .18398 .15367 .15370 .15272 .15275 60 59 58 57 + V 5 6 7 9.16598 .16606 .16614 .16621 .14655 .14658 .14660 .14663 9.17054 .17062 .17069 .17077 .14810 .14813 .14815 .14817 9.17507 .17515 .17522 .17530 .14965 .14968 .14970 .14973 9.17958 .17965 .17973 .17980 .15131 .15133 .15136 .16129 9.18405 .18413 .18420 .18428 .15278 .15380 .15383 .15285 56 55 54 63 + r 9 10 11 9.16629 .16637 .16644 .16652 .14665 .14668 .14670 .14673 9.17085 .17092 .17100 .17107 .14830 .14833 .14835 .14838 9.17538 .17545 .17553 .17560 .14975 .14978 .14981 .14983 9.17988 .17995 .18003 .18010 .15131 .15134 .15137 .15139 9.18435 .18443 .18450 .18457 .15288 .15291 .15293 .15296 52 51 50 49 + y 13 14 15 9.16659 .16667 .16675 .16682 .14676 .14678 .14681 .14683 9.17115 .17122 .17130 .17138 .14830 .14833 .14835 .14838 9.17568 .17575 .17583 .17590 .14986 .14988 .14991 .14993 9.18018 .18025 .18033 .18040 .15142 .15144 .15147 .15150 9.18465 .18472 .18480 .18487 .16298 .15301 .16304 .16306 48 47. 46 45 + i' 17 18 19 9.16690 .16697 .16705 .16713 .14686 .14688 .14691 .14693 9.17145 .17153 .17160 .17168 .14841 .14843 .14846 .14848 9.17598 .17605 .17613 .17620 .14996 .14999 .15001 .15004 9.18048 .18055 .18062 .18070 .16153 .15156 .16157 .15160 9.18495 .18502 .18509 .18517 .16309 .16312 .16314 .16316 U 43 42 41 + 5' 21 22 23 9.16720 .16728 .16735 .16743 .14696 .14699 .14701 .14704 9.17175 .17183 .17191 .17198 .14851 .14853 .14856 .14859 9.17628 .17635 .17643 .17650 .15006 .15009 .15013 .15014 9.18077 .18085 .18092 .18100 .16163 .15165 .15168 .15170 9.18524 .18532 .18539 .18547 .15319 .16322 .16325 .16327 40 39 38 37 + 6' 25 26 27 9.16751 .16758 .16766 .16774 .14706 .14709 .14713 .14714 9.17206 .17213 .17221 .17228 .14861 .14864 .14866 .14869 9.17658 .17665 .17673 .17680 .15017 .15019 .15033 .15035 9.18107 .18115 .18122 .18130 .15173 .16176 .16178 .16181 9.18554 .18561 .18569 .18576 .15330 .15333 .16335 .16337 S6 35 34 33 + r 29 SO 31 9.16781 .16789 .16796 .16804 .14717 .14719 .14733 .14734 9.17236 .17243 .17251 .17259 .14873 .14874 .14877 .14879 9.17688 .17695 .17703 .17710 .15037 .15030 .15032 .15035 9.18137 .18145 .18152 .18160 .16183 .16186 .16189 .16191 9.18584 .18591 .18598 .18606 .16340 .16343 .16346 .16348 32 31 SO 29 + S' S3 34 35 9.16812 .16819 .16827 .16834 .14737 .14730 .14733 .14735 9.17266 .17274 .17281 .17289 .14883 .14885 .14887 .14890 9.17718 .17725 .17733 .17740 .15038 .15040 .15043 .15045 9.18167 .18174 .18182 .18189 .16194 .15197 .15199 .16202 9.18613 .18621 .18628 .18636 .16361 .16353 .16356 .16359 28 27 26 25 + 9' 37 38 39 9.16842 .16850 .16857 .16865 .14737 .14740 .14743 .14745 9.17296 .17304 .17311 .17319 .14893 .14895 .14898 .14900 9.17748 .17755 .17763 .17770 .15048 .15051 .15053 .15056 9.18197 .18204 .18212 .18219 .15204 .15207 .16210 .16212 9.18643 .18650 .18658 .18665 .15361 .16364 .16367 .16369 24 23 22 21 + W 41 42 43 9.16872 .16880 .16887 .16895 .14748 .14750 .14753 .14755 9.17327 .17334 .17342 .17349 .14903 .14905 .14908 .14910 9.17778 .17785 .17793 .17800 .15058 .15061 .15064 .15066 9.18227 .18234 .18242 .18249 .16216 .15317 .15330 .15322 9.18673 .18680 .18687 .18695 .16372 .15374 .15377 .15379 20 19 18 17 + 11' 45 46 47 9.16903 .16910 .16918 .16925 .14758 .14760 .14763 .14766 9.17357 .17364 .17372 .17379 .14913 .14916 .14918 .14931 9.17808 .17815 .17823 .17830 .15069 .15071 .15074 .15077 9.18256 .18264 .18271 .18279 .15225 .16228 .15330 .16233 9.18702 .18710 .18717 .18724 .16382 .16386 .16388 .16390 16 15 14 IS + 13' 49 50 51 9.16933 .16941 .16948 .16956 .14768 .14771 .14773 .14776 9.17387 .17394 .17402 .17409 .14933 .14936 .14939 .14931 9.17838 .17845 .17853 .17860 .15079 .15083 .15084 .15087 9.18286 .18294 .18301 .18309 .15236 .15238 .15241 .15244 9.18732 .18739 .18747 .18754 .15393 .15395 .15398 .15401 12 11 10 9 8 7 6 5 + 13^ 53 64 55 9.16963 .16971 .16979 .16986 .14779 .14781 .14784 .14786 9.17417 .17425 .17432 .17440 .14934 .14936 .14939 .14943 9.17868 .17875 .17883 .17890 .15090 .15093 .15095 .15097 9.18316 .18324 .18331 .18338 .15246 .16349 .15251 .16254 9.18762 .18769 .18776 .18784 .15403 .15406 .15409 .15411 + W 57 58 59 9.16994 .17001 .17009 .17016 .14789 .14791 .14794 .14797 9.17447 .17455 .17462 .17470 .14944 .14947 .14949 .14953 9.17898 .17905 .17913 .17920 .15100 .15103 .15105 .15108 9.18346 .18353 .18361 .18368 .15257 .15259 .15263 .15364 9.18791 .18798 .18806 .18813 .15414 .15416 .15419 .15423 4 S 2 1 + 15^ 9.17024 .14799 9.17477 .14955 9.17928 .15110 9.18376 .15367 9.18821 .15424 20h 59m 20^ 58^ 20^ 57m 20h 56"» 20h 55m Page 848] TABLE 45. Haversinea. s 3h 5m 46° 15' 3h em 46° 30' 3^ im 46° 45' 3h gm 470 (K 3h 9m 47° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.18821 .18828 .18835 .18843 .15424 .15427 .15430 .15432 9.19263 .19270 .19278 .19285 .15582 .15585 .15588 .15590 9.19703 .19710 .19717 .19725 .15741 .15743 .15746 .15748 9.20140 .20147 .20154 .20162 .15900 .15903 .15905 .15908 9.20574 .20582 .20589 .20596 .16060 .16063 .16065 .16068 60 59 58 51 + r 5 6 1 9.18850 .18858 .18865 .18872 .15435 .15437 .15440 .15443 9.19292 .19300 .19307 .19315 .15593 .15595 .15598 .15601 9.19732 .19739 .19747 .19754 .15751 .15754 .15757 .15759 9.20169 .20176 .20184 .20191 .15911 .15913 .15916 .15919 9.20603 .20611 .20618 .20625 .16071 .16073 .16076 .16079 56 55 54 53 + 2' 9 10 11 9.18880 .18887 .18895 .18902 .15445 .15448 .15451 .15453 9.19322 .19329 .19337 .19344 .15603 .15606 .15609 .15611 9.19761 .19769 .19776 .19783 .15762 .15765 .15767 .15770 9.20198 .20205 .20213 .20220 .15921 .15924 .15927 .15929 .15932 .15935 .15937 .15940 9.20632 .20639 .20647 .20654 .16081 .16084 .16087 .16089 52 51 50 49 + 3' . IS 14 15 9.18909 .18917 .18924 .18932 .15456 .15458 .15461 .15464 9.19351 .19359 .19366 .19373 .15614 .15617 .15619 .15622 9.19790 .19798 .19805 .19812 .15773 .15775 .15778 .15781 9.20227 .20234 .20242 .20249 9.20661 .20668 .20675 .20683 .16092 .16095 .16097 .16100 48 41 46 45 + 4' 11 18 19 9.18939 .18946 .18954 .18961 .15466 .15469 .15472 .15474 9.19381 .19388 .19395 .19403 .15625 .15627 .15630 .15632 9.19820 .19827 .19834 .19842 .15783 .15786 .15789 .15791 9.20256 .20263 .20271 .20278 .15943 .15945 .15948 .15951 9.20690 .20697 .20704 .20712 .16103 .16105 .16108 .16111 44 43 42 41 + 5' 21 22 23 9.18968 .18976 .18983 .18991 .15477 .15479 .15482 .15485 9.19410 .19417 .19425 .19432 .15635 .15638 .15640 .15643 9.19849 .19856 .19863 .19871 .15794 .15796 .15799 .15802 9.20285 .20292 .20300 .20307 .15953 .15956 .15959 .15961 9.20719 .20726 .20733 .20740 .16113 .16116 .16119 .16121 40 39 38 31 + 6' 25 26 21 9.18998 .19005 .19013 .19020 .15487 .15490 .15493 .15495 9.19439 .19447 .19454 .19461 .15646 .15648 .15651 .15654 9.19878 .19885 .19893 .19900 .15804 .15807 .15810 .15812 9.20314 .20321 .20329 .20336 .15964 .15967 .15969 .15972 9.20748 .20755 .20762 .20769 .16124 .16127 .16129 .16132 36 35 34 33 + r 29 30 31 9.19027 .19035 .19042 .19050 .15498 .15501 .15503 .15506 9.19469 .19476 .19483 .19491 .15656 .15659 .15662 .15664 9.19907 .19914 .19922 .19929 .15815 .15818 .15820 .15823 9.20343 .20350 .20358 .20365 .15975 .15977 .15980 .15983 9.20776 .20784 .20791 .20798 .16135 .16137 .16140 .16143 32 31 SO 29 + 8' 33 34 35 9.19057 .19064 .19072 .19079 .15509 .15511 .15514 .15516 9.19498 .19505 .19513 .19520 .15667 .15670 .15672 .15675 9.19936 .19944 .19951 .19958 .15826 .15828 .15831 .15834 9.20372 .20379 .20386 .20394 .15985 .15988 .15991 .15993 9.20805 .20812 .20820 .20827 .16146 .16148 .16151 .16154 28 21 26 25 + 9' 31 38 39 9.19086 .19094 .19101 .19109 .15519 .15522 .15524 .15527 9.19527 .19535 .19542 .19549 .15677 .15680 .15683 .15685 9.19965 .19973 .19980 .19987 .15836 .15839 .15842 .15844 9.20401 .20408 .20415 .20423 .15996 .15999 .16001 .16004 9.20834 .20841 .20848 .20856 .16156 .16159 .16162 .16164 24 23 22 21 + 10' 41 42 43 9.19116 .19123 .19131 .19138 .15530 .15532 .15535 .15537 9.19557 .19564 .19571 .19579 .15688 .15691 .15693 .15696 9.19995 .20002 .20009 .20016 .15847 .15850 .15852 .15855 9.20430 .20437 .20444 .20452 .16007 .16009 .16012 .16015 9.20863 .20870 .20877 .20884 .16167 .16170 .16172 .16175 20 19 18 11 + 11' 45 46 41 9.19145 .19153 .19160 .19167 .15540 .15543 .15545 .15548 9.19586 .19593 .19600 .19608 .15699 .15701 .15704 .15706 9.20024 .20031 .20038 .20045 .15858 .15860 .15863 .15866 9.20459 .20466 .20473 .20481 .16017 .16020 .16023 .16025 9.20891 .20899 .20906 .20913 .16178 .16180 .16183 .16186 16 15 14 IS 12 11 10 9 + 12' 49 50 51 9.19175 .19182 .19190 .19197 .15551 .15553 .15556 .15559 9.19615 .19622 .19630 .19637 .15709 .15712 .15714 .15717 9.20053 .20060 .20067 .20075 .15868 .15871 .15874 .15876 9.20488 .20495 .20502 .20509 .16028 .16031 .16033 .16036 9.20920 .20927 .20935 .20942 .16188 .16191 .16194 .16196 + 13' 53 54 55 9.19204 .19212 .19219 .19226 .15561 .15564 .15566 .15569 9.19644 .19652 .19659 .19666 .15720 .15722 .15725 .15728 9.20082 .20089 .20096 .20104 .15879 .15881 .15884 .15887 9.20517 .20524 .20531 .20538 .16039 .16041 .16044 .16047 9.20949 .20956 .20963 .20971 .16199 .16202 .16204 .16207 8 1 6 5 + 14' 51 58 59 9.19234 .19241 .19248 .19256 9.19263 .15572 .15574 .15577 .15580 .15582 9.19674 .19681 .19688 .19696 .15730 .15733 .15736 .15738 9.20111 .20118 .20125 .20133 .15889 .15892 .15895 .15898 9.20546 .20553 .20560 .20567 .16049 .16052 .16055 .16057 9.20978 .20985 .20992 .20999 .16210 .16212 .16215 .16218 4 3 2 1 + 15' 9.19703 .15741 9.20140 .15900 9.20574 .16060 9.21006 .16220 20h 54m 20h 53m 20^ 52m 20h 5m 20^50m Page 860] TABLE 45. Haversines. s Sh urn 48° 45' S\ 16^ 49° 0' Sh J7m 49° 15/ 3h igm 49° 30^ Sh 19m 49° 45/ s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.23128 .23135 .23142 .23149 .17033 .17035 .17038 .17041 9.23545 .23552 .23559 .23566 .17197 .17200 .17203 .17205 9.23960 .23967 .23974 .23981 .17362 .17365 .17368 .17370 9.24372 .24379 .24386 .24393 .17528 .17530 .17533 .17536 9.24782 .24789 .24796 .24803 .17694 .17697 .17699 .17702 60 59 58 57 56 55 54 53 52 51 50 49 4S 47 46 45 44 43 42 41 + r 5 6 7 9.23156 .23163 .23170 .23177 .17044 .17046 .17049 .17053 9.23573 .23580 .23587 .23594 .17208 .17211 .17214 .17216 9.23988 .23994 .24001 .24008 .17373 .17376 .17379 .17381 9.24400 .24406 .24413 .24420 .17539 .17541 .17644 .17547 9.24809 .24816 .24823 .24830 .17706 .17708 .17710 .17713 + V 9 10 11 9.23184 .23191 .23198 .23205 .17055 .17057 .17060 .17063 9.23601 .23608 .23615 .23622 .17219 .17222 .17225 .17227 9.24015 .24022 .24029 .24036 .17384 .17387 .17390 .17392 9.24427 .24434 .24441 .24448 .17550 .17562 .17556 .17658 9.24837 .24843 .24850 .24857 .17716 .17719 .17722 .17724 + 3' 13 14 15 9.23212 .23219 .23226 .23233 .17066 .17068 .17071 .17074 9.23629 .23635 .23642 .23649 .17230 .17233 .17235 .17238 9.24043 .24050 .24056 .24063 .17395 .17398 .17401 .17403 9.24454 .24461 .24468 .24475 .17561 .17663 .17566 .17569 9.24864 .24871 .24877 .24884 .17727 .17730 .17733 .17736 + i' 17 18 19 9.23240 .23247 .23254 .23261 .17076 .17079 .17082 .17085 9.23656 .23663 .23670 .23677 .17241 .17244 .17246 .17249 9.24070 .24077 .24084 .24091 .17406 .17409 .17412 .17414 9.24482 .24489 .24495 .24502 .17672 .17675 .17577 .17680 9.24891 .24898 .24905 .24911 .17738 .17741 .17744 .17746 + h' 21 22 23 9.23268 .23275 .23282 .23289 .17087 .17090 .17093 .17096 9.23684 .23691 .23698 .23705 .17252 .17255 .17257 .17260 9.24098 .24105 .24111 .24118 .17417 .17420 .17423 .17425 9.24509 .24516 .24523 .24530 .17583 .17586 .17588 .17591 9.24918 .24925 .24932 .24939 .17749 .17752 .17756 .17758 40 39 38 37 + 6' 25 26 27 9.23295 .23302 .23309 .23316 .17098 .17101 .17104 .17107 9.23712 .23718 .23725 .23732 .17263 .17266 .17268 .17271 9.24125 .24132 .24139 .24146 .17428 .17431 .17434 .17436 9.24536 .24543 .24550 .24557 .17594 .17697 .17600 .17602 9.24945 .24952 .24959 .24966 .17760 .17763 .17766 .17769 36 35 34 33 + r 29 30 31 9.23323 .23330 .23337 .23344 .17109 .17112 .17115 .17117 9.23739 .23746 .23753 .23760 .17274 .17277 .17279 .17282 9.24153 .24160 .24166 .24173 .17439 .17442 .17445 .17447 9.24564 .24571 .24577 .24584 .17606 .17608 .17611 .17613 9.24973 .24979 .24986 .24993 .17772 .17774 .17777 .17780 32 31 30 29 + 8' 33 34 35 9.23351 .23358 .23365 .23372 .17120 .17123 .17126 .17128 9.23767 .23774 .23781 .23788 .17285 .17288 .17290 .17293 9.24180 .24187 .24194 .24201 .17450 .17453 .17456 .17458 9.24591 .24598 .24605 .24612 .17616 .17619 .17622 .17624 9.25000 .25007 .25013 .25020 .17783 .17785 .17788 .17791 28 27 26 25 24 23 22 21 + 9' 37 38 39 9.23379 .23386 .23393 .23400 .17131 .17134 .17137 .17139 9.23794 .23801 .23808 .23815 .17296 .17299 .17301 .17304 9.24208 .24215 .24221 .24228 .17461 .17464 .17467 .17470 9.24618 .24625 .24632 .24639 .17627 .17630 .17633 .17636 9.25027 .25034 .25040 .25047 .17794 .17797 .17799 .17802 + 10' 41 42 43 9.23407 .23414 .23421 .23427 .17142 .17145 .17148 .17150 9.23822 .23829 .23836 .23843 .17307 .17310 .17313 .17316 9.24235 .24242 .24249 .24256 .17472 .17475 .17478 .17481 9.24646 .24653 .24659 .24666 .17638 .17641 .17644 .17647 9.25054 .25061 .25068 .25074 .17805 .17808 .17811 .17813 20 19 18 17 + ir 45 46 47 9.23434 .23441 .23448 .23455 .17153 .17156 .17159 .17161 9.23850 .23857 .23863 .23870 .17318 .17321 .17323 .17326 9.24263 .24269 .24276 .24283 .17483 .17486 .17489 .17492 9.24673 .24680 .24687 .24694 .17649 .17662 .17656 .17658 9.25081 .25088 .25095 .25102 .17816 .17819 .17822 .17824 16 15 14 13 + 13' 49 50 51 9.23462 .23469 .23476 .23483 .17164 .17167 .17170 .17172 9.23877 .23884 .23891 .23898 .17329 .17332 .17335 .17337 9.24290 .24297 .24304 .24311 .17494 .17497 .17500 .17503 9.24700 .24707 .24714 .24721 .17661 .17663 .17666 .17669 9.25108 .25115 .25122 .25129 .17827 .17830 .17833 .17836 12 11 10 9 8 7 6 5 4 3 2 1 + 13' 53 54 55 9.23490 .23497 .23504 .23511 .17175 .17178 .17181 .17183 9.23905 .23912 .23919 .23926 .17340 .17343 .17346 .17348 9.24317 .24324 .24331 .24338 .17505 .17508 .17611 .17614 9.24728 .24734 .24741 .24748 .17672 .17674 .17677 .17680 9.25135 .25142 .25149 .25156 .17838 .17841 .17844 .17847 + 14' 57 58 59 9.23518 .23525 .23532 .23538 .17186 .17189 .17192 .17194 9.23932 .23939 .23946 .23953 .17351 .17354 .17367 .17359 9.24345 .24352 .24359 .24365 .17517 .17519 .17522 .17626 9.24755 .24762 .24768 .24775 .17683 .17686 .17688 .17691 9.25163 .25169 .25176 .25183 .17849 .17862 .17866 .17868 + 16' 9.23545 .17197 9.23960 .17362 9.24372 .17628 9.24782 .17694 9.25190 .17861 20^44'^ 20h43m 20h 42m 1 20h 41m 1 20^ 40m 1 TABLE 45. [Page 851 Haversines. s 5A :?0n» 50° (K 3^ 21m 50° 15' Sh 22m 50° 30' 3^ 23m 60° 45' 3h 24m 51° (K Log. Hav. Nat. Hav. Log. Hav.lXat. Hav. Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. s 1 2 3 9.25190 .25196 .25203 .25210 .17861 .17863 .17866 .17869 9.25595 .25602 .25608 .25615 .18028 .18031 .18034 .18036 9.25998 .26005 .26011 .26018 .18196 .18199 .18202 .18205 9.26398 .26405 .26412 .26418 .18365 .18368 .18370 .18373 9.26797 .26804 .26810 .26817 .18534 .18537 .18540 .18542 60 59 58 57 + r 5 6 7 9.25217 .25224 .25230 .25237 .17872 .17875 .17877 .17880 9.25622 .25629 .25635 .25642 .18039 .18042 .18045 .18048 9.26025 .26031 .26038 .26045 .18207 .18210 .18213 .18216 .18219 .18221 .18224 .18227 .18230 .18233 .18235 .18238 9.26425 .26432 .26438 .26445 .18376 .18379 .18382 .18384 9.26823 .26830 .26837 .26843 .18545 .18548 .18551 .18554 56 55 54 53 + -i' 9 10 11 9.25244 .25251 .25257 .25264 .17883 .17886 .17888 .17891 9.25649 .25655 .25662 .25669 .18050 .18053 .18056 .18059 9.26051 .26058 .26065 .26071 9.26078 .26085 .26091 .26098 9.26452 .26458 .26465 .26472 .18387 .18390 .18393 .18396 9.26850 .26856 .26863 .26870 9.26876 .26883 .26890 .26896 .18557 .18559 .18562 .18565 .18568 .18571 .18574 .18576 52 51 50 49 48 47 46 45 + 3' 13 14 15 9.25271 .25278 .25284 .25291 .17894 .17897 .17900 .17902 9.25676 .25682 .25689 .25696 .18062 .18064 .18067 .18070 9.26478 .26485 .26492 .26498 .18399 .18401 .18404 .18407 + 4' 17 18 19 9.25298 .25305 .25311 .25318 .17905 .17908 .17911 .17914 9.25703 .25709 .25716 .25723 .18073 .18076 .18078 .18081 9.26105 .26112 .26118 .26125 .18241 .18244 .18247 .18249 9.26505 .26512 .26518 .26525 .18410 .18413 .18415 .18418 9.26903 .26909 .26916 .26923 .18579 .18582 .18585 .18588 44 43 42 41 + 6' 21 22 23 9.25325 .25332 .25339 .25345 .17916 .17919 .17922 .17925 9.25729 .25736 .25743 .25750 9.25756^ .25763 .25770 .25776 .18084 .18087 .18090 .18092 .18095 .18098 .18101 .18104 9.26132 .26138 .26145 .26152 9.26158 .26165 .26172 .26178 .18252 .18255 .18258 .18261 .18263 .18266 .18269 .18272 9.26532 .26538 .26545 .26551 9.26558 .26565 .26571 .26578 .18421 .18424 .18427 .18430 .18432 .18435 .18438 .18441 9.26929 .26936 .26942 .26949 .18591 .18593 .18596 .18599 40 39 38 37 + 6' 25 26 27 9.25352 .25359 .25366 .25372 .17928 .17930 .17933 .17936 9.26956 .26962 .26969 .26975 .18602 .18605 .18608 .18610 36 35 34 33 32 31 30 29 + r 29 30 31 9.25379 .25386 .25393 .25399 .17939 .17941 .17944 .17947 9.25783 .25790 .25797 .25803 .18106 .18109 .18112 .18115 9.26185 .26192 .26198 .26205 .18275 .18277 .18280 .18283 9.26585 .26591 .26598 .26605 .18444 .18446 .18449 .18452 9.26982 .26989 .26995 .27002 .18613 .18616 .18619 .18622 + S' 33 34 35 9.25406 .25413 .25420 .25426 .17950 .17953 .17955 .17958 9.25810 .25817 .25823 .25830 .18118 .18120 .18123 .18126 9.26212 .26218 .26225 .26232 .18286 .18289 .18292 .18294 9.26611 .26618 .26625 .26631 9.26638 .26644 .26651 .26658 .18455 .18458 .18461 .18463 .18466 .18469 .18472 .18475 9.27008 .27015 .27022 .27028 .18624 .18627 .18630 .18633 28 27 26 25 + JK 37 38 39 9.25433 .25440 .25447 .25453 .17961 .17964 .17967 .17969 9.25837 .25844 .25850 .25857 .18129 .1S132 .18134 .18137 9.26238 .26245 .26252 .26259 .18297 .18300 .18303 .18306 9.27035 .27041 .27048 .27055 .18636 .18639 .18641 .18644 24 23 22 21 20 19 18 n + W 41 42 43 9.25460 .25467 .25474 .25480 .17972 .17975 .17978 .17981 9.25864 .25870 .25877 .25884 .18140 .18143 .18146 .18148 9.26265 .26272 .26279 .26285 .18308 .18311 .18314 .18317 9.26664 .26671 .26678 .26684 .18478 .18480 .18483 .18486 9.27061 .27068 .27074 .27081 .18647 .18650 .18653 .18656 + 11^ 45 46 47 9.25487 .25494 .25500 .25507 .17983 .17986 .17989 .17992 9.25891 .25897 .25904 .25911 .18151 .18154 .18157 .18160 9.26292 .26299 .26305 .26312 .18320 .18323 .18325 .18328 9.26691 .26697 .26704 .26711 .18489 .18492 .18494 .18497 9.27088 .27094 .27101 .27107 .18658 .18661 .18664 .18667 16 15 14 13 12 It 10 9 8 7 6 5 4 3 2 1 + 12' 49 50 51 9.25514 .25521 .25528 .25534 .17995 .17997 .18000 .18003 9.25917 .25924 .25931 .25938 .18162 .18165 .18168 .18171 9.26319 .26325 .26332 .26339 .18331 .18334 .18337 .18339 9.26717 .26724 .26731 .26737 .18500 .18503 .18506 .18509 9.27114 .27121 .27127 .27134 .18670 .18673 .18675 .18678 + 13' 53 54 55 9.25541 .25548 .25544 .25561 .18006 .18008 .18011 .18014 9.25944 .25951 .25958 .25964 .18174 .18176 .18179 .18182 9.26345 .26352 .26359 .26365 .18342 .18345 .18348 .18351 9.26744 .26751 .26757 .26764 .18511 .18514 .18517 .18520 9.27140 .27147 .27154 .27160 .18681 .18684 .18687 .18690 + 14' 57 58 59 9.25568 .25575 .25581 .25588 .18017 .18020 .18022 .18025 9.25971 .25978 .25984 .25991 .18185 .18188 .18190 .18193 9.26372 .26378 .26385 .26392 .18353 .18356 .18359 .18362 9.26770 .26777 .26784 .26790 .18523 .18526 .18528 .18531 9.27167 .27173 .27180 .27186 .18692 .18695 .18698 .18701 + 15' 9.22595 .18028 9.25998 .18196 9.26398 .18365 9.26797 .18534 9.27193 .18704 20^ 39m 20h 38m 20^ S7m J 20^ 36m 1 20^ 35m 1 Page 862] TABLE 45. Haversines. s 3h 25m 51° 15' 3h 26m 51° 30' Sh 27m 51° 45' 3^ 28m 52° 0' 3h 29m 52° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.27193 .27200 .27206 .27213 .18704 .18707 .18710 .18712 9.27587 .27594 .27600 .27607 .18874 .18877 .18880- .18883 9.27979 .27985 .27992 .27998 .19045 .19048 .19051 .19054 9.28368 .28375 .28381 .28388 .19217 .19220 .19223 .19226 9.28756 .28762 .28769 .28775 .19389 .19392 .19395 .19398 60 59 58 57 + r 5 6 7 9.27219 .27226 .27233 .27239 .18715 .18718 .18721 .18724 9.27613 .27620 .27626 .27633 .18886 .18888 .18891 .18894 9.28005 .28011 .28018 .28024 .19057 .19060 .19062 .19065 9.28394 .28401 .28407 .28414 .19228 .19231 .19234 .19237 9.28782 .28788 .28794 .28801 .19401 .19404 .19406 .19409 56 55 54 53 52 51 50 49 48 47 46 45 + 2^ 9 10 11 9.27246 .27252 .27259 .27265 .18727 .18729 .18732 .18735 9.27639 .27646 .27652 .27659 .18897 .18900 .18903 .18906 9.28031 .28037 .28044 .28050 .19068 .19071 .19074 .19077 9.28420 .28427 .28433 .28440 .19240 .19243 .19246 .19248 9.28807 .28814 .28820 .28827 .19412 .19415 .19418 .19421 + 3' 13 14 15 9.27272 .27279 .27285 .27292 .18738 .18741 .18744 .18746 9.27666 .27672 -.27679 .27685 .18908 .18912 .18914 .18917 9.28057 .28063 .28070 .28076 .19080 .19082 .19085 .19088 9.28446 .28453 .28459 .28465 .19251 .19254 .19257 .19260 9.28833 .28840 .28846 .28852 .19424 .19427 .19429 .19432 + i' 17 18 19 9.27298 .27305 .27311 .27318 .18749 .18752 .18755 .18758 9.27692 .27698 .27705 .27711 .18920 .18923 .18926 .18928 9.28083 .28089 .28096 .28102 .19091 .19094 .19097 .19100 9.28472 .28478 .28485 .28491 .19263 .19266 .19269 .19271 9.28859 .28865 .28872 .28878 .19435 .19438 .19441 .19444 44 43 42 41 + 5^ 21 22 23 9.27325 .27331 .27338 .27344 .18761 .18763 .18766 .18769 9.27718 .27724 .27731 .27737 .18931 .18934 .18937 .18940 9.28109 .28115 .28122 .28128 .19102 .19105 .19108 .19111 9.28498 .28504 .28511 .28517 .19274 .19277 .19280 .19283 9.28885 .28891 .28897 .28904 .19447 .19450 .19452 .19455 40 39 38 37 + 6' 25 26 27 9.27351 .27357 .27364 .27371 .18772 .18775 .18778 .18780 9.27744 .27751 .27757 .27764 .18943 .18945 .18948 .18951 9.28135 .28141 .28148 .28154 .19114 .19117 .19120 .19122 9.28524 .28530 .28537 .28543 .19286 .19289 .19291 .19294 9.28910 .28917 .28923 .28930 .19458 .19461 .19464 .19467 36 35 34 33 32 31 30 29 28 27 26 25 + r 29 30 31 9.27377 .27384 .27390 .27397 .18783 .18786 .18789 .18792 9.27770 .27777 .27783 .27790 .18954 .18957 .18960 .18963 9.28161 .28167 .28174 .28180 .19125 .19128 .19131 .19134 9.28549 .28556 .28562 .28569 .19297 .19300 .19303 .19306 9.28936 .28942 .28949 .28955 .19470 .19473 .19475 .19478 + 8' S3 34 35 9.27403 .27410 .27417 .27423 .18795 .18797 .18800 .18803 9.27796 .27803 .27809 .27816 .18965 .18968 .18971 .18974 9.28187 .28193 .28200 .28206 .19137 .19140 .19142 .19145 9.28575 .28582 .28588 .28595 .19309 .19311 .19314 .19317 9.28962 .28968 .28974 .28981 .19481 .19484 .19487 .19490 + 9' 37 38 39 9.27430 .27436 .27443 .27449 .18806 .18809 .18812 .18815 9.27822 .27829 .27835 .27842 .18977 .18980 .18983 .18985 9.28213 .28219 .28226 .28232 .19148 .19151 .19154 .19157 9.28601 .28608 .28614 .28620 .19320 .19323 .19326 .19329 9.28987 .28994 .29000 .29007 .19493 .19496 .19499 .19501 24 23 22 21 20 19 18 17 16 15 14 IS 12 11 10 9 + 10' 41 42 43 9.27456 .27463 .27469 .27476 .18817 .18820 .18823 .18826 9.27848 .27855 .27861 .27868 .18988 .18991 .18994 .18997 9.28239 .28245 .28252 .28258 .19160 .19163 .19165 .19168 9.28627 .28633 .28640 .28646 .19332 .19335 .19337 .19340 9.29013 .29019 .29026 .29032 .19504 .19507 .19510 .19513 + 11^ 45 46 47 9.27482 .27489 .27495 .27502 .18829 .18832 .18834 .18837 9.27875 .27881 .27888 .27894 .19000 .19002 .19005 .19008 9.28265 .28271 .28278 .28284 .19171 .19174 .19177 .19180 9.28653 .28659 .28666 .28672 .19343 .19346 .19349 .19352 9.29039 .29045 .29051 .29058 .19516 .19519 .19522 .19524 + 13' 49 50 51 9.27508 .27515 .27522 .27528 .18840 .18843 .18846 .18849 9.27901 .27907 .27914 .27920 .19011 .19014 .19017 .19020 9.28291 .28297 .28304 .28310 .19183 .19185 .19188 .19191 9.28679 .28685 .28691 .28698 .19355 .19358 .19360 .19363 9.29064 .29071 .29078 .29084 .19527 .19530 .19533 .19536 + 13' 53 54 55 9.27535 .27541 .27548 .27554 .18852 .18854 .18857 .18860 9.27927 .27933 .27940 .27946 .19022 .19025 .19028 .19031 9.28317 .28323 .28330 .28336 .19194 .19197 .19200 .19203 9.28704 .28711 .28717 .28724 .19366 .19369 .19372 .19375 9.29090 .29096 .29103 .29109 .19539 .19542 .19545 .19548 8 7 6 5 4 3 2 1 + 14' 57 58 59 9.27561 .27567 .27574 .27580 .18863 .18866 .18869 .18871 9.27953 .27959 .27966 .27972 9.27979 .19034 .19037 .19040 .19042 9.28342 .28349 .28355 .28362 .19205 .19208 .19211 .19214 9.28730 .28737 .28743 .28749 .19378 .19381 .19383 .19386 9.29116 .29122 .29128 .29135 .19550 .19553 .19556 .19559 + 16' 9.27587 .18874 .19045 9.28368 .19217 9.28756 .19389 9.29141 .19562 20Ji S4m 20h ssm 201^ 32m 20h Sim 20h30m TABLE 45. [Page 863 Haversines. s 3^ 30m 52° 30' 3^ 31^ 52° 45' 3^ 32m 53° (K 3h 33VI 63° 15' 5ft 34m 53° 30' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 ■ 2 S 9.29141 .29148 .29154 .29160 .19563 .19565 .19568 .19571 9.29524 .29531 .29537 .29543 .19735 .19738 .19741 .19744 9.29906 .29912 .29918 .29925 .19909 .19912 .19915 .19918 9.30285 .30291 .30207 .30303 .20084 .20087 .20090 .20093 9.30662 .30668 .30674 .30680 .30359 .30363 .30365 .30368 60 59 58 57 + r 5 6 7 9.29167 .29173 .29180 .29186 .19573 .19576 .19579 .19583 9.29550 .29556 .29563 .29569 .19747 .19750 .19753 .19756 9.29931 .29937 .29943 .29950 .19931 .19924 .19927 .19930 9.30310 .30316 .30322 .30329 .20095 .30098 .30101 .20104 9.30687 .30693 .30699 .30705 .30371 .30273 .30376 .20279 56 55 54 53 52 51 50 49 + -i' 9 10 11 9.29192 .29199 .29205 .29212 .19585 .19588 .19591 .19594 .19597 .19599 .19603 .19605 .19608 .19611 .19614 .19617 9.29575 .29582 .29588 .29594 .19758 .19761 .19764 .19767 9.29956 .29962 .29969 .29975 .19933 .19935 .19938 .19941 9.30335 .30341 .30348 .30354 .20107 .30110 .20113 .20116 9.30712 .30718 .30724 .30730 .20383 .30385 .30288 .30391 + 3' 13 14 15 9.29218 .29224 .29231 .29237 9.29601 .29607 .29614 .29620 9.29626 .29633 .29639 .29645 .19770 .19773 .19776 .19779 9.29981 .29988 .29994 .30000 .19944 .19947 .19950 .19953 9.30360 .30366 .30373 .30379 .20119 .20122 .20125 .20127 9.30737 .30743 .30749 .30755 .30394 .30397 .30300 .30303 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 17 18 19 9.29244 .29250 .29256 .29263 .19783 .19785 .19787 .19790 9.30007 .30013 .30019 .30026 .19956 .19959 .19963 .19964 9.30385 .30392 .30398 .30404 .20130 .20133 .20136 .20139 9.30762 .30768 .30774 .30780 .20306 .20309 .20312 .20314 + 6' 21 22 23 9.29269 .29276 .29282 .29288 .19630 .19633 .19635 .19638 9.29652 .29658 .29664 .29671 .19793 .19796 .19799 .19803 .19805 .19808 .19811 .19814 9.30032 .30038 .30045 .30051 .19967 .19970 .19973 .19976 9.30410 .30417 .30423 .30429 .20142 .20145 .20148 .20151 9.30787 .30793 .30799 .30805 .20317 .20320 .20323 .20326 + 6' 25 26 27 9.29295 .29301 .29307 .29314 .19631 .19634 .19637 .19640 .19643 .19646 .19649 .19651 9.29677 .29683 .29690 .29696 9.30057 .30064 .30070 .30076 .19979 .19982 .19985 .19988 9.30436 .30442 .30448 .30454 .20154 .20157 .30160 .30162 9.30812 .30818 .30824 .30830 .20339 .20333 .30335 .30338 + r 29 30 31 9.29320 .29327 .29333 .29339 9.29703 .29709 .29715 .29722 .19816 .19819 .19832 .19825 9.30083 .30089 .30095 .30102 .19991 .19994 .19996 .19999 .20002 .20005 .20008 .20011 9.30461 .30467 .30473 .30480 .20165 .30168 .20171 .30174 9.30837 .30843 .30849 .30855 .20341 .20344 .30347 .30350 32 31 SO 29 28 27 26 25 + 8' 33 34 35 9.29346 .29352 .29359 .29365 .19654 .19657 .19660 .19663 9.29728 .29734 .29741 .29747 .19838 .19831 .19834 .19837 .19840 .19843 .19845 .19848 9.30108 .30114 .30121 .30127 9.30133 .30139 .30146 .30152 9.30486 .30492 .30498 .30505 .30177 .30180 .20183 .20186 9.30862 .30868 .30874 .30880 .30353 .20355 .20358 .20361 + 9' 37 38 39 9.29371 .29378 .29384 .29391 .19666 .19669 .19672 .19675 9.29753 .29760 .29766 .29772 .30014 .30017 .30020 .30033 9.30511 .30517 .30524 .30530 .20189 .20192 .20195 .20198 9.30887 .30893 .30899 .30905 .20364 .20367 .20370 .20373 24 23 22 21 + 10' 41 42 43 9.29397 .29403 .29410 .29416 .19677 .19680 .19683 .19686 9.29779 .29785 .29791 .29798 .19851 .19854 .19857 .19860 9.30158 .30165 .30171 .30177 .30036 .30038 .30031 .20034 9.30536 .30542 .30549 .30555 .20200 .20203 .20206 .20209 9.30912 .30918 .30924 .30930 .20376 .20379 .20382 .20385 20 19 18 17 + 11^ 45 46 47 9.29422 .29429 .29435 .29442 .19689 .19693 .19695 .19698 9.29804 .29810 .29817 .29823 9.29829 .29836 .29842 .29848 .19863 .19866 .19869 .19873 .19874 .19877 .19880 .19883 .19886 .19889 .19892 .19895 9.30184 .30190 .30196 .30203 9.30209 .30215 .30222 .30228 9.30234' .30240 .30247 .30253 .30037 .30040 .30043 .30046 9.30561 .30567 .30574 .30580 .20212 .20315 .30318 .20221 9.30937 .30943 .30949 .30955 .30388 .30391 .20393 .30396 16 15 14 IS 12 11 10 9 + 13' 49 50 51 9.29448 .29454 .29461 .29467 .19701 .19703 .19706 .19709 .30049 .30053 .30055 .30058 9.30586 .30593 .30599 .30605 .30334 .30337 .20330 .30333 .30335 .30338 .30341 .30244 9.30962 .30968 .30974 .30980 .20399 .20402 .20405 .20408 + 13' 53 54 55 9.29473 .29480 .29486 .29493 .19713 .19715 .19718 .19731 9.29855 .29861 .29867 .29874 .30060 .30063 .30066 .30069 9.30611 .30618 .30624 .30630 9.30987 .30993 .30999 .31005 .20411 .20414 .20417 .20420 8 7 6 5 + U' 57 58 59 9.29499 .29505 .29512 .29518 .19734 .19737 .19730 .19733 9.29880 .29886 .29893 .29899 .19898 .19901 .19903 .19906 9.30259 .30266 .30272 .30278 .30073 .30075 .20078 .30081 9.30636 .30643 .30649 .30655 .30347 .30350 .30353 .30356 9.31012 .31018 .31024 .31030 .20423 .20426 .20429 .20432 4 3 2 1 "+ 15' 9.29524 .19735 9.29906 .19909 9.30285 .30084 9.30662 .30359 9.31036 .20435 20^ 29"^ 20^28rn 20^ 27-m 20^ 26m 20Ti 25^ Page 864] TABLE 45. Haversines. s 5^ 35m 53° 45' S^ 36m 54° 0' Sh 37m 54° 15/ 3^ 38m 54° 30^ 3^ 39m 54° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.31036 .31043 .31049 .31055 .30435 .30437 .30440 .30443 .30446 .30449 .30453 .30455 9.31409 .31416 .31422 .31428 .30611 .30614 .30617 .30630 9.31780 .31786 .31793 .31799 .30788 .30790 .30793 .30796 9.32149 .32155 .32161 .32168 .30965 .30968 .30971 .30974 9.32516 .32522 .32528 .32534 .31143 .31146 .31149 .31153 60 59 58 57 + r 5 6 7 9.31061 .31068 .31074 .31080 9.31434 .31440 .31447 .31453 9.31459 .31465 .31471 .31478 .30633 .30636 .30639 .30631 .30634 .30637 .30640 .30643 9.31805 .31811 .31817 .31823 .30799 .30803 .30805 .30808 9.32174 .32180 .32186 .32192 .30977 .30980 .30983 .30986 .30989 .30991 .30994 .30997 9.32541 .32547 .32553 .32559 .31155 .31158 .31161 .31164 56 55 54 53 + 2' 9 10 11 9.31086 .31093 .31099 .31105 .30458 .30461 .30464 .30467 9.31830 .31836 .31842 .31848 .30811 .30814 .30817 .30830 9.32198 .32204 .32210 .32217 9.32565 .32571 .32577 .32583 .31167 .31169 .31173 .31175 52 51 50 49 + 3' IS 14 15 9.31111 .31117 .31124 .31130 .30470 .30473 .30476 .30479 9.31484 .31490 .31496 .31502 .30646 .30649 .30653 .30655 9.31854 .31860 .31867 .31873 .30833 .30836 .30839 .30833 9.32223 .32229 .32235 .32241 .31000 .31003 .31006 .31009 9.32589 .32595 .32601 .32608 .31178 .31181 .31184 .31187 48 47 46 45 + ^' 17 18 19 9.31136 .31142 .31149 .31155 .30481 .30484 .30487 .30490 9.31508 .31515 .31521 .31527 .30658 .30661 .30664 .30667 9.31879 .31885 .31891 .31897 .30835 .30838 .30841 .30844 9.32247 .32253 .32259 .32266 .31013 .31015 .31018 .31031 9.32614 .32620 .32626 .32632 9.32638 .32644 .32650 .32656 .31190 .31193 .31196 .31199 44 43 42 41 + 5' 21 22 23 9.31161 .31167 .31173 .31180 .30493 .30496 .30499 .30503 9.31533 .31539 .31546 .31552 .30670 .30673 .30675 .30678 9.31903 .31910 .31916 .31922 .30847 .30850 .30853 .30855 9.32272 .32278 .32284 .32290 .31034 .31037 .31030 .31033 .31036 .31039 .31043 .31045 .31303 .31305 .31308 .31311 40 39 38 37 + 6' 25 26 27 9.31186 .31192 .31198 .31205 .30505 .30508 .305^11 .30514 9.31558 .31564 .31570 .31577 .30681 .30684 .30687 .30690 9.31928 .31934 .31940 .31947 .30858 .30861 .30864 .30867 9.32296 .32302 .32308 .32315 9.32662 .32668 .32675 .32681 .31314 .31317 .31330 .31333 36 35 34 S3 + r 29 30 SI 9.31211 .31217 .31223 .31229 .30517 .30530 .30533 .30535 9.31583 .31589 .31595 .31601 .30693 .30696 .30699 .30703 9.31953 .31959 .31965 .31971 .30870 .30873 .30876 .30879 9.32321 .32327 .32333 .32339 .31048 .31051 .31054 .31057 9.32687 .32693 .32699 .32705 .31336 .31339 .31333 .31335 32 31 30 29 + 8' SS 34 35 9.31236 .31242 .31248 .31254 .30538 .30531 .30534 .30537 9.31607 .31614 .31620 .31626 .30705 .30708 .30711 .30714 9.31977 .31983 .31990 .31996 .30883 .30885 .30888 .30891 9.32345 .32351 .32357 .32363 .31060 .31063 .31066 .31069 9.32711 .32717 .32723 .32729 .31338 .31341 .31344 .31347 28 27 26 25 24 23 22 21 20 19 18 17 + 9' 37 S8 39 9.31260 .31267 .31273 .31279 .30540 .30543 .30546 .30549 9.31632 .31638 .31644 .31651 .30717 .30730 .30733 .30736 9.32002 .32008 .32014 .32020 .30894 .30897 .30900 .30903 9.32370 .32376 .32382 .32388 .31073 .31074 .31077 .31080 9.32735 .32741 .32748 .32754 .31350 .31353 .31356 .31359 + W 41 42 43 9.31285 .31291 .31298 .31304 .30553 .30555 .30558 .30561 9.31657 .31663 .31669 .31675 .30739 .30731 .30734 .30737 9.32026 .32033 .32039 .32045 .30906 .30909 .30913 .30915 9.32394 .32400 .32406 .32412 .31083 .31086 .31089 .31093 9.32760 .32766 .32772 .32778 .31363 .31365 .31368 .31371 + ir 45 46 47 9.31310 .31316 .31323 .31329 .30564 .30567 .30570 .30573 9.31682 .31688 .31694 .31700 .30740 .30743 .30746 .30749 9.32051 .32057 .32063 .32069 .30918 .30930 .30933 .30936 9.32418 .32425 .32431 .32437 .31095 .31098 .31101 .31104 9.32784 .32790 .32796 .32802 .31374 .31377 .31380 .31383 16 15 14 IS + 13' 49 50 51 9.31335 .31341 .31347 .31354 .30575 .30578 .30581 .30584 9.31706 .31712 .31719 .31725 .30753 .30755 .30758 .30761 9.32076 .32082 .32088 .32094 .30939 .30933 .30935 .30938 9.32443 .32449 .32455 .32461 .31107 .31110 .31113 .31116 9.32808 .32814 .32820 .32827 .31385 .31388 .31391 .31394 12 11 10 9 + 13' 5S 54 55 9.31360 .31366 .31372 .31378 .30587 .30590 .30593 .20596 9.31731 .31737 .31743 .31749 .30764 .30767 .30770 .30773 9.32100 .32106 .32112 .32119 .30941 .30944 .30947 .30950 .30953 .30956 .30959 .30963 9.32467 .32473 .32480 .32486 .31119 .31123 .31135 .31138 9.32833 .32839 .32845 .32851 .31397 .31300 .31303 .31306 8 7 6 5 4 S 2 1 + 14' 57 58 59 9.31385 .31391 .31397 .31403 .30599 .30603 .30605 .30608 9.31756 .31762 .31768 .31774 .30776 .30779 .30783 .30785 9.32125 .32131 .32137 .32143 9.32149 9.32492 .32498 .32504 .32510 .31131 .31134 .31137 .31140 .31143 9.32857 .32863 .32869 .32875 .31309 .31313 .31315 .31318 + 15' 9.31409 .20611 9.31780 .30788 .30965 9.32516 9.32881 .31331 20h 24'^ 20^ 23'm 20^ 22^ 20h 21m 20^ 20"^ TABLE 45. [Page 866 Haversines. s Sh 40m 65"» r Sh 41m 550 15/ Sh 42m 55° 30' 3h 4Sm 65° 45' S^ 44™ 56° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Ha v. Nat. Hav. 1 2 3 9.32881 .32887 .32893 .32899 .31331 .31334 .31337 .31330 9.33244 .33250 .33256 .33262 .31500 .31503 .31506 .31509 9.33605 .33611 .33617 .33623 .31680 .31683 .31686 .31689 9.33965 .33971 .33976 .33982 .31860 .31863 .31866 .31869 9.34322 .34328 .34334 .34340 .33040 .33043 .33046 .33049 60 59 58 57 + V 5 6 7 9.32905 .32911 .32918 .32924 .31333 .31336 .31339 .31343 9.33268 .33274 .33280 .33286 .31513 .31515 .31518 .31531 9.33629 .33635 .33641 .33647 .31693 .31695 .31698 .31701 9.33988 .33994 .34000 .34006 .31873 .31875 .31878 .31881 9.-34346 .34352 .34358 .34363 .33053 .33055 .33058 .33061 56 55 54 53 + ^' 9 10 11 9.32930 .32936 .32942 .32948 .31345 .31348 .31351 .31354 9.33292 .33298 .33305 .33311 .31534 .31537 .31530 .31533 9.33653 .33659 .33665 .33671 .31704 .31707 .31710 .31713 9.34012 .34018 .34024 .34030 .31884 .31887 .31890 .31893 9.34369 .34375 .34381 .34387 .33064 .33067 .33071 .33074 52 51 50 49 + 3' IS 14 15 9.32954 .32960 .32966 .32972 .31357 .31360 .31363 .31366 9.33317 .33323 .33329 .33335 .31536 .31539 .31543 .31545 9.33677 .33683 .33689 .33695 .31716 .31719 .31733 .31735 9.34036 .34042 .34048 .34054 .31896 .31899 .31903 .31905 9.34393 .34399 .34405 .3441 1 .33077 .33080 .33083 .33086 48 47 46 45 + *^ 17 18 19 9.32978 .32984 .32990 .32996 .31369 .31373 .31375 .31378 9.33341 .33347 .33353 .33359 .31548 .31551 .31554 .31557 9.33701 .33707 .33713 .33719 .31738 .31731 .31734 .31737 9.34060 .34066 .34072 .34078 .31908 .31911 .31914 .31917 9.34417 .34423 .34429 .34435 .33089 .33093 .33096 .33098 44 43 42 41 + 5^ 21 22 23 9.33002 .33008 .33014 .33021 .31381 .31384 .31387 .31390 .31393 .31396 .31399 .31403 9.33365 .33371 .33377 .33383 9.33389 .33395 .33401 .33407 .31560 .31563 .31566 .31569 9.33725 .33731 .33737 .33743 .31740 .31743 .31746 .31749 9.34084 .34090 .34096 .34102 .31930 .31933 .31936 .31939 9.34441 .34446 .34452 .34458 .33101 .22104 .33107 .33110 40 39 38 37 + 6' 25 26 27 9.33027 .33033 .33039 .33045 .31573 .31575 .31578 .31581 9.33749 .33755 .33761 .33767 .31753 .31756 .31768 .31761 9.34108 .34114 .34120 .34126 .31933 .31936 .31938 .31941 9.34464 .34470 .34476 .34482 .32113 .33116 .33119 .33133 36 35 34 33 + r 29 SO 31 9.33051 .33057 .33063 .33069 .31405 .31408 .31411 .31414 9.33413 .33419 .33425 .33431 .31584 .31687 .31590 .31593 9.33773 .33779 .33785 .33791 .31764 .31767 .31770 .31773 9.34132 .34137 .34143 .34149 .31944 .31947 .31960 .31963 9.34488 .34494 .34500 .34506 .32125 .22128 .22131 .33134 32 SI 30 29 + 8' 33 34 35 9.33075 .33081 .33087 .33093 .31417 .31430 .31433 .31436 9.33437 .33443 .33449 .33455 .31596 .31599 .31603 .31605 9.33797 .33803 .33809 .33815 .31776 .31779 .31783 .31786 9.34155 .34161 .34167 .34173 .31966 .31969 .31963 .31965 9.34512 .34518 .34524 .34529 .33137 .32140 .33143 .33146 28 27 26 25 + r 37 38 39 9.33099 .33105 .33111 .33117 .31439 .31431 .31434 .31437 9.33461 .33467 .33473 .33479 .31608 .31611 .31614 .31617 9.33821 .33827 .33833 .33839 .31788 .31791 .31794 .31797 9.34179 .34185 .34191 .34197 .31968 .31971 .31974 .31977 9.34535 .34541 .34547 .34553 .32149 .22152 .22155 .33158 24 23 22 21 20 19 18 17 + W 41 42 43 9.33123 .33129 .33135 .33142 .31440 .31443 .31446 .31449 9.33485 .33491 .33497 .33503 .31630 .31633 .31636 .31639 9.33845 .33851 .33857 .33863 .31800 .31803 .31806 .31809 .31813 .31815 .31818 .31831 9.34203 .34209 .34215 .34221 .31980 .31983 .31986 .31989 9.34559 .34565 .34571 .34577 .33161 .32164 .22167 .22170 + ir 45 46 47 9.33148 .33154 .33160 .33166 .31453 .31455 .31458 .31461 9.33509 .33515 .33521 .33527 .31633 .31635 .31638 .31641 9.33869 .33875 .33881 .33887 9.33893 .33899 .33905 .33911 9.34227 .34233 .34239 .34245 .31993 .31996 .31998 .33001 9.34583 .34589 .34595 .34600 .33173 .33176 .33179 .33183 16 15 14 13 12 11 10 9 + ir 49 50 51 9.33172 .33178 .33184 .33190 .31464 .31467 .31470 .31473 9.33533 .33539 .33545 .33551 .31644 .31647 .31650 .31653 .31834 .31837 .31830 .31833 9.34251 .34256 .34262 .34268 .33004 .33007 .33010 .33013 9.34606 .34612 .34618 .34624 9.34630 .34636 .34642 .34648 .33185 .33188 .32191 .33194 + 13' 53 54 55 9.33196 .33202 .33208 .33214 .31476 .31479 .31483 .31485 9.33557 .33563 .33569 .33575 .31656 .31659 .31663 .31665 9.33917 .33923 .33929 .33935 .31836 .31839 .31843 .31845 9.34274 .34280 .34286 .34292 .33016 .33019 .32033 .33035 .33197 .33300 .33303 .33306 8 7 6 5 + 14' 57 58 59 9.33220 .33226 .33232 .33238 .31488 .31491 .31494 .31497 9.33581 .33587 .33593 .33599 .31668 .31671 .31674 .31677 9.33941 .33947 .33953 .33959 .31848 .31851 .31854 .31857 9.34298 .34304 34310 .34316 .33038 .33031 .33034 .33037 9.34654 .34660 .34666 .34671 .33309 .33313 .33315 .33318 4 3 2 1 + 15' 9.33244 .31500 9.33605 .31680 9.33965 .31860 9.34322 .33040 9.34677 .33331 20'h 19m 20fi 18™ 20^ 17™ 20^ 16m 20^ 15™ Page 856] TABLE 45. Haversines. s ^A 45m 56° 15' 3h 46m 56° 30' JA 47m 56° 45' Sh 48m. 57° (K 3^ 49m 57° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat .Hav. 1 2 3 9.34677 .34683 .34689 .34695 .22221 .22225 .22228 .22231 9.35031 .35037 .35043 .35049 .22403 .22406 .22409 .22412 9.35383 .35389 .35394 .35400 .22585 .22588 .22591 .22594 9.35733 .35738 .35744 .35750 .22768 .22771 .22774 .22777 9.36081 .36086 .36092 .36098 .22951 .22954 .22957 .22960 60 59 58 57 + r 5 6 7 9.34701 .34707 .34713 .34719 .22234 .22237 .22240 .22243 9.35054 .35060 .35066 .35072 .22415 .22418 .22421 .22424 9.35406 .35412 .35418 .35424 .22598 .22601 .22604 .22607 9.35756 .35762 .35767 .35773 .22780 .22783 .22786 .22789 9.36104 .36110 .36115 .36121 .22964 .22967 .22970 .22973 56 55 54 53 + r 9 10 11 9.34725 .34730 .34736 .34742 .22246 .22249 .22252 .22255 9.35078 .35084 .35090 .35096 .22427 .22430 .22433 .22437 9.35429 .35435 .35441 .35447 .22610 .22613 .22616 .22619 9.35779 .35785 .35791 .35797 .22792 .22795 .22799 .22802 9.36127 .36133 .36139 .36144 .22976 .22979 .22982 .22985 52 51 50 49 + 3' 13 14 15 9.34748 .34754 .34760 .34766 .22268 .22261 .22264 .22267 9.35101 .35107 .35113 .35119 .22440 .22443 .22446 .22449 9.35453 .35459 .35464 .35470 .22622 .22625 .22628 .22631 9.35802 .35808 .35814 .35820 .22805 .22808 .22811 .22814 9.36150 .36156 .36162 .36167 .22988 .22991 .22994 .22997 48 47 46 45 + 4' 17 18 19 9.34772 .34778 .34784 .34789 .22270 .22273 .22276 .22279 9.35125 .35131 .35137 .35143 .22452 .22455 .22458 .22461 9.35476 .35482 .35488 .35494 .22634 .22637 .22640 .22643 9.35826 .35831 .35837 .35843 .22817 .22820 .22823 .22826 9.36173 .36179 .36185 .36191 .23000 .23003 .23006 .23009 44 43 42 41 + 5' 21 22 23 9.34795 .34801 .34807 .34813 .22282 .22285 .22288 .22291 9.35148 .35154 .35160 .35166 .22464 .22467 .22470 .22473 9.35500 .35505 .35511 .35517 .22646 .22649 .22652 .22655 9.35849 .35855 .35860 .35866 .22829 .22832 .22835 .22838 .22841 .22844 .22847 .22850 9.36196 .36202 .36208 .36214 .23012 .23016 .23019 .23022 40 39 38 37 + 6' 25 26 27 9.34819 .34825 .34831 .34837 .22294 .22297 .22300 .22303 9.35172 .35178 .35184 .35189 .22476 .22479 .22482 .22485 9.35523 .35529 .35535 .35540 .22658 .22661 .22664 .22667 9.35872 .35878 .35884 .35889 9.36219 .36225 .36231 .36237 .23025 .23028 .23031 .23034 36 So 34 33 + r 29 30 31 9.34843 .34848 .34854 .34860 .22306 .22309 .22312 .22315 9.35195 .35201 .35207 .35213 .22488 .22491 .22494 .22497 9.35546 .35552 .35558 .35564 .22671 .22674 .22677 .22680 9.35895 .35901 .35907 .35913 .22853 .22857 .22860 .22863 .22866 .22869 .22872 .22875 9.36243 .36248 .36254 .36260 .23037 .23040 .23043 .23046 32 31 30 29 + 8' S3 34 35 9.34866 .34872 .34878 .34884 .22318 .22321 .22324 .22327 9.35219 .35225 .35230 .35236 .22500 .22503 .22506 .22509 9.35570 .35575 .35581 .35587 .22683 .22686 .22689 .22692 9.35918 .35924 .35930 .35936 9.36266 .36271 .36277 .36283 .23049 .23052 .23055 .23058 .23061 .23065 .23068 .23071 28 27 26 25 24 23 22 21 + 9' 37 38 39 9.34890 .34896 .34901 .34907 .22330 .22333 .22336 .22340 9.35242 .35248 .35254 .35260 .22512 .22515 .22518 .22522 9.35593 .35599 .35604 .35610 .22695 .22698 .22701 .22704 9.35942 .35947 .35953 .35959 .22878 .22881 .22884 .22887 9.36289 .36294 .36300 .36306 + 10' 41 42 43 9.34913 .34919 .34925 .34931 .22343 .22346 .22349 .22352 9.35266 .35271 .35277 .35283 .22525 .22528 .22531 .22534 9.35616 .35622 .35628 .35634 .22707 .22710 .22713 .22716 .22719 .22722 .22725 .22728 9.35965 .35971 .35976 .35982 9.35988 .35994 .36000 .36005 .22890 .22893 .22896 .22899 9.36312 .36318 .36323 .36329 .23074 .23077 .23080 .23083 20 19 18 17 16 15 14 13 + ir 45 46 47 9.34937 .34943 .34949 .34954 .22355 .22358 .22361 .22364 9.35289 .35295 .35301 .35307 .22537 .22540 .22543 .22546 9.35639 .35645 .35651 .35657 .22902 .22905 .22908 .22912 9.36335 .36341 .36346 .36352 .23086 .23089 .23092 .23095 + 12' 49 50 51 9.34960 .34966 .34972 .34978 .22367 .22370 .22373 .22376 9.35312 .35318 .35324 .35330 .22549 .22552 .22555 .22558 9.35663 .35669 .35674 .35680 .22731 .22735 .22738 .22741 9.36011 .36017 .36023 .36029 .22915 .22918 .22921 .22924 9.36358 .36364 .36369 .36375 .23098 .23101 .23104 .23107 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.34984 .34990 .34996 .35002 .22379 .22382 .22385 .22388 9.35336 .35342 .35348 .35353 .22561 .22564 .22567 .22570 9.35686 .35692 .35698 .35703 9.35709 .35715 .35721 .35727 .22744 .22747 .22750 .22753 .22756 .22759 .22762 .22765 9.36034 .36040 .36046 .36052 .22927 .22930 .22933 .22936 9.36381 .36387 .36392 .36398 .23110 .23114 .23117 .23120 + 14' 57 58 59 9.35007 .35013 .35019 .35025 .22391 .22394 .22397 .22400 9.35359 .35365 .35371 .35377 .22573 .22576 .22579 .22582 9.36058 .36063 .36069 .36075 .22939 .22942 .22945 .22948 ^.22951 9.36404 .36410 .36415 .36421 .23123 .23126 .23129 .23132 4 3 2 1 + 15' 9.35031 .22403 9.35383 .22585 9.35733 .22768 9.36081 9.36427 .23135 ^oh 14m 1 20'h' ISin 20h i£m 20^ lim 20Ji lOm TABLE 45. [Page 857 Haversines. s Sf^5am57°W 1 sh5msi°w 1 3^52^5%°^ 1 S^ 53m 58° 15' 3^ 54^ 58° 30' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat Hav. 1 2 S 9.36427 .36433 .36439 .36444 .23135 .23138 .23141 .23144 9.36772 .36777 .36783 .36789 .23319 .23322 .23325 .23329 9.37114 .37120 .37126 .37131 .23504 .23507 .23510 .23513 9.37455 .37461 .37467 .37472 .23689 .23692 .23695 .23699 9.37794 .37800 .37806 .37811 .23875 .23878 .23881 .23884 60 59 58 57 + r 5 6 7 9.36450 .36456 .36462 .36467 .23147 .23150 .23153 .23156 .23160 .23163 .23166 .23169 9.36794 .36800 .36806 .36812 .23332 .23335 .23338 .23341 9.37137 .37143 .37148 .37154 9.37160 .37166 .37171 .37177 .23516 .23519 .23523 .23526 .23529 .23532 .23535 .23538 .23541 .23544 .23547 .23550 9.37478 .37484 .37489 .37495 9.37501 .37506 .37512 .37518 9.37523 .37529 .37535 .37540 9.37546 .37552 .37557 .37563 .23702 .23705 .23708 .23711 .23714 .23717 .23720 .23723 .23726 .23729 .23733 .23736 .23739 .23742 .23745 .23748 9.37817 .37823 .37828 .37834 9.37840 .37845 .37851 .37856 .23887 .23891 .23894 .23897 56 55 54 53 + r 9 10 11 9.36473 .36479 .36485 .36490 9.36817 .36823 .36829 .36834 .23344 .23347 .23350 .23353 .23900 .23903 .23906 .23909 52 51 50 49 + 3" 13 14 15 9.36496 .36502 .36508 .36513 .23172 .23175 .23178 .23181 9.36840 .36846 .36852 .36857 .23356 .23359 .23362 .23365 9.37183 .37188 .37194 .37200 9.37862 .37868 .37873 .37879 9.37885 .37890 .37896 .37902 .23912 .23915 .23918 .23922 .23925 .23928 .23931 .23934 48 47 46 45 U 43 42 41 + i' 17 18 19 9.36519 .36525 .36531 .36536 .23184 .23187 .23190 .23193 9.36863 .36869 .36875 .36880 .23368 .23372 .23375 .23378 9.37205 .37211 .37217 .37222 .23553 .23556 .23560 .23563 + 6^ 21 22 23 9.36542 .36548 .36554 .36559 .23196 .23199 .23203 .23206 9.36886 .36892 .36897 .36903 .23381 .23384 .23387 .23390 .23393 .23396 .23399 .23402 9.37228 .37234 .37239 .37245 .23566 .23569 .23572 .23575 9.37569 .37574 .37580 .37585 .23751 .23754 .23757 .23760 9.37907 .37913 .37918 .37924 .23937 .23940 .23943 .23946 .23950 .23953 .23956 .23959 40 39 38 37 36 35 34 33 32 31 30 29 + 6' 25 26 27 9.36565 .36571 .36577 .36582 .23209 .23212 .23215 .23218 9.36909 .36915 .36920 .36926 9.37251 .37257 .37262 .37268 .23578 .23581 .23584 .23587 9.37591 .37597 .37602 .37608 .23764 .23767 .23770 .23773 9.37930 .37935 .37941 .37947 + r 29 SO 31 9.36588 .36594 .36599 .36605 .23221 .23224 .23227 .23230 9.36932 .36937 .36943 .36949 .23405 .23409 .23412 .23415 9.37274 .37279 .37285 .37291 .23590 .23594 .23597 .23600 9.37614 .37619 .37625 .37631 9.37636 .37642 .37648 .37653 .23776 .23779 .23782 .23785 .23788" .23791 .23795 .23798 9.37952 .37958 .37963 .37969 .23962 .23965 .23968 .23971 + 8' S3 34 35 9.36611 .36617 .36622 .36628 .23233 .23236 .23239 .23242 9.36955 .36960 .36966 .36972 .23418 .23421 .23424 .23427 9.37296 .37302 .37308 .37313 .23603 .23606 .23609 .23612 9.37975 .37980 .37986 .37992 .23974 .23977 .23981 .23984 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 + 9' 37 38 39 9.36634 .36640 .36645 .36651 .23246 .23249 .23252 .23255 9.36977 .36983 .36989 .36995 .23430 .23433 .23436 .23439 9.37319 .37325 .37330 .37336 .23615 .23618 .23621 .23624 9.37659 .37665 .37670 .37676 .23801 .23804 .23807 .23810 9.37997 .38003 .38008 .38014 .23987 .23990 .23993 .23996 .23999 .24002 .24005 .24009 .24012 .24015 .24018 .24021 + 10' 41 42 43 9.36657 .36663 .366B8 .36674 .23258 .23261 .23264 .23267 9.37000 .37006 .37012 .37017 .23442 .23445 .23449 .23452 9.37342 .37347 .37353 .37359 .23627 .23631 .23634 .23637 9.37682 .37687 .37693 .37699 .23813 .23816 .23819 .23822 9.38020 .38025 .38031 .38037 9.38042 .38048 .38053 .38059 + 11^ 45 46 47 + ir 49 50 51 9.36680 .36686 .36691 .36697 .23270 .23273 .23276 .23279 9.37023 .37029 .37034 .37040 1 .23455 i .23458 ! .23461 1 .23464 9.37364 1 .23640 .37370! .23643 .37376 .23646 .37382 .23649 9.37704 .37710 .37715 .37721 .23825 .23829 .23832 .23835 9.36703 .36708 .36714 .36720 .23282 .23285 .23289 .23392 9.37046 .37052 .37057 .37063 .23467 .23470 .23473 .23476 9.37387 .37393 .37399 .37404 .23652 .23055 .23658 .23661 9.37727 .37732 .37738 .37744 .23838 .23841 .23844 .23847 9.38065 .38070 .38076 .38081 9.3808f .38093 .38098 .38104 .24024 .24027 .24030 .24033 .24036 .24040 .24043 .24046 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.36726 .36731 .36737 .36743 .23295 .23298 .23301 .23304 9.37069 .37074 .37080 .37086 i .23479 .23482 .23486 .23489 9.37410 .37416 .37421 .37427 .23665 .23668 .23671 .23674 9.37749 .37755 .37761 .37766 .23850 .23853 .23856 .23860 + 14' 57 58 59 9.36749 .36754 .36760 .36766 .23307 .23310 .23313 .23316 9.37091 .37097 .37103 .37109 1 .23492 .23495 1 .23498 ' .23501 9.37433 .37438 .37444 .37450 .23677 .23680 .23683 .23686 9.37772 .37778 .37783 .37789 .23863 .23866 .23869 .23872 9.38110 .38115 .38121 .38126 .24049 .24052 .24055 .24058 4 3 2 1 + 15' 9.36772 .23819 9.37114 .23504 9.37455 .23689 9.37794 .23875 9.38132 .24061 20^ 9m 20^ 8'm 1 20^ 7"» 20^ 6"» 1 20fi 5m Page 858] TABLE 45. Haversines. s 5ft 55m 58° 45' Sh 56m 59° 0' 5ft 57m 59° 15' 5ft 58^ 59° 30' 5ft 59m 59° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.38132 .38138 .38143 .38149 .34061 .34064 .34068 .34071 9.38468 .38473 .38479 .38485 .34348 .34351 .34354 .34357 9.38802 .38807 .38813 .38819 .34435 .34438 .34443 .34445 9.39134 .39140 .39145 .39151 .34633 .34636 .34639 .34633 9.39465 .39470 .39476 .39481 .34811 .34814 .34818 .34831 60 59 58 57 + r 5 6 7 9.38154 .38160 .38166 .38171 .34074 .34077 .34080 .34083 9.38490 .38496 .38501 .38507 .34361 .34364 .34367 .34370 9.38824 .38830 .38835 .38841 .34448 .34451 .34454 .34457 9.39156 .39162 .39167 .39173 .34636 .34639 .34643 .34645 9.39487 .39492 .39498 .39503 .34834 .34837 .34830 .34833 56 55 54 53 + 3' 9 10 11 9.38177 .38182 .38188 .38194 .34086 .34089 .34093 .34096 9.38512 .38518 .38524 .38529 .34373 .34376 .34379 .34383 9.38846 .38852 .38857 .38863 .34460 .34463 .34467 .34470 9.39178 .39184 .39189 .39195 .34648 .34651 .34654 .34658 9.39509 .39514 .39520 .39525 .34836 .34840 .34843 .34846 52 51 50 49 + 3' 13 14 15 9.38199 .38205 .38210 .38216 .34099 .34103 .34105 .34108 9.38535 .38540 .38546 .38551 .34386 .34389 .34393 .34395 9.38868 .38874 .38880 .38885 .34473 .34476 .34479 .34483 9.39201 .39206 .39212 .39217 .34661 .34664 .34667 .34670 9.39531 .39536 .39542 .39547 .34849 .34853 .34855 .34858 48 47 46 45 + 4' 17 18 19 9.38222 .38227 .38233 .38239 .34111 .34114 .34117 .34130 9.38557 .38563 .38568 .38574 .34398 .34301 .34304 .34307 9.38891 .38896 .38902 .38907 .34485 .34488 .34493 .34495 9.39223 .39228 .39234 .39239 .34673 .34676 .34680 .34683 9.39553 .39558 .39564 .39569 .34863 .34865 .34868 .34871 44 43 42 41 + 5' 22 23 9.38244 .38250 .38255 .38261 9.38267 .38272 .38278 .38283 .34134 .34137 .34130 .34133 9.38579 .38585 .38590 .38596 .34310 .34314 .34317 .34330 9.38913 .38918 .38924 .38929 .34498 .34501 .34504 .34507 9.39245 .39250 .39256 .39261 .34686 .34689 .34693 .34695 9.39575 .39580 .39586 .39591 .34874 .34877 .34880 .34884 40 39 38 37 36 35 34 33 + 6' 26 27 .34136 .34139 .34143 .34145 9.38602 .38607 .38613 .38618 .34333 .34336 .34339 .34333 9.38935 .38941 .38946 .38952 .34510 .34514 .34517 .34530 9.39267 .39272 .39278 .39283 .34698 .34701 .34705 .34708 9.39597 .39602 .39608 .39613 .34887 .34890 .34893 .34896 + 7' 30 31 9.38289 .38295 .38300 .38306 .34148 .34153 .34155 .34158 9.38624 .38629 .38635 .38641 .34335 .34339 .34343 .34345 9.38957 .38963 .38968 .38974 .34533 .34536 .34539 .34533 9.39289 .39294 .39300 .39305 .34711 .34714 .34717 .34730 9.39619 .39624 .39630 .39635 .34899 .34903 .34906 .34909 32 31 30 29 + 8' 34 35 9.38311 .38317 .38322 .38328 .34161 .34164 .34167 .34170 9.38646 .38652 .38657 .38663 .34348 .34351 .34354 .34357 9.38979 .38985 .38990 .38996 .34535 .34539 .34543 .34545 9.39311 .39316 .39322 .39327 .34733 .34737 .34730 .34733 9.39641 .39646 .39652 .39657 .34913 .34915 .34918 .34931 28 27 26 25 24 23 22 21 + 9' 38 39 9.38334 .38339 .38345 .38350 .34173 .34176 .34180 .34183 9.38668 .38674 .38680 .38685 .34360 .34364 .34367 .34370 9.39002 .39007 .39013 .39018 .34548 .34551 .34554 .34557 9.39333 .39338 .39344 .39349 .34736 .34739 .34743 .34745 9.39663 .39668 .39674 .39679 .34934 .34938 .34931 .34934 + 10^ 42 43 9.38356 .38362 .38367 .38373 .34186 .34189 .34193 .34195 9.38691 .38696 .38702 .38707 .34373 .34376 .34379 .34383 9.39024 .39029 .39035 .39040 .34560 .34564 .34567 .34570 9.39355 .39360 .39366 .39371 .34749 .34753 .34755 .34758 9.39685 .39690 .39695 .39701 .34937 .34940 .34943 .34946 20 19 18 17 16 15 14 13 + 11' 45 46 47 9.38378 .38384 .38390 .38395 .34198 .34301 .34304 .34308 9.38713 .38719 .38724 .38730 .34385 .34388 .34393 .34395 9.39046 .39051 .39057 .39062 .34573 .34576 .34579 .34583 9.39377 .39382 .39388 .39393 .34761 .34764 .34767 .34770 9.39706 .39712 .39717 .39723 .34950 .34953 .34956 .34959 + 13' 49 50 51 9.38401 .38406 .38412 .38418 .34311 .34314 .34317 .34330 9.38735 .38741 .38746 .38752 .34398 .34401 .34404 .34^07 9.39068 .39073 .39079 .39085 .34586 .34589 .34593 .34595 9.39399 .39404 .39410 .39415 .34774 .34777 .34780 .34783 9.39728 .39734 .39739 .39745 .34963 .34965 .34969 .34973 .34975 .34978 .34981 .34984 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.38423 .38429 .38434 .38440 .34333 .34336 .34339 .34333 9.38757 .38763 .38769 .38774 .34410 .34413 .34417 .34430 9.39090 .39096 .39101 .39107 .34598 .34601 .34604 .34607 9.39421 .39426 .39432 .39437 .34786 .34789 .34793 .34796 9.39750 .39756 .39761 .39767 + 14' 57 58 59 9.38445 .38451 .38457 .38462 .34336 .34339 .34343 .34345 9.38780 .38785 ..38791 .38796 .34433 .34436 .34439 .34433 9.39112 .39118 .39123 .39129 .34611 .34614 .34617 .34630 9.39443 .39448 .39454 .39459 .34799 .34803 .34805 .34808 9.39772 .39778 .39783 .39789 .34987 .34991 .34994 .34997 4 S 2 1 + 15' 9.38468 .34348 9.38802 .34435 9.39134 .34633 9.39465 .34811 9.39794 .35000 20h 4m 20h sm 20^2'^ f Oft i"* 20^ 0^ TABLE 45. [Page 859 Haversines. s 4h Qm 60° V 4^ im 60° 15' 4h 2m 60° 30^ 4n sm 60° 45' 4h 4^ 61° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log.Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.39794 .39799 .39805 .39810 .25000 .25003 .25006 .25009 9.40121 .40127 .40132 .40138 .25189 .25192 .25195 .25199 9.40447 .40453 .40458 .40463 .25379 .25382 .25385 .25388 9.40771 .40777 .40782 .40787 .25569 .25572 .25575 .25578 9.41094 .41099 .41105 .41110 .25760 .25763 .25766 .25769 60 59 58 57 + r 5 6 7 9.39816 .39821 .39827 .39832 .25013 .25016 .25019 .25022 9.40143 .40149 .40154 .40159 .25202 .25205 .25208 .25211 9.40469 .40474 .40480 .40485 .25391 .25395 .25398 .25401 9.40793 .40798 .40804 .40809 .25582 .25585 .25588 .25591 9.41115 .41121 .41126 .41131 .25772 .25775 .25779 .25782 56 55 54 53 + r 9 10 11 9.39838 .39843 .39849 .39854 .25025 .25028 .25032 .25035 9.40165 .40170 .40176 .40181 .25214 .25218 .25221 .25224 9.40490 .40496 .40501 .40507 .25404 .25407 .25410 .25414 9.40814 .40820 .40825 .40831 .25594 .25597 .25601 .25604 9.41137 .41142 .41147 .41153 .25785 .25788 .25791 .25795 52 51 50 49 + 3^ 13 14 15 9.39860 .39865 .39871 .39876 .25038 .25041 .25044 .25047 9.40187 .40192 .40198 .40203 .25227 .25230 .25233 .25237 9.40512 .40518 .40523 .40528 .25417 .25420 .25423 .25426 9.40836 .40841 .40847 .40852 .25607 .25610 .25613 .25617 9.41158 .41163 .41169 .41174 .25798 .25801 .25804 .25807 48 47 46 45 + i' 17 18 19 9.39881 .39887 .39892 .39898 .25050 .25054 .25057 .25060 9.40208 .40214 .40219 .40225 .25240 .25243 .25246 .25249 9.40534 .40539 .40545 .40550 .25429 .25433 .25436 .25439 9.40858 .40863 .40868 .40874 .25620 .25623 .25626 .25629 9.41180 .41185 .41190 .41196 .25810 .25814 .25817 .25820 U 43 42 41 + 5^ 21 22 23 9.39903 .39909 .39914 .39920 .25063 .25066 .25069 .25072 9.40230 .40236 .40241 .40246 .25252 .25255 .25259 .25262 9.40555 .40561 .40566 .40572 .25442 .25445 .25448 .25452 9.40879 .40884 .40890 .40895 .25632 .25636 .25639 .25642 9.41201 .41206 .41212 .41217 .25823 .25826 .25830 .25833 40 39 38 37 36 35 34 S3 32 31 SO 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 + r 25 26 27 9.39925 .39931 .39936 .39942 .25076 .25079 .25082 .25085 .25088 .25091 .25095 .25098 9.40252 .40257 .40263 .40268 .25265 .25268 .25271 .26274 9.40577 .40582 .40588 .40593 .25455 .25458 .25461 .25464 9.40900 .40906 .40911 40917 .25645 .25648 .25651 .25655 9.41222 .41228 .41233 .41238 .25836 .25839 .25842 .25845 .25849 .25852 .25855 .25858 + r 29 SO 31 9.39947 .39952 .39958 .39963 9.40274 .40279 .40284 .40290 .25278 .25281 .25284 .25287 9.40599 .40604 .40609 .40615 .25467 .25471 .25474 .25477 9.40922 .40927 .40933 .40938 .25658 .25661 .25664 .25667 9.41244 .41249 .41254 .41260 + 8' 33 34 35 9.39969 .39974 .39980 .39985 .25101 .25104 .25107 .25110 9.40295 .40301 .40306 .40312 .25290 .25293 .25297 .25300 9.40620 .40626 .40631 .40636 .25480 .25483 .25487 .25490 9.40943 .40949 .40954 .40960 .25671 .25674 .25677 .25680 9.41265 .41270 .41276 .41281 .25861 .25865 .25868 .25871 + 9" 37 38 39 9.39991 .39996 .40002 .40007 .25113 .25117 .25120 .25123 9.40317 .40322 .40328 .40333 .25303 .25306 .25309 .25312 9.40642 .40647 .40653 .40658 .25493 .25496 .25499 .25502 9.40965 .40970 .40976 .40981 .25683 .25686 .25690 .25693 9.41287 .41292 .41297 .41303 .25874 .25877 .25880 .25884 + w 41 42 43 9.40012 .40018 .40023 .40029 .25126 .25129 .25132 .25136 9.40339 .40344 .40350 .40355 .25316 .25319 .25322 .25325 9.40663 .40669 .40674 .40680 .25506 .25509 .25512 .25515 9.40986 .40992 .40997 .41003 .25696 .25699 .25702 .25705 9.41308 .41313 .41319 .41324 .25887 .25890 .25893 .25896 + 11' 45 46 47 9.40034 .40040 .40045 .40051 .25139 .25142 .25145 .25148 9.40360 .40366 .40371 .40377 .25328 .25331 .25335 .25338 9.40685 .40690 .40696 .40701 .25518 .25521 .25525 .25528 9.41008 .41013 .41019 .41024 .25709 .25712 .25715 .25718 9.41329 .41335 .41340 .41345 .25900 .25903 .25906 .25909 ~+ 12' 49 50 51 9.40056 .40062 .40067 .40072 .25151 .25154 .25158 .25161 9.40382 .40388 .40393 .40398 .25341 .25344 .25347 .25350 9.40707 .40712 .40717 .40723 .25531 .25534 .25537 .25540 9.41029 .41035 .41040 .41046 .25721 .25724 .25728 .25731 9.41351 .41356 .41361 .41367 .25912 .25915 .25919 .25922 12 11 10 9 + m 53 54 55 9.40078 .40083 .40089 .40094 .25164 .25167 .25170 .25173 9.40404 .40409 .40415 .40420 .25354 .25357 .25360 .25363 9.40728 .40734 .40739 .40744 .25544 .25547 .25550 .25553 9.41051 .41056 .41062 .41067 .25734 .25737 .25740 .25744 9.41372 .41377 .41383 .41388 .25925 .25928 .25931 .25935 8 7 6 5 + U' 57 58 59 9.40100 .40105 .40111 .40116 .25177 .25180 .25183 .25186 9.40425 .4043] .40436 .40442 .25366 .25369 .25372 .25376 9.40750 .40755 .40761 .40766 .25556 .25559 .25563 .25566 9.41072 .41078 .41083 .41088 .25747 .25750 .25753 .25756 9.41393 .41399 .41404 .41409 .25938 .25941 .25944 .25947 4 S 2 1 + W 9.40121 .25189 9.40447 .25379 9.40771 .25569 9.41094 .25760 9.41415 .25951 19^ 59m 19^ 58m 19h 57m 19^ 56^ 19h 55m 21594°— 14 47 Page 860] TABLE 45. Haversines. s 4h 5m 61° 15' 4^ em 61° 30' 4^ 7m 61° 45' 4h 8m 62° 0' 4h 9m 62° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.41415 .41420 .41425 .41431 .35951 .25954 .25957 .25960 9.41734 .41739 .41745 .41750 .26142 .26145 .26148 .26152 9.42052 .42057 .42062 .42068 .26334 .26337 .26340 .36344 9.42368 .42373 .42378 .42384 .26526 .26530 .26533 .26536 9.42682 .42688 .42693 .42698 .26719 .26722 .36726 .26729 60 59 58 57 + r 5 6 7 9.41436 .41441 .41447 .41452 .25963 .25966 .25970 .25973 9.41755 .41761 .41766 .41771 .26155 .26158 .26161 .26164 9.42073 .42078 .42083 .42089 .36347 .36350 .26353 .36356 9.42389 .42394 .42399 .42405 .26539 .26543 .26546 .26549 9.42703 .42709 .42714 .42719 .26732 .26735 .26739 .26742 56 55 54 53 + 2^ > 9 10 11 9.41457 .41463 .41468 .41473 .25976 .25979 .25982 .25986 9.41776 .41782 .41787 .41792 .26168 .26171 .26174 .26177 9.42094 .42099 .42105 .42110 .36360 .36363 .26366 .36369 9.42410 .42415 .42420 .42426 .26552 .26555 .26559 .26562 9.42724 .42730 .42735 .42740 .26745 .26748 .26751 .26755 52 51 50 49 + 3' 13 14 15 9.41479 .41484 .41489 .41495 .25989 .25992 .25995 .25998 9.41798 .41803 .41808 .41814 .26180 .26184 .26187 .36190 9.42115 .42120 .42126 .42131 .36373 .36376 .26379 .26382 9.42431 .42436 .42441 .42447 .26565 .26568 .36571 .26575 9.42745 .42750 .42756 .42761 .26758 .26761 .26764 .26768 48 47 46 45 + 4' 17 18 19 9.41500 .41505 .41511 .41516 .26002 .26005 .26008 .26011 9.41819 .41824 .41829 .41835 .26193 .36196 .26200 .26203 9.42136 .42141 .42147 .42152 .26385 .26389 .36392 .26395 9.42452 .42457 .42462 .42468 .36578 .36581 .26584 .26587 9.42766 .42771 .42777 .42782 .26771 .26774 .36777 .26780 44 43 42 41 + 5' 21 22 23 9.41521 .41527 .41532 .41537 .26014 .26017 .26021 .26021 9.41840 .41845 .41851 .41856 .26206 .26209 .36313 .36316 9.42157 .42163 .42168 .42173 .26398 .26402 .26405 .36408 9.42473 .42478 .42483 .42489 .26591 .26594 .26597 .26600 9.42787 .42792 .42797 .42803 .26784 .26787 .26790 .26793 40 39 38 37 + 6' 25 26 27 9.41543 .41548 .41553 .41559 .26027 .26030 .26033 .26037 9.41861 .41867 .41872 .41877 .26219 .36333 .26225 .36338 9.42178 .42184 .42189 .42194 .26411 .26414 .36417 .26421 9.42494 .42499 .42504 .42510 .26604 .26607 .26610 .26613 9.42808 .42813 .42818 .42824 .26797 .26800 .26803 .26806 36 35 34 S3 + r 29 SO 31 9.41564 .41569 .41575 .41580 .26040 .26043 .26046 .26049 9.41882 .41888 .41893 .41898 .26232 .36335 .26238 .26241 9.42199 .42205 .42210 .42215 .26424 .26427 .26430 .26433 9.42515 .42520 .42525 .42531 .26616 .26620 .26623 .36626 9.42829 .42834 .42839 .42844 .26809 .26813 .26816 .26819 32 31 SO 29 + S' 33 34 35 9.41585 .41590 .41596 .41601 .26053 .26056 .26059 .26062 9.41904 .41909 .41914 .41920 .26244 .26248 .26251 .26254 9.42221 .42226 .42231 .42236 .26437 .26440 .26443 .26446 9.42536 .42541 .42546 .42552 .26629 .26632 .26636 .26639 9.42850 .42855 .42860 .42865 .26832 .26826 .26829 .26832 28 27 26 25 + V 37 38 39 9.41606 .41612 .41617 .41622 .26065 .26069 .36072 .26075 9.41925 .41930 .41935 .41941 .26257 .26260 .36264 .26267 9.42242 .42247 .42252 .42257 .26449 26453 .26456 .26459 9.42557 .42562 .42567 .42573 .26642 .26645 .26649 .26652 9.42870 .42876 .42881 .42886 .26835 .26838 .26842 .26845 24 23 22 21 + W 41 42 43 9.41628 .41633 41638 .41644 .26078 .26081 .26085 .26088 9.41946 .41951 .41957 .41962 .26270 .36373 .36376 .26280 9.42263 .42268 .42273 .42278 .26462 .26465 .26469 .26473 9.42578 .42583 .42588 .42593 .26655 .26658 .26661 .26665 9.42891 .42897 .42902 .42907 .26848 .26851 .26855 .26858 20 19 18 17 + 11' 45 46 47 9.41649 .41654 .41660 .41665 .26091 .26094 .26097 .26101 9.41967 .41972 .41978 .41983 .26283 .26286 .36389 .26292 9.42284 .42289 .42294 .42300 .26475 .26478 .26481 .26485 9.42599 .42604 .42609 .42614 .26668 .26671 .26674 .26677 9.42912 .42917 .42923 .42928 .26861 .26864 .26867 .26871 16 15 14 13 49 50 51 9.41670 .41676 .41681 .41686 .26104 .26107 .26110 .26113 9.41988 .41994 .41999 .42004 .36296 .26299 .36302 .26305 9.42305 .42310 .42315 .42321 .26488 .36491 .36494 .26498 9.42620 .42625 .42630 .42635 .26681 .26684 .26687 .26690 9.42933 .42938 .42943 .42949 .26874 .26877 .26880 .26883 12 11 10 9 + 13' 53 54 55 9.41692 .41697 .41702 .41707 .26117 .26120 .26123 .26126 9.42009 .42015 .42020 .42025 .26308 .26312 .26315 .26318 9.42326 .42331 .42336 .42342 .26501 .26504 .26507 .26510 9.42641 .42646 .42651 .42656 .26694 .26697 .26700 .26703 9.42954 .42959 .42964 .42969 .26887 .26890 .26893 .26896 8 7 6 5 + ir 57 58 59 9.41713 .41718 .41723 .41729 .26129 .26133 .36136 .26139 9.42031 .42036 .42041 .42046 .26321 .26324 .26328 .26331 9.42347 .42352 .42357 .42363 .26514 .26517 .26520 .26523 9.42662 .42667 .42672 .42677 .26706 .26710 .26713 .26716 9.42975 .42980 .42985 .42990 .26900 .36903 .36906 .36909 4 3 2 1 + W 9.41734 .26142 9.42052 .26334 9.42368 .26536 9.42682 .26719 9.42996 .36913 19Ji 54™' 19h 53m 19^ 52m i9ft 5lm 19^ 50m 1 TABLE 45. [Page 861 Haversines. s 4hl0m&i°W 4h 11m 62° 45' 4^ 12^ 63° 0' 4^ 13m 63° 15' 4h 14"^ 63° W s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.42996 .43001 .43006 .43011 .26913 .26916 .26919 .26922 9.43307 .43312 .43317 .43323 .27106 .27110 .27113 .27116 9.43617 .43622 .43627 .43632 .27300 .27304 .27307 .27310 9.43926 .43931 .43936 .43941 .27495 .27498 .27502 .27505 9.44232 .44238 .44243 .44248 .27690 .27693 .27697 .27700 60 59 58 57 56 55 54 53 52 51 50 49 + r 5 6 7 9.43016 .43022 .43027 .43032 .26925 .26929 .26932 .26935 9.43328 .43333 .43338 .43343 .27119 .27122 .27126 .27129 9.43638 .43643 .43648 .43653 .27313 .27317 .27320 .27323 9.43946 .43951 .43956 .43961 .27508 .27511 .27515 .27518 9.44253 .44258 .44263 .44268 .27703 .27706 .27710 .27713 + 2^ 9 10 11 9.43037 .43042 .43048 .43053 .26938 .26942 .26945 .26948 9.43348 .43354 .43359 .43364 .27132 .27135 .27139 .27142 9.43658 .43663 .43669 .43674 .27326 .27330 .27333 .27336 9.43967 .43972 .43977 .43982 .27521 .27524 .27528 .27531 9.44273 .44278 .44283 .44289 .27716 .27719 .27723 .27726 + 3^ 13 14 15 9.43058 .43063 .43068 .43074 .26951 .26955 .26958 .26961 9.43369 .43374 .43380 .43385 .27145 .27148 .27152 .27155 9.43679 .43684 .43689 .43694 .27339 .27343 .27346 .27349 9.43987 .43992 .43997 .44002 .27534 .27537 .27541 .27544 9.44294 .44299 .44304 .44309 .27729 .27732 .27736 .27739 48 47 46 45 17 18 19 9.43079 .43084 .43089 .43094 .26964 .26967 .26971 .26974 9.43390 .43395 .43400 .43405 .27158 .27161 .27165 .27168 9.43699 .43705 .43710 .43715 .27352 .27356 .27359 .27362 9.44008 .44013 .44018 .44023 .27547 .27550 .27554 .27557 9.44314 .44319 .44324 .44329 .27742 .27745 .27749 .27752 44 43 42 41 + 5' 21 22 23 9.43100 .43105 .43110 .43115 .26977 .26980 .26984 .26987 9.43411 .43416 .43421 .43426 .27171 .27174 .27177 .27181 9.43720 .43725 .43730 .43735 .27365 .27369 .27372 .27375 9.44028 .44033 .44038 .44043 .27560 .27563 .27567 .27570 9.44334 .44340 .44345 .44350 .27755 .27758 .27762 .27765 40 39 38 S7 36 35 34 S3 + 6' 25 26 27 9.43120 .43126 .43131 .43136 .26990 .26993 .26996 .27000 9.43431 .43436 .43442 .43447 .27184 .27187 .27190 .27194 9.43741 .43746 .43751 .43756 .27378 .27382 .27385 .27388 9.44048 .44054 .44059 .44064 .27573 .27576 .27580 .27683 9.44355 .44360 .44365 .44370 .27768 .27772 .27775 .27778 + r 29 SO 31 9.43141 .43146 .43151 43157 .27003 .27006 .27009 .27013 9.43452 .43457 .43462 .43467 .27197 .27200 .27203 .27207 9.43761 .43766 .43771 .43777 .27391 .27394 .27398 .27401 9.44069 .44074 .44079 .44084 .27586 .27589 .27593 .27596 9.44375 .44380 .44385 .44390 .27781 .27785 .27788 .27791 S2 SI 30 29 + 8' S3 34 S5 9.43162 .43167 .43172 .43177 .27016 .27019 .27022 .27025 9.43473 .43478 .43483 .43488 .27210 .27213 .27216 .27220 9.43782 .43787 .43792 .43797 .27404 .27407 .27411 .27414 9.44089 .44095 .44100 .44105 .27599 .27602 .27606 .27609 9.44396 .44401 .44406 .44411 .27794 .27798 .27801 .27804 28 27 26 25 + 9^ 37 38 39 9.43183 .43188 .43193' .43198 .27029 .27032 .27035 .27038 9.43493 .43498 .43504 .43509 .27223 .27226 .27229 .27232 9.43802 .43807 .43813 .43818 .27417 .27420 .27424 .27427 9.44110 .44115 .44120 .44125 .27612 .27615 .27619 .27622 9.44416 .44421 .44426 .44431 .27807 .27811 .27814 .27817 24 23 22 21 + W 41 42 43 9.43203 .43209 .43214 .43219 .27042 .27045 .27048 .27051 9.43514 .43519 .43524 .43529 .27236 .27239 .27242 .27245 9.43823 .43828 .43833 .43838 .27430 .27433 .27437 .27440 9.44130 .44135 .44141 .44146 .27625 .27628 .27632 .27635 9.44436 .44441 .44446 .44452 .27820 .27824 .27827 .27830 20 19 18 17 + n' 45 46 47 9.43224 .43229 .43234 .43240 .27055 .27058 .27061 .27064 9.43535 .43540 .43545 .43550 .27249 .27252 .27255 .27258 9.43843 .43849 .43854 .43859 .27443 .27446 .27450 .27453 9.44151 .44156 .44161 .44166 .27638 .27641 .27645 .27648 9.44457 .44462 .44467 .44472 .27833 .27837 .27840 .27843 16 15 14 IS + ir 49 50 51 9.43245 .43250 .43255 .43260 .27068 .27071 .27074 .27077 9.43555 .43560 .43565 .43571 .27262 .27265 .27268 .27271 9.43864 .43869 .43874 .43879 .27456 .27459 .27463 .27466 9.44171 44176 .44181 .44187 .27651 .27654 .27658 .27661 9.44477 .44482 .44487 .44492 .27846 .27850 .27853 .27856 12 11 10 9 + W 53 54 55 9.43266 .43271 .43276 .43281 .27080 .27084 .27087 .27090 9.43576 .43581 .43586 .43591 .27275 .27278 .27281 .27284 9.43884 .43890 .43895 .43900 .27469 .27472 .27476 .27479 9.44192 .44197 .44202 .44207 .27664 .27667 .27671 .27674 9.44497 .44502 .44507 .44513 .27859 .27863 .27866 .27869 8 7 6 6 4 S 2 1 + W 57 58 59 9.43286 .43291 .43297 .43302 .27093 .27097 .27100 .27103 9.43596 .43602 .43607 .43612 .27288 .27291 .27294 .27297 9.43905 .43910 .43915 .43920 .27482 .27485 .27489 .27492 9.44212 .44217 .44222 .44227 .27677 .27680 .27684 .27687 9.44518 .44523 .44528 .44533 .27873 .27876 .27879 .27882 + W 9.43307 .27106 9.43617 .27300 9.43926 .27495 9.44232 .27690 9.44538 .27886 19^ 49m 19h48m, ign 47m 19^46^ 19h45m Page 862] TABLE 45. Haversinea. s 4h 15m 63° 45' 4h 16m 64° 0' 4h 17m 64° 15' 4h 18m 64° 3^ 4h 19m 64° 45' 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.44538 .44543 .44548 .44553 .27886 .27889 .27892 .27895 9.44842 .44847 .44852 .44857 .28081 .38085 .28088 .28091 9.45144 .45149 .45155 .45160 .28278 .28281 .28284 .28288 9.45446 .45451 .45456 .45461 .28474 .28478 .28481 .28484 9.45745 .45750 .45755 .45760 .28672 .28675 .28678 .28681 60 59 58 57 + y 5 6 7 9.44558 .44563 .44568 .44573 .27899 .27902 .27905 .27908 9.44862 .44867 .44872 .44877 .28095 .28098 .28101 .28104 9.45165 .45170 .45175 .45180 .28291 .38394 .38397 .38301 9.45466 .45471 .45476 .45481 .38488 .38491 .38494 .38497 9.45765 .45770 .45775 .45780 .28685 .38688 .38691 .28695 56 55 54 53 + V 9 10 11 9.44579 .44584 .44589 .44594 .27912 .27915 .27918 .27921 9.44882 .44887 .44892 .44898 .28108 .28111 .28114 .28117 9.45185 .45190 .45195 .45200 .38304 .38307 .38310 .38314 9.45486 .45491 .45496 .45501 .38501 .38504 .38507 .38511 9.45785 .45790 .45795 .45800 .28698 .28701 .28704 .28708 52 51 50 49 + 3' 13 14 15 9.44599 .44604 .44609 .44614 .27925 .27928 .27931 .27935 9.44903 .44908 .44913 .44918 .28121 .28124 .28127 .28130 9.45205 .45210 .45215 .45220 .28317 .28320 .28324 .28337 9.45506 .45511 .45516 .45521 .38514 .38517 .38530 .28524 9.45805 .45810 .45815 .45820 .28711 .28714 .28718 .28721 48 47 46 45 + *' 17 18 19 9.44619 .44624 .44629 .44634 .27938 .27941 .27944 .27948 9.44923 .44928 .44933 .44938 .28134 .28137 .28140 .28144 9.45225 .45230 .45235 .45240 .28330 .28333 .28337 .28340 9.45526 .45531 .45536 .45541 .28527 .28530 .28534 .28537 9.45825 .45830 .45835 .45840 .28724 .28727 .28731 .38734 44 43 42 41 + 5' 21 22 23 9.44639 .44645 .44650 .44655 .27951 .27954 .27957 .27961 9.44943 .44948 .44953 .44958 .28147 .28150 .28153 .28157 9.45245 .45250 .45255 .45260 .28343 .28347 .28350 .28353 9.45546 .45551 .45556 .45561 .28540 .28543 .28547 .38550 9.45845 .45850 .45855 .45860 .38737 .38741 .28744 .28747 40 39 38 37 + 6' 25 26 27 9.44660 .44665 .44670 .44675 .27964 .27967 .27970 .37974 9.44963 .44968 .44973 .44978 .38160 .38163 .38166 .38170 9.45265 .45270 .45275 .45280 .28356 .28360 .28363 .28366 9.45566 .45571 .45576 .45581 .38553 .38557 .38560 .28563 9.45865 .45870 .45875 .45879 .28751 .28754 .28757 .28760 36 35 34 33 + r 29 30 31 9.44680 .44685 .44690 .44695 .27977 .27980 .27983 .27987 9.44983 .44988 .44993 .44998 .38173 .38176 .28180 .28183 9.45285 .45290 .45295 .45300 .28369 .28373 .28376 .28379 9.45586 .45591 .45596 .45601 .28566 .28570 .28573 .38576 9.45884 .45889 .45894 .45899 .28764 .28767 .28770 .28774 32 31 30 29 28 27 26 25 + 8' 33 34 35 9.44700 .44705 .44710 .44715 .27990 .27993 .37997 .28000 9.45003 .45009 .45014 .45019 .28186 .28189 .28193 .28196 9.45305 .45310 .45315 .45320 .28383 .28386 .28389 .28392 9.45606 .45610 .45615 .45620 .38580 .38583 .38586 .28589 9.45904 .45909 .45914 .45919 .38777 .38780 .28783 .28787 + 9^ 37 38 39 9.44721 .44726 .44731 .44736 .28003 .28006 .28010 .28013 9.45024 .45029 .45034 .45039 .28199 .28202 .28206 .28309 9.45325 .45330 .45335 .45340 .28396 .38399 .28402 .28406 9.45625 .45630 .45635 .45640 .28593 .28596 .28599 .28603 9.45924 .45929 .45934 .45939 .28790 .28793 .28797 .38800 24 23 22 21 41 42 43 9.44741 .44746 .44751 .44756 .28016 .28019 .28023 .28026 9.45044 .45049 .45054 .45059 .28213 .38316 .38319 .38223 9.45345 .45350 .45355 .45360 .28409 .28412 .28415 .28419 9.45645 .45650 .45655 .45660 .28606 .28609 .28612 .28616 9.45944 .45949 .45954 .45959 .38803 .38807 .38810 .38813 20 19 18 17 + 11^ 45 46 47 9.44761 .44766 .44771 .44776 .28039 .38033 .38036 .38039 9.45064 .45069 .45074 .45079 .28235 .38239 .28232 .28235 9.45365 .45370 .45375 .45380 .28423 .38435 .38439 .28432 9.45665 .45670 .45675 .45680 .28619 .28633 .38626 .38639 9.45964 .45969 .45974 .45979 .28816 .28820 .38833 .38836 16 15 14 13 + n' 49 50 51 9.44781 .44786 .44791 .44796 .28042 .28046 .28049 .28052 9.45084 .45089 .45094 .45099 .38338 .38342 .28245 .28248 9.45385 .45390 .45395 .45400 .28435 .28438 .38442 .28445 9.45685 .45690 .45695 .45700 .38633 .28635 .28639 .28642 9.45984 .45989 .45994 .45999 .38830 .28833 .28836 .28839 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.44801 .44807 .44812 .44817 .28055 .28059 .28062 .38065 9.45104 .45109 .45114 .45119 .28253 .28255 .28358 .38361 9.45405 .45410 .45415 .45420 .28448 .28451 .28455 .38458 9.45705 .45710 .45715 .45720 .38645 .38649 .28652 .28655 9.46004 .46009 .46014 .46019 .28843 .28846 .28849 .28853 + 1¥ 57 58 59 9.44822 .44827 .44832 .44837 .38068 .28072 .28075 .28078 9.45124 .45129 .45134 .45139 .38265 .28268 .28271 .28274 9.45426 .45431 .45436 .45441 .28461 .28465 .28468 .28471 9.45725 .45730 .45735 .45740 .28658 .28663 .28665 .28668 9.46023 .46028 .46033 .46038 .28856 .28859 .38863 .38866 4 3 2 "1 + 15' 9.44842 .28081 9.45144 .28278 9.45446 .28474 9.45745 .38672 9.46043 .28869 I9I1 44m IQJi 43m 19h 42m 19n 41m 19h4&m 1 TABLE 45. [Page 863 Haversines. s 41^ 2(y>n 65° (K 4h 21m 65° 15^ 4h 22m 65° W 41^ 23m 65° 45' 4^ 24^ 66° C s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.46043 .46048 .46053 .46058 .28869 .28872 .38876 .28879 9.46340 .46345 .46350 .46355 .29067 .29070 .29074 .29077 9.46635 .46640 .46645 .46650 .29265 .29269 .29272 .29275 9.46929 .46934 .46939 .46944 .29464 .29467 .29471 .29474 9.47222 .47227 .47231 .47236 .29663 .29666 .29670 .29673 60 59 58 57 + r 5 6 7 9.46063 .46068 .46073 .46078 .28882 .28886 .28889 .28892 9.46360 .46365 .46370 .46375 .29080 .29084 .29087 .29090 9.46655 .46660 .46665 .46670 .29279 .29282 .29285 .29289 .29292 .29295 .29298 .29302 9.46949 .46954 .46959 .46963 9.46968 .46973 .46978 .46983 .29477 .29481 .29484 .29487 9.47241 .47246 .47251 .47256 .29676 .29680 .29683 .29686 .29690 .29693 .29696 .29700 56 55 64 53 52 51 50 49 48 47 46 45 U 43 42 41 40 39 38 37 36 35 34 33 32 31 SO 29 28 27 26 25 24 23 22 21 + 3' 9 10 11 9.46083 .46088 .46093 .46098 .28895 .28899 .28902 .28905 9.46380 .46384 .46389 .46394 .29093 .29097 .29100 .29103 9.46675 .46680 .46684 .46689 .29491 .29494 .29497 .29501 9.47261 .47266 .47270 .47275 + 3^ IS 14 15 9.46103 .46108 .46113 .46118 .28909 .28912 .28915 .28918 9.46399 .46404 .46409 .46414 .29107 .29110 .29113 .29117 9.46694 .46699 .46704 .46709 .29305 .29308 .29312 .29315 9.46988 .46993 .46998 .47003 .29504 .29507 .29510 .29514 9.47280 .47285 .47290 .47295 .29703 .29706 .29710 .29713 + i' 17 18 19 9.46123 .46128 .46132 .46137 .28922 .28925 .28928 .28932 9.46419 .46424 .46429 .46434 .29120 .29123 .29126 .29130 9.46714 .46719 .46724 .46729 .29318 .29322 .29325 .29328 9.47007 .47012 .47017 .47022 .29517 .29520 .29524 .29527 9.47300 .47304 .47309 .47314 .29716 .29720 .29723 .29726 + 5' 21 22 23 9.46142 .46147 .46152 .46157 .28935 .28938 .28942 .28945 9.46439 .46444 .46448 .46453 .29133 .29136 .29140 .29143 9.46733 .46738 .46743 .46748 .29332 .29335 .29338 .29341 9.47027 .47032 .47037 .47042 .29530 .29534 .29537 .29540 9.47319 .47324 .47329 .47334 .29730 .29733 .29736 .2974* .29743 .29746 .29750 .29753 + 6^ 25 26 27 9.46162 .46167 .46172 .46177 .28948 .28952 .28955 .28958 9.46458 .46463 .46468 .46473 9.46478 .46483 .46488 .46493 9.46498 .46503 .46508 .46512 .29146 .29150 .29153 .29156 9.46753 .46758 .46763 .46768 .29345 .29348 .29351 .29355 9.47046 .47051 .47056 .47061 .29544 .29547 .29550 .29554 9.47338 .47343 .47345 .47353 + r 29 SO 31 9.46182 .46187 .46192 .46197 .28961 .28965 .28968 .28971 .29160 .29163 .29166 .29169 .29173 .29176 .29179 .29183 9.46773 .46778 .46782 .46787 9.46792 .46797 .46802 .46807 .29358 .29361 .29365 .29368 .29371 .29375 .29378 .29381 9.47066 .47071 .47076 .47081 .29557 .29560 .29564 .29567 9.47358 .47363 .47367 .47372 .29756 .29760 .29763 .29766 + 8' 33 34 35 9.46202 .46207 .46212 .46217 .28975 .28978 .28981 .28985 9.47085 .47090 .47095 .47100 .29570 .29573 .29577 .29580 9.47377 .47382 .47387 .47392 .29770 .29773 .29776 .29779 + 9^ 37 38 39 9.46222 .46226 .46231 .46236 .28988 .28991 .28994 .28998 9.46517 .46522 .46527 .46532 .29186 .29189 .29193 .29196 9.46812 .46817 .46822 .46827 .29385 .29388 .29391 .29394 9.47105 .47110 .47115 .47120 .29583 .29587 .29590 .29593 9.47397 .47401 .47406 .47411 .29783 .29786 .29789 .29793 + W 41 42 43 9.46241 .46246 .46251 .46256 .29001 .29004 .29008 .29011 9.46537 .46542 .46547 .46552 .29199 .29202 .29206 .29209 9.46831 .46836 .46841 .46846 .29398 .29401 .29404 .29408 9.47124 .47129 .47134 .47139 .29597 .29600 .29603 .29607 9.47416 .47421 .47426 .47431 .29796 .29799 .29803 .29806 .29809 .29813 .29816 .29819 20 19 18 17 16 15 14 13 + ir 45 46 47 9.46261 .46266 .46271 .46276 .29014 .29017 .29021 .29024 9.46557 .46562 .46567 .46571 .29212 .29216 .29219 .29222 9.46851 .46856 .46861 .46866 .29411 .29414 .29418 .29421 9.47144 .47149 .47154 .47159 .29610 .29613 .29617 .29620 9.47435 .47440 .47445 .47450 + n' 49 50 51 9.46281 .46286 .46291 .46296 .29027 .29031 .29034 .29037 9.46576 .46581 .46586 .46591 .29226 .29229 .29232 .29236 9.46871 .46875 .46880 .46885 .29424 .29428 .29431 .29434 9.47163 .47168 .47173 .47178 .29623 .29627 .29630 .29633 9.47455 .47460 .47464 .47469 .29823 .29826 .29829 .29833 12 11 10 9 8 7 6 5 + 13^ 53 54 55 9.46301 .46305 .46310 .46315 .29041 .29044 .29047 .29051 9.46596 .46601 .46606 .46611 .29239 .29242 .29245 .29249 9.46890 .46895 .46900 .46905 .29438 .29441 .29444 .29447 9.47183 .47188 .47193 .47197 .29637 .29640 .29643 .29647 9.47474 .47479 .47484 .47489 .29836 .29839 .29843 .29846 + W 57 58 59 9.46320 .46325 .46330 .46335 .29054 .29057 .29060 .29064 9.46616 .46621 .46626 .46630 .29252 .29255 .29259 .29262 9.46910 .46915 .46919 .46924 .29451 .29454 .29457 .29461 9.47202 .47207 .47212 .47217 .29650 .29653 .29657 .29660 9.47493 .47498 .47503 .47508 .29849 .29853 .29856 .29859 4 3 2 1 + 15^ 9.46340 .29067 9.46635 .29265 9.46929 .29464 9.47222 .29663 9.47513 .29863 19^ 39m 19h 38m 19h 37m 19^3&n 19h SSm 1 Page864J TABLE 45. Haversinea. s 4'^ 25^' 66° 15' 4^ 26^ 66° Sr 4h 27m 66° 45' 4h 28m 67° C 4h 29m 67° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.47513 .47518 .47523 .47527 .39863 .39866 .29869 .29873 9.47803 .47807 .47812 .47817 .30063 .30066 .30069 .30073 9.48091 .48096 .48101 .48105 .30263 .30266 .30269 .30273 9.48378 .48383 .48387 .48392 .30463 .30467 .30470 .30473 9.48664 .48668 .48673 .48678 .30664 .30668 .30671 .30675 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 + r 5 6 7 9.47532 .47537 .47542 .47547 .29876 .29879 .29883 .29886 9.47822 .47827 .47831 .47836 .30076 .30079 .30083 .30086 9.48110 .48115 .48120 .48124 .30276 .30280 .30283 .30286 9.48397 .48402 .48407 .48411 .30477 .30480 .30484 .30487 9.48683 .48687 .48692 .48697 9.48702 .48706 .48711 .48716 .30678 .30681 .30685 .30688 .30691 .30695 .30698 .30701 + 3' 9 10 11 9.47552 .47556 .47561 .47566 .29889 .29893 .29896 .29899 9.47841 .47846 .47851 .47856 .30089 .30093 .30096 .30099 9.48129 .48134 .48139 .48144 .30290 .30293 .30296 .30300 9.48416 .48421 .48426 .48430 .30490 .30494 .30497 .30500 + 3^ 13 14 15 9.47571 .47576 .47581 .47585 .29903 .29906 .29909 .29913 9.47860 .47865 .47870 .47875 .30103 .30106 .30109 .30113 9.48148 .48153 .48158 .48163 .30303 .30306 .30310 .30313 9.48435 .48440 .48445 .48449 .30504 .30507 .30510 .30514 9.48720 .48725 .48730 .48735 .30705 .30708 .30711 .30715 + 4^ 17 18 19 9.47590 .47595 .47600 .47605 .29916 .29919 .29923 .29926 9.47880 .47884 .47889 .47894 .30116 .30119 .30123 .30126 9.48168 .48172 .48177 .48182 .30316 .30320 .30323 .30326 9.48454 .48459 .48464 .48468 .30517 .30520 .30524 .30527 9.48739 .48744 .48749 .48754 .30718 .30721 .30725 .30728 U 43 42 41 + 5' 21 22 23 9.47610 .47614 .47619 .47624 .29929 .29933 .29936 .29939 9.47899 .47904 .47908 .47913 .30129 .30133 .30136 .30139 9.48187 .48192 .48196 .48201 .30330 .30333 .30336 .30340 9.48473 .48478 .48483 .48488 .30530 .30534 .30537 .30540 9.48758 .48763 .48768 .48773 .30732 .30735 .30738 .30742 40 39 38 37 + 6' 25 26 27 9.47629 .47634 .47639 .47643 .29943 .29946 .29949 .29953 9.47918 .47923 .47928 .47933 .30143 .30146 .30149 .30153 9.48206 .48211 .48215 .48220 .30343 .30346 .30350 .30353 9.48492 .48497 .48502 .48507 .30544 .30547 .30551 .30554 9.48777 .48782 .48787 .48792 .30745 .30748 .30752 .30755 36 35 34 33 32 31 SO 29 28 27 26 25 + r 29 SO 31 9.47648 .47653 .47658 .47663 .29956 .29959 .29963 .29966 9.47937 .47942 .47947 .47952 .30156 .30159 .30163 .30166 9.48225 .48230 .48235 .48239 .30356 .30360 .30363 .30366 9.48511 .48516 .48521 .48526 .30557 .30561 .30564 .30567 9.48796 .48801 .48806 .48811 .30758 .30762 .30765 .30768 + S' 33 34 35 9.47668 .47672 .47677 .47682 .29969 .29973 .29976 .29979 9.47957 .47961 .47966 .47971 .30169 .30173 .30176 .30179 9.48244 .48249 .48254 .48258 .30370 .30373 .30376 .30380 9.48530 .48535 .485^^0 .48545 .30571 .30574 .30577 .30581 9.48815 .48820 .48825 .48830 .30772 .30775 .30779 .30782 + 9' 37 38 39 9.47687 .47692 .47697 .47701 .29983 .29986 .29989 .29993 9.47976 .47981 .47985 .47990 .30183 .30186 .30189 .30193 9.48263 .48268 .48273 .48278 .30383 .30386 .30390 .30393 9.48549 .48554 .48559 .48564 .30584 .30587 .30591 .30594 9.48834 .48839 .48844 .48848 .30785 .30789 .30792 .30795 24 23 22 21 + W 41 42 43 9.47706 .47711 .47716 .47721 .29996 .29999 .30003 .30006 9.47995 .48000 .48005 .48009 .30196 .30199 .30203 .30206 9.48282 .48287 .48292 .48297 .30397 .30400 .30403 .30407 9.48568 .48573 .48578 .48583 .30597 .30601 .30804 .30607 9.48853 .48858 .48863 .48867 .30799 .30802 .30805 .30809 20 19 18 17 + 11' 45 46 47 9.47725 .47730 .47735 .47740 .30009 .30013 .30016 .30019 9.48014 .48019 .48024 .48029 .30209 .30213 .30216 .30219 9.48302 .48306 .48311 .48316 .30410 .30413 .30417 .30420 9.48587 .48592 .48597 .48602 .30611 .30614 .30618 .30621 9.48872 .48877 .48882 .48886 .30812 .30815 .30819 .30823 16 15 14 13 12 11 10 9 + 12' 49 50 51 9.47745 .47750 .47754 .47759 .30023 .30026 .30029 .30033 9.48033 .48038 .48043 .48048 .30223 .30226 .30229 .30233 9.48321 .48325 .48330 .48335 .30423 .30427 .30430 .30433 9.48607 .48611 .48616 .48621 .30624 .30628 .30631 .30634 9.48891 .48896 .48901 .48905 .30826 .30829 .30832 .30836 + 13^ 53 54 55 9.47764 .47769 .47774 .47778 .30036 .30039 .30043 .30046 9.48053 .48057 .48062 .48067 .30236 .30239 .30243 .30246 9.48340 .48344 .48349 .48354 .30437 .30440 .30443 .30447 9.48626 .48630 .48635 .48640 .30638 .30641 .30644 .30648 9.48910 .48915 .48919 .48924 .30839 .30842 .30846 .30849 8 7 6 5 + U' 57 58 59 9.47783 .47788 .47793 .47798 .30049 .30053 .30056 .30059 9.48072 .48077 .48081 .48086 .30249 .30253 .30256 .30259 9.48359 .48364 .48368 .48373 .30450 .30453 .30457 .30460 9.48645 .48649 .48654 .48659 .30651 .30655 .30658 .30661 9.48929 .48934 .48938 .48943 .30852 .30856 .30859 .30862 4 3 2 1 + 16' 9.47803 .30063 9.48091 .30263 9.48378 .30463 9.48664 .30664 9.48948 .30866 19Ji 34^ 19h SSm 19h s^ 19^ Sim igf^ som TABLE 45. [Page 866 Haversines. s 4^S0m%l°W 4^^ Sim 67" 45' .^ft S2m 68° C 4hSsm6S''W 4^ S4m 68" SO' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.48948 .48953 .48957 .48962 .30866 .30869 .30873 .30876 9.49231 .49235 .49240 .49245 .31068 .31071 .31074 .31078 9.49512 .49517 .49522 .49226 .31270 .31273 .31276 .31280 9.49793 .49797 .49802 .49807 .31472 .31475 .31479 .31482 9.50072 .50076 .50081 .50085 .31676 .31678 .31682 .31685 60 59 58 57 + r 5 6 7 9.48967 .48971 .48976 .48981 .30879 .30883 .30886 .30889 9.49250 .49254 .49259 .49264 .31081 .31084 .31088 .31091 9.49531 .49536 .49540 .49545 .31283 .31287 .31290 .31293 9.49811 .49816 .49821 .49825 .31486 .31489 .31492 .31496 9.50090 .50095 .50099 .50104 .31688 .31693 .31695 .31699 56 55 54 53 + 3^ 9 10 11 9.48986 .48990 .48995 .49000 .30893 .30896 .30899 .30903 9.49268 .49273 .49278 .49282 .31095 .31098 .31101 .31105 9.49550 .49554 .49559 .49564 .31297 .31300 .31303 .31307 9.49830 .49835 .49839 .49844 .31499 .31503 .31506 .31509 9.50109 .50113 .50118 ..50123 .31703 .31705 .31709 .31712 52 51 50 49 + 3' IS 14 15 9.49004 .49009 .49014 .49019 .30906 .30910 .30913 .30916 9.49287 .49292 .49297 .49301 .31108 .31111 .31115 .31118 9.49568 .49573 .49578 .49583 .31310 .31314 .31317 .31320 9.49849 .49853 .49858 .49862 .31513 .31516 .31619 .31523 9.50127 .50132 .50136 .50141 .31716 .31719 .31722 .31726 48 47 46 45 + 4^ 17 18 19 9.49023 .49028 .49033 .49038 .30920 .30923 .30926 .30930 9.49306 .49311 .49315 .49320 .31121 .31125 .31128 .31132 9.49587 .49592 .49597 .49601 .31324 .31327 .31330 .31334 9.49867 .49872 .49876 .49881 .31526 .31530 .31533 .31536 9.50146 .50150 .50155 .50160 .31729 .31732 .31736 .31739 44 43 42 41 + 6' 21 22 23 9.49042 .49047 .49052 .49056 .30933 .30936 .30940 .30943 9.49325 .49329 .49334 .49339 .31135 .31138 .31142 .31145 9.49606 .49611 .49615 .49620 .31337 .31341 .31344 .31347 9.49886 .49890 .49895 .49900 .31540 .31543 .31546 .31550 9.50164 .50169 .50174 .50178 .31742 .31746 .31749 .31753 40 39 38 37 + 6' 25 26 27 9.49061 .49066 .49071 .49075 .30946 .30950 .30953 .30957 9.49344 .49348 .49353 .49358 .31148 .31152 .31155 .31158 9.49625 .49629 .49634 .49639 .31351 .31354 .31357 .31361 9.49904 .49909 .49914 .49918 .31553 .31557 .31560 .31563 9.50183 .50187 .50192 .50197 .31756 .31760 .31763 .31766 36 35 34 SS + r 29 SO 31 9.49080 .49085 .49089 .49094 .30960 .30963 .30967 .30970 9.49362 .49367 .49372 .49376 .31162 .31165 .31169 .31172 9.49643 .49648 .49653 .49657 .31364 .31367 .31371 .31374 9.49923 .49928 .49932 .49937 .31567 .31670 .31573 .31677 9.50201 .50206 .50211 .50215 .31770 .31773 .31776 .31780 32 31 SO 29 + 8' S3 34 35 9.49099 .49104 .49108 .49113 .30973 .30977 .30980 .30983 9.49381 .49386 .49390 .49395 .31175 .31179 .31182 .31185 9.49662 .49667 .49671 .49676 .31378 .31381 .31384 .31388 9.49942 .49946 .49951 .49956 .31680 .31684 .31587 .31590 9.50220 .50224 .50229 .50234 .31783 .31787 .31790 .31793 28 27 26 25 + 9' 37 38 39 9.49118 .49122 .49127 .49132 .30987 .30990 .30994 .30997 9.49400 .49405 .49409 .49414 .31189 .31102 .3119G .31199 9.49681 .49685 .49690 .49695 .31391 .31394 .31398 .31401 9.4y9C0 .49965 .49969 .49974 .31694 .31597 .31601 .31604 9.50238 .50243 .50248 .50252 .31797 .31800 .31804 .31807 24 23 22 21 20 19 18 17 + W 41 42 43 9.49137 .49141 .49146 .49151 .31000 .31004 .31007 .31010 9.49419 .49423 .49428 .49433 .31302 .31206 .31209 .31212 9.49699 .49704 .49709 .49713 .31405 .31408 .31411 .31415 9.49979 .49983 .49988 .49993 .31607 .31611 .31614 .31617 9.50257 .50261 .50266 .50271 .31810 .31814 .31817 .31820 + ir 45 46 47 9.49155 .49160 .49165 .49170 .31014 .31017 .31020 .31024 9.49437 .49442 .49447 .49451 .31216 .31219 .31222 .31226 9.49718 .49723 .49727 .49732 .31418 .31431 .31435 .31428 9.49997 .50002 .50007 .50011 .31621 .31C24 .31628 .31631 9.50275 .50280 .50284 .50289 .31824 .31827 .31831 .31834 16 15 14 13 + W 49 50 51 9.49174 .49179 .49184 .49188 .31027 .31031 .31034 .31037 9.49456 .49461 .49465 .49470 .31229 .31233 .31236 .31239 9.49737 .49741 .49746 .49751 .31432 .314.35 .31438 .31442 9.50016 .50021 .50025 .50030 .31634 .31638 .31641 .31644 9.50294 .50298 .50303 .50308 .31837 .31841 .31844 .31848 12 11 10 9 + 13' 5S 54 55 9.49193 .49198 .49202 .49207 .31041 .31044 .31047 .31051 9.49475 .49480 .49484 .49489 .31243 .31246 .31249 .31253 9.49755 .49760 .49765 .49769 .31445 .31448 .31452 .31455 9.50034 .50039 .50044 .50048 .31648 .31651 .31655 .31658 9.50312 .50317 .50.322 .50326 .31851 .31854 .31858 .31861 8 7 6 5 + 14' 57 58 59 9.49212 .49217 .49221 .49226 .31054 .31057 .31061 .31064 9.49494 .49498 .49503 .49508 .31256 .31260 .31263 .31266 9.49774 .49779 .49783 .49788 .31459 .31462 .31465 .31469 9.50053 .50058 .50062 .50067 .31661 .31665 .31668 .31672 9.50331 .50335 .50340 .50345 .31865 .31868 .31871 .31876 4 3 2 1 + 15' 9.49231 .31068 9.49512 .31270 9.49793 .31472 9.50072 .31675 9.50349 .31878 19^ 29^ lOh 2Sm 19h 27m 19^ 26m i9^ 25m Page 866] TABLE 45. Haversines, s 4h 35m 68° 45' 4h SG-m 69° 0' 4h 37m 69° 15' 4Ji 38m 69° 30' 4h 39m 69° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3. 9.50349 .50354 .50358 .50363 .31878 .31881 .31885 .31888 9.50626 .50630 .50635 .50639 .32082 .32085 .32088 .32092 9.50901 .50905 .50910 .50914 .33285 .32289 .32292 .32296 9.51174 .51179 .51184 .51188 .32490 .32493 .33496 .33500 9.51447 .51452 .51456 .51461 .33694 .32698 .32701 .32704 60 59 58 57 66 65 64 63 52 61 50 49 + r 5 6 7 9.50368 .50372 .50377 .50382 .31892 .31895 .31898 .31902 9.50644 .50649 .50653 .50658 .32095 .32099 .32102 .32105 9.50919 .50924 .50928 .50933 .33299 .32302 .32306 .32309 9.51193 .51197 .51202 .51206 .33503 .32507 .32510 .32513 9.51465 .51470 .51474 .51479 .32708 .32711 .32715 .32718 + V 9 10 11 9.50386 .50391 .50395 .50400 .31905 .31909 .31912 .31915 9.50662 .50667 .50672 .50676 .32109 .32112 .32116 .32119 9.50937 .50942 .50946 .50951 .32313 .33316 .32319 .32323 9.51211 .51215 .51220 .51225 .32517 .33530 .33524 .32527 9.51483 .51488 .51492 .51497 .32721 .32735 .33728 .33732 + 3' 13 14 15 9.50405 .50409 .50414 .50418 .31919 .31922 .31926 .31929 9.50681 .50685 .50690 .50694 .32132 .32126 .32129 .32133 9.50956 .50960 .50965 .50969 .32326 .32330 .32333 .32336 9.51229 .51234 .51238 .51243 .32531 .32534 .32537 .32541 9.51501 .51506 .51510 .51515 .32735 .32738 .32743 .33745 48 47 46 45 44 ■43 42 41 + 4' 17 18 19 9.50423 .50428 .50432 .50437 .31932 .31936 .31939 .31942 9.50699 .50704 .50708 .50713 .32136 .32139 .32143 .32146 9.50974 .50978 .50983 .50988 .32340 .32343 .32347 .32350 9.51247 .51252 .51256 .51261 .33544 .32547 .32551 .32554 9.51519 .51524 .51529 .51533 .33749 .32762 .32756 .33759 + 5' 21 22 23 9.50442 .50446 .50451 .50455 .31946 .31949 .31953 .31956 9.50717 .50722 .50727 .50731 .32150 .33153 .32156 .32160 9.50992 .50997 .51001 .51006 .32353 .32357 .32360 .32364 9.51265 .51270 .51275 .51279 .32558 .32561 .32565 .32568 9.51538 .51542 .51547 .51551 .33762 .33766 .33769 .33773 40 39 38 37 + 6' 25 26 27 9.50460 .50465 .50469 .50474 .31959 .31963 .31966 .31970 9.50736 .50740 .50745 .50750 .33163 .32166 .32170 .32173 9.51010 .51015 .51019 .51024 .33367 .33370 .32374 .33377 9.51284 .51288 .51293 .51297 .33571 .33575 .32578 .32582 9.51556 .51560 .51565 .51569 .33776 .33779 .33783 .33786 36 36 34 33 + r 29 30 31 9.50478 .50483 .50488 .50492 .31973 .31976 .31980 .31983 .31987 .31990 .31993 .31997 9.50754 .50759 .50763 .50768 .32177 .33180 .32183 .32187 9.51029 .51033 .51038 .51042 .33381 .32384 .32388 .32391 9.51302 .51306 .51311 .51315 .32585 .33588 .32592 .33595 9.51574 .51578 .51583 .51587 .33790 .33793 .33797 .33800 32 31 SO 29 + 8' 33 34 35 9.50497 .50501 .50506 .50511 9.50772 .50777 .50782 .50786 .32190 .32194 .32197 .32200 9.51047 .51051 .51056 .51061 .33394 .32398 .32401 .33405 9.51320 .51325 .51329 .51334 .33599 .33602 .33605 .32609 9.51592 .51596 .51601 .51605 .33803 .32807 .33810 .33814 28 27 26 25 + 9^ 37 38 39 9.50515 .50520 .50524 .50529 .32000 .32004 .32007 .32010 9.50791 .50795 .50800 .50805 .33304 .33207 .33211 .32214 9.51065 .51070 .51074 .51079 .33408 .32411 .32415 .33418 9.51338 .51343 .51347 .51352 .32612 .32616 .32619 .32633 9.51610 .51614 .51619 .51623 .33817 .33830 .33834 .32837 24 28 22 21 20 19 18 11 + 10' 41 42 43 9.50534 .50538 .50543 .50547 .32014 .32017 .32021 .32024 9.50809 .50814 .50818 .50823 .32217 .33331 .33334 .32228 9.51083 .51088 .51092 .51097 .33422 .33435 .33438 .32432 9.51356 .51361 .51365 .51370 .33636 .33639 .33633 .33636 9.51628 .51633 .51637 .51642 .33831 .33834 .33838 .33841 + 11^ 45 46 47 9.50552 .50557 .50561 .50566 .32027 .32031 .32034 .32037 9.50827 .50832 .50837 .50841 .32231 .33335 .33338 .33341 9.51102 .51106 .51111 .51115 .33435 .33438 .32442 .32445 9.51374 .51379 .51384 .51388 .33640 .32643 .32646 .32650 9.51646 .51651 .51655 .51660 .33844 .33848 .33851 .33855 16 15 14 IS 12 11 10 9 8 7 6 5 + 12' 49 50 61 9.50570 .50575 .50580 .50584 .32041 .32044 .32048 .32051 9.50846 .50850 .50855 .50860 .32245 .32248 .32251 .32355 9.51120 .51124 .51129 .51133 .32449 .32452 .32456 .33459 9.51393 .51397 .51402 .51406 .32653 .32657 .32660 .32663 9.51664 .51669 .51673 .51678 .32858 .32861 .32865 .32868 + 13' 53 54 65 9.50589 .50593 .50598 .50603 .32054 .32058 .32061 .32065 9.50864 .50869 .50873 .50878 .32258 .32262 .32265 .32268 9.51138 .51143 .31147 .51152 .32462 .32466 .32469 .32473 9.51411 .51415 .51420 .51424 .32667 .32670 .32674 .32677 9.51682 .51687 .51691 .51696 .33873 .33875 .33878 .32882 + 14' 57 58 69 9.50607 .50612 .50616 .50621 .32068 .32071 .32075 .32078 9.50882 .50887 .50892 .50896 .33272 .32275 .32279 .32282 9.51156 .51161 .51165 .51170 .32476 .32479 .32483 .32486 9.51429 .51433 .51438 .51442 .32681 .33684 .33687 .33691 9.51700 .51705 .51709 .51714 .32885 .32889 .32892 .33896 4 8 2 1 + 15' 9.50626 .32082 9.50901 .32385 9.51174 .33490 9.51447 .32694 9.51718 .33899 jgh 24m igh 2Sm i9h 22m 19h 21m 19^ 20m. TABLE 45. [Page 867 Havereines. 3 4A 40TO 70° r 4h 41m 70° 15^ 4h 4pn 70° 30^ 411 43m 70° 45^ 4h 44m 710 0/ s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.51718 .51723 .51727 .51732 .32899 .32902 .32906 .32909 9.51988 .51993 .51997 .52002 .33104 .33108 .33111 .33114 9.52257 .52261 .52266 .52270 .33310 .33313 .33317 .33320 9.52525 .52529 .52533 .52538 .33515 .33519 .33522 .33526 9.52791 .52795 .52800 .52804 .33722 .33725 .33728 .33732 60 59 58 57 56 55 54 53 + 1' 5 6 7 9,51736 .51741 .51745 .51750 .32913 .32916 .32920 .32923 9.52006 .52011 .52015 .52020 .33118 .33121 .33125 .33128 9.52275 .52279 .52284 .52288 .33323 .33327 .33330 .33334 9.52542 .52547 .52551 .52556 .33529 .33533 .33536 .33540 9.52809 .52813 .52817 .52822 .33735 .33739 .33742 .33746 9 10 11 9.51754 .51759 .51763 .51768 .32926 .32930 .32933 .32937 9.52024 .52029 .52033 .52038 .33132 .33135 .33138 .33142 9.52293 .52297 .52302 .52306 .33337 .33341 .33344 .33347 9.52560 .52565 .52569 .52573 .33543 .33546 .33550 .33553 9.52826 .52831 .52835 .52839 .33749 .33753 .33756 .33759 52 51 50 49 48 47 46 45 + 9" IS 14 15 9.51772 .51777 .51781 .51786 .32940 .32943 .32947 .32950 9.52042 .52047 .52051 .52056 .33145 .33149 .33152 .33156 9.52311 .52315 .52320 .52324 .33351 .33354 .33358 .33361 9.52578 .52582 .52587 .52591 .33557 .33560 .33564 .33567 9.52844 .52848 .52853 .52857 .33763 .33766 .33770 .33773 + 4' 17 18 19 9.51790 .51795 .51799 .51804 .32954 .32957 .32961 .32964 9.52060 .52065 .52069 .52074 .33159 .33162 .33166 .33169 9.52328 .52333 .52337 .52342 .33365 .33368 .33371 .33375 9.52596 .52600 .52605 .52609 .33570 .33574 .33577 .33581 9.52862 .52866 .52870 .52875 .33777 .33780 .33783 .33787 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 + 5^ 21 22 23 9.51808 .51813 .51817 .51822 .32967 .32971 .32974 .32978 9.52078 .52082 .52087 .52091 .33173 .33176 .33179 .33183 9.52346 .52351 .52355 .52360 .33378 .33382 .33385 .33389 9.52G13 .52618 .52622 .52627 .33584 .33588 .33591 .33594 9.52879 .52884 .52888 .52893 .33790 .33794 .33797 .33801 + ^ 25 26 27 9.51826 .51831 .51835 .51840 .32981 .32984 .32988 .32991 9.52096 .52100 .52105 .52109 .33186 .33190 .33193 .33197 9.52364 .52369 .52373 .52378 .33392 .33395 .33399 .33402 9.52631 .52636 .52640 .52645 .33598 .33601 .33605 .33608 9.52897 .52901 .52906 .52910 .33804 .33808 .33811 .33814 + r 29 SO 31 9.51844 .51849 .51853 .51858 .32995 .32998 .33002 .33005 9.52114 .52118 .52123 .52127 .33200 .33203 .33207 .33210 9.52382 .52386 .52391 .52395 .33406 .33409 .33413 .33416 9.52649 .52653 .52658 .52662 .33612 .33615 .33618 .33622 9.52915 .52919 .52923 .52928 .33818 .33821 .33825 .33828 + 8^ 33 34 35 9.51862 .51867 .51871 .51876 .33008 .33012 .33015 .33019 9.52132 .52136 .52141 .52145 .33214 .33217 .33221 .33224 9.52400 .52404 .52409 .52413 .33419 .33423 .33426 .33430 9.52667 .52671 .52676 .52680 .33625 .33629 .33632 .33636 9.52932 .52937 .52941 .52946 .33832 .33835 .33839 .33842 + r 37 38 39 9.51880 .51885 .51889 .51894 .33022 .33025 .33029 .33032 9.52150 .52154 .52159 .52163 .33227 .33231 .33234 .33238 9.52418 .52422 .52427 .52431 .33433 .33436 .33440 .33444 9.52684 .52689 .52693 .52698 .33639 .33642 .33646 .33649 9.52950 .52954 .52959 .52963 .33845 .33849 .33852 .33856 + W 41 42 43 9.51898 .51903 .51907 .51912 .33036 .33039 .33043 .33046 9.52168 .52172 .52177 .52181 .33241 .33245 .33248 .33251 9.52436 .52440 .52444 .52449 .33447 .33450 .33454 .33457 9.52702 .52707 .52711 .52715 .33653 .33656 .33660 .33663 9.52968 .52972 .52976 .52981 .33859 .33863 .33866 .33869 + 11' 45 46 47 9.51916 .51921 .51925 .51930 .33049 .33053 .33056 .33060 9.52185 .52190 .52194 .52199 .33255 .33258 .33262 .33265 9.52453 .52458 .52462 .52467 .33461 .33464 .33467 .33471 9.52720 .52724 .52729 .52733 .33667 .33670 .33673 .33677 9.52985 .52990 .52994 .52999 .33873 .33876 .33880 .33883 + 12' 49 50 51 9.51934 .51939 .51943 .51948 .33063 .33067 .33070 .33073 9.52203 .52208 .52212 .52217 .33269 .33272 .33275 .33279 9.52471 .52476 .52480 .52484 .33474 .33478 .33481 .33485 9.52738 .52742 .52747 .52751 .33680 .33684 .33687 .33691 9.53003 .53007 .53012 .53016 .33887 .33890 .33894 .33897 + 13' 5,? 55 9.51952 .51957 .51961 .51966 .33077 .33080 .33084 .33087 9.52221 .52226 .52230 .52235 .33282 .33286 .33289 .33293 9.52489 .52493 .52498 .52502 .33488 .33491 .33495 .33498 9.52755 .52760 .52764 .52769 .33694 .33698 .33701 .33704 9.53021 .53025 .53029 .53034 .33900 .33904 .33907 .33911 8 7 6 5 + 14' 57 55 59 9.51970 .51975 .51979 .51984 .33090 .33094 .33097 .33101 9.52239 .52244 .52248 .52253 .33296 .33299 .33303 .33306 9.52507 .52511 .52516 .52520 .33502 .33505 .33509 .33512 9.52773 .52778 .52782 .52786 .33708 .33711 .33715 .33718 9.53038 .53043 .53047 .53051 .33914 .33918 .33921 .33925 4 3 2 1 + 15' 9.51988 .33104 9.52257 .33310 9.52525 .33515 9.52791 .33722 9.53056 .33928 19h 19m jgh igm 19h nm 19h lem 19^ 15m V Page 868] TABLE 45. Haversines. s 4h 4Sm 71° 15/ 471 46m 71° 30/ 4h 47m 71° 45/ 4^ 48^ 72° r 4^ 49m 72° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.53056 .53060 .53065 .53069 .33938 .33931 .33935 .33938 9.53320 .53324 .53328 .53333 .34135 .34138 .34142 .34145 9.53582 .53587 .53591 .53595 .34342 .34345 .34349 .34352 9.53844 .53848 .53852 .53857 .34549 .34553 .34556 .34560 9.54104 .54108 .54113 .54117 .34757 .34760 .34764 .34767 60 59 58 57 + 1^ 5 6 7 9.53073 .53078 .53082 .53087 .33913 .33945 .33949 .33953 9.53337 .53342 .53346 .53350 .34149 .34152 .34155 .34159 9.63600 .53604 .53609 .53613 .34356 .34359 .34363 .34368 9.53861 .53865 .53870 .53874 .34563 .34566 .34570 .34573 9.54121 .54126 .54130 .54134 .34771 .34774 .34778 .34781 56 55 54 53 + V 9 10 11 9.53091 .53096 .53100 .53104 .33956 .33959 .33962 .33966 9.53355 .53359 .53364 .53368 .34162 .34166 .34169 .34173 9.53617 .53622 .53626 .53630 .34369 .34373 .34376 .34380 9.53879 .53883 .53887 .53892 .34577 .34580 .34584 .34587 9.54139 .54143 .54147 .54152 .34784 .34788 .34791 .34795 52 51 50 49 + 3^ 13 14 15 9.53109 .53113 .53118 .53122 .33969 .33973 .33976 .33980 9.53372 .53377 .53381 .53385 .34176 .34180 .34183 .34186 9.53635 .53639 .53643 .53648 .34383 .34387 .34390 .34394 9.53896 .53900 .53905 .53909 .34591 .34594 .34598 .34601 9.54156 .54160 .54165 .54169 .34798 .34802 .34805 .34809 .34812 .34816 .34819 .34833 48 47 46 45 44 43 42 41 + 4^ 17 18 19 9.53126 .53131 .53135 .53140 .33983 .33986 .33990 .33993 9.53390 .53394 .53399 .53403 .34190 .34193 .34197 .34200 9.53652 .53657 .53661 .53665 .34397 .34400 .34404 .34407 9.53913 .53918 .53922 .53926 .34604 .34608 .34611 .34615 9.54173 .54177 .54182 .54186 + 5^ 21 22 23 9.53144 .53148 .53153 .53157 .33997 .34000 .34004 .34007 9.53407 .53412 .53416 .53421 .34204 .34207 .34211 .34214 9.53670 .53674 .53678 .53683 .34411 .34414 .34418 .34421 9.53931 .53935 .53939 .53944 .34618 .34622 .34625 .34629 9.54190 .54195 .54199 .54203 .34836 .34830 .34833 .34836 40 39 38 37 + 6' 25 26 27 9.53162 .53166 .53170 .53175 .34011 .34014 .34018 .34031 9.53425 .53429 .53434 .53438 .34218 .34321 .34224 .34228 9.53687 .53691 .53696 .53700 .34435 .34428 .34432 .34435 9.53948 .53952 .53957 .53961 .34633 .34636 .34639 .34643 9.54208 .54212 .54216 .54221 .34840 .34843 .34847 .34850 36 35 34 33 + r 29 SO 31 9.53179 .53184 .53188 .53192 .34034 .34038 .34031 .34035 9.53442 .53447 .53451 .53456 .34231 .34235 .34338 .34342 9.53704 .53709 .53713 .53718 .34439 .34442 .34445 .34449 9.53966 .53970 .53974 .53978 .34646 .34649 .34653 .34656 9.54225 .54229 .54234 .54238 .34854 .34857 .34861 .34864 32 31 30 29 + 8^ 33 34 35 9.53197 .53201 .53206 .53210 .34038 .34043 .34045 .34049 9.53460 .53464 .53469 .53473 .34245 .34249 .34252 .34256 9.53722 .53726 .53731 .53735 .34452 .34456 .34459 .34483 9.53983 .53987 .53991 .53996 .34660 .34663 .34667 .34670 9.54242 .54247 .54251 .54255 .34868 .34871 .34875 .34878 .34883 .34885 .34888 .34892 28 27 26 25 24 23 22 21 + 9^ 37 38 39 9.53214 .53219 .53223 .53228 .34053 .34055 .34059 .34063 9.53477 .53482 .53486 .53491 .34359 .34262 .34266 .34369 9.53739 .53744 .53748 .53752 .34466 .34470 .34473 .34477 9.54000 .54004 .54009 .54013 .34674 .34677 .34681 .34684 9.54260 .54264 .54268 .54272 + W 41 42 43 ■ 9.53232 .53236 .53241 .53245 .34066 .34069 .34073 .34076 9.53495 .53499 .53504 .53508 .34273 .34276 .34280 .34383 9.53757 .53761 .53765 .53770 .34480 .34483 .34487 .34490 9.54017 .54022 .54026 .54030 .34688 .34691 .34694 .34698 9.54277 .54281 .54285 .54290 .34895 .34899 .34902 .34906 20 19 18 17 16 15 14 13 + 11^ 45 46 47 9.53249 .53254 .53258 .53263 .34080 .34083 .34087 .34090 9.53512 .53517 .53521 .53526 .34287 .34290 .34293 .34297 9.53774 .53778 .53783 .53787 .34494 .34497 .34501 .34504 9.54035 .54039 .54043 .54048 .34701 .34705 .34708 .34712 9.54294 .54298 .54303 .54307 .34909 .34913 .34916 .34930 + W 49 50 51 9.53267 .53271 .53276 .53280 .34093 .34097 .34100 .34104 9.53530 .53534 .53539 .53543 .34300 .34304 .34307 .34311 9.53792 .53796 .53800 .53805 .34508 .34511 .34515 .34518 9.54052 .54056 .54061 .54065 .34715 .34719 .34722 .34726 9.54311 .54316 .54320 .54324 .34933 .34927 .34930 .34933 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.53285 .53289 .53293 .53298 .34107 .34111 .34114 .34118 9.53547 .53552 .53556 .53560 .34314 .34318 .34321 .34325 9.53809 .53813 .53818 .53822 .34521 .34525 .34528 .34532 9.54069 .54074 .54078 .54082 .34729 .34733 .34736 .34739 9.54329 .54333 .54337 .54341 .34937 .34940 .34944 .34947 + W 57 58 59 9.53302 .53307 .53311 .53315 .34131 .34124 .34128 .34131 9.53565 .53569 .53574 .53578 .34328 .34331 .34335 .34338 9.53826 .53831 .53835 .53839 .34535 .34539 .34542 .34546 9.54087 .54091 .54095 .54100 .34743 .34746 .34750 .34753 9.54346 .54350 .54354 .54359 .34951 .34954 .34958 .34961 4 3 2 1 + 15' 9.53320 .34135 9.53582 .34342 9.53844 .34549 9.54104 .34757 9.54363 .34965 i9h 14m 19h 13m 19hipn i9h lim 19hl0m TABLE 45. [Page 869 Haversines. s 4^ 50m. 72° w 4h 5im 72° 45^ 4h 52m 73° Q' 4^ 53m 73° 15^ 4h 54m 73° 3(K s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.54363 .54367 .54372 .54376 .34965 .34968 .34972 .34975 9.54621 .54625 .54629 .54634 .35173 .35176 .35180 .35183 9.54878 .54882 .54886 .54890 .35381 .35385 .35388 .35392 9.55133 .55137 .55142 .55146 .35590 .35594 .35597 .35601 9.55387 .55392 .55396 .55400 .35799 .35803 .35806 .35810 60 59 58 57 + r 5 6 7 9.54380 .54385 .54389 .54393 .34979 .34982 .34986 .34989 9.54638 .54642 .54647 .54651 .35187 .35190 .35194 .35197 9.54895 .54899 .54903 .54907 .35395 .35399 .35402 .35406 9.55150 .55154 .55159 .55163 .35604 .35608 .35611 .35615 9.55404 .55409 .55413 .55417 .35813 .35817 .35820 .35824 56 55 54 53 + 2' 9 10 11 9.54397 .54402 .54406 .54410 .34992 .34996 .34999 .35003 9.54655 .54659 .54664 .54668 .35201 .35304 .35308 .35311 9.54912 .54916 .54920 .54924 .35409 .35413 .35416 .35420 9.55167 .55171 .55176 .55180 .35618 .35622 .35625 .35638 9.55421 .55425 .55430 .55434 .35827 .35831 .35834 .35838 52 51 50 49 + 3' 13 14 15 9.54415 .54419 .54423 .54428 .35006 .35010 .35013 .35017 9.54672 .54677 .54681 .54685 .35215 .35218 .35322 .35225 9.54929 .54933 .54937 .54942 .35423 .35427 .35430 .35434 9.55184 .55188 .55192 .55197 .35632 .35635 .35639 .35642 9.55438 .55442 .55447 .55451 .35841 .35845 .35848 .35852 48 47 46 45 + 4' 17 18 19 9.54432 .54436 .54440 .54445 .35020 .35024 .35027 .35031 9.54689 .54694 .54698 .54702 .35228 .35232 .35235 .35239 9.54946 .54950 .54954 .54959 .35437 .35441 .35444 .35448 9.55201 .55205 .55209 .55214 .35646 .35649 .35653 .35656 9.55455 .55459 .55463 .55468 .35855 .35859 .35862 .35865 44 43 42 41 21 22 23 9.54449 .54453 .54458 .54462 .35034 .35038 .35041 .35044 9.54707 .54711 .54715 .54719 .35242 .35246 .35249 .35253 .35256 .35260 .35263 .35267 9.54963 .54967 .54971 .54976 .35451 .35454 .35458 .35461 9.55218 .55222 .55226 .55231 9.55235 .55239 .55243 .55248 .35660 .35663 .35667 .35670 9.55472 .55476 .55480 .55485 .35869 .35872 .35876 .35879 40 39 38 37 36 35 34 33 + 6^ 25 26 27 9.54466 .54471 .54475 .54479 .35048 .35051 .35055 .35058 9.54724 .54728 .54732 .54736 9.54980 .54984 .54988 .54993 .35465 .35468 .35472 .35475 .35674 .35677 .35681 .35684 9.55489 .55493 .55497 .55501 .35883 .35886 .35890 .35893 + r 29 30 31 9.54483 .54488 .54492 .54496 .35062 .35065 .35069 .35072 9.54741 .54745 .54749 .54754 .35270 .35274 .35377 .35281 9.54997 .55001 .55005 .55010 .35479 .35482 .35486 .35489 9.55252 .55256 .55260 .55265 .35688 .35691 .35695 .35698 9.55506 .55510 .55514 .55518 .35897 .35900 .35904 .35907 32 31 SO 29 28 27 26 25 + 8^ 33 34 35 9.51501 .54505 .54509 .54514 .35076 .35079 .35083 .35086 9.54758 .54762 .54766 .54771 .35284 .35288 .35291 .35294 9.55014 .55018 .55022 .55027 .35493 .35496 .35500 .35503 9.55269 .55273 .55277 .55282 .35702 .35705 .35709 .35712 9.55523 .55527 .55531 .55535 .35911 .35914 .35918 .35921 + 9^ 37 38 39 9.54518 .54522 .54526 .54531 .35090 .35093 .35097 .35100 9.54775 .54779 .54784 .54788 .35298 .35301 .35305 .35308 9.55031 .55035 .55039 .55044 .35507 .35510 .35514 .35517 9.55286 .55290 .55294 .55298 .35716 .35719 .3^723 .35726 9.55539 .55544 .55548 .55552 .35925 .35928 .35932 .35935 24 23 22 21 + 10^ 41 42 43 9.54535 .54539 .54544 .54548 .35103 .35107 .35110 .35114 9.54792 .54796 .54801 .54805 .35312 .35315 .35319 .35322 9.55048 .55052 .55057 .55061 .35521 .35524 .35528 .35531 9.55303 .55307 .55311 .55315 .35730 .35733 .35737 .35740 9.55556 .55561 .55565 .55569 .35939 .35942 .35946 .35949 20 19 18 17 + ir 45 46 47 9.54552 .54556 .54561 .54565 .36117 .35121 .35124 .35128 9.54809 .54813 .54818 .54822 .35326 .35329 .35333 .35336 9.55065 .55069 .55074 .55078 .35534 .35538 .35541 .35545 9.55320 .55324 .55328 .55332 .35743 .35747 .35750 .35754 9.55573 .55577 .55582 .55586 .35953 .35956 .35960 .35963 16 15 14 13 + 12' 49 50 51 9.54569 .54574 .54578 .54582 .35131 .35135 .35138 .35142 9.54826 .54831 .54835 .54839 .35340 .35343 .35347 .35350 9.55082 .55086 .55091 .55095 .35548 .35552 .35555 .35559 9.55337 .55341 .55345 .55349 .35757 .35761 .35764 .35768 9.55590 .55594 .55598 .55603 .35967 .35970 .35974 .35977 12 11 10 9 + 13^ 53 54 55 9.54587 .54591 .54595 .54599 .35145 .35149 .35152 .35156 9.54843 .54848 .54852 .54856 .35354 .35357 .35361 .35364 9.55099 .55103 .55108 .55112 .35562 .35566 .35569 .35573 9.55354 .55358 .55362 .55366 .35771 .35775 .35778 .35782 9.55607 .55611 .55615 .55620 .35981 .35984 .35988 .35991 8 7 6 5 4 3 2 1 57 58 59 9.54604 .54608 .54612 .54617 .35159 .35162 .35166 .35169 9.54860 .54865 .54869 .54873 .35368 .35371 .35374 .35378 9.55116 .55120 .55125 .55129 .35576 .35580 .35583 .35587 9.55370 .55375 .55379 .55383 .35785 .35789 .35792 .35796 9.5562'4 .55628 .55632 .55636 .35995 .35998 .36002 .36005 + 15' 9.54621 .35173 9.54878 .35381 9.55133 .35590 9.55387 .35799 9.55641 .36009 19^ 9m 19h 8m m 7m 19h6Jn 19h5m Page 870] TABLE 45. Havereines. s ^A 55m 73° 45' 4h 56m 74° 0' 4h 57m 740 15/ 4h 58m 740 3(K 4^ 59m 74° 45' Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav.j Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. s 1 2 S 9.55641 .55645 .55649 .55653 .36009 .36012 .36016 .36019 9.55893 .55897 .55901 .55905 .36318 .36333 .36335 .36339 9.56144 .56148 .56152 .56156 .36438 .36431 .36435 .36438 9.56393 .56397 .56402 .56406 .36638 .36643 .36645 .36649 9.56642 .56646 .56650 .56654 .36848 .36853 .36855 .36859 60 59 58 57 + r 5 6 7 9.55657 .55662 .55666 .55670 .36033 .36036 .36030 .36033 9.55909 .55914 .55918 .55922 .36333 .36336 .36339 .36343 9.56160 .56164 .56169 .56173 .36443 .36445 .36449 .36453 9.56410 .56414 .56418 .56422 .36653 .36656 .36659 .36663 9.56658 .56663 .56667 .56671 .36862 .36866 .36869 .36873 56 55 54 53 + 2' 9 10 11 9.55674 .55678 .55683 .55687 .36036 .36040 .36043 .36047 9.55926 .55930 .55935 .55939 .36346 .36350 .36353 .36357 9.56177 .56181 .56185 .56189 .36456 .36459 .36463 .36466 9.56426 .56431 .56435 .56439 .36666 .36670 .36673 .36677 9.56675 .56679 .56683 .56687 .36877 .36880 .36884 .36887 52 51 50 49 + 3' IS 14 15 9.55691 .55695 .55699 .55704 .36050 .36054 .36057 .36061 9.55943 .55947 .55951 .55955 .36360 .36364 .36367 .36371 9.56194 .56198 .56202 .56206 .36470 .36473 .36477 .36480 9.56443 .56447 .56451 .56456 .36680 .36684 .36687 .36691 9.56692 .56696 .56700 .56704 .36891 .36894 .36898 .36901 48 47 46 45 + 4' 17 18 19 9.55708 .55712 .55716 .55721 .36064 .36068 .38071 .36075 9.55960 .55964 .55968 .55972 .36374 .36378 .36381 .36385 9.56210 .56214 .56219 .56223 .36484 .36487 .36491 .36494 9.56460 .56464 .56468 .56472 .36694 .36698 .36701 .36705 9.56708 .56712 .56716 .56720 .36905 .36908 .36913 .36915 44 43 42 41 + r 21 22 2S 9.55725 .55729 .55733 .55737 .36078 .36083 .36085 .36089 9.55976 .55981 .55985 .55989 .36288 .36393 .36295 .36299 9.56227 .56231 .56235 .56239 .36498 .36501 .36505 .36508 9.56476 .56480 .56485 .56489 .36708 .36713 .36715 .36719 9.56725 .56729 .56733 .56737 9.56741 .56745 .56749 .56753 .36919 .36922 .36926 .36939 .36933 .36936 .36940 .36943 40 39 38 37 36 35 34 33 + 6' 25 26 27 9.55742 .55746 .55750 .55754 .36093 .36096 .36099 .36103 9.55993 .55997 .56001 .56006 .36303 .36306 .36309 .36313 9.56244 .56248 .56252 .56256 .36512 .36515 .36510 .36522 9.56493 .56497 .56501 .56505 .36733 .36736 .36729 .36733 + r 29 SO SI 9.55758 .55763 .55767 .55771 .36106 .36110 .36113 .36117 9.56010 .56014 .56018 .56022 .36316 .36320 .36323 .36327 9.56260 .56264 .56269 .56273 .36526 .36529 .36533 .36536 9.56509 .56514 .56518 .56522 .36736 .36740 .36743 .36747 9.56758 .56762 .56766 .56770 .36947 .36950 .36954 .36957 32 31 30 29 + S' SS S4 S5 9.55775 .55779 .55784 .55788 .36130 .36134 .36137 .36131 9.56027 .56031 .56035 .56039 .36330 .36334 .36337 .36341 9.56277 .56281 .56285 .56289 .36540 .36543 .36547 .36551 9.56526 .56530 .56534 .56538 .36750 .36754 .36757 .36761 9.56774 .56778 .56782 .56786 .36961 .36964 .36968 .36971 28 27 26 25 + 9' S7 38 39 9.55792 .55796 .55800 .55805 .36134 .36138 .36141 .36145 9.56043 .56047 .56052 .56056 .36344 .36348 .36351 .36355 9.56294 .56298 .56302 .56306 .36554 .36558 .36561 .36565 9.56543 .56547 .56551 .56555 .36764 .36768 .36771 .36775 9.56791 .56795 .56799 .56803 .36975 .36978 .36983 .36985 24 23 22 21 + 10' 41 42 43 9.55809 .55813 .55817 .55821 .36148 .36153 .36155 .36159 9.56060 .56064 .56068 .56073 .36358 .36363 .36365 .36368 9.56310 .56314 .56318 .56323 .36568 .36572 .36575 .36579 9.56559 .56563 .56567 .56572 .36778 .36782 .36785 .36789 9.56807 .56811 .56815 .56819 .36989 .36993 .36996 .36999 .37003 .37006 .37010 .37013 20 19 18 n 16 15 14 IS 12 11 10 9 + 11' 45 46 47 9.55826 .55830 .55834 .55838 .36163 .36166 .36169 .36173 9.56077 .56081 .56085 .56089 .36373 .36376 .36379 .36383 9.56327 .56331 .56335 .56339 .36582 .36586 .36589 .36593 9.56576 .56580 .56584 .56588 .36792 .36796 .36799 .36803 9.56824 .56828 .56832 .56836 + 13' 49 50 51 9.55842 .55846 .55851 .55855 .36176 .36180 .36183 .36187 9.56093 .56098 .56102 .56106 .36386 .36389 .36393 .36396 9.56343 .56348 .56352 .56356 .36596 .36600 .36603 .36607 .36610 .36614 .36617 .36631 9.56592 .56596 .56601 .56605 .36806 .36810 .36813 .36817 9.56840 .56844 .56848 .56852 .37017 .37030 .37034 .37037 + 13' 53 54 55 9.55859 .55863 .55867 .55872 .36190 .36194 .36197 .36301 9.56110 .56114 .56118 .56123 .36400 .36403 .36407 .36410 9.56360 .56364 .56368 .56373 9.56609 .56613 .56617 .56621 .36820 .36834 .36837 .36831 9.56856 .56861 .56865 .56869 .37031 .37034 .37038 .37041 .37045 .37049 .37053 .37055 8 7 6 5 4 3 2 1 + 14' 57 58 59 9.55876 .55880 .55884 .55888 .36304 .36308 .36311 .36215 9.56127 .56131 .56135 .56139 .36414 .36417 .36431 .36434 9.56377 .56381 .56385 .56389 .36634 .36638 .36631 .36635 9.56625 .56630 .56634 .56638 .36834 .36838 .36841 .36845 9.56873 .56877 .56881 .56885 + 15' 9.55893 .36318 9.56144 .36438 9.56393 .36638 9.56642 .36848 9.56889 .37059 19h 4m igh sm ighpn 1 19h im 1 ighom TABLE 45. [Page 871 Haversines. s 5A Orm 75° C 5* Jn» 75° 15' 5fc 2^ 75° 3(K 5h Sm 75° 45' 5h 4m 76° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.56889 .56893 .56898 .56902 .37059 .37063 .37066 .37070 9.57136 .57140 .57144 .57148 .37270 .37273 .37277 .37280 9.57381 .57385 .57389 .57393 .37481 .37485 .37488 .37492 9.57625 .57629 .57633 .57637 .37692 .37696 .37699 .37703 9.57868 .57872 .57876 .57881 .37904 .37907 .37911 .37914 60 59 58 57 + r 5 6 7 9.56906 .56910 .56914 .56918 .37073 .37077 .37080 .37084 9.57152 .57156 .57160 .57165 .37284 .37287 .37291 .37295 9.57397 .57402 .57406 .57410 .37495 .37499 .37502 .37506 9.57642 .57646 .57650 .57654 .37706 .37710 .37713 .37717 9.57885 .57889 .57893 .57897 .37918 .37922 .37925 .37029 56 55 54 53 52 51 50 49 48 47 46 45 + V 9 10 11 9.56922 .56926 .56931 .56935 .37087 .37091 .37094 .37098 9.57169 .57173 .57177 .57181 .37298 .37302 .37305 .37309 9.57414 .57418 .57422 .57426 .37509 .37513 .37516 .37520 9.57658 .57662 .57666 .57670 .37721 .37724 .37728 .37731 9.57901 .57905 .57909 .57913 .37932 .37936 .37939 .37943 + 3' 13 14 15 9.56939 .56943 .56947 .56951 .37101 .37105 .37108 .37113 9.57185 .57189 .57193 .57197 .37312 .37316 .37319 .37323 9.57430 .57434 .57438 .57442 .37523 .37527 .37530 .37534 9.57674 .57678 .57682 .57686 .37735 .37738 .37742 .37745 9.57917 .57921 .57925 .57929 .37946 .37950 .37953 .37957 + 4' 17 18 19 9.56955 .56959 .56963 .56968 .37U5 .37119 .37122 .37126 9.57201 .57205 .57210 .57214 .37326 .37330 .37333 .37337 9.57446 .57450 .57454 .57459 .37537 .37541 .37544 .37548 9.57690 .57694 .57698 .57702 .37749 .37752 .37756 .37759 9.57933 .57937 .57941 .57945 .37960 .37964 .37967 .37971 44 43 42 41 + 5' 21 22 23 9.56972 .56976 .56980 .56984 .37129 .37133 .37136 .37140 9.57218 .57222 .57226 .57230 .37340 .37344 .37347 .37351 9.57463 .57467 .57471 .57475 .37551 .37555 .37558 .37562 9.57706 .57711 .57715 .57719 .37763 .37766 .37770 .37773 9.57949 .57953 .57957 .57961 .37974 .37978 .37982 .37985 40 39 38 37 + 6' 25 26 27 9.56988 .56992 .56996 .57000 .37143 .37147 .37150 .37154 9.57234 .57238 .57242 .57246 .37354 .37358 .37361 .37365 9.57479 .57483 .57487 .57491 .37566 .37569 .37573 .37576 9.57723 .57727 .57731 .57735 .37777 .37780 .37784 .37788 9.57965 .57969 .57973 .57977 9.57981 .57986 .57990 .57994 .37989 .37992 .37996 .37999 36 35 34 S3 + r 29 30 31 9.57005 .57009 .57013 .57017 .37157 .37161 .37164 .37168 9.57250 .57255 .57259 .57263 .37368 .37372 .37375 .37379 9.57495 .57499 .57503 .57507 .37580 .37583 .37587 .37590 9.57739 .57743 .57747 .57751 .37791 .37794 .37798 .37802 .38003 .38006 .38010 .38013 32 31 30 29 + 8' 33 34 35 9.57021 .57025 .57029 .57033 .37171 .37175 .37179 .37182 9.57267 .57271 .57275 .57279 .37382 .37386 .37389 .37393 9.57511 .57516 .57520 .57524 .37594 .37597 .37601 .37604 9.57755 .57759 .57763 .57767 .37805 .37809 .37812 .37816 9.57998 .58002 .58006 .58010 .38017 .38020 .38024 .38027 28 27 26 25 + 9^ 37 38 39 9.57037 .57042 .57046 .57050 .37186 .37189 .37193 .37196 9.57283 .57287 .57291 .57295 .37397 .37400 .37404 .37407 9.57528 .57532 .57536 .57540 .37608 .37611 .37615 .37618 9.57771 .57775 .57779 .57783 .37819 .37823 .37826 .37830 9.58014 .58018 .58022 .58026 .38031 .38034 .38038 .38042 24 23 22 21 + W 41 42 43 9.57054 .57058 .57062 .57066 .37200 .37203 .37207 .37210 9.57299 .57304 .57308 .57312 .37411 .37414 .37418 .37421 9.57544 .57548 .57552 .57556 .37622 .37625 .37629 .37632 9.57787 .57792 .57796 .57800 .37833 .37837 .37840 .37844 9.58030 .58034 .58038 .58042 .38045 .38049 .38052 .38056 20 19 18 17 + 11' 45 46 47 9.57070 ,57074 .57078 .57083 .37214 .37217 .37221 .37224 9.57316 .57320 .57324 .57328 .37425 .37428 .37432 .37435 9.57560 .57564 .57568 .57572 .37636 .37639 .37643 .37647 9.57804 .57808 .57812 .57816 .37847 .37851 .37855 .37858 9.58046 .58050 .58054 .58058 9.58062 .58066 .58070 .58074 .38059 .38063 .38066 .38070 16 15 14 13 + 12' 49 50 51 9.57087 .57091 .57095 .57099 .37228 .37231 .37235 .37238 9.57332 .57336 .57340 .57344 .37439 .37442 .37446 .37449 9.57577 .57581 • .57585 .57589 .37650 .37654 .37657 .37661 9.57820 .57824 .57828 .57832 .37862 .37865 .37869 .37872 .38073 .38077 .38080 .38084 12 11 10 9 + 13' 53 54 55 9.57103 .57107 .57111 .57115 .37242 .37245 .37249 .37252 9.57348 .57353 .57357 .57361 .37453 .37456 .37460 .37463 9.57593 .57597 .57601 .57605 .37664 .37668 .37671 .37675 9.57836 .57840 .57844 .57848 .37876 .37879 .37883 .37886 9.58078 .58082 .58086 .58090 .38087 .38091 .38095 .38098 8 7 6 5 + W 57 58 59 9.57119 .57124 .57128 .57132 .37256 .37259 .37263 .37266 9.57365 .57369 .57373 .57377 .37467 .37470 .37474 .37477 9.57609 .57613 .57617 .57621 .37678 .37682 .37685 .37689 9.57852 .57856 .57860 .57864 .37890 .37893 .37897 .37900 9.58094 .58098 .58102 .58106 .38102 .38105 .38109 .38112 4 3 2 1 + 15' 9.57136 .37270 9.57381 .37481 9.57625 .37692 9.57868 .37904 9.58110 .38116 18T^59m 18^58:^ 18h 57m 18}i56m 18^ 55m Page 872] TABLE 45. Haversines, 8 Sh 5m U° 15' 1 5ft em 76° W 5h 7m 76° 45' 5h gm 77° O' 5h gm 77° W s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.58110 .58114 .58118 .58122 .38116 .38119 .38123 .38126 9.58351 .58355 .58359 .58363 .38328 .38331 .38335 .38338 9.58591 .58595 .58599 .58603 .38540 .38544 .38547 .38551 9.58830 .58834 .58838 .58842 .38752 .38756 .38760 .38763 9.59068 .59072 .59076 .59079 .38965 .38969 .38972 .38976 60 59 58 57 + r 5 6 7 9.58126 .58131 .58135 .58139 .38130 .38133 .38137 .38140 9.58367 .58371 .58375 .58379 .38342 .38345 .38349 .38352 9.58607 .58611 .58615 .58619 .38554 .38558 .38561 .38565 9.58846 .58850 .58854 .58858 .38767 .38770 .38774 .38777 9.59083 .59087 .59091 .59095 .38979 .38983 .38986 .38990 56 55 54 53 + It'' 9 10 11 9.58143 .58147 .58151 .58155 .38144 .38148 .38151 .38155 9.58383 .58387 .58391 .58395 .38356 .38360 .38363 .38367 9.58623 .58627 .58631 .58635 .38568 .38572 .38575 .38579 9.58862 ..58866 .58870 .58874 .38781 .38784 .38788 .38791 9.59099 .59103 .59107 .59111 .38994 .38997 .39001 .39004 52 51 50 49 + 3' IS 14 15 9.58159 .58163 .58167 .58171 .38158 .38162 .38165 .38169 9.58399 .58403 .58407 .58411 .38370 .38374 .38377 .38381 9.58639 .58643 .58647 .58651 .38582 .38586 .38590 .38593 9.58878 .58882 .58885 .58889 .38795 .38799 .38802 .38806 9.59115 .59119 .59123 .59127 .39008 .39011 .39015 .39018 48 47 46 45 + 4' 17 18 19 9.58175 .58179 .58183 .58187 .38172 .38176 .38179 .38183 9.58415 .58419 .58423 .58427 .38384 .38388 .38391 .38395 9.58655 .58659 .58663 .58667 .38597 .38600 .38604 .38607 9.58893 .58897 .58901 .58905 .38809 .38813 .38816 .38820 9.59131 .59135 .59139 .59143 .39022 .39025 .39029 .39033 44 43 42 41 + 5' 21 22 2S 9.58191 .58195 .58199 .58203 .38186 .38190 .38193 .38197 9.58431 .58435 .58439 .58443 .38398 .38402 .38406 .38409 9.58671 .58675 .58679 .58683 .38611 .38614 .38618 .38621 9.58909 .58913 .58917 .58921 .38823 .38827 .38830 .38834 9.59147 .59151 .59155 .59158 .39036 .39040 .39043 .39047 40 39 38 37 + 6' 25 26 27 9.58207 .58211 .58215 .58219 .38200 .38204 .38208 .38211 9.58447 .58451 .58455 .58459 .38413 .38416 .38420 .38423 9.58687 .58691 .58695 .58699 .38625 .38628 .38632 .38636 9.58925 .58929 .58933 .58937 .38837 .38841 .38845 .38848 9.59162 .59166 .59170 .59174 .39050 .39054 .39057 .39061 36 35 34 SS + r 29 SO SI 9.58223 .58227 .58231 .58235 .38215 .38218 .38222 .38225 9.58463 .58467 .58471 .58475 .38427 .38430 .38434 .38437 9.58703 .58707 .58711 .58715 .38639 .38643 .38646 .38650 9.58941 .58945 .58949 .58953 .38852 .38855 .38859 .38862 9.59178 .59182 .59186 .59190 .39064 .39068 .39072 .39075 S2 31 SO 29 + 8' SS S4 S5 9.58239 .58243 .58247 .58251 .38229 .38232 .38236 .38239 9.58479 .58483 .58487 .58491 .38441 .38444 .38448 .38451 9.58719 .58723 .58727 .58731 .38653 .38657 .38660 .38664 9.58957 .58961 .58965 .58969 .38866 .38869 .38873 .38876 9.59194 .59198 .59202 .59206 .39079 .39082 .39086 .39089 28 27 26 25 + 9' S7 S8 S9 9.58255 .58259 .58263 .58267 .38243 .38246 .38250 .38254 9.58495 .58499 .58503 .58507 .38455 .38459 .38462 .38466 9.58735 .58739 .58742 .58746 9.58750 .58754 .58758 .58762 .38667 .38671 .38675 .38678 9.58973 .58977 .58981 .58985 .38880 .38884 .38887 .38891 9.59210 .59214 .59218 .59222 .39093 .39096 .39100 .39103 24 23 22 21 + W 41 42 4S 9.58271 .58275 .58279 .58283 .38257 .38261 .38264 .38268 9.58511 .58515 .58519 .58523 .38469 .38473 .38476 .38480 .38682 .38685 .38689 .38692 9.58989 .58992 .58996 .59000 .38894 .38898 .38901 .38905 9.59225 .59229 .59233 .59237 .39107 .39111 .39114 .39118 20 19 18 17 + 11' 45 46 47 9.58287 .58291 .58295 .58299 .38271 .38275 .38278 .38282 9.58527 .58531 .58535 .58539 .38483 .38487 .38490 .38494 9.58766 .58770 .58774 .58778 .38696 .38699 .38703 .38706 9.59004 .59008 .59012 .59016 .38908 .38912 .38915 .38919 9.59241 .59245 .59249 .59253 .39121 .39125 .39128 .39132 16 15 14 13 49 50 51 9.58303 .58307 .58311 .58315 .38285 .38289 .38292 .38296 9.58543 .58547 .58551 .58555 .38498 .38501' .38505 .38508 9.58782 .58786 .58790 .58794 .38710 .38713 .38717 .38721 9.59020 .59024 .59028 .59032 .38923 .38926 .38930 .38933 9.59257 .59261 .59265 .59269 .39135 .39139 .39143 .39146 U 11 10 9 + 13' 5S 54 55 9.58319 .58323 .58327 .58331 .38299 .38303 .38307 .38310 9.58559 .58563 .58567 .58571 .38512 .38515 .38519 .38522 9.58798 .58802 .58806 .58810 .38724 .38728 .38731 .38735 9.59036 .59040 .59044 .59048 .38937 .38940 .38944 .38947 9.59273 .59277 .59281 .59285 .39150 .39153 .39157 .39160 8 7 6 5 + W 57 58 59 9.58335 .58339 .58343 .58347 .38314 .38317 .38321 .38324 9.58575 .58579 .58583 .58587 .38526 .38529 .38533 .38536 9.58814 .58818 .58822 .58826 .38738 .38742 .38745 .38749 9.59052 .59056 .59060 .59064 .38951 .38954 .38958 .38962 9.59289 .59292 .59296 .59300 .39164 .39167 .39171 .39174 4 S 2 1 + W 9.58351 .38328 9.58591 .38540 9.58830 .38752 9.59068 .38965 9.59304 .39178 18h 54"^ 18^ 5Sm 18h62m 18^ 5im 18h50m TABLE 45. [Page 873 Havereines. s 5hlom71°3(/ 5ft nm 77° 45' 5h 12m 78° C 5A ISm 78° 15' 5ft 14m 78° 30' 8 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.59304 .59308 .59312 .59316 .39178 .39182 .39185 .39189 9.59540 .59544 .59548 .59552 .39391 .39395 .39398 .39402 9.59774 .59778 .59782 .59786 .39604 .39608 .39612 .39615 9.60008 .60012 .60016 .60020 .39818 .39821 .39825 .39829 9.60240 .60244 .60248 .60252 .40032 .40035 .40039 .40042 + r 5 6 7 9.59320 .59324 .59328 .59332 .39193 .39196 .39199 .39203 9.59556 .59559 .59563 .59567 .39405 .39409 .39412 .39416 9.59790 .59794 .59798 .59802 .39619 .30622 .39626 .39629 9.60023 .60027 .60031 .60035 .39832 .39836 .39839 .39843 9.60256 .60260 .60263 .60267 .40046 .40049 .40053 .40057 56 55 54 53 + -y 9 10 11 9.59336 .59340 .59344 .59348 .39206 .39210 .39214 .39217 9.59571 .59575 .59579 .59583 .39420 .39423 .39427 .39430 9.59806 .59809 .59813 .59817 .39633 .39636 .39640 .39844 9.60039 .60043 .60047 .60051 .39846 .39850 .39854 .39857 9.60271 .60275 .60279 .60283 .40060 .40064 .40067 .40071 52 51 50 49 48 47 46 45 44 43 42 41 40 39 S8 37 + 3' IS 14 15 + 4' 17 18 19 9.59351 .59355 .59359 .59363 .39221 .39224 .39228 .39231 9.59587 .59591 .59595 .59599 .39434 .39437 .39441 .39444 9.59821 .59825 .59829 .59833 .39647 .39651 .39654 .39658 9.60054 .60058 .60062 .60066 .39861 .39864 .39868 .39871 9.60287 .60291 .60294 .60298 .40074 .40078 .40081 .40085 9.59367 .59371 .59375 .59379 .39235 .39238 .39242 .39245 9.59602 .59606 .59610 .59614 .39448 .39451 .39455 .39459 9.59837 .59841 .59845 .59848 .39661 .39665 .39668 .39672 9.60070 .60074 .60078 .60082 .39875 .39878 .39882 .39886 9.60302 .60306 .60310 .60314 .40089 .40092 .40096 .40099 + 5' 21 22 23 9.59383 .59387 .59391 .59395 .39249 .39253 .39256 .39260 9.59618 .59622 .59626 .59630 .39462 .3946G .39469 .39473 9.59852 .59856 .59860 .59864 .39676 .39679 .39683 .39686 9.60085 .60089 .60093 .60097 .39889 .39893 .39896 .39900 9.60318 .60321 .60325 .60329 .40103 .40106 .40110 .40114 + 6' 25 26 27 9.59399 .59403 .59406 .59410 .39263 .39267 .39270 .39274 9.59634 .59638 .59642 .59646 .39476 .39480 .39484 .39487 9.59868 .59872 .59876 .59880 .39690 .39693 .39697 .39700 9.60101 .60105 .60109 .60113 .39903 .39907 .39910 .39914 9.60333 .60337 .60341 .60345 .40117 .40121 .40124 .40128 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 + r 29 SO SI 9.59414 .59418 .59422 .59426 .39277 .39281 .39285 .39288 9.59649 .59653 .59657 .59661 .39491 .39494 .39498 .39501 9.59883 .59887 .59891 .59895 .39704 .39708 .39711 .39715 9.60116 .60120 .60124 .60128 .39918 .39921 .39925 .39928 9.60348 .60352 .60356 .60360 .40131 .40135 .40139 .40142 + 8' SS 34 35 9.59430 .59434 .59438 .59442 .39292 .39295 .39299 .39302 9.59665 .59669 .59673 .59677 .39505 .39508 .39512 .39516 9.59899 .59903 .59907 .59911 .39718 .39722 .39725 .39729 9.60132 .60136 .60140 .60144 .39932 .39935 .39939 .39943 9.60364 .60368 .60372 .60375 .40146 .40149 .40153 .40156 + 9^ 37 38 39 9.59446 .59450 .59454 .59458 .39306 .39309 .39313 .39317 9.59681 .59685 .59688 .59692 .39519 .39523 .39526 .39530 9.59915 .59918 .59922 .59926 .39732 .39736 .39739 .39743 9.60147 .60151 .60155 .60159 .39946 .39950 .39953 .39957 9.60379 .60383 .60387 .60391 .40160 .40163 .40167 .40171 + W 41 42 43 9.59461 .59465 .59469 .59473 .39320 .39324 .39327 .39331 9.59696 .59700 .59704 .59708 .39533 .39537 .39540 .39544 9.59930 .59934 .59938 .59942 .39746 .39750 .39754 .39757 9.60163 .60167 .60171 .60175 .39960 .39964 .39967 .39971 9.60395 .60399 .60402 .60406 .40174 .40178 .40181 .40185 + ir 45 46 47 9.59477 .59481 .59485 .59489 .39334 .39338 .39341 .39345 9.59712 .59716 .59720 .59724 .39548 .39551 .39555 .39558 9.59946 .59950 .59953 .59957 .39761 .39765 '39768 .39772 9.60178 .60182 .60186 .60190 .39975 .39978 .39982 .39985 9.60410 .60414 .60418 .60422 .40188 .40192 .40196 .40199 16 15 14 13 12 11 10 9 8 7 6 5 + ir 49 50 61 9.59493 .59497 .59501 .59505 .39348 .39352 .39356 .39359 9.59728 .59731 .59735 .59739 .39562 .39565 .39569 .39572 9.59961 .59965 .59969 .59973 .39775 .39779 .39782 .39786 9.60194 .60198 .60202 .60206 .39989 .39992 .39996 .40000 9.60426 .60429 .60433 .60437 .40203 .40206 .40210 .40213 + 13' 53 54 55 9.59508 .59512 .59516 .59520 .39363 .39366 .39370 .39373 9.59743 .59747 .59751 .59755 .39576 .39580 .39583 .39587 9.59977 .59981 .59985 .59988 .39789 .39793 .39796 .39800 9.60209 .60213 .60217 .60221 .40003 .40007 .40010 .40014 9.60441 .60445 .60449 .60452 .40217 .40220 .40224 .40228 + 14' 57 58 59 9.59524 .59528 .59532 .59536 .39377 .39380 .39384 .39388 9.59759 .59763 .59767 .59770 .39590 .39594 .39597 .39601 9.59992 .59996 .60000 .60004 .39803 .39807 .39811 .39814 9.60225 .60229 .60233 .60236 .40017 .40021 .40024 .40028 9.60456 .60460 .60464 .60468 .40231 .40235 .40238 .40242 4 3 2 1 + 15' 9.59540 .39391 9.59774 .39604 9.60008 .39818 9.60240 .40032 9.60472 .40245 18h 49m 18^48^ I8JI' 47m 18^ 4&^ 18^ 45^n Page 874] TABLE 45. Haversines. s 5h 15m 78° 45^ 5h 16m 79° 0^ 5h 17m 79° 15^ 5h 18m 79° 30^ 5h igm 79° 45/ s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.60472 .60476 .60479 .60483 .40345 .40349 .40353 .40356 9.60702 .60706 .60710 .60714 .40460 .40463 .40467 .40470 9.60931 .60935 .60939 .60943 .40674 .40677 .40681 .40685 9.61160 .61164 .61167 .61171 .40888 .40893 .40895 .40899 9.61387 .61391 .61395 .61399 .41103 .41106 .41110 .41114 60 59 58 57 + 1' 5 6 7 9.60487 .60491 .60495 .60499 .40360 .40363 .40367 .40370 9.60717 .60721 .60725 .60729 .40474 .40477 .40481 .40485 9.60947 .60951 .60954 .60958 .40688 .40693 .40695 .40699 9.61175 .61179 .61183 .61186 .40903 .40906 .40910 .40913 9.61402 .61406 .61410 .61414 .41117 .41131 .41134 .41138 56 55 54 53 + ■ 3^ 9 10 11 9.60502 .60506 .60510 .60514 .40374 .40377 .40381 .40385 9.60733 .60737 .60740 .60744 .40488 .40493 .40495 .40499 9.60962 .60966 .60970 .60973 .40703 .40706 .40710 .40713 9.61190 .61194 .61198 .61202 .40917 .40930 .40934 .40938 9.61417 .61421 .61425 .61429 .41131 .41135 .41139 .41143 52 51 50 49 + 3^ 13 14 15 9.60518 .60522 .60526 .60529 .40388 .40393 .40395 .40399 9.60748 .60752 .60756 .60760 .40503 .40506 .40510 .40513 9.60977 .60981 .60985 .60989 .40717 .40730 .40734 .40737 9.61205 .61209 .61213 .61217 .40931 .40935 .40938 .40943 9.61433 .61436 .61440 .61444 .41146 .41149 .41153 .41156 48 47 46 45 + 4^ n 18 19 9.60533 .60537 .60541 .60545 .40303 .40306 .40310 .40313 9.60763 .60767 .60771 .60775 .40517 .40530 .40534 .40537 9.60992 .60996 .61000 .61004 .40731 .40735 .40738 .40743 9.61221 .61224 .61228 .61232 .40945 .40949 .40953 .40956 9.61448 .61451 .61455 .61459 .41160 .41164 .41167 .41171 44 43 42 41 + 5^ 22 23 9.60549 .60552 .60556 .60560 .40317 .40330 .40334 .40338 9.60779 .60783 .60786 .60790 .40531 .40535 .40538 .40543 9.61008 .61012 .61015 .61019 .40745 .40749 '40753 .40756 9.61236 .61240 .61243 .61247 .40960 .40963 .40967 .40970 9.61463 .61467 .61470 .61474 .41174 .41178 .41183 .41185 40 39 38 37 + 6^ ^7 9.60564 .60568 .60572 .60576 .40331 .40335 .40338 .40343 9.60794 .60798 .60802 .60805 .40545 .40549 .40553 .40556 9.61023 .61027 .61031 .61034 .40760 .40763 .40767 .40770 9.61251 .61255 .61258 .61262 .40974 .40978 .40981 .40985 9.61478 .61482 .61485 .61489 .41189 .41193 .41196 .41199 36 35 34 33 + r 29 30 31 9.60579 .60583 .60587 .60591 .40345 .40349 .40353 .40356 9.60809 .60813 .60817 .60821 .40560 .40563 .40567 .40570 9.61038 .61042 .61046 .61050 .40774 .40777 .40781 .40785 9.61266 .61270 .61274 .61277 .40988 .40993 .40996 .40999 9.61493 .61497 .61500 .61504 .41303 .41307 .41310 .41314 32 31 SO 29 + 8^ 33 34 35 9.60595 .60599 .60602 .60606 .40360 .40363 .40367 .40370 9.60825 .60828 .60832 .60836 .40574 .40577 .40581 .40585 9.61053 .61057 .61061 .61065 .40788 .40793 .40795 .40799 9.61281 ..61285 .61289 .61293 .41003 .41006 .41010 .41013 9.61508 .61512 .61516 .61519 .41317 .41331 .41335 .41338 28 27 26 25 + 9^ 37 38 39 9.60610 .60614 .60618 .60622 .40374 .40377 .40381 .40385 9.60840 .60844 .60847 .60851 .40588 .40593 .40595 .40599 9.61069 .61072 .61076 .61080 .40803 .40806 .40810 .40813 9.61296 .61300 .61304 .61308 .41017 .41031 .41034 .41038 9.61523 .61527 .61531 .61534 .41333 .41335 .41239 .41342 24 23 22 21 + w 41 42 43 9.60625 .60629 .60633 .60637 .40388 .40393 .40395 .40399 9.60855 .60859 .60863 .60867 .40603 .40606 .40610 .40613 9.61084 .61088 .61091 .61095 .40817 .40830 .40834 .40837 9.61312 .61315 .61319 .61323 .41031 .41035 .41039 .41043 9.61538 .61542 .61546 .61549 .41346 .41250 .41353 .41357 20 19 18 17 + 11' ■45 47 9.60641 .60645 .60648 .60652 .40403 .40406 .40410 .40413 9.60870 .60874 .60878 .60882 .40617 .40630 .40634 .40637 9.61099 .61103 .61107 .61110 .40831 .40835 .40838 .40843 9.61327 .61330 .61334 .61338 .41046 .41049 .41053 .41056 9.61553 .61557 .61561 .61565 .41260 .41264 .41267 .41371 16 15 14 13 + 12^ 49 5i 9.60656 .60660 .60664 .60668 .40417 .40430 .40434 .40437 9.60886 .60890 .60893 .60897 .40631 .40635 .40638 .40643 9.61114 .61118 .61122 .61126 .40845 .40849 .40853 .40856 9.61342 .61346 .61349 .61353 .41060 .41063 .41067 .41071 9.61568 .61572 .61576 .61580 .41375 .41378 .41383 .41385 12 11 10 9 + 13^ 53 54 55 9.60671 .60675 .60679 .60683 .40431 .40434 .40438 .40443 9.60901 .60905 .60909 .60912 .40645 .40649 .40653 .40656 9.61129 .61133 .61137 .61141 .40860 .40863 .40867 .40870 9.61357 .61361 .61364 .61368 .41074 .41078 .41083 .41085 9.61583 .61587 .61591 .61595 .41389 .41393 .41396 .41300 8 7 6 5 57 55 59 9.60687 .60691 .60694 .60698 .40445 .40449 .40453 .40456 9.60916 .60920 .60924 .60928 .40660 .40663 .40667 .40670 9.61145 .61148 .61152 .61156 .40874 .40878 .40881 .40885 9.61372 .61376 .61380 .61383 .41089 .41093 .41096 .41099 9.61598 .61602 .61606 .61610 .41303 .41307 .41310 .41314 4 3 2 1 + 15^ 9.60702 .40460 9.60931 .40674 9.61160 .40888 9.61387 .41103 9.61614 .41318 18h44m 18fi 43^ 18^42^ 18h 4im 18h4am 1 TABLE 45. [Page 875 Haversinea. s 5fe 20'^ 80° (K 5h 21m 80° 15^ 5h 2pn 80° 30^ 5h 23m 80° 45' 5^^ 24'^ 81° O' 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.61614 .61617 .61621 .61625 .41318 .41331 .41325 .41338 9.61839 .61843 .61846 .61850 .41533 .41536 .41540 .41543 9.62063 .62067 .62071 .62074 .41748 .41751 .41755 .41758 9.62287 .62290 .62294 .62298 .41963 .41966 .41970 .41974 9.62509 .62513 .62516 .62520 .42178 .42182 .42185 .42189 60 59 58 57 + r 5 6 7 9.61629 .61632 .61636 .61640 .41332 .41335 .41339 .41343 9.61854 .61858 .61861 .61865 .41547 .41550 .41554 .41558 9.62078 .62082 .62086 .62089 .41762 .41766 .41769 .41773 9.62301 .62305 .62309 .62313 .41977 .41981 .41984 .41988 9.62524 .62527 .62531 .62535 .42193 .42196 .42200 .42303 56 55 54 53 + r 9 10 11 9.61644 .61647 .61651 .61655 .41346 .41350 .41353 .41357 9.61869 .61873 .61876 .61880 .41561 .41565 .41568 .41572 9.62093 .62097 .62100 .62104 .41776 .41780 .41783 .41787 9.62316 .62320 .62324 .62327 .41992 .41995 .41999 .42002 9.62538 .62542 .62546 .62550 .42307 .43311 .43314 .42218 52 51 50 49 48 47 46 45 44 43 42 41 + K 13 14 15 9.61659 .61662 .61666 .61670 .41361 .41364 .41368 .41371 9.61884 .61888 .61891 .61895 .41576 .41579 .41583 .41586 9.62108 .62112 .62115 .62119 .41791 .41794 .41798 .41801 9.62331 .62335 .62338 .62342 .42006 .42010 .42013 .42017 9.62553 .62557 .62561 .62564 .42221 .42225 .42239 .42333 + i' 17 18 19 9.61674 .61677 .61681 .61685 .41375 .41378 .41382 .41386 9.61899 .61903 .61906 .61910 .41590 .41593 .41597 .41601 9.62123 .62127 .62130 .62134 .41805 .41809 .41812 .41816 9.62346 .62350 .62353 .62357 .42020 .42024 .42027 .42031 9.62568 .62572 .62575 .62579 .42236 .43339 .43343 .43347 + 5' 21 22 23 9.61689 .61692 .61696 .61700 .41389 .41393 .41396 .41400 9.61914 .61917 .61921 .61925 .41604 .41608 .41611 .41615 9.62138 .62141 .62145 .62149 .41819 .41823 .41827 .41830 9.62361 .62364 .62368 .62372 .42035 .42038 .42042 .42045 9.62583 .62586 .62590 .62594 .43350 .42254 .42257 .42261 40 39 38 37 36 35 34 33 + 6^ 25 26 27 9.61704 .61708 .61711 .61715 .41404 .41407 .41411 .41414 9.61929 .61932 .61936 .61940 .41619 .41622 .41626 .41629 9.62153 .62156 .62160 .62164 .41834 .41837 .41841 .41844 9.62376 .62379 .62383 .62387 .42049 .42053 .42056 .42060 9.62598 .62601 .62605 .62609 .42264 .43368 .43373 .43375 + r 29 30 31 9.61719 .61723 .61726 .61730 .41418 .41421 .41425 .41429 9.61944 .61947 .61951 .61955 .41633 .41636 .41640 .41644 9.62168 .62171 .62175 .62179 .41848 .41852 .41855 .41859 9.62390 .62394 .62398 .62402 .42063 .42067 .42071 .42074 9.62612 .62616 .62620 .62623 .43379 .43383 .43386 .43290 32 31 30 29 28 27 26 25 24 23 22 21 + 8' 33 34 35 9.61734 .61738 .61741 .61745 .41432 .41436 .41439 .41443 9.61959 .61962 .61966 .61970 .41647 .41651 .41654 .41658 9.62182 .62186 .62190 .62194 .41862 .41866 .41870 .41873 9.62405 .62409 .62413 .62416 .42078 .42081 .42085 .42089 9.62627 .62631 .62634 .62638 .42293 .42297 .42300 .42304 + 9^ 37 38 39 9.61749 .61753 .61756 .61760 .41447 .41450 .41454 .41457 9.61974 .61977 .61981 .61985 .41662 .41665 .41669 .41672 9.62197 .62201 .62205 .62208 .41877 .41880 .41884 .41888 9.62420 .62424 .62427 .62431 .42092 .42096 .42099 .42103 9.62642 .62646 .62649 .62653 .42308 .42311 .42315 .42318 + W 41 42 43 9.61764 .61768 .61771 .61775 .41461 .41464 .41468 .41472 9.61989 .61992 .61996 .62000 .41676 .41679 .41683 .41687 9.62212 .62216 .62220 .62223 .41891 .41895 .41898 .41902 9.62435 .62439 .62442 .62446 .42106 .42110 .42114 .42117 9.62657 .62660 .62664 .62668 .43323 .43336 .43339 .43333 20 19 18 17 + 11^ 45 46 47 9.61779 .61783 .61786 .61790 .41475 .41479 .41482 .41486 9.62003 .62007 .62011 .62015 .41690 .41694 .41697 .41701 9.62227 .62231 .62234 .62238 .41905 .41909 .41913 .41916 9.62450 .62453 .62457 .62461 .42121 .42124 .42128 .42132 9.62671 .62675 .62679 .62682 .43336 .43340 .42344 .42347 16 15 14 IS 49 50 51 9.61794 .61798 .61801 .61805 .41490 .41493 .41497 .41500 9.62018 .62022 .62026 .62030 .41705 .41708 .41712 .41715 9.62242 .62246 .62249 .62253 .41920 .41923 .41927 .41931 9.62464 .62468 .62472 .62476 .42135 .42139 .42142 .42146 9.62686 .62690 .62693 .62697 .42351 .42354 .42358 .42361 12 11 10 9 + 13^ 53 54 55 9.61809 .61813 .61816 .61820 .41504 .41507 .41511 .41515 9.62033 .62037 .62041 .62045 .41719 .41722 .41726 .41730 9.62257 .62261 .62264 .62268 .41934 .41938 .41941 .41945 9.62479 .62483 .62487 .62490 .42150 .42153 .42157 .42160 9.62701 .62704 .62708 .62712 .42365 .42369 .43372 .42376 8 7 6 5 + W 57 58 59 9.61824 .61828 .61831 .61835 .41518 .41522 .41525 .41529 9.62048 .62052 .62056 .62059 .41733 .41737 .41740 .41744 9.62272 .62275 .62279 .62283 .41949 .41952 .41956 .41959 9.62494 .62498 .62501 .62505 .42164 .42168 .42171 .42175 9.62716 .62719 .62723 .62727 .42379 .42383 .42387 .42390 4 S 2 1 + 15^ 9.61839 .41533 9.62063 .41748 9.62287 .41963 9.62509 .42178 9.62730 .42394 18h 39m 18^ 38m J8h 37m 1 18^S6m 18^ 35-^ 21594°— 14- -48 TABLE 45. [Page 877 Haversines. s 5^50^82° 30' 5h 3lm 82° 45' 5ft 32m 83° 0' 5^ 33m 83° 15' 5h 34m 83° SO' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav 1 2 3 9.63823 .63826 .63830 .63833 .43474 .43477 .43481 .43485 9.64038 .64042 .64046 .64049 .43690 .43694 .43697 .43701 9.64253 .64256 .64260 .64264 .43907 .43910 .43914 .43917 9.64467 .64470 .64474 .64477 .44123 .44127 .44130 .44134 9.64679 .64683 .64686 .64690 .44340 .44343 .44347 .44351 60 59 58 57 + r 5 6 7 9.63837 .63841 .63844 .63848 .43488 .43492 .43495 .43499 9.64053 .64056 .64060 .64063 .43704 .43708 .43712 .43715 9.64267 .64271 .64274 .64278 .43921 .43925 .43928 .43932 9.64481 .64484 .64488 .64492 .44138 .44141 .44145 .44148 9.64694 .64697 .64701 .64704 .44354 .44358 .44362 .44365 56 55 54 53 + r 9 10 11 9.63851 .63855 .63859 .63862 .43503 .43506 .43510 .43513 9.64067 .64071 .64074 .64078 .43719 .43723 .43726 .43730 9.64281 .64285 .64289 .64292 .43935 .43939 .43943 .43946 9.64495 .64499 .64502 .64506 .44152 .44156 .44159 .44163 9.64708 .64711 .64715 .64718 .44369 .44372 .44376 .44380 52 51 50 49 48 47 46 45 + 3' 13 14 15 9.63866 .63869 .63873 .63877 .43517 .43521 .43524 .43528 9.64081 .64085 .64088 .64092 .43733 .43737 .43741 .43744 9.64296 .64299 .64303 .64306 .43950 .43953 .43957 .43961 9.64509 .64513 .64516 .64520 .44166 .44170 .44174 .44177 9.64722 .64725 .64729 .64732 .44383 .44387 .44390 .44394 + 4^ 17 18 19 9.63880 .63884 .63887 .63891 .43531 .43535 .43539 .43542 9.64096 .64099 .64102 .64106 .43748 .43751 .43755 .43759 9.64310 .64314 .64317 .64321 .43964 .43968 .43972 .43975 9.64523 .64527 .64531 .64534 .44181 .44185 .44188 .44192 9.64736 .64740 .64743 .64747 .44398 .44401 .44405 .44408 U 43 42 41 + 5' 21 22 23 9.63895 .63898 .63902 .63905 .43546 .43549 .43553 .43557 9.64110 .64113 .64117 .64121 .43762 .43766 .43769 .43773 9.64324 .64328 .64331 .64335 .43979 .43982 .43986 .43990 9.64538 .64541 .64545 .64548 .44195 .44199 .44203 .44206 9.64750 .64754 .64757 .64761 .44412 .44416 .44419 .44423 40 39 38 37 + 8' 25 26 27 9.63909 .63913 .63916 .63920 .43560 .43564 .43567 .43571 9.64124 .64128 .64131 .64135 .43777 .43780 .43784 .43787 9.64339 .64342 .64346 .64349 .43993 .43997 .44000 .44004 .44008 .44011 .44015 .44018 9.64552 .64555 .64559 .64563 9.64566 .64570 .64573 .64577 .44210 .44213 .44217 .44221 9.64764 .64768 .64771 .64775 .44427 .44430 .44434 .44437 36 35 34 33 + r 29 30 31 9.63923 .63927 .63931 .63934 .43575 .43578 .43582 .43585 9.64139 .64142 .64146 .64149 .43791 .43795 .43798 .43802 9.64353 .64356 .64360 .64363 .44224 .44228 .44231 .44235 9.64778 .64782 .64785 .64789 .44441 .44445 .44448 .44452 32 31 30 29 + 8' 33 34 35 9.63938 .63941 .63945 .63949 .43589 .43593 .43596 .43600 9.64153 .64156 .64160 .64164 .43805 .43809 .43813 .43816 9.64367 .64371 .64374 .64378 .44022 .44026 .44029 .44033 9.64580 .64584 .64587 .64591 .44239 .44242 .44246 .44250 9.64793 .64796 .64800 .64803 .44455 .44459 .44463 .44466 28 27 26 25 + 9' 37 38 39 9.63952 .63956 .63959 .63963 .43603 .43607 .43611 .43614 9.64167 .64171 .64174 .64178 .43820 .43824 .43827 .43831 9.64381 .64385 .64388 .64392 .44036 .44040 •44U44 .44047 9.64594 .64598 .64602 .64605 .44253 .44257 .44260 .44264 9.64807 .64810 .64814 .64817 .44470 .44474 .44477 .44481 24 23 22 21 + 10' 41 42 43 9.63966 .63970 .63974 .63977 .43618 .43622 .43625 .43629 9.64181 .64185 .64189 .64192 .43834 .43838 .43842 .43845 9.64396 .64399 .64403 .64406 .44051 .44055 .44058 .44062 9.64609 .64612 .64616 .64619 .44268 .44271 .44275 .44278 9.64821 .64824 .64828 .64831 .44484 .44488 .44492 .44495 20 19 18 17 + ir 45 46 ■^7 9.63981 .63984 .63988 .63992 .43632 .43636 .43640 .43643 9.64196 .64199 .64203 .64206 9.64210 .64214 .64217 .64221 .43849 .43852 .43856 .43860 .43863 .43867 .43870 .43874 9.64410 .64413 .64417 .64420 .44065 .44069 .44073 .44076 9.64623 .64626 .64630 .64633 .44282 .44286 .44289 .44293 9.64835 .64838 .64842 .64845 .44499 .44502 .44506 .44510 16 15 14 13 + 12' 49 50 51 9.63995 .63999 .64002 .64006 .43647 .43650 .43654 .43658 9.64424 .64428 .64431 .64435 .44080 .44083 .44087 .44091 9.64637 1 .44296 .64640 .44300 .64644 .44304 .64648 .44307 9.64849 .64852 .64856 .64860 .44513 .44517 .44521 .44524 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.64010 .64013 .64017 .64020 .43661 .43665 .43668 .43672 9.64224 .64228 .64231 .64235 .43878 .43881 .43885 .43888 9.64438 .64442 .64445 .64449 .44094 .44098 .44101 .44105 9.64651 .64655 .64658 .64662 .44311 .44315 .44318 .44322 9.64863 .64867 .64870 .64874 .44528 .44531 .44535 .44539 + 14' 57 68 59 9.64024 .64028 .64031 .64035 .43676 .43679 .43683 .43686 9.64239 .64242 .64246 .64249 .43892 .43896 .43899 .43903 9.64452 .64456 .64460 .64463 .44109 .44112 .44116 .44120 9.64665 .64669 .64672 .64676 .44325 .44329 .44333 .44336 9.64877 .64881 .64884 .64888 .44542 .44546 .44549 .44553 4 S 2 1 + 15' 9.64038 .43690 9.64253 .43907 9.64467 .44123 9.64679 .44340 9.64891 .44557 18h 29m 18J>'2S^ 18h 27m 18^ 26m 18h 25m Page 878] TABLE 45. Haversines. s 5h 35m 83° 45' 5A 36m 84° C 5h 37m 84° 15' 5h 38m 84° 3^ 5h 39m 84° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.64891 .64895 .64898 .64902 .M557 .44560 .44564 .44568 9.65102 .65106 .65109 .65113 .44774 .44777 .44781 .44784 9.65312 .65316 .65319 .65323 .44991 .44994 .44998 .45001 9.65521 .65525 .65528 .65532 .45308 .45311 .45315 .45319 9.65729 .65733 .65736 .65740 .45435 .45439 .45433 .45436 60 59 58 57 + r 5 6 7 9.64905 .64909 .64912 .64916 .44571 .44575 .44578 .44583 9.65116 1.65120 .65123 .65127 -.44788 .44793 .44795 .44799 9.65326 .65330 .65333 ♦.65337 .45005 .45009 .45013 .45016 9.65535 .65539 .65542 .65546 .45333 .45336 .45339 .45333 9.65743 .65747 .65750 .65754 .45439 .45443 .45447 .45450 56 55 54 53 + V 9 10 11 9.64919 .64923 .64926 .64930 .44586 .44589 .44593 .44596 9.65130 .65134 .65137 .65141 .44803 .44806 .44810 .44813 9.65340 .65344 .65347 .65351 .45030 .45033 .45037 .45030 9.65549 .65553 .65556 .65559 .45337 .45340 .45244 .45348 9.65757 .65761 .65764 .65767 .45454 .45458 .45461 .45465 52 51 50 49 + r 13 14 15 9.64934 .64937 .64941 .64944 .44600 .44604 .44607 .44611 9.65144 .65148 .65151 .65155 .44817 .44831 .44834 .44838 9.65354 .65358 .65361 .65365 .45034 .45038 .45041 .45045 9.65563 .65566 .65570 .65573 .45351 .45335 .45358 .45362 9.65771 .65774 .65778 .65781 .45468 .45472 .45476 .45479 48 47 46 45 44 43 42 41 + 4' 17 18 19 9.64948 .64951 .64955 .64958 .44614 .44618 .44623 .44635 9.65158 .65162 .65165 .65169 .44831 .44835 .44839 .44843 9.65368 .65372 .65375 .65378 .45048 .45053 .45056 .45059 9.65577 .65580 .65584 .65587 .45266 .45269 .45273 .45276 9.65785 .65788 .65792 .65795 .45483 .45486 .45490 .45494 + 5' 21 22 23 9.64962 .64965 .64969 .64972 .44639 .44633 .44636 .44640 9.65172 .65176 .65179 .65183 .44846 .44850 .44853 .44857 9.65382 .65385 .65389 .65392 .45063 .45067 .45070 .45074 9.65591 .65594 .65598 .65601 .45280 .45284 .45287 .45391 9.65799 .65802 .65806 .65809 .45497 .45501 .45505 .45508 40 39 38 37 + 6' 25 26 27 9.64976 .64979 .64983 .64986 .44643 .44647 .44651 .44654 9.65186 .65190 .65193 .65197 .44860 .44864 .44868 .44871 9.65396 .65399 .65403 .65406 .45077 .45081 .45085 .45088 9.65605 .65608 .65612 .65615 .45395 .45398 .45303 .45305 9.65812 .65816 .65819 .65823 .45513 .45515 .45519 .45523 36 35 34 33 + r 29 30 31 9.64990 .64993 .64997 .65000 .44658 .44661 .44665 .44669 9.65200 .65204 .65207 .65211 .44875 .44878 .44883 .44886 9.65410 .65413 .65417 .65421 .45093 .45096 .45099 .45103 9.65619 .65622 .65625 .65629 .45309 .45313 .45316 .45330 9.65826 .65830 .65833 .65837 .45526 .45530 .45534 .45537 32 31 SO 29 + 8' 33 34 35 9.65004 .65007 .65011 .65014 .44673 .44676 .44680 .44683 9.65214 .65218 .65221 .65225 .44889 .44893 .44897 .44900 9.65424 .65427 .65431 .65434 .45106 .45110 .45114 .45117 9.65632 .65636 .65639 .65643 .45334 .45337 .45331 .45334 9.65840 .65844 .65847 .65850 .45541 .45544 .45548 .45553 28 27 26 25 + 9^ 37 38 39 9.65018 .65021 .65025 .65028 .44687 .44690 .44694 .44698 9.65228 .65232 .65235 .65239 .44904 .44907 .44911 .44915 9.65438 .65441 .65445 .65448 .45131 .45134 .45138 .45133 9.65646 .65650 .65653 .65657 .45338 .45343 .45345 .45349 9.65854 .65857 .65861 .65864 .45555 .45559 .45563 .45566 24 23 22 21 + W 41 42 43 9.65032 .65035 .65039 .65043 .44701 .44705 .44708 .44713 9.65242 .65246 .65249 .65253 .44918 .44933 .44935 .44939 9.65452 .65455 .65459 .65462 .45135 .45139 .45143 .45146 9.65660 .65664 .65667 .65671 .45353 .45356 .45360 .45363 9.65868 .65871 .65875 .65878 .45570 .45573 .45577 .46581 20 19 18 17 16 15 14 13 + 11' 45 46 47 9.65046 .65050 .65053 .65057 .44716 .44719 .44733 .44737 9.65256 .65260 .65263 .65267 .44933 .44936 .44940 .44944 9.65466 .65469 .65473 .65476 .45150 .45153 .45157 .45161 9.65674 .65677 .65681 .65684 .45367 .45371 .45374 .45378 9.65881 .65885 .65888 .65892 .45584 .45f88 .45592 .45595 + ly 49 50 51 9.65060 .65064 .65067 .65071 .44730 .44734 .44737 .44741 9.65270 .65274 .65277 .65281 .44947 .44951 .44954 .44958 9.65480 .65483 .65486 .65490 .45164 .45168 .45173 .45175 9.65688 .65691 .65695 .65698 .45381 .45385 .45389 .45393 9.65895 .65899 .65902 .65906 .45599 .45603 .45606 .45610 12 11 10 9 + 13' 53 54 55 9.65074 .65078 .65081 .65085 .44745 .44748 .44753 .44755 9.65284 .65288 .65291 .65295 .44963 .44965 .44969 .44973 9.65493 .65497 .65500 .65504 .45179 .45183 .45186 .45190 9.65702 .65705 .65709 .65712 .45396 .45400 .45403 .45407 9.65909 .65913 .65916 .65919 .45613 .45617 .45630 .45634 8 7 6 5 + ir 57 58 59 9.65088 .65092 .65095 .65099 .44759 .44763 .44766 .44770 9.65298 .65302 .65305 .65309 .44976 .44980 .44983 .44987 9.65507 .65511 .65514 .65518 .45193 .45197 .45300 .45304 9.65716 .65719 .65722 .65726 .45410 .45414 .45418 .45431 9.65923 .65926 .65930 .65933 .45628 .45631 .45635 .45639 4 3 2 1 + W 9.65102 .44774 9.65312 .44991 9.65521 .45308 9.65729 .45435 9.65937 .45643 iSh 24^ ish 23m 18^ 22m 18h 2im 18^ 20m TABLE 45. [Page 879 Haversines. s 5ft 4^ 85° (K 1 5h 41"^ 85° 15' 5h 42^ 85° Sr 5h 43m 85° 45' 5A^'n86°0' 1 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. s 1 2 S 9.65937 .65940 .65944 .65947 .45642 .45646 .45649 .45653 9.66143 .66146 .66150 .66153 .45860 .45863 .45867 .45870 9.66348 .66352 .66355 .66359 .46077 .46081 .46084 .46088 9.66553 .66556 .66560 .66563 .46295 .46298 .46302 .46305 9.66757 .66760 .66763 .66767 .46512 .46516 .46519 .46523 60 59 58 57 56 55 54 53 + r 5 6 7 9.65950 .65954 .65957 .65961 .45657 .45660 .45664 .45668 9.66157 .66160 .66164 .66167 .45874 .45878 .45881 .45885 9.66362 .66366 .66369 .66372 .46092 .46095 .46099 .46102 9.66567 .66570 .66573 .66577 .46309 .46313 .46316 .46320 9.66770 .66774 .66777 .66780 .46527 .46530 .46534 .46538 + 3' 9 10 11 9.65964 .65968 .65971 .65975 .45671 .45675 .45678 .45682 9.66170 .66174 .66177 .66181 .45889 .45892 .45896 .45899 9.66376 .66379 .66383 .66386 .46106 .46110 .46113 .46117 9.66580 .66584 .66587 .66590 .46324 .46327 .46331 .46334 9.66784 .66787 .66791 .66794 .46541 .46545 .46548 .46552 52 51 50 49 1^ 14 15 9.65978 .65981 .65985 .65988 .45686 .45689 .45693 .45697 9.66184 .66188 .66191 .66194 .45903 .45907 .45910 .45914 9.66389 .66393 .66396 .66400 .46121 .46124 .46128 .46131 9.66594 .66597 .66601 .66604 .46338 .46342 .46345 .46349 9.66797 .66801 .66804 .66807 .46556 .46559 .46563 .46567 48 47 46 45 + 4^ 17 18 19 9.65992 .65995 .65999 .66002 .45700 .45704 .45707 .45711 9.66198 .66201 .66205 .66208 .45918 .45921 .45925 .45928 9.66403 .66407 .66410 .66413 .46135 .46139 .46142 .46146 9.66607 .66611 .66614 .66618 .46353 .46356 .46360 .46363 9.66811 .66814 .66818 .66821 .46570 .46574 .46577 .46581 44 43 42 41 + 5' 21 22 2S 9.66006 .66009 .66012 .66016 .45715 .45718 .45722 .45726 9.66212 .66215 .66218 .66222 .45932 .45936 .45939 .45943 9.66417 .66420 .66424 .66427 .46150 .46153 .46157 .46161 9.66621 .66624 .66628 .66631 .46367 .46371 .46374 .46378 9.66824 .66828 .66831 .66835 .46585 .46588 .46592 .46596 40 39 38 37 + 6' 25 26 27 9.66019 .66023 .66026 .66030 .46729 .45733 .45736 .45740 9.66225 .66229 .66232 .66236 .45947 .45950 .45954 .45957 9.66430 .66434 .66437 .66441 .46164 .46168 .46171 .46175 9.66635 .66638 .66641 .66645 .46382 .46385 .46389 .46392 9.66838 .66841 .66845 .66848 .46599 .46603 .46606 .46610 36 *65 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 + r 29 SO SI 9.66033 .66037 .66040 .66043 .45744 .45747 .45751 .45755 9.66239 .66242 .66246 .66249 .45961 .45965 .45968 .45972 9.66444 .66447 .66451 .66454 .46179 .46182 .46186 .46189 9.66648 .66652 .66655 .66658 .46396 .46400 .46403 .46407 9.66851 .66855 .66858 .66862 .46614 .46617 .46621 .46625 + 8^ SS S4 S5 9.66047 .66050 .66054 .66057 .45758 .45762 .45765 .45769 9.66253 .66256 .66260 .66263 .45976 .45979 .45983 .45986 9.66458 .66461 .66464 .66468 .46193 .46197 .46200 .46204 9.66662 .66665 .66669 .66672 .46411 .46414 .46418 .46421 9.66865 .66868 .66872 .66875 .46628 .46632 .46636 .46639 + 9^ S7 S8 S9 9.66061 .66064 .66067 .66071 .45773 .45776 .45780 .45783 9.66266 .66270 .66273 .66277 .45990 .45994 .45997 .46001 9.66471 .66475 .66478 .66482 .46208 .46211 .46215 .46218 9.66675 .66679 .66682 .66685 .46425 .46429 .46432 .46436 9.66878 .66882 .66885 .66889 .46643 .46646 .46650 .46654 + 1(K 41 42 4S 9.66074 .66078 .66081 .66085 .45787 .45791 .45794 .45798 9.66280 .66284 .66287 .66290 .46005 .46008 .46012 .46015 9.66485 .66488 .66492 .66495 .46222 .46226 .46229 .46233 9.66689 .66692 .66696 .66699 .46440 .46443 .46447 .46451 9.66892 .66895 .66899 .66902 .46657 .46661 .46665 .46668 + 11' 45 46 47 9.66088 .66092 .66095 .66098 .45802 .45805 .45809 .45812 9.66294 .66297 .66301 .66304 .46019 .46023 .46026 .46030 9.66499 .66502 .66505 .66509 .46237 .46240 .46244 .46247 9.66702 .66706 .66709 .66713 .46454 .46458 .46461 .46465 9.66905 .66909 .66912 .66916 .46672 .46675 .46679 .46683 16 15 14 13 12 11 10 9 8 7 6 5 49 50 51 9.66102 .66105 .66109 .66112 .45816 .45820 .45823 .45827 9.66307 .66311 .66314 .66318 .46034 .46037 .46041 .46044 9.66512 .66516 .66519 .66522 .46251 .46255 .46258 .46262 9.66716 .66719 .66723 .66726 .46469 .46472 .46476 .46480 9.66919 .66922 .66926 .66929 .46686 .46690 .46694 .46697 + W 53 54 55 9.66116 .66119 .66122 .66126 .45831 .45834 .45838 .45841 9.66321 .66325 .66328 .66331 .46048 .46052 .46055 .46059 9.66526 .66529 .66533 .66536 .46266 .46269 .46273 .46276 9.66730 .66733 .66736 .66740 .46483 .46487 .46490 .46494 9.66932 .66936 .66939 .66943 .46701 .46704 .46708 .46712 + 14' 57 58 59 9.66129 .66133 .66136 .66140 .45845 .45849 .45852 .45856 9.66335 .66338 .66342 .66345 .46063 .46066 .46070 .46073 9.66539 .66543 .66546 .66550 .46280 .46284 .46287 .46291 9.66743 .66747 .66750 .66753 .46498 .46501 .46505 .46509 9.66946 .66949 .66953 .66956 .46715 .46719 .46723 .46726 4 3 2 1 + 15' 9.66143 .45860 9.66348 .46077 9.66553 .46295 9.66757 .46512 9.66959 .46730 18^ 19m 18^ 18m 18^ 17m 18^ 16m 18^ 15m Page 880] TABLE 45. Haversines. s 5ft 45™ 86° 15' 5ft 46"» 86° 30' 5ft 47m 86° 45' 5ft 4^ 87° 0' 5ft ^9™ 87° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.66959 .66963 .66966 .66970 .46730 .46733 .46737 .46741 9.67161 .67165 .67168 .67171 .46948 .46951 .46955 .46958 9.67362 .67366 .67369 .67372 .47165 .47169 .47173 .47176 9.67562 .67566 .67569 .67572 .47383 .47387 .47390 .47394 9.67762 .67765 .67768 .67772 .47601 .47605 .47608 .47612 60 59 58 57 + r 5 6 7 9.66973 .66976 .66980 .66983 .46744 .46748 .46752 .46755 9.67175 .67178 .67181 .67185 .46962 .46966 .46969 .46973 9.67376 .67379 .67382 .67386 .47180 .47184 .47187 .47191 9.67576 .67579 .67582 .67586 .47398 .47401 .47405 .47409 9.67775 .67778 .67782 .67785 .47616 .47619 .47623 .47627 66 65 54 63 + r 9 10 11 9.66986 .66990 .66993 .66997 .46759 .46762 .46766 .46770 9.67188 .67192 .67195 .67198 .46977 .46980 .46984 .46987 9.67389 .67392 .67396 .67399 .47194 .47198 .47202 .47205 9.67589 .67592 .67596 .67599 .47412 .47416 .47420 .47423 9.67788 .67792 .67795 .67798 .47630 .47634 .47637 .47641 52 51 50 49 + 3' 13 14 15 9.67000 .67003 .67007 .67010 .46773 .46777 .46781 .46784 9.67202 .67205 .67208 .67212 .46991 .46995 .46998 .47002 9.67402 .67406 .67409 .67412 .47209 .47213 .47216 .47220 9.67602 .67606 .67609 .67612 .47427 .47430 .47434 .47438 9.67801 .67805 .67808 .67811 .47645 .47648 .47652 .47656 48 47 46 45 17 18 19 9.67013 .67017 .67020 .67023 .46788 .46792 .46795 .46799 9.67215 .67218 .67222 .67225 .47006 .47009 .47013 .47017 9.67416 .67419 .67422 .67426 .47223 .47227 .47231 .47234 9.67616 .67619 .67622 .67626 .47441 .47445 .47449 .47452 9.67815 .67818 .67821 .67825 9.67828 .67831 .67835 .67838 .47659 .47663 .47666 .47670 44 43 42 41 + 5' 21 22 23 9.67027 .67030 .67034 .67037 .46802 .46806 .46810 .46813 9.67228 .67232 .67235 .67238 .47020 .47024 .47027 .47031 9.67429 .67432 .67436 .67439 .47238 .47242 .47245 .47249 9.67629 .67632 .67636 .67639 .47456 .47459 .47483 .47467 .47674 .47677 .47681 .47685 40 39 38 37 36 36 34 33 32 31 30 29 28 27 26 25 + 6' «5 26 27 9.67040 .67044 .67047 .67050 .46817 .46821 .46824 .46828 9.67242 .67245 .67249 .67252 .47035 .47038 .47042 .47046 9.67443 .67446 .67449 .67452 .47252 .47256 .47260 .47263 9.67642 .67646 .67649 .67652 .47470 .47474 .47478 .47481 9.67841 .67844 .67848 .67851 .47688 .47692 .47696 .47699 + r 29 30 31 9.67054 .67057 .67060 .67064 .46831 .46835 .46839 .46842 9.67255 .67259 .67262 .67265 .47049 .47053 .47056 .47060 9.67456 .67459 .67462 .67466 .47267 .47271 .47274 .47278 9.67656 .67659 .67662 .67666 .47485 .47489 .47492 .47496 9.67854 .67858 .67861 .67864 .47703 .47706 .47710 .47714 .47717 .47721 .47725 .47728 + 8' 33 34 35- 9.67067 .67071 .67074 .67077 .46846 .46850 .46853 .46857 9.67269 .67272 .67275 .67279 .47064 .47067 .47071 .47075 9.67469 .67472 .67476 .67479 .47282 .47285 .47289 .47292 9.67669 .67672 .67675 .67679 .47499 .47503 .47507 .47510 9.67868 .67871 .67874 .67878 + 9' 37 38 39 9.67081 .67084 .67087 .67091 .46860 .46864 .46868 .46871 9.67282 .67285 .67289 .67292 .47078 .47082 .47086 .47089 9.67483 .67486 .67489 .67493 .47296 .47300 .47303 .47307 9.67682 .67685 .67689 .67692 .47514 .47518 .47521 .47525 9.67881 .67884 .67887 .67891 .47732 .47735 .47739 .47743 24 23 22 21 20 19 18 17 + lO' 41 42 43 9.67094 .67097 .67101 .67104 .46875 .46879 .46882 .46886 9.67295 .67299 .67302 .67305 .47093 .47096 .47100 .47104 9.67496 .67499 .67503 .67506 .47311 .47314 .47318 .47321 9.67695 .67699 .67702 .67705 .47528 .47532 .47536 .47539 9.67894 .67897 .67901 .67904 .47746 .47750 .47754 .47757 + 11' 45 46 47 9.67108 .67111 .67114 .67118 .46890 .46893 .46897 .46900 9.67309 .67312 .67315 .67319 .47107 .47111 .47115 .47118 9.67509 .67512 .67516 .67519 .47325 .47329 .47332 .47336 9.67709 .67712 .67715 .67719 .47543 .47547 .47550 .47554 9.67907 .67911 .67914 .67917 .47761 .47765 .47768 .47772 16 16 14 13 12 11 10 9 + 12' 49 50 51 9.67121 .67124 .67128 .67131 .46904 .46908 .46911 .46915 9.67322 .67326 .67329 .67332 .47122 .47125 .47129 .47123 9.67522 .67526 .67529 .67532 .47340 .47343 .47347 .47351 9.67722 .67725 .67729 .67732 .47558 .47561 .47565 .47568 9.67920 .67924 .67927 .67930 .47775 .47779 .47783 .47786 + 13' 53 54 55 9.67134 .67138 .67141 .67145 .46919 .46922 .46926 .46929 9.67336 .67339 .67342 .67346 .47136 .47140 .47144 .47147 9.67536 .67539 .67542 .67546 .47354 .47358 .47361 .47365 9.67735 .67738 .67742 .67745 .47572 .47576 .47579 .47583 9.67934 .67937 .67940 .67944 .47790 .47794 .47797 .47801 8 7 6 5 + 14' 57 55 59 9.67148 .67151 .67155 .67158 .46933 .46937 .46940 .46944 9.67349 .67352 .67356 .67359 .47151 .47155 .47158 .47162 9.67549 .67552 .67556 .67559 .47369 .47372 .47376 .47380 9.67748 .67752 .67755 .67758 .47587 .47590 .47594 .47597 9.67947 .67950 .67953 .67957 .47805 .47808 .47812 .47815 4 3 2 1 + 15' 9.67161 .46948 9.67362 .47165 9.67562 .47383 9.67762 .47601 9.67960 .47819 18h 14^ 15ft 13m 18 ft /^w ISh 11m Igh lO-m 1 TABLE 45. [Page 881 Haversines. s 5h 50m 87° 30' 5h Sm 87° 45' 5h 52m 88° 0' 5ft 53m 88° 15' 5fc 54™ 88° 30' s Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.67960 .67963 .67967 .67970 .47819 .47833 .47826 .47830 9.68158 .68161 .68164 .68167 .48037 .48041 .48044 .48048 9:68354 .68358 .68361 .68364 .48255 .48259 .48262 .48266 9.68550 .68553 .68557 .68560 .48473 .48477 .48480 .48484 9.68745 .68748 .68751 .68755 .48691 .48695 .48698 .48702 60 59 58 57 + r 5 6 7 9.67973 .67977 .67980 .67983 .47834 .47837 .47841 .47844 .47848 .47852 .47855 .47850 9.68171 .68174 .68177 .68181 .48053 .48055 .48059 .48062 9.68367 .68371 .68374 .68377 .48269 .48273 .48277 .48280 9.68563 .68566 .68570 .68573 .48488 .48491 .48495 .48499 9.68758 .68761 .68764 .68768 .48706 .48709 .48713 .48717 56 55 54 53 52 51 50 49 + V 9 10 11 9.67986 .67990 .67993 .67996 9.68184 .68187 .68190 .68194 9.68197 .68200 .68204 .68207 .48066 .48070 .48073 .48077 9.68380 .68384 .68387 .68390 .48284 .48288 .48291 .48295 9.68576 .68579 .68583 .68586 .48502 .48506 .48509 .48513 9.68771 .68774 .68777 .68781 .48720 .48724 .48728 .48731 + 3' 13 14 15 9.68000 .68003 .68006 .68010 .47863 .47866 .47870 .47874 .48081 .48084 .48088 .48092 9.68393 .68397 .68400 .68403 .48299 .48302 .48306 .48310 9.68589 .68592 .68596 .68599 .48517 .48520 .48524 .48528 9.68784 .68787 .68790 .68794 .48735 .48738 .48742 .48746 48 47 46 45 + 4' 17 18 19 9.68013 .68016 .68019 .68023 .47877 .47881 .47884 .47888 9.68210 .68213 .68217 .68220 .48095 .48099 .48102 .48106 9.68407 .68410 .68413 .68416 .48313 .48317 .48320 .48324 9.68602 .68605 .68609 .68612 .48531 .48535 .48538 .48542 9.68797 .68800 .68803 .68806 .48749 .48753 .48757 .48760 U 43 42 41 + 5' 21 22 23 9.68026 .68029 .68033 .68036 .47892 .47895 .47899 .47903 9.68223 .68227 .68230 .68233 .48110 .48113 .48117 .48121 9.68420 .68423 .68426 .68429 .48328 .48331 .48335 .48339 9.68615 .68618 .68622 .68625 .48546 .48549 .48553 .48557 9.68810 .68813 .68816 .68820 .48764 .48767 .48771 .48775 40 39 38 37 36 35 34 S3 + 6' 25 26 27 9.68039 .68042 .68046 .68049 .47906 .47910 .47913 .47917 9.68236 .68240 .68243 .68246 .48124 .48128 .48131 .48135 9.68433 .68436 .68439 .68442 .48342 .48346 .48350 .48353 9.68628 .68631 .68635 .68638 .48560 .48564 .48568 .48571 9.68823 .68826 .68829 .68832 .48778 .48782 .48786 .48789 + r 29 30 31 9.68052 .68056 .68059 .68062 .47921 .47924 .47928 .47932 9.68249 .68253 .68256 .68259 .48139 .48142 .48146 .48150 9.68446 .68449 .68452 .68456 .48357 .48360 .48364 .48368 9.68641 .68644 .68648 .68651 .48575 .48578 .48582 .48586 9.68836 .68839 .68842 .68845 .48793 .48797 .48800 .48804 32 31 30 29 28 27 26 25 + 8' 33 34 35 9.68066 .68069 .68072 .68075 .47935 .47939 .47943 .47946 9.68263 .68266 .68269 .68272 .48153 .48157 .48161 .48164 9.68459 .68462 .68465 .68469 .48371 .48375 .48379 .48382 9.68654 .68657 .68661 .68664 .48589 .48593 .48597 .48600 9.68849 .68852 .68855 .68858 .48807 .48811 .48815 .48818 + r 37 38 39 9.68079 .68082 .68085 .68089 .47950 .47953 .47957 .47961 9.68276 .68279 .68282 .68286 .48168 .48171 .48175 .48179 9.68472 .68475 .68478 .68482 .48386 .48389 .48393 .48397 9.68667 .68670 .68674 .68677 .48604 .48608 .48611 .48615 9.68862 .68865 .68868 .68871 .48822 .48826 .48829 .48833 24 23 22 21 20 19 18 17 -f W 41 42 43 9.68092 .68095 .68098 .68102 .47964 .47968 .47972 .47975 9.68289 .68292 .68295 .68299 .48182 .48186 .48190 .48193 9.68485 .68488 .68491 .68495 .48400 .48404 .48408 .48411 9.68680 .68683 .68687 .68690 .48618 .48622 .48626 .48629 9.68875 .68878 .68881 .68884 .48837 .48840 .48844 .48847 + 11' 45 46 47 9.68105 .68108 .68112 .68115 .47979 .47983 .47986 .47990 9.68302 .68305 .68308 .68312 .48197 .48201 .48204 .48208 9.68498 .68501 .68504 .68508 .48415 .48419 .48422 .48426 9.68693 .68696 .68700 .68703 .48633 .48637 .48640 .48644 9.68887 .68891 .68894 .68897 .48851 .48855 .48858 .48862 16 15 14 13 12 11 10 9 + n' 49 50 51 9.68118 .68121 .68125 .68128 .47993 .47997 .48001 .48004 9.68315 .68318 .68322 .68325 .48211 .48215 .48219 .48222 9.68511 .68514 .68517 .68521 .48429 .48433 .48437 .48440 9.68706 .68709 .68713 .68716 .48648 .48651 .48655 .48658 9.68900 .68904 .68907 .68910 .48866 .48869 .48873 .48877 + 13' 53 54 55 9.68131 .68135 .68138 .68141 .48008 .48012 .48015 .48019 9.68328 .68331 .68335 .68338 .48226 .48230 .48233 .48237 9.68524 .68527 .68531 .68534 .48444 .48448 .48451 .48455 9.68719 .68722 .68726 .68729 .48662 .48666 .48669 .48673 9.68913 .68917 .68920 .68923 .48880 .48884 .48887 .48891 8 7 6 5 + 14' 57 58 59 9.68144 .68148 .68151 .68154 .48022 .48026 .48030 .48033 9.68341 .68344 .68348 .68351 .48241 .48244 .48248 .48251 9.68537 .68540 .68544 .68547 .48459 .48462 .48466 .48469 9.68732 .68735 .68739 .68742 .48677 .48680 .48684 .466S8 9.68926 .68929 .68933 .68936 .48895 .48898 .48902 .48906 4 3 2 1 + 15' 9.68158 .48037 9.68354 .48255 9.68550 .48473 9.68745 .48691 9.68939 .48909 18h9m IghS^ 15A7TO 18^ em 18h5m Page 882] TABLE 45. Haversines. s 5A 55TO 88° 45' 6h S&m 89° r 5ft 57m 89° 15' 5ft 55W 89° 30' 5ft 59m 89° 45' s Log. Hav. Nat. Hav, Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. I-og. Hav. Nat. Hav. 1 2 S 9.68939 .68942 .68946 .68949 .48909 .48913 .48917 .48930 9.69132 .69136 .69139 .69142 .49137 .49131 .49135 .49138 9.69325 .69328 .69331 .69334 .49346 .49349 .49353 .49356 9.69516 .69520 .69523 .69526 .49564 .49567 .49571 .49575 9.69707 .69710 .69713 .69717 .49782 .49785 .49789 .49793 60 59 58 57 + y 5 6 7 9.68952 .68955 .68958 .68962 .48934 .48937 .48931 .48935 9.69145 .69148 .69152 .69155 .49143 .49146 .49149 .49153 9.69338 .69341 .69344 .69347 .49360 .49364 .49367 .49371 9.69529 .69532 .69535 .69539 .49578 .49583 .49585 .49589 9.69720 .69723 .69726 .69729 .49796 .49800 .49804 .49807 56 65 54 5S + 2^ 9 10 11 9.68965 .68968 .68971 .68975 .48938 .48942 .48946 .48949 9.69158 .69161 .69164 .69168 .49156 .49160 .49164 .49167 9.69350 .69354 .69357 .69360 .49375 .49378 .49383 .49386 9.69542 .69545 .69548 .69551 .49593 .49596 .49600 .49604 9.69732 .69736 .69739 .69742 .49811 .49815 .49818 .49822 52 51 50 49 + 3^ IS 14 15 9.68978 .68981 .68984 .68988 .48953 .48957 .48960 .48964 9.69171 .69174 .69177 .69181 .49171 .49175 .49178 .49182 9.69363 .69366 .69370 .69373 .49389 .49393 .49396 .49400 9.69555 .69558 .69561 .69564 .49607 .49611 .49615 .49618 9.69745 .69748 .69751 .69755 .49835 .49839 .49833 .49836 48 47 46 45 44 43 42 41 + 4' 17 18 19 9.68991 .68994 .68997 .69000 .48967 .48971 .48975 .48978 9.69184 .69187 .69190 .69193 .49186 .49189 .49193 .49196 9.69376 .69379 .69382 .69386 .49404 .49407 .49411 .49415 9.69567 .69570 .69574 .69577 .49632 .49635 .49639 .49633 9.69758 .69761 .69764 .69767 .49840 .49844 .49847 .49851 + ^ 21 22 2S 9.69004 .69007 .69010 .69013 .48983 .48986 .48989 .48993 9.69197 .69200 .69203 .69206 .49300 .49304 .49307 .49311 9.69389 .69392 .69395 .69398 .49418 .49433 .49436 .49439 9.69580 .69583 .69586 .69590 .49636 .49640 .49644 .49647 9.69770 .69774 .69777 .69780 .49855 .49858 .49863 .49865 40 39 38 37 + 6' 25 26 27 9.69017 .69020 .69023 .69026 .48997 .49000 .49004 .49007 9.69209 .69213 .69216 .69219 .49315 .49318 .49333 .49326 9.69402 .69405 .69408 .69411 .49433 .49436 .49440 .49444 9.69593 .69596 .69599 .69602 .49851 .49655 .49658 .49663 9.69783 .69786 .69789 .69793 .49869 .49873 .49876 .49880 36 35 S4 33 + r 29 SO SI 9.69029 .69033 .69036 .69039 .49011 .49015 .49018 .49033 9.69222 .69225 .69229 .69232 .49339 .49233 .49336 .49340 9.69414 .69417 .69421 .69424 .49447 .49451 .49455 .49458 9.69605 .69609 .69612 .69615 .49665 .49869 .49673 .49676 9.69796 .69799 .69802 .69805 .49884 .49887 .49891 .49895 32 31 SO 29 + 8' 5-5 S4 S5 9.69042 .69046 .69049 .69052 .49036 .49039 .49033 .49036 9.69235 .69238 .69242 .69245 .49244 .49247 .49251 .49355 9.69427 .69430 .69433 .69437 .49463 .49465 .49469 .49473 9.69618 .69621 .69625 .69628 .49680 .49684 .49687 .49691 9.69808 .69812 .69815 .69818 .49898 .49903 .49905 .49909 28 27 26 25 + 9^ S7 S8 S9 9.69055 .69058 .69062 .69065 .49040 .49044 .49047 .49051 9.69248 .69251 .69254 .69258 .49358 .49362 .49366 .49369 9.69440 .69443 .69446 .69449 .49476 .49480 .49484 .49487 9.69631 .69634 .69637 .69640 .49695 .49898 .49703 .49705 9.69821 .69824 .69827 .69831 .49913 .49916 .49930 .49934 24 23 22 21 + W 41 42 4S 9.69068 .69071 .69074 .69078 .49055 .49058 .490 i3 .49066 9.69261 .69264 .69267 .69270 .49273 .49276 .49380 .49284 9.69453 .69456 .69459 .69462 .49491 .49495 .49498 .49503 9.69644 .69647 .69650 .69653 .49709 .49713 .49716 .49730 9.69834 .69837 .69840 .69843 .49937 .49931 .49935 .49938 20 19 18 17 + 11' 45 46 47 9.69081 .69084 .69087 .69091 .49069 .49073 .49076 .49080 9.69274 .69277 .69280 .69283 .49287 .49291 .49295 .49298 9.69465 .69469 .69472 .69475 .49506 .49509 .49513 .49516 9.69656 .69659 .69663 .69666 .49734 .49727 .49731 .49735 9.69846 .69850 .69853 .69856 .49943 .49945 .49949 .49953 16 15 14 IS + 12' 49 50 51 9.69094 .69097 .69100 .69103 .49084 .49087 .49091 .49095 9.69286 .69290 .69293 .69296 .49302 .49306 .49309 .49313 9.69478 .69481 .69484 .69488 .49530 .49524 .49527 .49531 9.69669 .69672 .69675 .69678 .49738 .49743 .49745 .49749 9.69859 .69862 .69865 .69869 .49956 .49960 .49964 .49967 12 11 10 9 + 13' 5S 54 55 9.69107 .69110 .69113 .69116 .49098 .49103 .49106 .49109 9.69299 .69302 .69306 .69309 .49316 .49330 .49334 .49337 9.69491 .69494 .69497 .69500 .49535 .49538 .49542 .49545 9.69682 .69685 .69688 .69691 .49753 .49756 .49760 .49764 9.69872 .69875 .69878 .69881 .49971 .49975 .49978 .49983 8 7 6 5 + 14' 57 58 59 9.69120 .69123 .69126 .69129 .49113 .49116 .49130 .49134 9.69312 .69315 .69318 .69322 .49331 .49335 .49338 .49343 9.69504 .69507 .69510 .69513 .49549 .49553 .49556 .49560 9.69694 .69698 .69701 .69704 .49767 .49771 .49775 .49778 9.69884 .69888 .69891 .69894 .49985 .49989 .49993 .49997 4 3 2 1 + 16' 9.69132 .49137 9.69325 .49346 9.69516 .49564 9.69707 .49783 9.69897 .50000 18h4m 18^ Sm, 18h2m iShim IShQm TABLE 45. [Page 883 Haversines. s 6A Oni 90° (K 1 6Aim90°15' 1 6h 2m 90° SO' 6h sm 90° 45' | 6h 4m 91° (K 1 8 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.69897 .69900 .69903 .69906 .50000 .50004 .50007 .50011 9.70086 .70089 .70092 .70096 .50218 .50222 .50225 .50229 9.70274 .70277 .70281 .70284 .50436 .50440 .50444 .50447 9.70462 .70465 .70468 .70471 .50654 .50658 .50662 .50665 9.70648 .70652 .70655 .70658 .50873 .50876 .50880 .50884 60 59 68 57 + y 5 6 7 9.69910 .69913 .69916 .69919 .50015 .50018 .50022 .50025 9.70099 .70102 .70105 .70108 .50233 .50236 .50240 .50244 9.70287 .70290 .70293 .70296 .60451 .50455 .60458 .50462 9.70474 .70477 .70480 .70484 .50669 .50673 .60676 .50680 9.70661 .70664 .70667 .70670 .60887 .50891 .50894 .50898 56 55 54 5S 52 51 50 49 + V 9 10 11 9.69922 .69925 .69929 .69932 .50029 .50033 .50036 .50040 9.70111 .70114 .70118 .70121 .50247 .50251 .50255 .50258 9.70299 .70303 .70306 .70309 .50465 .50469 .60473 .50476 9.70487 .70490 .70493 .70496 .50684 .60687 .50691 .50694 9.70673 .70670 .70679 .70683 .50902 .50906 .50909 .60913 + 3' IS 14 15 9.69935 .69938 .69941 .69944 .50044 .50047 .50051 .50055 9.70124 .70127 .70130 .70133 .50262 .50265 .50269 .50273 9.70312 .70315 .70318 .70321 .50480 .50484 .50487 .50491 9.70499 .70502 .70505 .70509 .60698 .50702 .50706 .60709 9.70686 .70689 .70692 .70695 .50916 .60920 .60924 .60927 48 47 46 45 44 4S 42 41 40 39 38 37 + *' 17 18 19 9.69948 .69951 .69954 .69957 .50058 .50062 .50065 .50069 9.70136 .70140 .70143 .70146 .50276 .50280 .50284 .50287 9.70324 .70328 .70331 .70334 .50495 .50498 .50502 .50505 9.70512 .70515 .70518 .70521 .60713 .50716 .50720 .50724 9.70698 .70701 .70704 .70707 .50931 .50934 .60938 .50942 .60946 .50949 .60953 .50956 + 6' 21 22 2S 9.69960 .69963 .69966 .69970 .50073 .50076 .50080 .50084 9.70149 .70152 .70155 .70158 .50291 .50295 .50298 .50302 9.70337 .70340 .70343 .70346 .50509 .50513 .50616 .50620 9.70524 .70527 .70530 .70533 .50727 .60731 .60734 .50738 9.70710 .70714 .70717 .70720 + ^ 25 26 27 9.69973 .69976 .69979 .69982 .50087 .50091 .50095 .50098 9.70161 .70165 .70168 .70171 .50305 .50309 .50313 .50316 9.70349 .70353 .70356 .70359 .60524 .50627 .60531 .50534 9.70537 .70540 .70543 .70546 .50742 .50745 .50749 .60753 9.70723 .70726 .70729 .70732 .50960 .50964 .50967 .50971 36 35 34 33 32 31 30 29 + r 29 SO SI 9.69985 .69988 .69992 .69995 .50102 .50105 .50109 .50113 9.70174 .70177 .70180 .70183 .50320 .50324 .50327 .50331 9.70362 .70365 .70368 .70371 .50538 .60542 .50546 .50649 9.70549 .70552 .70555 .70558 .60756 .60760 .50764 .60767 9.70735 .70738 .70741 .70745 .60974 .60978 .60982 .50985 + 8' S3 S4 S5 9.69998 .70001 .70004 .70007 .50116 .50120 .50124 .50127 9.70187 .70190 .70193 .70196 .50335 .50338 .50342 .50345 9.70374 .70378 .70381 .70384 .60653 .60666 .60560 .50564 9.70561 .70565 .70568 .70571 .50771 .60774 .50778 .50782 9.70748 .70751 .70754 .70757 .50989 .50993 .50996 .51000 28 27 26 25 + 9^ S7 S8 ■ S9 9.70011 .70014 .70017 .70020 .50131 .50135 .5013S .50142 9.70199 .70202 .70205 .70209 .50349 .50353 .50356 .50360 9.70387 .70390 .70393 .70396 .50567 .50571 .50674 .50678 9.70574 .70577 .70580 .70583 .50785 .50789 .60793 .50796 9.70760 .70763 .70766 .70769 .51004 .61007 .51011 .51014 24 23 22 21 + W 41 42 4S 9.70023 .70026 .70029 .70033 .50145 .50149 .50153 .50156 9.70212 .70215 .70218 .70221 .50364 .50367 .50371 .50375 9.70399 .70402 .70406 .70409 .60682 .60585 .50589 .50693 9.70586 .70589 .70593 .70596 .60800 .50804 .50807 .50811 9.70772 .70775 .70779 .70782 .51018 .51022 .51026 .61029 20 19 18 17 + ir 45 46 47 9.70036 .70039 .70042 .70045 .50160 .50164 .50167 .50171 9.70224 .70227 .70230 .70234 .50378 .50382 .50385 .50389 9.70412 .70415 .70418 .70421 .50596 .50600 .60604 .60607 9.70599 .70602 .70605 .70608 .50814 .50818 .50822 .60826 9.70785 .70788 .70791 .70794 .51033 .51036 .61040 .61043 16 15 14 IS + nt' 49 50 51 9.70048 .70051 .70055 .70058 .50175 .50178 .50182 .50185 9.70237 .70240 .70243 .70246 .50393 .50396 .50400 .50404 9.70424 .70427 .70431 .70434 .60611 .60614 .60618 .50622 9.70611 .70614 .70617 .70620 .50829 .50833 .50836 .60840 9.70797 .70800 .70803 .70806 .51047 .51061 .51064 .51068 12 11 10 9 + 13' 5S 54 55 9.70061 .70064 .70067 .70070 .50189 .50193 .50196 .50200 9.70249 .70252 .70256 .70259 .50407 .50411 .50415 .50418 9.70437 .70440 .70443 .70446 .50626 .60629 .50633 .50636 9.70624 .70627 .70630 .70633 .50844 .60847 .50851 .50854 9.70809 .70813 .70816 .70819 .61062 .51065 .61069 .51073 8 7 6 5 4- W 57 58 59 9.70074 .70077 .70080 .70083 .50204 .50207 .50211 .50215 9.70262 .70265 .70268 .70271 .60422 .50425 .50429 .50433 9.70449 .70452 .70456 .70459 .60640 .50644 .50647 .60661 9.70636 .70639 .70642 .70645 .50868 .50862 .50865 .50869 9.70822 .70825 .70828 .70831 .61076 .51080 .51083 .61087 4 3 2 1 + 15' 9.70086 .50218 9.70274 .50436 9.70462 .50654 9.70648 .50873 9.70834 .51091 17h 59m 17n 58m 17h 57m 17h 56m 17h 55^ Page 884] TABLE 45. Haversines. s 6ft .5TO 91° 15^ 6h em 91° 30' eh Tm 91° 45' en gm 92° (y 6h gm 92° 15/ s Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.70834 .70837 .70840 .70843 .51091 .51094 .51098 .51102 9.71019 .71022 .71025 .71028 .51309 .51312 .51316 .51320 9.71203 .71206 .71210 .71213 .51527 .51531 .51534 .51538 9.71387 .71390 .71393 .71396 .51745 .51749 .51752 .51756 9.71569 .71572 .71575 .71579 .51963 .51967 .51970 .51974 60 59 58 57 + 1' 5 6 7 9.70847 .70850 .70853 .70856 .51105 .51109 .51113 .51116 9.71032 .71035 .71038 .71041 .51323 .51327 .51331 .51334 9.71216 .71219 .71222 .71225 .51541 .51545 .51549 .51552 9.71399 .71402 .71405 .71408 .51760 .51763 .51767 .51770 9.71582 .71585 .71588 .71591 .51978 .51981 .51985 .51988 56 55 64 53 + 3' 9 10 11 9.70859 .70862 .70865 .70868 .51120 .51123 .51127 .51131 9.71044 .71047 .71050 .71053 .51338 .51342 .51345 .51349 9.71228 .71231 .71234 .71237 .51556 .51560 .51563 .51567 9.71411 .71414 .71417 .71420 .51774 .51778 .51781 .51785 9.71594 .71597 .71600 .71603 .51992 .51996 .51999 .52003 52 51 50 49 + 3' 13 14 15 9.70871 .70874 .70877 .70881 .51134 .51138 .51142 .51145 9.71056 .71059 .71062 .71065 .51352 .51356 .51360 .51363 9.71240 .71243 .71246 .71249 .51571 .51574 .51578 .51581 9.71423 .71426 .71430 .7H33 .51789 .51792 .51796 .51799 9.71606 .71609 .71612 .71615 .62007 .62010 .52014 .52018 48 47 46 45 + r 17 18 19 9.70884 .70887 .70890 .70893 .51149 .51153 .51156 .51160 9.71068 .71072 .71075 .71078 .51367 .51371 .51374 .51378 9.71252 .71255 .71259 .71262 .51585 .51589 .51592 .51596 9.71436 .71439 .71442 .71445 .51803 .51807 .51810 .51814 9.71618 .71621 .71624 .71627 .52021 .52025 .52028 .62032 44 43 42 41 + 5' f5 9.70896 .70899 .70902 .70905 .51163 .51167 .51171 .51174 9.71081 .71084 .71087 .71090 .51382 .51385 .51389 .51392 9.71265 .71268 .71271 .71274 .51600 .51603 .51607 .51611 9.71448 .71451 .71454 .71457 .51818 .51821 .51825 .51829 9.71630 .71633 .71636 .71639 .52036 .52039 .52043 .52047 40 39 38 37 36 35 34 33 + 6' ;g7 9.70908 .70911 .70914 .70918 .51178 .51182 .51185 .51189 9.71093 .71096 .71099 .71102 .51396 .51400 .51403 .51407 9.71277 .71280 .71283 .71286 .51614 .51618 .51621 .51625 9.71460 .71463 .71466 .71469 .51832 .51836 .51839 .51843 9.71642 .71645 .71648 .71651 .52050 .52054 .52057 .52061 + r 29 . SI '' 9.70921 .70924 .70927 .70930 .51193 .51198 .51200 .51203 9.71105 .71108 .71111 .71114 .51411 .51414 .51418 .51422 9.71289 .71292 .71295 .71298 .51629 .51632 .51636 .51640 9.71472 .71475 .71478 .71481 .51847 .51850 .51854 .51858 9.71654 .71657 .71660 .71663 .62065 .52068 .52072 .52076 32 31 30 29 + 8' 34 I 35 9.70933 .70936 .70939 .70942 .51207 .51211 .51214 .51218 9.71118 .71121 .71124 .71127 .51425 .51429 .51432 .51436 9.71301 .71304 .71307 .71311 .51643 .51647 .51650 .51654 9.71484 .71487 .71490 .71493 .51861 .51865 .51869 .51872 9.71666 .71670 .71673 .71676 .52079 .52083 .62087 .52090 28 27 26 25 + ^ 37 s 38 39 9.70945 .70948 .70951 .70955 .51222 .51225 .51229 .51233 9.71130 .71133 .71136 .71139 .51440 .51443 .51447 .51451 9.71314 .71317 .71320 .71323 .51658 .51661 .51665 .51669 9.71496 .71500 .71503 .71506 .51876 .51879 .51883 .51887 9.71679 .71682 .71685 .71688 .62094 .62097 .62101 .52105 24 23 22 21 + W 41 42 43 9.70958 .70961 .70964 .70967 .51236 .51240 .51243 .51247 9.71142 .71145 .71148 .71151 .51454 .51458 .51462 .51465 9.71326 .71329 .71332 .71335 .51672 .51676 .51680 .51683 9.71509 .71512 .71515 .71518 .51890 .51894 .51898 .51901 9.71691 .71694 .71697 .71700 .62108 .52112 .52116 .52119 20 19 18 17 + tr 45 46 47 9.70970 .70973 .70976 .70979 .51251 .51254 .51258 .51262 9.71154 .71157 .71161 .71164 .51469 .51472 .51476 .51480 9.71338 .71341 .71344 .71347 .51687 .51690 .51694 .51698 9.71521 .71524 .71527 .71530 .51905 .51908 .51912 .51916 9.71703 .71706 .71709 .71712 .53123 .52126 .52130 .62134 16 15 14 13 12 11 10 9 + 12' 50 5i 9.70982 .70985 .70988 .70992 .51265 .51269 .51273 .51276 9.71167 .71170 .71173 .71176 .51483 .51487 .51491 .51494 9.71350 .71353 .71356 .71359 .51701 .51705 .51709 .51712 9.71533 .71536 .71539 .71542 .51919 .51923 .51927 .51930 9.71715 .71718 .71721 .71724 .52137 .62141 .52145 .52148 + 13' 53 54 55 9.70995 .70998 .71001 .71004 .51380 .51283 .51287 .51291 9.71179 .71182 .71185 .71188 .514d8 .51501 .51505 .51508 9.71362 .71365 .71369 .71372 .51716 .51720 .51723 .51727 9.71545 .71548 .71551 .71554 .51934 .51938 .51941 .51945 9.71727 .71730 .71733 .71736 .52152 .52156 .62159 .53163 i8 '.7 '6 '5 4 3 f + 14' 57 55 59 9.71007 .71010 .71013 .71016 .51294 .51298 .51302 .51305 9.71191 .71194 .71197 .71200 .51512 .51516 .51520 .51523 9.71375 .71378 .71381 .71384 .51730 .51734 .51738 .51741 9.71557 .71560 .71563 .71566 .61948 .61952 .51956 .51959 9.71739 .71742 .71745 .71748 .53166 .53170 .53174 .53177 4- 16' 9.71019 .51309 9.71203 .51527 9.71387 .51745 9.71569 .51963 9.71751 .52181 17h 54'^ 171). 5Sm 27A5fTO 17h 5im 17h50m ■> TABLE 45. [Page 886 Havereines. s 6h lom 93° SiK 6h im 92° 45' 6A 12m 93° 0' 6h 13m 93° 15' 6h 14m 930 3(K s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.71751 .71754 .71757 .71760 .52181 .52185 .52188 .52192 9.71932 .71935 .71938 .71941 .52399 .52403 .52406 .52410 9.72112 .72115 .72118 .72121 .52617 .52620 .52624 .52628 9.72292 .72295 .72298 .72301 .52835 .52838 .52842 .52846 9.72471 .72474 .72476 .72479 9.72482 .72485 .72488 .72491 .53052 .53056 .53060 .53063 60 59 58 57 + 1' 5 6 7 9.71763 .71766 .71769 .71772 .52196 .52199 .52203 .52206 9.71944 .71947 .71950 .71953 .52413 .52417 .52421 .52424 9.72124 .72127 .72130 .72133 .52631 .52635 .52639 .52642 9.72304 .72307 .72310 .72313 .52849 .52853 .52856 .52860 .53067 .53071 .53074 .53078 56 55 54 53 + 3' 9 10 11 9.71775 .71778 .71781 .71784 .52210 .52214 .52217 .52221 9.71956 .71959 .71962 .71965 .52428 .52432 .52435 .52439 9.72136 .72139 .72142 .72145 .52646 .52649 .52653 .52657 9.72316 .72319 .72322 .72325 .52864 .52867 .52871 .52875 9.72494 .72497 .72500 .72503 9.72506 .72509 .72512 .72515 .53081 .53085 .53089 .53092 .53096 .53100 .53103 .53107 52 51 50 49 48 47 46 45 + 3^ 13 14 15 9.71787 .71791 .71794 .71797 .52225 .52228 .52232 .52235 9.71968 .71971 .71974 .71977 .52442 .52446 ,52450 .52453 9.72148 .72151 .72154 .72157 .52660 .52664 .52668 .52671 9.72328 .72331 .72334 .72337 .52878 .52882 .52885 .52889 + 4' 17 18 19 9.71800 .71803 .71806 .71809 .52239 .52243 .52246 .52250 9.71980 .71983 .71986 .71989 .52457 .52461 .52464 .52468 9.72160 .72163 .72166 .72169 .52675 .52679 .52682 .52686 9.72340 .72343 .72346 .72349 .52893 .52896 .52900 .52904 9.72518 .72521 .72524 .72527 .53110 .53114 .53118 .53121 44 43 42 41 + 5' ^/ 22 23 9.71812 .71815 .71818 .71821 .52254 .52257 .52261 .52264 .52268 .52272 .52275 .52279 .52283 .52286 .52290 .52294 9 71992 .71995 .71998 .72001 9.72004 .72007 .72010 .72013 .52472 .52475 .52479 .52482 9.72172 .72175 .72178 .72181 .52689 .52693 .52697 .52700 9.72352 .72354 .72357 .72360 .52907 .52911 .52915 .52918 9.72530 .72533 .72536 .72539 .53125 .53129 .53132 .53136 40 39 38 37 + 6' ^7 9.71824 .71827 .71830 .71833 .52486 .52490 .52493 .52497 9.72184 .72187 .72190 .72193 .52704 .52708 .52711 .52715 9.72363 .72366 .72369 .72372 .62922 .52925 .52929 .52933 9.72542 .72545 .72548 .72551 .53140 .53143 .53147 .53150 36 35 34 S3 + r 29 30 31 9.71836 .71839 .71842 .71845 9.72016 .72019 .72022 .72025 .52501 .52504 .52508 .52511 9.72196 .72199 .72202 .72205 .52718 .52722 .52726 .52729 9.72375 .72378 .72381 .72384 .52936 .52940 .52944 .52947 9.72554 .72557 .72560 .72563 .53154 .53158 .53161 .53165 32 31 30 29 + 8' 33 34 35 9.71848 .71851 .71854 .71857 .52297 .52301 .52304 .52308 9.72028 .72031 .72034 .72037 .52515 .52519 .52522 .52526 9.72208 .72211 .72214 .72217 .52733 .52737 .52740 .52744 9.72387 .72390 .72393 .72396 .52951 .52954 .52958 .52962 9.72565 .72568 .72571 .72574 .53169 .53172 .53176 .53179 28 27 26 25 + 9' 59 9.71860 .71863 .71866 .71869 .52312 .52315 .52319 .52323 9.72040 .72043 .72046 .72049 .52530 .52533 .52537 .52541 9.72220 .72223 .72226 .72229 .52748 .52751 .52755 .52758 9.72399 .72402 .72405 .72408 .52965 .52969 .52973 .52976 9.72577 .72580 .72583 .72586 .53183 .53187 .53190 .53194 24 23 22 21 + 10^ 41 42 43 9.71872 .71875 .71878 .71881 .52326 .52330 .52334 .52337 9.72052 .72055 .72058 .72061 .52544 .52548 .52551 .52555 9.72232 .72235 .72238 .72241 .52762 .52768 .52769 .52773 9.72411 .72414 .72417 .72420 .52980 .52983 .52987 .52991 9.72589 .72592 .72595 .72598 .53198 .53201 .53205 .53208 20 19 18 17 + 11' 45 46 47 9.71884 .71887 .71890 .71893 .52341 .52344 .52348 .52352 9.72064 .72067 .72070 .72073 .52559 .52562 .52566 .52570 9.72244 .72247 .72250 .72253 .52776 .52780 .52784 .52787 9.72423 .72426 .72429 .72432 .52994 .52998 .53002 .53005 9.72601 .72604 .72607 .72610 .53212 .53216 .53219 .53223 .53227 .53230 .53234 .53238 16 15 14 13 12 11 10 9 + ir 49 50 51 9.71896 .71899 .71902 .71905 .52355 .52359 .52363 .52366 9.72076 .72079 .72082 .72085 .52573 .52577 .52580 .52584 9.72256 .72259 .72262 .72265 .52791 .52795 .52798 .52802 9.72435 .72438 .72441 .72444 .53009 .53013 .53016 .53020 9.72613 .72616 .72619 .72622 + 13' 53 54 55 9.71908 .71911 .71914 .71917 .52370 .52373 .52377 .52381 9.72088 .72091 .72094 .72097 .52588 .52591 .52595 .52599 9.72268 .72271 .72274 .72277 .52806 .52809 .52813 .52816 9.72447 .72450 .72453 .72456 .53023 .53027 .53031 .53034 9.72625 .72628 .72631 .72634 .53241 .53245 .53248 .53252 8 7 6 5 + 14' 57 58 59 9.71920 .71923 .71926 .71929 .52384 .52388 .52392 .52395 9.72100 .72103 .72106 .72119 .52602 .52606 .52610 .52613 9.72280 .72283 .72286 .72289 .52820 .52824 .52827 .52831 9.72459 .72462 .72465 .72468 .53038 .53042 .53045 .53049 9.72637 .72640 .72642 .72645 .55256 .53259 .53263 .53267 4 3 2 1 + 15' 9.71932 .52399 9.72112 .52617 9.72292 .52835 9.72471 .53052 9.72648 .53270 17h49m 17^ 48m 17h 47m 171^46^ 17^45^ Page 886] TABLE 45. Haversines. s 6J^ 15m 93° 45/ 6h 16m 94° 0' 6fe 17m 94° 15/ 6h 18m 94° 30' 6h 19m 94° 45 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.72648 .72651 .72654 .72657 .53:370 .53274 .53277 .53281 9.72825 .72828 .72831 .72834 .53488 .53491 .53496 .53499 9.73002 .73005 .73008 .73011 .63705 .63709 .63713 .63716 9.73177 .73180 .73183 .73186 .53923 .53927 .63930 .53934 9.73352 .73355 .73358 .73361 .54140 .54144 .54148 .64161 60 59 58 57 + r 5 6 7 9.72660 .72663 .72666 .72669 .53285 .53288 .53292 .53296 9.72837 .72840 .72843 .72846 .53502 .53606 .53610 .63513 9.73014 .73016 .73019 .73022 .53720 .63724 .63727 .63731 9.73189 .73192 .73195 .73198 .53937 .63941 .53945 .53948 9.73364 .73367 .73370 .73373 .54155 .54159 .64162 .64166 56 56 54 53 + 3" . 9 10 11 9.72672 .72675 .72678 .72681 .53299 .53303 .53306 .53310 9.72849 .72852 .72855 .72858 .63617 .63620 .53524 .53528 9.73025 .73028 .73031 .73034 .53734 .63738 .63742 .53746 9.73201 .73204 .73207 .73209 .53952 .63966 .53969 .53963 9.73375 .73378 .73381 .73384 .54169 .54173 .54177 .54180 52 51 50 49 + 3' 13 14 15 9.72684 .72687 .72690 .72693 .53314 .53317 .53321 .53325 9.72861. .72864 .72867 .72870 .63531 .63535 .53639 .63642 9.73037 .73040 .73043 .73046 .63749 .63753 .53756 .53760 9.73212 .73215 .73218 .73221 .63966 .63970 .53974 .53977 9.73387 .73390 .73393 .73396 .64184 .64188 .64191 .64195 48 47 46 45 + 4" 17 18 19 9.72696 .72699 .72702 .72705 .53328 .53332 .53335 .53339 9.72873 .72876 .72878 .72881 .63646 .63549 .53553 .53667 9.73049 .73052 .73055 .73057 .53763 .53767 .63771 .63774 9.73224 .73227 .73230 .73233 .63981 .53985 .53988 .63992 9.73399 .73402 .73404 .73407 .64198 .64202 .64206 .64209 44 43 42 41 40 39 38 37 + 5' 21 22 23 9.72708 .72710 .72713 .72716 .53343 .53346 .53350 .53354 9.72884 .72887 .72890 .72893 .53660 .53664 .63668 .63571 9.73060 .73063 .73066 .73069 .63778 .63782 .53786 .53789 9.73236 .73239 .73242 .73244 .63996 .63999 .64003 .64006 9.73410 .73413 .73416 .73419 .54213 .64217 .54220 .64224 + 6' 25 26 27 9.72719 .72722 .72725 .72728 .63357 .53361 .53364 .53368 9.72896 .72899 .72902 .72905 .63575 .53579 .53682 .53686 9.73072 .73075 .75078 .73081 .53792 .53796 .63800 .63803 9.73247 .73250 .73253 .73256 .54010 .64014 .64017 .54021 9.73422 .73425 .73428 .73431 .64227 .54231 .54236 .54238 36 35 34 33 + r 29 30 31 9.72731 .72734 .72737 .72740 .53372 .53375 ..53379 .53383 9.72908 .72911 .72914 .72917 .63689 .53593 .63597 .53600 9.73084 .73087 .73090 .73093 .63807 .53811 .63814 .53818 9.73259 .73262 .73265 .73268 .54024 .54028 .54032 .54035 9.73433 .73436 .73439 .73442 .54242 .64245 .64249 .64253 32 31 SO 29 + S' 33 34 35 9.72743 .72746 .72749 .72752 .53386 .53390 .53394 .53397 9.72920 .72923 .72926 .72928 .63604 .53608 .53611 .53616 9.73096 .73098 .73101 .73104 .53821 .53825 .53829 .63832 9.73271 .73274 .73277 .73280 .54039 .64043 .64046 .64050 9.73445 .73448 .73451 .73454 .64266 .54260 .54264 .54267 28 27 26 25 + 9" 37 38 39 9.72755 .72758 .72761 .72764 .53401 .53404 .53408 .53412 9.72931 .72934 .72937 .72940 .63618 .53622 .53626 .63629 9.73107 .73110 .73113 .73116 .63836 .53840 .53843 .53847 9.73282 .73285 .73288 .73291 .64063 .54057 .64061 .64064 9.73457 .73460 .73462 .73465 .54271 .54274 .64278 .54282 24 2S 22 21 + 10' 41 42 43 9.72767 .72770 .72772 .72775 .53415 .53419 .53423 .53426 9.72943 .72946 .72949 .72952 .63633 .63637 .63640 .63644 9.73119 .73122 .73125 .73128 .63850 .63854 .53858 .53861 9.73294 .73297 .73300 .73303 .54068 .54072 .64075 .54079 9.73468 .73471 .73474 .73477 .64285 .64289 .64293 .54296 20 19 18 17 + 11" 45 46 47 9.72778 .72781 .72784 .72787 .53430 .53433 .63437 .53441 9.72955 .72958 .72961 .72964 .63647 .53651 .53665 .63658 9.73131 .73134 .73136 .73139 .63865 .53869 .53872 .63876 9.73306 .73309 .73311 .73314 .64082 .64086 .64090 .54093 9.73480 .73483 .73486 .73489 .64300 .54303 .54307 .54311 16 15 14 13 + n' 49 50 51 9.72790 .72793 .72796 .72799 .53444 .53448 .53452 .53455 9.72967 .72970 .72972 .72975 .53662 .53666 .63669 .63673 9.73142 .73145 .73148 .73151 .53879 .63883 .63887 .63890 9.73317 .73320 .73323 .73326 .64097 .54101 .54104 .64108 9.73491 .73494 .73497 .73500 .64314 .54318 .64322 .64326 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.72802 .72805 .72808 .72811 .53459 .63462 .63466 .53470 9.72978 .72981 .72984 .72987 .53676 .63680 .63684 .63687 9.73154 .73157 .73160 .73163 .63894 .63898 .53901 .53905 9.73329 .73332 .73335 .73338 .64111 .54116 .54119 .64122 9.73503 .73506 .73509 .73512 .54329 .54332 .64336 .64340 + ir 57 58 59 9.72814 .72817 .72820 .72823 .63473 .63477 .53481 .53484 9.72990 .72993 .72996 .72999 .63691 .53696 .63698 .53702 9.73166 .73169 .73172 .73174 .63908 .63912 .63916 .53919 9.73341 .73343 .73346 .73349 .54126 .54130 .54133 .54137 9.73515 .73517 .73520 .73523 .64343 .64347 .54361 .54364 4 3 2 + 15' 9.72825 .63488 9,73002 .63705 9.73177 .53923 9.73352 .54140 9.73526 .54358 17h 44m nh 4sm 1 17h 42m 17h 41m 17h 40m 1 TABLE 45. [Page 887 Haversines. 3 6^20"* 95" C 1 6f^ 21m 95* 15' 6h 22m 95° 3r 6h 2Sm 96° 45' 6h 24^ 96° 0' 3 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.73526 .73529 .73532 .73535 .54358 .54361 .54365 .54369 9.73699 .73702 .73705 .73708 .54575 .54579 .54582 .54586 9.73872 .73875 .73878 .73881 .54792 .54796 .54800 .54803 9.74044 .74047 .74049 .74052 .55009 .55013 .55017 .55020 9.74215 .74218 .74220 .74223 .55226 .56230 .66234 .65237 + r 5 6 7 9.73538 .73541 .73544 .73546 .54372 .54376 .54380 .54383 9.73711 .73714 .73717 .73720 .54590 .54593 .54597 .54600 9.73883 .73886 .73889 .73892 .54807 .54810 .54814 .54818 9.74055 .74058 .74061 .74064 .55024 .55028 .55031 .55035 9.74226 .74229 .74232 .74235 .55241 .66245 .55248 .55252 56 55 54 53 52 51 50 49 + r 9 10 11 9.73549 .73552 .73555 .73558 .54387 .54390 .54394 .54398 9.73722 .73725 .73728 .73731 .54604 .54608 .54611 .54615 9.73895 .73898 .73901 .73903 .54821 .54825 .54828 .54832 9.74067 .74069 .74072 .74075 .55038 .55042 .55046 .55049 9.74237 .74240 .74243 .74246 .55265 .65259 .65263 .55266 + 3' 13 14 15 9.73561 .73564 .73567 .73570 .54401 .54405 .54409 .54412 9.73734 .73737 .73740 .73743 .54619 .54622 .54626 .54629 9.73906 .73909 .73912 .73915 .54836 .54839 .54843 .54847 9.74078 .74081 .74084 .74087 .55053 .55056 .55060 .55064 9.74249 .74252 .74254 .74257 .55270 .55273 .55277 .55281 48 41 46 45 + 4' 11 18 19 9.73572 .73575 .73578 .73581 .54416 .54419 .54423 .54427 9.73746 .73748 .73751 .73754 .54633 .54637 .54640 .54644 9.73918 .73921 .73924 .73926 .54850 .54854 .54857 .54861 9.74089 .74092 .74095 .74098 .55067 .55071 .55075 .55078 9.74260 .74263 .74266 .74269 .55284 .55288 .66292 .55295 U 43 42 41 + 5' 21 22 23 9.73584 .73587 .73590 .73593 .54430 .54434 .54437 .54441 9.73757 .73760 .73763 .73766 .54647 .54651 .54655 .54658 9.73929 .73932 .73935 .73938 .54865 .54868 .54872 .54876 9.74101 .74104 .74106 .74109 .55082 .55085 .55089 .55093 9.74272 .74274 .74277 .74280 .55299 .55302 .55306 .56310 40 39 38 31 + 6' 25 26 21 9.73596 .73598 .73601 .73604 .54445 .54448 .54452 .54456 9.73769 .73771 .73774 .73777 .54662 .54666 .54669 .54673 9.73941 .73944 .73946 .73949 .54879 .54883 .54886 .54890 9.74112 .74115 .74118 .74121 .55096 .55100 .55103 .55107 9.74283 .74286 .74289 .74291 .55313 .55317 .66320 .55324 36 35 34 33 + r 29 30 31 9.73607 .73610 .73613 .73616 .54459 .54463 .54466 .54470 9.73780 .73783 .73786 .73789 .54676 .54680 .54684 .54687 9.73952 .73955 .73958 .73961 .54894 .54897 .54901 .54904 9.74124 .74126 .74129 .74132 .55111 ,65114 .66118 .65122 9.74294 .74297 .74300 .74303 .56328 .66331 o65336 .55339 32 31 30 29 + 8' 33 34 35 9.73619 .73622 ,73624 .73627 .54474 .54477 .54481 .54485 9.73792 .73794 .73797 .73800 .54691 .54695 .54698 .54702 9.73964 .73967 .73969 .73972 .54908 .54912 .54915 .54919 9.74135 .74138 .74141 .74144 .65125 .65129 .65132 .55136 9.74306 .74308 .74311 .74314 .55342 .55346 .55349 .55353 28 21 26 25 + ^ 31 38 39 9.73630 .73633 .73636 .73639 .54488 .54492 .54495 .54499 9.73803 .73806 .73809 .73812 .54705 .54709 .54713 .54716 9.73975 .73978 .73981 .73984 .54923 .54926 .54930 .54933 9.74146 .74149 .74152 .74155 .55140 .65143 .66147 .56150 9.74317 .74320 .74323 .74325 .55357 .66360 .66364 .56367 24 23 22 21 + W 41 42 43 9.73642 .73645 .73648 .73650 .54503 .54506 .54510 .54514 9.73815 .73817 .73820 .73823 .54720 .54724 .54727 .54731 9.73987 .73989 .73992 .73995 .54937 .54941 .54944 .54948 9.74158 .74161 .74163 .74166 .55154 .55158 .55161 .55165 9.74328 .74331 .74334 .74337 .55371 .55375 .65378 .55382 20 19 18 11 + 11' 45 46 41 9.73653 .73656 .73659 .73662 .54517 .54521 .54524 .54528 9.73826 .73829 .73832 .73835 .54734 .54738 .54742 .54745 9.73998 .74001 .74004 .74007 .54952 .54955 .54959 .54963 9.74169 .74172 .74175 .74178 .66169 .66172 .65176 .56179 9.74340 .74342 .74345 .74348 .55386 .55389 .55393 .56396 16 15 14 13 + 13' 49 50 51 9.73665 .73668 .73671 .73674 .54532 .54535 .54539 .54542 9.73838 .73840 .73843 .73846 .54749 .54752 .54756 .54760 9.74009 .74012 .74015 .74018 .54966 .54970 .54973 .54977 9.74181 .74183 .74186 .74189 .55183 .55187 .66190 .66194 9.74351 .74354 .74357 .74359 .55400 .55404 .66407 .56411 12 11 10 9 + 13' 53 54 55 9.73676 .73679 .73682 .73685 .54546 .54550 .54553 .54557 9.73849 .73852 .73855 .73858 .54763 .54767 .54771 .54774 9.74021 .74024 .74027 .74029 .54980 .54984 .54988 .54991 9.74192 .74195 .74198 .74200 .65197 .56201 .55206 .55208 9.74362 .74365 .74368 .74371 .55414 .55418 .66422 .66426 8 1 6 5 + 14' 51 58 59 9.73688 .73691 .73694 .73697 .54561 .54564 .54568 .54571 9.73860 .73863 .73866 .73869 .54778 .54781 .54785 .54789 9.74032 .74035 .74038 .74041 .54995 .54999 .55002 .55006 9.74203 .74206 .74209 .74212 .55212 .55216 .55219 .55223 9.74374 .74376 .74379 .74382 .55429 .66433 .66436 .66440 4 3 2 1 + 15' 9.73699 .54575 9.73872 .54792 9.74044 .55009 9.74215 .55226 9.74385 .55443 llh 39m llhssm llh Sim 17h 36m nh 35m Page 888] TABLE 45. Haversines. s 6A 25m 96° W 6ft 26^ 96° 30' 6ft 27m 96° 45' 6ft 28m 97° 0' 6ft 29m 97° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.74385 .74388 .74391 .74393 .55443 .55447 .55451 .55454 9.74554 .74557 .74560 .74563 .55660 .55664 .55667 .55671 9.74723 .74726 .74729 .74732 .55877 .55880 .55884 .55888 9.74891 .74894 .748a7 .74900 .56093 .56097 .56101 .56104 9.75059 .75061 .75064 .75067 .56319 .56314 .56317 .56321 60 59 58 57 + r 5 6 7 9.74396 .74399 .74402 .74405 .55458 .55461 .55465 .55469 9.74566 .74569 .74571 .74574 .55675 .55678 .55682 .55685 9.74734 .74737 .74740 .74743 .55891 .55895 .55899 .55902 9.74902 .74905 .74908 .74911 .56108 .56112 .56115 .56119 9.75070 .75072 .75075 .75078 .56324 .56328 .56332 .56335 56 55 54 53 + ^' 9 10 11 9.74408 .74410 .74413 .74416 .55473 .55476 .55479 .55483 9.74577 .74580 .74583 .74585 .55689 .55693 .55696 .55700 9.74746 .74748 .74751 .74754 .55906 .55909 .55913 .55917 9.74914 .74916 .74919 .74922 .56122 .56126 .56130 .56133 9.75081 .75084 .75086 .75089 .56339 .56342 .56346 .56350 52 51 50 49 + 3' 13 14 15 9.74419 .74422 .74425 .74427 .55487 .55490 .55494 .55498 9.74588 .74591 .74594 .74597 .55704 .55707 .55711 .55714 9.74757 .74760 .74762 .74765 .55920 .55924 .55927 .55931 9.74925 .74928 .74930 .74933 .56137 .56140 .56144 .56147 9.75092 .75095 .75097 .75100 .56353 .56357 .56360 .56364 48 47 46 45 17 18 19 9.74430 .74433 .74436 .74439 .55501 .55505 .55508 .55512 9.74600 .74602 .74605 .74608 .55718 .55722 .55725 .55729 9.74768 .74771 .74774 .74776 .55935 .55938 .55942 .55945 9.74936 .74939 .74941 .74944 .56151 .56155 .56158 .56162 9.75103 .75106 .75109 .75111 .56368 .56371 .56375 .56378 44 43 42 41 + 5' 21 22 23 9.74442 .74444 .74447 .74450 .55516 .55519 .55523 .55526 9.74611 .74614 .74616 .74619 .55732 .55736 .55740 .55743 9.74779 .74782 .74785 .74788 .55949 .55953 .55956 .55960 9.74947 .74950 .74953 .74955 .56166 .56169 .56173 .56176 9.75114 .75117 .75120 .75122 .56382 .56386 .56389 .56393 40 39 38 37 + 6' 25 26 27 9.74453 .74456 .74458 .74461 .55530 .55534 .55537 .55541 9.74622 .74625 .74628 .74630 .55747 .55750 .55754 .55758 9.74791 .74793 .74796 .74799 .55964 .55967 .55971 .55974 9.74958 .74961 .74964 .74967 .56180 .56184 .56187 .56191 9.75125 .75128 .75131 .75134 .56397 .56400 .56404 .56407 36 35 34 33 + r 29 30 31 9.74464 .74467 .74470 .74473 .55545 .55548 .55552 .55555 9.74633 .74636 .74639 .74642 .55761 .55765 .55769 .55772 9.74802 .74805 .74807 .74810 .55978 .55982 .55985 .55989 9.74969 .74972 .74975 .74978 .56195 .56198 .56202 .56205 9.75136 .75139 .75142 .75145 .56411 .56415 .56418 .56422 32 31 30 29 28 27 26 25 + 8^ 33 34 35 9.74475 .74478 .74481 .74484 .55559 .55563 .55566 .55570 9.74645 .74647 .74650 .74653 .55776 .55779 .55783 .55787 9.74813 .74816 .74819 .74821 .55992 .55996 .56000 .56003 9.74981 .74983 .74986 .74989 .56209 .56213 .56216 .56220 9.75147 .75150 .75153 .75156 .56425 .56429 .56433 .56436 + 9' 37 38 39 9.74487 .74490 .74492 .74495 .55573 .55577 .55581 .55584 9.74656 .74659 .74661 .74664 .55790 .55794 .55797 .55801 9.74824 .74827 .74830 .74833 .56007 .56010 .56014 .56018 9.74992 .74994 .74997 .75000 .56223 .56227 .56231 .56234 9.75159 .75161 .75164 .75167 .56440 .56443 .56447 .56451 24 23 22 21 + 10^ 41 42 43 9.74498 .74501 .74504 .74506 .55588 .55592 .55595 .55599 9.74667 .74670 .74673 .74675 .55805 .55808 .55812 .55815 9.74835 .74838 .74841 .74844 .56021 .56025 .56029 .56032 9.75003 .75006 .75008 .75011 .56238 .56241 .56245 .56249 9.75170 .75172 .75175 .75178 .56454 .56458 .56461 .56465 20 19 IS 17 16 15 14 13 12 11 10 9 + 11^ 45 46 47 9.74509 .74512 .74515 .74518 .55603 .55606 .55610 .55613 9.74678 .74681 .74684 .74687 .55819 .55823 .55826 .55830 9.74846 .74849 .74852 .74855 .56036 .56039 .56043 .56047 9.75014 .75017 .75020 .75022 .56252 .56256 .56259 .56263 9.75181 .75183 .75186 .75189 .56469 .56472 .56476 .56479 49 50 51 9.74521 .74523 .74526 .74529 .55617 .55620 .55624 .55628 9.74690 .74692 .74695 .74698 .55834 .55837 .55841 .55844 9.74858 .74860 .74863 .74866 .56050 .56054 .56057 .56061 9.75025 .75028 .75031 .75033 .56267 .56270 .56274 .56277 9.75192 .75195 .75197 .75200 .56483 .56487 .56490 .56494 + 13^ 53 54 55 9.74532 .74535 .74538 .74540 .55631 .55635 .55638 .55642 9.74701 .74704 .74706 .74709 .55848 .55852 .55855 .55859 9.74869 .74872 .74874 .74877 .56065 .56068 .56072 .56075 9.75036 .75039 .75042 .75045 .56281 .56285 .56288 .56292 9.75203 .75206 .75208 .75211 .56497 .56501 .56505 .56508 8 7 6 5 + W 57 58 59 9.74543 .74546 .74549 .74552 .55646 .55649 .55653 .55657 9.74712 .74715 .74718 .74720 .55862 .55866 .55870 .55873 9.74880 .74883 .74886 .74888 .56079 .56083 .56086 .56090 9.75047 .75050 .75053 .75056 .56296 .56299 .56303 .56306 9.75214 .75217 .75220 .75222 .56512 .56516 .56519 .56523 4 3 2 1 + 15' 9.74554 .55660 9.74723 .55877 9.74891 .56093 9.75059 .56310 9.75225 .56526 i7A 34'^ 17^ 33m 17^ 3pn i7ft 3im i7ft 30^ TABLE 45. Haversines. [Page 889 s 6 A SOm 97° 3(K eft 3im 97° 45' 6h 32m 98° 0' 6^ 3Sm 98° 15' 6h 34m 98°3(K 8 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav, Log. Hav. Nat. Hav. 1 2 3 9.75225 .75228 .75231 .75233 .56526 .56530 .56534 .56537 9.75391 .75394 .75396 .75399 .56743 .58746 .56750 -56753 .56757 .56761 .56764 .56768 9.75556 .75559 .75561 .75564 9.75567 .75570 .75572 .75575 .56959 .58962 .56966 .56969 9.75720 .75723 .75726 .75729 9.75731 .75734 .75737 .75739 9.75742" .75745 .75748 .75750 .57175 .57178 .67182 .57185 .57189 .57193 .57196 .57200 .57203 .57207 .57211 .57214 .57218 .57221 .57225 .57229 9.75884 .75887 .75889 .75892 9.75895 .75898 .75900 .75903 .57390 .57394 .57398 .67401 60 59 58 57 + r 5 6 7 9.75236 .75239 .75242 .75244 .56541 .56544 .56.548 .56552 9.75402 .75405 .75407 .75410 .56973 .56977 .56980 .56984 .57406 .57408 .57412 .57416 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 36 34 33 32 31 30 29 28 27 26 25 '24 23 22 21 + 3' 9 10 11 9.75247 .75250 .75253 .75256 .56555 .58559 .56562 .56566 9.75413 .75416 .75418 .75421 9.75424 .75427 .75429 .75432 9.75435 .75438 .75440 .75443 9.75446 .75449 .75452 .75454 .56771 .56775 .56779 .56782 .56786 .56739 .56793 .56797 9.75578 .75581 .75583 .75586 9.75589 .75592 .75594 .75597 .56987 .56991 .56994 .56998 9.75906 .75908 .75911 .75914 .57419 .67423 .57426 .57430 .67434 .57437 .57441 .57444 .67448 .57462 .57456 .57459 .67462 .57466 .57470 .57473 .57477 .67480 .57484 .57488 + 3^ 13 14 15 9.75258 .75261 .75264 .75267 .56570 .56573 .56577 .56580 .57002 .57005 .57009 .57012 .57016 .57020 .57023 .57027 .57031 .57034 .57038 .57041 .57045 .57049 .57052 .57056 .57059 .57063 .57067 .57070 .57074 .57077 .57081 .57085 .57088 .57092 .57095 .57099 9.75753 .75756 .75759 .75761 9.75764 .75767 .75770 .75772 9.75917 .75919 .75922 .75925 9.75927 .75930 .75933 .75936 9.75938 .75941 .75944 .75947 + 4' 17 18 19 9.75269 .75272 .75275 .75278 .56584 .56588 .56591 .56595 .56598 .56602 .56606 .56609 .56800 .56804 .56807 .56811 9.75600 .75603 .75605 .75608 9.75611 .75614 .75616 .75619 9.75622 .75625 .75627 .75630 9.75633 .75636 .75638 .75641 9.75644 .75646 .75649 .75652 9.75655 .75657 .75660 .75663 .57232 .57236 .57239 .57243 .57247 .57250 .67254 .57267 + 5' 21 22 23 9.75280 .75283 .75286 .75289 .56815 .56818 .56822 .56825 9.75775 .75778 .75780 .75783 9.75786 .75789 .75791 .75794 + 6' 25 26 27 9.75291 .75294 .75297 .75300 .56613 .56616 .56620 .56624 9.75457 .75460 .75463 .75465 .56829 .56833 .56836 .56840 .56843 .56847 .56851 .56854 .56858 .56861 .56865 .56869 .67261 .57265 .57268 .57272 9.75949 .75952 .75955 .75957 + r 29 30 31 9.75303 .75305 .75308 .75311 .56627 .56631 .56634 .56638 9.75468 .75471 .75474 .75476 9.75797 .75800 .75802 .75805 9.75808 .75810 .75813 .75816 9.75819 .75821 .75824 .75827 .57275 .57279 .57283 .57286 .57290 .57293 .57297 .57301 .57304 .57308 .57311 .57315 9.75960 .75963 .75966 .75968 9.75971" .75974 .75976 .75979 9.75982 .75985 .75987 .75990 .57491 .67496 .57498 .57602 .57506 .57509 .57613 .57516 .57520 .57524 .57527 .57531 + 8' 33 34 35 9.75314 .75316 .75319 .75322 .56642 .56645 .56649 .56652 9.75479 .75482 .75485 .75487 + r 37 38 39 9.75325 .75327 .75330 .75333 .56656 .56660 .56663 .56667 9.75490 .75493 .75496 .75498 .56872 .56876 .56879 .56883 + W 41 42 43 9.75336 .75338 .75341 .75344 .56670 .56674 .56678 .56681 9.75501 .75504 .75507 .75509 .56887 .56890 .56894 .56897 9.75666 .75668 .75671 .75674 .57103 .57106 .57110 .57114 9.75S30 .75832 .75835 .75838 .67318 .57322 .57326 .57329 9.75993 .75995 .75998 .76001 .57534 .57538 .57541 .57545 20 19 18 17 + 11' 45 46 47 9.75347 .75350 .75352 .75355 .56685 .56689 .56692 .56696 9.75512 .75515 .75518 .75520 .56901 .56905 .56908 .56912 .56915 .56919 .56923 .56926 .56930 .56933 .56937 .56941 9.75677 .75679 .75682 .75685 9.75688 .75690 .75693 .75696 .57117 .57121 .57124 .57128 .57131 .57135 .57139 .57142 .57146 .57149 .57153 .57157 9.75840 .75843 .75846 .75849 .57333 .57337 .57340 .57344 .57347 .57351 .57355 .57358 .57362 .57365 .57369 .57373 9.76004 .76006 .76009 .76012 9.76014 .76017 .76020 .76023 9.76025' .76028 .76031 .76033 .57649 .57552 .57556 .57559 .57563 .57567 .57570 .57574 .57577 .57581 .57586 .57588 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 + n' 49 50 51 9.75358 .75361 .75363 .75366 9.75369 .75372 .75374 .75377 '9.75380' .75383 .75385 .75388 9.75391 .56699 .56703 .56707 .56710 .56714 .56717 .56721 .56725 .56728 .56732 .56735 .56739 9.75523 .75526 .75529 .75531 9.75534 .75537 .75540 .75542 9.75851 .75854 .75857 .75859 9.75862 .75865 .75868 .75870 9.75873 .75876 .75879 .75881 + 13^ 53 54 55 9.75698 .75701 .75704 .75707 57 58 59 9.75545 .75548 .75550 .75553 .56944 .56948 .56951 .56955 9.75709 .75712 .75715 .75718 .57160 .57164 .57167 .57171 .57376 .57380 .57383 .57387 .57390 9.76036 .76039 .76041 .76044 .57592 .57696 .57599 .57603 + 15' .56743 9.75556 .56959 9.75720 .67175 9.75884 9.76047 .57606 — nh 29m J7h 28m 17h 27m 17h 26m I7h 25m Page 890] TABLE 45. Haversines. s 6ft 55m 98° 45^ 6ft 36^ 99° 0^ 6ft 37m 99° 15^ 6ft 55™ 99° 30^ 6ft 39m 99° 45' 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 ■ 3 9.76047 .76050 .76052 .76055 .57606 .57610 .57613 .57617 9.76209 .76212 .76215 .76217 .57833 .57835 .57839 .57833 9.76371 .76373 .76376 .76379 .58037 .58041 .58044 .58048 9.76531 .76534 .76537 .76539 .58353 .58356 .58260 .58363 9 76691 76694 76697 76699 .58467 .58471 .58475 .58478 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 + r 5 6 7 9.76058 .76060 .76063 .76066 .57631 .57634 .57638 .57631 9.76220 .76223 .76225 .76228 .57836 .57840 .57843 .57847 9.76381 .76384 .76387 .76389 .58051 .58055 .58059 .58063 9.76542 .76545 .76547 .76550 .58367 .58370 .58374 .58377 9 76702 76705 76707 76710 .58483 .58485 .58489 .58493 .58496 .58500 .58503 .58507 + 2' 9 10 11 9.76069 .76071 .76074 .76077 .57635 .57639 .57643 .57646 9.76231 .76233 .76236 .76239 .57850 .57854 .57858 .57861 9.76392 .76395 .76397 .76400 .58066 .58069 .58073 .58077 9.76553 .76555 .76558 .76561 .58381 .58285 .58388 .58393 9 76713 .76715 .76718 .76721 + 3^ 13 14 15 9.76079 .76082 .76085 .76088 .57649 .57653 .57656 .57660 9.76241 .76244 -.76247 .76250 .57865 .57868 .57873 .57876 9.76403 .76405 .76408 .76411 .58080 .58084 .58087 .58091 9.76563 .76566 .76569 .76571 .58395 .58399 .58303 .58306 9 .76723 .76726 .76729 .76731 .58510 .58514 .58518 .58531 + 4' 17 18 19 9.76090 .76093 .76096 .76098 .57664 .57667 .57671 .57675 9.76252 .76255 .76258 .76260 .57879 .57883 .57886 .57890 9.76414 .76416 .76419 .76422 .58095 .58098 .58103 .58105 9.76574 .76577 .76579 .76582 .58310 .58313 .58317 .58331 9 .76734 .76737 .76739 .76742 .58535 .58538 .58533 .58536 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 + 5' 22 23 9.76101 .76104 .76106 .76109 .57678 .57683 .57685 .57689 9.76263 .76266 .76268 .76271 .57894 .57897 .57901 .57904 9.76424 .76427 .76430 .76432 .58109 .58113 .58116 .58130 9.76585 .76587 .76590 .76593 .58334 .58338 .58331 .58335 9 .76745 .76747 .76750 .76753 .58539 .58543 .58546 .58550 + 6^ 27 9.76112 .76115 .76117 .76120 .57693 .57696 .57700 .57703 9.76274 .76276 .76279 .76282 .57908 .57911 .57915 .57919 9.76435 .76438 .76440 .76443 .58133 .58137 .58130 .58134 9.76595 .76598 .76601 .76603 .58338 .58343 .58346 .58349 9 .76755 .76758 .76761 .76763 .58553 .58557 .58561 .58564 + 7' 31 9.76123 .76125 .76128 .76131 .57707 .57710 .57714 .57718 9.76285 .76287 .76290 .76293 .57933 .57936 .57939 .57933 9.76446 .76448 .76451 .76454 .58138 .58141 .58145 .58148 9.76606 .76609 .76611 .76614 .58353 .58356 .58360 .58364 9 .76766 .76769 .76771 76774 .58568 .58571 .58575 .58579 + 8^ 54 35 9.76134 .76136 .76139 .76142 .57731 .57735 .57738 .57733 9.76296 .76298 .76301 .76303 .57937 .57940 .57944 .57947 9.76456 .76459 .76462 .76464 .58153 .58156 .58159 .58163 9.76617 .76619 .76622 .76625 .58367 .58371 .58374 .58378 9 76777 76779 .76782 76784 .58583 .58586 .58589 .58593 28 27 26 25 24 23 22 21 + 9^ 57 55 39 9.76144 .76147 .76150 .76152 .57736 .57739 .57743 .57746 9.76306 .76309 .76311 .76314 .57951 .57955 .57958 .57963 9.76467 .76470 .76473 .76475 .58166 .58170 .58173 .58177 9.76627 .76630 .76633 .76635 .58381 .58385 .58389 .58393 9 76787 76790 76792 76795 .58596 .58600 .58604 .58607 + 1(K 43 9.76155 .76158 .76161 .76163 .57750 .57753 .57757 .57761 9.76317 .76320 .76322 .76325 .57965 .57969 .57973 .57976 9.76478 .76481 .76483 .76486 .58181 .58184 .58188 .58191 9.76638 .76641 .76643 .76646 .58396 .58399 .58403 .58407 9 76798 76800 76803 76806 .58611 .58614 .58618 .58633 20 19 18 17 + 11^ 45 46 47 9.76166 .76169 .76171 .76174 .57764 .57768 .57771 .57775 9.76328 .76330 .76333 .76336 .57980 .57983 .57987 .57990 9.76489 .76491 .76494 .76497 .58195 .58199 .58303 .58306 9.76649 .76651 .76654 .76657 .58410 .58414 .58417 .58421 9 76808 76811 76814 76816 .58625 .58639 .58633 .58636 16 15 14 13 + 12^ 49 50 51 9.76177 .76179 .76182 .76185 .57779 .57783 .57786 .57789 9.76338 .76341 .76344 .76346 .57994 .57998 .58001 .58005 9.76499 .76502 .76505 .76507 .58309 .58313 .58317 .58330 9.76659 .76662 .76665 .76667 .58424 .58438 .58433 .58435 9 76819 76822 76824 76827 .58639 .58643 .58647 .58650 12 11 10 9 8 7 6 5 + 13^ 55 54 55 9.76188 .76190 .76193 .76196 .57793 .57797 .57800 .57804 9.76349 .76352 .76354 .76357 .58008 .58013 .58016 .58019 9.76510 .76513 .76515 .76518 .58334 .58237 .58331 .58334 9.76670 .76673 .76675 .76678 .58439 .58443 .58446 .58450 9 76830 76832 76835 76838 .58654 .58657 .58661 .58665 + 14^ 57 55 59 9.76198 .76201 .76204 .76206 .57807 .57811 .57815 .57818 9.76360 .76363 .76365 .76368 .58033 .58036 .58030 .58034 9.76521 .76523 .76526 .76529 .58338 .58343 .58345 .58349 9.76681 .76683 .76686 .76689 .58453 .58457 .58460 .58464 9 76840 76843 76845 76848 .58668 .58671 .58675 .58679 4 3 2 1 + 15^ 9.76209 .57833 9.76371 .58037 9.76531 .58253 9.76691 .58467 9. 76851 .58682 nh 24m 1 17h 2Sm 17h 22^ 17h 2m J7h 20m 1 TABLE 45. [Page 891 Haversinea. s 6A 40™ 100° C 6h 41^ 100° 15' 6h 42m 100° 30' 6h 43m 100° 45' 6h 44m 101° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav.l Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.76851 .76853 .76856 .76859 .586S2 .58686 .58690 .58693 9.77009 .77012 .77015 .77017 9.77020 .77023 .77025 .77028 .58897 .58901 .58904 .58908 9.77167 .77170 .77173 .77175 .59112 .59115 .59119 .59123 9.77325 .77327 .77330 .77333 .59326 .59330 .59333 .59337 .59340 .59344 .59348 .59351 9.77481 .77484 .77486 .77489 9.77492 .77494 .77497 .77499 9.77502 .77505 .77507 .77510 .59540 .59544 .59548 .59551 60 59 58 67 + 1^ 5 6 7 9.76861 .76864 .76867 .76869 .58697 .58700 .58701 .58707 .58911 .58915 .58919 .58922 9.77178 .77181 .77183 .77186 .59126 .59130 .59133 .59137 9.77335 .77338 .77340 .77343 .59555 .59558 .59562 .59565 .59569 .59573 .59576 .59580 .59583 .59587 .59590 .59594 .59598 .59601 .59605 .59608 .59613 .59615 .59619 .59633 .59636 .59630 .59633 .59637 56 55 54 53 52 51 50 49 48 47 46 45 + 2' 9 10 11 9.76872 .76875 .76877 .76880 .58711 .58714 .58718 .58723 9.77031 .77033 .77036 .77038 .58926 .58929 .58933 .58937 .58940 .58944 ' .58947 .58951 .58954 .58858 .58962 .58965 9.77188 .77191 .77194 .77196 9.77199 .77202 .77204 .77207 .59140 .59144 .59148 .59151 9.77346 .77348 .77351 .77353 .59355 .59358 .59363 .59365 + y 13 14 15 9.76883 .76885 .76888 .76891 .58725 .58729 .58733 .58736 9.77041 .77044 .77046 .77049 .59155 .59158 .59163 .59165 9.77356 .77359 .77361 .77364 .59369 .59373 .59376 .59380 9.77512 .77515 .77518 .77520 + i' 17 18 19 9.76893 .76896 .76898 .76901 .58740 .58743 .58747 .58750 9.77052 .77054 .77057 .77060 9.77209 .77212 .77215 .77217 .59169 .59173 .59176 .59180 9.77366 .77369 .77372 .77374 .59383 .59387 .59391 .59394 .59398 .59401 .59405 .59408 9.77523 .77525 .77528 .77531 9.77533 .77536 .77538 .77541 44 43 42 41 40 39 38 37 36 35 34 S3 + 5' 21 22 23 9.76904 .76906 .76909 .76912 .58754 .58758 .58761 .58765 9.77062 .77065 .77067 .77070 .58969 .58972 .58976 .58979 9.77220 .77223 .77225 .77228 .59183 .59187 .59190 .59194 .59198 .59201 .59205 .59308 9.77377 .77380 .77382 .77385 + 6' 25 26 27 9.76914 .76917 .76920 .76922 .58768 .58772 .58776 .58779 9.77073 .77075 .77078 .77081 .58983 .58987 .58990 .58994 9.77230 .77233 .77236 .77238 9.77387 .77390 1 .77393 .77395 .59412 .59416 .59419 .59423 .59426 .59430 .59433 .59437 9.77544 .77546 .77549 .77551 9.77554 .77557 .77559 .77562 + r 29 30 31 9.76925 .76928 .76930 .76933 .58783 .58786 .58790 .58793 9.77083 .77086 .77089 .77091 .58997 .59001 .59005 .59008 9.77241 .77243 .77246 .77249 .59212 .59215 .59319 .59223 9.77398 .77400 .77403 .77406 .59640 .59644 .59648 .59651 .59655 .59658 .59663 .59665 32 31 30 29 28 27 26 25 + 8' 33 34 35 9.76936 .76938 .76941 .76943 .58797 .58801 .58864 .58808 9.77094 .77096 .77099 .77102 .59012 .59015 .59019 .59022 9.77251 .77254 .77257 .77259 .59226 .59230 .59233 .59237 .59240 .59244 .59248 .59251 9.77408 .77411 .77413 .77416 .59440 .59444 .59448 ^9451 9.77564 .77567 .77570 .77572 + 9^ 57 38 39 9.76946 .76949 .76951 .76954 .58811 .58815 .58818 .58822 9.77104 .77107 .77110 .77112 .59026 .59030 .59033 .59037 9.77262 .77264 .77267 .77270 9.77419 .77421 .77424 .77427 .59455 .59458 .59462 .59465 9.77575 .77577 .77580 .77583 .59669 .59673 .59676 .59680 .59683 .59687 .59690 .59694 24 23 22 21 20 19 18 17 + W 41 42 43 9.76957 .76959 .76962 .76965 .58826 .58829 .58833 .58836 .58840 .58843 .58847 .58851 9.77115 .77117 .77120 .77123 .59040 .59044 .59047 .59051 9.77272 .77275 .77278 .77280 .59255 .59258 .59263 .59365 9.77429 .77432 .77434 .77437 .59469 .59473 .59476 .59480 9.77585 .77588 .77590 .77593 + 11' 45 46 47 9.76967 .76970 .76972 .76975 9.77125 .77128 .77131 .77133 .59055 .59058 .59062 .59065 9.77283 .77285 .77288 .77291 .59369 .59373 .59376 .59380 9.77440 .77442 .77445 .77447 .59483 .59487 .59490 .59494 9.77596 .77598 .77601 .77603 .59697 .59701 .59705 .59708 16 15 14 13 12 11 10 9 8 7 6 5 + 12' 49 50 51 9.76978 .76980 .76983 .76986 .58854 .58858 .58861 .58865 9.77136 .77139 .77141 .77144 .59069 .59072 .59076 .59080 9.77293 .77296 .77298 .77301 .59283 .59387 .59390 .59294 9.77450 .77453 .77455 .77458 .59498 .59501 .59505 .59508 9.77606 .77609 .77611 .77614 .59713 .59715 .59719 .59733 .59736 .59730 .59733 .59737 + 13' 53 54 55 9.76988 .76991 .76994 .76996 .58869 .58872 .58876 .58879 9.77146 .77149 .77152 .77154 .59083 .59087 .59090 .59094 9.77304 .77306 .77309 .77312 .59298 .59301 .59305 .59308 9.77460 .77463 .77466 .77468 .59512 .59515 .59519 .59533 9.77616 .77619 .77622 .77624 + 14' 57 55 59 9.76999 .77002 .77004 .77007 .58883 .58886 .58890 .58894 9.77157 .77160 .77162 .77165 .59097 .59101 .59105 .59108 9.77314 .77317 .77319 .77322 .59312 .59315 .59319 .59323 9.77471 .77473 .77476 .77479 .59526 .59530 .59533 .59537 9.77627 .77629 .77632 .77634 .59740 .59744 .59747 .59751 4 3 2 1 + 15' 9.77009 .58897 9.77167 .59112 9.77325 .59326 9.77481 .59540 9.77637 .59755 ijh igm 17hi8m 17h 17m 17hl6m 17h 15m _ 21594°— 14- 49 Page 892] TABLE 45. Haversines. s 6h45m 101° 15' 6h46m 101° 30' 6h 47m 101° 45' 6h 48m, 103° 0' 6h 49m 103° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav Log. Hav. Nat. Hav. 1 2 3 9.77637 .77640 .77642 .77645 .59755 .59758 .59763 .59765 9.77792 .77795 .77797 .77800 .59968 .59973 .59976 .59979 9.77947 .77949 .77952 .77954 .60183 .60185 .60189 .60193 9.78101 .78103 .78106 .78108 .60396 .60399 .60403 .60406 9.78254 .78256 .78259 .78261 .60609 .60613 .60616 .60630 60 59 58 57 + r 5 6 7 9.77647 .77650 .77653 .77655 .59769 .59773 .59776 .59779 9.77803 .77805 .77808 .77810 .59983 .59986 .59990 .59993 9.77957 .77960 .77962 .77965 .60196 .60300 .60303 .60307 9.78111 .78113 .78116 .78118 .60410 .60414 .60417 .60430 9.78264 .78266 .78269 .78271 .60633 .60637 .60630 .60634 56 55 54 53 62 51 50 49 + 2^ 9 10 11 9.77658 .77660 .77663 .77666 .59783 .59787 .59790 .59794 9.77813 .77815 .77818 .77821 .59997 .60000 .60004 .60008 9.77967 .77970 .77972 .77975 .60311 .60314 .60318 .60331 9.78121 .78124 .78126 .78129 .60434 .60438 .60431 .60435 9.78274 .78277 .78279 .78282 .60637 .60641 .60644 .60648 + 3' IS 14 15 9.77668 .77671 .77673 .77676 .59797 .59801 .59804 .59808 9.77823 .77826 .77828 .77831 .60011 .60015 .60018 .60033 9.77978 .77980 .77983 .77985 .60335 .60338 .60333 .60335 9.78131 .78134 .78136 .78139 .60438 .60443 .60445 .60449 9.78284 .78287 .78289 .78292 .60653 .60655 .60659 .60663 48 47 46 45 + 4^ 17 18 19 9.77679 .77681 .77684 .77686 .59813 .59815 .59819 .59833 9.77834 .77836 .77839 .77841 .60035 .60039 .60033 .60036 9.77988 .77990 .77993 .77996 .60339 .60343 .60346 .60350 9.78141 .78144 .78147 .78149 .60453 .60456 .60460 .60463 9.78294 .78297 .78299 .78302 .60666 .60669 .60673 .60676 44 43 42 41 40 39 38 37 + 5^ 21 22 23 9.77689 .77691 .77694 .77697 .59836 .59839 .59833 .59837 9.77844 .77846 .77849 .77852 .60040 .60043 .60047 .60050 9.77998 .78001 .78003 .78006 .60353 .60357 .60360 .60364 9.78152 .78154 .78157 .78159 .60467 .60470 .60474 .60477 9.78305 .78307 .78310 .78312 .60680 .60684 .60687 .60691 + 6^ 26 27 9.77699 .77702 .77704 .77707 .59840 .59844 .59847 .59851 9.77854 .77857 .77859 .77862 .60054 .60057 .60061 .60065 9.78008 .78011 .78013 .78016 .60368 .60371 .60375 .60378 9.78162 .78164 .78167 .78170 .60481 .60484 .60488 .60493 9.78315 .78317 .78320 .78322 .60694 .60698 .60701 .60705 36 35 34 S3 + r 30 31 9.77710 .77712 .77715 .77717 .59854 .59858 .59861 .59865 9.77864 .77867 .77870 .77872 .60068 .60073 .60075 .60079 9.78019 .78021 .78024 .78026 .60383 .60385 .60389 .60393 9.78172 .78175 .78177 .78180 .60495 .60499 .60503 .60506 9.78325 .78327 .78330 .78332 .60708 .60713 .60715 .60719 32 31 30 29 + 8' 34 35 9.77720 .77723 .77725 .77728 .59869 .59873 .59876 .59879 9.77875 .77877 .77880 .77882 .60083 .60086 .60090 .60093 9.78029 .78031 .78034 .78037 .60396 .60300 .60303 .60307 9.78182 .78185 .78187 .78190 .60509 .60513 .60516 .60530 9.78335 .78338 .78340 .78343 .60733 .60736 .60730 .60733 28 27 26 25 + 9' 57 38 39 9.77730 .77733 .77735 .77738 .59883 .59886 .59890 .59894 9.77885 .77888 .77890 .77893 .60097 .60100 .60104 .60107 9.78039 .78042 .78044 .78047 .60310 .60314 .60317 .60331 9.78192 .78195 .78198 .78200 .60534 .60537 .60531 .60534 9.78345 .78348 .78350 .78353 .60737 .60740 .60744 .60747 24 23 22 21 + 1(K 42 43 9.77741 .77743 .77746 .77748 .59897 .59901 .59904 .59908 9.77895 .77898 .77900 .77903 .60111 .60114 .60118 .60133 9.78049 .78052 .78054 .78057 .60334 .60338 .60333 .60335 9.78203 .78205 .78208 .78210 .60538 .60541 .60545 .60548 9.78355 .78358 .78360 .78363 .60751 .60755 .60758 .60763 20 19 18 17 + ir 45 46 47 9.77751 .77754 .77756 .77759 .59911 .59915 .59919 .59933 9.77906 .77908 .77911 .77913 .60135 .60139 .60133 .60136 9.78060 .78062 .78065 .78067 .60339 .60343 .60346 .60349 9.78213 .78215 .78218 .78221 .60553 .60556 .60559 .69563 9.78365 .78368 .78371 .78373 .60765 .60769 .60773 .60776 16 15 14 13 + 12' 50 51 9.77761 .77764 .77766 .77769 .59936 .59939 .59933 .59936 9.77916 .77918 .77921 .77924 .60139 .60143 .60146 .60150 9.78070 .78072 .78075 .78077 .60353 .60356 .60360 .60364 9.78223 .78226 .78228 .78231 .60566 .60570 .60573 .60577 9.78376 .78378 .78.381 .78383 .60779 .60783 .60786 .60790 12 11 10 9 + 13^ 55 54 55 9.77772 .77774 .77777 .77779 .59940 .59943 .59947 .59951 9.77926 .77929 .77931 .77934 .60154 .60157 .60161 .60164 9.78080 .78083 .78085 .78088 .60367 .60371 .60374 .60378 9.78233 .78236 .78238 .78241 .60580 .60584 .60588 .60591 9.78386 .78388 .78391 .78393 .60794 .60797 .60801 .60804 8 7 6 5 + 14^ 57 58 59 9.77782 .77785 .77787 .77790 .59954 .59958 .59961 .59965 9.77936 .77939 .77942 .77944 .60168 .60171 .60175 .60179 9.78090 .78093 .78095 .78098 .60381 .60385 .60388 .60393 9.78243 .78246 .78249 .78251 .60595 .60598 .60603 .60605 9.78396 .78398 .78401 .78404 .60808 .60811 .60815 .60818 4 3 2 1 + 15' 9.77792 .59968 9.77947 .60183 9.78101 .60396 9.78254 .60609 9.78406 .60833 17h 14m ijh 13m 17h 12m 17h urn 17h 10m 1 TABLE 45. [Page 893 Haversines. s 6/1 50m 103° W 1 6^ 51^ 102° 45' 1 6/i 5;?™ 103° 0' | 6ft 55"t 103° 15' 1 6ft 54"» 103° 30' | s Log. Hav. Nat. Hav. Hav.Log. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.78406 .78409 .78411 .78414 .60823 .60825 .60829 .60833 9.78558 .78560 .78563 .78565 .61035 .61038 .61042 .61046 9.78709 .78711 .78714 .78716 .61248 .61251 .61255 .61258 9.78859 .78862 .78864 .78867 .61460 .61464 .61467 .61471 9.79009 .79011 .79014 .79016 .61672 .61676 .61679 .61683 60 59 58 57 56 55 54 53 52 51 50 49 + r 5 6 7 9.78416 .78419 .78421 .78424 .60836 .60840 .60843 .60847 9.78568 .78570 .78573 .78575 .61049 .61053 .61056 .61060 .61063 .61067 .61070 .61074 9.78719 .78721 .78724 .78726 .61262 .61265 .61269 .61272 9.78869 .78872 .78874 .78877 .61474 .61478 .61481 .61485 9.79019 .79021 .79024 .79026 .61686 .61690 .61693 .61697 + 2^ 9 10 11 9.78426 .78429 .78431 .78434 .60850 .60854 .60857 .60861 9.78578 .78581 .78583 .78586 9.78729 .78731 .78734 .78737 .61276 .61279 .61283 .61287 9.78879 .78882 .78884 .78887 .61488 .61492 .61495 .61499 9.79029 .79031 .79034 .79036 .61701 .61704 .61708 .61711 + 3' 13 14 15 9.78436 .78439 .78442 .78444 .60865 .60868 .60872 .60875 9.78588 .78591 .78593 .78596 .61077 .61081 .61085 .61088 9.78739 .78742 .78744 .78747 .61290 .61294 .61297 .61301 9.78889 .78892 .78894 .78897 .61502 .61506 .61510 .61513 9.79039 .79041 .79044 .79046 .61715 .61718 .61722 .61725 48 47 46 45 + *^ 17 18 19 9.78447 .78449 .78452 .78454 .60879 .60882 .60886 .60889 9.78598 .78601 .78603 .78606 .61092 .61095 .61099 .61102 9.78749 .78752 .78754 .78757 .61304 .61308 .61311 .61315 9.78899 .78902 .78904 .78907 .61517 .61520 .61524 .61527 9.79049 .79051 .79054 .79056 .61729 .61732 .61736 .61739 44 43 42 41 + 5' 21 22 ■ 23 9.78457 .78459 .78462 .78464 .60893 .60897 .60900 .60904 9.78608 .78611 .78013 .78616 .61106 .61109 .61113 .61116 9.78759 .78762 .78764 .78767 .61318 .61322 .61325 .61329 9.78909 .78912 .78914 .78917 .61531 .61534 .61538 .61541 9.79059 .79061 .79064 .79066 .61743 .61747 .61750 .61754 40 39 38 37 + 6' 25 26 27 9.78467 .78469 .78472 .78474 .60907 .60911 .60914 .60918 9.78618 .78621 .78623 .78626 .61120 .61124 .61127 .61131 9.78769 .78772 .78774 .78777 .61333 .61336 .61340 .61343 9.78919 .78922 .78924 .78927 .61545 .61548 .61552 .61556 9.79069 .79071 .79074 .79076 .61757 .61761 .61764 .61768 36 35 34 S3 + r 29 SO 31 9.78477 .78479 .78482 .78485 .60921 .60925 .60928 .60932 9.78628 .78631 .78633 .78636 .61184 .61138 .61141 .61145 9.78779 .78782 .78784 .78787 .61347 .61350 .61354 .61357 9.78929 .78932 .78934 .78937 .61559 .61563 .61566 .61570 9.79079 .79081 .79084 .79086 .61771 .61775 .61778 .61782 32 31 30 29 + 8' S3 34 35 9.78487 .78490 .78492 .78495 .60936 .60939 .60943 .60946 9.78638 .78641 .78643 .78646 .61148 .61152 .61155 .61159 9.78789 .78792 .78794 .78797 .61361 .61364 .61368 .61372 9.78939 .78942 .78944 .78947 .61573 .61577 .61580 .61584 9.79089 .79091 .79094 .79096 .61785 .61789 .61792 .61796 28 27 26 25 24 23 22 21 + 9' 37 38 39 9.78497 .78500 .78502 .78505 .60950 .60953 .60957 .60960 9.78649 .78651 .78654 .78656 .61163 .61166 .61170 .61173 9.78799 .78802 .78804 .78807 .61375 .61379 .61382 .61386 9.78949 .78952 .78954 .78957 .61587 .61591 .61594 .61598 9.79099 .79101 .79103 .79106 .61800 .61803 .61807 .61810 + W 41 42 43 9.78507 .78510 .78512 .78515 .60964 .60967 .60971 .60975 9.78659 .78661 .78664 .78666 .61177 .61180 .61184 .61187 9.78809 .78812 .78814 .78817 .61389 .61393 .61396 .61400 9.78959 .78962 .78964 .78967 .61602 .61605 .61609 .61612 9.79108 .79111 .79113 .79116 .61814 .61817 .61821 .61824 20 19 18 17 45 46 47 9.78517 .78520 .78522 .78525 .60978 .60982 .60985 .60989 9.78669 .78671 .78674 .78676 .61191 .61194 .61198 .61201 9.78819 .78822 .78824 .78827 .61403 .61407 .61410 .61414 9.78969 .78972 .78974 .78977 .61616 .61619 .61623 .61626 9.79118 .79121 .79123 .79126 .61828 .61831 .61835 .61838 16 15 14 13 + 13' 51 9.78528 .78530 .78533 .78535 .60992 .60996 .60999 .61003 9.78679 .78681 .78684 .78686 .61205 .61209 .61212 .61216 9.78829 .78832 .78834 .78837 .61418 .61421 .61425 .61428 9.78979 .78982 .78984 .78987 .61630 .61633 .61637 .61640 9.79128 .79131 .79133 .79136 .61842 .61845 .61849 .61853 12 11 10 9 + 13' 55 54 55 9.78538 .78540 .78543 .78545 .61007 .61010 .61014 .61017 9.78689 .78691 .78694 .78696 .61219 .01223 .61226 .61230 9.78839 .78842 .78844 .78847 .61432 .61435 .61439 .61442 9.78989 .78992 .78994 .78997 .61644 .61648 .61651 .61655 9.79138 .79141 .79143 .79146 .61856 .61860 .61863 .61867 8 7 6 5 + 14' 57 5S 59 9.78548 .78550 .78553 .78555 .61021 .61024 .61028 .61032 9.78699 .78701 .78704 .78706 .61233 .61237 .61240 .61244 9.78849 .78852 .78854 .78857 .61446 .61449 .61453 .61456 9.78999 .79002 .79004 .79007 .61658 .61662 .61665 .61669 9.79148 .79151 .79153 .79156 .61870 .61874 .61877 .61881 4 3 2 1 + 15' 9.78558 1 .61035 9.78709 .61248 9.78859 .61460 9.79009 .61672 9.79158 .61884 17^ 9m i7ft sm nh Tm nn&m, irhsm Page 894] TABLE 45. Haversines. s 6ft 55"* 103° 45' 6ft 56m 104° r 6h 5jm 104° 15^ 6h 58m 104° 30' 6h 59m 104° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.79158 .79161 .79163 .79165 .618S4 .61888 .61891 .61895 9.79306 .79309 .79311 .79314 .63096 .63100 .63103 .63107 .63110 .63114 .63117 .63131 9.79454 .79457 .79459 .79462 9.79464 .79466 .79469 .79471 .63308 .63311 .63315 .62318 9.79601 .79604 .79606 .79609 .62519 .62522 .63526 .63530 9.79748 .79750 .79752 .79755 .62730 .63734 .63737 .63741 60 59 58 57 66 55 64 63 62 61 60 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 SO 29 28 27 26 25 + r 5 6 7 9.79168 .79170 .79173 .79175 .61898 .61903 .61905 .61909 9.79316 .79319 .79321 .79324 .63333 .63335 .63339 .63333 .63336 .63339 .63343 .63346 9.79611 .79613 .79616 .79618 .63533 .63537 .62540 .63544 9.79757 .79760 .79762 .79765 .63744 .62748 .62751 .62755 .63758 .62762 .63765 .62769 + 2' 9 10 11 9.79178 .79180 .79183 .79185 .61913 .61916 .61930 .61933 9.79326 .79329 .79331 .79334 .63134 .63138 .63131 .63135 9.79474 .79476 .79479 .79481 9.79621 .79623 .79626 .79628 .63547 .63551 .63554 .63558 9.79767 .79770 .79772 .79774 + 3' 13 u 15 9.79188 .79190 .79193 .79195 .61927 .61930 .61931 .61937 9.79336 .79339 .79341 .79343 .63138 .63143 .63145 .63149 9.79484 .79486 .79489 .79491 .63350 .63353 .63357 .63361 9.79631 .79633 .79635 .79638 .63561 .63565 .62568 .63573 9.79777 .79779 .79782 .79784 .63773 .63776 .62779 .62783 + 4' 17 18 19 9.79198 .79200 .79203 .79205 .61941 .61944 .61948 .61951 9.79346 .79348 .79351 .79353 .62153 .62156 .62160 .62163 9.79493 .79496 .79498 .79501 .63364 .63368 .63371 .63375 9.79640 .79643 .79645 .79648 9.79650 .79653 .79655 .79657 .63575 .63579 .63582 .62586 .62589 .62593 .62596 .62600 9.79787 .79789 .79791 .79794 .63786 .63790 .63793 .63797 + 5' 21 22 23 9.79208 .79210 .79213 .79215 .61955 .61958 .61963 .61966 9.79356 .79358 .79361 .79363 .62167 .62170 .62174 .62177 9.79503 .79506 .79508 .79511 .62378 .62382 .62385 .62389 9.79796 .79799 .79801 .79804 .63800 .63804 .62807 .63811 + 6' 25 26 27 9.79217 .79220 .79222 .79225 .61969 .61973 .61976 .61980 9.79366 .79368 .79371 .79373 .62181 .62184 .62188 .62191 9.79513 .79516 .79518 .79520 .62393 .63396 .63399 .63403 9.79660 .79662 .79665 .79667 .62603 .63607 .63611 .63614 .63618 .63631 .63635 .63638 9.79806 .79808 .79811 .79813 9.79816 .79818 .79821 .79823 .62814 .63818 .62822 .63825 .62829 .63833 .62836 .62839 + r 29 30 31 9.79227 .79230 .79232 .79235 .61983 .61987 .61990 .61994 9.79376 .79378 .79380 .79383 .62195 .62198 .62303 .63205 9.79523 .79525 .79528 .79530 .63406 .63410 .63413 .63417 9.79670 .79672 .79674 .79677 + 8' 33 34 35 9.79237 .79240 .79242 .79245 .61997 .62001 .63004 .63008 9.79385 .79388 .79390 .79393 .62209 .62213 .62216 .62220 9.79533 .79535 .79538 .79540 .63430 .63434 .62427 .62431 9.79679 .79682 .79684 .79687 .63633 .63635 .63639 .63643 9.79825 .79828 .79830 .79833 .62843 .63846 .63850 .62853 + 9" 37 38 39 9.79247 .79250 .79252 .79255 .63011 .63015 .63018 .63032 9.79395 .79398 .79400 .79403 .62223 .62227 .62230 .62234 9.79542 .79545 .79547 .79550 .62434 .62438 .62442 .62445 9.79689 .79692 ,79694 .79696 .63646 .62649 .63653 .63656 9.79835 .79838 .79840 .79842 .62857 .63860 .63864 .63867 24 23 22 21 + W 41 42 43 9.79257 .79260 .79262 .79264 .62026 .62029 .62033 .62036 9.79405 .79407 .79410 .79412 .62237 .62241 .62244 .62348 9.79552 .79555 .79557 .79560 .62449 .63453 .63456 .63459 9.79699 .79701 .79704 .79706 .63680 .63663 .63687 .63670 9.79845 .79847 .79850 .79852 .63871 .63874 .63878 .63881 .63885 .63888 .63893 .63895 20 19 18 17 16 15 14 + ir 45 46 47 9.79267 .79269 .79272 .79274 .62040 .62043 .62047 .63050 9.79415 .79417 .79420 .79422 .63251 .63355 .63358 .63363 9.79562 .79565 .79567 .79569 .63463 .63466 .63470 .63473 .63477 .63480 .63484 .62487 9.79709 .79711 .79714 .79716 .62874 .63677 .63681 .63684 9.79855 .79857 .79859 .79862 + n' 49 50 51 9.79277 .79279 .79282 .79284 .62054 .62057 .62061 .62064 9.79425 .79427 .79430 .79432 .63365 .63369 .62272 .62276 9.79572 .79574 .79577 .79579 9.79718 .79721 .79723 .79726 .62688 .62691 .62695 .62698 9.79864 .79867 .79869 .79872 .63899 .63902 .62906 .62909 .63913 .63916 .63930 .63933 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.79287 .79289 .79292 .79294 .62068 .63071 .63075 .63078 9.79434 .79437 .79439 .79442 .62379 .63383 .63387 .63290 9.79582 .79584 .79587 .79589 9.79591 .79594 .79596 .79599 .63491 .63494 .63498 .63501 9.79728 .79731 .79733 .79735 .62703 .62706 .62709 .62713 9.79874 .79876 .79879 .79881 + 14' 57 58 59 9.79297 .79299 .79301 .79304 .63083 .63086 .63089 .63093 9.79444 .79447 .79449 .79452 .63394 .63397 .63301 .63304 .63505 .63508 .63512 .63515 9.79738 .79740 .79743 .79745 .62716 .62720 .62723 .62727 9.79884 .79886 .79888 .79891 .63937 .63930 .63934 .63937 4 S 2 1 + 15' 9.79306 .63096 9.79454 .63308 9.79601 .63519 9.79748 .62730 9.79893 .63941 171^ 4m 17^ 3m 17^ 2m i7him 17h0m TABLE 45. [Page 895 Haversines. s 7A Om 105° 0' 7ft im 105° 15' 7h 2m 105° 3r 7ft 3m 105° 45' 7ft 4^ 106° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 0- 1 2 3 9.79893 .79896 ,79898 .79901 .62941 .63944 .63948 .62951 9.80038 .80041 .80043 .80046 9.80048 .80050 .80053 .80055 .63153 .63155 .63159 .63162 .63166 .63169 .63173 .63176 9.80183 .80185 .80188 .80190 .63363 .63365 .63369 .63373 9.80.327 .80329 .80331 .80334 .63573 .63576 .63579 .63583 .63586 .63590 .63593 .63597 9.80470 .80472 .80474 .80477 .63782 .63785 .63789 .63792 60 59 58 57 + r 5 6 7 9.79903 .79905 .79908 .79910 .63955 .63958 .63963 .63965 9.80192 .80195 .80197 .80200 .63376 .63379 .63383 .63386 9.80336 .80339 .80341 .80343 9.80479 .80482 .80484 .80486 .63796 .63799 .63803 .63806 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 + 2' 9 10 11 9.79913 .79915 .79918 .79920 .63969 .63973 .63976 .63980 9.80058 .80060 .80063 .80065 .63180 .63183 .63187 .63190 9.80202 .80204 .80207 .80209 .63390 .63393 .63397 .63400 9.80346 .80348 .80351 .80353 9.80355" .80358 .80360 .80362 9.80365 .80367 .80370 .80372 .63600 .63604 .63607 .63611 .63614 .63618 .63631 .63635 .63638 .63633 .63035 .63639 .63642 .63646 .63649 .63653 .63656 .63660 .63663 .63666 .63670 .63673 .63677 .63680 .63684 .63687 .63691 .63694 9.80489 .80491 .80494 .80496 9.80498 .80501 .80503 .80505 9.80508 .80510 .80513 .80515 9.80517 .80520 .80522 .80524 9.80527 .80529 .80532 .80534 9.80536 .80539 .80541 .80543 9.80546 .80548 .80551 .80553 .63810 .63813 .63817 .63820 .63834 .63837 .63831 .63834 .63838 .63841 .63845 .63848 .63853 .63855 .6:J859 .63862 .63866 .63869 .63873 .63876 .63880 .63883 .63887 .63890 + 3' 13 14 15 9.79922 .79925 .79927 .79930 .63983 .62987 .63990 .63994 9.80067 .80070 .80072 .80075 9.80077 .80079 .80082 .80084 .63194 .63197 .63201 .63204 .63208 .63211 .63215 .63218 .63233 .63225 .63239 .63333 .63336 .63339 .63343 .63346 .63350 .63353 .63357 .63360 9.80212 .80214 .80216 .80219 .63404 .63407 .63411 .63414 + *' 17 18 19 9.79932 .79935 .79937 .79939 .63997 .63001 .63004 .63008 9.80221 .80224 .80226 .80228 .63418 .63431 .63435 .63438 + 5' 21 22 23 9.79942 .79944 .79947 .79949 .63011 .63015 .63018 .63033 9.80087 .80089 .80091 .80094 9.80096 .80099 .80101 .80103 9.80106 .80108 .80111 .80113 9.80116 .80118 .80120 .80123 9.80231 .80233 .80236 .80238 9.80240 .80243 .80245 .80248 9.80250 .80252 .80255 .80257 9.80260 .80262 .80264 .80267 9.80269 .80272 .80274 .80276 9.80279 .80281 .80284 .80286 .63433 .63435 .63439 .63443 .63446 .63450 .63453 .63457 .63460 .63464 .63467 .63471 9.80374 .80377 .80379 .80382 9.80384 .80386 .80389 .80391 9.80393 .80396 .80398 .80401 9.80403 .80405 .80408 .80410 25 26 27 9.79951 .79954 .79956 .79959 .63035 .63039 .63033 .63036 + r 29 30 31 9.79961 .79964 .79966 .79968 .63039 .63043 .63046 .63050 + 8' 33 34 35 9.79971 .79973 .79976 .79978 .63053 .63057 .63060 .63064 .63364 .63367 .63371 .63374 .63474 .63478 .63481 .63485 .63488 .63493 .63495 .63499 .63894 .63897 .63901 .63904 .63908 .63911 .63915 .63918 .63922 .63925 .63929 .63932 + 9' 37 38 39 9.79980 .79983 .79985 .79988 .63067 .63071 .63074 .63078 .63081 .63085 .63088 .63093 9.80125 .80128 .80130 .80132 9.80135" .80137 .80140 .80142 .63378 .63381 .63385 .63388 9.80413 .80415 .80417 .80420 9780422 .80424 .80427 .80429 9.80432 .80434 .80436 .80439 .63698 .63701 .63705 .63708 9.80555 .80558 .80560 .80562 + 10' 41 42 43 9.79990 .79993 .79995 .79997 .63393 .63295 .63299 .63302 .63503 .63506 .63509 .63513 .63713 .63715 .63719 .63722 .63726 .63729 .63733 .63736 9.80565 .80567 .80570 .80572 + 11' 45 46 47 9.80000 .80002 .80005 .80007 .63095 .63099 .63103 .63106 9.80144 .80147 .80149 .80152 .63306 .63309 .63313 .63316 9.80288 .80291 .80293 .80296 .63516 .63530 .63533 .63537 9.80574 .80577 .80579 .80581 9.80584 .80586 .80589 .80591 .63936 .63939 .63943 .6394fi .63950 .63953 .63957 .63960 16 15 14 13 12 11 10 9 + 13' 49 50 51 9.80009 .80012 .80014 .80017 .63109 .63113 .63116 .63120 9.80154 .80156 .80159 .80161 .63320 .63323 .63327 .63330 9.80298 .80300 .80303 .80305 .63530 .63534 .63537 .63541 9.80441 .80444 .80446 .80448 .63740 .63743 .63747 .63750 + 13^ 53 54 55 9.80019 .80022 .80024 .80026 .63133 .63127 .63131 .63134 9.80164 .80166 .80168 .80171 .63334 .63337 .63341 .63344 9.80307 .80310 .80312 .80315 .63544 .63548 .63551 .63555 9.80451 .80453 .80455 .80458 .63754 .63757 .63761 .63764 .63768 .63771 .63775 .63778 9.80593 .80596 .80598 .80600 .63964 .63967 .63971 .63974 8 7 6 5 + U' 57 58 59 9.80029 .80031 .80034 .80036 .63138 .63143 .63145 .63148 9.80173 .80176 .80178 .80180 .63348 .63351 .63355 .63358 9.80317 .80319 .80322 .80324 .63558 .63563 .63565 .63569 9.80460 .80463 .80465 .80467 9.80603 .80605 .80607 .80610 .63977 .63981 .63984 .63988 4 3 2 1 + W 9.80038 .63153 9.80183 .63363 9.80327 .63573 9.80470 .63782 9.80612 .63991 16h 59m 16Ji 58m 16^ 57m left 56m 16h 55m 1 Page 896] TABLE 45. Haversine.s. 7h 5m 106° 15' 7h em 106° 30' 7h 7m 106° 45' 7h gm 107° 0' 7h gm 107° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.80612 .80615 .80617 .80619 .63991 .63995 .63998 .64003 9.80754 .80756 .80759 .80761 .64201 .64204 .64308 .64211 9.80895 .80898 .80900 .80902 .64410 .64413 .64417 .64430 9.81036 .81038 .81040 .81043 .64619 .64622 .64626 .64629 9.81176 .81178 .81180 .81183 .64827 .64831 .64834 .64838 60 59 58 57 + r 5 6 7 9.80622 .80624 .80626 .80629 .64005 .64009 .64012 .64016 9.80763 .80766 .80768 .80771 .64215 .64218 .64222 .64225 9.80905 .80907 .80909 .80912 .64434 .64437 .64431 .64434 9.81045 .81047 .81050 .81052 .64632 .64636 .64639 .64643 9.81185 .81187 .81190 .81192 .64841 .64844 .64848 .64851 56 55 54 53 + V 9 10 11 9.80631 .80634 .80636 .80638 .64019 .64023 .64026 .64030 9.80773 .80775 .80778 .80780 .64229 .64232 .64236 .64239 9.80914 .80916 .80919 .80921 .64438 .64441 .64445 .64448 9.81054 .81057 .81059 .81081 .64646 .64650 .64653 .64657 9.81194 .81197 .81199 .81201 .64855 .64858 .64862 .64865 52 51 50 49 + y 13 14 15 9.80641 .80643 .80645 .80648 .64033 .64037 .64040 .64044 9.80782 .80785 .80787 .80789 .64343 .64246 .64250 .64253 9.80923 .80926 .80928 .80930 .64453 .64455 .64459 .64463 9.81064 .81066 .81068 .81071 .64660 .64664 .64667 .64671 9.81204 .81206 .81208 .81211 .64869 .64873 .64876 .64879 48 47 46 45 + 4^ 17 18 19 9.80650 .80652 .80655 .80657 .64047 .64051 .64054 .64058 9.80792 .80794 .807% .80799 .64257 .64260 .64384 .64367 9.80933 .80935 .80937 .80940 .64466 .64469 .64472 .64476 .81073 .81075 .81078 .81080 .64674 .64678 .64681 .64685 9.81213 .81215 .81217 .81220 .64883 .64886 .64890 .64893 44 43 42 41 + 5' 21 22 23 9.80660 .80662 .80664 .80667 .64061 .64065 .64068 .64072 9.80801 .80804 .80806 .80808 .64370 .64374 .64377 .64381 9.80942 .80944 .80947 .80949 .64479 .64483 .64486 .64490 9.81082 .81085 .81087 .81089 .64688 .64692 .64695 .64699 9.81222 .81224 .81227 .81229 .64897 .64900 .64903 .64907 40 39 38 37 + .89642 .78780 .89837 .79136 .90031 .79489 .90222 .79840 .90412 .80189 26 56+ 9 ,89645 .78786 .89840 .79142 .90034 .79495 .90225 .70846 .90415 .80195 24 S8 " ■> .89648 .78793 .89844 .79148 .90037 .79501 .90229 .79852 0.79858 .90418 .80201 0.80207 22 20 ^+10 9.89651 0.78798 9.89847 0.79153 9.90040 0.79507 9.90232 9.90421 42 .89655 .78804 .89850 .79159 .90044 .79513 .90235 .79864 .90425 .80213 18 ^+11 .89658 .78810 .89853 .79165 .90047 .79519 .90238 .79870 .90428 .80218 16 46 .89661 .78816 .89857 .79171 .90050 .79524 .90241 .79875 .90431 .80224 14 48+1% 9.89665 0.78822 9.89860 0.79177 9.90053 0.79530 9.90244 0.79881 9.90434 0.80230 12 50 .89668 .78828 .89863 .79183 .90056 .79536 .90248 .79887 .90437 .80236 10 62+13 .89671 .78834 .89866 .79189 .90060 .79542 .90251 .79899 .90440 .80242 8 54 .89674 .78839 .89870 .79195 .90063 .79548 0.79554 .90254 9.90257 .79893 0.79905 .90443 .80247 6 4 56+U 9.89678 0.78845 9.89873 0.79201 9.90066 9.90446 0.80253 58 9.89681 0.78851 9.89876 0.79207 9.90069 0.79560 9.90260 0.79910 .9.90449 0.80259 2 15A 39m 15^37^ 15^ S5m 15h SSm 15h Sim B -f 0+15 8h 21m 125° 0^ 8h 23m 125° 30^ 8h 25m 126° 0" 8h 27m 126° 30^ Sh 29m 127° r B 60 9.89684 0.78857 9.88879 : 0.79212 .9.90072 0.79565 9.90264 0.79916 9.90452 0.80265 2 .89687 .78863 .89883 i .79218 .90076 .79571 .90267 .79922 .90456 .80270 58 ^+16 .89691 .78869 .89886 i .79224 .90079 .79577 .90270 .79928 .90459 .80276 56 6 .89694 .78875 .89889 1 .79230 9.89892 0.79236 .90082 .79583 .90273 .79934 .90462 .80282 54 8+n 9.89697 0.78881 9.90085 0.79589 9.90276 0.79940 9.90465 0.80288 52 10 .89701 .78887 .89896 .79242 .90088 .79595 .90279 .79945 .90468 .80294 50 12+lS .89704 .78893 .89899 .79248 .90092 .79601 .90282 .79951 .90471 .80299 48 14 .89707 .78899 .89902 .79254 .90095 .79607 .90286 .79957 .90475 .80305 46 16+19 9.89710 0.78905 9.89905 0.79260 9.90098 0.79612 9.90289 0.79963 9.90478 0.80311 44 18 .89714 .78911 .89908 .79266 .90101 .79618 .90292 .79969 .90481 .80317 42 20+20 .89717 .78917 .89912 .79271 .90104 .79624 .90295 .79974 .90484 .80323 40 22 .89720 .78923 .89915 .79277 .90108 .79630 .90298 .79980 .90487 .80328 0.80334 38 36 24+21 9.89723 0.78328 9.89918 0.79283 9.90111 0.79636 9.90301 0.79986 9.90490 26 .89727 .78934 .89921 .79289 .90114 .79642 .90305 .79992 .90493 .80340 34 28+Zi .89730 .78940 .89925 .79295 .90117 .79648 .90308 .79998 .90496 .80346 32 SO .89733 .78946 .89928 .79301 .90120 .79653 .90311 .80004 .90499 .80351 30 5^+23 9.89736 0.78952 9.89931 0.79307 9.90124 0.79659 9.90314 0.80009 9.90503 0.80357 28 S4 .89740 .78958 .89934 .79313 .90127 .79665 .90317 .80015 .90506 .80363 26 S6+U .89743 .78364 .89938 .79319 .90130 .79671 .90320 .80021 .90509 .80369 24 S8 .89746 .78970 0.78976 .89941 .79325 .90133 .79677 .90324 .80027 0.80033 .90512 .990515 .80375 0.80380 22 20 40+15 9.89749 9.89944 0.79330 9.90136 0.79683 9.90327 42 .89753 .78982 .89947 .79336 .90140 .79688 .90330 .80038 .90518 .80386 18 4^+26 .89756 .78988 .89950 .79342 .90143 .79694 .90333 .80044 .90521 .80392 16 46 .89759 .78994 .89954 .79348 .90146 .79700 .90336 .80050 .90524 .80398 14 48+21 9.89763 0.79000 .9.89957 0.79354 9.90149 •0.79706 9.90339 0.80056 9.90527 0.80403 12 50 .89766 .79006 .89960 .79360 .90152 .79712 .90342 .80062 .90531 .80409 10 52+2S .89769 .79911 .89963 .79366 .90356 .79718 .90346 .80068 .90534 .80415 8 54 .89772 .79017 .89966 9.89970 .79372 .90159 .79724 0.79729 .90349 .80073 .90537 .80421 6 4 56+29 9.89776 0.79023 0.79377 9.90162 9.90352 0.80079 9.90540 0.80427 58 .89779 .79029 .89973 .79383 .90165 .79735 .90355 .80085 .90543 .80432 2 60+30 9.89782 0.79035 9.89976 0.79389 9.90168 0.79741 9.90358 0.80091 9.90546 0.80438 15^ 38m 15^ 36m 15A 34m 15fi 32m 15hS0m Page 910] TABLE 45. | Haversines. 1 s 8h som 127° 30' 8^1 3'2m 128° 0' gn 34m 128° 30^ 8h 36m 129° 0' 8h 38m 129° 30' s Log. Ilav.i Nat. Ilav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav.| Nat. Hav. Log. Hav. Nat. Hav. 9.90546 0.80438 9.90732 0.80783 9.90916 0.81126 9.91098 0.81466 9.91277 0.81804 60 ^ .90549 1 .80444 .90735 .80789 .90919 .81131 .91101 .81473 .91280! .81810 58 4+ 1 .90552 .80450 .90738 .80795 .90922 .81137 .91104 .81477 .91283 .81815 56 6 .90556 .80455 .90741 .80800 .90925 .81143 .91107 .81483 .91286 .81831 54 8+ 2 9.90559 0.80461 9.90744 0.90806 9.90928 0.81148 9.91110 0.81489 9.91289 0.81836 52 10 .90562 .80467 .90747 .80812 .90931 .81154 .91113 .81494 .91292 .81833 50 12^ 3 .90565 .80473 .90751 .80817 .90934 .81160 .91116 .81500 .91295 .81838 48 U .90568 .80478 .90754 .80823 .90937 .81165 .91119 .81506 .91298 .81843 46 16-\- 4 9.90571 0.80484 9.90757 0.80829 9.90940 0.81171 9.91122 0.81511 9.91301 6.81849 U 18 .90574 .80490 .90760 .80835 .90943 .81177 .91125 .81517 .91304 .81854 42 20-\- 5 .90577 .80496 .90763 .80840 .90946 .81183 .91128 .81533 .91307 .81860 40 22 .90580 .80503 .90766 .80846 .90949 .81188 .91131 .81538 .91310 .81866 0.81871 38 36 24+ 6 9.90584 0.80507 9.90769 0.80852 9.90952 0.81194 9.91134 0.81534 9.91313 26 .90587 .80513 .90772 .80858 .90955 .81300 .91137 .81539 .91316 .81877 34 28+ 7 .90590 .80519 .90775 .80863 .90958 .81205 .91140 .81545 .91319 .81883 32 ^0 .90593 .80525 .90778 .80869 .90962 .81211 .91143 1 .81551 .91322 .81888 30 32+ 8 9.90596 0.80530 9.90781 0.80875 9.90965 0.81217 9.91146 0.81556 9.91325 0.81894 28 5-^ .90599 .80536 .90784 .80880 .90968 .81222 .91149 .81563 .91328 .81899 26 56+ 9 .90602 .80542 .90787 .80886 .90971 .81228 .91152 .81568 .91331 .81905 24 38 .90605 .80548 .90790 .80892 0.80898 .90974 .81234 .91155 .81573 .91334 .81910 22 40+10 9.90608 0.80553 9.90794 9.90977 0.81239 9.91158 0.81579 9.91337 0.81916 20 42 .90611 .80559 .90797 .80903 .90980 .81245 .91161 .81585 .91340 .81933 18 U+11 .90615 .80565 .90800 .80909 .90983 .81251 .91164 .81590 .91343 .81937 16 46 .90618 .80571 .90803 .80915 .90986 .81356 .91167 .81596 .91346 .81933 14 48+12 9.90621 0.80576 9.90806 0.80920 9.90989 0.81363 9.91170 0.81601 9.91349 0.81938 12 50 .90624 .80582 .90809 .80926 .90992 .81268 .91173 .81607 .91352 .81944 10 52+13 .90627 .80588 .90812 .80932 .90995 .81273 .91176 .81613 .91355 .81950 8 54 .90630 .80594 .90815 .80938 .90998 .81279 .91179 .81618 .91358 .81955 6 56+14 9.90633 0.80599 9.90818 0.80943 9.91001 0.81285 9.91182 0.81634 9.91361 0.81961 4 58 9.90636 0.80605 9.90821 0.80949 9.91004 0.81291 9.91185 0.81630 9.91364 0.81966 2 15h 29m 15h 27m 15h 25m 15^ 23m 15h 21-m s ' 0+16 8^31^127° SO' Sh 33m 128° 0^ 8h 35m 128° 30^ 8h 37m 129° 0" 8h 39m 129° 30^ s 60 9.90639 0.80611 9.90824 0.80955 9.91007 0.81296 9.91188 0.81635 9.91367 0.81973 Jg .90642 .80617 .90827 .80960 .91010 .81302 .91191 .81641 .91369 .81978 58 4+16 .90646 .80622 .90830 .80966 .91013 .81308 .91194 .81647 .91372 .81983 56 6 .90646 .80628 .90833 .80972 .91016 .81313 .91197 .81653 .91375 .81989 0.81994 54 52 8+n 9.90652 0.80634 9.90836 0.80978 9.91019 0.81319 9.91200 0.81658 9.91378 10 .90655 .80640 .90840 .80983 .91022 .81325 .91203 .81663 .91381 .83000 50 12+18 .90658 .80645 .90843 .80989 .91025 .81330 .91206 .81669 .91384 .83005 48 14 .90661 .80651 .90846 .80995 .91028 .81336 .91209 .81675 .91387 .83011 46 16+19 9.90664 0.80657 9.90849 0.81000 9.91031 0.81343 9.91212 0.81680 9.91390 0.83017 44 18 .90667 .80663 .90852 .81008 .91034 .81347 .91215 .81686 .91393 .83033 42 20+20 .90670 .80668 .90855 .81012 .91037 .81353 .91218 .81693 .91396 .83038 40 22 .90673 .80674 .90858 .81017 .91040 9.91043 .81359 .91221 .81697 .91399 9.91402 .83033 38 36 24+21 9.90676 0.80680 9.90861 0.81023 0.81364 9.91224 0.81703 0.83039 26 .90680 .80686 .90864 .81029 .91046 .81370 .91227 .81708 .91405 .83045 34 28+22 .90683 .80691 .90867 .81035 .91049 .81376 .91230 .81714 .91408 .83050 32 SO .90686 .80697 .90870 .81040 .91052 .81381 .91233 .81730 .91411 .83056 30 32+23 9.90689 0.80703 9.90873 0.81046 9.91055 0.81387 9.91236 0.81735 9.91414 0.83061 28 34 .90692 .80709 .90876 .81052 .91058 .81393 .91239 .8?.731 .91417 .83067 26 36+24: .90695 .80714 .90879 .81057 .91061 .81398 .91242 .81737 .91420 .83073 24 38 .90698 .80720 .90882 .81063 .91064 .81404 .91245 .81742 .91423 .82078 22 20 40+25 9.90701 0.80726 9.90885 0.81068 9.91067 0.81409 9.91248 0.81748 9.91426 0.82084 42 .90704 .80731 .90888 .81074 .91071 .81415 .91251 .81753 .91429 .82089 18 U+26 .90707 .80737 .90892 .81080 .91074 .81431 .91254 .81759 .91432 .83095 16 46 .90710 .80743 .90895 .81086 .91077 .81436 .91257 .81765 .91435 .83100 14 48+21 9.90714 0.80749 9.90898 0.81092 9.91080 0.81432 9.91260 0.81770 9.91437 0.83106 12 50 .90717 .80754 .90901 .81097 .91083 .81438 .91263 .81776 .91440 .83113 10 52+28 .90720 .80760 .90904 .81103 .91086 .81443 .91265 .81781 .91443 .83117 8 54 .90723 .80766 0.80772 .90907 .81109 .91089 .81449 .91268 .81787 0.81793 .91446 .83133 6 4 56+29 9.90726 9.90910 0.81114 9.91092 0.81455 9.91271 9.91449 0.83138 58 .90729 .80777 .90913 .81120 .91095 .81460 .91274 .81798 .91452 .83134 2 60+30 9.90732 0.80783 9.90916 0.81126 9.91098 0.81466 9.91277 0.81804 9.91455 0.83139 /5'^ 28m 15h 26m n 15^ 24"^ 1 15^ 22m 1 15J>- 20m 1 TABLE 45. [Page 911 Haversines. s ' 5A 40''« 130° 0' 1 8^ 42^ 130° 30^ 8h U^ 131° iy 8^ 46m 131° 30^ | 8^ 4Sm 132° r 3 Log. Ilav. Nat. Ilav. Log. Hav. Nat. nav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.91455 0.83139 9.91631 0.82472 9.91805 0.82803 9.91976 0.83131 9.92146 0.83457 60 2 .91458 .83145 .91634 .82478 .91807 .82808 .91979 .83136 .92149 .83463 58 4+ 1 .91461 .83151 .91637 .82483 .91810 .82814 .91982 .83142 .92152 .83467 56 6 .91464 .82156 .91640 9.91643 .82489 0.82495 .91813 .82819 0.82825 .91985 9.91988 .83147 0.83153 .92154 .83473 54 52 8+ 3 9.91467 0.83163 9.91816 9.92157 0.83478 10 .91470 .83167 .91645 .82500 .91819 .83830 .91991 .83158 .92160 .83484 50 12+ 4 .91473 .83173 .91648 .82506 .91822 .83836 .91993 i .83164 .92163 .83489 48 U .91476 .83178 .91651 .82511 .91825 .83841 .91996 j .83169 .92166 .83494 46 16+ 4 9.91479 0.83184 9.91654 0.83517 9.91828 0.83847 9.91999 1 0.83175 9.92169 0.83500 44 18 .91482 .83189 .91657 .83533 .91830 .83853 .92002 .83180 .92171 .83505 42 20+ 5 .91485 .83195 .91660 .83538 .91833 .83858 .92005 .83185 .92174 .83511 40 22 .91488 .83200 .91663 9.91666 .83533 .91836 .83863 .92008 9.92010 .83191 .92177 .83516 38 24+ 6 9.91490 0.83306 0.83539 9.91839 0.82869 0.83196 9.92180 0.83531 36 26 .91493 .83312 .91669 .83544 .91842 .82874 .92013 .83203 .92183 .83527 34 28+ 7 .91496 .82217 .91672 .82550 .91845 .82880 .92016 .83307 .92185 .83532 32 SO .91499 .83333 .91674 .83555 .91848 .82885 .92019 .83313 .92188 .83538 30 S2+ 8 9.91502 0.82228 9.91677 0.83561 9.91851 0.82891 9.92022 0.83318 9.92191 0.83543 28 .54 .91505 .82234 .91680 .83566 .91853 .82896 .92025 .83334 .92194 .83548 26 56+ 9 .91508 .82240 .91683 .83573 .91856 .82902 .92027 .83329 .92197 .83554 24 38 .91511 .82345 .91686 .83577 .91859 .83907 .92030 .83334 .92199 9.92202 .83559 0.83564 22 20 40+10 9.91514 0.83351 9.91689 0.83583 9.91862 0.82913 9.92033 0.83340 42 .91517 .83356 .91692 .83588 .91865 .82918 .92036 .83345 .92205 .83570 18 44+11 .91520 .82362 .91695 .83594 .91868 .83934 .92039 .83351 .92208 .83575 16 46 .91523 .83367 .91698 .83599 .91871 .83939 .92042 .83356 .92211 .83581 14 45+13 9.91526 0.82273 9.91701 0.83605 9.91874 0.83934 9.92044 0.83263 9.92213 0.83586 12 50 .91529 .82278 .91703 .83610 .91876 .83940 .92047 ..83367 .92216 .83591 10 52+lZ .91532 .82284 .91706 .83616 .91879 .83945 .92050 .83373 .92219 .83597 8 54 .91534 .82290 .91709 .83631 .91882 9.91885 .83951 0:83956 .92053 9.92056 .83378 0.83383 .92222 9.92225 .83602 6 56+14 9.91537 0.83395 9.91712 0.83627 0.83608 4 58 9.91540 0.83301 9.91715 0.83632 9.91888 0.83963 9.92059 0.83389 9.92227 0.83613 2 15h igm 15h nm 15^ 15m 15h 13m loh 11m s ' 0+15 8h 4im 130° 0^ 8h 4sm 130° 30' Sh 45m 131° 0' 8h 47m 131° 30: 8h 49m 132° 0' s 60 9.91543 0.83306 9.91718 1 0.82638 9.91891 0.83967 9.92061 0.83394 9.92230 0.83618 2 .91546 .83312 .91721 1 .82644 .91894 .83973 .92064 .83300 .92233 .83624 58 4+ie .91549 .82317 .91724 i .82649 .91896 .83978 .92067 .83305 .92236 .83629 56 6 .91552 .82323 .91727 .82655 .91899 .83984 .92070 .83310 0.83316 .92239 .83635 54 52 8+11 9.91555 0.82328 9.91730 0.82660 9.91902 0.83989 9.92073 9.92241 0.83640 10 .91558 .82334 .91732 .82666 .91905 .83995 .92076 .83331 .92244 .83645 50 12+1% .91561 .82339 .91735 .82671 .91908 .83000 .92078 .83337 .92247 .83651 48 14 .91564 .83345 .91738 .82677 .91911 .83006 .92081 .83333 .92250 .83656 46 i6+19 9.91567 0.83351 9.91741 0.82682 9.91914 0.83011 9.92084 0.83337 9.92253 0.83661 U 18 .91570 .83356 .91744 .82688 .91916 .83016 .92087 .83343 .92255 .83667 42 20+29 .91573 .83363 .91747 .82693 .91919 .83033 .92090 .83348 .92258 .83673 40 22 .91575 .83367 .91750 .83699 .91922 9.91925 .83037 0.83033 .92093 9.92095 .83354 0.83359 .92261 .83678 38 36 24+21 9.91578 0.82373 9.91753 0.83704 9.92264 0.83683 26 .91581 .83378 .91756 .83710 .91928 .83038 .92098 .83365 .92266 .83688 34 28+n .91584 .83384 .91758 .82715 .91931 .83044 .92101 .83370 .92269 .83694 32 SO .91587 .82389 .91761 .82721 .91934 .83049 .92104 .83375 .92272 .83699 30 S2+29 9.91590 0.83395 9.91764 0.82726 9.91936 0.83055 9.92107 0.83381 9.92275 0.83704 28 S4 .91593 .83400 .91767 .82732 .91939 .83060 .92109 .83386 .92278 .83710 26 36+24: .91596 .83406 .91770 .82737 .91942 .83066 .92112 .83393 .92280 .83715 24 38 .91599 .83412 .91773 .82743 .91945 .83071 .92115 .83397 0.83402 .92283 9.92286 .83720 0.83726 22 20 40+25 9.91602 0.83417 9.91776 0.82748 9.91948 0.83077 9.92118 42 .91605 .83433 .91779 .83764 .91951 .83083 .92121 .83408 .92289 .83731 18 44+36 .91608 .83438 .91782 .83759 .91954 .83087 .92124 .83413 .92292 .83737 16 46 .91610 .83434 .91784 .83765 .91956 .83093 .92126 .83419 .92294 .83742 14 48+21 9.91613 0.83439 9.91787 0.82770 9.91959 0.83098 9.92129 0.83424 9.92297 0.83747 12 50 .91616 .83445 .91790 .83776 .91962 .83104 .92132 .83430 .92300 .83753 10 5^+38 .91619 .83450 .91793 .82781 .91965 .83109 .92135 .83435 .92303 .83758 8 54 .91622 .83456 .91796 .82786 .91968 9T91971 .83115 0.83130 .92138 9.92140 .83440 0.83446 .92305 .83763 6 66+29 9.91625 0.83461 9.91799 0.83792 9.92308 0.83769 4 58 .91628 .82467 .91802 .83797 .91973 .83126 .92143 .83451 .92311 .83774 2 60+30 9.91631 0.82472 9.91805 0.83803 9.91976 0.83131 9.92146 0.83457 9.92314 0.83780 15h 18m 15h 16m J5h 14m J5h 12m 15h lOm Page 912] TABLE 45. Haversines. s ' 8h 50m 132° 30' 5ft 5;?™ 133° 0' 5ft 54™ 133° 30^ 5ft 56m 134° 0' 5ft 58m 134° SO' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 2 4+ 1 6 '9.92314 .92317 .92319 .92322 0.S3780 .83785 .83790 .83796 0.83801 .83806 .83812 .83817 0.83832 .83828 .83833 .83838 0.83844 .83849 .83855 .83860 0.83865 .83871 .83876 .83881 9.92480 .92482 .92485 .92488 0.84100 .84105 .84111 .84116 9.92643 .92646 .92649 .92652 0.84418 .84423 .84428 .84434 0.84439 .84444 .84449 .84455 0.84460 .84465 .84470 .84476 9.92805 .92808 .92811 .92813 0.84733 .84738 .84743 .84749 9.92965 .92968 .92970 .92973 0.85045 .85051 .85056 .85061 60 58 66 54 8+ 2 10 12+ 3 14 16+ 4 18 20+ 5 22 9.92325 .92328 .92330 .92333 9.92336 .92339 .92342 .92344 9.92491 .92493 .92496 .92499 9.92502 .92504 .92507 .92510 0.84121 .84127 .84133 .84137 0.84142 .84148 .84153 .84158 9.92654 .92657 .92660 .92662 9 92665 .92668 .92670 .92673 9.92816 .92819 .92821 .92824 9.92827 .92829 .92832 .92835 0.84754 .84759 .84764 .84770 0.84775 .84780 .84785 .84790 9.92975 .92978 .92981 .92984 9.92986 .92989 .92992 .92994 0.85066 .85071 .85077 .85083 0.85087 .85092 .85097 .85102 62 60 48 46 44 42 40 38 24+ 6 26 28+ 7 30 32+ 8 34 36+ 9 38 9.92347 .92350 .92353 .92355 9.92358 .92361 .92364 .92366 9.92512 .92515 .92518 .92521 9.92523 .92526 .92529 .92532 0.84164 .84169 .84174 .84180 0.84185 .84190 .84196 .84301 9.92676 .92679 .92681 .92684 9.92687 .92689 .92692 .92695 0.84481 .84486 .84492 .84497 0.84502 .84507 .84513 .84518 9.92837 .92840 .92843 .92845 9.92848 .92851 .92853 .92856 0.84796 .84801 .84806 .84811 0.84817 .84822 .84827 .84832 9.92997 .93001 .93002 .93005 9.93007 .93010 .93013 .93015 0.85108 .85113 .85118 .85123 0.85128 .85134 .85139 .85144 36 34 32 30 28 26 24 22 40+10 42 U+11 46 48+12 50 52+n 54 9.92369 .92372 .92375 .92378 9.92380 .92383 .92386 .92389 0.83887 .83892 .83897 .83903 0.83908 .83913 .83919 .83924 9.92534 .92537 .92540 .92543 9.92545 ^2548 .92551 .92554 0.84206 .84211 .84217 .84222 0.84227 .84233 .84238 .84243 9.92698 .92700 .92703 .92706 9.92708 .92711 .92714 .92716 0.84523 .84528 .84534 .84539 0.84544 .84549 .84555 .84560 9.92859 .92861 .92864 .92867 9.92869 .92872 .92875 .92877 0.84837 .84843 .84848 .84853 0.84858 .84863 .84869 .84874 9.93018 .93021 .93023 .93026 9.93029 .93031 .93034 .93036 0.85149 .85154 .85159 .85165 0.85170 .85175 .85180 .85185 0.85190 0.85196 20 18 16 14 12 10 8 6 4 2 56+14 55 9.92391 9.92394 0.83929 0.83935 9.92556 9.92559 0.84249 0.84254 9.92719 9.92722 0.84565 0.84570 9.92880 9.92883 0.84879 0.84884 9.93039 9.93042 IShgm 15h7m 15115m 15h3m Uhlm 8 ' 5ft 5m 132° 30' 5ft 53m 133° 0' 5ft 55m 133° 30' 5ft 57TO 134° 0' 5ft 59m 134° 30' s 0+15 2 4+16 6 9.92397 .92400 .92402 .92405 0.83940 .83945 .83951 .83956 9.92562 .92564 .92567 .92570 0.84259 .84264 .84270 .84275 9.92725 .92727 .92730 .92733 0.84576 .84581 .84586 .84591 9.92885 .92888 .92891 .92893 0.84890 .84895 .84900 .84905 9.93044 .93047 .93050 .93052 0.85201 .85206 .85211 .85216 60 68 66 54 5+17 io 12+1% 14 16+19 i5 fO+20 22 9.92408 .92411 .92413 .92416 9.92419 .92422 .92425 .92427 0.83961 .83967 .83972 .83977 0.83983 .83988 .83993 .83999 9.92573 .92575 .92578 .92581 9.92584 .92586 .92589 .92592 0.84280 .84286 .84291 .84296 0.84302 .84307 .84312 .84317 9.92735 .92738 .92741 .92743 9.92746 .92749 .92751 .92754 0.84597 .84602 .84607 .84612 0.84618 .84623 .84628 .84633 9.92896 .92899 .92901 .92904 9.92907 .92909 .92912 .92915 0.84910 .84916 .84921 .84926 0.84931 .84936 .84942 .84947 9.93055 .93057 .93060 .93063 9.93065 .93068 .93071 .93073 0.85221 .85227 .85333 .85337 0.85343 .85247 .85252 .85358 62 50 48 46 44 42 40 38 24+21 26 28+22 SO 5^+23 34 56+24 55 9.92430 .92433 .92436 .92438 9.92441 .92444 .92447 .92449 0.84004 .84009 .84015 .84020 0.84025 .84031 .84036 .84041 9.92594 .92597 .92600 .92603 9.92605 .92608 .92611 .92613 0.84323 .84328 .84333 .84339 0.84344 .84349 .84354 .84360 9.92757 .92760 .92762 .92765 9.92768 .92770 .92773 .92776 0.84639 .84644 .84649 .84654 0.84660 .84665 .84670 .84675 9.92917 .92920 .92923 .92925 9.92928 .92931 .92933 .92936 0.84953 .84957 .84963 .84968 0.84973 .84978 .84983 .84988 9.93076 .93079 .93081 .93084 9.93086 .93089 .93092 .93094 0.85263 .85268 .85373 .85378 0.85283 .85288 .85394 .85399 36 34 32 30 28 26 24 22 40+25 42 44+26 46 45+27 50 5^+28 54 9.92452 .92455 .92458 .92460 9.92463 .92466 .92469 .92471 9.92474 .92477 9.92480 0.84047 .84052 .84057 .84063 0.84068 .84073 .84079 .84084 0.84089 .84095 0.84100 9.92616 .92619 .92622 .92624 9.92627 .92630 .92633 .92635 9.92638 .92641 9.92643 0.84365 .84370 .84376 .84381 0.84386 .84391 .84397 .84402 9.92778 .92781 .92784 .92786 9.92789 .92792 .92794 ,92797 0.84681 .84686 .84691 .84696 0.84702 .84707 .84712 .84717 9.92939 .92941 .92944 .92947 9.92949 .92952 .92955 .92957 9.92960 .92962 9.92965 0.84994 .84999 .85004 .85009 0.85014 .85030 .85025 .85030 9.93097 .93100 .93102 .93105 9.93107 .93110 .93113 .93115 0.85304 .85309 .85314 .85319 0.85324 .85330 .85335 .85340 0.85345 .85350 0.85355 20 18 16 14 12 10 8 6 4 g 56+29 55 60+30 0.84407 .84412 0.84418 9.92800 .92802 9.92805 0.84722 .84728 0.84733 0.85035 .85040 0.85045 9.93118 .93120 9.93123 15^ 8^ 15h6m 15^4.m IShgm 15^ Om TABLE 45. [Page 913 Havereines. s ' Qhom 135° 9A 4™ 136° 9h gm 137° 9^ 12m 138° 9hl6m 139° | Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 0.85967 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. I^g. Hav. Nat. Hav. s 60 9.93123 0.85355 9.93433 9.93736 0.86568 9.94030 0.87157 9.94318 0.87735 4 1 .93128 .85366 .93438 .85977 .93741 .86578 .94035 .87167 .94322 .87745 56 8 2 .93134 .85376 .93443 .85987 '.93746 .86588 .94040 .87177 .94327 .87755 52 12 3 .93139 .85386 .93448 .85997 .93751 .86597 .94045 .87186 .94332 .87764 48 16 4 9.93144 0.85396 9.93454 0.86007 9.93755 0.86607 9.94050 0.87196 9.94336 0.87774 U 20 5 .93149 .85407 .93459 .86017 .93760 .86617 .94055 .87206 .94341 .87783 40 24 6 .93154 .85417 .93464 .86028 .93765 .86627 .94059 .87216 .94346 .87793 36 28 7 .93160 .85427 .93469 .86038 .93770 .86637 .94064 .87225 .94351 .87802 32 32 8 9.93165 0.85438 9.93474 0.86048 9.93775 0.86647 9.94069 0.87235 9.94355 0.87812 28 36 9 .93170 .85448 .93479 .86058 .93780 .86657 .94074 .87245 .94360 .87821 24 40 10 ■ .93175 .85458 .93484 .86068 .93785 .86667 .94079 .87254 .94365 .87831 20 -^4 11 .93181 .85468 .93489 .86078 .93790 .86677 .94084 .87264 .94369 .87840 16 48 13 9.93186 0.85479 9.93494 0.86088 9.93795 0.86686 9.94088 0.87274 9.94374 0.87850 12 5^ 13 .93191 .85489 .93499 .86098 .93800 .86696 .94093 .87283 .94379 .87859 8 56 14 9.93196 0.85499 9.93504 0.86108 9.93805 0.86706 9.94098 0.87293 9.94383 0.87869 4 14h 59m i4h 55m 14^ 5im 14h 47m 14h4,sm s ' 9h im 135° 9^ 5m 136° 9fi 9m 137° 9h ism 138° 9h 17m 139° 8 15 9.93201 0.85509 9.93509 0.86118 9.93810 0.86716 9.94103 0.87303 9.94388 0.87878 60 4 16 .93207 .85520 .93515 .86128 .93815 .86726 .94108 .87313 .94393 .87888 56 5 17 .93212 .85530 .93520 .86138 .93820 .86736 .94112 .87322 .94398 .87897 52 12 18 .93217 .85540 .93525 .86148 .93825 .86746 .94117 .87332 .94402 .87907 48 iff 19 9.93222 0.85550 9.93530 0.86158 9.93830 0.86756 9.94122 0.87342 9.94407 0.87916 44 £0 20 .93227 .85560 .93535 .86168 .93835 .86765 .94127 .87351 .94412 .87926 40 24 21 .93232 .85571 .93540 .86178 .93840 .86775 .94132 .87361 .94416 .87935 36 f5 22 .93238 .85581 .93545 .86189 .93845 .88785 .94137 .87371 .94421 .87945 32 S2 23 9.93243 0.85591 9.93550 0.86199 9.93849 0.86795 9.94141 0.87380 9.94426 0.87954 28 56 24 .93248 .85601 .93555 .86209 .93854 .86805 .94146 .87390 .94430 .87964 24 40 25 .93253 .85612 .93560 .86219 .93859 .86815 .94151 .87400 .94435 .87973 20 44 26 .93258 .85622 .93565 .86229 .93864 .86825 .94156 .87409 .94440 .87983 16 4^ 27 9.93264 0.85632 9.93570 0.86239 9.93869 0.86834 9.94161 0.87419 9.94444 0.87992 12 52 28 .93269 .85642 .93575 .86249 .93874 .86844 .94165 .87428 .94449 .88001 8 56 29 9.93274 0.85652 9.93580 0.86259 9.93879 0.86854 9.94170 0.87438 9.94454 0.88011 4 14h 58m 14h 54m 14hsom 14h 46m 14h 42m 8 ' 9^ 2m 135° 9h6m 136° 9h 10m 1370 9^ 14m 138° 9^ 18m 139° s 30 9.93279 0.85663 9.93585 0.86296 9.93884 0.86864 9.94175 0.87448 9.94458 0.88020 60 4 31 .93284 .85673 .93590 .86279 .93889 .88874 .94180 .87457 .94463 .88030 56 8 32 .93289 .85683 .93595 .86289 .93894 .86884 .94184 .87467 .94468 .88039 52 J:? 33 .93295 .85693 .93600 .86299 .93899 .86893 .94189 .87477 .94472 .88049 48 i6 34 9.93300 0.85703 9.93605 0.86309 9.93904 0.86903 9.94194 0.87486 9.94477 0.88058 U 20 35 .93305 .85713 .93611 .86319 .93908 .86913 .94199 .87496 .94482 .88068 40 £4 36 .93310 .85724 .93616 .86329 .93913 .86923 .94204 .87505 .94486 .88077 36 28 37 .93315 .85734 .93621 .86339 .93918 .86933 .94208 .87515 .94491 .88086 32 5£ 38 9.93320 0.85744 9.93626 0.86349 9.93923 0.86942 9.94213 0.87525 9.94496 0.88096 28 56 39 .93326 .85754 .93631 .86359 .93928 .86952 .94218 .87534 .94500 .88105 24 40 40 .93331 .85764 .93636 .86369 .93933 .86962 .94223 .87544 .94505 .88115 20 44 41 .93336 .85774 .93641 .86379 .93938 .86972 .94227 .87554 .94509 .88124 16 48 42 9.93341 0.85785 9.93646 0.86389 9.93943 0.86982 9.94232 0.87563 9.94514 0.88133 12 52 43 .93346 .85795 .93651 .86399 .93948 .86991 .94237 .87573 .94519 .88143 8 56 44 9.93351 0.85805 9.93656 0.86409 9.93952 0.87001 9.94242 0.87582 9.94523 0.88152 4 14h sjm 14h 53m 14^ 49m 14h 4.5m 14h 41m s ' 9hsm 135° 9h 7m 136° gh 11m 137° 9h 15m 138° 9h 19m 139° s 45 9.93356 0.85815 9.93661 0.86419 9.93957 0.87011 9.94246 0.87592 9.94528 0.88162 60 4 46 .93362 .85825 .93666 .86429 .93962 .87021 .94251 .87602 .94533 .88171 56 S 47 .93367 .85835 .93671 .86438 .93967 .87030 .94256 .87611 .94537 .88180 52 i^ 48 .93372 .85846 .93676 .86448 .93972 .87040 .94261 .87621 .94542 .88190 4S 16 49 9.93377 0.85856 9.93681 0.86458 9.93977 0.87050 9.94265 0.87630 9.94546 0.88199 44 fO 50 .93382 .85866 .93686 .86468 .93982 .87060 .94270 .87640 .94551 .88209 40 24 51 .93387 .85876 .93691 .86478 .93987 .87070 .94275 .87649 .94556 .88218 36 £5 52 .93392 .85886 .93696 .86488 .93991 .87079 .94280 .87659 .94560 .88227 32 52 53 9.93397 0.85896 9.93701 0.86498 9.93996 0.87089 9.94284 0.87669 9.94565 0.88237 28 S6 54 .93403 .85906 .93706 .86508 .94001 .87099 .94289 .87678 .94570 .88246 24 40 55 .93408 .85916 .93711 .86518 .94006 .87109 .94294 .87688 .94574 .88255 20 44 56 .93413 .85926 .93716 .86528 .94011 .87118 .94299 .87697 .94579 .88265 16 45 57 9.93418 0.85937 9.93721 0.86538 9.94016 0.87128 9.94303 0.87707 9.94583 0.88274 12 52 68 .93423 .85947 .93726 .86548 .94021 .87138 .94308 .87716 .94588 .88284 8 66 69 .93428 .85957 .93731 .86558 .94026 .87148 .94313 .87726 .94593 .88293 4 60 60 9.93433 0.85967 9.93736 0.86568 9.94030 0.87157 9.94318 0.87735 9.94597 0.88302 14h 567n 1 J4h r,2m 1 14^ 4Sm 1 14^ 44m i 14* 40m 1 Page 914] TABLE 45. Haversines. s ' 9h 20m 140° 9h 24m 141° 9h 28m 143° 9h S2m 143° 9h 36m 144° s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.94597 0.88302 9.94869 0.88857 9.95134 0.89401 9.96391 0.89933 9.95641 0.90451 60 4 1 .94602 .88312 .94874 .88866 .95138 .89409 .95396 .89941 .95645 .90459 56 8 2 .94606 .88321 .94878 .88876 .95143 .89418 .95400 .89949 .95649 .90468 52 12 3 .94611 .88330 .94883 .88885 .95147 .89427 .95404 .89958 .95654 .90476 48 16 4 9.94616 0.88340 9.94887 0.88894 9.95151 0.89436 9.95408 0.89967 9.95658 0.90485 44 20 5 .94620 .88349 .94892 .88903 .95156 .89445 .95412 .89976 .95662 .90494 40 24 6 .94625 .88358 .94896 .88912 .95160 .89454 .95417 .89984 .95666 .90502 36 28 7 .94629 .88368 .94901 .88921 .95164 .89463 .95421 .89993 .95670 .90511 32 S2 8 9.94634 0.88377 9.94905 0.88930 9.95169 0.89473 9.95425 0.90003 9.95674 0.90519 28 S6 9 .94638 .88386 .94909 .88940 .95173 .89481 .95429 .90010 .95678 .90528 24 40 10 .94643 .88396 .94914 .86949 .95177 .89490 .95433 .90019 .95682 .90537 20 ^ 11 .94648 .88405 .94918 .88958 .95182 .89499 .95438 .90028 .95686 .90545 16 48 12 9.94652 0.88414 9.94923 0.88967 9.95186 0.89508 9.95442 0.90037 9.95690 0.90553 12 5f 13 .94657 .88423 .94927 .88976 .95190 .89517 .95446 .90045 .95694 .90563 8 56 14 9.94661 0.88433 9.94932 0.88985 9.95195 0.89536 9.95450 0.90054 9.95699 0.90570 4 14f>- S9m 14^ 35m 14^ 3im 14^ 27m 14h 23m s ' 15 9h 2im 140° 9h 25m 141° 9h 29m 142° 9h 33m 143° 9h 37m 144° s 60 9.94666 0.88442 9.94936 0.88994 9.95199 0.89534 9.95454 0.90063 9.95703 0.90579 4 16 .94670 .88451 .94941 .89003 .95203 .89543 .95459 .90071 .97507 .90588 56 5 17 .94675 .88461 .94945 .89012 .95208 .89552 .95463 .90080 .95711 .90596 52 12 18 .94680 .88470 .94950 .89022 .95212 .89561 .95467 .90089 .95715 .90604 48 16 19 9.94684 0.88479 9.94954 0.89031 9.95216 0.89570 9.95471 0.90097 9.95719 0.90613 U ^0 30 .94689 .88489 .94958 .89040 .95221 .89579 .95475 .90106 .95723 .90631 40 24 21 .94693 .88498 .94963 .89049 .95225 .89588 .95480 .90115 .95727 .90630 36 :25 22 .94698 .88507 .94967 .89058 .95229 .89597 .95484 .90124 .95731 .90638 32 32 23 9.94702 0.88516 9.94972 0.89067 0.95234 0.89606 9.95488 0.90132 9.95735 0.90647 28 56 24 .94707 .88526 .94976 .89076 .95238 .89614 .95492 .90141 .95739 .90655 24 40 25 .94711 .88535 .94981 .89085 .95242 .89623 .95496 .90150 .95743 .90664 20 44 26 .94716 .88544 .94985 .89094 .95246 .89632 .95501 .90158 .95747 .90673 16 45 27 9.94721 0.88553 9.94989 0.89103 9.95251 0.89641 9.95505 0.90167 9.95751 0.90680 12 62 28 .94725 .88563 .94994 .89112 .95255 .89650 .95509 .90176 .95755 .90689 8 56 29 9.94730 0.88572 9.94998 0.89121 9.95259 0.89659 9.95513 0.90184 9.95759 0.90697 4 Uf)- 38m 14^ 34m 14^ 30m 14h 26m 14h 22m s ' 30 9h 22m 140° 9h 26m 141° 9h som 143° 9h 34m 143° 9h ssm 144° s 60 9.94734 0.88581 9.95003 0.89130 9.95264 0.89668 9.95517 0.90193 9.95763 0.90706 4 31 .94739 .88590 .95007 .89139 .95268 .89677 .95521 .90201 .95768 .90714 56 8 32 .94743 .88600 .95011 .89149 .95272 .89685 .95526 .90210 .95772 .90733 52 :?f 33 .94748 .88609 .95016 .89158 .95276 .89694 .95530 .90219 .95776 .90731 48 i6 34 9.94752 0.88618 9.95020 0.89167 9.95281 0.89703 9.95534 0.90227 9.95780 0.90740 44 20 35 .94757 .88627 .95025 .89176 .95285 .89712 .95538 .90336 .95784 .90748 40 ^4 36 .94761 .88637 .95029 .89185 .95289 .89721 .95542 .90245 .95788 .90756 36 28 37 .94766 .88646 .95033 .89194 .95294 .89730 .95546 .90253 .95792 .90765 32 5^ 38 9.94770 0.88655 9.95038 0.89203 9.95298 0.89738 9.95550 0.90262 9.95796 0.90773 28 56 39 .94774 .88664 .95042 .89212 .95302 .89747 .95555 .90371 .95800 .90793 24 40 40 .94779 .88674 .95047 .89231 .95306 .89756 .95559 .90379 .95804 .90790 20 44 41 .94784 .88683 .95051 .89230 .95311 .89765 .95563 .90388 .95808 .90798 16 48 42 9.94788 0.88692 9.95055 0.89239 9.95315 0.89774 9.95567 0.90396 9.95812 0.90807 12 5;? 43 .94793 .88701 .95060 .89248 .95319 .89783 .95571 .90305 .95816 .90815 8 56 44 9.94797 0.88710 9.95064 0.89257 9.95323 0.89791 9.95575 0.90314 9.95820 0.90834 4 14h sjm ! i4h ssm 14^ 29m 14h 25m 1 14h 21m s ' 45 9h23m 140° 1 9h 27m 141° 9h Sim 143° 9h35m 143° | 9h 39m 144° s 60 9.94802 0.88720 9.95069 0.89266 9.95328 0.89800 9.95579 0.90322 9.95824 0.90832 4 46 .94806 .88729 .95073 .89275 .95332 .89809 .95584 .90331 .95828 .90840 56 5 47 .94811 .88738 .95077 .89284 .95336 .89818 .95588 .90339 .95832 .90849 52 i;? 48 .94815 .88747 .95082 .89293 .95340 .89827 .95592 .90348 .95836 .90857 48 16 49 9.94820 0.88756 9.95086 0.89302 9.75345 0.89835 9.95596 0.90357 9.95840 0.90866 U fO 50 .94824 .88766 .95090 .89311 .95349 .89844 .95600 .90365 .95844 .90874 40 24 51 .94829 .88775 .95095 .89320 .95353 .89853 .95604 .90374 .95848 .90882 36 ;?5 52 .94833 .88784 .95099 .89.329 .95357 .89862 .95608 .90382 .95852 .90891 32 5^ 53 9.94838 0.88793 9.95104 0.89338 9.95362 0.89870 9.95613 0.90391 9 95856 0.90899 28 36 54 .94842 .88802 .95108 .89347 .95366 .89879 .95617 .90399 .95860 .90907 24 40 55 .94847 .88811 .95112 .89356 .95370 .89888 .95621 .90408 .95864 .90916 20 U 56 .94851 .88821 .95117 .89365 .95374 .89897 .95625 .90417 .95868 .90924 16 45 57 9.94856 0.88830 9.95121 0.89374 9.95379 0.89906 9.95629 0.90425 9.95872 0.90933 12 5f 58 .94860 .88839 .95125 .89383 .95383 .89914 .95633 .90434 .95876 .90941 8 56 59 .94865 .88848 .95130 .89392 .95387 .89923 .95637 .90442 .95880 .90949 4 60 60 9.94869 0.88857 9.95134 0.89401 9.95391 0.89932 9.95641 0.90451 9.95884 0.90958 14^ 36m 1 14h S2m 1 14^ 28m 1 14^ 24^ 1 14f>' 20m 1 TABLE 45. [Page 916 Haversines. s ' 9h40m 145° 9h 44^ 146° 9h 48m 147° 9h S2m 148° 9h 56m 149° s Log. Hav. Nat. Hav. Log. IJav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.95884 0.90958 9.96119 0.91452 9.96347 0.91934 9.96568 0.92402 9.96782 0.93858 60 4 1 .95888 .90966 .96123 .91469 .96351 .91941 .96572 .92410 .96786 , .92666 56 8 It .95892 .90974 .96127 .91468 .96355 .91949 .96576 .92418 .96789 .92873 52 12 3 .95896 .90983 .96131 .91476 .96359 .91957 .96579 .92426 .96793 .92881 48 16 4 9.95900 0.90991 9.96135 0.91484 9.96362 0.91965 9.96583 0.92433 9.96796 0.92888 44 20 6 .95904 .90999 .96139 .91493 .96366 .91973 .96586 .92441 .96800 .93896 40 24 6 .95908 .91008 .96142 .91501 .96370 .91981 .96590 .92449 .96803 .92903 36 28 7 .95912 .91016 .96146 .91509 .96374 .91989 .96594 .92456 .96807 .92911 32 5^ 8 9.95916 0.91024 9.96150 0.91517 9.96377 0.91997 9.96597 0.92464 9.96810 0.93918 28 S6 9 .95920 .91033 .96154 .91525 .96381 .92005 .96601 .92472 .96814 .93936 24 40 le .95924 .91041 .96158 .91533 .96385 .92013 .96604 .92479 .96817 .93933 20 ■^4 11 .95928 .91049 .96162 .91541 .96388 .92020 .96608 .92487 .96821 .93941 16 48 12 9.95932 0.91057 9.96165 0.91549 9.96392 0.92028 9.96612 0.92495 9.96824 0.93948 12 5^ 13 .95936 .91066 .96169 .91557 .96396 .92036 .96615 .92502 .96827 .93955 8 56 14 9.95939 0.91074. 9.96173 0.91565 9.96400 0.92044 9.96619 0.92510 9.96831 0.93963 4 14h 19m 14h ism 14h 11m 14h7m 14h sm s ' 15 9h 41m 145° 9h 45m 146° 9h 49m 147° 9h SSm 148° 9h S7m 149° a 60 9.95943 0.91082 9.96177 0.91574 9.96403 0.92052 9.96622 0.92518 9.96834 0.93970 4 16 .95947 .91091 .96181 .91582 .96407 .92060 .96626 .92525 .96837 .93978 56 5 17 .95951 .91099 .96185 .91590 .96411 .92068 .96630 .92533 .96841 .93985 52 12 18 .95955 .91107 .96188 .91598 .96412 .92076 .96633 .92541 .96845 .93993 48 i6 19 9.95959 0.91115 9.96192 0.91606 9.96418 0.92083 9.96637 0.92548 9.96848 0.93000 U :?0 30 .95963 .91124 .96196 .91614 .96422 .92091 .96640 .92556 .96852 .93007 40 ;?4 21 .95967 .91132 .96200 .91622 .96426 .92099 .96644 .92563 .96855 .93015 36 f<§ 22 .95971 .91140 .96204 .91630 .96429 .92107 .96648 .92571 .96859 .93033 32 S2 23 9.95975 0.91149 9.96208 0.91638 9.96433 0.92115 9.96651 0.92579 9.96862 0.93030 28 56 24 .95979 .91157 .96211 .91646 .96437 .92123 .96655 .92586 .96866 .93037 24 40 25 .95983 .91165 .96215 .91654 .96440 .92130 .96658 .92594 .96869 .93045 20 44 26 .95987 .91173 .96219 .91662 .96444 .92138 .96662 .93603 .96873 .93053 16 45 27 9.95991 0.91182 9.96223 0.91670 9.96448 0.92146 9.96665 0.93609 9.96876 0.93059 12 52 28 .95995 .91190 .96227 .91678 .96451 .92154 .96669 .93617 .96879 .93067 8 56 29 9.95999 0.91198 9.96230 0.91686 9.96455 0.92162 9.96673 0.92624 9.96883 0.93074 4 14h 18m 14h 14m 14h 10m 14h6m 14h2m s ' 30 9h42m 145° | 9h 46m 148° 9h50m 147° 9h Sim 148° 9h sSm 149° s 60 9.96002 0.91206 9.96234 0.91694 9.96459 0.92170 9.96676 0.92633 9.96886 0.93081 4 31 .96006 .91215 .96238 .91702 .96462 .92177 .96680 .93640 .96890 .93089 56 8 32 .96010 .91223 .96242 .91710 .96466 .92185 .96683 .93647 .96894 .93096 52 i:g 33 .96014 .91231 .96246 .91718 .96470 .92193 .96687 .93655 .96897 .93104 48 :?6 34 9.96018 0.91239 9.96249 0.91726 9.96473 0.92301 9.96690 0.93663 9.96900 0.93111 44 20 35 .96022 .91247 .96253 .91734 .96477 .92209 .96994 .93670 .96904 .93118 40 ^4 36 .96026 .91256 .96257 .91742 .96481 .92216 .96697 .93678 .96907 .93126 36 28 37 .96030 .91264 .96261 .91750 .96484 .92224 .96701 .93685 .96910 .93133 32 5^ 38 9.96034 0.91272 9.96265 0.91758 9.96488 0.92232 9.96705 0.93693 9.96914 0.93110 28 56 39 .96038 .91280 .96268 .91766 .96492 .92240 .96708 .93700 .96917 .93148 24 40 40 .96042 .91289 .96272 .91774 .96495 .92248 .96712 .93708 .96921 .93155 20 44 41 .96046 .91297 .96276 .91782 .96499 .92255 .96715 .93715 .96924 .93162 16 48 42 9.96049 0.91305 9.96280 0.91790 9.96503 0.92263 9.96719 0.93733 9.96928 0.93170 12 52 44 .96053 .91313 .96283 .91798 .96506 .92271 .96722 .93731 .96931 .93177 8 56 44 9.96057 0.91321 9.96287 0.91806 9.96510 0.92279 9.96726 0.93738 9.96934 0.93184 4 i4h 17m 14h ism 14h 9m 14hsm 14h im i s ' 45 9h 43m 1450 9h 47m 146° 9h Sim 147° 9h SSm 148° 9h59m 149° | 60 9.96061 0.91329 9.96291 0.91814 9.96514 0.92286 9.96729 0.93746 9.96938 0.93193 4 46 .96065 .91338 .96295 .91822 .96517 .92294 .96733 .93753 .96941 .93199 56 5 47 .96069 .91346 .96299 .91830 .96521 .92302 .96736 .93761 .96945 .93306 52 J2 48 .96073 .91354 .96302 .91838 .96525 .92310 .96740 .93768 .96948 .93314 48 16 49 9.96077 0.91362 9.96306 0.91846 9.96528 0.92317 9.96743 0.93776 9,96951 0.93331 U ^0 60 .96081 .91370 .96310 .91854 .96532 .92325 .96747 .92783 .96955 .93338 40 24 51 .96084 .91379 .96314 .91862 .96536 .92333 .96750 .93791 .96958 .93336 36 f5 52 .96088 .91387 .96317 .91870 .96539 .93341 .96754 .93798 .96962 .93343 32 5:? 53 9.96092 0.91395 9.96321 0.91878 9.96543 0.92348 9.96758 0.93806 9.96965 0.93350 28 36 54 .96096 .91403 .96325 .91886 .96547 .92356 .98761 .93813 .96968 .93358 24 40 55 .96100 .91411 .96329 .91894 .96550 .93364 .96765 .93831 .96972 .93365 20 U 56 .96104 .91419 .96332 .91902 .96554 .93373 .96768 .93838 .96975 .93373 16 45 57 9.96108 0.91427 9.96336 0.91910 9.96557 0.93379 9.96772 0.92836 9.96979 0.93379 12 5f 58 .96112 .91436 .96340 .91918 .96561 .92387 .96775 .92843 .96982 .93387 8 50 59 .96115 .91444 .96344 .91926 .96565 .92394 .96779 .92851 .96985 .93394 4 60 60 9.96119 0.91452 9.96347 0.91934 9.96568 0.92402 9.96782 0.92858 9.96989 0.93301 14h 16m ~\ 14^ 12m 1 14h 8m 1 14h 4m 1 Uft Om 1 Page 916] TABLE 45. Haversines. s iOAOm 150° 1 lOh 4m 151° lOh 8m 153° ion 12m 153° ion 16m 154° 1 s Lor. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.96989 0.93301 9.97188 0.93731 9.97381 0.94147 9.97566 0.94550 9.97745 0.94940 60 4 1 .96992 .93309 .97192 .93738 .97384 .94154 .97569 .95557 .97748 .94946 56 8 3 .96996 .93316 .97195 .93^45 .97387 .94161 .97572 .94564 .97751 .94952 52 12 3 .96999 .93333 .97198 .93753 .97390 .94168 .97575 .94570 .97754 .94959 48 16 4 9.97002 0.93330 9.97201 0.93759 9.97393 0.94175 9.97578 0.94577 9.97756 0.94965 44 W 5 .97006 .93338 .97205 .93766 .97397 .94181 .97581 .94583 .97759 .94973 40 U 6 .97009 .93345 .97208 .93773 .97400 .94188 .97584 .94590 .97762 .94978 36 28 7 .97012 .93353 .97211 .93780 .97403 .94195 .97587 .94596 .97765 .94984 32 5:? 8 9.97016 0.93359 9.97214 0.93787 9.97406 0.94303 9.97591 0.94603 9.97768 0.94991 28 56 9 .97019 .93367 .97218 .93794 .97409 .94209 .97594 .94610 .97771 .94997 24 40 10 .97022 .93374 .97221 .93801 .97412 .94315 .97597 .94616 .97774 .95003 20 44 11 .97026 .93381 .97224 .93808 .97415 .94333 .97600 .94623 .97777 .95010 16 48 13 9.97029 0.93388 9.97227 0.93815 9.97418 0.94339 9.97603 0.94639 9.97780 0.95016 12 5f 13 .97033 .93395 .97231 .93833 .97422 .94336 .97606 .94636 .97783 .95033 8 56 14 9.97036 0.93403 9.97234 0.93839 9.97425 0.94343 9.97609 0.94642 9.97785 0.95039 4 13^ 59m isJi 55m ISh Sim isn 47m isn 4sm 8 ' 15 10^ im 150° lOh 5m 151° lOh 9m 153° ion 13m 153° ion 17m 154° s 60 9.97039 0.93410 9.97237 0.93836 9.97428 0.94349 9.97612 0.94649 9.97788 0.95035 4 16 .97043 .93417 .97240 .93843 .97431 .94356 .97615 .94655 .97791 .95041 56 5 17 .97046 .93434 .97244 .93850 .97434 .94363 .97618 .94663 .97794 .95048 52 i^ 18 .97049 .93433 .97247 .93857 .97437 .94370 .97621 .94669 .97797 .95054 48 16 19 9.97052 0.93439 9.97250 0.93864 9.97440 0.94376 9.97624 0.94675 9.97800 0.95060 44 ;gO 30 .97056 .93446 .97253 .93871 .97443 .94383 .97627 .94683 .97803 .95066 40 24 31 .97059 .93453 .97257 .93878 .97447 .94390 .97630 .94688 .97806 .95073 36 :?« 33 .97063 .93460 .97260 .93885 .97450 .94397 .97633 .94695 .97808 .95079 32 5f 33 9.97066 0.93468 9.97263 0.93893 9.97453 0.94303 9.97636 0.94701 9.97811 0.95085 28 36 34 .97069 .93475 .97266 .93899 .97456 .94310 .97639 .94708 .97814 .95093 24 40 35 .97073 .93483 .97269 .93906 .97459 .94317 .97642 .94714 .97817 .95098 20 U 26 .97076 .93489 .97273 .93913 .97462 .94334 .97645 .94731 .97820 .95104 16 4^ 37 9.97079 0.93496 9.97276 0.93930 9.97465 0.94330 9.97647 0.94737 9.97823 0.95111 12 5^ 38 .97083 .93503 .97279 .93937 .97468 .94337 .97650 .94734 .97826 .95117 8 56 39 9.97086 0.93511 9.97282 0.93934 9.97471 0.94344 9.97653 0.94740 9.97829 0.95133 4 13^ 58m 1 13h 54m 13h 50m 13n 46m I3n 42m s ' 30 10^ 2m 150° j lOh 6m 151° ion lOm 153° ion 14m 153° ion Igm 154° 3 60 9.97089 0.93518 9.97285 0.93941 9.97474 0.94351 9.97656 0.94747 9.97831 0.95139 4 31 .97093 .93535 .97289 .93948 .97478 .94357 .97659 .94753 .97834 .95136 56 5 33 .97096 .93533 .97292 .93955 .97481 .94364 .97662 .94760 .97837 .95143 52 12 33 .97099 .93539 .97295 .93963 .97484 .94371 .97665 .94766 .97840 .95148 48 i6 34 9.97103 0.93546 9.97298 0.93969 9.97487 0.94377 9.97668 0.94773 9.97843 0.95154 44 20 35 .97106 .93554 .97301 .93976 .97490 .94384 .97671 .94779 .97846 .95161 40 f4 36 .97109 .93561 .97305 .93983 .97493 .94391 .97674 .94786 .97849 .95167 36 ;?5 37 .97113 .93568 .97308 .93989 .97496 .94397 .97677 .94792 .97851 .95173 32 S2 38 9.97116 0.93575 9.97311 0.93996 9.97499 0.94404 9.97680 0.94799 9.97854 0.95179 28 56 39 .97119 .93583 .97314 .94003 .97502 .94411 .97683 .94805 .97857 .95185 24 40 40 .97123 .93589 .97317 .94010 .97505 .94418 .97686 .94811 .97860 .95193 20 44 41 .97126 .93596 .97321 .94017 .97508 .94424 .97689 .94818 .97863 .95198 16 45 43 9.97129 0.93603 9.97324 0.94034 9.97511 0.94431 9.97692 0.94824 9.97866 0.95304 12 52 43 .97132 .93611 .97327 .94031 .97514 .94438 .97695 .94831 .97868 .95310 8 56 44 9.97136 0.93618 9.97330 0.94038 9.97518 0.94444 9.97698 0.94837 9.97871 0.95217 4 ISh 57m ISh 5Sm isn 49m 13n 45m ISh 41m 45 10^ 3m 150° ion 7m 151° lOh llm 153° ion 15m 153° ion 19m 154° s 60 9.97139 0.93635 9.97333 0.94045 9.97521 0.94451 9.97701 0.94844 9.97874 0.95233 4 46 .97142 .93633 .97337 .94051 .97524 .94458 .97704 .94850 .97877 .95339 56 5 47 .97146 .93639 .97340 .94058 .97527 .94464 .97707 .94857 .97880 .95335 52 12 48 .97149 .93646 .97343 .94065 .97530 .94471 .97710 .94863 .97883 .95341 48 i6 49 9.97152 0.93653 9.97346 0.94073 9.97533 0.94477 9.97713 0.94869 9.97885 0.95348 44 20 50 .97156 .93660 .97349 .94079 .97536 .94484 .97716 .94876 .97888 .95354 40 ;?4 51 .97159 .93667 .97352 .94086 .97539 .94491 .97718 .94882 .97891 .95360 36 ;?5 53 .97162 .93674 .97356 .94093 .97542 .94497 .97721 .94889 .97894 .95266 32 32 53 9.97165 0.93683 9.97359 0.94099 9.97545 0.94504 9.97724 0.94895 9.97897 0.95272 28 56 54 .97169 .93689 .97362 .94106 .97548 .94511 .97727 .94901 .97899 .95378 24 40 55 .97172 .93696 .97365 .94113 .97551 .94517 .97730 .94908 .97902 .95385 20 44 56 .97175 .93703 .97368 .94130 .97554 .94534 .97733 .94914 .97905 .95391 16 45 57 9.97179 0.93710 9.97371 0.94137 9.97557 0.94531 9.97736 0.94931 9.97908 0.95397 12 52 58 .97182 .93717 .97575 .94134 .97560 .94537 .97739 .94927 .97911 .95303 8 56 59 .97185 .93734 .97378 .94141 .97563 .94544 .97742 .94933 .97914 .95309 4 60 60 9.97188 093731 9.97381 0.94147 9.97566 0.94550 9.97745 0.94940 9.97916 0.95315 13^ 56m 1 isn 52m isn48m isn 44m isn 40m 1 TABLE 45. [Page 917 Haversines. s ' lOh 2(pn. 155° lOh, 24m 156° lOh 2Sm 157° lOh 32m 158° lOhS&n 159° 1 8 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav.; Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.97918 0.95315 9.98081 0.95677 9.98239 0.96025 9.98389 0.96359 9.98533 0.96679 60 4 1 .97919 .95322 .98084 .95683 .98241 .96031 .98392 .96365 .98536 .96684 56 8 2 .97922 .95328 .98086 .95689 .98244 .96037 .98394 .96370 .98538 .96689 52 12 3 .97925 .95334 .98089 .95695 .98246 .96042 .98397 .96376 .98540 .96695 48 16 4 9.97927 0.95340 9.98092 0.95701 9.98249 0.96048 9.98399 0.96381 9.98543 0.96700 44 20 5 .97930 .95346 .98094 .95707 .98251 .96054 .98402 .96386 .98545 .96705 40 24 6 .97933 .95352 .98097 .95713 .98254 .96059 .98404 .96392 .98547 .96710 36 23 7 .97936 .95358 .98100 .95719 .98256 .96065 .98406 .96397 .98550 .96715 32 32 8 9.97939 0.95364 9.98102 0.95724 9.98259 0.96071 9.98409 0.96403 9.98552 0.96721 28 36 9 .97941 .95371 .98105 .95730 .98262 .96076 .98411 .96408 .98554 .96726 24 40 10 .97944 .95377 .98108 .95736 .98264 .96082 .98414 .96413 .98557 .96731 20 44 11 .97947 .95383 .98110 .95742 .98267 .96088 .98416 .96419 .98559 .96736 16 48 13 9.97950 0.95389 9.98113 0.95748 9.98269 0.96093 9.98419 0.96424 9.98561 0.96741 12 52 13 .97953 .95395 .98116 .95754 .98272 .96099 .98421 .96430 .98564 .96746 8 56 14 9.97955 0.95401 9.98118 0.95760 9.98274 0.96104 9.98424 0.96435 9.98566 0.96752 4 jfjft sgm 13f>' 35m ISh Sim 13h 27m ISh 23m 8 15 lOh 2im 155° lOh 25m 156° IQh 29m 151" lOh 33m 158° IQh Sim 1590 s 60 9.97958 0.95407 9.98121 0.95766 9.98277 0.96110 9.98426 0.96440 9.98568 0.96757 4 16 .97961 .95413 .98124 .95771 .98279 .96116 .98428 .96446 .98570 .96762 56 8 17 .97964 .95419 .98126 .95777 .98282 .96121 .98431 .96451 .98573 .96767 52 12 18 .97966 .95425 .98129 .95783 .98285 .96127 .98433 .96457 .98575 .96772 48 16 19 9.97969 0.95431 9.98132 0.95789 9.98287 0.96133 9.98436 0.96462 9.98577 0.96777 44 20 20 .97972 .95438 .98134 .95795 .98290 .96138 .98438 .96467 .98580 .96782 40 24 21 .97975 .95444 .98137 .95801 .98292 .96144 .98440 .96473 .98582 .96788 36 28 22 .97977 .95450 .98139 .95806 .98295 .96149 .98443 .96478 .98584 .96793 32 52 23 9.97980 0.95456 9.98142 0.95812 9.98297 0.96155 9.98455 0.96483 9.98587 0.96798 28 36 24 .97983 .95462 .98145 .85818 .98300 .96161 .98448 .96489 .98589 .96803 24 40 25 .97986 .95468 .98147 .95824 .98302 .96166 .98450 .96494 .98591 .96808 20 44 26 .97988 .95474 .98150 .95830 .98305 .96172 .98453 .96500 .98593 .96813 16 48 27 9.97991 0.95480 9.98153 0.95836 9.98307 0.96177 9.98455 0.96505 9.98596 0.96818 12 52 28 .97994 .95486 .98155 .95841 .98310 .96183 .98457 .96510 .98598 .96823 8 56 29 9.97997 0.95492 9.98158 0.95847 9.98312 0.96188 9.98460 0.96516 9.98600 0.96829 4 13^38^ 13h 54™ 1 13^30m ISh 26m 13h 22m 8 30 lOh 22m 155° lOfi 26m 156° IQh 30^ ► 157° IQh 34m 158° IQh SSm 159° s 60 9.97999 0.95498 9.98161 0.95853 9.98315 0.96194 9.98462 0.96521 9.98603 0.96834 4 31 .98002 .95504 .98163 .95859 .98317 .96200 .98465 .96526 .98605 .96839 56 8 32 .98005 .95510 .98166 .95865 .98320 .96205 .98467 .96532 .98607 .96844 52 12 33 .98008 .95516 .98168 .95870 .98322 .96211 .98469 ..96537 .98609 .96849 48 16 34 9.98010 0.95522 9.98171 0.95876 9.98325 0.96216 9.98472 0.96542 9.98612 0.96854 44 20 35 .98013 .95528 .98174 .95883 .98327 .96222 .98474 .96547 .98614 .96859 40 24 36 .98016 .95534 .98176 .95888 .98330 .96237 .98476 .96553 .98616 .96864 36 28 37 .98019 .95540 .98179 .95894 .98332 .96223 .98479 .96558 .98619 .96869 32 32 38 9.98021 0.95546 9.98182 0.95899 9.98335 0.96238 9.98481 0.96563 9.98621 0.96874 28 36 39 .98024 .95552 .98184 .95905 .98337 .96344 .98484 .96569 .98623 .96879 24 40 40 .98027 .95558 .98187 .95911 .98340 .96249 .98486 .96574 .98625 .96884 20 44 41 .98030 .95564 .98189 .95917 .98342 .96255 .98488 .96579 .98628 .96889 16 48 42 9.98032 0.95570 9.98192 0.95922 9.98345 0.96360 9.98491 0.96585 9.98630 0.96894 12 52 43 .98035 .95576 .98195 .95928 .98347 .96266 .98493 .96590 .98632 .96899 8 56 44 9.98038 0.95582 9.98197 0.95934 9.98350 0.96272 9.98496 0.96595 9.98634 0.96905 4 ISh 37m 13>>' 33m ISh 29m ISh 25m ISh 21m 1 8 45 10h23m 155° 1 J Oh 21m 156° lOh Sim 157° lOh 35m 158° IQh 39m 159° 1 3 60 9.98040 0.95588 9.98200 0.95940 9.98352 0.96277 9.98498 0.96600 9.98637 0.96910 4 46 .98043 .95594 .98202 .95945 .98355 .96283 .98500 .96606 .98639 .96915 56 8 47 .98046 .95600 .98205 .95951 .98357 .96288 .98503 .96611 .98641 .96930 52 12 48 .98049 .95606 .98208 .95957 .98360 .96294 .98505 .96616 .98643 .96935 48 16 49 9.98051 0.95612 9.98210 0.95962 9.98362 0.96299 9.98507 0.96621 9.98646 0.96930 U 20 50 .98054 .95618 .98213 .95968 .98365 .96305 .98510 .96627 .98648 .96935 40 24 51 .98057 .95624 .98215 .95974 .98367 .96310 .98512 .96632 .98650 .96940 36 28 52 .98059 .95630 .98218 .95980 .98370 .96315 .98514 .96637 .98652 .96945 32 32 53 9.98062 0.95636 9.98221 0.95985 9.98372 0.96331 9.98517 0.96642 9.98655 0.96950 28 36 54 .98065 .95642 .98223 .95991 .98375 .96326 .98519 .96648 .98657 .96955 24 40 55 .98067 .95648 .98226 .95997 .98377 .96332 .98521 .96653 .98659 .96960 20 44 56 .98070 .95654 .98228 .96002 .98379 .96337 .98524 .96658 .98661 .96965 16 48 57 9.98073 0.95660 9.98231 0.96008 9.98382 0.96343 9.98526 0.96663 9.98664 0.96970 12 52 58 .98076 .95665 .98233 .96014 .98384 .96348 .98529 .96669 .98666 .96975 8 56 59 .98078 .95671 .98236 .96020 .98387 .%354 .98531 .96674 .98668 .96980 4 60 60 9.98081 0.95677 9.98239 0.96025 9.98389 0.96359 9.98533 0.96679 9.98670 0.96985 13h 36^ 13h 32m 13h 28m 1 13h 24m 1 ISh gom 1 Page 918] TABLE 45. Havereines. s ' ion 40m 160° IQh 44m 161° lOh 48m 163° lOh 52m 163° lOh 56m 164° s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav.: Nat. Hav. Log. Hav. Nat. Hav. 9.98670 0.96985 9.98801 0.97276 9.98924 0.97553 9.99041 0.97815 9.99151 0.98063 60 4 1 .98673 .96990 .98803 .97381 .98926 .97557 .99043 .97819 .99152 .98067 56 8 1i .98675 .96995 .98805 .97385 .98928 .97562 .99044 .97824 .99154 .98071 52 12 3 .98677 .97000 .98807 .97390 .98930 .97566 .99046 .97828 .99156 .98075 48 16 4 9.98679 0.97005 9.98809 0.97395 9.98932 0.97571 9.99048 0.97832 9.99158 0.98079 44 20 5 .98681 .97009 .98811 .97300 .98934 .97575 .99050 .97836 .99159 .98083 40 24 6 .98684 .97014 .98813 .97304 .98936 .97580 .99052 .97841 .99161 .98087 36 28 1 .98686 .97019 .98815 .97309 .98938 .97584 .99054 .97845 .99163 .98091 32 S2 8 9.98688 0.97024 9.98817 0.97314 9.98940 0.97589 9.99056 0.97849 9.99165 0.98095 28 S6 9 .98690 .97029 .98819 .97318 .98942 .97593 .99058 .97853 .99166 .98099 24 40 10 .98692 .97034 .98822 .97333 .98944 .97598 .99059 .97858 .99168 .98103 20 ^ 11 .98695 .97039 .98824 .97338 .98946 .97602 .99061 .97862 .99170 .98107 16 48 13 9.98697 0.97044 9.98826 0.97333 9.98948 0.97606 9.99063 0.97866 9.99172 0.98111 12 5f 13 .98699 .97049 .98828 .97337 .98950 .97611 .99065 .97870 .99173 .98115 8 56 14 9.98701 0.97054 9.98830 0.97343 9.98952 0.97615 9.99067 0.97874 9.99175 0.98119 4 13h 19m ISh lorn ISh 11m ISh 7m ISh 3m s ' lOh 4im 160° lOh 45m 161° lOh 4m 162° IQh 53m 163° lOh 57m 164° s 15 9.98703 0.97059 9.98832 0.97347 9.98954 0.97620 9.99069 0.97879 9.99177 0.98133 60 4 16 .98706 .97064 .98834 .97351 .98956 .97624 .99071 .97883 .99179 .98137 56 5 17 .98708 .97069 .98836 .97356 .98958 .97629 .99072 .97887 .99180 .98131 52 12 18 .98710 .97074 .98838 .97361 .98960 .97633 .99074 .97891 .99182 .98135 48 i6 19 9.98712 0.97078 9.98840 0.97365 9.98962 0.97637 9.99076 0.97895 9.99184 0.98139 U ;?0 20 .98714 .97083 .98842 .97370 .98964 .97643 .99078 .97899 .99186 .98143 40 24 21 .98717 .97088 .98845 .97374 .98966 .97646 .99080 .97904 .99187 .98146 36 ^.^ 23 .98719 .97093 .98847 .97379 .98968 .97651 .99082 .97908 .99189 .98150 32 32 23 9.98721 0.97098 9.98849 0.97384 9.98970 0.97655 9.99084 0.97913 9.99191 0.98154 28 56 24 .98723 .97103 .98851 .97388 .98971 .97660 .99085 .97916 .99193 .98158 24 40 25 .98725 .97108 .98853 .97393 .98973 .97664 .99087 .97930 .99194 .98162 20 i4 26 .98728 .97113 .98855 .97398 .98975 .97668 .99089 .97924 .99196 .98166 16 45 27 9.98730 0.97117 9.98857 0.97403 9.98977 0.97673 9.99091 0.97939 9.99198 0.98170 12 62 28 .98732 .97123 .98859 .97407 .98979 .97677 .99093 .97933 .99200 .98174 8 56 29 9.98734 0.97127 9.98861 0.97413 9.98981 0.97681 9.99095 0.97937 9.99201 0.98178 4 ISh ism 13h 14m ISh 10m ISh 6m ISh 2m s ' lOh 42m 160° lOh 46m 161° IQh 50m 162° lOh 54'^ 163° IQh 58m 164° s 30 9.98736 0.97132 9.98863 0.97416 9.98983 0.97686 9.99096 0.97941 9.99203 0.98182 60 4 31 .98738 .97137 .98865 .97431 .98985 .97690 .99098 .97945 .99205 .98185 56 8 32 .98741 .97143 .98867 .97425 .98987 .97695 .99100 .97949 .99206 .98189 52 if 33 .98743 .97147 .98869 .97430 .98989 .97699 .99102 .97953 .99208 .98193 48 i6 34 9.98745 0.97151 9.98871 0.97435 9.98991 0.97703 9.99104 0.97957 9.99210 0.98197 U 20 35 .98747 .97156 .98873 .97439 .98993 .97708 .99106 .97962 .99212 .98301 40 ;g4 36 .98749 .97161 .98875 .97444 .98995 .97713 .99107 .97966 .99213 .98205 36 28 37 .98751 .97166 .98877 .97448 .98997 .97716 .99109 .97970 .99215 .98209 32 5f 38 9.98754 U97171 9.98880 0.97453 9.98999 0.97721 9.99111 0.97974 9.99217 0.98212 28 56 39 .98756 .97176 .98882 .97458 .99001 .97735 .99113 .97978 .99218 .98216 24 40 40 .98758 .97180 .98884 .97463 .99003 .97729 .99115 .97982 .99220 .98230 20 44 41 .98760 .97185 .98886 .97467 .99004 .97734 .99116 .97986 .99222 .98334 16 48 42 9.98762 0.97190 9.98888 0.97471 9.99006 0.97738 9.99118 0.97990 9.99223 0.98338 12 5:2 43 .98764 .97195 .98890 .97476 .99008 .97742 .99120 .97994 .99225 .98333 8 56 44 9.98766 0.97200 9.98892 0.97480 9.99010 0.97747 9.99122 0.97998 9.99227 0.98336 4 l,3h 17m ISh ism ISh gm ISh 5m ISh pn s ' lOh 43m 160° lOh 47m 161° IQh 5lm 162° lOh 55m 163° lOh 59m 164° s 45 9.98769 0.97204 9.98894 0.97485 9.99012 0.97761 9.99124 0.98002 9.99229 0.98339 60 4 46 .98771 .97209 .98896 .97490 .99014 .97755 .99126 .98007 .99230 .98343 56 5 47 .98773 .97214 .98898 .97494 .99016 .97760 .99127 .98011 .99232 .98347 52 if 48 .98775 .97219 .98900 .97499 .99018 .97764 .99129 .98015 .99234 .98351 48 16 49 9.98777 0.97224 9.98902 0.97503 9.99020 0.97768 9.99131 0.98019 9.99235 0.98355 44 fO 50 98779 .97238 .98904 .97508 .99022 .97773 .99133 .98033 .99237 .98358 40 24 51 .98781 .97333 .98906 .97513 .99024 .97777 .99135 .98037 .99239 .98263 36 f5 62 .98784 .97338 .98908 .97517 .99026 .97781 .99136 .98031 .99240 .98266 32 5f 63 9.98786 0.97343 9.98910 0.97531 9.99027 0.97785 9.99138 0.98035 9.99242 0.98270 28 S6 64 .98788 .97347 .98912 .97526 .99029 .97790 .99140 .98039 .99244 .98374 24 40 65 .98790 .97353 .98914 .97530 .99031 .97794 .99142 .98043 .99245 .98377 20 44 66 .98792 .97357 .98916 .97535 .99033 .97798 .99143 .98047 .99247 .98281 16 45 67 9.98794 0.97363 9.98918 0.97639 9.99035 0.97802 9.99145 0.98051 9.99249 0.98385 12 5f 68 .98796 .97366 .98920 .97544 .99037 .97807 .99147 .98055 .99250 .98389 8 56 59 .98798 .97371 .98922 .97548 .99039 .97811 .99149 .98059 .99252 .98393 4 60 60 9.98801 0.97376 9.98924 0.97553 9.99041 0.97815 9.99151 0.98063 9.99254 0.98396 ISh 16m ISh 12m ISh gm 1 ISh 4m 1 ISh om 1 TABLE 45. [Page 919 Haversines. s ' lin am 165° lin4m 166° llhgrn 167° llh 12m 168° llh 16m 169° s Log. Hav. Nat. I lav. Ix)g. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. llav. Nat. Hav. Log. Hav. Nat. Hav. 9.99254 0.98296 9.99350 0.98515 9.99440 0.98719 9.99523 0.98907 9.99599 0.99081 60 4 1 .99255 .98300 .99352 .98518 .99441 .98722 .99524 .98910 .99600 .99084 56 8 3 .99257 .98304 .99353 .98522 .99443 .98725 .99526 .98913 .99602 .99087 52 12 3 .99259 .98308 .99355 .98525 .99444 .98728 .99527 .98916 .99603 .99090 48 16 4 9.99260 0.98311 9.99356 0.98529 9.99446 0.98732 9.99528 0.98919 9.99604 0.99092 44 20 5 .99262 .98315 .99358 .98532 .99447 .98735 .99529 .98922 .99605 .99095 40 24 6 .99264 .98319 .99359 .98536 .99448 .98738 .99531 .98925 .99606 .99098 36 28 7 .99265 .98323 .99361 .98539 .99450 .98741 .99532 .98928 .99608 .99101 32 S2 8 9.99267 0.98326 9.99362 0.98543 9.99451 0.98745 9.99533 0.98931 9.99609 0.99103 28 36 9 .99269 .98330 .99364 .98546 .99453 .98748 .99535 .98934 .99610 .99106 24 40 10 .99270 .98334 .99366 .98550 .99454 .98751 .99536 .98937 .99611 .99109 20 U 11 .99272 .98337 .99367 .98553 .99456 .98754 .99537 .98940 .99612 .99112 16 48 12 9.99274 0.98341 9.99369 0.98557 9.99457 0.98757 9.99539 0.98943 9.99614 0.99114 12 52 13 .99275 .98345 .99370 .98500 .99458 .98761 .99540 .98946 .99615 .99117 8 56 14 9.99277 0.98349 9.99372 0.98564 9.99460 0.98764 9.99541 0.98949 9.99616 0.99120 4 1 12h 59m 1 12h 55m 12h5lm 12h 47m 12h 43m s '1 llhim 165° llhsm 166° llhgm 167° llh 13m 168° llh 17m 169° s 15 9.99278 0.98352 9.99373 0.98567 9.99461 0.98767 9.99543 0.98952 9.99617 0.99123 60 4 16 .99280 .98356 .99375 .98571 .99463 .98770 .99544 .98955 .99618 .99125 56 8 17 .99282 .98360 .99376 .98574 .99464 .98774 .99545 .98958 .99620 .99128 52 12 18 .99283 .98363 .99378 .98577 .99465 .98777 .99546 .98961 .99621 .99131 48 16 19 9.99285 0.98367 9.99379 0.98581 9.99467 0.98780 9.99548 0.98964 9.99622 0.99133 44 20 20 .99287 .98371 .99381 .98584 .99468 .98783 .99549 .98967 .99623 .99136 40 24 21 .99288 .98374 .99382 .98588 .99470 .98786 .99550 .98970 .99624 .99139 36 28 22 .99290 .98378 .99384 .98591 .99471 .98789 .99552 .98973 .99626 .99141 32 S2 23 9.99291 0.98382 9.99385 0.98595 9.99472 0.98793 9.99553 0.98976 9.99627 0.99144 28 S6 24 .99293 .98385 .99387 .98598 .99474 .98796 .99554 .98979 .99628 .99147 24 40 25 .99295 .98389 .99388 .98601 .99475 .98799 .99555 .98982 .99629 .99149 20 44 26 .99296 .98393 .99390 .98605 .99477 .98802 .99557 .98985 .99630 .99152 16 48 27 9.99298 0.98396 9.99391 0.98608 9.99478 0.98805 9.99558 0.98987 9.99631 0.99155 12 52 28 .99300 .98400 .99393 .98611 .99479 .98809 .99559 .98990 .99633 .99157 8 56 29 9.99301 0.98404 9.99394 0.98615 9.99481 0.98812 9.99561 0.98993 9.99634 0.99160 4 1 12h 58m 12h 54m 12h 50m 12h 46m 12h 42m s ' 1 llh2m 165° llhem 166° llhiom 167° llh 14m 168° llh 18m 169° s 60 30 9.99303 0.98407 9.99396 0.98619 9.99482 0.98815 9.99562 0.98996 9.99635 0.99163 4 31 .99304 .98411 .99397 .98622 .99484 .98818 .99563 .98999 .99636 .99165 56 8 32 .99306 .98415 .99399 .98625 .99485 .98821 .99564 .99002 .99637 .99168 52 12 33 .99308 .98418 .99400 .98629 .99486 .98824 .99566 .99005 .99638 .99171 48 16 34 9.99309 0.98422 9.99402 0.98632 9.99488 0.98827 9.99567 0.99008 9.99639 0.99173 44 20 35 .99311 .98426 .99403 .98635 .99489 .98830 .99568 .99011 .99641, .99176 40 24 36 .99312 .98429 .99405 .98639 .99490 .98834 .99569 .99014 .99642 .99179 36 28 37 .99314 .98433 .99406 .98642 .99492 .98837 .99571 .99016 .99643 .99181 32 S2 38 9.99316 0.98436 9.99408 0.98646 9.99493 0.98840 9.99572 0.99019 9.99644 0.99184 28 S6 39 .99317 .98440 .99409 .98649 .99495 .98843 .99573 .99022 .99645 .99186 24 40 40 .99319 .98444 .99411 .98652 .99496 .98846 .99575 .99025 .99646 .99189 20 44 41 .99320 .98447 .99412 .98656 .99497 .98849 .99576 .99028 .99648 .99193 16 48 42 9.99322 0.98451 9.99414 0.98659 9.99499 0.98852 9.99577 0.99031 9.99649 0.99194 12 52 43 .99324 .98454 .99415 .98662 .99500 .98855 .99578 .99034 .99650 .99197 8 56 44 9.99325 0.98458 9.99417 0.98666 9.99501 0.98858 9.99580 0.99036 9.99651 0.99199 4 12h 57m 12h 53m i2h 49m 12h 45m 12h 41m s ' llhsm 165° llhjm 166° llh llm 167° llh 15m 168° llh 19m 169° s 45 9.99327 0.98462 9.99418 0.98669 9.99503 0.98862 9.99581 0.99039 9.99652 0.99202 60 4 46 .99328 .98465 .99420 .98672 .99504 .98865 .99582 .99042 .99653 .99205 56 8 47 .99330 .98469 .99421 .98676 .99505 .98868 .99583 .99045 .99654 .99207 52 12 48 .99331 .98472 .99422 .98679 .99507 .98871 .99584 .99048 .99655 .99210 48 16 49 9.99333 0.98476 9.99424 0.98682 9.99508 0.98874 9.99586 0.99051 9.99657 0.99212 U 20 50 .99335 .98479 .99425 .98686 .99510 .98877 .99587 .99053 99658 .99215 40 24 51 .99336 .98483 .99427 .98689 .99511 .98880 .99588 .99056 .99659 .99217 36 28 52 .99338 .98487 .99429 .98692 .99512 .98883 .99580 .99059 .99660 .99220 32 S2 53 9.99339 0.98490 9.99430 0.98696 9.99514 0.98886 9.99591 0.99062 9.99661 0.99223 28 36 54 .99341 .98494 .99431 .98699 .99515 .98889 .99592 .99065 .99662 .99225 24 40 55 .99342 .98497 .99433 .98702 .99516 .98892 .99593 .99067 .99663 .99228 20 U 56 .99344 .98501 .99434 .98705 .99518 .98895 .99594 .99070 .99664 .99230 16 48 57 9.99345 0.98504 9.99436 0.98709 9.99519 0.98898 9.99596 0.99073 9.99666 0.99233 12 52 68 .99347 .98508 .99437 .98712 .99520 .98901 .99597 .99076 .99667 .99235 8 56 59 .99349 .98511 .99438 .98715 .99522 .98904 .99598 .99079 .99668 .99238 4 60 60 9.99350 0.98515 9.99440 0.98719 9.99523 0.98907 9.99599 0.99081 9.99669 0.99240 12^^ 56m 12h 52m 12h 48m 12h 44m 12h 40m Page 920] TABLE 45. | Haversines. 1 s ' llh20m 170° llh£4m 171° llh 28m 172° llh 32m 173° llh 36m 174° s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.99669 0.99240 9.99732 0.99384 9.997.88 0.99513 9.99838 0.99627 9.99881 0.99726 60 4 1 .99670 .99243 .99733 .99387 .99789 .99515 .99839 .99639 .99882 .99728 66 8 3 .99671 .99245 .99734 .99389 .99790 .99517 .99839 .99631 .99882 .99729 62 12 3 .99672 .99248 .99735 .99391 .99791 .99519 .99840 .99633 .99883 .99731 48 16 4 9.99673 0.99250 9.99736 0.99393 9.99792 0.99521 9.99841 0.99634 9.99884 0.99732 U 20 5 .99674 .99253 .99737 .99396 .99793 .99523 .99842 .99636 .99884 .99734 40 24 6 .99675 .99255 .99738 .99398 .99793 .99525 .99842 .99638 .99885 .99735 36 28 7 .99677 .99258 .99739 .99400 .99794 .99527 .99843 .99640 .99885 .99737 32 S2 8 9.99678 0.99260 9.99740 0.99402 9.99795 0.99539 9.99844 0.99641 9.99886 0.99738 28 S6 9 .99679 .99263 .99741 .99405 .99796 .99531 .99845 .99643 .99887 .99740 24 40 10 .99680 .99265 .99742 .99407 .99797 .99533 .99845 .99645 .99887 .99741 20 44 11 .99681 .99268 .99743 .99409 .99798 .99535 .99846 .99647 .99888 .99743 16 48 13 9.99682 0.99270 9.99744 0.99411 9.99799 0.99537 9.99847 0.99648 9.99889 0.99744 12 52 13 .99683 .99273 .99745 .99414 .99800 .99539 .99848 .99650 .99889 .99746 8 56 U 9.99684 0.99275 9.99746 0.99416 9.99800 0.99541 9.99848 0.99652 9.99890 1 0.99747 4 12^ S9m 12h s.sm 12hsim 12h 27m 12h 23m 8 1 llh2im 170° llfi'25'm 171° llh 29m 172° llh 33m 173° llh 37m 174° s '^ 15 9.99685 0.99278 9.99747 0.99418 9.99801 0.99543 9.99849 0.99653 9.99891 0.99748 60 4 16 .99686 .99280 .99748 .99420 .99802 .99545 .99850 .99655 .99891 .99750 66 8 17 .99687 .99283 .99748 .99422 .99803 .99547 .99851 .99657 .99892 .99751 62 12 18 .99688 .99285 .99749 .99425 .99804 .99549 .99851 .99659 .99893 .99753 48 16 19 9.99690 0.99288 9.99750 0.99427 9.99805 0.99551 9.99852 0.99660 9.99893 0.99754 44 20 20 .99691 .99290 .99751 .99429 .99805 .99553 .99853 .99663 .99894 .99756 40 24 21 .99692 .99293 .99752 .99431 .99806 .99555 .99854 .99664 .99894 .99757 36 28 1% .99693 .99295 .99753 .99433 .99807 .99557 .99854 .99665 .99895 .99759 32 S2 23 9.99694 0.99297 9.99754 0.99436 9.99808 0.99559 9.99855 0.99667 9.99896 0.99760 28 36 24 .99695 .99300 .99755 .99438 .99809 .99561 .99856 .99669 .99896 .99761 24 40 25 .99696 .99302 .99756 .99440 .99810 .99563 .99857 .99670 .99897 .99763 20 44 26 .99697 .99305 .99757 .99442 .99811 .99565 .99857 .99673 .99897 .99674 16 48 27 9.99698 0.99307 9.99758 0.99444 9.99811 0.99567 9.99858 0.99674 9.99898 0.99766 12 52 28 .99699 .99309 .99759 .99446 ' .99812 .99568 .99859 .99675 .99899 .99767 8 56 29 9.99700 0.99312 9.99760 0.99449 9.99813 0.99570 9.99859 0.99677 9.99899 0.99768 4 121 38m 12h S4m -* ... 12h30m '-*» 12h 26m 12h 22m 8 t llh22m 170° llh 26m 171° Ilh30m.^.n2° llh 34m 173° llh 38m 174° a 60 30 9.99701 0.99314 9.99761 0.99451 9.99814 0.99572 9.99860 0.99679 9.99900 0.99770 4 31 .99702 .99317 .99762 .99453 .99815 .99574 .99861 .99680 .99901 .99771 56 8 32 .99703 .99319 .99763 .99455 .99815 .99576 .99862 .99683 .99901 .99773 62 12 33 .99704 .99321 .99764 .99457 .99816 .99578 .99862 .99684 .99902 .99774 48 16 34 9.99705 0.99334 9.99765 0.99459 9.99817 0.99580 9.99863 0.99685 9.99902 0.99775 44 20 35 .99706 .99326 .99766 .99461 .99818 .99582 .99864 .99687 .99903 .99777 40 24 36 .99707 .99329 .99766 .99464 .99819 .99584 .99864 .99688 .99904 .99778 36 28 37 .99708 .99331 .99767 .99466 .99820 .99585 .99865 .99690 .99904 .99780 32 32 38 9.99710 0.99333 9.99768 0.99468 9.99820 0.99587 9.99866 0.99693 9.99905 0.99781 28 36 39 .99711 .99336 .99769 .99470 .99821 .99589 .99867 .99693 .99905 .99782 24 40 40 .99712 .99338 .99770 .99472 .99822 .99591 .99867 .99695 .99906 .99784 20 U 41 .99713 .99340 .99771 .99474 .99823 .99593 .99868 .99696 .99906 .99785 16 48 42 9.99714 0.99343 9.99772 0.99476 9.99824 0.99595 9.99869 0.99698 9.99907 0.99786 12 52 43 .99715 .99345 .99773 .99478 .99824 .99597 .99869 .99700 .99908 .99788 8 56 44 9.99716 0.99347 9.99774 0.99480 9.99825 0.99598 9.99870 0.99701 9.99908 0.99789 4 12h 37m 1 12h ssm 1 12h 29m 1 12h25m 1 12h 21m « ' llh23m 170° lift 27m 171° llh Sim 173° llh 35m 173° llh 39m 171° a 60 45 9.99717 0.99350 9.99774 0.99483 9.99826 0.99600 9.99871 0.99703 9.99909 0.99790 4 46 .99718 .99352 .99775 .99485 .99827 .99602 .99871 .99704 .99909 .99792 56 8 47 .99719 .99354 .99776 .99487 .99828 .99604 .99872 .99706 .99910 .99793 52 12 48 .99720 .99357 .99777 .99489 .99828 .99606 .99873 .99708 .99911 .99794 48 16 49 9.99721 0.99359 9.99778 0.99491 9.99829 0.99608 9.99874 0.99709 9.99911 0.99796 44 20 50 .99722 .99361 .99779 .99493 .99830 .99609 .99874 .99711 .99912 .99797 40 24 51 .99723 .99364 .99780 .99495 .99831 .99611 .99875 .99713 .99912 .99798 36 28 52 .99724 .99366 .99781 .99497 .99832 .99613 .99876 .99714 .99913 .99799 32 32 53 9.99725 0.99368 9.99782 0.99499 9.99832 0.99615 9.99876 0.99715 9.99913 0.99801 28 36 54 .99726 .99371 .99783 .99501 .99833 .99617 .99877 .99717 .99914 .99802 24 40 55 .99727 .99373 .99784 .99503 .99834 .99618 .99878 .99719 .99915 .99803 20 44 56 .99728 .99375 .99785 .99505 .99835 .99630 .99878 .99730 .99915 .99805 16 48 57 9.99729 0.99378 9.99786 0.99507 9.99836 0.99622 9.99879 0.99733 9.99916 0.99806 12 62 58 .99730 .99380 .99786 .99509 .99836 .99624 .99880 .99723 .99916 .99807 8 56 59 .99731 .99382 .99787 .99511 .99837 .99626 .99880 .99725 .99917 .99808 4 60 60 9.99732 0.99384 9.99788 0.99513 9.99838 0.99627 9.99881 0.99726 9.99917 0.99810 12h sem 1 12h 32m 1 12h 28m 1 12h 24m 1 12h 20m 1 TABLE 45. [Page 921 Haversines. a ' llh40m 175° llh44m 176° llh 48m 177° llh 52m 178° llh 56m 179° 3 60 Log. Ilav Nat. Hav. Log. Hav Nat. Hav. Log. Hav. Nat. Hav Log. Hav. Nat. Hav. 0.99970 lyog. Hav. 9.99997 Nat. Hav. 0.99992 9.99917 0.99810 9.99947 0.99878 9.99970 0.99931 9.99987 4 1 .99918 .99811 .99948 .99879 .99971 .99932 .99987 .99971 .99997 .99993 56 8 3 .99918 .99812 .99948 .99880 .99971 .99933 .99987 .99971 .99997 .99993 52 12 3 .99919 .99814 .99948 .99881 .99971 .99934 .99987 .99971 .99997 .99993 48 16 4 9.99919 0.99815 9.99949 0.99882 9.99972 0.99934 9.99988 0.99972 9.99997 0.99994 44 20 5 .99920 .99816 .99949 .99883 .99972 .99935 .99988 .99972 .99997 .99994 40 24 6 .99921 .99817 .99950 .99884 .99972 .99936 .99988 .99973 .99997 .99994 86 28 7 .99921 .99819 .99950 .99885 .99973 .99937 .99988 .99973 .99997 .99994 32 5^ 8 9.99922 0.99820 9.99951 0.99886 9.99973 0.99937 9.99988 0.99973 9.99998 0.99994 28 36 9 .99922 .99821 .99951 .99887 .99973 .99938 .99989 .99974 .99998 .99995 24 40 10 .99923 .99822 .99951 .99888 .99973 .99939 .99989 .99974 .99998 .99995 20 ■W 11 .99923 .99823 .99952 .99889 .99974 .99940 .99989 .99975 .99998 .99995 16 4S 12 9.99924 0.99825 9.99952 0.99890 9.99974 0.99940 9.99989 0.99975 9.99998 0.99995 12 5;? 13 .99924 .99826 .99953 .99891 .99974 .99941 .99989 .99976 .99998 .99995 8 56 U 9.99925 0.99827 9.99953 0.99892 9.99975 0.99942 9.99990 0.99976 9.99998 0.99996 4 12fi 19m 12h' 15m 12h lim 12h 7m 12hsm s ' llh4im 175° llh 4sm 176° llh 49m 177 llh5Sm 178° llh 57m 179° s 15 9.99925 0.99828 9.99953 0.99893 9.99975 0.99942 9.99990 0.99977 9.99998 0.99996 'W 4 16 .99926 .99829 .99954 .99894 .99975 .99943 .99990 .99977 .99998 .99996 56 5 17 .99926 .99831 .99954 .99895 .99976 .99944 .99990 .99978 .99998 .99996 52 12 18 .99927 .99832 .99954 .99896 .99976 .99944 .99990 .99978 .99998 .99996 48 i6 19 9.99927 0.99833 9.99955 0.99897 9.99976 0.99945 9.99991 0.99978 9.99998 0.99996 44 «0 20 .99928 .99834 .99955 .99898 .99976 .99946 .99991 .99979 .99999 .99997 40 24 21 .99928 .99835 .99956 .99899 .99977 .99947 .99991 .99979 .99999 .99997 36 «5 22 .99929 .99837 .99956 .99900 .99977 .99947 .99991 .99980 .99999 .99997 32 32 23 9.99929 0.99838 9.99957 0.99900 9.99977 0.99948 9.99991 0.99980 9.99999 0.99997 28 ■J6 24 .99930 .99839 .99957 .99901 .99978 .99949 .99992 .99981 .99999 .99997 24 40 25 .99931 .99840 .99958 .99902 .99978 .99949 .99992 .99981 .99999 .99997 20 44 26 .99931 .99841 .99958 .99903 .99978 .99950 .99992 .99981 .99999 .99998 16 4^ 27 9.99932 0.99842 9.99958 0.99904 9.99978 0.99950 9.99992 0.99982 9.99999 0.99998 12 52 28 .99932 .99844 .99959 .99905 .99979 .99951 .99992 .99982 .99999 .99998 8 56 29 9.99933 0.99845 9.99959 0.99906 9.99979 0.99952 9.99992 0.99982 9.99999 0.99998 4 12h 18m 12h 14m 12h 10m 12h6m 12h2m 8 ' llh42m 175° llh 46m 176° llhSOm 177° llh 54m 178° llh 58m 179° s 60 30 9.99933 0.99846 9.99959 0.99907 9.99979 0.99952 9.99993 0.99983 9.99999 0.99998 4 31 .99934 .99847 .99960 .99908 .99980 .99953 .99993 .99983 .99999 .99998 56 8 32 .99934 .99848 .99960 .99909 .99980 .99954 .99993 .99984 .99999 .99998 52 i;2 33 .99935 .99849 .99961 .99909 .99980 .99954 .99993 .99984 .99999 .99998 48 i6 34 9.99935 0.99850 9.99961 0.99910 9.99980 0.99955 9.99993 0.99984 9.99999 0.99999 44 20 35 .99935 .99851 .99961 .99911 .99981 .99956 .99993 .99985 .99999 .99999 40 ;g4 36 .99936 .99853 .99962 .99912 .99981 .99956 .99994 .99985 9.99999 .99999 36 28 37 .99936 .99854 .99962 .99913 .99981 .99957 .99994 .99985 0.00000 .99999 32 5^ 38 9.99937 0.99855 9.99963 0.99914 9.99981 0.99957 9.99994 0.99986 0.00000 0.99999 28 56 39 .99937 .99856 .99963 .99915 .99982 .99958 .99994 .99986 .00000 .99999 24 40 40 .99938 .99857 .99963 .99915 .99982 ► .99959 .99994 .99986 .00000 .99999 20 44 41 .99938 .99858 .99964 .99916 .99982 .99959 .99994 .99987 .00000 .99999 16 48 42 9.99939 0.99859 9.99964 0.99917 9.99983 0.99960 9.99994 0.99987 0.00000 0.99999 12 5:2 43 .99939 .99860 .99964 .99918 .99983 .99960 .99995 .99987 .00000 .99999 8 56 44 9.99940 0.99861 9.99965 0.99919 9.99983 0.99961 9.99995 0.99988 0.00000 0.99999 4 12h 17m 12h ism 1 12h9m 12h5m 12h im s ' llk4sm 175° j llh 47m 176° 1 llhsim 177° llh 55m 178° llh 59m 179° s 60 45 9.99940 0.99863 9.99965 0.99920 9.99983 0.99961 9.99995 0.99988 0.00000 1.00000 4 46 .99941 .99864 .99965 .99920 .99983 .99962 .99995 .99988 .00000 .00000 56 ^ 47 .99941 .99865 .99966 .99921 .99984 .99963 .99995 .99989 .00000 .OGOOO 52 1:? 48 .99942 .99866 .99966 .99922 .99984 .99963 .99995 .99989 .00000 .00000 48 16 49 9.99942 0.99867 9.99966 0.99923 9.99984 0.99964 9.99995 0.99989 0.00000 1.00000 44 ;20 50 .99943 .99868 .99967 .99934 .99984 .99964 .99996 .99990 .00000 .00000 40 24 51 .99943 .99869 .99967 .99924 .99985 .99965 .99996 .99990 .00000 .00000 36 ;g5 52 .99943 .99870 .99968 .99925 .99985 .99965 .99996 .99990 .00000 .00000 32 5:2 53 9.99944 0.99871 9.99968 0.99926 9.99985 0.99966 9.99996 0.99991 0.00000 1.00000 28 36 54 .99944 .99872 .99968 .99927 .99985 .99966 .99996 .99991 .00000 .00000 24 40 55 .99945 .99873 .99969 .99928 .99986 .99967 .99996 .99991 .00000 .00000 20 44 56 .99945 .99874 .99969 .99928 .99986 .99967 .99996 .99991 .00000 .00000 16 4i< Sun's Star's Sun's Star's Sun's Star's Sun's star's Sun's star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. COIT. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) o / 6 30 5 29 10 40 5 19 10 50 5 09 11 00 5 00 11 09 4 51 11 18 4 43 11 26 40 5 39 10 30 5 29 10 40 5 19 10 50 5 10 10 59 5 01 11 08 4 53 11 16 50 5 49 10 20 5 39 10 30 5 29 10 40 5 20 10 49 5 11 10 58 5 03 11 06 7 00 5 59 10 10 5 49 10 20 5 39 10 30 5 30 10 39 5 21 10 48 5 13 10 56 10 6 08 10 01 5 58 10 11 5 48 10 21 5 39 10 30 5 30 10 39 5 22 10 47 20 6 17 9 52 6 07 10 02 5 57 10 12 5 48 10 21 5 39 10 30 5 31 10 38 7 30 6 26 9 43 6 16 9 53 6 06 10 03 5 57 10 12 5 48 10 21 5 40 10 29 40 6 34 9 35 6 24 9 45 6 14 9 55 6 05 10 04 5 56 10 13 5 48 10 21 50 6 42 9 27 6 32 9 37 6 22 9 47 6 13 9 56 6 04 10 05 5 56 10 13 8 00 6 50 9 19 6 40 9 29 6 30 9 39 6 21 9 48 6 12 9 57 6 04 10 05 10 6 57 9 12 6 47 9 22 6 37 9 32 6 28 9 41 6 19 9 50 6 11 9 58 20 7 04 9 05 6 54 9 15 6 44 9 25 6 35 9 34 6 26 9 43 6 18 9 51 8 30 7 11 8 58 7 01 9 08 6 51 9 18 6 42 9 27 6 33 9 36 6 25 9 44 40 7 18 8 51 7 08 9 01 6 58 9 11 6 49 9 20 6 40 9 29 6 32 9 37 50 7 24 8 45 7 14 8 55 7 04 9 05 6 55 9 14 6 46 9 23 6 38 9 31 9 00 7 30 8 39 7 20 8 49 7 10 8 59 7 01 9 08 6 52 9 17 6 44 9 25 20 7 42 8 27 7 32 8 37 7 22 8 47 7 13 8 56 7 04 9 05 6 56 9 13 40 7 53 8 16 7 43 8 26 7 33 8 36 7 24 8 45 7 15 8 54 7 07 9 02 10 00 8 04 8 05 7 54 8 15 7 44 8 25 7 35 8 34 7 26 8 43 7 18 8 51 20 8 14 7 55 8 04 8 05 7 54 8 15 7 45 8 24 7 36 8 33 7 28 8 41 40 8 23 7 46 8 13 7 56 8 03 8 06 7 54 8 15 7 45 8 24 7 37 8 32 11 00 8 32 7 37 8 22 7 47 8 12 7 57 8 03 8 06 7 54 8 15 7 46 8 23 30 8 44 7 25 8 34 7 35 8 24 7 45 8 15 7 54 8 06 8 03 7 58 8 11 12 00 8 55 7 14 8 45 7 24 8 35 7 34 8 26 7 43 8 17 7 52 8 09 8 00 30 9 06 7 03 8 56 7 13 8 46 7 23 8 37 7 32 8 28 7 41 8 20 7 49 13 00 9 16 6 53 9 06 7 03 8 56 7 13 8 47 7 22 8 38 7 31 8 30 7 39 30 9 25 6 44 9 15 6 54 9 05 7 04 8 56 7 13 8 47 7 22 8 39 7 30 14 00 9 33 6 36 9 23 6 46 9 13 6 56 9 04 7 05 8 55 7 14 8 47 7 22 15 00 9 49 6 20 9 39 6 30 9 29 6 40 9 20 6 49 9 11 6 58 9 03 7 06 16 00 10 02 6 07 9 52 6 17 9 42 6 27 9 33 6 36 9 24 6 45 9 16 6 53 17 00 10 15 5 54 10 05 6 04 9 55 6 14 9 46 6 23 9 37 6 32 9 29 6 40 18 00 10 25 5 44 10 15 5 54 10 05 6 04 9 56 6 13 9 47 6 22 9 39 6 30 19 00 10 35 5 34 10 25 5 44 10 15 5 54 10 06 6 03 9 57 6 12 9 49 6 20 20 00 10 43 5 25 10 33 5 35 10 23 5 45 10 14 5 54 10 05 6 03 9 57 6 11 22 00 10 59 5 09 10 49 5 19 10 39 5 29 10 30 5 38 10 21 5 47 10 13 5 55 24 00 11 12 4 56 11 02 5 06 10 52 5 16 10 43 5 25 10 34 5 34 10 26 5 42 26 00 11 23 4 45 11 13 4 55 11 03 5 05 10 54 5 14 10 45 5 23 10 37 5 31 28 00 11 33 4 35 11 23 4 45 11 13 4 55 11 04 5 04 10 55 5 13 10 47 5 21 30 00 11 41 4 27 11 31 4 37 11 21 . 4 47 11 12 4 56 11 03 5 05 10 55 5 13 32 00 11 49 4 19 11 39 4 29 11 29 4 39 11 20 4 48 11 11 4 57 11 03 5 05 34 00 11 56 4 12 11 46 4 22 11 36 4 32 11 27 4 41 11 18 4 50 11 10 4 58 36 00 12 02 4 06 11 52 4 16 11 42 4 26 11 33 4 35 11 24 4 44 11 16 4 52 38 00 12 07 4 01 11 57 4 11 11 47 4 21 11 38 4 30 11 29 4 39 11 21 4 47 40 00 12 12 3 55 12 02 4 05 11 52 4 15 11 43 4 24 11 34 4 33 11 26 4 41 45 00 12 23 3 44 12 13 3 54 12 03 4 04 11 54 4 13 11 45 4 22 11 37 4 30 50 00 12 31 3 35 12 21 3 45 12 11 3 55 12 02 4 04 11 53 4 13 11 45 4 21 55 00 12 38 3 27 12 28 3 37 12 18 3 47 12 09 3 56 12 00 4 05 11 52 4 13 60 00 12 44 3 20 12 34 3 30 12 24 3 40 12 15 3 49 12 06 3 58 11 58 4 06 65 00 12 51 3 13 12 41 3 23 12 31 3 33 12 22 3 42 12 13 3 51 12 05 3 59 70 00 12 56 3 07 12 46 3 17 12 36 3 27 12 27 3 36 12 18 3 45 12 10 3 53 75 00 13 00 3 02 12 50 3 12 12 40 3 22 12 31 3 31 12 22 3 40 12 14 3 48 80 00 13 06 2 56 12 56 3 06 12 46 3 16 12 37 3 25 12 28 3 34 12 20 3 42 85 00 13 10 2 51 13 00 3 01 12 50 3 11 12 41 3 20 3 15 12 32 3 29 12 24 3 37 90 00 13 14 2 46 13 04 2 56 12 54 3 06 12 45 12 36 3 24 12 28 3 32 1 Additioi TAL COKR. Day of Month. Jan. Feb. Mar. Apr May. June July. Aug. Sept. Oct. Noi T. Dec. ,f r/ ,f „ // // f, „ tf // t ff FOR SU N's Alt. l8ttol5th.... +18 +15 +8 - 8 -13 -14 -11 -5 +3 +11 +16 16th to 31st... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *Thec orrections for theobserved altitude of a Star or Planet involves the di] )and the refraction; and for the observed altitude of the Sun s lower limb, the dip, refraction, parallax, and mean semidiameter, wi lich is taken as 16'. A supplementary correction taking acc( )unt of the variation of the Sun's semidiameter in the different month s of the year is given at the foot of the main table TABLE 46. [Page 923 CorrectioDfl to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. Ob8. Alt. HEIGHT OF THE EYE. 1 14 Feet. 16 Feet. 16 Feet. 17 Feet. 18 Feet. 19 Feet. 1 O * O * G * o * O :*> O if Sun's Star's Sun's Star's Sun's star's Sun's star's Sun's star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) / / // / // / // / // / // / // / // / // / // / // / // / // 6 30 4 35 11 34 4 27 11 42 4 20 11 49 4 13 11 56 4 06 12 03 3 59 12 10 40 4 45 11 24 4 37 11 32 4 30 11 39 4 23 11 46 4 16 11 53 4 09 12 00 50 4 55 11 14 4 47 11 22 4 40 11 29 4 33 11 36 4 26 11 43 4 19 11 50 7 00 5 05 11 04 4 57 11 12 4 50 11 19 4 43 11 26 4 36 11 33 4 29 11 40 10 5 14 10 55 5 06 11 03 4 59 11 10 4 52 11 17 4 45 11 24 4 38 11 31 20 5 23 10 46 5 15 10 54 5 08 11 01 5 01 11 08 4 54 11 15 4 47 11 22 7 30 5 32 10 37 5 24 10 45 5 17 10 52 5 10 10 59 5 03 11 06 4 56 11 13 40 5 40 10 29 5 32 10 37 5 25 10 44 5 18 10 51 5 11 10 58 5 04 11 05 50 5 48 10 21 5 40 10 29 5 33 10 36 5 26 10 43 5 19 10 50 5 12 10 57 8 00 5 56 10 13 5 48 10 21 5 41 10 28 5 34 10 35 5 27 10 42 5 20 10 49 10 6 03 10 06 5 55 10 14 5 48 10 21 5 41 10 28 5 34 10 35 5 27 10 42 20 6 10 9 59 6 02 10 07 5 55 10 14 5 48 10 21 5 41 10 28 5 34 10 35 8 30 6 17 9 52 6 09 10 00 6 02 10 07 5 55 10 14 5 48 10 21 5 41 10 28 40 6 24 9 45 6 16 9 53 6 09 10 00 6 02 10 07 5 55 10 14 5 48 10 21 50 6 30 9 39 6 22 9 47 6 15 9 54 6 08 10 01 6 01 10 08 5 54 10 15 9 00 6 36 9 33 6 28 9 41 6 21 9 48 6 14 9 55 6 07 10 02 6 00 10 09 20 6 48 9 21 6 40 9 29 6 33 9 36 6 26 9 43 6 19 9 50 6 12 9 57 40 6 59 9 10 6 51 9 18 6 44 9 25 6 37 9 32 6 30 9 39 6 23 9 46 10 00 7 10 8 59 7 02 9 07 6 55 9 14 6 48 9 21 6 41 9 28 6 34 9 35 20 7 20 8 49 7 12 8 57 7 05 9 04 6 58 9 11 6 51 9 18 6 44 9 25 40 7 29 8 40 7 21 8 48 7 14 8 55 7 07 9 02 7 00 9 09 6 53 9 16 11 00 7 38 8 31 7 30 8 39 7 23 8 46 7 16 8 53 7 09 9 00 7 02 9 07 30 7 50 8 19 7 42 8 27 7 35 8 34 7 28 8 41 7 21 8 48 7 14 8 55 12 00 8 01 8 08 7 53 8 16 7 46 8 23 7 39 8 30 7 32 8 37 7 25 8 44 30 8 12 7 57 8 04 8 05 7 57 8 12 7 50 8 19 7 43 8 26 7 36 8 33 13 00 8 22 7 47 8 14 7 55 8 07 8 02 8 00 8 09 7 53 8 16 7 46 8 23 30 8 31 7 38 8 23 7 46 8 16 7 53 8 09 8 00 8 02 8 07 7 55 8 14 14 00 8 39 7 30 8 31 7 38 8 24 7 45 8 17 7 52 8 10 7 59 8 03 8 06 15 00 8 55 7 14 8 47 7 22 8 40 7 29 8 33 7 36 8 26 7 43 8 19 7 50 16 00 9 08 7 01 9 00 7 09 8 53 7 16 8 46 7 23 8 39 7 30 8 32 7 37 17 00 9 21 6 48 9 13 6 56 9 06 7 03 8 59 7 10 8 52 7 17 8 45 7 24 18 00 9 31 6 38 9 23 6 46 9 16 6 53 9 09 7 00 9 02 7 07 8 55 7 14 19 00 9 41 6 28 9 33 6 36 9 26 6 43 9 19 6 50 9 12 6 57 9 05 7 04 20 00 9 49 6 19 9 41 6 27 9 34 6 34 9 27 6 41 9 20 6 48 9 13 6 55 22 00 10 05 6 03 9 57 6 11 9 50 6 18 9 43 6 25 9 36 6 32 9 29 6 39 24 00 10 18 5 50 10 10 5 58 10 03 6 05 9 56 6 12 9 49 6 19 9 42 6 26 26 00 10 29 5 39 10 21 5 47 10 14 5 54 10 07 6 01 10 00 6 08 9 53 6 15 28 00 10 39 5 29 10 31 5 37 10 24 5 44 10 17 5 51 10 10 5 58 10 03 6 05 30 00 10 47 5 21 10 39 5 29 10 32 5 36 10 25 5 43 10 18 5 50 10 11 5 57 32 00 10 55 5 13 10 47 5 21 10 40 5 28 10 33 5 35 10 26 5 42 10 19 5 49 34 00 11 02 5 06 10 54 5 14 10 47 5 21 10 40 5 28 10 33 5 35 10 26 5 42 36 00 11 08 5 00 11 00 5 08 10 53 5 15 10 46 5 22 10 39 5 29 10 32 5 36 38 00 11 13 4 55 11 05 5 03 10 58 5 10 10 51 5 17 10 44 5 24 10 37 5 31 40 00 11 18 4 49 11 10 4 57 11 03 6 04 10 56 5 11 10 49 5 18 10 42 5 25 45 00 11 29 4 38 11 21 4 46 11 14 4 53 11 07 5 00 11 00 5 07 10 53 5 14 50 00 11 37 4 29 11 29 4 37 11 22 4 44 11 15 4 51 11 08 4 58 11 01 5 05 55 00 11 44 4 21 11 36 4 29 11 29 4 36 11 22 4 43 11 15 4 50 11 08 4 57 60 00 11 50 4 14 11 42 4 22 11 35 4 29 11 28 4 36 11 21 4 43 11 14 4 50 65 00 11 57 4 07 11 49 4 15 11 42 4 22 11 35 4 29 11 28 4 36 11 21 4 43 70 00 12 02 4 01 11 54 4 09 11 47 4 16 11 40 4 23 11 33 4 30 11 26 4 37 75 00 12 06 3 56 11 58 4 04 11 51 4 11 11 44 4 18 11 37 4 25 11 30 4 32 80 00 12 12 3 50 12 04 3 58 11 57 4 05 11 50 4 12 11 43 4 19 11 36 4 26 85 00 12 16 3 45 12 08 3 53 12 01 4 00 11 54 4 07 11 47 4 14 11 40 4 21 90 00 12 20 3 40 12 12 3 48 12 05 3 55 11 58 4 02 11 51 4 09 11 44 4 16 1 Additional Core. Day of Month. Jan. Feb. Mar. Apr. May. lune. July. Aug. Sept. Oct. Nov. Dec. „ /, /, ,/ rr „ // // // // n /' FOE Sun's Alt. let to 15th... - +18 +15 H -8 -8 - -13 -14 -11 -5 +3 + 11 +16 16thto3l8t... +17 +12 H -4 -4 -11 - -14 -13 - 9 -1 +7 +14 +18 * The corrections for the observed altitude of a Star or Pla net involves the dip and the refraction; and for the observed altitude of the Sun's lower limb, the dip, refraction, parallax, and me£ in semidiameter, which is taken as 16'. A supplementary correction Ekt the foot of the main table. taking account of the variation of the Sun's semidiameter in t iie different months of the year is given 21594°— 14- -51 Page 824] TABLE 46. Corrections to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. Ob3. Alt. HEIGHT OF THE EYE. i 20 Feet. j 21 Feet. | 22 Feet. 1 23 Feet. 1 24 Feet. 1 25 Feet. j O * O * * O * * O * Sun's star's Sun's Star's Sun's Star's Sun's star's Sun's Star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) o ' 6 30 3 52 12 17 3 46 12 23 3 39 12 30 3 33 12 36 3 27 12 42 3 21 12 48 40 4 .2 12 07 3 56 12 13 3 49 12 20 3 43 12 26 3 37 12 32 3.31 12 38 50 4 12 11 57 4 06 12 03 3 59 12 10 3 53 12 16 3 47 12 22 3 41 12 28 7 00 4 22 11 47 4 16 11 53 4 09 12 00 4 03 12 06 3 57 12 12 3 51 12 18 10 4 31 11 38 4 25 11 44 4 18 11 51 4 12 11 57 4 06 12 03 4 00 12 09 20 4 40 11 29 4 34 11 35 4 27 11 42 4 21 11 48 4 15 11 54 4 09 12 00 7 30 4 49 11 20 4 43 11 26 4 36 11 33 4 30 11 39 4 24 11 45 4 18 11 51 40 5b 4 57 11 12 4 51 11 18 4 44 11 25 4 38 11 31 4 32 11 37 4 26 11 43 5 05 11 04 4 59 11 10 4 52 11 17 4 46 11 23 4 40 11 29 4 34 11 35 8 00 5 13 10 56 5 07 11 02 5 00 11 09 4 54 11 15 4 48 11 21 4 42 11 27 10 5 20 10 49 5 14 10 55 5 07 11 02 5 01 11 08 4 55 11 14 4 49 11 20 20 5 27. 10 42 5 21 10 48 5 14 10 55 5 08 11 01 5 02 11 07 4 56 11 13 8 30 5 34 10 35 5 28 10 41 5 21 10 48 5 15 10 54 5 09 11 00 5 03 11 06 40 5 41 10 28 5 35 10 34 5 28 10 41 5 22 10 47 5 16 10 53 5 10 10 59 50 5 47 10 22 5 41 10 28 5 34 10 35 5 28 10 41 5 22 10 47 5 16 10 53 9 00 5 53 10 16 5 47 10 22 5 40 10 29 5 34 10 35 5 28 10 41 5 22 10 47 20 6 05 10 04 5 59 10 10 5 52 10 17 5 46 10 23 5 40 10 29 5 34 10 35 40 6 16 9 53 6 10 9 59 6 03 10 06 5 57 10 12 5 51 10 18 5 45 10 24 10 00 6 27 9 42 6 21 9 48 6 14 9 55 6 08 10 01 6 02 10 07 5 56 10 13 20 6 37 9 32 6 31 9 38 6 24 9 45 6 18 9 51 6 12 9 57 6 06 10 03 40 6 46 9 23 6 40 9 29 6 33 9 36 6 27 9 42 6 21 9 48 6 15 9 54 11 00 6 55 9 14 6 49 9 20 6 42 9 27 6 36 9 33 6 30 9 39 6 24 9 45 30 7 07 9 02 7 01 9 08 6 54 9 15 6 48 9 21 6 42 9 27 6 36 9 33 12 00 7 18 8 51 7 12 8 57 7 05 9 04 6 59 9 10 6 53 9 16 6 47 9 22 30 7 29 8 40 7 23 8 46 7 16 8 53 7 10 8 59 7 04 9 05 6 58 9 11 13 00 7 39 8 30 7 33 8 36 7 26 8 43 7 20 8 49 7 14 8 55 7 08 9 01 30 7 48 8 21 7 42 8 27 7 35 8 34 7 29 8 40 7 23 8 46 7 17 8 52 14 00 7 56 8 13 7 50 8 19 7 43 8 26 7 37 8 32 7 31 8 38 7 25 8 44 15 00 8 12 7 57 8 06 8 03 7 59 8 10 7 53 8 16 7 47 8 22 7 41 8 28 16 00 8 25 7 44 8 19 7 50 8 12 7 57 8 06 8 03 8 00 8 09 7 54 8 15 17 00 8 38 7 31 8 32 7 37 8 25 7 44 8 19 7 50 8 13 7 56 8 07 8 02 18 00 8 48 7 21 8 42 7 27 8 35 7 34 8 29 7 40 8 23 7 46 8 17 7 52 19 00 8 58 7 11 8 52 7 17 8 45 7 24 8 39 7 30 8 33 7 36 8 27 7 42 20 00 9 06 7 02 9 00 7 08 8 53 7 15 8 47 7 21 8 41 7 27 8 35 7 33 22 00 9 22 6 46 9 16 6 52 9 09 6 59 9 03 7 05 8 57 7 11 8 51 7 17 24 00 9 35 6 33 9 29 6 39 9 22 6 46 9 16 6 52 9 10 6 58 9 04 7 04 26 00 9 46 6 22 9 40 6 28 9 33 6 35 9 27 6 41 9 21 6 47 9 15 6 53 28 00 9 56 6 12 9 50 6 18 9 43 6 25 9 37 6 31 9 31 6 37 9 25 6 43 30 00 10 04 6 04 9 58 6 10 9 51 6 17 9 45 6 23 9 39 6 29 9 33 6 35 32 00 10 12 5 56 10 06 6 02 9 59 6 09 9 53 6 15 9 47 6 21 9 41 6 27 34 00 10 19 5 49 10 13 5 55 10 06 6 02 10 00 6 08 9 54 6 14 9 48 6 20 36 00 10 25 5 43 10 19 5 49 10 12 5 56 10 06 6 02 10 00 6 08 9 54 6 14 38 00 10 30 5 38 10 24 5 44 10 17 5 51 10 11 5 57 10 05 6 03 9 59 6 09 40 00 10 35 5 32 10 29 5 38 10 22 5 45 10 16 5 51 10 10 5 57 10 04 6 03 45 00 10 46 5 21 10 40 5 27 10 33 5 34 10 27 5 40 10 21 5 46 10 15 5 52 50 00 10 54 5 12 10 48 5 18 10 41 5 25 10 35 5 31 10 29 5 37 10 23 5 43 55 00 11 01 5 04 10 55 5 10 10 48 5 17 10 42 5 23 10 36 5 29 10 30 5 35 60 00 11 07 4 57 11 01 5 03 10 54 5 10 10 48 5 16 10 42 5 22 10 36 5 28 65 00 11 14 4 50 11 08 4 56 11 01 5 03 10 55 5 09 10 49 5 15 10 43 5 21 70 00 11 19 4 44 11 13 4 50 11 06 4 57 11 00 5 03 10 54 5 09 10 48 5 15 75 00 11 23 4 39 11 17 4 45 11 10 4 52 11 04 4 58 10 58 5 04 10 52 5 10 80 00 11 29 4 33 11 23 4 39 11 16 4 46 11 10 4 52 11 04 4 58 10 58 5 04 85 00 11 33 4 28 11 27 4 34 11 20 4 41 11 14 4 47 11 08 4 53 11 02 4 59 90 00 11 37 4 23 11 31 4 29 11 24 4 36 11 18 4 42 11 12 4 48 11 06 4 54 1 Additional Core Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. ft It t> // >> II II II II II II " FOE Sun's Alt. 1st to 15th.... +18 +15 +8 C 1 -8 -13 -14 -11 -5 +3 +11 +16 16th to 31st... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 * The corrections for the observed altitude of a Star or Planet involves the di] ~> and the refraction; and for the observed altitude of the Sun's lower IL mb, the dip, refraction, parallax, and mean semidiametar, w hichistakenas 16'. A supplementary correction I at the toot of the main table. taking account of th e variation of the Sun's semidiameter in the different montl sof the year is giver TABLE 46. [Page 926 1 Correctiona* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find | the True Altitude — Continued. 1 Obs. Alt. HEIGHT OF THE EYE. | 26 Feet. 27 Feet. 28 Feet. 29 Feet. 30 Feet. 1 O * O « O « O * O * Sun's star's Sun's star's Sun's Star's Sun's star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 3 15 12 54 3 09 13 00 3 04 / // 13 05 2 58 13 11 2 53 13 16 40 3 25 12 44 3 19 12 50 3 14 12 55 3 08 13 01 3 03 13 06 50 3 35 12 34 3 29 12 40 3 24 12 45 3 18 12 51 3 13 12 56 7 00 3 45 12 24 3 39 12 30 3 34 12 35 3 28 12 41 3 23 12 46 10 3 54 12 15 3 48 12 21 3 43 12 26 3 37 12 32 3 32 12 37 20 4 03 12 06 3 57 12 12 3 52 12 17 3 46 12 23 3 41 12 28 7 30 4 12 11 57 4 06 12 03 4 01 12 08 3 55 12 14 3 50 12 19 40 4 20 11 49 4 14 11 55 4 09 12 00 4 03 12 06 3 58 12 11 50 4 28 11 41 4 22 11 47 4 17 11 52 4 11 11 58 4 06 12 03 . 8 00 4 36 11 33 4 30 11 39 4 25 11 44 4 19 11 50 4 14 11 55 10 4 43 11 26 4 37 11 32 4 32 11 37 4 26 11 43 4 21 11 48 20 4 50 11 19 4 44 11 25 4 39 11 30 4 33 11 36 4 28 11 41 8 30 4 57 11 12 4 51 11 18 4 46 11 23 4 40 11 29 4 35 11 34 40 5 04 11 05 4 58 11 11 4 53 11 16 4 47 11 22 4 42 11 27 50 5 10 10 59 5 04 11 05 4 59 11 10 4 53 11 16 4 48 11 21 9 00 5 16 10 53 5 10 10 59 5 05 11 04 4 59 11 10 4 54 11 15 20 5 28 10 41 5 22 10 47 5 17 10 52 5 11 10 58 5 06 11 03 40 5 39 10 30 5 33 10 36 5 28 10 41 5 22 10 47 5 17 10 52 10 00 5 50 10 19 5 44 10 25 5 39 10 30 5 33 10 36 5 28 10 41 20 6 00 10 09 5 54 10 15 5 49 10 20 5 43 10 26 5 38 10 31 40 6 09 10 00 6 03 10 06 5 58 10 11 5 52 10 17 5 47 10 22 11 00 6 18 9 51 6 12 9 57 6 07 10 02 6 01 10 08 5 56 10 13 30 6 30 9 39 6 24 9 45 6 19 9 50 6 13 9 56 6 08 10 01 12 00 6 41 9 28 6 35 9 34 6 30 9 39 6 24 9 45 6 19 9 50 30 6 52 9 17 6 46 9 23 6 41 9 28 6 35 9 34 6 30 9 39 13 00 7 02 9 07 6 56 9 13 6 51 9 18 6 45 9 24 6 40 9 29 30 7 11 8 58 7 05 9 04 7 00 9 09 6 54 9 15 6 49 9 20 14 00 7 19 8 50 7 13 8 56 7 08 9 01 7 02 9 07 6 57 9 12 15 00 7 35 8 34 7 29 8 40 7 24 8 45 7 18 8 51 7 13 8 56 16 00 7 48 8 21 7 42 8 27 7 37 8 32 7 31 8 38 7 26 8 43 17 00 8 01 8 08 7 55 8 14 7 50 8 19 7 44 8 25 7 39 8 30 18 00 8 11 7 58 8 05 8 04 8 00 8 09 7 54 8 15 7 49 8 20 19 00 8 21 7 48 8 15 7 54 8 10 7 59 8 04 8 05 7 59 8 10 20 00 8 29 7 39 8 23 7 45 8 18 7 50 8 12 7 56 8 07 8 01 22 00 8 45 7 23 8 39 7 29 8 34 7 34 8 28 7 40 8 23 7 45 24 00 8 58 7 10 8 52 7 16 8 47 7 21 8 41 7 27 8 36 7 32 26 00 9 09 6 59 9 03 7 05 8 58 7 10 8 52 7 16 8 47 7 21 28 00 9 19 6 49 9 13 6 55 9 08 7 00 9 02 7 06 8 57 7 11 30 00 9 27 6 41 9 21 6 47 9 16 6 52 9 10 6 58 9 05 7 03 32 00 9 35 6 33 9 29 6 39 9 24 6 44 9 18 6 50 9 13 6 55 34 00 9 42 6 26 9 36 6 32 9 31 6 37 9 25 6 43 9 20 6 48 36 00 9 48 6 20 9 42 6 26 9 37 6 31 9 31 6 37 9 26 6 42 38 00 9 53 6 15 9 47 6 21 9 42 6 26 9 36 6 32 9 31 6 37 40 00 9 58 6 09 9 52 6 15 9 47 6 20 9 41 6 26 9 36 6 31 45 00 10 09 5 58 10 03 6 04 9 58 6 09 9 52 6 15 9 47 6 20 50 00 10 17 5 49 10 11 5 55 10 06 6 GO 10 00 6 06 9 55 6 11 55 00 10 24 5 41 10 18 5 47 10 13 5 52 10 07 5 58 10 02 6 03 60 00 10 30 5 34 10 24 5 40 10 19 5 45 10 13 5 51 10 08 5 56 65 00 10 37 5 27 10 31 5 33 10 26 5 38 10 20 5 44 10 15 5 49 70 00 10 42 5 21 10 36 5 27 10 31 5 32 10 25 5 38 10 20 5 43 75 00 10 46 5 16 10 40 5 22 10 35 5 27 10 29 5 33 10 24 5 38 80 00 10 52 5 10 10 46 5 16 10 41 5 21 10 35 5 27 10 30 5 32 85 00 10 56 5 05 10 50 5 11 10 45 5 16 10 39 5 22 10 34 5 27 90 00 11 00 5 00 10 54 5 06 10 49 5 11 10 43 5 17 10 38 5 22 1 Additionai, Cc EB. Day of Month. Jan. Feb. Mai . Apr. ] May. June July. -Aug. Sept. Oct. Nov. Dec. // ,> / // ^/ // // " // f' // FOB Sun's Ai -T. Isl t to 15th.... +18 +15 +J 5 - - 8 -13 v-14 -11 -5 +3 +11 +16 16 thto3l8t... +17 +12 +^ t -4 - -11 -14 -13 - 9 -1 +7 +14 +18 * The correct ons for the observed altitude of a £ )tar or Planet involves the dip and the refraction; and for t, and mean semidiameter, which is talcen as 16'. A supp imeter in the different months of the year is given at the fc the observed altitude of the Sun's lowe rlimb, the dip, refraction, parallaj lementary correction taking account of the variati on of the Sun'ssemidia ot of the main table. Page 926] TABLE 46. Corrrections to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. HEIGHT OF THE EYE. 1 31 Feet. 32 Feet. 33 Feet. 34 Feet. 1 35 Feet. 1 Obs. Alt. O * O * O * * O ♦ Sun's star's Sun's star's Sun's star's Sun's star's Sun's star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) o / > n / // / II / i> / // / II / // / // / // / 11 6 30 2 48 13 21 2 42 13 27 2 37 13 32 2 32 13 37 2 27 13 42 40 2 58 13 11 2 52 13 17 2 47 13 22 2 42 13 27 2 37 13 32 50 3 08 13 01 3 02 13 07 2 57 13 12 2 52 13 17 2 47 13 22 7 00 3 18 12 51 3 12 12 57 3 07 13 02 3 02 13 07 2 57 13 12 10 3 27 12 42 3 21 12 48 3 16 12 53 3 11 12 58 3 06 13 03 20 3 36 12 33 3 30 12 39 3 25 12 44 3 20 12 49 3 15 12 54 7 30 3 45 12 24 3 39 12 30 3 34 12 35 3 29 12 40 3 24 12 45 40 3 53 12 16 3 47 12 22 3 42 12 27 3 37 12 32 3 32 12 37 50 4 01 12 08 3 55 12 14 3 50 12 19 S 45 12 24 3 40 12 29 8 00 4 09 12 00 4 03 12 06 3 58 12 11 3 53 12 16 3 48 12 21 10 4 16 11 53 4 10 11 59 4 05 12 04 4 00 12 09 3 55 12 14 20 4 23 11 46 4 17 11 52 4 12 11 57 4 07 12 02 4 02 12 07 8 30 4 30 11 39 4 24 11 45 4 19 11 50 4 14 11 55 4 09 12 00 40 4 37 11 32 4 31 11 38 4 26 11 43 4 21 11 48 4 16 11 53 50 4 43 11 26 4 37 11 32 4 32 11 37 4 27 11 42 4 22 11 47 9 00 4 49 11 20 4 43 11 26 4 38 11 31 4 33 11 36 4 28 11 41 20 5 01 11 08 4 55 11 14 4 50 11 19 4 45 11 24 4 40 11 29 40 5 12 10 57 5 06 11 03 5 01 11 08 4 56 11 13 4 51 11 18 10 00 5 23 10 46 5 17 10 52 5 12 10 57 5 07 11 02 5 02 11 07 20 5 33 10 36 5 27 10 42 5 22 10 47 5 17 10 52 5 12 10 57 40 5 42 10 27 5 36 10 33 5 31 10 38 5 26 10 43. 5 21 10 48 11 00 5 51 10 18 5 45 10 24 5 40 10 29 5 35 10 34 5 30 10 39 30 6 03 10 06 5 57 10 12 5 52 10 17 5 47 10 22 5 42 10 27 12 00 6 14 9 55 6 08 10 01 6 03 10 06 5 58 10 11 5 53 10 16 30 6 25 9 44 6 19 9 50 6 14 9 55 6 09 10 00 6 04 10 05 13 00 6 35 9 34 6 29 9 40 6 24 9 45 6 19 9 50 6 14 9 55 30 6 44 9 25 6 38 9 31 6 33 9 36 6 28 9 41 6 23 9 46 14 00 6 52 9 17 6 46 9 23 6 41 9 28 6 36 9 33 6 31 9 38 15 00 7 08 9 01 7 02 9 07 6 57 9 12 6 52 9 17 6 47 9 22 16 00 7 21 8 48 7 15 8 54 7 10 8 59 7 05 9 04 7 00 9 09 17 00 7 34 8 35 7 28 8 41 7 23 8 46 7 18 8 51 7 13 8 56 18 00 7 44 8 25 7 38 8 31 7 33 8 36 7 28 8 41 7 23 8 46 19 00 7 54 8 15 7 48 8 21 7 43 8 26 7 38 8 31 7 33 8 36 20 00 8 02 8 06 7 56 8 12 7 51 8 17 7 46 8 22 7 41 8 27 22 00 8 18 7 50 8 12 7 56 8 07 8 01 8 02 8 06 7 57 8 11 24 00 8 31 7 37 8 25 7 43 8 20 7 48 8 15 7 53 8 10 7 58 26 00 8 42 7 26 8 36 7 32 8 31 7 37 8 26 7 42 8 21 7 47 28 00 8 52 7 16 8 46 7 22 8 41 7 27 8 36 7 32 8 31 7 37 30 00 9 00 7 08 8 54 7 14 8 49 7 19 8 44 7 24 8 39 7 29 32 00 9 08 7 00 9 02 7 06 8 57 7 11 8 52 7 16 8 47 7 21 34 00 9 15 6 53 9 09 6 59 9 04 7 04 8 59 7 09 8 54 7 14 36 00 9 21 6 47 9 15 6 53 9 10 6 58 9 05 7 03 9 00 7 08 38 00 9 26 6 42 9 20 6 48 9 15 6 53 9 10 6 58 9 05 7 03 40 00 9 31 6 36 9 25 6 42 9 20 6 47 9 15 6 52 9 10 6 57 45 00 9 42 6 25 9 36 6 31 9 31 6 36 9 26 6 41 9 21 6 46 50 00 9 50 6 16 9 44 6 22 9 39 6 27 9 34 6 32 9 29 6 37 55 00 9 57 6 08 9 51 6 14 9 46 6 19 9 41 6 24 9 36 6 29 60 00 10 03 6 01 9 57 6 07 9 52 6 12 9 47 6 17 9 42 6 22 65 00 10 10 5 54 10 04 6 00 9 59 6 05 9 54 6 10 9 49 6 15 70 00 10 15 5 48 10 09 5 54 10 04 5 59 9 59 6 04 9 54 6 09 75 00 10 19 5 43 10 13 5 49 10 08 5 54 10 03 5 59 9 58 6 04 80 00 10 25 5 37 10 19 5 43 10 14 5 48 10 09 5 53 10 04 5 58 85 00 10 29 5 32 10 23 5 38 10 18 5 43 10 13 5 48 10 08 5 53 90 00 10 33 5 27 10 27 5 33 10 22 5 38 10 17 5 43 10 12 5 48 1 Additional C( )ER. Day of Month. Jan. Feb. Mar. Apr. May. June . July. Aug. Sept. Oct. Nov. Dec. „ // „ If II // " // /' " " II FOR Sun's A LT. Is t to 15th.... +18 +15 +8 - - 8 -13 -14 -11 -5 +3 +■ 11 +16 16 th to 31st. . . +17 +12 +4 -4 - -11 -14 -13 - 9 -1 +7 + 14 +18 * Thecorrect onsforthe< jhserved altitude of a S tar or Planet involves the dip and the refraction; and for , and mean semidiameter, which is taken as 16'. A supp meter In the diflerent months of the year is given at the fc the observe d altitude of the Sun's lowe r limb, the lip, refraction, parallax lementary correction taking account of thevarlati( )n of the Sun's semldla »ot of the n: tain table. TABLE 46. [Page 927 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. OBfl. Alt. HEIGHT OF THE EYE. 1 36 Feet. 37 Feet. 1 38 Feet. 1 39 Feet. 40 Feet. | O * O * * O iii O * ■ Sun's star's Sun's star's Sun's Star's Sun's star's Sun's star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) o / 6 30 t n 2 22 13 47 2 17 13 52 2 13 13 56 2 08 14 01 2 03 / II 14 06 40 2 32 13 37 2 27 13 42 2 23 13 46 2 18 13 51 2 13 13 56 50 2 42 13 27 2 37 13 32 2 33 13 36 2 28 13 41 2 23 13 46 7 GO 2 52 13 17 2 47 13 22 2 43 13 26 2 38 13 31 2 33 13 36 10 3 01 13 08 2 56 13 13 2 52 13 17 2 47 13 22 2 42 13 27 20 3 10 12 59 3 05 13 04 3 01 13 08 2 56 13 13 2 51 13 18 7 30 3 19 12 50 3 14 12 55 3 10 12 59 3 05 13 04 3 00 13 09 40 3 27 12 42 3 22 12 47 3 18 12 51 3 13 12 56 3 08 13 01 50 3 35 12 34 3 30 12 39 3 26 12 43 3 21 12 48 3 16 12 53 8 00 3 43 12 26 3 38 12 31 3 34 12 35 3 29 12 40 3 24 12 45 10 3 50 12 19 3 45 12 24 . 3 41 12 28 3 36 12 33 3 31 12 38 20 3 57 12 12 3 52 12 17 3 48 12 21 3 43 12 26 3 38 12 31 8 30 4 04 12 05 3 59 12 10 3 55 12 14 3 50 12 19 3 45 12 24 40 4 11 11 58 4 06 12 03 4 02 12 07 3 57 12 12 3 52 12 17 50 4 17 11 52 4 12 11 57 4 08 12 01 4 03 12 06 3 58 12 11 9 00 4 23 11 46 4 18 11 51 4 14 11 55 4 09 12 00 4 04 12 05 20 4 35 11 34 4 30 11 39 4 26 11 43 4 21 11 48 4 16 11 53 40 4 46 11 23 4 41 11 28 4 37 11 32 4 32 11 37 4 27 11 42 10 00 4 57 11 12 4 52 11 17 4 48 11 21 4 43 11 26 4 38 11 31 20 5 07 11 02 5 02 11 07 4 58 11 11 4 53 11 16 4 48 11 21 40 5 16 10 53 5 11 10 58 5 07 11 02 5 02 11 07 4 57 11 12 11 00 5 25 10 44 5 20 10 49 5 16 10 53 5 11 10 58 5 06 11 03 30 5 37 10 32 5 32 10 37 5 28 10 41 5 23 10 46 5 18 10 51 12 00 5 48 10 21 5 43 10 26 5 39 10 30 5 34 10 35 5 29 10 40 30 5 59 10 10 5 54 10 15 5 50 10 19 5 45 10 24 5 40 10 29 13 00 6 09 10 00 6 04 10 05 6 00 10 09 5 55 10 14 5 50 10 19 30 6 18 9 51 6 13 9 56 6 09 10 00 6 04 10 05 5 59 10 10 14 00 6 26 9 43 6 21 9 48 6 17 9 52 6 12 9 57 6 07 10 02 15 00 6 42 9 27 6 37 9 32 6 33 9 36 6 28 9 41 6 23 9 46 16 00 6 55 9 14 6 50 9 19 6 46 9 23 6 41 9 28 6 36 9 33 17 00 7 08 9 01 7 03 9 06 6 59 9 10 6 54 9 15 6 49 9 20 18 00 7 18 8 51 7 13 8 56 7 09 9 00 7 04 9 05 6 59 9 10 19 00 7 28 8 41 7 23 8 46 7 19 8 50 7 14 8 55 7 09 9 00 20 00 7 36 8 32 7 31 8 37 7 27 8 41 7 22 8 46 7 17 8 51 22 00 7 52 8 16 7 47 8 21 7 43 8 25 7 38 8 30 7 33 8 35 24 00 8 05 8 03 8 00 8 08 7 56 8 12 7 51 8 17 7 46 8 22 26 00 8 16 7 52 8 11 7 57 8 07 8 01 8 02 8 06 7 57 8 11 28 00 8 26 7 42 8 21 7 47 8 17 7 51 8 12 7 56 8 07 8 01 30 00 8 34 7 34 8 29 7 39 8 25 7 43 8 20 7 48 8 15 7 53 32 00 8 42 7 26 8 37 7 31 8 33 7 35 8 28 7 40 8 23 7 45 34 00 8 49 7 19 8 44 7 24 8 40 7 28 8 35 7 33 8 30 7 38 36 00 8 55 7 13 8 50 7 18 8 46 7 22 8 41 7 27 8 36 7 32 38 00 9 00 7 08 8 55 7 13 8 51 7 17 8 46 7 22 8 41 7 27 40 00 9 05 7 02 9 00 7 07 8 56 7 11 8 51 7 16 8 46 7 21 45 00 9 16 6 51 9 11 6 56 9 07 7 00 9 02 7 05 8 57 7 10 50 00 9 24 6 42 9 19 6 47 9 15 6 51 9 10 6 56 9 05 7 01 55 00 9 31 6 34 9 26 6 39 9 22 6 43 9 17 6 48 9 12 6 53 60 00 9 37 6 27 9 32 6 32 9 28 6 36 9 23 6 41 9 18 6 46 65 00 9 44 6 20 9 39 6 25 9 35 6 29 9 30 6 34 9 25 6 39 70 00 9 49 6 14 9 44 6 19 9 40 6 23 9 35 6 28 9 30 6 33 75 00 9 53 6 09 9 48 6 14 9 44 6 18 9 39 6 23 9 34 6 28 80 00 9 59 6 03 9 54 6 08 9 50 6 12 9 45 6 17 9 40 6 22 85 00 10 03 5 58 9 58 6 03 9 54 6 07 9 49 6 12 9 44 6 17 90 00 10 07 5 53 10 02 5 58 9 58 6 02 9 53 6 07 9 48 6 12 1 Additional C 3RR. Day of Month. | Jan. 1 Feb. Mar. Apr. May. June. 1 July. Aug. Sept. Oct. Nov. Dec. ,/ „ ,, // // n » " " " " If FOE Sun's A LT. Is t to 15th +18 +15 +8 - - 8 -13 -14 -11 -5 +3 + 11 +16 16 thto3l8t... +17 +12 +4 -4 - -11 -14 -13 - 9 -1 +7 + 14 +18 * The correct ions for the observed altitude of a 3tar or Planet involves the dip and the refraction; and foi theobserv ed altitude of the Sun's lowe r limb, the dip, refraction, paralla t, and mean semidiameter, which is taken as 16'. A sup plementary oot of the n correction taking account of thevariati( )n of the Sun's semidia meter in the different months of the year is given at the i lain table. Page 928] TABLE 46. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. HEIGHT OF THE EYE. 1 41 Feet. 42 Feet. 43 Feet. 44 Feet. 45 Feet. 46 Feet. 1 *-\__ A T*H 1 KjDO, JVltl.. .o * O * O * O * O * O ♦ Sun's Star's Sun's Star's Sun's Star's Sim's Star's Sun's star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 1 58 / ft 14 11 1 54 14 15 1 49 1 n 14 20 1 44 14 25 1 39 14 30 1 35 14 34 40 2 08 14 01 2 04 14 05 1 59 14 10 1 54 14 15 1 49 14 20 1 45 14 24 50 2 18 13 51 2 14 13 55 2 09 14 00 2 04 14 05 1 59 14 10 1 55 14 14 7 00 2 28 13 41 2 24 13 45 2 19 13 50 2 14 13 55 2 09 14 00 2 05 14 04 10 2 37 13 32 2 33 13 36 2 28 13 41 2 23 13 46 2 18 13 51 2 14 13 55 20 2 46 13 23 2 42 13 27 2 37 13 32 2 32 13 37 2 27 13 42 2 23 13 46 7 30 2 55 13 14 2 51 13 18 2 46 13 23 2 41 13 28 2 36 13 33 2 32 13 37 40 3 03 13 06 2 59 13 10 2 54 13 15 2 49 13 20 2 44 13 25 2 40 13 29 50 3 11 12 58 3 07 13 02 3 02 13 07 2 57 13 12 2 52 13 17 2 48 13 21 8 00 3 19 12 50 3 15 12 54 3 10 12 59 3 05 13 04 3 00 13 09 2 56 13 13 10 3 26 12 43 3 22 12 47 3 17 12 52 3 12 12 57 3 07 13 02 3 03 13 06 20 3 33 12 36 3 29 12 40 3 24 12 45 3 19 12 50 3 14 12 55 3 10 12 59 8 30 3 40 12 29 3 36 12 33 3 31 ]2 38 3 26 12 43 3 21 12 48 3 17 12 52 40 3 47 12 22 3 43 12 26 3 38 12 31 3 33 12 36 3 28 12 41 3 24 12 45 50 3 53 12 16 3 49 12 20 3 44 12 25 3 39 12 30 3 34 12 35 3 30 12 39 9 00 3 59 12 10 3 55 12 14 3 50 12 19 3 45 12 24 3 40 12 29 3 36 12 33 20 4 11 11 58 4 07 12 02 4 02 12 07 3 57 14 12 3 52 12 17 3 48 12 21 40 4 22 11 47 4 18 11 51 4 13 11 56 4 08 12 01 4 03 12 06 3 59 12 10 10 00 4 33 11 36 4 29 11 40 4 24 11 45 4 19 11 50 4 14 11 55 4 10 11 59 20 4 43 11 26 4 39 11 30 4 34 11 35 4 29 11 40 4 24 11 45 4 20 11 49 40 4 52 11 17 4 48 11 21 4 43 11 26 4 38 11 31 4 33 11 36 4 29 11 40 11 00 5 01 11 08 4 57 11 12 4 52 11 17 4 47 11 22 4 42 11 27 4 38 11 31 30 5 13 10 56 5 09 11 00 5 04 11 05 4 59 11 10 4 54 11 15 4 50 11 19 12 00 5 24 10 45 5 20 10 49 5 15 10 54 5 10 10 59 5 05 11 04 5 01 11 08 30 5 35 10 34 5 31 10 38 5 26 10 43 5 21 10 48 5 16 10 53 5 12 10 57 13 00 5 45 10 24 5 41 10 28 5 36 10 33 5 31 10 38 5 26 10 43 5 22 10 47 30 5 54 10 15 5 50 10 19 5 45 10 24 5 40 10 29 5 35 10 34 5 31 10 38 14 00 6 02 10 07 5 58 10 11 5 53 10 16 5 48 10 21 5 43 10 26 5 39 10 30 15 00 6 18 9 51 6 14 9 55 6 09 10 00 6 04 10 05 5 59 10 10 5 55 10 14 16 00 6 31 9 38 6 27 9 42 6 22 9 47 6 17 9 52 6 12 9 57 6 08 10 01 17 00 6 44 9 25 6 40 9 29 6 35 9 34 6 30 9 39 6 25 9 44 6 21 9 48 ]8 00 6 54 9 15 6 50 9 19 6 45 9 24 6 40 9 29 6 35 9 34 6 31 9 38 19 00 7 04 9 05 7 00 9 09 6 55 9 14 6 50 9 19 6 45 9 24 6 41 9 28 20 00 7 12 8 56 7 08 9 00 7 03 9 05 6 58 9 10 6 53 9 15 6 49 9 19 22 00 7 28 8 40 7 24 8 44 7 19 8 49 7 14 8 54 7 09 8 59 7 05 9 03 24 00 7 41 8 27 7 37 8 31 7 32 8 36 7 27 8 41 7 22 8 46 7 18 8 50 26 00 7 52 8 16 7 48 8 20 7 43 8 25 7 38 8 30 7 33 8 35 7 29 8 39 28 00 8 02 8 06 7 58 8 10 7 53 8 15 7 48 8 20 7 43 8 25 7 39 8 29 30 00 8 10 7 58 8 06 8 02 8 01 8 07 7 56 8 12 7 51 8 17 7 47 8 21 32 00 8 18 7 50 8 14 7 54 8 09 7 59 8 04 8 04 7 59 8 09 7 55 8 13 34 00 8 25 7 43 8 21 7 47 8 16 7 52 8 11 7 57 8 06 8 02 8 02 8 06 36 00 8 31 7 37 8 27 7 41 8 22 7 46 8 17 7 51 8 12 7 56 8 08 8 00 38 00 8 36 7 32 8 32 7 36 8 27 7 41 8 22 7 46 8 17 7 51 8 13 7 55 40 00 8 41 7 26 8 37 7 30 8 32 7 35 8 27 7 40 8 22 7 45 8 18 7 49 45 00 8 52 7 15 8 48 7 19 8 43 7 24 8 38 7 29 8 33 7 34 8 29 7 38 50 00 9 00 7 06 8 56 7 10 8 51 7 15 8 46 7 20 8 41 7 25 8 37 7 29 55 00 9 07 6 58 9 03 7 02 8 58 7 07 8 53 7 12 8 48 7 17 8 44 7 21 60 00 9 13 6 51 9 09 6 55 9 04 7 00 8 59 7 05 8 54 7 10 8 50 7 14 65 00 9 20 6 44 9 16 6 48 9 11 6 53 9 06 6 58 9 01 7 03 8 57 7 07 70 00 9 25 6 38 9 21 6 42 9 16 6 47 9 11 6 52 9 06 6 57 9 02 7 01 75 00 9 29 6 33 9 25 6 37 9 20 6 42 9 15 6 47 9 10 6 52 9 06 6 56 80 00 9 35 6 27 9 31 6 31 9 26 6 36 9 21 6 41 9 16 6 46 9 12 6 50 85 00 9 39 6 22 9 35 6 26 9 30 6 31 9 25 6 36 9 20 6 41 9 16 6 45 90 00 9 43 6 17 9 39 6 21 9 34 6 26 9 29 6 31 9 24 6 36 9 20 6 40 1 Additio SAL CORR Day of Month. Jan. Feh. Mar. Apr May. June. July. Aug. Sept. Oct. Nov. Dee. II „ // „ „ // II II II II II II FOB 8V •n's Alt. l3tt x)15th.... +18 +15 - F8 - 8 -13 -14 -11 -5 +3 +11 +16 16th to 3l8t... +17 +12 - f-4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *The< jorrection. > for the oh served altitude of a Star or Pk met involves the dip and the refraction; and for the observed altitude of the Sun s lower liu Qh, thedi] p, refraction, paralla X, and me an semidiameter, w hichis takenasie'. A supplementary correction at the foot of the main table. taking accc )unt of the variation of the Sun's semidi ameter in the diflerent mouth s of the year is given TABLE 46. [Page 929 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun 'a Lower Limb, to Find the True Altitude — Continued. Obs. Alt. HEIGHT OF THE EYE. 1 47 Feet. 48 Feet. 49 Feet. 50 Feet. 51 Feet. 52 Feet. 1 O * O * O * O * O * O * Sun's Star's Sun's Star's Sun's Star's Sun's star's Sun's Star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) ( + ) (-) ( + ) (-) (+) (-) (+) (-) (+) (-) 6 30 1 31 / // 14 38 1 27 14 42 1 23 14 46 1 19 14 50 1 15 / II 14 54 1 II 1 11 14 58 40 1 41 14 28 1 37 14 32 1 33 14 36 1 29 14 40 1 25 14 44 1 21 14 48 50 1 51 14 18 1 47 14 22 1 43 14 26 1 39 14 30 1 35 14 34 1 31 14 38 7 00 2 01 14 08 1 57 14 12 1 53 14 16 1 49 14 20 1 45 14 24 1 41 14 28 10 2 10 13 59 2 06 14 03 2 02 14 07 1 58 14 11 1 54 14 15 1 50 14 19 20 2 19 13 50 2 15 13 54 2 11 13 58 2 07 14 02 2 03 14 06 1 59 14 10 7 30 2 28 13 41 2 24 13 45 2 20 13 49 2 16 13 53 2 12 13 57 2 08 14 01 40 2 36 13 33 2 32 13 37 2 28 13 41 2 24 13 45 2 20 13 49 2 16 13 53 50 2 44 13 25 2 40 13 29 2 36 13 33 2 32 13 37 2 28 13 41 2 24 13 45 8 00 2 52 13 17 2 48 13 21 2 44 13 25 2 40 13 29 2 36 13 33 2 32 13 37 10 2 59 13 10 2 55 13 14 2 51 13 18 2 47 13 22 2 43 13 26 2 39 13 30 20 3 06 13 03 3 02 13 07 2 58 13 11 2 54 13 15 2 50 13 19 2 46 13 23 8 30 3 13 12 56 3 09 13 00 3 05 13 04 3 01 13 08 2 57 13 12 2 53 13 16 40 3 20 12 49 3 16 12 53 3 12 12 57 3 08 13 01 3 04 13 05 3 00 13 09 50 3 26 12 43 3 22 12 47 3 18 12 51 3 14 12 55 3 10 12 59 3 06 13 03 9 00 3 32 12 37 3 28 12 41 3 24 12 45 3 20 12 49 3 16 12 53 3 12 12 57 20 3 44 12 25 3 40 12 29 3 36 12 33 3 32 12 37 3 28 12 41 3 24 12 45 40 3 55 12 14 3 51 12 18 3 47 12 22 3 43 12 26 3 39 12 30 3 35 12 34 10 00 4 06 12 03 4 02 12 07 3 58 12 11 3 54 12 15 3 50 12 19 3 46 12 23 20 4 16 11 53 4 12 11 57 4 08 12 01 4 04 12 05 4 00 12 09 3 56 12 13 40 4 25 11 44 4 21 11 48 4 17 11 52 4 13 11 56 4 09 12 00 4 05 12 04 11 00 4 34 11 35 4 30 11 39 4 26 11 43 4 22 11 47 4 18 11 51 4 14 11 55 30 4 46 11 23 4 42 11 27 4 38 11 31 4 34 11 35 4 30 11 39 4 26 11 43 12 00 4 57 11 12 4 53 11 16 4 49 11 20 4 45 11 24 4 41 11 28 4 37 11 32 30 5 08 11 01 5 04 11 05 5 00 11 09 4 56 11 13 4 52 11 17 4 48 11 21 13 00 5 18 10 51 5 14 10 55 5 10 10 59 5 06 11 03 5 02 11 07 4 58 11 11 30 5 27 10 42 5 23 10 46 5 19 10 50 5 15 10 54 5 11 10 58 5 07 11 02 14 00 5 35 10 34 5 31 10 38 5 27 10 42 5 23 10 46 5 19 10 50 5 15 10 54 15 00 5 51 10 18 5 47 10 22 5 43 10 26 5 39 10 30 5 35 10 34 5 31 10 38 16 00 6 04 10 05 6 00 10 09 5 56 10 13 5 52 10 17 5 48 10 21 5 44 10 25 17 00 6 17 9 52 6 13 9 56 6 09 10 00 6 05 10 04 6 01 10 08 5 57 10 12 18 00 6 27 9 42 6 23 9 46 6 19 9 50 6 15 9 54 6 11 9 58 6 07 10 02 19 00 6 37 9 32 6 33 9 36 6 29 9 40 6 25 9 44 6 21 9 48 6 17 9 52 20 00 6 45 9 23 6 41 9 27 6 37 9 31 6 33 9 35 6 29 9 39 6 25 9 43 22 00 7 01 9 07 6 57 9 11 6 53 9 15 6 49 9 19 6 45 9 23 6 41 9 27 24 00 7 14 8 54 7 10 8 58 7 06 9 02 7 02 9 06 6 58 9 10 6 54 9 14 26 00 7 25 8 43 7 21 8 47 7 17 8 51 7 13 8 55 7 09 8 59 7 05 9 03 28 00 7 35 8 33 7 31 8 37 7 27 8 41 7 23 8 45 7 19 8 49 7 15 8 53 30 00 7 43 8 25 7 39 8 29 7 35 8 33 7 31 8 37 7 27 8 41 7 23 8 45 32 00 7 51 8 17 7 47 8 21 7 43 8 25 7 39 8 29 7 35 8 33 7 31 8 37 34 00 7 58 8 10 7 54 8 14 7 50 8 18 7 46 8 22 7 42 8 26 7 38 8 30 36 00 8 04 8 04 8 00 8 08 7 56 8 12 7 52 8 16 7 48 8 20 7 44 8 24 38 00 8 09 7 59 8 05 8 03 8 01 8 07 7 57 8 11 7 53 8 15 7 49 8 19 40 00 8 14 7 53 8 10 7 57 8 06 8 01 8 02 8 05 7 58 8 09 7 54 8 13 45 00 8 25 7 42 8 21 7 46 8 17 7 50 8 13 7 54 8 09 7 58 8 05 8 02 50 00 8 33 7 33 8 29 7 37 8 25 7 41 8 21 7 45 8 17 7 49 8 13 7 53 55 00 8 40 7 25 8 36 7 29 8 32 7 33 8 28 7 37 8 24 7 41 8 20 7 45 60 00 8 46 7 18 8 42 7 22 8 38 7 26 8 34 7 30 8 30 7 34 8 26 7 38 65 00 8 53 7 11 8 49 7 15 8 45 7 19 8 41 7 23 8 37 7 27 8 33 7 31 70 00 8 58 7 05 8 54 7 09 8 50 7 13 8 46 7 17 8 42 7 21 8 38 7 25 75 00 9 02 7 00 8 58 7 04 8 54 7 08 8 50 7 12 8 46 7 16 8 42 7 20 80 00 9 08 6 54 9 04 6 58 9 00 7 02 8 56 7 06 8 52 7 10 8 48 7 14 85 00 9 12 6 49 9 08 6 53 9 04 6 57 9 00 7 01 8 56 7 05 8 52 7 09 90 00 9 16 6 44 9 12 6 48 9 08 6 52 9 04 6 56 9 00 7 00 8 56 7 04 1 Additio NAL CORB Day of Month. Jan. Feh. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. /, // ,, , // „ // n 11 It II It FOE St. rN's Alt. Ist1 to 15th.... +18 +15 +8 - 8 -13 -14 -11 -5 +3 + 11 +16 16th I to 31st... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 ♦The 3orrectlon 3 for the oV served altitude of a Star or Planet involves the dij and the refraction; and for the observed altitude of the Sun 's lower lii nb.thedi p, refraction, paralle IX, and mean semidiameter, w hich is taken as 16'. A supplementary conection at the foot of the main table. taking ace ountof th 3 variation of the Sun's semid ameter in the different month s of the year is given Page 930] TABLE 46. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued . 1 Obs. Alt. HEIGHT OF THE EYE. 1 53 Feet. 54 Feet. 55 Feet. 1 56 Feet. 57 Feet. | 58 Feet. 1 O * O * O * O * O * O * Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 / 1) 1 07 15 02 1 03 15 06 59 15 10 55 15 14 51 15 18 1 II 48 15 21 40 1 17 14 52 1 13 14 56 1 09 15 00 1 05 15 04 1 01 15 08 58 15 11 50 1 27 14 42 1 23 14 46 1 19 14 50 1 15 14 54 1 11 14 58 1 08 15 01 7 00 1 37 14 32 1 33 14 36 1 29 14 40 1 25 14 44 1 21 14 48 1 18 14 51 10 1 46 14 23 1 42 14 27 1 38 14 31 1 34 14 35 1 30 14 39 1 27 14 42 20 1 55 14 14 1 51 .14 18 1 47 14 22 1 43 14 26 1 39 14 30 1 36 14 33 7 30 2 04 14 05 2 00 14 09 1 56 14 13 1 52 14 17 1 48 14 21 1 45 14 24 40 2 12 13 57 2 08 14 01 2 04 14 05 2 00 14 09 1 56 14 13 1 53 14 16 50 2 20 13 49 2 16 13 53 2 12 13 57 2 08 14 01 2 04 14 05 2 01 14 08 8 00 2 28 13 41 2 24 13 45 2 20 13 49 2 16 13 53 2 12 13 57 2 09 14 00 10 2 35 13 34 2 31 13 38 2 27 13 42 2 23 13 46 2 19 13 50 2 16 13 53 20 2 42 13 27 2 38 13 31 2 34 13 35 2 30 13 39 2 26 13 43 2 23 13 46 8 30 2 49 13 20 2 45 13 24 2 41 13 28 2 37 13 32 2 33 13 36 2 30 13 39 40 2 56 13 13 2 52 13 17 2 48 13 21 2 44 13 25 2 40 13 29 2 37 13 32 50 3 02 13 07 2 58 13 11 2 54 13 15 2 50 13 19 2 46 13 23 2 43 13 26 9 00 3 08 13 01 3 04 13 05 3 00 13 09 2 56 13 13 2 52 13 17 2 49 13 20 20 3 20 12 49 3 16 12 53 3 12 12 57 3 08 13 01 3 04 13 05 3 01 13 08 40 3 31 12 38 3 27 12 42 3 23 12 46 3 19 12 50 3 15 12 54 3 12 12 57 10 00 3 42 12 27 3 38 12 31 3 34 12 35 3 30 12 39 3 26 12 43 3 23 12 46 20 3 52 12 17 3 48 12 21 3 44 12 25 3 40 12 29 3 36 12 33 3 33 12 36. 40 4 01 12 08 3 57 12 12 3 53 12 16 3 49 12 20 3 45 12 24 3 42 12 27 11 00 4 10 11 59 4 06 12 03 4 02 12 07 3 58 12 11 3 54 12 15 3 51 12 18 30 4 22 11 47 4 18 11 51 4 14 11 55 4 10 11 59 4 06 12 03 4 03 12 06 12 00 4 33 11 36 4 29 11 40 4 25 11 44 4 21 11 48 4 17 11 52 4 14 11 55 30 4 44 11 25 4 40 11 29 4 36 11 33 4 32 11 37 4 28 11 41 4 25 11 44 13 00 4 54 11 15 4 50 11 19 4 46 11 23 4 42 11 27 4 38 11 31 4 35 11 34 30 5 03 11 06 4 59 11 10 4 55 11 14 4 51 11 18 4 47 11 22 4 44 11 25 14 00 5 11 10 58 5 07 11 02 5 03 11 06 4 59 11 10 4 55 11 14 4 52 11 17 15 00 5 27 10 42 5 23 10 46 5 19 10 50 5 15 10 54 5 11 10 58 5 08 11 01 16 00 5 40 10 29 5 36 10 33 5 32 10 37 5 28 10 41 5 24 10 45 5 21 10 48 17 00 5 53 10 16 5 49 10 20 5 45 10 24 5 41 10 28 5 37 10 32 5 34 10 35 18 00 6 03 10 06 5 59 10 10 5 55 10 14 5 51 10 18 5 47 10 22 5 44 10 25 19 00 6 13 9 56 6 09 10 00 6 05 10 04 6 01 10 08 5 57 10 12 5 54 10 15 20 00 6 21 9 47 6 17 9 51 G 13 9 55 6 09 9 59 6 05 10 03 6 02 10 06 22 00 6 37 9 31 6 33 9 35 6 29 9 39 6 25 9 43 6 21 9 47 6 18 9 50 24 00 6 50 9 18 6 46 9 22 6 42 9 26 6 38 9 30 6 34 9 34 6 31 9 37 26 00 7 01 9 07 6 57 9 11 6 53 9 15 6 49 9 19 6 45 9 23 6 42 9 26 28 00 7 11 8 57 7 07 9 01 7 03 9 05 6 59 9 09 6 55 9 13 6 52 9 16 30 00 7 19 8 49 7 15 8 53 7 11 8 57 7 07 9 01 7 03 9 05 7 00 9 08 32 00 7 27 8 41 7 23 8 45 7 19 8 49 7 15 8 53 7 11 8 57 7 08 9 00 34 00 7 34 8 34 7 30 8 38 7 26 8 42 7 22 8 46 7 18 8 50 7 15 8 63 36 00 7 40 8 28 7 36 8 32 • 7 32 8 36 7 28 8 40 7 24 8 44 7 21 8 47 38 00 7 45 8 23 7 41 8 27 7 37 8 31 7 33 8 35 7 29 8 39 7 26 8 42 40 00 7 50 8 17 7 46 8 21 7 42 8 25 7 38 8 29 7 34 8 33 7 31 8 36 45 00 8 01 8 06 7 57 8 10 7 53 8 14 7 49 8 18 7 45 8 22 7 42 8 25 50 00 8 09 7 57 8 05 8 01 8 01 8 05 7 57 8 09 7 53 8 13 7 50 8 16 55 00 8 16 7 49 8 12 7 53 8 08 7 57 8 04 8 01 8 00 8 05 7 57 8 08 60 00 8 22 7 42 8 18 7 46 8 14 7 50 8 10 7 54 8 06 7 58 8 03 8 01 65 00 8 29 7 35 8 25 7 39 8 21 7 43 8 17 7 47 8 13 7 51 8 10 7 54 70 00 8 34 7 29 8 30 7 33 8 26 7 37 8 22 7 41 8 18 7 45 8 15 7 48 75 00 8 38 7 24 8 34 7 28 8 30 7 32 8 26 7 36 8 22 7 40 8 19 7 43 80 00 8 44 7 18 8 40 7 22 8 36 7 26 8 32 7 30 8 28 7 34 8 25 7 37 85 00 8 48 7 13 8 44 7 17 8 40 7 21 8 36 7 25 8 32 7 29 8 29 7 32 90 00 8 52 7 08 8 48 7 12 8 44 7 16 8 40 7 20 8 36 7 24 8 33 7 27 1 Additio NAL Core Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. „ n // „ II II II ,/ „ ,/ „ II FOR SX Hi's Alt. I8t1 to 15th.... +18 +15 +8 - 8 -13 -14 -11 -5 +3 +11 +16 IBtll I to 31st... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 + 14 +18 ♦The correction 3 for the ol )served altitude of a Star or Planet involves the dij ) and the refraction; and for the observed altitude of the Sun 's lower lii ■nb,thedi p, refraction, paralla X, and mean semidiameter, w hich is taken as 16'. A supplementary correction IS of the year is given at the foot of the main table. taking ace cunt of th evariatior I of the Sun's semid lameter in the diilerent montl TABLE 46. [Page 931 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun 'a Lower Limb, to Find the True Altitude — Continued. 1 Obs. Alt. HEIGHT OF THE EYE. 1 59 Feet. 60 Feet. 61 Feet. 62 Feet. 63 Feet. 64 Feet. 1 O >•> O * O ♦ O « O « O « Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 44 / // 15 25 40 / II 15 29 36 / n 15 33 32 15 37 29 > II 15 40 25 15 44 40 54 15 15 50 15 19 46 15 23 42 15 27 39 15 30 35 15 34 50 1 04 15 05 1 00 15 09 56 15 13 52 15 17 49 15 20 45 15 24 7 00 1 14 14 55 1 10 14 59 1 06 15 03 1 02 15 07 59 15 10 55 15 14 10 1 23 14 46 1 19 14 50 1 15 14 54 1 11 14 58 1 08 15 01 1 04 15 05 20 1 32 14 37 1 28 14 41 1 24 14 45 1 20 14 49 1 17 14 52 1 13 14 56 7 30 1 41 14 28 1 37 14 32 1 33 14 36 1 29 14 40 1 26 14 43 1 22 14 47 40 1 49 14 20 1 45 14 24 1 41 14 28 1 37 14 32 1 34 14 35 1 30 14 39 60 1 57 14 12 1 53 14 16 1 49 14 20 1 45 14 24 1 42 14 27 1 38 14 31 8 00 2 05 14 04 2 01 14 08 1 57 14 12 1 53 14 16 1 50 14 19 1 46 14 23 10 2 12 13 57 2 08 14 01 2 04 14 05 2 00 14 09 1 57 14 12 1 53 14 16 20 2 19 13 50 2 15 13 54 2 11 13 58 2 07 14 02 2 04 14 05 2 00 14 09 8 30 2 26 13 43 2 22 13 47 2 18 13 51 2 14 13 55 2 11 13 58 2 07 14 02 40 2 33 13 36 2 29 13 40 2 25 13 44 2 21 13 48 2 18 13 51 2 14 13 55 50 2 39 13 30 2 35 13 34 2 31 13 38 2 27 13 42 2 24 13 45 2 20 13 49 9 00 2 45 13 24 2 41 13 28 2 37 13 32 2 33 13 36 2 30 13 39 2 26 13 43 20 2 57 13 12 2 53 13 16 2 49 13 20 2 45 13 24 2 42 13 27 2 38 13 31 40 3 08 13 01 3 04 13 05 3 00 13 09 2 56 13 13 2 53 13 16 2 49 13 20 10 00 3 19 12 50 3 15 12 54 3 11 12 58 3 07 13 02 3 04 13 05 3 00 13 09 20 3 29 12 40 3 25 12 44 3 21 12 48 3 17 12 52 3 14 12 55 3 10 12 59 40 3 38 12 31 3 34 12 35 3 30 12 39 3 26 12 43 3 23 12 46 3 19 12 50 11 00 3 47 12 22 3 43 12 26 3 39 12 30 3 35 12 34 3 32 12 37 3 28 12 41 30 3 59 12 10 3 55 12 14 3 51 12 18 3 47 12 22 3 44 12 25 3 40 12 29 12 00 4 10 11 59 4 06 12 03 4 02 12 07 3 58 12 11 3 55 12 14 3 51 12 18 30 4 21 11 48 4 17 11 52 4 13 11 56 4 09 12 00 4 06 12 03 4 02 12 07 13 00 4 31 11 38 4 27 11 42 4 23 11 46 4 19 11 50 4 16 11 53 4 12 11 57 30 4 40 11 29 4 36 11 33 4 32 11 37 4 28 11 41 4 25 11 44 4 21 11 48 14 00 4 48 11 21 4 44 11 25 4 40 11 29 4 36 11 33 4 33 11 36 4 29 11 40 15 00 5 04 11 05 5 00 11 09 4 56 11 13 4 52 11 17 4 49 11 20 4 45 11 24 16 00 5 17 10 52 5 13 10 56 5 09 11 00 5 05 11 04 5 02 11 07 4 58 11 11 17 00 5 30 10 39 5 26 10 43 5 22 10 47 5 18 10 51 5 15 10 54 5 11 10 58 18 00 5 40 10 29 5 36 10 33 5 32 10 37 5 28 10 41 5 25 10 44 5 21 10 48 19 00 5 50 10 19 5 46 10 23 5 42 10 27 5 38 10 31 5 35 10 34 5 31 10 38 20 00 5 58 10 10 5 54 10 14 5 50 10 18 5 46 10 22 5 43 10 25 5 39 10 29 22 GO 6 14 9 54 6 10 9 58 6 06 10 02 6 02 10 06 5 59 10 09 5 55 10 13 24 00 6 27 9 41 6 23 9 45 6 19 9 49 6 15 9 53 6 12 9 56 6 08 10 00 26 00 6 38 9 30 6 34 9 34 6 30 9 38 6 26 9 42 6 23 9 45 6 19 9 49 28 00 6 48 9 20 6 44 9 24 6 40 9 28 6 36 9 32 6 33 9 35 6 29 9 39 30 00 6 56 9 12 6 52 9 16 6 48 9 20 6 44 9 24 6 41 9 27 6 37 9 31 32 00 7 04 9 04 7 00 9 08 6 56 9 12 6 52 9 16 6 49 9 19 6 45 9 23 34 00 7 11 8 57 7 07 9 01 7 03 9 05 6 59 9 09 6 56 9 12 6 52 9 16 36 00 7 17 8 51 7 13 8 55 7 09 8 59 7 05 9 03 7 02 9 06 6 58 9 10 38 00 7 22 8 46 7 18 8 50 7 14 8 54 7 10 8 58 7 07 9 01 7 03 9 05 40 00 7 27 8 40 7 23 8 44 7 19 8 48 7 15 8 52 7 12 8 55 7 08 8 59 45 00 7 38 8 29 7 34 8 33 7 30 8 37 7 26 8 41 7 23 8 44 7 19 8 48 50 00 7 46 8 20 7 42 8 24 7 38 8 28 7 34 8 32 7 31 8 35 7 27 8 39 55 00 7 53 8 12 7 49 8 16 7 45 8 20 7 41 8 24 7 38 8 27 7 34 8 31 60 00 7 59 8 05 7 55 8 09 7 51 8 13 7 47 8 17 7 44 8 20 7 40 8 24 65 00 8 06 7 58 8 02 8 02 7 58 8 06 7 54 8 10 7 51 8 13 7 47 8 17 70 00 8 11 7 52 8 07 7 56 8 03 8 00 7 59 8 04 7 56 8 07 7 52 8 11 75 00 8 15 7 47 8 11 7 51 8 07 7 55 8 03 7 59 8 00 8 02 7 56 8 06 80 00 8 21 7 41 8 17 7 45 8 13 7 49 8 09 7 53 8 06 7 56 8 02 8 00 85 00 8 25 7 36 8 21 7 40 8 17 7 44 8 13 7 48 8 10 7 51 8 06 7 55 90 00 8 29 7 31 8 25 7 35 8 21 7 39 8 17 7 43 8 14 7 46 1 8 10 7 50 1 Addition f AL COKR. Day of Month. Jan. Feb. Mar. Apr May. lune. July. Aug. Sept. Oct. Nov . 1 Dec. „ II II n // „ II II II II 1 1 n FOR Su N's Alt. Istt ol5th.... +18 +15 1-8 - 8 ■ -13 -14 -11 -5 +3 +1] . +16 16th to 3l8t... + 17 +12 h4 -4 -11 ■ -14 -13 - 9 -1 +7 +1^ [ +18 *Thec orrections for the ob served altitude of a Star or Pla net involves the dip and the refraction; and for the observed altitude of the Sun' s lower limb, the dij ), refraction, paralla X, and me an semidiameter, w tiich is taken as 16'. A supplementary correction 3 of the year is given at the foot of the main table. taking accc )unt of the variation of the Sun's semidi ameter in the different month. Page 932] TABLE 46. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find f the True Altitude — Continued. 1 Obs. Alt. HEIGHT OF THE EYE. 1 65 Feet. 1 66 Feet. 1 67 Feet. 1 68 Feet. 1 69 Feet. 1 70 Feet. 1 O * O * O * O * O * G * Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) O 1 6 30 21 15 48 18 1 II 15 51 14 15 55 10 15 59 07 16 02 03 16 06 40 31 15 38 28 15 41 24 15 45 20 15 49 17 15 52 13 15 56 50 41 15 28 38 15 31 34 15 35 30 15 39 27 15 42 23 15 46 7 00 51 15 18 48 15 21 44 15 25 40 15 29 37 15 32 33 15 36 10 1 00 15 09 57 15 12 53 15 16 49 15 20 46 15 23 42 15 27 20 1 09 15 00 1 06 15 03 1 02 15 07 58 15 11 55 15 14 51 15 18 7 30 1 18 14 51 1 15 14 54 1 11 14 58 1 07 15 02 1 04 15 05 1 00 15 09 40 1 26 14 43 1 23 14 46 1 19 14 50 1 15 14 54 1 12 14 57 1 08 15 01 50 1 34 14 35 1 31 14 38 1 27 14 42 1 23 14 46 1 20 14 49 1 16 14 53 8 00 1 42 14 27 1 39 14 30 1 35 14 34 1 31 14 38 1 28 14 41 1 24 14 45 10 1 49 14 20 1 46 14 23 1 42 14 27 1 38 14 31 1 35 14 34 1 31 14 38 20 1 56 14 13 1 53 14 16 1 49 14 20 1 45 14 24 1 42 14 27 1 38 14 31 8 30 2 03 14 06 2 00 14 09 1 56 14 13 1 52 14 17 1 49 14 20 1 45 14 24 40 2 10 13 59 2 07 14 02 2 03 14 06 1 59 14 10 1 56 14 13 1 52 14 17 50 2 16 13 53 2 13 13 56 2 09 14 00 2 05 14 04 2 02 14 07 1 58 14 11 9 00 2 22 13 47 2 19 13 50 2 15 13 54 2 11 13 58 2 08 14 01 2 04 14 05 20 2 34 13 35 2 31 13 38 2 27 13 42 2 23 13 46 2 20 13 49 2 16 13 53 40 2 45 13 24 2 42 13 27 2 38 13 31 2 34 13 35 2 31 13 38 2 27 13 42 10 00 2 56 13 13 2 53 13 16 2 49 13 20 2 45 13 24 2 42 13 27 2 38 13 31 20 3 06 13 03 3 03 13 06 2 59 13 10 2 55 13 14 2 52 13 17 2 48 13 21 40 3 15 12 54 3 12 12 57 3 08 13 01 3 04 13 05 3 01 13 08 2 57 13 12 11 00 3 24 12 45 3 21 12 48 3 17 12 52 3 13 12 56 3 10 12 59 3 06 13 03 30 3 36 12 33 3 33 12 36 3 29 12 40 3 25 12 44 3 22 12 47 3 18 12 51 12 00 3 47 12 22 3 44 12 25 3 40 12 29 3 36 12 33 3 33 12 36 3 29 12 40 30 3 58 12 11 3 55 12 14 3 51 12 18 3 47 12 22 3 44 12 25 3 40 12 29 13 00 4 08 12 01 4 05 12 04 4 01 12 08 3 57 12 12 3 54 12 15 3 50 12 19 30 4 17 11 52 4 14 11 55 4 10 11 59 4 06 12 03 4 03 12 06 3 59 12 10 14 00 4 25 11 44 4 22 11 47 4 18 11 51 4 14 11 55 4 11 11 58 4 07 12 02 15 00 4 41 11 28 4 38 11 31 4 34 11 35 4 30 11 39 4 27 11 42 4 23 11 46 16 00 4 54 11 15 4 51 11 18 4 47 11 22 4 43 11 26 4 40 11 29 4 36 11 33 17 00 5 07 11 02 5 04 11 05 5 00 11 09 4 56 11 13 4 53 11 16 4 49 11 20 18 00 5 17 10 52 5 14 10 55 5 10 10 59 5 06 11 03 5 03 11 06 4 59 11 10 19 00 5 27 10 42 5 24 10 45 5 20 10 49 5 16 10 53 5 13 10 56 5 09 11 00 20 00 5 35 10 33 5 32 10 36 5 28 10 40 5 24 10 44 5 21 10 47 5 17 10 51 22 00 5 51 10 17 5 48 10 20 5 44 10 24 5 40 10 28 5 37 10 31 5 33 10 35 24 00 6 04 10 04 6 01 10 07 5 57 10 11 5 53 10 15 5 50 10 18 5 46 10 22 26 00 6 15 9 53 6 12 9 56 6 08 10 00 6 04 10 04 6 01 10 07 5 57 10 11 28 00 6 25 9 43 6 22 9 46 6 18 9 50 6 14 9 54 6 11 9 57 6 07 10 01 30 00 6 33 9 35 6 30 9 38 6 26 9 42 6 22 9 46 6 19 9 49 6 15 9 53 32 00 6 41 9 27 6 38 9 30 6 34 9 34 6 30 9 38 6 27 9 41 6 23 9 45 34 00 6 48 9 20 6 45 9 23 6 41 9 27 6 37 9 31 6 34 9 34 6 30 9 38 36 00 6 54 9 14 6 51 9 17 6 47 9 21 6 43 9 25 6 40 9 28 6 36 9 32 38 00 6 59 9 09 6 56 9 12 6 52 9 16 6 48 9 20 6 45 9 23 6 41 9 27 40 00 7 04 9 03 7 01 9 06 6 57 9 10 6 53 9 14 6 50 9 17 6 46 9 21 45 00 7 15 8 52 7 12 8 55 7 08 8 59 7 04 9 03 7 01 9 06 6 57 9 10 50 00 7 23 8 43 7 20 8 46 7 16 8 50 7 12 8 54 7 09 8 57 7 05 9 01 55 00 7 30 8 35 7 27 8 38 7 23 8 42 7 19 8 46 7 16 8 49 7 12 8 53 60 00 7 36 8 28 7 33 8 31 7 29 8 35 7 25 8 39 7 22 8 42 7 18 8 46 65 00 7 43 8 21 7 40 8 24 7 36 8 28 7 32 8 32 7 29 8 35 7 25 8 39 70 00 7 48 8 15 7 45 8 18 7 41 8 22 7 37 8 26 7 34 8 29 7 30 8 33 75 00 7 52 8 10 7 49 8 13 7 45 8 17 7 41 8 21 7 38 8 24 7 34 8 28 80 00 7 58 8 04 7 55 8 07 7 51 8 11 7 47 8 15 7 44 8 18 7 40 8 22 85 00 8 02 7 59 7 59 8 02 7 55 8 06 7 51 8 10 7 48 8 13 7 44 8 17 90 00 8 06 7 54 8 03 7 57 7 59 8 01 7 55 8 05 7 52 8 08 7 48 8 12 1 Additio NAL Cork Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. „ „ „ , „ „ n ,/ „ ^ /, 1, FOE St [N's Alt. Istl X)15th.... + 18 +15 +8 c - 8 -13 -14 -11 -5 +3 +11 +16 16th to 31st... +17 +12 +4 -A -11 -14 -13 - 9 -1 +7 +14 +18 *The( jorrection 5 for the olj served altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude of the Sun s lower lii nb, thedi p, refraction, paralls IX, and mean semidiameter, which is taken as 16'. A supplementary correction ameter in the different months of the year is given at the Toot of the main table. taking ace Duntof th B variation of the Sun's semid TABLE 46. [Page 933 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find 1 the True Altitude— Continued. 1 Obs. Alt HEIGHT OF THE EYE. 1 71 Feet. 72 Feet. 73 Feet. 74 Feet. 75 Feet. 76 Feet. 1 Sun's Corr. (+) * Star's Corr. (-) Sun's Corr. * Star's Corr. (-) Sun's Corr. * star's Corr. (-) Sun's Corr. * Star's Corr. (-) n©, Sun's Corr. * Star's Corr. (-) Sun's Corr. 4< Star's Corr. (-) 6 30 00 16 09 -0 04 16 13 -0 08 16 17 -0 11 16 20 / II -0 14 16 23 -0 17 16 26 40 10 15 59 +0 06 16 03 +0 02 16 07 -0 01 16 10 -0 04 16 13 -0 07 16 16 50 20 15 49 16 15 53 12 15 57 +0 09 16 00 +0 06 16 03 +0 03 16 06 7 00 30 15 39 26 15 43 22 15 47 1 19 15 50 16 15 53 13 15 56 10 39 15 30 35 15 34 31 15 38 1 28 15 41 25 15 44 22 15 47 20 48 15 21 44 15 25 40 15 29 1 37 15 32 34 15 35 31 15 38 7 30 57 15 12 53 15 16 49 15 20 1 46 15 23 43 15 26 40 15 29 40 1 05 15 04 1 01 15 08 57 15 12 1 54 15 15 51 15 18 48 15 21 50 1 13 14 56 1 09 15 00 1 05 15 04 1 02 15 07 59 15 10 56 15 13 8 00 1 21 14 48 1 17 14 52 1 13 14 56 1 10 14 59 1 07 15 02 1 04 15 05 10 1 28 14 41 1 24 14 45 1 20 14 49 1 17 14 52 1 14 14 55 1 11 14 58 20 1 35 14 34 1 31 14 38 1 27 14 42 1 24 14 45 1 21 14 48 1 18 14 51 8 30 1 42 14 27 1 38 14 31 1 34 14 35 1 31 14 38 1 28 14 41 1 25 14 44 40 1 49 14 20 1 45 14 24 1 41 14 28 1 38 14 31 1 35 14 34 1 32 14 37 50 1 55 14 14 1 51 14 18 1 47 14 22 1 44 14 25 1 41 14 28 1 38 14 31 9 00 2 01 14 08 1 57 14 12 1 53 14 16 1 50 14 19 1 47 14 22 1 44 14 25 20 2 13 13 56 2 09 14 00 2 05 14 04 2 02 14 07 1 59 14 10 1 56 14 13 40 2 24 13 45 2 20 13 49 2 16 13 53 2 13 13 56 2 10 13 59 2 07 14 02 10 00 2 35 13 34 2 31 13 38 2 27 13 42 2 24 13 45 2 21 13 48 2 18 13 51 20 2 45 13 24 2 41 13 28 2 37 13 32 2 34 13 35 2 31 13 38 2 28 13 41 40 2 54 13 15 2 50 13 19 2 46 13 23 2 43 13 26 2 40 13 29 2 37 13 32 11 00 3 03 13 06 2 59 13 10 2 55 13 14 2 52 13 17 2 49 13 20 2 46 13 23 30 3 15 12 54 3 11 12 58 3 07 13 02 3 04 13 05 3 01 13 08 2 58 13 11 12 00 3 26 12 43 3 22 12 47 3 18 12 51 3 15 12 54 3 12 12 57 3 09 13 00 30 3 37 12 32 3 33 12 36 3 29 12 40 3 26 12 43 3 23 12 46 3 20 12 49 13 00 3 47 12 22 3 43 12 26 3 39 12 30 3 36 12 33 3 33 12 36 3 30 12 39 30 3 56 12 13 3 52 12 17 3 48 12 21 3 45 12 24 3 42 12 27 3 39 12 30 14 00 4 04 12 05 4 00 12 09 3 56 12 13 3 53 12 16 3 50 12 19 3 47 12 22 15 00 4 20 11 49 4 16 11 53 4 12 11 57 4 09 12 00 4 06 12 03 4 03 12 06 16 00 4 33 11 36 4 29 11 40 4 25 11 44 4 22 11 47 4 19 11 50 4 16 11 53 17 00 4 46 11 23 4 42 11 27 \% 11 31 4 35 11 34 4 32 11 37 4 29 11 40 18 00 4 56 11 13 4 52 11 17 11 21 4 45 11 24 4 42 11 27 4 39 11 30 19 00 5 06 11 03 5 02 11 07 4 58 11 11 4 55 11 14 4 52 11 17 4 49 11 20 20 00 5 14 10 54 5 10 10 58 5 06 11 02 5 03 11 05 5 00 11 08 4 57 11 11 22 00 5 30 10 38 5 26 10 42 5 22 10 46 5 19 10 49 5 16 10 52 5 13 10 55 24 00 5 43 10 25 5 39 10 29 5 35 10 33 5 32 10 36 5 29 10 39 5 26 10 42 26 00 5 54 10 14 5 50 10 18 5 46 10 22 5 43 10 25 5 40 10 28 5 37 10 31 28 00 6 04 10 04 6 00 10 08 5 56 10 12 5 53 10 15 5 50 10 18 5 47 10 21 30 00 6 12 9 56 6 08 10 00 6 04 10 04 6 01 10 07 5 58 10 10 5 65 10 13 32 00 6 20 9 48 6 16 9 52 6 12 9 56 6 09 9 59 6 06 10 02 6 03 10 05 34 00 6 27 9 41 6 23 9 45 6 19 9 49 6 16 9 52 6 13 9 55 6 10 9 58 36 00 6 33 9 35 6 29 9 39 6 25 9 43 6 22 9 46 6 19 9 49 6 16 9 52 38 00 6 38 9 30 6 34 9 34 6 30 9 38 6 27 9 41 6 24 9 44 6 21 9 47 40 00 6 43 9 24 6 39 9 28 6 35 9 32 6 32 9 35 6 29 9 38 6 26 9 41 45 00 6 54 9 13 6 50 9 17 6 46 9 21 6 43 9 24 6 40 9 27 6 37 9 30 50 00 7 02 9 04 6 58 9 08 6 54 9 12 6 51 9 15 6 48 9 18 6 45 9 21 55 00 7 09 8 56 7 05 9 00 7 01 9 04 6 58 9 07 6 55 9 10 6 52 9 13 60 00 7 15 8 49 7 11 8 53 7 07 8 57 7 04 9 00 7 01 9 03 6 58 9 06 65 00 7 22 8 42 7 18 8 46 7 14 8 50 7 11 8 53 y 08 8 56 7 05 8 59 70 00 7 27 8 36 7 23 8 40 7 19 8 44 7 16 8 47 7 13 8 50 7 10 8 53 75 00 7 31 8 31 7 27 8 35 7 23 8 39 7 20 8 42 7 17 8 45 7 14 8 48 80 00 7 37 8 25 7 33 8 29 7 29 8 33 7 26 8 36 7 23 8 39 7 20 8 42 85 00 7 41 8 20 7 37 8 24 7 33 8 28 7 30 8 31 7 27 8 34 7 24 8 37 90 00 7 45 8 15 +7 41 8 19 +7 37 8 23 +7 34 8 26 +7 31 8 29 +7 28 8 32 1 Additioi vTAL Core. Day of Month Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. 3ct. Nov. Dec. It // II „ „ „ ~ II „ II „ II FOR SU n's Alt. Istt ol5th.... +18 +15 H ^8 - 8 -13 -14 -11 -5 +3 +11 +16 16th to 31st... +17 +12 H h4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *Thec orrections for the oh served altitude of a K StarorPla net invoh ^es the dip and the refraction; and for the observed altitude of the Sun' s lower limb, the dij 3, refraction, paralla X, and me an semidi ameter, which is taken as 16'. A supplementary correction taking accc unt of the variation of the Sun's semid ameter in the diiier< jit months of the year is given at the foot of the main table. Page 934] TABLE 46. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find | the True Altitude — Continued. 1 Obs. Alt. HEIGHT OF THE EYE. 1 77 Feet. 78 Feet. 1 79 Feet. 1 80 Feet. 1 81 Feet. 1 82 Feet. 1 * * * * >K ii< Sun's Corr. Star's Corr. (-) Sun's COTI. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) 6 30 -0 21 16 30 -0 24 16 33 -0 28 16 37 -0 31 16 40 -0 34 16 43 -0 37 16 46 40 -0 11 16 20 -0 14 16 23 -0 18 16 27 -0 21 16 30 -0 24 16 33 -0 27 16 36 50 -0 01 16 10 -0 04 16 13 -0 08 16 17 -0 11 16 20 -0 14 16 23 -0 17 16 26 7 00 +Q 09 16 00 +0 06 16 03 +0 02 16 07 -0 01 16 10 -0 04 16 13 -0 07 16 16 10 18 15 51 15 15 54 11 15 58 +0 08 16 01 +0 05 16 04 +0 02 16 07 20 27 15 42 24 15 45 20 15 49 17 15 52 14 15 55 11 15 58 7 30 36 15 33 33 15 36 29 15 40 26 15 43 23 15 46 20 15 49 40 44 15 25 41 15 28 37 15 32 34 15 35 31 15 38 28 15 41 50 52 15 17 49 15 20 45 15 24 42 15 27 39 15 30 36 15 33 8 00 1 00 15 09 57 15 12 53 15 16 50 15 19 47 15 22 44 15 25 10 1 07 15 02 1 04 15 05 1 00 15 09 57 15 12 54 15 15 51 15 18 20 1 14 14 55 1 11 14 58 1 07 15 02 1 04 15 05 1 01 15 08 58 15 11 8 30 1 21 14 48 1 18 14 51 1 14 14 55 1 11 14 58 1 08 15 01 1 05 15 04 40 1 28 14 41 1 25 14 44 1 21 14 48 1 18 14 51 1 15 14 54 1 12 14 57 50 1 34 14 35 1 31 14 38 1 27 14 42 1 24 14 45 1 21 14 48 1 18 14 51 9 00 1 40 14 29 1 37 14 32 1 33 14 36 1 30 14 39 1 27 14 42 1 24 14 45 20 1 52 14 17 1 49 14 20 1 45 14 24 1 42 14 27 1 39 14 30 1 36 14 33 40 2 03 14 06 2 00 14 09 1 56 14 13 1 53 14 16 1 50 14 19 1 47 14 22 10 00 2 14 13 55 2 11 13 58 2 07 14 02 2 04 14 05 2 01 14 08 1 58 14 11 20 2 24 13 45 2 21 13 48 2 17 13 52 2 14 13 55 2 11 13 58 2 08 14 01 40 2 33 13 36 2 30 13 39 2 26 13 43 2 23 13 46 2 20 13 49 2 17 13 52 11 00 2 42 13 27 2 39 13 30 2 35 13 34 2 32 13 37 2 29 13 40 2 26 13 43 30 2 54 13 15 2 51 13 18 2 47 13 22 2 44 13 25 2 41 13 28 2 38 13 31 12 00 3 05 13 04 3 02 13 07 2 58 13 11 2 55 13 14 2 52 13 17 2 49 13 20 30 3 16 12 53 3 13 12 56 3 09 13 00 3 06 13 03 3 03 13 06 3 00 13 09 13 00 3 26 12 43 3 23 12 46 3 19 12 50 3 16 12 53 3 13 12 56 3 10 12 59 30 3 35 12 34 3 32 12 37 3 28 12 41 3 25 12 44 3 22 12 47 3 19 12 50 14 00 3 43 12 26 3 40 12 29 3 36 12 33 3 33 12 36 3 30 12 39 3 27 12 42 15 00 3 59 12 10 3 56 12 13 3 52 12 17 3 49 12 20 3 46 12 23 3 43 12 26 16 00 4 12 11 57 4 09 12 00 4 05 12 04 4 02 12 07 3 59 12 10 3 56 12 13 17 00 4 25 11 44 4 22 11 47 4 18 11 51 4 15 11 54 4 12 11 57 4 09 12 00 18 00 4 35 11 34 4 32 11 37 4 28 11 41 4 25 11 44 4 22 11 47 4 19 11 50 19 00 4 45 11 24 4 42 11 27 4 38 11 31 4 35 11 34 4 32 11 37 4 29 11 40 20 00 4 53 11 15 4 50 11 18 4 46 11 22 4 43 11 25 4 40 11 28 4 37 11 31 22 00 5 09 10 59 5 06 11 02 5 02 11 06 4 59 11 09 4 56 11 12 4 53 11 15 24 00 5 22 10 46 5 19 10 49 5 15 10 53 5 12 10 56 5 09 10 59 5 06 11 02 26 00 5 33 10 35 5 30 10 38 5 26 10 42 5 23 10 45 5 20 10 48 5 17 10 51 28 00 5 43 10 25 5 40 10 28 5 36 10 32 5 33 10 35 5 30 10 38 5 27 10 41 30 00 5 51 10 17 5 48 10 20 5 44 10 24 5 41 10 27 5 38 10 30 5 35 10 33 32 00 5 59 10 09 5 56 10 12 5 52 10 16 5 49 10 19 5 46 10 22 5 43 10 25 34 00 6 06 10 02 6 03 10 05 5 59 10 09 5 56 10 12 5 53 10 15 5 50 10 18 36 00 6 12 9 56 6 09 9 59 6 05 10 03 6 02 10 06 5 59 10 09 5 56 10 12 38 00 6 17 9 51 6 14 9 54 6 10 9 58 6 07 10 01 6 04 10 04 6 01 10 07 40 00 6 22 9 45 6 19 9 48 6 15 9 52 6 12 9 55 6 09 9 58 6 06 10 01 45 00 6 33 9 34 6 30 9 37 6 26 9 41 6 23 9 44 6 20 9 47 6 17 9 50 50 00 6 41 9 25 6 38 9 28 6 34 9 32 6 31 9 35 6 28 9 38 6 25 9 41 55 00 6 48 9 17 6 45 9 20 6 41 9 24 6 38 9 27 6 35 9 30 6 32 9 33 60 00 6 54 9 10 6 51 9 13 6 47 9 17 6 44 9 20 6 41 9 23 6 38 9 26 65 00 7 01 9 03 6 58 9 06 6 54 9 10 6 51 9 13 6 48 9 16 6 45 9 19 70 00 7 06 8 57 7 03 9 00 6 59 9 04 6 56 9 07 6 53 9 10 6 50 9 13 75 00 7 10 8 52 7 07 8 55 7 03 8 59 7 00 9 02 6 57 9 05 6 54 9 08 80 00 7 16 8 46 7 13 8 49 7 09 8 53 7 06 8 56 7 03 8 59 7 00 9 02 85 00 7 20 8 41 7 17 8 44 7 13 8 48 7 10 8 51 7 07 8 54 7 04 8 57 90 00 +7 24 8 36 +7 21 8 39 +7 17 8 43 +7 14 8 46 +7 11 8 49 +7 08 8 52 1 Additio NAL CORB. Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. „ ,/ „ / tr // t) " '1 II " " FOR St jN's Alt. 1st to 15th.... +18 +15 +8 C ) - 8 -13 -14 -11 -5 +3 +11 +^^ 16tl 1 to 31st... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *The corrections for the ol ^served altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude of the Sun 's lower limb, the di p, refraction, paralk IX, and mean semidiameter, which is taken as 10'. A supplementary correction ameter in the different months of the year is given at the foot of the main table. taking ace ount of the variatior 1 of the Sun's semid TABLE 46. [Page 935 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find 1 the True Altitude — Continued. HEIGHT OF THE EYE. | 83 Feet. 84 Feet. 85 Feet. 86 Feet. 87 Feet. 88 Feet. 1 Obs. Alt Sun's Corr. * Star's Corr. (-) G Sun's Corr. * Star's Corr. (-) Sun's Corr. * Star's Corr. (-) Sun's Corr. * Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) 6 30 -0 41 / // 16 50 -0 44 16 53 -0 47 16 56 -0 50 1 II 16 59 -0 63 17 02 -0 57 17 06 40 -0 31 16 40 -0 34 16 43 -0 37 16 46 -0 40 16 49 -0 43 16 62 -0 47 16 56 50 -0 21 16 30 -0 24 16 33 -0 27 16 36 -0 30 16 39 -0 33 16 42 -0 37 16 46 7 00 -0 11 16 20 -0 14 16 23 -0 17 16 26 -0 20 16 29 -0 23 16 32 -0 27 16 36 10 -0 02 16 11 -0 05 16 14 -0 08 16 17 -0 11 16 20 -0 14 16 23 -0 18 16 27 20 +0 07 16 02 +0 04 16 05 +0 01 16 08 -0 02 16 11 -0 05 16 14 -0 09 16 18 7 30 16 15 53 13 15 56 10 15 59 +0 07 16 02 +0 04 16 05 00 16 09 40 24 15 45 21 15 48 18 15 51 15 15 54 12 16 67 +0 08 16 01 50 32 15 37 29 15 40 26 15 43 23 15 46 20 16 49 16 16 63 8 00 40 15 29 37 15 32 34 15 35 31 15 38 28 15 41 24 15 46 10 47 15 22 44 15 25 41 15 28 38 15 31 35 15 34 31 15 38 20 54 15 15 51 15 18 48 15 21 45 15 24 42 16 27 38 15 31 8 30 1 01 15 08 58 15 11 55 15 14 52 15 17 49 16 20 46 15 24 40 1 08 15 01 1 05 15 04 1 02 15 07 59 15 10 56 15 13 52 15 17 50 1 14 14 55 1 11 14 58 1 08 15 01 1 05 15 04 1 02 15 07 58 15 11 9 00 1 20 14 49 1 17 14 52 1 14 14 55 1 11 14 58 1 08 16 01 1 04 15 05 20 1 32 14 37 1 29 14 40 1 26 14 43 1 23 14 46 1 20 14 49 1 16 14 53 40 1 43 14 26 1 40 14 29 1 37 14 32 1 34 14 35 1 31 14 38 1 27 14 42 10 00 1 54 14 15 1 51 14 18 1 48 14 21 1 45 14 24 1 42 14 27 1 38 14 31 20 2 04 14 05 2 01 14 08 1 58 14 11 1 55 14 14 1 52 14 17 1 48 14 21 40 2 13 13 56 2 10 13 59 2 07 14 02 2 04 14 05 2 01 14 08 1 57 14 12 11 00 2 22 13 47 2 19 13 50 2 16 13 53 2 13 13 56 2 10 13 59 2 06 14 03 30 2 34 13 35 2 31 13 38 2 28 13 41 2 25 13 44 2 22 13 47 2 18 13 51 12 00 2 45 13 24 2 42 13 27 2 39 13 30 2 36 13 33 2 33 13 36 2 29 13 40 30 2 56 13 13 2 53 13 16 2 50 13 19 2 47 13 22 2 44 13 26 2 40 13 29 13 00 3 06 13 03 3 03 13 06 3 00 13 09 2 57 13 12 2 54 13 15 2 50 13 19 30 3 15 12 54 3 12 12 57 3 09 13 00 3 06 13 03 3 03 13 06 2 59 13 10 14 00 3 23 12 46 3 20 12 49 3 17 12 52 3 14 12 55 3 11 12 58 3 07 13 02 15 00 3 39 12 30 3 36 12 33 3 33 12 36 3 30 12 39 3 27 12 42 3 23 12 46 16 00 3 52 12 17 3 49 12 20 3 46 12 23 3 43 12 26 3 40 12 29 3 36 12 33 17 00 4 05 12 04 4 02 12 07 3 59 12 10 3 56 12 13 3 53 12 16 3 49 12 20 18 00 4 15 11 54 4 12 11 57 4 09 12 00 4 06 12 03 4 03 12 06 3 69 12 10 19 00 4 25 11 44 4 22 11 47 4 19 11 50 4 16 11 53 4 13 11 66 4 09 12 00 20 00 4 33 11 35 4 30 11 38 4 27 11 41 4 24 11 44 4 21 11 47 4 17 11 61 22 00 4 49 11 19 4 46 11 22 4 43 11 25 4 40 11 28 4 37 11 31 4 33 11 35 24 00 5 02 11 06 4 59 11 09 4 56 11 12 4 53 11 15 4 60 11 18 4 46 11 22 26 00 5 13 10 55 6 10 10 58 5 07 11 01 5 04 11 04 6 01 11 07 4 57 11 11 28 00 5 23 10 45 5 20 10 48 5 17 10 51 5 14 10 54 5 11 10 57 5 07 11 01 30 00 5 31 10 37 5 28 10 40 5 25 10 43 5 22 10 46 5 19 10 49 5 16 10 63 32 00 5 39 10 29 5 36 10 32 5 33 10 35 5 30 10 38 5 27 10 41 5 23 10 46 34 00 5 46 10 22 5 43 10 25 5 40 10 28 5 37 10 31 5 34 10 34 6 30 10 38 36 00 5 52 10 16 5 49 10 19 5 46 10 22 5 43 10 25 5 40 10 28 5 36 10 32 38 00 5 57 10 11 5 54 10 14 5 51 10 17 5 48 10 20 6 45 10 23 5 41 10 27 40 00 6 02 10 05 5 59 10 08 5 56 10 11 5 53 10 14 5 50 10 17 5 46 10 21 45 00 6 13 9 54 6 10 9 57 6 07 10 00 6 04 10 03 6 01 10 06 5 57 10 10 50 00 6 21 9 45 6 18 9 48 6 15 9 51 6 12 9 54 6 09 9 57 6 05 10 01 55 00 6 28 9 37 6 25 9 40 6 22 9 43 6 19 9 46 6 16 9 49 6 12 9 53 60 00 6 34 9 30 6 31 9 33 6 28 9 36 6 25 9 39 6 22 9 42 6 18 9 46 65 00 6 41 9 23 6 38 9 26 6 35 9 29 6 32 9 32 6 29 9 36 6 26 9 39 70 00 6 46 9 17 6 43 9 20 6 40 9 23 6 37 9 26 6 34 9 29 6 30 9 33 75 00 6 50 9 12 6 47 9 15 6 44 9 18 6 41 9 21 6 38 9 24 6 34 9 28 80 00 6 56 9 06 6 53 9 09 6 50 9 12 6 47 9 15 6 44 9 18 6 40 9 22 85 00 7 00 9 01 6 57 9 04 6 54 9 07 6 51 9 10 6 48 9 13 6 44 9 17 90 00 +7 04 8 56 +7 01 8 59 +6 58 9 02 +6 55 9 05 +6 62 9 08 +6 48 9 12 1 Additio] ■^AL Core. Day of Month Jan. Feb. Mar. Apr May. June. July. Aug. Sept. ( 3ct. Nov. 1 Dec. 1 // '/ " '/ ti " " II " " " FOR SU :sj'3 Alt. Istt o 15th.. .-+18 +15 +8 - 8 - -13 -14 -11 -5 +3 +11 +16 16th to 31st. ..+17 +12 +4 -4 -11 - -14 -13 - 9 -1 +7 +14 +18 *Thec orrections for the oh served altitude of a » Star or Planet involves the dip and the refraction; and for the observed altitude of the Sun s lower limb, the di p, refraction, paralla X, and mean semidiameter, which is taken as 16'. A supplementary correction taking ace )unt of the variation of the Sun's semid ameter in the different months of the year is given at the foot of the main table. Page 936] TABLE 46. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find 1 the True Altitude — Continued. 1 Obs. Alt. HEIGHT OF THE EYE. 1 89 Feet. 90 Feet. 91 Feet. 92 Feet. 93 Feet. 94 Feet. 1 * * * * * :|c Sim's Con. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) O Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) 6 30 -1 00 17 09 -1 03 17 12 -1 06 17 15 -1 09 17 18 -1 12 17 21 -1 15 1 It 17 24 40 -0 60 16 59 -0 53 17 02 -0 56 17 05 -0 59 17 08 -1 02 17 11 -1 05 17 14 50 -0 40 16 49 -0 43 16 52 -0 46 16 55 -0 49 16 58 -0 52 17 01 -0 55 17 04 7 00 -0 30 16 39 -0 33 16 42 -0 36 16 45 -0 39 16 48 -0 42 16 51 -0 45 16 54 10 -0 21 16 30 -0 24 16 33 -0 27 16 36 -0 30 16 39 -0 33 16 42 -0 36 16 45 20 -0 12 16 21 -0 15 16 24 -0 18 16 27 -0 21 16 30 -0 24 16 33 -0 27 16 36 7 30 -0 03 16 12 -0 06 16 15 -0 09 16 18 -0 12 16 21 -0 15 16 24 -0 18 16 27 40 +0 05 16 04 +0 02 16 07 -0 01 16 10 -0 04 16 13 -0 07 16 16 -0 10 16 19 50 13 15 56 10 15 59 +0 07 16 02 +0 04 16 05 +0 01 16 08 -0 02 16 11 8 00 21 15 48 18 15 51 15 15 54 12 15 57 09 16 00 +0 06 16 03 10 28 15 41 25 15 44 22 15 47 19 15 50 16 15 53 13 15 56 20 35 15 34 32 15 37 29 15 40 26 15 43 23 15 46 20 15 49 8 30 42 15 27 39 15 30 36 15 33 33 15 36 30 15 39 27 15 42 40 49 15 20 46 15 23 43 15 26 40 15 29 37 15 32 34 15 35 50 55 15 14 52 15 17 49 15 20 46 15 23 43 15 26 40 15 29 9 00 1 01 15 08 58 15 11 55 15 14 52 15 17 49 15 20 46 15 23 20 1 13 14 56 1 10 14 59 1 07 15 02 1 04 15 05 1 01 15 08 58 15 11 40 1 24 14 45 1 21 14 48 1 18 14 51 1 15 14 54 1 12 14 57 1 09 15 00 10 00 1 35 14 34 1 32 14 37 1 29 14 40 1 26 14 43 1 23 14 46 1 20 14 49 20 1 45 14 24 1 42 14 27 1 39 14 30 1 36 14 33 1 33 14 36 1 30 14 39 40 1 54 14 15 1 51 14 18 1 48 14 21 1 45 14 24 1 42 14 27 1 39 14 30 11 00 2 03 14 06 2 00 14 09 1 57 14 12 1 54 14 15 1 51 14 18 1 48 14 21 30 2 15 13 54 2 12 13 57 2 09 14 00 2 06 14 03 2 03 14 06 2 00 14 09 12 00 2 26 13 43 2 23 13 46 2 20 13 49 2 17 13 52 2 14 13 55 2 11 13 58 30 2 37 13 32 2 34 13 35 2 31 13 38 2 28 13 41 2 25 13 44 2 22 13 47 13 00 2 47 13 22 2 44 13 25 2 41 13 28 2 38 13 31 2 35 13 34 2 32 13 37 30 2 56 13 13 2 53 13 16 2 50 13 19 2 47 13 22 2 44 13 25 2 41 13 28 14 00 3 04 13 05 3 01 13 08 2 58 13 11 2 55 13 14 2 52 13 17 2 49 13 20 15 00 3 20 12 49 3 17 12 52 3 14 12 55 3 11 12 58 3 08 13 01 3 05 13 04 16 00 3 33 12 36 3 30 12 39 3 27 12 42 3 24 12 45 3 21 12 48 3 18 12 51 17 00 3 46 12 23 3 43 12 26 3 40 12 29 3 37 12 32 3 34 12 35 3 31 12 38 18 00 3 56 12 13 3 53 12 16 3 50 12 19 3 47 12 22 3 44 12 25 3 41 12 28 19 00 4 06 12 03 4 03 12 06 4 00 12 09 3 57 12 12 3 54 12 15 3 51 12 18 20 00 4 14 11 54 4 11 11 57 4 08 12 00 4 05 12 03 4 02 12 06 3 59 12 09 22 00 4 30 11 38 4 27 11 41 4 24 11 44 4 21 11 47 4 18 11 50 4 15 11 53 24 00 4 43 11 25 4 40 11 28 4 37 11 31 4 34 11 34 4 31 11 37 4 28 11 40 26 00 4 54 11 14 4 51 11 17 4 48 11 20 4 45 11 23 4 42 11 26 4 39 11 29 28 00 5 04 11 04 5 01 11 07 4 58 11 10 4 55 11 13 4 52 11 16 4 49 11 19 30 00 5 12 10 56 5 09 10 59 5 06 11 02 5 03 11 05 5 00 11 08 4 57 11 11 32 00 5 20 10 48 5 17 10 51 5 14 10 54 5 11 10 57 5 08 11 00 5 05 11 03 34 00 5 27 10 41 5 24 10 44 5 21 10 47 5 18 10 50 5 15 10 53 5 12 10 56 36 00 5 33 10 35 5 30 10 38 5 27 10 41 5 24 10 44 5 21 10 47 5 18 10 50 38 00 5 38 10 30 5 35 10 33 5 32 10 36 5 29 10 39 5 26 10 42 5 23 10 45 40 00 5 43 10 24 5 40 10 27 5 37 10 30 5 34 10 33 5 31 10 36 5 28 10 39 45 00 5 54 10 13 5 51 10 16 5 48 10 19 5 45 10 22 5 42 10 25 5 39 10 28 50 00 6 02 10 04 5 59 10 07 5 56 10 10 5 53 10 13 5 50 10 16 5 47 10 19 55 00 6 09 9 56 6 06 9 59 6 03 10 02 6 00 10 05 5 57 10 08 5 54 10 11 60 00 6 15 9 49 6 12 9 52 6 00 9 55 6 06 9 58 6 03 10 01 6 00 10 04 65 00 6 22 9 42 6 19 9 45 6 16 9 48 6 13 9 51 6 10 9 54 6 07 9 57 70 00 6 27 9 36 6 24 9 39 6 21 9 42 6 18 9 45 6 15 9 48 6 12 9 51 75 00 6 31 9 31 6 28 9 34 6 25 9 37 6 22 9 40 6 19 9 43 6 16 9 46 80 00 6 37 9 25 6 34 9 28 6 31 9 31 6 28 9 34 6 25 9 37 6 22 9 40 85 00 6 41 9 20 6 38 9 23 6 35 9 26 6 32 9 29 6 29 9 32 6 26 9 35 90 00 +6 45 9 15 +6 42 9 18 +6 39 9 21 +6 36 9 24 +6 33 9 27 +6 30 9 30 1 Additio (TAL Cork. Day of Month. Jan. Feb. Mar. Apr. May. . Fune. Ju y. Aug. Sept. ( Dct. Nov . Dec. // // „ /, f // // // „ n > 1, roB Stj 'n's Alt. Istt o 15th.... +18 +15 +8 - 8 - -13 -1 4 -11 -5 +3 +11 +16 16th to 3l8t.. +17 +12 +4 -4 -11 - -14 -1 3-9 -1 f7 + 14 +18 ♦The 3oiTections for the ot served altitude of a Star or Planet involves the dip and the r< sfraction; and for the observed altitude of the Sun 3 lower limb, the di p, refraction, paralla X, and mean semidiameter, which is tak en as 16'. A supplementary correction ir is given at the loot of the main table. taking ace }UQt of thev ariation of the Sun's semidi ameter in the different months of the yes TABLE 46. [Page 937 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. | HEIGHT OF THE EYE. 1 95 Feet. 96 Feet. 1 97 Feet. 1 98 Feet. 1 99 Feet. 1 100 Feet. 1 Obs. Alt. oO, Sun's Corr. Star's Corr. (-) „o Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) «o. Sun's Corr. star's Corr. (-) oO, Sun's Corr. Star's Corr. (-) oO, Sun's Corr. Star's Corr. (-) o , / // / t, / II / // / n / II / II 1 II / // / // / II / II 6 30 -1 18 17 27 -1 21 17 30 -1 24 17 33 -1 27 17 36 -1 30 17 39 -1 33 17 42 40 -1 08 17 17 -1 11 17 20 -1 14 17 23 -1 17 17 26 -1 20 17 29 -1 23 17 32 50 -0 58 17 07 -1 01 17 10 -1 04 17 13 -1 07 17 16 -1 10 17 19 -1 13 17 22 7 00 -0 48 16 57 -0 51 17 00 -0 54 17 03 -0 57 17 06 -1 00 17 09 -1 03 17 12 10 -0 39 16 48 -0 42 16 51 -0 45 16 54 -0 48 16 57 -0 51 17 00 -0 54 17 03 20 -0 30 16 39 -0 33 16 42 -0 36 16 45 -0 39 16 48 -0 42 16 51 -0 45 16 54 7 30 -0 21 16 30 -0 24 16 33 -0 27 16 36 -0 30 16 39 -0 33 16 42 -0 36 16 45 40 -0 13 16 22 -0 16 16 25 -0 19 16 28 -0 22 16 31 -0 25 16 34 -0 28 16 37 50 -0 05 16 14 -0 08 16 17 -0 11 16 20 -0 14 16 23 -0 17 16 26 -0 20 16 29 8 00 +0 03 16 06 00 16 09 -0 08 16 12 -0 06 16 15 -0 09 16 18 -0 12 16 21 10 10 15 59 +0 07 16 02 +0 04 16 05 +0 01 16 08 -0 02 16 11 -0 05 16 14 20 17 15 52 14 15 55 11 15 58 08 16 01 +0 05 16 04 +0 02 16 07 8 30 24 15 45 21 15 48 18 15 51 15 15 54 12 15 57 09 16 00 40 31 15 38 28 15 41 25 15 44 22 15 47 19 15 50 16 15 53 50 37 15 32 34 15 35 31 15 38 28 15 41 25 15 44 22 15 47 9 00 43 15 26 40 15 29 37 15 32 34 15 35 31 15 38 28 15 41 20 55 15 14 52 15 17 49 15 20 46 15 23 43 15 26 40 15 29 40 1 06 15 03 1 03 15 06 1 00 15 09 57 15 12 54 15 15 51 15 18 10 00 1 17 14 52 1 14 14 55 1 11 14 58 1 08 15 01 1 05 15 04 1 02 15 07 20 1 27 14 42 1 24 14 45 1 21 14 48 1 18 14 51 1 15 14 54 1 12 14 57 40 1 36 14 33 1 33 14 36 1 30 14 39 1 27 14 42 1 24 14 45 1 21 14 48 11 00 1 45 14 24 1 42 14 27 1 39 14 30 1 36 14 33 1 33 14 36 1 30 14 39 30 1 57 14 12 1 54 14 15 1 51 14 18 1 48 14 21 1 45 14 24 1 42 14 27 12 00 2 08 14 01 2 05 14 04 2 02 14 07 1 59 14 10 1 56 14 13 1 53 14 16 30 2 19 13 50 2 16 13 53 2 13 13 56 2 10 13 59 2 07 14 02 2 04 14 05 13 00 2 29 13 40 2 26 13 43 2 23 13 46 2 20 13 49 2 17 13 52 2 14 13 55 30 2 38 13 31 2 35 13 34 2 32 13 37 2 29 13 40 2 26 13 43 2 23 13 46 14 00 2 46 13 23 2 43 13 26 2 40 13 29 2 37 13 32 2 34 13 35 2 31 13 38 15 00 3 02 13 07 2 59 13 10 2 56 13 13 2 53 13 16 2 50 13 19 2 47 13 22 16 00 3 15 12 54 3 12 12 57 3 09 13 00 3 06 13 03 3 03 13 06 3 00 13 09 17 00 3 28 12 41 3 25 12 44 3 22 12 47 3 19 12 50 3 16 12 53 3 13 12 56 18 00 3 38 12 31 3 35 12 34 3 32 12 37 3 29 12 40 3 26 12 43 3 23 12 46 19 00 3 48 12 21 3 45 12 24 3 42 12 27 3 39 12 30 3 36 12 33 3 33 12 36 20 00 3 59 12 12 3 53 12 15 3 50 12 18 3 47 12 21 3 44 12 24 3 41 12 27 22 00 4 12 11 56 4 09 11 59 4 06 12 02 4 03 12 05 4 00 12 08 3 57 12 11 24 00 4 25 11 43 4 22 11 46 4 19 11 49 4 16 11 52 4 13 11 55 4 10 11 58 26 00 4 36 11 32 4 33 11 35 4 30 11 38 4 27 11 41 4 24 11 44 4 21 11 47 28 00 4 46 11 22 4 43 11 25 4 40 11 28 4 37 11 31 4 34 11 34 4 31 11 37 30 00 4 54 11 14 4 51 11 17 4 48 11 20 4 45 11 23 4 42 11 26 4 39 11 29 32 00 5 02 11 06 4 59 11 09 4 56 11 12 4 53 11 15 4 50 11 18 4 47 11 21 34 00 5 09 10 59 5 06 11 02 5 03 11 05 5 00 11 08 4 57 11 11 4 54 11 14 36 00 5 15 10 53 5 12 10 56 5 09 10 59 5 06 11 02 5 03 11 05 5 00 11 08 38 00 5 20 10 48 5 17 10 51 5 14 10 54 5 11 10 57 5 08 11 00 5 05 11 03 40 00 5 25 10 42 5 22 10 45 5 19 10 48 5 16 10 51 5 13 10 54 5 10 10 57 45 00 5 36 10 31 5 33 10 34 5 30 10 37 5 27 10 40 5 24 10 43 5 21 10 46 50 00 5 44 10 22 5 41 10 25 5 38 10 28 5 35 10 31 5 32 10 34 5 29 10 37 55 00 5 51 10 14 5 48 10 17 5 45 10 20 5 42 10 23 5 39 10 26 5 36 10 29 60 00 5 57 10 07 5 54 10 10 5 51 10 13 5 48 10 16 5 45 10 19 5 42 10 22 65 00 6 04 10 00 6 01 10 03 5 58 10 06 5 55 10 09 5 52 10 12 5 49 10 15 70 00 6 09 9 54 6 06 9 57 6 03 10 00 6 00 10 03 5 57 10 06 5 54 10 09 75 00 6 13 9 49 6 10 9 52 6 07 9 55 6 04 9 58 6 01 10 01 5 58 10 04 80 00 6 19 9 43 6 16 9 46 6 13 9 49 6 10 9 52 6 07 9 55 6 04 9 58 85 00 6 23 9 38 6 20 9 41 6 17 9 44 6 14 9 47 6 11 9 50 6 08 9 53 90 00 6 27 9 33 +6 24 9 36 +6 21 9 39 +6 18 9 42 +6 15 9 45 +6 12 9 48 1 Additio NAL Cork Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. „ „ „ // ti II 1, // II " II FOR Sr in's Alt. Ist to 15th.... +18 +15 +8 C I - 8 -13 -14 -11 -5 +3 +11 +16 16tl I to 31st... +17 +12 +4 -A -11 -14 -13 - 9 -1 +7 +14 +18 *The correction s for the o >served altitude of a Star or Planet involves the di X, and mean semidiameter, v [) and the refraction; and for the observed altitude of the Sun 's lower li Hb, thedi p, refraction, paralla •hich is taken as 16'. A supplementary correction s of the year is given at the foot of the main table. taking ace ountof th 8 variation of the Sun's semidi ameter in the diflerent month Page 938] TABLE 47. Longitude Factors. F Is the change in longitude due to a change of 1' in latitude. Latitude. Bear- 0° 1° 2° 4° 6° 8° 10° 12° Bear- ing. ing. / / / / / / / / o 1 57.29 57.30 57.32 57.43 57.61 57.85 58.17 58.57 1 2 28.64 28.64 28.65 28.71 28.79 28.92 29.08 29.28 2 3 19.08 19.08 19.09 19.13 19.19 19.27 19.38 19.51 3 4 14.30 14.30 14.31 14.34 14.38 14.44 14.52 14.62 4 5 11.43 11.43 11.44 11.46 11.49 11.54 11.61 11.69 5 6 9.51 9.52 9.52 9.54 9.57 9.61 9.66 9.73 6 7 8.14 8.15 8.15 8.16 8.19 8.22 8.27 8.33 7 8 7.12 7.12 7.12 7.13 7.15 7.18 7.22 7.27 8 10 5.67 5.67 5.68 5.69 5.70 5.73 5.76 5.80 10 12 4.71 4.71 4.71 4.72 4.73 4.75 4.78 4.81 12 14 4.01 4.01 4.01 4.02 4.03 4.05 4.07 4.10 14 16 3.49 3.49 3.49 3.50 3.51 3.52 3.54 3.56 16 18 3.08 3.08 3.08 3.08 3.10 3.11 3.13 3.15 18 20 2.75 2.75 2.75 2.75 2.76 2.77 2.79 2.81 20 n 2.47 2.47 2.48 2.48 2.49 2.50 2.51 2.53 22 U 2.25 2.25 2.25 2.25 2.26 2.27 2.28 2.30 24 m 2.05 2.05 2.05 2.05 2.06 2.07 2.08 2.10 26 28 1.88 1.88 1.88 1.88 1.89 1.90 1.91 1.92 28 30 1.73 1.73 1.73 1.74 1.74 1.75 1.76 1.77 30 32 1.60 1.60 1.60 1.60 1.61 1.62 1.63 1.64 32 34 1.48 1.48 1.48 1.49 1.49 1.50 1.50 1.52 34 36 1.38 1.38 1.38 1.38 1.38 1.39 1.40 1.41 36 38 1.28 1.28 1.28 1.28 1.29 1.29 1.30 1.31 38 40 1.19 1.19 1.19 1.19 1.20 1.20 1.21 1.22 40 42 1.11 1.11 1.11 1.11 1.12 1.12 1.13 1.14 42 44 1.04 1.04 1.04 1.04 1.04 1.05 1.05 1.06 44 46 .97 .97 .97 .97 .97 .98 .98 .99 46 48 .90 .90 .90 .90 .90 .91 .91 .92 48 50 .84 .84 .84 .84 .84 .85 .85 .86 50 52 .78 .78 .78 .78 .79 .79 .79 .80 52 54 .73 .73 .73 .73 .73 .73 .74 .74 54 56 .67 .67 .67 .68 . .68 .68 .68 .69 56 58 .63 .63 .63 .63 .63 .63 .63 .64 58 60 .58 .58 .58 .58 .58 .58 .59 .59 60 62 .53 .53 .53 .53 .53 .54 .54 .54 62 64 .49 .49 .49 .49 .49 .49 .50 .50 64 66 .45 .45 .45 .45 .45 .45 ,45 .46 66 68 .40 .40 .40 .40 .40 .41 .41 .41 68 70 .36 .36 .36 .36 .37 .37 .37 .37 70 72 .33 .33 .33 .33 .33 .33 .33 .33 72 74 .29 .29 .29 .29 .29 .29 .29 .29 74 76 .25 .25 .25 .25 .25 .25 .25 .25 76 78 .21 .21 .21 .21 .21 .21 .22 .22 78 80 .18 .18 .18 .18 .18 .18 .18 .18 80 81 .16 .16 .16 .16 .16 .16 .16 .16 81 82 .14 .14 .14 .14 .14 .14 .14 .14 82 83 .12 .12 .12 .12 .12 .12 .12 .13 83 84 .10 .10 .10 .10 .10 .10 .11 .11 84 85 .09 .09 .09 .09 .09 .09 .09 .09 85 86 .07 .07 .07 .07 .07 .07 .07 .07 86 87 .05 .05 .05 .05 .05 .05 .05 .05 87 88 .03 .03 .03 .03 .03 .03 .03 .04 88 89 .02 .02 .02 .02 .02 .02 .02 .02 89 90 .00 .00 .00 .00 .00 .00 .00 .00 90 0° 1° 2° 4° 6° 8° 10° 12° Co rr. to Long. = Error in Lat.) CF. 21594°— 14- Pag e940] TABLE 47. Longitude Factors. F is the change In longitude due to a change of 1' in latitude. Latitude. Bear- 30° 32° 34° 36° 38° 40° 42° 44° Bear- ing. ing. o / / / / / / / / o 1 66.15 67.56 69.10 70.81 72.70 74.79 77.09 79.64 1 S 33.07 33.77 34.54 35.40 36.34 37.38 38.53 39.81 2 3 22.03 22.50 23.02 23.59 24.21 24.91 25.68 26.53 3 4 16.51 16.86 17.25 17.68 18.15 18.67 19.24 19.88 4 5 13.20 13.48 13.79 14.13 14.50 14.92 15.38 15.89 5 6 10.99 11.22 11.48 11.76 12.07 12.42 12.80 13.23 6 7 9.40 9.60 9.82 10.07 10.34 10.63 10.96 11.32 7 8 8.22 8.39 8.58 8.79 9.03 9.29 9.57 9.89 8 10 6.55 6.69 6.84 7.01 7.20 7.40 7.63 7.88 10 13 5.43 5.55 5.67 5.81 5.97 6.14 6.33 6.54 12 14 4.63 4.73 4.84 4.96 5 09 5.24 5.40 5.58 14 16 4.03 4.11 4.21 4.31 4.43 4.55 4.69 4.85 16 18 3.55 3.63 3.71 3.80 3.91 4.02 4.14 4.28 18 20 3.17 3.24 3.31 3.40 3.49 3.59 3.70 3.82 20 22 2.86 2.92 2.98 3.06 3.14 3.23 3.33 3.44 22 24 2.59 2.65 2.71 2.78 2.85 2.93 3.02 3.12 24 26 2.37 2.42 2.47 2.53 2.60 2.68 2.76 2.85 26 28 2.17 2.22 2.27 2.32 2.39 2.45 2.53 2.61 28 30 2.00 2.04 2.09 2.14 2.20 2.26 2.33 2.41 30 32 1.85 1.89 1.93 1.98 2.03 2.09 2.15 2.22 32 34 1.71 1.75 1.79 1.83 1.88 1.93 1.99 2.06 34 36 . 1.59 1.62 1.66 1.70 1.75 1.80 1.85 1.91 36 38 1.48 1.51 1.54 1.58 1.62 1.67 1.72 1.78 38 40 1.38 1.41 1.44 1.47 1.51 1.56 1.60 1.66 40 42 1.28 1.31 1.34 1.37 1.41 1.45 1.49 1.54 42 44 1.20 1.22 1.25 1.28 1.31 1.35 1.39 1.44 44 46 1.11 1.14 1.16 1.19 1.23 1.26 1.30 1.34 46 48 1.04 1.06 1.09 1.11 1.14 1.17 1.21 1.25 48 50 .97 .99 1.01 1.04 1.06 1.09 1.13 1.17 50 62 .90 .92 .94 .97 .99 1.02 1.05 1.09 52 54 .84 .86 .88 .90 .92 .95 .98 1.01 54 56 .78 .79 .81 .83 .86 .88 .91 .94 56 58 .72 .74 .75 .77 .79 .82 .84 .87 58 60 .67 .68 .70 .71 .73 .75 .78 .80 60 62 .61 .63 .64 .66 .67 .69 .72 .74 62 64 .56 .57 .59 .60 .62 .64 .66 .68 64 66 .51 .52 .54 .55 .56 .58 .60 .62 66 68 .47 .48 .49 .50 .51 .53 .54 .56 68 70 .42 .43 .44 .45 .46 .47 .49 .51 70 72 .37 .38 .39 .40 .41 .42 .44 .45 72 74 .33 .34 .35 .35 .36 .37 .39 .40 74 76 .29 .29 .30 .31 .32 .32 .34 .35 76 78 .24 .25 .26 .26 .27 .28 .29 .29 78 80 .20 .21 .21 .22 .22 .23 .24 .24 80 81 .18 .19 .19 .20 .20 .21 .21 .22 81 82 .16 .17 .17 .17 .18 .18 .19 .19 82 83 .14 .14 .15 .15 .16 .16 .16 .17 83 84 .12 .12 .13 .13 .13 .14 .14 .15 84 85 .10 .10 .11 .11 .11 .11 .12 .12 85 86 .08 .08 .08 .09 .09 .09 .09 .10 86 87 .06 .06 .06 .06 .07 .07 .07 .07 87 88 .04 .04 .04 .04 .04 .05 .05 .05 88 89 .02 .02 .02 .02 .02 .02 .02 .02 89 90 .00 .00 .00 .00 .00 .00 .00 .00 90 30° 32° 34° 36° 38° 40° 42° 44° Corr. to Long.=EiTor in Lat.xF. 1 TABLE 47. [Page 941 Longitude Factors. F Is the cbange In longitude due to a change of 1' in latitude. Latitude. Bear- 46° 48° 50° 52° 54° 56° 58° 60° Bear- ing. ing. o / / / / / / / / o' 1 82.47 85.62 89.13 93.05 97.47 102.5 108.1 114.6 1 2 41.22 42.80 44.55 46.51 48.72 51.21 54.04 67.27 2 3 27.47 28.52 29.68 30.99 32.46 34.12 36.01 38.16 3 4 20.59 21.37 22.25 23.23 24.33 •25. 57 26.99 28.60 4 5 16.45 17.08 17.78 18.57 19.45 20.44 21.57 22.86 5 6 13.70 14.22 14.80 15.45 16.19 17.01 17.95 19.03 6 7 11.72 12.17 12.67 13.23 13.86 14.56 15.37 16.29 7 8 10.24 10.63 11.07 11.56 12.11 12.72 13.43 14.23 8 10 8.16 8.48 8.82 9.21 9.65 10.14 10.70 11.34 10 12 6.77 7.03 7.32 7.64 8.00 8.41 8.88 9.41 12 14 5.77 5.99 6.24 6.51 6.82 7.17 7.57 8.02 14 16 5.02 5.21 5.42 5.66 5.93 6.24 6.58 6.97 16 18 4.43 4.60 4.79 5.00 5.24 5.50 5.81 6.15 18 20 3.95 4.11 4.27 4.46 4.67 4.91 5.19 5.49 20 22 3.56 3.70 3.85 4.02 4.21 4.43 4.67 4.95 22 24 3.23 3.36 3.49 3.65 3.82 4.02 4.24 4.49 24 26 2.95 3.06 3.19 3.33 3.49 3.66 3.87 4.10 26 28 2.71 2.81 2.93 3.05 3.20 3.36 3.55 3.76 28 30 2.49 2.59 2.69 2.81 2.95 3.10 3.27 3.46 30 32 2.30 2.39 2.49 2.60 2.72 2.86 3.02 3.20 32 34 2.13 2.22 2.31 2.41 2.52 2.65 2.80 2.96 34 36 1.98 2.06 2.14 2.24 2.34 2.46 2.60 2.75 36 38 1.84 1.91 1.99 2.08 2.18 2.29 2.41 2.56 38 40 1.71 1.78 1.85 1.94 2.03 2.13 2.25 2.38 40 42 1.60 1.66 1.73 1.80 1.89 1.99 2.09 2.22 42 44 1.49 1.55 1.61 1.68 1.76 1.85 1.95 2.07 44 46 1.39 1.44 1.50 1.57 1.64 1.73 1.82 1.93 46 48 1.30 1.35 1.40 1.46 1.53 1.61 1.70 1.80 48 50 1.21 1.25 1.31 1.36 1.43 1.50 1.58 1.68 50 52 1.12 1.17 1.22 1.27 1.33 1.40 1.47 1.56 52 54 1.05 1.09 1.13 1.18 1.23 1.30 1.37 1.45 54 56 .97 1.01 1.05 1.10 1.15 1.21 1.27 1.35 56 58 .90 .93 .97 1.01 1.06 1.12 1.18 1.25 58 60 .83 .86 .90 .94 .98 1.03 1.09 1.15 60 62 .77 .79 .83 .86 .90 .95 1.00 1.06 62 64 .70 .73 .76 .79 .83 .87 .92 .97 64 66 .64 .66 .69 .72 .76 .79 .84 .89 66 68 .58 .60 .63 .65 .69 .72 .76 .81 68 70 .52 .54 .57 .59 .62 .65 .68 .73 70 72 .47 .49 .51 .53 .55 .58 .61 .65 72 74 .41 .43 .45 .46 .49 .51 .54 .57 74 76 .36 .37 .39 .40 .42 .45 .47 .50 76 78 .31 .32 .33 .34 .36 .38 .40 .42 78 80 .25 .26 .27 .29 .30 .31 .33 .35 80 81 .23 .24 .25 .26 .27 .28 .30 .32 81 82 .20 .21 .22 .23 .24 .25 .26 .28 82 83 .18 .18 .19 .20 .21 .22 .23 .25 83 84 .15 .16 .16 .17 .18 .19 .20 .21 84 85 .13 .13 .14 .14 .15 .16 .16 .17 85 86 .10 .10 .11 .11 .12 .12 .13 .14 86 87 .08 .08 .08 .08 .09 .09 .10 .10 87 88 .05 .05 .05 .06 .06 .06 .07 .07 88 89 .02 .03 .03 .03 .03 .03 .03 .03 89 90 .00 .00 .00 .00 .00 .00 .00 .00 90 46° 48° 50° 52° 54° 66° 58° 60° doi T. to Long.=Error in Lat.X r. Page 942] TABLE 48. Latitude Factors. t is the change in latitude due to a change of 1' in longitude. Latitude. Bear- 0" 1° 3° 4° 6° 8° 10° 13° Bear- ing. ing. o / / / / / / f / o 1 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 1 3 .03 .03 .03 .03 .03 .03 .03 .03 3 3 .05 .05 .05 .05 .05 .05 .05 .05 3 4 .07 .07 .07 .07 .07 .07 .07 .07 4 5 .09 .09 .09 .09 .09 .09 .09 .09 5 6 .11 .11 .11 .10 .10 .10 .10 .10 6 1 .12 .12 .12 .12 .12 .12 .12 .12 7 8 .14 .14 .14 .14 .14 .14 .14 .14 8 10 .18 .18 .18 .18 .18 .17 .17 .17 10 13 .21 .21 .21 .21 .21 .21 .21 .21 13 14 .25 .25 .25 .25 .25 .25 .25 .24 14 16 .29 .29 .29 .29 .28 .28 .28 .28 16 18 .32 .32 .32 .32 .32 .32 .32 .32 18 20 .36 .36 .36 .36 .36 .36 .36 .36 30 33 .40 .40 .40 .40 .40 .40 .40 .40 33 34 .44 .44 .44 .44 .44 .44 .44 .43 34 36 .49 .49 .49 .49 .49 .48 .48 .48 36 38 .53 .53 .53 .53 .53 .53 .52 .52 38 30 .58 .58 .58 .57 .57 .57 .57 .56 30 33 .63 .63 .63 .63 .62 .62 .61 .61 33 34 .68 .68 .68 .67 .67 .67 .67 .66 34 36 .72 .72 .72 .72 .72 .72 .71 .71 36 38 .78 .78 .78 .78 .78 .78 .77 .76 38 40 .84 .84 .84 .84 .83 .83 .83 .82 40 43 .90 .90 .90 .90 .89 .89 .88 .88 43 44 .96 .96 .96 .96 .96 .95 .95 .94 44 46 1.04 1.04 1.04 1.03 1.03 1.03 1.02 1.01 46 48 1.11 1.11 1.11 1.11 1.11 1.10 1.10 1.09 48 50 1.19 1.19 1.19 1.19 1.19 1.18 1.17 1.17 50 53 1.28 1.28 1.28 1.28 1.27 1.27 1.26 1.25 53 54 1.38 1.38 1.38 1.37 1.37 1.36 1.36 1.35 54 56 1.48 1.48 1.48 1.48 1.47 1.47 1.46 1.45 56 58 1.60 1.60 1.60 1.60 1.59 1.58 1.58 1.57 58 60 1.73 1.73 1.73 1.73 1.72 1.72 1.71 1.69 60 63 1.88 1.88 1.88 1.88 1.87 1.86 1.85 1.84 63 64 2.05 2.05 2.05 2.05 2.04 2.03 2.02 2.01 64 66 2.25 2.25 2.24 2.24 2.23 2.22 2.21 2.20 66 68 2.48 2.48 2.47 2.47 2.46 2.45 2.44 2.42 68 70 2.75 2.75 2.75 2.74 2.73 2.72 2.71 2.69 70 73 3.08 3.08 3.08 3.07 3.06 3.05 V 3.03 3.01 73 74 3.49 3.49 3.49 3.48 3.47 3.45 3.43 3.41 74 76 4.01 4.01 4.01 4.00 3.99 3.97 3.95 3.92 76 78 4.70 4.70 4.70 4.69 4.68 4.66 4.63 4.60 78 80 5.67 5.67 5.67 5.66 5.64 5.62 5.59 5.55 80 81 6.31 6.31 6.31 6.30 6.28 6.25 6.22 6.18 81 83 7.12 7.11 7.11 7.10 7.07 7.05 7.01 6.96 83 83 8.15 8.14 8.14 8.13 8.10 8.07 8.02 7.97 83 84 9.52 9.51 9.51 9.49 9.46 9.42 9.37 9.31 84 85 11.43 11.43 11.42 11.40 11.37 11.32 11.25 11.18 85 86 14.30 14.30 14.29 14.27 14.22 14.16 14.08 13.99 86 87 19.08 19.08 19.07 19.03 18.98 18.91 18.79 18.66 87 88 28.63 28. '63 28.62 28.57 28.48 28.35 28.20 28.01 88 89 57.29 57.28 57.26 57.15 56.98 56.73 56.42 56.04 89 0° 1° 3° 4° 6° 8° 10° 13° C< )r. to Lat.= Error in Long.> ;f. TABLE 48. Latitude Factors. [Page 943 t is the change in latitude due to a change 3f 1' in longitude. Latitude. Bear- 14° 16° 18° 20° 22° 24° 26° 28° Bear- ing. ing. / f / / / / f / o 1 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 1 2 .03 .03 .03 .03 .03 .03 .03 .03 2 3 .05 .05 .05 .05 .05 .05 .05 .05 3 4 .07 .07 .07 .07 .06 .06 .06 .06 4 5 .08 .08 .08 .08 .08 .08 .08 .08 5 6 .10 .10 .10 .10 .10 .10 .09 .09 6 7 .12 .12 .12 .12 .11 .11 .11 .11 7 8 .14 .14 .13 .13 .13 .13 .13 .12 8 10 .17 .17 .17 .17 .16 .16 .16 .16 10 13 .21 .20 .20 .20 .20 .19 .19 .19 12 14 .24 .24 .24 .23 .23 .23 .22 .22 14 16 .28 .28 .27 .27 .27 .26 .26 .25 16 18 .32 .31 .31 .30 .30 .30 .29 .29 18 20 .35 .35 .35 .34 .34 .33 .33 .32 20 Zt .39 .39 .38 .38 .38 .37 .36 .36 22 U .43 .43 .42 .42 .41 .41 .40 .39 24 26 .47 .47 .46 .46 .45 .45 .44 .43 26 28 .52 .51 .51 .50 .49 .49 .48 .47 28 30 .56 .56 .55 .54 .53 .53 .52 .51 30 32 .61 .60 .60 .59 .58 .57 .56 .55 32 34 .65 .65 .64 .63 .63 .62 .61 .59 34 36 .70 .70 .69 .68 .68 .66 .65 .64 36 38 .76 .75 .74 .74 .72 .71 .70 .69 38 40 .81 .81 .80 .79 .78 .77 .75 .74 40 42 .88 .87 .85 .85 .83 .82 .81 .79 42 44 .93 .93 .92 .91 .89 .88 .87 .85 44 46 1.01 1.00 .99 .97 .96 .95 .93 .91 46 48 1.08 1.07 1.06 1.04 1.03 1.02 1.00 .98 48 50 1.16 1.15 1.13 1.12 1.10 1.09 1.07 1.05 50 52 1.24 1.23 1.22 1.20 1.19 1.17 1.15 1.13 52 54 1.34 1.32 1.31 1.29 1.28 1.26 1.24 1.22 54 56 1.44 1.43 1.41 1.39 1.38 1.35 1.33 1.31 56 58 1.55 1.54 1.52 1.50 1.48 1.46 1.44 1.41 58 60 1.68 1.67 1.65 1.63 1.61 1.58 1.56 1.53 60 62 1.83 1.81 1.79 1.77 1.74 1.72 1.69 1.66 62 64 1.99 1.97 1.95 1.93 1.90 1.87 1.84 1.81 64 66 2.18 2.16 2.14 2.11 2.08 2.05 2.02 1.98 66 68 2.40 2.38 2.35 2.33 2.30 2.26 2.23 2.18 68 70 2.67 2.64 2.61 2.58 2.55 2.51 2.47 2.43 70 72 2.99 2.96 2.93 2.89 2.85 2.81 2.77 2.72 72 74 3.38 3.35 3.32 3.28 3.23 3.19 3.14 3.08 74 76 3.89 3.86 3.81 3.77 3.72 3.66 3.61 3.54 76 78 4.56 4.52 4.47 4.42 4.36 4.30 4.23 4.15 78 80 5.50 5.45 5.39 5.33 5.26 5.18 5.10 5.01 80 81 6.13 6.07 6.01 5.93 5.86 5.77 5.68 5.58 81 82 6.90 6.84 6.77 6.69 6.60 6.50 6.40 6.28 82 83 7.90 7.83 7.75 7.65 7.55 7.44 7.32 7.19 83 84 9.23 9.15 9.05 8.94 8.82 8.69 8.55 8.40 84 85 11.09 10.99 10.87 10.74 10.60 10.44 10.26 10.09 85 86 13.88 13.75 13.60 13.44 13.26 13.07 12.86 12.63 86 87 18.51 18.34 18.15 17.93 17.69 17.43 17.15 16.85 87 88 27.78 27.52 27.23 26.91 26.55 26.16 25.74 25.28 88 89 55.59 55.07 54.49 53.84 53.12 52.33 51.50 50.58 89 14° 16° 18° 20° 22° 24° 26° 28° Ck) rr. to Lat.=Error in Long.)